Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Thermal performance of a solar hot water system : model versus measurement Naegele, Timothy Paul 1984

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1984_A6_7 N33.pdf [ 14.73MB ]
Metadata
JSON: 831-1.0096148.json
JSON-LD: 831-1.0096148-ld.json
RDF/XML (Pretty): 831-1.0096148-rdf.xml
RDF/JSON: 831-1.0096148-rdf.json
Turtle: 831-1.0096148-turtle.txt
N-Triples: 831-1.0096148-rdf-ntriples.txt
Original Record: 831-1.0096148-source.json
Full Text
831-1.0096148-fulltext.txt
Citation
831-1.0096148.ris

Full Text

THERMAL PERFORMANCE OF A SOLAR DOMESTIC HOT WATER HEATING SYSTEM: MODEL VERSUS MEASUREMENT by TIMOTHY PAUL NAEGELE B.Sc, The University of B r i t i s h Columbia, 1980 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Geography Department) We accept th i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March 1984 © Timothy Paul Naegele, 1984 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements fo r an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s t h e s i s for s c h o l a r l y purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s for f i n a n c i a l gain s h a l l not be allowed without my written permission. T i m o t h y P a u l N a e g e l e Department of G e o g r a p h y  The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 0 D a t e A p r i l 2, 1984 DE-6 (3/81) i i ABSTRACT A commercially available solar domestic hot water heating system i n s t a l l e d in a private residence in Vancouver, B.C. has operated continously and r e l i a b l y since i t was commissioned in A p r i l 1981. The system employs a water-based, double tank, drainback design; components include a f l a t plate c o l l e c t o r array, solar storage tank with immersed c o i l heat exchanger, c i r c u l a t i o n pump, d i f f e r e n t i a l c o n t r o l l e r , and a u x i l i a r y hot water tank. Project monitoring of the system using an automatic data acqui s i t i o n and logging system commenced in June 1981 and continued to December 1982. Storage tank, water supply l i n e and ambient a i r temperatures, together with solar radiation, hot water consumption, solar / t o t a l heat delivered, and a u x i l i a r y fuel consumption were integrated or averaged hourly; pump operating hours were recorded d a i l y . The completeness, consistency, and quality of the data c o l l e c t e d over the 19 month monitoring period has been established. The system's thermal performance and operating c h a r a c t e r i s t i c s are evaluated and analyzed. Results incorporate information on: the hot water heating load and fraction supplied by solar energy, the operating e f f i c i e n c y of the system and i t s components, the storage tank and water supply l i n e temperatures, and the amount of conventional energy saved.. A separate account i s given of the users' hot water consumption patterns. Over the monitoring period the system u t i l i z e d 38.0% of the solar radiation incident on the c o l l e c t o r array. The resul t i n g solar energy contribution to the hot water heating load was 47.5%. However, there was large diurnal, day-to-day, and seasonal v a r i a b i l i t y in the system's thermal performance. This was a direct result of the highly variable combination of load and meteorological conditions imposed on the system, together with i t s limited thermal storage c a p a b i l i t y . A problem was encountered in evaluating the system's performance during the late f a l l and early winter months due to the existence of standby heat gain. The l a t t e r resulted from the storage tank temperature decreasing below that of the surrounding basement a i r during periods of low and zero solar energy input. Simulation of the system was performed using a modified version of the WATSUN-3 Domestic Hot Water (DHWA) model (Chandrashekar and Wylie, 1981a). This model assumes that the storage tank is f u l l y mixed and isothermal at a l l times, and that the system variables remain constant over each one hour time step. Modifications made to the model include changes to the input data s p e c i f i c a t i o n s , c o l l e c t o r control strategy, immersed c o i l exchanger and standby heat loss c a l c u l a t i o n s . Input data for the model were derived from three sources: measured hourly data for the load and meteorological variables, manufacturer's sp e c i f i c a t i o n s for the system component parameters, and externally performed test results for the co l l e c t o r e f f i c i e n c y parameters. Model predictions are compared against actual system measurements for both a two month and a year long simulation period. Although the model was able to consistently track thermal conditions in the storage tank, i t exhibited a seasonally dependent negative bias. This i v limited i t s a b i l i t y to predict the system's long term thermal performance; the estimated annual solar f r a c t i o n deviated by -15.8 percent. I d e n t i f i c a t i o n of the cause(s) of the model bias was hindered by lack of s u f f i c i e n t monitoring data. A s e n s i t i v i t y analysis, undertaken to assess user-effect errors, revealed that several of the input variables associated with the c o l l e c t o r component model were potential sources of inaccuracy. Thus further testing and evaluation of the simulation model, using more rigorous and detailed measurement data, i s required before the model can be used with confidence. V TABLE OF CONTENTS Page ABSTRACT i i LIST OF TABLES v i i i LIST OF FIGURES ix ACKNOWLEDGEMENTS xiv CHAPTER 1 INTRODUCTION 1 A. Solar Heating as an Alternative 1 B. Project Background and Objectives 2 C. General Description of the System Under Investigation 6 D. Reporting Format 8 CHAPTER 2 SYSTEM DESCRIPTION, TERMINOLOGY, AND METHODOLOGY 11 A. System Configuration and Operating Strategy 11 B. Thermal Performance Evaluation 12 1. Thermal Energy Quantities 12 2. Solar Radiation, Fuel and Pump Energy 17 3. Temperatures 19 4. Hot Water Consumption 20 5. Thermal Performance Indicators 21 a. Heat Exchanger Effectiveness 21 b. Conventional Energy Saved 24 CHAPTER 3 MONITORING PROGRAM 29 A. Monitoring Requirements 29 B. Automatic Data Acquisition and Logging System . . . . 29 1 . Data Logger 29 2. Instrumentation 30 C. Data Reduction and Quality Control 33 D. Monitoring Period 35 E. Equipment F a i l u r e , Data Gaps, and Logger Saturation . 36 F. System Operation and Maintenance 37 v i Page CHAPTER 4 PRESENTATION AND DISCUSSION OF MONITORING RESULTS 4 3 A. Overview of Presentation 43 B. Overall Thermal Performance Summary 43 C. Monthly / Seasonal Thermal Performance Results . . . 45 1. Solar Heat Delivered, Pump Operation, and Solar Radiation 48 2. Solar Fraction 49 3. Solar Conversion E f f i c i e n c y 50 4. Au x i l i a r y Water Heater 52 5. Conventional Energy Saved and Pump Energy Consumption 54 6. Heat Exchanger Effectiveness 55 7. Storage Tank Temperature 58 8. Water Supply Line Temperatures 59 D. Daily Thermal Performance 61 1. September 1981 62 2. March 1982 64 3. December 1981 65 4. June 1982 66 E. Diurnal Variation in System Operation and Performance 68 1. Sunday, September 13, 1981 69 2. Thursday, March 11, 1982 72 3. Monday, December 7, 1982 75 4. Thursday, June 17, 1982 76 F. Hot Water Consumption Patterns 79 1 . Frequency D i s t r i b u t i o n of Hot Water Draws . . . . 79 2. Diurnal Hot Water Consumption Pattern 80 3. Intra-Weekly Hot Water Consumption Pattern . . . . 81 CHAPTER 5 SIMULATION MODEL 124 A. Simulation Modelling of Solar Heating Systems - An Overview 124 B. Solar Heating System Simulation Models 124 1. Advantages and Limitations 124 2. Developing and Modifying 126 C. Selecting a Simulation Model 127 D. Detailed Description of the Simulation Model . . . . 128 1. General Approach and Solution Technique 128 2. Collector Model 129 3. Standby Heat Loss Model 136 4. Heat Exchanger Model 138 5. Domestic Hot Water Model 140 6. Storage Tank Equation 141 7. Model Input / Output 143 v i i Page CHAPTER 6 MODEL VALIDATION 147 A. Model V a l i d a t i o n i n P r e s e n t S t u d y 147 B. E r r o r S t a t i s t i c s 148 C. I n i t i a l S i m u l a t i o n R e s u l t s 150 1. S t o r a g e Tank T e m p e r a t u r e Time S e r i e s 150 2. S t o r a g e Tank T e m p e r a t u r e E r r o r S t a t i s t i c s . . . . 153 3. S o l a r Hot Water Heat 155 D. Model B i a s 157 1. S o u r c e s of E r r o r 157 2. U s e r - E f f e c t E r r o r s 158 E. S e n s i t i v i t y A n a l y s i s 159 1. System P a r a m e t e r s 159 2. System V a r i a b l e s 171 3. Summary o f U s e r - E f f e c t E r r o r s 178 4. D i s c u s s i o n and S u g g e s t i o n s f o r F u r t h e r I n v e s t i g a t i o n 179 F. S i m u l a t i o n R e s u l t s f o r a One Y e a r P e r i o d 180 1. P r e d i c t e d S e a s o n a l T h e r m a l E n e r g y Regime 180 2. S t o r a g e Tank T e m p e r a t u r e 182 3. S o l a r Hot Water Heat 184 4. C o l l e c t o r O p e r a t i o n 185 5. S o l a r F r a c t i o n 186 CHAPTER 7 CONCLUSIONS 218 A. System T h e r m a l P e r f o r m a n c e and O p e r a t i n g C h a r a c t e r i s t i c s 218 B. Model V a l i d a t i o n R e s u l t s 222 C. Recommendations f o r F u r t h e r R e s e a r c h 224 FOOTNOTES 226 REFERENCES 229 APPENDIX A DETAILED DESCRIPTION OF THE SYSTEM COMPONENTS 234 APPENDIX B CR21 INPUT / OUTPUT TABLE CODING FORMS . . . . 246 APPENDIX C ERROR ANALYSIS 251 APPENDIX D DETAILED CALCULATION OF THE THEORETICAL HEAT LOSS COEFFICIENT FOR THE SOLAR STORAGE TANK . 259 APPENDIX E DETERMINATION OF A SURROGATE VARIABLE FOR THE BASEMENT AIR TEMPERATURE 261 APPENDIX F SAMPLE PRINTOUT OF HOURLY SIMULATION RESULTS . 271 v i i i LIST OF TABLES Table T i t l e Page 2.1 Thermal Performance Evaluation Terms 25 3.1 Summary of Instrumentation 39 4.1 Monthly Thermal Performance Summary - Part I . . . 82 4.2 Monthly Thermal Performance Summary - Part II . . . 83 4.3 Monthly Average Heat Exchanger Effectiveness . . . 84 4.4 Diurnal D i s t r i b u t i o n of Hot Water Consumption for the Overall Monitoring Period 85 4.5 Hot Water Consumption S t a t i s t i c s for the Overall Monitoring Period 86 5.1 Storage Tank Heat Loss Coefficient - Empirical Evaluation Results 137 5.2 Input Data Requirements for the Simulation Model . 145 6.1 Storage Tank Temperature Error S t a t i s t i c s Simulaton Period: August - September, 1982 . . . . 154 6.2 Solar Hot Water Heat Error S t a t i s t i c s Simulation Period: August - September, 1982 . . . 156 6.3 Summary of User-Effect Errors 187 6.4 Simulation Results for a One Year Period 188 6.5 Storage Tank Temperature Error S t a t i s t i c s Simulation Period: June 1981 - July 1982 189 6.6 Solar Hot Water Heat Error S t a t i s t i c s Simulation Period: June 1981 - July 1982 1 90 6.7 Collector Operation Error S t a t i s t i c s Simulation Period: June 1981 - July 1982 191 A.1 Heat Exchanger Specifications 236 A.2 Collector Specifications & E f f i c i e n c y Test Results 238 C. 1 Monthly Error Analysis Summary 256 D. 1 Thermal Resistance Values for the Storage Tank . . 259 E. 1 Agreement Between the Daily Cold Water and Basement Air Temperatures 262 ix LIST OF FIGURES Figure Capt ion Page 1.1 Solar Domestic Hot Water Heating System - Simplified Schematic 6 1.2 Solar Domestic Hot Water Heating System - Dr. John E. Hay's Residence 9 1.3 Flat Plate Collector Array Mounted on Roof . . . . 10 2.1 System Configuration 27 2.2 Energy and Water Flow within the Solar Domestic Hot Water Heating System 28 2.3 Evaluation of Thermal Energy Flow 28 3.1 Monitoring Equipment Layout - Automatic Data Acquisition and Data Logging System 40 3.2 Pyranometer Positioned Immediately Below Collector Array 41 3.3 L i s t i n g of Data Logger Output Tables for Julian Day 248 (September 5) 1981 42 4.1 Solar and Thermal Energy Totals for Overall Monitoring Period 87 4.2 Monthly Integrals of Solar (QSDHW), Au x i l i a r y (QAUXW) and Total (QDHW) Heat Delivered to the Domestic Hot Water Supply 88 4.3 Monthly Integrals of Incident Solar Radiation and Pump Operating Hours 89 4.4 Monthly Solar Fraction 90 4.5 Monthly Solar Energy Conversion E f f i c i e n c y . . . . 91 4.6 Monthly Integrals of Fuel Energy Consumption (QFUEL), Au x i l i a r y Heat Delivered (QAUXW), and Au x i l i a r y Tank Heat Loss (QAUXL) 92 4.7 Monthly Auxiliary Tank E f f i c i e n c y 93 4.8 Monthly Integrals of Fuel (QFSAVE) and Net (QESAVE) Energy Saved, and Pump Energy Consumption (QPUMP) 94 4.9 Monthly Flow-Weighted Heat Exchanger Effectiveness 95 X Figure Capt ion Page 4.10 Frequency D i s t r i b u t i o n of Hourly Heat Exchanger Effectiveness for the Overall Monitoring Period . 96 4.11 Heat Exchanger Effectiveness as a Function of Flow Conditions for a Random Sample of Hourly Hot Water Draws Selected from the Overall Monitoring Period 97 4.12 Daily Mean Storage Tank (mid-height), Basement Air and Incoming Cold Water Temperatures 98 4.13 Daily Mean Storage Tank and Solar Heated Water Temperatures: (a) June - December, 1981 99 (b) January - June, 1982 100 (c) July - December, 1982 101 4.14 Daily Mean Incoming Cold Water (TM), Solar Heated Water (TSDHW) and Hot Water Delivery (TDHW) Temperatures: (a) June - December, 1981 102 (b) January - June, 1982 103 (c) July - December, 1982 104 4.15 Daily Integrals of Solar (QSDHW), Aux i l i a r y (QAUXW) and Total (QDHW) Heat Delivered: September 1981 105 4.16 Time Series Plot of Storage Tank Temperature: September 1981 106 4.17 Daily Integrals of Solar (QSDHW), Aux i l i a r y (QAUXW) and Total (QDHW) Heat Delivered: March 1982 107 4.18 Time Series Plot of Storage Tank Temperature: March 1982 108 4.19 Daily Integrals of Solar (QSDHW), Aux i l i a r y (QAUXW) and Total (QDHW) Heat Delivered: December 1981 109 4.20 Time Series Plot of Storage Tank and Basement Air Temperatures: December 1981 . . . . 110 4.21 Daily Integrals of Solar (QSDHW), Au x i l i a r y (QAUXW) and Total (QDHW) Heat Delivered: June 1982 111 4.22 Time Series Plot of Storage Tank Temperature: June 1 982 112 4.23 Diurrtal Variation in System Operation and Performance on September 13, 1981 113 xi Figure Capt ion Page 4.24 Diurnal Variation in System Operation and Performance on March 1 1 , 1982 114 4.25 Diurnal Variation in System Operation and Performance on December 7, 1981 115 4.26 Diurnal Variation in System Operation and Performance on June 17, 1982 116 4.27 Cumulative Frequency D i s t r i b u t i o n of Hourly Hot Water Draws for the Overall Monitoring Period . . 117 4.28 Diurnal P r o f i l e of Hourly Hot Water Draws: October 1981 118 4.29 Diurnal P r o f i l e of Hourly Hot Water Draws: January 1982 119 4.30 Diurnal P r o f i l e of Hourly Hot Water Draws: A p r i l 1982 120 4.31 Diurnal P r o f i l e of Hourly Hot Water Draws: June 1982 121 4.32 Diurnal P r o f i l e of Monthly Hot Water Consumption . 122 4.33 Diurnal D i s t r i b u t i o n of Hot Water Consumption for the Overall Monitoring Period 123 5.1 Collector Model Flowchart . 146 6.1 Time Series Plot of Predicted and Measured Storage Tank Temperatures: (a) August 1 - 15, 1982 192 (b) August 16 - 31, 1982 193 (c) September 1 - 1 5 , 1982 194 (d) September 16 - 30, 1982 195 6.2 Daily Integrals of Predicted and Measured Solar Hot Water Heat: (a) August 1982 196 (b) September 1982 . . . 197 6.3 Model S e n s i t i v i t y to a Decrease in the D i f f e r e n t i a l Controller Turn ' O f f Set Point . . . 198 6.4 Model S e n s i t i v i t y to an Increase in Collector Area 199 6.5 Model S e n s i t i v i t y to a Decrease in Collector F l u i d Capacitance 200 6.6 Model S e n s i t i v i t y to Changes in Storage Volume . . 201 x i i Figure Caption Page 6.7 Model S e n s i t i v i t y to an Increase in the Collector Zero-Point E f f i c i e n c y Parameter . . . . 202 6.8 Model S e n s i t i v i t y to a Decrease in the Collector Slope E f f i c i e n c y Parameter 203 6.9 Model S e n s i t i v i t y to a Decrease in the Storage Tank Heat Loss Coefficient 204 6.10 Model S e n s i t i v i t y to an Increase in Basement Air Temperature 205 6.11 Model S e n s i t i v i t y to an Increase in Solar Radiation Incident on the Collector Array . . . . 206 6.12 Hemispherical Sky View from Centre of Collector Array 207 6.13 Model S e n s i t i v i t y to an Increase in Ambient Air Temperature 208 6.14 Model S e n s i t i v i t y to an Increase in Incoming Cold Water Temperature 209 6.15 Model S e n s i t i v i t y to a Decrease in the Volume of Hot Water Drawn 210 6.16 General Strategy for Validating the Simulation Model 211 6.17 Predicted Monthly Thermal Energy Quantities for the One Year Simulation Period 212 6.18 Time Series Plot of Predicted and Measured Storage Tank Temperatures for the One Year Simulation Period 213 6.19 Storage Tank Temperature Error S t a t i s t i c s . . . . 214 6.20 Monthly Integrals of Predicted and Measured Solar Hot Water Heat for the One Year Simulation Period 215 6.21 Solar Hot Water Heat Error S t a t i s t i c s 216 6.22 Collector Operation Error S t a t i s t i c s 217 A.1 System Configuration Schematic 240 A.2 Flat Plate Collector Panels 241 A.3 Collector Panel Details 242 xi i i Figure Caption Page A.4 Collector E f f i c i e n c y Curve 243 A.5 D i f f e r e n t i a l Controller 244 A.6 Section Through Storage Tank 244 A.7 Insulated Solar Storage Tank and Monitoring Equipment 245 C.1 Uncertainty in the Monthly Thermal Energy Quantities 257 C.2 Uncertainty in the Monthly Solar Fractions 258 E.I Time Series Plot of Predicted and Measured Basement Air Temperature: (a) August 1 - 15, 1982 264 (b) August 16 - 31, 1982 265 (c) September 1 - 15, 1982 266 (d) September 16 - 30, 1982 267 (e) October 1 - 15, 1982 268 (f) October 16 - 31, 1982 269 E.2 Cold Water Inlet Pipe in Relation to Space Heating Furnace, Ductwork, and Basement C e i l i n g 270 x i v ACKNOWLEDGEMENTS I would l i k e to thank my supervisor, Dr. John E. Hay, for providing me with the the opportunity to undertake t h i s project and for rendering much assistance, advice, and suggestions. I would also l i k e to thank Dr. M. Iqbal for reviewing the thesis. Further thanks are extended to E. Hoffman, V. Flannery, and R. S t i t t of Solarsystems Industries Ltd.; D. Blythe, L. McClelland, and G. Matthews of B.C. Hydro (Energy Use Engineering Department); and Trevor Jones of the B.C. Ministry of Energy, Mines and Petroleum (Conservation and Renewable Energy Branch). Their technical assistance and advice was most appreciated. Financial assistance was provided by a post-graduate scholarship from the Natural Sciences and Engineering Research Council of Canada. 1 CHAPTER 1 INTRODUCTION A. Solar Heating as an Alternative Solar heating at present offers a technically viable alternative to conventional heating methods. Domestic hot water heating, in pa r t i c u l a r , i s favourably suited as a solar heating application because i t constitutes a year round, r e l a t i v e l y low temperature energy requirement, allowing u t i l i z a t i o n of the available solar resource during a l l seasons of the year. In addition, the solar c o l l e c t o r area and storage volume required are generally small, and the associated a n c i l l i a r y equipment is f a i r l y compact and manageable. Hence a solar domestic hot water (SDHW) heating system can usually be i n s t a l l e d into a home quite e a s i l y , often by only one experienced tradesperson. Site assembly b a s i c a l l y involves l i f t i n g and mounting c o l l e c t o r panels onto the roof, laying out piping, hooking up a pump and co n t r o l l e r , and connecting a storage tank with the domestic water supply. R e t r o f i t t i n g with a SDHW heating system - by incorporating the exi s t i n g (conventional) water heater as an au x i l i a r y or backup - i s also common practice and offers additional advantages to the homeowner. Maintenance of SDHW heating systems is usually minimal and their construction i s most often designed to l a s t at least 20 years. Reliable and durable systems have been marketed in many regions of the world for the past decade. In Canada, various government funding programs (Grignon, 1979; Jones, 1982) together with individual i n i t i a t i v e s have helped a small, yet productive solar engineering and manufacturing 2 industry develop within the last five years. Fostering and promotion of the related technology has been a c t i v e l y pursued by the Solar Energy Society of Canada and the Canadian Solar Industries Association as well as by other private and public organizations. Thus, the use of SDHW heating systems is l i k e l y to become more widespread in the future, especially as the costs of conventional energy sources ( e l e c t r i c i t y , natural gas, and o i l ) r i s e , and as energy-conscious consumers become more aware of alternative heating methods. This w i l l act to reduce the demand for expensive non-renewable energy resources and w i l l result in potential long term savings for consumers. B. Project Background and Objectives In order to increase the current knowledge about solar heating systems, potential designs must be f i e l d tested and monitored so that their performance can be evaluated and compared against systems of d i f f e r e n t design. A selection process w i l l then occur, whereby the more e f f i c i e n t system designs w i l l propagate and become competitive in the marketplace. In Canada, an intensive f i e l d t r i a l and monitoring program administered by the National Research Council (NRC) was i n i t i a t e d in 1978. Data from several solar heating systems has since been co l l e c t e d and analyzed (Barakat et a l . , 1978; Onno, 1980). These data are subsequently used to evaluate the thermal and economic performance of the systems and to formulate design guidelines. This information i s then disseminated to the solar energy community, a s s i s t i n g engineers in improving their designs. Thus, monitoring of f i e l d t r i a l s 3 plays an important role in the o v e r a l l design / learning cycle inherent in system development. Hence the f i r s t objective of the present study is to report the monitoring results of a SDHW heating system which has been operating in a single family residence for the past two years. Included w i l l be an evaluation of the system's thermal performance, an analysis of i t s operating c h a r a c t e r i s t i c s , and an account of the users' hot water consumption patterns. While monitoring of f i e l d t r i a l s allows important knowledge to be gained about the performance and operation of solar heating systems, i t has limited usefulness in developing improved system designs. This i s primarily due to the time and expense involved in undertaking a monitoring program, prior to interpreting and u t i l i z i n g the r e s u l t s . Moreover, the results obtained are d i r e c t l y dependent upon the s p e c i f i c load and meteorological conditions experienced during the monitoring period. Therefore they are not always suitable for making generalizations. Consequently, mathematical models have been developed which are capable of simulating solar heating systems quickly and inexpensively for a wide range of system configurations, operating strategies, and component types. These simulation models are used as numerical tools in developing improved system designs since they permit systematic variation of parameter values and optimization of system performance. Hence they provide substantial cost benefit to engineers by quantifying the consequences of design decisions before they are put into e f f e c t . They also give researchers greater understanding of system operation and component 4 behaviour since they allow the int e r - r e l a t i o n s h i p s among system variables to be studied in d e t a i l . As well, simulation models provide resource managers with a predictive tool for use in energy conservation and planning. Many individuals and i n s t i t u t i o n s around the world who are involved in solar energy u t i l i z a t i o n recognize the large potential benefits to be drawn from simulation models (Jorgensen , 1 979; SERI.,1980; Beckman , 1 981 ; Chandrashekar , 1 982) . In Canada, the ongoing use and development of simulation models is supported by the Solar Energy Program of the NRC's Divis i o n of Energy. Currently a s i g n i f i c a n t part of t h i s e f f o r t relates to the WATSUN simulation model (Chandrashekar and Wylie, 1981b; Ferguson and Sul l i v a n , 1982). Developed at the University of Waterloo with NRC funding ( O r g i l l and Hollands, 1976; Le and Chandrashekar, 1978), WATSUN i s a design-oriented simulation model capable of predicting the thermal and economic performance of a variety of a i r and liquid-based systems used in space, DHW, and process solar heating. It has evolved through several stages of growth and refinement, and now combines considerable v e r s a t i l i t y in programming with economy and s i m p l i c i t y of use. In order to evaluate the c a p a b i l i t i e s and l i m i t a t i o n s of simulation models, such as WATSUN, a number of comparisons between simulated and measured performance for di f f e r e n t systems have been undertaken (Winn et a l . , 1978; Hedstrom, 1981; Jorgensen, 1982; Si b b i t t and Wylie, 1982). However, very few SDHW heating systems have been intensively monitored over a s u f f i c i e n t period of time to permit such an evaluation. Therefore, the second objective of the present 5 study is to simulate the system under investigation and compare the resulting model predictions against actual system measurements. This comparison w i l l allow the precision and accuracy of the simulation model to be assessed, and w i l l indicate how much confidence can be placed in i t s predictions. Additional analysis w i l l demonstrate the s e n s i t i v i t y of the model to variations in the input data. This w i l l permit potential users to become more familiar with the effects that the d i f f e r e n t system parameters and variables have on the model predictions. The simulation model used in thi s study i s a modified version of the WATSUN-3 Domestic Hot Water (DHWA) model (Chandrashekar and Wylie, 1981a). The l a t t e r model is widely used as a design, teaching and research tool in Canada at present. Hence the study results hold a broader relevance. In summary, the objectives of the research project are l i s t e d below. (1) To evaluate the thermal performance of a SDHW heating system including - the hot water heating load and the fraction supplied by solar energy - the operating e f f i c i e n c y of the system and i t s components - the amount of conventional energy saved (2) To analyze the system's operating c h a r a c t e r i s t i c s (3) To record the occupants' use of the system by p r o f i l i n g the amount and d i s t r i b u t i o n of hot water consumption (4) To validate a simulation model which can be used to predict the system's thermal performance (5) To examine the s e n s i t i v i t y of the simulation model to variations in the input data 6 C. General Description of the System Under Investigation The main function of a SDHW heating system i s to convert the variable supply of solar energy into a r e l a t i v e l y steady source of thermal energy for use in heating potable water. To accomplish this task, a system requires a means of c o l l e c t i n g , storing and transfering the available solar energy. This requirement is universal to a l l system designs, while in cold climates a method of freeze protection is also needed. The system under investigation employs a water-based, double tank, drainback design to meet both of these requirements. A si m p l i f i e d schematic is presented in Figure 1.1 below, and a cross-sectional drawing i l l u s t r a t i n g the house and the system is shown in Figure 1.2. The system incorporates a solar storage tank with an immersed c o i l heat exchanger, an a u x i l i a r y hot water tank, and a f l a t plate c o l l e c t o r array mounted on the roof ( t i l t angle = 41° from horizontal, azimuth = 172° from North; Figure 1.3). The system was manufactured and i n s t a l l e d by Solarsystems Industries Ltd. of Richmond, B.C. It i s sold commercially as Model SOL 840. Figure 1.1 Solar Domestic Hot Water Heating System Simplified Schematic (Solarsystems Industries Ltd., 1980) <— —> a u x i l i a r y tank c o l l e c t o r array storage tank 7 The system is located in the single family residence of Dr. John E. Hay in Vancouver, B.C.1 The Hay household i s an urban middle class family with one employed parent, one domestic parent, two teen-aged school children, and occasional house guests. Hot water consumption i s oriented toward a variety of uses, as l i s t e d below. - laundering of clothes using automatic washer - washing dishes, pots, and pans (performed manually) - house cleaning; washing f l o o r s , windows, bathtubs, sinks - personal hygiene; bathing, showering, hand/face washing The purchase of the system was p a r t i a l l y funded under the B.C. Solar Domestic Hot Water Demonstration Program (Jones, 1982). As a participant in th i s program, the system owner was required to permit public viewing of the system and to f u l f i l l a weekly monitoring obligation over a one year period. Procurement of the system and the necessary c i t y permits was administered by the Demonstration Program managers. I n s t a l l a t i o n and commissioning of the system was performed by Solarsystems Industries Ltd. in A p r i l 1981. The system has operated continously and r e l i a b l y since then. Monitoring became f u l l y operational in June 1981, and continued to December 1982. Formulation of the monitoring program and instrumentation of the system preceeded the present study; as such, they were i n d i r e c t l y incorporated into the project design. 8 D. Reporting Format The project report i s comprised of seven basic sections. The f i r s t section is a description of the system being investigated. This is presented in Chapter 2 and Appendix A. Also in Chapter 2 is section two - an outline of the evaluation methodology and d e f i n i t i o n of the associated terminology. The t h i r d section (Chapter 3 and Appendix B) provides d e t a i l s of the monitoring program, including the instrumentation used and the data set c o l l e c t e d . The fourth section presents a comprehensive account of the monitoring results (Chapter 4) and an analysis of error in the measured data values (Appendix C). The f i f t h section combines a detailed description of the simulation model together with a general discussion on simulating solar heating systems (Chapter 5 and Appendices D & E). Section six then provides an extensive account of the simulation results and analyzes the agreement between model and measurement (Chapter 6 and Appendix F). Lastly, the major findings of the project are summarized in Chapter 7. Figure 1.2 Solar Domestic Hot Water Heating System Dr. John E. Hay Residence s o l a r c o l l e c t o r a r r a y on r o o f f a c i n g s o u t h c o l l e c t o r l o o p p i p i n g hot water to f a u c e t s w a t e r s u p p l y l i n e n i n c o m i n g c o l d w a t e r from l o c a l mains a u x i l i a r y hot water tanffl s u p p l i e d bv_ rnatu*raT"Ras £ 1W u c i r c u d i f f e r e n t i a l '. j I c o n t r o l l c r a t i o n 'pump s o l a r s t o r a g e tank w i t h immersed c o i l h e a t e x c h a n g e r 10 F i g u r e 1.3 F l a t P l a t e C o l l e c t o r A r r a y Mounted on Roof 11 CHAPTER 2 SYSTEM DESCRIPTION, TERMINOLOGY, AND METHODOLOGY A. System Configuration and Operating Strategy As shown in the configuration diagram presented in Figure 2.1, the components of the SDHW heating system include a solar c o l l e c t o r array, c i r c u l a t i o n pump, d i f f e r e n t i a l c o n t r o l l e r , solar storage tank with immersed c o i l heat exchanger, a u x i l i a r y hot water tank, and piping. (A detailed description of each of the system components - including their s p e c i f i c a t i o n s - can be found in Appendix A.) The system i s en t i r e l y water-based. Moreover, the same water is used as both the heat transfer f l u i d and the storage medium. The pump draws the water from the bottom of the storage tank and c i r c u l a t e s i t through the c o l l e c t o r loop. The water absorbs solar energy as i t flows through the co l l e c t o r panels and then transfers this energy in the form of sensible heat to the storage tank. The c i r c u l a t i o n pump is turned 'on' and 'off' by a d i f f e r e n t i a l c o n t r o l l e r , depending on whether or not useful energy i s available from the c o l l e c t o r . The d i f f e r e n t i a l c o n t r o l l e r i s an electronic device which senses the temperature difference between the c o l l e c t o r and the water in the bottom of the solar storage tank. Whenever the temperature difference exceeds a pre-set value (TDIF1) the c i r c u l a t i o n pump is turned on and co l l e c t o r operation is i n i t i a t e d . Solar energy c o l l e c t i o n continues u n t i l the temperature difference f a l l s below a second pre-set value (TDIF2), at which time the d i f f e r e n t i a l c o n t r o l l e r turns the pump off and the water drains back to the storage tank via gravity. Air from the top of the storage tank 1 2 then bubbles up through the vent tube and f i l l s the c o l l e c t o r loop. This draining operation provides freeze protection for the solar c o l l e c t o r ; to ensure proper drainage, the piping i s continuously sloped back to the tank. The heat exchanger consists of a long length of co i l e d copper pipe immersed within the solar storage tank. When hot water i s being drawn, the pressurized supply of incoming cold water passes through th i s 'demand' heat exchanger and picks up whatever heat is ava i l a b l e . The 'solar' heated water then passes to the a u x i l i a r y hot water tank, which supplies additional heat as required in order to maintain the set-point delivery temperature. B. Thermal Performance Evaluation This section defines and describes the terms and methods used in evaluating the thermal performance of the SDHW heating system. A comprehensive l i s t of the evaluation terms and methods i s condensed in Table 2.1. It i s intended to complement the discussion below and serve as a cross reference for other chapters. 1. Thermal Energy Quantities The most important group of evaluation terms to define are the thermal energy quantities. They are shown in Figure 2.2 by arrows, which represent the flow of energy into and out of each system component. For example, QSDHW represents the flow of heat out of the solar storage tank and into the a u x i l i a r y hot water tank. The energy flows depicted are net quantities, integrated over a s u f f i c i e n t period of time such that thermal storage in the c o l l e c t o r and piping i s n e g l i g i b l e . However, in 1 3 g e n e r a l , i t may be s t a t e d t h a t t h e amount o f e n e r g y i n p u t i n t o a s y s t e m component i s e q u a l t o t h e e n e r g y o u t p u t p l u s or minus any change i n s t o r e d e n e r g y . T h i s s t a t e m e n t s i m p l y d e f i n e s t h e e n e r g y b a l a n c e e q u a t i o n - an a n a l y t i c a l t o o l u s e f u l i n d e c i d i n g t h e l o c a t i o n and c h o i c e o f e n e r g y measurements. Thus F i g u r e 2.2 i n d i c a t e s t h e t h e r m a l e n e r g y q u a n t i t i e s t h a t must be e i t h e r m e a sured or e s t i m a t e d i n o r d e r t o d e t e r m i n e t h e component and s y s t e m e n e r g y b a l a n c e s . The e n e r g y b a l a n c e e q u a t i o n c a n a l s o be u s e d as an i n d i r e c t c h e c k on t h e i n s t a l l e d i n s t r u m e n t a t i o n . By s o l v i n g t h e e n e r g y b a l a n c e e q u a t i o n f o r a s y s t e m component, an a s s e s s m e n t of measurement a c c u r a c y i s p o s s i b l e . I f t h e e n e r g y b a l a n c e c l o s u r e e r r o r e x c e e d s a c c e p t a b l e l i m i t s t h e n a c o n t r o l l e d i n v e s t i g a t i o n o f i t s c a u s e s i s r e q u i r e d . The s t a n d a r d e x p r e s s i o n f o r d e t e r m i n i n g t h e q u a n t i t y of h e a t d e l i v e r e d t o a f l u i d f l o w i n g t h r o u g h a p i p e or a tank i s g i v e n by i n t e g r a t i n g t h e i n s t a n t a n e o u s r a t e o f h e a t t r a n s f e r as f o l l o w s : 11 Q = J mCp(Tout - T i n ) d t (1) t2 where Q = q u a n t i t y o f h e a t t r a n s f e r r e d m = mass f l o w r a t e Cp = s p e c i f i c h e a t o f f l u i d ( a t c o n s t a n t p r e s s u r e ) T o u t - T i n = t e m p e r a t u r e change of f l u i d and t 1 , t 2 = i n i t i a l and f i n a l t i m e s of i n t e g r a t i o n p e r i o d In g e n e r a l , b o t h T o u t and T i n a r e f u n c t i o n s o f t i m e , Cp i s a f u n c t i o n o f t e m p e r a t u r e , and m i s a f u n c t i o n o f b o t h t i m e and t e m p e r a t u r e . However, f o r t h e s y s t e m under i n v e s t i g a t i o n , b o t h t h e d e n s i t y and s p e c i f i c h e a t o f t h e f l u i d ( w a t e r ) c a n be t r e a t e d as c o n s t a n t o v e r t h e a p p l i c a b l e t e m p e r a t u r e r a n g e , 0°C 100°C. Hence, Cp becomes c o n s t a n t , and m r e d u c e s t o a t i m e 1 4 dependent variable. The above expression can therefore be rewritten as follows: 11 Q = pCp / V(Tout - Tin) dt (2) t2 where p = density of f l u i d and V = volumetric flow rate Figure 2.3 i l l u s t r a t e s a generalized instrument setup to evaluate t h i s equation. It assumes that no accumulation of f l u i d occurs between cross sections 1 and 2 - a condition s a t i s f i e d within the SDHW heating system. Ideally continuous temperature measurements are required since heat flow in the system i s unsteady with respect to time. However, temporal sampling l i m i t a t i o n s in the monitoring equipment r e s t r i c t e d the instantaneous measurements to discrete i n t e r v a l s . Thus, fluctuations in the water temperatures between measurements were not resolved, introducing a potential source of error into the evaluation procedure (Appendix C). Changing the mathematical notation to indicate discrete temporal sampling, equation 2 can be rewritten as follows: <>t Q = pCp I V(Tin - Tout) (3) where V = volumetric flow during sampling in t e r v a l and <>t = summation period The following thermal energy equations can then be derived for the SDHW heating system using equation 3 and the nomenclature designated in Table 2.1: (i) Solar energy col l e c t e d and transferred to storage <>t QCSS = CMC Z (TCO - TCI) (4) 15 ( i i ) Solar heat delivered to the incoming cold water <>t QSDHW = ROWCP Z FLOW*(TSDHW - TM) (5) ( i i i ) A u x i liary heat delivered to the solar heated water <>t QAUXW = ROWCP Z FLOW*(TDHW - TSDHW) (6) (iv) Total (solar and au x i l i a r y ) heat delivered to the domestic hot water supply <>t QDHW = ROWCP Z FLOW*(TDHW - TM) (7) Appropriate measurement locations for the water flow and temperature sensors are indicated in Figure 2.2. Once the temperature sensors are i n s t a l l e d in the system, they delineate the thermal boundaries between system components. Thus, i f the boundary between the solar storage and a u x i l i a r y hot water tanks i s demarcated by the point at which TSDHW i s measured, then equation 6 can be replaced by the following equat ion: QAUXW = QDHW - QSDHW (6a) A rigorous monitoring program would involve measuring a l l the flow and temperature variables l i s t e d above. Unfortunately equipment constraints limited such a procedure. Consequently the water flow and i n l e t / o u t l e t temperatures in the c o l l e c t o r loop were not measured, precluding evaluation of the amount of solar energy c o l l e c t e d and transferred to storage (equation 4). However the flow and temperature variables appearing in equations 5 to 7 were measured, permitting the thermal energy quantities associated with these variables (QSDHW, QAUXW, and QDHW) to be evaluated. An hourly evaluation frequency i s used. This time interval was chosen 16 in order to e l i c i t diurnal variations in the system's thermal performance and to match the time step used in the simulation model. Additional summations enable d a i l y , monthly, and ove r a l l t o t a l s of these thermal energy quantities to be reported. Further examination of Figure 2.2 reveals a heat loss term for both the solar storage and a u x i l i a r y hot water tanks. 2 This term equals the difference between the heat that enters each tank and the heat that is subsequently delivered to the domestic hot water supply. For the solar storage tank, QSENV represents standby heat loss to the surrounding basement a i r through the tank insulation; for the a u x i l i a r y hot water tank, QAUXL i s a combination of jacket, pipe and flue heat losses. Since the tank heat losses are d i f f i c u l t quantities to measure d i r e c t l y , they are generally determined i n d i r e c t l y , either as residuals or from calculations using an appropriate temperature gradient and heat loss c o e f f i c i e n t . Over a period of a month, the change in heat content of the a u x i l i a r y tank is i n s i g n i f i c a n t r e l a t i v e to the fuel energy consumed and the hot water heat delivered. Hence QAUXL is evaluated on a monthly basis - as a residual. Since QCSS i s not evaluated, a similar c a l c u l a t i o n for QSENV i s not possible. The change in heat content of the solar storage tank (QSTOR) is the la s t term in the energy balance equation for this system component. It i s also a d i f f i c u l t quantity to determine; i t i s usually estimated by measuring the change in temperature of the storage medium and then multiplying by an applicable heat capacity value. However, s p a t i a l sampling 1 7 error becomes inherent in such a procedure, especially i f thermal s t r a t i f i c a t i o n i s prevalent in the storage tank and the instrumentation f a i l s to adequately integrate the temperature v a r i a t i o n . The change in heat content of the solar storage tank together with the standby heat loss were only evaluated with respect to determining an empirical value for UAS (Chapter 5 ) . The resulting QSTOR and QSENV values were very imprecise. This then precludes the energy balance equation for the storage tank from being used as an indicator of measurement accuracy. However, t h i s equation w i l l be seen to form the basis for the simulation model (Chapter 5 ) . Moreover, a numerical error analysis w i l l provide an assesment of uncertainty in the evaluated thermal energy quantities (Appendix C). In summary, evaluation of the thermal energy quantities is largely concerned with determining the amount of heat delivered by the solar storage and a u x i l i a r y hot water tanks to the incoming cold water. This allows the thermal performance of the SDHW heating system to be quantified in terms of the solar contribution to the hot water heating load. 2. Solar Radiation, Fuel and Pump Energy Three remaining energy variables in Figure 2.2 require d e f i n i t i o n . The t o t a l solar radiation incident on the. c o l l e c t o r array is evaluated by summing an instantaneous point measurement over time and multiplying by the c o l l e c t o r area as follows: 18 <>t QHT = AREAC I HT (8) Again, discrete temporal sampling rather than continuous integration i s due to lim i t a t i o n s in the monitoring equipment. Spatial sampling error also warrants consideration for th i s variable since a point measurement is used to represent a s p a t i a l l y integrated value. (This i s discussed in more d e t a i l in Chapter 6 and Appendix C.) QHT i s evaluated on an hourly basis, with further summations providing d a i l y , monthly, and ov e r a l l t o t a l s . It i s an extremely important quantity to evaluate since i t establishes the potential amount of solar energy which can be converted into hot water heat. Consequently, QHT is used as the prime meteorological variable in the simulation model; i t i s also used to determine the system's solar energy conversion e f f i c i e n c y . The volume of natural gas consumed by the a u x i l i a r y hot water tank (FUEL) i s d i r e c t l y measured at point of use. It i s a continuously integrated variable and i s evaluated on an hourly basis. In order to determine the corresponding amount of fuel energy consumption (QFUEL), the heat content of the natural gas (HCF) is required. This quantity is measured d a i l y by an independent testing firm. The d i s t r i b u t o r then ari t h m e t i c a l l y averages the d a i l y values over the two-month b i l l i n g period, enabling bi-monthly average HFC values to be determined from the regular b i l l i n g statement. QFUEL i s subsequently evaluated on a monthly basis as follows: QFUEL = HCF J* FUEL dt (9) (Note - The same HFC value i s used for the two consecutive 19 months to which i t applies.) As with a l l active solar heating systems, user supplied energy must be expended in order to convert the available solar energy into useful heat. For the SDHW heating system this quantity is represented by the pump energy consumption (QPUMP).3 This term i s evaluated on a monthly basis by summing the daily accumulated pump operating hours (PPHR) and multiplying by the pump's power consumption rating (PCDOT). QPUMP and QFUEL are both evaluated in order to ascertain the amount of energy consumed by the SDHW heating system. These quantities are then used in conjunction with the thermal energy quantities above to determine the amount of conventional energy saved by the system and to calculate certain component e f f i c i e n c e s (as outlined below). 3. Temperatures Evaluation of the temperatures within the SDHW heating system can be divided into three d i f f e r e n t methods: Arithmetical averaging i s used to evaluate hourly values for the ambient and basement a i r temperatures (TA and TBSM) and for the storage tank temperatures (TS). The appropriate expression for this type of averaging is given by <>t T = ( Z T) / n (10) where T = instantaneous temperature measurement T = arithmetical average value and n = number of temperature measurements during averaging period (<>t) Again, discrete temporal sampling is a l i m i t a t i o n of the monitoring equipment. The three temperature variables l i s t e d above are primarily evaluated in order to generate input and 20 comparison data for the simulation model. Accordingly, they are averaged on an hourly basis to provide compatibility with the model. For those periods when the basement a i r temperature was not being monitored, a surrogate variable i s used to estimate values for TBSM (Chapter 5 and Appendix E). Temperatures measured in the water supply l i n e (TM, TSDHW, and TDHW) are evaluated on an hourly basis using the following flow-weighted averaging approach: <>t <>t T = ( L FLOW * T) / Z FLOW (11) where FLOW = volume of hot water drawn during sampling in t e r v a l If no hot water i s drawn during a given hour, these temperatures are evaluated using arithmetical averaging ( i e . equat ion 10). Evaluation of the water supply l i n e and storage tank temperatures permits analysis of the system's thermal operating c h a r a c t e r i s t i c s . In addition, evaluation of TM (a system boundary variable) provides required input data for the simulation model. As previously mentioned, temperatures within the co l l e c t o r loop (TCI, TCO, and TCP) were not evaluated. 4. Hot Water Consumption Hot water consumption (FLOW) is evaluated on an hourly basis by continously integrating the volumetric flow through the water supply l i n e . As demonstrated above, evaluation of FLOW forms an integral step in determining the amount of heat transferred within the SDHW heating system. Furthermore, i t 21 provides necessary input data for the simulation model since i t defines one of the system's operating conditions. It also permits analysis of the day-to-day and diurnal hot water consumption patterns, including the resultant effects on the system's thermal performance. Summation of the hourly FLOW values yields d a i l y , monthly, and ove r a l l hot water consumption t o t a l s . 5. Thermal Performance Indicators The evaluation terms which t y p i c a l l y attract most interest are the thermal performance indicators. They indicate the e f f i c i e n c y with which the system components operate (ACEF, AUXE, HXEF, and SCOP), the a b i l i t y of the system to convert available solar energy into hot water heat (SCEF), the solar contribution to the hot water heating load (SFRAC), and the amount of conventional energy saved (QFSAVE and QESAVE). In order for representative values to be determined, the evaluation period must be s u f f i c i e n t l y long such that short term storage effects are n e g l i g i b l e . Consequently, the thermal performance indicators are only evaluated for periods of at least one month. The majority of the thermal performance indicators are defined as simple ratios (Table 2.1) involving the energy quantities l i s t e d above. However, d e f i n i t i o n of the heat exchanger effectiveness and the amount of conventional energy saved require f u l l e r explanation, a. Heat Exchanger Effectiveness The effectiveness of a heat exchanger i s defined by the r a t i o of 'actual heat transfer' to 'maximum possible heat 22 transfer' (TES Limited, 1981). For water flowing through a c o i l e d pipe heat exchanger immersed within a large and thermally conservative storage tank, t h i s r a t i o reduces to 'actual change in water temperature' divided by 'maximum possible change'. This s i m p l i f i c a t i o n results from being able to treat the density and s p e c i f i c heat of the water in the heat exchanger as constant over the temperature ranges involved, and by recognizing that temperature changes occurring within the storage tank, due to the withdrawal of heat by the heat exchanger, tend to be r e l a t i v e l y small (at least over a one hour i n t e r v a l ) . The actual change in temperature of the water as i t flows through the heat exchanger i s a complex function of the variable thermal and physical conditions existing within both the storage tank and the heat exchanger i t s e l f . Several of the factors which are thought to have an influence are l i s t e d below. - temperature of the water entering the heat exchanger - flow rate of the water through the heat exchanger, including i t s residency times during periods of intermittent flow - thermal gradient between the water in the storage tank and that in the heat exchanger - thermal s t r a t i f i c a t i o n and convective a c t i v i t y within the storage tank Fortunately, the o v e r a l l e f f e c t of these time-dependent factors i s integrated on an hourly basis through the simultaneous measurement of both the heat exchanger i n l e t (TM) 23 and o u t l e t (TSDHW) t e m p e r a t u r e s . Thus t h e t e m p e r a t u r e d i f f e r e n c e (TSDHW-TM) r e p r e s e n t s t h e a c t u a l change i n water t e m p e r a t u r e a c r o s s t h e h e a t e x c h a n g e r . However, d e t e r m i n a t i o n of t h e maximum p o s s i b l e t e m p e r a t u r e change i s more d i f f i c u l t . T h e o r e t i c a l l y , t h e water p a s s i n g t h r o u g h t h e h e a t e x c h a n g e r c a n o n l y a t t a i n a t e m p e r a t u r e a s h i g h as t h a t i n t h e warmest r e g i o n of t h e s t o r a g e t a n k . E v a l u a t i o n of t h i s l a t t e r t e m p e r a t u r e p r e s e n t s a p r o b l e m . In t h e p r e s e n t s t u d y i t i s a p p r o x i m a t e d by u s i n g t h e s t o r a g e t a n k t e m p e r a t u r e m easured a t th e m i d - h e i g h t l e v e l . Hence h e a t e x c h a n g e r e f f e c t i v e n e s s i s d e t e r m i n e d on an h o u r l y b a s i s u s i n g t h e f o l l o w i n g m a t h e m a t i c a l e x p r e s s i o n : HXEF = (TSDHW - TM) / (TSmid - TM) (12) B o t h f l o w - w e i g h t e d and a r i t h m e t i c a l a v e r a g i n g of t h e h o u r l y HXEF v a l u e s a r e t h e n u s e d t o e v a l u a t e m o n t h l y h e a t e x c h a n g e r e f f e c t i v e n e s s . [ Note - The above e x p r e s s i o n a d h e r e s t o t h e method f o r e v a l u a t i n g h e a t e x c h a n g e r e f f e c t i v e n e s s a s g i v e n i n S t r e e d ( 1 9 7 9 ) . I t d i f f e r s from t h e o r e t i c a l l y d e v e l o p e d f o r m u l a t i o n s of h e a t e x c h a n g e r e f f e c t i v e n e s s w h i c h a r e d e f i n e d i n terms of f l u i d c a p a c i t a n c e r a t e s (Kays and London, 1964). E v a l u a t i o n of ' e f f e c t i v e n e s s ' u s i n g e q u a t i o n 12 i s s i m p l y i n t e n d e d t o p r o v i d e i n s i g h t i n t o t h e o p e r a t i n g c h a r a c t e r i s t i c s of t h e h e a t e x c h a n g e r a s s y s t e m component; i t i s n o t meant t o d e f i n e a r i g o r o u s t h e r m a l e f f i c i e n c y f u n c t i o n f o r t h e h e a t e x c h a n g e r p e r s e . As w i l l be seen i n C h a p t e r 4, t h e r e s u l t i n g HXEF v a l u e s do n o t a l w a y s f a l l w i t h i n t h e l i m i t s o f z e r o t o u n i t y . T h e r e f o r e , c a u t i o n i s r e q u i r e d when i n t e r p r e t t i n g t h e s e v a l u e s . ] 24 b. Conventional Energy Saved In order to determine the amount of conventional energy saved, one f i r s t has to measure the amount of energy consumed by the SDHW heating system (QFUEL and QPUMP). Next, the stand-alone e f f i c i e n c y of the a u x i l i a r y hot water tank in the absence of any solar heating equipment (ACEF) must be evaluated." The evaluation method used is the same as for AUXE (Table 2.1), except that the solar components are now decoupled from the heating system. Having a value for ACEF allows one to calculate the amount of fuel energy that would have been consumed by the a u x i l i a r y hot water tank had i t been operating as a conventional water heater under i d e n t i c a l load conditions as the SDHW heating system. One simply divides the to t a l amount of heat delivered to the domestic hot water supply by ACEF, i e . QDHW/ACEF. The fuel energy saved (QFSAVE) i s then the difference between the calculated fuel energy p o t e n t i a l l y required to operate a conventional water heater and the measured fuel energy actually consumed by the SDHW heating system. F i n a l l y , the net energy saved (QESAVE) i s evaluated by subtracting the pump energy consumption from the fuel energy saved. Since QESAVE accounts for the amount of e l e c t r i c a l energy needed to operate the SDHW heating system, i t gives a 'truer' indication of the amount of conventional energy saved. 