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Development of a design procedure for greenhouse solar heating systems Lau, Anthony Ka-Pong 1988

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D E V E L O P M E N T O F A DESIGN P R O C E D U R E F O R G R E E N H O U S E HEATING  SYSTEMS  by ANTHONY K A - P O N G L A U B. Sc. (Eng), University of Guelph, Ontario, 1981 M . Sc., University of Guelph, Ontario, 1983 A THESIS SUBMITTED IN P A R T I A L F U L F I L M E N T O F T H E REQUIREMENTS DOCTOR  FOR THE DEGREE OF  OF  PHILOSOPHY  in F A C U L T Y O F G R A D U A T E STUDIES Department of Interdisciplinary Studies (Field: Bio-Resource Engineering) We accept this thesis as conforming to the required standard  T H E UNIVERSITY O F BRITISH  COLUMBIA  March 1988 ©  Anthony Ka-pong Lau, 1988  SOLAR  In  presenting  degree  at the  this  thesis  in partial  University of  fulfilment  of  department  this thesis for or  by  his  or  the  requirements  for  an  advanced  British Columbia, I agree that the Library shall make it  freely available for reference and study. copying  of  scholarly her  I further agree that permission for  purposes  may be  representatives.  It  is  granted  by  understood  extensive  the head of that  publication of this thesis for financial gain shall not be allowed without  copying my  l-nh^M^ajylllAiW^  The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date  DE-6(3/81)  M^cM  ,  lf*8  fyil$ * ^'"'^Uuj'oc  or  written  permission.  Department of  my  kMjA^'^  ABSTRACT The techniques of computer modeling and simulations are used to* develop a design procedure for greenhouse solar heating systems. In this study a flexible computer program was written based on mathematical models that describe the various subsystems of the solar heating system that uses the greenhouse  as  the  solar  predicting system thermal  collector. Extensive simulation runs performance,  and  subsequently  were  carried  correlations were  out  for  established  between dimensionless variables and long term system performance. The combined greenhouse with  the  empirical  relationships  thermal environment and  the  values  thermal storage model along  of constants approximated  in  the  simulation yielded reasonably accurate computed results compared to observed data. The computer average  model was then climatological  investigate thermal  the  energy  effects  data of  applied to predict the as  forcing  various  functions.  factors  storage characteristics  on  system behaviour using long-term A parametric  pertinent system  to  study  greenhouse  performance.  was  made  construction  The - key  to and  performance  indices were defined in terms of the 'total solar contribution' and the 'solar heating fraction'. Correlations were developed between  monthly solar load ratio and total solar  contribution, and between total solar contribution and solar heating fraction. The result is a simplified  design method that covers a number of alternative design options. It  requires users to obtain monthly average climatological data and determine the solar heating fraction in a sequence of computational steps. A crop photosynthesis model was used to compute the net photosynthetic rate of a greenhouse tomato canopy; the result may be used to compare crop performance under  different  aerial  environments  in  system.  i i  greenhouses  equipped  with  a  solar  heating  This research program had attempted to generate technical information for a number of design alternatives, and as design optimization of greenhouse solar heating is subject to three major criteria of evaluation: thermal performance, crop yield and cost, recommendations were put forward for future work on economic analysis as the final step required for selecting the most cost effective solution for a given design problem.  Tahle of Contents ABSTRACT '. ACKNOWLEIXJEMENTS  ii  LIST O F TABLES  iv  LIST O F FIGURES  vii  1.  2.  INTRODUCTION  1  1.1  General  1  1.2  Objectives  5  1.3  Scope of the Study  5  1.4 Organization of the Manuscript  6  U T E R A T U R E REVIEW  8  2.1 Greenhouse Solar Heating Systems  „  8  2.1.1 Internal collection  8  2.1.2 External collection  14  2.2 Mathematical Modeling of Solar Greenhouses 2.2.1 Greenhouse thermal environment  21 21  2.2.1.1 Solar radiation level inside the greenhouse  23  2.2.1.2 Convective heat exchange  33  2.2.1.3 Evapotranspiration  35  2.2.2 Thermal energy storage  .... 37  2.2.2.1 Rockbed thermal storage  37  2.2.2.2 Soil thermal storage  39  2.3 Design Methods  42  2.3.1 f-chart method  42  2.3.2 SLR-method  44  2.3.3 Direct simulations as design method  44  2.4 Effects of Environmental Factors on Greenhouse Plant Growth 2.4.1 Environmental factors  46 46  iv  2.4.2 Mathematical models  -.56  NOTATION  62  3.  64  C O M P U T E R M O D E L I N G A N D SIMULATIONS 3.1 System I Storage  -  Augmented  Internal  Collection  With  Rockbed Thermal 64  3.1.1 Greenhouse thermal environment  64  3.1.2 Rockbed thermal storage  71  3.2 System II -  Internal Collection With Soil Thermal Storage  73  3.2.1 Greenhouse thermal environment  73  3.2.2 Soil thermal storage  73  3.3 The Simulation Method  77  3.4 Model Validation -  82  Results and Discussion  3.4.1 Solar radiation transmission and interception  82  3.4.2 Greenhouse thermal environment and thermal storage  83  3.4.2.1 System I  „  85  3.4.2.2 System II  -.  NOTATION 4.  114 140  SIMULATION F O R L O N G - T E R M SOLAR H E A T I N G SYSTEMS  PERFORMANCE  4.1 Modification to the Simulation Method  OF  GREENHOUSE 142 144  4.1.1 Solar radiation  144  4.1.2 Temperature  147  4.1.3 Relative humidity  148  4.2 Parametric Study  148  4.2.1 Greenhouse  148  4.2.2 Rockbed thermal storage  151  4.2.3 Soil thermal storage  153  4.2.4 Results and discussion  154  v  4.2.4.1 Effect of greenhouse construction parameters  .156  4.2.4.2 Effect of locations  175  4.2.4.3 Effect of rockbed thermal storage parameters  179  4.2.4.4 Effect of soil thermal storage parameters  186  4.3 Sensitivity Analysis  195  4.4 Crop Canopy Photosynthesis  200  4.4.1 The simulation method  200  4.4.2 Results and discussion  203  4.5 Development of A Simplified Design Method  219  4.5.1 Introduction  219  4.5.2 Regression method  224  4.5.3 Outline of the design procedure  225  4.5.4 Example calculation  «  233  NOTATION  235  5.  238 '  CONCLUSIONS A N D R E C O M M E N D A T I O N S  BIBLIOGRAPHY APPENDICES  244 ,  -  v i  257  LIST O F TABLES Title  Table number  1.1  Greenhouse solar heating systems  3.1  Values of parameters  Page  2  used in validating the  simulation model for  78  The effect of wind speed and ventilator position on air exchange in  80  systems I and II 3.2  the greenhouse (from: Whittle and Lawrence, 1960) 3.3  Means and standard deviations of differences between predicted and observed temperatures  91  and relative humidities on three occasions for  systems I and II 3.4  Relative humidity as  a  function  of humidity ratio  and  dry-bulb  93  temperature 3.5  Sample outputs of model validation runs  113  4.1  Greenhouse dimensions and related quantities  150  4.2  Rockbed thermal storage characteristics  152  4.3  Soil thermal storage characteristics  155  4.4  Effect of greenhouse shape on system thermal performance  158  4.5  Effect of cover material on system thermal performance  163  4.6  Collection efficiency for shed-type and conventional greenhouse  with  164  glass or double acrylic covers 4.7  Effect of greenhouse roof tilt on system thermal performance  4.8  Effect  of  greenhouse  length-to-width  ratio  on  166  system  thermal  167  system  thermal  168  4.10  System thermal performance for various greenhouse sizes (floor area)  169  4.11  Monthly average values of  172  performance 4.9  Effect  of  greenhouse  orientation  shape  on  performance  and K yii  D  4.12  Effect  of  locations  on  system  thermal  performance  -  shed-type  176  conventional  178  greenhouse 4.13  Effect  of locations on system thermal performance  -  shape greenhouse 4.14  Effect of rockbed storage capacity on system thermal performance  180  4.15  Effect of rockbed air flow rate on system thermal performance  184  4.16  Effect  187  of pipe wall area-to-greenhouse  floor area ratio on system  thermal performance 4.17  Effect of pipe air flow rate on system thermal performance  4.18  Effect  of  soil  type  and  moisture  content  on  system  191 thermal  193  performance 4.19  Thermal properties of clay and sand  4.20  Sensitivity  test  results  -  194  ventilation rate,  leaf  Bowen  ratio  and  196  shading factor 4.21  Sensitivity test results -  initial thermal storage  temperatures  197  4.22  Sensitivity test results -  solar radiation processing algorithm  198  4.23  Crop canopy photosynthesis model parameters  202  4.24  Monthly average daily net photosynthetic rate - Vancouver  208  4.25  Monthly average daily net photosynthetic rate -  Guelph  209  4.26  Effective  solar heat collection  214  transmissivity for different greenhouse  systems 4.27  Values of coefficients in eqn. 4.21  4.28  Combined  226 on  231  Combined effect of soil storage pipe wall area and air flow rate  232  rockbed storage  capacity and  air  flow  rate  effect  system thermal performance 4.29  on system thermal performance  viii  4.30  Average local climatological data for Vancouver, and solar load ratio  234  for a C V / G S collection system 4.31  Solar heating fraction, f, for eight design options  ix  234  LIST O F FIGIIRF.S Title  Figure number 2.1  Solar  heating  Page  system  for  a  shed-type  greenhouse  with  rocked  10  system  for  a  conventional greenhouse  earth  12  Schematic diagram of the latent heat storage unit (from: Nishina  15  thermal storage 2.2  Solar  heating  with  thermal storage 2.3  and Takakura, 1984) 2.4  Greenhouse solar heating system with active collector and thermal  16  storage (redrawn from: Mears et al., 1977). 2.5  Schematic  of  the  solar  pond-greenhouse  heating  system  which  18  included a direct exchange loop and a heat pump loop (from: Fynn et al., 1980) 2.6  Cross-section through greenhouse and solar energy collector (from:  20  Dale et al., 1984) 2.7  Brace-style greenhouse (redrawn from: La wand et al., 1975)  27  2.8  Greenhouse types evaluated by Turkewitsch and Brundrett (1979)  29  2.9  The f-chart for an air system (from: Klein et al., 1976)  43  2.10  Monthly solar heating fraction versus solar load ratio for buildings  45  with south-facing collector-storage wall systems (from: Balcomb and McFarland, 1978) 2.11  Nomographs for design of greenhouse-rock  storage-collector  system  47  Computer predicted seasonal performance of a solar collector-heating  48  (from: Puri, 1981) 2.12  system  for three commercial type greenhouses  U.S.A. and in Malaga, Spain (redrawn from: 1984)  in Wooster, Ohio, Short and Montero,  2.13  Photosynthesis  of a cucumber  leaf at  limiting  and saturating  C0  2  50  enrichment on C O , fixation in a sugar  51  concentrations under incandescent light (Gaastra, 1963) 2.14  Effects of atmospheric C 0  2  beet leaf (Salisbury. and Ross, 1978) 2.15  Photosynthetic  and  transpirational  various light intensities  and C 0  2  responses  of  levels (from:  tomato  plants  Bauerle and  to  53  Short,  1984) 3.0  Principal components of the greenhouse thermal environment model  66  3.1  Rocked thermal storage divided into N segments  72  3.2  Soil thermal storage -  75  3.3  Total transmission  modeled region  factor and effective  transmissivity -  experimental  84  and simulated results for the period Sept 1983 to Aug 1984 3.4  External climatic conditions during the week of Feb 18-24, 1984  86  3.5  System I -  87  photosynthetically active radiation at plant canopy level,  Feb 18-24 3.6  System  I  -  solar  radiation  incident  at  plant  canopy  level  and  88  environment,  89  absorber plate, Feb 18-24 3.7  System  I -  temperatures of the  greenhouse thermal  Feb 18-24 3.8  System I -  greenhouse relative humidity, Feb 18-24  90  3.9  System I -  Rockbed temperatures at three sections, Feb 18-24  95  3.10  System I -  simulated results of spatial temperature distribution in  97  the rockbed, Feb 18-24 3.11  External climatic conditions during the week of Mar 25-31, 1984  3.12  System I -  3.13  System  I -  PAR at plant canopy level, Mar 25-31 temperatures of the  Mar 25-31 xi  greenhouse thermal  99 100  environment,  101  3.14  System I - greenhouse relative humidity, Mar 25-31  102  3.15  System I - Rockbed temperatures at three sections, Mar 25-31  103  3.16  System I  104  - simulated  results of spatial temperature distribution in  the rockbed, Mar 25-31 3.17  External climatic conditions during the week of Apr 18-24, 1984  107  3.18  System I - PAR at plant canopy level, Apr 8-14  108  3.19  System Apr  I  -  temperatures of the  greenhouse  thermal  environment,  109  8-14  3.20  System I - greenhouse relative humidity, Apr 8-14  110  3.21  System I - Rockbed temperatures at three sections, Apr 8-14  111  3.22  System I  112  -  simulated  results of spatial temperature distribution in  the rockbed, Apr 8-14 3.23  System  II -•  solar  radiation  incident  at  plant  canopy  level,  Feb  115  environment,  117  18-24 3.24  System II  -• temperatures of the  greenhouse  thermal  Feb 18-24 3.25  System II - greenhouse relative humidity, Feb 18-24  118  3.26  System II - soil temperatures at three locations in the storage zone,  119  Feb 18-24 3.27  System II - isotherms of simulated soil temperatures, Feb 18-24  121  3.28  System II - pipe oudet air temperature, Feb 18-24  122  3.29  System  II  --  solar  radiation  incident  at  plant  canopy  level, Mar  124  environment,  125  25-31 3.30  System II Mar  3.31  -• temperatures of the  greenhouse  thermal  25-31  System II - greenhouse relative humidity, Mar 25-31  xii  126  3.32  System II -  soil temperatures at three locations in the storage zone,  127  pipe outlet air temperature. Mar 25-31  129  Mar 25-31 3.33  System II -  3.34  System II -  isotherms of simulated soil temperatures at the center  130  region, Mar 25-31 3.35  System II -  isotherms  of simulated soil temperatures at the edge  131  region, Mar 25-31 3.36  System  II -  solar  radiation  incident at  plant  canopy  level,  Apr •  133  8-14 3.37  System II -  temperatures of the greenhouse thermal  environment,  134  Apr 8-14 3.38  System II -  greenhouse relative humidity, Apr 8-14  135  3.39  System II -  soil temperatures at three locations in the storage zone,  136  Apr 8-14 3.40  System II -  isotherms of simulated soil temperatures, Apr 8-14  137  •3.41  System II -  pipe outlet air temperature, Apr 8-14  138  4.1  Shed-type  glasshouse  -  total  transmission  factor  calculated  using  159  factor calculated using  160  average solar radiation data for eight geographic locations 4.2  Conventional glasshouse  -  total transmission  average solar radiation data for eight geographic locations 4.3  Effective transmissivity for a shed-type glasshouse  170  4.4  Effective transmissivity for a conventional glasshouse  171  4.5  Variation of net canopy photosynthesis with P A R and C 0  4.6  Variation of net canopy photosynthesis (leaf area index =  204  2  8.6) with  206  2.1) with  207  temperature and P A R 4.7  Variation of net canopy photosynthesis (leaf area index = temperature and P A R xiii  4.8  Mean hourly inside P A R flux density on the typical design day of  210  each month - Vancouver 4.9  Mean hourly net photosynthetic rate on the typical design day of  211  each month for a greenhouse tomato crop grown in Vancouver 4.10  Mean  hourly  rates  of  gross  photosynthesis,  respiration  and  net  213  solar  221  photosynthesis on the representative day in September 4.11  Simulated  values  of  solar  heating  fraction  versus  total  contribution 4.12  Simulated values of total solar contribution versus solar load ratio -  222  rockbed thermal storage 4.13  Simulated values of total solar contribution versus solar load ratio -  223  soil thermal storage 4.14  Design curves fitted to the simulated data points of Fig. 4.12  227  4.15  Design curves fined to the simulated data points of Fig. 4.13  228  4.16  Function fitted to the simulated data of Fig. 4.11  229  xlv  ACKNOWT.FnfiffMFNTS  I wish to express my sincere gratitude to my supervisor, Professor L . M . Staley, for his continuous guidance and encouragement  throughout the course of this research  programme. Professor Staley made himself available from time to time for discussions and gave me timely advice on a number of key points. I would also like to thank him for giving me the opportunity to join the team working on the solar greenhouse research project. Much appreciation is also due to other members of the supervisory committee for  their  constructive  comments  Dr. N.R.  development  Bulley  and  criticisms  served on the  at  various  committee  stages  of  the  thesis  previously and pointed  out  some practical aspects of concern. I thank Dr. G.W. Eaton for stressing the importance of the clarity of the project objectives at the outset Dr. M . Iqbal was instrumental in identifying the need of a design procedure for solar heating systems for and was helpful in reminding the  author  to bring the  greenhouses,  simulation results  down to  earth. Dr. P.A. Jolliffe exposed me to the intriguing field of plant physiology, and was -  supportive of my attempts to model plant response under different aerial environments. I thank Dr. K . V . Lo for participating in the cornmittee to replace Dr. Bulley, and for his assistance  in the  capacity of former  graduate advisor. Dr. M . D . Novak made  some valuable suggestions and introduced alternative methods regarding the modeling of the greenhouse  thermal environment and soil thermal storage. The author expresses his  hearty  to  thanks  each  and  every  one  of  them  for  making  this interdisciplinary  programme more complete and meaningful. Special thanks are extended to a number of individuals who provided assistance in  various  greenhouse Mr.  ways. Mr. G.J. Monk research  D. Thomas  carried  out  the  engineering  management  of  the  facilities, and paved the way for me to acquire additional data.  untiringly updated  me  with  details  of the  status of sensors and  recorded data during the 1983/1984 experimental period. Dr. E M . van Zinderen Bakker  xy  supplied the crop productivity data and other details of the research operation. Mr. E Charter, Ms. T. DeLaurier, Mr. B. Ewert and Mr. A . Wakelin working in the summer on  the  UBC,  greenhouse  project  have contributed  Dr. T.A. Black of the  to data collection and analysis. Here  Soil Science Department  M r . J. Pehlke has  has kindly let me use  consistently rendered  me  prompt  at  some  laboratory  equipment  technical  assistance.  Ms. C. Moore, Mr. T. Nicol, Mr. D . Townsend and Mr. B. Wong have  each given me some good advice on using the packaged programs available from the Computing Center. Appreciation is also due to Dr. J.M. Molnar, former Director of Agriculture Canada Saanichton Research Station for permission to use the experimental data. The continuous support and encouragement of my parents is greatly appreciated. And,  to  my  friends  and  fellow  graduate  students,  my  cordial  thanks  for  their  companionship and care. And,  as Rome is not built in one  day, I am indebted  to all my teachers  during these years of education • and training for laying the foundation which me to overcome the obstacles that I encountered  enables  on the road, and to accept  future  challenges. The  financial  University Graduate Staley  from  the  assistance  of  the  University of British  Fellowship, and the  Columbia  through  the  financial support made available to Professor  Faculty of Agricultural  Sciences  Research  Fund, and  the  Natural  Sciences and Engineering Research Council of Canada are gratefully acknowledged. Last, but  not  least,  I  want  to  thank  Ms. J. Blake  administrative assistant  xv i  for  her  help  in the  capacity of  Chapter 1 INTRODI TfTTON  1.1  fisnsial The greenhouse  industry in Canada is centred  primarily in Southern Ontario  and secondly in South Western B.C. Salad vegetables and flower crops are the main products followed by ornamentals and tree seedlings. The survival and expansion of a viable commercial greenhouse  industry is largely dependent on the  production  costs,  some thirty to forty percent of which are due to heating. To reduce the reliance of greenhouse  heating on fossil fuels, research efforts have concentrated along two major  paths: developing energy conservation techniques such as double skin coverings, lower operating temperatures and use of thermal screens;  and. developing alternative  energy  sources like solar heat and waste heat Optimizing the use of solar energy to partially fulfil the heating of  greenhouses has  stimulated  a number  requirements  of investigations of collection and storage  systems in combination since the 1970's. A summary of some greenhouse  solar heating  systems is shown in Table 1.1. Solar radiation may be converted into useful heat gain by means of passive or active collections. Passive collection makes use of the greenhouse resource to collect excess heat trapped within the greenhouse  itself as an existing  during the daytime. On  the other hand, active collection usually involves external solar collectors placed near the greenhouse; part  of  the  alternatively, an internal collector can be incorporated as an integral  greenhouse  design. Furthermore,  to  match  solar  energy  availability  to  energy needs requires the provision of sensible or latent heat storage in rock beds, wet  soil,  water  tanks, salt ponds, containers  of phase-change  materials, and so on.  Thus, active systems require additional electrical inputs to facilitate solar heat capture.  1  T A B L E 1.1  Greenhouse solar heating systems  Greenhouse  Cover  Collection  Brace-style  Double polyethylene  Internal (Q-mats with water)  Hemispheric Quonset  Polyethylene Corrugated f ibreglass/ plastic-  Shed-type Quonset  Corrugated fibreglass/ Tedlar Double polyethylene  Semi-cylindrical  Double acrylic  Quonset  Double polyethylene  Gutter-connected Brace-style Quonset  Glass Double polyethylene Double polyethylene  Yenlo-type  Glass  Shed-type  Glass  Conventional Quonset  Glass Fibreglass  Solar fraction*  Storage  Authors  10%  Albright et al. (1979)  —  —  External air solar collector with reflective wings External (flat plate air collector) Solar pond (brine solution) Internal (solar air heater and fan) External (plastic film solar collector) Internal (fan)  Soil  9:,% (estimated) 4%  Begin et al. (1984) Daleet al. (1980)  Soil  43%  D a l e e t a l . (1984)  Solar pond  G2%  F y n n e t a l . (1980)  Rock  84%  Garzoli and Shell (1984)  Rock and water CaCl,-10H O a  —  —  External (plastic film solar collector) Internal (fan)  Gravel and water  Internal (solar air heater and fan) Internal (fan) Internal (fan)  Na SO,-10H,0 with additives Rock 2  Soil Rock  r>%  Ingratta and Blom (1981)  60% 35% 53%  Jaffrinand Cadier (1982) L a w a n d e t a l . (1975) M e a r s e t a l . (1977)  100%  Nishina and Takakura (1984) Staley and M o n k (1984)  35% 20% 33%  Staley and Monk (1984) W i l l i t s e t a l . (1980)  'measured over a period (month, season or annual).  to  3  Internal Wigstroem Shell  collection  has  (1980), Blackwell  (1984), Jaffrin  been  tested  by Albright  et al. (1982), Caffell  and Cadier (1982), Kozai  et al. (1979), Areskoug and  and MacKay  et  (1981), Garzoli  al. (1986), Milburn  and  and  Aldrich  (1979), Nishina and Takakura (1984), Portales et al. (1982). Staley et al. (1984), Willits et al. (1980), and Wilson et al. (1977). The collected solar heat was transferred to the storage, and the air returned to the greenhouse generates a closed-loop cooling effect to some extent Experiments with an external collection scheme were conducted by Chiapale et al. (1977), Connellan (1985), Dale et al. (1980, 1984), Fynn et al. (1980), Ingratta and Blom (1981), McCormick (1976) and Mears et al. (1977). Internal  greenhouse  collection  systems have  to operate  at  lower  temperatures  than external collectors, so that healthy plant growth will not be jeopardized under relatively  hot  and  humid conditions. However, the  merits  of an  internal  collection  scheme are primarily two-fold Firstly, it saves on capital cost and secondly, no extra land is required. It was noted by van Die (1980) that i f a solar heating system were ever to be used by the greenhouse industry, growers would prefer it to be an integral component Greenhouses studied  by  with  Ben-Abdallah  shapes (1983),  quite Begin  different et  from  conventional ones  al. (1984),  Lawand  et  have  al. (1975)  been and  Turkewitsch and Brundrett (1979). As summarized in Table 1.1, with these active and passive systems, the solar heating  fraction,  f,  defined  as  the  percentage  of greenhouse  supplied by solar energy, was reported to vary from  heating  load  4% to 100%, measured  that is on a  monthly, seasonal or annual basis. It should be noted that some of the high f-values encompassed the contribution from other energy conservation measures such as nighttime use of retractable thermal curtains.  4  Some researchers (Arinze et al., 1984; Cooper and Fuller, 1983; Duncan et al., 1981;  Santamouris and Lefas, 1986, Shah et al., 1981 and Willits et al., 1985) have  coordinated their experimental and theoretical works using mathematical models to study the thermal performance are  pertinent  to  the  of their research greenhouse  thermal  greenhouses.  Others presented  environment  (Avissar and  models that  Mahrer, 1982;  Chandra et al., 1981; Froehlich et al., 1979; Kimball, 1973; Kindelan, 1980; Short and Montero, 1984; Soribe and Curry,  1973 and Takakura et al., 1971). Kimball  (1981)  developed perhaps the most detailed computer model thus far, which is similar to the modular TRNSYS program (Klein  et al., 1975) written primarily for residential solar  heating systems. His model can couple the thermal environment of greenhouses with some  energy-related  external  devices such as heat exchangers  and rock bed thermal  storage. Whereas  experimental  results  indicated  that  a  solar  heating  system  had  satisfactory or poor performance at a specific location, it is not known how the same or  a  similar  system  with  modified design parameters might behave  under climatic  conditions that prevail in other places. Experiments with each plausible design are too expensive because of the  high costs of heating  a greenhouse,  let alone monitoring  full-scale tests over many years to assess the system performance. Computer modeling and simulations can implement a systematic approach to solve these uncertainties and enable  designers  alternatives. reduced  to  engineers  The  to evaluate  long-term average  simulation results  generate  serving the  a  simplified  greenhouse  system behavior  derived  from  extensive  design  procedure,  for  different  design  simulations may also  through  industry can readily extract  which the  designers  be and  necessary technical  informatioa While many more innovations are yet to appear and be tested, research work in greenhouse solar heating has provided a reasonably broad base for the development of design methods for greenhouse solar heating systems as an extension to the 'f-chart  5  method'  for active solar residential space  and  water  heating  systems  (Klein,  et al.,  1976) or the 'solar load ratio method' for similar but passive systems (Balcomb and MacFarland, 1978). Design  optimization of  greenhouse  solar  heating  is  subject  to  three  major  criteria: thermal performance, crop yield and cost With adequate technical information generated  for a number  of design alternatives,  economic analysis is the  final  step  required for selecting the most cost-effective solution for a given design problem.  1.2 Objectives The objectives of this research work reflect, in part, the steps leading to the establishment  of a simplified design procedure  for solar greenhouse  design. They are  listed as follows: 1.  to develop mathematical models that describe the greenhouse thermal environment and thermal storage,  2.  to develop a computer program based on the overall mathematical model that is capable of interconnecting various subsystems of the solar heating system,  3.  to carry out simulations for validating the models with existing experimental data and predicting long-term system thermal performance,  4.  to  quantify  the  effects  of  important  design  parameters  on  system  thermal  performance and crop net photosynthesis, 5.  to develop correlations between dimensionless variables and the system long-term thermal performance.  1.3 Scope of the Study While enabling a designer to readily predict the solar fraction, the development of the f-chart  and solar load ratio methods  for systems with standard  configurations  necessarily put restrictions on their usage. Since no 'standard' greenhouse  solar heating  6 system  has  simplified  yet  been  defined,  design method  intermittent  the  present  work  aims  at  the  establishment  of a  for two generic systems that have each been subjected  testing at the  Agriculture Canada Saanichton Research  Station located  to at  Sidney, B.C. (latitude 48.5 ° N , longitude 123.3 ° W ) between 1980 and 1984.  1.4 Organization of the Manuscript The thesis is organized into five chapters. A brief outline of the rationale for the research programme is presented in chapter 1, where the objectives and scope of the study are also specified. In chapter 2, a critical review of the work done by other researchers is made. Experiments collection  with  greenhouse  methods  mathematical environment  are  cited  solar heating and  modeling of solar and  thermal  energy  systems  described  greenhouses, storage.  in  using the  detail,  which  internal  followed  includes the  A n account  by  and a  external  review  greenhouse  of  thermal  is also given of the existing  design methods for solar heating systems, for residences and greenhouses alike. Finally, effects  of  environmental  factors  on  greenhouse  plant  growth  are  introduced,  and  research works in the area of modeling crop growth are described. Chapter 3 presents the simulation models for two generic solar heating systems for  greenhouses.  System I represents 'augmented  internal collection with sensible heat  (rockbed) storage' while system II is representative  of 'internal collection with sensible  heat (wet soil) storage'. Results of model validation with existing experimental data are reported separately for the two systems investigated. A parametric study is launched in chapter 4 to study the variation of system behaviour under different conditions as affected  by parameters pertinent to  greenhouse  construction and thermal storage characteristics. Modifications to the simulation method employed in chapter 3 are explained, and some uncertainties of the modeling technique are  examined by a sensitivity analysis. Results of the parametric study are analyzed  7  and  used  for the synthesis of a simplified  design procedure.  A n example is given  demonstrating the steps to be followed in using the proposed design method. A special section is assigned to study crop performance by means of a net photosynthesis model as derived from literature review. Lastly,  the  thesis  is  concluded  with  suggestions  for  future  theoretical  and  experimental research work in chapter 5. The  appendices  contain listings of the  computer  program  developed  in this  project for simulating system performance, as well as a small program that implements the  simplified  design  procedure.  Psychrometric equations,  and  expressions  for  direct  (beam) radiation interception factor and diffuse radiation view factor are also included.  Chapter 2 LITERATI TRF RFVTFW  2.1 Greenhouse SolaT Heating Systems  2.1.1 Internal collection Wilson et al. (1977) adopted the notion of the greenhouse as a solar collector; they attempted to find ways to improve the collection efficiency which for the greenhouse under study at Ithaca, N.Y.  was found to be 32%. They proposed to  increase this percentage by modifying the greenhouse shape similar to the Brace-style design. For a given floor area, the authors suggested that taller structures will enhance temperature stratification without endangering plants at the bench level. Albright et al. (1979) tested yet another method of improving the greenhouse as a passive solar collector, whereby a number of 12.2 m long x 0.254 m wide flat polyethylene tubings known as Q-mats were filled with water and laid between rows of potted poinsettias and chrysanthemum plants inside a Brace-type greenhouse. These mats increase the thermal mass within the greenhouse by 9 MJ/°K. The authors pointed out that regions with severe winter weather cannot expect to have enough excess solar heat during even the best of days to provide a significant portion of the nighttime heat in a conventional greenhouse without adapting other energy conservation techniques. They further noted that if day and night greenhouse temperatures are permitted to vary according to ambient conditions, passive solar systems could be more beneficial. For the Q-mat system, contribution of stored energy to the nighttime heating demand was found to be 10% and it increased to 50% for the same house with highly insulated night cover that has reduced the heating load by 80%. Milbum and Aldrich (1979) tested a collection system using a plastic tube with perforations along the greenhouse ridge, while a fan helps to circulate the warm air 8  9  from there to the rockbed heat storage. The authors found that with this method of collection, a single cover greenhouse located in Pennsylvania could have 10 to 20% of the  annual  heating  load  met  by solar  energy.  The  system performance  relied  on  outdoor temperature, crop zone temperature and air flow rate. Staley et al. (1982) designed an air-type solar heating system for a shed-type glasshouse (that is, glass greenhouse) located at Sidney, B.C. (Fig. 2.1). The 6.4m x 18.3m structure is formed from one half of a conventional gable roof greenhouse that has had its north roof eliminated and north wall insulated. The greenhouse is used as .the collector whereby a 97 m inside north opened  wall  to different  surface extents  }  low-cost black thermal shade cloth mounted against its  acts as the  absorber  plate. The roof and side vents  when inside air temperature  reaches  are  28° C or above in  order to cool the greenhouse by way of natural ventilation Heated air that rises up the absorber plate is drawn by a centrifugal fan into a slotted duct and conveyed downwards to be stored in two parallel underground horizontal rockbeds. Cooled air returns  to  the  greenhouse  to  complete  the  closed circuit  At night,  the  air  flow  direction is reversed and the stored energy is recovered to heat the greenhouse. This system represents the method of 'augmented internal collection with sensible (rockbed) heat  storage'.  The  annual  energy  savings  amounted  to  29% and  35% during  the  operating periods of 1980-81 and 1983-84 respectively. All  equipment designed to adjust  the indoor environment including the solar  heating systems, were controlled by a microprocessor which performed  the  following  tasks: to integrate indoor and outdoor climatic information to control the greenhouse temperature to precise but flexible set-points to adjust ventilation and auxiliary heating systems to conserve energy to optimize solar energy collection, storage and recovery to control nutrient supplies to plants grown with the Nutrient Film Technique  section view toward east w a l l  1: tapered a i r duct  2: v e r t i c a l a i r duct  A: v e r t i c a l absorber plate 7: rockbed storage p a r t i t i o n 10: polytube ^  3: h o r i z o n t a l a i r duct  5: rockbed thermal storage 8: side vent  11: a u x i l l i a r y heater  6: storage a i r i n l e t / o u t l e t  9: roof vent  12: l i g h t weight pipe s t r u t s  a i r f l o w d i r e c t i o n (storage charging) *  Fig.  schematic diagram  2.1  a i r f l o w d i r e c t i o n (storage discharging) Solar heating system for a shed-type  greenhouse  with rockbed thermal storage  11 (NFT) to collect experirnental data on a continuously integrated basis Blackwell et al. (1982) described a simple system that stores the heat generated within a tunnel-type greenhouse covered with fiberglass reinforced polyester. A solar air heater consisted of ten air channels formed from overlapping five sheets of galvanized roofing  materials  inclination  of  mounted  the  in  absorber  the  northern  varies  from  side  21.5°  of  the  apex,  along the  thus  northern  the  edge  angle to  of  almost  horizontal at the top. During the day, a fan draws the heated air into a rock bed thermal  storage,  which  acts as  the  solar  heat sink. At m'ghttime,  its  function  is  reversed. Areskoug and Wigstroem (1980) reported findings of experimental investigations of an earth heat accumulation system directly beneath a greenhouse. During July and August  in  Alnarp,  Sweden  (62  °N)  excess  solar  heat  from  the  greenhouse  was  collected by heat pumps. Heat exchange takes place between water that flows through a system o f buried polyethylene pipes and the moist soil. The soil temperature at 2 m deep reached 42° C during the loading period. In the rest period of September and October,  before  unloading  actually  took  place,  bottom, as well as heat flow to greenhouse  heat  losses  through  via the soil surface  the  sides  and  led to a drop of  temperature to 28° C. By early January, the temperature fell further  to below 10° C .  Seasonal storage of solar heat as originally desired did not seem to be feasible with the system studied. They suggested that if the soil storage was intended to capture all excess solar heat during the summer, a network of vertical pipes that extended to a depth of 10-15 m might be necessary. Staley  et al. (1984) monitored the  performance  of an  earth  thermal storage  coupled to a conventional gable roof glasshouse that collects excess daytime heat (Fig. 2.2). Design and construction  details  were  reported  by Monk  et  al. (1983). When  interior air temperature rises above 22° C, warm air is drawn through a network of  •cctioa view towards east gable 1. 2.  acheBatlc dlagn  v e r t i c a l a i r ducts bolted to the top o f west gable plenum chamber c e n t r i f u g a l fan housing  3. e a r t h (heavy c l a y loam) thermal storage  4.  100 mm diameter FVC pipes, t o t a l 17 rows on 0.63 m centres  5.  polytube  7.  75 mm porous concrete f l o o r »•  Fig. 2.2  6. energy truss f o r sloped thermal c u r t a i n s 8.  SO mm g r a v e l l a y e r  a i r f l o w d i r e c t i o n (storage charging) a i r f l o w d i r e c t i o n (storage discharging)  Solar healing system for a conventional greenhouse with earth thermal storage  ^  13  34, 0.1m diameter PVC sewer pipes buried in two layers longitadinally in the  soil  beneath the greenhouse porous concrete floor. Excess irrigation wateT is allowed to seep through this floor thereby keeping the soil wet Heat is transferred the  pipe  to  the  soil  storage.  At night, when greenhouse  from the air in  temperature  drops below  17° C, cool air is circulated through the pipes to pick up heat from the storage and deliver it to the greenhouse. This system is representative  of 'internal collection with  sensible (soil) heat storage'. During the 1983-84 heating seasons, stored heat was able to supply 20% of the heat demand of the greenhouse. The concept of latent heat storage applied to horticulture was tested at the La Baronne solar greenhouse  complex (42° N) in France (Jaffrin and Cadier, 1982). The  experiment was run in a 500 m  multispan glasshouse devoted to rose production. The  5  excess solar heat available inside the greenhouse is extracted from the top of the roof ridges, thence transferred for storage in an underground network of flat bags made of a  polyester-aluminum-polyethylene complex and  chloride  decahydrate  (CaCl .10HjO) 2  filled  with  as a phase change  melts at 25° C and half solidification occurs at 15° C  13.5 tonnes  of Calcium  material (PCM).  This P C M  The storage capacity due to the  latent (PCM) and sensible (soil) heat of the materials add to a total of 155.4 M J / m . 3  At night, fans forced cool greenhouse air through the storage to recover stored heat Heat flux across the soil surface also contributed to nighttime heating supply to the insulated greenhouse -  April  fitted with inflated polyethylene film. During the December 1979  1980 heating  cunsumption  compared  season, to  the  this  solar  control, and  greenhouse net  achieved  60% savings  in  gas  savings of 50% when electricity is  accounted for. Nishina and Takakura (1984) also presented preliminary results of studies in a solar  greenhouse  experiment  station.  with The  latent  heat  experiments  storage were  system carried  at out  glasshouse. During day time, when the inside temperature  the in  Kanagawa Horticultural a  352  m  2  Venlo  type  was above 22° C, air was  14  drawn by fans into the Warm  air  exchanged  (Na SO,.10H O) 2  with  3  heat storage unit placed within heat  with  chemical  2.5  tonnes  additives  that  greenhouse  (Fig. 2.3).  sodium  sulphate  decahydrate  encapsulated  in  of  are  the  200  duminum  laminated polyethylene bags. This P C M has a melting point around 20° C and a heat of  fusion  of  235.2  MJ/m .  The  3  roof  ventilators  were  temperature reached 28° C. During the December 1982 -  opened  when  inside  air  March 1983 period, 50 % of  the night time heating requirement was supplied by P C M while the other 50 % was met  by heat released  heating  from the soil surface.  load is already  reduced  No auxiliary heating was needed since  by two energy  conservation measures:  one  to two  layers of thermal screens depending on outside air temperature, and splitting night time set-point temperatures between 12 and 8 ° C .  2.1.2 External collection Mears  et  al.  (1977)  developed  a  low-cost  solar  collector  for  v  greenhouse  applications using plastic films (Fig. 2.4). A black polyethylene layer serves as absorber  plate  and  is  sandwiched  between  four  layers  of  6 w  the  clear, ultraviolet  stabilized polyethylene films that form two air inflated pillows on each side of the black sheet  The  dead  insulator. Warm water concrete  floor  air space  created  leaving the  in a stone/water  by the  inflated  collector is stored  section acts as a  under  the  mix. The heat capacity of the  modest  greenhouse  porous  stone water  mix is  about 3550 kJ/m K. The composite floor also acts as the primary heat exchanger for 3  transfering heat to the greenhouse. Vertical curtains (double sheets of polyethylene) with warm water  in between  trickling down from the  distribution pipe to the  floor  are  placed between rows of plants and act as secondary heat exchanger units that increase the  thermal  coupling between  environment  at  researchers  found  night that  Over stored  the four solar  water full  in the heating  energy  met  floor seasons  storage and from  44.8% of  the  1976  the to  greenhouse 1980,  greenhouse  the  heating  North 14 (m)  Air outlet  25 (m)  Polyethelene film duct  Arrangement of the heat storage units in the greenhouse.  A i r inlet L Heat storage unit South Air  Fig. 2.3  inlet  Schematic diagram of the latent heat storage unit (Nishina and Takakura, 1984)  S  pump  Fie. 2.4  Greenhouse solar heating system with active collector and thermal storage (Mears et al., 1977)  17  requirement  that had been reduced by 44% through nighttime deployment of thermal  curtains. Ingratta and Blom (1981) evaluated the performance of a similar system for the climatic conditions at the Ontario.  