25 T a b l e 2.1 T h e r m a l P e r f o r m a n c e E v a l u a t i o n Terms C a t e g o r y / A b b r e v i a t i o n S y s t e m V a r i a b l e s T e m p e r a t u r e s D e f i n i t i o n E v a l u a t i o n Method E v a l u a t i o n F r e q u e n c y TA a m b i e n t a i r measurement h o u r l y TBSM basement a i r measurement/ h o u r l y / e s t i m a te d a i l y TCI c o l l e c t o r i n l e t N/A TCO c o l l e c t o r o u t l e t N/A TCP c o l l e c t o r a b s o r b e r p l a t e N/A TM i n c o m i n g c o l d w a ter measurement h o u r l y TS s o l a r s t o r a g e t a n k measurement h o u r l y ( b o t t o m and m i d - h e i g h t ) TSDHW s o l a r h e a t e d water measurement h o u r l y TDHW h o t water d e l i v e r y measurement h o u r l y Hot water c o n s u m p t i o n FLOW volume o f hot water drawn S o l a r r a d i a t i o n HT QHT s o l a r r a d i a t i o n i n c i d e n t on c o l l e c t o r s l o p e p e r u n i t a r e a t o t a l s o l a r r a d i a t i o n i n c i d e n t on c o l l e c t o r a r r a y T h e r m a l e n e r g y QCSS s o l a r e n e r g y c o l l e c t e d a nd t r a n s f e r r e d t o s t o r a g e QSDHW s o l a r h e a t d e l i v e r e d QSENV s t a n d b y h e a t l o s s from t h e s o l a r s t o r a g e t a n k QSTOR change i n h e a t c o n t e n t o f th e s o l a r s t o r a g e t a n k QAUXW a u x i l i a r y h e a t d e l i v e r e d QAUXL a u x i l i a r y tank h e a t l o s s QDHW t o t a l h e a t d e l i v e r e d A u x i l i a r y w a t e r h e a t e r FUEL volume o f f u e l consumed QFUEL f u e l e n e r g y c o n s u m p t i o n measurement h o u r l y measurement h o u r l y HT*AREAC h o u r l y N/A measurement UAS*(TS-TBSM) ATS*CVS QDHW-QSDHW QFUEL-QAUXW measurement measurement FUEL*HCF h o u r l y h o u r l y m o n t h l y h o u r l y h o u r l y m o n t h l y Pump o p e r a t i o n PPHR pump o p e r a t i n g h o u r s QPUMP pump e n e r g y c o n s u m p t i o n measurement PPHR*PCDOT d a i l y m o n t h l y 26 T a b l e 2.1 c o n t i n u e d C a t e g o r y / A b b r e v i a t i o n Def i n i t i o n S y stem P a r a m e t e r s P h y s i c a l AREAC c o l l e c t o r a r e a ( g r o s s ) VOLS volume of water i n s o l a r s t o r a g e t a n k T h e r m a l CMC c o l l e c t o r f l u i d c a p a c i t a n c e CVS h e a t c a p a c i t y of s t o r a g e HCF h e a t c o n t e n t o f f u e l ( p e r u n i t volume) ROWCP h e a t c a p a c i t y of water ( p e r u n i t volume) UAS s t o r a g e tank h e a t l o s s c o e f f i c i e n t Pump o p e r a t i o n PCDOT power c o n s u m p t i o n o f pump TDIF1 c o n t r o l l e r 'on' d i f f e r e n t i a l TDIF2 c o n t r o l l e r ' o f f d i f f e r e n t i a l C o l l e c t o r e f f i c i e n c y p a r a m e t e r s F R ( t a ) e z e r o - p o i n t e f f i c i e n c y FRUL s l o p e e f f i c i e n c y T h e r m a l P e r f o r m a n c e I n d i c a t o r s E f f i c i e n c i e s ACEF s t a n d - a l o n e e f f i c i e n c y o f a u x i l i a r y h o t wa t e r ta n k AUXE a u x i l i a r y tank e f f i c i e n c y HXEF h e a t e x c h a n g e r e f f e c t i v e n e s s SFRAC s o l a r f r a c t i o n o f t o t a l h e a t d e l i v e r e d SCEF s o l a r c o n v e r s i o n e f f i c i e n c y SCOP s o l a r c o e f f i c i e n t o f p e r f o r m a n c e C o n v e n t i o n a l e n e r g y s a v e d QFSAVE f u e l e n e r g y s a v e d QESAVE n e t e n e r g y s a v e d E v a l u a t i o n Method E v a l u a t i o n F r e q u e n c y measurement measurement d e s i g n v a l u e VOLS*ROWCP e x t e r n a l l i t e r a t u r e e m p i r i c a l / t h e o r e t i c a l d e s i g n v a l u e d e s i g n v a l u e d e s i g n v a l u e e x t e r n a l e x t e r n a l empi r i c a l / 1 i t e r a t u r e QAUXW/QFUEL (TSDHW-TM)/ (TSmid-TM) QSDHW/QDHW QSDHW/QHT QSDHW/QPUMP (QDHW/ACEF) -QFUEL QFSAVE-QPUMP m o n t h l y m o n t h l y m o n t h l y m o n t h l y m o n t h l y m o n t h l y m o n t h l y 27 F i g u r e 2.1 System C o n f i g u r a t i o n ( S o l a r s y s t e m s I n d u s t r i e s L t d . , 1980) 28 F i g u r e 2^2 Energy and Water Flow w i t h i n the SDHW H e a t i n g System TA c o l l e c t o r a r r a y / / T C P c o l l e c t o r l o o p TCO o u t l e t QCSS CMC c i r c u l a t i o n pump QPUMP FLOW i n c o m i n g c o l d w a ter from l o c a l mains TM w a t e r s u p p l y l i n e —••— > •'-TSDHW QSDHW solar heated water TBSM QSENV hot water to f a u c e t s QAUXL Q FUEL s o l a r s t o r a g e tank w i t h immersed c o i l h e a t e x c h a n g e r a u x i l i a r y hot water tank F i g u r e 2.3 E v a l u a t i o n of T h e r m a l E n e r g y Flow <2> t e m p e r a t u r e s e n s o r 1 f l o w meter sy s tern component eg. s t o r a g e tank t e m p e r a t u r e s e n s o r 29 CHAPTER 3 MONITORING PROGRAM A. M o n i t o r i n g R e q u i r e m e n t s The l e v e l of m o n i t o r i n g r e q u i r e d f o r a g i v e n s y s t e m depends p r i m a r i l y on t h e s u b s e q u e n t use t o be made of t h e d a t a c o l l e c t e d . In t h e p r e s e n t s t u d y , d e t a i l e d measurements a r e needed i n o r d e r t o r i g o r o u s l y e v a l u a t e t h e t h e r m a l p e r f o r m a n c e of t h e s y s t e m and t o p r o v i d e h o u r l y i n p u t and c o m p a r i s o n d a t a f o r t h e s i m u l a t i o n m o d e l . Hence a f a i r l y i n t e n s i v e l e v e l o f m o n i t o r i n g i s r e q u i r e d . The a c t u a l i n s t r u m e n t a t i o n i n s t a l l e d on t h e SDHW h e a t i n g s y s t e m r e p r e s e n t s a compromise w i t h r e s p e c t t o e q u i pment a v a i l a b i l i t y . C o n s e q u e n t l y , c o n s t r a i n t s a r e imposed on t h e c o m p r e h e n s i v e n e s s of t h e t h e r m a l p e r f o r m a n c e e v a l u a t i o n and t h e model v a l i d a t i o n . P a r t i a l l y o f f s e t t i n g t h i s l i m i t a t i o n , i s t h e l e v e l of r e l i a b i l i t y and r e s o l u t i o n a c h i e v e d i n t h e i n s t r u m e n t a t i o n . T h i s l e a d s t o a r e l a t i v e l y c o m p l e t e and a c c u r a t e d a t a s e t b e i n g o b t a i n e d o v e r a c o m p a r a t i v e l y l e n g t h y p e r i o d of t i m e . B. A u t o m a t i c D a t a A c q u i s i t i o n and L o g g i n g S y s t e m 1. D a t a l o g g e r In o r d e r t o g a t h e r , p r o c e s s and s t o r e t h e l a r g e volume of d a t a b e i n g c o l l e c t e d , an a u t o m a t i c d a t a a c q u i s i t i o n and l o g g i n g s y s t e m i s u s e d . The c e n t r a l u n i t i n t h i s s y s t e m i s a C a m p b e l l S c i e n t i f i c CR21 d a t a l o g g e r , c a p a b l e of h a n d l i n g i n p u t from n i n e d i f f e r e n t s e n s o r s . I t f u n c t i o n s a s b o t h a m i c r o -p r o c e s s o r and r e c o r d e r , and comes e q u i p p e d w i t h a r e a l t i m e c l o c k , s e r i a l d a t a i n t e r f a c e , i n t e r n a l programming, 30 analog-to-digital converter, and a l i q u i d c r y s t a l display. Every ten seconds the data logger scans the input channels, rapidly sampling the sensor signals; i t then processes and accumulates the data in an intermediate memory. At the end of each hour (n=360), the processed data is transferred to the logger's storage memory where i t awaits periodic 'dumping' to a cassette tape recorder. Operation of the data logger is controlled by internal programs spec i f i e d via user-entered input and output tables (Appendix B). The logger i t s e l f only performs a minor amount of processing on the data p r i o r to storing i t in a form suitable for use by a d i g i t a l computer. 2. Instrumentation The instrumentation associated with the data logger -temperature, flow and radiation sensors - is summarized in Table 3.1 and b r i e f l y discussed below. Consideration was given to choosing representative locations for a l l sensors p r i o r to i n s t a l l a t i o n , since thermal and radiative conditions can vary quite considerably over short distances within the system. The location of the various sensors i s indicated in Figure 3.1. Temperature transducers (two-terminal; integrated c i r c u i t ) are used to measure temperatures within the water supply l i n e and the storage tank. They e f f e c t i v e l y act as high impedance, constant current regulators, passing 1 MA per degree C and having a pre-set output of 298.2 jxA at 25°C. Thus they produce a current output d i r e c t l y proportional to absolute temperature. The temperature transducers u t i l i z e highly sensitive f i l m r e s i s t o r s (sensor chips) which have a time response constant (for 62.3% adjustment) reported to be less 31 t h a n 1.5 s e c o n d s ( A n a l o g D e v i c e s , 1979). P r i o r t o i n s t a l l a t i o n , a c u r r e n t - t o - v o l t a g e c o n v e r s i o n r e s i s t o r was use d t o t r i m t h e i r c a l i b r a t i o n e r r o r t o z e r o . They were t h e n t e s t e d f o r a c c u r a c y o v e r t h e i r o p e r a t i n g r a n g e , and matched t o w i t h i n ± 0 . 2 5 ° C o f ea c h o t h e r . 5 The t h r e e t r a n s d u c e r s w h i c h measure t e m p e r a t u r e s i n t h e water s u p p l y l i n e a r e a l l s e a t e d i n i n s u l a t e d p i p e f i x t u r e s , w i t h t h e i r s e n s o r c h i p s e x t e n d i n g w e l l i n t o t h e main f l o w s t r e a m . The TM t r a n s d u c e r i s i n s e r t e d i n t o t h e c o l d water i n l e t p i p e a p p r o x i m a t e l y 90 cm from t h e e n t r a n c e t o t h e s o l a r s t o r a g e t a n k , w h i l e t h e TSDHW t r a n s d u c e r i s l o c a t e d on t h e warm s i d e of t h e water s u p p l y l i n e , 5 cm from t h e s t o r a g e tank e x i t . The TDHW t r a n s d u c e r i s p o s i t i o n e d i n t h e hot wa t e r o u t l e t p i p e , 14 cm from t h e a u x i l i a r y t a n k e x i t . The two t e m p e r a t u r e t r a n s d u c e r s i n t h e s o l a r s t o r a g e t a n k a r e s e a t e d i n t h e r m o - w e l l s w h i c h a r e a t t a c h e d t o t h e tank a t bot t o m and m i d - h e i g h t l e v e l s . T h e i r v e r t i c a l p o s i t i o n s a r e 0.05 and 0.70 of i n s i d e t a n k h e i g h t r e s p e c t i v e l y . A t h e r m i s t o r p r o b e i s u s e d t o measure t h e ambient a i r t e m p e r a t u r e . I t i s ho u s e d w i t h i n a l o u v r e d S t e v e n s o n s c r e e n l o c a t e d on t h e su n d e c k , 3 m e t r e s ( i n v e r t i c a l d i s t a n c e ) below t h e c o l l e c t o r a r r a y . A s i m i l a r s e n s o r i s u s e d t o measure t h e basement a i r t e m p e r a t u r e ; t h e l a t t e r i s p o s i t i o n e d w i t h i n 1 met r e o f t h e s o l a r s t o r a g e t a n k , a t a p p r o x i m a t e l y m i d - h e i g h t l e v e l . A p o s i t i v e d i s p l a c e m e n t f l o w meter i s u s e d t o measure h o t wat e r c o n s u m p t i o n . T h i s meter i s e q u i p p e d w i t h an i m p u l s e head w h i c h p r o d u c e s 200 s w i t c h c l o s u r e s ( p u l s e s ) f o r e v e r y g a l l o n 32 (U.S.) of water flowing through the i n l e t pipe. It i s located on the cold side of the water supply l i n e due i t s temperature sensitive p l a s t i c housing. Since there i s no accumulation of water in t h i s l i n e , the flow meter measures the equivalent volume of hot water drawn from the taps. Its exact position i s 60 cm from the entrance to the solar storage tank, and i t is s u f f i c i e n t l y displaced from pipe elbows and temperature sensors to prevent any flow disturbance from biasing i t s measurements. A standard displacement gas meter i s used to measure the volume of natural gas consumed by the a u x i l i a r y hot water tank. A two part, magnetic pulse encoder provides a non-contact interface between the gas meter register and the data logger. The encoder u t i l i z e s a c i r c u l a r , multiple pole magnet and a s o l i d state 'Hall E f f e c t ' sensor encapsulated in a small, l i g h t weight housing. A saturating open-collector NPN transistor in the encoder produces an output of 5 pulses for every cubic foot of gas registered by the meter. Pulses from both the water flow and gas meters are fed to the data logger where they are temporarily held in an input buffer u n t i l being accumulated and stored in memory. A pyranometer i s mounted on the roof to measure the amount of solar radiation incident on the c o l l e c t o r array. It i s positioned immediately below the c o l l e c t o r array yet i s oriented in the same plane and with the same t i l t angle (Figure 3.2). The pyranometer was c a l i b r a t e d by the Canadian Atmospheric Environment Service prior to monitoring, and again after the data set had been c o l l e c t e d . A t i l t angle multiplying factor and a temperature dependence c o e f f i c i e n t (used in 33 conjunction with the measured ambient a i r temperatures) were applied to the hourly solar radiation values (Latimer, 1980). An electronic t o t a l i z i n g clock i s used to measure the cumulative number of hours that the c i r c u l a t i o n pump operates. This clock i s independent from the data logger; i t s d i g i t a l l y displayed readout is recorded manually once each day. Two integrating heat (BTU) meters and a second flow meter (Neptune) were also i n s t a l l e d on the system, as part of the B. C. SDHW Demonstration Program. Their d i g i t a l and d i a l displays are read on a daily basis, and their cumulative values recorded manually. While monitoring results from the BTU and Neptune meters are not reported in the present study, their measurements were used during quality control of the logger data as discussed in the next section. On-site plumbing and e l e c t r i c a l modification of the system to prepare i t for instrumentation was performed by Solarsystems Industries Ltd. I n s t a l l a t i o n of the flow meter, gas meter, encoder, and the five temperature transducers was carri e d out by technical staff involved in the B.C. SDHW Demonstration Program. None of the sensors required replacement or servicing during the monitoring period except for the pyranometer, which had i t s dessicant ( s i l i c a gel) changed. C. Data Reduction and Quality Control When the hourly data values are transmitted from the logger's memory to the cassette tape recorder, they are preceeded by a two d i g i t i d e n t i f i c a t i o n number and a blank 34 space. The data values themselves are f i t t e d into a five-place numeric f i e l d (four d i g i t s including p o l a r i t y , plus a flo a t i n g point decimal), and then entered into one of three output tables as spec i f i e d by the user. The format of the output tables i s shown in the sample printout l i s t i n g presented in Figure 3.3; i t can be interpretated using the CR21 output table coding forms found in Appendix B. A l l data are recorded for the hour ending in l o c a l clock time, which together with the Jul i a n day number are displayed in the second and t h i r d entries respectively, of input table #1. (The f i r s t entry of each table is reserved for the table number.) There are two important points to note about the tabulated data. F i r s t l y , the numerical values for the thermal energy quantities, together with the values for hot water and fuel consumption, are a l l recorded in logger units. These values were subsequently converted into appropriate SI units prior to analysis. Secondly, the data contains duplication in the water supply l i n e temperatures and hot water consumption values. For example, i f one knows the hourly value for TM from output table #1 and the value for TDHW-TM from output table #3, then a missing value for TDHW can be eas i l y calculated as a residual. S i m i l a r l y , i f one knows the hourly values for TDHW and TM from output table #1 (or a l t e r n a t i v e l y TDHW-TM from output table #3), as well as the value for FLOW from output table #1, then a missing value for QDHW can be estimated by assuming that the difference in water temperature across the two tanks remains independent of flow during the hour. ( i e . Assume that flow-weighted and arithmetical average TDHW-TM values are equal 35 to each other.) Conversely, i f hourly values for QDHW and TDHW-TM (or TDHW and TM) are known, then a missing value for FLOW can be estimated using the same assumption as above. Similar duplication in the recorded data exists for the hourly values of TSDHW and QSDHW. Quality control of the data included a vi s u a l inspection of a l l values after transposing them into a more readable format. This revealed any missing data and displayed the 'playback noise' introduced during r e t r i e v a l of the data from the cassette tapes. It also provided confirmation that the data values were within reasonable bounds. Comparison checks were then made in order to find any inconsistencies between the logger data and the BTU and Neptune meter measurements. These entailed p l o t t i n g scatter diagrams and ca l c u l a t i n g correlation s t a t i s t i c s for the da i l y values of hot water consumption and thermal energy. This again points out the duplication of data recorded for several of the system variables - this time by diff e r e n t sets of instrumentation. The duplication provided greater r e l i a b i l i t y of data continuity and an ongoing check of the monitoring r e s u l t s . Following quality control, a l l data were saved for permanent record on "magnetic tape. The archived data set i s available from the University of B r i t i s h Columbia Data Library. D. Monitoring Period I n i t i a l monitoring of the system using the data logger commenced in late A p r i l 1981. However, f u l l data logging was not in operation u n t i l June 19, 1981. The results reported 36 in the present study include data c o l l e c t e d up to December 16, 1982. The monitoring period therefore covers 546 days, spanning a t o t a l of 19 months.6 E. Equipment Fa i l u r e , Data Gaps, and Logger Saturation While the overall monitoring procedure went very smoothly with no major problems occurring, three d i f f e r e n t disruptive events did occur during c o l l e c t i o n of the data. A l l three were minor in extent and did not seriously a f f e c t the subsequent analysis. The f i r s t event involved a poor quality cassette tape recording on March 23, 1982 in which a small percentage of the data could not be recovered. Randomly missing data for this day were interpolated or estimated using data that were present. In the second incident, human error resulted in the complete loss of data for a 78 hour i n t e r v a l from October 15 to October 18, 1982. These data were irrecoverable and represent the only gap in the quality controlled data set. The t h i r d problem stemmed from storage constraints in the logger's memory, which l i m i t s the maximum size of the recorded data values to 7935.7 For the hot water consumption values t h i s i s equivalent to an hourly draw of 150.2 l i t r e s . Unfortunately, there were f i f t e e n separate hourly occurrences during the monitoring period when the flow meter exceeded 7935 pulses. This resulted in saturation of the logger's memory for the QSDHW, QDHW and FLOW values. (None of the other variables were affected by the 7935 storage l i m i t . ) Ammendments were made to the relevant data by estimating hot water consumption using the BTU meter readings and by assuming that the water supply l i n e 37 temperatures remained independent of flow during each of the affected hours. (The l a t t e r i s a reasonable assumption since water flow would have occurred during a majority of the temperature sampling intervals.) The maximum resul t i n g increase in the ammended data values was 30%. This indicates that the largest hourly hot water draw was approximately 195 l i t r e s . F. System Operation and Maintenance The system functioned continuously and without f a i l u r e during the entire monitoring period. There were no occurrences of snow accumulation on the solar c o l l e c t o r , and frequent r a i n f a l l was s u f f i c i e n t to keep the glazing clean. Condensation was occasionally observed under the panel covers, but frost and dust were never a problem. Corrosion and leakage in the piping was not in evidence, nor was there any sign of mechanical breakdown in the c i r c u l a t i o n pump. Furthermore, no maintenance work was required on the system or i t s components. In summary, mechanical performance of the system was very r e l i a b l e , with no problems a r i s i n g . Two items concerning system operation require mention. F i r s t l y , the d i f f e r e n t i a l c o n t r o l l e r turn 'on' set-point was lowered from 2 to 1 degree C on March 19, 1982 during a periodic inspection of the system by technicians from Solarsystems Industries Ltd. This e f f e c t i v e l y allowed i n i t i a t i o n of c o l l e c t o r operation under s l i g h t l y lower i n t e n s i t i e s of solar radiation, and therefore acted to increase the amount of solar energy c o l l e c t e d by the system. Secondly, there was a 12 l i t r e v a r i a t i o n (.405 - 417 l i t r e s ) in the volume 38 of water in the storage tank (VOLS) during the monitoring period. This was primarily due to evaporation of water from the tank i t s e l f , which i s vented free to the atmosphere. Topping up of the tank was performed on July 29, 1982 using the manual f i l l v alve. 8 Table 3.1 Summary of Instrumentation Design System Variables Sensor Type Operating Range Manufacturer/Trade Name/Model Sensor Uncertainty Temperatures water supply storage tank ambient a i r basement a i r F l u i d flows hot water consumption f u e l consumption Solar radiation transducers thermistors flowmeter gas meter/ encoder pyranometer -55°C - +150°C -10°C - +45 °C 1 - 100 1/min 0 - 85 1/min -40 eC - +40 °C 0 - 1100 W/mZ Analog Devices AD590 K T0-52 package; designation H Campbell S c i e n t i f i c CSI Model 101 Rho Sigma RS 807A Canadian Meter Company Darcom Model D010 Kipp and Zonen CM6 + 0.25 °C ((? 0°C) + 1.0 °C (@ 100°C) + 0.09PC + 1.5% + 0.5% ( f i f t h order polynomial curve f i t ) (over design operating range) (over f u l l operating range) +5.0% (Latimer, 1980) Pump operation t o t a l i z i n g clock 10,000 hours ( d i g i t a l display) +0.1 hour (output resolution) 40 Figure 3.1 Monitoring Equipment Layout -Automatic Data Acquisition and Data Logging System solar collector array H T jfy r anome|t £~^F\ thermistojr 3 i probe d i f f cont e rent t i a l roller f | PPHB | i t o t a l i z i n g clock data logger CR21 lead FLOW flow meter cassette tape recorder • wires Incoming[cold wat from local mains ••< * — TM temperature transducers TSDHW TBSM thermistor probe TDHW hot water to faucets gas meter. circ u l a t i o n pump s o l a r s t o r a g e tank w i t h immersed c o i l heat exchanger a u x i l i a r y hot water tank F i g u r e 3.2 Pyranome t e r B e l o w P o s i t i o n e d I m m e d i a t e l y C o l l e c t o r A r r a y 42 10609 701 0001 . 02 0248. 03 0100. 04 106 10 709 27 .99 10 34.99 1 1 2.000 12 1061 1 701 0002. 02 14 .42 03 0.072 10612 701 0003. 02 37 .46 03 0.211 04 10613 701 0001 . 02 0248. 03 0200. 04 10614 709 27 .99 10 34 .99 11 0 .000 12 10615 701 0002. 02 14.86 03 0.000 10616 701 0003. 02 36.89 03 0.000 04 10617 701 OOOI . 02 0248. 03 0300. 04 10618 709 27.99 10 34.99 1 1 0 .000 12 10619 701 0002. 02 14 .78 03 O.OOO 10620 701 0003. 02 36.35 03 0 .000 04 10621 70.1 0001 . 02 0248. 03 0400. 04 10622 709 27.99 10 34 .99 1 1 O.OOO 12 10623 701 0002. 02 14.21 03 0 .000 10624 701 0003. 02 35.96 03 O.OOO 04 10625 701 0001 . 02 0248. 03 0500. 04 10626 709 27 .99 10 34 .99 1 1 O.OOO 12 10627 701 0002. 02 14 .08 03 0 .000 10628 701 0OO3. 02 35.81 03 O.OOO 04 10629 701 0001 . 02 0248. 03 0600. 04 10630 709 27.99 10 34 .99 1 1 0 .000 12 10631 701 0002. 02 14.00 03 0 .000 10632 701 0003. 02 35.36 03 0 .000 04 10633 701 0001 . 02 0248. 03 0700. 04 10634 709 27.99 10 34.99 11 0 .000 12 10635 701 0002. 02 14 . 16 03 0 .000 10636 701 0003. 02 35.30 03 0 .000 04 10637 701 0001 . 02 0248. 03 0800. 04 10638 709 27 .99 10 34 .99 1 1 0 .000 12 10639 701 0002. 02 14.03 03 0 .000 10640 701 0003. 02 34 .91 03 0 .000 04 1064 1 701 OOOI . 02 0248. 03 0900. 04 10642 709 27.99 10 34.35 1 1 O.OOO 12 10643 701 0002. 02 13.58 03 0 .000 10644 701 0003. 02 34 .55 03 O.OOO 04 10645 701 0O01 . 02 0246. 03 1000. 04 10646 709 27.99 10 33.99 1 1 6.000 12 10647 701 0002. 02 13.03 03 0 . 188 10648 701 0003. 02 34 .23 03 0.572 04 10649 701 0001 . 02 0248. 03 1100. 04 10650 709 30.31 10 33.27 11 1252. 12 10651 701 0002. 02 16. 19 03 63.62 10652 701 0003. 02 41.11 03 157 .2 04 10653 701 0001. 02 0248. 03 1200. 04 10654 709 34 .31 10 35. 1 1 1 1 1 140. 12 10655 701 0002. 02 18.75 03 64 .99 10656 701 0O03. 02 46.85 03 154 .5 04 10657 701 0001 . 02 0248. 03 1300. 04 10658 709 37.26 10 38.64 1 1 412 .0 12 10659 701 0002. 02 19.99 03 28.82 10660 701 0003. 02 43.56 03 54. 14 04 - 5 . 7 8 ' 05 12.55 06 19.39 07 33.81 08 56.86 0.319 5.000 -2 .25 05 12.90 06 19.12 07 33.9B 08 56.01 0.000 4.000 -3.01 05 13.28 06 18\99 07 33.78 08 55.35 0.000 5.000 -2 .66 05 13.43 06 18.99 07 33.21 08 54.96 0.000 4 .000 -3 .29 05 13.53 06 18.93 07 33.01 08 54.74 0.000 5.000 -3.34 05 13.48 06 18.99 07 32.99 08 54.36 O.OOO 4.000 5.040 05 13.28 06 18.83 07 32.99 08 54.14 0.000 4.000 115.7 05 13.3B 06 18.93 07 32.96 08 53.85 0.000 5.OOO 262.7 05 14:00 06 18.99 07 32.58 08 53.54 0.000 4.OOO 338.O 05 14.63 06 18.99 07 32.03 08 53.23 0.888 5.000 1086. 05 15.71 06 17.22 07 33.41 08 58.33 214.3 20.00 1832. 05 17.52 06 16.77 07 35.52 08 63.62 206 .2 21 .00 2446. 05 18.58 06 17.27 07 37.26 08 60.83 73.00 4.000 F i g u r e 3.3 L i s t i n g of f o r J u l i a n Data L o g g e r Output Day 248 (September T a b l e s 5) 1981 43 CHAPTER 4 PRESENTATION AND DISCUSION OF MONITORING RESULTS A. Overview of Presentation The aim of this chapter i s to provide a q u a l i t a t i v e and quantitative account of the system's thermal performance based on the evaluation methodology outlined in Chapter 2 and the data set described in Chapter 3. The presentation is arranged in descending order of d e t a i l . Overall and monthly results are presented f i r s t ; these provide a general perspective on system performance. They are followed by an examination of the system on a dai l y and diurnal basis, y i e l d i n g more s p e c i f i c information on the system's operating c h a r a c t e r i s t i c s . Lastly, the users' hot water consumption patterns are analyzed. B. Overall Thermal Performance Summary The o v e r a l l thermal performance of the SDHW heating system is diagrammed in Figure 4.1. Over the 19 month long monitoring period, 35.97 GJ of solar radiation was incident on the c o l l e c t o r array. From th i s t o t a l amount of available solar energy, the system usefully converted 38%, or 13.66 GJ, and delivered i t in the form of sensible heat to the domestic hot water supply. This required an external expenditure of 0.68 GJ of e l e c t r i c a l energy in order to power the c i r c u l a t i o n pump and transfer the useful solar energy gains to the storage tank during the 1761.2 hours of c o l l e c t o r operation. Accordingly, the system had an overall c o e f f i c i e n t of performance of 20.1 with respect to solar operation; i e . one unit of 'purchased' energy was expended for every twenty units of 'free' solar 44 energy u t i l i z e d . In comparison, the a u x i l i a r y hot water tank expended 35.85 GJ of fuel energy, equivalent to a volume of 914.5 m3 of natural gas. Forty-two percent of t h i s a u x i l i a r y energy input (15.08 GJ) was converted and delivered as sensible hot water heat, while 58% (20.77 GJ) was subsequently dissipated and lost to the surrounding environment. The combined t o t a l of solar and a u x i l i a r y heat delivered to, and retained by, the 145.0 m3 of water flowing through the system amounted to 28.74 GJ. This quantity represents the t o t a l domestic hot water heating load during the monitoring period. The corresponding solar f r a c t i o n of t h i s load was 47.5%. The stand-alone e f f i c i e n c y of the a u x i l i a r y hot water tank was evaluated following termination of the monitoring period. Since a representative ACEF value requires a s u f f i c i e n t l y lengthy period of t y p i c a l hot water consumption to be monitored, a t o t a l of three weeks in January 1983 were employed. During t h i s period the solar components were decoupled from the heating system, allowing the a u x i l i a r y tank to supply the t o t a l hot water heating requirement. The resultant (empirical) ACEF value was 0.54. This compares favourably with the findings of Farahan (1977) for an average r e s i d e n t i a l gas water heater in good working condition, as l i s t e d below. Jacket losses D i s t r i b u t i o n losses F l u e / p i l o t l i g h t losses (25 f t . hot water pipe) 12% 3% 33% i e . o v e r a l l gas water heater e f f i c i e n c y = 52% For the system under investigation, the d i s t r i b u t i o n losses are 45 minimal since the hot water delivery temperature is measured in close proximity to the a u x i l i a r y tank e x i t . Thus, i f one discounts the d i s t r i b u t i o n losses reported above, the two ACEF values can be seen to be in close agreement. Application of the empirical ACEF value y i e l d s an accumulated fuel energy savings of 17.37 GJ for the o v e r a l l monitoring period. The net amount of conventional energy saved - i e . subtracting the amount of e l e c t r i c a l energy needed to operate the c i r c u l a t i o n pump - was 16.69 GJ, or approximately 46% of the t o t a l amount of a u x i l i a r y energy consumed. Tables 4.1 and 4.2 summarize the monthly and overall thermal performance of the system. Several of the thermal energy quantities and performance indicators follow a d e f i n i t e seasonal cycle, while others show a pronounced v a r i a b i l i t y independent of season. This i s discussed in f u l l e r d e t a i l in the presentation which follows. The above tables should be used as a reference for s p e c i f i c monthly values. C. Monthly / Seasonal Thermal Performance Results Figure 4.2 presents a bar graph of the monthly integrals of solar, a u x i l i a r y , and t o t a l heat delivered to the domestic hot water supply. 9 The lower portion of each monthly bar (with one exception as noted below) i s the amount of solar heat delivered (QSDHW), while the upper portion i s the amount of a u x i l i a r y heat delivered (QAUXW). Summed together they indicate the t o t a l amount of heat delivered by the system to the incoming cold water (QDHW). This l a t t e r quantity varied from month to month depending on the volume of hot water 46 consumed and the temperature increase between the cold water entering the system and the hot water ex i t i n g i t , as was mathematically expressed by equation 7 in Chapter 2. Monthly volumes of hot water consumption can be read from Table 4.1, while the magnitude of the temperature increase across the two tanks can be ascertained on a dail y basis from Figure 4.14. February 1982 experienced the largest monthly QDHW value (2.019 GJ), although only the fourth largest hot water consumption value (9.117 m 3). May, June, and September of 1982 a l l experienced greater hot water consumption (9.422, 9.188, and 9.765 m3 respectively), yet delivered less t o t a l hot water heat. The reason was due to smaller increases in the temperature of the water as i t flowed through the system. This sit u a t i o n i s v e r i f i e d by Figure 4.14, which reveals generally higher TM and lower TDHW temperatures during the l a t t e r three months. In fact, a downward step change in hot water delivery temperature i s seen to occur in early March 1982; while the day-to-day v a r i a b i l i t y does not v i s i b l y change, the average TDHW temperature appears to be systematically lower after t h i s date. 1 0 Total hot water heat delivered was consistently greater than i t s solar component for a l l months of the monitoring period except August 1981. This l a t t e r month experienced predominantly sunny weather, which combined with favourable angles of incidence for beam radiation on the c o l l e c t o r slope to produce the highest monthly solar radiation value (3.51 GJ) . While the actual quantity of solar energy co l l e c t e d was not measured, the large number of pump operating hours (142.0) and 47 the elevated storage tank temperatures (Figure 4.13a) indicate that a r e l a t i v e l y large amount of solar energy was gained by the system during t h i s month. Unfortunately this month also experienced the lowest volume of hot water consumption (excluding the two incomplete months) due to summer holidays and the consequent absence of household members. Hence the abundant supply of heat which existed in the solar storage tank was not f u l l y u t i l i z e d . The resultant d a i l y mean storage tank temperatures, for both the bottom and mid-height measurement lev e l s , remained above 50°C for most of th i s month; for a one week period the mid-height temperature was in fact above 70°C. Consequently, the solar heated water was r e l a t i v e l y hot as i t flowed out of the heat exchanger from the storage tank. Figure 4.14a indicates that the temperature of t h i s water was c h a r a c t e r i s t i c a l l y above the temperature of the hot water exiting from the a u x i l i a r y tank. Thus the amount of heat extracted from the solar storage tank and delivered to the incoming cold water exceeded the t o t a l amount of heat added to and retained by the hot water drawn from the a u x i l i a r y tank. The l a t t e r tank was in ef f e c t acting as a heat sink since more heat was l o s t (0.873 GJ) than was gained from combustion of fuel (0.834 GJ). The heat loss i t s e l f was largely standby loss through the poorly insulated a u x i l i a r y tank jacket as well as from the 4 metre long insulated entry pipe included within the a u x i l i a r y tank's thermal boundary. The fuel consumption in turn was largely a result of continuous p i l o t l i g h t o p eration. 1 1 Because of the net heat loss for the a u x i l i a r y hot water tank, the month of August 1981 recorded a negative a u x i l i a r y 48 tank e f f i c i e n c y (-0.046) and a solar f r a c t i o n greater than unity (1.040). In contrast, a l l other months had positi v e AUXE values, and solar fractions less than unity. 1. Solar Heat Delivered, Pump Operation, and Solar Radiation The amount of solar heat delivered to the incoming cold water exhibits a d e f i n i t e seasonal pattern. It varies as a function of both the amount of solar radiation incident on the col l e c t o r array and the volume of hot water consumed. The two highest monthly QSDHW values occurred in May (1.296 GJ) and June (1.282 GJ) of 1982. They were a result of r e l a t i v e l y large hot water consumption in combination with abundantly available solar energy. The two lowest monthly QSDHW values occurred in December 1981 (0.216 GJ) and January 1982 (0.170 GJ). They d i r e c t l y correspond with minimal values of solar radiation incident on the c o l l e c t o r array. It i s interesting to note how the volume of hot water consumed can s i g n i f i c a n t l y influence the amount of solar heat delivered by the system, irrespective of the magnitude of available solar energy. v i z . During the summer of 1981, each of the months of July, August, and September experienced greater QHT values than th e i r counterparts in 1982 (+6%, +21%, and +2% respectively) yet produced lower QSDHW values (-13%, -6%, and -9%). Thus, the greater amount of available solar energy during the f i r s t summer of system operation was simply not being u t i l i z e d as e f f e c t i v e l y . The primary reason was the much smaller volume of hot water consumed: -19%, -42%, and -33% for the three months respectively. QSDHW i s strongly correlated with the number of pump 49 operating hours (PPHR). The l a t t e r variable is i n d i r e c t l y a measure of the amount of solar energy col l e c t e d and transferred to the storage tank. It also varies as a function of the interacting e f f e c t s of available solar energy and hot water consumption, and therefore exhibits a seasonal pattern similar to QSDHW (Figure 4.3). The maximum PPHR value of 190.5 hours was recorded in June 1982, yie l d i n g an average of 6.35 hours per day of solar energy c o l l e c t i o n for this month. The minimum PPHR value occurred in January 1982 - a monthly t o t a l of only 7.1 hours. Examination of the seasonal d i s t r i b u t i o n in the amount of solar radiation incident on the c o l l e c t o r array (Figure 4.3) reveals that each of the spring and summer months, A p r i l through September inclusive, can record comparatively large QHT values. Hence during these months, the number of pump operating hours and the amount of solar heat delivered are largely a function of the variable load and meteorological conditions imposed on the system, and less a function of earth-sun geometry. In fact, late A p r i l and August are ra d i a t i v e l y the most ideal times of the year for solar energy c o l l e c t i o n given clear sky conditions, due to the t i l t angle of the c o l l e c t o r (41°). The period between October and March becomes increasingly less favourable for solar energy a v a i l a b i l i t y , e s p e c i a l l y as the winter s o l s t i c e i s approached, exclusive of the overcast skies which generally p r e v a i l at this time of year. 2. Solar Fraction The monthly solar fractions are graphed in Figure 4.4. 50 They d i s p l a y a s e a s o n a l p a t t e r n s i m i l a r t o t h e QSDHW v a l u e s w i t h w h i c h t h e y a r e d i r e c t l y r e l a t e d . S o l a r f r a c t i o n s f o r t h e months J u l y and September 1981, t o g e t h e r w i t h t h e months A p r i l t h r o u g h A u g ust 1982, were a l l c l o s e t o 0.7. E x c e p t i o n s t o t h i s p a t t e r n were June and A u g u s t o f 1981. The f o r m e r o f t h e s e two months e x p e r i e n c e d r e l a t i v e l y c l o u d y w eather d u r i n g i t s l i m i t e d p e r i o d of m o n i t o r i n g and t h e r e f o r e had a s e a s o n a l l y d e p r e s s e d s o l a r f r a c t i o n ( 0 . 5 1 5 ) ; t h e l a t t e r month e x p e r i e n c e d a s m a l l hot w ater h e a t i n g l o a d r e l a t i v e t o s o l a r e n e r g y i n p u t and t h e r e f o r e had a s o l a r f r a c t i o n g r e a t e r t h a n u n i t y , as was d i s c u s s e d a b o v e . The s p r i n g and f a l l months had i n c r e a s i n g and d e c r e a s i n g s o l a r f r a c t i o n s r e s p e c t i v e l y , w i t h v a l u e s r a n g i n g between 0.2 and 0.7. The two w i n t e r months of December 1981 and J a n u a r y 1982 r e c o r d e d t h e l o w e s t s o l a r f r a c t i o n s - 0.133 and 0.092 r e s p e c t i v e l y - i n r e s p o n s e t o m i n i m a l s o l a r e n e r g y a v a i l a b i l i t y ; i e . s h o r t d a y l e n g t h s , p e r s i s t e n t c l o u d , and l a r g e a n g l e s o f i n c i d e n c e f o r beam r a d i a t i o n . 3. S o l a r C o n v e r s i o n E f f i c i e n c y M o n t h l y v a l u e s o f t h e s y s t e m ' s s o l a r e n e r g y c o n v e r s i o n e f f i c i e n c y a r e g r a p h e d i n F i g u r e 4.5. V a l u e s r a n g e from 0.29 t o 0.48 and e x h i b i t an a p p a r e n t b i - m o d a l s e a s o n a l d i s t r i b u t i o n . Maximum SCEF v a l u e s o c c u r r e d d u r i n g t h e f a l l and w i n t e r months, w i t h a s e c o n d a r y maximum i n e a r l y summer; a c y c l i c a l p a t t e r n of l o w e r v a l u e s o c c u r r e d d u r i n g t h e i n t e r v e n i n g s p r i n g and summer months. A u g u s t 1981/82 and March 1982 r e c o r d e d t h e minimum v a l u e s d u r i n g t h e m o n i t o r i n g p e r i o d . L e s s e f f i c i e n t use o f t h e a v a i l a b l e s o l a r e n e r g y d u r i n g t h e s e months can be p a r t i a l l y e x p l a i n e d i n terms o f t h e v a r i a b l e l o a d c o n d i t i o n s 51 imposed on the system. Compare June and August 1982. Total solar radiation incident on the c o l l e c t o r array was s l i g h t l y greater for August (1.5%) yet the number of pump operating hours and the amount of solar heat delivered were s i g n i f i c a n t l y greater in June (14% and 19% respectively). The cause of t h i s discrepancy was a larger average d a i l y consumption of hot water in June (7.0%). During t h i s month, large hot water draws in the morning tended to decrease storage tank temperatures prior to commencement of solar energy c o l l e c t i o n (Section E). This lead to more e f f i c i e n t c o l l e c t o r operation and therefore greater solar energy input and u t i l i z a t i o n . The apparent a b i l i t y of the system to make more e f f i c i e n t use of the available solar energy during the f a l l and winter months i s somewhat incongruous. One could reason that the system should be less e f f i c i e n t at th i s time of year since a greater proportion of the solar radiation i s dif f u s e and the angles of incidence for beam radiation are less favourable. Further investigation of t h i s situation reveals that the system on average delivered 0.023 GJ of solar heat for each hour of co l l e c t o r operation in January 1982 yet only 0.007 GJ per hour in June 1982 - the most e f f i c i e n t spring / summer month. In addition, the system's solar c o e f f i c i e n t of performance was 39.4 and 60.2 in December 1981 and January 1982 respectively, markedly above the o v e r a l l average value of 20.1 for the monitoring period. The incongruity can be p a r t i a l l y explained based on the evidence that the solar storage tank actually gained a considerable amount of heat from the surrounding basement a i r during the f a l l and winter months. Examination of 52 Figure 4.12 for the period November 1981 through February 1982 reveals that the d a i l y mean storage tank temperature (mid-height level) was frequently below that of the surrounding basement a i r (as estimated by the surrogate variable TMNF5 -Appendix E). In fact, during January 1982 the daily mean storage tank temperature remained below that of the surrounding basement a i r for the entire month, creating a per s i s t e n t l y negative tank-to-air temperature gradient. The l i m i t i n g factor determining the minimum storage tank temperature i s the a b i l i t y of the incoming cold water to extract heat from the tank as i t flows through the heat exchanger. Heat can be transferred as long as a temperature gradient e x i s t s . Thus, the storage tank temperature was depressed below that of the surrounding basement a i r and approached that of the incoming cold water during periods of low and zero solar energy input. It therefore follows that heat was frequently transferred from the warmer basement a i r to the cooler water in the storage tank during the f a l l and winter months. Some of t h i s standby heat gain would have been subsequently transferred to the water supply. With respect to the evaluation terminology, th i s heat was i m p l i c i t l y included in the amount of 'solar' heat delivered to the incoming cold water. Accordingly, the values for QSDHW fa l s e l y represent the actual solar performance of the system during the f a l l and winter months; values for SFRAC and SCEF should also be interpretted with t h i s l i m i t a t i o n in mind. 4. A u x i l i a r y Water Heater The amount of a u x i l i a r y heat delivered to the domestic hot• water supply also exhibits a d e f i n i t e seasonal pattern since i t 53 acts as a conjugate to the amount of solar heat delivered (Figure 4.6). Small monthly QAUXW values occurred from A p r i l through August and were consistently below 0.5 GJ. Large monthly values occurred during the winter months; QAUXW for both January and February 1982 exceeded 1.6 GJ. In turn, fuel energy consumption varied as a function of the au x i l i a r y hot water heating demand. Large monthly values of QFUEL coincided with those of QAUXW and were in excess of 3.0 GJ. Small monthly values were generally close to 1.4 GJ, although August 1981 recorded a value only s l i g h t l y greater than that required to maintain p i l o t l i g h t operation. The e f f i c i e n c y of the au x i l i a r y hot water tank varied in direct proportion to fuel energy consumption. The maximum AUXE values - which occurred during the winter months - were t y p i c a l l y around 0.5, while those for the other times of the year were considerably lower (Figure 4.7). The seasonal v a r i a b i l i t y in the AUXE values relates to fuel consumption being comprised of an approximately constant p i l o t l i g h t component and a variable main burner component. As fuel consumption increases, a r e l a t i v e l y larger proportion i s u t i l i z e d by the main burner, which i s more e f f i c i e n t at converting fuel energy into hot water heat. This resulted in fuel energy consumption being seasonally less variable than a u x i l i a r y hot water heating demand (on a re l a t i v e b a s i s ) . The heat content of the natural gas - a parameter used in converting volumetric fuel consumption into i t s thermal equivalent - varied over a range of 5.1% (2.00 MJ/m3) on a bi-monthly basis. The highest HFC value (40.55 MJ/m3) 54 occurred during the two months July/August 1982; the lowest value (38.55 MJ/m3) during the two months March/April 1982. A c y c l i c a l pattern of intermediate values occurred during other months of the monitoring period. The seasonal v a r i a b i l i t y in HFC is related to well-head supply. A single, high quality well i s used to supply natural gas in summer. During the winter heating season this high quality gas i s mixed with gas from a well of lower quality to provide for the extra heating demand. The day-to-day v a r i a b l i l i t y in HFC during any given two-month b i l l i n g period i s usually quite small - t y p i c a l l y less than 1.5% (personal communication - G. Matthews). Hence the v a r i a b i l i t y in HFC i s largely seasonal in character. Accordingly, neg l i g i b l e error was introduced into the monthly QFUEL quantities through the use of average HFC values, i e . Fuel consumption was never concentrated on only a limited number of days; rather i t was dis t r i b u t e d over a l l days of each month. 5. Conventional Energy Saved and Pump Energy Consumption Monthly values for both fuel and net conventional energy saved varied seasonally in close unison with the QSDHW values, to which they are i n d i r e c t l y related (Figure 4.8). The maximum monthly QFSAVE and QESAVE values (1.794 and 1.724 GJ respectively) occurred in May 1982, coincident with the maximum value of QSDHW. Values for the months A p r i l through September 1982 were consistently above 1.35 GJ for QFSAVE and above 1.29 GJ for QESAVE. Values for corresponding summer months in 1981 (July - September) were approximately one t h i r d lower, r e f l e c t i n g the lower QSDHW values experienced during t h i s 55 summer. The minimum m o n t h l y QFSAVE and QESAVE v a l u e s (0.168 and 0.162 GJ) o c c u r r e d i n December 1981 and were c o m e n s u r a t e w i t h t h e s m a l l amount of s o l a r h e a t d e l i v e r e d d u r i n g t h i s month. The o c c u r r e n c e o f s i m i l a r QFSAVE and i d e n t i c a l QESAVE v a l u e s f o r t h e two months of A u g u s t and September 1982, d e s p i t e a 13.7% l a r g e r QSDHW v a l u e i n A u g u s t , r e l a t e s t o t h e v a r i a b i l i t y i n t h e AUXE v a l u e s . Pump e n e r g y c o n s u m p t i o n - r e p r e s e n t e d g r a p h i c a l l y by t h e d i f f e r e n c e between t h e QFSAVE and QESAVE v a l u e s - v a r i e d s e a s o n a l l y i n a c c o r d a n c e w i t h t h e number of pump o p e r a t i n g h o u r s . On a m o n t h l y b a s i s , QPUMP had a maximum v a l u e of 73.4 MJ i n June 1982 and a minimum v a l u e o f 2.7 MJ i n J a n u a r y 1982. 6. Heat E x c h a n g e r E f f e c t i v e n e s s M o n t h l y f l o w - w e i g h t e d h e a t e x c h a n g e r e f f e c t i v e n e s s a l s o e x h i b i t s a d e f i n i t e s e a s o n a l p a t t e r n ( F i g u r e 4 . 9 ) . V a l u e s f o r t h e months June t h r o u g h O c t o b e r 1981 and March t h r o u g h September 1982 were a l l above 0.9. The maximum mo n t h l y HXEF v a l u e of 1.014 o c c u r r e d i n A u g u s t 1981. T h i s was t h e o n l y month w h i c h r e c o r d e d a HXEF v a l u e g r e a t e r t h a n u n i t y . The f a l l a nd w i n t e r months e x p e r i e n c e d c y c l i c a l l y l o w e r HXEF v a l u e s . December 1981 and J a n u a r y 1982 had t h e l o w e s t HXEF v a l u e s : 0.617 and 0.589 r e s p e c t i v e l y . To e x p l a i n t h e s e a s o n a l v a r i a b i l i t y i n h e a t e x c h a n g e r e f f e c t i v e n e s s , i t i s u s e f u l t o i n i t i a l l y examine t h e f r e q u e n c y d i s t r i b u t i o n o f t h e i n d i v i d u a l ( h o u r l y ) HXEF v a l u e s o v e r t h e m o n i t o r i n g p e r i o d . T h i s d i s t r i b u t i o n i s g r a p h e d i n F i g u r e 4.10. I t i s s l i g h t l y skewed w i t h a modal c l a s s (19.6% o f t o t a l 56 hourly values) between 1.025 and 1.075. However, a s i g n i f i c a n t number of values l i e below 0.025 (8.14%) as well as above 1.275 (3.86%). (They are highlighted as d i s t i n c t classes in the d i s t r i b u t i o n graph by dashed lines.) It i s important to ascertain why these 'deviant' HXEF values e x i s t . Such an investigation w i l l also provide the reason for the seasonal v a r i a b i l i t y in heat exchanger effectiveness. F i r s t l y , r e c a l l that the denominator of the HXEF r a t i o was set equal to the temperature difference between the storage tank (mid-height level) and the cold water entering the immersed c o i l heat exchanger, i e . TSmid-TM. During the f a l l and winter months this temperature difference was often negative, indicating that the incoming cold water was frequently warmer than the water residing in the storage tank. This si t u a t i o n predominantly occurred under low-flow conditions. v i z . Stagnant cold water in the un-insulated i n l e t pipe would equilibrate in temperature with the warmer surrounding basement a i r . A small amount of hot water would then be drawn and 'pre-heated' water would flow into the heat exchanger and lose heat to the cooler water in the storage tank. This would consequently result in a non-positive hourly HXEF v a l u e . 1 2 The d i s t r i b u t i o n of non-positive hourly HXEF values on a seasonal basis can be examined by comparing the monthly flow-weighted average HXEF values with those evaluated using arithmetical averaging (Table 4.3). During December 1981/82 the arithmetical average HXEF value was less than -1.7. 1 3 Hence many of the hourly HXEF values were non-positive. This calender month represented the extreme case. Other f a l l 57 and w i n t e r months e x p e r i e n c e d n o n - p o s i t i v e h o u r l y HXEF v a l u e s w i t h l e s s f r e q u e n c y . T h e r e f o r e t h e i r a r i t h m e t i c a l a v e r a g e HXEF v a l u e s were not as low. T h i s t h e n e x p l a i n s t h e e x i s t e n c e and s e a s o n a l v a r i a b i l i t y o f t h e n o n - p o s i t i v e HXEF v a l u e s . To c o m p l e t e t h e d i s c u s s i o n , t h e m o n t h l y d i v e r g e n c e between t h e f l o w - w e i g h t e d and a r i t h m e t i c a l a v e r a g e HXEF v a l u e s r e q u i r e s e x p l a n a t i o n . Under h i g h - f l o w c o n d i t i o n s t h e volume of h o t w a t e r drawn g r e a t l y e x c e e d s t h e volume o f c o l d water i n i t i a l l y r e s i d i n g i n t h e i n l e t p i p e . C o n s e q u e n t l y , t h e t e m p e r a t u r e of t h e i n c o m i n g c o l d water r e f l e c t s t h a t of t h e l o c a l mains s u p p l y and not t h a t of t h e basement a i r ( S e c t i o n E ) . Thus h i g h - f l o w c o n d i t i o n s a l m o s t a l w a y s e x p e r i e n c e a p o s t i v e TSmid-TM t e m p e r a t u r e d i f f e r e n c e and t h e r e f o r e y i e l d p o s i t i v e h o u r l y HXEF v a l u e s . Hence d u r i n g t h e w i n t e r months t h e f l o w - w e i g h t e d a v e r a g e HXEF v a l u e s s i g n i f i c a n t l y e x c e e d t h e a r i t h m e t i c a l a v e r a g e v a l u e s . D u r i n g t h e s p r i n g and summer months t h i s s i t u a t i o n c h a n g e s . Even under l o w - f l o w c o n d i t i o n s , t h e s e months a l w a y s e x p e r i e n c e a p o s i t i v e TSmid-TM t e m p e r a t u r e d i f f e r e n c e due t o g r e a t e r s o l a r e n e r g y i n p u t and warmer s t o r a g e t a n k t e m p e r a t u r e s . F u r t h e r m o r e , under l o w - f l o w c o n d i t i o n s t h e s o l a r h e a t e d water e x i t i n g t h e h e a t e x c h a n g e r t e n d s t o r e f l e c t t h e t e m p e r a t u r e e x i s t i n g i n t h e upper r e g i o n of t h e s t o r a g e t a n k and i s t h e r e f o r e o f t e n s l i g h t l y warmer t h a n t h e t e m p e r a t u r e measured a t t h e m i d - h e i g h t l e v e l ( S e c t i o n E ) . Hence h o u r l y HXEF v a l u e s under l o w - f l o w c o n d i t i o n s f r e q u e n t l y e x c e e d e d 1 . 0 d u r i n g t h e s p r i n g and summer months. In c o m p a r i s o n , h i g h f l o w - c o n d i t i o n s a r e n o r m a l l y a s s o c i a t e d w i t h s m a l l e r TSDHW-TM t e m p e r a t u r e d i f f e r e n c e s s i n c e r e l a t i v e l y c o l d 58 mains water now c o m p l e t e l y r e p l a c e s t h e volume of ( t h e r m a l l y e q u i l i b r a t e d ) water i n i t i a l l y r e s i d i n g i n t h e i n l e t p i p e and t h e immersed c o i l h e a t e x c h a n g e r . The i n c r e a s e i n t e m p e r a t u r e of t h i s water as i t f l o w s t h r o u g h t h e s t o r a g e tank i s u s u a l l y l e s s t h a n t h e 'maximum p o s s i b l e i n c r e a s e ' ( i e . TSmid-TM) s i n c e i t s f l o w - t h r o u g h t i m e i s r e l a t i v e l y s h o r t . T h i s r e s u l t s i n h o u r l y HXEF v a l u e s c h a r a c t e r i s t i c a l l y l e s s t h a n 1.0 under h i g h - f l o w c o n d i t i o n s , as i n d i c a t e d by F i g u r e 4.11. Hence d u r i n g t h e s p r i n g and summer months t h e f l o w - w e i g h t e d a v e r a g e HXEF v a l u e s a r e t y p i c a l l y l e s s t h a n t h e a r i t h m e t i c a l a v e r a g e v a l u e s . 7. S t o r a g e Tank T e m p e r a t u r e E x a m i n a t i o n of t h e d a y - t o - d a y v a r i a b i l i t y i n s t o r a g e t a n k t e m p e r a t u r e ( F i g u r e 4.13) r e v e a l s t h r e e t h e r m a l l y d i s t i n c t s e a s o n a l p e r i o d s f o r t h e s t o r a g e t a n k . The f i r s t p e r i o d , w h i c h i n c l u d e s t h e s p r i n g and summer months A p r i l t h r o u g h A u g u s t , e x h i b i t s wide swings i n d a i l y mean s t o r a g e t a n k t e m p e r a t u r e -f r e q u e n t l y by as much as 3 0 ° C . T h i s o c c u r r e n c e r e l a t e s t o t h e l a r g e d a y - t o - d a y v a r i a b i l i t y i n t h e l o a d and m e t e o r o l o g i c a l c o n d i t i o n s imposed on t h e s y s t e m as w e l l as t h e s h o r t - t e r m t h e r m a l c h a r a c t e r i s t i c o f t h e s t o r a g e t a n k . D u r i n g t h i s p e r i o d t h e d a i l y mean tank m i d - h e i g h t t e m p e r a t u r e r a n g e d from a low o f 24°C ( A p r i l 13, 1982) t o a h i g h o f 78°C ( A u g u s t 11, 1981). S i m i l a r y , t h e t a n k b o t t o m t e m p e r a t u r e r a n g e d f r o m 19°C t o 69°C. No month d u r i n g t h i s p e r i o d e x p e r i e n c e d c o n s i s t e n t l y h i g h e r d a y - t o - d a y t e m p e r a t u r e s t h a n any o t h e r month. However, A u g u s t 1981 d i d r e c o r d a s i g n i f i c a n t l y h i g h e r m o n t h l y a v e r a g e s t o r a g e t a n k t e m p e r a t u r e due t o i t s u n i q u e c o m b i n a t i o n of r e l a t i v e l y 59 large solar energy input and small hot water heating load. The second period, which includes the calendar months February/March and September/October/November, exhibits a transitory increase and decrease in daily mean storage tank temperature. This relates to the large seasonal change in the amount of available solar energy during this period. --Day-to-day temperature swings decrease during the three f a l l months, while during the two spring months they increase. As well, the ove r a l l range in da i l y mean temperature i s substantially reduced during t h i s period. The t h i r d period, consisting of the two winter months December and January, exhibits a comparatively uniform da i l y mean storage tank temperature; i t fluctuates within the narrow range 10°C - 25°C, and i s r e l a t i v e l y close to that of the surrounding basement a i r . This period experienced the least degree of thermal s t r a t i f i c a t i o n within the storage tank. Daily mean temperature differences between the tank bottom and mid-height measurement level s averaged only 2 degrees C. This compares with an average 5 degrees C during the f i r s t period and 3 degrees C during the second. 8. Water Supply Line Temperatures Figures 4.14 depicts the day-to-day and seasonal v a r i a b i l i t y in the water supply l i n e temperatures. The d a i l y mean incoming cold water temperature TM exhibits the least amount of v a r i a b i l i t y . Confined within .the comparatively narrow temperature range 10°C - 20°C, i t s day-to-day temperature swings are c h a r a c t e r i s t i c a l l y less than 3 degrees C. Futhermore, they are largely influenced by da i l y differences in 60 the water flow regime ( i e . residency time of the cold water in the i n l e t pipe coupled with the heating effect of the surrounding basement a i r ) and not by temperature v a r i a b i l i t y in the l o c a l mains supply. Correspondingly, seasonal v a r i a b i l i t y in the incoming cold water temperature i s only very s l i g h t , as can be seen most e a s i l y during the summer and f a l l months of 1981 (Figure 4.14a). The hot water delivery temperature TDHW experiences r e l a t i v e l y larger day-to-day temperature swings ( t y p i c a l l y 2 - 5 degrees C), r e f l e c t i n g the influence of flow conditions and the i n a b i l i t y of the a u x i l i a r y hot water tank to maintain a constant delivery temperature. The dail y mean TDHW temperature ranged from a low of 47°C (March 22, 1982) to a high of 69°C (October 8, 1981) and had an ove r a l l average of 58°C for the monitoring period. The solar heated water temperature exhibits the greatest amount of v a r i a b i l i t y , both on a day-to-day and a seasonal basis. Daily mean TSDHW temperatures tended to closely match those of TSmid, as evidenced in Figure 4.13. An apparent exception to this trend is the two month period December 1981 - January 1982. The positiv e divergence between the TSDHW and TSmid temperature curves during these two winter months was caused by evaluation l i m i t a t i o n s such that the hourly (flow-weighted) TSDHW temperatures were precluded from being less than the corresponding TM temperatures (Appendix C). Therefore, the result i n g d a i l y mean TSDHW temperatures plotted for these two months are p o s i t i v e l y biased. Additional periods can be seen when the da i l y mean TSDHW temperature curve i s noticeably below the TSmid curve - eg. mid-August 1981 and mid-March 1982. 61 These negative divergences relate to differences in the computational data sets used to calculate the dail y mean temperatures. For the storage tank temperatures, a l l hours of the day are included in the da i l y mean values. In contrast, the daily mean solar heated water temperature includes only those hours in which flow occurred. Hence days which experienced r e l a t i v e l y warmer temperatures in the storage tank during (mid-day) hours in which no hot water was drawn, tended to y i e l d higher daily mean TSmid than TSDHW temperatures. The d a i l y mean temperature difference between the cold water entering the heat exchanger and the solar heated water exiting i t i s indicated by the separation between the TSDHW and TM temperature curves (Figure 4.14). During August 1981 this temperature difference averaged 48°C - the largest monthly difference. On a day-to-day basis i t was subject to large v a r i a b i l i t y , predominantly as a function of the v a r i a b i l i t y in TSDHW. Seasonally, t h i s temperature difference was largest and most variable during the spring and summer months A p r i l through August. It decreased and became less variable during the f a l l and winter months. D. Daily Thermal Performance Figures 4.15, 4.17, 4.19 & 4.21 present bar graphs of the da i l y integrals of solar, a u x i l i a r y , and t o t a l heat delivered to the domestic hot water supply. Four separate months are shown, representing d i f f e r e n t radiative and thermal conditions for the system during the monitoring period. Accompanying the thermal energy bar graphs are time series plots of the storage 62 tank temperatures for a two week period during each of the four months (Figures 4.16, 4.18, 4.20 & 4.22). The thermal performance of the system during each of the months i s discussed below. 1. September 1981 (Figures 4.15 & 4.16) The mean da i l y quantity of solar heat delivered during t h i s month was 29.5 MJ. (Note - There was no hot water drawn on Sept. 19.) This compares with a corresponding value of 43.4 MJ for t o t a l heat delivered. However, these monthly averages conceal the large day-to-day v a r i a b i l i t y in the amounts of solar and t o t a l heat delivered. For QSDHW, the individual d a i l y values ranged from a minimum of 13 MJ on Sept. 5 to a maximum of 57 MJ on Sept. 14. Intermediate d a i l y QSDHW values were f a i r l y evenly di s t r i b u t e d within this monthly range. For QDHW, the individual d a i l y values varied between 18 MJ (Sept. 6) and 75.5 MJ (Sept. 25). Daily solar fractions can be v i s u a l l y estimated by comparing the heights of the s o l i d (QDHW) and dashed (QSDHW) bars. During the f i r s t half of September 1981 the d a i l y solar fractions tended to be high; there were a t o t a l of five days on which the solar fraction exceeded 1.0, and no day had a solar fra c t i o n less than 0.6. This was a result of r e l a t i v e l y large d a i l y solar energy input, in combination with small to moderate hot water consumption. In contrast, the second half of the month had larger d a i l y volumes of hot water consumption and less solar energy input; t h i s resulted in lower da i l y solar fractions (0.3 - 0.8). The time series plot of storage tank temperatures v e r i f i e s the large amount of solar energy that was gained by the system 63 d u r i n g t h e f i r s t h a l f of t h i s month. The d a i l y number o f pump o p e r a t i n g h o u r s i s l i s t e d a c r o s s t h e t o p o f t h e f i g u r e . Hours d u r i n g w h i c h t h e pump i s o p e r a t i n g a r e a c c o m p a n i e d by an i n c r e a s e i n s t o r a g e t a n k t e m p e r a t u r e i n d i c a t i n g s o l a r e n e r g y c o l l e c t i o n ; h o u r s w h i c h show l a r g e d e c l i n e s i n s t o r a g e t a n k t e m p e r a t u r e - e s p e c i a l l y t a n k b o t t o m t e m p e r a t u r e - i n d i c a t e h e a t b e i n g w i t h d r a w n from t h e tank and d e l i v e r e d t o t h e i n c o m i n g c o l d w a t e r . D a i l y maximum t e m p e r a t u r e s were t y p i c a l l y between 60°C and 75°C, w h i l e d a i l y minimum t e m p e r a t u r e s were g e n e r a l l y between 30°C - 45°C f o r t h e tank b o t t o m and 40°C -55°C f o r t h e tank m i d - h e i g h t l e v e l . The s t o r a g e t a n k t e n d s t o be i s o t h e r m a l d u r i n g p e r i o d s of s o l a r e n e r g y c o l l e c t i o n , and t h e r m a l l y s t r a t i f i e d d u r i n g p e r i o d s of h e a t w i t h d r a w a l ( i n t h e a b s e n c e o f c o n c u r r e n t pump o p e r a t i o n ) . T h e r m a l s t r a t i f i c a t i o n i s p a r t i a l l y a t t r i b u t a b l e t o h e a t b e i n g p r e f e r e n t i a l l y w i t h d r a w n from t h e low e r r e g i o n of th e s t o r a g e t a n k a s water f l o w s t h r o u g h t h e immersed c o i l h e a t e x c h a n g e r . S t r a t i f i c a t i o n i s a l w a y s s t a b l e and can become v e r y w e l l d e v e l o p e d ; t h e maximum measured t h e r m o c l i n e ( T S m i d - T S b o t ) d u r i n g t h e f i r s t two weeks o f September was 21 d e g r e e s C. Under t h e s e c o n d i t i o n s t h e b o t t o m and m i d - h e i g h t t e m p e r a t u r e s become r e p r e s e n t a t i v e of o n l y s m a l l z o n e s w i t h i n t h e t a n k . P e r i o d s d u r i n g w h i c h t h e s t o r a g e t a n k t e m p e r a t u r e s a r e r e l a t i v e l y s t e a d y , o r d e c l i n e o n l y s l i g h t l y , i n d i c a t e t h e a b s e n c e of b o t h h o t water draws and s o l a r e n e r g y c o l l e c t i o n . S t a n d b y h e a t l o s s becomes t h e o n l y a c t i v e e n e r g y i n p u t / o u t p u t t e r m f o r t h e s t o r a g e t a n k d u r i n g t h e s e p e r i o d s . The d a i l y number of pump o p e r a t i n g h o u r s i s s t r o n g l y 64 c o r r e l a t e d w i t h t h e d a i l y i n c r e a s e i n s t o r a g e tank t e m p e r a t u r e . F u r t h e r m o r e , t h e d a i l y amount of s o l a r h e a t d e l i v e r e d i s c o r r e l a t e d w i t h t h e d e c r e a s e i n s t o r a g e t a n k t e m p e r a t u r e . However, s i n c e t h e tank i s c a p a b l e of s t o r i n g more h e a t t h a n i s t y p i c a l l y r e q u i r e d by t h e u s e r s d u r i n g a g i v e n day, t h e d a i l y PPHR v a l u e s a r e n o t a l w a y s matched w i t h t h e c o r r e s p o n d i n g QSDHW v a l u e s . Compare September 8 and 9. On t h e fo r m e r of t h e s e two d a y s t h e tank bottom t e m p e r a t u r e i n c r e a s e d by 30 d e g r e e s C t o a a h i g h o f 76°C d u r i n g a c o m p a r a t i v e l y l e n g t h y 6.1 h o u r s of pump o p e r a t i o n . On t h e n e x t day no s o l a r e n e r g y was c o l l e c t e d and t h e t a n k b o t t o m t e m p e r a t u r e s u b s e q u e n t l y d e c r e a s e d t o a low of 27°C. Y e t b o t h t h e amount o f s o l a r h e a t d e l i v e r e d and t h e s o l a r f r a c t i o n s f o r t h e s e two days were v e r y s i m i l a r . T h i s o c c u r r e n c e i n d i c a t e s t h a t t h e s y s t e m i s c a p a b l e of m a i n t a i n i n g h i g h t h e r m a l p e r f o r m a n c e f o r an e n t i r e day i n t h e a b s e n c e of s o l a r e n e r g y i n p u t , and t h a t t h e tank i s a b l e t o s t o r e a two day s u p p l y o f h e a t under f a v o u r a b l e r a d i a t i v e c o n d i t i o n s . 2. M a r c h 1982 ( F i g u r e s 4.17 & 4.18) A l t h o u g h a p p r o x i m a t e l y e q u i v a l e n t t o September 1981 w i t h r e s p e c t t o t h e m o n t h l y t o t a l s of i n c i d e n t s o l a r r a d i a t i o n and s o l a r h e a t d e l i v e r e d , M a r c h 1982 e x p e r i e n c e d g r e a t e r d a y - t o - d a y v a r i a b i l i t y i n b o t h t h e amount of s o l a r e n e r g y i n p u t t o t h e s t o r a g e t a n k and t h e volume of h o t water consumed. T h i s r e s u l t e d i n a g r e a t e r d a y - t o - d a y v a r i a b i l i t y i n t h e sy s t e m ' s t h e r m a l p e r f o r m a n c e . D u r i n g t h e f i r s t two weeks o f t h i s month t h e d a i l y number of pump o p e r a t i n g h o u r s r a n g e d between 0 and 6, i n d i c a t i n g a h i g h l y v a r i a b l e i n p u t of s o l a r e n e r g y f o r t h e s y s t e m . C o r r e s p o n d i n g l y , t h e r e was wide f l u c t u a t i o n i n t h e 65 d a i l y storage tank temperature regimes and in the amount of solar heat delivered. The f i r s t three days of this month experienced cloudy weather and hence low solar energy input (PPHR < 1). This resulted in storage tank temperatures remaining r e l a t i v e l y steady and below 20°C. Since the hot water heating loads during these days were r e l a t i v e l y large and there was only marginal stored heat available, the da i l y solar fractions were less than 0.15. However, toward the end of the f i r s t week, solar energy input increased considerably and the da i l y hot water heating loads decreased. Consequently, the storage tank temperatures increased to the 40°C - 55°C range and the da i l y solar fractions exceeded 0.5. A frequent occurrence in March 1982 during periods of brief solar energy c o l l e c t i o n was an increase in tank bottom temperature without a corresponding increase in tank mid-height temperature. (These periods have been marked by upward pointing arrows in Figure 4.18.) This occurrence was due to the c i r c u l a t i o n pump turning on and operating only long enough to mix the water in the storage tank without adding s i g n i f i c a n t amounts of c o l l e c t e d solar energy. 3. December 1981 (Figures 4.19 & 4.20) The mean da i l y quantity of solar heat delivered during th i s winter month was only 7.0 MJ. On a d a i l y basis the QSDHW values never exceeded 15.5 MJ - roughly equivalent to the minimum value experienced during September 1981. In comparison, the d a i l y quantities of t o t a l heat delivered averaged 52.4 MJ and ranged from 14 MJ (Dec. 27) to 102 MJ (Dec. 24). As was stated e a r l i e r , a portion of the solar heat 66 delivered during this winter month was in effect standby heat gain derived from the surrounding basement a i r . This i s further v e r i f i e d by examining the hourly sequence of storage tank temperatures in conjunction with the d a i l y mean basement a i r temperature. Nearly half of the f i f t e e n days shown experienced storage tank temperatures several degrees cooler than the surrounding basement a i r . Hence standby heat was both lo s t and gained during t h i s month. The lack of large fluctuations in storage tank temperature and the r e l a t i v e l y few pump operating hours r e f l e c t the small amount of solar energy col l e c t e d during December. Collector operation was r e s t r i c t e d to less than three hours per day, even under clear sky conditions, due to short daylengths, large angles of incidence for beam radiation, and shading by trees. Moreover, temperatures in the storage tank were frequently depressed toward those of the incoming cold water. For the tank bottom, a minimum temperature of 12°C was measured; for the tank mid-height l e v e l , 14°C was the minimum temperature recorded. Maximum temperatures in the storage tank during the infrequent periods of solar energy c o l l e c t i o n never exceeded 27°C. As well, thermal s t r a t i f i c a t i o n persisted in the storage tank for several days at a time when there was no intervening pump operation to cause mechanical mixing of the water. During these periods the bottom of the tank remained 2 to 4 degrees C cooler than the mid-height l e v e l . 4. June 1982 (Figures 4.21 S< 4.22) This month recorded the longest i n t e r v a l of consistently sunny and warm weather during the monitoring period together 67 with the largest average d a i l y volume of hot water consumption (306 L ) . Accordingly, i t experienced the largest mean dail y quantity of solar heat delivered (43.7 MJ). On a da i l y basis, the QSDHW values ranged from a minimum of 11.5 MJ to a maximum of 97 MJ, r e f l e c t i n g the large day-to-day v a r i a b i l i t y in hot water consumption. Daily solar fractions were correspondingly variable, although c h a r a c t e r i s t i c a l l y above 0.5; a t o t a l of eight days had values greater than 1.0. The d a i l y storage tank temperature regime was f a i r l y r e p e t i t i v e for those days experiencing 7 to 9 hours of solar energy c o l l e c t i o n - a t y p i c a l operating period for the co l l e c t o r on the majority of clear days during t h i s month. (The maximum number of pump operating hours recorded was 8.8, occurring on June 11..) Increases in storage tank temperature during periods of solar energy c o l l e c t i o n averaged 31 degrees C for the tank bottom and 20 degrees C for the tank mid-height l e v e l ; the resulting d a i l y maximum tank temperatures were in the range 65°C - 83°C. On June 16 the tank bottom temperature increased from 25°C to 67°C - a t o t a l increase of 42 degrees C. This represented the largest d a i l y increase in storage tank temperature during the monitoring period. As the tank became warmer over a series of days during which there was greater solar energy input than heat withdrawal (eg. June 16 - 20) i t s temperature approached a l i m i t i n g maximum value. This value was a function of both the intensity of solar radiation incident on the c o l l e c t o r array and the ambient a i r temperature, and therefore was dependent on the time of year. For mid-June i t was 83°C; for mid-August i t was 86°C. 68 Withdrawal of large amounts of heat from the storage tank caused equally large temperature decreases. This was accompanied by the development of highly s t r a t i f i e d conditions within the tank; the thermocline t y p i c a l l y ranged between 10 and 25 degrees C during the evening hot water draw periods. One of the largest decreases in storage tank temperature occurred after cessation of solar energy c o l l e c t i o n on June 24: the tank bottom temperature decreased from 71°C to 31°C over an 18 hour period during which there was 47.5 MJ of stored heat withdrawn. The subsequent two days (June 25 and 26) experienced very small amounts of solar energy input ( i e . 1.0 and 0.3 pump hours respectively). However, as in September 1981, the solar storage tank had acquired a s u f f i c i e n t thermal store such that i t was able to deliver s i g n i f i c a n t amounts of heat on these two days. Complete depletion of available stored heat would . have occurred on June 27 had solar energy c o l l e c t i o n not resumed. Instead, the storage tank increased in temperature on th i s day (and the following two days) as solar energy input surpassed heat withdrawal. E. Diurnal Variation in System Operation and Performance Figures 4.23 - 4.26 present graphs of the diurnal variation in system operation and performance. Four d i f f e r e n t diurnal regimes are included - one for each of the months previously discussed. The graphs themselves are divided into three temporally aligned sections. In the top section, the hourly water supply l i n e and storage tank temperatures are plotted. The l a t t e r includes temperatures for a l l hours of the day, while 69 the former includes temperatures only for those hours during which water was drawn. The middle section presents the hourly amounts of solar and t o t a l heat delivered, together with the values of solar radiation incident on the c o l l e c t o r array. Also l i s t e d are the accumulated d a i l y t o t a l s of these three energy quantities. The bottom section displays the hourly hot water draws, and indicates d a i l y t o t a l consumption. Each of the four diurnal regimes is analyzed separately below. 1. Sunday, September 13, 1981 (Figure 4.23) The variation in system operation and performance during th i s day was t y p i c a l of a day in early spring / late summer experiencing abundant solar energy input, large solar fractions, and the c h a r a c t e r i s t i c diurnal pattern of hot water consumption (Section F). From midnight to 0700 hour a well developed thermal s t r a t i f i c a t i o n was maintained in the storage tank; the thermocline from the tank bottom to mid-height l e v e l remained at a constant 12 degrees C. Prior to 0800 hour there was a very small volume of hot water drawn (0.1 L). Accordingly, the water supply l i n e temperatures exhibited the eff e c t s of low-flow conditions. The incoming cold water was r e l a t i v e l y warm (19°C), having been stagnant in the i n l e t pipe and consequently heated by the surrounding basement a i r ; the solar and a u x i l i a r y heated water temperatures were r e l a t i v e l y cool (44°C and 52°C respectively), r e f l e c t i n g thermal conditions exi s t i n g in the tank outlet pipes. During the following hour, 0800 to 0900 hour, a large volume (101.1 L) of hot water was drawn. Since the storage tank was f a i r l y warm, the amount of 70 solar heat delivered (15.7 MJ) comprised a large fracti o n of the t o t a l (18.3 MJ). Both the TSDHW and TDHW temperatures increased during t h i s hour, r e f l e c t i n g temperatures more c h a r a c t e r i s t i c of the i n t e r i o r of the two tanks. The increase in TDHW was also partly due to the main burner of the a u x i l i a r y tank supplying heat. (The inte r v a l 0800 - 1000 hour was the only time during t h i s day in which the main burner operated.) The storage tank temperatures decreased during this hour in response to the withdrawal of heat, with the lower region of the tank supplying a greater amount as indicated by the thermocline increasing to 14 degrees C. The incoming cold water temperature also decreased due the effect of high-flow conditions; the TM temperature for this hour was largely influenced by the temperature of the lo c a l mains supply. For the hour ending 1000 hour there was both a small amount of solar heat withdrawn from the storage tank (1.8 MJ) and a small amount of solar energy added. I n i t i a t i o n of solar energy c o l l e c t i o n during t h i s hour i s indicated by the decrease in thermal s t r a t i f i c a t i o n within the storage tank; once the c i r c u l a t i o n pump i s turned on, water i s mechanically c i r c u l a t e d throughout the tank and an isothermal condition i s established. September 13, 1981 was a r e l a t i v e l y clear day as indicated by the large mid-day QHT values and the general bell-shape of the solar radiation curve. Accordingly, there were 5.5 hours of pump operation during this day and solar energy c o l l e c t i o n continued to 1600 hour, by which time the amount of ' solar radiation had begun to rapidly decrease. During the period of pump operation the storage tank remained f u l l y mixed 71 ( i s o t h e r m a l ) and s t e a d i l y i n c r e a s e d i n t e m p e r a t u r e , as s o l a r e n e r g y i n p u t s i g n i f i c a n t l y e x c e e d e d h e a t w i t h d r a w a l . The tank b o t t o m i n c r e a s e d by 31 d e g r e e s C t o a maximum t e m p e r a t u r e of 71°C, w h i l e t h e t a n k m i d - h e i g h t l e v e l i n c r e a s e d by 23 d e g r e e s C. D u r i n g t h e l a s t t h r e e m o r n i n g h o u r s and t h e f i r s t hour of t h e a f t e r n o o n t h e r e were d e c r e a s i n g l y s m a l l e r v o l u m e s o f h o t water drawn (13.3 L, 3.7 L, 2.8 L, and < 0.1 L ) . T h i s r e f l e c t s t h e c h a r a c t e r i s t i c a l l y l o w e r c o n s u m p t i o n of h o t wa t e r d u r i n g t h i s t i m e of day ( S e c t i o n F ) . S i n c e t h e s t o r a g e t a n k was w e l l s u p p l i e d w i t h h e a t (and t h e h o t water draws were s m a l l ) s o l a r h e a t c o m p r i s e d a m a j o r i t y of t o t a l h e a t d e l i v e r e d ( i e . h o u r l y s o l a r f r a c t i o n s > 0.65). The r e a s o n why t h e TSDHW t e m p e r a t u r e e x c e e d e d t h e c o r r e s p o n d i n g TS t e m p e r a t u r e s d u r i n g two o f t h e mo r n i n g h o u r s (1000 - 1200 h o u r ) i s most l i k e l y due t o t h e a s s o c i a t e d h o t water draws o c c u r r i n g n e a r t h e end of t h e hour i n t e r v a l s i n v o l v e d . A t t h e s e t i m e s t h e s t o r a g e t a n k t e m p e r a t u r e would have been c o r r e s p o n d i n g l y h i g h e r , a s can be j u d g e d from i n t e r p o l a t i o n of t h e g r a p h . (The r e v e r s e s i t u a t i o n a p p l i e s f o r t h e hour e n d i n g 1300 h o u r . ) D u r i n g t h e l a t e a f t e r n o o n hour e n d i n g 1700 hour a l a r g e volume (67.3 L) of h o t water was drawn. S i n c e t h e s o l a r s t o r a g e t a n k t e m p e r a t u r e was s e v e r a l d e g r e e s warmer t h a n t h a t of t h e a u x i l i a r y h o t water t a n k , t h e TSDHW t e m p e r a t u r e (64.5°C) e x c e e d e d t h e c o r r e s p o n d i n g TDHW t e m p e r a t u r e ( 6 1 . 5 ° C ) . T h i s r e s u l t e d i n an h o u r l y s o l a r f r a c t i o n g r e a t e r t h a n 1.0. The TM t e m p e r a t u r e showed a d e c r e a s e f o r t h i s hour due t o t h e e f f e c t s of h i g h - f l o w c o n d i t i o n s ; i t s u b s e q u e n t l y i n c r e a s e d when t h e h o u r l y v o l u m e s o f h o t water draw d e c r e a s e d , o n l y t o r e p e a t t h e 72 cycle when they increased again. The TDHW temperature showed a reverse cycle; with larger hot water draws i t tended to increase u n t i l the a u x i l i a r y tank began to be depleted of heat, at which time i t decreased. The TSDHW temperature was also affected by flow conditions, although thermal conditions in the storage tank had an ov e r a l l dominating effect on TSDHW. The evening hot water draw period was associated with solar fractions greater than 1.0, r e f l e c t i n g the large input of solar energy to the storage tank during the day. As well, this period was accompanied by strong development of thermal s t r a t i f i c a t i o n . From 1600 - 2300 hour the tank bottom temperature decreased by 25 degrees C to 46°C, while the mid-height temperature cooled 10 degrees C to 61.5°C. Thus a 15.5 degree C thermocline developed in the storage tank. 2. Thursday, March 11, 1982 (Figure 4.24) The variation in system operation and performance during this late winter day was characterized by non-continuous solar energy c o l l e c t i o n , variable solar fractions, and small hot water draws. Again the storage tank exhibited persistant thermal s t r a t i f i c a t i o n during the nighttime hours, although the thermocline was smaller at only 4 degrees C. Early morning household a c t i v i t y followed and was accompanied by the usual demand for hot water; 79.5 L of water were drawn during the two hour i n t e r v a l 0600 - 0800 hour. (This represented 74% of the dai l y t o t a l . ) Very small volumes of hot water were also drawn during the two contiguous morning hours - as indicated by the presence of water supply l i n e temperatures on the graph. Since 73 the storage tank was largely depleted of available heat at thi s time, the amount of solar heat delivered was only a small fractio n of the t o t a l (0.26 for the 4 hours combined). The very small hot water draw for the hour ending 0600 hour meant that the water supply l i n e temperatures for this hour were affected by stagnant conditions in the i n l e t / o u t l e t pipes. Hence the hot water delivery temperature was depressed and the incoming cold water temperature was elevated. The TM temperature then displayed i t s c h a r a c t e r i s t i c inverse dependence on flow conditions during the remainder of the early morning draw period; i t decreased from 16°C to 7.5°C when the volume of hot water drawn increased, and then rose back up to 16°C when hot water consumption was reduced. The TDHW temperature increased by 15 degrees C (49°C to 64°C) during th i s same period, in response to the main burner of the au x i l i a r y tank operating between 0600 and 0800 hour and adding heat to the hot water tank. Lastly, the solar heated water temperature reflected temperatures measured within the storage tank during t h i s period (20°C - 23°C) with one exception. For the small hot water draw (1.6 L) during the hour ending 0900 hr the TSDHW temperature (24°C) exceeded the TSmid temperature (22°C). This exemplifies an hourly HXEF value greater than 1.0 under low-flow conditions. It accompanies s t r a t i f i e d thermal conditions in the storage tank such that the water exiting the heat exchanger tends to acquire a temperature similar to that in the upper region of the tank. The reason why a similar condition did not occur for the hour ending 0600 hour, when a very small volume (0.1 L) of hot water was drawn, relates to the 74 small distance (5 cm) between the heat exchanger exit from the storage tank and the point at which TSDHW i s measured in the outlet pipe. Water in this (insulated) pipe region tends to be cooled s l i g h t l y by the surrounding basement a i r under stagnant conditions. The same situ a t i o n applies to the au x i l i a r y hot water tank, where the separation between the sensor in the (un-insulated) outlet pipe and the tank exit is 14 cm. Consequently, the TSDHW and TDHW temperatures fluctuated by 5 to 10 degrees C during the late afternoon and evening hot water draw period in response to whether the water flow was 'small' or 'very small'. S i m i l a r l y , the TM temperature traced a reverse fluctuating pattern since i t was sourced below basement a i r temperature. For the daytime on March 11, 1982 there was a six to seven hour period (0800 - 1500 hour) during which solar energy was collected, as evidenced by the isothermal and increasing temperatures within the storage tank. During t h i s period solar energy input controlled the changes in storage tank temperature since hot water consumption was n e g l i g i b l e . Accordingly, the tank bottom increased by 28 degrees C and the mid-height l e v e l by 24 degrees C. The f i n a l maximum (isothermal) storage tank temperature was 46°C. Since the t o t a l number of pump operating hours recorded for th i s day was 4.2, solar energy c o l l e c t i o n can be deduced as having been intermittent or non-continuous. This i s in agreement with the observed reduction in solar radiation for the hour ending 1100 hour (indicating attenuation by clouds) and the slower rate of increase in storage tank temperature during the morning hours. 75 Moreover, since the storage tank remained e s s e n t i a l l y isothermal for a t o t a l of eight hours, i t can be concluded that there are times following or interspersed between periods of pump operation when thermal s t r a t i f i c a t i o n does not develop. Such times p r e f e r e n t i a l l y occur in the absence of hot water draws since the l a t t e r tend to promote thermal s t r a t i f i c a t i o n within the storage tank. During the late afternoon and evening hours the small amount of heat withdrawal, together with convective a c t i v i t y , re-established a small (5 degrees C) thermocline within the storage tank; i e . the tank bottom temperature decreased to 39°C while the mid-height temperature remained r e l a t i v e l y unchanged at 44°C. The solar fractions associated with the afternoon and evening hot water draws were a l l . close to unity, r e f l e c t i n g the elevated storage tank temperatures. However the daily solar fraction was dominated by the larger hot water draws during the morning hours, and therefore was less than 0.4. 3. Monday, December 7, 1982 (Figure 4.25) The va r i a t i o n in system operation and performance during th i s day was t y p i c a l of a late f a l l / early winter day, the majority of which experienced low or zero solar energy input. There are two notable features which distinguish the diurnal regime for t h i s day from the two previous ones. F i r s t l y , there was considerably less solar energy input and hence lower storage tank temperatures throughout the day. With only 1.0 hour of pump operation during this day (as reflected by the changeover from s t r a t i f i e d to isothermal conditions within the storage tank), the amount of solar energy collected 76 and t r a n s f e r r e d t o s t o r a g e was m i n i m a l . A c c o r d i n g l y , t h e tank t e m p e r a t u r e s v a r i e d w i t h i n a c o m p a r a t i v e l y narrow r a n g e (14°C -2 1 ° C ) , and r e m a i n e d r e l a t i v e l y c l o s e t o t h a t o f t h e s u r r o u n d i n g basement a i r . S e c o n d l y , s i n c e t h e s t o r a g e t a n k had a m i n i m a l h e a t c o n t e n t t h r o u g h o u t t h e day, t h e s o l a r f r a c t i o n s a s s o c i a t e d w i t h t h e h o u r l y hot water draws were a l l l e s s t h a n 0.2. C o r r e s p o n d i n g l y , t h e main b u r n e r of t h e a u x i l i a r y tank s u p p l i e d h e a t d u r i n g t h e m a j o r i t y of h o u r s i n w h i c h h o t water was drawn. A f i n a l o b s e r v a t i o n f o r t h i s day c o n c e r n s t h e e a r l i e r d i s c u s s i o n on n o n - p o s i t i v e h o u r l y HXEF v a l u e s . Such a v a l u e o c c u r r e d f o r t h e hour e n d i n g 1200 h o u r . T h i s hour e x p e r i e n c e d l o w - f l o w c o n d i t i o n s and t h e r e s u l t i n g i n c o m i n g c o l d water t e m p e r a t u r e e x c e e d e d t h e t e m p e r a t u r e measured a t t h e m i d - h e i g h t l e v e l i n t h e s t o r a g e t a n k . S i n c e t h e TM t e m p e r a t u r e was e q u a l t o t h e ( p o s i t i v e l y b i a s e d ) TSDHW t e m p e r a t u r e , t h e HXEF v a l u e computed f o r t h i s hour was 0.0. 4. T h u r s d a y , June 17, 1982 ( F i g u r e 4.26) The v a r i a t i o n i n s y s t e m o p e r a t i o n and p e r f o r m a n c e d u r i n g t h i s day was t y p i c a l of a s p r i n g / summer day e x p e r i e n c i n g l e n g t h y s o l a r e n e r g y c o l l e c t i o n , s o l a r f r a c t i o n s g r e a t e r t h a n u n i t y , and t h e c h a r a c t e r i s t i c d i u r n a l p a t t e r n of h o t water c o n s u m p t i o n ( S e c t i o n F ) . D u r i n g t h e t h r e e h o u r s from 0600 - 0900 hour t h e r e was t h e u s u a l e a r l y m o r n i n g demand f o r h o t w a t e r . A l a r g e volume o f water (208 L) was drawn d u r i n g t h i s p e r i o d . Hence t h e s t o r a g e tank t e m p e r a t u r e s d e c r e a s e d m a r k e d l y from t h e i r c o m p a r a t i v e l y warm n i g h t t i m e v a l u e s . By 0800 hour t h e tank b o t t o m t e m p e r a t u r e had d e c r e a s e d 20 d e g r e e s C, w h i l e t h e m i d - h e i g h t l e v e l 77 was 7 d e g r e e s C c o o l e r compared t o two h o u r s e a r l i e r . C o r r e s p o n d i n g l y , t h e t a n k t h e r m o c l i n e i n c r e a s e d f r o m 8 d e g r e e s C t o 19 d e g r e e s C. D u r i n g t h e f o l l o w i n g h o u r , pump o p e r a t i o n was i n i t i a t e d and s o l a r e n e r g y c o l l e c t i o n commenced. Thus t h e s t o r a g e tank became i s o t h e r m a l even t h o u g h t h e r e was c o n c u r r e n t f l o w of water t h r o u g h t h e h e a t e x c h a n g e r and a c c o m p a n y i n g w i t h d r a w a l of h e a t . The d e c r e a s e i n s t o r a g e t a n k t e m p e r a t u r e p r i o r t o c o l l e c t o r o p e r a t i o n a l l o w e d t h e e f f i c i e n c y of t h e s y s t e m t o be e f f e c t i v e l y i n c r e a s e d d u r i n g t h i s day; i e . t h e lo w e r tank t e m p e r a t u r e s meant t h a t t h e s y s t e m was a b l e t o c o n v e r t and u t i l i z e a g r e a t e r p r o p o r t i o n o f t h e a v a i l a b l e s o l a r e n e r g y t h a n i t would have i f t a n k t e m p e r a t u r e s had r e m a i n e d e l e v a t e d . T h i s r e l a t e s t o g r e a t e r c o l l e c t o r e f f i c i e n c y , and t h e r e f o r e g r e a t e r s o l a r e n e r g y i n p u t t o t h e s t o r a g e t a n k , when t h e c o l l e c t o r i n l e t t e m p e r a t u r e i s low ( C h a p t e r 5 ) . T h e r e were a t o t a l of 8.4 pump o p e r a t i n g h o u r s on June 11, 1982 - 2.9 h o u r s more t h a n on September 13, 1981 d e s p i t e t h e f a c t t h a t t h e r e was 6.5% l e s s a v a i l a b l e s o l a r e n e r g y . L o n g e r pump o p e r a t i o n on t h i s day was p a r t l y due t o h i g h e r amounts of s o l a r r a d i a t i o n i n c i d e n t on t h e c o l l e c t o r a r r a y d u r i n g t h e e a r l y m o r n i n g and l a t e a f t e r n o o n h o u r s . ( T h i s i n t u r n r e s u l t e d f r o m s m a l l e r a n g l e s of i n c i d e n c e f o r beam r a d i a t i o n d u r i n g t h e s e h o u r s o f t h e day i n Jun e . ) Thus s o l a r e n e r g y c o l l e c t i o n commenced p r i o r t o 0800 hour and c o n t i n u e d p a s t 1600 h o u r , i n c r e a s i n g t a n k t e m p e r a t u r e t o a maximum o f 74°C . However, c o l l e c t i o n was b r i e f l y i n t e r r u p t e d d u r i n g t h e hour e n d i n g 1500 hour when t h e r e was a l a r g e r e d u c t i o n i n s o l a r r a d i a t i o n (due t o c l o u d s ) . S i n c e t h e r e was a l s o a 30 L draw o f h o t water d u r i n g 78 t h i s h o u r , t h e r e was a s m a l l e r i n c r e a s e i n s t o r a g e t a n k t e m p e r a t u r e t h a n d u r i n g t h e p r e v i o u s h o u r s . The e v e n i n g h o t wa t e r draws r e - e s t a b l i s h e d a l a r g e t h e r m o c l i n e w i t h i n t h e s t o r a g e t a n k . W h i l e t h e s m a l l h ot water draws d u r i n g t h e i n t e r v a l 1700 - 2100 hour c o n t r i b u t e d t o i n i t i a l d e v e l o p m e n t of t h e r m a l s t r a t i f i c a t i o n , t h e l a r g e h ot wa t e r draw (64 L) d u r i n g t h e hour e n d i n g 2200 hour m a r k e d l y i n c r e a s e d t h e tank t h e r m o c l i n e . By m i d n i g h t t h e t h e r m o c l i n e was a c o m p a r a t i v e l y l a r g e 25 d e g r e e s C. The v e r y warm s u p p l y of s o l a r h e a t e d w a t e r a s s o c i a t e d w i t h t h e e v e n i n g draw p e r i o d was a r e s u l t of t h e e l e v a t e d s t o r a g e t a n k t e m p e r a t u r e s . F o r t h e hour e n d i n g 1900 h o u r , TSDHW was 20 d e g r e e s C warmer t h a n TDHW. As t h e e v e n i n g p r o g r e s s e d and more h o t water was drawn, t h e TSDHW t e m p e r a t u r e s t e a d i l y d e c r e a s e d from 74°C t o 57°C . In c o n t r a s t , t e m p e r a t u r e s f o r b o t h t h e i n c o m i n g c o l d w a ter and e x i t i n g h o t water v a r i e d a s f u n c t i o n s of t h e f l o w c o n d i t i o n s : TM r a n g e d between 8°C - 24°C, and TDHW between 52°C - 60°C. W h i l e t h e o v e r a l l s o l a r f r a c t i o n f o r t h i s day was f a i r l y c l o s e t o u n i t y ( 1 . 0 3 ) , t h e r e was a c l e a r d i v i s i o n i n t h e h o u r l y s o l a r f r a c t i o n s between p r e - and p o s t - s o l a r e n e r g y c o l l e c t i o n ; i e . t h e s o l a r f r a c t i o n s f o r t h e m o r n i n g h o u r s were a l l l e s s t h a n 1.0, w h i l e t h o s e f o r t h e a f t e r n o o n and e v e n i n g h o u r s were a l l g r e a t e r t h a n 1.0. F u r t h e r m o r e , s i n c e t h e m o r n i n g s o l a r f r a c t i o n s were n o t s i g n i f i c a n t l y l e s s t h a n 1.0, t h e r e was o n l y a s m a l l demand f o r a u x i l i a r y h e a t . T h i s was s u p p l i e d by h e a t s t o r e d w i t h i n t h e a u x i l i a r y t a n k . As a r e s u l t , t h e main b u r n e r of t h e a u x i l i a r y tank d i d n o t o p e r a t e d u r i n g t h i s d ay. 79 F. Hot Water C o n s u m p t i o n P a t t e r n s In a s i n g l e f a m i l y r e s i d e n c e t h e demand f o r h o t water c a n be q u i t e v a r i a b l e on b o t h an h o u r - t o - h o u r and a d a y - t o - d a y b a s i s . T h i s i s due t o d i v e r s i t y i n t h e use o f t h e h o t water consumed ( C h a p t e r l ) and t h e h a b i t s of t h e u s e r s . Thus, an a c c o u n t of t h e u s e r s ' h o t w ater c o n s u m p t i o n p a t t e r n s i s i n c l u d e d h e r e t o p r o v i d e i n f o r m a t i o n on t h e volume and d i s t r i b u t i o n of h o t water draws. The p r e s e n t a t i o n b e g i n s w i t h an o v e r a l l e x a m i n a t i o n of t h e f r e q u e n c y d i s t r i b u t i o n of h o t w a ter u t i l i z a t i o n . T h i s i s f o l l o w e d by an a n a l y s i s of t h e d i u r n a l hot w ater c o n s u m p t i o n p a t t e r n s . L a s t l y , s i n c e t h e h o u s e h o l d members a d h e r e t o a r e l a t i v e l y r e g u l a r w o r k i n g week r o u t i n e , a c h e c k i s made t o a s c e r t a i n whether t h e r e were any s i g n i f i c a n t d i f f e r e n c e s i n h o t w ater c o n s u m p t i o n between t h e d a y s of t h e week. 1. F r e q u e n c y D i s t r i b u t i o n o f Hot Water Draws W h i l e i n d i v i d u a l h o t w a t e r draws were i n t h e o r d e r o f s e c o n d s t o m i n u t e s , f o r t h e p u r p o s e s o f e v a l u a t i o n t h e y were i n t e g r a t e d on an h o u r l y b a s i s . A c c o r d i n g l y , a g i v e n h o u r l y FLOW v a l u e can be composed o f one o r many i n d i v i d u a l h o t w ater draws. F u r t h e r m o r e , no measurements were made of t h e f l o w r a t e s a s s o c i a t e d w i t h t h e i n d i v i d u a l draws, a l t h o u g h t h e s e were known t o v a r y f r o m t a p d r i p p i n g t o a l i m i t i n g f l o w r a t e of 18 l i t r e s / m i n . F i g u r e 4.27 p r e s e n t s a c u m u l a t i v e f r e q u e n c y d i s t r i b u t i o n g r a p h of t h e h o u r l y h o t w ater draws f o r t h e o v e r a l l m o n i t o r i n g p e r i o d . I t r e v e a l s t h a t 26% o f t h e h o u r l y draws were l e s s t h a n 0.5 l i t r e s , w h i l e fewer t h a n 2% were g r e a t e r t h a n 100 l i t r e s . The median h o u r l y h o t w ater draw 80 volume was 6.4 l i t r e s ; t h i s compares w i t h a mean h o u r l y draw volume of 18.6 l i t r e s . Hence h o u r l y h o t water c o n s u m p t i o n was skewed t o w a r d numerous s m a l l draws, w i t h r e l a t i v e l y few l a r g e draws o c c u r r i n g . However, t h e l a t t e r s i g n i f i c a n t l y c o n t r i b u t e d t o t h e t o t a l volume of h o t water consumed, as w i l l be shown i n t h e n e x t s e c t i o n . 2. D i u r n a l Hot Water C o n s u m p t i o n P a t t e r n F i g u r e s 4.28 - 4.31 p r e s e n t d i u r n a l p r o f i l e s of h o t water c o n s u m p t i o n f o r s e l e c t e d months d u r i n g t h e m o n i t o r i n g p e r i o d . The number and volume o f h o t water draws f o r e a c h hour of t h e day a r e i n d i c a t e d by t h e h o r i z o n t a l b a r s . (The v e r t i c a l s e p a r a t i o n between i n d i v i d u a l b a r s e q u a l s t h e volume of h o t water drawn d u r i n g a g i v e n h o u r ; c u m u l a t i v e bar h e i g h t e q u a l s t h e t o t a l m o n t h l y volume f o r e a c h hour o f t h e day.) The d i s t r i b u t i o n o f t h e h o r i z o n t a l b a r s g r a p h i c a l l y i l l u s t r a t e s t h e g r e a t e r f r e q u e n c y of s m a l l draws a s w e l l as t h e s i z e a b l e c u m u l a t i v e e f f e c t of a s e r i e s o f l a r g e draws. W h i l e t h e r e i s no u n i f o r m d a y - t o - d a y p a t t e r n i n t h e h o u r l y draw v o l u m e s , a d e f i n i t e d i u r n a l d i s t r i b u t i o n of h o t w a t e r c o n s u m p t i o n i s e v i d e n t . I t i s c h a r a c t e r i z e d by e a r l y m o r n i n g (0700 - 0900 h r ) and e v e n i n g (1800 - 2100 h r ) p e a k s , an a f t e r n o o n t r o u g h , and a n i g h t t i m e a b s e n c e of h o t water c o n s u m p t i o n . The r e l a t i v e d ominance o f t h e m o r n i n g and e v e n i n g p e a k s v a r i e d from month t o month. In A p r i l and June o f 1982 t h e m o r n i n g peak was by f a r t h e l a r g e r ; d u r i n g O c t o b e r 1981 and J a n u a r y 1982 t h e two p e a k s were more even i n m a g n i t u d e . F o r t h e o v e r a l l m o n i t o r i n g p e r i o d , t h e m o r n i n g peak was t h e g r e a t e r o f t h e two. T h i s i s shown i n F i g u r e 4.32 w h i c h g r a p h s t h e a c c u m u l a t e d m o n t h l y 81 v o l u m e s of h o t water consumed f o r e a c h hour o f t h e day. The l a r g e s t a c c u m u l a t e d volume o c c u r r e d f o r t h e hour e n d i n g 0800 h r . On a r e l a t i v e b a s i s , t h i s h o u r r e c o r d e d 12.3% of t o t a l h o t water c o n s u m p t i o n . The e v e n i n g hour w h i c h r e c o r d e d t h e ( s e c o n d a r y ) l a r g e s t a c c u m u l a t e d volume was t h e hour e n d i n g 2100 h o u r . I t s p e r c e n t a g e o f t o t a l h o t water c o n s u m p t i o n was 9.2%. R e l a t i v e v a l u e s f o r t h e o t h e r h o u r s of t h e day a r e shown g r a p h i c a l l y i n F i g u r e 4.33 and a r e l i s t e d i n T a b l e 4.4. (The n o t i c e a b l e d i p d u r i n g t h e hour e n d i n g 2000 hour r e p r e s e n t s a p e r i o d of l o w e r hot water demand f o l l o w i n g c o m p l e t i o n o f d i s h w a s h i n g and p r e c e d i n g commencement of e v e n i n g b a t h i n g and w a s h i n g . ) 3. I n t r a - W e e k l y Hot Water C o n s u m p t i o n P a t t e r n The maximum, minimum, mean, and s t a n d a r d d e v i a t i o n o f d a i l y h ot w a t e r c o n s u m p t i o n a r e l i s t e d i n T a b l e 4.5 f o r e a c h o f t h e i n d i v i d u a l d a y s of t h e week. Monday e x p e r i e n c e d t h e l a r g e s t a v e r a g e d a i l y volume o f h o t water c o n s u m p t i o n (326.0 L ) , w h i l e Sunday e x p e r i e n c e d t h e s m a l l e s t (226.9 L ) . Hence t h e r e was an a v e r a g e d i f f e r e n c e of 100 l i t r e s (36%) i n d a i l y h o t wa t e r c o n s u m p t i o n between t h e s e two n e i g h b o u r i n g d a y s of t h e week. In c o n t r a s t , d a i l y v a r i a b i l i t y i n h o t w a t e r c o n s u m p t i o n was c o m p a r i t i v e l y s i m i l a r f o r a l l d a y s of t h e week; t h e s t a n d a r d d e v i a t i o n r a n g e d from 112.3 L on F r i d a y t o 91.3 L on T u e s d a y . The mean d a i l y volume of h o t water consumed d u r i n g t h e m o n i t o r i n g p e r i o d was 265.8 L ( i n c l u d i n g t h r e e d a y s d u r i n g w h i c h no h o t water was d r a w n ) . T h i s c o r r e s p o n d s t o a p p r o x i m a t e l y 66 L p e r p e r s o n p e r day when a v e r a g e d o v e r f o u r h o u s e h o l d members. TABLE 4. 1 MONTHLY THERMAL PERFORMANCE SUMMARY - PART I MONTH QHT QSDHW QDHW QAUXW QAUXL FLOW FUEL HCF QFUEL (GJ) (GJ) (GJ) (GJ) (GJ) (m]) (m') (MJ/m') (GJ) 1981 *JUN 1 092 0 392 0 .762 0 370 0 .500 3 496 22 382 38 .85 0 870 JUL 2 889 0 926 1 298 0 372 1 .072 6 449 35 781 40 35 1 444 AUG 3 513 1 014 0 975 -0 039 0 .873 5 136 20 671 40 35 0 834 SEP 2 497 0 856 1 258 0 402 1 043 6 498 37 010 39 05 1 445 OCT 1 512 0 646 1 712 1 066 1 390 8 288 62 909 39 05 2 457 NOV 0 747 0 342 1 631 1 290 1 305 8 286 67 117 38 65 2 594 DEC 0 469 0 216 1 623 1 407 1 430 7 567 73 420 38 65 2 838 1982 JAN 0 353 0 170 1 837 1 667 1 546 8 058 82 062 39 15 3 213 FEB 0 937 0 399 2 019 1 620 1 416 9 117 77 549 39 15 3 036 MAR 2 391 0 792 1 533 0 741 1 152 7 346 49 1 13 38 55 1 893 APR 3 014 1 123 1 612 0 489 1 001 8 235 38 664 38 55 1 490 MAY 3 064 1 296 1 771 0 475 1 010 9 422 38 233 38 85 1 485 JUN 2 870 1 282 1 696 0 414 0 957 9 188 35 288 38 85 1 371 JUL 2 726 1 059 1 462 0 403 0 949 7 991 33 352 40 55 1 352 AUG 2 913 1 075 1 543 0 468 0 963 8 860 35 305 40 55 1 432 SEP 2 458 0 945 1 693 0 748 0 974 9 765 42 991 40 05 1 722 +OCT 1 454 0 622 1 497 0 875 1 034 8 108 47 669 40 05 1 909 NOV 0 789 0 374 1 887 1 513 1 409 8 972 75 215 38 85 2 922 •DEC 0 283 0 130 0 928 0 799 0 746 4 226 39 757 38 85 1 545 00 N3 TOTAL 35.973 13.658 28.737 15.080 20.771 145.008 914.485 39.20 35.851 + + + + + + + + + + + * - INCOMPLETE MONTH + - 4 DAYS OF MISSING DATA NOMENCLATURE QHT - TOTAL SOLAR RADIATION QSDHW - SOLAR HEAT DELIVERED QDHW - TOTAL HEAT DELIVERED QAUXW - AUXILIARY HEAT DELIVERED QAUXL - AUXILIARY TANK HEAT LOSS FLOW - VOLUME OF HOT WATER CONSUMED FUEL - VOLUME OF NATURAL GAS CONSUMED HCF - HEAT CONTENT OF NATURAL GAS QFUEL - FUEL ENERGY CONSUMPTION TABLE 4.2 MONTHLY THERMAL PERFORMANCE SUMMARY - PART II MONTH SFRAC SCEF SCOP HXEF AUXE PPHR (HR) OPUMP (GJ) QFSAVE (Gd) QESAVE (GO) 1981 *JUN 0. .515 0 .359 24 .8 0 .959 0 .425 4 1 . 1 0 .0158 0 .542 0 .526 JUL 0. ,714 0 . 321 21 .0 0 .991 0 .257 1 14 . 5 0 .0441 0 .960 0 .915 AUG 1 . .040 0. .289 18 .5 1 .014 -0. .046 142 .0 0 .0547 0 .972 0 .917 SEP 0. .680 0. .343 22 .4 0 .968 0 .278 99 . 1 0 .0382 0 .884 0 .845 OCT o .377 0 .427 26 . 1 0 . 923 0 .434 64 . 2 0 .0247 0 .714 0 .690 NOV 0. .209 0 .457 34 .2 0 .864 0 .497 25 .9 0 .0100 0 . 427 0 .417 DEC 0. . 133 0. .460 39 .4 0 .617 0 .496 14 . 2 0 .0055 0 . 168 0 . 162 1982 JAN 0. 092 0. ,481 62 .0 0, .589 0, .519 7 . 1 0. .0027 0 . 189 0, . 186 FEB 0. 198 0. 425 31 .4 0, .785 0, .534 33 .0 0, .0127 0, . 702 0, ,689 MAR 0. 516 0. 331 21 .8 0. .916 0. 392 94. . 1 0, .0362 0. .946 0. .910 APR 0. 697 0. 373 19 .5 0. 921 0. 328 149 .4 0. 0575 1 , 495 1 . 438 MAY 0. 732 0. 423 18, , 7 0. 953 0. 320 179, 7 0. 0692 1 . 794 1 . 724 JUN 0. 756 0. 447 17 , .5 0. 963 0. 302 190. 5 0. 0734 1 . 770 1 . 696 JUL 0. 724 0. 388 17 , .5 0. 962 0. 298 156. 7 0. 0604 1 . 355 1 . 295 AUG 0. 697 0. 369 16. ,7 0. 948 0. 327 167 . 2 0. 0644 1 . 426 1 . 361 SEP 0. 558 O. 385 17 , .8 0. 913 O. 434 137 . 5 O. 0530 1 . 4 14 1 . 36 1 • OCT 0. 416 0. 428 19. , 1 0. 855 0. 458 84 . 8 0. 0327 0. 863 0. 831 NOV 0. 198 0. 474 22 . 1 0. 790 0. 518 43. 9 0. 0169 0. 573 0. 556 *DEC 0. 140 0. 458 20. ,7 0. 650 0. 517 16. 3 0. 0063 0. 175 0. 168 TOTAL 0. 475 0. 380 20. 1 0. 872 0. 421 1761 . 2 0. 6784 17 . 366 16 . 688 INCOMPLETE MONTH 4 DAYS OF MISSING DATA NOMENCLATURE SFRAC - SOLAR FRACTION OF TOTAL HEAT DELIVERED SCEF - SOLAR ENERGY CONVERSION EFFICIENCY SCOP - SOLAR COEFFICIENT OF PERFORMANCE HXEF - HEAT EXCHANGER EFFECTIVENESS AUXE - AUXILIARY TANK EFFICIENCY PPHR - NUMBER OF PUMP OPERATING HOURS QPUMP - PUMP ENERGY CONSUMPTION QFSAVE - FUEL ENERGY SAVED QESAVE - NET (CONVENTIONAL) ENERGY SAVED 84 T a b l e 4.3 M o n t h l y A v e r a g e Heat E x c h a n g e r E f f e c t i v e n e s s A r i t h m e t i c a l F l o w - W e i g h t e d A v e r a g e A v e r a g e 1981 June 0.983 0.959 J u l y 0.995 0.991 Au g u s t 0.980 1.014 September 0.993 0.968 O c t o b e r 1 .059 0.923 November 0.293 0.864 December -1.711 0.617 1982 J a n u a r y -0.250 0.589 F e b r u a r y 0.032 0.785 March 0.565 0.916 A p r i l 0.941 0.921 May 0.983 0.953 June 1.000 0.963 J u l y 0.971 0.962 Au g u s t 0.957 0.948 September 0.944 0.913 O c t o b e r 0.835 0.855 November 0.707 0.790 December -1.774 0.651 85 T a b l e 4.4 D i u r n a l D i s t r i b u t i o n o f Hot Water Consumption f o r t h e O v e r a l l M o n i t o r i n g P e r i o d Hour E n d i n g P e r c e n t a g e o f T o t a l Hot Water C o n s u m p t i o n 0100 0.172 0200 0.060 0300 0.011 0400 0.010 0500 0.004 0600 1.215 0700 7.324 0800 12.272 0900 1 1 .059 1 000 7.835 1 1 00 4.833 1 200 3.676 1 300 3.263 1 400 2.511 1 500 2.242 1 600 2.567 1 700 4.685 1 800 5.275 1900 7.338 2000 4.648 21 00 9. 199 2200 6.482 2300 2.782 2400 0.569 T a b l e 4.5 Hot Water Consumption S t a t i s t i c s f o r o v e r a l l m o n i t o r i n g p e r i o d A l l v a l u e s a r e i n L i t r e s Day of the Week Monday Tuesday Wednesday T h u r s d a y F r i d a y S a t u r d a y Sunday O v e r a l l Maximum 576 . 1 471.5 528 . 1 489 .8 638.6 595.6 555.7 638 . 6 Mean 326 .0 238 .4 286 .5 281.5 248.7 252.8 226.9 265.8 Minimum 63.9 35 .3 96 . 7 49 . 7 0.0 0.0 0 . 0 0.0 S t a n d a r d D e v i a t i o n 102 .4 91.3 96 .5 93.7 112.3 99.5 100.-3 104 . 6 Figure 4*1 Solar and Thermal Energy Totals for Overall Monitoring Period Heat Loss QSENV Standby Heat Loss QAUXL Heat Loss A QHT 35.973 GJ Solar Radiation Co l l e c t o r Loop A u 00 QCSS N/A A Solar Energy Input 53 Storage Tank Heat Exchanger QSDHW 13.658 GJ Solar Hot Water Heat A o QAUXW A u x i l i a r y Hot Water Heat 15.080 GJ A CO QDHW 28.737 GJ > T o t a l Hot Water Heat QPUMP QFUEL Operating Energy Fuel Energy 2.4-t 2.2 -2.D -].B -=3 i-M o i— i - H tr a) UJ § i.oH i -o x 0.8 -i r MONTHLY TOTAL, SOLAR, ANO AUXILIARY HOT WATER HEAT QDHW QAUXW QSDHW QSDHW r --QAUXU QDHU 0.6 -0.4-0.2 -0.0 J _Li T I III III ' I M l l l l i I l i r J L l 11 111 11 II JUN JUL RUG SEP OCT NOV DEC JflN FEB IWR APR HAY JUN JUL BU» SEP OCT NOV DEC 1381 1982 F i g u r e 4.2 M o n t h l y I n t e g r a l s of S o l a r (QSDHW), A u x i l i a r y (QAUXW), and T o t a l (QDHW) Heat D e l i v e r e d to the D o m e s t i c Hot Water S u p p l y MONTHLY SOLAR RADIATION AND PUMP OPERATING- HOURS QHT - SOLAR RADIATION INCIDENT ON COLLECTOR ARRAY — B -PPHR - NUMBER OF PUflP OPERATING HOURS —x — 03 JUN JUL HUG SEP OCT NOV DEC JBN FEB MRR RPR IWY JUN JUL AUG SEP OCT NOV DEC 1981 1982 F i g u r e 4.3 Monthly I n t e g r a l s of I n c i d e n t S o l a r R a d i a t i o n and Pump O p e r a t i n g Hours MONTHLY SOLAR FRACTION JUH JUL BUC SEP OCT NO» DEC JBK FE6 BRH BPft HftY JUN JUL AU6 SEP OCT NOV DEC 1981 1982 F i g u r e 4.4 M o n t h l y S o l a r F r a c t i o n MONTHLY SOLAR ENERGY CONVERSION EFFICIENCY J.0-, p 0.3-0.8-0.7-z UJ o 0.5-M U-U-w 0.4-1 0.3-0.2-0.1-0.0-i i i r i i r i i i i r i r -1.0 -0.3 -0.8 h-0.7 -0.6 m -n ~n M m z o hO.4 -c -0.3 -0.2 -0.1 -0.0 JUN JUL flUC SEP OCT NOV DEC JAN FEB flflR APR HAY JUN JUL flUC SEP OCT NOV DEC 198) 1982 ' VO F i g u r e 4.5 M o n t h l y S o l a r E n e r g y C o n v e r s i o n E f f i c i e n c y MONTHLY AUXILIARY ENERGY QUANTITIES QFUEL QAUXL QAUXL -QAUXW JUN JUL RUC SEP OCT NOV DEC JflN FEB ftflR APR ftflY JUN JUL flUC SEP OCT NOV DEC 1981 1982 F i g u r e 4.6 M o n t h l y I n t e g r a l s of F u e l E n e r g y Consumption (QFUEL), A u x i l i a r y Heat D e l i v e r e d (QAUXW), and A u x i l i a r y Tank Heat L o s s (QAUXL) MONTHLY AUXILIARY TANK EFFICIENCY 1.0 0.9-0.8-D.T-0.6->-o M O C 0.4H ui 0.3 0.2-0.1-0.0' -0.1 1 ~T i r i 1 1 r i r u 1.0 -0.9 -0.8 -0.7 -0.6 m h0.5 2 n o -0.3 J I I L J L _L I J I -0.2 -0.1 •0.0 •-0.1 JUN JUL BUG SEP OCT NOV 0EC JflN FEB nflR APR nflY JUN JUL BUG SEP OCT NOV OEC 1981 1982 F i g u r e 4.7 M o n t h l y A u x i l i a r y Tank E f f i c i e n c y MONTHLY CONVENTIONAL ENERGY SAVED OFSAVE OPUnP QESAVE 2.4 JUN JUL flUC SEP OCT NOV DEC JflN FEB flRR APR HAY JUN JUL flUC SEP OCT NOV DEC 198! 1982 F i g u r e 4.8 Monthly I n t e g r a l s of F u e l (QFSAVE) and Net (QESAVE) Energy Saved, and Pump Energy Consumption (QPUMP)' Figure 4.9 MONTHLY FLOW-WEIGHTED HEAT EXCHANGER EFFECTIVENESS 1.2-1.1-1.0-0.9-V) 0.8-i/l UJ Z £ 0.7-| (_) £ 0.6-u. UJ 0.5-_ 0.4-< * 0.3-0.2-0.1-I u o.o-i r 1 ~T i r i—n 1 r 1.2 h l . l •1.0 -0.8 i m > -0.7 -0.6 X n x n -0.5 n n - h -0.4 n •z n ' (/> -0.3 W -0.2 -0.1 •0.0 JUN JUL AUG SEP OCT NOV DEC JAN FEB MA ft APS MAY JUN JUL AUG SEP OCT NOV DEC 1981 1982 96 16-]S • 14 • 13 -12 -11 -CO a S. io a z CO tr O o a: u. o <r IX) m Z 9 -B -3 2 1 -FREQUENCY DISTRIBUTION OF HOURLY HEAT EXCHANGER EFFECTIVENESS _L JL _L <0.02S 0.1 0.2 0.3 0.4 tt.S 0.6 0.7 0.B 0.9 HEAT EXCH. EFFECTIVENESS 1.0 1.1 1.2 >1.27S F i g u r e 4.10 F r e q u e n c y D i s t r i b u t i o n o f H o u r l y Heat E x c h a n g e r E f f e c t i v e n e s s f o r the O v e r a l l M o n i t o r i n g P e r i o d F i g u r e 4.11 J . 3 -3.7-J . J J-D W f l . 3 -UJ z tjj 0 . 8 - { o u. Ld X 0 . 6 -O 0 . 5 H 0 . 4 -0 . 3 -0 . 2 -o.i-Heat E x c h a n g e r E f f e c t i v e n e s s as a F u n c t i o n o f F l o w C o n d i t i o n s f o r a Random Sample o f H o u r l y Hot Water Draws S e l e c t e d f r o m t h e O v e r a l l M o n i t o r i n g P e r i o d ( N e g a t i v e v a l u e s not shown) D - H t 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 . 10. 20. 3 0 . 40. 50. 6 0 . 70. 8 0 . SO. 100. 1J0. 120. 130. 140. 150. FLOW (LITRES) DAILY HEAN TEMPERATURES F i g u r e 4.12 D a i l y Mean S t o r a g e Tank ( m i d - h e i g h t ) , Basement A i r and I n c o m i n g C o l d Water T e m p e r a t u r e s DAILY riEAN TEMPERATURES SOLfiR STORAGE TANK TS DID BOT UflTER SUPPLY LINE TSDHU VO JUN JUL AUG SEP OCT NOV DEC 1981 F i g u r e 4.13 D a i l y Mean S t o r a g e Tank and S o l a r Heated Water T e m p e r a t u r e s (a) June - December, 1981 DAILY MEAN TEHPERATURES SOLAR STORRGE TANK TS HID BOT UATER SUPPLY LINE TSDHU i i i n i o o JON FEB tlAR RPR flAY JUN 1981 Figure 4.13 (continued) Daily Mean Storage Tank and Solar Heated Water Temperatures (b) January - June, 1982 DOILY HERN TEMPERATURES SOLAR STORAGE TRNK TS HID - BOT URTER SUPPLY UNE T5DHV JUL RU& SEP OCT NOV U82 Figure 4.13 Daily Mean Storage Tank and Solar Heated Water Temperatures (continued) (c) July - December, 1982 DAILY HERN TEMPERATURES UflTER SUPPLY LINE Ttl TSDHU TOHU o 1381 Figure 4.14 Daily Mean Incoming Cold Water (TM), Solar Heated Water (TSDHW) and Hot Water Delivery (TDHW) Temperatures: (a) June - December, 1981 DAILY HERN TEMPERATURES URTER SUPPLY LINE TH TSOHU TOHU JRN FEB HflR APR MAY JUN 1981 Figure 4.14 Daily Mean Incoming Cold Water (TM), Solar Heated Water (TSDHW) and (continued) Hot Water Delivery (TDHW) Temperatures: (b) January - June, 1982 DRILY flERN TErlPERRTURES UflTER SUPPLY LINE TO - TSDHV —r- 70HU j n ! j — 1 [ — — 1392 Figure 4.14 Daily Mean Incoming Cold Water (TM), Solar Heated Water (TSDHW) and (continued) Hot Water Delivery (TDHW) Temperatures: (c) July - December, 1982 105 r*t — DAILY HOT UATER HEAT 1HJ) « / ) 0 l / ) 0 l / ) Q m 0 l / > Q v i Q l / ? 0 l / ) 0 u ? 0 UJ X cn o X >-a: CE M _ i M X D cc a cr af <x _j o to _J cc in o v> o to a n n ^ « o a (rU) 1U3H cJ3iHM 10H A1100 F i g u r e 4.15 D a i l y I n t e g r a l s o f S o l a r (QSDHW), A u x i l i a r y (QAUXW) and T o t a l (QDHW) Heat D e l i v e r e d : September, 1981 106 TEHPERRTURE (DEG. C) o i n o W o t n o i n o o '030) synibusdiai F i g u r e 4.16 Time S e r i e s P l o t o f S t o r a g e Tank T e m p e r a t u r e : September 1981 ( D a i l y Pump O p e r a t i n g H o u r s a r e l i s t e d a c r o s s t o p ) 107 DRILY HOT WATER HEAT IrtJ) LO o m o o o to o o m a ai ai aa co r- r~ cr LL) x CE LU O CE cr M I H x ZD CX a cr a: CX I o CO, cr o a ID x co cr a OCT C7 I 3 X X a cr co CTC7 cr -T m a CM r>4 -i 1 i i 1 1 1 1 1 1 1 1 1 i 1 I 1 1 i 1 I 1 r iTU) 1U3H U3im 10H A1IUQ F i g u r e 4.17 D a i l y I n t e g r a l s o f S o l a r (QSDHW), A u x i l i a r y (QAUXW) and T o t a l (QDHW) Heat D e l i v e r e d : March, 1982 108 TEMPERATURE (DEC C) 9 JO O .^•r-z — " CO CD <X CC o CO o to o CD to O d CN <r CM d rO d o o \D 00 CM OS CM CO CO _ / ..l • >• ^ (M CD CO CP I <_) CE ro O o r -9 IO T -9 F i g u r e 4.18 Time S e r i e s P l o t o f S t o r a g e Tank T e m p e r a t u r e : March 1982 ( D a i l y Pump O p e r a t i n g Hours a r e l i s t e d a c r o s s t o p ) 109 DAILY HOT UATER HEAT iriJ) T 1 r m o tn o 10 N M « T" i r t o m o « n o t o o i o o i Q Q > n o v > p i o o (PU) 1U3H a a i b n IOH AHUO 19 D a i l y I n t e g r a l s of S o l a r (QSDHW), A u x i l i a r y (QAUXW) and T o t a l (QDHW) Heat D e l i v e r e d : December, 1981 110 TEMPERATURE (DEC. O U J cc ex CC St z CC cc a co O to O u. z cc cc 2 LLi UJ to G "030) 3anid<J3dU3l F i g u r e 4.20 Time S e r i e s P l o t o f S t o r a g e Tank and Basement A i r T e m p e r a t u r e s : December 1981 ( D a i l y Pump O p e r a t i n g H o u r s a r e l i s t e d a c r o s s t o p ) W c to TOTAL, SOLAR, AND AUXILIARY HOT UATER HEAT a tu H-(D M 3 Q. H H 3 O rt rt (0 to OQ M H .O W O K O S3 H » SS O IB M rt n e> ^ a < se n s: n ^ ro « a. .. > c X t-t H> C H 3 H-ro o> M vO ^ 00 O N3 > c X S3 cr UJ re cr UJ a x >-_i H cr a 125 J20 115-JJQ-105-100 95 H 90 85 H 60 75 70 65 60 SS SO 45 40 35 30 H 2S 20 15 10 5 0 QDHU QAUXU QSDHU T 1 1 1 1 1 I 1 I QSDHU -QAUXU QDHU i — i — i — i — i — i — i — i — i i i 1 1 1 r • | l i | l i | •!• !•! !•! ill lil '•' lil lil lil Lu ul u Ll u Lu—Ui—III Ml—III l i — U 125 -120 -1J5 -1J 0 105 -100 95 r90 85 hBO 75 70 -65 -60 55 SO 45 -40 -35 -30 25 20 15 10 5 0 1 2 3 4 S 6 7 8 9 10 11 12 13 14 15 16 1T18 19 20 21 22 23 2 4 25 26 27 28 29 30 JUNE 1982 112 TEMPERATURE (DEC C) (3 '930) 3aniuy3dU3i F i g u r e 4.22 Time S e r i e s P l o t o f S t o r a g e Tank T e m p e r a t u r e : June 1982 ( D a i l y Pump O p e r a t i n g H o u r s a r e l i s t e d a c r o s s t o p ) 113 F i g u r e 4.23 D3URNRL VARIATION IN SYSTEM OPERATION AND PERFORMANCE ON SEPTEMBER 13. 