Vineland Station of the  No vertical curtains  were  used  to  Horticultural Research Institute  enhance  heat transfer  between  of  thermal  storage and greenhouse environment The system is comparatively inexpensive, and could be installed for a cost of $35 to $40/m  2  (1980 value) of greenhouse  floor area. A  water flow rate of 1.86 1/s produced a collector efficiency of 49.3%. Y e t only 4.9% savings in fossil fuel consumption was achieved during the period September  1979 to  May 1980. Based on these figures alone, the authors suggested that active solar heating of  greenhouses in Ontario did not  appear to  be  feasible;  however,  refinement  of  collection and long term storage technology may alter this situation Another type of active solar collection system is the solar pond (Fig. 2.5). Fynn et al. (1980) carried out experiments using a salt gradient pond for  greenhouse  heating. An 18.3 m long, 8.5 m wide and 3 m deep pond with vertical walls was constructed. The pond was lined  with a layer of high density polyethylene material  that was able to meet the stringent physical and biological requirements. The bottom half of the  pond is a 20% salt (sodium chloride) solution convective zone  whereas  the  top half is a non-convective zone (NCZ) due to a salt  gradient  that  varies  from  fresh  water  at  the  top  to  20% salt  at  the  (LCZ),  concentration LCZ/NCZ  interface. The gradient zone is transparent to incoming shortwave radiation and opaque to re-radiated thermal energy, and it provides good insulation against conductive losses from the top. Heat was normally extracted from the pond by pumping the hot brine from the L C Z through a shell and tube heat exchanger. When the brine temperature was low (typically between 20 and 40 ° C in the middle of winter at Wooster, Ohio), the fresh water leaving the heat exchanger was manually switched to circulate through a  heat pump evaporator. The higher source temperature compared to outside air or  rl. COIL  Fig. 2.5  H.W. STORAGE  HEAT PUMP  S/f HEAT EXCHANGER  Schematic of the solar pond-greenhouse heating system which included a direct exchange loop and a heat pump loop (Fynn et al., 1980)  19  well water improves the coefficient of performance of the heat pump. The fresh water circuit transferred  heat from the heat exchanger or the heat pump to a storage tank  that eventually supplies heat to the greenhouse. The solar pond started to collect and store energy in mid-March of 1979. During the fall period, solar contribution to the greenhouse  heating load was found to be 79%, although this amount of solar heat  represents merely 4.5% of the solar radiation that fell on the pond in 1979. Dale  et  storage system  al. (1980) for  heating  investigated  a  greenhouses.  solar The  air  collection -  collector was  fabricated  wings at the top and bottom, and its tilt was 30 and 60° months at West Lafayette, Indiana. The subterranean  ground  water  with  heat  reflective  for summer and winter  groundwater soil storage unit was  enclosed in an impermeable pond liner and sealed to prevent vapor leaks. To reduce heat losses to the surroundings, it was insulated on the sides and top. The warm air from  the  collector outlet  was  circulated  through  a  network  of  corrugated  0.1  m  diameter P V C drainage pipes buried in the storage unit, thus heating up the soil. The average soil temperature around mid-September was 32.2° C, but reached only 15.5 ° C by late January. Hence, the soil storage subsystem was unable to retain heat for an extended  time period. During  barely 4% of the  greenhouse  the  winter of 1979-1980, stored  heat load. Aside  from the  soil  solar heat  supported  heat losses, this low  percentage could be due to the inefficiency incurred by simultaneously subjecting  the  soil storage unit to regeneration and extraction modes using two sets of alternating hot and cold pipes. A similar project was initiated by Dale et al. (1984) in October 1980 with the goal of developing an energy flat-plate  efficient greenhouse,  collector (Fig. 2.6). A shed-type  and combined with  greenhouse  an air type  was constructed with a vertical  south wall and a tilted north roof. The north wall is insulated, while the rerraining walls and roof are covered with Filon coated corrugated fiberglass on the outside and a  layer of tedlar (polyvinylfluoride) on the  inside. Thermal curtains were closed at  Fig. 2.6  Cross-section thiough greenhouse and solar energy collector (Dale et al.. 1984)  21 night The 40.7 m  2  greenhouse  roof  with  greenhouse  floor  area  storage  underneath  collector is fabricated of the same type of cover materials as the a  blackened  aluminum  absorber  plate.  Collector  area  ratio is 1:2. Transfer of collected heat to the saturated  the  greenhouse  is  achieved  by  means  of  45.  0.1m  to soil  diameter  non-perforated plastic tiles that extend in two layers through the soil. For the heating season between November 1980 to February 1981, energy contribution from heated soil amounted to 43.4% of total greenhouse heating demand. It should be noted, however, that this percentage conservation  is based  measures  on reduced heat load  mentioned  earlier.  brought about  Without these measures,  by the  energy  solar  heating  the  fraction would have been 10.7 %. They suggested that the auxiliary solar collector may be eliminated; instead, air from within the greenhouse during the daylight period can be circulated through the heat transfer pipes when the greenhouse approaches 28 to 30° C.  2.2 Mathematical Modeling of Solar Greenhouses  2.2.1 Greenhouse thermal environment Very  little glasshouse (greenhouse)  climate research  had been reported during  the many years of their use until Businger (1963) gave a detailed description of the energy budget of the glasshouse, which involved the usual heat transfer mechanisms, as well  as evaporation, condensation and ventilation. He partitioned the greenhouse  into  three components: the greenhouse cover, the air and the soil surface. Walker  (1965) presented  ventilated  greenhouses  as  Neglecting  the  associated  energy  a  single equation  environmental with  conditions  for predicting air temperature or  respiration and  air  flow  rate  photosynthesis,  is and  in  changed. the  heat  22  released by equipment, the energy balance for inside air is given as  Qs  The at  ±  Qau  -f  Qcn  + Q,  +  Qv  +  Qt  (2.1)  o  =  symbols used in the above equation are defined in the 'Notation' section placed the  end  Symbols  of  found  therein. This ventilation  this  chapter.  in figures  In  and  subsequent  tables  chapters,  separate  entire  manuscript  in the  notations are  are  used.  also explained  expression also permits some preliminary determination of heating and  requirements  of greenhouses.  However, the  impact of changes  in design  parameters on .the microclimate cannot be assessed. Models that divide the greenhouse  into its essential elements started  perhaps  with Takakura et al. (1971). The authors realised that measured leaf temperature and inside  air  temperature  were  not  the  same,  especially  during  daytime,  and  as  photosynthetic rate depends on the former, they introduced the plant canopy into the heat (energy) and mass (moisture) balance models. From  top  to  bottom, these components  are:  the  cover (inside and  outside  surfaces), the inside air, the plant canopy, floor surface and the soil. Heat balances are then given by: Qso  +  Qto  +  Qcvo  Qt,  -r  Qt,  +  Qcv,  +  Q cvp  Qcvf  +  +  +  Qcd  Qcd,  Qau  ~  Q „  +  Q t p - Q c v p - Q x ,  Q,j  +  Qti  Qn-Qn  -  Qc/  =  +  0  =  -  Qcvt  Qcn  -  =  (2-2) =  Qv  Q mp  —  0  (2-3) 0  (2-4) (2.5) (2.6)  Qcdj  (2.7)  Q  and mass balance for the inside air given by M, - M  v  - M\ t4  = M „ m  Since then, similar models were presented  (2.8) by Kimball (1973), Maher and O'Flaherty  23  (1973), Takami and  Uchijima  (1977), Scribe and  Curry  (1973),  Seginer and  Levav  (1970), Froehlich et al. (1979), Chandra et al. (1981), Kindelan (1980), and Avissar and Mahler (1982). These models differed in the degree of complexity with which they treat the various fluxes involved in the above equations, with some improving on the shortcomings  of  others.  Each  model  was  able  to  bring about  reasonably  accurate  predictions of the greenhouse environmental conditions that did not deviate considerably from  measured  data, as collected from experiments that lasted from a three-day  to  six-month period. This tends to suggest that these models may not be very sensitive to  the  magnitudes  of  certain  of their  parameters,  and  therefore  very complicated  models might not be warranted, depending on the objectives of the research. The greenhouse  extension solar  of these energy  heating  system  balance  models to incorporate  was presented  by  Duncan  et  features of a  al. (1981),  Kimball  (1981), Cooper and Fuller (1983), Arinze et al. (1984) and Willits et al. (1985). The computer model presented greenhouses. exchangers, (2.2)  by Kimball was developed for both conventional and solar  It couples the greenhouse rockbeds,  through  infrared  (2.8)  are  to energy-related  heaters, and  again  valid  for  evaporative solar  devices such as curtain heat coolers. In  greenhouses,  essence,  except  that  the  equations energy  balance of inside air must now include the heat transferred to storage during charging or recovered from storage during discharging, thus  Qcvp  +  Qcvf  +  Qau  ~  Qcv\  ~ Q  V  - Q t 6  =  (0.9)  0  2.2.1.1 Solar radiation level inside the greenhouse In the energy budget, solar radiation constitutes the major heat input to the  greenhouse  and  it  should  following review is concentrated greenhouses.  In  fact,  many  performance  of  greenhouses  be  as  accurately  as  possible.  The  on solar radiation transmission characteristics of  studies in  calculated  have  transmitting  been  carried  light, and  out results  to  evaluate were  the  generally  24  presented the  with regard to the glazing level transmittance, r , or more  effective transmissivity, r  . Whereas r  g  showed mainly the  frequently  effects  of the  optical properties of glazing materials, sky clearness and solar angle of incidence, r  g  is strongly influenced by the greenhouse  structures.  Though various authors used different terminologies in reporting their  research outcomes, r (broadband that  geometric configuration and internal  can generally be defined as the amount of solar radiation  g  or PAR) received on an inside horizontal surface  falling  on an  outside  horizontal surface  of the  same  as a percent of area.  The inside  horizontal surface may be taken at any height, but the plant canopy level is the most  appropriate  reference  while  floor  level  measurements  have  also  been  reported. Research works pertinent t o r  are reviewed first, followed by those that  concern r e  Walker and  Slack (1970) made  a  comparative  summary  of the optical  properties of selected rigid and film greenhouse covering materials, including glass, fiberglass, PVC, polyvinyl, polyester, UV-polyethylene and ordinary polyethylene. Spectral  transmittance  spectrophotometer. rigid have  values  Several  were  of the  measured  materials,  with  polyvinyl,  a  Bausch  polyester,  and  Lomb  fiberglass  and  P V C show a reduced transparency in the 735 nm wavelength, which would a  significant  effect  upon  flowering  and  stem  elongation  of  plants.  Transmittance of global (direct and diffuse) solar radiation for all materials with the exception of standard fiberglass was about 90 percent; fiberglass exhibited a marked difference between direct and global transmittance. Later  in  the  decade,  Godbey  et  experimental work to determine values of r  al.  (1979)  carried  out  extensive  for a variety of glazing materials.  Global as well as direct solar energy transmission were measured for six angles of incidence ranging from the normal (0 ° ) to 67°. Results were presented  for  25 single-layer samples and two-layer combinations. Measurements of long wavelength transmission were also included in their project In  his comprehensive  introduced  a  daylight  study  coefficient  of the  which  greenhouse climate, Businger  related  inside  and  outside  (1963)  short-wave  radiations, taking into account the optical losses through glass and the influence of the  construction, the  orientation  and  the  location of the  greenhouse on a  lumped basis. This coefficient varies from 0.55 under diffuse light conditions to 0.70  when  direct  light predominates  for  glass panes 0.6  construction greenhouses; a larger size of glasspane  m  wide in wooden  (0.72 m) favored a higher  value. Edwards large-span  and  1800 m  radiations,  2  as well  Lake (1965)  measured  east-west oriented as the  solar  radiation  transmission  greenhouse. Outside  transmission  onto  in  global and  a  diffuse  an inside horizontal surface  were  measured at various positions in the greenhouse. Obstructions to diffuse radiation caused  by  various  components  of  the  structure  was  found  by  making  measurements on overcast days at various stages of construction. The mean daily transmissivity of the diffuse component was found to be 64 to 69%; that of the beam  component,  changes  in  57% in summer  shape  rather  than  and  68% in winter. He  structure  could  lead  to  pointed  out  improvements  that in  transmission, particularly that of direct radiation.  direct  Manbeck and Aldrich  (1967) were probably the first ones to  generalize  visible  transmission  analytical  procedure.  solar  energy  Computations were  done  in  greenhouses  using  an  with various planar and curvilinear surfaces  that represent rigid plastic greenhouses. Results showed that at a latitude of 45 ° N , an E - W oriented gable-roof surface transmitted more solar radiation in the winter months and slightly less in early fall and spring than one oriented N - S . However, a greenhouse with  ridge aligned N - S is superior  to an E - W one  26  when it is located at a more southern latitude of 35 ° N . A latitude of 40.8 ° N is about the neutral location where E - W and N - S houses are more or less equally effective in light transmission. These results are similar for the vault-type fiberglass greenhouse. A  more detailed analytical method was outlined by Smith and Kingham  (1971) for calculating the solar radiation components falling within a single-span glasshouse  located at  K.ew, England. They  introduced an  angle-factor  F  and  separately evaluated this factor using geometric and trigonometric analyses for the direct and diffuse radiations transmitted by a glass surface (roof or wall) and subsequently intercepted by the floor of the house. Two glasshouses, one with lumber construction and the other a more modern wide-span metal type were compared in terms of percentage transmission of total radiation at the floor level. For  the  modern greenhouse  aligned E - W , the calculated values of r  range  g  from 0.66 in June to 0.70 in January, and were said to be in good agreement to within 5% with the observed values of Edwards and Lake (1965). Experimental rigid plastic greenhouses ranging in size from 20 m m  J  2  to 40  were used by Aldrich and White (1973) to study the relationship between  structural  form  greenhouses.  and  quality and quantity of transmitted  Measurements  were  taken  on  selected  solar energy  days  during  in such  two  winter  growing seasons. Results showed that there is an insignificant difference in r g due to single acrylic sheet cover or glass, with values ranging from 0.64 to 0.84, compared to that of a fiberglass cylindrical vault which varied from 0.58 to 0.74. The Brace Research Institute style greenhouse was proposed by Lawand et al. (1975) as an unconventionally shaped greenhouse for colder (northern) regions. The  basis  reducing illustrated  for  high  the heat  new  design was to  losses  in Fig. 2.7, the  associated  with  greenhouse  maximize solar radiation input conventional greenhouse  is oriented on an  while  designs. As  east-west  axis,  the  double-layer cl polyethylene  Fig. 2.7  Brace-style greenhouse (Lawand et al., 1975)  28  south-faring roof and wall is transparent, and the inclined north wall is insulated with a reflective cover on the interior face. The angle of the transparent roof and  the  inclined wall  are  chosen to meet the  experimental unit with 40 m  2  design criteria. Tests with  an  floor area showed that a 30 to 40% reduction in  heating requirements was achieved compared to conventional double layered plastic greenhouses.  Solar irradiance incident on north side of the house was observed  to be higher than that on south side, giving an average r  g  value of 0.54 in  April and 0.90 in December. They further reported higher yields of tomato and lettuce grown in the new design greenhouse, possibly due to increased luminosity in winter. Kozai et al. (1977) developed a computer model to predict the effects of orientation  and  latitude  conventional glasshouse.  on  the  overall  transmissivity  He concluded that the  difference  of  a  free-standing  in greenhouse  direct  transmissivity (the ratio of daily integrated direct solar light at floor level to that outside)  between  east-west  and  north-south  oriented  greenhouses is larger  at  higher latitudes; when comparing Amsterdam (52.3 ° N ) to Tokyo (35.7 ° N ) , the E-W  orientation  locations.  That  was greater by 22% for the the  E - W oriented  greenhouse  former performs  and 7% for better  than  the  latter  the  N-S  oriented one at the more southern latitude of Tokyo contradicts somewhat with the calculated results of Manbeck and Aldrich (1967) as mentioned earlier. Turkewitsch and Brundrett (1979) used the computer simulation technique to  predict  conventional  solar  energy  ( E - W and  admission  of  N - S oriented),  four  one  single-span  Brace style and  glasshouses:  two  an asymmetrical  glasshouse ('Greensol') retaining the north roof and insulating only the north wall (Fig.  2.8). Floor  level  or  plant  canopy  level  irradiance  were  the  outputs of  computer simulations, and a 'net transmission factor' was defined accordingly to compare collection efficiency. Their results indicated that reflecting insulation walls  #  K a.  X  X  *  10 m SPAN TRUSS E/w or N/S RIDGE  Fig. 2.8  Greenhouse types evaluated by Turkewitsch and Brundrett (1979)  30 augment winter light levels and reduce summer ventilating heat load. The Brace design  was  found  alternatives  during  studied, whereas  to  have  winter  the months  transmitted  greatest collection in  both  efficiency  locations  radiation per unit floor  among  (Toronto area  the  four  and Winnipeg)  in summer was  the  lowest Its disadvantage is the higher penalty under completely overcast conditions compared to Greensol; the  latter has a larger transparent  cover area to floor  area ratio. In this regard, though, Lawand (1975) suggested that new greenhouse designs should have every effort made to reduce the exposed transparent cover surface  area and hence  the  conductive heat loss, while maximizing solar gain.  The authors cautioned that care should be taken to ensure a reasonably uniform distribution of the radiation across the greenhouse floor as variations as high as 60% were calculated for the Brace design. Light  intensity  measured  directly  above  the  top  heating  pipes  was  compared by Amsen (1981) for double glass and double acrylic greenhouses with reference to a single glasshouse. No absolute values of r g  were reported, rather,  light level was found to be 20% and 22% less under double glass and double acrylic respectively. Stoffers,  as cited by Critten (1984) showed that transmissivity increased  steadily as the roof tilted more from the horizontal. The latter used computer modeling techniques to study the effects of geometric changes in a 'structureless* greenhouse hence  cross  average  conditions.  section greenhouse  Parameters  on  transmissivity patterns across transmissivity  investigated  were  under wall  diffuse height  the and  roof  greenhouse direct  height  and  irradiance and  roof  symmetry with one to three spans. He concluded that in houses with one or two spans, average direct light transmissivity can exceed unity, under low angle direct sunlight conditions, and a vertical south roof that reflects light downwards instead of upwards as in conventional multispans would also improve this value.  31  On the other hand, diffuse light transmissivity varied from 0.88 to 0.92 for both the conventional roofed house and the vertical south roofed house. Ferare and Goldsberry (1984) reported level ( l m above floor) under  values of r  measured at plant  g  double glazings. The percent  of global radiation  transmitted ranged from 0.55 to 0.65 for double polyethylene (Monsanto 603) and 0.62 to 0.72 for double P V C (4mil) between October and April. In Hannover (52.5 ° N ) , Bredenbeck (1985) measured light transmissivity at the  plant canopy level in three N - S oriented greenhouses  each covered with  single glass, double glass and double acrylic over a period of two years. The transmissivity of the single glass house was about 0.60 in summer and 0.55 in winter. It was noted that the transmissivity for diffuse radiation in winter time was higher  than  greenhouse  that  for  direct radiation, a  well  known connection  between  orientation and light transmissivity. The corresponding values of the  double glass house were about 0.10 less. He suggested that cleaning the glasses in the roof area could increase r cover  had  difference  a  transmissivity  g  ranging  by 0.03. On the other hand, double acrylic from  0.60  to  0.64  between summer and winter months. That r  better than double glass was attributed  g  with  no  significant  for double acrylic is  to the placing of less bars (aluminum  with rubber profiles) in the roof area and the treatment of the cladding material with a 5% ' S U N - C L E A R ' solution Ben-Abdallah shed-type TTF  glasshouses  by means  radiation input to conventional and  of two factors,  the  'total transmission  factor,  and the 'total capture factor, T C F . T T F was defined as follows:  TTF The  (1983) analyzed solar  numerator  through  = ZUAtMi represents the  all glazing  surfaces,  + uIuh sum of beam while  the  and  diffuse  denominator  is  radiations global  transmitted  solar radiation  32  incident on an outside horizontal surface. He used this factor to compare solar input efficiency of greenhouses having different values of construction parameters. Since  geometric  appropriate  losses  are  excluded in this  expression, the  indicator of actual solar input efficiency.  T T F is not  The author  an  then applied  view factors to compute solar radiation absorbed by the plant canopy (similar to r  g  in concept);  compared  to  unfortunately,  standard  values  the for  values of T C F thus derived are conventional  greenhouses  because  too high of  the  assumption that all beam radiation transmitted through the cover is intercepted by an  inside  horizontal  surface.  Nevertheless,  the  concept  behind  the  T T F is  important in that the transmitted solar radiation is an essential secondary quantity that leads to the computation of tertiary results such as I  and If. .  Another piece of research work that dealt with bothr  and r  g  was due  to Ting and Giacomelli (1987) who found that air-inflated double polyethylene transmitted range  a  higher percentage  (83%) than  in the  when measured  P A R range  in the  global  solar radiation  (76%). Moreover, effective transmissivity  based on the P A R range is much reduced at the canopy level, and is only 0.48 (that is, 48%). A number of greenhouse steady state or unsteady state modeling studies adopted  a simple method to  estimate  the  solar radiation level  horizontal surface and incorporated this estimated value in the  on an inside energy balance,  thus  Iik = rI r , the  (2.H)  oh  transmittance  of the greenhouse  depends  on the  type of cover  material and is assigned an average value regardless of greenhouse construction, orientation and latitude. While this approach is appropriate for the determination of an adequate ventilation rate required to maintain healthy plant growth (Walker et al., 1983) based on maximum solar heat input at noon, it is not applicable  33  for in  the purpose of this research work. Not only would large errors be induced the  estimation of solar gain if an average r  detailed  hour-by-hour  simulations, but  more  equivalent to the effective transmissivity r All  the  above  experimental  value is used throughout  importantly, r  is by  no  the  means  of the greenhouse as a whole.  g  and  simulation studies  have  one  idea  in  common despite the use of different terminologies: transmissivity is based on the solar radiation incident on an inside horizontal surface. The knowledge of this property of the greenhouse provides useful information for preliminary greenhouse design. Yet, when the  actual  amount  of solar  gain is needed  in a  detailed  greenhouse thermal environment model that incorporates a number of construction parameters, the previous research findings are not readily applicable as they  are  specific to the greenhouses studied. 2.2.1.2 Convective heat exchange F o r . the heat convection terms relevant to inside air, several  expressions  have been reported in the literature, all of which are of the form h where AT  ka  a,(Arr  =  denotes the  (2.12)  temperature difference  greenhouse air. The values of &i and a  2  between a component  are  well established  surface  for flat  and  surfaces  (Kreith and Black, 1980). They depend on the physical conditions of the heated 1/4 surface  and air flow, and the suggested  Zemansky, 1960); 1.38 1.52  ( AT)  1 7 3  ( AT. )  for cover and  1978). The values of ai = 1/3) are representative the  empirical value  experimental  1 / 3  values are  2.56 ( AT )  (Jakob, 1949); 4.87 ( AT ) 1.90  ( AT/B ) P  1 / 4  conditions,  ai  (Kimball, 1973);  for plant (Seginer  and  Livne,  1.38 and 1.52 corresponding to turbulent flow (a  of the air thermal properties (%, of  1 / 3  (Sears and  =  which  4.87  obtained  probably  by  includes  v, n  Kimball  2  =  and Pr) whereas  is  contribution  specific from  to  his  forced  convection due to ventilation. Seginer and Livne (1978) treated the problem of a  34  ventilated greenhouse  with a typical air flow velocity of 0.5 m s"  mixed convection regime; they added the contribution from the  expressions  as one of  1  shown  above  for  free  convection,  forced convection to  based  on  principles  of  momentum transfer across a boundary layer over a flat plate. A  testing  of  model  sensitivity  led  Avissar  and  Mahrer  (1982)  emphasize the need of accurately determining the inside air transfer since  the  computed  plant  and air temperatures  and  thus the  to  coefficients  convective heat  fluxes are stongly influenced. External heat exchange coefficient due to wind governs the heat loss from the  greenhouse.  Iqbal  pentagonal-shaped coefficients boundary  and  model  for. bluff layer.  Khatry  (1977)  greenhouse  to  bodies that are  Based  on  power-law  conducted determine  subjected profiles,  wind the  to the they  tunnel  tests on  wind-induced flow  from  presented  transfer  the an  a  earth's  empirical  relationship K  =  17.9u°-  567  ( 2.13)  van Bavel et al. (1980) found that this heat transfer coefficient led to too large a heat loss when compared to actual data for their multispan greenhouse. They adopted Jurges' (cited by McAdams, 1954) expression for a 0.5 x 0.5 m vertical flat plate oriented along the air flow K  =  5.7 + 3.8u,„  (2.14)  However, in their review of heat loss from flat plate solar collectors due to outside winds, Duffle and Beckman (1980) cautioned that it is not reasonable to assume eqn  2.14 is valid at other plate lengths. Garzoli and Black (1981)  and Willits et al. (1985) presented slightly different expressions, which are derived by linear regression on data given in the ASHRAE Handbook of Fundamentals (1981). Calculated h  values are practically the same as that due to eqn (2.14).  35 2.2.1.3 Evapotranspiration Quantitative description of the evapotranspiration process in greenhouses is one area where authors appeared to differ widely in their approach. Morris carnations  et  al. (1957)  to determine  the  carried out  experiments  on tomatoes,  relationship of transpiration to  the  lettuce  and  solar radiation  impinging upon the crop. Their results indicated a high degree of correlation of transpiration with radiation observed when the water supply is non-limiting. They recommended a ratio of 0.5 for freely transpiring, well-watered crops. Walker et al.  (1983)  adopted  requirements,  this  but added  value  in  their  procedure  of  evaluating  ventilation  that it should be reduced by a varying factor when  plants are very small or when the ratio of active growing space to aisle space is low. Businger  (1963)  suggested  that  the  latent  heat  flux  associated  transpiration may be expressed as a function of net radiation in the and the Bowen ratio 0  with  greenhouse  (the ratio of sensible heat flux to latent heat flux). Yet,  Seginer and Levav (1971) had made a thorough review of the models existing at that time, pointing out the need to develop models which only include primary boundary (environmental) conditions that are easy to measure and unaffected by the  existence of the  greenhouse.  These  include, among other  climatic  factors,  outside solar radiation and air temperature. Net radiation should therefore not be used as the  driving  function. Garzoli  and  Shell (1973) conducted a series of  experiments at the C.S.I.R.O. Division of Irrigation Research, Griffith, and found that the latent heat percentage  of the enthalpy increase for a fully  greenhouse  cotton crop varied between  under  summer  the  conditions of high  48 and 75% with an average solar  radiation intensities  temperatures, characteristics of the semi-arid area of inland Australia.  and  developed of 57%, ambient  36 Milbum from  (1981) stated  that  for  typical  greenhouse  operations, 0  ranged  about 0.4 for dense crops, such as roses and tomatoes to 4.0 for very  sparse crops, such as bedding plants. If absorbed  solar radiation by the  plant  canopy is partitioned into sensible and latent heat exchanges only, then for 0  =  (0.33, 0.4, 1, 2 and 4), the proportion that is latent heat flux will be 1/(1-H?) =  (75%, 70%, 50%, 33% and 20%). A 0 value of 0.4 therefore  seems too high  compared to the findings of other authors. Bello greenhouse,  (1982)  made  an  in-depth  study  of  evapotranspiration  in  a  and concluded that a constant Bowen ratio should not be assumed  over a seasonal period. Another fundamental  way  of  method,  and  evaluating is used  transpiration  by Takakura et  may  be  called  the  direct  al. (1971), Chandra  et al.  (1981), Cooper and Fuller (1983), Kindelan (1980), Kimball (1981) and Arinze et al. (1984). Basically it is the Ohm's law approach  M,  -  *»•"•-'>  ( 2  in which the canopy resistance (r stomatal resistance  .  I S )  ) to water vapor diffusion is made up of a  in series with a boundary layer air resistance  and weighted  according to leaf area index. These investigators used very different values for r^ , ranging from 250 to 900 s m* , and not necessarily depending on the stage of 1  plant growth. Parameterization of the and  Mahrer (1982)  who introduced  taking into account the temperature,  vapor diffusion  effects  an  process  empirical expression  of environment factors  vapor pressure gradient, C 0  was outlined by Avissar  2  for a  rose crop,  including solar radiation,  concentration and soil water potential.  The constants in their expression were specific for rose and not available for  37 other plants in the literature.  2.2.2 Thermal energy storage There are basically two types of thermal energy storage systems, sensible heat storage and latent heat storage. The latter is outside the scope of this study, and two sensible heat storage media will be covered in this section. 2.2.2.1 Rockbed thermal storage Rockbed thermal storage is also known as a packed bed, pebble bed or rock pile storage, whereby a fluid (usually air) is circulated through the bed of loosely packed material to add or remove heat  A variety of solids may be  used, rock being the most common. Its specific heat ranges within narrow limits from 800 to 920 J/kg.C. With a void ratio of 0.25 to 0.40, the effective density varies from 1600 to 2300 kg n r  (Telkes, 1977).  3  Schumann (1929) formulated the classic equations for the solid and fluid phases  ^  c)fiAn  ~df  (vc) (l-e)^  =  r  Underlying  these  one-dimensional  -{™)f-^  =  plug  dispersion; no mass transfer;  v  n  r  (2.16)  f  K(T -T ) }  governing  fluid  + h A {T -T )  (2.17)  T  equations  flow;  are  constant  no temperature  the  properties;  following no  axial  assumptions: conduction or  gradient within the solid particles;  internal heat generation is absent; and radiation effects are negligible. Since then, many  studies  packed (Mumma  beds. and  have  been  made  Works that link Marvin,  on with  the  heating  and  cooling  characteristics of  solar applications include transient analysis  1976; Hughes et  al., 1976; White and  Korpela, 1979;  Coutier and Farber, 1982; Saez and McCoy, 1982), and pressure drop estimation  38 (Chandra and Willits,  1981; Parker et al., 1983). In particular, Hughes et al.  (1976) found that the long-term performance of a solar air heating system with N T U (number of heat transfer  units) equal to 25 is virtually the same as that  with N T U equal to infinity, where h A I  (?hc) (l+0.2Bi)  c  a  Bi  =  h d /]2k  h  =  6r>0(m/A d) -  v  2  v  r  0  7  n  (2.18) and thus eqns (2.16) and (2.17) can be combined into a single P D E since Tj, and T  r  are everywhere the same. With the addition of a heat loss term and  another one for axial conduction, the simplified equation becomes  (2.19); where  T^  is  now  the  effective  storage  empirical expression for heat transfer  temperature.  coefficient h  y  It  is  noted  that  the  is due to Lbf and Hawley  (1948). Close et al. (1968, cited by Klein, 1976) observed experimentally that up to  25% more  heat  could  be  discharged  as  pebbles  adsorb  water,  and  thus  increases the bed's apparent storage capacity. Kimball (1986) attempted to consider condensation of moisture on the rock particles thereby was  assumed  that  no  significant absorption  of  releasing latent heat  moisture  occurs  and  It  that all  condensed water drains away so evaporation cannot take place during discharging. He did not check his model with actual data, though. Willits et al. (1985) also realized the need to modify the rockbed model to include latent heat exchange since their inspection of the bed at the end of a charging period revealed that condensation has occured. The amount of water condensed in each rock layer in  39  their model was assumed to remain in that layer, and was calculated by means of a mass balance using the humidity ratio of moist air. However, details of the modeling were not given.  2.2.2.2 Soil thermal storage Theoretical work on heat transfer between a pipe and soil were done by researchers such as Ingersoll et al. (1948) and Pappas and Freberg (1949). They found that heat transfer to the soil became difficult as the soil dried out In  the  area  of  waste  heat  utilization,  Kendrick  and  Haven  (1973)  considered the steady-state radial flow of heat from the water in pipes into a semi-infinite  soD  body.  The  key  assumption  in  their  work  was  that  the  temperature field established by each pipe acting as a line source at an arbitrary cross section is independent of all the other pipes in the field. Parker et al. (1981) presented moisture transfer  a computer  model to predict  heat and  in the soil produced by a subsurface network" of warm water  pipes. A finite difference scheme was used to implement the soil model on the computer. Soil thermal properties that change with moisture content were updated at each time step. The water flow rate in the pipes was assumed high enough so that the temperature gradient in the longitudinal direction was negligible. Puri (1984) applied the finite element method to analyze the simultaneous diffusion  of  moisture  and  heat  in  soils.  A  time-dependent  axisymmetric  formulation for a single tube was used to evaluate the thermal performance of an earth tube heat exchanger system. Based on numerical results, he concluded that the single tube analysis can be extended to multiple tubes using addition provided a minimum distance of eight tube diameters is maintained between the tubes.  The author  soil-pipe interface  also noted  that for  a pipe air temperature  volumetric moisture content is reduced from  of 38° C,  the  the initial 30%  (near saturation) to 28.75% after 12 hours of continuous operation and result in  40  only a 4% change in soil thermal conductivity. This is inconsequential and does not affect the overall system performance. Furthermore, he studied two initial moisture regimes, 30% and 20% and suggested that the preliminary design curves developed for 30% are equally valid for a 6  of 20%, since C varies linearly w s  with moisture content, whereas k  g  has an approximately linear variation with the  range of moisture content considered; in other words, the thermal diffusivity of soil, a  , does not change significantly. The study made by Lei et al. (1985) on the characteristics of a single  underground pipe for tempering ventilation air for plant and animal shelters falls along the same line as Puri (1984). They considered more parameters and the combined effects of pipe diameter, pipe length and air velocity were quantified. As experimental data revealed that the soil temperature gradient in the radial direction is on the average at least 100 times greater that that along the pipe's, they restricted the region of interest to a semi-cylindrical section The latent heat released due to condensation of moist air on the inside of the pipe was handled by calculating the increase in the convective  heat transfer  coefficient  using heat and mass transfer analogy. The simulated data indicated that the overall soil effects on the temperature differential between inlet and outlet air are not significant Model validation of their work was based on simulated and measured outlet aiT temperatures, which agreed fairly well with each other. Areskoug and Wigstroem (1980) used the general heat conduction equation to simulate soil temperatures in an earth thermal storage system directly beneath a  greenhouse.  centerline  The  of the  modeled  greenhouse  region  was  constructed  with  symmetry  and was discretized in a two-dimensional  at  the finite  difference scheme. Predicted values compared favorably with actual data measured at depths up to 7 m on days with charging and discharging operations.  41  Simulation study of a soil heat storage system for a solar greenhouse was also carried out by Dale et al. (1980) and Boulard and Bailie (1986a.b). The former  researchers  heat transfer  used  a three-dimensional  to or from  finite difference  pipes. The standard  actual hourly soil temperatures  model to predict  deviation between  predicted and  on two typical days, one each in summer and  winter, was reported to be within 1 ° C . Boulard and Bailie quoted the work of Person: 'At low soil temperatures gradients, heat diffusion  (30 ° C ) and with small soil water potential  due to moisture movement can be safely ignored'. This  observation agreed with the experimental steady-state silt loam soil  temperatures  obtained from a controlled laboratory system, as reported by FJwell et al. (1985), where it was shown that a soil/pipe interface temperature  of 30.0 ° C did not  lead to dry core formation while raising it to 43.3 ° C caused a dry core region of  approximately 9  cm in diameter  to  form  around  each  electrically heated  copper tube 2.5 cm in diameter, and hence steep temperature  gradients around  the pipes were produced. They adopted Fourier's heat conduction equation as the governing equation and discretized it in two dimensions using the implicit Finite difference method. The time-varying boundary conditions were measured values of surface  soil temperature,  temperature. treated  as  temperature  Of these a  secondary  pipe/soil three  interface  sets of data,  boundary  temperature surface  condition as  it  and  pipe is  underground  temperature affected  by  water  shall the  be fluid  inside the pipe and conduction process in the soil itself. Hence their  model is not suitable for a complete simulation study integrating the soil thermal storage with the greenhouse thermal environment.  42  2.3 Design Methods The present research program aims at the establishment of a simplified design procedure for greenhouse solar heating systems, along the lines of the 'f-chart' method for active collection systems or the 'SLR-method' for passive collection systems, both coupling to storage and other equipment in the overall residential solar heating system. Also presented  in this section is a discussion of some design-oriented studies related  to solar greenhouses that appeared  in the literature previous to the proposed design  procedure.  2.3.1 f-chart method The f-chart method proposed by Klein et al. (1976) and Beckman et al. (1977) which  is now widely  adopted  in flat-plate  solar collector designs  is a generalized  design method that results from numerous computer simulations. The conditions of the simulations  were  varied  over  appropriate  ranges  of parameters  of practical  system  designs. For an air heating system, the fraction, f, of the monthly total heating load supplied by the solar heating system is given as a function of X and Y which are respectively the ratio of absorbed solar radiation to total heating load and the ratio of collector loss to total heating load. The relationship between X , Y and f in equation form is /  =  1.04K - 0 . 0 6 3 X - 0 . 1 5 9 7 + 0 . 0 0 1 8 7 X * - 0 . 0 0 9 5 F 2  3  (2.20)  Fig. 2.9 illustrates the design curves in two graphical forms. Given the basic design characteristics of the system, such as collector area, the storage size, heat-exchanger  parameters, air flow rate, and the collector performance, as  well as the monthly climatological averages, solar insolation and heat load data based on the degree-days method (ASHRAE, 1981), the f-chart will predict the monthly and hence annual solar fraction of the system. These can then be used for design decisions  Fig. 2.9  The f-chart for an air system (Klein et al., 1976) above: f as a function of X and Y below: f versus X with Y as parameter  44  and economic evaluation.  2.3.2 SLR-method The SLR (solar load ratio) method devised by Balcomb and McFarland (1978) is a simplified method for estimating the performance of a collector-storage wall (also called  Trombe  wall  or  Trombe-Michel  wall)  passive  heating  system.  The  SLR is  defined as the ratio of monthly solar energy absorbed on the storage wall surface to the monthly building heat load. It is calculated for each month and a monthly solar heating fraction, SHF, is obtained from Fig. 2.10 for the particular system.  2.3.3 Direct simulations as design method Both  the  performance methods  f-chart  and  SLR  methods  allow  designers  to  estimate  system  based on local weather data i f they are readily available. However, these  are  not  arrangements or  applicable  when the  to  unconventional  magnitudes  of the  designs  that  involve  other  system  design parameters deviate significantly  from the specified ranges. Under these conditions, dynamic simulations by means of a computer model are still necessary. Rotz et al. (1979) extended their computer models written for conventional and solar  greenhouses  alternative  to  insulating  predict and  solar  energy  requirements  heating  modeled, which included a solar water  systems.  for Four  greenhouses solar  equipped  with  systems  were  heating  system with uninsulated or insulated external  collectors, a solar air system, and an internal greenhouse  collection system. Insulation  options  Computer runs  with  were:  only  one  double acrylic cover and fixed  set  of  design  thermal  blanket  parameters  and  for  an  average  were  made  location in  Pennsylvania, hence results were very specific They concluded that the system with the least  potential  (about  9%)  for  fuel  saving was  that based  on  internal  greenhouse  collection of excess solar heat alone, whereas the most promising one (about 90%) was  A,SN/L. Solar load ratio  Fig. 2.10  Monthly solar heating fraction versus solar load ratio for buildings with south-facing collector-storage wall systems (Balcomb and McFarland, 1978)  46 a system that combined heavy thermal blankets, double acrylic cover and external solar collection. Solar  greenhouses  number of researchers,  with  a  rockbed  thermal  storage  have  been  tested  by  a  as pointed out in an earlier section. Puri (1981) presented  a  few design curves (Fig. 2.11) as a quick means of predicting the long-term thermal performance  of  a  solar  heating  system  that  makes  collector. The design parameters considered are  the  areas, the ratio of storage volume to greenhouse  use  of  an  external  flat-plate  ratio of collector to  greenhouse  area, as well as collector tilt and  azimuth angles. Though the results are specific for the location at Lafayette, Indiana, and  have  limited  applications, it was the  first  of its kind  that aims at providing  designers with some guidelines in sizing a solar heating system for their customers. Montero and Short (1984) tested plastic solar collectors similar to the Rutgers design (Mears et al., 1977). After an efficiency curve was established a collector model was combined with a computer simulation program for greenhouses in order to predict the thermal performance of the system in two distinctly different areas -  Ohio (USA)  and Malaga (Spain), which subsequently led to two sets of curves that may be used as design tools. These charts, as depicted in Fig. 2.12, relate the solar heating fraction to the collector areargreenhouse area ratio for various kinds of greenhouse covers.  