1981 TIME OF DAY IHOURJ O 1 2 3 4 5 6 1 B 3 JO J l J2 JJ J4 J5 JG il IB IS 20 2J 22 2J 80 13 •50 63 60 o 33 t- 50 LU 45 CC ZD 40 )— ex cc 33 UJ a . E 30 LU 1- 25 20 13 10 3 0 20 — i i 13 1— CE . 10 LU X 5 0 110 100 90 O) eo LU cc: t— •JO 60 30 3 a 4) _ J 30 20 10 0 -I I I ' 1 • I I I I I . I I • • • 24 -Vao ST0BAGE TRNK T TS BJD •L TS BOT WATER SUPPLY a TDHU A TSDHW » Tn —i 1 1 1 1 1 r DAILY TOTALS »' QHT ' 32B.6 HJ QOHU " 42.1 nJ —'- QSDHU - 40.2 flJ - i 1 1 1 i 1 r -T 1 I 1 I — I HOT UATEH CONSUMPTION OAILY TOTAL - 229 L a i 1 1 1 1 1 1—i—l—l—"i—* 1 1 1—r 0 J t J 4 5 6 "7 i 3 JO JJ J l JJ J I JS j« J l J8 JS 20 2J 22 23 13 h ">» 63 - eo - 55 30 h 15 40 - 35 •30 - 25 20 - 13 - 10 3 I- 0 20 - 13 10 - 5 0 h no loo 90 BO 10 eo 50 40 I- 30 20 10 0 24 TIHE OF DAY IHOURJ 114 F i g u r e 4.24 DIURNAL VARIATION IN SYSTEM OPERATION AND PERFORMANCE ON MARCH 11. 1982 TIME OF DAY (HOUR) 0 1 2 3 4 5 6 1 B 9 10 11 32 13 34 15 16 17 18 19 20 21 22 23 24 80 UJ cx or ui LU 7? 70 63 60 53 30 43 40 35 30 23 -Zfl 35 10 3 -0 -• 1 1 1—• • • • - i — i ' • STORAGE TANK j TS HID TS BOT WATER SUPPLY o TDHU A TSDHW » Til 11111 H-ri cc LU X co UJ d I— 3 O 0 no 100 ao 80 •70 60 50 40 30 20 -\ 30 0 HOT WATER CONSUMPTION DAILY TOTAL - 107L r—1 n 1-73 70 63 r 60 33 -30 - 43 40 1-33 30 23 -20 - 15 30 3 0 80 0 3)0 - 100 - ao 80 70 60 30 r 40 30 ZD 10 0 3 -o m TO 33 m o m 33 O TO m CO 0 1 2 3 4 5 6 7 8 9 30 3 3 32 33 3 4 35 36 11 38 39 20 23 22 23 24 TIME OF DAY (HOUR) 115 F i g u r e 4.25 DIURNAL VARIATION IN SYSTEM OPERATION AND PERFORMANCE ON DECEMBER 7, 1981 TIME OF DAY (HOUR) UJ cc cc LU Q_ rr UJ so "73 70 63 60 53 50 45 10 33 30 23 20 13 10 5 0 20 13 -0 J 2 3 4 5 6 7 fi a JO JJ 12 13 14 15 J 6 11 18 J9 20 21 22 23 24 -J > 1 1 1 1 1 1 1 1 1 I I I I I I I 1 I 1 1 L s *° 1 3 -0 -110 100 30 -BO -70 60 30 -40 -30 -20 -JO 0 CO UJ cc o ST0RACE TANK T TS AID * TS BOT WATER SUPPLY a TOHU a TSDHU « Tfl I I I I I I —i i 1 1 1 1 i t 1 r DAILY TOTALS x QHT - 24.6 11J — QDHW = 65.0J1J --- QSDHU = 3.8MJ - i 1 1 1 1 1 1 1 1 1 1 r 73 70 63 60 - 33 - 30 - 43 - 40 • 33 30 -23 - 20 - JS - W. -5 0 l 1 1 1 r HOT WATER CONSUMPTION DAILY TOTAL - 298L 0 1 —r-2 4 = P 80 - 20 - IS 10 0 110 - 100 90 -60 - 70 60 50 40 30 h 20 10 0 5 6 7 B 9 10 11 12 13 14 IS 16 17 IB 19 20 21 22 23 24 TIME OF DAY (HOUR) 116 F i g u r e 4.26 DJURNflL VARIATION IN SYSTEM OPERATION AND PERFORMANCE ON JUNE 17, \3n 0 1 2 3 4 5 6 7 BO 1 1 1 ' >-TJHE OF DAY (HOUR) B 3 JO 11 11 13 J i J5 j « J i J i JJ 20 11 11 13 11 10 U 60 5J 50 45 4) 35 30 2J 20 13 10 0 20 M H 10 3 i Q no too ga • ftQ • 10 60 50 « 30 70 10 0 ] ] o—a l a STORAGE TANK TS HID 1 TS BOT WTEft SUPPLY o TDHU a TSOHU » T n \ / i i i i i i ~i—i—i—i—i—i— DRILY TOTAL J QHT - i70.JI1J — QDHU = 13.5 rtJ • — QSDHU =» i5.3 TU i—i—•}—r—*i—r—r HOT WATER CONSUnPTTON DAILY TOTfiL - 324 L —i 1 1 1 r 1 2 3 4 5 6 7 f—1—r -i—r a • J no ISO as tn u ea a « - 39 2D JO —I 1 1 r B 3 JO JJ J7. J3 J4 JJ Jt JT JJ JJ 20 2J 71 13 H TlHE OF DAY (HOUR) CUMULATIVE FREQUENCY DISTRIBUTION OF HOURLY HOT WATER DRAWS JQO 90 -to • m cn Q I CC UJ o CE UJ O cn UJ 40 SO 60 10 AO VOLUME OF HOT WATER DRAWS JOu 110 (LITRES) J5Q O BC a. o rt 118 5 in z o u X 1800 1750 1700 1650 1600 1550 150O 1450 1400 1350 1300 1250 1200 1150 1100 1050 • 1000 • 350 • 330 B50 BOO 750 700 • 550 500 • 550 • 500 • 450 400 • 350 • 300 • 250 • 200 • 150 • 100 50 • 0 _ OCTOBER 1981 TOTAL (L) = 8287 DAILY AVERAGE (L/DAY) = 267 19 20 21 22 23 24 F i g u r e 4.28 D i u r n a l P r o f i l e o f H o u r l y Hot Water Draws: O c t o b e r 1981 119 If) z o u < o X 1800 -1150 -n o o -1650 -1600 -1S50 -I50O -1450 -1400 -1350 -1300 -1250 -1200 -1 ISO -1100 -10S0 -1000 -950 -goo -aso -800 -750 -700 -E50 -GOO -550 -500 -450 -430 -3S0 -300 -250 -200 -ISO -too -50 -0 0 JANUARY 1982 TOTAL (L) = 8057 DAILY AVERAGE (L/DAY) = 260 H—I—I—I—r 1 2 3 4 5 6 7 8 9 10 11 12 13,14 1 TIME OF DAY (HR) 5 IB 17 IB 19 20 21 22 23 24 F i g u r e 4.29 D i u r n a l P r o f i l e o f H o u r l y Hot Water Draws: J a n u a r y 1982 120 APRIL 19B2 TOTAL (L) = 8234 DAILY AVERAGE (L/DAY) = 274 Q UJ 3S Z3 cn z o u or UJ t— < o a: 8 9 10 11 12 13.14 J5 16 17 18 19 20 21 22 23 24 TIME OF DAY , 4 IS (HR) F i g u r e 4.30 D i u r n a l P r f i l e o f H o u r l y Hot Water Draws: A p r i l 1982 121 =3 o < o X JUNE 1982 TOTAL (L) S 9187 DAILY AVERAGE (L/DAY) = 306 2 3 8 9 10 II 12 13,14 11 TIME OF DAY (HR) 18 19 20 21 22 23 24 F i g u r e 4.31 D i u r n a l P r o f i l e o f H o u r l y Hot Water Draws: June 1982 122 20 - i 11 " ja -17 -ia 15 14 -13 -2 3 10 IO z. o U 8 Q£ 5 • 5 7 I • 6 -5 -4 -2 " 1 -° P I I I I I .1 I I I I I I • - I . . . . . 1 S 1 7, 3 4 5 « 7 8 3 10 11 12 33 14 IS J6 17 IB 19 20 21 72 23 24 TIME OF DAY (HR) F i g u r e 4.32 D i u r n a l P r o f i l e o f M o n t h l y Hot Water C o n s u m p t i o n 123 15 -14 -13 -6 -S -4 -3 -2 -1 -0 0 1 2 3 4 5 € 7 fl 9 10 11 12 J3 J4 15 16 17 J8 39 20 21 22 23 24 TIME OF DAY (HR) F i g u r e 4.33 D i u r n a l D i s t r i b u t i o n o f Hot Water C o n s u m p t i o n f o r the O v e r a l l M o n i t o r i n g P e r i o d 1 24 CHAPTER 5 SIMULATION MODEL A. S i m u l a t i o n M o d e l l i n g o f S o l a r H e a t i n g Systems - An O v e r v i e w S i m u l a t i o n m o d e l l i n g of s o l a r h e a t i n g s y s t e m s i n v o l v e s t h e f o l l o w i n g s i x s t e p s : (1) D e f i n i n g a s y s t e m i n terms o f t h e p h y s i c a l , t h e r m a l , and m e c h a n i c a l c h a r a c t e r i s t i c s o f i t s components and t h e p r o c e s s e s w h i c h o p e r a t e w i t h i n i t ; (2) F o r m u l a t i n g t h e s y s t e m p r o c e s s e s and components ( i n c l u d i n g t h e i r c o n n e c t i o n s , i n t e r a c t i o n s , and c o n t r o l mechanisms) u s i n g s e t s o f m a t h e m a t i c a l e q u a t i o n s ; (3) C o n s t r u c t i n g a p p r o p r i a t e a l g o r i t h m s and r e c u r s i v e methods t o s o l v e t h e e q u a t i o n s ; (4) Computer c o d i n g , programming, and d e b u g g i n g ; (5) O b t a i n i n g t h e n e c e s s a r y i n p u t d a t a , i n c l u d i n g v a l u e s f o r t h e s y s t e m p a r a m e t e r s and v a r i a b l e s ; (6) E x e c u t i n g t h e p r o g r a m arid a n a l y z i n g t h e r e s u l t s . S t e p 1 was c o v e r e d i n C h a p t e r s 2 & 3 and A p p e n d i x A; s t e p 6 w i l l be d e a l t w i t h i n C h a p t e r 6. The c o n t e n t o f t h i s c h a p t e r i s c o n c e r n e d w i t h s t e p s 2, 3 & 5. The d i s c u s s i o n b e g i n s w i t h an i n t r o d u c t o r y comment on t h e use o f models t o s i m u l a t e s o l a r h e a t i n g systems,, and t h e n f o c u s s e s on s e l e c t i n g and m o d i f y i n g an e x i s t i n g model f o r t h e p u r p o s e of s i m u l a t i n g t h e s y s t e m under i n v e s t i g a t i o n . B. S o l a r H e a t i n g System S i m u l a t i o n M o d e l s 1. A d v a n t a g e s and L i m i t a t i o n s As was b r i e f l y d i s c u s s e d i n t h e I n t r o d u c t i o n , t h e 1 25 p e r f o r m a n c e of s o l a r h e a t i n g s y s t e m s can be e v a l u a t e d e i t h e r e x p e r i m e n t a l l y t h r o u g h m o n i t o r i n g of f i e l d t r i a l s o r m a t h e m a t i c a l l y u s i n g s i m u l a t i o n m o d e l s . The a d v a n t a g e s o f t h e l a t t e r a r e many, as i n d i c a t e d by t h e f o l l o w i n g p o i n t s : (1) S i m u l a t i o n models a r e a b l e t o p r e d i c t a s y s t e m ' s l o n g t e r m p e r f o r m a n c e , i n c l u d i n g e n e r g y and d o l l a r s a v i n g s , w i t h o u t a y e a r o r more of a c t u a l s y s t e m o p e r a t i o n and m o n i t o r i n g . (2) S i m u l a t i o n models p r o d u c e r e s u l t s q u i c k l y and i n e x p e n s i v e l y a l l o w i n g immediate e v a l u a t i o n and m o d i f i c a t i o n of s y s t e m d e s i g n ; t h e y p r o v i d e f r e e d o m from e quipment p r o b l e m s w h i c h o f t e n c a u s e major d e l a y s d u r i n g m o n i t o r i n g of f i e l d t r i a l s . (3) S i m u l a t i o n models a l l o w p a r a m e t e r v a l u e s t o be e a s i l y a l t e r e d and o p t i m a l d e s i g n s t o be r e a d i l y i d e n t i f i e d f o r v a r i o u s l o a d and m e t e o r o l o g i c a l c o n d i t i o n s ; t h e y a l l o w c o m p l e t e f l e x i b i l i t y of s y s t e m c o n f i g u r a t i o n , o p e r a t i n g s t r a t e g y , and component t y p e s . (4) S i m u l a t i o n m o d e ls can p r o v i d e i n d e p t h a n a l y s i s o f s y s t e m o p e r a t i o n and component b e h a v i o u r , i n c l u d i n g t h e s e n s i t i v i t y o f a s y s t e m t o v a r y i n g i n p u t c o n d i t i o n s , w i t h o u t t h e need f o r d e t a i l e d i n s t r u m e n t a t i o n . Thus s i m u l a t i o n models p r o v i d e a c o n v e n i e n t t o o l w i t h w h i c h t o d e s i g n s y s t e m s , p r e d i c t t h e i r p e r f o r m a n c e , and a n a l y z e t h e i r o p e r a t i o n and b e h a v i o u r . However, i n a d d i t i o n t o a l l t h e i r a d v a n t a g e s , s i m u l a t i o n models e x h i b i t c e r t a i n l i m i t a t i o n s . They o n l y p o r t r a y a c t u a l s y s t e m s u s i n g a p p r o x i m a t e m a t h e m a t i c a l r e p r e s e n t a t i o n s ; e x a c t r e p l i c a t i o n i s i m p o s s i b l e ( o r a t l e a s t i m p r a c t i c a l a s s u c h ) . Hence s i m u l a t i o n m o d e ls a r e i n h e r e n t l y i m p e r f e c t . They g e n e r a l l y i n c o r p o r a t e many s i m p l i f i c a t i o n s i n 1 26 o r d e r t o r e n d e r t h e c o m p l e x i t y of r e a l s y s t e m s t r a c t a b l e . T h e s e i n c l u d e l i n e a r i z i n g f u n c t i o n a l l y complex r e l a t i o n s h i p s , s e t t i n g some s y s t e m v a r i a b l e s c o n s t a n t , and i g n o r i n g r e l a t i v e l y m i n o r i n t e r a c t i o n s and f e e d b a c k e f f e c t s . E a c h s i m p l i f i c a t i o n a c t s t o l e s s e n a model's p r e c i s i o n and u l t i m a t e l y a f f e c t s i t s a c c u r a c y . The o v e r a l l c h a l l e n g e t h e n , i s t o d e v e l o p a s i m u l a t i o n model w h i c h p r o v i d e s an a p p r o p r i a t e t r a d e - o f f between a c c u r a c y and c o m p l e x i t y , w h i l e a t t h e same t i m e s a t i s f y i n g u s e r r e q u i r e m e n t s i n terms of i t s a p p l i c a b i l i t y . In t h e p r e s e n t s t u d y a model was sought w h i c h c o u l d a c c u r a t e l y p r e d i c t t h e s y s t e m ' s l o n g t e r m t h e r m a l p e r f o r m a n c e a s w e l l as t r a c k i t s dynamic b e h a v i o u r t o a l i m i t e d d e g r e e . 2. D e v e l o p i n g and M o d i f y i n g T h e r e a r e s e v e r a l f a c t o r s w h i c h must be c o n s i d e r e d when d e v e l o p i n g o r m o d i f y i n g a s i m u l a t i o n model. F i r s t l y , t h e r e a r e d i m i n i s h i n g r e t u r n s i n p r e c i s i o n and a c c u r a c y , and i n c r e a s i n g c o s t s i n programming and c o m p u t a t i o n , a s t h e l e v e l of model d e t a i l and r e s o l u t i o n a r e i n c r e a s e d and t h e number o f a s s u m p t i o n s r e d u c e d . S e c o n d l y , s i n c e t h e t h e r m a l p r o c e s s e s b e i n g m o d e l l e d c a n be complex and not e n t i r e l y u n d e r s t o o d , e m p i r i c a l r e l a t i o n s h i p s must o f t e n be i n c o r p o r a t e d . (Hence d e v e l o p m e n t of s i m u l a t i o n models f r e q u e n t l y p r o c e e d s i n u n i s o n w i t h e x p e r i m e n t a l work.) T h i r d l y , t h e component models s h o u l d be matched i n t h e i r l e v e l o f d e t a i l and a c c u r a c y . F o r example, a complex s t o r a g e t a n k model s h o u l d n o t be c o u p l e d w i t h a p o o r l y d e f i n e d h e a t e x c h a n g e r m o d e l . T h i s would r e s u l t i n c o m p u t a t i o n a l i n e f f i c i e n c y . 1 27 C. S e l e c t i n g a S i m u l a t i o n Model A s u r v e y o f a v a i l a b l e s i m u l a t i o n m o d e ls and t h e i r s o l a r h e a t i n g a p p l i c a t i o n s was u n d e r t a k e n p r i o r t o s e l e c t i n g a s p e c i f i c model f o r use i n t h e p r e s e n t s t u d y . T h e r e was a v a r i e t y o f d i f f e r e n t models from w h i c h t o c h o o s e ( J o r g e n s e n , 1979; SERI, 1980). They m a i n l y d i f f e r e d i n t h e i r s o l u t i o n methods, w h i c h c an be c a t e g o r i z e d under t h e f o l l o w i n g t y p e s : l i n e a r / n o n - l i n e a r , d e t e r m i n i s t i c / p r o b a b i l i s t i c / s t o c h a s t i c , s t a t i c / t r a n s i e n t / dynami c , and d i s c r e t e / lumped / c o n t i n u o u s ( C h a n d r a s h e k a r , 1982). However, t h e main c o n c e r n d i d not r e s t w i t h t h e p a r t i c u l a r s o l u t i o n method of a model, but r a t h e r w i t h i t s a b i l i t y t o match t h e c o n f i g u r a t i o n , o p e r a t i n g s t r a t e g y , and components e x i s t i n g w i t h i n t h e s y s t e m under i n v e s t i g a t i o n . The WATSUN-3 D o m e s t i c Hot Water (DHWA) model ( C h a n d r a s h e k a r and W y l i e , 1981a) came c l o s e s t t o m e e t i n g t h i s r e q u i r e m e n t , a l t h o u g h t o t a l c o n f o r m i t y was f a r from c o m p l e t e . WATSUN DHWA i s an h o u r - b y - h o u r s i m u l a t i o n model c a p a b l e of p r e d i c t i n g t h e t h e r m a l and economic p e r f o r m a n c e of l i q u i d - b a s e d d o u b l e t a n k SDHW h e a t i n g s y s t e m s . I t s mo d u l a r p r o g r a m s t r u c t u r e i s b a s e d on a number o f i n t e r a c t i n g component models and s u p p o r t i n g s u b r o u t i n e s . W h i l e e x a c t d e t a i l s o f t h e component models and t h e i r c o n t r o l l o g i c were n ot a d o p t e d , s u f f i c i e n t m e t h o d o l o g y ( i n c l u d i n g t h e g e n e r a l a p p r o a c h and b a s i c a s s u m p t i o n s ) was r e t a i n e d , s u c h t h a t t h e s i m u l a t i o n model p r e s e n t e d below r e p r e s e n t s a m o d i f i c a t i o n and n o t a new d e v e l o p m e n t . A l l s i g n i f i c a n t d i f f e r e n c e s between t h e o r i g i n a l WATSUN DHWA model and t h e m o d i f i e d v e r s i o n a r e c l e a r l y i d e n t i f i e d ; i n some c a s e s 128 t h e y a r e f e l t t o be o f s p e c i a l i n t e r e s t and a r e d i s c u s s e d i n d e t a i l . F i n a l l y , i t s h o u l d be n o t e d t h a t o n l y t h e a c t u a l h e a t t r a n s f e r models c o n t a i n e d w i t h i n WATSUN DHWA were u t i l i z e d ; i t s e conomic a n a l y s i s , programming p a c k a g e , and i n p u t / o u t u t r o u t i n e s were not e m p l o y e d . D. D e t a i l e d D e s c r i p t i o n o f t h e S i m u l a t i o n M odel 1. G e n e r a l A p p r o a c h and S o l u t i o n T e c h n i q u e The s i m u l a t i o n model c a n be l o o s e l y d e s c i b e d as u s i n g a component ' b l a c k box' e n e r g y b a l a n c e a p p r o a c h . In t h i s a p p r o a c h , a t h e r m a l e q u i l i b r i u m i s m a i n t a i n e d i n t h e s y s t e m by b a l a n c i n g t h e e n e r g y i n p u t s and o u t p u t s f o r t h e c o l l e c t o r , h e a t e x c h a n g e r , and s o l a r s t o r a g e t a n k . The m o d e l ' s s o l u t i o n t e c h n i q u e i s b a s e d on a s e q u e n t i a l c a l c u l a t i o n o f t h e e n e r g y i n p u t / o u t p u t t e r m s f o r t h e s e t h r e e i n t e r a c t i n g components; t h e c a l c u l a t i o n i s r e p e a t e d e v e r y hour o v e r t h e e n t i r e s i m u l a t i o n p e r i o d . Two s i m p l i f i c a t i o n s a r e made: i n l e t and o u t l e t t e m p e r a t u r e s o f n e i g h b o u r i n g components a r e s e t e q u a l t o e a c h o t h e r , and t h e v a l u e s from t h e p r e v i o u s c a l c u l a t i o n a r e u s e d as i n i t i a l c o n d i t i o n s . Hence f o r e a c h c a l c u l a t i o n , t h e c o l l e c t o r i n l e t t e m p e r a t u r e and t h e h e a t e x c h a n g e r o u t l e t t e m p e r a t u r e a r e s e t e q u a l t o t h e s t o r a g e t a n k t e m p e r a t u r e as d e t e r m i n e d a t t h e end of t h e p r e v i o u s c a l c u l a t i o n . The e f f e c t s of c o l l e c t o r o p e r a t i o n ( e n e r g y i n p u t ) and h o t water draws ( e n e r g y o u t p u t ) a r e i n c o r p o r a t e d i n t o e a c h c a l c u l a t i o n as t h e y o c c u r ; t h e y s u b s e q u e n t l y a f f e c t t h e s t o r a g e t a n k t e m p e r a t u r e and t h e r e f o r e t h e i n l e t and o u t l e t t e m p e r a t u r e s f o r t h e n e x t c a l c u l a t i o n . E a c h c a l c u l a t i o n c o v e r s a t i m e s t e p of one h o u r ; 129 t h e u n d e r l y i n g a s s u m p t i o n i s t h a t t h e s y s t e m v a r i a b l e s r e m a i n c o n s t a n t o v e r t h i s t i m e i n t e r v a l . Hence t h e s o l u t i o n t e c h n i q u e can be d e s c r i b e d . a s b e i n g q u a s i - s t a t i o n a r y , and t h e model c a n be c l a s s i f i e d under t h e t r a n s i e n t and d e t e r m i n i s t i c c a t e g o r i e s l i s t e d a b o v e . The one hour t i m e s t e p a d o p t e d i n t h e model i s l o n g e r t h a n t h e t i m e r e q u i r e d f o r water c i r c u l a t i n g t h r o u g h t h e c o l l e c t o r l o o p t o f l o w t h r o u g h t h e p a n e l s , as w e l l a s f o r i n c o m i n g c o l d w ater t o p a s s t h r o u g h t h e h e a t e x c h a n g e r . One hour i s a l s o l o n g e r t h a n t h e t i m e c o n s t a n t s f o r b o t h of t h e s e s y s t e m components. T h i s s i t u a t i o n i s compounded by t h e f a c t t h a t even t h o u g h s w i t c h i n g of t h e c i r c u l a t i o n pump c a n be r e s o l v e d t o w i t h i n one h o u r , t h e r m a l waves c a n p e r s i s t i n t h e a c t u a l s t o r a g e t a n k w h i c h may n o t n e c e s s a r i l y be r e p l i c a t e d by the model i n o n l y one or two t i m e s t e p s . C o n s e q u e n t l y , s h o r t t e r m s i m u l a t i o n s o f t h e s y s t e m ( h o u r s - d a y s ) a r e u n l i k e l y t o p r o d u c e r e l i a b l e r e s u l t s . P r e c i s i o n and r e s o l u t i o n o f t h e model have t h e r e f o r e been r e d u c e d i n f a v o u r of l o w e r c o m p u t a t i o n a l c o s t s and e a s i e r programming - a n e c e s s a r y t r a d e - o f f when s i m u l a t i n g a s y s t e m o v e r a p e r i o d of a y e a r o r l o n g e r . (The p r o b l e m a d d r e s s e d i n t h e n e x t c h a p t e r i s t o d e t e r m i n e t o what e x t e n t model p r e c i s i o n has been r e d u c e d , and t o f i n d o u t whether model a c c u r a c y has been p r e s e r v e d o v e r t h e l o n g term.) 2. C o l l e c t o r M odel WATSUN DHWA u s e s a s i m p l i f i e d a n a l y t i c a l model w h i c h c h a r a c t e r i z e s t h e s t e a d y s t a t e t h e r m a l p e r f o r m a n c e of a f l a t p l a t e c o l l e c t o r . T h i s model was o r i g i n a l l y d e v e l o p e d by H o t t e l 1 30 and Woertz ( 1 9 4 2 ) , and l a t e r r e f i n e d by H o t t e l and W h i l l i e r (1958) and W h i l l i e r ( 1 9 7 7 ) . I t c a n be e x p r e s s e d m a t h e m a t i c a l l y i n t e r m s o f an e n e r g y b a l a n c e e q u a t i o n : QC = A R E A C * F R [ H T ( t a ) e - UL(TCI - T A ) ] (13) where QC = u s e f u l e n e r g y g a i n ( s o l a r e n e r g y c o l l e c t e d ) AREAC = c o l l e c t o r a r e a FR = c o l l e c t o r h e a t r e m o v a l f a c t o r HT = s o l a r r a d i a t i o n i n c i d e n t on c o l l e c t o r s u r f a c e p e r u n i t a r e a ( t a ) e = c o v e r t r a n s m i t t a n c e and p l a t e a b s o r p t a n c e p r o d u c t UL = o v e r a l l c o l l e c t o r h e a t l o s s c o e f f i c i e n t TCI = c o l l e c t o r i n l e t t e m p e r a t u r e TA = ambient a i r t e m p e r a t u r e T h i s e q u a t i o n i n d i c a t e s t h a t t h e s o l a r r a d i a t i o n i n c i d e n t on a c o l l e c t o r i s p a r t i t i o n e d i n t o : u s e f u l e n e r g y g a i n , h e a t l o s s e s (by c o n d u c t i o n , c o n v e c t i o n , and t h e r m a l r a d i a t i o n ) , and s o l a r r a d i a t i o n l o s s e s . The h e a t l o s s e s from t h e c o l l e c t o r t o t h e s u r r o u n d i n g s a r e r e p r e s e n t e d by an o v e r a l l h e a t l o s s c o e f f i c i e n t UL m u l t i p l i e d by t h e t e m p e r a t u r e g r a d i e n t between t h e c o l l e c t o r i n l e t and t h e ambient a i r (TCI - T A ) . T h i s i s a c o n v e n i e n t r e p r e s e n t a t i o n f o r m o d e l l i n g t h e c o l l e c t o r b e c a u s e i t s i n l e t t e m p e r a t u r e c a n be d e r i v e d f r o m t h e s t o r a g e t a n k t e m p e r a t u r e . However, h e a t l o s s e s b a s e d on t h e i n l e t t e m p e r a t u r e u n d e r - e s t i m a t e a c t u a l h e a t l o s s e s b e c a u s e t h e t e m p e r a t u r e g r a d i e n t between t h e c o l l e c t o r and t h e ambient a i r i n c r e a s e s i n t h e d i r e c t i o n of f l o w ; i e . a t t h e c o l l e c t o r o u t l e t , t h i s t e m p e r a t u r e g r a d i e n t (TCO - TA) i s much l a r g e r t h a n a t t h e i n l e t . T h e r e f o r e , a h e a t r e m o v a l f a c t o r FR i s i n c l u d e d i n t h e above e q u a t i o n . T h i s t e r m r e d u c e s t h e u s e f u l e n e r g y g a i n f r o m what i t p o t e n t i a l l y would be i f t h e whole c o l l e c t o r was o p e r a t i n g a t t h e i n l e t t e m p e r a t u r e t o what i t a c t u a l l y i s f o r t h e c o l l e c t o r o p e r a t i n g w i t h a t e m p e r a t u r e 131 g r a d i e n t from i n l e t t o o u t l e t . S i m i l a r l y , t h e c o v e r t r a n s m i t t a n c e and p l a t e a b s o r p t a n c e p r o d u c t ( t a ) e i s i n c l u d e d i n t h i s e q u a t i o n t o a c c o u n t f o r t h e f r a c t i o n o f i n c i d e n t s o l a r r a d i a t i o n w h i c h i s a t t e n u a t e d by t h e g l a s s c o v e r and r e f l e c t e d by t h e a b s o r b e r p l a t e ; t h i s r a d i a t i o n i s e f f e c t i v e l y l o s t by t h e c o l l e c t o r . 1 ' When t h e two terms FR and ( t a ) e a r e m u l t i p l i e d t o g e t h e r , t h e y i n d i c a t e t h e f r a c t i o n of i n c i d e n t s o l a r r a d i a t i o n w h i c h i s a b l e t o p e n e t r a t e t h r o u g h t h e g l a s s c o v e r , be a b s o r b e d by t h e p l a t e , and t h e n be t r a n s f e r r e d ( i n t h e form of s e n s i b l e h e a t ) t o t h e water c i r c u l a t i n g t h r o u g h t h e c o l l e c t o r p a s s a g e s . In o t h e r words, F R ( t a ) e r e p r e s e n t s t h e f r a c t i o n of i n c i d e n t s o l a r r a d i a t i o n w h i c h i s a b s o r b e d by t h e c o l l e c t o r i n t h e a b s e n c e of any h e a t l o s s e s . The l a t t e r a r e r e p r e s e n t e d by FRUL, w h i c h i n d i c a t e s t h e r a t e a t which a b s o r b e d h e a t i s l o s t f r o m t h e c o l l e c t o r . T h e s e two p a r a m e t e r s -F R ( t a ) e and FRUL - can e i t h e r be d e r i v e d a n a l y t i c a l l y f r o m b a s i c p r i n c i p l e s , o r e v a l u a t e d e m p i r i c a l l y u s i n g s p e c i a l a p p a r a t u s d e s i g n e d t o t e s t c o l l e c t o r e f f i c i e n c y . S i n c e t h e l a t t e r t e c h n i q u e was u s e d t o g e n e r a t e v a l u e s f o r t h e c o l l e c t o r p a r a m e t e r s u s e d i n t h e p r e s e n t s t u d y , i t s method w i l l be b r i e f l y d i s c u s s e d . F i r s t l y , e q u a t i o n 13 needs t o be r e - a r r a n g e d i n terms o f an ' i n s t a n t a n e o u s ' c o l l e c t o r e f f i c i e n c y ( n ) , d e f i n e d by t h e r a t i o o f u s e f u l e n e r g y g a i n t o t o t a l s o l a r e n e r g y a v a i l a b l e , a s f o l l o w s : n = QC/(HT*AREAC) = F R ( t a ) e - FRUL(TCI - TA)/HT (14) E q u a t i o n 14 forms t h e b a s i s f o r c o l l e c t o r e f f i c i e n c y t e s t s u s e d i n e v a l u a t i n g t h e t h e r m a l p e r f o r m a n c e o f f l a t p l a t e 1 32 c o l l e c t o r s . The g e n e r a l p r o c e d u r e i s t o s e t t h e c o l l e c t o r up i n a t e s t f a c i l i t y , o p e r a t e i t under r e l a t i v e l y s t e a d y t h e r m a l and r a d i a t i v e c o n d i t i o n s , and p e r f o r m a s e r i e s o f m e a s u r e m e n t s . 1 5 The v a r i a b l e s w h i c h a r e m e a s u r e d i n c l u d e t h e t h r e e a p p e a r i n g on t h e r i g h t hand s i d e of e q u a t i o n 14 - T C I , TA, and HT - as w e l l as TCO and CMC. The l a t t e r two, when combined w i t h T C I , a l l o w e v a l u a t i o n of QC u s i n g t h e f o l l o w i n g s t e a d y s t a t e h e a t t r a n s f e r e q u a t i o n : QC = CMC(TCO - TCI) (15) M easurements must be made o v e r t h e range of c o l l e c t o r i n l e t t e m p e r a t u r e s t y p i c a l l y e x p e r i e n c e d when t h e c o l l e c t o r o p e r a t e s a s p a r t of an a c t u a l s y s t e m . I n s t a n t a n e o u s e f f i c i e n c i e s (n) a r e t h e n e v a l u a t e d u s i n g e q u a t i o n s 14 & 15, and p l o t t e d as a f u n c t i o n of t h e c o l l e c t o r o p e r a t i n g p o i n t s (TCI - TA)/HT. I f UL, FR, and ( t a ) e were a l l c o n s t a n t , t h e p l o t t e d p o i n t s would f a l l on a p e r f e c t l y s t r a i g h t l i n e w i t h i n t e r c e p t F R ( t a ) e and s l o p e -FRUL. However t h e c o l l e c t o r p a r a m e t e r s a r e not c o n s t a n t , and t h e d a t a p o i n t s t e n d t o e x h i b i t a l i m i t e d amount of s c a t t e r due t o t e m p e r a t u r e d e p endence, wind e f f e c t s , and a n g l e o f i n c i d e n c e v a r i a t i o n s . 1 6 Hence a b e s t f i t ( l e a s t s q u a r e s ) l i n e i s g e n e r a l l y drawn t h r o u g h t h e d a t a p o i n t s ; i t u s u a l l y f i t s t h e d a t a t o w i t h i n ± 5 % ( D u f f i e and Beckman, 1980). T h i s l i n e i s known a s t h e c o l l e c t o r e f f i c i e n c y c u r v e , and i t s i n t e r c e p t and a b s o l u t e s l o p e a r e commonly r e f e r r e d t o as t h e z e r o - p o i n t and s l o p e e f f i c i e n c y p a r a m e t e r s , r e s p e c t i v e l y . T hese two p a r a m e t e r s a r e w i d e l y u s e d t o r e p o r t t h e t h e r m a l p e r f o r m a n c e of f l a t p l a t e c o l l e c t o r s . A c c o r d i n g l y , t h e y form t h e b a s i s f o r t h e s i m p l e c o l l e c t o r model u s e d i n b o t h WATSUN 1 33 DHWA and t h e m o d i f i e d v e r s i o n . T h e i r dependence on s t e a d y r a d i a t i v e and t h e r m a l c o n d i t i o n s i s n e c e s s a r i l y i n c o r p o r a t e d i n t o t h e c o l l e c t o r model a s a s i m p l i f i c a t i o n . T h i s i s i n agreement w i t h t h e u n d e r l y i n g b a s i s of t h e s i m u l a t i o n model, w h i c h assumes s t e a d y s t a t e o p e r a t i o n o f t h e s y s t e m o v e r e a c h one hour i n t e r v a l d e s p i t e t h e dynamic n a t u r e o f t h e l o a d and m e t e o r o l o g i c a l v a r i a b l e s . WATSUN DHWA i n c l u d e s an a d d i t i o n a l t e r m i n i t s c o l l e c t o r m odel; an i n c i d e n t a n g l e m o d i f i e r i s i n c o r p o r a t e d t o a c c o u n t f o r i n c r e a s i n g s o l a r r a d i a t i o n l o s s e s a t i n c i d e n t a n g l e s g r e a t e r t h a n 40 d e g r e e s o f f n o r m a l . T h i s t e r m was n o t i n c o r p o r a t e d i n t h e m o d i f i e d v e r s i o n s i n c e i t was c o n s i d e r e d t o be a s e c o n d - o r d e r c o r r e c t i o n f a c t o r , m i s - m a t c h i n g t h e o v e r a l l f i r s t - o r d e r l e v e l of d e t a i l s o u g h t f o r t h e s i m u l a t i o n model. A d d i t i o n a l s e c o n d - o r d e r c o r r e c t i o n f a c t o r s would a l s o r e q u i r e i n c l u s i o n i n t h e model i f t h i s l e v e l o f d e t a i l were d e s i r e d . Examples would be c o r r e c t i o n s f o r t h e e f f e c t s of c o l l e c t o r h e a t c a p a c i t y , c o l l e c t o r s h a d i n g , and n o n - u n i f o r m i t y of f l o w t h r o u g h t h e p a n e l s . ( T h i r d - o r d e r e f f e c t s would i n c l u d e d i s s i p a t i o n o f pump e n e r g y i n t o t h e water c i r c u l a t i n g t h r o u g h t h e c o l l e c t o r l o o p and r e d u c t i o n of c o v e r t r a n s m i t t a n c e due t o d u s t a c c u m u l a t i o n and o p t i c a l d e t e r i o r a t i o n . ) In b o t h WATSUN DHWA and t h e m o d i f i e d v e r s i o n , p i p e h e a t l o s s a nd c a p a c i t a n c e e f f e c t s w i t h i n t h e c o l l e c t o r l o o p a r e i g n o r e d . However, r e s e a r c h e r s i n v o l v e d w i t h WATSUN have s i n c e a l l o w e d f o r t h e s e e f f e c t s i n t h e i r c o l l e c t o r model ( p e r s o n a l c o m m u n i c a t i o n - M. C h a n d r a s h e k a r ) . F o r t h e s y s t e m under i n v e s t i g a t i o n , t h e s e e f f e c t s were a g a i n c o n s i d e r e d t o be 134 s e c o n d - o r d e r s i n c e b o t h t h e i n l e t and o u t l e t p i p e s a r e w e l l i n s u l a t e d , run a l m o s t e n t i r e l y i n d o o r s ( w i t h i n h e a t e d s p a c e ) , and a r e d r a i n e d of water when t h e c o l l e c t o r i s n o t o p e r a t i n g . Hence a l l s o l a r e n e r g y c o l l e c t e d i s assumed t o be t r a n s f e r r e d t o t h e s t o r a g e tank w i t h o u t any i n t e r m e d i a t e l o s s e s , i e . QCSS = QC. From e q u a t i o n 13, a n e g a t i v e s o l a r e n e r g y g a i n c o u l d be c a l c u l a t e d f o r a g i v e n h o u r . C o n s e q u e n t l y , an e q u i l i b r i u m a b s o r b e r p l a t e t e m p e r a t u r e (TCP) e v a l u a t e d f o r ' n o - f l o w ' c o n d i t i o n s (QC=0) i s u s e d a s a c o n t r o l v a r i a b l e t o d e t e r m i n e whether c o l l e c t o r o p e r a t i o n s h o u l d be i n i t i a t e d . TCP i s c a l c u l a t e d f o r e a c h h o u r o f t h e s i m u l a t i o n p e r i o d u s i n g t h e f o l l o w i n g e q u a t i o n : TCP = TA + H T [ F R ( t a ) e ] / F R U L (16) I t s v a l u e w i l l a l w a y s be g r e a t e r t h a n a mbient a i r t e m p e r a t u r e d u r i n g d a y l i g h t h o u r s , w h i l e a t n i g h t TCP w i l l a l w a y s e q u a l TA. In t h e p r e s e n t s t u d y , a c t u a l measured d a t a a r e u s e d a s i n p u t v a l u e s f o r t h e two m e t e o r o l o g i c a l v a r i a b l e s on t h e r i g h t hand s i d e o f e q u a t i o n 16. In s y s t e m d e s i g n s t u d i e s u s i n g WATSUN DHWA t h e i n p u t v a l u e s f o r TA must n e c e s s a r i l y be d e r i v e d f r o m c l i m a t o l o g i c a l r e c o r d s , w h i l e v a l u e s f o r HT must be c a l c u l a t e d u s i n g a p p r o p r i a t e s l o p e r a d i a t i o n f o r m u l a e i n c o n j u n c t i o n w i t h a r c h i v e d r a d i a t i o n d a t a . G i v e n a v a l u e f o r TCP, e q u a t i o n 13 c a n be r e w r i t t e n and s o l v e d a s QCSS = AREAC*FRUL(TCP - T C I ) + (17) where t h e '+' s i g n i n d i c a t e s t h a t c o n t r o l l o g i c i s b e i n g a p p l i e d , s u c h t h a t o n l y p o s i t i v e QCSS v a l u e s above a t h r e s h o l d l e v e l a r e c a l c u l a t e d by t h e c o l l e c t o r m odel. The t h r e s h o l d 1 35 l e v e l i s s e t by t h e f o l l o w i n g i n e q u a l i t y : TCP - TCI > TDIF1 (18) S o l a r e n e r g y c o l l e c t i o n c o n t i n u e s u n t i l a s e c o n d i n e q u a l i t y i s no l o n g e r s a t i s f i e d . T h i s i n e q u a l i t y s e t s t h e minimum c o l l e c t o r - t o - t a n k t e m p e r a t u r e d i f f e r e n c e r e q u i r e d t o m a i n t a i n pump o p e r a t i o n and c i r c u l a t i o n of water t h r o u g h t h e c o l l e c t o r l o o p . I t r e p r e s e n t s a f u r t h e r m o d i f i c a t i o n t o WATSUN DHWA s i n c e t h e l a t t e r o n l y a l l o w s s p e c i f i c a t i o n of a s i n g l e t e m p e r a t u r e d i f f e r e n t i a l t o c o n t r o l o p e r a t i o n of t h e c i r c u l a t i o n pump; i e . TDIF2 = T D I F 1 . In t h e a c t u a l s y s t e m , a two s t a g e d i f f e r e n t i a l c o n t r o l l e r i s u s e d . Hence t h e model was m o d i f i e d t o p e r m i t ' o n - o f f o p e r a t i o n o f t h e pump u s i n g two t e m p e r a t u r e d i f f e r e n t i a l s . In b o t h i n e q u a l i t i e s 18 & 19, TCI i s s e t e q u a l t o t h e s t o r a g e t a n k t e m p e r a t u r e as c a l c u l a t e d a t t h e end of t h e p r e v i o u s h o u r . TCO i n t u r n i s e v a l u a t e d by s o l v i n g a r e - a r r a n g e d f o r m of e q u a t i o n 15 as f o l l o w s : The c o n t r o l l o g i c f o r t h e c o l l e c t o r model i s o u t l i n e d i n F i g u r e 5.1. I t can be se e n t h a t i n e q u a l i t y 18 i s o n l y c h e c k e d i f t h e r e was no s o l a r e n e r g y c o l l e c t e d f o r t h e p r e v i o u s h o u r . In c o n t r a s t , i n e q u a l i t y 19 i s c h e c k e d i f e i t h e r i n e q u a l i t y 18 i s c u r r e n t l y s a t i s f i e d , o r i f t h e r e was s o l a r e n e r g y c o l l e c t e d d u r i n g t h e p r e v i o u s h o u r . In e i t h e r c a s e , s o l a r e n e r g y c o l l e c t i o n c o n t i n u e s u n t i l i n e q u a l i t y 19 c e a s e s t o be s a t i s f i e d . An a d d i t i o n a l c h e c k v e r i f i e s t h a t TCO i s below a maximum v a l u e of 100°C ( b o i l i n g p o i n t o f w a t e r ) f o r a l l TCO - TCI > TDIF2 (19) TCO = TCI + QCSS/CMC (20) 1 36 h o u r s of c o l l e c t o r o p e r a t i o n . 1 7 3. S t a n d b y Heat L o s s Model The s t a n d b y h e a t l o s t ( o r g a i n e d ) from t h e s o l a r s t o r a g e t a n k t o t h e s u r r o u n d i n g basement a i r i s c a l c u l a t e d u s i n g t h e f o l l o w i n g s t e a d y s t a t e h e a t t r a n s f e r e q u a t i o n : QSENV = UAS(TS - TBSM) (21) WATSUN DHWA expands t h i s e q u a t i o n by a l l o w i n g an a r e a -w e i g h t e d p o r t i o n of t h e s t a n d b y h e a t t o be l o s t t h r o u g h t h e ta n k b o t t o m t o t h e basement f l o o r a t a t e m p e r a t u r e d i f f e r e n t t o t h a t of TBSM. T h i s d i v i s i o n o f t h e s t a n d b y h e a t l o s s was n o t i n c o r p o r a t e d i n t h e m o d i f i e d v e r s i o n of t h e model; t h e l a t t e r assumes t h a t a l l h e a t l o s t f r o m t h e s t o r a g e t a n k o c c u r s t o ambient a i r a t t e m p e r a t u r e TBSM. The s t o r a g e t a n k h e a t l o s s c o e f f i c i e n t (UAS) was e v a l u a t e d b o t h e m p i r i c a l l y and t h e o r e t i c a l l y . The l a t t e r e v a l u a t i o n i s p r e s e n t e d i n A p p e n d i x D. E m p i r i c a l e v a l u a t i o n of UAS i n v o l v e d s o l v i n g UAS = QSENV/(TS - TBSM) = (A T S * C V S ) / ( T S - TBSM) (22) f o r t h o s e p e r i o d s when no s o l a r e n e r g y c o l l e c t i o n (QCSS) o r h o t wat e r draws (QSDHW) were o c c u r r i n g - i e . g e n e r a l l y d u r i n g n i g h t t i m e h o u r s when s t a n d b y h e a t l o s s became t h e o n l y a c t i v e e n e r g y i n p u t / o u t p u t t e r m f o r t h e s t o r a g e t a n k . A t o t a l o f 60 i n d i v i d u a l e v a l u a t i o n s were p e r f o r m e d ; t h e y u s u a l l y e x t e n d e d o v e r an i n t e r v a l o f 6 t o 7 h o u r s . F o r a l l c a s e s , t h e c h a n g e s i n s t o r a g e t a n k t e m p e r a t u r e (ATS) were a r i t h m e t i c a l l y a v e r a g e d o v e r t h e b o t t o m and m i d - h e i g h t l e v e l s . In a d d i t i o n , t h e measured h o u r l y t e m p e r a t u r e g r a d i e n t s between t h e water i n t h e s t o r a g e t a n k and t h e s u r r o u n d i n g basement a i r (TS - TBSM) were 1 37 a v e r a g e d o v e r t h e e v a l u a t i o n i n t e r v a l . The r e s u l t s a r e summarized i n t h e T a b l e 5.1 below. T a b l e 5.1 S t o r a g e Tank Heat L o s s C o e f f i c i e n t E m p i r i c a l E v a l u a t i o n R e s u l t s A l l v a l u e s a r e i n kJ/hr°C Mean S t d . Dev. Max imum Minimum 16.0 3.0 24.2 10.5 A l a r g e d i s c r e p a n c y e x i s t s between t h e e m p i r i c a l and t h e o r e t i c a l UAS v a l u e s - 16.0 v e r s u s 4.6 k J / h r ° C . W h i l e t h e t h e o r e t i c a l v a l u e i s b a s e d on c e r t a i n a s s u m p t i o n s , t h e r e i s a l s o c o n s i d e r a b l e u n c e r t a i n t y a s s o c i a t e d w i t h t h e e m p i r i c a l v a l u e as i s i n d i c a t e d by i t s d e g r e e of d i s p e r s i o n . P a r t of t h e r e a s o n f o r t h i s u n c e r t a i n t y i s due t o t h e f a c t t h a t t h e t e m p e r a t u r e t r a n s d u c e r measurements were o n l y r e s o l v e d t o ±0.5°C by t h e m o n i t o r i n g equipment ( A p p e n d i x C ) , w h i l e t e m p e r a t u r e c h a n g e s i n t h e s t o r a g e t a n k o v e r t h e e v a l u a t i o n i n t e r v a l s were u s u a l l y l e s s t h a n 5.0 d e g r e e s C. Hence t h e m a g n i t u d e o f t h e h o u r l y t e m p e r a t u r e c h a n g e s a p p r o a c h e d i n s t r u m e n t r e s o l u t i o n . S i n c e t h i s l i m i t a t i o n was n o t c u m u l a t i v e o v e r an e v a l u a t i o n i n t e r v a l , i t i s more a p p r o p r i a t e t o s t a t e t h a t an a v e r a g e r e s o l u t i o n e r r o r e x c e e d i n g 10% e x i s t s w i t h i n t h e e m p i r i c a l UAS v a l u e . A n o t h e r r e a s o n f o r t h e t h e u n c e r t a i n t y i n t h e e m p i r i c a l v a l u e i s t h a t n i g h t t i m e i s t y p i c a l l y c h a r a c t e r i z e d by w e l l - d e v e l o p e d t h e r m a l s t r a t i f i c a t i o n w i t h i n t h e s t o r a g e t a n k ( C h a p t e r 4 ) . Thus, p a r t o f t h e m easured TS t e m p e r a t u r e change may be due t o c o n v e c t i v e a c t i v i t y a s o p p o s e d t o s t a n d b y h e a t l o s s - m o n i t o r i n g o f t h e 1 38 tank was s i m p l y n ot i n t e n s i v e enough t o d i f f e r e n t i a t e between t h e s e two t h e r m a l p r o c e s s e s . D e s p i t e t h e l a r g e amount o f e r r o r i n t h e e m p i r i c a l UAS v a l u e , t h e r e i s s u f f i c i e n t i n d e p e n d e n t e v i d e n c e t o s u g g e s t t h a t t h i s v a l u e i s more a c c u r a t e t h a n t h e t h e o r e t i c a l one. F i r s t l y , t h e m a n u f a c t u r e r d i d q u o t e two UAS v a l u e s - 14.3 and 18.0 kJ/hr°C - o b t a i n e d f r o m more r i g o r o u s e x p e r i m e n t a l t e s t s p e r f o r m e d on a s i m i l a r s t o r a g e t a n k . S e c o n d l y , i t has been r e p o r t e d by C u r t i s and L a F o n t a i n e (1981) t h a t s t o r a g e t a n k h e a t l o s s e s " a r e g e n e r a l l y 2 t o 3 t i m e s h i g h e r t h a n e x p e c t e d f r o m c a l c u l a t i o n s b a s e d on i n s u l a t i o n t h i c k n e s s " . T h e r e f o r e , a g r e a t e r d e g r e e of c o n f i d e n c e c a n be p l a c e d i n t h e e m p i r i c a l UAS v a l u e t h a n i n i t s t h e o r e t i c a l c o u n t e r p a r t . W h i l e t h e model c a l c u l a t e s t h e h o u r l y v a l u e s of TS u s e d i n e q u a t i o n 21, t h e v a l u e s f o r TBSM a r e e n t e r e d as i n p u t d a t a . U n f o r t u n a t e l y , t h e basement a i r t e m p e r a t u r e was measured d u r i n g o n l y a l i m i t e d p a r t o f t h e m o n i t o r i n g p e r i o d . Hence a s u r r o g a t e v a r i a b l e i s u s e d t o e s t i m a t e TBSM v a l u e s f o r s i m u l a t i o n p e r i o d s when t h e measured h o u r l y v a l u e s a r e not a v a i l a b l e ( A p p e n d i x E ) . The s u r r o g a t e v a r i a b l e i s o n l y c a p a b l e o f e s t i m a t i n g basement a i r t e m p e r a t u r e on a d a i l y b a s i s . S t i l l , t h i s d i f f e r s from WATSUN DHWA w h i c h assumes t h a t TBSM i s c o n s t a n t o v e r t h e e n t i r e s i m u l a t i o n p e r i o d . A c t u a l d i u r n a l and d a y - t o - d a y v a r i a t i o n s i n t h e basement a i r t e m p e r a t u r e a r e documented i n A p p e n d i x E . 4. Heat E x c h a n g e r Model WATSUN DHWA models t h e t r a n s f e r of h e a t from t h e wa t e r r e s i d i n g i n t h e s t o r a g e t a n k t o t h a t f l o w i n g t h r o u g h t h e 139 immersed c o i l h e a t e x c h a n g e r by u s i n g an e m p i r i c a l c o r r e l a t i o n e q u a t i o n . T h i s e q u a t i o n was o r i g i n a l l y d e v e l o p e d t o model f r e e c o n v e c t i v e h e a t t r a n s f e r away f r o m a h o r i z o n t a l p i p e immersed i n a f l u i d h a v i n g l a m i n a r f l o w . I t i s c o n s i d e r e d t o be an i n a p p r o p r i a t e a p p l i c a t i o n i n t h e c u r r e n t s i t u a t i o n s i n c e t h e f o l l o w i n g a s s u m p t i o n s must n e c e s s a r i l y be made: (1) Water i n t h e s t o r a g e t a n k i s assumed t o be i n a f r e e c o n v e c t i v e s t a t e a t a l l t i m e s ; i n t h e a c t u a l s y s t e m t h i s i s n e g a t e d by t h e c i r c u l a t i o n pump, w h i c h c a u s e s f o r c e d c o n v e c t i o n and t h o r o u g h m i x i n g of t h e water i n t h e tank d u r i n g p e r i o d s o f s o l a r e n e r g y c o l l e c t i o n . (2) The e n t i r e l e n g t h o f h e a t e x c h a n g e r p i p e i s assumed h o r i z o n t a l ; no a c c o u n t i s made f o r t h e v e r t i c a l e n t r a n c e s e c t i o n , t h e s l i g h t g r a d e i n t h e c o i l e d s e c t i o n , nor f o r th e e f f e c t o f v e r t i c a l l y n e i g h b o u r i n g c o i l s . F u r t h e r m o r e , WATSUN DHWA makes t h e f o l l o w i n g s i m p l i f i c a t i o n s i n a d o p t i n g t h i s e q u a t i o n a s a h e a t e x c h a n g e r m o d e l : (3) The o u t s i d e p i p e w a l l t e m p e r a t u r e i s assumed c o n s t a n t o v e r t h e e n t i r e l e n g t h of t h e h e a t e x c h a n g e r . (4) No a c c o u n t i s made f o r t h e t h e r m a l r e s i s t a n c e between t h e o u t s i d e p i p e w a l l and t h e main s t r e a m of water f l o w i n g w i t h i n t h e h e a t e x c h a n g e r . (5) Water i s assumed t o f l o w t h r o u g h t h e h e a t e x c h a n g e r a t a c o n s t a n t r a t e ; no a c c o u n t i s made f o r i t s r e s i d e n c y t i m e d u r i n g p e r i o d s o f i n t e r m i t t e n t f l o w . (6) The t h e r m a l and p h y s i c a l p r o p e r t i e s o f water a r e assumed i n d e p e n d e n t o f t e m p e r a t u r e . 1 40 T h e r e f o r e , i t was d e c i d e d i n s t e a d t o assume c o n s t a n t h e a t e x c h a n g e r e f f e c t i v e n e s s . ( T h i s a g a i n i s i n agreement w i t h t h e o v e r a l l f i r s t - o r d e r l e v e l of d e t a i l s o u g h t f o r t h e s i m u l a t i o n model.) The h e a t e x c h a n g e r e f f e c t i v e n e s s was s e t t o a c o n s t a n t v a l u e of u n i t y by e q u a t i n g t h e o u t l e t t e m p e r a t u r e (TSDHW) t o th e s t o r a g e t a n k t e m p e r a t u r e a s c a l c u l a t e d a t t h e end of th e p r e v i o u s h o u r . 1 8 The s t a n d - a l o n e a c c u r a c y of t h i s s i m p l i f i c a t i o n c a n be a s s e s s e d by r e f e r r i n g t o t h e m o n t h l y a v e r a g e HXEF v a l u e s r e p o r t e d i n C h a p t e r 4 ( e x c l u d i n g t h o s e months e x p e r i e n c i n g n o n - p o s i t i v e h o u r l y HXEF v a l u e s ) . These v a l u e s were seen t o ran g e between 0.91 and 1.01 on a f l o w - w e i g h t e d b a s i s . A l t e r n a t i v e l y , an a v e r a g e e m p i r i c a l HXEF v a l u e c o u l d have been u s e d f o r h e a t e x c h a n g e r e f f e c t i v e n e s s . However, u s i n g s u c h a v a l u e would l i m i t t h e g e n e r a l a p p l i c a b i l i t y o f t h e model s i n c e e m p i r i c a l HXEF v a l u e s a r e not n o r m a l l y known. The p r e d i c t e d amount of h e a t e x t r a c t e d from t h e s t o r a g e t a n k and d e l i v e r e d t o t h e i n c o m i n g c o l d water ( s o l a r h o t water h e a t ) i s c a l c u l a t e d u s i n g t h e f o l l o w i n g s t e a d y s t a t e h e a t t r a n s f e r e q u a t i o n : QSDHW = ROWCP*FLOW(TSDHW - TM) (23) M e a s u r e d h o u r l y v a l u e s f o r b o t h FLOW and TM a r e e n t e r e d as i n p u t d a t a f o r e q u a t i o n 23 f o r e a c h hour o f t h e s i m u l a t i o n p e r i o d . T h i s d i f f e r s from WATSUN DHWA, w h i c h i s programmed t o o p e r a t e on a u s e r - e n t e r e d d i u r n a l h o t wa t e r c o n s u m p t i o n s c h e d u l e and a s e a s o n a l l y v a r y i n g c o l d water t e m p e r a t u r e c y c l e . 5. D o m e s t i c Hot Water Model WATSUN DHWA c a l c u l a t e s t h e t o t a l amount o f ( s o l a r and 141 a u x i l i a r y ) h e a t d e l i v e r e d t o t h e d o m e s t i c h o t wa t e r s u p p l y u s i n g t h e f o l l o w i n g s t e a d y s t a t e h e a t t r a n s f e r e q u a t i o n : QDHW = ROWCP*FLOW(TDHW - TM) (24) where TDHW i s s e t e q u a l t o a c o n s t a n t t e m p e r a t u r e v a l u e . S i n c e p r e d i c t i o n and measurement would a g r e e i f a c t u a l h o u r l y v a l u e s f o r TM, TDHW, and FLOW were us e d as i n p u t d a t a , t h i s e q u a t i o n becomes s u p e r f l u o u s i n t h e m o d i f i e d model. The amount of h e a t d e l i v e r e d by t h e a u x i l i a r y h o t water tank i s s i m p l y c a l c u l a t e d a s a r e s i d u a l i n WATSUN DHWA; i e . QAUXW = QDHW - QSDHW (25) P r e d i c t e d v a l u e s f o r t h i s t h e r m a l e n e r g y q u a n t i t y were a l s o n ot e v a l u a t e d i n t h e p r e s e n t s t u d y s i n c e t h e y p r o v i d e no a d d i t i o n a l i n f o r m a t i o n a b o u t t h e model's c a p a b i l i t e s . 6. S t o r a g e Tank E q u a t i o n The s t o r a g e tank e q u a t i o n r e p r e s e n t s t h e c o r e o f t h e s i m u l a t i o n m odel; i t a s s e m b l e s t h e t h r e e component models t o g e t h e r . The r e s u l t i s a s i n g l e a l g e b r a i c e q u a t i o n d e s c r i b i n g t h e e n e r g y b a l a n c e of t h e s t o r a g e t a n k : QSTOR = QCSS - QSDHW - QSENV (26) T h i s e q u a t i o n s t a t e s t h a t t h e change i n h e a t c o n t e n t o f t h e s t o r a g e t a n k i s e q u a l t o t h e d i f f e r e n c e between i t s e n e r g y i n p u t s and o u t p u t s ( as c a l c u l a t e d u s i n g t h e component m o d e l s ) . The s i m u l a t i o n model assumes t h a t t h e s t o r a g e t a n k i s f u l l y m i xed and i s o t h e r m a l a t a l l t i m e s . Hence t h e t e m p e r a t u r e change o f t h e s t o r a g e tank o v e r e a c h one hour t i m e s t e p c a n be c a l c u l a t e d u s i n g t h e f o l l o w i n g e q u a t i o n : ATS = QSTOR/CVS (27) C o r r e s p o n d i n g l y , t h e t e m p e r a t u r e o f t h e s t o r a g e t a n k a t t h e end 1 42 of a g i v e n hour i s c a l c u l a t e d as f o l l o w s : TS | = TS | + ATS (28) t 2 t1 where TS | = s t o r a g e t a n k t e m p e r a t u e c a l c u l a t e d a t end o f p r e v i o u s hour t i The s t o r a g e t a n k t e m p e r a t u r e i s i n i t i a l i z e d a t t h e s t a r t of t h e s i m u l a t i o n p e r i o d u s i n g an a c t u a l measured v a l u e ( T START). A f t e r t h i s i n i t i a l i z a t i o n , TS i s d e t e r m i n e d s o l e l y by t h e h o u r l y s i m u l a t i o n s e q u e n c e . S t a b i l i t y i n t h e r e s u l t i n g TS v a l u e s i s a s s u r e d by t h e m o d e l ' s a l g e b r a i c s o l u t i o n method and by t h e n e g a t i v e f e e d b a c k e f f e c t s d i s c u s s e d below, a. N e g a t i v e F e e d b a c k E f f e c t s U n d o u b t e d l y , i t w i l l not be p o s s i b l e f o r t h e s i m u l a t i o n model t o p r e c i s e l y t r a c k t h e r m a l c o n d i t i o n s w i t h i n t h e a c t u a l s t o r a g e t a n k b e c a u s e of t h e h o u r l y d i s c r e t i z a t i o n i n h e r e n t i n t h e m o d e l . F o r i n s t a n c e , a d e v i a t i o n of o n l y a f r a c t i o n of a d e g r e e i n t h e c o l l e c t o r - t o - t a n k t e m p e r a t u r e d i f f e r e n c e may a d v a n c e or d e l a y t h e s w i t c h i n g o f t h e ( s i m u l a t e d ) c i r c u l a t i o n pump by an h o u r . T h i s c a n t h e n c a u s e s i g n i f i c a n t s h o r t t e r m d e v i a t i o n between p r e d i c t i o n and measurement. F o r t u n a t e l y t h e s e d e v i a t i o n s a r e l a r g e l y s e l f - c o r r e c t i n g b e c a u s e o f n e g a t i v e f e e d b a c k e f f e c t s w h i c h e x i s t w i t h i n t h e s y s t e m , and w h i c h e n s u r e s t a b i l i t y i n t h e s i m u l a t i o n m o d e l . F o r example, w i t h h i g h s t o r a g e t a n k t e m p e r a t u r e s , c o l l e c t o r e f f i c i e n c y and s o l a r e n e r g y i n p u t t o s t o r a g e d e c r e a s e . As w e l l , t h e r e i s an i n c r e a s e i n t h e amount o f h e a t e x t r a c t e d and l o s t f r o m s t o r a g e . T h e s e e f f e c t s w i l l t e n d t o s u p p r e s s f u r t h e r i n c r e a s e s i n s t o r a g e t a n k t e m p e r a t u r e . C o r r e s p o n d i n g l y , w i t h low t a n k t e m p e r a t u r e s , c o l l e c t o r e f f i c i e n c y and s o l a r e n e r g y i n p u t 1 43 i n c r e a s e , a c c o m p a n i e d by a d e c r e a s e i n s t o r a g e h e a t o u t p u t . Hence i n t h i s s i t u a t i o n t h e f e e d b a c k e f f e c t s w i l l a c t t o s u p p r e s s f u r t h e r t e m p e r a t u r e d e c r e a s e s . F o r t h e model, t h e s e e f f e c t s mean t h a t even t h o u g h s i m u l a t e d and a c t u a l t h e r m a l c o n d i t i o n s w i t h i n t h e s y s t e m may d i v e r g e f o r a w h i l e , t h e r e i s a t e n d e n c y f o r them t o c o n v e r g e a g a i n . T h i s t e n d e n c y s h o u l d a c t t o d i m i n i s h l o n g t e r m d e v i a t i o n between model and measurement, t h e r e b y p e r m i t t i n g a c c u r a t e p r e d i c t i o n of t h e s y s t e m ' s m o n t h l y and s e a s o n a l t h e r m a l p e r f o r m a n c e . 7. Model I n p u t / O u t p u t The s i m u l a t i o n model r e q u i r e s two g e n e r a l t y p e s of i n p u t d a t a as l i s t e d i n T a b l e 5.2. I n p u t v a l u e s f o r t h e s y s t e m p a r a m e t e r s a r e e n t e r e d i n t o t h e model a t t h e s t a r t of t h e s i m u l a t i o n p e r i o d and r e m a i n c o n s t a n t t h r o u g h o u t . In c o n t r a s t , i n p u t v a l u e s f o r t h e s y s t e m v a r i a b l e s a r e r e a d i n by t h e model on an h o u r l y b a s i s i n a c c o r d a n c e w i t h i t s c a l c u l a t i o n s e q u e n c e . They form a l i n k between t h e s i m u l a t e d and a c t u a l s y s t e m s . As s u c h , t h e y c an be c o n s i d e r e d a s f o r c i n g f u n c t i o n s , d r i v i n g t h e s e t of m a t h e m a t i c a l e q u a t i o n s w h i c h d e s c r i b e s y s t e m o p e r a t i o n and b e h a v i o u r . The s i m u l a t i o n model c a l c u l a t e s t h r e e s y s t e m v a r i a b l e s o f d i r e c t i n t e r e s t - t h e s t o r a g e t a n k t e m p e r a t u r e ( T S ) , t h e amount of s o l a r h e a t d e l i v e r e d t o t h e i n c o m i n g c o l d w a t e r (QSDHW), and t h e number o f pump o p e r a t i n g h o u r s (PPHR). P r e d i c t e d v a l u e s f o r t h e s e t h r e e v a r i a b l e s a r e compared a g a i n s t a c t u a l s y s t e m measurements on an h o u r l y , d a i l y , and m o n t h l y b a s i s ( C h a p t e r 6 ) . As w e l l , t h e p r e d i c t e d QSDHW v a l u e s a r e summed o v e r a one y e a r s i m u l a t i o n p e r i o d , a l l o w i n g e s t i m a t i o n of an a n n u a l s o l a r 1 44 f r a c t i o n (SFRAC) f o r t h e s y s t e m . A d d i t i o n a l s y s t e m v a r i a b l e s c a l c u l a t e d by t h e model i n c l u d e t h e f o l l o w i n g : (1) TCP - c o l l e c t o r a b s o r b e r p l a t e t e m p e r a t u r e (2) TCI - c o l l e c t o r i n l e t t e m p e r a t u r e (3) TCO - c o l l e c t o r o u t l e t t e m p e r a t u r e (3) QCSS - s o l a r e n e r g y c o l l e c t e d and t r a n s f e r r e d t o s t o r a g e (4) QSENV - s t a n d b y h e a t l o s s f r o m t h e s t o r a g e t a n k (5) . QSTOR - change i n h e a t c o n t e n t o f t h e s t o r a g e t a n k However, t h e s e v a r i a b l e s were n o t measured i n t h e a c t u a l s y s t e m and t h e r e f o r e t h e i r p r e d i c t e d v a l u e s c a n n o t be compared o r v e r i f i e d i n t h e p r e s e n t s t u d y . A sample p r i n t o u t of h o u r l y i n p u t and o u t p u t v a l u e s f o r t h r e e d i f f e r e n t s i m u l a t i o n d a y s i s p r e s e n t e d i n A p p e n d i x F. The o u t p u t v a l u e s a r e i d e n t i f i e d by t h e i r v a r i a b l e names b e i n g u n d e r l i n e d i n t h e h e a d i n g s . A n e g a t i v e TCO v a l u e i n d i c a t e s t h a t no p r e d i c t e d s o l a r e n e r g y c o l l e c t i o n o c c u r r e d f o r t h a t hour ( i e . QCSS = 0). N e g a t i v e v a l u e s f o r t h e water s u p p l y l i n e t e m p e r a t u r e s (TM, TSDHW, and TDHW) a r e p r i n t e d when no h o t water was drawn d u r i n g a g i v e n h o u r , a s i n d i c a t e d by t h e i n p u t v a l u e o f FLOW. F i n a l l y , a p o s i t i v e TCI v a l u e o c c u r s whenever i n e q u a l i t y 18 i s s a t i s f i e d f o r t h e c u r r e n t h o u r , o r was s a t i s f i e d f o r a p r e v i o u s hour w i t h o u t i n t e r r u p t i o n . S i n c e i n e q u a l i t y 19 might n ot be c o n c u r r e n t l y s a t i s f i e d , t h e s i m u l a t e d c o l l e c t o r may n o t be o p e r a t i n g and t h e r e f o r e t h e c o r r e s p o n d i n g TCO v a l u e may be n e g a t i v e ( e g . h o u r s 14 & 19 on J u l i a n day 2 1 4 ) . 1 45 T a b l e 5.2 I n p u t D a t a R e q u i r e m e n t s f o r t h e S i m u l a t i o n M o d e l System P a r a m e t e r s AREAC F R ( t a ) e FRUL TDIF1 TDIF2 CMC UAS ROWCP VOLS TSTART System V a r i a b l e s HT TA TBSM TM FLOW A s s o c i a t e d Component Model C o l l e c t o r C o l l e c t o r C o l l e c t o r C o l l e c t o r C o l l e c t o r C o l l e c t o r S t a n d b y Heat L o s s Heat E x c h a n g e r / S t o r a g e Tank S t o r a g e Tank S t o r a g e Tank C o l l e c t o r C o l l e c t o r S t a n d b y Heat l o s s Heat E x c h a n g e r Heat E x c h a n g e r 146 F i g u r e 5.1 C o l l e c t o r Model F l o w c h a r t START I CONTINUE NO SOLAR ENERGY COLLECTED (QCSS=0) # 1 <-NO ? TCP - TCI =»-TDIFl (18) j YES NO ? TCO - TCI >TDIF2 (19) I YES COLLECTOR OPERATION INITIATED CONTINUE SOLAR ENERGY COLLECTED (QCSS>0) COLLECTOR OPERATION MAINTAINED YES COLLECTOR OPERATION CEASES ? TCO - TCI > TDIF2 (19) NO 147 CHAPTER 6 MODEL VALIDATION A. M o d e l V a l i d a t i o n i n t h e P r e s e n t S t u d y In t h e c o u r s e o f d e v e l o p i n g t h e s i m u l a t i o n model s e v e r a l a s s u m p t i o n s and a p p r o x i m a t i o n s were made i n o r d e r t o r e n d e r t h e c o m p l e x i t y of t h e r e a l s y s t e m t r a c t a b l e . T e s t i n g and e v a l u a t i o n of t h e s e s i m p l i f i c a t i o n s becomes n e c e s s a r y i n o r d e r t o a s c e r t a i n whether t h e model can p r o d u c e r e a l i s t i c and r e l i a b l e r e s u l t s . T h i s p r o c e d u r e i s commonly r e f e r r e d t o as model v a l i d a t i o n . In t h e p r e s e n t s t u d y , i t i n v o l v e s c o m p a r i n g model p r e d i c t i o n s a g a i n s t a c t u a l s y s t e m measurements. By p e r f o r m i n g t h i s c o m p a r i s o n one s u b s t a n t i a t e s o r d i s p r o v e s t h e m o d e l ' s a b i l i t y t o m a t h e m a t i c a l l y r e p l i c a t e t h e t r a n s f e r and s t o r a g e of h e a t w i t h i n t h e s y s t e m . As w e l l , one d e m o n s t r a t e s t h e model's c a p a b i l i t y t o a c c u r a t e l y p r e d i c t s y s t e m p e r f o r m a n c e . C o n f i d e n c e i n t h e model can t h e n be e s t a b l i s h e d o r r e j e c t e d . Hence model v a l i d a t i o n c o n s t i t u t e s a r e q u i s i t e p r o c e d u r e p r i o r t o a m odel's s u b s e q u e n t use as an a n a l y t i c a l o r p r e d i c t i v e t o o l . C o m p r e h e n s i v e and r i g o r o u s v a l i d a t i o n would i n c l u d e e v a l u a t i n g t h e p r e c i s i o n and a c c u r a c y o f t h e s i m u l a t i o n model o v e r t h e a p p l i c a b l e range o f p a r a m e t e r v a l u e s and o p e r a t i n g c o n d i t i o n s f o r w h i c h t h e s y s t e m was d e s i g n e d . However, s u c h an a n a l y s i s was beyond the s c o p e of t h e p r o j e c t o b j e c t i v e s The p r e s e n t s t u d y was r e s t r i c t e d t o an i n d i v i d u a l s y s t e m c h a r a c t e r i z e d by a g i v e n s e t of p h y s i c a l and t h e r m a l p a r a m e t e r s w h i c h , when s u b j e c t e d t o a u n i q u e c o m b i n a t i o n o f l o a d and m e t e o r o l o g i c a l c o n d i t i o n s , o p e r a t e d i n a s p e c i f i c 1 48 manner. I t i s q u i t e p o s s i b l e t h a t w h i l e t h e s i m u l a t i o n model may g i v e r e a s o n a b l e r e s u l t s f o r t h i s p a r t i c u l a r s y s t e m , i t s i n h e r e n t c h a r a c t e r i s t i c s may c a u s e i t t o r e a c t i m p r o p e r l y i f one o r more of t h e s y s t e m p a r a m e t e r s a r e s u b s t a n t i a l l y v a r i e d o r i f t h e o p e r a t i n g c o n d i t i o n s a r e s i g n i f i c a n t l y c h a n g e d . T h e r e f o r e , a c o n c l u s i v e s t a t e m e n t a b o u t t h e range of a p p l i c a b i l i t y o f t h e s i m u l a t i o n model c a n n o t be made. A c c o r d i n g l y , t h e a n a l y s i s p r e s e n t e d below c o u l d more a p p r o p r i a t e l y be termed model v e r i f i c a t i o n s i n c e i t f a i l s t o p r o v i d e v a l i d a t i o n of t h e model under t h e b r o a d e r c r i t e r i a . N e v e r t h e l e s s , i t r e p r e s e n t s an i m p o r t a n t p a r t of t h e v a l i d a t i o n p r o c e s s s i n c e i t i s a b l e t o i n d i c a t e whether t h e component a l g o r i t h m s have been p r o p e r l y i n c o r p o r a t e d i n t o t h e s i m u l a t i o n model and i t i s a b l e t o e l i c i t any g r o s s m o d e l l i n g e r r o r s . F u r t h e r m o r e , i t does q u a n t i f y t h e a b i l i t y of t h e s i m u l a t i o n model t o p r e d i c t t h e t h e r m a l p e r f o r m a n c e of t h e s y s t e m under i n v e s t i g a t i o n - one o f o n l y a l i m i t e d number of s y s t e m s m o n i t o r e d o v e r a s u f f i c i e n t p e r i o d of t i m e t o p e r m i t s u c h an e v a l u a t i o n . Thus i t forms a b a s i s f o r d e c i d i n g whether t o use t h e model t o p r e d i c t t h e t h e r m a l p e r f o r m a n c e o f o t h e r s y s t e m s h a v i n g s i m i l a r d e s i g n and o p e r a t i n g c o n d i t i o n s , and f o r a s s e s s i n g t h e i mpact of f u r t h e r m o d i f i c a t i o n s and improvements t o t h e m o d e l . B. E r r o r S t a t i s t i c s The s i m u l a t i o n model p r e s e n t e d i n t h i s s t u d y i s i n h e r e n t l y an i m p e r f e c t m a t h e m a t i c a l r e p r e s e n t a t i o n o f t h e a c t u a l s y s t e m ; t h e model g e n e r a t e d ' v a l u e s a r e c e r t a i n t o d e v i a t e f r o m t h e i r 1 49 measured c o u n t e r p a r t s . The e r r o r s t a t i s t i c s s e l e c t e d t o q u a n t i f y t h e m a g n i t u d e of t h e s e d e v i a t i o n s a r e t h e r o o t mean s q u a r e e r r o r (RMSE) and t h e mean b i a s e r r o r (MBE). B o t h a r e w i d e l y a c c e p t e d e r r o r s t a t i s t i c s (Won, 1981; W i l l m o t t , 1982), w h i c h , when u s e d t o g e t h e r , p r o v i d e a r e a s o n a b l y c o m p r e h e n s i v e e v a l u a t i o n of model p e r f o r m a n c e . The RMSE p r o v i d e s a measure of t h e i n d i v i d u a l d e v i a t i o n s between p r e d i c t e d and measured v a l u e s ; i t g i v e s an i n d i c a t i o n o f t h e p r e c i s i o n o f a mod e l . The f o r m u l a f o r c a l c u l a t i n g t h i s e r r o r s t a t i s t i c i s g i v e n by n 2 L ( Y i - X i ) i = 1 RMSE = SQRT[ ] (29) n where n i s t h e number o f v a l u e s i n t h e v e r i f i c a t i o n d a t a s e t , and Y i and X i a r e t h e ' i ' t h m o d e l l e d and measured v a l u e s r e s p e c t i v e l y . B e c a u s e of t h e s q u a r e d t e r m , p o s i t i v e and n e g a t i v e d e v i a t i o n s do n o t c a n c e l . M o r e o v e r , l a r g e d e v i a t i o n s t e n d t o a m p l i f y t h e RMSE. The MBE p r o v i d e s an i n d i c a t i o n o f s y s t e m a t i c e r r o r o r i n a c c u r a c y i n a model. A p o s i t i v e MBE v a l u e i n d i c a t e s a t e n d e n c y f o r t h e model t o o v e r - e s t i m a t e ; a n e g a t i v e v a l u e i n d i c a t e s a t e n d e n c y t o u n d e r - e s t i m a t e . T h i s e r r o r s t a t i s t i c i s e x p r e s s e d a s f o l l o w s : n E ( Y i - X i ) i = 1 MBE = (30) n 1 50 S i n c e p o s t i v e and n e g a t i v e d e v i a t i o n s a c t t o c a n c e l e a c h o t h e r , a z e r o MBE i n d i c a t e s as much n e g a t i v e d e v i a t i o n as p o s i t i v e o v e r t h e l o n g t e r m . T h i s s i t u a t i o n s i g n i f i e s an u n b i a s e d model, a l t h o u g h not n e c e s s a r i l y a p r e c i s e one. C. I n i t i a l S i m u l a t i o n R e s u l t s The s i m u l a t i o n p e r i o d s e l e c t e d t o i n i t i a l l y t e s t t h e model was t h e two month i n t e r v a l A u g u s t t h r o u g h September 1982. T h i s p e r i o d c o v e r e d a wide r a n g e of l o a d and m e t e o r o l o g i c a l c o n d i t i o n s f o r t h e s y s t e m . In a d d i t i o n , m e asured h o u r l y basement a i r t e m p e r a t u r e s were a v a i l a b l e f o r t h i s p e r i o d . S t o r a g e t a n k t e m p e r a t u r e p l o t s and e r r o r s t a t i s t i c s were j u d g e d t o be t h e most i n f o r m a t i v e t o o l s w i t h w h i c h t o a s s e s s t h e s i m u l a t i o n model d u r i n g t h e two month t e s t p e r i o d . T h i s r e l a t e s t o t h e f a c t t h a t t h e model e s s e n t i a l l y c o n s t i t u t e s an e n e r g y b a l a n c e on t h e s t o r a g e t a n k . Thus i t was of i n t e r e s t t o a s c e r t a i n how c l o s e l y t h e model c o u l d t r a c k t h e r m a l c o n d i t i o n s w i t h i n t h e a c t u a l s t o r a g e t a n k . T h i s would u l t i m a t e l y d e t e r m i n e i t ' s a b i l i t y t o p r e d i c t t h e t h e r m a l p e r f o r m a n c e o f t h e s y s t e m . 1. S t o r a g e Tank T e m p e r a t u r e Time S e r i e s F i g u r e 6.1 i s a t i m e s e r i e s p l o t o f t h e p r e d i c t e d and m e a s u r e d h o u r l y s t o r a g e t a n k t e m p e r a t u r e s . B o t h t h e t a n k b o t t o m and m i d - h e i g h t t e m p e r a t u r e measurements a r e i n c l u d e d . In c o n t r a s t , o n l y one t e m p e r a t u r e i s shown f o r t h e s i m u l a t i o n model s i n c e i t assumes t h a t t h e s t o r a g e t a n k i s f u l l y mixed and i s o t h e r m a l a t a l l t i m e s . Such a c o n d i t i o n o n l y e x i s t s w i t h i n t h e a c t u a l s t o r a g e t a n k d u r i n g p e r i o d s of pump o p e r a t i o n , when 151 f o r c e d c o n v e c t i o n c a u s e s t h e w ater c i r c u l a t i n g t h r o u g h t h e t a n k t o become t h o r o u g h l y m i x e d . T h i s c o n d i t i o n i s d e p i c t e d i n t h e t i m e s e r i e s p l o t s when t h e t e m p e r a t u r e i s s t e a d i l y r i s i n g (due t o s o l a r e n e r g y i n p u t ) and t h e t a n k b o t t o m and m i d - h e i g h t c u r v e s o v e r l a p . W h i l e i t i s o b v i o u s t h a t t h e p r e d i c t e d t e m p e r a t u r e c u r v e n e i t h e r f u l l y c o i n c i d e s w i t h nor p a r a l l e l s e i t h e r of t h e two measured t e m p e r a t u r e c u r v e s , i t c a n be s e e n t h a t t h e s i m u l a t i o n model i s a b l e t o c o n s i s t e n t l y t r a c k t h e r m a l c o n d i t i o n s w i t h i n t h e a c t u a l s t o r a g e t a n k . T h i s i s i n d i c a t e d by t h e a b s e n c e of any l a r g e t i m e s h i f t s , and by t h e p r e d i c t e d t e m p e r a t u r e c u r v e g e n e r a l l y s t a y i n g w i t h i n t h e bounds of t h e measured c u r v e s . T h i s t h e n v e r i f i e s t h a t t h e component a l g o r i t h m s do i n t e r a c t p r o p e r l y and t h a t t h e s i m u l a t i o n model i s f r e e of any g r o s s e r r o r s . F u r t h e r v i s u a l i n s p e c t i o n o f t h e s t o r a g e t a n k t e m p e r a t u r e p l o t - a l l o w s s e v e r a l m i n o r d i f f e r e n c e s between t h e p r e d i c t e d and measured t e m p e r a t u r e c u r v e s t o be n o t e d . (1) The h o u r l y d i s c r e t i z a t i o n i n h e r e n t i n t h e model d i d c a u s e t e m p o r a l d e v i a t i o n s t o o c c u r w i t h r e s p e c t t o t h e c o l l e c t o r o p e r a t i n g p e r i o d s . ( S m a l l t i m e l a g s i n commencement of s o l a r e n e r g y c o l l e c t i o n have been i d e n t i f i e d by upward p o i n t i n g a r r o w s . In a d d i t i o n , t h e p r e d i c t e d and measured d a i l y pump o p e r a t i n g h o u r s have been l i s t e d a c r o s s t h e t o p o f e a c h p l o t . ) T h e s e d e v i a t i o n s a p p e a r t o have been somewhat s e l f - c a n c e l l i n g t h o u g h , s i n c e o n l y a s m a l l c u m u l a t i v e d e p a r t u r e e r r o r (-0.9%) was r e c o r d e d f o r t h e t o t a l number of c o l l e c t o r o p e r a t i n g h o u r s o v e r t h e two month t e s t p e r i o d . 1 9 However, i t s h o u l d be n o t e d t h a t s y s t e m a t i c r e - d i s t r i b u t i o n o f t h e c o l l e c t o r o p e r a t i n g 152 p e r i o d s can s i g n i f i c a n t l y a f f e c t t h e m o d e l ' s a b i l t i t y t o p r e d i c t t h e amount o f s o l a r e n e r g y i n p u t t o t h e s t o r a g e t a n k . T h u s , a c c u r a c y i n s y s t e m s t a t u s d o e s n o t n e c e s s a r i l y mean a c c u r a c y i n s y s t e m p e r f o r m a n c e . (2) A n o t h e r c o n s e q u e n c e of t h e model's d i s c r e t i z a t i o n i s i t s i n a b i l i t y t o c o n s i s t e n t l y r e p l i c a t e b r i e f o r f l u c t u a t i n g p e r i o d s of low i n t e n s t i y s o l a r e n e r g y c o l l e c t i o n . ( These t i m e s have been marked by downward p o i n t i n g a r r o w s . ) T h i s r e c u r r e n c e does not s e r i o u s l y e r o d e t h e model's p r e d i c t i v e c a p a b i l i t y t h o u g h , s i n c e t h e s e p e r i o d s a r e n o r m a l l y a s s o c i a t e d w i t h low s o l a r e n e r g y i n p u t t o s t o r a g e and t h e model w i l l t e n d t o compensate i f any marked d i v e r g e n c e of t a n k t e m p e r a t u r e o c c u r s . (3) D u r i n g t h e s e c o n d h a l f of A u g u s t 1982 t h e r e was a p e r i o d o f p r e d o m i n a n t l y sunny weather w h i c h was c h a r a c t e r i z e d by a d a i l y p a t t e r n of i n t e n s e s o l a r e n e r g y c o l l e c t i o n . However, t h e s i m u l a t i o n model c o n s i s t e n t l y u n d e r - e s t i m a t e d t h e d u r a t i o n and amount of e n e r g y c o l l e c t i o n . The r e a s o n f o r t h i s b i a s c a n be i n f e r r e d t o e x i s t w i t h i n t h e c o l l e c t o r m o d e l . I f o t h e r model components were a t f a u l t t h e n t h e p r e d i c t e d s t o r a g e t a n k t e m p e r a t u r e would have t e n d e d t o f a l l below t h e measured tan k b o t t o m t e m p e r a t u r e d u r i n g p e r i o d s when t h e c o l l e c t o r was n o t o p e r a t i n g ( i e . l a t e a f t e r n o o n and e v e n i n g h o u r s when h o t water was b e i n g drawn, and n i g h t t i m e h o u r s when o n l y s t a n d b y h e a t l o s s was o c c u r r i n g ) . O v e r - p r e d i c t i o n of t h e amount o f s o l a r e n e r g y c o l l e c t e d was a l s o i n e v i d e n c e , e s p e c i a l l y d u r i n g t h e l a t t e r h a l f of September 1982 when a more v a r i a b l e w e a t h e r r e g i m e p r e v a i l e d . Thus, a v i s u a l e x a m i n a t i o n o f t h e s t o r a g e t a n k t e m p e r a t u r e p l o t s c a n n o t e s t a b l i s h an o v e r a l l b i a s i n 153 t h e c o l l e c t o r m odel. As p o i n t e d out above, t h e p r e d i c t e d t e m p e r a t u r e c u r v e i s n o t p e r f e c t l y c o n g r u e n t w i t h e i t h e r t h e t a n k b o t t o m o r m i d - h e i g h t t e m p e r a t u r e c u r v e s . O n l y d u r i n g p e r i o d s of s o l a r e n e r g y c o l l e c t i o n does i t u s u a l l y c o i n c i d e w i t h or c l o s e l y p a r a l l e l t h e two measured c u r v e s . P e r i o d i c a l l y i t w i l l r i s e a d e g r e e or more above them - a l t h o u g h o n l y f o r a few h o u r s . D u r i n g p e r i o d s when h o t water i s b e i n g drawn and no s o l a r e n e r g y i s b e i n g c o l l e c t e d i t t e n d s t o o c c u p y an i n t e r m e d i a t e p o s i t i o n . O c c a s i o n a l l y i t d r o p s below t h e t a n k bottom c u r v e ; however, s u c h d i v e r g e n c e s a r e g e n e r a l l y r e s t r i c t e d t o 1 - 5 d e g r e e s C and n e v e r p e r s i s t f o r more than 24 h o u r s . T h i s l a s t s i t u a t i o n m a i n l y o c c u r s d u r i n g p e r i o d s of low s o l a r e n e r g y i n p u t . 2. S t o r a g e Tank T e m p e r a t u r e E r r o r S t a t i s t i c s In o r d e r t o compute t h e h o u r l y s t o r a g e t a n k t e m p e r a t u r e e r r o r s t a t i s t i c s , a s e t of measurement v a l u e s has t o be a c c e p t e d as b e i n g r e p r e s e n t a t i v e o f t h e r m a l c o n d i t i o n s w i t h i n t h e a c t u a l s t o r a g e t a n k . One c o u l d a r g u e t h a t t h e t a n k m i d - h e i g h t t e m p e r a t u r e v a l u e s a r e s u f f i c i e n t l y r e p r e s e n t a t i v e and t h e r e f o r e t h e y s h o u l d be u s e d i n t h e s t a t i s t i c a l c o m p a r i s o n a g a i n s t t h e p r e d i c t e d v a l u e s . A l t e r n a t i v e l y , one c o u l d i n t e r p o l a t e a v e r a g e v a l u e s u s i n g a w e i g h t e d f u n c t i o n o f t h e t a n k b o t t o m and m i d - h e i g h t t e m p e r a t u r e s . However, b o t h t h e s e a p p r o a c h e s were deemed u n a c c e p t a b l e . R e c o g n i z i n g t h a t n e i t h e r p o i n t measurements nor w e i g h t e d a v e r a g e v a l u e s were l i k e l y t o be h i g h l y r e p r e s e n t a t i v e , i t was d e c i d e d i n s t e a d t o q u a n t i f y t h e model d e v i a t i o n s u s i n g o n l y t h o s e t e m p e r a t u r e s m easured 1 54 when t h e s t o r a g e t a n k was i s o t h e r m a l . T h i s t h e n would c o r r e s p o n d t o t h e f u l l y mixed a s s u m p t i o n o f t h e model, and would a l l o w e v a l u a t i o n o f t h e model on i t s own t e r m s , t h e r e b y d e - e m p h a s i z i n g i t s s h o r t t e r m i m p r e c i s i o n s w h i l e a t t h e same t i m e u n c o v e r i n g any i n h e r e n t b i a s e s . The s t o r a g e tank was d e f i n e d t o be i s o t h e r m a l when t h e t e m p e r a t u r e d i f f e r e n c e between t h e b o t t o m and m i d - h e i g h t l e v e l s was e q u a l t o or l e s s t h a n t h e a s s o c i a t e d measurement e r r o r ( A p p e n d i x C, S e c t i o n B ) . The t o t a l number of h o u r s d u r i n g t h e two month t e s t p e r i o d was 1464; a p p l y i n g t h e i s o t h e r m a l r e s t r i c t i o n r e d u c e d t h e number of h o u r s i n t h e s t a t i s t i c a l sample t o 345, s l i g h t l y l e s s t h a n 1/4 of t h e t o t a l . By c o m p a r i s o n , t h e r e were 302 p r e d i c t e d and 304.7 measured h o u r s of c o l l e c t o r o p e r a t i o n . T a b l e 6.1 below l i s t s t h e r e l e v a n t e r r o r s t a t i s t i c s . T a b l e 6.1 S t o r a g e Tank T e m p e r a t u r e E r r o r S t a t i s t i c s S i m u l a t i o n P e r i o d : A u g u s t - September, 1982 A l l v a l u e s a r e i n d e g r e e s C e l c i u s . RMSE MBE M i d Bottom M i d Bottom 3.49 3.25 -2.49 -2.16 The n e g a t i v e MBE v a l u e s i n d i c a t e t h a t t h e model t e n d s t o s y s t e m a t i c a l l y u n d e r - e s t i m a t e t h e t e m p e r a t u r e of t h e s t o r a g e t a n k - a t l e a s t d u r i n g t h o s e h o u r s when t h e t a n k i s i s o t h e r m a l . 2 0 However, n o t a l l o f t h e d e v i a t i o n between t h e p r e d i c t e d and measured t e m p e r a t u r e s i s s y s t e m a t i c . T h i s i s i n d i c a t e d by t h e RMSE v a l u e s , w h i c h i n r e l a t i v e t e r m s a r e 40% - 50% l a r g e r t h a n t h e MBE v a l u e s . The s i g n i f i c a n t number o f h o u r s when t h e p r e d i c t e d t a n k t e m p e r a t u r e c u r v e r i s e s above t h e c o r r e s p o n d i n g 1 55 measured curves also attests to the presence of non-systematic error in the model. Nevertheless, systematic error dominates the model's temperature deviations. 3. Solar Hot Water Heat Existence of a negative bias in the model's storage tank temperature predictions suggests that the predicted values of solar hot water heat (QSDHW) w i l l also tend to be under-estimated. This can be deduced by r e c a l l i n g that the simulation model equates the temperature of the solar heated water to that of the storage tank as calculated at the end of the previous hour. A systematic error in the l a t t e r temperature w i l l therefore d i r e c t l y affect the heat exchanger model and p o t e n t i a l l y cause a corresponding error in QSDHW. This error can be further speculated upon by v i s u a l l y comparing the divergence between the predicted and measured (mid-height) tank temperature curves during periods of s i g n i f i c a n t hot water draw ( i e . those hours during which the temperature curves experience sharp declines). The majority of these periods show a 0 to 10 degree C temperature deviation, with the measured curve being consistently higher. The associated average temperature gradient between the storage tank and the incoming cold water i s in the order of 25 degrees C. Hence the average difference between the predicted and measured tank-to-water temperature gradient is approximately (negative) 20%. As outlined in the previous chapter, the model assumes a constant heat exchanger effectiveness equal to unity. In comparison, the average flow-weighted HXEF value for the two month test period (based on the tank mid-height temperature) i s 0.93 - a 156 ( p o s i t i v e ) 7% d i f f e r e n c e . Thus one c o u l d r o u g h l y p r e d i c t a 10% t o 15% s y s t e m a t i c u n d e r - e s t i m a t i o n i n t h e model ' s QSDHW v a l u e s . F i g u r e 6.2 p r e s e n t s b ar g r a p h s w h i c h i n d i c a t e t h e d e v i a t i o n between t h e p r e d i c t e d and measured d a i l y v a l u e s o f s o l a r h ot water h e a t . As e x p e c t e d , t h e r e i s a d e f i n i t e n e g a t i v e b i a s i n th e m o d e l ' s QSDHW v a l u e s . T h i s i s v e r i f i e d by t h e e r r o r s t a t i s t i c s l i s t e d i n T a b l e 6.2 below. (Note - The s t a t i s t i c s a r e computed u s i n g o n l y n o n - z e r o QSDHW v a l u e s . ) T a b l e 6.2 S o l a r Hot Water Heat E r r o r S t a t i s t i c s S i m u l a t i o n P e r i o d : A u g u s t - September, 1982 N MEAN RMSE MBE I n t e g r a t i o n Sample Meas. P r e d . Abs. R e l . Abs. R e l . P e r i o d s i z e (MJ) (MJ) (MJ) % (MJ) % H o u r l y 954 2.117 1 .872 0.557 26.3 -0.245 - 11.6 D a i l y 61 33.116 29.283 4.602 13.9 -3.833 - 11.6 F o r t u n a t e l y , i n t e r a c t i o n among t h e component a l g o r i t h m s i n t h e s i m u l a t i o n model p r e v e n t s t h e d e v i a t i o n i n t h e p r e d i c t e d QSDHW v a l u e s from becoming e x c e s s i v e ; i e . u n d e r - e s t i m a t i o n of s o l a r h e a t e x t r a c t e d from s t o r a g e w i l l t e n d t o s u p p r e s s s u b s e q u e n t d e c r e a s e s i n s t o r a g e t a n k t e m p e r a t u r e , w h i c h i n c o m b i n a t i o n w i t h g r e a t e r s t o r a g e i n p u t , w i l l a c t t o m i n i m i z e f u r t h e r n e g a t i v e d e v i a t i o n s i n QSDHW. T h i s e x e m p l i f i e s one of th e n e g a t i v e f e e d b a c k e f f e c t s w h i c h e x i s t w i t h i n b o t h t h e a c t u a l s y s t e m and t h e s i m u l a t i o n model ( C h a p t e r 5 ) , and whi c h e f f e c t i v e l y l i m i t l o n g t e r m d e v i a t i o n between p r e d i c t i o n and measurement. 1 57 D. Model B i a s 1. S o u r c e s o f E r r o r The n e x t q u e s t i o n t o ask i s why does t h e d e t e c t e d i n a c c u r a c y i n t h e model p r e d i c t i o n s e x i s t , and can c o r r e c t i v e s t e p s be t a k e n t o e l i m i n a t e or r e d u c e i t . U n f o r t u n a t e l y , t h e g r a p h i c a l and s t a t i s t i c a l t o o l s u s e d t o e v a l u a t e t h e s i m u l a t i o n model f a i l t o i d e n t i f y o r i s o l a t e t h e c a u s e ( s ) of i t s b i a s - a p r o b l e m not i m m e d i a t e l y r e s o l v a b l e due t o l a c k o f s u f f i c i e n t m o n i t o r i n g d a t a . In t h e model, t h e t h e r m a l p e r f o r m a n c e of a l l components i s i n t e r c o n n e c t e d s u c h t h a t an e r r o r i n s i m u l a t i n g one component c a u s e s d i s a g r e e m e n t between p r e d i c t i o n and measurement f o r a l l components. E i t h e r s t a n d - a l o n e component t e s t s a r e r e q u i r e d o r a d d i t i o n a l s y s t e m v a r i a b l e s must be m o n i t o r e d i n o r d e r t o p e r m i t a more e x t e n s i v e e v a l u a t i o n of t h e model and i d e n t i f y t h e c a u s e ( s ) o f i t s b i a s . In p a r t i c u l a r , t h e water f l o w and i n l e t / o u t l e t t e m p e r a t u r e s i n t h e c o l l e c t o r l o o p s h o u l d be measured, a l l o w i n g d i r e c t c o m p a r i s o n of t h e e n e r g y i n p u t t e r m f o r t h e s t o r a g e t a n k . However, an i n i t i a l a t t e m p t a t r e s o l v i n g t h e b i a s can be made i f one f i r s t r e c o g n i z e s two g e n e r a l s o u r c e s o f e r r o r i n t h e m o d e l . (1) E x t r i n s i c e r r o r i n t r o d u c e d i n t o t h e model's i n p u t d a t a by th e u s e r - T h i s c o m p r i s e s e r r o r i n t h e i n p u t v a l u e s f o r t h e s y s t e m p a r a m e t e r s and v a r i a b l e s . E r r o r s i n t h e s y s t e m p a r a m e t e r s can o r i g i n a t e i n b o t h t h e m a n u f a c t u r e r ' s s p e c i f i c a t i o n s and t h e i n d e p e n d e n t l y p e r f o r m e d c o l l e c t o r e f f i c i e n c y t e s t s , w h i l e e r r o r s i n t h e s y s t e m v a r i a b l e s a r e c a u s e d by measurement e r r o r ( A p p e n d i x C ) . In a d d i t i o n , e r r o r s r e s u l t i n g f r o m c o n v e r s i o n and i n t e r p r e t a t i o n of t h e 1 58 i n p u t d a t a a r e p o s s i b l e . E r r o r s w i t h i n t h i s c a t e g o r y a r e c o l l e c t i v e l y r e f e r r e d t o as u s e r - e f f e c t e r r o r s . (2) I n t r i n s i c e r r o r r e s u l t i n g from t h e i n h e r e n t i m p e r f e c t i o n s o f t h e m o d e l . 2. U s e r - e f f e c t E r r o r s Immediate c o n c e r n r e s t s w i t h u s e r - e f f e c t e r r o r s . In p r e v i o u s v a l i d a t i o n s t u d i e s of s i m u l a t i o n m o d e ls t h e y have been f o u n d t o be v e r y s i g n i f i c a n t ( H e d s t r o m , 1981). O f t e n t h e y can c a u s e more u n c e r t a i n t y i n t h e p r e d i c t e d r e s u l t s t h an t h e m o d e l ' s m a t h e m a t i c a l f o r m u l a t i o n . Hence t h e y c a n c o n c e a l a m o del's ' t r u e ' p r e d i c t i v e c a p a b i l i t i y . They a r e a l s o a l m o s t u n a v o i d a b l e i n p r a c t i c e , g i v e n t h e l a r g e amount of d a t a t h a t must be g a t h e r e d and t h e n i n p u t by t h e u s e r i n t o model. T h i s p r o m p t e d one team of r e s e a r c h e r s t o s t a t e t h a t "much more e m p h a s i s s h o u l d be put i n t o t h e g e n e r a t i o n o f i m p r o v e d i n p u t schemes f o r t h e models r a t h e r t h a n t o t h e c o r r e c t m a t h e m a t i c a l f o r m u l a t i o n o f a c e r t a i n phenomenon . . . F o r example, i f you s t a r t q u e s t i o n i n g t h e c o l l e c t o r f l o w r a t e and t h e h e a t e x c h a n g e r e f f i c i e n c y and m o d i f y t h e s e p a r a m e t e r s , t h e model p r e d i c t i o n s w i l l v a r y d r a s t i c a l l y " ( J 0 r g e n s e n e t a l . , 1982). They s u b s e q u e n t l y c o n c l u d e d t h a t "a s y s t e m p r o v i d i n g d a t a f o r v a l i d a t i o n p u r p o s e s has t o be measured and m o n i t o r e d t o s u c h a d e g r e e t h a t ( i n t h e i d e a l s i t u a t i o n ) t h e r e i s no doubt a t a l l as t o what t h e s y s t e m p a r a m e t e r s a r e " . T hus, commencing t h e p r e s e n t model v a l i d a t i o n w i t h an i n i t i a l two month t e s t p e r i o d was p r i m a r i l y done i n o r d e r t o i d e n t i f y any o b v i o u s u s e r - e f f e c t e r r o r s p r i o r t o s i m u l a t i n g l o n g e r p e r i o d s of s y s t e m o p e r a t i o n . 159 E. S e n s i t i v i t y A n a l y s i s I t was d e c i d e d t h a t t h e most p r o d u c t i v e method of u n c o v e r i n g p o t e n t i a l u s e r - e f f e c t e r r o r s was t o s y s t e m a t i c a l l y v a r y t h e i n p u t v a l u e of e a c h s y s t e m p a r a m e t e r and v a r i a b l e w h i l e h o l d i n g a l l o t h e r s u nchanged. The i n p u t v a l u e s were o n l y v a r i e d i n t h e d i r e c t i o n w h i c h t e n d e d t o r e d u c e t h e model's s t o r a g e t a n k t e m p e r a t u r e d e v i a t i o n . M o r e o v e r , a l l v a l u e s were c o n f i n e d w i t h i n r e a s o n a b l e l i m i t s . The s u b s e q u e n t c h a n g e s i n t h e model p r e d i c t i o n s were examined by c o m p u t i n g and g r a p h i n g t h e e r r o r s t a t i s t i c s f o r s t o r a g e t a n k t e m p e r a t u r e ( m i d - h e i g h t ) and c o l l e c t o r o p e r a t i n g h o u r s . Thus, t h i s a n a l y s i s i n d i c a t e s t h e s e n s i t i v i t y of t h e model t o v a r i a t i o n s i n t h e i n p u t d a t a . I t a l s o s e r v e s t o i d e n t i f y t h o s e s y s t e m p a r a m e t e r s and v a r i a b l e s w h i c h must be a c c u r a t e l y d e t e r m i n e d i n o r d e r t o e n s u r e t h a t u s e r - e f f e c t e r r o r s do not d o m i n a t e t h e model's u n c e r t a i n t y - s p e c i a l a t t e n t i o n w i l l be p a i d t o t h e i r i n p u t v a l u e s . 1 . System P a r a m e t e r s (1) TDIF1 - The model was t o t a l l y i n s e n s i t i v e t o a l l c h a n g e s i n t h e d i f f e r e n t i a l c o n t r o l l e r t u r n 'on' s e t - p o i n t w h i c h would t e n d t o i n c r e a s e t h e t e m p e r a t u r e o f t h e s t o r a g e t a n k ; v a r y i n g TDIF1 from 10 t o 0 d e g r e e s C had no e f f e c t on model p r e d i c t i o n s . T h i s means t h a t l o w e r i n g t h e c o n t r o l l e r 'on' s e t -p o i n t does n o t a l t e r t h e number o r d i s t r i b u t i o n o f h o u r s t h a t t h e s i m u l a t e d c o l l e c t o r o p e r a t e s , and t h e r e f o r e i t d o e s not i n c r e a s e t h e amount of s o l a r e n e r g y c o l l e c t e d nor t h e a v e r a g e s t o r a g e t a n k t e m p e r a t u r e . More s p e c i f i c a l l y , i t i n d i c a t e s t h a t whenever t h e s i m u l a t e d c o l l e c t o r - t o - t a n k t e m p e r a t u r e d i f f e r e n c e 160 e x c e e d s t h e minimum a l l o w a b l e v a l u e t o m a i n t a i n c o l l e c t i o n , t h e r e i s a l w a y s s u f f i c i e n t s o l a r e n e r g y i n c i d e n t on t h e c o l l e c t o r f o r i t t o t u r n on. C o n v e r s e l y , t h e r e c a n be s u f f i c i e n t s o l a r e n e r g y a v a i l a b l e f o r t h e c o l l e c t o r t o t u r n on, y e t not enough f o r c o l l e c t i o n t o be m a i n t a i n e d . Thus, i t i s t h e d i f f e r e n t i a l c o n t r o l l e r t u r n ' o f f ' s e t - p o i n t , TDIF2, w h i c h e f f e c t i v e l y c o n t r o l s c o l l e c t o r o p e r a t i o n . T h i s s i t u a t i o n i s v e r i f i e d by e x a m i n i n g t h e h o u r l y s i m u l a t i o n p r i n t o u t f o r J u l i a n day 214 l i s t e d i n A p p e n d i x F. I t s u g g e s t s t h a t t h e r e a r e t i m e s d u r i n g a c t u a l s y s t e m o p e r a t i o n when t h e c i r c u l a t i o n pump t u r n s on and t h e n s h o r t l y a f t e r w a r d s t u r n s o f f due t o f a i l u r e o f t h e c i r c u l a t i n g w a ter t o be s u f f i c i e n t l y h e a t e d b e f o r e r e a c h i n g t h e c o n t r o l l e r ' s t e m p e r a t u r e s e n s o r i n t h e c o l l e c t o r o u t l e t . T h i s of c o u r s e w i l l happen more f r e q u e n t l y d u r i n g p e r i o d s of f l u c t u a t i n g s o l a r i r r a d i a n c e a s o p p o s e d t o p e r i o d s o f s t e a d y r a d i a t i v e i n p u t w h i c h t h e model assumes. Such o c c u r r e n c e s have been r e p e a t e d l y o b s e r v e d o n - s i t e . I t must be e m p h a s i z e d t h a t t h e c o l l e c t o r - t o - t a n k t e m p e r a t u r e d i f f e r e n c e measured by t h e d i f f e r e n t i a l c o n t r o l l e r d oes n o t i d e n t i c a l l y c o r r e s p o n d w i t h t h e t e m p e r a t u r e d i f f e r e n c e r e p r e s e n t e d i n t h e m o d e l . The model c a l c u l a t e s an e q u i l i b r i u m a b s o r b e r p l a t e t e m p e r a t u r e under n o - f l o w c o n d i t i o n s ( T C P ) , and t h e n compares t h i s t e m p e r a t u r e w i t h t h e i s o t h e r m a l s t o r a g e t a n k t e m p e r a t u r e t o d e t e r m i n e whether c o l l e c t o r o p e r a t i o n s h o u l d be i n i t i a t e d . In t h e a c t u a l s y s t e m , t h e c o l l e c t o r t e m p e r a t u r e i s measured i n t h e o u t l e t m a n i f o l d . T h i s t e m p e r a t u r e - w h i c h w i l l t e n d t o be s l i g h t l y c o o l e r t h a n TCP - i s t h e n compared a g a i n s t a t e m p e r a t u r e measured i n t h e e n t r a n c e t o t h e c o l l e c t o r i n l e t 161 p i p e n e a r t h e b o t t o m o f t h e s t o r a g e t a n k . In b o t h c a s e s i f t h e t e m p e r a t u r e d i f f e r e n c e e x c e e d s T D I F 1 , t h e c o l l e c t o r pump t u r n s on and s o l a r e n e r g y c o l l e c t i o n commences. The i n s e n s i t i v i t y of t h e model t o r e d u c t i o n s i n TDIF1 t h e r e f o r e i n d i c a t e s t h a t t h e r e p r e s e n t a t i v e n e s s of t h e m o d e l l e d c o l l e c t o r - t o - t a n k t e m p e r a t u r e d i f f e r e n c e i s not c r u c i a l ; i t a l s o p e r m i t s t h e u s e r t o be l e s s c o n c e r n e d a b o u t s e c u r i n g an a c c u r a t e v a l u e f o r T D I F 1 . However, i f t h e v a l u e of TDIF1 was s e t h i g h e r s u c h t h a t i t d i d a f f e c t t h e number and d i s t r i b u t i o n o f h o u r s t h a t t h e s i m u l a t e d c o l l e c t o r o p e r a t e d , t h e n a c c u r a t e s p e c i f i c a t i o n of TDIF1 would be i m p o r t a n t and improvement i n m o d e l l i n g t h e a c t u a l c o l l e c t o r - t o - t a n k t e m p e r a t u r e d i f f e r e n c e would be i n o r d e r . (2) TDIF2 ( F i g u r e 6.3) - U n l i k e T D I F 1 , t h e model d i d r e s p o n d t o c h a n g e s i n t h e d i f f e r e n t i a l c o n t r o l l e r t u r n ' o f f ' s e t p o i n t . D e c r e a s i n g TDIF2 from i t s s p e c i f i e d v a l u e of 1.0 d e g r e e C down t o a l i m i t i n g v a l u e o f z e r o r e d u c e d t h e MBE v a l u e by 0.5°C. The r e s u l t a n t s m a l l i n c r e a s e i n t h e a v e r a g e t e m p e r a t u r e of t h e s t o r a g e t a n k was a c c o m p a n i e d by a d r a m a t i c r i s e i n t h e number o f c o l l e c t o r o p e r a t i n g h o u r s - o v e r 19% - e x h i b i t e d on t h e s e n s i t i v i t y p l o t by t h e i n c r e a s e i n t h e ( c u m u l a t i v e ) pump hour d e p a r t u r e e r r o r . B a s i c a l l y t h i s r e p r e s e n t s a m a r g i n a l i n c r e a s e i n s t o r a g e h e a t i n p u t t h r o u g h t h e a d d i t i o n of many h o u r s o f low i n t e n s i t y s o l a r e n e r g y c o l l e c t i o n . Even l o w e r i n g TDIF2 by o n l y 0.25 d e g r e e C c a u s e d t h e number o f c o l l e c t o r o p e r a t i n g h o u r s t o i n c r e a s e by o v e r 7%. T h i s outcome s u g g e s t s t h a t t h e t r u e v a l u e of TDIF2 i s f a i r l y c l o s e t o t h a t s p e c i f i e d , and t h e r e f o r e t h e u s e r - e f f e c t e r r o r a s s o c i a t e d w i t h t h i s 162 p a r a m e t e r i s l i k e l y t o be s m a l l . I t a l s o i n d i c a t e s t h a t t h e u s e r s h o u l d be c a r e f u l i n a s c e r t a i n i n g a c o r r e c t v a l u e f o r TDIF2 s i n c e o n l y a s m a l l e r r o r c an l e a d t o c o n s i d e r a b l e i n a c c u r a c y i n p r e d i c t i n g c o l l e c t o r o p e r a t i o n . The m o d e l ' s c o l l e c t o r - t o - t a n k t e m p e r a t u r e d i f f e r e n c e u s e d i n c o n j u n c t i o n w i t h TDIF2 i s i n c l o s e r agreement w i t h t h e a c t u a l s y s t e m t h a n was t h e c a s e f o r T D I F 1 . The model's c o l l e c t o r o u t l e t t e m p e r a t u r e now d i r e c t l y c o r r e s p o n d s w i t h t h e t e m p e r a t u r e measured i n t h e c o l l e c t o r o u t l e t m a n i f o l d ; t h e model's c o l l e c t o r i n l e t t e m p e r a t u r e m a i n t a i n s i t s c o r r e s p o n d e n c e w i t h t h e t e m p e r a t u r e m easured n e a r t h e b o t t o m o f t h e s t o r a g e t a n k ( w h i c h i s s e t e q u a l t o t h e i s o t h e r m a l s t o r a g e tank t e m p e r a t u r e ) . T h i s c l o s e r m a t c h i n g of t h e t e m p e r a t u r e d i f f e r e n c e r e i n f o r c e s t h e need t o a s c e r t a i n a c o r r e c t i n p u t v a l u e f o r TDIF2.. O t h e r w i s e , u s e r - e f f e c t e r r o r w i l l g o v e r n t h e a c c u r a c y o f t h e c o l l e c t o r m o d e l . (3) AREAC ( F i g u r e 6.4) - As e x p e c t e d , i n c r e a s i n g t h e c o l l e c t o r a r e a c a u s e d t h e amount o f s o l a r e n e r g y c o l l e c t e d t o i n c r e a s e , and a l o n g w i t h i t , t h e a v e r a g e s t o r a g e t a n k t e m p e r a t u r e . T h i s i s e v i d e n c e d by t h e 0.4 d e g r e e C d e c r e a s e i n t h e MBE v a l u e when t h e c o l l e c t o r a r e a i s i n c r e a s e d by 2.0%. At t h e same t i m e t h e number o f c o l l e c t o r o p e r a t i n g h o u r s s t a y e d r e l a t i v e l y c o n s t a n t . T h i s i s a l o g i c a l r e s u l t , s i n c e w i t h o u t a c o r r e s p o n d i n g i n c r e a s e i n s t o r a g e volume, t h e r i s e i n h e a t c o n t e n t o f t h e s t o r a g e t a n k w i l l t e n d t o s u p p r e s s any a d d i t i o n a l h o u r s of c o l l e c t o r o p e r a t i o n . C o n s e q u e n t l y , s m a l l i n c r e a s e s i n c o l l e c t o r a r e a s i m p l y mean c o l l e c t i n g s l i g h t l y more e n e r g y d u r i n g e a c h hour o f pump o p e r a t i o n . 1 63 Measurement of t h e c o l l e c t o r a r e a i s a s i m p l e and a c c u r a t e p r o c e d u r e ; o n - s i t e d e t e r m i n a t i o n matched t h e m a n u f a c t u r e r ' s s p e c i f i c a t i o n t o w i t h i n 0.08%. T h i s f a c t s h o u l d be s u f f i c i e n t t o r u l e o ut any u s e r - e f f e c t e r r o r i n t h i s p a r a m e t e r . C a u t i o n i s s t i l l r e q u i r e d t h o u g h i f t h e u s e r i s summing t h e a r e a o f s e v e r a l i n d i v i d u a l p a n e l s or i s c o n v e r t i n g u n i t s , s i n c e m e a s u r a b l e d e v i a t i o n s c an r e s u l t when t h e e r r o r i n AREAC i s o n l y a few p e r c e n t . (4) CMC ( F i g u r e 6.5) - D e c r e a s i n g t h e c o l l e c t o r f l u i d c a p a c i t a n c e by as much as 20% c a u s e d o n l y a v e r y s m a l l r e d u c t i o n (0.25 d e g r e e C) i n t h e MBE v a l u e . A d j u s t i n g CMC downward w i l l a l l o w t h e water c i r c u l a t i n g t h r o u g h t h e c o l l e c t o r l o o p t o h e a t up t o a h i g h e r t e m p e r a t u r e s i n c e i t s r e s i d e n c y t i m e i n t h e p a n e l s w i l l be i n c r e a s e d . 2 1 Accompanying t h e h i g h e r c o l l e c t o r o u t l e t t e m p e r a t u r e w i l l be l o n g e r p e r i o d s o f c o l l e c t o r o p e r a t i o n , due t o t h e p r o p o r t i o n a t e l y g r e a t e r number of h o u r s when t h e c o l l e c t o r - t o - t a n k t e m p e r a t u r e d i f f e r e n c e e x c e e d s TDIF2. T h i s i s v e r i f i e d on t h e s e n s i t i v i t y p l o t by t h e 6.25% i n c r e a s e i n t h e number of c o l l e c t o r o p e r a t i n g h o u r s . C o u n t e r a c t i n g t h e e f f e c t of h i g h e r c o l l e c t o r o u t l e t t e m p e r a t u r e i s t h e f a c t t h a t by d e c r e a s i n g CMC, t h e r a t e a t w h i c h t h e c i r c u l a t i n g w a t e r i s a b l e t o t r a n s f e r h e a t t o s t o r a g e i s r e d u c e d . The n e t r e s u l t t h e n i s a v e r y s m a l l i n c r e a s e i n a v e r a g e t a n k t e m p e r a t u r e . A c c u r a c y i n t h e s p e c i f i e d v a l u e of CMC i s s u b j e c t t o t h e p r o p e r s e t t i n g o f a c o n t r o l o r i f i c e w h i c h l i m i t s t h e c i r c u l a t i o n f l o w r a t e t o t h e d e s i g n v a l u e . W h i l e o n - s i t e d e t e r m i n a t i o n o f CMC was n o t p o s s i b l e , t h e s e n s i t i v i t y p l o t 1 64 shows t h a t a 10% e r r o r i n t h e s p e c i f i e d v a l u e i s c e r t a i n l y t o l e r a b l e s i n c e i t has no s i g n i f i c a n t i n f l u e n c e on model p r e d i c t i o n s . Hence t h e u s e r - e f f e c t e r r o r a s s o c i a t e d w i t h t h i s p a r a m e t e r c a n be c o n s i d e r e d r e l a t i v e l y m i n o r . (5) VOLS ( F i g u r e 6.6) - S i n c e i t was i m p o s s i b l e t o p o s i t i v e l y d e duce i n w h i c h d i r e c t i o n t o v a r y t h e s t o r a g e volume i n o r d e r t o r e d u c e t h e model's s t o r a g e tank t e m p e r a t u r e d e v i a t i o n , t h e v a l u e f o r t h i s p a r a m e t e r was b o t h i n c r e a s e d and d e c r e a s e d . One c a n r e a s o n t h a t i n c r e a s i n g t h e s t o r a g e volume w i l l l e a d t o lower t a n k t e m p e r a t u r e s s i n c e t h e r e w i l l be g r e a t e r t h e r m a l i n e r t i a t o i n h i b i t t e m p e r a t u r e c h a n g e s . However, l o w e r t a n k t e m p e r a t u r e s w i l l i n c r e a s e c o l l e c t o r e f f i c i e n c y and t h e r e f o r e i n c r e a s e s u b s e q u e n t s t o r a g e i n p u t v i a t h e n e g a t i v e f e e d b a c k e f f e c t s d i s c u s s e d e a r l i e r . In c o n t r a s t , d e c r e a s i n g t h e s t o r a g e volume w i l l i n i t i a l l y l e a d t o h i g h e r t a n k t e m p e r a t u r e s . A g a i n t h i s s e t s i n m o t i o n n e g a t i v e f e e d b a c k e f f e c t s : h i g h e r tank t e m p e r a t u r e s w i l l d e c r e a s e c o l l e c t o r e f f i c i e n c y w h i c h i n t u r n w i l l d e c r e a s e s t o r a g e i n p u t and t e n d t o l o w e r t a n k t e m p e r a t u r e s . T h u s , i n b o t h c a s e s t h e e v e n t u a l outcome i s d i f f i c u l t t o p r e d i c t w i t h c e r t a i n t y . The s e n s i t i v i t y r e s u l t s were needed i n o r d e r t o v e r i f y t h a t t h e l a t t e r c a s e does i n d e e d i n c r e a s e t h e s t o r a g e t a n k t e m p e r a t u r e on a v e r a g e , w h i l e t h e f o r m e r c a s e r e d u c e s i t . They show t h a t a d e c r e a s e i n s t o r a g e volume of 40 l i t r e s r e d u c e s t h e MBE v a l u e by a p p r o x i m a t e l y 0.6 d e g r e e C, w h i l e an i n c r e a s e i n s t o r a g e volume of an e q u i v a l e n t amount i n c r e a s e s t h e MBE by 0.5 d e g r e e C. Thus t h e r e s u l t s i n d i c a t e t h a t t h e model i s o n l y s l i g h t l y s e n s i t i v e t o s m a l l v a r i a t i o n s i n VOLS, s u g g e s t i n g t h a t t h e u s e r need o n l y employ 165 r e a s o n a b l e c a r e when m e a s u r i n g t h e volume of water i n t h e s t o r a g e t a n k . The s e n s i t i v i t y r e s u l t s a l s o i l l u s t r a t e two a d d i t i o n a l p o i n t s . F i r s t l y , i n n e i t h e r c a s e does t h e number o f c o l l e c t o r o p e r a t i n g h o u r s s u b s t a n t i a l l y c h a n g e . T h e r e f o r e , t h e s m a l l v a r i a t i o n s i n a v e r a g e t a n k t e m p e r a t u r e r e s u l t from c h a n g e s i n e n e r g y i n p u t / o u t p u t f o r t h e s t o r a g e t a n k d u r i n g a l l h o u r s o f s y s t e m o p e r a t i o n , and not from an o v e r a l l i n c r e a s e or d e c r e a s e i n c o l l e c t o r o p e r a t i o n . S e c o n d l y , t h e minimum RMSE v a l u e o c c u r s a t a s t o r a g e volume j u s t s l i g h t l y g r e a t e r t h a n t h a t u s e d i n t h e c o n t r o l s i m u l a t i o n r u n . (RMSE i n c r e a s e s s l i g h t l y a s t h e s t o r a g e volume i s d e c r e a s e d ; i t a l s o shows a m a r g i n a l r i s e when VOLS i s i n c r e a s e d t o w a r d s t o r a g e t a n k c a p a c i t y . ) The volume of water i n t h e s t o r a g e t a n k was measured p r i o r t o and s h o r t l y a f t e r t h e two month t e s t p e r i o d . I t was e q u a l t o 417 ± 2 l i t r e s on b o t h o c c a s i o n s . C o n t r a r y t o t h i s e v a l u a t i o n , t h e a v e r a g e m o n i t o r i n g p e r i o d volume o f 410 l i t r e s was i n a d v e r t e n t l y u s e d i n t h e c o n t r o l r u n . Thus, a d e m o n s t r a b l e s o u r c e of u s e r - e f f e c t e r r o r was i n t r o d u c e d i n t o t h e model. The f a c t t h a t t h e RMSE s t a t i s t i c c o n f o r m e d w i t h e x p e c t a t i o n s adds some c o n f i d e n c e t o t h e method o f a n a l y s i s . (6) F R ( t a ) e ( F i g u r e 6.7) - I n c r e a s i n g t h e c o l l e c t o r z e r o - p o i n t e f f i c i e n c y p a r a m e t e r from 0.725 t o 0.825 l e a d t o a v e r y l a r g e r e d u c t i o n i n t h e MBE v a l u e - i t i n f a c t became p o s i t i v e above an ( i n t e r p o l a t e d ) F R ( t a ) e v a l u e o f 0.79. T h i s i n d i c a t e s t h a t t h e model i s e x t r e m e l y s e n s t i v e t o t h i s p a r a m e t e r . Hence t h e u s e r s h o u l d pay p a r t i c u l a r a t t e n t i o n t o o b t a i n i n g an a c c u r a t e v a l u e f o r F R ( t a ) e . 1 66 W h i l e t h e c o l l e c t o r e f f i e n c y t e s t s were p e r f o r m e d on a SOL 100 c o l l e c t o r i d e n t i c a l t o t h e ones b e i n g u s e d i n t h e s y s t e m , t h e y i n v o l v e d o n l y a s i n g l e p a n e l and not an a r r a y of t h r e e . M o r e o v e r , t h e r e i s l a c k of c e r t a i n t y t h a t t h e t e s t s were p e r f o r m e d u s i n g p r e c i s e l y t h e same c i r c u l a t i o n f l o w r a t e a s o c c u r s i n t h e a c t u a l s y s t e m . ( F o r b o t h c a s e s t h e f l o w r a t e was r e p o r t e d l y s e t t o t h e m a n u f a c t u r e r ' s d e s i g n v a l u e . ) F u r t h e r m o r e , t h e f l o w o f w ater t h r o u g h t h e c o l l e c t o r a r r a y i n t h e s y s t e m may not be as u n i f o r m as t h e f l o w t h r o u g h th e s i n g l e p a n e l t e s t e d ; any r e g i o n s w i t h i n t h e c o l l e c t o r a r r a y w h i c h r e c e i v e r e d u c e d water c i r c u l a t i o n w i l l c o l l e c t p r o p o r t i o n a l l y l e s s s o l a r e n e r g y . C o n s e q u e n t l y , t h e v a l u e r e p o r t e d f o r F R ( t a ) e may n o t a c c u r a t e l y r e p r e s e n t t h e z e r o - p o i n t e f f i c i e n c y o f t h e s o l a r c o l l e c t o r u s e d i n t h e s y s t e m . To a s s e s s t h e l i k e l i h o o d t h a t i n a c c u r a c y i n t h e v a l u e o f F R ( t a ) e c a u s e s t h e model b i a s one has t o s c r u t i n i z e t h e s e n s i t i v i t y p l o t w i t h c a r e . I t c a n be seen t h a t t h e i n c r e a s e i n t h e t e m p e r a t u r e o f t h e s t o r a g e t a n k i s l a r g e l y a t t r i b u t a b l e t o g r e a t e r s o l a r e n e r g y i n p u t d u r i n g e a c h hour of c o l l e c t o r o p e r a t i o n . T h i s i s i n d i c a t e d by t h e f a c t t h a t t h e number o f c o l l e c t o r o p e r a t i n g h o u r s i n c r e a s e s by o n l y 2.6% when F R ( t a ) e i s i n c r e a s e d by 13.8% ( s u c h t h a t the'MBE = 0.0 d e g r e e C ) . Thus s y s t e m a t i c e r r o r i n t h e p r e d i c t e d s t o r a g e t a n k t e m p e r a t u r e c o u l d be e l i m i n a t e d by i n c r e a s i n g t h e v a l u e o f F R ( t a ) e w i t h o u t c a u s i n g any s i g n i f i c a n t d e v i a t i o n i n c o l l e c t o r o p e r a t i o n . I n d e e d , i n c r e a s i n g F R ( t a ) e by 0.05 r e d u c e s t h e s t o r a g e t a n k t e m p e r a t u r e b i a s t o l e s s t h a n 0.65 d e g r e e C, m i n i m i z e s s h o r t t e r m t e m p e r a t u r e d e v i a t i o n s , and o n l y i n c r e a s e s t h e number o f 1 67 c o l l e c t o r o p e r a t i n g h o u r s by 1.3%. However, t h e r e i s no s u p p o r t i n g e v i d e n c e t o p e r m i t one t o i n c r e a s e t h e v a l u e o f F R ( t a ) e . (No o n - s i t e c o l l e c t o r e f f i c e n c y t e s t s were p o s s i b l e . ) Hence any upward a d j u s t m e n t i n F R ( t a ) e would s t r i c t l y be an a t t e m p t t o f o r c e model a g r e e m e n t . T h e r e f o r e , i t can o n l y be r e - i t e r a t e d t h a t t h i s p a r a m e t e r i s a p o t e n t i a l s o u r c e o f s i g n i f i c a n t u s e r - e f f e c t e r r o r . (7) FRUL ( F i g u r e 6.8) - The r e p r e s e n t a t i v e n e s s of t h e v a l u e r e p o r t e d f o r FRUL may a l s o be a f f e c t e d by t h e c o l l e c t o r e f f i c i e n c y t e s t s b e i n g p e r f o r m e d on a s i n g l e p a n e l as o p p o s e d t o an a r r a y o f t h r e e , and by t h e p o s s i b i l i t y t h a t t h e f l o w r a t e u s e d i n t h e t e s t s may have d i f f e r e d f r o m t h a t a c t u a l l y o c c u r r i n g i n t h e s y s t e m . M o r e o v e r , t h e r e i s u s u a l l y a c e r t a i n amount o f s c a t t e r a b o u t t h e c o l l e c t o r e f f i c i e n c y c u r v e i t s e l f . Hence t h e r e i s p o t e n t i a l i n a c c u r a c y a s s o c i a t e d w i t h t h e v a l u e of t h e s l o p e e f f i c i e n c y p a r a m e t e r u s e d i n t h e model. A 20% i n a c c u r a c y was deemed t o be t h e maximum p o s s i b l e e r r o r . D e c r e a s i n g FRUL by t h i s amount c a u s e d a m o d e r a t e r e d u c t i o n i n t h e MBE v a l u e ; t h e m o d e l ' s s t o r a g e tank t e m p e r a t u r e b i a s was r e d u c e d t o l e s s t h a n -0.75 d e g r e e C. A t t h e same t i m e t h e number o f c o l l e c t o r o p e r a t i n g h o u r s i n c r e a s e d by o v e r 6.5%. T hus, v a r i a t i o n s i n t h e s l o p e e f f i c i e n c y p a r a m e t e r c a u s e g r e a t e r c h a n g e s i n c o l l e c t o r o p e r a t i o n t h a n do e f f e c t i v e l y e q u i v a l e n t v a r i a t i o n s i n t h e z e r o - p o i n t e f f i c i e n c y p a r a m e t e r ; i e . when F R ( t a ) e was v a r i e d so t h a t t h e MBE v a l u e d e c r e a s e d t o -0.75 d e g r e e C, t h e number of c o l l e c t o r o p e r a t i n g h o u r s i n c r e a s e d by l e s s t h a n 1.3%. The r e a s o n f o r t h i s d i f f e r e n c e i s t h a t i n c r e a s e s i n F R ( t a ) e d i r e c t l y i n c r e a s e t h e amount o f s o l a r 1 68 r a d i a t i o n a b s o r b e d by t h e c o l l e c t o r ( a l t h o u g h t h e e f f e c t s a r e p a r t i a l l y o f f s e t b e c a u s e h i g h e r c o l l e c t o r o p e r a t i n g t e m p e r a t u r e s mean g r e a t e r c o l l e c t o r h e a t l o s s e s ) . In c o n t r a s t , r e d u c i n g FRUL means d e c r e a s i n g t h e r a t e a t w h i c h h e a t i s l o s t f r o m t h e c o l l e c t o r - no e x t r a s o l a r r a d i a t i o n i s i n i t i a l l y a b s o r b e d . T h e r e f o r e i t s e f f e c t s a r e p r o p o r t i o n a l l y s m a l l e r , and t h e number of c o l l e c t o r o p e r a t i n g h o u r s has t o be i n c r e a s e d c o n s i d e r a b l y b e f o r e c h a n g e s i n FRUL w i l l d e l i v e r a s much a d d i t i o n a l u s e f u l h e a t t o s t o r a g e as c h a n g e s i n F R ( t a ) e . C o n s e q u e n t l y , by i n c r e a s i n g t h e v a l u e of FRUL i n o r d e r t o e l i m i n a t e t h e s y s t e m a t i c e r r o r i n s t o r a g e t a n k t e m p e r a t u r e , one s i g n i f i c a n t l y r e d u c e s t h e agreement i n c o l l e c t o r o p e r a t i n g h o u r s . T h i s f a c t s u g g e s t s t h a t u s e r - e f f e c t e r r o r i n FRUL i s p r o b a b l y l i m i t e d . The s e n s i t i v i t y p l o t i n d i c a t e s t h a t t h e e r r o r must be l e s s t h a n 4% i f c l o s e agreement i n c u m u l a t i v e c o l l e c t o r o p e r a t i o n i s t o be m a i n t a i n e d o v e r t h e two month t e s t p e r i o d . A g a i n t h e r e i s no s u p p o r t i n g e v i d e n c e t o i n d i c a t e t h a t t h e ' t r u e ' v a l u e o f FRUL i s l e s s t h a n t h a t r e p o r t e d f o r t h e c o l l e c t o r e f f i c i e n c y t e s t s . T h e r e f o r e , one c a n o n l y s t a t e t h a t t h e model i s m o d e r a t e l y s e n s i t i v e t o v a r i a t i o n s i n t h i s p a r a m e t e r and t h a t t h e u s e r s h o u l d e x e r c i s e c a u t i o n when o b t a i n i n g or i n t e r p r e t i n g an FRUL v a l u e . (8) UAS ( F i g u r e 6.9) - D e c r e a s i n g t h e s t o r a g e t a n k h e a t l o s s c o e f f i c i e n t f r o m i t s e m p i r i c a l l y d e t e r m i n e d v a l u e o f 16.0 kJ/hr°C down t o a p h y s i c a l l y l i m i t i n g v a l u e o f z e r o c a u s e d a l a r g e r e d u c t i o n i n t h e MBE v a l u e - i t i n f a c t became p o s i t i v e below an ( i n t e r p o l a t e d ) UAS v a l u e o f 3.3 k J / h r ° C . Hence t h e model i s e x t r e m e l y s e n s i t i v e t o t h i s p a r a m e t e r , and t h e u s e r i s 1 69 w e l l a d v i s e d t o c a r e f u l l y d e s i g n any e x p e r i m e n t u n d e r t a k e n i n o r d e r t o a s c e r t a i n i t s v a l u e . UAS i s t h e p a r a m e t e r i n t h e model w h i c h a c t s t o r e g u l a t e t h e amount of s t a n d b y h e a t l o s t from t h e s t o r a g e tank t o t h e s u r r o u n d i n g basement a i r . By d e c r e a s i n g t h e i n p u t v a l u e o f UAS t h e s i m u l a t e d s t o r a g e tank l o s e s l e s s h e a t and t h e r e f o r e e x p e r i e n c e s a h i g h e r a v e r a g e t e m p e r a t u r e . However, n e g a t i v e f e e d b a c k e f f e c t s f o l l o w . The h i g h e r s t o r a g e t a n k t e m p e r a t u r e means t h a t t h e c o l l e c t o r i n l e t t e m p e r a t u r e i s i n c r e a s e d . T h i s c o n s e q u e n t l y d e c r e a s e s c o l l e c t o r e f f i c i e n c y and s t o r a g e i n p u t , w h i c h i n c o m b i n a t i o n w i t h i n c r e a s e d s t o r a g e o u t p u t , a c t t o s u p p r e s s t h e t h e t e n d e n c y t o w a r d h i g h e r t a n k t e m p e r a t u r e s . D e s p i t e t h e s e n e g a t i v e f e e d b a c k e f f e c t s , t h e n e t r e s u l t of d e c r e a s i n g t h e s t o r a g e t a n k h e a t l o s s c o e f f i c i e n t i s a s h a r p i n c r e a s e i n a v e r a g e t a n k t e m p e r a t u r e . The main e f f e c t o f t h e n e g a t i v e f e e d b a c k s i s t o p r o p o r t i o n a t e l y d e c r e a s e t h e number of c o l l e c t o r o p e r a t i n g h o u r s . They i n f a c t d e c r e a s e d by o v e r 6.5% when UAS was r e d u c e d t o z e r o . T h i s was c a u s e d by t h e s u b s e q u e n t l y s m a l l e r c o l l e c t o r - t o - t a n k t e m p e r a t u r e d i f f e r e n c e ; fewer h o u r s now o c c u r r e d when t h i s t e m p e r a t u r e d i f f e r e n c e e x c e e d e d TDIF2. The t h e o r e t i c a l UAS v a l u e o f 4.58 kJ/hr°C i s a l s o shown on t h e s e n s i t i v i t y p l o t . I t c o r r e s p o n d s t o an MBE v a l u e o f -0.28 d e g r e e C and an RMSE v a l u e o f 2.83 d e g r e e s C. T h e s e d e v i a t i o n s a r e s u b s t a n t i a l l y s m a l l e r t h a n t h e d e v i a t i o n s a s s o c i a t e d w i t h t h e e m p i r i c a l h e a t l o s s c o e f f i c i e n t . (The l a t t e r v a l u e s a r e -2.49 and 3.49 d e g r e e s C r e s p e c t i v e l y . ) In f a c t t h e l o n g t e r m d e v i a t i o n i n s t o r a g e t a n k t e m p e r a t u r e c a n 1 70 be a l m o s t e n t i r e l y e l i m i n a t e d , and t h e s h o r t t e r m d e v i a t i o n s p a r t i a l l y r e d u c e d , i f one were t o a c c e p t t h e t h e o r e t i c a l UAS v a l u e f o r use i n t h e model. The c o n s e q u e n c e o f s u c h a d e c i s i o n t h o u g h , would be t o l e s s e n t h e agreement between t h e number o f p r e d i c t e d and measured c o l l e c t o r o p e r a t i n g h o u r s ; i e . t h e c u m u l a t i v e d e p a r t u r e e r r o r would d e c r e a s e t o -5.15%. As d i s c u s s e d e a r l i e r , t h e d i f f e r e n c e between t h e e m p i r i c a l and t h e o r e t i c a l UAS v a l u e s i s q u i t e p r o n o u n c e d . C o n s i d e r a b l e measurement e r r o r i s known t o e x i s t i n t h e e m p i r i c a l v a l u e , s u g g e s t i n g t h a t i n a c c u r a c y i n t h e s t o r a g e t a n k h e a t l o s s c o e f f i c i e n t i s v e r y p r o b a b l e . U n f o r t u n a t e l y t h e s y s t e m was not s u f f i c i e n t l y m o n i t o r e d t o p e r m i t e v a l u a t i o n of s t a n d b y h e a t l o s s as a r e s i d u a l - a method w h i c h would have y i e l d e d a more a c c u r a t e UAS v a l u e . T h e r e f o r e , one must r e l y upon i n d e p e n d e n t t e s t r e s u l t s and t h e documented f i n d i n g s of o t h e r s a s s u p p o r t i n g e v i d e n c e t h a t t h e e m p i r i c a l v a l u e i s i n d e e d t h e more a c c u r a t e o f t h e two UAS v a l u e s a v a i l a b l e . An added a t t e m p t a t q u i c k l y c h e c k i n g t h e a c c u r a c y of t h e e m p i r i c a l v a l u e i s t o r e - e x a m i n e t h e s t o r a g e t a n k t e m p e r a t u r e p l o t ( F i g u r e 6.1) as f o l l o w s . D u r i n g t h e n i g h t t i m e s t r a t i f i c a t i o n p e r i o d s when no h o t w a t e r i s b e i n g drawn, s t a n d b y h e a t l o s s becomes t h e o n l y a c t i v e e n e r g y i n p u t / o u t p u t t e r m f o r t h e s t o r a g e t a n k . The s l o p e of t h e p r e d i c t e d t e m p e r a t u r e c u r v e s h o u l d t h e n p a r a l l e l t h e two m easured c u r v e s i f t h e UAS v a l u e i s a c c u r a t e . S u r v e y i n g t h e s e t i m e p e r i o d s one s e e s t h a t t h e p r e d i c t e d c u r v e t e n d s t o be s l i g h t l y s t e e p e r t h a n t h e t a n k b o t t o m c u r v e , y e t g e n e r a l l y no s t e e p e r t h a n t h e m i d - h e i g h t c u r v e . B a s i c a l l y t h i s v i s u a l c o m p a r i s o n s e r v e s o n l y t o r e - e m p h a s i z e t h e u n c e r t a i n t y 171 a s s o c i a t e d w i t h d e t e r m i n i n g t h e e m p i r i c a l UAS v a l u e . To c o n c l u d e t h e n , u s e r - e f f e c t e r r o r i n t h e s t o r a g e tank h e a t l o s s c o e f f i c i e n t i s v e r y p r o b a b l e and i t s p o t e n t i a l e f f e c t q u i t e s i g n i f i c a n t . 