2.4 Effects of Environmental Factors on Greenhouse Plant Growth  2.4.1 Environmental factors The hence  major  growth  temperature, practices.  and  environmental development  factors of  that  affect  greenhouse  the  plants  physiological processes are  light,  carbon  and humidity, which are in turn influenced by cultural and  and  dioxide,  engineering  47  1.0  I  I  I  I  l  I  I  r-60°  0.9 0.8 0.7  -  ^ - 9 0 ° (Vertical)  -  | 0.6 u- 0.5  .-  ~ N o Collector  0.4 0.3  •*-  0.2 _  Due South  0.1 0 0  i I I 0 . 5 1.0 1.5 A  I 2.0 c /  A  l l I 2.5 3.0 3 . 5 4.0 g — -  1.0 0.9  Azimuth = 0  0.8 0.7 |  0.6  LL. 0 . 5  No  Collector  0.4 0.3 Tilt = 45°  0.2 0.1 0  Fig. 2.11  0  0.5  1.0  1.5  2.0 2.5 3.0 3.5 4.0  Nomographs for greenhouse-rock storage-collector system (Puri, 1981) above: for vertical and 60° tilt collectors below: fot 45° tilt collector and various azimuth angles  Fig. 2.12  Computer predicted seasonal performance of a solar collector-heating system for three commercial type greenhouses (Short and Montero, 1984) left: Wooster, Ohio, U.S.A. right: Malaga, Spain  49  Blackman (cited by Mastalerz, 1979) stated the 'principle of limiting factors' as follows: "When a process is conditioned as to its rapidity by a number of separate factors,  the  rate of the  process  is limited  by the  pace  of the  slowest  factor." This principle may be illustrated by the photosynthesis of a cucumber leaf at limiting and saturating C 0 ppm  (  level  (about  concentrations under 500 W incandescent light (Fig. 2.13). At 300  2  C0  level, the saturation rate is reached at comparatively lower light  2  100 W n r  PAR), regardless  2  enrichment to 1300 ppm, marked difference  of air temperature. is seen under  However, with C 0  two different  2  temperature  regimes. Looking at this phenomenon stimulated  C0  2  fixation  more  at  from another increasing  angle, higher carbon dioxide levels  light  intensities.  This  relationship,  as  depicted in Fig. 2.14 for sugar beet (a C - 3 dicot), has been well known for many years. At normal C 0 126 W / m  2  level of 330 ppm, a drop in P A R level from 308 W / m  leads to a very slight reduction in C 0  2  in light level to 35 W / m  2  2  fixation rate, while a further  2  to  drop  brings about an additional 50 % rate reduction. In other  words, photosynthetic rate saturation occurs at a PAR of about 120 W n r . 2  For  tomato  plants  (also  C-3  concentration  show  one-half full  sunlight, that is, 150 -  horizontal  surface;  photosynthetic  young  tomato  dicots)  rate  single leaves  saturation 200 W n r  plants  do  not  at 2  to  P A R intensities  (or 30 need  exposed  the  normal C 0 one-third  2  to  40 klx) on an exposed light intensities  of  full  sunlight For  an entire crop, though, light saturation occurs at much higher intensities.  For instance, typical values for two C - 3 crops, wheat (monocot) and cotton (dicot) are about 280 and 420 W m demonstrated  2  respectively. On the other hand, many experiments  that the optimum C 0  2  have  concentration ranges between 1000 and 1500 ppm  Fig. 2.13  Photosynthesis of a cucumber leaf at limiting and saturating C O : concentrations under incandescent light (Gaastra, 1965)  51  J  I  500 C0  Fig. 2.14  2  ! _  1,000  concentration (ppm)  Effects of atmospheric C 0 2 enrichment on C0 2 fixation in a sugar beet leaf (Salisbury and Ross. 1982)  52 (Wittwer and Honma, 1979). Bauerle and Short (1984) studied the C 0 greenhouses.  At 200  ppm  C0  and  2  600  depletion effects  2  P A R light  intensity  in energy efficient (130  W  nr ), 2  net  photosynthesis of tomato plants was found to be 35% less than that at 300 ppm C 0 . 2  At the more  same time, transpiration rate was 4% higher (Fig. 2.15) since stomates open at  occured  low C 0 with  2  concentrations.  increasing  Larger photosynthesis  light levels. In  stomatal opening with changes in C 0 (1965)  and  many  other  the  2  transpiration  phenomenon  differences  of transpiration  and  content of the air had been observed by Pallas  2  physiologists. Lettuce  photosynthetic rate at reduced C 0  showed  less  of  a  reduction  in  net  concentrations than did tomato.  Reduction in net photosynthetic and  fact,  and  even a longer growing season,  rate would likely lead to reduced  fruit size,  thus posing scheduling problems. On the  other  hand, higher transpiration rate means more ventilation is needed for humidity control, and watering should be more  frequent  The temperature range over which plants can photosynthesize is large. Increases in temperature usually stimulate photosynthetic rates until the stomates close or enzyme denaturation begins to occur. Each species or variety has therefore, at any given stage in  its life cycle, an optimum range of temperatures that promotes  maximum growth  rate. For C - 3 plants photorespiration activity increases with temperature rise because of a higher ratio of dissolved 0  2  compared to C 0 , thus counteracting 2  the stimulating  effect of a temperature rise, resulting in a rather flat and broad temperature response curve between 1978).  15 and  Klapwijk  (1987)  30 ° C  when compared  commented  temperature range can lie between cause besides,  stomatal such  membranes.  closure conditions  in  most destroy  that  under  18 and plants  unsaturated  35 ° C . Very  and  proteins,  to C - 4 plants (Salisbury and Ross,  therefore  inactivate  light  conditions,  this  high temperatures usually  affect enzymes  photosynthetic and  activity;  disintegrate  cell  200  400  600 2  PAR light intensity, uE/m s  200  400  600  800  1000  ? PAR light intensity, pE/m s Phoiosynlheu'c (above) and transpiralional (below) responses of tomato plants to various light intensities and CO, levels  54 Many plants, especially woody ones, grow better when the night temperature lower  than  the  day temperature.  These plants have two optimum temperatures,  is one  during the day and the other and more crucial one at night, for each stage of plant development temperature  Moore  (cited  for tomatoes  by  Alrich  et  al.,  1983)  during flowering and fruiting  reported  that  is 15 to  the  optimum  19 ° C for cloudy  days and at night, and 20 to 27 ° C on sunny days, whereas Wittwer and Honma (1979)  suggested  correspondingly. tomatoes  slightly  different  Salisbury and  ranges  of  Ross (1978)  15°  noted  to  17° C,  that the  is at a maximum when night temperature  and  18°  to  relative growth  24° C rate of  is around 20 ° C for a typical  optimum day temperature of 26 ° C . Relative humidity level of 70-80% is considered most desirable for  greenhouse  plants. This optimum range allows adequate transpiration to take place and effectively cool the leaves. Above 80%, if water vapor condenses on the foliage, disease organisms are more likely to be a problem; the situation could deteriorate when combined with high  temperatures.  During cold weather, condensation frequently  occurs on the inside  surface of the greenhouse cover, it does not pose a problem until it builds up to the point  of  dripping  accumulates  in  the  onto  the  house  leaves.  because  In of  plastic-covered less  exchange  structures, of  air  more  through  moisture infiltration.  Condensed moisture spreads out into a thin film on glass while it remains in droplet form  on  the  plastic surface.  Polyethylene  films  can  now be  made  with  modified  surface tension properties that can reduce the size of the droplets thereby bringing the condensation problem under some control. Aside from these primary environmental factors, air movement is a factor that cannot be overlooked in greenhouse environment control. Greenhouses that are designed to be used as solar collectors for the solar heating system still need ventilation for temperature, maximize  C0  the  2  level  collection  and of  humidity control, while every effort trapped  solar  heat  The  is being made  ventilation system  should  to be  55  designed to provide adequate air mixing and distribution. The boundary  layer resistance  of air moving across a leaf surface  with increasing air speed, thus increasing transpiration, heat transfer and C 0  decreases movement  2  into the leaf. Aldrich et al. (1983) pointed out that air speeds of 0.1 to 0.25 m s"  1  facilitate C 0  2  uptake, as air speed increases above this value, C 0  2  uptake is reduced,  growth is inhibited and eventually may even cause damages to plants, whereas below this value, uniform mixing in all sections of the greenhouse is not assured (Mastalerz, 1979). Welles et al. (1983) studied the effect of thermal screens and wall insulation on yield. For an east-west aligned glasshouse, cropping near the north-facing wall was little affected  by the cladding materials compared to those  grown near  the  opposite  wall, probably due to a reduction in temperature near the walls. Buitelaar et al. (1984) made  further  investigations on the  effects  of four insulation materials placed against  single-glazed glasshouse walls on growth and production of tomatoes. Materials in the south wall have a more profound effect on the production. It appeared that the less the  light  is  transmitted  by  the  insulating  material,  the  greater  is  the  loss  in  production; flowering rate was hardly influenced. Papadopoulos and Jewett (1984) compared tomato growth, development and yield in twin-wall P V C panel and single glass greenhouses.  Plant growth and  development  were found to be better under glass during the light-deficient months of the Final marketable yields depend  on the season  In all experiments, harvests  from  year. the  P V C house had larger and higher percent grade #1 fruits. van Winden greenhouses  on  et al. (1984) compared  production  of  tomato.  In  the  effects  spring  and  of single and autumn,  plants  double inside  glass the  double-glazed house yielded respectively 10-15% and 4-13% less in comparison with single glass.  56  The above findings indicated that a definite trend could not yet be observed with regard to the enhanced  the  techniques  of double glazing on greenhouse  conclusion made  tested  single-skinned  effect  by  and  a  by  number  Hurd  of  (1983)  researchers,  double-skinned plastic or  tomato production. They  from his survey that  differences  of energy in  yields  glass greenhouses have  saving between  not consistently  favoured the former houses.  2.4.2 Mathematical models The variation of greenhouse  designs in shape, size, orientation, type and layers  of cover may lead to a variety of internal environmental conditions, and it is desirable to work with a crop growth model that incorporates the essential environmental factors such as light, C 0  2  and temperature. Other factors (e.g. irrigation and nutrient supplies)  are assumed to follow normal practice and sound management assures that they are at their optimal quantities for plant growth so as to reduce the complexity involved in modeling. France and Thornley (1984) made a critical survey of crop growth models that can be  operated  categorized the somewhere  over a whole growing season  to predict growth  and  yield. They  models into empirical or mechanistic types, though many models  in between.  Empirical  models attempt to  directly to various aspects of climate, weather  relate  crop  and environment;  growth  the  major  and  fall yield  objectives  are to account for observed yield variations and to discover which factors affect yield most greatly. Mechanistic models are constructed by assuming that the system has a certain  structure,  processes  and  assigning  to  the  components  of  the  system  properties  and  which can be assembled within a mathematical model. The submodels of a  mechanistic model may be either empirical or mechanistic A simple mechanistic model may just consist of photosynthesis and respiration (for instance, Johnson et al.. 1983), while  a  comprehensive  model  would  attempt to account  for all the  processes  (for  57 instance Meyei et al, 1979). The authors deemed that sound mechanistic models are suitable for applied scientists whose aim is to use current knowledge for their research and development activities. Soribe and Curry (1973) extended the dynamic modelling established by Curry and Chen (1971) to simulate lettuce growth in an air-supported plastic greenhouse. The major processes considered in their model were photosynthesis and respiration. Modeling of gross photosynthetic rate is based on Monteith (1965a):  ^  . l* + JLY  l  dt  PAR;  \c  r  (2.2i)  As suggested by Saeki (cited by Charles-Edwards, 1981), the light flux density incident on the surface of a leaf within a canopy can be described by PAR  =  PAR K exp(-K L,) p  (2.22)  f  p  which is an adaptation of Bouguer's law of light attenuation. The rate of respiration that is made up of two parts, maintenance and conversion (growth) respiration, is temperature dependent and is given by  =  cWQ\l'-^'"  +  ^  ,2.23,  while the rate of dry matter accumulation is  which represents the difference between the quantity of carbohydrates synthesized and their consumption during dark respiration. The rate of leaf area expansion may be empirically expressed in terms of increments of leaf weight ratio, LWR. and specific leaf area, SLA: dA.  dW  =  LWR(t).SLA(t).—  (2.25)  58  and it acts as a positive feedback term for photosynthesis, via expanding the base for light interception. Acock et al. (1978) evaluated two models of canopy net photosynthesis of a tomato  crop.  Tomato  plants  were  grown  techniques. The glasshouse was heated  in  a  glasshouse  using  nutrient  culture  to 16.5° C at night and maintained at 20° C  during the day. Primarily the gross photosynthesis part of the model for a single leaf takes the  form of Monteith's expression  except that the  temperature function F is  removed: P.  where a  aPAR^C  =  a P A R + cC  is the leaf light utilization efficiency and J  transfer. The coefficients a (Pg -  (2.26)  is the leaf conductance to C 0  and $ are evaluated on the assumption that P  3  stands for  Rj ), where Rj is the photorespiration rate and & , $) corresponds to (1/B,  1/A) in equation 2.21. The simple model assumed that the canopy was composed of leaves  with  identical photosynthetic  and  respiratory  characteristics, whereas  the  more  detailed model allows explicitly for variation in $ and R^ within the canopy. The rate of canopy net photosynthesis per unit ground area, P P  n  =  g l n f ___«* PAR + (l-r,kC K {aK PAR exp(-K L )-r(l-r ^cj P  v  where  p  p  is expressed as  Q  P  p  t  K  j  p  (2-27)  R^ includes 'dark* respiration by stems, fruits and roots besides that of the  leaves. Equation 2.27 may be derived by integrating over the entire leaf area of the canopy from the expression of P from  Soribe and Curry's procedure  for a single leaf along with eqn (2.22). It differed of numerically solving their ordinary differential  equations. Experimentally, P The canopy with L.  =  Q  was measured over a range of natural light flux  densities.  8.6 was divided into three layers for progressive defoliation  tests. In this way, the uppermost layer, occupying 23% of total leaf area, was found to  59  assimilate  66% of the net C 0  percentage  of the total  coefficient  decreased  leaf  2  fixed  by the canopy  respiration.  with depth  Measured  and accounted  values  for a similar  of the canopy  in the canopy, ranging from 0.63 from  extinction  the top to  0.52 at the bottom layer, corresponding to L of 2.0 and 8.6. Estimated values of o and $  from fitting experimental  data  to equation  2.27 were  10.1+1.0  x 10' [mg  COj/J]  and 1.6±0.4 x 10~ [m/s] respectively. A mean value of 0.15 for the leaf  3  3  transmission coefficient, m, was used in all analyses. Subsequently, Charles-Edwards (1981) concluded that the simple canopy model (equation 2.27) adequately quantify the photosynthetic response of the canopy to light, and that detailed modeling of leaf photosysthesis  by incorporating the photorespiration  effect precludes simple analytical solutions upon integration and results in crop models too cumbersome for general use. Seginer and Albright (1983) worked on an optimization method operation  that  reasonably  simple growth function, which  and  influence  temperature. They  canopy,  of  an  the  adopted  reintroducing  photosynthesis terms  can  the  climate.  incorporates  function  that  Soribe and Curry,  they  function  in  temperature  The procedure  the key factors  the model of Acock  temperature  term, and like exponential  greenhouse  for equipment  et al. (1978) is  attached  expressed  with  a  Q  dark 1 0  of  required  a  of P A R , COj for the  entire  to  gross  the  respiration in 2.0  for  leaf  temperatures between 10 and 35 ° C (Enoch and Hurd, 1977), thus R*  where  R  2 0  =  R2oQ[ o'- ' ° T  is the value of R  (- )  T ]/1  d  at 20 ° C  2  Charles-Edwards (1981)  expressed  28  this  variable as  Rio =  where R .  ~£l-exp(-AW]  (2-29)  is the dark respiration rate of an unshaded leaf at the top of the canopy.  60  Their proposed temperature  function, F, reflects the optimum temperature  relevant to  tomato growth in the greenhouse as different from that grown in the field, and is of a parabolic form F This  formula  =  1.25 - 0 . 0 0 7 ( T - 26)  ( - )  2  2  P  suggests  that  at  the  optimum  temperature  of  26  °C  for  3 0  gross  photosynthesis, F is at the maximum of 1.25, its value is 1.0 at 20 ° C and 32 ° C . They therefore  claimed that a deviation of 6 ° C from the optimum results in a loss  of production of 20%, which is typical of tomato plants at the vegetative stage (Went, 1945). Yet, they did not hesitate  to point out that if net photosynthesis follows a  parabolic trend, then gross photosynthesis should not be so, although  they  did not  suggest any modification. Almost concurrent with the Sacks (1978) presented  study made. by Acock et al. (1978), Enoch and  an empirical  carnation) in relation to light, C 0  model of C 0  2  exchange of a C  concentration and  2  leaf  plant (spray  3  temperature.  The model  stems from a customary equation for photosynthate balance P. In  order  to  -  P.-R.-R.  minimize  the  ('» J 3  number  of parameters,  the  authors  made  the  following  assumptions: 1.  Pg is a multiplicative function of PAR, C 0  2  and Tj , so that the variables are  allowed to modify each other 2.  Rj is related  to  depending on C 0 3.  Pg by 2  a  function  whose  value varies  between  0  and  1,  concentration and  R^ is the rate during the first hour of dark respiration, and is a function of Tp and P A R in a previous period. 120 combinations of PAR, C 0  45 to 450 W / m , C 0 J  measurements  of P  2  2  and T  n  200 to 3100 ppm and T  were tested, with P A R varying from p  were recorded. Besides, R .  10 to 35° C. For each combination, was measured  during a  one-hour  61  period of induced darkness when leaf temperature stabilized at 20° C. They fitted a linear logarithmic model to their data, which takes the following form: P  n  = exp(-C)PAR C 'r,f- (rrt + 4  s  rt\ ?AR')Q%- ° T  n  )/i0  (2.32)  The authors noted that the constants a', b\ c\ d\ m\ and n* may be experimentally determined for other C plants using similar methods. 3  62  NOTATION Dimension  A A  Area Leaf area Area normal to fluid flow  m m m  Constants used in eqn. 2.21 Biot number COj concentration Temperature-correction factor Hourly solar irradiance Extinction coefficient Length Leaf area index  -mg -W  nr  nr m m  nr  P  Leaf weight ratio Moisture flow rate Net photosynthetic rate  g g" kg smg n r W  n  -mg  nr  2  P  Hourly photosynthetically active irradiance Prandtl number Net photosynthetic rate  g  Gross photosynthetic rate  mg n r  2  P  'g  Gross photosynthesis  mg n r  2  P  Respiration ratio  -  \  A \ B' Bi C F I K L i LWR M L  n PAR Pr  Qio Q Qa  R  'd  SLA SLR o W X, Y TCF TTF U T  AT  ai,a a, c a'.b' c'.d' m\n' e f h 2  Heat flow rate Conduction heat gain of a soil layer  2 2 2  nr 2  1  2  2  1  1  nr  2  2  W W  Conduction heat loss of a soil layer  W  Dark respiration rate  mg n r  Dark respiration  mg m  Specific leaf area Solar load ratio Reference temperature for respiration  m  Dry matter weight Dimensionless variables used in eqn. 2.23 Total capture factor Total transmission factor Overall heat loss coefficient Temperature difference Constants used in eqn 2.12 Constants used in eqn 2.23 ) Constants used in eqn. 2.32 ) ) greenhouse air vapor pressure Monthly solar heating fraction Convective (surface) heat transfer coefficient  3  2  3  g  1  nr  2  nr  2  -° C mg  -W °C  -  kPa  -W  2  63  h  y  Convective (volumetric) heat transfer  coefficient  k m  Thermal conductivity Air flow rate  ^  Plant resistance to water vapor diffusion  t u  Time Ambient wind velocity W  x,y,z a e M v T T£ X  Cartesian coordinates Leaf light utilization efficiency Void ratio Absolute viscosity Density Solar radiation transmittance Effective transmissivity Volumetric thermal expansion coefficient Subscripts  a au b cd cn cv d e f g i ih k m o oh p r rs s t td v w X 0  inside air supplemental heat beam radiation condensation conduction convection diffuse radiation transpiration floor, fluid transferred to or from ground inside cover inside horizontal surface component surface accumulated quantity outside cover outside horizontal surface plant canopy rock rockbed storage solar gain thermal radiation transferred to storage ventilation and infiltration wind latent heat inclined surface  Superscript  saturated value  W m" K "  1  W m kg s" s m  1  3  1  K  1  s  1  1  s m s"  1  m kg n r kg m  °K  -  1  3  1  Chapter 3 C O M P U T E R M O D E L I N G A N D SIMULATIONS Computational simplicity is needed generation  of a simplified  in the  design procedure  simulation model intended  to allow an examination of the  for  the  thermal  performance of many system designs in a variety of climates, so that computing time can be minimized. On the other hand, care must be taken in constructing and making simplifications to the mathematical models that any essential processes  or mechanisms  are not precluded. Since  sufficient  experimental  data  are  readily available  for  model validation  purposes, the present study is focused upon the following two generic systems of the internal collection type. System I -  augmented internal collection with rockbed thermal storage  System II -  internal collection with wet soil thermal storage  The design and operation of these two systems have been described in Chapter 2, and each system with its key features has-been schematically shown in Fig. 2.1 and 2.2.  3.1 System I -  Augmented Internal Collection With Rrekbed Thermal Storage  3.1.1 Greenhouse thermal environment The principal components considered to play an important role in the analysis are: the inside air, the plant canopy, the cover, the absorber plate and the  concrete  floor (Fig.D3.1). During most of the growing period, the latter can be excluded from the  model since the  vegetation  cover shades the  floor.  At the  seedlings and  early  transplanting stages this assumption may lead to minor errors in predicting the inside temperature since the solar absorptivity and thermal erhissivity of concrete differ from those of plant materials.  64  65  Energy balances of the cover (inside and outside surfaces), the absorber plate, the plant canopy, the floor and the inside air yield the following equations:  (  m  c  )  c  ,  ' ^ r  Sci+  =  KiaA  ( m c ) „ ^ = S  CQ  +]  ~-(t^  ^  Ta  T  +  A  + h A {T - T ) + ( w  C0  0  < '° ~  +  co  {T  T c i )  — J A (Tti - T ) c  co  + QrCo*  (me), ^  S  =  q  +  (3.2)  2h A {T qa  q  U A {T  - T) +  a  q  q  q  0  - T) + Q  ( m c ) ? = 5 + 2(1 + i)/i ^ (^a - T ) + Q P  p  at  dT ^'Iti  =  5  /  +  h  f ^ aA  ( m c ) , ^ = h A {T  at  cia  +QaU  pa  /J  ci  -  ci  ~ ^  Ta  p  P  T  +  +  q  r p  +  (3-3)  + Q <,  rq  rq  (3.4)  Qrpi,  ^  (3.5)  - T ) + 2/i, A,(T, - T ) + 2/ 4 (r - T ) fl  Qtd  -  W  a  fl  p  Qv  p  a  , „ -  x  (3.6)  The mass balance on the inside air gives / i / \ dW  a  The convective heat transfer coefficient, h  , for air is included in eqns. (3.1)  a  and (3.2) for analyzing twin-walled covers that are separated by air. Basic assumptions of the model are: 1.  The system is vertically layered.  2.  A l l the  component  surfaces  are  homogeneous,  having  uniform  temperature  horizontally and vertically. 3.  Horizontal fluxes are neglected.  4.  The physical properties of the various layers do not vary during the simulation.  66 5.  The air flow in the greenhouse is uniform.  6.  Greenhouse crops are grown in hydroponics systems placed on concrete floor. Of the heat and moisture accumulation terms on the left-hand side of Eqns.  (3.1) to (3.7), those  for the cover, air, floor and plate are negligible compared to  existing fluxes, either due to small mass or small heat capacities. Heat capacity per unit volume of plant materials (4200 kJ/m K) as reported by Takakura et al. (1971) is 3  essentially that of water. When solar radiation is high, exceeding 600 W n r plant  canopy  comparison  to  level,  the  amount  diurnal energy  of energy  fluxes.  For  stored the  radiation and large change in leaf temperature  over an  situation  hour  at the  J  is insignificant in  of moderate  to  low solar  with time, this storage term cannot be  overlooked. However, this condition rarely occurs and hence, energy storage in leaves can  also  be  neglected.  Eqns. (3.1)  to  (3.7)  therefore  equations that may be solved to predict greenhouse  degenerate  into steady-state  environmental conditions on an  hourly basis. A similar approach was used by Kindelan (1980), Kimball (1981) and Avissar and Mahler (1982). Description of how the various heat fluxes in the model are evaluated follows. Solar radiation absorbed by the various surfaces are computed from global and diffuse  irradiances incident on an outside horizontal surface.  difference  between  transposed  to  the  radiation  two  quantities.  incident  upon  Diffuse an  and  inclined  beam plane  Beam irradiance is the components (the  were  greenhouse  each cover).  Transmitted solar irradiance is then calculated for each hour using the incidence angle at  mid-hour, by means of FresnePs relations and Bouguer's law of attenuation  account for reflectance and absorptance  that  respectively. The above computational formulae  are presented in detail by Iqbal (1983). The diffuse component is relatively independent of the sun's position and is assumed to be incident at a constant 60 degrees (Duffie and Beckman, 1980). The total primary solar energy input is the sum of beam and diffuse  radiations transmitted through the cover (roof, wall and gable ends), I.  67 and and  t  . The latter originates from 1^ which consists of sky diffuse irradiance  ground reflected irradiance, assumed perfectly  diffused. An anisotropic model  (Klucher, 1979 cited by Iqbal, 1983) was used to transform 1^ to I  ^ ; this model  d  approximates partly cloudy sky conditions, and may vary from clear skies on one extreme to entirely cloudy skies on the other. The admitted solar radiation has to be traced further to arrive at quantities of solar energy incident on an inside horizontal surface (plant canopy or floor level) or absorber plate surface. Two separate factors are determined for this end, one being called the 'interception factor (P^ )' for beam radiation and the other is the well known 'configuration factor (F^ necessary transmitted  because the direct  )'  for diffuse radiation. The interception factor is  dimensions of  sunrays  that  is  the  greenhouse  captured  inside  dictate  the  the  percentage  greenhouse,  of  whereas the  configuration factor accounts for diffuse radiation that does not reach the surface in question. Based on the method outlined by Smith and Kingham (1971), Pj^ was formulated for each of the inside horizontal surface and the absorber plate surface; it is a function of the solar altitude, the solar azimuth, as well as the cover surface azimuth and slope, and the greenhouse dimensions. The expression for F^. between two rectangles having a common edge and forming an arbitrary angle was first derived by Hamilton and Morgan (1952) and later corrected numerically by Feingold (1965). Fy varies with the greenhouse dimensions and the relevant cover surface area involved in the radiation interchange. The equations associated with P^ and  are derived or  otherwise reproduced in appendix A. Absorbed solar radiations by the plant canopy Sp , and the absorber plate S are surnrnarized in the following two expressions:  S = <*p £ P  *k [{nhePkp + r I F ) d  d0  kp  S, = a, £ *k [{nhpPkq + r I F ) d  d0  kq  + p F„{r hpPk q  h  q  + f> F (nh P P  M  fi  kp  + ul^F^)]  (3.8)  + r I F )}  (3.9)  d  dp  kp  68 where k denotes each cover surface. Two assumptions were made: 1.  only one internal reflection is considered, as subsequent  multiple reflections are  much weakened because of low albedo values of the various participating surfaces 2.  a surface reflects radiation diffusely The evaluation of internal convective heat transfer  coefficients follows Seginer  and Livre's (1978) rational approach, which considers the combined effects of free and forced convection Thus h  = i.43|r -r |  h  =  qa  cla  h?  The  a  7  a  +5  I/3  .2(^y/:  1.52|T ,-r | / + 5 . 2 ( ^ ) c  = 1.90  T -T p  a  1  3  1/4  /  between  .10)  (3.H)  1 / 2  1/2  a  +  3  - 'f)  (3-12)  2  dimensions of the cover (or the absorber  difference  X  (3  plate)  and the larger  inside air and the cover (or absorber  enough Grashof number that in turn causes  plate)  leads  temperature to a large  turbulent free convection between these  elements. On the other hand, the much smaller dimension of the leaf and a less pronounced temperature difference between the air and plant canopy would likely result in  laminar  free  convection near  the plant  canopy. Thus, the forms  of the  free  convection coefficients differ slightly in equations 3.10 to 3.12. The external convective heat transfer coefficient h  w  is evaluated using eqn 2.13 when wind speed is between  4 and 20 m s" . Below the lower limit, h 1  is obtained from eqn. 2.14.  W  Thermal (long-wave) radiation exchange among the various component  surfaces  (assumed gray diffuse) is calculated by the two relationships (Siegel and Howell, 1965)  69  for isothermal surfaces that form an enclosure:  Qrk  =  A -^(oe\-J )  (3.13)  Qrk  =  A (j -t.F J,)  (3.14)  k  k  k  k  ki  The sign convention is such that a negative value of  represents heat gain by the  surface k. Eqns. (3.13) and (3.14) are written for the enclosure formed by the absorber plate, the plant canopy and the cover. In addition, thermal radiation exchange between each surface and the sky is treated as a two-body system, thus  (3.15)  where T J  is the long wavelength transmittance of the cover. Typical values are 0.04  for glass and 0.80 for polyethylene, whereas acrylic material transmits virtually no thermal radiation. This expression excludes the sky emissivity since the surface area A^ small compared to the sky dome's thus A^ /A — >  is negligibly temperature, 6.  0. The sky  , then is related to outside air temperature (Swinbank, 1963) by flw, =  1.5  0.05520,  (3.16)  Although it is certain that both the clouds and the ground will tend to increase the effective sky temperature over that for a clear sky, it makes little difference upon evaluating collector long-term performance when their influence is not reflected in Eqn. (3.16) (Duffle and Beckman, 1980).  The terms that are common in both the heat and mass transfer processes include M  g  , the rate of the inside air moisture loss by condensation on the cover,  , the rate of transpiration and M  ventilation and infiltration  y  , the rate of moisture transfer due to  70  The  expression for M . is cd  h«a  M  cd  '  s  g i v e n  a  z e r o  v a  *  u e  w  Le /c 067  a  ^  e  n  i l  ^  (3.17)  n e  8 ' v e . Humidity ratio, W, is evaluated using a t  psychrometric equations obtained by Wilhelm (1976) through curve fitting to data points on  the psychrometric chart (appendix B). Implicit calculations are necessary here since  it is a function of inside temperatures and relative humidity that are to be solved at the same time. Heat of condensation is then calculated asX M  y  M . . cd is also expressed in terms of humidity ratio as follows: M,  =  (v V)*N{W  - Wg/3600  a  (3.18)  where N is the number of air changes per hour. When no ventilation is required, N assumes the values pertinent to infiltration, typical values are 0.75 to 1.50 for newly constructed  glass  structure,  and  1 to  2  for  well-maintained old glass  construction  (ASHRAE, 1981). The corresponding rate of sensible heat loss can be determined as Qv  =  [y,cV)  a  N {T - r ) / 3 6 0 0 a  (3.19)  o  (3.20)  when the humidity ratio of the leaf (assumed inside air. But when the reverse condition W  &  at saturation) is greater than that of >  W  p  is encountered, transpiration will  be assigned a zero value, and condensation on the canopy is neglected.  71 3.1.2 Rockbed thermal storage Rock size (25-38 mm) and air flow rate (0.11 m3 s 1 area) used  in the solar  shed  experiments  were within  per m3 cross-sectional  the range  of experimental  conditions investigated by Lof and Hawley (1948) and hence their empirical expression (eqn. 2.18) for h y , the volumetric heat transfer coefficient is valid for this study. Moreover, with a cross- sectional area of 4.57 x 0.91 m, NTU was calculated to be c 56  for  each  storage  chamber.  Thus,  the  necessary  condition  for  using  the  one-dimensional heat flow equation for packed beds (eqn. 2.19) is met Another point that  has  to  be  addressed  before  applying  this  equation  to  analyze  storage  of  greenhouse excess solar heat concerns the assumption of no occurence of mass transfer and thus release of latent heat possessed by the moist inlet air. Condensed vapor in the storage was in fact drained into a sump so that the rockbed thermal properties are not significantly altered by the presence of water. The amount of condensate was not measured, thus the importance of the latent heat term as compared to the sensible heat cannot be assessed. During the charging operation, the release of latent heat would lead to more heat being stored, and improves the performance of the solar heating system The assumption of no mass transfer is therefore conservative and this simplified rockbed model is considered sufficient for the present investigation Using the finite difference method, the bed may be divided into a numer of segments along the flow direction, as shown in Fig. 3.1. The boundary and initial conditions are: T ,(x,t) = T  at i = 0  j£(j-,£) = 7„  at x = L ,  T  r B (x,0)  a  =T,  m  r  charging discharging (3-21)  Since airflow direction is reversed during the discharging operation, the first term on the right-hand-side of eqn. 2.19 is negated. Besides, when the rockbed is in neutral  airflow direction (charging)  N  m  m  ta = L /N rs  I  Fig. 3.1  -  Rocked thermal storage divided into N segments  airflow direction (discharging)  73 mode, this term will be omitted in the calculations. The rockbed is assumed to be well insulated such that heat transfer through the greenhouse floor is negligible.  3.2 System II -  Internal Collection With Soil Thermal Storage  3.2.1 Greenhouse thermal environment The heat and mass balances that constitute the greenhouse thermal environment model are similar to those of the solar shed, except for the absence of a vertical absorber plate that will modify the conventional greenhouse are therefore  climate. Eqns. 3.1 to 3.7  applicable to this system, with the exception of eqn. 3.3 and excluding  terms that are related to the absorber plate.  3.2.2 Soil thermal storage The subsurface  choice pipe  of  an  system  appropriate  depends  on  model its  for  the  soil  cost-effectiveness.  thermal  storage  with  Three-dimensional  a  (3-D)  computer models should give the most accurate results, however, they need much more computing time than  either  the  two-dimensional (2-D) or axisymmetric formulations  that require more assumptions. Since many simulation runs are anticipated for model validation and subsequently the prediction of long term system performance,  the  3-D  method was ruled out Unfortunately, the more powerful axisymmetric formulation about a single pipe does not appear to suit the existing network of buried pipes, a 2 - D scheme was therefore considered most applicable for the present work. Further savings in  computational  cost  can be  achieved  by neglecting moisture  fluxes. The possible  problem of soil becoming dried around the pipe is ameliorated by the excess irrigation water that seeps through the porous concrete floor to keep the soil moist The use of the 2 - D model is also justified by observed soil temperature data along the pipes. Thermistors located in the longitudinal direction measured temperature difference in the  74 order of 2 to 4°C, indicating that the thermal gradient and therefore heat transfer was quite small in this direction compared to the lateral (x) and vertical (y) directions. With the above assumptions, the governing equation of transient heat transfer in the wet soil thermal storage is the Fourier equation for systems that have no heat generation  C, = (0.315 + 0.) x 4.18 k,  a,6, + b  =  t  The thermal conductivity is assumed to be independent of the x and y coordinates for a homogeneous soil, and its relation with moisture content is approximated by a linear expression The modeled region of the storage is shown in Fig. 3.2 along with all the boundary conditions. The temperature gradient vanishes ( 3T/3x axis of symmetry (centerline of the greenhouse, x=d  2  = 0)  across the  + w/2), since the greenhouse  with its components is modeled as a one-dimensional entity, and is assumed to be so at the insulation edge. Other boundary conditions are  dy  = 0  at y = di + si +}d f \  J±=0 dx  d  r,  - kf— = ~k.-—^ = U (T - T,) 1  ox  ay  -  dT  p  = «..(r  a  a  - T.)  2  at i = 0,y >2di + 5i at x = d ,y <2di + si 2  at pipe/soil interface  at y = 0 , i > d  t  (3.23)  The diurnal damping depth, d , for the clay soil with 30% moisture content was 2  calculated to be 0.124 m, and perturbation was considered insignificant at a depth of three times d . 2  75  Fig. 3.2  Soil thermal storage - modeled region w: dj: d: Si: Sj2  greenhouse width = 10.8 m depth of upper row pipes = 0.35 m damping depth of wet clay soil » 0.12 m vertical spacing between upper and lower rows = 0.20 m horizontal spacing between two neighbouring pipes = 0.65 m  Ax = Ay • finite difference scheme grid size = D/2 D: pipe diameter = 0.10 m  76  The convective heat transfer coefficient for pipe air, h Dittos-Boelter  empirical equation  for  turbulent  flow  in  smooth  Raghaven, 1984). Preliminary calculations also showed that h to  experimental  values  obtained  by  Eckhoff  circumstances. Incorporating the thermal resistance  and  , was evaluated by the  p  p  pipes  (Sibley  and  so calculated was close  Okos  (1980)  under  similar  of the P V C pipe wall, the overall  heat transfer coefficient between pipe air and soil/pipe interface may be expressed as  (3.25)  whereas  the  overall heat transfer  coefficient between greenhouse  air and soil  surface  underneath the porous concrete floor (y = 0) is calculated from  (3.24)  This expression for U transferred  from  p  along with the related boundary condition calculates the heat  greenhouse  air to  the  soil,  thus bypassing the  use  of the  floor  temperature. Psychrometric equations  were applied to determine  i f condensation  would  place inside the pipe which would cause an increase in the convective heat coefficient h  P  latent  transfer  . A n augmented value of h_ can be calculated based on the latent heat P  removed from the condensate, and  take  heat  transfers.  assuming that the area is the same for both sensible  Again,  the  latent  heat  is  calculated  from  the  Lewis  relationship (3.26)  Qx a  '  77  3.3 The Simulation Method Computer  simulations were  models presented  earlier for the  simulations were either measured  performed  aiming  at  validating the  mathematical  two systems. Values of the constants used in the or approximated from  literature, and are listed in  Table 3.1. Actual hourly data collected by Staley et al. (1984) include: global and diffuse solar  radiation on an outside  horizontal surface,  solar radiation transmitted  through  various greenhouse surfaces, solar radiation striking the absorber plate, photosynthetically active radiation (PAR) at the gutter height level, inside air dry bulb temperature various positions) and relative humidity, outdoor dry bulb temperature, discharging air flow  absorber plate  temperature  (at  temperatures  and soil temperatures (at a number of locations), storage inlet and outlet  temperatures,  various heights), charging and  (at  supplemental energy consumption and soil temperature  bed. These measurements  rates, rock bed  outside the rock  were taken regularly and. recorded on the control computer.  In addition, plant canopy temperature and greenhouse cover temperature were measured separately  on  a  few  occasions between  February  and  May 1984. The  instruments  employed  for data acquisition are listed in appendix D, along with the location of  relevant sensors. Data for wind speed and outside relative humidity were obtained from the  weather  records maintained by the  Victoria  International Airport, located 2 km  from the greenhouse research station. Preliminary computer runs used these actual data to calibrate the greenhouse model and the thermal storage model separately, while the two models are subsequently combined during validation runs. In the  greenhouse  model, the most difficult  variable to be evaluated is the  ventilation rate N (number of air changes per hour) due to natural ventilation, which is  a  function  of  wind  speed,  vent  location  and  size  of  vent " opening. Another  parameter that was not precisely measured is the Bowen ratio 0 , which was allowed to assume values between 1.0 and 2.5 for an actively growing crop, and between 2.5  78  T a b l e 3.1  V a l u e s of p a r a m e t e r s u s e d i n v a l i d a t i n g t h e model f o r s y s t e m s I and I I  Greenhouse  Area  orientarion roof t i l t eave h e i g h t  E-W 26.6 2.6 m  length  18.3  19.3  plant  height  volume  area bed mass rock bulk void  wall  m m  2 2  I: 131 m II 232 m I: 47 tn I I : 100 m 54 m I: 85 m II  2  2  2  g a b l e ends absorber p l a t e insulation  (per chamber.)  normal to length flow rate diameter density ratio  radiation  reflectivity absorptivity transmissivity  flow  Soil  4.16 m 4.57 m 0.56 kg s" 25-38 mm 1760 kg nf 0.37  2  2  1  plant  880 J kg" 0.93 W m" 0.60 W m"  1  1  2  absorber plate  0.15 0.75 0.10  0.05 0.90 0.05  0.95  0.90  96 m 106 m  3  K" K" K"  1  1 1  2  2  storage  pipe  2  Thermal r a d i a t i o n emi s s i v i t y  105 140  3  s p e c i f i c heat thermal conductivuty heat l o s s c o e f f i c i e n t  Solar  I: II  2  3  Rockbed storage  canopy  cover roof  m m  6.4 m 10.8 m 5.8 m 5.3 m 490 m 820 m  width ridge  simulation  wall thickness thermal c o n d u c t i v i t y diameter length number of l a y e r s spacing depths t o t a l mass f l o w r a t e soi 1 thermal c o n d u c t i v i t y thermal capacity moisture content  2.5 mm 0.145 W m" K" 0.1 m 18 m 2 0..63 m 0. 4 and 0.^6 m 1 ,78 kg s" 1  W nf 1C-l 1 ,40 . 2. .57 MJ nf K" 30% 1  3  Cover number of l a y e r s r e f r a c t i o n index thickness extinction coefficient  1  .526 mm . 1 0 m'  1  79 and 4.0 for relatively sparse plants. A checking guideline for N is the values measured by  Whittle  and  Lawrence  (1960),  which  are  shown  in  Table  3.2.  The  program  algorithm was directed to keep checking how much ventilation was needed during each hour to attain the measured put N and 0 the  absorber  measured the  inside air temperature and relative humidity level, which  into iterations. During calibration, measured plate  and  plant  canopy  were  used  in  solar radiation incident on  eqns.  (3.3)  storage inlet and outlet temperatures were substituted  and  (3.4),  into eqn. (3.6) during  hour when charging took place for calculating the rate of heat transfer  storage. The measured (3.1) were  while  to  the  external climatic conditions were precribed at each hour. Eqns.  (3.7) along with all other expressions for the evaluation of various heat fluxes  simultaneously  solved iteratively by  the  modified  secant method  as  a  set  of  nonlinear algebraic equations. The solving package, NDINVT, is also documented by the U B C computing center (Moore, 1984). Predicted inside air temperature, relative humidity and absorber cover  plate temperature, and occasionally, plant canopy temperature as well as  temperature  will  be  compared  to  the  actual  data.  Besides,  simulated  solar  radiation inside the greenhouse will also be verified.  more  Values of N and 0  were modified within the allowable limits in order to get  accurate  greenhouse  continue  until  temperature  results the  and  of  difference relative  between  humidity  temperature predicted  falls  within  and  and  relative  measured  specified  humidity. values  tolerance  of  Iterations inside  intervals.  air For  temperature, a maximum difference of 10% (from an engineering point of view) was used as the criterion for good prediction accuracy. As relative humidity depends on air temperature, it would likely be less accurately predicted; the tolerance interval for R H was set at  15%. At a particular hour  when computed  and measured  values  cannot  converge, possibly due to factors involved in the greenhouse operation and not indicated in data collection, the model may be deemed unable to yield reasonably accurate results.  T A B L E 3 . 2 T H E E F F E C T O F WIND S P E E D A N D V E N T I L A T O R POSITION O N AIR E X C H A N G E I N T H E G R E E N H O U S E (from Whittle and Lawrence, 1960) Vent position Roof Shut Lee aide V* open Both sides full open Both sides full open Both sides full open Both sides full open Both sides full open  Sides  Wind speed, kmh  A i r exchange per hour  Shut Shut Shut Shut Shut Open Open  21.6 21.4 4.3 9.7 10.5 2.3 3J.  2.9 9.1 14. 20. 34. 41. 45.  81 In the rock bed model, measured hourly air inlet temperature was prescribed as the boundary condition at calibration stage. As for initial conditions, spline Fitting to the  measured  rockbed  temperatures  at  various  sections  was  performed  to  generate  continuous values for all rockbed segments. A U B C general purpose program, M O L 1 D (Nicol, 1987) was used for simulation, it provided a Runge-Kutta integration scheme to solve the differential equation. Rock bed temperatures and the temperature of the air passage outlet during storage charging and discharging are the outputs that are verified with measured data. For the soil model, soil temperature was assumed to be uniform throughout the storage when the cluster of thermistors placed at two strategic locations all recorded similar  temperatures.  Eqn. 3.22  together  discretized by an explicit finite difference  with  the  various  scheme;  boundary  conditions  details of all representative  was nodal  equations can be found in the computer program listing in appendix C. The explicit scheme is less costly than an implicit one, but the time step A t  has to be selected  in such a way that no solution stability criterion is jeopardized. A t Fourier number a A t / A x  2  depends on the  which in turn is a function of soil thermal properties (and  thus the type of soil and its moisture content) and pipe diameter. Computed hourly soil temperatures and pipe outlet air temperature are checked with actual data. The two models are then coupled together, whereby the thermal storage models are coded as subroutines in the computer program Another major subroutine computed the solar radiation striking the glass cover, the plant canopy and the absorber At  this stage of simulation, only those  environmental  conditions unaffected  plate.  by  the  presence of the greenhouse were read as inputs to the computer program. Examination of  experimental  temperature T j R  T  data  showed  was within 1-3  that  for  system  I,  the  rockbed  storage  ° C of the contemporary greenhouse  inlet  air  air temperature  , and for system II, the pipe inlet air temperature was lower than the  greenhouse  air temperature by 2 to 7 ° C . The attenuation of air temperature might be associated  82  with the pressure drop as air passes through pipe network. For an air flow rate of 0.74 m  the 3  vertical ducts  °C  decrease  in  During  the  _1  each  iteration  a Q n  is sufficient to cause a thermal  storage  subroutine was activated to compute the air outlet temperature and hence the  amount  of heat transferred  temperature.  entering  s , calculations show that at constant  density, the associated drop of 2.2 kPa in pressure from P 6.5  before  step,  the  to the storage.  3.4 Model Validation -  Results and Discussion  3.4.1 Solar radiation transmission and interception Before making any comparison between simulated and measured data, the latter were analyzed and transformed into two factors, the total transmission factor T T F (eqn. 2.10), and the effective transmissivity r  e PAR)/0.45  A  v  given by (3.27)  The constant 0.45 is the conversion factor between PAR and broadband solar radiation (Salisbury and Ross, 1978). Values of TTF deduced from measured solar radiation data inside and outside than  the greenhouse for the shed-type structure are consistently higher  those for the control (conventional gable house). The shed has a TTF ranging  from 2.16 in December to 1.03 in June, whereas the control house achieved a value declining from 1.66 in December to 0.93 in July. During the period Oct 83 to Sept 84, solar GJ/m  2  energy  input  into  the  compared to 4.22 G J / m  2  shed  with north  insulated  amounted  to  5.11  for the conventional house. On a per unit floor area  basis, the shed received 32% more radiation than Oct 83 to Mar 84, though  wall  the conventional gable house from  this margin is reduced to 18% for the months covering  Apr to Sept 84. Since the two houses have almost the same transparent cover surface to  floor area  ratio  (1.98  vs. 2.02),  the  shed-type  glasshouse  appears to  be  more  83  efficient  in  attributed  adrnitting  solar  radiation  than  the  conventional  shape.  This  may  be  to the shed's larger area (131 m ) of the south roof as the major cover J  surface compared to 110 m  J  for the control house. Simulations were then carried out  using one week's data from each month, and results of TTF are plotted in Fig. 3.3. The very good agreement between measured and predicted values may be credited to the  well  established  mathematical  relations  used  radiation through non-diffusing materials. Values of T  for G  calculating  transmitted  solar  derived from experimental data  are plotted in Fig. 3.3 along with the TTF values. Two trends that are not possessed by T T F can now be realized. The effective transmissivity of each greenhouse vary  more  than  25%  annually,  and  the  shed-type  glasshouse  has  an  does not effective  transmissivity insignificantly different from its conventional counterpart. These results are not particularly surprising considering the dimensions of the solar shed that limit the percentage of transmitted beam radiation to be intercepted at the plant canopy level. Simulations produced r  values that have a maximum difference  g  of 12% from  the  experimentally derived values, and these computed results are also plotted in Fig. 3.3. More  details about  the  inside solar radiation that forms the  basis of r  may  be  e  found in the next section  3.4.2 Greenhouse thermal environment and thermal storage A greenhouse  number  of  validation runs  environment -  have  been  carried  out  started  on  the  combined  thermal storage model for the growing period from January  to May 1984. In the solar shed, tomato plants were transplanted harvesting  using  April  16.  During  this  period,  the  on February 10 and  conventional  greenhouse  equipped with soil storage had some grape plants. Results for system I and system II are presented  in separate sections. Among a large number of observational data that  are available for model verification, three weeks with different climatic conditions and system performances were examined in detail for purpose of illustration  84  3.0  -t  Month Fig. 3.3  Total transmission factor and effective transmissivity - experimental and simulated results for the period Sept 1983 to Aug 1984  85 3.4.2.1 System I Case 1. Feb 18-24 This week recorded a sequence of medium to low hourly solar radiation (I  =  300 -  daily I Fig.  500 W nr ), which was mostly (81%) diffuse in nature. Average 2  was found to be 6.2 M J n r . Other climatic conditions are shown in 2  3.4, where diurnal outdoor  temperatures are seen to vary from - 1  to 10  ° C , and the first half of the week was very windy and gusts of up to 60 km tr  1  were not uncommon. Predicted values, based on eqns. (3.8) and (3.9), of hourly solar radiation  inside  the  represented  greenhouse by the  are  plotted  interval between  in  Fig. 3.5.  A  day  within  two ticks. Since the  number  the of  hours  with measurable  differ  in width. A l l the figures that illustrate model validation results  chapter  plate, surface  that the  daytime  in this  Conversion of P A R to global solar radiation radiation  magnitude  of I  was very close to I  , solar  radiation  incident on the  absorber  , solar radiation incident on an inside horizontal  at the plant canopy (gutter height)  Weekly total I  is  solar radiation varied from day to day, these intervals  bear this feature.  revealed  week  level, as demonstrated  in Fig. 3.6.  is 8421 M J and is 5% greater than the measured value of 8015  M J . As for Iq , simulated and actual data differ by 9%. Daytime  greenhouse  environmental  temperature  regimes  and  relative  humidity are presented in Figs. 3.7 and 3.8. The computed and measured of inside air temperature T  &  , and absorber  plate temperature T^ are in very  good agreement, with a maximum difference of 4.6 ° C for T T  . The means and standard  values  deviations of the  differences  fl  and 3.7 ° C for between  simulated  and actual greenhouse temperature data are found in Table 3.3. This table also contains statistical results for measured and predicted greenhouse relative humidity and thermal storage temperatures in this case (Feb 18-24) and two others to be  86  Date Fig. 3.5  System I -  photosynthetically  active radiation at plant canopy  level.  900-1  Legend 800-  predicted. Incident on Inside horlzontol surfaco measured, Incident on Inside horizontal surface measured, Incident on absorber plate  700  CN  E  predicted, tncldent on absorber plate  600  Date Fig. 3.6  System I -  solar radiation incident at plant canopy level and absorber plate, Feb 18-24  CO CO  Legend pradlctad, Inalda olr "  maoaurad, Inslda olr pradlctad, abaorbar plota  •  maaaurad. obao'bar plota pradlctad, ptont conopy  *  maaaurad. plant canopy pradlctad, covar  o  0  -f  1  1  1  1  1  1  maaaurad, covar  f  Date Fig. 3.7  System 1 -  temperatures of the greenhouse thermal environment, Feb 18-24  ^  Relative Humidity, %  06  Table 3.3  Means and standard d e v i a t i o n s of d i f f e r e n c e s between observed temperatures and r e l a t i v e h u m i d i t i e s on 3 occasions f o r 2 systems  Variable  System I  System  Case 1  2  predicted/  II  Case 3  1  2  3  T  q  ,°C  mean S.D.  2.1 3 . 8 2 . 3 1 . 3 2 . 8 1.6  T  a  ,°C  mean S.D.  2.0 1.0  1.6 1.0  1.6 0.9  1.8 1.2  1.5 1.0  1.6 1.3  RH , %  mean S.D.  3.8 3.8  4.7 2.2  3.7 2.6  3.5 2.3  5.3 3.7  4.8 3.0  T  mean S.D.  1.0 0.8  1 . 0 0 . 9 0.9 0.7  mean S.D.  -  -  1.0 0.7  1.3 1.1  a  T  rs  s  ,°C  ,°c  -  -  0.9 0.6  92 discussed  later.  During  the  hours  with  higher  solar  radiation,  plant  canopy  temperature T is greater than T by 3 to 5 ° C . Measured leaf temperatures p a are lower than those calculated, and a difference  of up to 6 ° C is obtained.  Near sunrise and sunset times when supplemental heating was supplied from the furnace, calculated T falls below T p a , T  q  and T  p  by 2 to 4 ° C . The highest values of T a  occurred on day 6 at 1200 hr (31.0, 48.7 and 33.8 ° C ) when I  rose to 495 W n r  2  to produce values of ( I  , I  q  Q  ) as (550, 582 W nr )- The 2  plant canopy receives slightly more solar radiation, but transpiration serves to cool it down substantially while the absorber plate stays at a high temperature. Relative humidity prediction has a larger error when compared to actual data. Discarding faulty constant-value readings (59.5 percent) on days 1 and 2, a maximum difference between  computed  of 10 percent and  measured  is obtained. The statistics of the  difference  values  3.3.  is  also  found  in  Table  prediction accuracy is directly linked to the moisture balance of the  The  greenhouse  as governed mainly by crop transpiration, which in turn, is a complex function of  interacting  greenhouse  environmental  conditions  -  light,  velocity and carbon dioxide level. The dominating factors) determine  the  extent  of  stomatal  activity.  represented  by the Bowen ratio 0 . Even  In  the  though 0  temperature,  among them  model,  air  would  transpiration  is  is allowed to vary within  reasonable bounds during the simulation runs, it is still not capable of detecting such events on a small time scale. A n indirect cause for the discrepancy between measured  and  predicted  values  is  related  to  the  accuracy  in greenhouse  air  temperature estimation. Assuming constant  moisture quantity and hence humidity  ratio W„ , the extent of A T = a a  T  T  a  -  a  values, depending on the magnitude  of T  values  function  of  relative  humidity  as  a  would lead to quite different R H ^ a itself. Table 3.4 gives some typical of  humidity  temperature as derived from the psychrometric chart  ratio  and  dry-bulb  The variation of R H with  Table 3.4  R e l a t i v e humidity bulb temperature W,  kg/kg  f u n c t i o n of humidity  T  db,  c  ratio  RH  0.010  20 25 30 35  68 50 37 28  0.015  20 25 30 35  100 75 56  0.020  20 25 30 35  100 100 75  and dry  94  db  cuminishes  as  W  becomes  smaller.  Therefore,  as  W  changes  with  the  moisture balance calculations, the degree of accuracy in predicting R H also varies. Considering  temperature  profiles  at  various positions  of the  rock  bed  storage as shown in Fig. 3.9, it is evident that the storage capacity was not fully  utilized as some one-quarter  of the storage had little rise in temperature  during the charging hours to reach its potential value. The low air flow rate of 0.56 kg s"  led to a high N T U and hence transfer to storage was only effective  1  for the anterior portion of the bed. Duncan et al. (1981) noted that long flow paths were inefficient for the typical time-temperature unless larger  air  flow  rates or  heat transfer  patterns of a  coefficients  could  be  greenhouse used. The  maximum storage entrance temperature was 33.5 ° C at 1200 hr on day 6 when solar irradiance was at its peak, and was 2.5 ° C higher than the greenhouse air temperature. giving rockbed  Energy stored was computed to be 1910 M J per storage chamber,  a total  of  3820  temperatures  M J . Agreement  is better  between  during the  the  predicted  charging process,  and  measured  whereas  predicted  temperatures are generally lower than measured values upon discharging. Although the  mean  temperature  value is  of  the  difference  only  1.0  °C  with  between a  predicted  standard  and  deviation  measured of  0.8  rockbed °C,  the  temperature of the bed anterior is less accurately predicted compared to either the middle or the posterior section. The means and standard deviations for each of these three sections are (1.5, 0.7), (1.0, 0.9) and (0.6, 0.6) ° C . The whole week had 48 cumulative nighttime hours during which time storage discharging took place and a total of 2960 M J was recovered. This represents 75% of that stored during daytime. The second half of the nights required supplemental heat when storage exit temperature was lower than or barely reached the nighttime setpoint temperature of 18 ° C .  greenhouse  Legend p r e d i c t e d , ot  1/4 d i s t a n c e  m e a s u r e d , a t 1/4  distance  p r e d i c t e d , o t 1/2 d i s t o n c e _  o  o ^ CD D  "o CD Q.  E r^ "O CD JD  O o  Date Fig. 3.9  System I -  Rockbed temperatures at three sections, Feb 18-24  m e a s u r e d , a t 1/2  distance  p r e d i c t e d , a t 3/4  distance  m e a s u r e d , a t 3/4  distance  96 The thermal stratification of the rockbed based on calculated values on day 3 is shown in Fig. 3.10. Discharging took place between 0000 and 0400 hours  while  the  charging process  occured  from  0800 to  1500 hours, beyond  which the discharging mode resumed. As time progressed, the temperature  front  passed through the bed and fluctuated in accordance with the operation modes. While the peak charging inlet temperature was 30.5 ° C at 1200 and 1300 hours, the subsequent two hours of charging had lower inlet temperatures 25.5 ° C , thus causing a drop in temperature  of 27.5 and  of the anterior rockbed segments.  However, effective charging still occured in other parts of the bed. On this day, there  was  considerable  heat  discharge  between  1600 and  2000 hours  as  the  greenhouse air temperature fell below 18 ° C in the evening. Auxiliary energy requirement  for the shed-type  greenhouse  was recorded  to be 3710 M J . On the other hand, the control house recorded a total heat supply of 60.5 M J n r \ which translated to 7080 M J for the solar shed were it operated  as a conventional glasshouse  without insulation. Hence, energy savings  for this week amounted to 3370 M J and is basically met by the stored solar heat. This value is 410 M J more than the calculated from the rockbed temperature temperature difference  energy recovered from  storage  as  history. Aside from the slight inside air  difference between the two houses, it seems at first glance that the could be attributed to the north wall insulation. While it is certain  that energy savings may be nullified without the insulation, the ( U A ) ^ value of the shed being 13.9 W ° C control house with (UA)^ = itself  likely  per m  2  floor  13.7 W ° C ~  1  area is higher than that for  the  n r . In other words, the shed by J  needs as much heating requirement  as a conventional  greenhouse.  Therefore, predicted energy savings for this week is 11% less than the actual data.  L6  98  By  fixing  the  inside air temperature at  and nighttime energy  requirement  18 ° C at night, total daytime  was computed to be 7650 M J , marking a  difference of 8% from the experimental value of 7080 M J .  Case 2. Mar 25-31 Fig.  3.11 depicts the  outside climatic conditions. Wind  speeds were  the  lowest among the three weeks under study. Global solar radiation averaged 14.4 MJ nr  per day, and beam radiation constitutes 70% of I  2  this week had abundant sunshine when I  . The second half of  attained values of up to 800 W n r o  for  three consecutive  inside  solar  r  days. These driving  radiation,  greenhouse  air  2  forces produced simulation results of  temperature  and  relative  humidity  and  rockbed temperature profiles which are separately illustrated in Figs. 3.12 to 3.16. Except for day 1 when solar radiation level was very low, greenhouse air temperature T exceeded well  &  was consistently above 30 ° C during daytime hours with I  that  temperature T  was  500 W n r . 2  above  T  , and  Correspondingly, the it  managed  to  absorber  acquire  a  plate value  as  high as  63  °C.  a  Predicted temperatures are in favorable agreement with measured  data, and  the  patterns of rises and falls are similar for all temperature terms involved in the greenhouse  energy balance. Some experimental data of T , and T  on day 7 when measurements were taken these are and T °C  p  were available  between 0900 and 1700 hours, and  also indicated in Fig. 3.13. The temperature differential between  T  p  varies from 2 to 8 ° C . While simulated leaf temperature approaches 40  on one  occasion, measurement  with  the  infrared  value of 33 ° C . As for glass cover temperature,  thermometer  indicated a  inside and outside surfaces did  not differ by more than 3 ° C , and agree reasonably well with computed values. The  trend  of predicted inside relative humidity appears to be  with the actual values. Relative humidity is kept below 80 percent  in line  because of  99  900.0-. I  E „« 600.0 H  « u c '-5 o 300.0H  k_ a o  0  0.0  0 35.0-  2  25.0-  E  15.0-  ©  Tern  a.  5.0-5.0-  i>?  100.0-1  >. "D  E  70.0-  ive  X  40.0-  0 ©  or  10.08O.O-1  1  1 _c  E  60.0-  ©  40.0-  Q. (/> "D C  20.0-  j* O  0.0-  1  1  1  1  1  1  1  Date Fig. 3.11  External climatic conditions during the week of Mar 25-31. 1984  Legend  9001  predicted, Inside PAR measured, Inside PAR measured, Incident on absorber plate  800-  predicted. Incident on absorber plate  700  Date Fig.  3.12  System I -  PAR at plant canopy level. Mar 25-31  70 -,  Legend pr*dlct«d, Intld* olr '  m « o t u r « d , Intld* air predicted, a b * o r b « r plat*  '  m * o t u r * d , o b i o ' b i r plat* pr*dlc**d. plant canopy m*asur*d, plant canopy pr*dlct*d, cov*r m * o t u r * d , cov*r  Date Fig. 3.13  System I -  temperatures of the greenhouse thermal environment. Mar 25-31  Relative Humidity, %  201  •N  CD  CD  >sj  CO  CD  o  o  o  o  o  o  o o  Legend predicted, ot 1/4 distonce measured, at 1/4 d i s t a n c e p r e d i c l e d , at 1/2 distonce_ measured, at 1/2 distance predicted, at 3/4 distance measured, at 3/4 distance  Fig. 3.15  Date System 1 -  Rockbed temperatures at three sections. Mar 25-31  40-i  Legend  1  2  3  4  5  6  7  V  t  +  t — 04 hr  A  t  X  t  O  t  16 hr  •  t  20 hr  8  =  00 hr  =  08 hr  =  12 hr  9  10  Rockbed Segment Fig. 3.16  System I  simulated results of spatial temperature distribution in the rockbed. M a r  25-31  (day  6)  2  105 ventilation, though it is chiefly for temperature control purpose. Examination of RH  a  values seems to suggest that the relatively high plant temperature on days  with high solar radiation level may be another factor for lower R H (below 70 percent) during those sunlit hours when stomates opened less to conserve water. On the whole, simulated rock temperatures are rather close to  measured  values, exhibiting a maximum difference of 4.5 ° C on day 5. Simulation started at 0000 hr of day 1 when temperatures of the rockbed ranged from 19.5 ° C at one end of the storage to 16.5 ° C on the other. On the solar  radiation  that  recorded  more  than  500  W  nr , 2  days with outside the  storage  inlet  temperature, T . , during daytime charging attained peak values ranging from 30 to 33.5  ° C . Higher values of  could not be realized due  to greenhouse  ventilation. In fact, the gross useful heat gain of the greenhouse acting as the solar collector was estimated  to be 6320 M J , based on convective heat  transfer  between the various surfaces  and air. Calculations show that about 60% of this  available energy is dissipated through conduction, infiltration and ventilation heat losses. Such high percentage of heat loss could be partly reduced by minimizing ventilation.  However,  in  this  week,  much  ventilation  was  required  to  avoid  excessively high air and leaf temperatures and to ensure an adequate supply of C 0 , since no C 0 2  2  enrichment was provided in these research greenhouses.  Computations using transient value of 2530 M J as energy during  57 hours  changes in rockbed temperatures returned  being stored, subsequently,  of discharging operation.  2000 M J is recovered  Energy consumption  week indicated that the control house used 47.9 M J n r  J  a  record  for  this  whereas the solar shed  required 31.9 M J n r . The energy savings of 1870 M J compared well with the 2  energy discharged from the storage.  Case 3. Apr 8-14  106 The  solar radiation of this week is characterized by the approximately  equal magnitudes of the beam and diffuse components, the latter making up 54% of I  . Other outside climatic conditions that prevailed during the period are  also shown in Fig. 3.17. Discussion of results will focus on Figs. 3.18 to 3.22 in sequence. Simulated  values of inside solar radiation fall  within  7% and  12% of  measured values in regard to that incident on the absorber plate and the plant canopy respectively. Like other cases presented earlier, when outside solar radiation level is at a  low level of less than  200 W n r , 2  temperatures  of the  various component  surfaces in the greenhouse environment model are close to each other. On days with strong sunshine, the maximum temperature differentials between plant canopy and air, and absorber plate and air range from 5 to 7 ° C and 13 to 22 ° C respectively. By comparison with the week of Mar 25-31 (Fig. 3.13), it is readily seen that even though I for  the  present  Q  is of. the same magnitude, both T  week. For instance, on Mar 29, (T  ,  p  and  are less  ) had maximum  values of (39 ° C , 58 ° Q , but on Apr 8, they were (35 ° C , 50 ° C ) as I peaked at 760 W n r  2  on each occasion, and both days recorded total I  =  4870 W n r . Sample outputs of model validation runs for these two days may 2  be found in Table 3.5. Iterations during the solving of the energy and moisture balance equations indicated that for convergence to take place, values of the leaf Bowen ratio ranged from 1.3 to 1.5 on Mar 29, whereas it varied between 1.0 and 2.2 on Apr 8. The lower 0 possibly influenced  due  to  a  denser  by the diffuse  value of 1.0 reflects higher transpiration rate,  canopy.  Furthermore,  system  and direct composition of the  behaviour  is  also  global solar radiation.  Whereas the diffuse radiation view factor between the cover (south roof) and the vertical absorber plate is only 0.26, the beam radiation interception factor is 0.34  107  Legend  900  pr«dlcUd, Intld* PAR measured, Insldo PAR m«asiir«d. Incldont on obsorbor plot* pr< dlcUd, Incident on absorber plot*  Date Fig. 3.18  System I -  P A R at plant canopy level, Apr  8-14  70  -i  Legend pfidieted, inttde olr •  measured, inside olr predicted, absorber plote  *  measured, absorber plot* predicted, plant conopy  •  measured, plant conopy predicted, cover  o measured, cover  Date Fig. 3.19  System 1 -  temperatures of the greenhouse thermal environment, Apr 8-14  Relative Humidity, %  on  Legend predicted, at 1/4 distonce *  measured, at 1/4 distance predicted, at 1/2 distonce  Date Fig.  3.21  System I - Rockbed temperatures at three sections, Apr 8-14  Zll  Table  3«5  Sample o u t p u t s o f model System  Hour 7 8 9 10 1 1 12 13 14 15 16 17 18  System Hour 7 8 9 10 1 1 12 13 14 15 16 17 18  I - Mar  29.  validation  runs  •  r  --21 . 5 30 34 35 33 31 31 29 23  o 0  o .0 .. 5 .5 .0 .0  •  20. 0 20 .7 20. 2 33 3 39. 4 38 . 3 37 .0 35. 1 33 .5 27 ,,2 19. 2 18. 4  I - Apr  •  20 22 21 29 33 32 32 31 29 27 22 19  .5 .0 ..0 0 5 .5 .0 .5 .5 .0 .5 0  8.  1984  •  •  15 . 1 17..0 19 .9 30 7 34 .6 32 .. 7 32 .6 35 .6 31 .8 25 .0 24 .5 21 . 4  19 0 20 5 19 .0 28 5 28 5 27 5 26 5 27 .5 27 5 24 . 5 25 0 23 .O  • p T  thermal  environment  1984  A* T  - greenhouse  Symbols a r e d e f i n e d  •  16 19 18 28 33 31 31 29 28 24 18 17  4 . B .5 9 . 3 .9 .2 5 .4 .6 . 3 8  TA,  18. 1 19. 5 19. 8 27 . 1 29. 5 27 . 5 27 . 6 29. 3 27 . 6 21 . 9 22. 2 20. 2  in  •  1  •  22 23 22 43 56 57 52 49 37 29 21 18  . 3 . 5 . 7 .0 .0 .5 .5 .0 . 7 .7 .5  T  8  •  20 . 5 21 ..7 28 . 7 41 . 5 48 .2 46 0 45..5 49..3 43 .0 29 .5 28 .2 23 . 5  %  •  22 . 1 23 . 3 24 ..0 49 .3 62 .9 60 .5 58..5 55.. 1 44 ..0 36 . 4 24 ..9 18 ..5  1  T  .  19.. 1 20..9 25 .0 49.. 1 52 ,,9 48 ..2 46 . 1 50..5 42 .5 28 .0 30..7 22 ,9  \  •  --15 .. 1 24 28 29 26 29 27 21 19  --  T  .4 , 7 .6 ,4 ,5 . 7 2 .0  C  ------------  the ' n o t a t i o n '  •  11 16 17 28 32 30 28 27 26 23 17 12  . 7 .8 .8  . 3 .0 .4 6 .8  .2 .3 .5 .6  •  17 .8 17 .4 19 ..3 26 .5 28..2 27 .. 1 26 6 28 .2 26 . 1 21 .2 21 .3 18 . 7  RH^  .  62 .0 66 .0 7 1 .0 70 .5 64 .0 62 .O 62 .0 62 .0 64 O 62 .0 64 .0 65 .O  RH*  70 73 77 72 62 62 64 62 64 68 71 73  67 67 80 72 67 64 66 65 65 63 70 69  .  .5 .5 .0 . 5 .0  .O  .0 .0  .O  .5 .0 .5  section,  A* R H , X.  c  .5 . 3 .2 .6 .6 . 3 .3 . 7 .6 .7 .0  1 8 1 .5 1 .5 2.3 2.6 2.4 2.4 2.3 2 . 3 2.0 1 .6 1. 1  O  RH*.  65 76 69 73 66 66 71 59 63 67 74 68  si .  . 3 .7 .7 . 1 . 1 .9 .6 .8 .7 .6 .3 .5  ,  J  T  1 .5 1 .5 1.7 2. 2 2 , .4 2 . 2 2 . 1 2 .3 2 . 1 1 .7 1 .8 1 .6  p.136-137  1 .7 1 .4 1 .5 1 .8 2. 0 2 .O 2. 0 1 .9 1 .8 1 .7 1 .5 1 .1  <J  O .8 1 .3 1.3 1 .6 1. 7 1 .6 1 .5 1 .5 1 .5 1 .5 1. 3 o.4  C'  1. 3 1 :3 1 .5 1 .8 1 .9 1 .8 1 .8 1 .9 1 .7 1 .6 1 .6 1 .5  1.3 1.3 1 .4 1 .5 1.5 1. 5 1 .5 1 .5 1 .5 1 .4 1 .4 1. 3  N. 7 5 5 8 9 12 10 9 10 12 5  r 1 1 1 1 1 1 1  i 1 1 1  6  1  N.  t  5 4 11 9 9 10 8 10 9 6 4 4  .3 .3 .3 . 3 .4 .5 .5 .5 . 5 .5 .4 .4  2 . 2 1 .6 1 O 1 .0 1. 1 1. 2 1. 2 1.3 1.3 1. 1 1 .0 1. 1  114  at noon at this time of the year. The shed-type beam radiation more effectively than  diffuse  greenhouse  therefore  captures  radiation during most of the day.*  Solar radiation on Mar 29 is predominantly direct in nature (78%), by contrast, it is 40% diffuse on Apr 8. Hence, the plate is heated to a higher temperature in the former case. As shown in Fig. 3.21, the posterior portion of the rockbed has more temperature variation in this week. On day 5, it attained a maximum value of 24 ° C during charging, a mere 2 ° C short of the storage inlet temperature.  It  may just be an incidence of erratic measured data since similar behaviour is not observed on the following day with even higher solar radiation and outdoor air temperature.  Spatial temperature distribution within the  rockbed is displayed in  Fig. 3.22 for day 3. Although solar radiation happened to reach a high value of 730 W n r ,  it was a typical  2  subjected  day  with  intermittent  sunshine.  The storage is  to charging for nine hours, but the inlet temperature stays relatively  constant (22.5 ±  1.5  0  C), resulting in little movement of the temperature - front  in the bed. The week of April 8-14 the  shed  and  the  was warmer and energy consumption of both  control house  were less than the  previous two cases.  The  difference in recorded supplemental heat (45.8 versus 28.6 M J n r ) implies total 2  energy  savings of 2020 M J . This value is 260 M J more  than  the  predicted  recovery of 1760 M J from the storage. 3.4.2.2 System II Case 1. Feb 18-24 Fig.  3.23  shows  the  solar  radiation  incident  on  an  inside horizontal  surface at the plant canopy level. Qimatological data for this week have been given previously in Fig. 3.4. Simulation results expressed in terms of temperature and relative humidity of the  greenhouse  thermal environment are illustrated in  900-1  Legend predicted. Incident on Inside horizontal surface measured, Incident on Inside horizontal surface  Date Fig. 3.23  System II -  solar radiation incident at plant canopy level, Feb  18-24  116  Figs. 3.24 and 3.25 together  with the measured points. Because of a relatively  sparse crop canopy, the leaf Bowen ratio 0  is found to lie between 2.5 and 3.5  when the iteratively computed hourly inside air temperature and relative humidity converged with respect to measured values. Due to less transpiration heat loss, plant temperature  is higher than air temperature  by as much as 15 ° C , and  radiative heat exchange between the plant canopy and glass surface could only lower Tp by 1 to 3 ° C . Gates and Benedict (1962) measured heat exchange for various broad-leaved deciduous trees under still air conditions in the laboratory. The surface temperature of Maple and Poplar leaves (characteristics dimension = 62 and 96 mm) was observed to be 9 and 15 ° C higher than air temperature when energy lost through transpiration represented  10 and 20% of total energy  absorbed by the plant Measured R H  experienced a narrow range of 62 to 68%, whereas R H  is seen to vary from 58 to 74%, suggesting that a fixed value of 0 could have been used for this week, but for consistency in the simulation, 0  was allowed to  possess different values when necessary. Simulated soil temperatures are presented in two forms. Fig. 3.26 depicts the measured temperatures along with the simulated values at three representative locations in the region near the centre of the storage. Location A coincides with the  immediate neighbourhood of the  upper  pipe (that is, soil/pipe interface),  location B is at a depth of 0.2 m between the soil surface and the upper pipe, and location C is midway between the  upper and the lower pipes. For this  week, the soil temperatures are seen to be bound within a narrow belt of 15 to 19  ° C , due  to  the  low-grade  heat  transferred  from  pipe  air  to  the  soil.  Temperature of air at the pipe inlet varied from 18 to 23 ° C , and is up to 7 ° C less than the daytime greenhouse air temperature. Calculated values have a mean  difference  of 0.9  °C  from  actual  data.  Again,  like  the  case  of  the  70-. Legend p r « d l c U d , l n » l d « olr «  60  m « a t u r * d , I n i l d * olr p r » d l c l « d , plonl conopy  •  m t a t u r t d . plant canopy p r « d l c l « d , eov  o  m a o t u r « d , oovar  50 O O  Q>  40 H  O  CD Q_  30 H  ,CD  20 H 10-f '  v  s  \  V  N  0  Date Fig. 3.24  System II - temperatures of the greenhouse thermal environment. Feb 18-24  Legend predicted, inside air X measured, inside air  -  80-  50-  40 -)  1  1  1  1  1  1  Date Fig. 3.25  System II - greenhouse relative humidity, Feb 18-24  r  24-i  Legend predicted, locotion A measured, location A p r e d i c t e d , l o c o t i o n B_ measured, location B predicted, location C measured, location C  Date Fig.  3.26  System II -  soil temperatures at three locations in the storage zone, Feb 18-24  120  rockbed thermal storage, the mean and standard deviation vary with the point of interest  Prediction accuracy  associated  with  the  largest  is  best  with  discrepancy.  location  B, whereas  location  shows  isotherms  Fig. 3.27  the  C  is that  represent the calculated soil temperatures in the entire region near the edge of the  storage.  SCATCN  The  (Mair,  contours  were  generated  by  1984). Heat loss to the  down to 14 ° C at  the  a  ambient  insulation boundary,  packaged soil  whereas  computer  drives the  program  temperature  a large portion of this  region is close to 17 ° C . Predicted pipe outlet air temperature is compared with the measured  data  in Fig. 3.28. When storage charging takes place in the day, a temperature drop of 7.5 ° C between the inlet and outlet air can be realized. At night measured greenhouse air temperature centers upon 17 ° C with a variation of 1.5 ° C , and is close to T ^  . On the whole, the prediction of T ^  during both charging  and discharging agrees reasonably well with observed values. The difference averaged  2.5  difference  ±  2  between the soil/pipe interface and pipe air temperatures ° C , which  is within  20% of the  air  temperature.  Less  is observed when pipe air temperature is higher. The magnitude of  this temperature differential indicates that heat exchange between soil and air is quite  efficient  The overall heat transfer  value of about 20 W m air  occurs,  its  J  computed  ° C value  coefficient was calculated to  have  a  most of the time. When condensation of moist increased  by  up  to  three  fold,  however,  no  significant effect on this temperature differential was found. Heat transferred from soil to air during 66 hours of discharging operation in this week amounts to a total of 1830 M J , and is 11% less than the actual. energy  savings  of  2060  greenhouse heating demand.  M J . Stored  solar  heat  provided  17% of  the  total  121  Fig. 3.27  System II (day  6,  isotherms of simulated soil temperatures, Feb 18-24 0900  hr)  Legend predicted pipe outlet air temperature measured pipe outlet air temperature measured greenhouse air temperature  Date Fig. 3.28  System II - pipe outlet air temperature, Feb 18-24  123 Case 2. Mar 25-31  For  the  greenhouse  thermal  environment,  values  of  measured and  computed inside solar radiation, air temperature and relative humidity are plotted in Figs. 3.29, 3.30 and 3.31. Predicted inside solar radiation is greater than the measured data on days when outside solar radiation are high and shows opposite trend on other days. The overall prediction differs 8% from the measured weekly quantity of 5540 MJ (weekly .1  = 8035 MJ).  On the days with high solar radiation, inside air temperature did not get past 30 °C, in contrast to the conditions inside the shed-type greenhouse in System I, which is 6 to 8 °C higher. This demonstrates the combined effect of absorber plate and plant cover on greenhouse temperature regime. In fact, a dense canopy by itself has already added thermal mass to the greenhouse and therefore convective heat exchange with inside air. In this aspect, Avezov et al. (1985) analyzed daily  variations in T  in a solar-heated greenhouse. With a  identical values of solar radiation input and outside temperature, T  was found  to be lower in the absence of plant cover than it is when plants are present, exhibiting a maximum difference of 8 °C in the early afternoon. Again, one can observe from Fig. 3.31 that the actual relative humidity again did not vary much -  between 60% and 72%, and is quite well predicted  by the model. Since less natural ventilation is required for climate control in this conventional greenhouse, air movement is reduced and subsequently, plant temperature rose well above air temperature. Soil temperatures have more variation in this week, as illustrated by the wider spreading of data points that appear in Fig. 3.32. Among the three sensor locations, location C has values that are least accurately predicted. Measured soil temperature here ranged from 14.0 to 20.8 °C and the corresponding predicted  70 Legend p r « d l c t « d , l n » l d « olr *  60  m « a « u r « d , Intldo air p r « d l c t » d , plant canopy  »  m « a t u r « d , plant canopy pr«dlct«d. covr  •  50-  m«otur«d, cov«r  O O <D  ^_  40-  D  E 20-i 10-  0-  Date Fig. 3.30  System II -  temperatures of the greenhouse thermal environment, Mar 25-31  Legend predicted, inside air X measured, inside air  l  1  1  1  1  1  Date Fig. 3.31  System II -  greenhouse relative humidity, Mar 25-31  24  -i  Legend predicted, locotion A °  measured, location A p r e d i c t e d , l o c a t i o n B_  XX A A  x  measured, location B predicted^ location C  AAA  xx  Date Fig. 3.32  System II -  soil temperatures at three locations in the storage zone. Mar 25-31  A  measured, location C  128 values  are  15.9  to  19.2  °C;  the  maximum  difference  is  2.2  °C  or  in  percentage, 15%. The maximum difference between measured and computed results is  2.1  °C  (11%)  for  location  A  and  1.8  °C  (8%)  for  location  B. The  discrepancy can be partly explained by the unequal inlet air temperature in the pipes. Measurements indicated that air in an upper pipe had consistently higher temperature than  that in a lower pipe by 0.5 to 2.0 ° C . In the simulation,  however, all pipes are assumed to have uniform air temperature at the entry. Predicted and measured pipe outlet air temperature is plotted in Fig. 3.33. The maximum difference  in T  and T  p Q  is 2.7 ° C for nighttime discharging  p Q  mode, and 2.1 ° C with daytime charging operatioa The outlet air temperature is calculated as a function of enthalpy change between inlet and outlet air due to ,  the  heat  two-dimensional  exchange model  per  meter  assumes q  $  pipe  is the  longitudinal direction, whereas in practice, q length. Consequently, the  length same at  g  between any  air  and  soil.  cross section in  A the  should be different along the pipe  pipe outlet air temperature cannot be predicted very  accurately, though it is better predicted than the soil temperatures. Figs. 3.34 and 3.35 show the isotherms that represent two regions in the same cross section of the soil thermal storage. For the region near the  center  line, more uniform temperature distributions result in the symmetrical shapes of the contour lines, whereas thermal gradient is larger near the edge, as expected. The model is then checked on a macroscopic basis. Supplemental energy consumption data for this week indicated that 2490 M J was saved, or 26% of the 9580 M J consumed by the control house. Calculated heat transfer from soil to pipe air during 70 hours of discharging totalled 2180 M J , and is 12.5 % less than the actual energy savings. Computed quantity of heat being stored during daytime  amounts  appropriate  to  2570  M J , however, the  concept  of  'stored  heat'  is  not  for model validation as it is not as well defined as the rockbed  Legend predicted pipe outlet air temperature measured pipe outlet air temperature measured greenhouse air temperature  i  1  1  1  1  Date Fig. 3.33  System II -  pipe outlet air temperature, Mar  25-31  r  I  ~I 0.05 Fig. 3.35  1 0.22  1 Lateral  System II -  1  0.39  1  0.56  0.73  distance, m  isotherms of simulated soil temperatures  at the edge region. Mar 25-31 ( d a y * ,  n  9 °  n  hr)  I 0.9  Fig. 3.34  System II - isotherms of simulated soil temperatures at the center region. Mar 25-31  132 thermal storage that has a closed boundary.  Case 3. Apr 8-14  This week has medium solar radiation as compared to the other two weeks. Predicted and measured inside solar radiation agrees well and is within 9% of one another, as observed from Fig. 3.36. Fig. 3.37 demonstrates once again that plant temperature can be very close to air temperature when solar radiation is low. Predicted inside humidity is more accurate for this week, the measured values range from 59 to 73%, while prediction has a range of 55 to 75 %, as seen in Fig. 3.38. Figs. 3.39 and 3.40 present simulated results of soil temperatures. Soil temperature has gradually increased from about 18 °C in the beginning of the week to about 20 °C on the last day. This pattern follows the temperature of the soil outside the storage zone. Records show that measured T ^ was 3 to 4.5 so °C in the week of Feb 18-24, 6 to 6.5 °C during Mar 25-31 and 6 to 7 °C in the period Apr 8-14. Predicted soil temperature is most accurate for location B, followed by locations A  and then C.  The  difference  between calculated and measured  soil/pipe interface temperature is large on days 5 and 6 (more than 3 °C or 15% on a few occasions). In fact, the mean difference between simulated and observed data is 1.3 °C with a standard deviation of 1.1 °C. When considered on an individual basis, calculated means and S.D.'s are (1.3, 0.9), (0.5, 0.4) and (2.2, 1.1) °C respectively for the temperature nodes that correspond to the three thermistor locations. The pipe air temperature reached 29 °C during charging, and a small dry core region could have been formed around the pipe, leading to a reduction of the soil thermal conductivity and hence a steeper temperature gradient than that computed.  Legend predicted, Incident on Inside horizontal turfoco measured, Incident on Intld* horizontal turfao*  Date Fig. 3.36  System II -  solar radiation incident at plant canopy level, Apr 8-14  Legend pradlctad, Inalda olr »  moaaured, Inslda air pradlctad, plont canopy  »  maosurad, plant canopy pradlctad, cover  a  maoiurad, eovar  Date Fig. 3.37  System II -  temperatures of the greenhouse thermal environment, Apr 8-14  100  Legend predicted, inside air X measured, inside air  40  H Date Fig. 3.38  System II -  greenhouse relative humidity, Apr 8-14  136  LO O O  0.05  0.22  0.39 Lateral  Fig. 3.40  System II (day  6,  0.56  0.73  0.9  distance, m  isotherms of simulated soil temperatures, Apr 8-14 1400  hr)  24  n  Date Fig. 3.39  System II -  soil temperatures at three locations in the storage zone, Apr 8-14  Legend predicted pipe outlet air temperature measured pipe outlet air temperature measured greenhouse air temperature  1  r  Date Fig. 3.41  System II - pipe outlet air temperature, Apr 8-14  139  Isotherms reaches 21 ° C  are  plotted  in  Fig. 3.40. Soil  because of higher  higher pipe air temperature,  greenhouse  the lateral depth  temperature temperature.  