2. System V a r i a b l e s (1) TBSM ( F i g u r e 6.10) - S y s t e m a t i c a l l y i n c r e a s i n g t h e i n p u t v a l u e s of basement a i r t e m p e r a t u r e by as much as 2.5 d e g r e e s C c a u s e d a s m a l l r e d u c t i o n (0.35 d e g r e e C) i n t h e MBE v a l u e . By i n c r e a s i n g TBSM t h e t e m p e r a t u r e g r a d i e n t between t h e water i n t h e s t o r a g e t a n k and t h e s u r r o u n d i n g basement a i r d e c r e a s e s . The s i m u l a t i o n model u s e s t h i s t e m p e r a t u r e g r a d i e n t i n c o n j u n c t i o n w i t h t h e s t o r a g e t a n k h e a t l o s s c o e f f i c i e n t t o c a l c u l a t e t h e m a g n i t u d e of t h e s t a n d b y h e a t l o s s . C o n s e q u e n t l y , i f t h i s t e m p e r a t u r e g r a d i e n t i s d e c r e a s e d , t h e s t a n d b y h e a t l o s s w i l l be r e d u c e d and a h i g h e r t e m p e r a t u r e w i l l be m a i n t a i n e d w i t h i n t h e s t o r a g e t a n k . A g a i n n e g a t i v e f e e d b a c k e f f e c t s e n s u e . The h i g h e r h e a t c o n t e n t of t h e s t o r a g e t a n k w i l l t e n d t o d e c r e a s e c o l l e c t o r e f f i c i e n c y and s o l a r e n e r g y i n p u t , as w e l l as i n c r e a s e s t o r a g e h e a t o u t p u t . A l s o , t h e number of c o l l e c t o r o p e r a t i n g h o u r s w i l l t e n d t o d e c r e a s e due t o t h e s m a l l e r c o l l e c t o r - t o - t a n k t e m p e r a t u r e d i f f e r e n c e , w h i c h w i l l n o t e x c e e d TDIF2 q u i t e a s o f t e n . T h i s i s e v i d e n c e d i n t h e s e n s i t i v i t y p l o t by a 0.65% d e c r e a s e i n c u m u l a t i v e c o l l e c t o r o p e r a t i o n . Hence t h e n e g a t i v e f e e d b a c k e f f e c t s p a r t i a l l y c o u n t e r a c t t h e r e d u c t i o n of s t a n d b y h e a t l o s s . The n e t r e s u l t f o r t h e p r e s e n t c a s e i s o n l y a s l i g h t i n c r e a s e i n a v e r a g e t a n k t e m p e r a t u r e , i n d i c a t i n g t h a t t h e model i s q u i t e i n s e n s i t i v e t o s m a l l v a r i a t i o n s i n TBSM. T h i s r e s u l t w i l l v a r y d u r i n g o t h e r 172 t i m e s of t h e y e a r , d e p e n d i n g on t h e m a g n i t u d e of t h e t a n k - t o - a i r t e m p e r a t u r e g r a d i e n t ; i e . i n w i n t e r , t h e s i m u l a t i o n model may be more s e n s i t i v e t o t h i s v a r i a b l e due t o t h e l a r g e r r e l a t i v e e f f e c t of TBSM on s t a n d b y h e a t l o s s and t h e g r e a t e r r e l a t i v e i m p o r t a n c e of QSENV i n t h e s t o r a g e t a n k e n e r g y b a l a n c e . W h i l e p r e c i s i o n of t h e basement a i r t e m p e r a t u r e s e n s o r i s ±0.1°C ( T a b l e 3 . 1 ) , s p a t i a l s a m p l i n g e r r o r i s somewhat l a r g e r . T h i s a r i s e s f r o m t h e f a c t t h a t by s a m p l i n g TBSM a t a s i n g l e p o i n t i t s s p a t i a l v a r i a b i l i t y i s n o t c a p t u r e d . Hence t h e v a l u e s m easured f o r TBSM may d i f f e r f r o m ' t r u e ' s p a t i a l l y i n t e g r a t e d v a l u e s . However, t h e s p a t i a l v a r i a b i l i t y i n TBSM i s not g r e a t - one t r i a l e v a l u a t i o n y i e l d e d a range o f 2 d e g r e e s C. At t h e same t i m e , t h e s e n s i t i v i t y p l o t p o i n t s o u t t h a t a s y s t e m a t i c e r r o r o f up t o 2.5 d e g r e e s C i n t h e i n p u t v a l u e s of TBSM i s c e r t a i n l y t o l e r a b l e s i n c e i t has no s i g n i f i c a n t i n f l u e n c e on t h e model's p r e d i c t i o n s . Thus, any u s e r - e f f e c t e r r o r i n t r o d u c e d i n t o t h e model t h r o u g h t h i s v a r i a b l e c a n be c o n s i d e r e d s m a l l . The i n i t i a l two month t e s t p e r i o d p r o v i d e d an o p p o r t u n i t y t o a s s e s s t h e model's s e n s i t i v i t y t o t h e s u r r o g a t e TBSM v a r i a b l e - TMNF5. As s t a t e d e a r l i e r , TMNF5 i s t h e 5-day r u n n i n g mean o f t h e c o l d water t e m p e r a t u r e under n o - f l o w c o n d i t i o n s - a v a r i a b l e w h i c h p r o v i d e d t h e b e s t e s t i m a t e o f basement a i r t e m p e r a t u r e . S u b s t i t u t i n g t h e d a i l y TMNF5 v a l u e s i n p l a c e o f t h e h o u r l y TBSM v a l u e s had v i r t u a l l y no impact on t h e m o del's s h o r t or l o n g t e r m t e m p e r a t u r e d e v i a t i o n s . B o t h t h e RMSE and MBE v a l u e s i n c r e a s e d by o n l y 0.02 d e g r e e C, t o 3.51 and -2.51 d e g r e e s C r e s p e c t i v e l y , w h i l e t h e t o t a l number 1 73 of c o l l e c t o r o p e r a t i n g h o u r s d e c l i n e d by 1. T h i s i n d i c a t e s t h a t t h e r e i s n e g l i g i b l e u s e r - e f f e c t e r r o r a s s o c i a t e d w i t h u s i n g TMNF5 as a s u r r o g a t e v a r i a b l e f o r TBSM ( a t l e a s t o v e r t h e i n i t i a l two month t e s t p e r i i o d ) . I t a l s o s u g g e s t s t h a t t h e basement a i r t e m p e r a t u r e can be i n p u t i n t o t h e model on a d a i l y as o p p o s e d t o an h o u r l y b a s i s w i t h o u t i n t r o d u c i n g any s i g n i f i c a n t a d d i t i o n a l b i a s . (2) HT ( F i g u r e 6.11) - S y s t e m a t i c a l l y i n c r e a s i n g t h e i n p u t v a l u e s o f s o l a r r a d i a t i o n i n c i d e n t on t h e c o l l e c t o r a r r a y by up t o 10 p e r c e n t r e s u l t e d i n a l a r g e d e c r e a s e i n t h e MBE v a l u e . A 9.2% i n c r e a s e i n HT r e d u c e d t h e m odel's s t o r a g e t a n k t e m p e r a t u r e b i a s t o z e r o . Hence t h e model i s v e r y s e n s i t i v e t o t h i s v a r i a b l e , and t h e u s e r s h o u l d pay p a r t i c u l a r a t t e n t i o n t o s e c u r i n g a c c u r a t e p y r a n o m e t r i c d a t a . HT i s t h e p r i m e m e t e o r o l o g i c a l v a r i a b l e i n t h e s i m u l a t i o n m o del; i t s e t s t h e p o t e n t i a l amount of s o l a r e n e r g y w h i c h c a n be c o n v e r t e d i n t o h o t w a ter h e a t . By i n c r e a s i n g t h e i n p u t v a l u e s of HT, more s o l a r e n e r g y becomes a v a i l a b l e t o h e a t t h e w a t e r f l o w i n g t h r o u g h t h e c o l l e c t o r p a n e l s . A t t h e same t i m e , t h e c o l l e c t o r - t o - t a n k t e m p e r a t u r e d i f f e r e n c e becomes l a r g e r , c a u s i n g a g r e a t e r number of h o u r s t o o c c u r when t h i s t e m p e r a t u r e d i f f e r e n c e e x c e e d s TDIF1 and T D IF2. C o n s e q u e n t l y , i f none o f t h e o t h e r s y s t e m p a r a m e t e r s a r e v a r i e d , t h e model w i l l show an i n c r e a s e i n t h e amount of s o l a r e n e r g y c o l l e c t e d and t r a n s f e r r e d t o s t o r a g e , and t h e r e f o r e an i n c r e a s e i n t a n k t e m p e r a t u r e . Thus t h e r e i s a d i r e c t r e l a t i o n s h i p between t h e h e a t c o n t e n t of t h e s t o r a g e t a n k and t h e amount of s o l a r r a d i a t i o n i n c i d e n t on t h e c o l l e c t o r a r r a y . I t i s t h i s 174 r e l a t i o n s h i p w h i c h c a u s e d th e p r o p o r t i o n a l r e d u c t i o n i n t h e MBE v a l u e and t h e s m a l l i n c r e a s e i n t h e number of c o l l e c t o r o p e r a t i n g h o u r s as HT was i n c r e a s e d . The s e n s i t i v i t y p l o t shows t h a t by s y s t e m a t i c a l l y i n c r e a s i n g t h e s o l a r r a d i a t i o n v a l u e s , t h e model's l o n g t e r m t e m p e r a t u r e d e v i a t i o n c a n be e l i m i n a t e d and i t s s h o r t t e r m t e m p e r a t u r e d e v i a t i o n s m i n i m i z e d , w h i l e a t t h e same t i m e t h e c l o s e agreement i n t h e number of c o l l e c t o r o p e r a t i n g h o u r s can be m a i n t a i n e d . However, t h e s e n s i t i v i t y p l o t does not p r o v i d e any e v i d e n c e s u p p o r t i n g s u c h an i n c r e a s e . T h e r e f o r e one has t o examine t h e c o l l e c t o r ' s r a d i a t i v e e n v i r o n m e n t i n o r d e r t o a s s e s s t h e l i k l i h o o d t h a t i n a c c u r a c y i n t h e measured HT v a l u e s c a u s e s t h e model b i a s . I t c a n be seen from F i g u r e 6.12 t h a t t h e l o c a l sky h o r i z o n s o f b o t h t h e c o l l e c t o r a r r a y and t h e p y r a n o m e t e r a r e p a r t i a l l y b l o c k e d by a n e a r b y dormer t o t h e e a s t , and s u r r o u n d i n g t a l l t r e e s t o t h e s o u t h and west. Hence b o t h t h e c o l l e c t o r a r r a y and t h e p y r a n o m e t e r a r e s u b j e c t t o non-random shadowing d u r i n g e a r l y m o r n i n g and l a t e a f t e r n o o n . In summer, t h e s e p e r i o d s o f t h e day c a n o f t e n e x p e r i e n c e s o l a r e n e r g y c o l l e c t i o n . S i n c e t h e p y r a n o m e t e r i s p o s i t i o n e d below t h e c o l l e c t o r a r r a y i t t e n d s t o r e c e i v e , on a v e r a g e , more r e c u r r e n t shadow c a s t i n g t h a n o t h e r a r e a s o f t h e c o l l e c t o r ; i e . t h e p y r a n o m e t e r c a n be i n t o t a l shadow w h i l e t h e c o l l e c t o r a r r a y i s o n l y i n p a r t i a l shadow. T h i s o b s e r v e d o c c u r r e n c e w i l l r e s u l t i n l o n g t e r m u n d e r - e s t i m a t i o n of t h e ' t r u e ' s p a t i a l l y i n t e g r a t e d amount of s o l a r r a d i a t i o n i n c i d e n t on t h e c o l l e c t o r a r r a y . I t a g a i n i l l u s t r a t e s t h e p r o b l e m o f s p a t i a l s a m p l i n g e r r o r w h i c h o f t e n a r i s e s when one t r i e s t o use a p o i n t 175 measurement t o r e p r e s e n t a s p a t i a l l y i n t e g r a t e d v a l u e . W h i l e t h e m a g n i t u d e of t h e e r r o r i n t h i s p a r t i c u l a r c a s e c a n n o t be q u a n t i f i e d , i t i s n o t e d t h a t i t s e f f e c t w i l l o c c u r most f r e q u e n t l y under s m a l l i n c i d e n t a n g l e s . T h e s e p e r i o d s a r e g e n e r a l l y not h o u r s o f i n t e n s e s o l a r e n e r g y c o l l e c t i o n . T h e r e f o r e , a maximum s y s t e m a t i c e r r o r o f +10% was assumed f o r t h e HT v a l u e s . The s e n s i t i v i t y p l o t i n t u r n r e v e a l s t h a t even a s o l a r r a d i a t i o n b i a s s u b s t a n t i a l l y l e s s t h a n +10% can i n t r o d u c e s i g n i f i c a n t u s e r - e f f e c t e r r o r i n t o t h e model. Hence s p e c i a l a t t e n t i o n must be p a i d t o t h e r e p r e s e n t a t i v e n e s s of t h e i n p u t v a l u e s f o r t h i s v a r i a b l e . (3) TA ( F i g u r e 6.13) - S y s t e m a t i c a l l y i n c r e a s i n g t h e i n p u t v a l u e s o f ambient a i r t e m p e r a t u r e by as much as 5.0 d e g r e e s C c a u s e d l a r g e r e d u c t i o n s i n b o t h t h e MBE and RMSE v a l u e s ; t h e m o d e l ' s l o n g t e r m s t o r a g e t a n k t e m p e r a t u r e d e v i a t i o n was r e d u c e d by 2.3 d e g r e e s C and i t s s h o r t t e r m t e m p e r a t u r e d e v i a t i o n s were r e d u c e d by 0.75 d e g r e e C. Thus t h e model i s v e r y s e n s i t i v e t o v a r i a t i o n s i n TA. A c c o r d i n g l y , i n p u t v a l u e s f o r t h i s v a r i a b l e must a c c u r a t e l y r e p r e s e n t ambient t h e r m a l c o n d i t i o n s . As a c o r o l l a r y , t h e s e n s i t i v i t y r e s u l t s s u g g e s t t h a t s l i g h t c h a n g e s i n ambient a i r t e m p e r a t u r e c a n s i g n i f i c a n t l y a f f e c t t h e u s e f u l s o l a r e n e r g y g a i n s o f t h e c o l l e c t o r . The a i r s u r r o u n d i n g t h e c o l l e c t o r p a n e l s a c t s as a t h e r m a l s i n k r e c e i v i n g h e a t l o s t f r o m a l l p a r t s o f t h e c o l l e c t o r , i n c l u d i n g t h e a b s o r b e r p l a t e and t h e water c i r c u l a t i n g t h r o u g h t h e p a s s a g e s b e n e a t h i t . By i n c r e a s i n g TA, t h e t e m p e r a t u r e g r a d i e n t between t h e c o l l e c t o r and t h e ambient a i r i s 176 d e c r e a s e d . The s i m u l a t i o n model i n c o r p o r a t e s t h i s t e m p e r a t u r e g r a d i e n t i n c o n j u n c t i o n w i t h an o v e r a l l h e a t l o s s c o e f f i c i e n t t o c a l c u l a t e t h e c o l l e c t o r h e a t l o s s e s . C o n s e q u e n t l y , i f t h i s t e m p e r a t u r e g r a d i e n t i s d e c r e a s e d , t h e c o l l e c t o r h e a t l o s s e s w i l l be r e d u c e d and p o t e n t i a l l y more s o l a r e n e r g y w i l l be i n p u t t o s t o r a g e . In a d d i t i o n , t h e a b s o r b e r p l a t e t e m p e r a t u r e under n o - f l o w c o n d i t i o n s (TCP) w i l l be h i g h e r a t a l l t i m e s . T h i s w i l l r e s u l t i n a p r o p o r t i o n a t e l y g r e a t e r number o f h o u r s d u r i n g w h i c h t h e c o l l e c t o r - t o - t a n k t e m p e r a t u r e d i f f e r e n c e w i l l e x c e e d TDIF1, p e r m i t t i n g e n e r g y c o l l e c t i o n t o commence under s l i g h t l y l o w e r l e v e l s o f s o l a r i r r a d i a n c e . F u r t h e r m o r e , s i n c e t h e c o l l e c t o r o u t l e t t e m p e r a t u r e w i l l t e n d t o be h i g h e r , t h e r e w i l l be an i n c r e a s e i n t h e number of h o u r s t h a t t h e c o l l e c t o r - t o - t a n k t e m p e r a t u r e d i f f e r e n c e e x c e e d s TDIF2. These two e f f e c t s w i l l l e a d t o more f r e q u e n t and l o n g e r c o l l e c t o r o p e r a t i o n . T h i s i s i n d i c a t e d i n t h e s e n s i t i v i t y p l o t by t h e 8.9% i n c r e a s e i n t h e number of c o l l e c t o r o p e r a t i n g h o u r s . N e g a t i v e f e e d b a c k e f f e c t s w i l l p a r t i a l l y o f f s e t t h e t e n d e n c y of h i g h e r TA v a l u e s t o i n c r e a s e s t o r a g e i n p u t . However, f o r t h e s m a l l v a r i a t i o n s i n TA examined, t h e i r e f f e c t a p p e a r s t o be f a i r l y m i n i m a l . Hence a d e f i n i t e i n c r e a s e i n a v e r a g e s t o r a g e t a n k t e m p e r a t u r e o c c u r s , as r e f l e c t e d by t h e l o w e r MBE v a l u e s . I n s t r u m e n t e r r o r i n h e r e n t i n t h e a m b i e n t a i r t e m p e r a t u r e s e n s o r i s a p p r o x i m a t e l y ± 0.1°C ( T a b l e 3 . 1 ) . However, t h e r e p r e s e n t a t i v e n e s s of t h e measured TA t e m p e r a t u r e s i s much l e s s c e r t a i n . D u r i n g p e r i o d s of c o l l e c t o r o p e r a t i o n t h e a i r i n t h e immediate v i c i n i t y of t h e p a n e l s may w e l l be s e v e r a l d e g r e e s 177 warmer t h a n t h a t r e c o r d e d i n t h e S t e v e n s o n s c r e e n on t h e s u n d e c k . T h i s s i t u a t i o n depends upon t h e a b i l i t y o f t h e r o o f t o h e a t t h e n e a r s u r f a c e a i r l a y e r s , and on d i f f e r e n c e s i n a d v e c t i v e e f f e c t s between t h e two e x p o s u r e s . A +5 d e g r e e C t e m p e r a t u r e b i a s was j u d g e d t o be t h e maximum e r r o r l i k e l y t o o c c u r i n t h i s v a r i a b l e . The s e n s i t i v i t y p l o t r e v e a l s t h a t a s y s t e m a t i c v a r i a t i o n i n TA of t h i s m a g n i t u d e l e a d s t o v i r t u a l e l i m i n a t i o n of t h e model's l o n g t e r m t e m p e r a t u r e d e v i a t i o n . However a t t h e same t i m e , t h e p r e d i c t e d number o f c o l l e c t o r o p e r a t i n g h o u r s s i g n i f i c a n t l y d i f f e r s from t h a t m easured. T h i s outcome s u g g e s t s t h a t u s e r - e f f e c t e r r o r i n t h i s v a r i a b l e i s p r o b a b l y l i m i t e d t o l e s s t h a n +1.0 d e g r e e C. (4) TM ( F i g u r e 6.14) - S y s t e m a t i c a l l y i n c r e a s i n g t h e i n c o m i n g c o l d w ater t e m p e r a t u r e v a l u e s by t w i c e t h e m a g n i t u d e of t h e i r measurement u n c e r t a i n t y ( A p p e n d i x C) c a u s e d o n l y a s m a l l r e d u c t i o n (0.35 d e g r e e C) i n t h e MBE v a l u e . By i n c r e a s i n g TM, t h e t e m p e r a t u r e g r a d i e n t between t h e c o l d w ater e n t e r i n g t h e immersed c o i l h e a t e x c h a n g e r and t h e warmer water r e s i d i n g i n t h e s t o r a g e t a n k d e c r e a s e s . The s i m u l a t i o n model u s e s t h i s t e m p e r a t u r e g r a d i e n t t o c a l c u l a t e t h e amount o f h e a t t h a t i s e x t r a c t e d f r o m s t o r a g e and d e l i v e r e d t o t h e i n c o m i n g c o l d w a t e r . C o n s e q u e n t l y , i f t h i s t e m p e r a t u r e g r a d i e n t i s d e c r e a s e d , t h e amount o f h e a t t r a n s f e r r e d from s t o r a g e i s r e d u c e d and h i g h e r s t o r a g e tank t e m p e r a t u r e s w i l l r e s u l t . However, as t h e s e n s i t i v i t y p l o t i n d i c a t e s , t h e model i s o n l y s l i g h t l y s e n s i t i v e t o t h e u n c e r t a i n t y w h i c h e x i s t s i n t h e measured v a l u e s of TM. Hence i t i s u n l i k e l y t h a t s i g n i f i c a n t u s e r - e f f e c t e r r o r i s i n t r o d u c e d i n t o t h e model t h r o u g h t h i s 178 v a r i a b l e . (5) FLOW ( F i g u r e 6.15) - D e c r e a s i n g t h e i n p u t v a l u e s of t h e h o u r l y h o t water draws by up t o 2.5 p e r c e n t c a u s e d o n l y a v e r y s m a l l r e d u c t i o n (0.26 d e g r e e C) i n t h e MBE v a l u e . By s y s t e m a t i c a l l y d e c r e a s i n g FLOW, t h e volume of water f l o w i n g t h r o u g h t h e h e a t e x c h a n g e r i s r e d u c e d . T h i s v a r i a b l e i s a l s o u s e d by t h e s i m u l a t i o n model t o p r e d i c t t h e amount of s t o r e d h e a t t h a t i s d e l i v e r e d t o t h e i n c o m i n g c o l d w a t e r . I f i t s v a l u e s a r e s y s t e m a t i c a l l y d e c r e a s e d , t h e amount of h e a t e x t r a c t e d from s t o r a g e i s p r o p o r t i o n a t e l y r e d u c e d , and a h i g h e r a v e r a g e s t o r a g e t a n k t e m p e r a t u r e r e s u l t s . As l i s t e d i n T a b l e 3.1, t h e measurement e r r o r f o r t h e f l o w meter i s ± 1 . 5 % o v e r t h e rang e 1 - 1 0 0 l i t r e s p e r m i n u t e . As t h e f l o w r a t e d r o p s below 1 l i t r e p e r m i n u t e , t h e m a n u f a c t u r e r ' s l i t e r a t u r e i n d i c a t e s t h a t u n d e r - e s t i m a t i o n becomes i n c r e a s i n g l y s i g n i f i c a n t . B e c a u s e 29% o f t h e h o u r l y h o t water draws were l e s s t h a n 1 l i t r e i n volume, many of w h i c h were p r o b a b l y 1 m i n u t e o r more i n d u r a t i o n , low f l o w r a t e s c o n s t i t u t e a f a i r l y f r e q u e n t o c c u r r e n c e . Thus t h e i r i m p a c t on model p r e d i c t i o n s c a n n o t be i g n o r e d . However, t h e s e n s i t i v i t y p l o t r e v e a l s t h a t t h e model i s o n l y m a r g i n a l l y s e n s i t i v e t o t h e p o t e n t i a l b i a s w h i c h e x i s t s i n t h e measured v a l u e s o f FLOW. I t a l s o i n d i c a t e s t h a t t h e f l o w meter must o v e r - e s t i m a t e , n ot u n d e r - e s t i m a t e , t h e volume of h o t water drawn i n o r d e r f o r t h e model's s h o r t and l o n g t e r m t e m p e r a t u r e d e v i a t i o n s t o be r e d u c e d . T h e r e f o r e , u s e r - e f f e c t e r r o r a s s o c i a t e d w i t h t h i s v a r i a b l e c a n be c o n s i d e r e d m i n i m a l . 3. Summary o f U s e r - E f f e c t E r r o r s T a b l e 6.3 p r o v i d e s a q u a l i t a t i v e summary o f t h e 179 p r o b a b i l i t y o f u s e r - e f f e c t e r r o r s b e i n g i n t r o d u c e d i n t o t h e s i m u l a t i o n model by t h e c u r r e n t s e t o f i n p u t v a l u e s f o r t h e d i f f e r e n t s y s t e m p a r a m e t e r s and v a r i a b l e s . 4. D i s c u s s i o n and S u g g e s t i o n s f o r F u r t h e r I n v e s t i g a t i o n A t t h i s s t a g e i n t h e model v a l i d a t i o n p r o c e s s i t becomes e v i d e n t t h a t u s e r - e f f e c t e r r o r i n t h e i n p u t d a t a p r o b a b l y c o n t r i b u t e s t o t h e model b i a s . The most l i k e l y s o u r c e s o f u s e r - e f f e c t e r r o r i n c l u d e t h e s o l a r r a d i a t i o n and ambient a i r t e m p e r a t u r e v a r i a b l e s t o g e t h e r w i t h t h e c o l l e c t o r e f f i c i e n c y p a r a m e t e r s . Hence i t would be a p p r o p r i a t e a t t h i s p o i n t t o p e r f o r m a s t a n d - a l o n e t e s t on t h e c o l l e c t o r l o o p i n o r d e r t o a s c e r t a i n w h i c h of t h e s e p a r a m e t e r s or v a r i a b l e s r e q u i r e r e - e v a l u a t i o n p r i o r t o f u r t h e r model v a l i d a t i o n . A s e c o n d p y r a n o m e t e r and a m bient a i r t e m p e r a t u r e p r o b e , p o s i t i o n e d above t h e c o l l e c t o r a r r a y , c o u l d be i n s t a l l e d i n o r d e r t o o b t a i n a s y n c h r o n o u s s e t o f m e t e o r o l o g i c a l d a t a w i t h w h i c h t o a s s e s s t h e s p a t i a l s a m p l i n g e r r o r i n HT and TA. As w e l l , t h e i n l e t / o u t l e t t e m p e r a t u r e s and w ater f l o w i n t h e c o l l e c t o r l o o p c o u l d be measured, p e r m i t t i n g v e r i f i c a t i o n o f t h e p r e d i c t e d q u a n t i t y of s o l a r e n e r g y c o l l e c t e d and t r a n s f e r r e d t o s t o r a g e . Due t o p r o j e c t c o n s t r a i n t s and t h e n o n - e x p e r i m e n t a l d e s i g n of t h e m o n i t o r i n g p r o g r a m , t h e s e p r o c e d u r e s were n o t i m p l e m e n t e d i n t h e p r e s e n t s t u d y . The b a s i c o b j e c t i v e was s i m p l y t o e v a l u a t e t h e s i m u l a t i o n model and a n a l y z e i t s s e n s i t i v i t y u s i n g t h e c u r r e n t s e t o f measurement d a t a . However, t h e f l o w c h a r t p r e s e n t e d i n F i g u r e 6.16 i n d i c a t e s t h e g e n e r a l s t r a t e g y one w o u l d f o l l o w i n c o m p l e t i n g a more t h o r o u g h v a l i d a t i o n o f t h e m o d e l . S i n c e t h e o u t l i n e d c o u r s e o f a c t i o n c o u l d not be 180 a d h e r e d t o , and s i n c e i t was f e l t t h a t a d d i t i o n a l t e s t i n g o f t h e model u s i n g t h e a v a i l a b l e d a t a s e t c o u l d p r o v i d e f u r t h e r i n s i g h t i n t o t h e model b i a s , a y e a r l o n g s i m u l a t i o n o f t h e s y s t e m was p e r f o r m e d . The r e s u l t s a r e d e t a i l e d i n t h e n e x t s e c t i o n . F. S i m u l a t i o n R e s u l t s f o r a One Ye a r P e r i o d 1. P r e d i c t e d S e a s o n a l T h e r m a l E n e r g y Regime The y e a r l o n g s i m u l a t i o n p e r i o d e x t e n d s f r o m J u l y 1981 t o June 1982, i n c l u s i v e . P r e d i c t e d m o n t h l y and a n n u a l v a l u e s f o r t h e t h e r m a l e n e r g y q u a n t i t i e s w h i c h c o m p r i s e t h e s t o r a g e t a n k e n e r g y b a l a n c e , t o g e t h e r w i t h t h e p r e d i c t e d number of pump o p e r a t i n g h o u r s , a r e l i s t e d i n T a b l e 6.4. A l s o t a b u l a t e d a r e th e measured v a l u e s o f i n c i d e n t s o l a r r a d i a t i o n , t o t a l h e a t d e l i v e r e d , and h o t wa t e r c o n s u m p t i o n . F i g u r e 6.17 d e p i c t s t h e l a r g e s e a s o n a l v a r i a t i o n i n t h e p r e d i c t e d t h e r m a l e n e r g y q u a n t i t i e s . S o l a r e n e r g y i n p u t t o s t o r a g e (QCSS) i s t h e dominant q u a n t i t y f o r a l l t i m e s o f t h e y e a r e x c e p t l a t e f a l l and e a r l y w i n t e r . D u r i n g t h i s l a t t e r p e r i o d t h e amount of s o l a r h e a t d e l i v e r e d t o t h e i n c o m i n g c o l d w a t e r (QSDHW) s u r p a s s e s t h e amount o f s o l a r e n e r g y c o l l e c t e d and t r a n s f e r r e d t o s t o r a g e . The d i f f e r e n c e i s d e r i v e d from a n e g a t i v e s t a n d b y h e a t l o s s (QSENV); i e . h e a t i s e f f e c t i v e l y t r a n s f e r r e d f r o m t h e warmer basement a i r t o t h e c o o l e r w ater i n t h e s t o r a g e t a n k , a l l o w i n g QSENV t o a c t as a s o u r c e o f e n e r g y i n p u t . T h i s s i t u a t i o n was d e d u c e d i n C h a p t e r 4. Thus, t h e s i m u l a t i o n r e s u l t s s u p p o r t e a r l i e r e v i d e n c e t h a t n ot a l l o f th e h e a t e x t r a c t e d f r o m t h e s t o r a g e t a n k and d e l i v e r e d t o 181 t h e i n c o m i n g c o l d w ater i s d e r i v e d from s o l a r e n e r g y . ( C o r r e s p o n d i n g l y , t h e d e s i g n a t i o n ' s o l a r h e a t d e l i v e r e d ' i s more i n c l u s i v e t h a n i t s name i m p l i e s s i n c e i t c o n t a i n s a component of s t a n d b y h e a t g a i n d u r i n g t h e l a t e f a l l and e a r l y w i n t e r months.) S o l a r e n e r g y i n p u t t o t h e s t o r a g e tank e x h i b i t s a s l i g h t l y b i - m o d a l s e a s o n a l v a r i a t i o n . The two h i g h e s t m o n t h l y QCSS v a l u e s o c c u r i n May (1.29 GJ) and A u g u s t (1.31 G J ) , c o i n c i d e n t w i t h t h e maximum v a l u e s o f s o l a r r a d i a t i o n i n c i d e n t on t h e c o l l e c t o r a r r a y ( T a b l e 6 . 4). The minimum m o n t h l y QCSS v a l u e o c c u r s i n J a n u a r y (0.09 G J ) , c o i n c i d e n t w i t h t h e minimum QHT v a l u e . The s e a s o n a l v a r i a t i o n i n t h e amount o f s o l a r h e a t d e l i v e r e d t o t h e i n c o m i n g c o l d w a t e r f o l l o w s t h a t of s o l a r e n e r g y i n p u t , a l t h o u g h not i n a d i r e c t l y p r o p o r t i o n a l manner. The QSDHW v a l u e s a r e 20%-30% s m a l l e r t h a n t h e c o r r e s p o n d i n g QCSS v a l u e s i n summer, but a r e l a r g e r by a r o u g h l y e q u i v a l e n t amount i n December and J a n u a r y . Standby h e a t l o s s from t h e s t o r a g e t a n k a l s o e x h i b i t s s e a s o n a l v a r i a t i o n . Heat l o s s i s l a r g e when t h e s t o r a g e t a n k t e m p e r a t u r e i s h i g h . T h i s g e n e r a l l y c o i n c i d e s w i t h months w h i c h have l a r g e s o l a r e n e r g y i n p u t . Heat l o s s d e c r e a s e s , and even becomes n e g a t i v e , as t h e t e m p e r a t u r e o f t h e s t o r a g e t a n k i s r e d u c e d below t h a t o f t h e s u r r o u n d i n g basement a i r d u r i n g months of low s o l a r e n e r g y i n p u t . L a s t l y , t h e m o n t h l y change i n h e a t c o n t e n t of t h e s t o r a g e t a n k (QSTOR) n e v e r e x c e e d s 0.05 G J . QSTOR i s u s u a l l y t h e s m a l l e s t t e r m i n t h e e n e r g y b a l a n c e f o r t h e s t o r a g e t a n k ; i t i s r e l a t i v e l y i n s i g n i f i c a n t compared t o t h e o t h e r e n e r g y i n p u t / o u t p u t t e r m s . T h i s r e f l e c t s t h e s h o r t t e r m s t o r a g e 182 d e s i g n of t h e s y s t e m . 2. S t o r a g e Tank T e m p e r a t u r e F i g u r e 6.18 i s a t i m e s e r i e s p l o t of t h e p r e d i c t e d and measured d a i l y mean s t o r a g e tank t e m p e r a t u r e s f o r t h e one y e a r s i m u l a t i o n p e r i o d . A g a i n t h e p r e d i c t e d t e m p e r a t u r e c u r v e n e i t h e r f u l l y c o i n c i d e s w i t h nor p a r a l l e l s e i t h e r of t h e two measured c u r v e s , a l t h o u g h i t i s a b l e t o c o n s i s t e n t l y t r a c k d a y - t o - d a y t e m p e r a t u r e c h a n g e s w i t h i n t h e a c t u a l s t o r a g e t a n k . The p r e d i c t e d t e m p e r a t u r e c u r v e c h a r a c t e r i s t i c a l l y l i e s b e n e a t h t h e measured t a n k m i d - h e i g h t c u r v e and o n l y i n t e r m i t t e n t l y r i s e s above t h e tank bottom c u r v e . P e r i o d s o f s i g n i f i c a n t u n d e r - e s t i m a t i o n i n t h e d a i l y mean s t o r a g e t a n k t e m p e r a t u r e o c c u r i n t h e s p r i n g and summer months, e s p e c i a l l y d u r i n g d a y s of l a r g e s o l a r e n e r g y i n p u t . In c o n t r a s t , t h e r e i s c l o s e r agreement between p r e d i c t e d and measured t e m p e r a t u r e s d u r i n g t h e w i n t e r months, when d a y - t o - d a y t e m p e r a t u r e c h a n g e s a r e l e s s v a r i a b l e and s o l a r e n e r g y i n p u t c e a s e s t o be t h e dominant t e r m i n t h e s t o r a g e t a n k e n e r g y b a l a n c e . T h i s i s v e r i f i e d by t h e s t o r a g e t a n k t e m p e r a t u r e e r r o r s t a t i s t i c s l i s t e d i n T a b l e 6.5 and p l o t t e d i n F i g u r e 6.19. They a r e computed on a m o n t h l y and a n n u a l b a s i s u s i n g t h e p r e d i c t e d and measured d a i l y mean s t o r a g e tank t e m p e r a t u r e s . 2 2 B o t h s h o r t (RMSE) and l o n g t e r m (MBE) d e v i a t i o n s i n t h e p r e d i c t e d d a i l y mean s t o r a g e t a n k t e m p e r a t u r e show marked s e a s o n a l v a r i a t i o n . The l o n g t e r m d e v i a t i o n w i t h r e s p e c t t o t h e t a n k b o t t o m t e m p e r a t u r e i s l e s s t h a n +0.75 d e g r e e C f o r t h e f a l l and w i n t e r months ( O c t o b e r - M a r c h ) . However, d u r i n g t h e t h r e e s p r i n g months ( A p r i l - J u n e ) i t becomes i n c r e a s i n g l y 183 n e g a t i v e . The c o r r e s p o n d i n g d e v i a t i o n w i t h r e s p e c t t o t h e tank m i d - h e i g h t t e m p e r a t u r e i s n e g a t i v e d u r i n g a l l months of t h e y e a r ; t h e m i d - h e i g h t MBE i n c r e a s e s from a minimum v a l u e o f -1.76 d e g r e e s C i n J a n u a r y t o a maximum v a l u e o f -10.41 d e g r e e s C i n J u n e . T h e s e n e g a t i v e MBE v a l u e s i n d i c a t e t h a t t h e model t e n d s t o s y s t e m a t i c a l l y u n d e r - e s t i m a t e t h e t e m p e r a t u r e of t h e s t o r a g e t a n k , as was c o n c l u d e d from t h e s i m u l a t i o n r e s u l t s f o r t h e i n i t i a l two month t e s t p e r i o d . The s e a s o n a l v a r i a t i o n i n t h e m a g n i t u d e o f t h e MBE s u g g e s t s t h a t t h e m o d e l ' s p r e d i c t i o n s of s o l a r e n e r g y i n p u t a r e i n a c c u r a t e . A s s u m i n g u s e r - e f f e c t e r r o r i s t h e major c o n t r i b u t i n g c a u s e , t h e most l i k e l y s o u r c e of e r r o r would a g a i n be t h e i n p u t d a t a f o r t h e c o l l e c t o r model ( i e . t h e s o l a r r a d i a t i o n and a m b i e n t a i r t e m p e r a t u r e v a r i a b l e s t o g e t h e r w i t h t h e c o l l e c t o r e f f i c i e n c y p a r a m e t e r s ) . In t h e a b s e n c e of u s e r - e f f e c t e r r o r , t h e s i m p l i f i c a t i o n s a s s o c i a t e d w i t h t h e c o l l e c t o r model ( e g . s t e a d y s t a t e a s s u m p t i o n ) would be t h e p o t e n t i a l s o u r c e of s i m u l a t i o n i n a c c u r a c y . D e v i a t i o n i n t h e p r e d i c t e d s t o r a g e t a n k t e m p e r a t u r e s i s n o t e n t i r e l y l i m i t e d t o s y s t e m a t i c e r r o r . S h o r t term d e v i a t i o n s w i t h r e s p e c t t o t h e t a n k b o t t o m t e m p e r a t u r e f a l l w i t h i n t h e r a n g e 0.99 - 4.36 d e g r e e s C. T h i s compares w i t h a c o r r e s p o n d i n g r a n g e i n t h e l o n g t e r m d e v i a t i o n of 0.05 - 3.80 d e g r e e s C ( i g n o r i n g t h e s i g n of t h e MBE). Hence a component of n o n - s y s t e m a t i c e r r o r i s e v i d e n t i n t h e m o d e l ' s t e m p e r a t u r e d e v i a t i o n s on a d a i l y b a s i s - a t l e a s t i f one i s making th e e v a l u a t i o n w i t h r e s p e c t t o t e m p e r a t u r e s m easured i n t h e b o t t o m of t h e s t o r a g e t a n k . F o r a s i m i l a r e v a l u a t i o n , but u s i n g t e m p e r a t u r e s measured a t t h e t a n k m i d - h e i g h t l e v e l , 184 n o n - s y s t e m a t i c e r r o r i s seen t o be r e l a t i v e l y l e s s s i g n i f i c a n t . T h i s i s a r e s u l t o f t h e model c o n s i s t e n t l y p r e d i c t i n g much lo w e r d a i l y mean t e m p e r a t u r e s t h a n o c c u r a t t h e m i d - h e i g h t l e v e l i n t h e s t o r a g e t a n k . Thus, even t h o u g h t h e tank m i d - h e i g h t RMSE v a l u e s c a n e x c e e d t h e c o r r e s p o n d i n g MBE v a l u e s by a s much as 0.5 d e g r e e C, i n r e l a t i v e t e r m s t h i s d i f f e r e n c e i s q u i t e s m a l l . 3. S o l a r Hot Water Heat The b a r g r a p h p r e s e n t e d i n F i g u r e 6.20 i n d i c a t e s t h e d e v i a t i o n between t h e p r e d i c t e d and measured m o n t h l y t o t a l s of s o l a r h o t water h e a t o v e r t h e one y e a r s i m u l a t i o n p e r i o d . As was t h e c a s e f o r t h e i n i t i a l two month t e s t p e r i o d , t h e model s y s t e m a t i c a l l y u n d e r - e s t i m a t e s t h e QSDHW v a l u e s . The y e a r l o n g s i m u l a t i o n r e s u l t s f u r t h e r r e v e a l t h a t t h i s s y s t e m a t i c e r r o r i s s e a s o n a l l y d e p e n d e n t . B o t h t h e a b s o l u t e and r e l a t i v e d e v i a t i o n s i n m o n t h l y s o l a r h o t water h e a t a r e l a r g e s t d u r i n g t h e s p r i n g and summer months, and s m a l l e s t d u r i n g t h e f a l l and w i n t e r months. T h i s i s v e r i f i e d by t h e m o n t h l y MBE v a l u e s l i s t e d i n T a b l e 6.6 and p l o t t e d i n F i g u r e 6.21. Th e s e v a l u e s e q u a l t h e d e v i a t i o n between t h e p r e d i c t e d and measured mean d a i l y q u a n t i t i e s of s o l a r h o t water h e a t . The s m a l l e s t d e v i a t i o n o c c u r s i n J a n u a r y , when t h e a b s o l u t e MBE v a l u e i s -0.32 MJ/day and t h e r e l a t i v e MBE v a l u e i s -5.9%. The l a r g e s t d e v i a t i o n o c c u r s i n J u n e , a t w h i c h t i m e t h e a b s o l u t e MBE v a l u e has i n c r e a s e d t o -10.4 MJ/day and t h e r e l a t i v e MBE v a l u e t o -24.3%. T h i s s e a s o n a l v a r i a t i o n i n t h e s y s t e m a t i c e r r o r of s o l a r h o t water h e a t c o i n c i d e s w i t h t h a t o c c u r r i n g i n s t o r a g e t a n k t e m p e r a t u r e . I t c a n be d e d u c e d t h a t 185 i f t h e s t o r a g e t a n k t e m p e r a t u r e i s b e i n g s y s t e m a t i c a l l y u n d e r - e s t i m a t e d , t h e n t h e p r e d i c t e d amount of h e a t t h a t i s a b l e t o be e x t r a c t e d from s t o r a g e and d e l i v e r e d t o t h e i n c o m i n g c o l d w a t e r w i l l a l s o be u n d e r - e s t i m a t e d . Hence s y s t e m a t i c e r r o r i n t h e s e two v a r i a b l e s i s d i r e c t l y r e l a t e d . The s o u r c e of t h e i n a c c u r a c y a g a i n a p p e a r s t o o r i g i n a t e i n t h e c o l l e c t o r model s i n c e s y s t e m a t i c e r r o r i n QSDHW i s s i g n i f i c a n t l y r e d u c e d d u r i n g t h e w i n t e r months when s o l a r e n e r g y i n p u t l o s e s i t s d o minance. S e a s o n a l v a r i a t i o n i n t h e a b s o l u t e RMSE v a l u e s f o r QSDHW c o r r e s p o n d s w i t h t h a t i n t h e MBE v a l u e s . The s m a l l e s t a b s o l u t e RMSE v a l u e o c c u r s i n J a n u a r y (1.39 M J / d a y ) , w h i l e t h e l a r g e s t v a l u e o c c u r s i n June (11.28 M J / d a y ) . In c o n t r a s t , t h e r e l a t i v e RMSE v a l u e s e x h i b i t a b i - m o d a l s e a s o n a l v a r i a t i o n . Maximum v a l u e s o c c u r i n b o t h J a n u a r y and Jun e , 25.4% and 26.4% r e s p e c t i v e l y ; minimum v a l u e s o c c u r i n March and September, 11.8% and 13.4% r e s p e c t i v e l y . The w i n t e r maximum r e l a t e s t o s e a s o n a l v a r i a t i o n i n t h e m a g n i t u d e o f s o l a r h o t water h e a t . D u r i n g . w i n t e r t h e d a i l y QSDHW v a l u e s a v e r a g e l e s s t h a n 15 MJ. Thus , even s m a l l a b s o l u t e d e v i a t i o n s i n t h e p r e d i c t e d v a l u e s c a n c a u s e l a r g e r e l a t i v e e r r o r s . 4. C o l l e c t o r O p e r a t i o n W h i l e t h e s i m u l a t i o n model s y s t e m a t i c a l l y u n d e r - e s t i m a t e s b o t h t h e s t o r a g e t a n k t e m p e r a t u r e and t h e s o l a r h o t water h e a t , i t o v e r - e s t i m a t e s t h e number o f c o l l e c t o r o p e r a t i n g h o u r s . T h i s r e s u l t i s v e r i f i e d by e x a m i n i n g t h e e r r o r s t a t i s t i c s l i s t e d i n T a b l e 6.7 and p l o t t e d i n F i g u r e 6.22. On an i n d i v i d u a l m o n t h l y b a s i s , t h e pump hour d e p a r t u r e e r r o r r a n g e s f r o m a minimum o f -1 hour i n June t o a maximum of +40 h o u r s 186 i n M a r c h and September. The s p r i n g and f a l l maxima e x i s t s o n l y f o r t h e a b s o l u t e e r r o r . The r e l a t i v e pump hour d e p a r t u r e e r r o r f o l l o w s an a n n u a l c y c l e ; i t i s l a r g e s t i n J a n u a r y (+182%) and s m a l l e s t i n June (-1%). I t s v a r i a b i l i t y i s r e l a t e d t o t h e l a r g e s e a s o n a l v a r i a t i o n i n c o l l e c t o r o p e r a t i o n : 7.1 h o u r s i n J a n u a r y v e r s u s 190.5 h o u r s i n June ( f o r t h e a c t u a l c o l l e c t o r ) . C u m u l a t i v e pump hour d e p a r t u r e e r r o r o v e r t h e one y e a r s i m u l a t i o n p e r i o d was +246 h o u r s , o r +22.1%. I t i s d i f f i c u l t t o deduce why t h e a b s o l u t e pump hour d e p a r t u r e e r r o r e x h i b i t s a b i - m o d a l s e a s o n a l v a r i a t i o n . N e g a t i v e f e e d b a c k e f f e c t s i n t h e model w i l l t e n d t o i n c r e a s e t h e p r e d i c t e d number of c o l l e c t o r o p e r a t i n g h o u r s above t h a t a c t u a l l y measured d u r i n g any e x t e n d e d p e r i o d f o r wh i c h t h e s i m u l a t e d s t o r a g e t a n k t e m p e r a t u r e i s t o o low. S i n c e t h e month of June has t h e l a r g e s t n e g a t i v e t a n k t e m p e r a t u r e b i a s , one would e x p e c t i t t o have a f a i r l y l a r g e pump hour d e p a r t u r e e r r o r . The f a c t t h a t i t does n o t , i n d i c a t e s t h a t t h e c o n j e c t u r e d i n a c c u r a c y i n t h e c o l l e c t o r model i s s e a s o n a l l y d e p e n d e n t - w h a t e v e r i t s s p e c i f i c c a u s e ( s ) . 5. S o l a r F r a c t i o n The p r e d i c t e d s o l a r f r a c t i o n f o r t h e one y e a r s i m u l a t i o n p e r i o d - b a s e d on t h e measured q u a n t i t y o f t o t a l h e a t d e l i v e r e d - was 0.402. T h i s compares w i t h a measured s o l a r f r a c t i o n f o r t h e same p e r i o d o f 0.478, r e p r e s e n t i n g a r e l a t i v e d e v i a t i o n o f -15.8%. Thus, t h e n e g a t i v e b i a s i n t h e model r e s t r i c t s i t s a b i l i t y t o p r e d i c t t h e s y s t e m ' s l o n g t e r m t h e r m a l p e r f o r m a n c e . C o n f i d e n c e i n t h e model t h e r e f o r e a w a i t s i d e n t i f i c a t i o n and c o r r e c t i o n o f i t s s o u r c e o f i n a c c u r a c y . 187 T a b l e 6.3 Summary of U s e r - E f f e c t E r r o r s P a r a m e t e r / V a r i a b l e L i k l i h o o d o f U s e r - E f f e c t E r r o r T D I F 1 TDIF2 AREAC CMC VOLS FRTA FRUL UAS TBSM TMNF5 HT TA TM FLOW a b s e n t s m a l l n e g l i g i b l e v e r y s m a l l v e r y s m a l l l a r g e moderate l a r g e s m a l l s m a l l l a r g e m oderate v e r y s m a l l n e g l i g i b l e TABLE 6.4 SIMULATION RESULTS FOR A ONE YEAR PERIOD MONTH OHT (MO) QCSS (MJ) OSTOR (MJ) QSENV (MJ) QSDHW (MJ) QDHW (MJ) FLOW (m' ) PUMP (HR) 1981 JUL 2889 . 159 106 1 . 104 17 .211 298 .051 745 . 839 1297 . 770 6 . 4490 133 . AUG 3512 . 562 1312 .268 -5 . 754 435 . 345 882 . 674 975 . 179 5 . 1359 167 . SEP 2496 .971 1022 . 509 -14. .938 280 .887 756 . 558 1257 . 531 6 . 4976 140. OCT 1512 .041 619 .429 -14. . 306 102 .625 531 . 108 1712 . 294 8 . 2876 92 . NOV 747 .429 290. .006 -6 . .080 12 . 159 283 .926 1631 . 231 8 . 2863 42 . DEC 468. .784 147 . 682 2 . 925. -41 . . 789 186 . 547 1623. .047 7 . 5670 30. 1982 JAN 352 .771 90. .961 1 . . 325 -70 .016 159 .652 1836 .689 8 .0577 20. FEB 937 . 114 372 . 559 1 1 . 217 -3 . .915 365 . 256 2018 . 512 9. , 1 173 59 . MAR 2391 . 230 910. 691 -10. 203 196 . 851 724 . 041 1533 . 108 7 . 3460 134 . APR 3013. .823 1250. 818 51 . 288 236 . 214 963 . ,314 1612 . 195 8 . 2348 168 . MAY 3063 . 766 1286 . 977 -12. 056 242 . 516 1056 . 515 1770. .664 9 , .4223 186 . JUN 2869. 981 1202 . 576 -3 . 212 235 . 730 970. .056 1695 . 930 9 . 1877 189 . YEAR 24255. 613 9567 . 566 17 . 416 1924 . 656 7625 . 477 18964. 137 93 . 5891 1360. CO CO NOMENCLATURE QHT - TOTAL SOLAR RADIATION INCIDENT ON COLLECTOR ARRAY QSDHW QCSS - SOLAR ENERGY COLLECTED AND TRANSFERRED TO STORAGE QDHW QSTOR - CHANGE IN HEAT CONTENT OF THE STORAGE TANK FLOW QSENV - STANDBY HEAT LOSS FROM THE STORAGE TANK PUMP - SOLAR HOT WATER HEAT - TOTAL (SOLAR AND AUXILIARY) HOT WATER HEA - VOLUME OF HOT WATER CONSUMED - NUMBER OF PUMP OPERATING HOURS 189 T a b l e 6.5 S t o r a g e Tank T e m p e r a t u r e E r r o r S t a t i s t i c s S i m u l a t i o n P e r i o d : June 1981 - J u l y 1982 A l l v a l u e s a r e i n d e g r e s s C e l c i u s Mean D a i l y T e m p e r a t u r e MBE RMSE Month M e a s u r e d P r e d i c t e d M i d Bot M i d Bot M i d Bot 1981 J u l 52.05 44.69 44. 1 6 -7.89 -0.53 8.12 2.48 Aug 63.93 55.56 57. 21 -6.73 1 .64 6.97 2.59 Sep 49.27 41 .67 44. 00 -5.26 2.34 5.53 3.46 Oct 32.09 26.68 26. 88 -5.21 0.20 5.63 1 .43 Nov 22.34 1 9.02 19. 07 -3.27 0.05 3.66 1.15 Dec 17.03 1 4.09 14. 62 -2.41 0.53 2.72 0.99 1 982 J a n 1 3.32 10.83 1 1 . 56 -1.76 0.73 2.05 1 .09 Feb 19.59 1 5.73 16. 38 -3.21 0.66 . 3.94 1 .44 Mar 38.43 32.77 32. 99 -5.44 0.21 5.91 2.19 Apr 44.73 38.05 37. 32 -7.42 -0.73 7.96 1 .30 May 46. 17 39.67 37. 90 -8.2 -1 .77 8.37 2.39 Jun 50.78 44. 1 7 40. 37 -10.4 -3.80 1 0.93 4.36 Y e a r 37.58 32.00 31.96 -5.62 -0.04 6.49 2.30 190 T a b l e 6.6 S o l a r Hot Water Heat E r r o r S t a t i s t i c s S i m u l a t i o n P e r i o d : June 1981 - J u l y 1982 Month Mean D a i l y QSDHW MBE RMSE Meas. P r e d . Abs. R e l Abs. R e l . (MJ/day) (MJ/day) (%) (MJ/day) (%) 1981 J u l 29.871 24.059 -5.812 -19. 5 6.323 21.2 Aug 32.703 28.473 -4.230 -12. 9 4.762 14.6 Sep 28.518 25.219 -3.299 -11. 6 3.826 13.4 Oct 20.843 17. 133 -3.710 -17. 8 4.347 20.9 Nov 1 1 . 389 9.464 -1.925 -16. 9 2.510 22.0 Dec 6.955 6.018 -0.937 -13. 5 1 .670 24.0 1 982 Ja n 5.470 5.150 -0.320 -5. 9 1 .387 25.4 Feb 14.241 13.045 -1.196 -8. 4 2.851 20.0 Mar 25.542 23.356 -2. 186 -8. 6 3.004 11.8 Apr 37.436 32.110 -5.326 -14. 2 6.438 17.2 May 41 .797 34.081 -7.716 -18. 5 8.316 19.9 Jun 42.735 32.335 -10.399 -24. 3 11.284 26.4 Y e a r 24.820 20.891 -3.929 -15.8 5.494 22.1 191 T a b l e 6.7 C o l l e c t o r O p e r a t i o n E r r o r S t a t i s t i c s S i m u l a t i o n P e r i o d : J u n e 1981 - J u l y 1982 No. of Pump O p e r a t i n g H o u r s D e p a r t u r e E r r o r Month M e a s u r e d P r e d i c t e d M o n t h l y C u m u l a t i v e I n d . Cumul. I n d . Cumul. Abs. R e l . Abs. R e l . ( H o u r s ) ( H o u r s ) ( H r s ) (%) ( H r s ) (%) 1981 J u l 114.5 114.5 1 33. 133. 18.5 1 6.2 18.5 16.2 Aug 1 42.0 256.5 1 67. 300. 25.0 17.6 43.5 17.0 Sep 99. 1 355.6 1 40. 440. 40. 9 41 .3 84.4 23.7 Oct 64.2 419.8 92. 532. 27.8 43.3 112.2 26.7 Nov 25.9 445.7 42. 574. 16.1 62.2 128.3 28.8 Dec 14.2 459.9 30. 604. 15.8 111.3 144. 1 31.3 1982 Ja n 7.1 467.0 20. 624. 12.9 181.7 1 57.0 33.6 Feb 33.0 500.0 59. 683. 26.0 78.8 183.0 36.6 Mar 94. 1 594. 1 1 34. 817. 39.9 42.4 222.9 37.5 Apr 1 49.4 743.5 168. 985. 18.6 12.4 241 .5 32.5 May 179.7 923.2 186. 1171. 6.3 3.5 247.8 26.8 Jun 190.5 1113.7 189. 1 360. -1.5 -0.8 246.3 22. 1 192 9 a LU CC I— <x cc LU a: LU o cc cc a • i—• CQ CC a _ J Q CQ a • i-t a a LU UJ (— cc <-> 73 s l-t • cc CL. M £ 1 T E H P E R H T U R E ( D E C C ) 3 S S3 3 9 9 # 2 a . a a « 9 • a R ' a s ( 3 " 0 3 0 ) 3HnibH3dU31 F i g u r e 6.1 Time S e r i e s P l o t o f P r e d i c t e d and Measured S t o r a g e Tank T e m p e r a t u r e s : (a) A u g u s t 1 - 15, 1982 ( D a i l y Pump O p e r a t i n g H o u r s a r e l i s t e d a c r o s s t o p) 193 o CO a M a U J cc ZD a U J a UJ I— • LU a. a a U J a; " a; U J L U as c a. TEHPERflTURE (DEC, C). 8 . 3 3 9 9 3 9 9 to •93Q) 3 a n i « y 3 d u 3 i F i g u r e 6.1 ( c o n t i n u e d ) Time S e r i e s P l o t o f P r e d i c t e d and Measured S t o r a g e Tank T e m p e r a t u r e s : (b) August 16 - 30, 1982 ( D a i l y Pump O p e r a t i n g H o u r s a r e l i s t e d a c r o s s t o p ) 194 ^ ! o LU a LU CC cc cc •z cc o CO • U J o Q a LU § a s CO LU CC CC ^ ^ CC _J . a Q 3 TEfiPERflTURE (DEC C) S 13 S 3 9 _ J I L_ L _ _ L H a s a -1 » ± 1 in CO •O) CO cc 00 LU CO to 3 9 3 S S (3 -33Q) 3 U r U B « 3 d U 3 1 F i g u r e 6.1 Time S e r i e s P l o t o f P r e d i c t e d and Measured S t o r a g e ( c o n t i n u e d ) Tank T e m p e r a t u r e s : (c) September 1 - 15, 1982 ( D a i l y Pump O p e r a t i n g Hours a r e l i s t e d a c r o s s top) 195 F i g u r e 6.1 ( c o n t i n u e d ) Time S e r i e s P l o t o f P r e d i c t e d and Measured S t o r a g e Tank T e m p e r a t u r e s : (d) September 16 - 30, 1982 ( D a i l y Pump O p e r a t i n g Hours a r e l i s t e d a c r o s s t o p ) SOLAR HOT UATER HEAT c M (0 ON w a o CO H« H-P> M H v$ 33 M 0 3 rt rt (D SI (TO Co H rt Co (0 M M CD W O (B i-h la rt •• M (D CL, 01 o ^ rt ID > CL C Ot) p> c a co a. rt (D vo Co 00 CO to C M n cv. 60 55 50-45-40H E 35-1 X 30 Q CO ° 25 20 15-10-5-MEflSURED PREDICTED "i 1 1 — i — i — i — i — i — r r — n — i — i — i — r - i — i i i — i — i — I I -i 1 — i — r il Ml lil in lit lil lil lil ii •' '•' '•' ••' '•' ••' '•' '•' '•' •'' 111 '"—u 60 55 •50 4S 40 X C 30 r25 y •20 •IS •JO •5 1 2 3 4 S 6 7 8 9 JO JJ 12 13 14 15 16 17 J8 19 20 21 22 23 24 25 26 21 2fl 2S 30 3J AUGUST 1982 •—N * i o H-o W o C rt H- fl> 3 C Ox (D • CU ro cn O o f» H" 03 M H M o 3 rt rt ro SI OP Co l-l rt p> ro M •1 S3 O pi rt »tJ ro cr o ^ rt n> w a. ro •O 0) rt 3 ro a S a- s ro ro 11 o> co c VO H co ro SOLAR HOT UflTER HEAT tlERSURED PREDICTED 60 55 50 45 40 B 35-I 30-3 X a CO Cr as 2D-15-10 5 • i l l — • i i i i i i i i i 1 r- ~i 1 i 1 1 1 r • '•' LU LU LU LU LU III III ! • ! III 111 I.I !• JJ U l " I I " " I U l I " i 60 55 50 45 40 O IS CO X C 1-30 25 <= 20 IS JO 5 I 2 3 4 S 6 7 8 9 10 11 12 13 14 15 16 11 18 19 20 21 22 23 24 25 26 21 20 23 30 SEPTflBER 1982 VO 198 MODEL SENSITIVITY TO TDIF2 o TS - ROSE l-C) • TS - MBE r a A PPHR - DEPARTURE ERROR 12) 1.00 0.75 0.5O TDIF2 CO 0.25 0 .00 F i g u r e 6.3 Model S e n s i t i v i t y t o a D e c r e a s e i n t h e D i f f e r e n t i a l C o n t r o l l e r T u r n ' O f f ' Set P o i n t ( E r r o r S t a t i s t i c s p l o t t e d i n c l u d e t h e RMSE and MBE f o r S t o r a g e Tank T e m p e r a t u r e ( m i d - h e i g h t ) and the C u m u l a t i v e D e p a r t u r e E r r o r f o r Pump O p e r a t i n g H o u r s ; A u g u s t - September, 1982) 199 MODEL SENSITIVITY TO AREAC a IS - RMSE !*CJ « 1 5 - MBE CC] & PPHR - DEPARTURE ERROR U) 4 -G 2 l -co ID CJ _J LU O CO UJ o LU • D -2 - 3 -•4--0- -o-h 20 15 10 o.o ^ i i i i r 0.5 1.0 1.5 PERCENT DEVIATION AREAC 2.0 25 5 2 -m n 0 z - 5 >* •10 - - 1 5 --20 -25 F i g u r e 6.4 M o d e l S e n s i t i v i t y t o an I n c r e a s e i n C o l l e c t o r A r e a ( E r r o r S t a t i s t i c s p l o t t e d i n c l u d e t h e RMSE and MBE f o r S t o r a g e Tank T e m p e r a t u r e ( m i d - h e i g h t ) and t h e C u m u l a t i v e D e p a r t u r e E r r o r f o r Pump O p e r a t i n g H o u r s ; A u g u s t - September,, 1982) 200 MODEL SENSITIVITY TO CttC a IS - RMSE VQ Q IS - MBE CCJ * PPHR - DEPARTURE EfiROH U J U 2 -1 -H o _J UJ 0 o LU -1 cr: co LU -3 --4 --Cr-CI. 1 1 1 1 1 :  -4. - 8 . -17. PERCENT DEVIATION -it. -20. 25 - 20 - J5 - JO n 0 2 --5 - -jo --15 --20 -25 CMC F i g u r e 6.5 M o d e l S e n s i t i v i t y t o a D e c r e a s e i n C o l l e c t o r F l u i d C a p a c i t a n c e ( E r r o r S t a t i s t i c s p l o t t e d i n c l u d e t h e RMSE and MBE f o r S t o r a g e Tank T e m p e r a t u r e ( m i d - h e i g h t ) and t h e C u m u l a t i v e D e p a r t u r e E r r o r f o r Pump O p e r a t i n g H o u r s ; A u g u s t - S e p t e m b e r , 1982) MODEL SENSITIVITY TO VOLS a TS - RflSE I'Cl » TS - m e 1X1 a PPHR - DEPARTURE ERROR CX) Figure 6.6 Model S e n s i t i v i t y to Changes i n Storage Volume (Error S t a t i s t i c s p l o t t e d include the RMSE and MBE f o r Storage Tank Temperature (mid-height) and the Cumulative Departure E r r o r f o r Pump Operating Hours; August - September, 1982) 2 0 2 HODEL SENSITIVITY TO Ff^"fJ e a TS - RflSE i*C) « IS - MBE I'CJ A PPHR - DEPARTURE ERROR (%) 3 -_J UJ CO UJ LU cr o UJ Q -1 --5 i r _ — A A — i r 0.725 0.750 1 1 0.715 FRTA — i T 0.800 0.B25 25 h 20 15 10 h 5 ^ m ro o rn 0 -z -5 -10 15 — 2 0 -25 F i g u r e 6.7 Model S e n s i t i v i t y to an I n c r e a s e i n t h e C o l l e c t o r Z e r o - P o i n t E f f i c i e n c y P a r a m e t e r ( E r r o r S t a t i s t i c s p l o t t e d i n c l u d e t h e RMSE and MBE f o r S t o r a g e Tank T e m p e r a t u r e ( m i d - h e i g h t ) and the C u m u l a t i v e D e p a r t u r e E r r o r f o r Pump O p e r a t i n g H o u r s ; A u g u s t - September, 1982) 203 MODEL SENSITIVITY TO FRUL o TS - RUSE f'CJ « TS - MBE CCJ A PPHR - DEPARTURE ERROR CO F i g u r e 6.8 Model S e n s i t i v i t y t o a D e c r e a s e i n t h e C o l l e c t o r S l o p e E f f i c i e n c y . P a r a m e t e r ( E r r o r S t a t i s t i c s p l o t t e d i n c l u d e t h e RMSE and MBE f o r S t o r a g e Tank T e m p e r a t u r e ( m i d - h e i g h t ) and t h e C u m u l a t i v e D e p a r t u r e E r r o r f o r Pump O p e r a t i n g H o u r s ; A u g u s t - September, 1982) 204 MODEL SENSITIVITY TO UAS O T S - R M S E I 'CJ « T S - J I B E (°CJ A P P H R - j D E P H R T U R E E R R O R (X) 16.0 12.0 8.0 4.0 UflS KJ/HR-C 0.0 F i g u r e 6.9 Model S e n s i t i v i t y t o a D e c r e a s e i n the S t o r a g e Tank Heat L o s s C o e f f i c i e n t ( E r r o r S t a t i s t i c s p l o t t e d i n c l u d e the RMSE and MBE f o r S t o r a g e Tank T e m p e r a t u r e ( m i d - h e i g h t ) and the C u m u l a t i v e D e p a r t u r e E r r o r f o r Pump O p e r a t i n g H o u r s ; August - September, 1982) 2 05 MODEL SENSITIVITY TO TBSM e> TS - RMSE 1'CJ • TS - flBE ra A PPHR - DEPARTURE ERROR 00 i r 4-G 2 -1 -CO ID M U UJ 0 • o CO ui -1-cc CD U J o _2-- 3 --4 — -5-O.O T i r fl.S J.O 1.5 DEGREES-C DEVIATION TBSM 2.0 2.5 25 - 20 - 15 10 h 5 ~J> m o m 0 z --5 •-10 — 1 5 — 2 0 -25 F i g u r e 6.10 Model S e n s i t i v i t y to an I n c r e a s e i n Basement A i r T e m p e r a t u r e ( E r r o r S t a t i s t i c s p l o t t e d i n c l u d e the RMSE and MBE f o r S t o r a g e Tank T e m p e r a t u r e ( m i d - h e i g h t ) and t h e C u m u l a t i v e D e p a r t u r e E r r o r f o r Pump O p e r a t i n g H o u r s ; August - September, 1982) 206 MODEL SENSITIVITY TO HT a TS - RnsE CO o IS - JIBE I'C) a PPHR - DEPARTURE ERROR U) F i g u r e 6.11 Model S e n s i t i v i t y to an I n c r e a s e i n S o l a r R a d i a t i o n I n c i d e n t on t h e C o l l e c t o r A r r a y ( E r r o r S t a t i s t i c s p l o t t e d i n c l u d e t h e RMSE and MBE f o r S t o r a g e Tank T e m p e r a t u r e ( m i d - h e i g h t ) and the C u m u l a t i v e D e p a r t u r e E r r o r f o r Pump O p e r a t i n g H o u r s ; August - September, 1982) 207 Figure 6 . 12 Hemispherical Sky View from Centre of Collector Array 208 MODEL SENSITIVITY TO TP ca TS - RtlSE fCJ « TS - MBE fCJ A PPHR - DEPARTURE ERROR CS) O.O 1.0 2.0 3.0 4.0 5.0 DEGREES-C DEVIATION F i g u r e 6.13 Model S e n s i t i v i t y t o an I n c r e a s e i n Ambient A i r T e m p e r a t u r e ( E r r o r S t a t i s t i c s p l o t t e d i n c l u d e the RMSE and MBE f o r S t o r a g e Tank T e m p e r a t u r e ( m i d - h e i g h t ) and t h e C u m u l a t i v e D e p a r t u r e E r r o r f o r Pump O p e r a t i n g H o u r s ; August - September, 1982) 209 MODEL SENSITIVITY TO TM o TS - WISE ra • TS - MBE rCJ A PPHR - DEPARTURE ERROR (U 4 -3-i 1 1 1 — i 1 1 1 1 r 25 20 J5 O 2 - - JO 3 ' H M O _J LU 0 to LU . LU "J GC LU Q - 2 - 3 -- 4 -- 5 A — D.O 0.5 n 1 r~ 1.0 <>TH DEVIATION 1^ J .5 i r 2.0 5 "3 53 o _ m 0 2 —5 v« — J O - J 5 I—20 - 2 5 F i g u r e 6.14 Model S e n s i t i v i t y t o an I n c r e a s e i n Incoming C o l d Water T e m p e r a t u r e ( E r r o r S t a t i s t i c s p l o t t e d i n c l u d e the RMSE and MBE f o r S t o a r g e Tank T e m p e r a t u r e ( m i d - h e i g h t ) and the C u m u l a t i v e D e p a r t u r e E r r o r f o r Pump O p e r a t i n g H o u r s ; August - September, 1982) 210 MODEL SENSITIVITY TO FLOW a TS - RUSE r c l « TS - MBE l-CJ a PPHR - DEPARTURE ERROR (X,) i i T i r i r 4 -3 -G 2 1-co z> o _1 UJ o CO LU - J . " CC CD LU o _2--3--4-0.0 -0.5 -1.0 -1.5 PERCENT DEVIATION FLOW -2.0 i r~ -2.5 25 h 20 JS 10 m TO r> 0 Z —) — 5 5 -10 --15 --20 -25 F i g u r e 6.15 Model S e n s i t i v i t y t o a D e c r e a s e i n t h e Volume of Hot Water Drawn ( E r r o r S t a t i s t i c s p l o t t e d i n c l u d e t h e RMSE and MBE f o r S t o r a g e Tank T e m p e r a t u r e ( m i d - h e i g h t ) and the C u m u l a t i v e D e p a r t u r e E r r o r f o r Pump O p e r a t i n g H o u r s ; August - September, 1982) 211 Figure 6.16 General Strategy for V a l i d a t i n g the Simulation Model St a r t Monitoring Program Measured System Performance Manufacturer's S p e c i f i c a t i o n s Independently performed t e s t s On-site system measurements Input values f o r System Parameters & V a r i a b l e s Simulation Model Pr e d i c t e d System Performance Comparison of Results End Yes Results Acceptable ? No I d e n t i f y i n g Source of E r r o r i n the model z U s e r - E f f e c t E r r o r X I n t r i n s i c E r r o r Re-evaluation of input data Model M o d i f i c a t i o n 212 PREDICTED MONTHLY THERMAL ENERGY QUANTITIES QCSS — o — QSDHW—*— QSENV--*-- QSTOR- -* -JUL RUG SEP OCT NOV DEC JflN FEB flfifl RPR HflY JUN 138] 1382. F i g u r e 6.17 P r e d i c t e d M o n t h l y T h e r m a l E n e r g y Q u a n t i t i e s f o r t h e One Y e a r S i m u l a t i o n P e r i o d : J u l y 1981 - June 1982 STORAGE TANK TEMPERATURE JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY JUN 1981 1982 F i g u r e 6.18 Time S e r i e s P l o t of P r e d i c t e d and Measured S t o r a g e Tank T e m p e r a t u r e s f o r the One Year S i m u l a t i o n P e r i o d 214 F i g u r e 6.19 STORAGE TANK TEMPERATURE ERROR STATISTICS ROOT MEAN SQUARE ERROR --ID--niD-HEICnT --+--BOTTOM flEAN BIAS ERROR I I I I I I I I I I 1 JUL RUC SEP OCT NOV DEC JfiN FEB MflR RPR rW JUN 1381 1982 215 riONTHLY SQLRR HOT WTER rlERT "3 1.4" 1.3 -1.2 -1.1 -1.0 -O.J s £ -o.JH > GJ O.T H S O.-E cc o CO 0.4 0.3 -0.7 -0.1 0.0 MEASURED PREDICTED "1 r T T i r 1-4 h l - 3 1--2 -1-1 -1-0 0.3 co D 3 r-0.8 g C3 r-O.T m M 0.€ I rn o -0.5 ^ CD -0.+ -O.J -0.-2 -0.1 0.0 JUL PUG SEP OCT ND"V DEC JRN FEB mR flPfl HAr" JUN JJfll 1382 F i g u r e 6.20 M o n t h l y I n t e g r a l s of P r e d i c t e d and Measured S o l a r Hot Water Heat f o r t h e One Year S i m u l a t i o n P e r i o d 216 F i g u r e 6.21 SOLAR HOT WATER HEAT ERBOR STATISTICS ROOT MEAN SQUARE ERROR —CD—F&SQ LITJ E --+--RELATIVE JIEAN BIAS ERROR —A—ABSOLUTE —X~RELATIVE i 1 1 1 1 1 1 1 1 r i i i i i i i i i i i JUL RUG SEP OCT NOV DEC JAN FEB MAR RPR MAY JUN 1381 1382 217 cc CC o cc a: LU LU tx: r-cr: ex CL LU Q Figure 6.22 COLLECTOR OPERATION ERROR STATISTICS PUflP HOUR DEPARTURE ERROR O FB50LWE - HOURS + RELRTJVE - PERCENT JUL RU6 SEP OCT NOV DEC 1381 OflN FEB m n RPR 1382 rWY JUN 218 CHAPTER 7 CONCLUSIONS T h i s f i n a l c h a p t e r p r e s e n t s a c o n c l u d i n g s t a t e m e n t on t h e p r o j e c t ' s major f i n d i n g s . I t i s d i v i d e d i n t o t h r e e s e c t i o n s . The f i r s t s e c t i o n r e c a p i t u l a t e s t h e t h e r m a l p e r f o r m a n c e o f t h e s y s t e m , t h e s e c o n d summarizes t h e model v a l i d a t i o n r e s u l t s , and t h e t h i r d l i s t s r e c o m medations f o r f u r t h e r r e s e a r c h . A. System T h e r m a l P e r f o r m a n c e and O p e r a t i n g C h a r a c t e r i s t i c s The t h e r m a l p e r f o r m a n c e of t h e SDHW h e a t i n g s y s t e m was c h a r a c t e r i z e d by l a r g e d i u r n a l , d a y - t o - d a y , and s e a s o n a l v a r i a b i l i t y . T h i s was a d i r e c t r e s u l t of t h e h i g h l y v a r i a b l e c o m b i n a t i o n o f l o a d and m e t e o r o l o g i c a l c o n d i t i o n s imposed on t h e s y s t e m . The l i m i t e d t h e r m a l s t o r a g e c a p a b i l i t y of t h e s y s t e m a c t e d o n l y a s a s h o r t t e r m b u f f e r . Thus t h e s y s t e m a l t e r n a t e d between p e r i o d s ( h o u r s - d a y s ) of h i g h and low s o l a r e n e r g y c o n t r i b u t i o n t o t h e h o t water h e a t i n g l o a d , as m o d i f i e d by t h e s e a s o n . D u r i n g t h e s p r i n g and summer months, A p r i l t h r o u g h September, s o l a r e n e r g y s u p p l i e d between 56 and 104 p e r c e n t o f t h e u s e r s ' h o t water h e a t i n g demand. In a d d i t i o n , t h e s y s t e m d e m o n s t r a t e d t h a t i t was c a p a b l e of u t i l i z i n g up t o 45 p e r c e n t of t h e a v a i l a b l e s o l a r e n e r g y a t t h i s t i m e o f y e a r , d e p e n d i n g on t h e volume o f h o t water consumed. In o r d e r t o t r a n s f e r t h e u s e f u l s o l a r e n e r g y g a i n s t o t h e s t o r a g e t a n k , t h e s y s t e m r e q u i r e d an i n p u t of e l e c t r i c a l e n e r g y e q u i v a l e n t t o a p p r o x i m a t e l y 5 t o 6 p e r c e n t o f t h e amount o f s o l a r h e a t d e l i v e r e d . R e s u l t i n g f u e l e n e r g y s a v i n g s v a r i e d between 60 219 and 130 p e r c e n t of m o n t h l y a u x i l i a r y e n e r g y c o n s u m p t i o n . C o n t i n u o u s p i l o t l i g h t o p e r a t i o n p r e c l u d e d t h e l a t t e r q u a n t i t y f r o m a p p r o a c h i n g z e r o d u r i n g p e r i o d s of abundant s o l a r e n e r g y a v a i l a b i l i t y . F o r one p a r t i c u l a r month, i n w h i c h t h e r e was an o v e r - s u p p l y of s o l a r e n e r g y r e l a t i v e t o t h e hot w a t e r h e a t i n g l o a d , t h e a u x i l i a r y tank e f f e c t i v e l y a c t e d as a h e a t s i n k s i n c e more h e a t was l o s t t o t h e s u r r o u n d i n g basement a i r t h a n was g a i n e d from c o m b u s t i o n of f u e l . The e f f i c i e n c y of t h e a u x i l i a r y t a n k i t s e l f v a r i e d as a f u n c t i o n of f u e l c o n s u m p t i o n ( i e . r e l a t i v e w e i g h t i n g o f p i l o t l i g h t l o s s e s ) ; when o p e r a t e d a l o n e under t y p i c a l l o a d c o n d i t i o n s , i t y i e l d e d a maximum e f f i c i e n c y of 54 p e r c e n t . D u r i n g t h e f a l l and w i n t e r months, O c t o b e r t h r o u g h March, t h e s o l a r p e r f o r m a n c e of t h e s y s t e m was s u b s t a n t i a l l y r e d u c e d due t o lower amounts o f s o l a r r a d i a t i o n i n c i d e n t on t h e c o l l e c t o r a r r a y . M o n t h l y s o l a r f r a c t i o n s d e c r e a s e d t o between 0.13 and 0.52; t h e number of pump o p e r a t i n g h o u r s and t h e amount o f c o n v e n t i o n a l e n e r g y s a v e d were a l s o much l o w e r . In a d d i t i o n , t h e s t o r a g e t a n k t e m p e r a t u r e s f l u c t u a t e d w i t h i n a much n a r r o w e r r a n g e - b o t h on a d i u r n a l and a d a y - t o - d a y b a s i s . A p r o b l e m e n c o u n t e r e d i n e v a l u a t i n g t h e s y s t e m ' s t h e r m a l p e r f o r m a n c e d u r i n g t h i s p a r t o f t h e y e a r was t h e e x i s t e n c e o f s t a n d b y h e a t g a i n , s u c h t h a t a p o r t i o n of t h e ' s o l a r h e a t d e l i v e r e d ' was i n e f f e c t d e r i v e d f r o m t h e s u r r o u n d i n g basement a i r and n o t from s o l a r e n e r g y c o l l e c t i o n . N e g a t i v e t a n k - t o - a i r t e m p e r a t u r e g r a d i e n t s a s s o c i a t e d w i t h s t a n d b y h e a t g a i n were t h e r e s u l t o f c o n t i n u e d h e a t w i t h d r a w a l from t h e s t o r a g e tank by t h e i n c o m i n g c o l d w ater d u r i n g p e r i o d s o f low and z e r o s o l a r 220 e n e r g y i n p u t . T h e s e p e r i o d s were a f a i r l y f r e q u e n t o c c u r r e n c e d u r i n g t h e l a t e f a l l and e a r l y w i n t e r months. The l a r g e t e m p o r a l v a r i a b i l i t y i n t h e s y s t e m ' s t h e r m a l p e r f o r m a n c e was a s s o c i a t e d w i t h h i g h l y v a r i a b l e t h e r m a l c o n d i t i o n s w i t h i n t h e s t o r a g e t a n k . D i u r n a l f l u c t u a t i o n s i n s t o r a g e t a n k t e m p e r a t u r e were c a p a b l e of e x c e e d i n g 30 d e g r e e s C when t h e r e was l a r g e s o l a r e n e r g y i n p u t and h e a t w i t h d r a w a l . When s o l a r e n e r g y a v a i l a b i l i t y was low, t a n k t e m p e r a t u r e s r e m a i n e d d e p r e s s e d and r e l a t i v e l y c o n s t a n t . Maximum s t o r a g e t a n k t e m p e r a t u r e s r e c o r d e d d u r i n g t h e m o n i t o r i n g p e r i o d r e a c h e d 86°C, w h i l e minimum t e m p e r a t u r e s were as low as 12°C. F u r t h e r m o r e , s i n c e h e a t i s p r e f e r e n t i a l l y w i t h d r a w n from t h e l o w e r r e g i o n of t h e s t o r a g e t a n k , t h e r m a l s t r a t i f i c a t i o n was a p r e v a l e n t and p e r s i s t e n t f e a t u r e , o f t e n b ecoming v e r y w e l l d e v e l o p e d . L a r g e f l o w s o f water t h r o u g h t h e h e a t e x c h a n g e r were c a p a b l e o f p r o d u c i n g a 20 d e g r e e C t h e r m o c l i n e between t h e t a n k b o t t o m and m i d - h e i g h t measurement l e v e l s i n t h e a b s e n c e o f pump o p e r a t i o n . Whenever t h e c i r c u l a t i o n pump d i d o p e r a t e , an i s o t h e r m a l c o n d i t i o n was e s t a b l i s h e d and m a i n t a i n e d i n t h e s t o r a g e t a n k . T e m p e r a t u r e s measured i n t h e water s u p p l y l i n e a l s o e x h i b i t e d t e m p o r a l v a r i a b i l i t y - p a r t i c u l a r l y on a d i u r n a l b a s i s . The s o l a r h e a t e d water t e m p e r a t u r e was t h e most v a r i a b l e of t h e t h r e e , b e i n g s t r o n g l y d e p e n d e n t on t h e r m a l c o n d i t i o n s i n t h e s t o r a g e t a n k . I t was most f r e q u e n t l y e q u a l t o o r s l i g h t l y warmer t h a n t h e t a n k m i d - h e i g h t t e m p e r a t u r e . V a r i a b i l i t y i n t h e i n c o m i n g c o l d w ater t e m p e r a t u r e was l a r g e l y a f u n c t i o n of f l o w c o n d i t i o n s , w h i l e a d d i t i o n a l v a r i a b i l i t y i n 221 t h e h o t water d e l i v e r y t e m p e r a t u r e r e s u l t e d f r o m t h e i n a b i l i t y o f t h e a u x i l i a r y tank t o m a i n t a i n a c o n s t a n t water t e m p e r a t u r e . Flow c o n d i t i o n s i n d i r e c t l y a f f e c t e d t h e water s u p p l y l i n e t e m p e r a t u r e s s i n c e t h e y d e t e r m i n e d t h e r e s i d e n c y t i m e o f t h e w a t e r i n t h e i n l e t / o u t l e t p i p e s , h e a t e x c h a n g e r and a u x i l i a r y t a n k . S t a g n a t i o n of water i n t h e i n l e t / o u t l e t p i p e s was a s s o c i a t e d w i t h a t e n d e n c y f o r t h e water t o e q u i l i b r a t e i n t e m p e r a t u r e w i t h t h e s u r r o u n d i n g basement a i r . S u b s e q u e n t s m a l l draws o f hot water r e s u l t e d i n water s u p p l y l i n e t e m p e r a t u r e s t h a t were e i t h e r e l e v a t e d o r d e p r e s s e d , d e p e n d i n g on whether t h e water was s o u r c e d above o r below basement a i r t e m p e r a t u r e . W i t h l a r g e h o t water draws, t h e water s u p p l y l i n e t e m p e r a t u r e s more c l o s e l y r e f l e c t e d t h e r m a l c o n d i t i o n s e x i s t i n g w i t h i n the s t o r a g e / a u x i l i a r y t a n k s and t h e l o c a l m a i n s . The t h e r m a l p e r f o r m a n c e r e s u l t s o b t a i n e d f o r t h e s y s t e m under i n v e s t i g a t i o n were d i r e c t l y d e p e n d e n t upon t h e s p e c i f i c l o a d and m e t e o r o l o g i c a l c o n d i t i o n s e x p e r i e n c e d d u r i n g t h e m o n i t o r i n g p e r i o d . T h i s makes i t d i f f i c u l t t o compare them a g a i n s t r e s u l t s r e p o r t e d i n t h e l i t e r a t u r e f o r o t h e r SDHW h e a t i n g s y s t e m s . F u r t h e r m o r e , t h e t h e r m a l p e r f o r m a n c e o f t h e s y s t e m was s i g n i f i c a n t l y i n f l u e n c e d by i t s p a r t i c u l a r c o n f i g u r a t i o n , component t y p e s , c o n t r o l s e t t i n g s , c o l l e c t o r e x p o s u r e and i n s t a l l a t i o n l a y o u t . Thus t h e r e p r e s e n t a t i v e n e s s o f t h e v a l u e s measured i s l i m i t e d , even i f a p p l i e d t o o t h e r s y s t e m s h a v i n g i d e n t i c a l d e s i g n and s i m i l a r o p e r a t i n g c o n d i t i o n s . C o r r e s p o n d i n g l y , t h e r e s u l t s o b t a i n e d c a n n o t be u s e d as a b a s i s f o r g e n e r a l i z i n g t h e t h e r m a l p e r f o r m a n c e o f t h e s y s t e m d e s i g n . 222 However, t h e o v e r a l l o p e r a t i n g c h a r a c t e r i s t i c s and p e r f o r m a n c e c a p a b i l i t i e s o f t h e s y s t e m , as e v a l u a t e d o v e r t h e n i n e t e e n month m o n i t o r i n g p e r i o d , can be u s e d as a r e f e r e n c e i n d e v e l o p i n g an i m p r o v e d s y s t e m d e s i g n . B. M odel V a l i d a t i o n R e s u l t s C o m p a r i s o n o f model p r e d i c t i o n s a g a i n s t a c t u a l s y s t e m measurements l e a d t o t h r e e major c o n c l u s i o n s c o n c e r n i n g t h e s i m u l a t i o n model and t h e v a l i d a t i o n p r o c e d u r e . F i r s t l y , t h e s i m u l a t i o n model i s a b l e t o c o n s i s t e n t l y t r a c k t h e r m a l c o n d i t i o n s w i t h i n t h e a c t u a l s t o r a g e t a n k . However, i t i s u n a b l e t o c o n t i n u o u s l y r e p l i c a t e t e m p e r a t u r e s a t any one l e v e l i n t h e t a n k s i n c e i t assumes f u l l y mixed and i s o t h e r m a l c o n d i t i o n s a t a l l t i m e s whereas t h e a c t u a l s t o r a g e t a n k e x p e r i e n c e s f r e q u e n t and p r o n o u n c e d t h e r m a l s t r a t i f i c a t i o n . F u r t h e r m o r e , t h e h o u r l y d i s c r e t i z a t i o n i n h e r e n t i n t h e s i m u l a t i o n model does c a u s e t e m p o r a l d e v i a t i o n s t o o c c u r w i t h r e s p e c t t o c o l l e c t o r o p e r a t i o n , e s p e c i a l l y d u r i n g p e r i o d s o f b r i e f o r f l u c t u a t i n g s o l a r e n e r g y c o l l e c t i o n . N e v e r t h e l e s s , i t may be s t a t e d t h a t t h e m o d e l ' s component a l g r o r i t h m s do i n t e r a c t p r o p e r l y and t h a t t h e model i s f r e e of any g r o s s e r r o r s . S e c o n d l y , t h e s i m u l a t i o n model e x h i b i t e d a n e g a t i v e b i a s l i m i t i n g i t s a b i l i l t y t o p r e d i c t t h e s y s t e m ' s l o n g t e r m t h e r m a l p e r f o r m a n c e . F o r t h e i n i t i a l two month t e s t p e r i o d , t h e p r e d i c t e d s t o r a g e tank t e m p e r a t u r e was on a v e r a g e 2.16 and 2.49 d e g r e e s C l e s s t h a n t h a t m e asured a t t h e t a n k b o t t o m and m i d - h e i g h t l e v e l s r e s p e c t i v e l y (when compared under i s o t h e r m a l 223 c o n d i t i o n s ) . F o r t h e y e a r l o n g s i m u l a t i o n p e r i o d , t h e model s y s t e m a t i c a l l y u n d e r - e s t i m a t e d t h e m o n t h l y v a l u e s o f s o l a r hot w a t e r h e a t by -6 t o -24 p e r c e n t d e p e n d i n g on t h e t i m e of y e a r . T h i s r e s u l t e d i n t h e p r e d i c t e d a n n u a l s o l a r f r a c t i o n d e v i a t i n g by -15.8 p e r c e n t ; i e . 0.402 v e r s u s a measured v a l u e o f 0.478. F u r t h e r m o r e , s e a s o n a l v a r i a t i o n i n t h e m a g n i t u d e of t h e s t o r a g e t a n k t e m p e r a t u r e d e v i a t i o n s s u g g e s t e d t h a t t h e p r e d i c t e d v a l u e s of s o l a r e n e r g y i n p u t were a l s o u n d e r - e s t i m a t e d . In c o n t r a s t , n e g a t i v e f e e d b a c k e f f e c t s i n t h e model c a u s e d i t t o o v e r - e s t i m a t e t h e m o n t h l y number o f c o l l e c t o r o p e r a t i n g h o u r s by up t o +180 p e r c e n t ; when a c c u m u l a t e d o v e r t h e y e a r , t h e d e v i a t i o n was +22 p e r c e n t . T h i r d y , i d e n t i f i c a t i o n of t h e c a u s e ( s ) of t h e model b i a s was h i n d e r e d by l a c k o f s u f f i c i e n t m o n i t o r i n g d a t a . In p a r t i c u l a r , u n a v a i l a b i l i t y o f measured water f l o w and i n l e t / o u t l e t t e m p e r a t u r e s i n t h e c o l l e c t o r l o o p p r e c l u d e d d i r e c t c o m p a r i s o n of t h e e n e r g y i n p u t t e r m f o r t h e s t o r a g e t a n k . G i v e n t h a t u s e r - e f f e c t e r r o r s were a p o t e n t i a l s o u r c e o f model b i a s , an a n a l y s i s was u n d e r t a k e n t o a s s e s s t h e m odel's s e n s i t i v i t y t o v a r i a t i o n s i n t h e i n p u t d a t a . R e s u l t s i n d i c a t e d t h a t t h e s o l a r r a d i a t i o n and a m bient a i r t e m p e r a t u r e v a r i a b l e s t o g e t h e r w i t h t h e c o l l e c t o r e f f i c i e n c y p a r a m e t e r s were t h e most l i k e l y s o u r c e s o f u s e r - e f f e c t e r r o r s . A c c u r a c y i n model p r e d i c t i o n s was v e r y s e n s i t i v e t o t h e i r i n p u t v a l u e s . M o r e o v e r , t h e s e t e r m s were a s s o c i a t e d w i t h l a r g e s a m p l i n g e r r o r . O n l y f u r t h e r t e s t i n g and e v a l u a t i o n of t h e s i m u l a t i o n m o d e l, u s i n g more r i g o r o u s and d e t a i l e d measurement d a t a , can p o s i t i v e l y i d e n t i f y t h e s o u r c e o f t h e model b i a s . 224 The p r e s e n t model v a l i d a t i o n r e s u l t s were p r e c e e d e d by an e a r l i e r s t u d y e x a m i n i n g t h e WATSUN DHWA s i m u l a t i o n model ( S i b b i t t and W y l i e , 1982). In t h e e a r l i e r s t u d y , p r e d i c t e d and measured t h e r m a l p e r f o r m a n c e r e s u l t s f o r a s o l a r h o t water h e a t i n g s y s t e m i n s t a l l e d i n a c o m m e r c i a l l a u n d r y f a c i l t i y were compared f o r p e r i o d s r a n g i n g from two weeks t o f i v e months. U s i n g s i t e - m e a s u r e d l o a d and m e t e o r o l o g i c a l d a t a , WATSUN DHWA o v e r - e s t i m a t e d t h e amount of s o l a r h e a t d e l i v e r e d by 12% f o r t h e two week p e r i o d and by 14% f o r a t h r e e month p e r i o d . F u r t h e r m o r e , i t was r e p o r t e d t h a t t h e a c c u r a c y o f t h e s i m u l a t i o n r e s u l t s were v e r y s e n s i t i v e t o t h e a c c u r a c y o f t h e i n p u t d a t a ; l a r g e d i s c r e p a n c i e s between model and measurement o c c u r r e d when t h e c o l l e c t o r e f f i c i e n c y p a r a m e t e r s , s t o r a g e t a n k h e a t l o s s c o e f f i c i e n t , and h e a t e x c h a n g e r e f f e c t i v e n e s s were i n c o r r e c t l y s p e c i f i e d . The p r e s e n t s t u d y r e i t e r a t e s t h e s e f i n d i n g s . M o r e o v e r , i t i n d i c a t e s t o p o t e n t i a l u s e r s t h e d e g r e e o f a c c u r a c y r e q u i r e d f o r e a c h of t h e d i f f e r e n t s y s t e m p a r a m e t e r s and v a r i a b l e s i n o r d e r f o r r e a s o n a b l e s i m u l a t i o n r e s u l t s t o be o b t a i n e d . C. Recommendations f o r F u r t h e r R e s e a r c h G i v e n t h a t more r i g o r o u s and d e t a i l e d measurement d a t a a r e r e q u i r e d i n o r d e r t o p o s i t i v e l y i d e n t i f y t h e s o u r c e o f t h e model b i a s ( S e c t i o n B ) , t h e f o l l o w i n g r e commendations a r e made w i t h r e s p e c t t o f u r t h e r r e s e a r c h . 1. I n s t a l l a t i o n of A d d i t i o n a l I n s t r u m e n t a t i o n I n s t r u m e n t a t i o n r e q u i r e d t o up g r a d e m o n i t o r i n g o f t h e SDHW h e a t i n g s y s t e m t o IEA p r i m a r y s t a n d a r d s ( S t r e e d , 1979) i n c l u d e s 225 t h e i n s t a l l a t i o n of one f l o w meter and two t e m p e r a t u r e s e n s o r s i n t h e c o l l e c t o r l o o p . T h e s e s e n s o r s would e n a b l e t h e amount of s o l a r e n e r g y c o l l e c t e d and t r a n s f e r r e d t o s t o r a g e t o be e v a l u a t e d . A s e c o n d p y r a n o m e t e r and a m bient a i r t e m p e r a t u r e p r o b e ( p o s i t i o n e d above t h e c o l l e c t o r a r r a y on t h e r o o f ) s h o u l d a l s o be i n s t a l l e d i n o r d e r t o o b t a i n a s y n c h r o n o u s s e t o f d a t a w i t h w h i c h t o . a s s e s s t h e s p a t i a l s a m p l i n g e r r o r i n t h e m e t e o r o l o g i c a l v a r i a b l e s . S y s t e m m o n i t o r i n g s h o u l d t h e n be resumed f o r a p e r i o d of s i x t o t w e l v e months u s i n g t h e c u r r e n t d a t a l o g g i n g equipment and a r e c o r d i n g i n t e r v a l of one h o u r . A more f r e q u e n t r e c o r d i n g i n t e r v a l c o u l d be u s e d t o d e t e r m i n e s i t e - m e a s u r e d v a l u e s f o r t h e c o l l e c t o r e f f i c i e n c y p a r a m e t e r s d u r i n g s h o r t e x p e r i m e n t a l p e r i o d s . 2. S e c o n d Round of V a l i d a t i o n S i m u l a t i o n of t h e s y s t e m s h o u l d t h e n be r e p e a t e d u s i n g t h e newly o b t a i n e d s e t o f i n p u t v a l u e s , f o l l o w e d by a s t a t i s t i c a l c o m p a r i s o n between model p r e d i c t i o n s and a c t u a l s y s t e m measurements. The s y s t e m v a r i a b l e o f p r i m e i n t e r e s t w i l l be t h e s o l a r e n e r g y i n p u t t e r m f o r t h e s t o r a g e t a n k ; emphasis s h o u l d be p l a c e d i n d e t e r m i n i n g t h e m o d e l ' s a c c u r a c y i n p r e d i c t i n g t h i s v a r i a b l e . An a s s e s s m e n t s h o u l d a l s o be made t o d e t e r m i n e t h e e x t e n t o f u s e r - e f f e c t e r r o r s i n t h e i n p u t d a t a f o r t h e c o l l e c t o r m o d e l . T h i s would i n v o l v e p e r f o r m i n g s e v e r a l s i m u l a t i o n r u n s u s i n g b o t h s e t s o f s o l a r r a d i a t i o n and ambient a i r t e m p e r a t u r e d a t a . In a d d i t i o n , any d i f f e r e n c e s between t h e s i t e - m e a s u r e d and i n d e p e n d e n t l y r e p o r t e d (NRC t e s t f a c i l i t y ) v a l u e s f o r t h e c o l l e c t o r e f f i c i e n c y p a r a m e t e r s would need t o be a n a l y z e d i n o r d e r t o d e t e r m i n e t h e i r e f f e c t on model p r e d i c t i o n s . 226 FOOTNOTES 1 V a n c o u v e r has a west c o a s t m a r i t i m e t y p e c l i m a t e , w i t h p r e d o m i n a n t l y c l o u d y and o v e r c a s t s k i e s i n w i n t e r and r e l a t i v e l y c l e a r s k i e s i n summer. R a i n f a l l i s f r e q u e n t d u r i n g w i n t e r , but o n l y o c c a s i o n a l s n o w f a l l o c c u r s . T e m p e r a t u r e s a r e t y p i c a l l y m i l d i n summer and above f r e e z i n g i n w i n t e r . S u r f a c e winds i n t h e v i c i n i t y of t h e s o l a r c o l l e c t o r a r e g e n e r a l l y l i g h t and v a r i a b l e a t a l l t i m e s of t h e y e a r . 2 Heat l o s s terms a r e a l s o a s s o c i a t e d w i t h t h e s o l a r c o l l e c t o r and t h e p i p i n g . F o r t h e c o l l e c t o r , h e a t l o s s i s a c o m b i n a t i o n of back, edge, and t o p l o s s e s - t h e l a s t one b e i n g t h e most s i g n i f i c a n t ; f o r t h e p i p i n g , h e a t l o s s i s t h r o u g h t h e p o l y u r e t h a n e i n s u l a t i o n t o t h e s u r r o u n d i n g a i r . N e i t h e r of t h e s e two h e a t l o s s terms were e v a l u a t e d i n t h e p r e s e n t s t u d y . However, p i p e h e a t l o s s on t h e warm s i d e o f t h e water s u p p l y l i n e was i m p l i c i t l y i n c l u d e d i n t h e e n e r g y b a l a n c e of t h e a u x i l i a r y h o t w a t e r tan k s i n c e i t o c c u r r e d w i t h i n t h i s component's t h e r m a l b o u n d a r y . S i m i l a r l y , h e a t g a i n on t h e c o l d s i d e o f t h e water s u p p l y l i n e was i n d i r e c t l y added t o t h e e n e r g y b a l a n c e of t h e s o l a r s t o r a g e t a n k . T h e s e p i p e h e a t l o s s / g a i n s a r e a p p r o x i m a t e l y two o r d e r s of m a g n i t u d e s m a l l e r t h a n t h e q u a n t i t y of h e a t t r a n s f e r r e d w i t h i n t h e SDHW h e a t i n g s y s t e m . 3 The e n e r g y c o n s u m p t i o n of t h e d i f f e r e n t i a l c o n t r o l l e r - an o r d e r o f m a g n i t u d e l e s s t h a n QPUMP - i s i g n o r e d i n e v a l u a t i n g t h e s y s t e m o p e r a t i n g e n e r g y and t h e n e t e n e r g y s a v e d . 4 S i n c e t h e e f f i c i e n c i e s o f gas water h e a t e r s a s r e p o r t e d i n t h e l i t e r a t u r e ( e g . F a r a h a n , 1977) a r e b a s e d on measurements t a k e n under c o n t r o l l e d c o n d i t i o n s , t h e y u s u a l l y d i f f e r somewhat from e f f i c i e n c i e s measured f o r water h e a t e r s i n a c t u a l u s e . T h e r e f o r e , i n o r d e r t o e n s u r e t h a t an a c c u r a t e ACEF v a l u e was o b t a i n e d , an i n - s i t u e v a l u a t i o n of t h e a u x i l i a r y t a n k s t a n d - a l o n e e f f i c i e n c y was p e r f o r m e d ( C h a p t e r 4 ) . 5 R e f e r e n c e t e m p e r a t u r e s e n s o r s i n c l u d e d a F l u k e t h e r m i s t o r ( Model 8 0 T - 1 5 0 ) , an IMC t h e r m o c o u p l e , and a hand h e l d b i m e t a l l i c thermometer ( T r e r i c e C o . ) . 6 The basement a i r t e m p e r a t u r e was measured d u r i n g o n l y a l i m i t e d p a r t of t h e m o n i t o r i n g p e r i o d ( J u l y 30, 1982 - November 14, 1982) due t o equipment c o n s t r a i n t s . 7 D u r i n g i n i t i a l p r o c e s s i n g and a c c u m u l a t i o n of t h e d a t a v a l u e s , t h e l o g g e r h o l d s t h e numbers i n a 4 b y t e f l o a t i n g p o i n t f o r m a t h a v i n g an exp o n e n t r a n g e o f 10" 1 8 t o 1 0 + 1 8 , and a r e s o l u t i o n c a p a c i t y of 7 d e c i m a l d i g i t s . T h i s g r e a t l y e x c e e d s t h e r e s o l u t i o n c a p a b a l i t i e s o f t h e i n s t r u m e n t s e n s o r s and t h e A/D c o n v e r t e r . However, t h e l o g g e r ' s s t o r a g e memory i s l i m i t e d t o o n l y 16 b i t s (2 b y t e s ) p e r d a t a v a l u e . Of t h e s e 16 b i t s , two a r e u s e d a s d e c i m a l p o i n t l o c a t o r s and one i s u s e d a s a 227 p o l a r i t y i n d i c a t o r . In a d d i t i o n , a s p e c i a l b i t c o n f i g u r a t i o n i n t h e f i r s t b y t e i s u s e d a s a d a t a a r r a y m a r k e r . Hence, t h e l a r g e s t a b s o l u t e number t h a t c an be s t o r e d as a d a t a v a l u e i s 7395; t h e s m a l l e s t number i s 0.001. The d e c i m a l p o i n t s h i f t s whenever t h e 7935 d i g i t p a t t e r n i s e n c o u n t e r e d ; o n l y t h r e e d i g i t s a r e t h e n s t o r e d u n t i l t h e 999 d i g i t p a t t e r n i s p a s s e d . F o r example, a i r t e m p e r a t u r e c o u l d r i s e t o 7.935°C, s u d d e n l y change t o 7.94°C, and t h e n s t a y w i t h t h r e e d i g i t s u n t i l 9.99°C i s p a s s e d - a f t e r w h i c h p o i n t , 4 d i g i t s w ould a g a i n be s t o r e d . The t e m p e r a t u r e s e n s o r , however, m i g h t o n l y be a c c u r a t e t o 2 s i g n i f i c a n t f i g u r e s ( i e . 7 . 9 ° C ) . T h e r e f o r e , t h e l o g g e r d a t a must be i n t e r p r e t t e d w i t h c a r e . 8 The maximum volume of water t h a t t h e s t o r a g e t a n k can h o l d i s l e s s t h a n i t s t o t a l c a p a c i t y . The o v e r f l o w p i p e s e t s t h e volume l i m i t . I t a l l o w s t h e water i n t h e s t o r a g e t a n k t o expand upon h e a t i n g w i t h o u t c a u s i n g damage t o t h e t a n k . 9 The months of June 1981 and December 1982 have i n c o m p l e t e r e c o r d s . The form e r month - o c c u r r i n g a t t h e s t a r t of t h e m o n i t o r i n g p e r i o d - i n c l u d e s o n l y 12 d a y s of d a t a ; t h e l a t t e r month - t e r m i n a t i n g t h e m o n i t o r i n g p e r i o d - c o n t a i n s 16 d a y s . In a d d i t i o n , t h e month o f O c t o b e r 1982 has 4 d a y s of m i s s i n g d a t a . 10 The downward s t e p change i n TDHW does not r e l a t e t o a l o w e r i n g o f t h e s e t - p o i n t d e l i v e r y t e m p e r a t u r e ; r a t h e r i t i s a s s o c i a t e d w i t h l e s s f r e q u e n t o p e r a t i o n of t h e main b u r n e r i n t h e a u x i l i a r y h o t water t a n k . 11 The p i l o t l i g h t on a v e r a g e consumes an e s t i m a t e d 0.715 GJ of f u e l e n e r g y p e r month. 12 T h i s o b s e r v a t i o n s u g g e s t s t h a t t h e n u m e r a t o r of t h e HXEF r a t i o - e q u a l t o t h e d i f f e r e n c e i n water t e m p e r a t u r e a c r o s s t h e h e a t e x c h a n g e r ( i e . TSDHW-TM) - i s c o n t r a d i c t o r i l y n o n - n e g a t i v e . As o u t l i n e d i n A p p e n d i x C, s u c h a c o n d i t i o n a l w a y s a p p l i e s s i n c e TSDHW i s n e v e r l e s s t h a n TM when e v a l u a t e d on a f l o w - w e i g h t e d b a s i s u s i n g t h e l o g g e r d a t a . A c c o r d i n g l y , t h e minimum TSDHW-TM t e m p e r a t u r e d i f f e r e n c e i s z e r o . 13 I n s t a b i l i t y i n t h e HXEF r a t i o o c c u r s when TSmid-TM a p p r o a c h e s z e r o . Thus t h e e x i s t e n c e o f a few l a r g e n e g a t i v e h o u r l y v a l u e s t e n d e d t o d e p r e s s t h e a v e r a g e HXEF v a l u e t o a g r e a t e r e x t e n t i n December 1981/82 t h a n i n J a n u a r y 1982. F u r t h e r m o r e , l a r g e p o s i t i v e h o u r l y v a l u e s o c c u r when TSmid-TM a p p r o a c h e s z e r o and TSDHW - TM i s n o n - z e r o . F o u r v a l u e s e x c e e d i n g +25 were f l a g g e d ; t h e y were s u b s e q u e n t l y removed from t h e c o m p u t a t i o n a l d a t a s e t . In c o n t r a s t , no h o u r l y v a l u e s l e s s t h a n -25 were f o u n d . Thus a l l n e g a t i v e HXEF v a l u e s were i n c l u d e d i n t h e c o m p u t a t i o n s . 14 The p o s t s c r i p t 'e' on ( t a ) e i s u s e d t o t o i n d i c a t e a s m a l l c o r r e c t i o n f o r t h e e f f e c t of s o l a r r a d i a t i o n a b s o r b e d by t h e g l a s s c o v e r . S i n c e t h i s a b s o r b e d e n e r g y t e n d s t o i n c r e a s e 228 t h e c o v e r t e m p e r a t u r e , and t h e r e f o r e r e d u c e t h e c o l l e c t o r h e a t l o s s e s , i t r e s u l t s i n a s l i g h t i n c r e a s e i n u s e f u l e n e r g y g a i n . However, t h i s i n c r e a s e i s n e g l i g i b l e f o r l o w - i r o n g l a s s ( D u f f i e and Beckman, 1980), s u c h as u s e d i n t h e g l a z i n g of t h e SOL 100 c o l l e c t o r . 15 The p r o c e d u r e u s u a l l y n e c e s s i t a t e s t h a t t h e t e s t s be p e r f o r m e d d u r i n g mid-day h o u r s on c l e a r d a y s , s u c h t h a t t h e i n c i d e n t s o l a r r a d i a t i o n i s i n t e n s e ( HT >630 W/m2 ), l a r g e l y d i r e c t , and n e a r l y n o r m a l t o t h e c o l l e c t o r s u r f a c e ( 8 < 30° ). T h e s e r a d i a t i v e c o n d i t i o n s a r e assumed t o be s i m i l a r t o t h o s e u nder w h i c h t h e c o l l e c t o r w i l l p r o d u c e most of i t s u s e f u l e n e r g y g a i n when i n a c t u a l u s e . 16 FR i s a weak f u n c t i o n o f t e m p e r a t u r e , a l t h o u g h i t c a n u s u a l l y be c o n s i d e r e d c o n s t a n t f o r a g i v e n f l o w r a t e ; UL i s a moderate f u n c t i o n of t e m p e r a t u r e and wind s p e e d , and ( t a ) e i s an i n c r e a s i n g f u n c t i o n of i n c i d e n t a n g l e when 9 > 4 0 ° . 17 TCO n e v e r e x c e e d e d 100°C d u r i n g s i m u l a t i o n of t h e a c t u a l s y s t e m . T h i s was l a r g e l y due t o t h e r e g u l a r i t y o f t h e h o t wa t e r draws ( w h i c h m o d e r a t e d t h e s t o r a g e tank and c o l l e c t o r i n l e t t e m p e r a t u r e s ) and t h e a b s e n c e o f any p r o l o n g e d i n t e r v a l s of e x t r e m e l y i n t e n s e s o l a r r a d i a t i o n i n c i d e n t on t h e c o l l e c t o r p a n e l s . 18 T h i s s i m p l e h e a t e x c h a n g e r model was i n f a c t u s e d i n an e a r l i e r v e r s i o n o f WATSUN ( O r g i l l and H o l l a n d s , 1976). 19 ' C o l l e c t o r o p e r a t i n g h o u r s ' w i l l g e n e r a l l y be u s e d i n p l a c e o f 'pump o p e r a t i n g h o u r s ' i n o r d e r t o improve c l a r i t y . The two t e r m s a r e e q u i v a l e n t i n t h a t t h e c o l l e c t o r o n l y o p e r a t e s when t h e pump i s on. 20 The s m a l l (0.33 d e g r e e s C) d i f f e r e n c e between t h e two MBE v a l u e s s u g g e s t s e i t h e r a s l i g h t measurement b i a s e x i s t s i n one of t h e t e m p e r a t u r e s e n s o r s ( t h e y were matched t o w i t h i n ± 0.25°C of e a c h o t h e r p r i o r t o i n s t a l l a t i o n ) , o r t h a t under f u l l y m i x e d c o n d i t i o n s t h e bo t t o m r e g i o n of t h e s t o r a g e t a n k i s , on a v e r a g e , m a r g i n a l l y c o o l e r t h a n t h e upper r e g i o n . 21 I t i s assumed t h a t t h e h e a t c a p a c i t y component of CMC s t a y s c o n s t a n t a t a v a l u e o f 4186 kJ/m 3 and t h a t o n l y t h e f l o w r a t e o f t h e water c i r c u l a t i n g t h r o u g h t h e c o l l e c t o r l o o p i s v a r i e d . 22 The i s o t h e r m a l r e s t r i c t i o n ( f o r c o n d i t i o n s w i t h i n t h e a c t u a l s t o r a g e t a n k ) was n o t a p p l i e d i n c o m p u t i n g t h e d a i l y mean s t o r a g e t a n k t e m p e r a t u r e s ; i e . a l l h o u r l y v a l u e s a r e i n c l u d e d i n t h e d a i l y mean t e m p e r a t u r e s . 229 REFERENCES A n a l o g D e v i c e s , 1979: T w o - T e r m i n a l I n t e g r a t e d C i r c u i t T e m p e r a t u r e T r a n s d u c e r , T e c h n i c a l D a t a B u l l e t i n . Anand, K.D., W.J. K e n n i s h , T.M. K n a s e l , and A.C. S t o l a r z , 1979: V a l i d a t i o n m e t h o d o l o g y f o r s o l a r h e a t i n g and c o o l i n g s y s t e m s . E n e r g y , 4 ( 4 ) , 549-560. ASHRAE, S t a n d a r d 93-77, 1977: Methods of T e s t i n g t o D e t e r m i n e t h e T h e r m a l P e r f o r m a n c e of S o l a r C o l l e c t o r s . A m e r i c a n S o c i e t y o f H e a t i n g , R e f r i g e r a t i o n , and A i r C o n d i t i o n i n g E n g i n e e r s , New Y o r k . B a r a k a t , S. A., W. E . C a r s c a l l e n , and B.E. S i b b i t t , 1978a: NRC s o l a r m o n i t o r i n g p r o g r a m . Renewable A l t e r n a t i v e s , P r o c e e d i n g s o f t h e F o u r t h A n n u a l C o n f e r e n c e of t h e S o l a r E n e r g y S o c i e t y o f Canada I n c . B a r a k a t , S. A., W. E. C a r s c a l l e n , and B.E. S i b b i t t , 1978b: NRC S o l a r M o n i t o r i n g P rogram. N a t i o n a l R e s e a r c h C o u n c i l of Canada, D i v i s i o n o f B u i l d i n g R e s e a r c h , B u i l d i n g R e a s e a r c h Note No. 136. Beckman, W. A., 1981: S i m u l a t i o n and m o d e l l i n g . S o l a r W o r l d Forum, P r o c e e d i n g s of t h e I n t e r n a t i o n a l S o l a r E n e r g y S o c i e t y C o n g r e s s , B r i g h t o n , E n g l a n d , 2505-2506. B e l l , J . M. and J . T. S t r a c k , 1978: M e a s u r e d and p r e d i c t e d p e r f o r m a n c e of s o l a r d o m e s t i c h o t water h e a t e r s . Renewable A l t e r n a t i v e s , P r o c e e d i n g s of t h e F o u r t h A n n u a l C o n f e r e n c e o f t h e S o l a r E n e r g y S o c i e t y of Canada I n c . B r a n d o n , R. J . and P. R. MacKinnon, 1982: I n s t a l l a t i o n and M o n i t o r i n g of 20 S o l a r D o m e s t i c Hot Water S y s t e m s . N a t i o n a l R e s e a r c h C o u n c i l o f Canada, S o l a r E n e r g y Program, INSTAL-2. B u c k l e s , W.E. and S.A. K l e i n , 1980: A n a l y s i s o f s o l a r d o m e s t i c h o t w ater h e a t e r s . S o l a r E n e r g y , 25, 417-424. C a m p b e l l S c i e n t i f i c I n c . , 1981: CR21 D a t a L o g g e r Programming M a n u a l . C h a n d r a s h e k a r , M. and R. H. W y l i e , 1981a: WATSUN-3 S o l a r H e a t i n g S i m u l a t i o n and Economic E v a l u a t i o n Program, U s e r ' s Manual and Program D o c u m e n t a t i o n f o r S o l a r D o m e s t i c Hot Water System w i t h P r e - H e a t i n g S t o r a g e and E x c h a n g e r s , U n i v e r s i t y o f W a t e r l o o R e s e a r c h I n s t i t u t e . C h a n d r a s h e k a r , M. and R.H. W y l i e , 1981b: A n a l y s i s o f D e s i g n s o f Phase I I System T r i a l s U s i n g WATSUN-3. N a t i o n a l R e s e a r c h C o u n c i l o f Canada, S o l a r E n e r g y Program, P r o j e c t No. 811-06-03. 230 C h a n d r a s h e k a r , M., 1982: System s i m u l a t i o n a s a m e t h o d o l o g y i n s o l a r e n e r g y s y s t e m d e s i g n . E n e r g e x ' 8 2 , C o n f e r e n c e P r o c e e d i n g s of t h e S o l a r E n e r g y S o c i e t y of Canada I n c . , 1039-1043. C u r t i s , D. M. and S.G.T. L a F o n t a i n e , 1981: Model v a l i d a t i o n -i t s p u r p o s e , v a l u e and r e s u l t s . S o l a r W o r l d Forum, P r o c e e d i n g s of t h e I n t e r n a t i o n a l S o l a r E n e r g y S o c i e t y C o n g r e s s , B r i g h t o n , E n g l a n d , 2659-2663. Darcom, 1979: M e t e r E n c o d e r D010, P r o d u c t B u l l e t i n . D u f f i e , J . A. and W. A. Beckman, 1980: S o l a r E n g i n e e r i n g of T h e r m a l P r o c e s s e s . John W i l e y & Sons, New Y o r k . Fanney, A. H. and S. T. L i u , 1980: C o m p a r i s o n o f e x p e r i m e n t a l computer p r e d i c t e d p e r f o r m a n c e f o r s i x s o l a r d o m e s t i c h o t water s y s t e m s . ASHRAE T r a n s a c t i o n s , 86, P a r t 1, 823-835. F a r a h a n , E . , 1977: R e s i d e n t i a l E l e c t r i c and Gas Water H e a t e r s . Argonne N a t i o n a l L a b o r a t o r y , R e p o r t 77-2. F e r g u s o n , J . E. and H. F. S u l l i v a n , 1982a: O p t i m i z a t i o n of S e v e r a l S o l a r D o m e s t i c Hot Water System P a r a m e t e r s U s i n g t h e WATSUN S i m u l a t i o n P r o g r a m . N a t i o n a l R e s e a r c h C o u n c i l of Canada, S o l a r E n e r g y Program, SOLWAT-2. F e r g u s o n , J . E. and H. F. S u l l i v a n , 1982b: O p t i m i z a t i o n of s e v e r a l s o l a r d o m e s t i c h o t water s y s t e m p a r a m e t e r s . E n e r g e x ' 8 2 , C o n f e r e n c e P r o c e e d i n g s of t h e S o l a r E n e r g y S o c i e t y o f Canada, I n c . , 536-541. F r a s e r , A. J . , F.R. L i v i n g s t o n e , and W.R. D a v i s , 1980: D e s i g n g u i d e l i n e s f o r s o l a r s y s t e m c o n f i g u r a t i o n and c o n t r o l s . S o l w e s t ' 8 0 , C o n f e r e n c e P r o c e e d i n g s of t h e S o l a r E n e r g y S o c i e t y o f Canada I n c . , 448-452. G r i g n o n , A.A., 1979: The N a t i o n a l R e s e a r c h C o u n c i l S o l a r E n e r g y Program. N a t i o n a l R e a s e a r c h C o u n c i l o f Canada, SEP Note 1. Hedstrom, J . C. e t a l . , 1981: V a l i d a t i o n o f S i m u l a t i o n M o d e l s U s i n g M e a s u r e d P e r f o r m a n c e D a t a from t h e L o s Alamos S t u d y C e n t e r . I n t e r n a t i o n a l E n e r g y Agency S o l a r H e a t i n g and C o o l i n g Program, L o s Alamos N a t i o n a l L a b o r a t o r y . H o t t e l , H. C. and B. B. W o e r t z , 1942: P e r f o r m a n c e of f l a t - p l a t e s o l a r - h e a t c o l l e c t o r s . T r a n s a c t i o n s o f t h e A m e r i c a n S o c i e t y o f M e c h a n i c a l E n g i n e e r s , 64, 91. H o t t e l , H. C. and A. W h i l l i e r , 1958: E v a l u a t o n of f l a t p l a t e c o l l e c t o r p e r f o r m a n c e . T r a n s a c t i o n s of t h e C o n f e r e n c e on t h e Use of S o l a r E n e r g y , 2, P a r t 1, 74. 231 Hunn, B. D., G. J . E. W i l l c u t t , and T. B. McSweeney, 1977: S i m u l a t i o n and c o s t o p t i m i z a t i o n of s o l a r h e a t i n g i n b u i l d i n g s i n a d v e r s e s o l a r r e g i o n s . S o l a r E n e r g y , 19, 33-44. IBI G r o u p and W a t e r s h e d E n e r g y Systems L t d . , 1982: Hot Water Lo a d P r o f i l e s . N a t i o n a l R e s e a r c h C o u n c i l of Canada, S o l a r E n e r g y Program, SOLWAT-4. I r e t o n , V. M., 1978: D o m e s t i c w a t e r p r e h e a t i n g u s i n g s o l a r e n e r g y . Renewable A l t e r n a t i v e s , P r o c e e d i n g s o f t h e F o u r t h A n n u a l C o n f e r e n c e of t h e S o l a r E n e r g y S o c i e t y o f Canada I n c . I s a k s o n , P., W. K e n n i s h and E. O f v e r h o l m , 1980: R e p o r t i n g Format f o r T h e r m a l P e r f o r m a n c e of S o l a r H e a t i n g and C o o l i n g Systems i n B u i l d i n g s . I n t e r n a t i o n a l E n e r g y Agency S o l a r H e a t i n g and C o o l i n g Program, S w e d i s h C o u n c i l f o r B u i l d i n g R e s e a r c h S t o c k h o l m . J o n e s , T., 1982: S o l a r D o m e s t i c Hot Water D e m o n s t r a t i o n Program; d e s c r i p t i o n and p r e l i m i n a r y r e s u l t s . E n e r g e x ' 8 2 , C o n f e r e n c e P r o c e e d i n g s of t h e S o l a r E n e r g y S o c i e t y o f Canada I n c . , 519-522. J 0 r g e n s e n , 0. C. ( e d i t o r ) , 1979: M o d e l l i n g and S i m u l a t i o n . I n t e r n a t i o n a l E n e r g y Agency S o l a r H e a t i n g and C o o l i n g Program, T h e r m a l I n s u l a t i o n L a b o r a t o r y , T e c h n i c a l U n i v e r s i t y of Denmark. J 0 r g e n s e n , 0. C , 1981: IEA S o l a r H e a t i n g and C o o l i n g Program Task I , I n v e s t i g a t i o n of t h e P e r f o r m a n c e of S o l a r H e a t i n g and and C o o l i n g S y s t e m s . S o l a r W o r l d Forum, P r o c e e d i n g s o f t h e I n t e r n a t i o n a l S o l a r E n e r g y C o n g r e s s , B r i g h t o n , E n g l a n d , 2507-2512. J 0 r g e n s e n , 0. C. e t a l . , 1982: S i m u l a t i o n P rogram V a l i d a t i o n U s i n g D o m e s t i c Hot Water System D a t a . I n t e r n a t i o n a l E n e r g y Agency S o l a r H e a t i n g and C o o l i n g Programme, T h e r m a l L a b o r a t o r y , T e c h n i c a l U n i v e r s i t y o f Denmark. Kaye, J . E. and A. J . Z a i d i , 1982: M o n i t o r i n g r e s u l t s on t h e p e r f o r m a n c e of two s o l a r e n e r g y h o t water h e a t i n g s y s t e m s i n Canada. E n e r g e x ' 8 2 , C o n f e r e n c e P r o c e e d i n g s o f t h e S o l a r E n e r g y S o c i e t y of Canada I n c . , 523-528. Kays, W. M. and A. L. London, 1964: "Compact Heat E x c h a n g e r s " , M c G r a w - H i l l , New Y o r k . L a t i m e r , J . R., 1980: C a n a d i a n p r o c e d u r e s f o r m o n t i o r i n g s o l a r r a d i a t i o n . P r o c e e d i n g s F i r s t C a n a d i a n S o l a r R a d i a t i o n D a t a Workshop, J . E. Hay and T. K. Won ( e d i t o r s ) , C a n a d i a n A t m o s p h e r i c E n v i r o n m e n t S e r v i c e and t h e N a t i o n a l R e s e a r c h C o u n c i l o f Canada, 21-31. 232 Le, N. T. and M. C h a n d r a s h e k a r , 1978: WATSUN-II S i m u l a t i o n Program f o r S o l a r A s s i s t e d H e a t i n g Systems, U s e r ' s Manual and Program D o c u m e n t a t i o n , U n i v e r s i t y o f W a t e r l o o R e s e a r c h I n s t i t u t e . L e s l i e , S.F., D.V. B l y t h e , and G.W. Matthews, 1980: A c o m p a r i s o n of f - c h a r t e s t i m a t e s w i t h o p e r a t i o n a l p e r f o r m a n c e of s i x s o l a r water h e a t i n g s y s t e m s i n t h e V a n c o u v e r r e g i o n . S o l w e s t ' 8 0 , C o n f e r e n c e P r o c e e d i n g s of t h e S o l a r E n e r g y S o c i e t y of Canada I n c . , 218-222. N a t i o n a l R e s e a r c h C o u n c i l of Canada, 1982: S o l a r E n e r g y Program, P u b l i c a t i o n L i s t and C o n t r a c t R e g i s t r y . N o r g a t e , G., V. H. N i e l s o n , D. M. Dean, and J.D. Savage, 1980: M o n i t o r i n g o f a s o l a r h o t water s y s t e m . S o l w e s t ' 8 0 , C o n f e r e n c e P r o c e e d i n g s o f t h e S o l a r E n e r g y S o c i e t y of Canada I n c . , 377-381. Onno, T., 1980: O b j e c t i v e s and m e t h o d o l o g y f o r m o n i t o r i n g of NRC a c t i v e and p a s s i v e s o l a r s y s t e m f i e l d t r i a l s . S o l w e s t ' 8 0 , P r o c e e d i n g s o f t h e S o l a r E n e r g y S o c i e t y of Canada I n c . , 212-217. O r g i l l , J . F . and K.G.T. H o l l a n d s , 1976: WATSUN S o l a r H e a t i n g S i m u l a t i o n and Economic E v a l u a t i o n Program, U s e r ' s Manual, U n i v e r s i t y of W a t e r l o o R e s e a r c h I n s t i t u t e . P a r k e r , G.J., 1981: P e r f o r m a n c e of a s o l a r water h e a t i n g s y s t e m i n a d w e l l i n g i n C h r i s t c h u r c h , New Z e a l a n d . S o l a r E n e r g y , 26, 189-197. Rho Sigma I n c : P r o d u c t I n f o r m a t i o n B u l l e t i n s . SERI, 1980: A n a l y s i s Methods f o r S o l a r H e a t i n g and C o o l i n g A p p l i c a t i o n s - P a s s i v e and A c t i v e S y s t e m s . S o l a r E n e r g y R e s e a r c h I n s t i t u t e , G o l d e n , C o l o r a d o . S i b b i t t , B.E. and R.H. W y l i e , 1982: S i m u l a t e d and measured p e r f o r m a n c e of a c o m m e r c i a l s o l a r w a t e r h e a t i n g s y s t e m . E n e r g e x ' 8 2 , C o n f e r e n c e P r o c e e d i n g s o f t h e S o l a r E n e r g y S o c i e t y o f Canada I n c . , 1181-1185. S o l a r D o m e s t i c Hot Water D e m o n s t r a t i o n Program, P r o g r e s s R e p o r t , 1981: C o n s e r v a t i o n and Renewable. E n e r g y D i v i s i o n , E n e r g y R e s o u r c e s B r a n c h , M i n i s t r y o f E n e r g y , M i n e s and P e t r o l e u m R e s o u r c e s , P r o v i n c e of B r i t i s h C o l u m b i a . S o l a r s y s t e m s I n d u s t r i e s L t d . , 1980: S o l a r P r o d u c t D a t a S h e e t s No. 5 and 19. Sp r a g u e E l e c t r i c Company, 1978: Type UGN-3501M S o l i d - S t a t e L i n e a r O u t p u t ' H a l l E f f e c t ' S e n s o r s , E n g i n e e r i n g B u l l e t i n 27500. 1 . 233 S t r e e d , E. R. ( e d i t o r ) , 1979: D a t a R e q u i r e m e n t s and T h e r m a l P e r f o r m a n c e E v a l u a t i o n P r o c e d u r e s f o r S o l a r H e a t i n g and C o o l i n g S y s t e m s . I n t e r n a t i o n a l E n e r g y Agency S o l a r H e a t i n g and C o o l i n g Program, (U.S.) N a t i o n a l B u r e a u of S t a n d a r d s , W a s h i n g t o n , D.C. T a y l o r , P. J . and E. M i c h e l s o n , 1981: V a l i d a t i o n of computer models of a water h e a t i n g s y s t e m . S o l a r W o r l d Forum, P r o c e e d i n g s o f t h e I n t e r n a t i o n a l S o l a r E n e r g y S o c i e t y C o n g r e s s , B r i g h t o n , E n g l a n d , 2646-2650. TES L i m i t e d , 1981: Development of M o n i t o r i n g Methods f o r S o l a r D o m e s t i c Hot Water S y s t e m s . N a t i o n a l R e s e a r c h C o u n c i l of Canada, S o l a r E n e r g y Program, R e p o r t C331-2. Timko, M.P., 1976: A t w o - t e r m i n a l i n t e g r a t e d c i r c u i t t e m p e r a t u r e t r a n s d u c e r . I E E E J . S o l i d S t a t e C i r c u i t s , SC-11, 784-788. W h i l l i e r , A., 1977: P r e d i c t i o n o f p e r f o r m a n c e of s o l a r c o l l e c t o r s . A m e r i c a n S o c i e t y of H e a t i n g , R e f r i g e r a t i o n , and A i r C o n d i t i o n i n g E n g i n e e r s , New Y o r k . W i l k i n s o n , R. G., 1982: A n a l y s i s o f F a c t o r s A f f e c t i n g T h e r m a l P e r f o r m a n c e i n S o l a r D o m e s t i c Hot Water S y s t e m s . N a t i o n a l R e s e a r c h C o u n c i l of Canada, S o l a r E n e r g y Program, SOLWAT-2. W i l l m o t t , C. J . , 1982: Some commments on t h e e v a l u a t i o n of model p e r f o r m a n c e . B u l l e t i n of t h e A m e r i c a n M e t e o r o l o g i c a l S o c i e t y , 6 3 ( 1 1 ) , 1309-1313. Winn, C. B., B.W. P a r k i n s o n , and N. Duong, 1978: V a l i d a t i o n of s o l a r s y s t e m s i m u l a t i o n p r o g r a m s . P r o c e e d i n g s o f t h e A n n u a l M e e t i n g o f t h e I n t e r n a t i o n a l S o l a r E n e r g y S o c i e t y , D enver, C o l o r a d o , 120-124. Won, T.K., 1981: Model v a l i d a t i o n methods. Handbook of R a d i a t i o n E s t i m a t i o n Methods, I n t e r n a t i o n a l E n e r g y Agency S o l a r H e a t i n g and C o o l i n g Program, A t m o s p h e r i c E n v i r o n m e n t S e r v i c e , Canada. W. R. D a v i s E n g i n e e r i n g L i m i t e d , 1980: G u i d e f o r t h e C o n f i g u r a t i o n and C o n t r o l of S o l a r H e a t i n g S y s t e m s . N a t i o n a l R e s e a r c h C o u n c i l of Canada, S o l a r E n e r g y Program, CON-2. W y l i e , R. H., M. C h a n d r a s h e k a r , and W. E . C a r s c a l l e n , 1981: S i m u l a t i o n , a n a l y s i s and d e s i g n p r e d i c t i o n s o f a number o f b u i l t s o l a r h e a t i n g s y s t e m s . S o l a r W o r l d Forum, P r o c e e d i n g s of t h e I n t e r n a t i o n a l S o l a r E n e r g y S o c i e t y C o n g r e s s , B r i g h t o n , E n g l a n d , 2651-2658. Z a i d i , A. J . , J . E . Kaye, and J . N o s t e d t , 1982: P e r f o r m a n c e of s o l a r e n e r g y h o t water s y s t e m s . E n e r g e x ' 8 2 , C o n f e r e n c e P r o c e e d i n g s o f t h e S o l a r E n e r g y S o c i e t y o f Canada I n c . , 529-535. 234 APPENDIX A DETAILED DESCRIPTION OF THE SYSTEM COMPONENTS R e f e r e n c e - S o l a r s y s t e m s I n d u s t r i e s L t d . , 1980: S o l a r P r o d u c t D a t a S h e e t s No. 5 & 19. S y s t e m Components - The SDHW h e a t i n g s y s t e m i n c o r p o r a t e s a s o l a r c o l l e c t o r a r r a y , c i r c u l a t i o n pump, d i f f e r e n t i a l c o n t r o l l e r , s o l a r s t o r a g e t a n k w i t h immersed c o i l h e a t e x c h a n g e r , a u x i l i a r y h o t water t a n k , p i p i n g , and i n s u l a t i o n . (See t h e s y s t e m c o n f i g u r a t i o n s c h e m a t i c i n F i g u r e A.1) (1) C o l l e c t o r A r r a y ( F i g u r e s A.2 and A.3) - T h i s component c o n s i s t s of t h r e e f l a t p l a t e c o l l e c t o r p a n e l s c o n n e c t e d i n p a r a l l e l by i n t e r n a l h e a d e r p i p e s w h i c h a r e s l i g h t l y s l o p e d t o a l l o w d r a i n a g e . The s i n g l e - g l a z e d p a n e l c o v e r s a r e composed of l o w - i r o n t e m p e r e d g l a s s w h i c h has been l i g h t l y t e x t u r e d t o r e d u c e r e f l e c t i o n . The b e v e l l e d g l a s s edges a r e s e a l e d u s i n g a U-shaped g a s k e t which i s h e l d i n p l a c e by a snap-on c a p . The a b s o r b e r p l a t e c o n s i s t s of c o p p e r s t r i p s w h i c h a r e formed t o wrap p a r t i a l l y a r o u n d , and w h i c h a r e c o n t i n u o u s l y s o l d e r e d t o , e i g h t c o p p e r r i s e r t u b e s . The r i s e r t u b e s i n t u r n , a r e b r a z e d t o c o p p e r h e a d e r p i p e s w h i c h e x t e n d beyond t h e c o l l e c t o r frame and a r e e x p a n d e d t o r e c e i v e s t a n d a r d 13 mm p i p i n g ; s u p p l y and r e t u r n p i p i n g c o n n e c t i o n s a r e t o d i a g o n a l l y o p p o s i t e c o r n e r s . The a b s o r b e r p l a t e i s h e l d i n p l a c e by t h e m a n i f o l d p i p i n g , w h i c h i s s e c u r e d by s i l i c o n e r u b b e r s l e e v e s t o t h e frame. The a b s o r b e r s u r f a c e i s s e l e c t i v e b l a c k chrome e l e c t r o p l a t e d o n t o a n i c k e l s u b s t r a t e and t h e n o n t o t h e c o p p e r s t r i p s . Back and edge i n s u l a t i o n i s medium d e n s i t y , h i g h - t e m p e r a t u r e f i b r e g l a s s f i t t e d b e n e a t h t h e a b s o r b e r p l a t e . The s i d e s o f e a c h c o l l e c t o r p a n e l a r e made of e x t r u d e d aluminum, w i t h c o r n e r s r e i n f o r c e d by m e t a l b r a c k e t s . The back p l a t e i s u t i l i t y g r a d e aluminum s h e e t , i n s e r t e d i n t o a g r o o v e and r i v e t e d t o t h e s i d e s . V e n t i l a t i n g h o l e s a r e l o c a t e d a l o n g t h e upper s i d e s o f t h e c o l l e c t o r and weep h o l e s a l o n g t h e bottom; a i r w h i c h e n t e r s t h e p a n e l i n t e r i o r i s f i l t e r e d t h r o u g h t h e f i b r e g l a s s i n s u l a t i o n , t h e r e b y k e e p i n g d u s t o u t . The e n t i r e c o l l e c t o r a s s e m b l y i s mounted on t h e r o o f u s i n g aluminum b r a c k e t s and s p a c e r s w h i c h a r e c l i p p e d i n t o g r o o v e s a r o u n d t h e p e r i m e t e r of t h e frame and t h e n b o l t e d o n t o t h e r o o f r a f t e r s w i t h g a l v a n i z e d s t e e l l a g s c r e w s . F l a s h i n g i s l a i d a r o u n d t h e o u t s i d e b a s e o f t h e c o l l e c t o r f r a m e, and a l l e x p o s e d aluminum i s f i n i s h e d i n brown ba k e d enamel t o r e d u c e w e a t h e r i n g . T a b l e A.2 summarizes t h e c o l l e c t o r s p e c i f i c a t i o n s and e f f i c i e n c y t e s t r e s u l t s . (2) P i p i n g ( F i g u r e A.1) - The p i p i n g l a y o u t i s d i v i d e d i n t o two h a l v e s : a c o l l e c t o r l o o p c o n n e c t i n g t h e c o l l e c t o r a r r a y w i t h t h e s o l a r s t o r a g e t a n k , and a water s u p p l y l i n e e x t e n d i n g from t h e l o c a l m a i n s t o t h e a u x i l i a r y t a n k e x i t . E a c h h a l f i n t u r n , has b o t h a c o l d o r i n l e t s i d e , and a warm o r o u t l e t s i d e . The 38 m e t r e l o n g c o l l e c t o r l o o p u t i l i z e s a d r a i n b a c k d e s i g n t o p r o v i d e f r e e z e p r o t e c t i o n . T h i s means t h a t t h e c o l l e c t o r l o o p o n l y c o n t a i n s w ater when t h e c i r c u l a t i o n pump i s 235 o p e r a t i n g and s o l a r e n e r g y c o l l e c t i o n i s o c c u r r i n g . When t h e pump s t o p s , a i r i s a d m i t t e d t o t h e c o l l e c t o r o u t l e t p i p e t h r o u g h a s e p a r a t e i n v e r t e d U - t u b e . T h i s u n b a l a n c e s t h e wa t e r f l o w i n g t h r o u g h t h e c o l l e c t o r l o o p and c a u s e s i t t o d r a i n back t o t h e s o l a r s t o r a g e t a n k v i a g r a v i t y . (Most o f t h e water d r a i n s back t h r o u g h t h e c i r c u l a t i o n pump.) The i n v e r t e d U-tube a l s o a c t s as an a i r v e n t , a l l o w i n g a i r t o be f l u s h e d from t h e c o l l e c t o r p a s s a g e s when t h e pump s t a r t s up, and p r e v e n t i n g any a i r l o c k s f r o m o c c u r r i n g d u r i n g c o l l e c t o r o p e r a t i o n . T h e r e a r e no c o n t r o l o r p r e s s u r e r e l i e f v a l v e s i n t h e c o l l e c t o r l o o p ; t h e p i p i n g i s open t o t h e a t m o s p h e r e and c a n n o t b u i l d up any p r e s s u r e . P r o p e r l y s l o p i n g p i p e s p r o v i d e f a i l - s a f e o p e r a t i o n ; i f t h e e l e c t i c a l s e r v i c e i s d i s r u p t e d , t h e pump s t o p s and wa t e r i n t h e c o l l e c t o r l o o p d r a i n s b a c k . A g a t e v a l v e c an be u s e d t o c l o s e o f f t h e c o l l e c t o r i n l e t p i p e , a l l o w i n g t h e pump t o be s e r v i c e d . A l l c o l l e c t o r l o o p p i p i n g i s Type M c o p p e r t u b i n g , 19 mm i n d i a m e t e r . I n s u l a t i o n i s p r o v i d e d on b o t h t h e i n l e t and o u t l e t p i p e s by c l o s e d c e l l f l e x i b l e p o l y u r e t h a n e foam, 13 mm t h i c k and h a v i n g a RSI v a l u e o f 0.9. P i p i n g i n t h e water s u p p l y l i n e i s Type L c o p p e r t u b i n g , 19 mm i n d i a m e t e r . The 4 metre l o n g p i p e on t h e warm s i d e ( t h a t s e c t i o n of p i p e between t h e s o l a r s t o r a g e and a u x i l i a r y t a n k e x i t s ) i s e n c a s e d i n p o l y u r e t h a n e i n s u l a t i o n . T h r e e b y p a s s v a l v e s on t h e c o l d s i d e of t h e water s u p p l y l i n e p e r m i t i s o l a t i o n of t h e s t o r a g e t a n k ; however t h e r e i s no t e m p e r i n g v a l v e t o e n a b l e i n c o m i n g c o l d w a ter t o p a r t i a l l y b y p a s s t h e t a n k . A water f i l l v a l v e a l l o w s manual f i l l i n g and t o p p i n g up of t h e s t o r a g e t a n k . L a s t l y , an o i l f i l l v a l v e i s u s e d t o po u r a s m a l l amount o f motor o i l i n t o t h e t o p o f t h e tank t o r e d u c e e v a p o r a t i o n from t h e water s u r f a c e . (3) C i r c u l a t i o n pump - A r o t a r y s e a l c e n t r i f u g a l pump, t r a d e name H a r t e l l M odel GPPS-45H-1, i s u s e d t o l i f t w ater from t h e bo t t o m of t h e s t o r a g e t a n k and c i r c u l a t e i t t h r o u g h t h e s o l a r c o l l e c t o r p a n e l s . A c o n t r o l o r i f i c e l i m i t s t h e c i r c u l a t i o n f l o w r a t e t o t h e d e s i g n v a l u e . The pump i s power r a t e d a t 107 W and o p e r a t e s on s t a n d a r d h o u s e h o l d e l e c t r i c c u r r e n t . (4) D i f f e r e n t i a l c o n t r o l l e r ( F i g u r e A.5) - The c i r c u l a t i o n pump i s a c t i v a t e d by an ' o n - o f f ' d i f f e r e n t i a l c o n t r o l l e r , t r a d e name S o l a r s y s t e m s M odel DT-11. T h i s i s a p r e - a s s e m b l e d e l e c t r o n i c d e v i c e w h i c h u t i l i z e s two remote t e m p e r a t u r e s e n s o r s . One s e n s o r i s i n s e r t e d i n t o t h e c o l l e c t o r o u t l e t m a n i f o l d ; i t i s s e a t e d i n p o l y u r e t h a n e i n s u l a t i o n h e l d i n p l a c e by a s t e e l c l a m p . The o t h e r s e n s o r i s i n s e r t e d i n t o t h e e n t r a n c e of t h e c o l l e c t o r i n l e t p i p e , n e a r t h e b o t t o m o f t h e s o l a r s t o r a g e t a n k . B o t h s e n s o r s a r e p r e c i s i o n matched t h e r m i s t o r s , t r a d e name Fenwal UUA41-J1. They have a r e s i s t a n c e o f 10 kfi a t 25°C, a s e n s i t i v i t y of 4.3% p e r d e g r e e C, and a r e i n t e r c h a n g e a b l e t o w i t h i n ±0.2°C o v e r t h e t e m p e r a t u r e r a n g e 0°C - 70°C . They come e n c a s e d i n s i l i c o n e r u b b e r and have l e a d w i r e s i n s u l a t e d w i t h T e f l o n . The d i f f e r e n t i a l c o n t r o l l e r a l s o u t i l i z e s s o l i d s t a t e c i r c u i t r y , a r e l a y o u t p u t , and an LED l i g h t t o i n d i c a t e i f t h e c o n t r o l l e r i s 'on'. I t o p e r a t e s on s t a n d a r d h o u s e h o l d e l e c t r i c c u r r e n t and draws l e s s t h a n 10 W power when 'on'; when ' o f f , 236 n e g l i g i b l e power i s consumed. The 'on' t e m p e r a t u r e d i f f e r e n t i a l (TDIF1) i s a d j u s t a b l e between 5 - 1 5 d e g r e e s C, th e ' o f f d i f f e r e n t i a l (TDIF2) between 0 - 4 d e g r e e s C. The c o n t r o l l e r c u r r e n t l y has 'on' s e t a t 10 d e g r e e s C, and ' o f f s e t a t 1 d e g r e e C. Thus, t h e minimum a l l o w a b l e c o l l e c t o r - t o - t a n k t e m p e r a t u r e d i f f e r e n c e t o i n i t i a t e pump o p e r a t i o n i s 10 d e g r e e s C, and t h e minimum a l l o w a b l e t e m p e r a t u r e d i f f e r e n c e t o m a i n t a i n o p e r a t i o n i s 1 d e g r e e C. (5) S t o r a g e Tank ( F i g u r e s A.6 and A.7) - An u p r i g h t s e a l e d p o l y e t h y l e n e c y l i n d e r f i l l e d w i t h water i s u s e d t o s t o r e c o l l e c t e d s o l a r e n e r g y . T h i s s t o r a g e tank i s m a n u f a c t u r e d by S o l a r s y s t e m s I n d u s t r i e s L t d . and i s 450 l i t r e s i n t o t a l c a p a c i t y . I t o p e r a t e s a t a t m o s p h e r i c p r e s s u r e and t h e r e f o r e no e x p a n s i o n t a n k o r p r e s s u r e r e l i e f v a l v e i s n e c e s s a r y . The wa t e r l e v e l i n t h e tank i s i n d i c a t e d by a s i g h t g l a s s . The t a n k can be t o p p e d up u s i n g t h e manual f i l l v a l v e ; any e x c e s s w a t e r s i m p l y d r a i n s o ut t h e o v e r f l o w p i p e . P o l y e t h y l e n e p i p e b o s s e s a r e w e l d e d t o t h e o u t s i d e tank w a l l t o a l l o w screw-on c o n n e c t i o n w i t h e x t e r n a l p i p i n g . F i b r e g l a s s i n s u l a t i o n , t h i c k n e s s 15 cm and RSI 3.70, s u r r o u n d s t h e s t o r a g e t a n k . I t i s h e l d i n p l a c e by a v i n y l s l i p - o n c o v e r . Two s t y r o f o a m d i s c s , t h i c k n e s s 7.5 cm and RSI 2.64, i n s u l a t e t h e t o p and bo t t o m of t h e t a n k . Maximum o p e r a t i n g t e m p e r a t u r e i s 80°C on a c o n t i n u o u s b a s i s ; i n t e r m i t e n t l y , t e m p e r a t u r e s up t o 100°C c an be t o l e r a t e d . C omplete r e - c i r c u l a t i o n of w a t e r t h r o u g h t h e s t o r a g e t a n k d u r i n g c o l l e c t o r o p e r a t i o n t a k e s a t l e a s t 3 h o u r s . (6) Heat e x c h a n g e r - A s i n g l e - w a l l , p i p e h e a t e x c h a n g e r made of Type L s o f t c o p p e r i s c o i l e d i n s i d e t h e f u l l h e i g h t o f t h e s t o r a g e t a n k . I t r e s t s on t h e bottom of t h e tank w i t h i t s c o n n e c t i o n s e x t e n d i n g t h r o u g h t h e t o p . M a n u f a c t u r e d by S o l a r s y s t e m s I n d u s t r i e s L t d . , i t s d i m e n s i o n s and o t h e r s p e c i f i c a t i o n s a r e l i s t e d i n T a b l e A.1 below. T a b l e A.1 Heat E x c h a n g e r S p e c i f i c a t i o n s p i p e l e n g t h 30.48 m p i p e d i a m e t e r 19 mm w a l l t h i c k n e s s 0.254 mm s u r f a c e a r e a 1 .82 m 2 volume 8.64 l i t r e s t h e r m a l c o n d u c t i v i t y 385 W / m ° C max. f l o w r a t e 75 l i t r e s / m i n max. o p e r a t i n g p r e s s u r e 1000 kPa (7) A u x i l i a r y Hot Water Tank - A c o n v e n t i o n a l , n a t u r a l gas f i r e d h o t w a t e r t a n k , p r e - e x i s t i n g on t h e p r e m i s e s , s e r v e s as th e a u x i l i a r y w a ter h e a t e r . I t i s a s t o r a g e t y p e h e a t e r h o l d i n g 150 l i t r e s of h o t w a t e r ; o u t s i d e d i m e n s i o n s a r e 1.22 m i n h e i g h t by 0.51 m i n d i a m e t e r . S o l a r h e a t e d water e n t e r s t h r o u g h a d i p t u b e e x t e n d i n g 1.04 m down f r o m t h e t o p of t h e t a n k . F i b r e g l a s s i n s u l a t i o n , t h i c k n e s s 2.54 cm and RSI 0.53, 237 i s f i t t e d between t h e t a n k ' s g l a s s - l i n i n g and t h e t h i n m e t a l s h e l l w h i c h e n c a s e s i t . (The l a t t e r i s e n a m e l l e d w h i t e on t h e o u t s i d e ) . The a u x i l i a r y hot w a t e r t a n k i s a s t a n d a r d m o del, power r a t e d a t 10.3 kW. A t e m p e r a t u r e / p r e s s u r e r e l i e f v a l v e p r o v i d e s s a f e t y i n t h e e v e n t of o v e r - h e a t i n g . 