near  the  Yet, even  of penetration  surface with  a  of temperature is  less than three pipe diameters. In other words, the lateral pipe spacing of 0.63 m  used in the  experiments is sufficient to avoid undesirable influence of one  pipe on the other in the same layer. On the other hand, thermal gradient is restricted  in the  vertical direction since the  pipes are  only 0.20 m apart A  larger vertical pipe spacing would be able to expand the  region available for  heat storage, but more insulation is required. Lastly, whereby  energy  savings  1910 M J of stored  due  to  the  soil  thermal  storage  is  calculated,  heat is recovered during 34 hours of discharging  operation. This value is 9.5 % higher than the actual savings of 1740 M J which in turn is equivalent to 19% of the total weekly heating demand of 9180 M J .  140  NOTATION Dimension  Area Thermal capacity of soil  1  3  K  I J  Hourly solar irradiance Radiosity Length Characteristic length of cover Lewis number Moisture flow rate Number of air changes Number of heat transfer units for rockbed thermal storage  L c Le M N NTU L  c PAR Q RH S T TTF U V W  W W m m  nr nr  2 1  kg sh-  1  1  Beam radiation interception factor between two surfaces Hourly photosynthetically active irradiance Heat flow rate Relative humidity Absorbed solar radiation Temperature Total transmission factor Overall heat loss coefficient Volume Humidity ratio  s ' s Constants in soil thermal conductivity c Specific heat d„ d Vertical separation distances h Convective (surface) heat transfer coefficient v Convective (volumetric) heat transfer coefficient Mass transfer coefficient D k Thermal conductivity Mass m Number of glazing covers c Heat transfer rate per unit length of pipe  W rrr W  2  W o  W nr K m kg kg" 2  l  3  1  b  h  J kg- K m W nr K" W nr K kg n r  2  h  s"  W nr kg  1  K  2  1  1  2  1  3  1  n  % Sj  t u x,y,z a I  e e_ V  1  Configuration factor between two surfaces  kj  a  m MJ nr  W nr  Lateral separation distance Time Air velocity inside greenhouse Cartesian coordinates Solar radiation absorptance Leaf Bowen ratio Thermal emittance Absolute temperature Volumetric moisture content of soil  m s m m  Latent heat of vaporization Density Thickness  J kg" kg n r m  s  1  % 1  3  1  1  141  p a T 9 A  Solar radiation reflectance Stefan-Boltzmann constant Transmittance Differential operator Difference  Subscripts  a au b ci cd co d e f g h i ih kj lw m o oh p q r rs s td v w \j> 0  inside air supplemental heat beam radiation inside cover condensation outside cover diffuse radiation transpiration floor glazing greenhouse inlet inside horizontal surface glazing surfaces long-wave radiation measured value outlet, outside outside horizontal surface pipe, plant canopy absorber plate radiative heat transfer rockbed storage soil transferred to storage ventilation and infiltration wind, pipe wall sky inclined surface  Superscript  saturated value predicted value  .  W  nr  2  °K  4  Chapter 4 SIMULATION FOR I£>NG-TERM P E R F O R M A N C E O F G R F F N H O I J S E SOLAR HEATING  SYSTEMS  System thermal performance is of primary concern to a designer who wants to find out what percentage of energy savings can be attained with each different design It is necessary to carry out simulations using long-term average climatic data as the driving force. The computer models validated in chapter 3 were used to predict solar heating  contributions  under  different  climatic  conditions  and  for  varying  design  parameters. The computer program was modified to make it general and flexible enough to handle  a variety of inputs. From  meet nighttime heating  the  requirements,  outputs of energy  it is possible to  recovered  find  out  from storage to  what  magnitude  of  design parameters in combination are required to bring about a desired level of solar contribution for different locations. The effects of design variations on crop canopy net photosynthetic  rate shall be  assessed  and  compared  by means of a' simple growth  function Based upon the availability of solar radiation and ambient temperature regimes, eight  Canadian  and  US  locations  were  selected  for  the  simulation  experiments:  Albuquerque, N M ; Edmonton, A L T A ; Guelph, O N T ; Montreal, PQ; Nashville, T N ; St John's, N F D ; Vancouver, B C and Winnipeg, M A N . Mean (monthly average) meteorological data include the following: daily (H) or hourly (I) global solar radiation incident on an outside horizontal surface, maximum and minimum outside air temperatures (T „ and T . ), outside relative humidity or max min v  dew point temperature, albedo  is  needed  to  wind speed, and soil temperatures at various depths. Ground compute  reflected  diffuse  radiation  from  the  greenhouse  surroundings, and mean values were cited by Iqbal (1983). Some weather stations also recorded diffuse or direct radiation in addition to global radiation, and these were used 142  143  as inputs so as to reduce the error incurred by estimating either with  empirical  (1983)  for  relations. These  many  weather  data  are  Canadian locations, whereas  form of radiation  published by Environment Canada  soil  temperatures  were  obtained  from  Ouellet et al. (1975). In the United States, hourly 'typical meteorological year (TMY)' data are recorded on a magnetic tape for 26 locations (National Climatic Center, 1983) so that minimal data processing is required before using them as inputs. However, soil temperature  monthly normals could not be obtained and values are assumed  in the  simulation studies. Design variations considered in this study pertain mainly to the greenhouse, the rockbed thermal storage and the soil thermal storage. 1.  Greenhouse a.  shape:  conventional gable  roof,  quonset,  shed-type  and  Brace-style (all  single-span)  2.  3.  b.  roof tilt: 18.4° (1:4), 26.7° (1:2) and 33.7° (1:1.5)  c.  glazing material: glass, polyethylene and twin-walled acrylic -  Rockbed thermal storage a.  storage capacity: 0.19, 0.24 and 0.38 m  b.  air flow rate: 6, 12 and 18 L s* n r A^. 1  3  n r Aj. 2  2  Soil thermal storage a.  pipe diameter: 0.10 and 0.15 m  b.  ratio of total pipe wall area to greenhouse floor area: 0.5, 1.0 and 1.5  c.  air flow rate: 6, 12 and 18 L s  d.  soil type: clay, sand  e.  soil moisture content: 20% - 40%  1  nr  2  Aj.  144 4.1 Modification tn thp Simulation Mpthori Certain algorithms had to be rearranged  for long-term simulations. Simulation  starts with a minimum ventilation rate of 1.0 air change per when  computed  inside  relative  humidity  temperature rises above 30 ° C after  exceeds  85%  or  if  hour, and is altered the  greenhouse  air  excess heat has been delivered to the thermal  storage. The value of net useful heat gain, that is, the excess solar energy available for storage, is computed based on the criterion that the solar fan is turned on when T  attains 22 ° C or above. Predicted plant canopy temperature  links the greenhouse  thermal environment model with the crop growth function. The  Bowen ratio is assumed  to have a 1-2-3-4 variation from  and  between  a 4-3-2-1  is the variable that  pattern  January  and  September to December  May, matching the  cropping practices. Hourly values of climatic data must be generated  usual  greenhouse  when only daily  values are available. Initial temperatures are needed in the thermal storage models. The rockbed  is assumed  initially  to  be  at  a  uniform temperature  of  15  °C,  whereas  undisturbed soil temperatures at various depths are used as initial values. The program simulates the hourly performance of the solar heating system over a typical design-day each month for the heating season which starts in September and ends in May, and its  performance  was assumed  to be  the  average  performance  of that  month. The  typical day has average climatological conditions. Carnegie et al. (1982) noted that the design-day analysis leads to quite optimistic results during the  colder months when  large weather fluctuations are more common.  4.1.1 Solar radiation The aim is to obtain I, and either 1^ or 1^ , depending on several cases.  Case 1. only hourly global radiation (I) is available  145  Hay's  method  as  summarized  by Iqbal  (1983)  may be  used  to compute  the  hourly diffuse component 1^ in the following manner:  (4J)  /' = /{l-p[p.(B/JVi)+Ml-0/^)l} h  =  /; +  l'  =  (0.9702 + 1.6688u - 21.303u  d  (/-/) 2  + 51.288u - 50.081K' + 17.551u )l' 3  u  =  5  /'//„  where N . is the modified daylength which excludes the fraction when the solar altitude is less than 5 ° A',7  p  and p 3  =  /cos 85° - sin 0sin 6 C \  1  — arccos 7.5 \  cos^coscS  4.2  /  c  (  '  are clear sky albedo and cloud albedo, and have values of 0.25 and  C  0.6 respectively. I and 1^ are the global and diffuse reflections between the  ground and the sky. p  radiations before multiple  is the monthly average ground  albedo measured for large geographic areas. Case 2. global and diffuse radiations (I and 1^ ) are both available  This  is  the  most  straight-forward  situation, and  no  solar  data  processing  is  necessary. Case 3. only daily global radiation (H) is available  A  few correlations have to be applied in sequence to achieve our aim in this  case.  For  locations  situated  between  40  °N  and  40  °S,  the  daily  diffuse  radiation can be calculated from Page's correlation (1979) H  d  =  //[1.00-1.13(/////„)J  (4.3)  146  whereas Iqbal's correlation may be used for Canadian  H  where  7/(0.791 - 0 . 6 3 5 ( 3 / ^ ) ]  is the average N  The  =  4  next  —  d  step  locations  (  4  4  )  daylength defined by  2 — a r c c o s ( - t a n r/>tan 6 ) 15  (4.5)  C  is to estimate hourly  diffuse  radiation  from  using  L i u and  Jordan's method (1967)  ~  d  Finally,  24  hourly  - w,(7r/180)cosu;J  [sinu,  d  global  radiation  can  be  (  calculated  by  the  expression  4  "  6  )  of  Collares- Pereira and Rabl (1979):  (4.7)  /  =  ^-H(a'+b'cosu;,)  a'  =  0.409 4 0.5016 s i n (a-, - 60°)  where  b' =  0.6609 - 0.4767 s i n ( w , - 60°)  Case 4. only the number o f bright sunshine  hours (m) is available  This  radiation  case  rather,  applied  sunshine  to locations  records  where  solar  is not routinely  are maintained. The correlation  measured,  due to Rietveld  (1978)  will be adopted H  Thence, the  above  =  H [0.18 ex  + 0.62(6/TV,)]  (4.8)  , 1^ and I are estimated as outlined i n case 3 above. cases,  hourly  beam  radiation  is calculated  simply  as the difference  147  between I and I  Case  5.  both  hourly  global  and  direct  normal  radiations  (I  and  I  )  are  available  This case refers to the US locations where I I,  is measured  by a pyrheliometer.  may be calculated in terms of the solar azimuth h  =  I  —  sin <p sin b + cos 0 cos 6 cos w,  where cos 6  Z  n  cos  0  (4.9)  t  c  C  Then 1^ is subtracted from I to get 1^ .  4.1.2 Temperature For Canadian stations, diurnal temperature patterns can be generated from daily maximum and minimum temperatures using the model of Parton and Logan (1981) that accounts  for  monthly variation in daylength  and  modified by  Kimball  and  Bellamy  (1986) to provide for a continuity in temperature between the end of the night and the beginning of the day.  daytime: -  T  where n  nun  N  d  "nun)  (4.10)  + 2a  , the hour of the lowest temperature is given by =  n„ + c  -  (^,n-<?) + [ r ,  nighttime: T  e t  -(7 , -e)]exp m  n  24 - N + c d  (4.11)  148  where T *and n  is the temperature at sunset computed from eqn. (4.10) with n  g e t  and n  g r  =  n^ ,  are sunrise and sunset hours. After midnight, 24 h is added to n  g s  for use in eqn. (4.11). Also, «  =  (7-.,, - T )/[exp(b)  - 1]  min  (4.12)  Values of a, b and c are 1.86 h, 2.20 and -0.17 h respectively. Kimball and Bellamy (1986) noted that some caution should be exercised when applying this model to desert areas. Their model is preferred Close (1967)  and  subsequently  over a simpler sinusoidal function first proposed by used  by various researchers in solar  heating  system  simulations, such as FJdighidy and Taha (1983).  4.1.3 Relative humidity The Therefore,  Canadian stations the  recorded  cubic-spline curve  outdoor  fitting  relative humidity  technique  may  be  four  employed  times to  a  day.  interpolate  hourly values. For this end, the program DSPLFT is used (Moore, 1981). In  the  case  of  US  psychrometric variables, T ^  locations,  and T^  relative  humidity  is  calculated  . The psychrometric equations  from  two  were similar to  those used earlier in chapter 3, and are listed in Appendix B.  4.2 Parametric Study Before the simulation results can be reduced to some simplified design tools, it is  useful  to carry out a parametric  study  to examine the effects  of a number of  design parameters on system thermal performance, and eventually eliminate those found to have minimal influence.  4.2.1 Greenhouse Variations  of  greenhouse  design  parameters  (construction)  are  confined  to  greenhouse shape, orientation, glazing material, roof tilt and length-to-width ratio. Table  149  4.1 gives the greenhouse dimensions, and associated view factors and overall heat loss coefficients. The majority of conventional glasshouses constructed for commercial use have a roof tilt of 1:2 or 1:1.5. The steeper slope is usually found in greenhouses that are narrower than 8 m (Mastalerz, 1979), while a slope less than 1:2 is not recommended for  snowfall  areas; also, condensate  on the inside cover surface  will have a higher  tendency to drip onto the plants below unless the glazing has been pre-treated  with  products such as the 'sun-clear solution' (Bredenbeck, 1984) that would permit filmwise condensation. Unsymmetrical  roof tilts are  characteristics of the  shed-type  and Brace-style  greenhouses. A l l three roof tilts (1:1.5, 1:2 and 1:3) were included in the parametric study for the  south  roof of the shed, while the north wall is at 9 0 ° . The roof  slopes were fixed at a constant 35° (south side)/65° (north side) configuration for the Brace-style house. Glazing transparent diffusion  materials are  materials are as  light  generally classified  homogeneous  passes  through  as transparent  with a planar surface  them.  Typical  or translucent.  Highly  and cause virtually  examples  are  glass  and  no  acrylic  (plexiglas). Translucent materials may diffuse the light up to 90%. Clear polyethylene, polycarbonate, polyester and P V C film are materials that diffuse light slightly, whereas fibreglas and striated glass are much more diffusing. To maximize solar energy input for  subsequent  storage,  fibreglass  structures  are  not  desirable.  In  this  study,  glass,  polyethylene and twin-walled acrylic are considered. The foremost requirement for computing the capture of solar radiation is the transmittance  of  the  cover  material  of  (absorption) coefficient K. Information of t handbooks. 1  1  However, values  known  refractive  index t  and  extinction  for most glazing materials is published in  of K for plastics are  not  immediately available. This  typical values may be found in User's practical selection handbook for optimum plastics, rubbers and adhesives.  T a b l e 4.1 shape/ cover CV/GS CV/DA SS/GS SS/DA BS/GS CV/GS CV/GS SS/GS SS/GS CV/GS CV/GS SS/GS SS/GS CV/GS CV/GS SS/GS SS/GS  G r e e n h o u s e d i m e n s i o n s and r e l a t e d A  f  l (m200 )  200 200 200 200 2O0 200 200 200 200 200 200 200 500 10O0 500 1000  L:W  2 2 2 2 2 4 8 4 8 2 2 2 2 2 2 2 2  Symbols found i n t h i s t a b l e explained tn the 'Notation'  *1 26 .6 26 .6 26 .6 26 .6 35..0 26. 6 26..6 26..6 26 .6 18 . 4 33.. 7 18 . 4 33., 7 26. 6 26. 6 26 .6 26. 6  ^2 26 .6 26 .6 90 .0 90 .0 65..0 26 .6 26..6 90..0 90 .0 18 .4 33 .7 90 .0 90..0 26 6 26..6 90..0 90..0  V I( H I  3  quantities Agz  )  650 650 900 900 930 575 525 755 650 565 735 735 1065 1990 4800 2980 7600  1 (m ) 370  370 355 355 315 380 410 335 335 345 395 325 390 810 1510 810 1545  A  NW  Cm 2 )  0 0 140 140 160 0 0 155 180 0 0 105 175 0 0 315 590  and a l l o t h e r t a b l e s o f c h a p t e r s e c t i o n o n p a g e s 235 t o 237-  4 are  12  F  0..86 0..86 0..67 0..67 0..66 0. 81 0. 82 0. 61 0. 62 0. 93 0. 79 0. 77 0. 58 0. 86 0. 86 o. 67 0. 67  13  UA  F  w/°c  0 .09 0 .09 0..25 0..25 0..24 0.. 16 o.. 16 0.. 34 0 35 0..05 0.. 15 0. 17 0. 32 0.,09 0. 09 0.. 25 0. 25  2430 1505 2475 1590 2280 2465 2660 2325 2335 2275 2600 2235 2740 5500 10595 5955 12015  151 problem  was resolved by determining  the  value of K using Fresnel's  relation and  Bouguer's law of attenuation as described in chapter 3, along with the measured values of  direct  transmittance  at  various  incident  angles  (Godbey  et  al.,  1979)  for  polyethylene; for acrylic, Russell (1985) suggested that the K-value is small. Using this method, K was estimated to be 400 n r  1  and 10 n r  1  for polyethylene and acrylic, of  thickness 0.1 mm and 16mm (two 2mm sheets with 12mm air space) respectively. Also, using the total and direct transmittance values, the diffusing power of polyethylene was estimated  to be 10% for an angle of incidence 6.  below 6 0 ° , and 15% when  i  0. i  exceeds 6 0 ° .  4.2.2 Rockbed thermal storage The rockbed storage capacity and the air flow rate are the two major design concerns. Values chosen for a particular system would govern the size of the bed and the fan to deliver the quantity of air. Table 4.2 shows the rockbed dimensions and information relevant to the heat transfer characteristics. The variables involved in these two design parameters are: Pr  : rock density ( M / V ) r  r  e : void ratio (void volume/total volume) L d  . W r  A  , h  r  : bed dimensions (length, width, depth)  : rock size (equivalent diameter) storage capacity  corresponds to 350 kJ n r  2  (SC °C  r  )  of 0.25  m  3  rock  per  m  J  collector area,  which  was used by Beckman et al. (1977) as the standard  size to develop the f-chart for solar air heating system Also, a base air flow rate of 10 L s  _1  nr  2  was adopted.  ^cont'd) 1976. The International Technical Information Institute, Tokyo, Japan Handbook of tables for applied engineering science. Ed. R . E Bolz and G . L . Ture. 1979. C R C Press, Inc., Florida, U S A  Table  4.2  Rockbed  thermal  storage  variables  Greenhouse A (m ) (m)  W (m)  Rockbed L (m) W „ (m)  SC.  200 200 200 200 200 200 200 200 200 200 200 200 200 500 1000  10.0 7. 1 5.0 10.O 10.0 10.0 10.0 10.0 10.0 10.0 10.0 7. 1 5.0 15.8 22 . 4  6.8 9.6 13.5 5. 1 3.4 6.8 6.8 6.8 6.8 6.8 6.8 9.6 13.5 10. 7 15.1  0. 38 0. 38 0. 38 0. 28 0. 19 O. 38 0. 28 O. 19 0. 38 O. 28 0. 19 0. 38 0. 38 0. 38 O. 38  f  S  20 .0 28 . 3 40 .0 20 .0 20 .0 20 o 20..0 20 .0 20..0 20 .0 20 .0 28.. 3 40. 0 31 .6 44 .7  5  8 .0 5 .7 4 .0 8 .0 8 .0 8 .0 8. 0 8 .0 8. 0 8 .0 8 .0 5. 7 4 .o 12! . 7 17 .9  kJ/m C  fn kg/s  L/s.m  800 800 800 600 400 800 600 400 800 600 400 800 800 800 800  4 .5 4 .5 4 .5 4 .5 4 .5 1 .5 1 .5 1 .5 3. 0 3 .O 3. 0 3. 0 3. 0 7 .5 15.0  18.7 18 . 7 18.7 18.7 18.7 6 . 25 6.25 6 . 25 12.5 12.5 12.5 12.5 12.5 12.5 12.5  1  r t  NTU W/m  1  3  71 91 1 16 54 36 99 75 50 81 61 40 103 131 11 1 142  C  3009 3835 4889 30O9 3009 1395 1395 1395 2266 2266 2266 2888 368 1 3122 3980  W/nf^C 15.8 20. 1 25 . 7 15.8 15.8 7.3 7.3 7.3 11.9 11.9 11.9 15.2 19.3 16.4 20.9  153 The air flow rate determines the pressure drop AP  in the packed bed for  given e , L and d values. Expressions for AP depend on the nature of the flow regimes. In the laminar regime, the Blake- Kozeny (Bird et al., 1960) equation gives  A P l  =  1 5 0  ^Ml-')  ;  (4.13)  For highly turbulent flow, the Burke- Plummer (Bird et aL, 1960) equation governs  iM&ihgz*  A*..  at  (4.14)  3  whereas for flow in the transition zone, the Ergun equation (Sissom and Pitts, 1972) may be used, which is simply AP3  =  A f i + APj  (4-15)  In the long-term simulations, the bed's depth was fixed at 1.0 m, and its width as 0.8 x house width. Other fixed quantities arep = 2400 kg m \e r  =  = 0.30 and d  25 to 38 mm. When SC is specified, the bed volume and therefore the bed r  length can be calculated. Air flow rate is selected to give a high enough NTU value so that eqn (2.19) is valid.  4.2.3 Soil thermal storage Again, the key design parameters are storage capacity and air flow rate. But unlike the rockbed storage which has a fixed size, the 'size' of the soil storage is represented by the layout of the pipe network. The following factors are involved: N : number of pipes P D: pipe diameter Sp : pipe spacing n^ : number of layers of pipe Lp : pipe length d  f  : depth of pipe  154 d. : depth of insulation material Table  4.3  lists  the  various  arrangements  together  with  characteristics. In the simulations, the fixed variables are n ^ = length, dj. = greenhouse  0.4 m and dj  floor area A  p  =  some  heat* transfer  2, L =  greenhouse  1.0 m. When the ratio of total pipe wall area to  / A j . and total air flow rate are specified, the number of  pipes and air flow rate in each pipe can be calculated. Furthermore, for a given pipe diameter, pipe spacing is also determined.  4.2.4 Results and discussion For long-term system thermal performance, the ultimate output from simulations is the annual solar heating fraction for the heating period from September Before the  simulation results are presented  in this section, it is necessary  to May. to define  several terms. Two concepts are requirements  involved  in defining the  percentage of greenhouse  heating  met by solar energy. Internal collection systems use the greenhouse  as a  passive solar collector, and admitted solar radiation could therefore counteract the whole or  part  of  its  daytime  heat  losses.  If this  solar  contribution is to  be  explicitly  recognized, then the term 'total solar contribution, s' may be defined as passive solar gain + solar heat recovered from storage daytime and nighttime heating load  s  —  Q  P  A  S  Q  S  T  QDL + QNL In  the  program, Q p § A  (4.16)  is set equal to Q  D  L  when the passive solar gain  exceeds  daytime gross heating load, so that the 'passive solar gain' term does not include the portion of useful heat gain that is stored. However,  if only  fuel  savings  is  concerned,  then  the  term  'solar  heating  Table  4.3  Soil  thermal  greenhouse f l o o r area: 200 m  ,  1  network r  1 ayout  I S  1. 5 1.0 0.5 1.5 1 .0 0.5 1.5 1 .0 0.5 1.5 1 .0 0.5  N  P  46 30 14 46 30 14 30 20 10 30 20 10  storage  length-to-width r a t i o :  = 20 .0 m)  D  S  0. 10  0 . 35 0 .61 1 .55 0 . 35 0 .61 1 .55 0 .53 o .90 2 .31 0 .53 0 .90 2 .31  0 . 10 0. 15 0. 15  variabl  P  m  NTU  kg/s  L/s.rtr*  4. 5  18.7  1 .5  6.2  4. .5  18.7  1 .5  6.2  2  Up  m  W/m C  kg/s  21.8 27.3 38 . 2 1 1 .0 14.6 23.8 16.4 20.8 30.5 7.8 10.4 16.8  0. 10 0. 15 0.32 0.03 0.05 0.11 0.15 0.23 0.45 0.05 0.08 0.15  1  1 .40 . 1 .. 14 0 . 75 2 . 12 1 .83 1 .35 1 .04 0 .88 0 .63 1..48 1..31 1,,04  p  156  fraction, f applies, and is defined as _  solar heat recovered from storage daytime net heating load -f nighttime heating load  _  QST  QDN + QNL  Daytime  net  heating  load  (4-17)  is the  auxiliary  heat  supplied to  the  greenhouse  when  passive solar gain cannot meet the total daytime heat losses induced by transmission and ventilation (including infiltration). The f value corresponds to the  energy savings  achieved against a control greenhouse in research experiments. The denominator of the above expression is also directly linked to the cost of greenhouse space heating borne by the grower. Results of the greenhouse  construction  detailed parametric parameters  will  study be  are  now presented.  discussed  first,  and  Effects followed  of  the  by  an  examination of the influence of thermal storage design parameters on long-term system performance. Typical simulation results will be tabulated where necessary and the values of the fixed parameters  used in each cluster of computer runs are also indicated in  the relevant tables. 4.2.4.1 Effect of greenhouse construction parameters The greenhouse greenhouse.  major  design  parameters  that  affect  the  useful  heat  gain  of a  being used as a solar collector are the shape and glazing of the As mentioned  earlier, embedded  in the  parameter  'shape'  is  the  energy collection or absorption method. The shape SS represents method I that features  a  shed-type  greenhouse  with  north  wall  insulation  and  a vertical  absorber plate with high short-wave absorptivity for augmenting heat collection. Method II is implied by the shape C V where a conventional greenhouse (gable roof or quonset type) is built without modification. The curved surface of the quonset house could be approximated by polygons, but the resulting profile would  157  complicate the  determination of view factors and interception factors. Thus, the  quonset shape is assumed to have straight sloping surfaces like the gable-roofed greenhouse.  BS refers  to  energy  greenhouse  having an insulated  collection method north  surface  U l whereby  and  lined  a Brace-style  inside with  a highly  reflective material is used for energy collection. Table 4.4 shows the simulation results for a glass greenhouse of different shapes  C V , SS  and  BS  and  located  at  greenhouse effective transmissivity. Values of r  Montreal. First,  we  consider  the  typically range from 0.65 to 0.75  g  for an east-west aligned greenhouse and a small difference in the magnitude of inside solar radiation exists between the SS and C V greenhouses, suggesting that modification  of the  greenhouse  shape alone cannot  bring about  an  appreciable  improvement in the effective transmissivity. At an early stage of this project, the total  transmission  comparing  factor  greenhouse  (TTF)  solar  input  as  proposed  efficiency  by  was  Ben-Abdallah calculated  for  (1983) some  for  North  American locations. Two representative plots for the shed-type glasshouse and the conventional glasshouse are shown in Figs. 4.1 and 4.2. It can be readily seen that TTF is well above 1.0 for the SS house in certain locations. The drastic difference in the magnitudes of TTF and r  g  of the same greenhouse points out  the phenomenon that even though the solar shed can admit substantially greater amount of solar radiationat the glazing level, the loss induced by the  greenhouse  geometry itself on both the direct and diffuse components eventually erodes this advantage  if  solar  radiation  at  argument has been substantiated location  of  Vancouver, and  the  the  plant  canopy  level  is  considered.  This  with experimental evidence in chapter 3 for the results  here  show  that  it  applies  to  other  locations. Besides, on an equal floor area basis, the glazing area of a SS house is close to that of a C V house, and has greater volume (Table 4.1  refers).  Therefore, were the absorber plate not installed in the solar shed, this modified  Table  4.4  Effect  of greenhouse  greenhouse  storage  shape on system  thermal  performance  - l o c a t i o n : M o n t r e a l , f l o o r a r e a : 200 nr , o r i e n t a t i o n : E-W, l e n g t h - t o - w i d t h r a t i o : 2, r o o f t i l t : 26.6 (SS a n d CV) - medium: r o c k b e d , c a p a c i t y : 0.38  /m?  , a i r flow  cover:  rate:  12.5 L/s.m^  May  Year  Sep  Oct  Nov  Dec  Jan  Feb  Mar  Apr  ss  0.78 0.79 0.88  o. 76 0. 78 0. 90  O. 74  0. 75 O. 87  o. 74 0. 77 0. 91  0. 77 0. 83 0. 93  O. 79  0. 81 0. 88  0. 78 0. 77 O. 80  O. 7  BS  0.77 0. 79 0.84  1 0. 73 0. 81  0.76 0. 78 0.85  [MJ]  CV SS BS  2031 2084 2216  1287 1304 1452  681 699 806  565 573 665  789 821 970  1329 1433 1605  1962 2012 2186  2512 2479 2576  2670 2745 2857  13826 14150 15333  0 ,[MJ]  CV SS BS  349 361 306  774 798 678  1440 1483 1259  1659 1709 1450  1863 1917 1627  2299 2366 2007  2205 2269 1925  1594 1642 1394  711 723 615  CV SS BS  609 629 535  1413 1458 1238  2351 2422 2056  3992 4112 3489  4599 4732 4015  3975 4092 3472  2679 2758 2340  1512 1557 1321  810 21940 823 22583 701 19167  CV SS BS  958 990 84 1  2187 2256 1916  3791 3905 3315  5651 5821 4939  6462 6649 5642  6274 6458 5479  4884 5027 4265  3106 3199 2715  1521 1546 1316  34834 35851 30428  0. 80 O .77 0 .94  1 .76 . 1.77 2 . 17  0.40 0.40 0.50  .60 0 .71 O .61  0 . 75 0 .92 0 .89  0. 33 0.40 0. 37  0 .30 0 .47 0 .32  0 .54 0 .86 0 .79  0.07 0.14 0.11  X  Hp  CV  e  D  U  L.  °rJI NL  0  T  L  [  M  J  ]  [MJ]  SLR  CV SS BS  2.11 2.09 2.63  0.59 0.58 0. 76  0 . 18 O . 18 0 . 24  O..  10 0 . 10 0 . 13  0.. 12 0 . 12 0 . 17  0 .21 O .22 0 .29  0. 40 O .40 0 .51  s  CV SS BS  0.91 0.96 0.93  0.50 0.62 0.56  0 . 22 0 .33 O . 22  0 . 13 0 . 18 o . 11  o . 15 0 .24 0 . 16  O  . 25 0 .35 0 . 27  0 . 39 0 .48 0 .42  f  CV SS BS  0.77 0.92 0.88  0.22 0.43 0.29  0 .00 0 .06 0 .03  0 .00 0 .00 0 .00  0 .00 0 .02 0 .02  0 .00 0 .05 0 .03  0 .05 0 . 15 0 .07  O  glass  12894 13268 1 1261  CO  159  / A  Albuquerquo  ' 'X  Lexington  •  Tucson  H  Edmonton  2  Winnipeg  X"  Voncouver  ^  MontreoJ  ©  Guolph  Month Fig. 4.1  Shed-type glasshouse -  total uansmission factor calculated using  average solar radiation data for eight geographic locations  160  o c  o 'to  'E c o CO  o .o  Legend A  Albuquerque  X  Lexington  •  Tuoeon  53  Edmonton  2  Winnipeg  X  Voncouver  ^ ©  Montreal Guelph  3 ^ ^^^w^^^w^w^  0.4 H  Month  Fig. 4.2  Conventional glasshouse -  total transmission factor calculated using  average solar radiation data  for eight geographic locations  161  structure would have claimed no advantage over a conventional greenhouse shape for the "sake of collection. With these solar heat gain and building heat loss values, the solar load ratio (SLR) defined as the quotient of Hp , the mean daily total solar radiation incident on an inside horizontal surface at the plant canopy  level  divided by  ,  the  mean  daily  gross heating  load  before  discounting passive solar gain was calculated for each greenhouse shape. Since the daytime setpoint temperature of the greenhouse is 22 ° C while it is 17 ° C at nighttime, during the warmer spring period in Montreal, daytime heating load is comparable to that at night,  . SLR has the highest value for the  BS greenhouse, while the CV and SS come very close to each other in terms of the solar load ratio. Over the heating season from September to May, the SS and CV houses admit 10% less solar radiation than the BS house, and at the same time, lose 14% more heat, since the latter has the least glazing-to-floor area ratio. To demonstrate  that the better solar admission of the Brace-style  greenhouse is credited primarily to the reflective aluminum foil mounted on the inside of the insulated north surface rather than the shape itself, a short-wave reflectivity of 0.05 (equal to that used for the vertical absorber plate of the SS house) was then used in the input in the simulation runs involving the BS house. It was noticed that T  became even less than that of the SS house.  e However, when the entire solar heating system is considered, the annual total solar contribution s favourable  for  the  y  and hence the solar heating fraction f  SS greenhouse,  followed  by  the  greenhouse collection method. As seen in Table 4.4, f and 0.07  BS and lastly  are more the CV  is 0.14 for SS and 0.11  for CV and BS houses respectively. Expectedly, the presence of the  absorber plate is beneficial  for solar heat gain and collection. The reflective  coating characteristics of the BS collection method permits greater luminosity, but is less effective in enhancing convective  heat exchange and thus solar energy  162  collection compared to the SS design. The merits of the SS collection system is more obvious if the  greenhouse  is located in Vancouver where the fraction of heating load supplied by solar is 0.32, which  is 39% more  than  the  BS method  and 60% more than the C V  greenhouse collection. The effect of cover (glazing) material on system thermal performance is next shown in Table 4.5 for a C V greenhouse  located in the Vancouver area.  Whereas the effective transmissivity of a polyethylene covered quonset house is close to that of a gable roof glasshouse, due in part to the assumption of a straight  edge for the  greenhouse  with  curved surface,  it is about  double acrylic cover. On the  cover retards the  10% less  other  rate of heat loss by about  hand,  for a gable roof the  double  acrylic  45% relative to either glass or  polyethylene. Hence, its solar load ratio is considerably higher; the annual solar heating  fraction turns out to be 0.31, compared to 0.20 for a glasshouse  0.17 for a polyethylene greenhouse November  to February, the  and  in the same location During the months of  C V collection method  is the  limiting  factor  even  when glass is replaced by double acrylic. However, the impact of twin-walled acrylic material is significant in early fall and spring time, when some marked increase in solar heating fraction is sufficient to boost the annual energy savings. Another  way  to  compare  the  thermal  performance  of  one collection  method with the other is via the collection efficiency rj which is defined as the percentage of inside solar radiation, Hp that is converted into useful heat gain, Q  u  . Some calculated values of TJ  based on simulated results of H  p  and  Q  u  can be found in Table 4.6 for the SS and C V collection systems with glass or double acrylic cover. Substituting double acrylic for glass would let a SS house improve its collection efficiency by 12% whereas a C V house will be 20% more efficient  Viewing from another  angle, if the  SS collection system is preferred  Table  4.5  Effect  of cover  m a t e r i a l on s y s t e m  thermal  greenhouse - l o c a t i o n : Vancouver, f l o o r s h a p e : CV, l e n g t h - t o - w i d t h storage cover  - medium:  performance  a r e a : 200 m^ , o r i e n t a t i o n : r a t i o : 2, r o o f t i l t : 26.6  c a p a c i t y : 0.38 m^/m^  rockbed,  , a i r flow  E-W,  rate:  12.5 L/s.m^  Sep  Oct  Nov  Dec  Jan  Feb  Mar  Apr  May  Year  0.76 0.74 0.69  0.76 0.74 0.69  0.71 0.71 0.65  0.71 0.72 0.66  0.71 0.71 0.65  0.76 0.75 0.70  0.79 0.77 0.72  0.77 0.75 0.69  0.78 0.75 0.71  0.75 0.75 0.69  [MJ]  GS PE DA  2009 1957 1830  1122 1092 1029  514 507 471  318 323 296  418 423 382  863 848 777  1585 1515 1444  2318 2221 2077  2936 2823 2743  12064 11976 11032  0 . [MJ]  GS PE DA  593 601 274  875 884 413  1008 1021 470  1163 1178 552  1260 1362 592  1401 1513 677  1491 1507 736  1349 1363 667  1074 1086 526  8075 8160 4907  0  [MJ]  GS PE DA  564 537 366  1087 1125 671  1743 1804 1051  2023 2094 1224  2215 2293 1324  1796 1859 1089  1407 1456 873  951 984 606  561 582 374  12463 12602 7578  [MJ]  GS PE DA  1157 1188 640  1962 2009 1084  2751 2825 1521  3187 3472 1776  3475 3655 1916  3197 3372 1766  2898 3013 1609  2300 2447 1273  1635 1668 900  22562 23299 12485  GS PE DA  1 74 1 65 2 86  0 57 0 54 0 95  0 19 0 18 0 31  0 10 0 09 0. 17  0 0  12 12 20  O 27 0 25 0 44  0 55 0 50 0 90  1 01 0 91 1 63  1 80 1 69 3 05  0 54 0 51 0 88  S  GS PE DA  0 88 0 83 1 00  0 54 0 50 0 76  0 28 0 24 0 24  0 0 0  18 17 12  0 20 0 19 0 17  0 34 0 30 0 39  0 52 0 50 0 67  0 71 0 62 0 89  0 92 0 86 1 00  0 44 0 40 0 51  f  GS PE DA  0 78 0 66 1 00  0 21 0 16 0 57  0 02 0 00 0 02  0 00 O 00 0 00  0 02 o 00 0 03  0 05 O 03 0 08  0 23 o 19 0 43  0 48 0 38 0 78  0 85 O .75 1 00  0 20 0 17 0 31  Hp  n  NI  0. L  SLR  o  cover:  glass  T a b l e 4.6  C o l l e c t i o n e f f i c i e n c y f o r s h e d - t y p e and c o n v e n t i o n a l with g l a s s or double a c r y l i c covers greenhouse  location  shape/cover  -  greenhouses  f l o o r a r e a : 200 , o r i e n t a t i o n : E-W l e n g t h - t o - w 1 d t h r a t i o : 2, r o o f t i l t : 26 6  Sep  Oct  Nov  Dec  Jan  Feb  Mar  Apr  May  Year  2116 1215  1180 883  522 289  336 146  418 237  888 429  1604 930  2318 1402  3020 1693  12402 7223  0. 58  1983 1 184  1107 941  492 328  314 225  394 319  844 490  1505 1072  2197 1496  2818 1644  1 1654 7729  0. 66  2009 804  1122 514  514 113  318 0  418 0  863 144  1585 485  2318 835  2936 1028  12064 3920  o . 33  1830 770  1029 547  471 149  296 0  382 174  777 202  1444 571  2077 896  2743 1014  1 1049 4324  0. 39  2208 1312  1474 979  754 149  664 O  976 156  1693 683  2161 1061  2510 1310  2956 1746  15396 7391  0 .48  Hp Q u H OP u  2068 1286  1399 941  714 270  620 201  915 321  1575 775  2000 11 17  2353 1366  2795 1724  14439 7656  0 . 53  2152 996  1455 681  734 0  655 0  940 0  1609 1 13  2161 464  2576 753  3077 1 149  15359 4106  H  1956 881  1343 725  675 174  601 48  868 92  1484 351  1945 534  2340 842  2794 101 1  14006 4658  n » 0 /H u  VAN  SS/GS u SS/DA  Hp u  CV/GS  H  p  cr  GPH  CV/DA  >  SS/GS  H  u  u  u SS/DA  CV/GS CV/DA  w  u  o .27 0 . 33  p  165 over the CV method, a glasshouse would experience a 77% increase in efficiency while a double acrylic greenhouse would see its collection efficiency be raised by 65%. Aside from the shape and cover material, other construction parameters investigated are: roof tilt, length-to-width ratio (L:W), orientation and floor area. Each of these variables would modify the greenhouse climate to a different extent Simulation results are presented in turn in Tables 4.7 to 4.10. Holding the floor area constant as the roof tilt is lowered from 33.7° to 18.4°, the glazing area is reduced by 10% and greenhouse volume gets smaller as well, hence there is slightly less heat loss. It was found that the effective transmissivity is not appreciably affected over the range of roof slopes studied. Figs. 4.3 and 4.4 illustrate this point when monthly r  is plotted for the  shed-type and conventional glasshouses at three locations Vancouver, Edmonton and Winnipeg. For the conventional gable roof house, T  g  increases very mildly  with roof tilt during the winter months, when the effect is most obvious for Edmonton, followed by Winnipeg, while Vancouver exhibits the least variation. Similar behaviour is observed for the shed. The difference in the pattern between Vancouver and the other two locations may be explained by different composition of solar radiation received at Vancouver, as demonstrated by two indices: Kj , the ratio of global horizontal radiation to extraterrestrial radiation and K  d  , the ratio of diffuse to global radiation that are depicted in Table  4.11. As shown, Vancouver has the highest K.^ and the lowest K j in the winter months, indicating the domination by the diffuse component Coupled to the fact that direct radiation interception factor has different value from the diffuse radiation view factor, a greenhouse located at Vancouver and Winnipeg therefore differs in solar radiation capture characteristics, though the two locations are at the same latitude.  Table  4.7  Effect  of greenhouse  greenhouse storage roof  tin  -  roof  tilt  on system  thermal  performance  l o c a t i o n : V a n c o u v e r , f 1 o o r a r e a : 20O s h a p e : SS. l e n g t h - t o - w i d t h r a t to : 2  - medium: r o c k b e d ,  m  c a p a c i t y : 0. 38 m^/m  2  ,  o r i e n t a t i o n : E-W.  , air  2  f1ow r a t e :  Sep  Oct  Nov  Dec  Jan  Feb  Mar  Apr  12.5  May  Year  33 . 7  s f  1 .OO 1 .OO  0.63 0.44  0. 33 0. 10  0.21 0.05  0.25 0.06  0.44 0. 16  0.61 0.32  0.84 0.68  1 .00 1 .00  0.54 0.31  26 .6  s f  1 .00 1 .OO  0.65 0.47  0.34 0.09  0.20 0.04  0.24 0.06  0.44 0. 15  0.63 0.34  0.87 0.70  1 .00 1 .OO  0.54 0.32  18 .4  s f  1 .00 1 .00  0.69 0.52  0.33 0.08  0. 19 0.04  0.21 0.04  0.45 0. 14  0.64 0. 38  0.90 0.78  1 .00 1 .00  0.55 0. 34  SC  m  s  18. 4 33..7  0. 38  12 . 50  0. 45 0. 44  0. 17 0. 15  18 .. 4 33 .7  0. 19  6 .25 .  0. 31 0. 31  0. 10 0. 09  18 .4 33 . 7  0. 38  12 .50  0..44 0 .43  0 .21 0 . 19  18 . 4 33 . 7  0 , 19  6 . 25  0 .33 0 . 33  0 .1 1 0.1 1  other  cases  location GPH  VAN  shape/cover SS/GS  CV/GS  roof  tilt  f  Table 4.8  E f f e c t of greenhouse greenhouse  storage  l e n g t h - t o - w l d t h r a t i o on s y s t e m  thermal  performance  - l o c a t i o n : V a n c o u v e r , f l o o r a r e a : 200 nr orientation: s h a p e : CV, r o o f t i l t : 26.6, c o v e r : d o u b l e a c r y l i c  E-W,  - mediumi:  12.5  y  rockbed,  c a p a c i t y : 0.38  m /m 3  2  , air  flow rate:  Nov  Dec  Jan  Feb  Mar  Apr  May  Year  0.69 0.71 0.70  0.65 0.67 0.66  0.66 0.67 0.67  0.65 0.66 0.66  0.70 0.71 0.70  0.72 O. 73 0.73  0.69 O. 70 0.70  0.71 0.71 0.70  0.69 0.70 0.69  1830 1850 1850  1029 1048 1033  471 486 479  296 301 301  382 388 388  777 788 777  1444 1464 1464  2077 2107 2107  2743 2743 2704  1 1032 1 1 175 1 1 103  2 4 8  274 275 295  413 414 444  470 471 505  552 554 594  592 594 636  677 679 728  736 739 791  667 670 717  526 531 569  4907 4927 5278  [MJ]  2 4 8  366 367 393  671 673 721  1051 1055 1 129  1224 1229 1317  1324 1329 1423  1089 1093 1 170  873 876 938  606 608 650  374 377 403  7578 7607 8145  [MJ]  2 4 8  640 642 688  1084 1087 1 165  1521 1526 1634  1776 1783 191 1  1916 1923 2059  1766 1772 1898  1609 1615 1729  1273 1278 1367  900 908 972  12485 12534 13423  SLR  2 4 8  2 .86 2 .88 2 .69  0. 95 0. 96 0. 89  0. 31 0. 32 0. 29  0. 17 0. 17 0. 16  0. 20 0. 20 0. 19  0. 44 0. 44 0. 41  0. 90 0. 91 0. 84  1 .63 1 .65 1 .54  3 .05 3 .02 2 .78  0. 88 0. 89 0. 83  s  2 4 8  1 .OO 1 .00 1 .00  0. 76 0 84 O 82  o. 24 0. 27 0. 28  O. 12 0. 14 O. 17  0. 17 0. 20 0..22  0. 39 0..41 O .41  0. 67 0.,70 0 .69  1 .OO 1 .00 . 1 ,OO  1 .OO 1 .00 1 .00  O. 51 0. 53 O..49  f  2 4 8  1 .00 1 .OO 1 .00  0 .57 0 .66 O .52  0 .02 0 .04 0 .02  0 .00 0..00 0 .00  0 .03 0 .04 0 .03  0 .08 0.1 1 0 .07  0 .43 o .48 0 .41  0 .78 0 .83 0 .73  1 .00 1 .00 1 .00  0 .31 0 . 34 0 .30  L:W  Sep  Oct  2 4 8  0.69 0.70 0. 70  [MJ]  2 4 8  'DL  [MJ]  NL  Hp  0  L  T a b l e 4.9  Effect  of greenhouse  greenhouse  storage  [MJ]  Hp  orientation  on s y s t e m  thermal  performance  - l o c a t i o n : V a n c o u v e r , f l o o r a r e a : 200 m , cover: glass s h a p e : CV, l e n g t h - t o - w i d t h r a t i o : 2, r o o f t i l t : 26.6 l  - medium: r o c k b e d , c a p a c i t y :  0.38  m /m 3  2  , a i r flow  rate:  12.5  Sep  Oct  Nov  Dec  Jan  Feb  Mar  Apr  May  Year  E-W N-S  0. 76 0. 56  0. 76 O. 58  0.71 O. 58  0. 71 O. 62  0. 71 O. 60  0.76 0.60  O. 79 O. 60  O. 77 O. 63  0. 78 0. 66  0.75 0. 62  E-W N-S  2009 1431  1 122 856  514 420  318 278  418 353  844 666  1585 1204  2318 2197  2936 2484  12064 9939  Q  D L  [MJ]  E-W) N-S)  593  875  1008  1 163  1260  1401  1491  1349  1074  8075  0  N L  [MJ]  E-W) N-S)  564  1087  1743  2023  2215  1796  1407  951  561  12463  0  L  E-W) N-S)  1 157  1962  2751  3187  3475  3197  2898  2300  1635  22562  SLR  E-W N-S  1 .74 1 . 29  0.57 0.43  0. 19 0. 15  0. 10 0. 08  0. 12 0. 10  0.27 0.21  0. 55 0. 4 1  1 .01 0 96  1 .80 1 .78  0.54 0.44  s  E-W N-S  0.88 0.76  0.54 0.45  0. 28 0.22  0 . 18 0 . 15  0,.20 0 . 18  0. 34 0.26  0. 52 0,.46  O .71 0 .68  0 .92 0 .87  0. 44 0.41  f  E-W N-S  0. 78 0.62  0.21 0. 15  0.02 0.01  0 .00 0 .00  0 .02 0 .00  0.05 0.02  0 .23 0 . 13  0 .48 0 .42  0 .85 0 .80  0. 20 0.16  [MJ]  a n o t h e r c a s e - 1ocat1 on :  Albuquerque  E-W  s f  1 .00 1 .OO  0.95 0.90  0.64 0.31  0 .47 O . 24  0 .45 0 . 18  0.53 0. 22  O .67 0 .40  0 .86 0 . 76  1 .00 1 .00  0.64 0. 35  N-S  s f  1 .00 1 .00  1 .00 1 .OO  0.55 0. 19  0 . 39 0 . 10  0 .39 0.1 1  0.46 0. 14  0 .64 0 .32  1 .00 1 .00  1 .00 1 .00  0.49 0.30  L/s.m  Table  4.10  System  thermal  greenhouse  -  storage f l o o r ,area  performance  f o r v a r i o u s greenhouse  l o c a t i o n : Vancouver, o r i e n t a t i o n : s h a p e : SS. l e n g t h - t o - w i d t h r a t I o :  - medium: r o c k b e d , c a p a c i t y : 0.38  sizes  (floor  area)  E-W, c o v e r : g l a s s 2, r o o f t i l t : 26 .6  m /m 3  2  ,, a i r f l o w  r a t e : 12.5  Sep  Oct  Nov  Dec  dan  Feb  Mar  Apr  May  Year  200  m  2  s f  1 .00 1 .00  0.65 0.47  0.34 0.09  0.20 0.04  0.24 0.06  0.44 O. 15  0.63 0.34  0.87 0.70  1.00 1 .00  0.54 0. 32  500  m  2  s f  1 .00 1 .00  0.63 0.41  0.28 0.06  0.17 0.02  0. 19 0..03  0.39 0.12  0.58 O. 28  0.83 0.61  1 .00 1 .OO  0.51 O. 29  1000  m2  s f  1 .OO 1 .00  0.61 0.40  O. 23 0.04  0.14 0.00  O. 16 0.02  0. 33 0.09  0.51 0.24  O. 76 0.53  1 .00 1 .00  O. 49 0.27  Other  cases  shape/cover  area (m ) 200 500 1000  0.44 0.41 0.37  0.20 0. 18 0. 17  200 500 1000  0.51 0.48 0.45  0.31 0.29 0.27  2  CV/GS  CV/DA  1.0 v >~ 0.8  H  B  8  V)  I  0.6 H  CO  C  o a) > o 4)  0.4 0.2  0.0  T  1  r  1.0 CD  o  £ > to  •I  0  8  - '$ 8  Legend  0 6  CO  c o ^  CD >  „ 0.4  o.o  i  i  A  c= -°  X  £ = 26.6°  O  £ = 33.7  18  r  1.0 <D  *>^ 0.8 <  8  o  0  N  >  CO CO  £CO  0.6 -  c o i_  0.4 -  > o  0.2 -  ~ — * <D U— J  0.0  —r M  -r  M  J  J  -  A  Month Fig. 4.3  Effective transmissivity for a shed-type glasshouse ( . t o p : V A N , m i d d l e : E D M , b o t t o m : WNG)  4  C  1.0  6  >  '</) to  £  B  ft  0.6 -I  c D  0.4H  > o  0.2  H  0.0  I.Oi  5  0.8-1  05  ©  9  8 A  ~  0.6  0.4 -\  Legend  A  % = 18.4(  X  5 = 26.6  O  £ = 33.7  0.2  0.0-  -i  r  1.0-,  0.8  2  » s  6 § A  0.6 H  0.4 -J  0.2 H  0.0  —r~  M  —T-  A  i M  r J  0  N  D  Month Fig. 4.4  Effective transmissivity for a conventional glasshouse (top:  VAN, m i d d l e :  EDM, b o t t o m :  WNG)  172  T a b l e 4.11  Monthly average values  Location  Latitude °N  Edmonton  53..5  Winnipeg  50,.0 49 .3  Jul  Oct  Dec  T Kd  0. 58 0. 39  0. 58 0. 39  0. 