238 T a b l e A.2 C o l l e c t o r S p e c i f i c a t i o n s & E f f i c i e n c y T e s t R e s u l t s T r a d e Name - S o l a r s y s t e m s SOL 100 L i q u i d F l a t C o l l e c t o r P a n e l d i m e n s i o n s s i d e s l e n g t h 2470 mm d e p t h 131 mm t h i c k n e s s 1 .6 mm t o p / b o t t o m w i d t h 895 mm d e p t h 131 mm t h i c k n e s s 0.51 mm g r o s s f r o n t a l a r e a p e r p a n e l 2.21 m 2 t o t a l a r r a y 6.64 m2 n e t a p e r t u r e a r e a p e r p a n e l 2.02 m 2 t o t a l a r r a y 6.06 m 2 h e a d e r p i p e d i a m e t e r 1 9 mm r i s e r t u b e d i a m e t e r 7 mm r i s e r tube s p a c i n g 1 06 mm g l a s s c o v e r t h i c k n e s 4 mm a b s o r b e r p l a t e t h i c k n e s s 0.254 mm I n s u l a t i o n t h i c k n e s s back 75 mm s i d e s 1 2 mm t h e r m a l r e s i s t a n c e back 2.1 RSI s i d e s 0.34 RSI R a d i a t i v e C h a r a c t e r i s t i c s g l a s s c o v e r r e f r a c t i v e i n d e x 1 .5 t r a n s m i t t a n c e ( s h o r t w a v e ) 89.6% a b s o r b e r p l a t e a b s o r p t a n c e ( s h o r t w a v e ) 95% ± 2% e m i t t a n c e ( l o n g w a v e ) 10% ± 2% Heat T r a n s f e r F l u i d medium b o i l i n g p o i n t (max. o p e r a t i n g temp.) d e n s i t y s p e c i f i c h e a t mass f l o w r a t e ( p e r p a n e l ) f l u i d c a p a c i t a n c e ( t o t a l a r r a y ) max. o p e r a t i n g p r e s s u r e w a t e r 100 °C 1.0 k g / l i t r e 4.186 kJ/kg°C 2.27 kg/min 1711 kJ/hr°C 670 kPa 239 T a b l e A.2 - c o n t i n u e d E f f i c i e n c y P a r a m e t e r s ( F i g u r e A.4) [NRC s o l a r c o l l e c t o r t e s t f a c i l i t y ; ASHRAE S t a n d a r d 93-77 (1977) p r o c e d u r e s f o l l o w e d . V a l u e s a r e b a s e d on s i n g l e c o l l e c t o r p a n e l and g r o s s f r o n t a l a r e a . ] z e r o - p o i n t e f f i c i e n c y s l o p e e f f i c i e n c y 0.725 5.21 W/m2 °C Solarsystems Drain Back Domestic Hot Water System F i g u r e A.1 System C o n f i g u r a t i o n ( S o l a r s y s t e m s I n d u s t r i e s L t d . , S c h e m a t i c 1980) Piping System Schematic Diagram 241 F i g u r e A.2 F l a t P l a t e C o l l e c t o r P a n e l s Figure A.3 Collector Panel D e t a i l s (Solarsystems Industries Ltd., 1980) 7 side connections aluminum (tamo single glazed tempered tow-iron glass copper stnp absorber with blncK chrome soleclfvo surtaca . copper risers .copper header 892 mm It t - - ~ . tempered glazing - , EPDM gasket Surface Mounting Details snap-on aluminum glazing cap . copper strip absorber copper riser copper header silicone rubber sleeve extruded aluminum l/ome gglvanired )fe in. lag bolt Aluminum mounting bracket clipped into frame aluminum spacer roof suiface high-temperature tiberglass insulation sheet aluminum backing collector frame Between Collectors End of Array 243 F i g u r e A.4 C o l l e c t o r E f f i c i e n c y C urve (NRC s o l a r c o l l e c t o r t e s t f a c i l i t y ; ASHRAE S t a n d a r d 93-77 (1977) p r o c e d u r e s f o l l o w e d . V a l u e s a r e b a s e d on s i n g l e c o l l e c t o r p a n e l and g r o s s f r o n t a l a r e a . 2 4 4 F i g u r e A.5 Differential Controller ( S o l a r s y s t e m s I n d u s t r i e s L t d . , 1980) F i g u r e A.6 Section Through Storage Tank ( S o l a r s y s t e m s I n d u s t r i e s L t d . , 1980) Sfyrolbam insulation level sight thermometer white vinyl jacket frbreglass insulation polyethylene tank copper coil heat exchanger pump suction drain a n d * l Styiofoam Insulation collector return cold water Tn Ti collector vent hot water out Ic; TH = 610 mm ^ — D o • 914 mm Storage Tank 2 4 5 F i g u r e A.7 I n s u l a t e d S o l a r S t o r a g e Tank and M o n i t o r i n g Equipment 246 APPENDIX B CR21 INPUT / OUTPUT TABLE CODING FORMS 247 CR21 Input Table Coding Form CR21 (D SDHW Heating System S t a r t D a t c June 19, 1981 S t a r t T i m e 00:00 Hours /VOTE: Select Input program numbers from appendix A of the CR2I Operator's Manual. Specify a multiplier (a) and offset (b) (or each sensor using the equation EU = aX + b to convert the sensor output (X) to engineering units. EU = Final Output Engineering Units. IU = Input Units e.g. volts (V). millivolts (MV). and counts. Sensor Number Sensor Description and Calibration Final Output (EU) Range (EU) Input Program Program No. Multiplier (EU/IU) Offset (EU) (V. MV, DC Resistance) 1 _2 Solar Radiation <* HT Kipp Pyranometer 10.88 uV/Wm KJ/mZ * Max. Rad. 1.3kW/tn' DC M i l l i v o l t s 11: 2 12; 0.9189 13: 0 (V, MV. DC Resistance) 2 Outside Ambient A i r Temp. - TA CSI Model 101 Thermistor Probe °C -40 C to +60 C Temperature 21: 7 22: 1-0 23: 0 (V. MV, DC Resistance) 3 Inlet Cold Water Temperature «• TM AD590 Integrated C i r c u i t Temperature Transducer °C -55 C to +150 C DC Volts 31: 1 32; 1000. 33: -273. (V. MV. DC Resistance) 4 Solar Heated Water Temperature - TSDHW AD590 Integrated C i r c u i t Temperature Transducer °C -55 C to +150 C DC Volts 41: 1 42: 1000. 43: -273. (V. MV. DC & AC Resistance) 5 Hot Water Delivery Temperature = TDHW AD590 Integrated C i r c u i t ' r Temperature Transducer °C -55 C to +150 C DC Volts 51: 1 52: 1000. 53: "273. (V. MV. DC & AC Resislance) 6 AD5 Q0.Integrated Solar Storage Tank Temperature - Bottom - TS_„_ C i r c u i t Tefflper-6 v BOT acure Transducer •c -55 C to +150 C DC Volts 61: 1 62: 1000. 63: -273. (V. MV, DC & AC Resistance) 7 AD5 Solar Storage Tank Temperature - Middle =• T S M T n gjj 90.Integrated c u l t Teflper-re Transducer •a' -55 C to +150 C DC Volts 71: 1 72: 1000. 73. -273. Pulse counter (4095 counts per scan maximum) 8 Volume of Hot Water Drawn - FLOW RS805 Flow Meter 200 gogntg^ Counts 60 Gal./ min Pulse Counts 81: 6 82: 1.0 83: 0 Pulse counter (15 counts per scan maximum) 9 Volume of Natural Gas Consumed = FUEL Darcqm Model Encoder "> CO 101 Meter,_ tints/ cu.ft. Counts Variable Pulse Counts 91: 6 92: 1.0 93. 0 CAMPBELL SCIENTIFIC, INC. Logan. Utah 248 CR21 Output Table Coding Form CR21 ID SDHW Heating System Start Date June 19, 1981 Start Time QQxQQ H n n r » NOTE: Select output program number and parameters from appendix B of the CR21 Operator's Manual Output ID numbers 1. 2 and 3 identify table number, day and time. ID numbers 4 and greater identify data generated by ouput programs. Only positive integers are used to program the output table. Output Table Number (1,2 or 3) 1 OutputTime Interval (minutes) CK-  60  Table Entry Number Output Program and Data Description Output ID No. Param 1 descrip. Param 2 descrip. Program No. Parameter 1 Parameter 2 1 2 Totalize - Solar Radiation = HT KJ/m 4 4 Input Channel 11: 5 2 12: 1 13: 2 Averaging - Outside Ambient A i r Temperature = TA °C 5 Input Channel 21: 5 1 22: 2 23: 3 Averaging - Inlet Cold Water'Temperature = TM 8C 6 Input Channel 31: 51 32: 3 33: 4 Averaging - Solar Heated Water Temperature = TSDHW °C 7 Input Channel 41: 51 42: 4 43: 5 Averaging - Hot Water Delivery Temperature = TDHW *C 8 Input Channel 51: 51 52: 5 53: 6 Averaging - Solar Storage Tank Temperature - Bottom = TS n„_ 'c 9 Input Channel 61: 51 62: 6 63. 7 Averaging - Solar Storage Tank Temperature - Middle » TS.,,.-. "c MID 10 Input Channel 71: 51 72: 7 73: 8 Totalize - Volume of Hot Water Drawn = FLOW Flow Counts 11 Input Channel 81: 52 82: 8 83: 9 Intermediate X*Y = TDHW*FLOW/360 0C-Counts 12 Input Channel Input Channel 91: 68 92: 5 93: 8 C A M P B E L L S C I E N T I F I C I N C . LOGAN, UTAH 249 CR21 Output Table Coding Form SDHW Heating System ^  r w J u n e 1 9 » 1 9 8 1 Start Time 0 0 ; 0 ° H o u r 8 NOTE: Select output program number and parameters from appendix B of the CR21 Operator's Manual. Output ID numbers 1. 2 and 3 identify table number, day and time. ID numbers 4 and greater identify data generated by oupul programs. Only positive integers are used to program the output table. Output Table Number (1,2 or 3) ? Output Time Interval (minutes) 03: £0 Table Entry Number Output Program and Data Description Output ID No. Param 1 descrip. Param 2 descrip. Program No. Parameter 1 Parameter 2 1 Intermediate X-Y = TSDHW-TM °C 4 2 Input Channel Input Channel 11: 66 12: A 13: 3 2 Intermediate X*Y = (TSDHW-TM)*FL0W/360 °C-Counts 3 Input Channel Input Channel 21: 6 8 22: " 23: 8 3 31: 32: 33: 4 41: 42: 43: 5 51: 52: 53: 6 61: 62: 63: 7 71: 72: 73: 8 81: 82: 83: 9 91: 92: 93: CAMPBELL SCIENTIFIC. INC. Logan. Utah 250 CR21 Output Table Coding Form SDHW Heating System S t a r t D a t e June 19, 1981 S { a r t T x m e 00:00 Hours NOTE: Select output program number and parameters from appendix B of the CR21 Operator's Manual. Output ID numbers 1. 2 and 3 identify table number, day and time. ID numbers 4 and greater identify data generated by ouput programs. Only positive integers are used to program the output table. Output Table Number (1,2 or 3) Output Time Interval (minutes) 03: 6Q Table Entry Number Output Program and Data Description Output ID No. Param 1 descrip. Param 2 descrip. Program No. Parameter 1 Parameter 2 1 Intermediate X-Y » TDHW-TM °C 4 2 Input Channel Input Channel 11: 66 12: 5 13: 3 2 Intermediate X*Y = (TDHW-TM)*FL0W/360 "C-Counts 3 Input Channel Input Channel 21: 68 22: n 23: 8 3 Totalize - Volume of Natural Gas Consumed = FUEL Counts 4 Input Channel 31: 52 32: 9 33: 4 41: 42: 43: 5 51: 52: 53: 6 61: 62: 63: 7 71: 72: 73: 8 81: 82: 83: 9 91: 92: 93: CAMPBELL SCIENTIFIC, INC. Logan. Utah 251 APPENDIX C ERROR ANALYSIS R e f e r e n c e s - A n a l o g D e v i c e s , 1979: T w o - T e r m i n a l I n t e g r a t e d C i r c u i t T e m p e r a t u r e T r a n s d u c e r , T e c h n i c a l D a t a B u l l e t i n . C a m p b e l l S c i e n t i f i c I n c . , 1981: CR21 D a t a L o g g e r Programming M a n u a l . Rho Sigma I n c : P r o d u c t I n f o r m a t i o n B u l l e t i n s . A. Measurement E r r o r T h r e e g e n e r a l s o u r c e s o f measurement e r r o r c o n t r i b u t e t o t h e u n c e r t a i n t y i n t h e d a t a v a l u e s r e c o r d e d by t h e l o g g e r . They i n c l u d e t h e f o l l o w i n g : (1) S e n s o r e r r o r s - i n c l u d e s e r r o r s due t o s e n s o r s e n s i t i v i t y , t i m e r e s p o n s e , c a l i b r a t i o n , s t a b i l i t y , n o n - l i n e a r i t y , t e m p e r a t u r e d e p e n d e n c e , d r i f t , and z e r o - p o i n t a d j u s t m e n t (2) S i g n a l c o n d i t i o n i n g e r r o r s - e r r o r s due t o t h e e l e c t r o n i c c i r c u i t r y w h i c h c o n v e r t s t h e s e n s o r s i g n a l s i n t o measurement v a l u e s (3) S a m p l i n g e r r o r s - b o t h t e m p o r a l and s p a t i a l 1. I n s t r u m e n t E r r o r s E r r o r s w i t h i n c a t e g o r i e s 1 and 2 above a r e c o l l e c t i v e l y t e r m e d i n s t r u m e n t e r r o r s . The m a g n i t u d e of t h e s e e r r o r s f o r t h e f l o w meter and t e m p e r a t u r e t r a n s d u c e r s a r e l i s t e d below. (1) Flow meter S e n s o r e r r o r = ± 1 . 5 % o v e r r a n g e 1 - 100 l i t r e s / m i n - u n d e r - e s t i m a t i o n becomes i n c r e a s i n g l y s i g n i f i c a n t as t h e f l o w r a t e d r o p s below 1 l i t r e / m i n , and as t h e d u r a t i o n o f i n d i v i d u a l draws s h o r t e n s t o < one m i n u t e S i g n a l c o n d i t i o n i n g e r r o r = a b s e n t - no c o n v e r s i o n of d i g i t a l p u l s e s i g n a l (2) T e m p e r a t u r e t r a n s d u c e r s S e n s o r e r r o r - a b s o l u t e = ± ( 0 . 0 0 7 5 * T + 0.25)°C where 0 ° C < T < 1 0 0 ° C - r e l a t i v e = a l l s e n s o r s matched t o w i t h i n ± 0 . 2 5 ° C S i g n a l c o n d i t i o n i n g e r r o r = ± 0 .5°C - s o u r c e = r e s o l u t i o n o f t h e l o g g e r ' s v o l t a g e a m p l i f i e r and A/D c o n v e r t e r - t h i s i s an i n s t a n t a n e o u s e r r o r ; i t w i l l t e n d t o c a n c e l o v e r a s e r i e s of measurements ( l o g g e r s c a n s ) p r o v i d e d t h e t e m p e r a t u r e v a r i e s o v e r a r a n g e of a t l e a s t 1.0 d e g r e e C. 252 2. S a m p l i n g E r r o r s (1) T e m p o r a l s a m p l i n g e r r o r o c c u r s when a s i g n a l i s not sampled f r e q u e n t l y enough f o r i t s e x a c t waveform t o be r e p r o d u c e d . B e c a u s e t h e r m a l and r a d i a t i v e c o n d i t i o n s w i t h i n t h e s y s t e m and i t s e n v i r o n m e n t can change q u i t e r a p i d l y w i t h t i m e , i t i s n o t p o s s i b l e t o d u p l i c a t e t h e p r e c i s e waveform of t h e t h e t e m p e r a t u r e and s o l a r r a d i a t i o n s i g n a l s u s i n g t h e a v a i l a b l e m o n i t o r i n g e q u i p m e n t . N e v e r t h e l e s s , by s a m p l i n g f a i r l y f r e q u e n t l y , a m a j o r i t y of t h e s m a l l e r v a r i a t i o n s i n t h e waveform ( as w e l l as a l l t h e l a r g e r ones) a r e c a p a b l e o f b e i n g d e t e c t e d . W i t h a 10 s e c o n d s a m p l i n g i n t e r v a l and an hour l o n g summation p e r i o d , t h e d a t a v a l u e s r e c o r d e d by t h e l o g g e r a r e b a s e d on 360 s a m p l e s . Hence t e m p o r a l s a m p l i n g e r r o r s i n t h e h o u r l y a r i t h m e t i c a l a v e r a g e t e m p e r a t u r e s and t h e i n t e g r a t e d s o l a r r a d i a t i o n t o t a l s a r e assumed t o be n e g l i g i b l e . However, t e m p o r a l s a m p l i n g e r r o r p o t e n t i a l l y e x i s t s i n t h e h o u r l y f l o w - w e i g h t e d a v e r a g e t e m p e r a t u r e s s i n c e t h e y c a n be b a s e d on as few as one measurement sample. F o r t u n a t e l y , t h e a s s o c i a t e d e r r o r i n t h e t h e r m a l e n e r g y q u a n t i t i e s becomes r e l a t i v e l y s m a l l when summing o v e r p e r i o d s of a day o r l o n g e r . T h i s i s a r e s u l t o f h o u r s w i t h l a r g e f l o w , and t h e r e f o r e s m a l l t e m p o r a l s a m p l i n g e r r o r , d o m i n a t i n g t h e a c c u m u l a t e d t h e r m a l e n e r g y q u a n t i t i e s . (2) S p a t i a l s a m p l i n g e r r o r c a n a r i s e when a v a r i a b l e i s sampled a t o n l y a l i m i t e d number of p o i n t s w i t h i n i t s s p a t i a l f i e l d . E r r o r r e s u l t s i f t h e s a m p l i n g p o i n t ( s ) c h o s e n a r e n o t r e p r e s e n t a t i v e of t h e f i e l d i n g e n e r a l , o r do not a d e q u a t e l y c a p t u r e t h e v a r i a b i l i t y w i t h i n i t . S p a t i a l s a m p l i n g e r r o r i s assumed t o be n e g l i g i b l e f o r t h e t e m p e r a t u r e s measured i n t h e water s u p p l y l i n e (TM, TSDHW, and TDHW) s i n c e t h e t r a n s d u c e r c h i p s e x t e n d w e l l i n t o t h e main f l o w s t r e a m from p r o p e r l y s e a t e d and i n s u l a t e d t h e r m o - w e l l s . M o r e o v e r , r a d i a l t e m p e r a t u r e g r a d i e n t s w i t h i n t h e s m a l l d i a m e t e r water p i p e s a r e m i n i m a l . Hence b u l k f l o w t e m p e r a t u r e s c a n be a c c u r a t e l y m easured by s a m p l i n g a t a s i n g l e p o i n t . S p a t i a l s a m p l i n g e r r o r i s however a s s o c i a t e d w i t h s e v e r a l o f t h e o t h e r s y s t e m v a r i a b l e s . T h i s i s d i s c u s s e d f u r t h e r , i n r e f e r e n c e t o u s e r -e f f e c t e r r o r , i n S e c t i o n E of C h a p t e r 6. B. U n c e r t a i n t y i n S t o r a g e Tank T e m p e r a t u r e D i f f e r e n c e The u n c e r t a i n t y a s s o c i a t e d w i t h e v a l u a t i n g t h e t e m p e r a t u r e d i f f e r e n c e between t h e bott o m and m i d - h e i g h t l e v e l s i n t h e s t o r a g e t a n k ( u s i n g t h e measured h o u r l y TSmid and TSbo t v a l u e s ) i s e s t i m a t e d a s f o l l o w s : a ( T S m i d - T S b o t ) = S Q R T [ ( 0 . 2 5 ) 2 + ( 0 . 5 ) 2 + ( 0 . 5 ) 2 ] = ±0.75°C where a s i g n i f i e s p r o b a b l e e r r o r ( S t r e e d , 1979). Here i t i s assumed t h a t t h e i n s t a n t a n e o u s s i g n a l c o n d i t i o n i n g e r r o r s do n o t c a n c e l o v e r t h e h o u r ; i e . b o t h t e m p e r a t u r e s i g n a l s a r e i n d e p e n d e n t of e a c h o t h e r and a r e s u b j e c t t o t h e maximum s i g n a l c o n d i t i o n i n g e r r o r o f ± 0 . 5 ° C . T h i s s i t u a t i o n w i l l y i e l d t h e 253 maximum p r o b a b l e e r r o r i n d e t e r m i n i n g T S m i d - T S b o t . (The minimum p r o b a b l e e r r o r i s s i m p l y e q u a l t o t h e r e l a t i v e u n c e r t a i n t y between t h e two t e m p e r a t u r e t r a n s d u c e r s = ± 0 . 2 5 ° C . ) C. U n c e r t a i n t y i n t h e T h e r m a l E n e r g y Q u a n t i t i e s and Water S u p p l y L i n e T e m p e r a t u r e s H o u r l y d a t a r e c o r d e d by t h e l o g g e r i n c l u d e t h e f o l l o w i n g t h r e e t h e r m a l e n e r g y q u a n t i t i e s ( A p p e n d i x B ) : DELTOT = [E(TDHW*FLOW)]/360 (C1) DELDHW = [I(TDHW-TM)*FLOW]/360 (C2) DELSDHW = [E(TSDHW-TM)*FLOW]/360 (C3) A l l a r e i n u n i t s of D e g r e e C - C o u n t s . The l a t t e r two t h e r m a l e n e r g y q u a n t i t i e s c a n be e x p r e s s e d i n SI u n i t s a s f o l l o w s : (1) T o t a l h e a t d e l i v e r e d QDHW = DELDHW*CONSTANT* 3 60 (C4) = [I(TDHW-TM)*FLOW]*CONSTANT where CONSTANT = c o n v e r s i o n f a c t o r f r o m Deg. C - C o u n t s t o k J = (4186 kJ/m 3 °C)*(1 U.S. G a l / 200 C o u n t s ) * ( 3 . 7 8 5 4 1 x 1 0 - 3 m 3/U.S. G a l ) = 0.07923 kJ/°C-Count (2) S o l a r h e a t d e l i v e r e d QSDHW = DELSDHW*CONSTANT*360 (C5) = [E(TSDHW-TM)*FLOW]*CONSTANT S i n c e t h e l o g g e r o n l y a c c u m u l a t e s p o s i t i v e t e m p e r a t u r e d i f f e r e n c e s , h o u r l y v a l u e s o f DELSDHW (and t h e r e f o r e QSDHW) a r e ne v e r n e g a t i v e . Hence t h e m o n t h l y t o t a l s o f s o l a r h e a t d e l i v e r e d r e p r e s e n t g r o s s q u a n t i t i e s and do n o t i n c l u d e any he a t l o s t by i n c o m i n g ' p r e - h e a t e d ' water t o t h e s t o r a g e t a n k ( C h a p t e r 4 ) . T h i s d a t a l o g g i n g l i m i t a t i o n i s n o t a p p l i c a b l e t o t h e DELDHW (and QDHW) v a l u e s s i n c e t h e TDHW-TM t e m p e r a t u r e d i f f e r e n c e was n e v e r n e g a t i v e ( o r even c l o s e t o z e r o ) . H o u r l y f l o w - w e i g h t e d a v e r a g e t e m p e r a t u r e s c a n be d e r i v e d f r o m t h e l o g g e r d a t a a s f o l l o w s : (3) Hot wat e r d e l i v e r y t e m p e r a t u r e TSHffi = (DELTOT*360) / Z FLOW = [E(TDHW*FLOW)] / Z FLOW (C6) 254 (4) I n c o m i n g c o l d water t e m p e r a t u r e T"R = TBRW - (DELDHW*360) / I FLOW (C7) = {[Z(TDHW*FLOW)]-[E(TDHW-TM)*FLOW]} / L FLOW (5) S o l a r h e a t e d water t e m p e r a t u r e TS"DHVJ = TM + (DELSDHW*360) / L FLOW (C8) = {[L(TDHW*FLOW)]-[L(TDHW-TM)*FLOW] +[Z(TSDHW-TM)*FLOW]} / Z FLOW H o u r l y v a l u e s o f TSDHW computed u s i n g e q u a t i o n C8 can n e v e r be l e s s t h a n t h e c o r r e s p o n d i n g h o u r l y v a l u e s o f TM. T h i s e v a l u a t i o n l i m i t a t i o n i s a d i r e c t r e s u l t of t h e DELSDHW v a l u e s a l w a y s b e i n g n o n - n e g a t i v e as s t a t e d a b o v e . Thus, h o u r l y f l o w - w e i g h t e d a v e r a g e TSDHW t e m p e r a t u r e s have t h e p o t e n t i a l t o be p o s i t i v e l y b i a s e d ( C h a p t e r 4 ) . Assumin g t h a t s e n s o r e r r o r s f o r t h e f l o w meter and t e m p e r a t u r e t r a n s d u c e r s a r e i n d e p e n d e n t of e a c h o t h e r , and t h a t s i g n a l c o n d i t i o n i n g e r r o r s f o r t h e t e m p e r a t u r e t r a n s d u c e r s c a n c e l o v e r e a c h h o u r , t h e f o l l o w i n g e x p r e s s i o n s c a n be w r i t t e n f o r t h e h o u r l y t h e r m a l e n e r g y q u a n t i t i e s and water s u p p l y l i n e t e m p e r a t u r e s ( t h e summation and a v e r a g i n g symbols have been o m i t t e d f o r c l a r i t y ) : (6) QDHW = (TDHW-TM)*FLOW*CONSTANT ± AQDHW (C9a) where AQDHW = f|FLOW*A(TDHW-TM)|+|(TDHW-TM)*AFLOW|] (C9b) *CONSTANT AFLOW = ±(0.015 * FLOW) and A(TDHW-TM) = ±0.25°C H e r e , t h e a b s o l u t e method ( S t r e e d , 1979) has been u s e d f o r c o m b i n i n g i n d i v i d u a l e r r o r t e r m s i n a f u n c t i o n a l r e l a t i o n s h i p . (7) QSDHW = (TSDHW-TM)*FLOW*CONSTANT ± AQSDHW ( C l O a ) where AQSDHW = [|FLOW*A(TSDHW-TM)| + (C l O b ) |(TSDHW-TM)*AFLOW|] * CONSTANT AFLOW = ±(0.015 * FLOW) and A(TSDHW-TM) = ±0.25°C (8) TDHW = TDHW ± ATDHW (C11) where ATDHW = ±(0 . 0 0 7 5 * T D H W + 0.25)°C (9) TM = TDHW - (TDHW-TM) ± aTM (C12) where aTM = SQRT[(ATDHW) 2 + A(TDHW-TM) 2] = SQRTf(0.0075*TDHW + 0 . 2 5 ) 2 + ( 0 . 2 5 ) 2 ] 255 (10) TSDHW = TDHW - (TDHW-TM) + (TSDHW-TM) ± aTSDHW (C13) where aTSDHW = SQRT[(ATDHW)2 + A(TDHW-TM)2 + A(TSDHW-TM)2] = SQRT[(0.0075*TDHW + 0.25) 2 + (0.25) 2 + (0.25) 2] Table C.1 l i s t s the maximum and minimum monthly uncertainty estimates for QSDHW and QDHW. They were evaluated by summing the hourly QSDHW and QDHW values computed using equations C9a/b and ClOa/b above. Also l i s t e d are monthly integrals of the measured QSDHW and QDHW values. Figure C.1 presents a corresponding graph of the monthly uncertainty estimates. On an absolute basis, they are dependent on the magnitude of the thermal energy quantities. In p a r t i c u l a r , they are large when the temperature differences are at a maximum, and are small when the temperature differences are at a minimum. This r e f l e c t s the dominance of flow meter error in the uncertainty estimates. On a r e l a t i v e basis, this error e f f e c t i v e l y sets the uncertainty in the thermal energy quantities at a constant ±1.5%. D. Uncertaintity in the Solar Fraction If the solar frac t i o n i s defined as SFRAC = QSDHW/QDHW (C14) and the 'true' values of QSDHW and QDHW are expressed in terms of the measured values, i e . QSDHW. = QSDHW (1 +' 5) = C1*QSDHW (CI 5) t m m QDHWfc = QDHWm(l + £) = C2*QDHWm (C16) where 6 = AQSDHW/QSDHW and £ = AQDHW/QDHW are the estimated f r a c t i o n a l errors (evaluated using equations C9a/b and ClOa/b), then by substituting equations C15 and C16 into equation C14, the 'true' solar frac t i o n can be expressed as follows: SFRAC. = (C1*QSDHW )/(C2*QDHW ) (C17) t m m = (C1/C2) * SFRAC m Hence the difference between the 'true' solar fraction and that measured is equal to ASFRAC = SFRACm - SFRACfc = SFRAC^* f1 - (C1/C2)] (C18) Evaluation of t h i s l a s t equation y i e l d s the estimated uncertainty in the measured solar f r a c t i o n s . On a r e l a t i v e basis t h i s uncertainty is approximately ±3%. This i s shown graphically for the monthly solar fractions in Figure C.2. The corresponding maximum and minimum uncertainty estimates are l i s t e d in Table C.1. TABLE C.1 MONTHLY ERROR ANALYSIS SUMMARY MONTH QSDHW OSDHW QSDHW QDHW QDHW QDHW SFRAC SFRAC SFRAC MAXIMUM MEAS. MINIMUM MAXIMUM MEAS. MINIMUM MAXIMUM MEAS. MINIMUM (GJ) (GJ) (GJ) (GJ) (GJ) (GJ) 1981 + *JUN 0. . 398 0 . 392 0 . 387 0 .774 0 . 762 0 . 751 0 . 531 0 .515 0, .500 JUL 0 .940 0 .926 0 .912 1 .317 1 .298 1 . 278 0 . 735 0 .714 0 .692 AUG 1 .029 1 .014 0 .998 0 .990 0 .975 0 .960 1 .071 1 .040 1 .009 SEP 0, .869 0 .856 0 .843 1 .277 1 . 258 1 . 239 0 .701 0 .680 0 .660 OCT 0. .656 0 .646 0 .636 1 .738 1 .712 1 .686 0 .389 0. . 377 0, . 366 NOV 0, , 347 0 .342 0. . 336 1 .656 1 .631 1 .607 0, .216 0, .209 0, .203 DEC 0. .219 0 .216 0, .212 1 .648 1 . .623 1 .599 0, . 137 0, . 133 0. . 129 1982 JAN 0. . 172 0. . 170 0. , 167 1 .864 1 . .837 1 . 809 0. .095 0. 092 0. .089 FEB 0. .405 0. .399 0. . 393 2 .049 2 . 019 1 .988 0, .204 0. . 198 0. , 192 MAR 0. ,804 0. .792 0. , 780 1 .556 1 . .533 1 , .510 0. . 532 0. 516 0. 501 APR 1 . , 140 1 . . 123 1 . . 106 1 . .637 1 . 612 1 , .588 0. ,718 0. 697 0. 676 MAY 1 . .315 1 . .296 1 . 276 1 . . 797 1 . ,771 1 . . 744 0. 754 0. 732 0. 710 JUN 1 . 301 1 . .282 1 . 263 1 . . 722 1 . 696 1 . .670 0. 779 0. 756 0. 733 JUL 1 . 075 1 . .059 1 . 043 1 . 484 1 . 462 1 . .440 0. 746 0. 724 0. 703 AUG 1 . 091 1 . 075 1 . 058 1 . 566 1 . 543 1 . 520 0. 718 0. 697 0. 676 SEP 0. 960 0. 945 0. 931 1 . 719 1 . 693 1 . 668 0. 576 0. 558 0. 542 +OCT 0. 632 0. 622 0. 613 1 . .520 1 . 497 1 . ,474 0. 429 0. 416 0. 403 NOV 0. 380 0. 374 0. 368 1 . .916 1 . 887 1 . 859 0. 204 0. 198 0. 192 *DEC 0. 132 0. 130 0. 128 0. 942 0. 928 0. 914 0. 144 0. 140 0. 136 TOTAL 13 . 865 13. 658 13. 450 29. 171 28. 737 28 . 303 0. 490 0. 475 0. 461 * - INCOMPLETE MONTH + - 4 DAYS OF MISSING DATA QSDHW - SOLAR HOT WATER HEAT SFRAC - SOLAR FRACTION OF TOTAL HOT WATER HEAT QDHW - TOTAL (SOLAR AND AUXILIARY) HOT WATER HEAT F i g u r e C.1 F i g u r e C.2 UNCERTAINTY IN THE MONTHLY SOLAR FRACTIONS o M r— U <x cc u. QL cr _J o co 1.2 1. M 1.0 0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1-0.0-i 1 1 r i r i r 1.2 -1.1 1.0 -0.9 -0.8 co o (-0.7 £ •X) ho.6 Z> D o hO.S M o 2 -0.4 -0.3 -0.2 -0.1 -0.0 JUN JUL RUC SEP OCT NOV DEC JRN FEB ttAR RPR MRY JUN JUL RUG SEP OCT NOV DEC 1981 1982 ho oo 259 APPENDIX D DETAILED CALCULATION OF THE THEORETICAL HEAT LOSS COEFFICIENT FOR THE SOLAR STORAGE TANK R e f e r e n c e s - Bennet,C.O. and J . E . M y e r s , 1974: "Momentum, Heat and Mass T r a n s e r " , M c G r a w - H i l l , New Y o r k , 2nd ed. K r e i t h , E. and W.Z. B l a c k , 1980: " B a s i c Heat T r a n s f e r " , H a r p e r & Row, New Y o r k . S o l a r s y s t e m s I n d u s t r i e s L t d . , 1980: S o l a r P r o d u c t D a t a S h e e t No. 19. The s t o r a g e t a n k h e a t l o s s c o e f f i c i e n t i s a p a r a m e t e r w h i c h i n d i c a t e s t h e a b i l i t y of t h e water i n t h e s t o r a g e tank t o l o s e h e a t t o ( o r g a i n h e a t from) t h e s u r r o u n d i n g basement a i r . I t s v a l u e depends upon t h e s i z e and shape o f t h e s t o r a g e t a n k , t h e t h e r m a l and p h y s i c a l p r o p e r t i e s of t h e water i n t h e t a n k , and - most i m p o r t a n t l y - on t h e t y p e and t h i c k n e s s of t h e m a t e r i a l i n s u l a t i n g i t . The a p p r o a c h t a k e n h e r e i s t o d e r i v e UAS u s i n g t h e network r e s i s t a n c e method. S t e a d y s t a t e c o n d i t i o n s a r e assumed and t h e r e s i s t a n c e o f t h e t a n k w a l l ( p o l y e t h y l e n e ) i s i g n o r e d . The network c o n s i s t s o f t h r e e t h e r m a l r e s i s t a n c e s : R i , R and Ro. R i r e p r e s e n t s t h e i n s i d e f i l m r e s i s t a n c e f r o m t h e main body of water i n t h e s t o r a g e tank t o t h e t a n k w a l l . R r e p r e s e n t s t h e r e s i s t a n c e t o h e a t f l o w a c r o s s t h e i n s u l a t i o n , and Ro r e p r e s e n t s t h e o u t s i d e f i l m r e s i s t a n c e f r o m t h e tank c o v e r t o t h e f r e e l y c i r c u l a t i n g a m b i e n t a i r . V a l u e s u s e d f o r t h e s e r e s i s t a n c e t e r m s a r e l i s t e d i n T a b l e B.1 b e l o w . T a b l e D.1 T h e r m a l R e s i s t a n c e V a l u e s f o r t h e S t o r a g e Tank R i = 0.0035 ° C m 2 / W water t o t a n k R = 2.64 " s t y r o f o a m - t a n k ends = 3.70 " f i b r e g l a s s - t a n k s i d e s Ro = 0.12 " c o v e r t o a i r Heat l o s s i s assumed t o o c c u r from t h e ends and s i d e s of t h e s t o r a g e t a n k i n p a r a l l e l . T hus, t h e o v e r a l l s t o r a g e a r e a h e a t l o s s c o e f f i c i e n t i s c a l c u l a t e d as f o l l o w s : UAS = ( U A ) t b + (UA)s where ( U A ) t b = t o p and b o t t o m a r e a h e a t l o s s c o f f i c i e n t s and (UA)s = t o t a l s i d e a r e a h e a t l o s s c o e f f i c i e n t The s t o r a g e t a n k d i m e n s i o n s u s e d i n t h e f o l l o w i n g c a l c u l a t i o n s a r e shown i n F i g u r e A.6. 260 (1) C a l c u l a t i o n o f ( U A ) t b R t b = R i + R + Ro = 0.0035 + 2.64 + 0.12 = 2.76 °C m2/W A i = 7T D i 2 / 4 = t t ( 0 . 6 1 0 ) 2 / 4 = 0.292 m 2 ( U A ) t b = A i / Rtb = 0.292/2.76 = 0.106 W / ° C (2) C a l c u l a t i o n o f (UA)s Ao = ff Do L i = 7.(0.914) ( 1 .710) = 4.91 m 2 r = ( r o - r i ) / In ( r o / r i ) = ( 0 . 4 5 7 - 0 . 3 0 5 ) / l n ( 0 . 4 5 7 / 0 . 3 0 5 ) = 0.152 / 0.404 .= 0.376 m (UA)s = Ao / ( R i * r o / r i + R * r o / r + Ro ) = 4.91/(0.0035*0.457/0.305 + 3.70*0.457/0.376 + 0.12) = 4.91/(0.00524 + 4.50 + 0.12) = 4.91/4.63 = 1.061 W / ° C T h e r e f o r e , UAS = 0.106 + 0.106 + 1.061 = 1.273 W / ° C or 4.58 kJ/hr°C 261 APPENDIX E DETERMINATION OF A SURROGATE VARIABLE FOR THE BASEMENT AIR TEMPERATURE S i n c e t h e basement a i r t e m p e r a t u r e was measured d u r i n g o n l y a l i m i t e d p a r t o f t h e m o n i t o r i n g p e r i o d , a s u b s t i t u t e method f o r e v a l u a t i n g TBSM had t o be u s e d d u r i n g o t h e r p e r i o d s o f s y s t e m s i m u l a t i o n . T h e r e were two d i f f e r e n t a p p r o a c h e s t o t a k e . One was t o assume t h a t t h e basement a i r t e m p e r a t u r e r e m a i n e d c o n s t a n t o v e r t h e s i m u l a t i o n p e r i o d ( as was done i n WATSUN DHWA). The a l t e r n a t i v e was t o e s t i m a t e v a l u e s f o r TBSM u s i n g a s u r r o g a t e v a r i a b l e . T h i s l a t t e r a p p r o a c h was a c t i v e l y p u r s u e d i n t h e p r e s e n t s t u d y . A n a l y s i s o f t h e measured TBSM v a l u e s r e v e a l e d t h a t t h e basement a i r t e m p e r a t u r e had a maximum ran g e o f a p p r o x i m a t e l y 10 d e g r e e s C, and was s u b j e c t t o c o n s i d e r a b l e d i u r n a l and d a y - t o - d a y v a r i a b i l i t y . In w i n t e r , v a r i a b i l i t y i n t h e basement a i r t e m p e r a t u r e can mean t h e d i f f e r e n c e between p o s i t i v e and n e g a t i v e s t a n d b y h e a t l o s s s i n c e t h e t e m p e r a t u r e of t h e s t o r a g e t a n k i s o f t e n v e r y c l o s e t o t h a t of t h e s u r r o u n d i n g basement a i r . In summer, v a r i a b i l i t y i n TBSM i s r e l a t i v e l y l e s s i m p o r t a n t ( w i t h r e s p e c t t o s t a n d b y h e a t l o s s ) s i n c e t h e m a g n i t u d e of t h e t a n k - t o - a i r t e m p e r a t u r e g r a d i e n t a v e r a g e s 25 d e g r e e s C, and can even be a s l a r g e a s 50 d e g r e e s C f o r s h o r t p e r i o d s of t i m e . N e v e r t h e l e s s , i f t h e v a r i a b i l i t y i n TBSM i s n o t a c c o u n t e d f o r , s u b s t a n t i a l u s e r - e f f e c t e r r o r can be i n t r o d u c e d i n t o t h e s t a n d b y h e a t l o s s m odel. Thus s u b s t i t u t e t e m p e r a t u r e s w h i c h c a p t u r e t h e v a r i a b i l i t y i n TBSM a r e d e s i r a b l e . I t s h o u l d be e m p h a s i z e d , however, t h a t p r e c i s i o n i n TBSM does n o t by i t s e l f y i e l d a c c u r a c y i n t h e s t a n d b y h e a t l o s s m o d e l . E r r o r i n TBSM c a n be e i t h e r o f f s e t o r compounded by i n a c c u r a c i e s e x i s t i n g w i t h i n t h e UAS and TS t e r m s o f e q u a t i o n 21 ( C h a p t e r 5 ) . T h i s means t h a t t h e p r e d i c t e d QSENV v a l u e s c a n i n f a c t be g r e a t e r t h a n o r l e s s t h a n t h e ' t r u e ' v a l u e s i n d e p e n d e n t o f t h e e r r o r i n TBSM. Hence o b t a i n i n g p r e c i s e e s t i m a t e s of TBSM does not n e c e s s a r i l y improve t h e a c c u r a c y o f t h e s t a n d b y h e a t l o s s m odel; i t o n l y r e d u c e s t h e p o t e n t i a l u s e r - e f f e c t e r r o r a s s o c i a t e d w i t h t h i s v a r i a b l e . D u r i n g q u a l i t y c o n t r o l o f t h e d a t a i t was n o t i c e d t h a t t h e t e m p e r a t u r e o f t h e i n c o m i n g c o l d w a ter t e n d e d t o i n c r e a s e and e q u i l i b r a t e w i t h t h a t of t h e basement a i r d u r i n g t h o s e h o u r s i n w h i c h t h e r e was no h o t water c o n s u m p t i o n . In o t h e r words, s t a g n a n t c o l d water i n t h e u n - i n s u l a t e d i n l e t p i p e was b e i n g h e a t e d q u i t e r e a d i l y by t h e s u r r o u n d i n g basement a i r . Thus i t was t h o u g h t t h a t i f t h e c o l d w a t e r t e m p e r a t u r e s measured d u r i n g p e r i o d s of ' n o - f l o w ' were a v e r a g e d on a d a i l y b a s i s , t h e y c o u l d p r o v i d e a r e a s o n a b l e e s t i m a t e o f t h e basement a i r t e m p e r a t u r e . M o n i t o r i n g o f t h e basement a i r t e m p e r a t u r e was i n f a c t i n i t i a t e d i n o r d e r t o t e s t t h i s h y p o t h e s i s . A t o t a l of 3 1/2 months of h o u r l y v a l u e s f o r TBSM were r e c o r d e d u s i n g a s e p a r a t e d a t a l o g g e r . T h i s p r o v i d e d a s u f f i c i e n t l y e x t e n s i v e s e t o f t e m p e r a t u r e d a t a w i t h w h i c h t o examine t h e agreement between t h e e s t i m a t e d and measured v a l u e s . 262 M e a s u r e d h o u r l y TBSM v a l u e s f o r t h e 3 months, A u g u s t t h r o u g h O c t o b e r 1982, a r e r e p r e s e n t e d by t h e s o l i d c u r v e i n F i g u r e E.1; t h e d a s h e d l i n e i n d i c a t e s d a i l y a v e r a g i n g of t h e s e v a l u e s . [ N o t e : The h o u r l y v a l u e s a r e p l o t t e d u s i n g t h e o u t p u t r e s o l u t i o n o f t h e l o g g e r (±0.01°C) - not t h e p r e c i s i o n of t h e t e m p e r a t u r e s e n s o r ( ± 0 . 1 ° C ) ] . Warming of t h e basement a i r d u r i n g t h e d a y t i m e , and i t s s u b s e q u e n t c o o l i n g a t n i g h t , i s t r a c e d by t h e d i u r n a l c y c l e s i n t h e h o u r l y t e m p e r a t u r e c u r v e . Up u n t i l September 27, t h e s e d i u r n a l t e m p e r a t u r e c y c l e s - w h i c h a v e r a g e d 2.3 d e g r e e s C i n range - were ' n a t u r a l l y ' o c c u r i n g . A f t e r t h i s d a t e , t h e s p a c e h e a t i n g f u r n a c e came i n t o s e a s o n a l o p e r a t i o n . I t t h e n e f f e c t i v e l y c o n t r o l l e d t e m p e r a t u r e f l u c t u a t i o n s , c a u s i n g a d d i t i o n a l peaks and t r o u g h s t o o c c u r b e s i d e s t h o s e i n t h e d i u r n a l t e m p e r a t u r e c y c l e s . P r i o r t o t h e end o f September, t r a n s i t o r y warming and c o o l i n g t r e n d s c a n be o b s e r v e d . They l a s t f o r p e r i o d s o f a week o r l o n g e r , and a r e a c c o m p a n i e d by marked c h a n g e s i n t h e d i u r n a l t e m p e r a t u r e c y c l e s . S i n c e t h e y a r e a f u n c t i o n of t h e p r e v a i l i n g w e a t h e r c o n d i t i o n s , t h e y d i s a p p e a r once t h e f u r n a c e commences s e a s o n a l o p e r a t i o n . The d o t t e d l i n e i n F i g u r e E.1 r e p r e s e n t s t h e d a i l y a v e r a g e c o l d w a ter t e m p e r a t u r e u n d e r n o - f l o w c o n d i t i o n s (TMNF). The a c t u a l l i n e p l o t t e d i s a 5-day r u n n i n g mean. (Hence t h e d a t a gap i n O c t o b e r e x t e n d s o v e r s e v e n d a y s i n s t e a d of t h r e e . ) T h i s a v e r a g i n g p e r i o d p r o v i d e s s l i g h t l y g r e a t e r agreement between t h e e s t i m a t e d and measured t e m p e r a t u r e s , as i n d i c a t e d by t h e s t a t i s t i c s i n T a b l e E.1 below. C o n s e q u e n t l y , TMNF5 was c h o s e n a s t h e s u r r o g a t e v a r i a b l e f o r TBSM. T a b l e E.1 Agreement Between t h e D a i l y C o l d Water and Basement A i r T e m p e r a t u r e s ( J u l y 30 t o November 14, 1982) T e m p e r a t u r e A v e r a g i n g Mean Max. Dev. RMSE MBE C o r r . V a r i a b l e P e r i o d (°C) (°C) (°C) (°C) C o e f f . TBSM d a i l y 18.63 TMNF1 d a i l y 18.89 1.86 0.69 +0.26 0.785 TMNF3 3-day 18.88 1.78 0.35 +0.25 0.862 r u n n i n g mean TMNF5 5-day 18.88 1.23 0.31 +0.25 0.879 r u n n i n g mean TMNF7 7-day 18.90 1.69 0.36 +0.27 0.852 r u n n i n g mean 263 S i n c e TMNF5 c a n n o t be e v a l u a t e d on an h o u r l y b a s i s , i t i s u n a b l e t o i n c o r p o r a t e t h e d i u r n a l t e m p e r a t u r e c y c l e s i n t o t h e s t a n d b y h e a t l o s s m odel. However, i t i s a b l e t o c a p t u r e t h e s m a l l amount of d a y - t o - d a y v a r i a b i l i t y i n t h e basement a i r t e m p e r a t u r e . T h i s i s i n d i c a t e d by t h e c o r r e l a t i o n c o e f f i c i e n t v a l u e o f 0.88. F u r t h e r m o r e , t h e d a i l y TMNF5 v a l u e s were a l l w i t h i n 1.23 d e g r e e s C o f t h e d a i l y mean TBSM v a l u e s ; i n d i v i d u a l (RMSE) and l o n g t e r m (MBE) d e v i a t o n s a v e r a g e d 0.31 and 0.25 d e g r e e s C r e s p e c t i v e l y . T h i s compares w i t h a range of 5.6 d e g r e e s C and a s t a n d a r d d e v i a t i o n of 1.3 d e g r e e s C i n t h e d a i l y mean TBSM v a l u e s . A v i s u a l e x a m i n a t i o n of t h e t e m p e r a t u r e c u r v e s shows t h a t t h e maximum d e v i a t i o n between t h e e s t i m a t e d d a i l y and measured h o u r l y v a l u e s i s 3.0 d e g r e e s C. S i n c e basement a i r t e m p e r a t u r e i s an h o u r l y i n p u t v a r i a b l e , t h i s d e v i a t i o n i n d i c a t e s t h e maximum e r r o r i n e s t i m a t i n g t h e TBSM v a l u e s f o r t h e s t a n d b y h e a t l o s s m odel; t h e a s s o c i a t e d a v e r a g e (RMSE) e r r o r i s 0.9 d e g r e e C. In c o m p a r i s o n , i f one had assumed a c o n s t a n t basement a i r t e m p e r a t u r e e q u a l t o t h e measured mean TBSM v a l u e o f 18.6°C, t h e maximum e r r o r would have i n c r e a s e d t o 4.8 d e g r e e s C and t h e a v e r a g e e r r o r t o 1.5 d e g r e e s C. Hence t h e s u r r o g a t e v a r i a b l e p r o v i d e s s l i g h t l y more p r e c i s e e s t i m a t e s o f TBSM t h a n does an u n b i a s e d c o n s t a n t t e m p e r a t u r e v a l u e ( a t l e a s t o v e r t h e p e r i o d e x a m i n e d ) . An a d d i t i o n a l comment i s i n c l u d e d t o e x p l a i n why t h e mean TMNF v a l u e s a r e s l i g h t l y g r e a t e r (+0.26 d e g r e e C) t h a n t h e mean TBSM v a l u e ( T a b l e E . 1 ) , even t h o u g h t h e f o r m e r a r e b a s e d l a r g e l y on n i g h t t i m e h o u r s when t h e basement a i r t e m p e r a t u r e t e n d s t o be c o o l e r . T h e r e a r e two r e a s o n s . F i r s t l y , t h e c o l d w a t e r i n l e t p i p e i s s i t u a t e d n e a r t h e basement c e i l i n g and i s t h e r e f o r e s u r r o u n d e d by g e n e r a l l y warmer a i r t h a n e x i s t s a t t h e ta n k m i d - h e i g h t l e v e l where TBSM was measured. S e c o n d l y , t h e i n l e t p i p e i s i n c l o s e p r o x i m i t y t o t h e s p a c e h e a t i n g f u r n a c e and i t s a c c o m p a n y i n g d u c t w o r k ( F i g u r e E . 2 ) , w h i c h h e a t t h e basement a i r n o n - u n i f o r m l y . E x a m i n a t i o n o f i n d i v i d u a l h o u r l y TMNF v a l u e s r e v e a l e d t h a t when t h e f u r n a c e i s o p e r a t i n g , s t a g n a n t water i n t h e i n l e t p i p e c a n a t t a i n t e m p e r a t u r e s as h i g h a s 26°C. However, t h e s e e l e v a t e d t e m p e r a t u r e s a r e o f f s e t by c o o l e r t e m p e r a t u r e s when t h e s t a g n a n t c o l d w ater i s f i r s t warming. T h i s i s t h e r e a s o n why t h e 5-day r u n n i n g mean p r o d u c e d t h e c l o s e s t e s t i m a t e of basement a i r t e m p e r a t u r e ; d a y s w i t h a b n o r m a l l y h i g h o r low TMNF v a l u e s were a v e r a g e d o u t . c W > H H-i-l 3 ro H fD CO 3 ro 13 H CD H* (D Co 01 rt C • t i r—1 rt> O •? f t O i-h CO v ' • t i n > ro c 09 H-c o CO rt rt ft) i—• Co 1 3 ro 1—» cn VO c CO l-t ro ro w CO ro a ro 3 rr BASEMENT AIR TEMPERATURE DAILY HERN MEflSURED HOURLY PREDICTED DAILY i I I I L 21 -26 -25 -24 -23 -22 -21 -20 -19 M6 his •14 € i a AUGUST 1382 10 11 12 13 14 15 TJ m 33 TO m a m CD r-J8 ~ ro CTv 4> 265 TEflPERRTURE (DEC 0 (3 "330) 3binibcd3dUI31 F i g u r e E . l Time S e r i e s P l o t of P r e d i c t e d and Measured Basement ( c o n t i n u e d ) A i r T e m p e r a t u r e : (b) August 16 - 31, 1982 266 TEMPERATURE (DEC P a *03a) 3aniby3dU3X F i g u r e E.1 Time S e r i e s P l o t of P r e d i c t e d and Measured Basement ( c o n t i n u e d ) A i r T e m p e r a t u r e : (c) September 1 - 15, 1982 267 F i g u r e E.1 ( c o n t i n u e d ) Time S e r i e s P l o t A i r T e m p e r a t u r e : of P r e d i c t e d and Measured Basement (d) September 16 - 30, 1982 n o OQ 0 C rt H H* ro C w ro • — !> H-i-l 3 ro H ro CO ro X) H ro tu cn rt C TJ i-l h-1 ro o •• rt O ro Hi —^ •rj H o ro o (X rt H-O o a ' rt ro ro i-l Cu i—* 3 BASEMENT M R TEMPERATURE i a -u i ro * cu cn >- e H oo ro a . w CO ro 3 ro 3 flEflSURED HOURLY PREDICTED DRILY D R I L Y MEAN 71 26 -25 -2 4 -23 -T 5 € 1 S 3 OCTOBER 1982 O |cw c 1-1 H-lfo 3 C |W (D > H H 3 ft) H ft) C/3 BASEMENT AIR TEMPERflTURE 3 ft) i-l CO 05 rt C ^ r i r-> fD O O l-h l-i ro ex H-n o n o c r ri-ft) ro i-i a . I—» CO a . I 3 o j ro I—' CO - CD c 1— 1-1 vo ro CO cx ho w co cn ro 3 ro 3 flEflSURED HOURLY PREDICTED DAILY DAILY MEAN 16 17 18 19 20 21 22 23 24 OCTOBER 1982 25 26 27 28 29 30 F i g u r e E .2 C o l d W a t e r I n l e t P i p e i n R e l a t i o n t o Space H e a t i n g F u r n a c e , D u c t w o r k , and Basement C e i l i n g 271 APPENDIX F SAMPLE PRINTOUT OF HOURLY SIMULATION RESULTS J U L I A N D A Y 4 8 F E B R U A R Y 1 7 . 1 9 8 2 • • • H R T A T C P T C I T C O T B S M T M T S T S D H W TDHW ( C ) ( C ) ( C ) ( C ) . ( C ) ( C ) ( C ) ( C ) ( C ) 1 8 . 3 8 . 3 - 9 . 6 - 9 . G 1 7 . 7 - 1 6 . 1 9 . 7 - 1 S . 1 - S 4 . 6 2 7 . 9 7 . 9 - 9 . 7 - 9 7 1 7 . 7 - 1 7 : 0 9 . 8 - 1 7 . 0 - 5 3 . S 3 7 . 6 7 . 6 - 9 . 8 - 9 . 8 1 7 . 7 - 1 7 . 0 9 . 8 - 1 7 . 0 - 5 2 . 7 4 7 . 4 7 . 4 - 9 . 8 - 9 . 8 1 7 . 7 - 1 6 . 9 9 . 9 - 1 6 . 9 - 5 2 . 1 5 7 . 2 7 . 2 - 9 . 9 - 9 . 9 1 7 . 7 - 1 6 . 0 1 0 . 0 - 1 6 . 0 - 5 1 . 3 6 6 . 9 6 . 9 - 1 0 . 0 - 1 0 . 0 1 7 . 7 1 6 . 0 1 0 . 1 1 0 . 0 5 0 . 2 7 6 . 7 6 . 7 - 1 0 . 1 - 1 0 . 1 1 7 . 7 6 . 9 9 . 9 1 0 . 1 5 6 . 9 8 6 . 5 8 . 1 - 9 . 9 - 9 . 9 1 7 . 7 8 . 0 9 . 8 9 . 9 6 5 . 0 9 6 . 6 2 8 . 2 9 . B - 1 1 . 2 1 7 . 7 7 . 5 9 . 8 9 . 8 6 7 . 0 1 0 7 . 9 3 8 . 7 9 . 8 t l . 9 1 7 . 7 1 4 . 3 1 2 . 0 9 . 8 6 2 . 8 11 8 . 6 7 5 . 1 1 2 . 0 1 6 . 6 1 7 . 7 - 1 7 . 0 1 6 . 6 - 1 7 . 0 - 5 8 . 1 1 2 1 0 . 2 1 1 5 . 4 1 6 . 6 2 3 . 8 1 7 . 7 8 . 6 2 3 . 5 1 6 . 6 6 2 . 5 1 3 1 1 . 3 1 3 8 . 6 2 3 . 5 3 1 . 9 1 7 . 7 1 0 . 3 3 1 . 5 2 3 . 5 6 1 . 7 1 4 1 1 . 6 1 0 6 . 3 3 1 . 5 3 7 . 0 1 7 . 7 9 . 8 3 6 . 3 3 1 . 5 5 9 . 6 1 5 1 0 . 2 2 9 . 3 3 6 . 3 - 3 5 . 8 1 7 . 7 1 0 . 3 3 5 . 5 3 6 . 3 5 7 . 3 1 6 9 . 6 4 1 . 5 - 3 5 . 5 - 3 5 . 5 1 7 . 7 7 . 7 3 3 . 9 3 5 . 5 5 4 . 7 1 7 8 . 6 1 3 . 5 - 3 3 . 9 - 3 3 . 9 1 7 . 7 9 . 4 3 3 . 0 3 3 . 9 5 6 . 3 1 8 7 . 3 7 . 5 - 3 3 . 0 - 3 3 . 0 1 7 . 7 6 . 8 2 9 . 7 3 3 . 0 5 4 . 5 1 9 6 . 1 6 . 1 - 2 9 . 7 - 2 9 . 7 1 7 . 7 8 . 7 2 8 . 2 2 9 . 7 5 9 . 6 2 0 5 . 9 5 . 9 - 2 8 . 2 - 2 8 . 2 1 7 . 7 1 5 . 8 2 8 . 0 2 8 . 2 5 6 . 0 2 1 5 . 1 5 . 1 - 2 8 . 0 - 2 8 . 0 1 7 . 7 7 . 5 1 8 . 2 2 8 . 0 6 7 . 4 2 2 5 . 0 5 0 - 1 8 . 2 - 1 8 . 2 1 7 . 7 1 8 . 8 1 8 . 2 1 8 . 2 5 7 . 7 2 3 4 . 7 4 . 7 - 1 8 2 - 1 8 . 2 1 7 . 7 1 2 . 9 1 8 . 1 1 8 . 2 5 5 . 0 2 4 3 . 9 3 . 9 - 1 8 . 1 - 1 8 . 1 1 7 . 7 1 5 . 1 1 8 . 1 1 8 . 1 5 4 . 0 D A I L Y T O T A L S O H T ( K J ) O . 0 . o. 0 . 0 . 0 . o. 2 8 1 . 3 7 2 6 . 5 2 9 2 . 1 1 4 2 4 . 1 8 0 8 7 . 2 1 8 7 5 . 1 6 2 7 3 . 3 2 8 6 . 5 4 8 6 . 8 4 0 . 3 4 . O . O . O . 0 . 0 . 0 . ( M J ) 8 6 . 6 0 2 O C S S ( K O ) O . 0 . O . 0 . O . O . O . O . O . 3 5 9 7 . 7 8 7 0 . 1 2 3 1 1 . 1 4 3 3 7 . 9 3 0 9 . O . O . O . O . O . O . O . O . 0 . 0 . ( M J ) 4 7 . 4 2 5 Q S T O R ( K J ) 1 2 9 . 1 2 8 . 1 2 7 . 1 2 6 . 1 2 5 . 1 2 5 . - 1 9 4 . - 1 9 5 . - 7 1 . 3 7 2 6 . 7 9 6 2 . 1 1 8 0 6 . 1 3 8 2 1 . 8 2 2 5 . - 1 4 7 5 . - 2 7 4 6 . - 1 5 3 8 . - 5 6 7 5 . - 2 4 3 3 . - 3 8 8 . 1 6 8 9 2 . - 2 . - 1 4 3 . - 3 5 . ( M J ) 1 4 . 5 1 4 O S E N V ( K J ) - 1 2 9 . - 1 2 8 . - 1 2 7 . - 1 2 6 . - 1 2 5 . - 1 2 4 . - 1 2 2 . - 1 2 4 . - 1 2 6 . - 1 2 7 . - 9 2 . - 1 8 . 9 2 . 2 2 I . 2 9 8 2 8 4 . 2 5 9 . 2 4 4 . 1 9 1 . 1 6 9 . 1 6 5 . 8 . 8 . 6 ( M J ) 0 . 5 7 7 O S D H W ( K J ) O . O . O . O . 0 . - 2 . 3 1 6 . 3 1 9 . 1 9 7 . - 3 . 0 . 5 2 3 . 4 2 4 . 8 6 3 . 1 1 7 7 . 2 4 6 2 . 1 2 8 0 . 5 4 3 I . 2 2 4 1 . 2 1 9 . 1 6 7 2 7 . - 5 . 1 3 6 28. ( M J ) 3 2 . 3 3 4 O D H W ( K J ) O . O . o. O . o. 1 1 . 4 9 9 7 . 9 3 5 2 . 5 0 2 6 . 2 7 . O . 3 5 1 1 . 1 6 5 3 . 1 9 7 9 . 2 1 2 3 . 4 1 6 7 . 2 4 5 3 . 9 9 0 3 . 5 4 5 3 . 7 1 0 . 4 8 8 8 7 . 3 0 2 . 1 0 8 7 . 3 6 7 . ( M J ) 1 0 2 . O O B F L O W ( L ) 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 O . 1 2 3 . 8 3 9 . 2 2 0 . 2 O . 1 0 . 0 1 5 . 5 7 . 7 9 . 5 1 0 . 8 2 1 . 2 1 2 . 5 4 9 . 6 2 5 . 6 4 . 2 1 9 5 . 2 1 . 9 6 . 2 2 . 3 ( M 3 ) 0 . 4 4 5 4 t o CO • • * J U L I A N D A Y 2 1 4 A U G U S T 2 . 1 9 8 2 H R T A T C P T C I T C O T B S M T M T S T S D H W TDHW ( C ) ( C ) ( C ) ( C ) < C ) ( C ) ( C ) ( C I < C ) 1 1 2 . 3 1 2 . 3 - 2 2 . 4 - 2 2 . 4 1 8 . 8 1 8 . 3 2 2 . 4 2 2 . 4 5 7 . 4 2 1 2 . 3 1 2 . 3 - 2 2 . 4 - 2 2 . 4 1 8 . 7 1 8 . 0 2 2 . 4 2 2 . 4 5 5 . 6 3 1 2 . 2 1 2 . 2 - 2 2 . 4 - 2 2 . 4 1 8 . 6 1 8 . 0 2 2 . 3 2 2 . 4 5 5 . 0 4 1 2 . 2 1 2 . 2 - 2 2 . 3 - 2 2 . 3 1 8 . 6 1 8 . 0 2 2 . 3 2 2 . 3 5 4 . 2 5 1 2 . 2 1 2 . 2 - 2 2 . 3 - 2 2 . 3 1 8 . 5 1 8 . 0 2 2 . 2 2 2 . 3 5 4 . 0 6 1 2 . 2 1 2 . 2 - 2 2 . 2 - 2 2 . 2 1 8 . 4 1 9 . 0 2 2 . 2 2 2 . 2 5 3 . 4 7 1 2 . 3 1 3 . 3 - 2 2 . 2 - 2 2 . 2 1 8 . 4 1 8 . 5 2 2 . 2 2 2 . 2 5 3 . 0 8 1 2 . 6 1 6 . 6 - 2 2 . 2 - 2 2 . 2 1 8 . 4 1 8 . 2 2 2 . 1 2 2 . 2 5 2 . 6 9 1 2 . 9 2 2 . 7 - 2 2 . 1 - 2 2 . 1 1 8 . 4 1 8 . 3 2 2 . 1 2 2 . 1 5 2 . 0 1 0 1 3 . 2 2 4 . 7 - 2 2 . 1 - 2 2 . 1 1 8 . 3 1 8 . 4 2 2 . 0 2 2 . 1 5 2 . 0 11 1 3 . 4 2 5 . 3 - 2 2 . 0 - 2 2 . 0 1 8 . 4 1 5 . 0 2 0 . 8 2 2 . 0 5 5 . 2 1 2 1 3 . 9 2 7 . 9 - 2 0 . 8 - 2 0 . 8 1 8 . 9 1 5 . 2 2 0 . 4 2 0 . 8 6 0 . 4 1 3 1 4 . 8 3 5 . 1 2 0 . 4 2 1 . 4 1 9 . 4 1 4 . 7 2 0 . 8 2 0 . 4 6 1 . 7 1 4 1 5 . 1 3 1 . 2 2 0 . 8 - 2 1 . 5 1 9 . 6 1 7 . 5 2 0 . 7 2 0 . 8 6 0 . 9 1 5 1 5 . 7 3 8 . 9 2 0 . 7 2 2 . 0 1 9 . 5 1 5 . 5 2 1 . 9 2 0 . 7 6 0 . 4 1 6 1 6 . 2 3 6 . 9 2 1 . 9 2 3 . 0 1 9 . 2 1 8 . 4 2 2 . 9 2 1 . 9 5 3 . 0 1 7 1 6 . 6 4 6 . 2 2 2 . 9 2 4 . 6 1 9 . 1 1 5 . 2 2 3 . 3 2 2 . 9 5 9 . 8 1 8 1 7 . 1 4 3 . 5 2 3 . 3 2 4 . 8 1 9 . 2 1 6 . 9 2 4 . 6 2 3 . 3 6 4 . 3 1 9 1 6 . 7 3 0 . 6 2 4 . 6 - 2 5 . 0 1 9 . 1 1 6 . 0 2 4 . 4 2 4 . 6 6 0 . 3 2 0 1 6 . 6 2 4 . 3 - 2 4 . 4 - 2 4 . 4 1 9 . 0 1 8 . 7 2 4 . 3 2 4 . 4 4 9 . 7 2 1 1 5 . 6 1 6 . 3 - 2 4 . 3 - 2 4 . 3 1 8 . 6 1 9 . 3 2 4 . 3 2 4 . 3 4 9 . 9 2 2 1 4 . 7 1 4 . 7 - 2 4 . 3 - 2 4 . 3 1 8 . 7 1 3 . 2 2 1 . 7 2 4 . 3 5 6 . 8 2 3 1 3 . 9 1 3 . 9 - 2 1 . 7 - 2 1 . 7 1 9 . 0 1 4 . 0 2 1 . 7 2 1 . 7 5 9 . 8 2 4 1 3 . 2 1 3 . 2 - 2 1 . 7 - 2 1 . 7 1 9 . 0 - 1 9 . 2 2 1 . 7 - 1 9 . 2 - 5 5 . 3 O A I L Y T O T A L S Q H T ( K J ) O . O . 0 . 0 . O . O . 1 6 9 . 7 0 0 . 1 6 7 7 . 1 9 6 3 . 2 0 4 5 . 2 3 9 4 . 3 4 9 4 . 2 7 7 2 . 3 9 8 3 . 3 5 6 3 . 5 0 7 5 . 4 5 3 7 . 2 3 8 6 . 1 3 2 3 . 1 2 9 . 0 . O . 0 . ( M J ) 3 6 . 2 0 9 Q C S S ( K J ) O . O . 0 . O . 0 . O . O . O . 0 . 0 . O . 0 . 1 8 3 7 . O . 2 2 6 9 . 1 8 7 5 . 2 8 9 7 . 2 5 1 0 . O . O . O . O . O . O . ( M J ) 1 1 . 3 8 7 O S T O R ( K d ) - 6 4 . - 6 4 . - 6 3 . - 6 4 . - 6 2 . - 6 4 . - 6 6 . - 7 4 . - 7 6 . - 7 6 . - 2 1 3 8 . - 7 2 7 . 6 7 9 . - 1 2 1 . 2 0 0 2 . 1 8 3 1 . 6 6 4 . 2 1 9 8 . - 4 0 3 . - 8 6 . - 9 5 . - 4 3 6 4 . - 4 4 . - 4 3 . ( M J ) - 1 . 3 1 9 Q S E N V ( K J ) 5 9 . 5 9 . 6 0 . 6 0 . 6 0 . 6 1 . 6 1 . 6 1 . 6 0 . 6 0 . 5 8 . 3 1 . 1 5 . 1 9 . 2 0 . 4 2 . 6 1 . 6 6 . 88 8 5 . 9 2 . 8 9 . 4 3 . 4 3 . ( M J ) 1 . 3 5 4 O S D H W ( K J ) 5 . 5 . 3 . 4 . 2 . 3 . 5 . 1 3 . 1 6 . 1 5 . 2 0 8 0 . 6 9 6 . 1 1 4 3 . 1 0 2 . 2 4 7 . 2 . 2 1 7 1 . 2 4 6 . 3 1 4 . 0 . 3 . 4 2 7 4 . 1 . O . ( M J ) 1 1 . 3 5 2 ODHW ( K J ) 5 0 . 4 2 . 2 9 . 3 4 . 1 7 . 3 3 . 4 9 . 1 1 5 . 1 3 6 . 1 3 8 . 1 1 8 3 4 . 5 6 6 4 . 9 4 3 2 . 1 3 4 5 . 2 1 3 6 . 1 6 . 1 2 4 7 0 . 1 8 1 2 . 1 6 2 8 . 2 . 1 9 . 1 6 8 5 4 . 4 . 0 . ( M J ) 6 3 . 8 5 9 F L O W ( L ) 0 . 3 0 . 3 0 . 2 0 . 2 0 . 1 0 . 2 0 . 3 0 . 8 1 . 0 1 . 0 7 0 . 2 3 0 . 0 4 7 . 9 7 . 4 1 1 . 4 0 . 1 6 6 . 8 9 . 1 8 . 8 0 . 0 0 . 2 9 2 . 2 0 . 0 0 . 0 ( M 3 ) 0 . 3 4 8 5 » • * J U L I A N D A Y 2 3 1 A U G U S T 1 9 , 1 9 8 2 * * • H R T A T C P T C I T C O T B S M T M T S T S D H W TDHW Q H T ^ O C S S O S T O R O S E N V Q S D H W QDHW F L O W ( C ) ( C ) ( C ) ( C ) ( C ) ( C ) ( C ) ( C ) I C ) ( K J ) ( K J ) ( K J ) ( K J ) ( K J ) ( K J ) ( L ) 1 1 4 . 2 1 4 . 2 - 5 7 . 8 - 5 7 . 8 1 9 . 7 - 1 9 . 0 5 7 . 4 - 1 9 . 0 - 5 0 . 1 O . O . - 6 0 9 . 6 0 9 . 0 . 0 . 0 . 0 2 1 3 . 7 1 3 . 7 - 5 7 . 4 - 5 7 . 4 1 9 . 5 - 1 9 . 0 5 7 . 0 - 1 9 . 0 - 5 0 . 3 0 . O . - 6 0 6 . 6 0 6 . 0 . 0 . 0 . 0 3 1 2 . 9 1 2 . 9 - 5 7 . 0 - 5 7 . 0 1 9 . 3 - 1 9 . 0 5 6 . 7 - 1 9 . 0 - 4 9 . 7 0 . 0 . - 6 0 4 . 6 0 4 . 0 . O . 0 . 0 4 1 2 . 4 1 2 . 4 - 5 6 . 7 - 5 6 . 7 1 9 . 1 - 1 9 . 9 5 6 . 3 - 1 9 . 9 - 5 0 . 2 0 . 0 . - 6 0 1 . 6 0 1 . 0 . O . 0 . 0 5 1 1 . 9 1 1 . 9 - 5 6 . 3 - 5 6 . 3 1 8 . 9 - 1 9 . 7 5 6 . 0 - 1 9 . 7 - 5 0 . 2 O . O . - 5 9 9 . 5 9 9 . 0 . O . 0 . 0 6 1 1 . 8 1 1 . 8 - 5 6 . 0 - 5 6 . 0 1 8 . 8 1 6 . 6 5 3 . 3 5 6 . 0 5 8 . 6 O . O . - 4 5 8 3 . 5 9 6 . 3 9 8 7 . 4 2 5 0 . 2 4 . 2 7 1 1 . 5 1 3 . 2 - 5 3 . 3 - 5 3 . 3 1 8 . 6 - 1 8 . 6 5 3 . 0 - 1 8 . 6 - 5 0 . 7 2 9 6 . 0 . - 5 5 6 . 5 5 6 . O . O . 0 . 0 8 1 2 . 4 2 1 . 2 - 5 3 . 0 - 5 3 . 0 1 8 . 5 1 6 . 6 5 0 . 2 5 3 . 0 5 8 . 5 1 5 1 3 . 0 . - 4 8 3 5 . 5 5 2 . 4 2 8 3 . 4 9 2 9 . 2 8 . 1 9 1 5 . 2 5 7 . 1 - 5 0 . 2 - 5 0 . 2 1 8 . 8 1 5 . 2 4 0 . 8 5 0 . 2 5 8 . 8 7 1 9 7 . O . - 1 6 1 0 8 . 5 0 2 . 1 5 6 0 6 . 1 9 4 6 6 . 1 0 6 . 5 1 0 1 8 . 1 9 0 . 8 4 0 . 8 4 4 . 4 1 9 . 3 1 5 . 4 4 3 . 7 4 0 . 8 5 7 . 5 1 2 4 9 8 . 6 2 3 3 . 4 9 5 8 . 3 4 4 . 9 3 0 . 1 5 4 4 . 8 . 8 11 1 9 . 8 1 2 1 . 5 4 3 . 7 4 9 . 4 1 9 . 6 1 6 . 8 4 8 . 7 4 3 . 7 5 5 . 1 1 7 4 8 0 . 9 6 9 9 . 8 6 4 0 . 3 8 5 . 6 7 4 . 9 6 0 . 6 . 0 1 2 2 1 . 6 1 4 5 . 1 4 8 . 7 5 5 . 7 1 9 . 9 1 6 . 3 5 5 . 0 4 8 . 7 5 3 . 2 2 1 2 2 1 . 1 2 0 0 2 . 1 0 7 4 9 . 4 6 1 . 7 9 2 . 9 0 2 . 5 . 8 1 3 2 3 . 0 1 5 8 . 9 5 5 . 0 6 2 . 5 2 0 . 0 1 7 . 6 6 1 . 9 5 5 . 0 5 1 . 8 2 3 3 3 9 . 1 2 9 4 1 . 1 1 8 6 0 . 5 5 9 . 5 2 1 . 4 7 7 . 3 . 3 1 4 2 4 . 0 1 6 1 . 4 6 1 . 9 6 9 . 1 2 0 . 2 . 1 9 . 9 6 8 . 7 6 1 . 9 4 6 . 9 2 3 6 1 8 . 1 2 3 9 9 . 1 1 7 2 2 . 6 6 7 . 1 0 . 6 . 0 . 1 1 5 2 4 . 6 1 4 0 . 0 6 8 . 7 7 3 . 9 2 0 . 4 - 2 0 . 7 7 3 . 4 - 2 0 . 7 - 4 7 . 1 1 9 8 2 3 . 8 8 7 3 . 8 1 0 0 . 7 7 3 . O . O . 0 . 0 1 6 2 5 . 0 6 2 . 4 7 3 . 4 - 7 2 . 6 2 0 . 5 - 2 1 . 3 7 2 . 9 - 2 1 . 3 - 4 7 . 4 6 4 2 7 . 0 . - 8 4 7 . 8 4 7 . O . O . 0 . 0 1 7 2 3 . 8 7 4 . 0 - 7 2 . 9 - 7 2 . 9 2 0 . 7 - 2 2 . 0 7 2 . 5 - 2 2 . 0 - 4 7 . 5 8 6 1 5 . O . - 8 3 6 . 8 3 6 . O . 0 . 0 . 0 1 8 2 3 . 3 4 0 . 0 - 7 2 . 5 - 7 2 . 5 2 0 . 8 1 8 . 1 7 1 . 5 7 2 . 5 5 3 . 7 2 8 6 4 ! O . - 1 6 6 7 . 8 2 7 . 8 4 0 . 5 5 0 . 3 . 7 1 9 2 2 . 7 2 8 . 1 - 7 1 . 5 - 7 1 . 5 2 1 . 1 1 5 . 0 6 8 . 7 7 1 . 5 5 5 . 1 9 1 5 . O . - 4 7 4 7 . 8 0 7 . 3 9 4 0 . 2 8 0 1 . 1 6 . 7 2 0 2 1 . 1 2 4 . 6 - 6 8 . 7 - 6 8 . 7 2 0 . 8 1 4 . 0 6 6 . 9 6 8 . 7 5 6 . 6 5 9 7 . O . - 3 1 9 8 : 7 6 7 . 2 4 3 1 . 1 8 9 2 . 1 0 . 6 2 1 1 9 . 7 1 9 . 9 - 6 6 . 9 - 6 6 . 9 2 0 . 7 1 3 . 3 6 4 . 0 6 6 . 9 5 8 . 4 3 9 . O . - 4 8 9 5 . 7 3 9 . 4 1 5 6 . 3 5 0 3 . 1 8 . 5 2 2 18.5 1 8 . 5 - 6 4 . 0 - 6 4 . 0 2 0 . 8 1 3 . 0 6 1 . 8 6 4 . 0 5 9 . 8 O . O . - 3 8 1 7 . 6 9 1 . 3 1 2 7 . 2 8 6 9 . 1 4 . 6 2 3 1 7 . 5 1 7 . 5 - 6 1 . 8 - 6 1 . 8 2 0 . 8 1 8 . 0 6 1 . 4 6 1 . 8 5 3 . 4 O . O . - 6 8 7 . 6 5 5 . 3 1 . 2 5 . 0 . 2 2 4 1 6 . 5 1 6 . 5 - 6 1 . 4 - 6 1 . 4 2 0 . 6 - 2 0 . 0 6 1 . 0 - 2 0 . 0 - 5 2 . 2 O . O . - 6 5 2 . 6 5 2 . 0 . 0 . 0 . 0 ( M J ) ( M J ) I M J ) ( M J ) ( M J ) ( M J ) ( M 3 ) D A I L Y T O T A L S 1 4 6 . 4 4 0 6 2 . 1 4 6 5 . 5 8 3 1 5 . 2 3 6 4 1 . 3 2 7 4 4 . 1 7 4 0 . 2 4 7 1 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0096148/manifest

Comment

Related Items