59 0. 38  0. 55 0. 42  0. 49 0. 47  T d  0. 63 0. 34  0. 56 0. 4 1  0. 58 0,. 39  0..49 0. 47  0. 50 0.,47  *<i  T  0..38 0..59  0. 48 0.,49  0. 57 0.,40  0,,42 0..54  0..28 0.,68  T Kd  0.,50 0.,47  0. 49 0. 48  0. 52 0.,45  0. 43 0.,54  0.,37 0. 60  T K  0. 56 0. 41  0. 49 0. 48  0. 55 0. 42  0. 46 0.,51  0. 39 0. 58  T K  0. 41 0. 53  0..48 0..46  0..52 0.,42  0. 51 0. 43  0. 37 0. 58  T K  0. 66 0. 26  0. 71 0. 20  0. 70 0. 21  0..70 0. 21  0. 63 0. 29  K  K  K  45..5  K  Guelph  43. 5  K  d  38 .0  K  d  A l b u q u e r q u e 35 . 1  and K-  Apr  Montreal  Lexington  d  Feb  K  Vancouver  of K  K  d  173  In terms of system thermal performance as a whole, annual solar heating fraction  increases with  with roof tilt  =  decreasing roof slope. In fact, additional computer  45.0°  runs  confirm that energy saving is inversely proportional to  roof tilt, albeit insignificant within the range of slopes found in practice. Thus, unlike the important role of latitude-dependent  collector slope in optimizing the  design of flat plate solar collectors, the greenhouse geometry renders the roof tilt a minor factor in solar heating system design considerations. •  Solar load ratio is essentially unchanged when L : W increases from 2 to  4, and decreases somewhat when L : W is further Table 4.8. For a 200 m  s  raised to 8, as illustrated in  greenhouse, the shift in house length is from 20 m to  28 m and then 40 m, and correspondingly from 10 m to 7 m and then 5 m in width. With a high L : W ratio, the apparent advantage of relatively greater south facing glazing area is offset by the interception of less direct radiation at the  gutter height level as the result of a narrower greenhouse.  At the same  time, heat loss increases by 8% as the L : W ratio is changed from 2 to 8. On the whole, length-to-width ratio of a greenhouse system thermal performance  for a 200 m  J  has no perceptible effect on  greenhouse,  and it has more visible  influence as the floor area expands. Table attained  by  4.9 a  summarizes  greenhouse  the  difference  equipped  with  in  annual  rockbed  solar  thermal  heating  storage  fraction  when  the  structure is oriented either with its long axis lying east-west or north-south. The effective  transmissivity of a greenhouse  is reduced by 13% to 26% when it is  moved from the E - W to N - S orientation, depending on the time of the year. The decrease in inside solar radiation is less pronounced in the winter months when diffuse since  radiation dominates  heat loss is assumed  to  for the Vancouver area. On the be  independent  of greenhouse  reduction in solar input is solely responsible for the  other  orientation,  hand, the  20% reduction in energy  174  savings. For Albuquerque where direct sunlight constitutes  a major part of the  global solar radiation during most of the heating season, the decrease of 38% in solar heating fraction for a N - S aligned greenhouse compared to one oriented otherwise is more significant. Lastly, greenhouse collection is studied  with various floor areas. Results  depicted in Table 4.10 show that it is not necessarily true for the greenhouse solar heating system to perform  independently  of greenhouse floor area, which  might be desirable from the point of view of developing a generalized design procedure. As the floor area expands from 200 m  2  to 500 m  and 1000 m , the  2  2  annual solar heating fraction is predicted to decrease from 0.32 to 0.29 and 0.27 respectively. While solar radiation transmission is unaffected  by the  floor  area,  the size of the greenhouse varies. As indicated in Table 4.1, the volume-to-floor area ratio does not stay constant with different floor areas. For the SS house, it increases from 6 to 8 when a 200 m  2  SS greenhouse is increased to 500 m , 2  and a further increase to 10 occurs when the greenhouse floor area reaches 1000 m . The difference in house volume is expected to cause a different  extent of  natural  fact,  2  ventilation, and  thus affects  the  useful  heat gain, Q  . In  u  collection efficiency drops from 58% to 53% when one compares the of a 200 m  2  the  performance  house to one occupying 1000 m . Less difference is observed for a 2  C V collection system. Since the shed can attain a higher inside temperature, for a  given  storage  capacity,  humidity  control.  With  more  natural  ventilation ventilation,  is the  required associated  for  temperature  heat  loss  and  depends  strongly on the greenhouse volume. The volume increase per unit floor area is greater in the case of a solar shed  compared  to the  conventional greenhouse.  Thus, as floor area gets larger, the efficiency of a SS system reduces more than a C V system and is reflected in the solar heating fractioa  175 4.2.4.2 Effect of locations Table 4.12 presents simulation results of a SS collection system with glass cover  for  distinctly  three  locations  different  -  Vancouver, Guelph  climatic  conditions  and  throughout  Albuquerque  the  heating  that  season  have from  September to May. The solar radiation and outside temperature regimes of the regions represented  by these locations may be classified as (low, cool), (medium,  cold) and (high, cool) respectively, and their relative magnitudes are reflected by the solar load ratio. Not only is the outside solar radiation more abundant in Albuquerque, the simulated effective  transmissivity for this location is also 10%  higher than either Vancouver or Guelph. This is likely due to the capture of more  direct sunlight; the  higher  for  interception  Albuquerque compared  to  factor  for  the  other  direct radiation is consistently sites.  For  the  SS collection  system, a greenhouse located at Guelph saves approximately 50% less energy than one  operating  at  Vancouver,  while  Albuquerque. Results for other  the  latter  locations are  saves  40%  less  energy  than  also found, in Table 4.12. It is  readily seen that although the total solar contribution can exceed 0.35 in the colder regions of Canada, the annual solar heating fraction is short of 0.15. On the  other  hand,  the  solar  heating  fraction  for  Nashville  is computed  to  be  higher than that of Albuquerque, even though its characteristic solar load ratio are  lower  directly  than  the  proportional  latter's, to  the  indicating that solar  load  energy  ratio.  The  savings  is not  nighttime  necessarily  temperature  September in Nashville is higher than the inside setpoint temperature,  in  thus SLR  need not be calculated for this month. The behaviour of the solar greenhouse with a C V collection system was also studied, and results for four locations -  Vancouver, Guelph, Montreal and  Albuquerque are listed in Table 4.13. A reduction of the solar heating fraction ranging from 35% to 50% is realized upon comparing the thermal  performance  T a b l e 4.12  E f f e c t o f l o c a t i o n s on s y s t e m shed-type greenhouse  thermal  performance -  g r e e n h o u s e - f l o o r a r e a : 200 m . orientation: s h a p e : SS, l e n g t h - t o - w i d t h r a t i o :  E-W. c o v e r : g l a s s 2, r o o f t i l t : 26.6  2  storage  location  - medium: r o c k b e d ,  c a p a c i t y : 0.38  m /n> 3  2  . a i r flow  rate:  12.5  Sep  Oct  Nov  Dec  dan  Feb  Mar  Apr  May  Year  VAN GPH ALB  0.80 0.79 0.80  0. 80 O. 79 0. 85  0. 72 o. 77 0. 87  0. 75 0. 74 0. 91  0. 71 0. 81 0. 87  0. 80 0. 81 0. 93  0. 80 O. SO 0. 82  0.77 O. 76 0.79  0.75 0.73 0.80  0.78 O. 77 0.84  [MJ]  VAN GPH ALB  2116 2208 3552  1 180 1474 3077  522 754 231 1  336 664 1962  418 976 1937  888 1693 2466  1604 2161 3246  2318 2510 4108  3020 2956 4688  12402 15306 27347  [MJ]  VAN GPH ALB  605 482 22  892 978 634  1028 1735 1 167  1 187 1883 1579  1285 2609 1518  1430 254 1 1439  1521 2504 1373  1376 1847 723  1096 1032 91  8409 12934 8546  [MJ]  VAN GPH ALB  575 642 0  1 109 1437 587  1778 2289 1555  2064 3564 2180  2260 3603 2295  1832 3505 2102  1435 2521 1502  970 1456 928  572 862 180  12984 20555 1 1329  [MJ]  VAN GPH ALB  1 180 1 124 22  2001 2415 1221  2806 4025 2722  3251 5447 3759  3545 6212 3813  3262 6046 3541  2956 5025 2875  2346 3302 1651  1668 1894 271  23015 33489 19875  SLR  VAN GPH ALB  1 . 79 1 .96 161 .5  0 . 59 0 .61 2 .52  O . 19 0 .19 0 .85  0 . 10 0 . 12 0 .52  O . 12 0 . 16 0 .51  O .27 0 .28 0 .70  0 .54 0 .43 1 . 13  0.99 0.76 2.49  1.81 1 .56 15.37  0.54 0.46 1 .38  s  VAN GPH ALB  1 .00 1 .OO 1 .00  0 .65 0 .66 1 .00  0 .34 0 .34 0 .73  0 .20 0 .21 0 .56  0 .24 0 . 30 0 .56  0 .44 0 . 39 0 .64  0 .63 O .51 0 .81  0.87 0.71 0.96  1 .00 0.96 1 .00  0.52 0. 44 0.71  f  VAN GPH ALB  1 .00 0.94 1 .00  0 .47 O .49 1 .00  0 .09 O .06 0 .56  0 .04 0 .OO 0 .29  0 .06 0 .04 0 .30  0 . 15 O . 10 0 .41  0 . 34 0 .20 0 . 74  0.70 0.48 0.95  1 .00 0.88 1 .00  0.32 0. 17 0.54  Hp  °DL UL  °NL  0,  L  L/s.m  Table  4.12  Other  EDM  (continued)  locations Sep  Oct  0. 84  Nov  Dec  Jan  Feb  Mar  Apr  May  Year  s f SLR  0. 68 1. 01  0 .51 0 .25 0. 41  0 .23 0 .03 0 . 12  0.. 14 0..00 0.,07  0.. 13 0 00 0..08  0. 32 0. 03 0. 17  0. 44 0. 13 0. 36  0.,72 0. 44 0. 77  0.,96 0. 84 1 ,40 .  0., 36 0., 1 1 O. 38  WNG  s f SLR  0. 94 0. 82 1. 19  0.. 53 0..30 0 .42  0 . 25 0..03 0. 12  0.. 18 0..00 0..09  0 . 19 0..00 0.. 10  0..33 0..04 0. 17  0. 48 0. 13 O. 33  O,.70 0,.42 0,.69  0. 91 0..74 1..34  0..37 0.. 10 0.. 35  MTL  s f SLR  1. OO 0. 92 1. 88  o. 62 0..43 0. 53  0., 33 0..06 0.. 17  O., 18 0..00 0..09  O . 24 0 .02 0.. 12  0., 35 0.,05 0.,22  O. 48 0. 15 0. 38  0,.74 0 .47 0..74  o,.97 0..86 1,.64  0 . 4 1 0 . 14 0..40  1. OO 1. 0 0 2 . 24  0. 82 0. 77 o. 65  O. 57 0. 38 O. 30  O. 60 0. 40 0. 32  0. 69 0.,52 0. 50  0. 89 0. 84 0. 89  1 1 2  • • -  .OO . ,00 29  1.,00 1.,00 12 .57  0. 73 0. 58 1. 03  Table  4.13  E f f e c t o f l o c a t i o n s on s y s t e m t h e r m a l c o n v e n t i o n a l shape greenhouse greenhouse  storage  performance  -  - f l o o r a r e a : 200 m^ , o r i e n t a t i o n : E-W, c o v e r : g l a s s s h a p e : CV, l e n g t h - t o - w i d t h r a t i o : 2. r o o f t i l t : 26.6 - medium: r o c k b e d , c a p a c i t y : 0.38 m /m 3  Sep  Oct  Nov  Dec  Jan  Feb  2  , a i r flow  rate:  12.5 L/s.m  Mar  Apr  May  Year  VAN  s f  0 .88 0 .78  0. 54 0. 21  0. 28 0. 02  0. 18 0 .00  0.20 0.00  0.34 0.05  0. 52 0. 23  0. 71 0. 48  0. 92 0. 85  0.44 0. 20  GPH  s f  0 .94 0 .85  0. 52 0.. 20  0. 23 0. 00  0.. 15 0..00  0.22 O.OO  0.30 0.02  0. 43 0. 06  0. 61 0. 29  0. 69 0 .46  0. 36 0.09  YUL  s f  0 .91 0 . 77  0.. 50 0..22  O..22 0 .00  0 . 13 0..00  O. 15 0.00  0.25 0.00  0 39 0 .05  O .60 0.,30  O,.75 0 .54  0.33 0.07  ALB  s f  1 .OO 1 OO  0 .95 0 .90  0 .61 0 .31  0 .47 0 .24  0.45 O. 18  0. 53 O. 22  0 .67 0 .40  O .86 0 .76  1 .OO 1 .00  0.64 0.35  2  179 with  that of a SS collection system. Without some means to augment  energy  collection, the colder regions cannot save energy by more than 10% even with a relatively large rockbed storage capacity of 0.38 m  3  per m  2  greenhouse floor area.  4.2.4.3 Effect of rockbed thermal storage parameters The (volume)  dependence  is demonstrated  of  system  in Table  thermal 4.14.  performance  on  Simulation results,  storage  capacity  expressed  as  the  fraction of the monthly total heating load supplied by solar energy, are shown along with various heat flow quantities: Q  u  , the useful heat gain;  , the  amount of heat transferred to storage during daytime; and Q g j , the amount of heat subsequently  recovered from storage during nighttime. Q g j is the variable  common  calculation of both  to  the  the  monthly total  solar  contribution and  monthly solar heating fraction. In general, the solar heating fraction varies directly with storage capacity at any given air flow rate and the behaviour follows the return. For instance, f  for a SS greenhouse  law of diminishing  located in Vancouver increases by  24% from 0.29 to 0.36 as the storage capacity is enlarged from 0.19 to 0.28 m nr , 2  whereas  further  expansion of the  rocked volume to 0.38 m  leads to a change of 8% more energy savings. In early fall  3  nr  2  3  merely  and late spring,  excess solar heat is available for storage during most of the day. Although solar heat gain in May is more than double that in October and May is a slightly warmer month, the amount of excess solar heat available for storage is only 40% more  for  the  May climatic conditions. Collection  efficiency for  the  month of  May is 56% compared to 75% for October. The occurence of this phenomenon in the simulation experiments is due to the seasonal variation in the leaf Bowen ratio p  in accordance with the stage of plant growth. For the fall crop, Bowen  ratio 0  is set at 2.0 in October, whereas 0  is assigned a value of 1.0 in May  for a fully developed canopy that is transpiring more to induce less sensible heat  Table  4.14  Effect  of  greenhouse  storage storage capaclty  SC  r  »  Sep  0.19 'td  s f SC  0.28  r  J  SC  r  »  ST  O.38 .ST  rockbed  s t o r a g e c a p a c i t y on  system  thermal  - l o c a t i o n : V a n c o u v e r , f l o o r a r e a : 200 shape;: SS. l e n g t h - tO-w1dth r a t I o : 2, - a i r flow Oct  rate:  18. 75  Nov  Dec  L/s.m  performance  m , orientation: r o o f t i l t : 26.6 2  E-W.  2  dan  Feb  Mar  Apr  May  Year  1215 7 10 575 1 .00 1 .00  883 576 510 0.66 0.45  289 198 155 0.35 0. 10  146 121 100 0. 18 0.03  237 193 141 0.25 0.06  429 267 206 0.45 0.17  930 539 517 0.59 0. 30  1402 660 615 0.71 0.49  1693 662 572 1 .00 1 .00  0. 53 0. 29  1215 966 575 1 .00 1 .00  883 697 594 0. 77 0.61  289 211 182 0.36 0. 12  146 122 100 0. 19 0.03  237 194 143 0.25 0.06  429 363 279 0.49 0.23  930 784 726 0.67 0.42  1402 1055 921 0.86 0.72  1693 1087 572 1 .00 1 .00  0. 60' 0. 36  1215 1 140 575 1 .00 1 .OO  883 776 715 0.82 0.72  289 214 183 0.36 0.12  146 123 102 0.20 0.04  237 195 148 0.25 0.06  429 376 294 0.49 0. 24  930 872 833 0.71 0. 49  1402 1 185 970 0.91 0. 78  1693 1296 572 1 .00 1 .00  0..65 0 . 39  cover:  glass  Table  4.14  Other  cases  locat ion VAN  (continued)  shape/cover SS/GS  m 6.25  CV/DA  GPH  SS/DA  f  0. 19 O. 28 0.38  0.51 O. 53 0.53  0.23 0.24 0.24  0. 19 O. 28 O. 38  0.49 0.51 0.54  0. 27 O. 30 0.32  O. 19 0.38  O. 52 O. 55  O. 30 0.32  12.50  O. 19 0.38  0.61 0.66  0.41 0.44  18.75  0. 19 O. 38  0.63 O. 76  0.42 0.53  G.25  O. 19 O. 28 O. 38  0.48 0.51 0.52  0.20 0.22 0.22  12 .50  O. 19 0.28 0.38  0.44 0.47 0.51  0.23 O. 26 0.31  O. 19 O. 38  0.47 0.49  0.20 0.20  12.50  O. 19 O. 38  0.52 O. 55  0.27 0.31  18.75  O. 19 O. 38  0.54 0.60  O. 29 0.38  12.50  SS/DA  s  6.25  6.25  182  exchange with greenhouse air, thus useful heat gain is reduced. In some months, the quantity of heat transferred to storage during charging can be less than 50% of the useful heat gain if the storage capacity is relatively small. A portion of the latent heat could be reclaimed if condensation takes place in the rockbed. The  bed  temperature  however  may  dew-point  temperature  of  incoming  the  increase air,  to  a  value  consequently,  higher  than  the  excess  greenhouse  moisture still needs to be removed via ventilation. For the months of September and May, nighttime heat demand is less than 600 M J per night, and in theory can be met entirely by the heat retrieved from storage. On the other hand, in the winter, excess solar heat is only available for a fraction of the daytime hours. Under such circumstances, greenhouse becomes limiting and enlargement improvement in energy retrieved  from  storage  of the storage  savings. It during  should be  discharging  volume does not induce any  noted that the may  collection  well  exceed  amount  of heat  the  nighttime  requirement in September and May for the Vancouver climate. In calculating the monthly solar fractions, though, Q  S T  is set equal to Q ^  L  when this situation  arises so as to suppress the impossibility of f-values being greater than unity. In practice, then, this manipulation is equivalent to invoking additional venting of daytime surplus solar heat  This partly confirms the findings of Ben- Abdallah  (1983) that excess solar heat accumulated  inside the  shed-type  glasshouse can  indeed supply more than its own heating demand. Nevertheless, this is only true for  a short period within  the  heating season. Hence, in September  and May  when nighttime heating load is small, a large storage is bound to be wasteful. The merits of larger storage capacity lie mainly in the months of October and February  through  energy storage,  April.  The  rockbed  storage  is  not  designed  and collection of excessive energy would affect  for  long-term  the  subsequent  thermal performance of the rockbed itself, and has to be avoided by means of  183 appropriate computer control algorithm. In other words, dumping of excess heat is  necessary  so  that  the  bed  would  not  be  cooled  prematurely  during  the  daytime. Results of simulation runs that incorporate variation in storage capacity for other  cases  are  also summarized in Table 4.14. When  relatively low (6.25 L s"  nr  1  the  meritorious collection  :  the  or equivalent to 1.5 kg s" possessed  by  a  flow  for A^. =  1  potentials  air  SS collection  rate is 200 m ), J  system  or  twin-walled acrylic cover material cannot be fully utilized; solar heating fraction is found to be quite independent of storage capacity and only 5% increase in f may be realized for a change of S C from 0.19 to 0.38 m r  air flow rate to 12.5 and 18.75 L s f  raised  to  an  average  of  nr  _l  2  14% and  3  n r . Increasing the 1  would see this percentage increase in 31% respectively  for  three  different  collection methods and two locations. These average values can be expected to be reasonably valid for other situations unless the collection system becomes the limiting factor. How air flow from  rate affects  system thermal performance  can be inferred  the energy flows tabulated in Table 4.15 for a double acrylic  shed-type  greenhouse located at Guelph. Together with condensed results pertinent to other cases that are presented in the same table, it can be deduced that for the SS and C V methods of collection, average percentage change of annual solar heating fraction amounts to a 36% increase as flow rate is tripled from 6.25 to 18.75 L s"  1  n r , for a fixed storage capacity of 0.19 m 2  to 76% if a larger storage of 0.38 m the  Brace-style greenhouse  3  nr  2  3  n r . The increase in f 2  jumps  is in place. The number of runs for  is limited, but a consistent pattern  is observed, in  Vancouver and Montreal alike. The interaction of storage capacity and air flow rate may be elaborated in  greater  detail. With  respect  to heat exchange, a lower N T U value means  T a b l e 4.15  Effect  of  r o c k b e d a i r f l o w r a t e on s y s t e m  thermal  g r e e n h o u s e - l o c a t i o n : G u e l p h , f l o o r a r e a : 200 m s h a p e : SS, 1 e n g t h - t o - w i d t h r a t i o : 2, 2  itorage air f1ow rate  m »  cover: double  m /m 3  2  Oct  Nov  Dec  Jan  Feb  Mar  Apr  May  Year  1286 583 424 1 .OO 1 .00  941 391 268 0. 59 0.39  270 101 82 0.32 0.06  201 67 45 0.22 0.02  321 126 89 0.28 0.04  775 208 167 0. 38 0.09  1117 295 242 0.48 0. 17  1366 418 373 0. 64 0.38  1724 663 562 O. 96 0.93  0. 49 0. 20  OST s f  1286 942 424 1 .00 1 .00  941 653 539 0.85 0.77  270 182 151 0.36 0.11  201 118 82 0.23 0.04  321 193 159 0.31 0.07  775 386 357 0.44 0. 18  1 1 17 541 493 0.58 0. 33  1366 829 736 0.86 0.75  1724 1101 592 1 .00 1 .00  0..55 o. 31  f  1286 1 137 424 1 .00 1 .00  94 1 836 747 1 .00 1 .00  270 243 209 0.40 0. 16  201 144 1 15 0. 25 0.06  321 290 240 0. 34 0. 11  775 582 531 0. 50 0.27  1117 837 742 0.68 0.48  1366 1 1 10 966 1 .00 1 .00  1724 1262 592 1 .00 1 .00  0..60 0 .40  J  12.50  0 .38  , o r i e n t a t i o n : E-W, r o o f t i l t : 26 . 6  Sep  6 . 25  m•  - capacity:  performance  ST  Ou  18.75  acrylic  Table  Other  4.15  (continued)  cases  s c a t 1 on VAN  shape/cover SS/GS  SC 0. 19  m 6..25 12 .50 18..75  s 0.51 0. 54 0.53  f 0.23 0. 27 0.29  SS/GS  0. 38  6. 25 12..50 18..75  0.53 0.59 0.60  0. 24 0.32 0. 39  SS/DA  0. 38  6 .25 12..50 18..75  O. 57  0.66 0. 7G  0. 32 0. 44 O. 52  BS/GS  0. 38 .  6..25 12 ..50 18. 75  0. 39 0.46 0.51  0. 15 0.24 0. 32  CV/DA  0. 19  6..25 12 .,50 18 , 75  0.48 0.54 0. 58  0. 20 0.23 0. 25  0. 38  6 , 25 12 .,50 18..75  0.42 0.51 0.59  0.22 0.31 0. 38  GPH  SS/DA  0. 19  6..25 12..50 18 .75  0.47 0.52 0.54  0.20 0. 27 0.30  MTL  BS/GS  0.38  6 .25 12 .50 18 .75  0.29 0. 35 0. 39  0.08 0.12 0.17  CO 1^1  186  more uniform distribution of heat transfer through the entire rockbed, whereas a high N T U value leads to more effective transfer in the anterior portion. Thus, the  temperature  rise  of the  bed near  the  former case, which implies less temperature outlet  Now, as air flow  temperature  air exit passage  is more for  the  drop takes place between inlet and  rate increases, N T U decreases  asymtotically, and  drop diminishes more. Hence the increase in the  the  amount of heat  transferred to the storage dampens with flow rate upsurge. However, when more storage volume is used, the number of heat transfer units is sufficiently large to sustain  a  temperature  drop  that  varies  little  with  increasing  flow  rate.  Consequently, energy savings increase more linearly with air flow rate.  4.2.4.4 Effect of soil thermal storage parameters The volume of a soil thermal storage medium is indefinite and thus the effect  of storage  capacity has  been  investigated indirectly  via the  pipe heat  exchange system and the soil type and its moisture content Table 4.16 contains the simulation results that indicate how system behaviour varies with r  g  , the  ratio of total pipe wall area to greenhouse floor area. Again, heat flow quantities are included in the table along with annual performance indices for a typical case  of a C V glasshouse  located at  Vancouver, followed  by results of other  cases. For the entire heating season, the amount of excess solar energy made available for storage adds up to 4325 M J per day in a month, or 55% of what a  SS collection system can accumulate. In December and January, virtually no  energy saving can be expected. These long-term average  estimations of system  performance are more conservative than the observed experimental values, partly because  there were few plants in the  research greenhouse  equipped with  soil  thermal storage. The system configuration that is compatible with the research unit is one  of D  =  0.10 m, m  =  6.25 L s  1  nr , 2  and r  g  =  greenhouse 1.0. The  Table  4.16  Effect  of pipe wall  greenhouse  storage  Ou Otd  QST f f  °ST s f  area-to-greenhouse  floor  area  ratio  on system  thermal  - l o c a t i o n : V a n c o u v e r , f l o o r a r e a : 200 m2 , o r i e n t a t i o n : s h a p e : CV, l e n g t h - t o - w i d t h r a t i o : 2. r o o f t i l t : 26.6 - medium: c l a y  soil,  6_  = 30%. a i r f l o w  rate:  E-W.  performance cover:  glass  6.25 L/s.m , p i p e d i a m e t e r :  Sep  Oct  Nov  Dec  Jan  Feb  Mar  Apr  804 536 34 3 0.66 0.54  514 302 176 0.42 0. 16  113 49 26 0.23 0.00  0 0 0 0. 18 0.00  0 0 0 0.21 0.00  144 97 66 0.30 0.02  485 288 169 0.46 O. 1 1  804 518 352 0. 70 0.59  514 315 182 0.42 0. 16  113 57 28 0.25 0.01  0 0 0 O. 18 0..00  0 0 0 O. 22 0 .02  144 99 67 0.30 0.02  804 571 333 0.71 0.62  514 328 207 0.43 0.17  1 13 76 31 0.25 0.01  0 0 0 0. 18 0..00  0 0 0 0.,22 0.,02  144 101 85 0.31 0.03  2  May  Year  835 546 339 0.61 O. 29  1028 561 415 0.68 0.57  0.33 0.09  485 281 180 0.46 0.12  835 529 365 0.62 0.31  1028 530 443 O. 7 1 0.60  O..34 0..09  485 300 186 0.46 0. 12  835 561 376 0.63 0.32  1028 588 477 0.73 0.63  0. 35 0. 10  0.15 m  OO  Table  Other  4.16  cases  location VAN  (continued)  shape/cover CV/GS  D  m  r  s  s  f  NTUp  e. 25  0. 5 1 .0 1 .5  0. 32 0 . 35 0 . 36  0. 10 0 . 13 0 . 14  1 . 35 1 .83 2.12  18. 75  o. 5 1 .0 1 .5  0 . 33 0 . 36 0 . 38  O. 11 0 . 14 o . 17  0. 75 1 . 14 1 .40  6. 25  0. 5 1 ,0 . 1 .5 .  0 . 34 0 . 34 0 . 35  0 . 09 O. 09 0 . 10  1 .04 1.31 1 .48  18 . 75  0 .5 1 .0 1 .5  0. 35 0. 36 0. 37  0 . 10 0. 1 1 0. 13  0.63 0.88 1 .04  0 .5 1 .0 1. 5  0. . 33 0 .43 0 .50  0. 19 0, .23 o . 25  18 .75  1 .0 1 .5  0 .49 0 .54  0 .24 0 .31  0 . 15  6 .25  1 .0 1 .5  0 .42 0 .43  0 . 17 0 . 18  0. 10  0. 15  CV/DA  0. 10  SS/GS  0 . 10  6 . 25  GPH  SS/GS  0 . 10  18 .75  1 .0 1 .5  0 .41 0 .44  0 . 12 0 . 15  ALB  SS/GS  0 . 10  18 .75  1 .0 1 .5  0 .63 0 . 72  0 .41 o . 56  189 predicted annual solar heating fraction is 0.12, as compared to the 20% energy saving achieved with the Like  the  control  case of the  experimental set-up in the research  that was fine-tuned  credited  with  the  method  used  in this study  shed-type  greenhouse  to monitor the  improvement  in system  cannot  energy  thermal  1983/1984 heating unit, the  seasoa  microcomputer  flows should be partially performance.  effectively duplicate the  The simulation  corrective measures  taken by the microcomputer to achieve the desired greenhouse climate. Therefore the  present  estimates  of  long-term  average  system  performance  tends  to  be  conservative. Different combinations of pipe diameter, total flow rate and pipe wall to greenhouse  floor  area  ratio  would  lead to  different  values  of N T U p  ,  the  number of heat transfer units for each individual pipe, defined as U An  examination of the  greenhouse increasing r  floor §  variation of N T U with p  area  and  a  fixed  pipe, diameter  D , NTUp  increases  with  . As a result of the installation of more pipes the air flow rate in  each pipe gets smaller, and the heat transfer the  r s  A /rhC. p w revealed that for a given  pipe/soil interface  coefficient from the pipe air to  is reduced. However, the  decrease in Up is more  than  balanced by the decrease in air flow rate. The increase in NTUp together with the fact that more pipes are present eventually bring about an increase in the annual solar heating fraction. As r and a diminishing effect  increases further, N T U shows less increment s p  is seen in the energy savings. The algorithm used in  this study gives the maximum pipe spacing for a confined floor area, and given values of r pipe  g  spacings  and D. Computer runs with a fixed number of pipes, but varying indicated  that  affected as long as a S  system  thermal  performance  is  not  significantly  / D ratio of at least six is maintained. This low value  P can be attributed to the fact that the temperature gradient within the soil mass is not  large  enough  to  cause appreciable  interaction  between  pipes.  In  other  190  words, the influence of each pipe does not extend beyond three pipe diameters. Furthermore, it is noted that for the case of fixed heat exchange  surface  area and fixed total air flow rate, the adoption of a pipe network with larger pipe diameter  means less pipes are  required. As a result,  NTUp  simply gets  smaller and exert an opposite effect on energy savings. In order to compare the soil thermal storage with storage, the  the rockbed thermal  simulation runs were carried out for solar heating systems that couple  SS  collection method  to  either  storage  medium.  For  Vancouver, it is found that a design configuration of D = and m  =  18.75 L s"  nr  1  the  0.10 m, r  chosen for the pipe heat exchange  2  location g  at  =  1.0  system would  produce an annual solar heating fraction of 0.24 which can be matched by a rockbed storage with S C  r  = 0.28 m  3  nr  2  and m = 6.25 L s  _1  nr . 2  Table 4.17 shows the computed results based on inputs that involve two air  flow  rates, m  separately  =  6.25 and  18.75 L s"  nr .  1  Computer runs  2  with a total flow rate of 12.50 L s"  nr  2  1  nr ,  1  negligible increase over a flow rate of 6.25 L s" small. The average  percentage change  increasing flow rate is  +10%,  have shown that f 2  especially when r  in annual solar heating  +17% and  carried out  fraction  has g  due  is to  +26% respectively for values of r  g  equal to 0.5, 1.0 and 1.5. From the same table, one can detect an interesting similarity in the trend of annual solar heating coefficient U ,  and  upon  t  =  x  ranking  this  . For a given r coefficient  in  §  fraction and total heat  , f  y  transfer  is directly proportional to  descending  order,  the  effect  of  the  combination of pipe diameter and total air flow rate becomes visible. A system with  smaller  performs  betteT  pipe  diameter  coupled  with  higher  air  flow  rate  consistently  than one with larger pipe diameter and lower flow rate; as r  increases, the difference in performance also magnifies.  g  Table  4.17  Effect  of pipe a i r flow  greenhouse  storage  r a t e on s y s t e m  - medium: c l a y  soil,  es  Sep  Oct  Nov  = 30%, Jan  Dec  performance  a r e a : 200 m^ , o r i e n t a t i o n : E-W r a t i o : 2, r o o f t i l t : 26.6, c o v e r :  - l o c a t i o n : Vancouver, f l o o r Shape: CV, l e n g t h - t o - w i d t h  p i p e wal1/greenhouse f l o o r  a i r f1ow rate  thermal  pipe diameter:  0.10  m,  1.5  area  ratio:  Feb  Mar  Apr  May  Year  m = 6.25  s f  1 .00 1 .00  0.58 0. 35  0.23 0.00  0. 18 O.OO  0.20 0.00  0.32 0.04  0.53 0.26  0.73 0.57  1 .00 1 .00  0.50 0. 25  m = 12.50  s f  1 .00 1 .OO  0.63 0.42  0.24 o.oo  0. 18 O.OO  0.21 0.00  0. 35 0.06  0.58 O. 32  0.84 0.72  1 .00 1 .OO  0. 52 0. 28  m - 18.75  s f  1 .oo 1 .00  O. 66 0.45  O. 26 0.01  O. 19 0.00  0. 22 0.01  0.40 0.07  0.61 0. 36  0.86 0.80  1 .00 1.00  0. 53 0.30  Other  cases  Shape/cover  CV/GS  0.5  1.0  1.5  CV/DA  1.0  0.10  18.75  0.34  0.11  532  6.25  0.32  0.10  333  0.15  18.75 6.25  0.35 0.33  0.10 0.09  305 168  0.10  18.75 6.25  0.37 0.36  0.15 0.13  819 438  0.15  18.75 6.25  0.36 0.34  0.11 0.09  416 208  0.10  18.75 6.25  0.38 0.36  0.17 0.14  1003 506  0.15  18.75 6.25  0.37 0.35  0.13 0.10  492 234  0.10  18.75  0.34  0.26  0.29  0.23  6.25  double  acrylic  192  In floor  designing a pipe heat exchange system for a greenhouse  area,  consider  the  case  of  obtaining greater  solar  heating  of known fraction  by  increasing the total pipe wall area. Apparently, this may be accomplished in two ways:  using  installing  larger  more  pipes  pipes  while  but  keeping  retaining  the  the  number  original  of  pipes  diameter.  constant,  Both  or  approaches  introduce the same additional area of pipes. Consider for the moment the case of  a  C V house  located in Vancouver. From  Table 4.17, by  comparing  thermal performance of the various scenarios with the same air flow rate: (r 1.0, D =  0.10, N = p  30) with (r s  =  1.5, D = 0.15, N  =  the g  =  30) and (r = p s  1.5, D = 0.10, Np = 46), the first approach is seen to cause a decrease in f and thus destroy our purpose. While this phenomenon implies that it would be more effective to increase the  number of pipes than their diameter, a larger  pressure drop associated with smaller pipes needs to be considered upon sizing for the solar fan Lastly, we examine the effect of soil type and its moisture content on energy savings. Results of simulation runs are entered in Table 4.18. Although a limited  number  of runs  was carried out,  these results  suggested  that system  performance is not significantly affected by either parameter. In fact, even when the  volumetric moisture content 9  is raised to a fictitious  value of 80% as  w  compared  to  the  usual saturation  value  of 40% for clay  and  sand,  still  no  significant difference can be visualized. These results are not surprising because the thermal diffusivity of soil does not change significantly with moisture content, as indicated in Table 4.19. In the model, both the soil heat capacity C  §  and  thermal conductivity k are linear functions of moisture content; the increase in C with d is slightly more than that of k . The preference of a clay soil s w s g  medium over sand is due to the former's moisture holding capability, which is advantageous in keeping the soil wet from time to time.  Table 4.18  Effect  of s o i l  type/moisture  content  on s y s t e m  thermal  performance  g r e e n h o u s e - l o c a t i o n : V a n c o u v e r , f l o o r a r e a : 200 m , orientation: s h a p e : CV, l e n g t h - t o - w i d t h r a t i o : 2, r o o f t i l t : 2G.6 2  storage  - a i r flow  rate:  18.75 l/s.m , p i p e d i a m e t e r : 2  p i p e wal1/greenhouse f l o o r  so i) t y p e / moisture content  area  ratio:  Sep  Oct  Nov  Dec  Jan  Feb  E-W,  cover:  0.10 m,  1.5  Mar  Apr  May  Year  c 1 ay 20%  s f  0. 82 0. 70  0. 52 0. 23  0. 25 0..01  0. 18 0. 00  0. 20 0,.00  0. 32 0,.04  0. 50 0. 19  0.79 0,54  0. 83 0. 71  0. 38 0., 16  sand  s f  O. 89 0 . 77  O. 54 0..30  0.,25 0..01  0. 18 0,.00  0..20 0,.OO  O., 33 0 .05  0. 53 0 .23  0.82 0.61  O. 92 0 .83  0.,40 0,. 19  D  m  Other  20%  cases  Shape/cover CV/GS  CV/DA  0. 10  0 . 15  18.75  6.25  r  s  1.5  1.0  type  %  c i ay  20% 30% 40%  0 . 38 0. 38 o . 39  0. 16 0. 17 0. 19  sand  20% 40%  0. 39 0. 40  0. 19 0. 21  c l ay  20% 30% 40%  0. 34 0 35 0 . 36  0. , 17 0. 18 0. 19  sand  20% 40%  0 .34 0 . 36  0. . 18 0, .20  s  f  glass  T a b l e 4.19  soil type  Thermal  properties  volumetric moisture content  of c l a y  and  thermal conductivity W nr C 1  _ 1  sand  thermal capacity MJ  nT  3  C"  thermal diffusivlty 1  m  2  s  clay  20%  1.20  2.20  0.56  clay  40%  1.60  3.00  0.54  sand  20%  1.73  2.20  0.80  sand  40%  2.39  3.00  0.80  _ 1  195  4.3 Sensitivity Analysis  The  mathematical  experimentally  determined  models  contain  some  factors  that  have  not  in detail or variables that may be calculated by  methods. This section is devoted to test the influence of these uncertainties  been different on the  system performance at large. For the greenhouse  thermal environment model, sensitivity is tested upon  the  following: 1.  number of air changes per hour, N  2.  Bowen ratio,/}  3.  shading factor due to structural members,  4.  solar radiation as driving force  f^  The rockbed storage model has been used by many researchers and the level of uncertainty of the variables involved is the least in the overall modeling process. A sensitivity test was made of the initial rockbed temperature. The same test was applied to the soil storage model, the variables of which have also been widely evaluated by many researchers. Results of the model sensitivity testing are listed in Tables 4.20 to 4.22. With the method of natural ventilation, it is not always possible to keep the number of air changes per hour, N , at a desirable value that is associated with the extent of vent openings. If its maximum value should differ from 10 h" the  parametric  greenhouse 20% if N  study,  the  amount  of  useful  heat  gain  will  be  located at Vancouver, the annual solar heating fraction, f  1  as used in  affected.  For  a  would fall by  is 20 Ir . The percentage reduction in energy savings is larger for a 1  m  a  x  colder region such as Guelph and may be up to 50%. For the case of N max  =  pattern to a 4-2.5-1.5-1 pattern, f  10, as Bowen ratio 0 is altered from a  4-3-2-1  decreases by 7% from 0.27 to 0.25, and by 17%  from 0.29 to 0.24 respectively for a SS/GS system in Vancouver and a S S / D A system  Table  4.20  Senslt1/lty test results and s h a d i n g f a c t o r greenhouse  storage location  VAN  GPH  - ventilation rate,  SS/GS  SS/DA  Bowen  ratio  f l o o r a r e a : 200 m , o r i e n t a t i o n : E-W, c o v e r : l e n g t h - t o - w i d t h r a t i o : 2, r o o f t i l t : 26.6 2  - medium: r o c k b e d , c a p a c i t y :  cover/ shape  leaf  maximum number ooff a i r c h a n g e s p e r hour  0.38 m /m 3  Bowen rat 1 o  2  . a i r flow shadl ing factor  glass  rate:  12.5 L/s.m s  2  f  C C C  O.B5 0.90 0.95 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85  0. 35 0.37 0.38 0.42 0.50 0. 34 0.33 0.49 0. 32 0.35 0.40  O. 17 0. 18 0. 19 0.21 0.27 0. 16 0. 20 0.25 O. 14 0. 19 0. 24  A A A B B B  0.85 0.85 0.85 0.85 0.85 0.85  0.28 0.37 0.50 0.25 0.32 0.44  0. 16 0.22 0. 29 0.15 0. 18 0.24  20 20 20 15 10 20 15 10 20 15 10  A A A A A B B B  20 15 10 20 15 10  T a b l e 4.21  Sensitivity initial  test  results  rockbed  - initial  temperature  [°C]  12.5 10.0  initial clay,  sand,  6 « 30% S  9 = 30% S  soil  temperature  thermal  [°C]  storage  temperatures  s  f  0.515 0.516  0.282 0.283  s  f  12.0 16.0 18.0  0.53  0.30  0.52  0.29  12.0 16.0 18.0  0.55  0.33  0.53  0.31  Table  Sensitivity  4.22  greenhouse  storage  Sep  test  results - solar  radiation  processing  algorithm  - l o c a t i o n : M o n t r e a l , f l o o r a r e a : 200 m , orientation: l e n g t h - t o - w i d t h r a t i o : 2, r o o f t i l t : 26.6 2  - medium: r o c k b e d , c a p a c i t y : 0.38 m /m 3  2  , a i r flow  Oct  Nov  Dec  dan  Feb  Mar  Apr  May  Hp/H (T„) 0. 79 r c 0. 77 0. 76  0. 79 O. 77 0. 78  0. 78 O. 77 0. 79  0. 75 0. 76 0. 76  0. 77 0. 78 0. 77  0. 83 0. 84 0. 82  0. 81 0. 79 0. 78  0. 77 O. 75 0. 75  0. 73 0. 72 0. 73  Hq/H  0..72 0..70 0 .70  0. 85 0. 82 0. 83  1 .00 0. 99 1 .02  1 1 1  1 . 14 1 .. 13 1.1 1  0. 91 0. 92 0..89  0. 79 0..77 0. 76  0. 61 0. 61 0 .61  0..49 0,.50 0..50  f  0 .92 0 .89 0 .87  0. 43 0 .43 0 .45  0..06 0 .06 O .08  0..00 0 .00 o .00  0 .02 0 .02 0 .00  0 .05 0 .06 0 .05  0.. 15 0 . 14 0 . 13  0..47 0 .45 o .42  O .86 0 .87 O .81  .. 13 .. 14 .. 14  rate:  Year  O. 14 0. 13 0. 12  E-W,  cover:  12.5 L/s.m  glass  2  199  i n Guelph. A n  even lower Bowen  ratio throughout  the growing  season (3.5-2.5-1.5-0.5  pattern) practically does not affect the solar heating fraction any further. The  testing on  components heating 10%  of the greenhouse  fraction is  less  shading  energy is  provided  model sensitivity to shading  directly proportional savings  would  actually possible that  snow-cover As  framework  the  occur  with  greenhouse  , due to the structural  shows that the percentage to the  change  i f it is  acrylic cover is  factor, f ^  located  a  15%  which  in  in  the  value  shading  requires  places  like  variation in  in  of  f^  .  lieu o f  less  About  5%.  structural  Vancouver  solar  Less  members  with  nominal  in winter. for  the  thermal  storage,  results  indicate  that  the  overall  model  is  not  sensitive to initial rockbed temperature, and mildly sensitive to initial soil temperatures. Hence,  the  lack  of  soil  temperature  data  for  the  U.S.  locations is  not  expected to  generate unreasonable simulation results for sites such as Albuquerque and Nashville. Lastly, the due  model  energy  input  to  Results  for  number  of bright  only  is  the  solar  radiation processing,  Montreal,  tested on  different where  sunshine  greenhouse  negligible. The  is  its sensitivity to the variation of  processing  records  hours  of  algorithms global  simulation method  presented  diffuse  solar  are all available, are presented  effective transmissivity but also  and  as  its  in  the  used in this study  annual  solar  solar  section  4.1.1.  radiations in  relatively unaffected by  effect on  hourly  Table  and  the  4.22.  Not  the method  heating  can therefore provide  of  fraction is reasonable  estimates o f the energy savings for locations where solar energy data are less complete than Montreal, in which case solar radiation processing than direct computation.  requires more correlations other  200 4.4 Crop Canonv Photosynthesis Various crop growth mathematical models have been reviewed in Chapter 2. Modeling of various processes involved in plant growth and eventually the final marketable yield requires a combination of mechanistic and empirical models, and thus a good deal of experimental data for curve fitting purpose. Photosynthesis provides the driving force for most of these processes, and net photosynthetic rate may be regarded as an index of primary production. The present study does not incoporate experiments for generating measured data of the variables that are needed in plant growth analysis. However,  it  is  response  under  felt  that  different  a  growth  aerial  function  may  environment  be  in  developed  greenhouses  to  as  quantify  affected  plant  by  the  a  net  engineering parameters considered in the last section.  4.4.1 The simulation method The  model  photosynthesis Crops  function  Research  photosynthesis  esculentum  presented (eqn.  taken  Acock  2.27)  Institute,  were  Mill.  by  el  to experimental  Littlehampton, from  (cv. Kingley  al. (1978)  noon  to  data  U.K. dusk  based  on  collected at  Measurements  for  Cross) that were  is  the  placed  cabinet Air temperature was maintained at 20 ° C , the C 0  2  the' Glasshouse  of  tomato in a  fitting  net  plants,  canopy  Lycopersicon  controlled-environment  concentration at 400 ppm  and the vapor pressure deficit at 0.7 kPa. The  operation  of a  solar  greenhouse  alters  the  greenhouse  temperature and  moisture regimes. Though it is known that temperature exerts less influence on  net  photosynthesis  for  temperature's  compared role  to  in plant  light and response.  C O , , the Variation  in  growth  function  the  greenhouse  shall account  relative humidity  results in varying degrees of vapor pressure deficit, and thus the leaf conductance, t, , to  C0  2  transfer.  assumption that $  However, the  lack  of  specific  is independent  of greenhouse  experimental  data  results  in  the  relative humidity. Another assumption  201 made here is that for a given set of light and C 0 2 conditions, gross photosynthesis (deducting photorespiration), P maximum P  , is constant beyond a certain temperature  , as more dissolved oxygen is present to induce more photorespiration so  as to cancel the stimulating effect the  that yields  literature  review, the  temperature- correction  of temperature  temperature  factor,  at  on gross photosynthesis. Based on  this point is taken  F, is assumed  to have  the  as  26  following  ° C , and  the  value, which  is  light-dependent:  F = 1.00  F ~ 1.25 - 0.007(7; - 26)  P A R < 125Wm"2 PAR >  2  f = 1-25  P A R > \2bWm-> a n d T > 26°C  125 W n r  J  is the light saturation level  tomatoes. It is chosen to encompass the situation when temperature  effect on P  (4.18)  p  These expressions do not imply that PAR = for  m W m ^  has a mild  under medium light intensities.  Together with an expression for canopy dark respiration, which combines eqn. 2.28 (Enoch and Hurd, 1977) and eqn 2.29 (Charles-Edwards, 1981), the mathematical model used for canopy net photosynthesis is given by  P n  -F^  l n  i a A ' p P A R p e x P ( - / f p L , ) + (l-r )ccJ p  "rY/1  C X P (  (4.19) At  20 ° C , F has a value of 1.00 regardless of light level, and 2  1.00, so that with the right parameters, P  n  ( T  "  2 0 ) / 1 0  =  should have values that match the results  obtained by Acock et al. (1978) who carried out experiments under this condition It shall be noted that the leaf temperature is assumed to be equal to air temperature in their experiments. The parameters a,I 4.23  and K vary with L . , and are listed in Table  along with the estimated L . values over the two crop growing seasons. For the  202  T a b l e 4.23  Crop canopy  photosynthesis  model  parameters  Sep  Oct  Nov  Dec  Jan  Feb  Mar  p  0.52  0.53  0.56  0.60  0.63  0.60  0.55  0.52  Lj  8.6  7.6  5.8  3.4  2.0  3.4  6.6  8.6  a  1.6  1.5  1.2  1.6  2.1  1.6  1.4  1.6  t,  9.6  9.1  11.5  10.3  9.1  10.3  10.5  9.6  K  Apr  203  fall crop, plants are seeded in May/June, and a sizeable crop canopy is established by September; leaf area is assumed to decrease thereafter till December. The spring crop usually starts in November/December (later area  index is assumed  to have reached  seeding if fuel  its peak  price is high), and  value in April.  leaf  In the simulation,  PAR is taken as a constant percentage (45%) of broadband (total) solar radiation. The  engineering  parameters  considered  in  the  simulation  study  of  performance are mainly concerned with the greenhouse solar collection method -  crop shape,  cover material and absorption means. Computer runs were carried out for the locations of Vancouver and Guelph. The computer modeling does not include the prediction of the  time  simulation  history of the stage, net  C0  2  level within the  photosynthesis  as  greenhouse  affected  by  five  enclosure;  ambient  rather, at  C0  the  concentrations  2  (210, 240, 270, 300 and 330 ppm) were calculated.  4.4.2 Results and discussion Prior  to  using  the  average  climatic conditions  program, the combined effect of light and C 0 by  2  as  inputs  to  the  computer  only on net photosynthesis is evaluated  subjecting eqn. 2.27 to preliminary computer runs. Fig. 4.5 shows the variation of  canopy net photosynthetic rate at 20 ° C with PAR above the plant canopy, and C 0 is the additional parameter. As C 0  2  decreases from 330 to 240 ppm, P  n  2  is reduced  by 9.5%, 11% and 13% respectively for P A R fluxes of 90, 150 and 240 W n r . The 2  calculated percentage decrease is less pronounced  than  that reported  by Bauerle and  Short (1984) who found it to range from 22% to 35% for a single physiologically mature tomato (cv. MR-13) leaf. The computation is then extended to examine the effect of temperature using eqn. 4.19, and calculated results for two leaf area indices are illustrated in Figs. 4.6 and 4.7. At low P A R levels such as 90 W n r , P^ is unaffected 2  temperatures considered, whereas R , increases with temperature,  by the range of  thus P  is noticed to  Fig. 4.5  Variation of net canopy photosynthesis with P A R and C 0  2  205  decrease monotonically with rise in temperature. As light level increases, P  n  reaches a  maximum at 26 ° C , falling off to about 20% less at 20 ° C . Temperature exceeding 26 ° C also causes less net C 0 smaller influence on P  2  uptake, but to a less extent  Light intensity has a  for a relatively young plant Comparison of Figs. 4.6 and 4.7  n  reveals that at low light levels, net photosynthetic rate differs less markedly between a young crop and one  with  a fully  developed canopy. The difference  becomes more  obvious as P A R increases. The incorporated  crop as  net  photosynthesis  a subroutine  function  in the  overall  as  represented  computer  by  eqn.  4.19 is  then  program previously used  for  predicting the thermal performance of the solar heating system. For each month, mean hourly results are summed up to give mean daily values of P subsequently total value for each growing period (kg n r  2  Q  (g n r  2  d" ) and 1  period ). Tables 4.24 and -1  4.25 separately present these results for the Vancouver region and Guelph region. In each case, five solar greenhouse collection systems are studied. For the fall period in Vancouver, P d  _1  in September to 12.56 g n r  2  d'  1  Q  has a remarkable drop from 29.56 g m  J  in October as the corresponding leaf area index  changes from 8.6 to 7.6, and mean daily outside solar radiations are 13.40 M J n r  2  and 7.56 M J n r . The original model (eqn. 2.27) fitted to the experimental data by 2  Acock  et al. (1978) gives P  n  values that are  boosted by at  most  10% as  Lj is  increased from 5.2 to 8.6. Charles-Edwards (1981) and Ludwig et al. (1965) noted that canopy net photosynthesis (or crop metabolic rate activity) decreased appreciably only when  the  therefore  leaf  area  index was reduced  below 3. The large  decrease in P  n  may  be attributed primarily to the reduction in outdoor light intensity, which in  fact is the most important factor affecting photosynthesis. Fig. 4.8 sketches the mean hourly inside P A R flux  density profile  for the  months of September  through May,  while the mean hourly net photosynthetic rate is depicted in Fig. 4.9. It is obvious that  the  trend  of  P  follows  that  of  P A R very  closely.  Hourly  values  of  the  2.1-1  1.81.5-  1.2 0.9  Legend  0.6  P A R =30, CO2=330 p 0.3  PAR PAR PAR  0  =90  P  p  =150 =210 =270  ?AR P  -0.3 18  20  22  24  26  28  32  30  34  36  Temperature, C c  Fig. 4.6  Variation of net canopy  photosynthesis  (leaf area index  =  8.6) with temperature and P A R  Legend  2.1  PAR =30,-C02=330 .  p  1.8-4 P A R =90 p_  PAR p  _  _  _  =150  1.5 4|PAR =210 p  |PAR =270 1.2 H tr  0.9 H 0.6 0.3 H 0 -0.3 18  I  20  I  22  I  24  1  26  1  28  1—  30  Temperature,°C Fig. 4.7  Variation o f net canopy  photosynthesis  (leaf area index  =  32  34  36  2.1) with temperature and P A R  Table  4.24  monthly average d a l l y Sep  Oct  net photosynthetic  Nov  Dec  r a t e - Vancouver  Period total  dan  Feb  Mar  Apr  Period total  Annual total  Sol ar Greenhouse  SS/GS  C1 C2 C3  29. 56 27 . 43 24. 62  12. 56 1 1 .77 10. 69  6. 84 6. 41 5. 80  3. 17 3 02 2 81  1 56 1 46 1 32  2. 95 2 81 2 63  9. 94 9. 29 8. 42  23. 87 22 . 18 19. 94  33. 52 31 . 21 28. 15  2 .1 1 1 .96 1 .77  3. 67 3. 42 3. 09  SS/DA  C1 C2 C3  26. 68 24 84 22 36  1 1 .41 10 69 9 72  6 12 5 72 5 18  2 74 2 59 2 41  1 41 1 32 1 19  2 56 2 45 2 27  9 04 8 46 7 70  21 . 28 19 80 17 82  31 . 10 29 05 26 28  1 92 1 79 1 62  3 33 3 1 1 2 81  CV/GS  C1 C2 C3  28 33 26 32 23 69  1 1 74 10 98 9 97  6 66 6 26 5 65  2 95 2 81 2 59  1 49 1 39 1 26  2 99 2 84 2 66  9 29 8 68 7 88  23 54 21 85 19 62  33 23 30 92 27 90  2 07 1 93 1 74  3 56 3 32 3 00  CV/DA  CI C2 C3  25 20 23 51 21 20  10 66 10 01 9 1 1  5 98 5 62 5 1 1  2 52 2 38 2 20  1 33 1 25 1 . 13  2 59 2 48 2 30  8 42 7 88 7 16  19 91 18 50 16 67  30 28 28 30 25 63  1 84 1 72 1 .55  3 17 2 97 2 68  BS/GS  C1 C2 C3  31 50 29 12 25 .99  17 06 15 95 14 44  8 24 7 70 6 95  3 56 3 .38 3 . 13  1 .81 1 .68 1 .52  3 .67 3 .49 3 . 24  1 1 16 10 40 9 36  26 75 24 77 22 14  35 78 33 23 29 92  2 .32 2 . 16 1 .94  4 . 13 3 .84 3 .46  CV/GS  C1 C2 C3  30 . 28 28 .26 25 .63  12 . 56 1 1 .81 10 .80  6 .98 6 .55 5 • 98  3 . 10 2 .95 2 .74  1 .59 1 .49 1 .35  3 . 17 3 .02 2 .84  24 . 59 22 .90 20 .70  35 .03 32 .72 29 .70  2 . 18 2 .03 1 .85  3 .77 3 .52 3 .20  units:  g m~2 kg m~  ConventIonal Greenhouse 9 .76 9 . 14 8 .35  C1: 2  day period - 1  - 1  f o r monthly values f o r period total values  CO,  =  C 2 : CO2 • C 3 : CO2 «  330 ppm 2 7 0 ppm 2 1 0 ppm  Table  4.25  monthly Sep  average d a i l y Oct  net photosynthetic  Nov  Dec  Period total  r a t e - Guelph  Jan  Feb  Mar  Apr  Per 1od total  Annual total  SS/GS  30. 49 C1 19.26 28.30 C2 18.OO 25.34 16.27 C3  9 .97 9.29 8.39  7.56 7. 13 6.48  2 .02 1 .88 1 .69  7.85 7 .34 6.66  31 .75 36.36 20.88 29.20 33.77 19. 12 25.92 30. 38 16.85  2.91 2.68 2.39  4.93 4 .56 4.08  SS/DA  C1 28.40 C2 26.42 23.76 C3  16.13 15.08 13.64  9.00 8.39 7 .60  6.80 6.41 5.87  1.81 1 .69 1 .53  7. 13 19.48 29.70 32 .90 6.66 17 .93 27.40 30.64 24.41 6.05 15.84 27 .65  2.68 2.48 2.22  4 .49 4.17 3.75  CV/GS  C1 29.92 C2 27.76 24 .88 C3  18.94 17 .68 15 .95  9.61 8.96 8 . 10  7 . 38 6.95 6 .34  1 .98 1 .84 1 .66  7.56 7 .09 6.41  19.94 31 .50 37 .01 18 . 29 28 .98 34.34 16. 13 25. 70 30.85  2 .88 2 .66 2.37  4 . 86 .4 .50 4 .03  CV/DA  C 1 27 . 47 15 . 77 C2 25.56 14 .69 C3 23 .04 13.28  8 .68 8. 10 7.31  6 . 66 6.26 5.72  1 . 76 1 .64 1 .48  6.84 6.44 5.83  18.58 29. 20 33 . 12 17. 10 26 .93 30.82 15. 16 24.01 27 .76  2 .63 2.44 2 . 18  4 . 39 4 .08 3.66  BS/GS  CI 31 .93 C2 29.56 C3 26 . 39  8.86 8.28 7.49  2.20 2 .05 1 .83  33 . 48 37 . 26 10. 19 24.26 34.56 9.50 22. 10 30.67 8.57 19.37 27 . 1 1 31 .07  3. 16 2.91 2.58  5 . 36 4 .96 4.41  units:  g m" day , k g nf* p e r i o d  11.41 21 .28 19.76 10.58 17 .78 9.50 1  f o r monthly v a l u e s f o r period total values  7-.  Legend C02=340 C02=280 C02=220  Septl8 Fig. 4.9  Octl9  Novl8  HA  Decl3  Janl7  Month  Febl4  Marl5  Aprl5  Mayl5  Mean hourly net photosynthetic rate on the typical design day of each month for a greenhouse tomato crop grown in Vancouver  212 components  (P g  representative  and  R, d  )  that  constitute  P„ n  are  shown  in  Fig. 4.10  for  the  day in September. It is seen that dark respiration makes up about 30%  of gross photosynthesis around noon time. Sestik (1985) commented that although  the  process of dark respiration is partly inhibited by light in photosynthesizing cells, some 25% of the dark rate might be preserved. The  situation  is  somewhat  different  for  the  same  tomato  'numerically' in Guelph. Since inside PAR level is above 125 W n r the  difference  differences and  P  fl  in  September  in photosynthetic rate between  January  when  Vancouver. It simulation  between  solar  should be  program  and  October  is  2  less  the two locations are  plant d"  1  noted  processing  does not  consider  the  situation  when  Vast  found in December  twice as much  climatic data  in October,  pronounced.  radiation in Guelph is about that the  grown  as  that in  algorithm in  the  snow is present on  the  greenhouse roof. It is imperative that good management practice would be followed to minimize the duration of snow cover that induces static live load on the cover and blocks incoming solar radiation. The demonstrated  extent  of reduction  in P  fl  with  diminishing C 0  by the results in Tables 4.24 and 4.25. If C 0  normal 330 ppm to 210 ppm, P  2  2  concentration is depressed  is also from  the  lessens by 15% to 18%. On a monthly basis, less  Q  percentage decrease occurs in the winter months for Vancouver, but this percentage is relatively more uniform from month to month for Guelph. It is simply a reaffirmation of the fact that the effect of C 0  2  concentration is more significant when light is not  limiting. Comparison is next made between greenhouse collection methods, with to the pivotal case of C V / G S -  reference  solar collection with a conventional glasshouse and no  auxiliary features for absorption. Table 4.26 lists the effective transmissivity for various greenhouse  collection systems. For a glasshouse located in the Vancouver region, crop  performance is slightly better with a SS/GS collection system; total P  during the  fall  Legend Gross photosynthetic rate ftesgiratjon_rate_ Net photosynthetic rote  I  s CM  I  c Q _  Hour Fig. 4.10  Mean hourly rates of gross photosynthesis, respiration and net photosynthesis on the representative day in September  214  T a b l e 4.26  Effective  shape/cover  Vancouver  Guelph  transmissivity  for different  collection  systems  Mar  Apr  0. 80  0. 80  0. 77  0. 65  0. 74  0. 74  0. 71  0. 71  0. 71  0. 76  0. 79  0. 77  0. 65  0. 66  0. 65  0. 70  0. 72  0. 69  0. 92  0. 85  0. 81  0. 82  0. 91  0. 88  0. 81  0., 79  0., 79  0., 77  0..74  0. 81  0.,81  0..80  0 .76  SS/DA  0..72  0,.73  0 .71  0 .68  O .74  0 .75  0 . 73  0 .70  CV/GS  0 .77  0 . 78  .0 .75  0 .73  0 . 78  O . 77  0 .80  0 .78  CV/DA  0 .70  0..72  0 .69  0 .67  0 .72  0 .71  0 .72  0 .71  BS/GS  0..83  0 .88  0 .88  0 .85  0 .93  0 .92  0 .86  0 . 78  Sep  Oct  Nov  Dec  dan  Feb  SS/GS  O. 80  0. 80  0. 72  0. 75  0. 71  SS/DA  0. 74  0. 74  0. 66  0. 69  CV/GS  0. 76  0. 76  0. 71  CV/DA  0. 69  0. 69  BS/GS  0. 87  SS/GS  215  is increased by 5%, and only 2% improvement is achieved for the  spring growing  period. Upon modifying the greenhouse to bear the BS/GS configuration (with internal reflecting surface), the plant canopy would secure a 21% (0.32 kg n r ) and 12% (0.25 2  kg m ) increase in P J  Q  for the fall and spring respectively. On the other hand, i f one  decides to use double acrylic cover (the C V / D A arrangement), a 11% reduction in net C0  2  uptake may be expected throughout the entire heating season. Similarly, if the  SS/DA system is adopted, P In  general,  net  Q  would cut by 10% relative to a SS/GS system.  photosynthesis  is  about  35%  higher  in  Guelph  than  in  Vancouver. Departure from this trend lies in the BS/GS system where only 10% (fall: 0.22 kg n r , 2  spring: 0.28  kg n r ) J  more P  fl  is realized compared to the  CV/GS  method. It may be attributed to the months with a high leaf area index (Sept, Oct, Mar, Apr) which govern the overall performance in each growing season, when inside light level increases relatively more in Vancouver by adopting the BS/GS design. As far as leaf temperature  is concerned, the effect is coupled to light intensity  (and C 0 ) . The BS/GS setup leads to the most inside PAR level at the top of the 2  canopy, accordingly the temperature-correction factor F with values larger than unity is applied more frequently, and further enhance the net photosynthetic rate. For Guelph, temperature  effect is insignificant in the fall, but more influential in the winter months  of January and February, becoming insignificant again in later spring. The accuracy of the absolute value of P  fl  cannot be verified since the model  parameters are pertinent to a tomato plant not grown in Canada. Furthermore, to the knowledge of the author, there is very little information on net photosynthetic rate of greenhouse crops. Nevertheless, some endeavor was made to check with reported values of related information such as greenhouse crop yield. Moss (1983) found that there was a direct relationship between radiation level and yield. Tomatoes grown with N F T and subject to root-zone warming had a yield of 0.845 kg n r  2  per week in the first two weeks of picking when the average daily  216  radiation  outside  was 10.3 M J n r  d"  2  radiation in Vancouver is 10 M J n r C V / G S system is 23.5 g n r  in Australia. The mean  1  d"  2  daily  outside  in March, and the computed P  1  n  solar for a  d" . Enoch (1977) made an attempt to generalize yield,  2  1  Y , from primary production, P  . Based upon the assumption that one absorbed C O :  n  molecule is used to create one molecule of dry matter (CH 0), that 50% of this dry 2  matter  is  yield,  multiplication  and  factor  that  the  total  mass  of 7 is estimated  cucumbers. Thus for P  n  =  23.5 g n r  for 2  of  yield  greenhouse  contains  5%  dry  crops such as  matter,  a  tomatoes and  d~\ the yield is roughly 1.17 kg n r  2  per  week, a reasonable value compared to Moss' findings. Papadopalos and Jewett (1984) measured the marketable yield of tomatoes grown under  glass  Harrow  and  Research  twin-wall  P V C gable-roof  greenhouses at  Station, Ontario. In March  1982, the  yield  the  Agriculture Canada  of the  three cultivars  (CR-6, Vendor and MR-13) grown under glass are 0.23, 0.57 and 0.31 kg per plant, which, for a planting density of 0.281 m /plant can be translated J  35.0 g n r 21.6,  d" . For the  2  entire  1  to 26.0, 64.0 and  spring growing season, cumulative yield amounts  to  17.5 and 15.6 kg n r . The corresponding yield for those cultivars grown under 2  twin-wall P V C are 23.3, 16.0 and 16.8 kg n r . By comparison, the simulated total P 2  of  2.88  kg n r  2  for the  CV/GS  system  in the  Guelph region results  in a yield  estimate of 20.2 kg n r , and that for the C V / D A system, 18.4 kg n r . In the 2  n  2  fall  growing season of 1982, cultivar C R - 6 grown under P V C showed a reduction in yield compared to that grown under glass. These results suggest that crop yield may increase or  decrease when grown under  twin-wall  P V C cover, though  values of P  fl  energy-conserving greenhouses such as the one with no  conclusion may  be  drawn. In  contrast,  computed  in this study are always lower for the case of twin-wall acrylic cover  material, the light transmission characteristics of which is much like twin-wall P V C . Yield  records  obtained  from  the  Saanichton  research  station  (van  Zinderen  Bakker, 1986) indicated that annual tomato crop yield had an average of 17 and 20  217 kg n r  2  for two (fall 1983/spring 1984 and fall 1984/spring 1985) experimental periods;  the computed total (fall and spring) P  of 3.56 kg n r  Q  (yield estimate  2  = 25 kg n r ) 2  for the C V / G S system in the Vancouver region is therefore not an unreasonable value either.  Comparing the  without thermal  solar shed  storage),  occured during the Fall  actual  with  data  the  control house  (a conventional  also showed that 6% and  8% yield  1983/Spring 1984 growing period and Fall  glasshouse reduction  1984/Spring 1985  period respectively. Since no thermal storage is there to remove the surplus solar heat built up in a conventional greenhouse,  much ventilation is needed. Also given in Table 4.24 are  the simulation results of P  n  , with a maximum ventilation rate of 30 air changes per  hour. Comparing the values with those of the C V / G S solar heating system where less ventilation takes place to conserve captured solar energy, these net photosynthetic rates are  5% to  7% higher,  due  to  lower  greenhouse  air  temperature  and  thus  plant  temperature. Aside from the temperature effect, where depletion of COj occurs in a solar greenhouse  such as the solar shed (SS/GS system) with less ventilation and no C 0  enrichment, reduction in P  fl  can be  expected. Referring to Table 4.24 again, i f its  concentration is allowed to drop to 280 ppm, total P be 3.32 kg n r Suppose C 0  2  2  2  for both growing seasons would  Q  for a C V / G S collection system, and 3.42 kg n r  2  for a SS/GS system  level can be maintained at the normal level in a conventional greenhouse  with much ventilation, the associated P  is 3.77 kg n r , which is 14% and 10% more 2  Q  than each of the above system. If the depletion is more severe (down to 210 ppm), the loss in primary production is increased to 26% and 22% respectively. The actual depletion of C O  a  varies from month to month, and is a function  of the total leaf area and Q„ , the amount of excess solar heat not collected and e subsequently delivered to the thermal storage. A high L C 0 , and if coupled to a very small Q 2  means plants consume more  value, then ventilation must have been kept  218 to a ntinimum. It is therefore  expected that C 0  months, and most in October and April  2  will be depleted least in the winter  when leaf area index is large while at the  same time, collection of solar heat is to be maximized. Therefore,  for  a  known quantity  of  useful  heat  gain, Q  ,  u  that  can  achieved by a greenhouse solar collection system, as storage capacity increases,  be  more  heat can be collected over a longer time during the day with the right combination of  air  flow  rate  and  storage  extended  period, thus more  situation  has  not  been  capacity.  CO  depletion  a  developed  Accordingly,  vents  takes place.  in this study, and  will  The  the  be  closed  algorithm  effect  for  an  for  such a  of thermal  storage  parameters can only be described qualitatively with respect to the results of P  n  for  by  the  varying amount of C 0 . 2  The rate of C 0  2  consumption in a closed system may be estimated  following equation:  22AA P T f  (4.20)  n  (44)(273)V  The  area  used  in  the  shed-type glasshouse ( A mg  nr  2  s  minutes, C 0 the  at T =  1  2  above f  =  expression  is greenhouse  117 m , V =  490 m ), i f P  2  floor  3  n  area,  Aj. . For  the  has a typical value of 1.0  30 ° C and is assumed to stay constant with time, then in 15  will drop by 120 ppm Of course, C 0  2  depletion rate is not constant in  actual situation, but this simple calculation demonstrates one important point: for  collection  of solar heat to be  enrichment  is  necessary.  Willits  realistic such and  Peet  that vents are  (1987)  commented  not that  open  often,  the  cooling provided by storage during the day allows sufficient additional C 0  C0  2  closed-loop 2  enrichment  time over conventional ventilation systems such that significant yield increases can be expected  with some  greenhouse crops.  For a glasshouse  with tomatoes under U . K .  219 winter conditions, an average  of 416 kg C 0  2  ha"  y  1  1  was used to raise the C 0  2  concentration 1 ppm (Slack and Calvert, 1972). Enoch (1978) suggested that this would require 139 kg propane ha  -1  y . 1  4.5 Development of A Simplified Design Method  4.5.1 Introduction The parametric study described in detail in section 4.2 provides some insight into  the  extent  of  variation  of system  thermal  performance  with  the  key  design  variables. The most important observation is that in most cases, both the key indices of long-term system performance, the total solar contribution and solar heating fraction are  directly proportional to the  dimensionless solar load ratio which  represents the  characteristics of the greenhouse collection system. In greenhouses,  developing  a  simplified  design  method  for  solar  heating  systems  for  it is desirable to have a set of generalized design curves that cover as  many parameters as possible. Besides, a designer needs some guidelines to obtain the information related to the essential variables involved in the design procedure. From the results of the parametric study, the greenhouse construction parameters that bear minimal influence on system performance  have been identified to be roof  slope and length-to-width ratio. On the other hand, parameters that can induce large variation in system performance  by way of the solar load ratio include location and  cover material. Greenhouse orientation and floor area have some measurable effect on the solar  energy  savings too. The greenhouse  radiation  input,  rather,  it is  the  shape per se has no appreciable combination of the  shape and  effect on the  energy  absorption method that would either modify the solar load ratio or enhance the heat exchange process that ultimately leads to better system performance. Storage parameters affect  the  system  behaviour  independently  and  do  not  affect  the  solar  load ratio.  220 Results suggested that all the storage parameters with the exception of soil type and moisture  content are  significant  variables,  so  that  a  family of  design  curves  are  probably required for different choices of the storage configuration The approach adopted here is to establish a correlation between the solar load ratio and system thermal performance. Preliminary plottings of SLR versus s and f indicated that both s and f exhibit a positive correlation with SLR and that the former shows a more definitive pattern Moreover, V was found to be well correlated with 'f,  as seen in Fig. 4.11. It is therefore possible to establish a set of design  curves that permit s and f to be calculated in sequence. Although the solar heating fraction is of utmost concern for subsequent economic analysis of the results generated from  the  present  study,  the  total  solar  contribution can  provide complimentary  information for comparing alternative designs. Hence, it is necessary to estimate both indices of system thermal performance to assist in decision making. The simulation results in the form of .s and f of a large number of runs are plotted in Figs. 4.12 and 4.13. Fig. 4.12 pertains to the SS and CV collection systems with rockbed thermal storage. Each collection method is coupled to two combinations of the storage parameters, SC r =  0.38, m =  These  chosen  two sets of  values  are  to  12.50 and SC r = 0.19 and m = represent  some  6.25.  bounds within practical  consideration to the system performance with alternative storage designs. For a given collection system and storage configuration, it is realized that, by and large, variations in the following design parameters can be accomodated by a single curve that relates s to SLR: cover material, roof tilt, length-to-width ratio, orientation and floor area. Some  adjustment  on  the  annual  solar  heating  fraction  is  necessary  for  large  greenhouses. The same curve can account for the thermal performance of a particular design put to operation in regions with climatic conditions representative of the various locations covered in this study.  X X X *XX,  \ X  x X  x x x  x  A  A  X  A  mxx •  x  n  £ *  o  [  •  ?  •  •  •  g  o  o o  acx,  •  ••  o  A •  o  o  CP  o  o  o  o  o 'O o  Legend X  SS  0.38  12.5  A  SS  0.19  6.25  •  CV  0.38  O CV 0.19 s h a p e SC / cover  0.8  1.2  1.6  Solar load ratio =  2.0  2.4  12.5 6.25  m  2.8  3.2  AfHp/Qj_ to to  Fig. 4.12  Simulated values of total solar contribution versus solar load rauo -  rockbed thermal storage  1.0 - i X  0.9-  A X  x x  0.8-  X  A  B  CO  C O  0.7  2  0.6  O o  0-5  O  0.4  o  "D  A  B  o 8  Legend 0.3  X 0.10 1.5 18.75 A 0.10 1.0 18.75  X  0.2 H  •  82*  0.15 1.5  6.25  O 0.15 1.0  6.25  D  0.1-  m  0.0 0.0  0.4  0.8  1.2  1.6  Solar load ratio = Fig. 4.13  2.0  2.4  2.8  AfHp/Q|_  Simulated values of total solar contribution versus solar load ratio - soil thermal storage  to to  224  Total solar contribution as a function of solar load ratio is plotted in Fig. 4.13 for a CV collection system and wet soil thermal storage. Less simulation runs were executed for this solar heating system since it is not necessary to repeat the variation of those parameters that have nominal effect on system performance. Also, in view of the higher computing cost involved in the soil storage simulation, only the locations of Vancouver, Guelph and Albuquerque were included. The climatic conditions of other locations do not give rise to solar load ratios and hence solar fractions that are out of the range covered by the aforesaid locations.  4.5.2 Regression method At  this point, the performance curves that shall form the skeleton  of the  proposed simplified design procedure are ready to be synthesized through curve fitting. The desirable output is to produce a general empirical relation for a family of curves. However, this is only possible if the parameters of the curves can be fully quantified. The next desirable outcome is the generation of the same form of a certain equation, in which the constants (coefficients) are allowed to vary with different parameters. The situation that equations of different forms need to be fitted to these simulated data is to be avoided by all means because of possible confusion Mathematical expressions are required since a fair amount of computational work is still expected on the part of the user though he/she is no longer required to undertake the detailed simulations carried out herewith. For the correlation between monthly total solar contribution, s, and solar load ratio, SLR, since s has an upper limit of 1.00, the exponential form of equation is more appropriate than other forms such as hyperbolic which has an asymtotic locus, or parabolic which tends to fall off at some point Using the packaged program NLSUM at UBC (Moore, 1981), the data points of Fig. 4.12 and 4.13 function s =  a + a^e 0  T  ae 2  were fitted to the  225  where the coefficients for each case (rockbed thermal storage and soil thermal storage) with various combinations of storage characteristics are given in Table 4.27. The value of s is insensitive to round-off of decimal points for the coefficients, except case for which 5 decimal places need to be retained. F o r nonlinear regression correlation  index, P, was computed  SI,  analysis, the  and its values are shown in Table  4.27 as well.  Equation 4.21 is graphically shown i n F i g . 4.14 and 4.15 for the two cases. A  polynomial  function  was  fitted  to the correlation  between  monthly  solar  heating fraction, f, and s, and results i n the following quadratic equation: / = - 0 . 0 0 7 + 0.03 s + 0.92 s  (4.22)  2  A  slightly better fit was obtained with a cubic polynomial, however, a local  f  occurs  where  s  =  0.20, below  and above  which  f begins  minimum  to increase, which  is  unrealistic. Equation 4.22 is represented by Fig. 4.16.  4.5.3 Outline o f the design procedure The  use o f the design curves or the fitted equations for determining the solar  heating fraction involves a number o f calculation steps, as outlined below: 1.  Specify location, greenhouse  2.  Obtain  monthly  average  and thermal storage design characteristics.  climatic data  -  solar  radiation  [in M J  nr  J  d" ] and 1  temperature., 3.  Calculate total glazing area, A  , as  gz A  =  3Z  4.  The 24- hour hourly  A  gr  +A  greenhouse  +A  gw  heating  i- ) 4  3t  load  [in M J ]  is estimated  by summing  23  the  values, QL  =  E 24-hr  U A, (T„ -T.)(0.0OX) tM  M  t  (- ) 4  24  T a b l e 4.27 Case  Coefficients a  0  a  of equation  l  a  4.21  2  b  l  R1 R2 R3 R4  1 .03 1.15 1 . 13 0. 80  -1 .00 -0.89 -0.71 -0. 44  -0. 35 -0.44 -0. 39  -1 .96 -0. 82 -0. 61 -0. 73  S1 S2 S3 S4  0.873 0.85 0.79 0.77  -2151.478 -0.76 -0.59 -0.57  2150.697 0.06 -0.75 -1.19  -o. .83676 -1.. 19 -1 .00 -0 .98  b  I  2  2  -9. 18 -3.24 -6 . 38  0. 91 0. 92 0. 92 0. 88  -0.83657 -9 .76 -22 .4 -27 .6  0. 95 0. 91 0..94 0..93  LU  1.0  0.9-  Fig. 4.15  Design curves fitted to the simulated data points of  Fig. 4.13  K  230  where  T  is  the  set-point  temperature  (e.g.  22  C  daytime  and  17  °C  nighttime), and U is the overall heat loss coefficient of the greenhouse glazing (5.7,  5.8,  and  3.2  W  nr  K~  2  l  for  respectively). The outside temperature, T  glass, Q  polyethylene,  and  double  acrylic  , is calculated in accordance with eqns.  4.10 (daytime) and 4.12 (nighttime). 5.  Determine monthly greenhouse  effective transmissivity, r  . It is noted that r e  does not vary much from  e  month to month at a specific location, and. for a  given collection system (shape, cover and absorption means). Typical values may be found in Table 4.26. However, a computer program that only computes  r  &  can be made available POT users if so desired. 6.  Calculate the amount of solar radiation incident on an inside horizontal surface as HP  7.  rH  (4.25)  E  The monthly solar load ratio is then SLR  8.  =  From  Fig. 4.14  or  =  AjH IQ P  (4.26)  L  Fig. 4.15,  obtain  the  corresponding  monthly  total  solar  contribution, s. 9.  Estimate monthly solar heating fraction, f, from Fig. 4.16.  10.  Finally, the annual solar heating fraction, f  for the entire heating season may  be computed from  , _ Em/Qz. " Em QL  (4.27)  /V  11.  Design options that are reference  not covered by the performance  curves may have  the  system thermal performance estimated by the procedure outlined above,  and calculated results can be modified by consulting Tables 4.28 and 4.29.  Table  4.28  Combined  rockbed  greenhouse  1ocation VAN  GPH  YUL  ALB  s t o r a g e c a p a c i t y and a i r f l o w  rate effect  on system  thermal  performance  f l o o r a r e a : 200 m . o r l e n t a t I o n : E-W l e n g t h - t o - w i d t h r a t l o : 2!, r o o f t l i t : 26 .6 2  m  s  0. 19 0. 38  6. 25 12 .50  0. 51 0. 59  0. 23 o. 32  SS/DA  0. 19 0. 38  6 .25 12 .50  0. 54 0. 66  0. 30 0. 44  CV/GS  0. 19 o. 38  e. 25 12. 50  o.  0. 33 37  0. 12 0. 20  CV/DA  0. 19 0. 38  6 .25 12 .50  0. 48 0. 61  o.  CV/PE  0. 19 0. 38  6. 25 12 .50  0. 29 o. 34  0. 10 0. 17  SS/GS  0. 19 0. 38  6. 25 12 .50  0. 37 0. 44  0. 08 o. 17  SS/DA  0. 19 0. 38  6. 25 12. 50  o. 47 0. 57  0. 20 0. 35  CV/GS  0. 19 0. 38  6 25 12 .50  0. 27 0..36  0. 05 0.,09  CV/DA  0. 19 0. 38  6 .25 12 .50  0 .37 0 .44  0.. 10 0 .21  SS/GS  0 , 19 0 .38  6 .25 12 .50  0 .35 0 .40  0 .07 0 . 14  8S/GS  0 . 19 0 . 38  6 .25 12 .50  0 .31 0 .35  0 .07 0 . 12  CV/DA  0 . 19 0 .38  6 .25 12 .50  0 .39 0 .41  0.1 1 o .20  SS/GS  0 . 19 0 . 38  6 .25 12 .50  0 .57 0 .70  CV/GS  0 . 19 0 .38  6 .25 12 .50  o . 43 0 .57  0 .20 o .35  0 . 19 0 .38  6 .25 12 .50  0 .41 0 .52  0 . 17 0 .31  shape/cover  SC  SS/GS  CV/PE  r  f  20 0. 31  o .28 0 .54  to  Table  4.29  Combined e f f e c t o f s o i l s t o r a g e p i p e w a l l on s y s t e m t h e r m a l p e r f o r m a n c e g r e e n h o u s e - f l o o r a r e a : 200 length- to-wldth storage  location VAN  GPH  ALB  - medium: c l a y  shape/cover  area  and a i r flow  rate  m . o r i e n t a t i o n : E-W r a t 1o : 2, r o o f t i l t : 26 .6 2  soil.  Di  e  8  30%  r.5  m  f  s  SS/GS  0. 10 0. 15  1 .5 1 .0  18 . 75 6.25  0. 54 0. 42  0. 31 0. 17  CV/GS  0. 10 0. 15  1 .5 1 .0  18.75 6.25  0. 38 0. 34  0. 17 0. 09  CV/DA  0. 10 0. 15  1 .5 1.0  18 . 75 6.25  0. 53 0. 44  0. 30 0. 18  CV/PE  0. 10 0. 15  1 .5 1 .0  18.75 6.25  0. 32 0. 19  0. 14 0. 06  SS/GS  0. 10 0. 15  1 .5 . 1 .0 ,  18.75 6.25  0. 44 0.,39  0. 15 0.,09  CV/DA  0. 10 0. 15  1 .5 , 1 .0  18.75 6.25  0 43 0 .37  0.,20 0 . 13  CV/PE  0., 10 0.. 15  1 .5 1 .0  18.75 6.25  0 .36 0 .28  0 .09 0 .05  SS/GS  0 . 10 0 . 15  1.5 1 .0  18.75 6.25  0 .72 0 .51  0 . 56 0 .27  CV/PE  0 . 10 0 . 15  1 .5 1 .0  18.75 6.25  0 .46 0 . 40  0 . 23 0 . 15  233 4.5.4  Example ralrtilatirtn  In this section, an example is given showing how the used to determine  design curves can be  the annual solar heating fraction during the period of  September  through May, for the following specifications: location: Vancouver greenhouse floor area: 500 m  1  length-to-width ratio: 2 wall height: 2 m roof tilt: 26.6 ° glazing: single layer glass daytime setpoint temperature: nighttime setpoint temperature:  22 ° C 17 ° C  By working through the steps outlined in section 4.5.3, we shall be able to come up with a set of f-values for various options provided in the design curves. The local climatological data for Vancouver is given in Table 4.30, also shown here are the calculated monthly solar load ratio values. The fraction of the load supplied by solar energy  during each month can then  heating  be obtained from Figs.  4.12 or 4.13, and Fig. 4.11. A small computer program as listed in appendix E has been written to facilitate the computation procedure. Users need to prepare a short list of  inputs that correspond to the design specifications. The estimated  performance for each design alternative is given in Table 4.31.  system  thermal  T a b l e 4.30  Average l o c a l c l i m a t o l o g i c a l data f o r Vancouver, s o l a r l o a d r a t i o f o r a CV/GS c o l l e c t i o n s y s t e m  Sep H  13 .22 18.47 9.90 0.76 10.05 2838 1 .77  Tmax T  min  Hp  QL SLR  Table  4.31  Oct 7 .38 13.74 6.46 0.76 5.61 4814 0.58  Nov  Dec  3.59 9.06 2 .90 0.71 2.55 6749 0. 19  2 .28 6.61 1 .24 0.71 1 .62 7821 0. 10  Solar heating fraction,  Jan 2 .94 5.29 -0.27 0.71 2 .09 8528 O. 12  Feb 5 .53 7 .56 0.96 0.76 4 . 20 7847 0.27  f for eight design  and  Mar 10.03 9 .65 2.30 0.79 7 .92 71 10 0.56  Apr 15.09 13. 19 4.83 0.77 1 1 .62 5642 1 .03  May 20. 15 16 .83 7.84 0.78 15.72 4008 1 .96  options  Sep  Oct  Nov  Dec  Jan  Feb  Mar  Apr  May  Year  R1 R2 R3 R4  0. 94 0. 84 0. 78 0..45  0. 48 0. 34 o. 33 0. 25  0. 11 0. 10 0. 07 0. 09  0. 04 0. 03 0. 02 0..04  0. 05 0. 05 O. 03 0. 05  0. 18 0. 16 O. 13 0. 14  0. 46 0. 32 0. 32 0. 25  0. 76 0. 56 0. 55 O. 35  0. 96 0. 89 o. 83 0. 47  0. 35 0. 28 0. 26 0. 19  S1 S2 S3 S4  0 0 0 0  0 0 0 0  0 .08 O .07 0 .09 0 .08  0 0 0 0  0. 12 O. 10 0. 12 0.. 1 1  0. 29 O., 22 0..21 0 . 19  0 .53 0..40 0 .34 0 .32  o .75 o .60  0..25 0..20 0 . 18 0.. 17  Case  .72 .57 .47 .44  .30 .23 .22 .20  .04 .04 .04 .04  0 0 0 0  .05 .04 .05 .05  0 .49 0 .46  235  NOTATION Dimension  A  Greenhouse floor area  F  Monthly average number of bright sunshine hours C 0 concentration Pipe diameter Temperature-correction factor View factor between one roof surface and plant canopy  f B C D F  2  12  13 H I K F  K  m  d  View factor between two roof surfaces Daily global solar radiation incident on a horizontal surface Hourly global radiation incident on a horizontal surface Extinction coefficient The ratio H . / H d ex Clearness parameter (cloudiness index) = H / H g x  L L. i L:W N N  d  j N N  p NTU' g P n PAR P  QDL QDN Q  L  QNL QPAS QST  Length Leaf area index  J  mg n r m  3  -  M J n r d" kJ n r hnr 2  2  1  1  -  m m  2  nr  2  greenhouse length-to-width ratio Number of air changes per hour Day length  -h r  Modified day length  h  Number of pipes Number of heat transfer units Gross photosynthetic rate  -mg  nr  2  Net photosynthetic rate  mg n r  2  Photosynthetically active radiation Daytime heating load  kJ n r MJ d  Daytime net heating load  M J d-  1  24-hour gross heating load  M J d"  1  Nighttime heating load  M J d"  1  Passive solar gain  M J d"  1  Solar heat recovered from storage  M J d"  1  1  h  Heat transferred to storage (charging)  M J d-  1  Q  Useful heat gain  M J d"  1  u  Dark respiration rate  mg n r  2  Pipe spacing  m  Storage capacity Solar load ratio Temperature Total transmission factor Overall heat transfer coefficient Width  m  S  P  sc  SLR  T TTF U W  3  nr  -° C -W n r m  S"  1  1  1  t d  d  1  h-  2  Q  R  S"  2  S"  1  2  K-  1  236  Pressure drop a,b,c,e Constants used in equations 4.10 and 4.11 a\ b' Constants used in equation 4.7 Constants used in eqn. 4.21 o  kN  nr  2  a  bi.bj  d f  Rock equivalent diameter Monthly solar heating fraction shading factor due to greenhouse structural members  m  Annual solar heating fraction 'sh h n rh  shading factor due to greenhouse structural members Depth Hour Air flow rate Number of layers of pipe  m 00-24 L s' n r 1  2  Total pipe wall area to greenhouse floor area ratio s s  y  V  a  *c e S e_  i M »>  P  P„  Monthly total solar contribution Annual total solar contribution Superficial fluid velocity Leaf light utilization efficiency Leaf Bowen ratio Declination on characteristic days Void ratio Leaf conductance to C 0 transfer Collection efficiency Soil volumetric moisture content 2  m s" mg J" 1  1  Degrees m  s  _1  %  Zenith angle  Degrees  Angle of incidence  Degrees  Refractive index Absolute viscosity Density slope of roof surface 1 slope of roof surface 2 Ground albedo Cloudless sky albedo  kg n r s kg n r Degrees Degrees 1  3  Cloud albedo Effective transmissivity Leaf transmittance  0  Latitude Hour angle at the middle of an hour Sunset-hour angle for a horizontal surface Subscripts  Degrees Degrees Degrees  _1  1,2,3 ex f g ge gr gz i m max min n o p r rs set sr ss w y  for pressure drop expressions extraterrestrial floor, fluid greenhouse greenhouse gable ends greenhouse roof greenhouse glazing insulation month maximum minimum direct normal outside plant canopy, pipe rock rockbed storage setpoint sunrise sunset wall year Abbreviations  BS CV SS  Brace-style greenhouse conventional gable roof or quonset greenhouse shed-type greenhouse  DA GS PE  twin-walled (double) acrylic glass polyethylene  ALB Albuquerque E D M Edmonton GPH Guelph MTL Montreal NSV Nashville STJ SL John's V A N Vancouver W N G Winnipeg  Chapter 5 CONCLUSIONS The  computer program  heating systems alternatives.  made  has been made flexible to include a number o f  parameters  characteristics, most  of  include  which  for the processing  are  The with  the  the  better  allowed  to have  design  characteristics and  variable  values.  Provision  storage is  also  also written to deal with canopy  net photosynthesis  A of  tomato crop. combined  empirical  simulation has for  location, greenhouse  solar  of climatological data that are available in different forms.  subroutine of the program was a greenhouse  RECOMMENDATIONS  written for predicting the thermal performance of  for greenhouses  Design  AND  two  greenhouse  thermal environment  relationships  and  yielded reasonably specific  agreement  systems  with  temperatures, whereas  the  values  of  thermal storage constants  values,  relative humidity  solar  followed shows  radiation  by  more  and  rockbed  model  approximated  accurate computed results compared  studied. Inside  actual  -  in  temperature  from  the  to observed  temperatures  deviations  along  the  data  are  and  in soil  experimental  data. Nevertheless, the prediction of energy savings due to each solar heating system  is  within 15% of measured energy savings data. Based on simulated data, a concise set of design curves have been obtained for estimating  the  system. With knowing  long-term  average  thermal performance  these curves, the annual  the average  of  greenhouse  solar  heating  solar heating fraction can be directly calculated  climatic conditions of a certain design  is also quantified for various  a  greenhouse  location. Crop  collection systems. A  performance  detailed economics  study  based on the predicted thermal and crop performances pertinent to a particular system design would then enable a designer  to evaluate design alternatives in the early  phase  of a project Specific findings of this study are: 1.  Accurately  predicted  greenhouse  temperature  238  and  relative  humidity  cannot  be  239 attained simultaneously as relative humidity depends on temperature. 2.  Latent  heat  release  by  the  moist  inlet  air  in  the  rockbed  storage  is  significant as the calculated rockbed temperatures are not vastly different  not from  measured values. 3.  Of the width  greenhouse ratio  have  construction parameters investigated, roof least  influence  on  effective  tilt and length  transmissivity  and  hence  to  solar  heating fraction. The collection method that comprises the shape, cover material and solar radiation absorption means has transmissivity of a solar greenhouse  obvious effects.  Besides, the  effective  does not vary appreciably from month  to  month, in contrast to the trend of the total transmission factor. 4.  Solar irradiation on the plant canopy does not differ significantly, regardless of shape, unless internal reflection is increased considerably.  5.  With the rockbed thermal storage, larger storage capacity is warranted only i f a higher air flow rate is used. System thermal performance diminishing  return'  with  regard  to air  flow  follows the  rate. A more  'law of  linear variation is  obtained, however, for the range of storage capacity investigated. 6.  With the soil thermal storage, if the pipe wall-to-greenhouse fixed,  a system with smaller pipe diameter  floor area ratio is  coupled with higher air flow rate  performs better than one with larger pipe diameter and lower air flow rate. To obtain greater solar heating fraction by increasing the total pipe wall area, it is more effective to increase the number of pipes than their diameter. 7.  For most (colder) regions in Canada, annual 10% with conventional greenhouse  solar heating  fraction  lies below  collection system and no auxiliary feature  to  augment solar .heat collection. Double-acrylic cover improves energy savings, but not significantly over the winter months either. 8.  In months  with more  solar radiation, the  crop canopy has  more  transpiration  heat loss, which constitutes a good portion of incoming solar radiation Collection  240 efficiency  is therefore  lower than it could otherwise achieve with a less dense  canopy. 9.  As far as model sensitivity is concerned, thermal performance  is sensitive to the  Bowen ratio and the maximum allowable ventilation rate. The model is mildly sensitive initial  to the storage  shading  factor  temperatures,  due  and  to structural  practically  members.  so  for  It is insensitive  different  solar  to  radiation  processing algorithms. 10.  Given  the  photosynthetic  same  plant  and  cultural  rate is higher in the  practices,  tomato  Guelph region than  crop  the  canopy  net  Vancouver region  because of better natural light conditions. 11.  If C O ; is replenished  in solar  greenhouses, net  photosynthesis  is greater  for  collection systems that use modified greenhouse shapes, whereby one with internal reflective  surface  has  the  best  performance.  However,  reduction  in  primary  relation  between  production can be expected with twin-walled cover. 12.  Correlations are monthly  solar  developed load  for  ratio and  design  curves  monthly  total  that depict solar  the  contributioa  They are  also  generated for monthly solar heating fraction as a function of monthly total solar contribution. 13.  There  exists  a  value  of  total  solar  contribution,  below  which  solar  heating  fraction is essentially zero. 14.  The system thermal performance  can be characterized by a location's solar load  ratio, so that the design curves so developed are location-independent  For the  Canadian locations, the solar load ratio for most months in the heating seasons is low because of medium to low solar radiation and high heating demand. Though the design curves are presented as the final results of this study, it is by no means the only tool for evaluating alternative  designs. The computer  program  developed by the author can indeed be used as a direct tool in design, provided that  241  users have access to alternative solving packages for various submodels.  Possible  future  works are  suggested  in the  following  section. They may  be  divided into analytical work and experimental work. 1.  analytical work The computer modeling and simulation method can be improved in order to get more accurate  estimates  of the absolute  indices. Additional modeling efforts  values of system thermal  performance  can be made within the framework of the  present study. The following areas may be addressed: a.  A transient  model of the greenhouse  thermal environment is needed  for  more precise prediction of storage charging and discharging times, and for determining when ventilation is required after surplus solar heat is collected and  delivered to  estimating  the  storage.  This  transient  ventilation requirement  analysis can  for C 0  2  also be  replenishment  used  in a  for solar  greenhouse. The set of simultaneous nonlinear equations have to be solved at time intervals shorter than one hour, and may therefore necessitate  the  solving of simultaneous ordinary differential equations. b.  Other pipe network configurations can be considered, such as vertical pipe settings. With this arrangement, by  an  the soil thermal storage may be analyzed  axisymmetric finite element  length can be properly assessed.  program  so  that the  This would need  effect  of pipe  the assumption of no  interaction between adjacent pipes, which is likely the case if space permits pipes to be separated by at least six pipe diameters. c  energy required by fan during the charging and discharging operations.  d.  use average hour-by-hour year-long climatological data (such as the typical meteorological year) as inputs for simulation and compare results with the present study. This method, however, is only feasible for U.S. locations at  242  present e.  More detailed modeling on various stages of crop growth and development, as affected by aerial environmental factors.  f.  Economic modeling to assess the overall costs and benefits  of alternative  designs. The scope of the study may also be expanded to cover the following cases:  2.  a.  multispan greenhouses  b.  plastic covers with much light diffusive power  c  external solar collection systems  d.  other sensible heat storage devices like water and solar pond  e.  latent heat storage device  experimental work a.  The 'rate of decay tracer gas technique' can be applied to measure  the  ventilation rate, N , due to natural ventilation method. Accurate values of N need  to be obtained for different  extents • of openings of the ventilation  panels located at the ridge or the side. These values can then be used in the control algorithm of the microprocessor for more precise control of the requirement for ventilation of uncollected surplus solar heat If COj is used as the tracer gas, the rate of C 0  2  replenishment can be measured at the  same time. b.  C O enrichment :  experiments can be carried out to study the effect of C 0  2  enrichment time  on system thermal performance and crop performance, while minimizing the ventilation requirement c.  latent heat recovery While the collection efficiency  could be improved i f less ventilation takes  place, humidity control is still necessary. The recovery of latent heat serves  243  the  dual purpose  enhancing  the  of removing excessive greenhouse  collection  efficiency.  It  is  moisture and  preferred  accomplish this task be located inside the greenhouse  that  further  devices  that  rather than having  moisture condensed in the storage medium, which is less effective and even undesirable. d.  The leaf Bowen ratio of greenhouse  crops shall be measured during the  entire heating season so that a seasonal variation pattern can be obtained under solar greenhouse climates. Alternatively, the plant resistance to water vapour diffusion can be measured. 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Agriculture Canada Saanichton Research and Plant Quarantine Station, Sidney, B.C.  APPENDICES  A.  Direct radiation interception factor diffuse r a d i a t i o n view factor  B.  Psychrometric  C.  L i s t i n g of  D.  Sensors  E.  L i s t i n g of  and  equations  computer their  program  *OVERALL*  locations  computer  257  program  *DESIGN*  and  258  Appendix C  259  "OVERALL* to simulate long-term average performance of s o l a r h e a t i n g systems f o r greenhouses, with rockbed or s o i l thermal s torage. by  Anthony  K.  Lau  u n i t s : 3:  input  5:  outputs  data -  6:  -  7:  -  8:  -  IMPLICIT  greenhouse c i n t e r c e p t i o n greenhouse t temperature, e f f e c t i v e t r absorbed s o l amounts of t net p h o t o s y n  REAL*-8(A-H.  h a r a c t e r i s t i c s , including s o l a r r a d i a t i o n f a c t o r and view factor emperatures, r e l a t i v e humidity, storage o u t l e t useful heat gain, heat t r a n s f e r r e d to/from storage, a n s m i s s i v i t y , s o l a r load r a t i o , s o l a r h e a t i n g f r a c t i o n s a r r a d i a t i o n s , heat t r a n s f e r c o e f f i c i e n t s , r a n s p i r a t i o n and c o n d e n s a t i o n t h e t i c rate  0-Z)  C O M M O N / D A T A / T O U T , R H T ( 2 4 ) . VW, R H S E T C O M M O N / E N V / C L , BOWEN COMMON/GEOM/GHL,GHW.BH,WH, R T I L T 1 , R T I L T 2 , S 1 , S 3 , GVOL COMMON/GROWTH/RK,RLAI,TAUC,EFLITE,TRANSM,RDO, PN(10) COMMON/INDEX/I, J C O M M O N / H E A T / T M A X ( 1 2 ) , T M I N ( 1 2 ) . H E A T L D . OSUP, QPASS COMMON/L0GIC/F0R3. ALIGN COMMON/MAT/THCRC, RKCRC. R K P , T H P I P E COMMON/OCCUR/ICALL. ICAL COMMON/OUT/RHINS. T R P N , T R S P . SUMOU. T P O U T . OTRAN. PN1 COMMON/PROP/RHOP. A L P P , RHOG, R K G , T H G , TAULW, E P C , EPP COMMON/PSYC/TDP. T C , T P , RH.WA, WCSAT.WPSAT.WOUT, TIN C O M M O N / R A O I A N / P S I , R D E L C ( 1 2 ) , R L A T , R W I ( 2 4 ) , R B D N , R G A M ( 6 ) , R B E T A ( G) COMMON/ROCK/STCAP, FRATE, T I N I T , RHOR COMMON/SOI L V / T S ( 6 ) . T S O U T ( 1 2 ) . V M C . C 1 , C 2 . D I A . D P I P E , D I N S , V S E P , R A R E A . TRATE.DT,TF,LAYER,NL,NP C O M M O N / S O L A R / H B T . H O T . H P S , H B S . S C O , S C I , S P . SB COMMON/SUN/SR.SS. D A , WS, I R I S E . ISET COMMON/SYSTEM/INSN. ISTDEV C0MM0N/TRMT/TAUD2. ALPD2, TAUA, TAUB2, ALPB2 COMMON/VENT/NAE. NAEMAX COMMON/VIEW/F1P.FP1, F 3 P . F P 3 . FGP.FPG, F13.F31, F3G.FG3. ANGLE,RL,RN DIMENSION DBETA(S). DGAM(6) DIMENSION DELC(12), E ( 1 2 ) , DWI(24) DIMENSION SUNHR(12), BSUNHR(12), RH0(12) DIMENSION RHO1(12).RH07(12),RH13(12),RH19(12).VW(12) DIMENSION H I 1 2 . 2 4 ) . H D ( 1 2 . 2 4 ) , H B ( 1 2 . 2 4 ) . D(12), DBAR(12) DIMENSION F ( 6 ) . P ( 6 ) , REFLEC(6) DIMENSION SPN(10). WPN(10). FPN(10) LOGICAL INSN. ALIGN READ Group  15  70  16 C  INPUTS 1  inputs:  climatic  data  R E A D ( 3 , 18)1 RUN, NFM. NLM FORMAT(516) R E A D ( 3 . 16 ) D L A T READ(3.15) (DE L C ( I ) . 1 = 1 . 1 2 ) R E A D O . 15) ( E ( I ) . 1=1,12) READ(3,15) (RHO(I). I 12) R E A D O . 15 ) ( S U N H R ( I ) , 1.12) FORMAT)15F10.0) R E A D O . 18) IAVSOL IF ( I A V S O L EO. 2 ) G 0 T 0 IF ( I A V S O L .EO. 3 ) G 0 T 0 DO 7 0 1 = 1 , 12 READ ( 3 . 1 6 ) (H(I.J) J = 4.21 ) CONTINUE GOTO 6 R E A D O . 16) ( D B A R ( I ) . 1. 12) R E A D O . 16) (TMAX(I ) . 1. 1 2 ) R E A D O . 16) ( T M I N ( I ) . 1.12) R E A D O , 16) ( R H O K I ) . 1.12) R E A D O . 16) ( R H 0 7 I I ) . 1. 1 2 ) R E A D O . 16) ( R H 1 3 ( 1 ) , 1.12) R E A D O . 16) ( R H 1 9 ( I ) , 1.12) 1= READ* 3. 16) ( V W ( I ) . 12) FORMAT* 2 0 F 6 . 0 )  2  Group  inputs:  greenhouse  thermal  environment  parameters  READ(3,17)IN5N 17  FORMA T ( L 1 ) READ(3.18)  I5T0EV  READ(3.18)  NAEMAX  READ(3,  12)NS,  RLWR.  READ(3,12)NC. 12  FORMAT(16,  AP.  RKL, RI,  WH.  16 ) ( D B E T A ( I ) ,  R E A D O ,  16)RHOP,  R E A D O .  16)CW1.  1 = 1.  ALPP. CW2.  (ISTDEV  . E Q .  1(GOTO  1  (ISTDEV  . E O .  2)GOT0  2  inputs:  rockbed  16)STCAP.  FRATE.  38  inputs:  s o i l  12)NL.  R E A D O .  12)LAYER,  R E A D O ,  16)VMC.  R E A D O .  1G)THCRC.  R E A D O ,  16 )  (TS(I ) .  R E A D O ,  16)  (TSOUT(I).  Group  4  T F .  TINIT,  16)  DPIPE.  RKCRC. 1 =  RHOR  crop  TRANSM.  RHOCLD =  RHOA  growth RDO  O . 25 O. 6 1012.5 1 . 204 =  ALIGN  =  RDO  RDO  = 160  0 .TRUE. *  1.0-3  KL= 1 ,  FPN(KL)  =  O  WPN(KL)  =  O  5  CONTINUE  C Conversion  to  radians  C RLAT  =  01  =  DSIN(RLAT)  DLAT  •  02  =  DCOS(RLAT)  PI/180  RTILT1  =  TILT1  PI/180.  RTILT2  =  TILT2  PI/180.  90  1=1,12  RDELC(I  )  =  DINS  .  RAREA,  DELCCI)  RKP  f u n c t i o n  =  =  parameters  1=1.12)  =  ICALL  VSEP.  THPIPE.  PI=3.14159 RHOCLR  storage  1.6)  HSC=4.921  DO  parameters  C2  Constants  C  storage  DT DIA.  C I .  inputs:  R E A D O .  160  ALPB  thermal  thermal  R E A D O .  DO  SHADE  3  Group  CPA  TAULW.  CW3  IF  GOTO  RKG.  NS)  APFACT,  IF  REAO(3  TILT2 THG.  1= 1.NS)  READ(3.  3A  1,  RH03,  10FG.O)  READ(3,1G) (DGAM(I),  Group  TILT  RHO1.  PI/180.  parameters  TRATE  261  BSUNHR(I) 90  =  00  80  I  1.  =  RGAM(I)  =  RBETA(I) 80  SUNHR(11/30.  CONTINUE NS  DGAM(I) =  •  PI/180.  DBETA(I)  «  PI/180.  CONTINUE  C C  sum  up  hourly  global  solar  r a d i a t i o n  to  obtain  d a i l y  value  C IF  (IAVSOL  DO  40  D(I) 00  = SO  40  1)G0T0  83  12  0. J=4.  D(I) 50  .NE.  1=1.  =  2 1  D(I)  +  H(I.J)  CONTINUE CONTINUE  C 83  RKL2 NC2 NNC IF  =  RKL  =  NC  =  NC  (NC  *  *  0 5 0.5  .EO.  1)NC2  =  NC  GHW  =  DSORT(AP/RLWR)  GHL  =  AP/GHW  C IF(TILT1  EO.  90.JT21  =  1./DTAN(RTILT2)  IF(TILT2  .EO.  90.JT21  =  1./DTAN(RTILT1)  IF(TILT2  .NE.  90.)T21  =  BH  •  S1  =  S3  =  AC3  =  S1*GHL S3*GHL 0.  IF(INSN)AB AG  =  GVOL  1./DTAN(RTILT2)  BH/DSIN(RTILT2) »  =  •  BH/DSIN(RTILT1)  AC 1 AB  1./DTAN<RTILT1)  GHW/T21  BH =  =  AC3  *  GHW  (AG  +  *  0.5  WH'GHW)  •  GHL  C C  set  ALIGN  =  FALSE,  for  N-S  o r i e n t e d  gnhse  C IF  (DBETA(I)  GT.  80.)  ALIGN  =  FALSE.  C CALL  FDFSE  C C  Print  -  echoed  inputs  and  others  C IF IF  34 35 61 62 63 C 64 51  (ISTDEV (ISTDEV  EO. EO  1) 2)  WRITE(6.34) WRITE<6,35)  IRUN I RUN  FORMAT(/'RR'.15/) FORMAT(/'RS'.15/) WRITE(5.61)DLAT FORMAT(/'Latitude =', F10.2/) WRITE(5.62)(DGAM(I). 1=1. NS) FORMAT(/'Surface azimuth: ', WRITE(5.63)(0BETA(I). 1-1. NS) FORMAT(/'Surface  t i l t :  '.  10F10.0)  10F10.1/)  IF (1NSN) WR1TE15.64) RH03 F0RMAT(/'Insulated 3rd (North-facing) Surface. WRITE(5.51) F ORMA T ( / ' LWR GHL GHW BH WH  RHO  ='.F10.2/)  TILT1  TILT2  SHADE  NAEMAX'/)  262  WRITE(5.65)RLWR, 65  F0RMAT(8F7.2,  GHL,GHW,BH,WH,TILT1.TILT2.SHADE.  NAEMAX  17)  WRITE(5.52) 52  FORMAT(/'  AC1  AC3  AB  AP  F3P  FP3  A G ' / )  WRITE(5.66)AC1.AC3.AB.AP.AG 66  FORMAT(5F7.  1 )  WRITE(5.53) 53  FORMAT(/'  F1P  FP1  FGP  FPG  F13  F31  F3G  FG3' /)  WRITE(5,67)F1P.FP1,F3P,FP3,FGP,FPG,F13,F31,F3G,FG3 67  FORMAT(10F7.3)  C C  d i f f u s e  i r r a d i a n c e  transmittance  (angle  of  Incidence  =  60  deg)  C AINCD -AUD  =  P I / 3 .  =  TRANS(AINCD.  RKL. NC.  TAUD2  =  TRANS(AINCD.  ALPD2  =  1.  -  RI)  RKL, NC2,  RI)  TAUA  C C  OUTERMOST  DO-LOOP  (10)  FOR A L L MONTHS  (index  I)  C DO  10  IK  =  NFM.  NLM  IF  (IK  .GT.  12)  I  =  IK  IF  (IK  . L E . 12)  I  =  IK  ICAL  =  -  12  O  C C  r e a d  other  crop  parameters  from  month  to  month  C READ(3.16)B0WEN.  RK.  RLAI.  TAUC,  EFLITE  C CALL  RISET  CALL  SPLINE(RH01.  C RH07.  RH13.  RH19.  I)  C T1  = BSUNHR!I)/DA  C VW(I) HW  =  =  VW1I)  CW1  +  *  1 0 0 0 / 3 6 0 0 .  CW2  *  (VW(I)  CW3)  C WRITE(6.32)I WRITE(7.32)I WRITE(8.32)I 32  F O R M A T ( / 1 0 0 ! ' * ' ) /  'Month  ='.  15)  C TAUC  =  TAUC  EFLITE  =  DO  KA  170  SPN(KA) 170  *  1.D-3  EFLITE = =  *  1.D-3  1.5 0.  CONTINUE  C WRITE(5.58) 58  FORMAT!/' IF  (INSN)  WRITE(6.4 41  HR H P A R I N GOTO  TP  F  PG340  RC  PN220  PN250  PN280  PN310  PN340'/)  26  1)  FORMAT(/'HR  NAE  BOWEN  TCO  TCI  TP  RHIN  TIN  SP  TRPN  %SP  TPOUT  OTRAN  WRITE(7.43) 43  FORMAT!/' GOTO  HR  SCO  SCI  SP  HCA  HPA  TRPN  %SP  CONDS'/)  27  26  WRITEI6.42)  42  FORMAT ( / '  HR N A E  WRITE(7.44)  BOWEN  TCO  TCI  TP  TB  RHIN  TIN  SP  SB  TRPN  °/,SP  263  44  FORMAT(/'  HR  SCO  SCI  SP  SB  HCA  HPA  HBA  TRPN  %SP'/>  C 27  0 1 1 = 012  OCOS(WS)  =  OSIN(WS)  05  =  O S I M RDELC ( I ) )  OS  =  DCOS(RDELC(I))  IF  (IAVSOL  EO.  1)GOTO  8  C C  d a i l y  d i f f u s e  r a d i a t i o n  on  o u t s i d e  horizontal  surface  f o r  IAVSOL  .NE.  1  C T34  =  012  OHBAR IF  «  -  WS*Q11  24.*HSC*E(I)*Q2*06*T34/PI  (IAVSOL  EO. 3)DBAR(I)  RKT  =  T31  = 0.409  T32  = 0.6609  =  DHBAR  *  (O.18+0.62*T1)  DBAR(I)/DHBAR +  0.5016 -  •  0.4767  DSIN(WS *  -  DSIN(WS  P I / 3 . ) -  P I / 3 . )  C IF  (DLAT  CHI  =  CH2  =  9  CH1  9 0.958  3  CH2  =  0.982  DDBAR  =  (CH1 -  RA1  7  1.13  GOTO 7  . G T . 40.1G0T0 1.0  =  CH2*RKT)  *  DBAR(I)  DOBAR/DBAR(I)  C 8  THPS  »  THBS  = O.  O.  SUMHD  = O.  SUMQU  = O.  SUMQTD  -  O.  SUMOTN  =  0.  SUMNL  = O.  SUMDL  = O.  SUMPN  = O.  SUMOSP SUMQP  =  0.  = 0 .  C C  OUTER  DO LOOP  (20)  FOR HOURS  (index  d)  C IR1=IRISE IR24 DO  =  20  +  1  IRISE JA  IF  (JA  IF  (JA  =  +  24  IK1 .  . L E .  IR24  24)  G T . 24)  J J  = JA =  JA  -  D W I ( J ) = ( 1 2 - J ) * 1 5 . RWI(J)  =  OWIIJ)  *  07  =  DSIN(RWKJ))  08  =  DCOStRWI(J))  T33  =  HEXT  08 =  -  24 + 7 . 5  PI/180.  011  HSC *  Ed)*  06  *  02  *  T33  C SCO  *  0.  SCI  =  0.  HPS  = O.  HBS  *  0.  C  C  IF  (J  IF  (JA  GT  1RISE  .AND. J  G E . ISET1G0T0  25  L T . 1SET  .AND. H ( I . J )  . L E .0.01  . A N D . IAVSOL  EO.  1)GOTO  20  264  Compute  daytime  T18  =  T19  =  TOUT CALL  TMIN(I))  +  T19  =  d i f f u s e global  IAVSOL  HEATLD 1)GOTO  r a d i a t i o n r a d i a t i o n  .NE. =  H ( I , J )  =  (J  DDBAR HEXT  DSIN(T18/T20)  *  *  PI  IRISE  r a d i a t i o n  RHOCLR  '  T 1  RHOCLD  '  (1.-T1)  T4  =  RHO(I)  <  =  HPI/HEXT  T6  =  1  T7  =  21.303*(T5'*2)  T8  =  51  T9  =  5O.081  and  hence  method  * J  •  (T31 . L T .  +  T34) T32*Q8J/DHBAR  ISET  .AND.  H ( I . J )  .LE.  O.OOGOTO  horizontal  surface  (Hay's  method)  6688*T5 . 2 8 8 M T 5 " 3 ) *(T5•'4)  17.551*(T5**5) 0.9702 =  HPI  HO(I.J)  =  *  *  *  T6  -  T7  +  T8  -  T9  +  T10  T11  HDP I  (HD(I.J)  SUMHD  method,  Rabl's  (1.-T4)  =  =  Jordan's and  (T2+T3) •  H( I . J )  T5  T11  and  T33/(24.  on  =  HDP I  *  AND.  =  =  L i u  Col lares  DBAR(I)  T3  T10  81  -  T2  IF  model  82  d i f f u s e  HPI  Bellamy's  1  . G T .  GOTO  82  +  EO.  SUMDL  hourly  hourly  and  NTLOAO(JA)  (IAVSOL  IF  Kimball  IHRMIN)  •  TMIN(I)  HO(I.J)  81  (J  using  -  hourly for  c c c  *  TOUT  (TMAX(I) =  SUMDL IF  PI  hourly  *  H ( I . J )  -  HPI  . L T . O . ) H D ( I . J )  SUMHD  *  =  O.  HO(I.J)  C C  hourly  beam  r a d i a t i o n  on  horizontal  surface  C HB(I . J)=  H ( I . J )  I F ( H B ( I . J ) INNER  DO  LOOP  DO  30  K=1.  IF  ( N O T .  IF(K  (30)  HD(I,J) O.)HB(I.J)=0.  FOR  ALL CONTRIBUTING  SURFACES  (index  K)  NS (ALIGN)(GOTO  EO.  3  AND.  IF  (K  EO.  1)AREA  IF  (K  .EO.  IF  (K  .EO.  GOTO 84  -  L T .  84  INSN)GOTO =  AC 1  3)AREA  =  ACS  2  OR.  K  .EO  1  .OR.  K  30  4 ) AREA  = AG  89  IF  (K  EO.  IF  (K  .EO.  2)  AREA  IF  (K  . E O .  4)  AREA  03  =  DSIN(RBETA(K))  04  =  DCOS(RBETA(K ) )  09  =  .EO. AC 1 = AC3  3)  AREA  = AG  =  C 89  010 hourly  DSIN(RGAMIK)) =  DCOS(RGAM(K))  r a d i a t i o n  on  t i l t e d  surface  ( c a l c  RB  for  each  surface)  20  265  UP2t=((01*04)  -  (02*03*010))  •  UP22=((Q2'Q4)  +  (01*03*010))  *  UP23=Q6  *  03  *  RBUP  =  UP2 1  RBDN  =  (01*05)  RB  =  •  09  *  UP22 +  05 06  *  08  07 +  UP23  (02*06*08)  RBUP/RBDN  IF(RB  LT .  O.)RB  =  O.  C C  beam  r a d i a t i o n  C HBT  =  H B ( I . J )  •  RB  C C  sky  ( a n i s o t r o p i c  model),  and  ground  r e f l e c t e d  diffuse  r a d i a t i o n  C F A  =  1 .  F1  =  1.  +  F A * ( D S l N ( R B £ T A ( K ) / 2 . ) * * 3 )  ( H D ( I . J ) / H ( I , J ) ) * * 2  F2  =  1.  +  FA*(RBUP**2)*((1.  -  HST  =  0.5  '  HD(I.J)  DCOS(RBETA(K)))  HRT  =  0.5  *  H ( I . J )  HDT  =  HST  + HRT  * *  (1.  +  RHO(I)  *  RBDN**2)* * (1.  -  1.5) *  F1  *  F2  DC0S(RBETA(K)))  C C  Angle  of  incidence  for  beam  r a d i a t i o n  C AINCB TAUB  = =  DARCOS(RBUP) TRANS(AINCB.  RKL. NC.  TAUB2  •  TRANS(AINCB,  ALPB2  =  1 .  -  RI)  RKL. NC2,  RI )  TAUA  IF  (TAUB  IF  (TAUB2  . L T . 0.) . L T . O.)  TAUB  TAUB2  =  =  0. O.  IF  (ALPB2  L T . O.)  ALPB2  =  O.  C C  Total  (beam  & diffuse)  transmitted  i r r a d i a n c e  thru  surface  . L T . 0.001  . A N O . AINCB  . L T .  1.047)FRB  =  0.90  .AND.  . G E .  1.047)FRB  -  0.85  C FRB  =  1.  IF  (THG  IF  (THG . L T . 0.001  HTB  =  TAUB*HBT  HTD  =  (  *  TAUD'HDT  FRB +  *  AINCB  SHADE  TAUB*HBT*(1.-FRB)*TAUD  )  •  SHADE  (Plant  using  r e s u l t s  rad  reaching  C C C  Extend  onto  *FBEAM-  h o r i z o n t a l  and  *FDFSE *  ("/.BEAM  canopy)  and  C IF  (RB  IF  (RB  GOTO  GT.  O. )CALL  . L E . O.)G0T0  FBEAM 24  88  C C  SURFACE  NOTATION:  C C  1,3:  South  C  2.4:  East  and and  North West  faces faces  C 24  IF  (K  .NE.  3)  REFLEC(I)  =  IF  (K  . E O .  3)  REFLEC(1)  = RHO1  REFLEC(2) DO  110  P(II) 110  =  CONTINUE GOTO  29  =  11=1. O.  RHOP 4  surface  %0IFFUSE  RH03  solar  from It)  266  88  21  IF  ((ALIGN  .AND.  K.EQ.1)  .OR.  (.NOT.(ALIGN)  .AND.  K.E0.2))GOTO  21  IF  ((ALIGN  .AND.  K.EO.3)  .OR.  (.NOT.(ALIGN)  .AND.  K.E0.4))G0T0  22  IF  ((ALIGN  .AND.  (K.EO.2  .OR.  K.EO.4))  (.NOT.(ALIGN)  (P(M),  M M .  4)  M»1.  4)  F< 1 )  *  F(2)  =  F13  F(3)  =  F3P  P(1)  •  PIP  P(2)  =  P13  F1P  W R I T E ( 5 . 7 9 ) I . J , K , 79  F0RMAT(3I5. REFLEC(1) IF(  *  F(4)  «  F13  F(5)  -  F1P  F(6)  »  FP3  P(3)  =  P13  P(4)  =  P1P  REFLEC(2 ) 22  -  «  F(2)  »  F31  F(3)  *  FIP  1 )  GOTO  RHOP  P3P  •  P31  REFLEC(1) GOTO  =  RHOI  =  RH03  29  F ( 1 ) .=  FGP  F(2)  -  FG3  F(3)  -  F3P  P(  »  PGP  =•  PG3  1 )  P(2)  REFLEC( 1 )  W R I T E ( 5 . 7 9 ) I . J , K ,  (P(M),  IF(.NOT.(INSN))GOTO F(4)  =  FG3  F(5)  =  FGP  F(6)  «  FP3  P(3)  =  PG3  P(4)  -  PGP  REFLEC(2 ) GOTO 29  60  DO  »  RHOP  29  60  L  •  1,6 . L T .  O . ) P ( L )  =  IF(P(L)  .GT.  1.)P(L)  -  1.  IF(F(L)  . L T .  O. )F(L)  -  0.  O.  IF(F(L)  .GT.  1.)F(L)  -  1.  CONTINUE T15  =  HTB  *  P(1)  T16  -  HTD  *  F(1)  '  (HTB*P(2)  IF  ((INSN  .AND.  +  HT0*F(2))  K  .EO.  3)  »  F(3)  .OR.  •  REFLEC(1)  (.NOT.(INSN)))GOTO  T12  =  HTB  •  P(3)  T13  =  HTO  *  F(4)  T14  =  ( H T B « P ( 4 )  HBS  «  (T12  •  T13  •  T14)  «  AREA/AB  +  HBS  HPS  '  (T15  +  T16  +  T17)  •  AREA/AP  +  HPS  +  C CALL  SCOVER  C 30  29  IF(P(L)  T17  28  29  F3P  -  P(2)  23  RH03  29  F(1)  P(  10F7.2)  .NOT.(INSN))  GOTO  .OR.  CONTINUE  (AREA)  HTD* F(5))  •  F(6)  •  REFLEC(2)  28  .AND.  (K.EO.1  .OR.  K.EO.3)))GOTO  23  267  c SCO  3  SCI  SCO  +  SCI  +  '  RHOP-HPS*AP*FPC*TAUD2*ALPD2 RHOP*HPS*AP*FPC*ALPD2  SP  •  HPS  *  AP  *  ALPP  SB  «  HBS  •  AB  *  ALPB  IF  (SCO  . L T . O.  OR.  SCI  . L T . 0.  .OR.  SP  . L T . 0.)GOTO  C C  convert  [MJ/hr]  to  [W  d/s]  3  C SCO  •  SCI  1  SCO  *  1.06/3600.  SCI  *  1.D6/36O0.  SP  •  SP  SB  «  SB  *  1.06/3600.  *  1.D6/3600.  THPS  -  THPS  +  HPS  THBS  •  THBS  +  HBS  C CALL  NLE  SUMQTD SUMOSP SUMOP  »  SUMOTO  +  »  SUMOSP  +  SUMOP  3  +  OTRAN OSUP  OPASS  C CALL  PSRATE  C 00  150  KN  SPN(KN) 150  " 1 , 5 «  SPN(KN)  •  PN(KN)  CONTINUE GOTO  20  C C  C a l c u l a t i o n s  for  nite-tiroe  hours  only  C 25  CALL  NTLOAD  SUMNL TIN  -  •  (JA)  SUMNL  +  HEATLD  17.  IF  (ISTOEV  .EO.  2)CALL  LTSOIL  IF  (ISTOEV  EO.  D C A L L  LTROCK  SUMOTN  »  SUMQTN  +  DABS(OTRAN)  C 20  CONTINUE  C IF  (IAVSOL  .EO.  1)  THBAR  IF  (IAVSOL  .NE.  1)  THBAR  TCF  »  TCFB XI X2  •  THBS/THBAR  THPS  *  AP/SUMNL  •  AP/(SUMOL*SUMNL)  »  (SUMOP  FM2  »  SUMQTD/(SUMOSP  •  SUMQTD)/(SUMDL  (FM1  GT.  1.)FM1  »  IF  (FM2  . G T .  1.)FM2  »  IF  (FM1  L T .  IF  (FM2 3  O.)  . L T . 0.) SUMOL  +  FM1  SUMA  *  SUMC  3  SUMOSP  SUMD  3  FM2  *  FORMAT(15. FYUP1 FYUP2 FYDN1  3  • 3  •  SUMNL)  SUMNL) 1. 1.  FM1  =  0.  FM2  »  O.  SUMNL •  SUMNL  SUMC  WRITE(7.69)IRUN. 69  +  IF  SUMB  0(1) DBAR(I)  THPS  FM1  SUMA  •  THPS/THBAR •  3  3  X1.X2.FM1.FM2.  10F10.2)  FYUP1  *  FYUP2  •  SUMB SUMD  FYDN1  •  SUMA  SUMA.SUMB.SUMC.SUMD  20  FVDN2  =  FYDN2  +  SUMC  WRITEO.45) 45 33  FORMAT(/'monthly:  QU[MJ)  OTO[MJ]  QTN(MJ]  WRITEO,33)SUMQU.  SUMOTD.  SUMQTN.  SUMDL.  FORMAT(8X.  5F8.0.  ODL(MJ] SUMNL.  QNL[MJ]  D(I).  HBAR  TCF. TCFB.  TCF X I .  X2.  TCFB FM1.  XI  X2  FM1  FM2'/)  FM2  10FB.2)  C IF  (IAVSOL  NE  1)  W R I T E O . 77 ) D B A R ( I ),  IF  (IAVSOL  EO.  1)  W R I T E O , 77)D(  W R I T E O . 76)1 77  .  ( H D ( I . J ) .  I ) .  SUMHD.  OOBAR  SUMHO  J - 4 . 2 1 )  FORMAT(5F7.2)  76  FORMAT(13,  20F7.2)  C (I  GE.  140  KK =1.  WPN(KK)  •  140  CONTINUE  91  00  GOTO  WPN(KK)  SPN(KK)  KM>1. •  •  SPN(KM)  5  FPN(KM)  WRITEO.49)  49 78  FORMAT!/'monthly.  PN220  WRITEO.78)  K J - 1 .  (SPN(KJ).  F0RMAT(8X,  PN250  PN280  P N 3 IO  PN340'/)  5)  10F8.2)  CONTINUE FY 1  =  FYUP1/FYDN1  F Y2  *  FYUP2/FYDN2  WRITEO.31)FY1. 31  •  CONTINUE  93  10  91  GOTO 5  93  120  FPN(KM) 120  9)  IF 00  FY2  F 0 R M A T ( / 1 0 O ( ' * ' ) / / ' A n n u a l  solar  heating  fractions  " ' .  2F10.2)  W R I T E O . 5 6 ) 56  FORMAT(/100('*')/' WRITEO,71  7 1  FPN220  )(FPN( KK) ,  FPN250  K K » 1 , 5 ) .  FPN280  (WPN(KK).  FPN310  FPN340  WPN220  WPN250  WPN280  WPN310  WPN340'/)  KK»1,5)  F0RMAT(20F8.2)  C IF  (ISTDEV  1)G0T0  EO.  4  WRITEO.39)TRATE 39  FORMAT(/'tota1 GOTO  4  FRAP  mass  flow  r a t a  for  s o i l  storage  (kg/sj  rock  storage  [kg/s]  F10.2/)  85 •  FRATE  •  1000./(AP  WRITEO.38)FRATE. 38  F O R M A T ! / ' t o t a l  85  STOP  •  RHOA)  FRAP  mass  flow  rate  for  » ' .  F10.2,  '  or  [L/s.m2]  =  ' .  F6.1)  END C C  FUNCTION  SUBPROGRAM  'TRANS*  for  solar  r a d i a t i o n  transmittance  C FUNCTION  TRANS(X,  IMPLICIT  REAL*8(A-H,  RKL, NC,  C0MM0N/TRMT/TAUD2.  RI)  0-Z)  ALPD2,  TAUA.  TAUB2,  ALPB2  AREF=DARSIN(DSIN(X)/RI) DIFF = AREF-X ADD"= A R E F +X R H O P D » ( D S I N ( D I F F ) * * 2 ) / ( D S I N ( A D D ) * * 2 ) RHOPL*(DTAN(DlFF)**2)/(DTAN(ADD)* TAUR-0.5 &  *  *2)  ((1-RH0PD)/(1+(2*NC-1)*RH0P0)  +  (1-RH0PL)/(1*(2*NC-1)'RH0PL)) TAUA=DEXP(-RKL TRANS=TAUR*TAUA RETURN END  *  NC/DC0S(AREF))  0  0  269  c C C  10  30  50 99 C C C  C C C  C  SUBROUTINE 'SPLINE * t o f i t c u b i c  s p l i n e to RHOUT data(4 v a l u e s p e r day)  SUBROUTINE SPLINE(RH01, RH07, RH13, RH19, I) IMPLICIT REAL*8(A-H. 0-Z) COMMON/OATA/TOUT, RHT(24). VW. RHSET DIMENSION X ( 4 ) . Y ( 4 ) . DY(4). W(58). XX(24), YY(24), YY1(24), YY2(24) DIMENSION R H O K 1 5 ) . RH07(15). RH13(15). RH19(15) DO 10 J'1,4 X ( J ) « DFLOAT(J-1) * 6. • 1. DY(d) * 2. CONTINUE Y( 1 ) » R H O K I ) Y(2)=RH07(I) Y(3)»RH13(I) Y(4)»RHI9(I) S'O. CALL 0SPLFT(X,Y.0Y,S.4.W. g.99) DO 30 K«1,19 XX(K)»0FL0AT(K) CONTINUE CALL DSPLN(XX,YY,YY1.YY2, 19, S99) DO 50 L=1 , 19 RHT(L) => YY(L) CONTINUE RETURN END SUBROUTINE  *RISET* t o compute s u n r i s e  and sunset  hours  SUBROUTINE RISET IMPLICIT REAL *8(A-H, 0-2) COMMON/RAD IAN/PSI,RDELC(12),RLAT.RWI(24).RBDN.RGAM(6),RBETA(G) COMMON/SUN/SR.SS, DA, WS. IRISE. ISET COMMON/INOEX/I. d PI « 3.14159 WS » OARCOS(-DTAN(RLAT) • DTAN(RDELC(I))) DWS - WS • 180./PI DA » DWS * 2./15. SR - 12. - DWS/15. SS - SR + DA IRISE - DINT(SR + 0.5) ISET » DINT(SS + 0.5) RETURN END SUBROUTINE  'FBEAM* t o compute beam r a d i a t i o n  Interception  factors  SUBROUTINE FBEAM IMPLICIT REAL * 8(A-H, 0-Z) COMMON/BEAM/NS. K, PIP. P3P, PGP. P13. P31 . PG3 COMMON/GEOM/GHL.GHW.BH.WH. RTILT1.RTILT2.S1.S3 . GVOL COMMON/INDEX/I. d C0MM0N/L0GIC/F0R3. ALIGN COMMON/RADIAN/PSI,RDELC( 12) .RLAT , RWI (24),RBDN,RGAM(6),RBETA(6) LOGICAL F0R3. ALIGN PI =• 3 . 14 159 BH2 • BH • 0.5 ALPHA DARSIN(RBDN) 3  270  ALPHA2 F0R3  =  PI*0.5  =  -  ALPHA  FALSE.  C  c c  s o l a r  azimuth  angle  PSIUP  =  DSIN(ALPHA)  *  DSIN(RLAT)  PSIDN  =  OCOS(ALPHA)  *  DCOS(RLAT)  PSI  •  -  OSIN(RDELC(I))  DARCOS(PSIUP/PSIDN)  C  c c c  1  For  Surfaces  *1  and  #3.  use  f u n c t i o n  subprogram  *FB12*  Surfaces  #2  and  #4,  use  f u n c t i o n  subprogram  *FB34*  IF  ((ALIGN  .AND.  K . E 0 . 1 )  .OR.  (.NOT.(ALIGN)  .AND.  K.EQ.2))GOTO  1  IF  ((ALIGN  .AND.  K.EQ.3)  .OR.  (.NOT.(ALIGN)  .AND.  K.E0.4))GOTO  2  IF  ((ALIGN  AND.  (K.EQ.2  .OR.  K . E 0 . 4 ) )  (.NOT.(ALIGN)  P1P  «  F0R3 P13  FB12(GHW. •  BH.  K.  ALPHA)  GHW.  K,  ALPHA2)  .AND.  TRUE.  •  FB12(BH,  SUP 1  '  1.  SUP2  »  1.  IF  GHL.  .OR.  (P13  GHL.  -  PIP  -  P13  .GT.  SUP1)P13  »  DMIN1(SUP 1,SUP2)  RETURN 2  P3P  •  FB12(GHW.  P31  -  1.  IF  -  (P3P  GHL.  BH.  K.  ALPHA)  P3P  . L E .  O.)  P31  *  O.  RETURN 3  PGP  =  FOR3 PG3  FB34(GHW. »  '  FB34(BH2.  SUP 1  =  1 . -  SUP2  -  1 .  IF  GHL,  BH2,  K,  ALPHA)  GHL,  GHW,  K.  ALPHA2)  .TRUE.  (PG3  PGP -  PG3  GT.  SUP 1)PG3  «  DMIN1(SUP 1,SUP2)  RETURN END C C  FUNCTION  *FB12*  for  roof  C FUNCTION  FB12(A.  IMPLICIT  REAL*8(A-H,  LOGICAL  FOR3,  B,  C.  N,  ELEV)  O-Z)  ALIGN  COMMON/GEOM/GHL.GHW.BH.WH. COMMON/RADI AN/PS  RTILT1,RTILT2.S1.S3 ,  COMMON/LOGIC/FOR3,  ALIGN  C THETA EX  1  »  «  PSI  -  RGAM(N)  C/OTAN(ELEV)  CR1  •  DABSfEX  •  DSIN(THETA))  CR2  "  DABSfEX  •  DCOS(THETA))  W1  »  IF  (FOR3)  W1  AX  =  C/OTANIRTILT1) CR2  W1  +  =  A  IF(CR1  .GE.  B)GOTO  1  IF(CR1  . L T .  B)GOTO  2  IF(N  EO.  1)FB12  »  B/(2.*CR1)  1F(N  .EQ.  3)FB12  •  O.  RETURN 2 3  IF(AX  GT.  A)GOTO  3  IF(AX  . L E .  A)GOTO  4  IF(N T1  =  EQ.  3)G0T0  (A**2)  *  GVOL  I.RDELC(12).RLAT.RWI(24),RBDN.RGAM(6),RBETA(6)  CR1  1  (K.E0.1  .OR.  K.EQ.3)))GOTO  3  271  4 C C C  T2 = 2. • AX T3 = (A * B) - T1/T5 FB12 = T3/(B * AX) RETURN FB12 » 1. - CR1/(2.*B) RETURN END FUNCTION  »FB34» f o r g a b l e ends  FUNCTION FB34(A, B.C. N.ELEV) IMPLICIT REAL*8(A-H. O-Z) LOGICAL FOR3, ALIGN COMMON/GEOM/GHL.GHW.BH.WH, RTILT1,RTILT2.S1.S3. GVOL COMMON/RADI AN/PSI.RDELC(12).RLAT,RWI(24),RBDN,RGAM(6).RBETA(6) C0MM0N/L0GIC/F0R3. ALIGN C  1 2  3 5 7  C C C  THETA = PSI - RGAM(N) EX » C/DTAN1ELEV) CR1 = DABS(EX « DSIN(THETA)) CR2 - DABS(EX * DCOS(THETA)) W1 - C/DTAN(RTILT1) IF (F0R3) W1 = A AX = W1 + CR1 IF(CR2 .LT. B)GOTO 1 IF(CR2 GE. B)GOTO 7 IF(AX .GT. A)GOTO 2 IF(AX .LE. A)GOTO 3 IF(CR1 .LE. W1)FB34 » 1. - 0.5*CR1/A IF(CR1 .GE. A)FB34 « 0.5*A/CR1 IF(CR1 .GT. W1 .AND. CR1 .LT. A)GOTO 5 RETURN FB34 - 1. RETURN T1 = (CR1 - W1)*-*2 FB34 » i . - T1/(A«CR1) RETURN T1 » 0.5«(B**2)*DTAN(THETA) T2 * (A*B) - T1 FB34 « T2/(A*CR2) RETURN END SUBROUTINE  *FOFSE* t o compute d i f f u s e r a d i a t i o n view  factors  SUBROUTINE FDFSE IMPLICIT REAL*8(A-H, O-Z) COMMON/AREAS/AB. AP. AC 1, AC3, AG. APFACT COMMON/GEOM/GHL.GHW,BH,WH. RTILT 1 .RTILT2.S1.S3. GVOL COMMON/VIEW/F1P,FP1.F3P.FP3.FGP.FPG.F13.F31.F3G.FG3. ANGLE.RL.RN PI»3.14159 EPSLN " P I - (RTILT1 + RTILT2) FIP » F12(GHW. GHL,SI. RTILT1 ) FP1 * F I P • AC 1/AP F3P » F12(GHW. GHL. S3, RTILT2) FP3 = F3P • AC3/AP FPG =• ( 1 . - FF 1 - FP3) • 0.5 FGP * FPG * AP/AG F13 ' F12CS3. GHL, S I . EPSLN) F31 » F13 * AC1/AC3  272  F3G  =  FG3  =• F 3 G *  (1.  -  F31  -  F3P)  *  0.5  AC3/AG  RETURN ENO C C  FUNCTION  «F12*  c a l l e d  by  FDFSE  C FUNCTION  F12(A,  IMPLICIT  REAL*8(A-H.  B,  C .  EXTERNAL  G  PHI) 0-Z)  COMMON/VIEW/FIP,FP1,  F3P.FP3,  FGP.FPG,  F13.F31.  F3G.FG3,  ANGLE,RL.RN  C PI  =  3.14159  ANGLE  •  PHI  RL  •  C / B  RN  » A / B  RLS=RL»*2 RNS=RN'«2 T1  »  (RL -  T2  »  DATAN(T1)  T3  «  (RN -  T4  »  DATAN(T3)  • RLS  (0.5*PI  PHI)  T5 •• TG  =• R N •  RN«DCOS(PHI))/(RL«DSIN(PHI •  ))  RNS  RL*DCOS(PHI))/(RL«DSIN(PHI)) -  RL •  *  (RNS+RLS)  DSIN(PHI)  T7  •  -(T2+T4+T5+T6)  T8  -  RNS +  T9  »  RLS -  *  0SIN(2*PHI)  *  0.25  2*RN*RL"0C0S(PHI)  RLS*(T8+1)/((1+RLS)*T8)  T10  »  T11  »  T9  * • RLS  (1+RNS)"(1*RLS)/(T8+1)  T12  =  ( 1 ./OSIN(PHI  T13  «  T11  T14  -  DL0G(T13*T10)  T15  »  (1 + R N S ) / ( T 8 - M )  T16  -  T15  T17  '  RNS/T8  • *  ) )*«2  +  ( 1 ./DTAN(PHI))*«2  T12  * •  •  (DSIN(PHI)**2)  0.25  «  RNS •  (DCOS(PHI)«*2)  T18  -  T19  »  T20  -  DSORT(T8)  T21  -  RN *  DATAN(1./RN)  T22  -  RL -  RN-DCOS(PHI)  T23  •  DS0RT(1.  T24  =  DL0G(T17«T16)  *  (DSIN(PHI)**2)  0.25  DATAN(1./DSORT(T8)) «  +  T19 -  T20  RNS*(DSIN(PHI)••2))  OATAN(T22/T23)  T25  =  DATAN(RN*DCOS(PHI)/T23)  T26  »  T23  *  (T25  +  T27  -  0.5  *  RN •  DSIN(PHI)  T28  »  RL  AREA  »  »  •  =  AREA  F12  =  (T7  *  DSIN(2*PHI)  *  T26  DATAN(1./RL)  CADRE  T33  T24)  (G.  * +  O . .  R L . 0.OO0O1,  0.0001.  ERROR)  DCOS(PHI) T14  +  T18  +  T21  +  T27  +  T28  +  T33)/(PI*RL)  RETURN ENO C C  FUNCTION  * G * as  r e q u i r e d  by  «F12*  C FUNCTION IMPLICIT  G(X) REAL*8(A-H.  COMMON/VIEW/F1P,FP1,  0-Z) F3P.FP3,  »  DS0RT(1.  +  (X'*2)  T30  »  DATAN  •  DCOS(ANGLE)/T29)  T31  =  RN -  (X  X'DCOS(ANGLE)  •  FGP.FPG.  T29  F13.F31,  (DSIN(ANGLE)**2))  F3G.FG3.  ANGLE,RL.RN  273  T32  -  G  T29  =  DATAN •  (T31/T29)  (T32  •  T30)  RETURN END C C C  SUBROUTINE outer  *SCOVER»  and  inner  to  compute  absorbed  solar  rad  by  cover  surfaces  C SUBROUTINE IMPLICIT  SCOVER  (AREA)  REAL*8(A-H,  COMMON/AREAS/AB, COMMON/INDEX/1  O-Z)  AP,  ,  A C 1,  AC3,  COMMON/PROP/RHOP,  ALPP.  COMMON/SOLAR/HBT,  HOT, HPS,  COMMON/TRMT/TAUD2. Tl  •  AREA  *  HBT  *  ALPB2  »  AREA  •  HOT •  ALPD2  '  T1  +  T2  +  RHOG,  ALPD2.  T2 SCO  AG,  R K G . T H G , TAULW.  HBS.  TAUA,  •  AREA  *  HBT  •  TAUB2  *  ALPB2  T4  »  AREA  *  HOT *  TAUD2  »  ALPD2  •=  T3  •  T4  SCO.  SCI.  TAUB2.  E P C , EPP  SP.  SB  ALPB2  SCO  T3 SCI  APFACT  J  +  SCI  RETURN END C C  SUBROUTINE  C  *NLE•  to  solve  the  system  of  nonlinear  heat  and  equations  C SUBROUTINE  NLE  IMPLICIT  REAL*8(A-H,  EXTERNAL  FCN  COMMON/AREAS/AB.  O-Z)  AP.  A C 1,  AC3,  AG.  APFACT  COMMON/COVER/NNC COMMON/CONV/CW1  ,  CW2 ,  COMMON/OATA/TOUT. COMMON/ENV/  C L ,  CW3,  HW .  RHT(24),  H C A , H P A , HBA  VW.  RHSET  BOWEN  COMMON/INDEX/I,  J  COMMON/HEAT/TMAX(12),  TMIN(12).  HEATLD,  OSUP.  COMMON/OUT/RHINS.  TRPN.  TRSP.  SUMOU.  COMMON/PROP/RHOP,  ALPP.  RHOG.  R K G . T H G . TAULW,  COMMON/PSYC/TDP.  TC.TP,  RH.WA.  COMMON/SOLAR/HBT.  HOT. HPS.  COMMON/SUN/SR.SS.  DA.  COMMON/SYSTEM/INSN.  WS.  COMMON/VENT/NAE,  NAEMAX F(10),  X(10).  INSN.  NEWY,  IRISE.  SCO,  SCI,  ISET  ACCEST(IO)  NEWA,  NEWB  C C  I n i t i a l i z a t i o n  of  unknown  (X)  values  C IF  (INSN)  AC  IF  ('.NOT.  (INSN))AC  NAEMIN JM  >  IF  (J  IF  ( J  AC 1  L E . JM) .GT. =  BINCPT '  JM)  -  JN  «  JN  =  2.*(NAEMAX «  =  AC1  +  AC3  2  (IRISE+ISET)  SLOPE NAE  «  =  NAEMIN  -  OINT(SLOPE»JN  X( 1)  =  15.  X(2)  =  15.  0.5 J 24 -  -  J  NAEMIN)/(I  SET-IRISE)  (SLOPE•IRISE) +  BINCPT  OPASS  OTRAN.  +  0.5)  SP,  PN1  E P C . EPP  WCSAT.WPSAT.WOUT.  HBS,  ISTDEV  DIMENSION LOGICAL  TPOUT.  TIN SB  mass  balance  X(3)  =  X(4)  =  8000. 15.  X(5)  =  70.  X(6)  »  15.  X(7)  •  450.  X(8)  -  450.  X(9)  »  450.  ERR  ' 0 . 1  IF  (INSN)  N  IF  (  (INSN))  NOT.  MAX I T CL  '  -  =  6 N  =  5  50  O.10  C CALL  NDINVT  (N.  X,  F.  ACCEST.  MAX I T ,  ERR.  FCN.  &2)  C C  P r i n t  outputs  C IF  (.NOT.  SUMH TIN  = -  X(3) IF  22. «  GOTO  SUMQU  »  O.  HCA-AC  +  HBA*AB*2.  36O0.  *  1.D-6  O.(GOTO  1  DABS(X(3)) •  HEATLO  +  X(3)  9  OPASS QSUP  *  GT.  -  +  X(3)/SUMH  X(3)  OPASS  9  +  (X(3)  QSUP  1  (INSN))HBA  HPA'AP*2  =  HEATLD  =  O.  »  SUMQU  +  X(3)  TP  =  X(4)  IF  (ISTDEV  . E Q .  1)  GOTO  5  IF  (ISTOEV  . E Q .  2)  GOTO  6  RETURN C 5 6 B  CALL  LTROCK  GOTO  8  CALL  LTSOIL  IF  (INSN)  GOTO  3  W R I T E ( 6 . 10)vJ.  NAE.BOWEN.  WRITE(7.20)J.  SCO.  X ( l ) . X ( 2 ) .  SCI.  SP.  X(4),  HCA. HPA,  X(5).  TRPN.  TIN.  SP.  TRPN.  ,  TPOUT,  QTRAN.  X(3)  TRSP  RETURN 3  WRITE(6.50)J.  NAE.BOWEN.  WR1TE(7.30)J.  SCO.  X ( 1 ) . X ( 2 ) .  SCI.  SP,  20  FORMAT(13.  3F7.0.  10F7.2)  30  FORMA T ( I 3 .  4F7.0.  10F7.2)  10  FORMAT(2I3.  GF7.1,  F7.0,  50  F0RMAT(2I3,  7F7.1.  2F7.0.  2  RETURN  SB.  X(4),  HCA. HPA.  2F7.2.  X(6). HBA,  X(5). TRPN,  TIN,  SP.  TRPN.  TRSP.  TPOUT.  OTRAN.  X(3)  TRSP  3F7.1)  2F7.2.  3F7.1)  ENO C C  SUBROUTINE  *FCN*  c a l l e d  by  *NLE*  for  e v a l u a t i o n  of  X's  and  F's  C SUBROUTINE IMPLICIT  FCN(X.  F)  REAL*8(A-H.  COMMON/AIR/CPA, COMMON/AREAS/AB. COMMON/BEAM/NS,  0-Z)  RHOA. AP. K,  FRMASS A C 1.  PIP.  ACS.  P3P,  AG.  PGP.  APFACT P13,  P31.  COMMON/COVER/NNC C0MM0N/C0NV/CW1. COMMON/DATA/TOUT, COMMON/ENV/  C L ,  CW2.  CW3.  RHT(24), BOWEN  HW, VW,  H C A . H P A . HBA RHSET  PG3  to -O  275  COMMON/GEOM/GHL.GHW,BH,WH, COMMON/INDEX/I.  RTILT1.RTILT2,S1.S3,  COMMON/OUT/RHINS.  TRPN.  TRSP,  SUMQU.  COMMON/PROP/RHOP.  ALPP.  RHOG.  R K G , T H G . TAULW.  COMMON/PSYC/TDP.  T C . T P .  COMMON/SOLAR/HBT. COMMON/VENT/NAE.  TPOUT.  QTRAN.  WCSAT,WPSAT,WOUT.  HBS.  SCO.  SCI.  PN1  EPC. EPP  SP.  TIN  SB  ISTDEV  NAEMAX  COMMON/VIEW/F1P.FP1, LOGICAL  RH.WA.  HOT. HPS.  COMMON/SYSTEM/INSN.  DIMENSION  GVOL  J  X(10).  F3P.FP3,  FGP.FPG.  F13.F31.  F3G.FG3.  ANGLE.RL,RN  F(IO)  INSN  C IF  (INSN)  AC  IF  (.NOT.  (INSN))AC  EPB  -  EPC  -  EPP  »  UB  O  -  AC 1 »  AC1  +  AC3  91  0.95 0 9 5  •  0.6  RLEWIS  *  RHOV  RHOA  «  RLATNT  0.89  *  •  GVOL  2.450+6  TC  -  X(2)  TP  =  X(4)  RH  •=  X(5)  TB  =  X(6)  RUB  *  RJP  •=  X(7) X(8)  RJC  =  X(9)  T28  '  0.  C CALL  PSY1  C C  C o n v e c t i v e  heat  t r a n s f e r  c o e f f i c i e n t s  C CALL  FORCE(HFPA,  HCA  -  1.52  HPA  *  1.9  IF(  NOT.  HBA  =  » *  HFCA. -  X(2))  **  (DABS(X(4)-22. ) / C L )  (INSN))G0T0  1.52  AC)  DABS(22.  *  0.333 * •  +  0.25  HFCA •  HFPA  2  0ABS(22.  -  X ( 6 ) ) * ' 0 . 3 3 3  +  HFPA  C C  Cover  outside  surface  temperature,  »  -  X(1)  C 2  T1  •  SCO  T2  "  HW *  IF  (NNC  . E O .  1)  RHCHR  *  O.  IF  (NNC  .EO.  2)  RHCHR  »  0.16666667  RST T3  = »  T51 F(  (TOUT  NNC'THG/RKG AC  « 1 )  AC  *  (X(2)  SKYRAD *  T1  •  +  +  RHCHR  X(1))/RST  (TCO, T2  X(1))  EPC. AC)  T3  +  T51  C C  Cover  Inside  surface  temp,  X(2)  C T4  =  SCI  T5  «  HCA •  T6  *  -T3  AC  *  (22.  -  X(2))  C CALL  PSY2  T7  RLATNT  C =  •  HCA  *  AC  »  ( R L E W I S • » 0 . 6 7 )  •  (WA  -  WCSAT)/CPA  276  IF  (X(2)  GT.  T22  =  IF(  NOT.  TOP  THRAD(TC.  F(2)  =  .OR.  R J C ,  (INSN))T22  T4  +  T5  +  T6  T7  . L T . 0.1T7  *  O.  AC. EPC) =  0.  +  T7  •  T22  C C  Useful  heat  g a i n  (greenhouse (X(2)  a i r ) ,  X(3)  C  1  T8  =  HCA »  AC  *  T9  *  HPA  AP  *  IF  (.NOT.  •  =  HBA  T12  •  RHOV =•  •  T8  AE *  +  •  T9  •  +  22.)  *  2.  1  (X(6)  CPA  22.) -  (INSN)(GOTO  T28 F(3)  -  (X(4)  - 2 2 . )  NAE • T28  +  (TOUT T12  *  2.  -  22.)/3600.  -  X(3)  *  0.5  C C  Plant  canopy  temp.  X(4)  C T13  =  SP  T14  =•  T9  =  DABS(T14/B0WEN)  T15 IF  (WPSAT  TAU IF  -  . L T . WA)  (T7  . L T . O.)  T20  =  SKYRAD(TP,  T23  *  THRA0(TP,  IF(.NOT. T21  «  F(4)  T15  =  O.  TAULW  +  T13  TAULW  EPP. RJP.  (INSN))T23  T20 «  TAU -  AP) AP,  =  * TAU EPP)  0.  T23 -  T14  -  T15  +  T21  C C  Greenhouse  r e l a t i v e  humidity.  X(5)  C T16  »  T15/RLATNT  T17  =  T7/RLATNT  T18  =  F(5)  RHOV  *  NAE  •  (WA  T16  -  T17  -  T18  »  -  W0UT)/36OO.  C C C  Convert  T r a n s p i r a t i o n  condensation  in  from  kg/sec  to  mm/hr:  a l s o  c a l c u l a t e  kg/sec  C CONOS TRPN IF  ' •  T17 T1G  (T13  TRSP  •  3600./AP  EO.  =  O  )G0T0  5  T15/T13  C 5  IF(.NOT.  ( I N S N ) ) R E TURN  C C  Absorber  p l a t e  temp.  X(6)  C T24  =  SB  T25  =  THRAD(TB.  T26  =  HBA  T27  •  UB  F(6)  =  RJB.  ' A C *  AB  T24  +  *  T25  AB.  (22.  -  (TOUT  -  +  T26  EPB) X(6))  *  2.  X(6)) •  T27  C C  R a d i o s l t y .  X(7).  X(8).  X(9)  for  surfaces  ( q . p . c i . )  C F(7)  «  X(7)  -  T25/AB  -  F3P'X(8)  -  F(8)  -  X(8)  -  T21/AP  -  FP1*X(9)  -  FP3«X(7)  F(9)  -  X(9)  -  T22/AB  -  F 1 3 » X ( 7 )  -  F31*X(8)  RETURN  F31*X(9)  or  ( 3 , 2 , 1 )  277  END C C  FUNCTION  SUBPROGRAMS  f o r  psychrometr1cs  C FUNCTION  PRESS(T)  IMPLICIT  2  REAL'8(A-H.  (T  OR.  T  IF  (T  . L E . 273.)  GOTO  1  IF  (T  . G T . 273.)  GOTO  2  T1  GT.  =  373.  0-Z)  IF  T2  = =  1.1655E-5  T4  =  1.281E-8  T5  *  2.1E-11  T6  »  12.151  =  173.)  RETURN  -7511.52/T  T3  V  . L T.  0.024  T1  PRESS  •  «  T * * •  (T  *  ** • *  **  2) 3)  4)  DLOG(T)  89.631  •  {T (T  *  T2  -  T3  -  T4  •  T5  -  T6  DEXP(Y)  RETURN 1  T1  »  T2  »  Y  =  -6238.64/T 0.3444  »  24.278  PRESS  -  +  DLOG(T) T1  -  T2  DEXP(Y)  RETURN END C FUNCTION  HUMIO(PS)  IMPLICIT  REAL*8(A-H.  HUMID  »  0.622  *  0-Z)  PS/(101.3  -  PS)  RETURN END C FUNCTION  ENTLPY(T.W)  IMPLICIT  REAL * 8 ( A - H .  ENTLPY  1.006*T  »  •  0-Z)  W*(2501.  +  1.775*T).  RETURN END C FUNCTION  PVAP(W)  IMPLICIT  REAL*8(A-H.  PVAP  =  101.3/(1.  •  0-Z) 0.622/W)  RETURN ENO C C  SUBROUTINE  »PSY2*  to  compute  WCSAT.  WPSAT,  WOUT.  TOP  C SUBROUTINE IMPLICIT  PSY2  REAL*8(A-H.  COMMON/DATA/TOUT. COMMON/INDEX/I,  0-Z)  RHT(24),  COMMON/PSYC/TDP.  TC.TP.  IF  =  (J  . G T .  RHOUT  «  TPK  -  TP  TCK  «  TC +  TUK  »  TOUT  PPSAT  19)  J  19  RHT(J) +  273. 273. •  VW.  RHSET  J  273.  •  PRESS(TPK) PRESS(TCK)  PCSAT  -  PUSAT  •  WPSAT  •  HUMID(PPSAT)  WCSAT  »  HUMIO(PCSAT)  PRESS(TUK)  RH,WA.  WCSAT.WPSAT.WOUT.  TIN  278  PVOUT WOUr  =  RHOUT  =  '  PUSAT/100.  HUMID(PVOUT)  RETURN END C C  SUBROUTINE  *PSY1 *  to  compute  psychrometr1cs  f o r  greenhouse  a i r  C SUBROUTINE IMPLICIT  PSY 1  REAL*8(A-H.  COMMON/DATA/TOUT, COMMON/PSYC/TDP.  1  TINK  *  PSAT  =  O - Z )  RHT(24), T C . T P ,  VW,  RH.WA,  RHSET WCSAT,WPSAT.WOUT,  TIN  295. PRESS(TINK)  IF  (RH  PV  =  . G T . 100.)  RH»100.  RH*PSAT/1O0.  IF  (PV  IF  (TINK  . LE .  . G T . 273.)TDP  •  G.983  +  14.38•DLOG(PV)  +  1 .079*(DLOG(PV)**2)  IF  (TINK  . L E . 273.)TDP  "  5.994  +  12.41*OLOG(PV)  +  O. 4273*(DLOG(PV)*«2)  WA  «  HUMID  0.)GOTO  1  (PV)  RETURN END  C C  FUNCTION  C  a  *SKYRAD*  component  to  s u r f a c e  compute and  thermal  r a d i a t i o n  exchange  between  sky  C FUNCTION  SKYRAD  IMPLICIT  REAL*8(A-H,  (T.  COMMON/DATA/TOUT. COMMON/BEAM/NS.  EMIS.  AREA)  O - Z )  RHT(24),  K.  P1P.  VW,  P3P.  C O M M O N / G E O M / G H L , GHW. B H , WH, COMMON/VIEW/F1P.FP1. BOLTZ FCS  =  -  TSKY  1  •  P31.  PG3  I L T 1 . RT I L T 2 . S 1 . S 3 .  F3P.FP3,  DC0S(RTILT1))  0.0552  IF  (TSKY  T1  •  AREA  T2  =  (1.  SKYRAD  R  FGP.FPG.  F13.F31,  GVOL F3G.FG3.  ANGLE.RL.RN  5.6697D-8  (1. «  RHSET  PGP. P13.  *  . L T . O. -  *  0.5  (T0UT+273.) .OR.  BOLTZ  •  T  **  1.5  . L T . -273.)G0T0  ((TSKY**4.)  EMIS)/EMIS  +  -  1  ( T + 2 7 3 . ) « * 4 . )  1./FCS  » T 1 / T 2  RETURN  END C C  FUNCTION  *THRAD*  to  compute  thermal  r a d i a t i o n  exchange  among  s u r f a c e s  C FUNCTION  THRADfT.  IMPLICIT  REAL*8(A-H,  BOLTZ  »  A,  E)  O - Z )  5.6697D-8  TK  «  T  +  273.  T1  -  A  •  E  T2  =  1.  THRAD  R.  -  *  (R  -  B0LTZ*(TK**4))  E  = T 1 / T 2  RETURN END C C  SUBROUTINE  'FORCE*  to  compute  FORCE  ( F P .  the  component  of  HCA/HPA  C SUBROUTINE IMPLICIT  REAL*8(A-H.  COMMON/AREAS/AB, COMMON/BEAM/NS. COMMON/ENV/  AP, K.  F C . AC)  O - Z ) A C 1,  P1P,  C L . BOWEN  A C 3 , A G , APFACT  P3P.  PGP. P13.  P31.  PG3  due  to  f o r c e d  convection  279  COMMON/GEOM/GHL.GHW,BH,WH. COMMON/VENT/NAE. PLNTHT AFR  =  GVOL  1.5  * A C / 3 .  IF  (NAE  UM  '  UP  RTILT1,RTILT2,S1,S3,  NAEMAX  K  . L T .  '  1  NAE/(AFR  1)NAE  *  GVOL  *  UM *  (PLNTHT ' A P / G V O D * *  3600.)  FC  =  5.2  *  0S0RT(UM/S1)  FP  =  5.2  *  OSORT(UP/CL)  (0.6667)  RETURN END C C  SUBROUTINE  *PSRATE*  to  compute  net  photosynthetic  r a t e  for  tomato  plants  C SUBROUTINE IMPLICIT  PSRATE REAL*8(A-H,  0-Z)  COMMON/GROWTH/RK, R L A I , T A U C , E F L I T E , T R A N S M , R D O . COMMON/INDEX/I, COMMON/OUT/RHINS.  TRPN,  COMMON/PSYC/TDP,  TR  0  •= »  «  HPS  •  1.D6  . L T .  IF  (HPARIN  IF T2  HBS.  SCO.  SCI,  »  SP.  PN1  TIN SB  0.45/36OO.  125.)  EFF »  1.OO  G E .  125.  .AND.  TP  . G T .  (HPARIN  G E .  125.  AND.  TP  . L E . 26.)  «  *  EFLITE -  -  RK  OEXP(-RK T2  «  *  *  •  26.)  EFF-1.25 EFF«1.25  -  O.0O7*((TP-26.)**2)  HPARIN  RLAI)  T i l  RDO *  (1.  -  T11)/RK  T8  «  (TP  -  TR)/10.  RC  •  RD1  •  (0  DO  10  I d » 1 .  T8)  5  CD(Id)  '  220.  CD(Id)  -  CD(Id) •  +  (Id *  T1  -  TAUC  T3  =  (1.-TRANSM)  T5  •  -  1)*30.  1.83  CO(Id)/RK *  TAUC  *  CD(Id)  (T2+T3)/(T4+T3)  T6  •  DL0G(T5)  PG  =  T1  PN(Id) IF  QTRAN.  20.  (HPARIN  ROI  « •  T6 PG  (PN(Id)  * -  EFF RC  . L T . 0.)  PN(Id)  =  O.  CONTINUE WRITE(5.11)d.  11  HOT, HPS.  TPOUT,  WCSAT.WPSAT.WOUT.  CD(10)  IF  T11  10  SUMQU.  RH.WA.  2.  HPARIN  T4  TRSP,  TC,TP,  COMMON/SOLAR/HBT. DIMENSION  PN(10)  J  FORMA T( 1 7 ,  HPARIN,  F 7 . 0 .  TP,  F 7 . 1 .  EFF.PG,  RC,  F7.2,  10F7.3)  compute  amount  (PN(K),  K - 1 . 5 )  RETURN ENO C C C  SUBROUTINE to  s o i l  *LTSOIL* (daytime)  to and  recovered  from  of  heat  s o i l  t r a n s f e r r e d  (nighttime)  C SUBROUTINE IMPLICIT  LTSOIL REAL*8(A-H,  COMMON/AIR/CPA. COMMON/AREAS/AB. COMMON/BEAM/NS.  0-Z)  RHOA. AP. K,  FRMASS A C 1,  P1P.  COMMON/GEOM/GHL,GHW.BH.WH. COMMON/INDEX/I.J  AC3.  P3P,  AG.  PGP.  APFACT P13,  P31.  PG3  RTILT1.RTILT2.S1.S3.  GVOL  280  COMMON/MAT/THCRC,  RKCRC.  COMMON/OCCUR/ICALL. COMMON/OUT/RHINS. COMMON/PAR/FUW,  TRPN,  THPIPE  TRSP.  HP, UP.  COMMON/PSYC/TDP, COMMON/RAD1  RKP,  ICAL U l .  T C . T P .  SUMOU.  TPOUT,  OTRAN,  PN1  BII  RH.WA,  W C S A T . W P S A T , WOUT .  TIN  AN/PSI,RDELC(12),RLAT,RWI(24).RBDN,RGAM(G),RBETA(6)  COMMON/SOILV/TS(6).TSOUT(12).VMC.C1,C2.DIA,DPIPE.DINS,VSEP.RAREA, COMMON/SUN/SR  SS.  D A . WS.  IRISE.  TRATE,DT.TF.LAYER.NL.NP  ISET  COMMON/TEMP/T(100.350) DIMENSION  T K 1 0 0 . 3 5 0 ) ,  DIMENSION  MP(5).MPP(5),MPM(5), LC(20).LCP(20),LCM(20)  IF  ( ( d  . L E . IRISE  TPOUT  =  OTRAN  «  N0DE(20)  .OR. J  . G E . ISET)  .OR.  TIN  . G T . 22.)  GOTO  99. O.  RETURN 5  NF  =• N L  IF  (ICALL  -  15 . N E . 0)GOTO  4  C C  c a l c u l a t e  Cs  [ d / m * « 3  C]  and  ks  [W/m C j  C CS  »  (0.315  RKS  =  RKW  » RKS  RKO PI  -  +  C1*VMC  VMC) • +  4.18  •  1.D6  C2  RKS 3.14159  C C  c a l c u l a t e  the  number  C  f o r  g i v e n  ' t o ' a l  C  a n d  greenhouse  of  pipe  pipes  (total  a r e a - t o - f l o o r  length-to-width  2  layers)  area'  r e q u i r e d ,  r a t i o ,  r a t i o  C APIPE NP  «  *  PI  *  DIA  DINT(RAREA  FRMASS  »  NPHALF  *  HSEP  (GHW -  RSP  » -  • GHL •  AP/APIPE)/LAYER  TRATE/(NP*LAYER) NP  *  0.5 NP*DIA)/(NP-1)  HSEP/DIA  C C  C a l c u l a t e  thermal  d l f f u s l v l t y  and  C DX«DIA  •  0.5  IX  »  DINT(HSEP/DX  +  IY  -  DINT((VSEP  0IA)/DX  IDP  =  INSD  +  0.5)  DINT(0INS/DX  •  0.5)  =  •  30  INSD  K I - 1,  MP(KI)  »  +  •  O S )  1  LAYER  IDP •  (KI-1)*(lY+2)  MPP(KI)*MP(KI) MPM(KI)»MP(KI) 30  0.5)  DINT(DPIPE/DX  INSDP1 DO  -  + 1 -  1  CONTINUE ALPHAW«RKW/CS ALPHAD*RKD/CS FUW«ALPHAW«DT/(DX«*2) FU0-ALPHAD*DT/(0X««2)  C CALL XNTU  TXPIPE -  (UP*APIPE)/(FRMASS*CPA)  BIP=UP*DX/RKW C HI  - 6 . 1 3  F o u r i e r  number  floor  area,  5  281  UI  -  1 / ( 1 . / H I  +  THCRC/RKCRC)  BII=UI*DX/RKW C C  E s t a b l i s h  C  an  s t a b i l i t y  error  message  c r i t e r i a .  w i l l  be  If  any  of  p r i n t e d  and  program  them  1s  v i o l a t e d  w i l l  exit  C CR1  •=  FUW  •  (2  •  BI I )  CR2  *  FUW  *  (2.  .  •  BIP)  CR3  =  FUW  *  (3.  +  BIP)  CR4  =  FUW  CR5  •  3.*FUW  +  FUD  IF(CR1  .GT.  0.5)CAIL  ERROR  (1.CR1,  &2)  IF(CR2  .GT.  0.5)CALL  ERROR  (2.CR2,  » 2 )  IF(CR3  .GT.  0.75)CALL  ERR0R(3,CR3,  42)  IF(CR4  .GT.  0.25)CALL  ERR0R(4,CR4.  82)  IF(CR5  .GT.  1.0)CALL  ERROR  (5.CR5.  42)  WRITE(5,33)CR1.CR2.CR3.CR4,CR5 33  F O R M A T ( ' s t a b 111ty  c r i t e r i a .  CR1  to  CR5  » ' .  5 F 7 . 2 / )  C C  C a l c u l a t e  C  and  Y  C  i n s i g n i f i c a n t  take  3  as  a  f u n c t i o n  times  damping  ( l e s s  than  of  damping  depth  as  5%)  a l s o  ;  depth  where  based  on  d a i l y  p e r t u r b a t t o n  c a l c  NX.  NY  c y c l e  1s  etc.  C DAMP DAM  » «  DSQRT(2.  *  ALPHAW/7.30-5) VSEP*(LAYER-1)  3.'DAMP  Y  »  DAM  •  DPIPE  +  X  »  GHW  •  0.5  DAM  INX  •  +  0INT(DAM/DX  INXM1  »  INX  -  •  0.5)  »  DINT  (GHW/(DX'2)  NY  •  DINT  ((Y/DX)  NXM1  »  NX  -  1  »  NY  -  1  NM  (NX  •  -  OX  1  NX  NYM1  +  INX)  +  •  +  0.5)  0.5)  +  +  INX  +  1  1  0.5  C WRITE(5.55) 55  FORMAT ( / '  X  Y  DINS  W R I T E O . 3 5 ) X , Y . D I N S . D I A , D P I P E ,  VSEP.  DIA  DPIPE  HSEP.  FRMASS.  VSEP XNTU.  HSEP  FRMASS  XNTU  RAREA'  /)  RAREA  W R I T E O . 5 6 ) 56  F0RMAT(/'  VMC  WRITEO.36)VMC.  RKW.  KW RKO,  CS.  KO ALPHAW.  CS  ALPHAD.  FUW.  ALPHAW  ALPHAD  FUD  W R I T E O . 5 7 ) 57  F0RMAT(/'NX(*N00ES)  NY(#N0DES)'/)  WRITEO.37)NX.NY W R I T E O . 5 2 ) 52  F0RMAT(/'  NP/LAYER  W R I T E O , 3 7 )  NP.  37  F0RMATOI10)  36  FORMAT(F10.1,  35  NPHALF  NPHALF,  2F10.3,  LAYER'/)  LAYER  3E10.2,  2F10.3)  FORMAT(10F8.2)  C C  A f t e r  C  h o u r ' s  ther  1st  f i n a l  hour,  i n i t i a l  computed  T's  at  s o i l  temperatures  time  •  TF  (hence  Just s k i p  equal  C DO  10  M=1.NY  YO  -  DO  M*DX  20  N-1.NX  IF  (M  IF  (YD  . L T . .GE  INSD 0.  IF  (YD  .GT.  0.05  .AND.  N  AND. AND.  . L T . YO  INX)G0T0  20  . L E . 0.05)T(M,N) YD  L E .  *  0.15)T(M.N)  TS(1) «  last  I n i t i a l i z a t i o n )  TS(2)  FUW  FUD'  /)  282  20  IF  (YD  . GT .  0.  15  .AND.  YD  L E .  0.35)T(M,N)  =  TS(3)  IF  (YD  .GT .  0. 35  .AND.  YD  . L E .  0.75)T(M,N)  »  TS(4)  IF  (YD  . GT.  YD  . L E .  1.25)T(M.N)  '  TS(5)  IF  (YD  . GT.  .AND. 0. 75 1 . 25)T(M.N)  '  TS(6)  CONTINUE  IO  c  CONTINUE  4  TPIPE  «  TIN  STORE=0. TIME'O. 99  CONTINUE TRANS 1  -  O.  TRANS3  -  0.  C C  Compute  nodal  temperatures  at  t i m e » t + d t  (through  v a r i a b l e  FUW)  C 00  GO M » 1 .  DO  NY  70  N= 1 ,  N>:  IF(M  . E O .  1)G0T0  IF(M  .GT.  1  IF(M  . G T .  INSD  IF(M  . E O .  NY JGOTO  81  AND.  M  . L E .  AND.  M  INSD)G0T0  84  . L T . NY)GOT0  87  89  C C  s u r f a c e  nodes,  f a c i n g  greenhouse  (M»1)  C 81  IF  (N  L T .  INX)GOT0  93  IF  (N  . E O .  INX)GOTO  82  IF  (N  .EO.  NXJGOTO  T K M . N ) GOTO  =  83  SURF( 1 . 0 .  1 .2.  T I N . B I I . FUW. M . N)  70  C C  s u r f a c e  ( l e f t  and  right  corner  nodes)  C 82  T K M . N ) GOTO  83  »  SURF(0.0.2.2.  T I N . B 1 1 , FUW . M . N )  =  SURF(2.0,0.2.  T I N . BI I . FUW, M . N )  70  T K M . N ) GOTO  70  C C  I n t e r i o r  nodes  (M  •  2  TO M -  INSD)  C 84  IF(M  . L T .  INSD  .AND.  N.LT.INX)GOT0  93  IF(M  . E O .  INSD  AND.  N.LT.INX)GOT0  88  IF(N  . E O .  INX)GOTO  IF(N  . E O .  T K M . N ) GOTO 93  8G  SOIL( 1 . 1 . 1 . 1 .  FUW,M.N)  70  T K M . N GOTO  NX)GOTO -  85  )=-0. 70  C C  i n s u l a t i o n  boundary  nodes  (AT  N=INX,  M-1  TO M=INSD:  and  N=1.  C 85  TI(M.N)  -  IF(M  . E O .  GOTO  70  S O I L ( 0 . 1 . 2 . 1 . INSD)TI(M.N)  FUW,M.N) •  S O I L ( 1 . 1 . 1 . 1 .  FUW.M.N)  C C  symmetry  boundary  nodes  (AT  N=NX,  M«1  C 86  T K M . N ) GOTO  C  70  =  S0IL(2.  1.0,  1.  FUW,M.N)  TO M=NY,  dT/dx  =  O)  M-INSD  T O M=NY:  dT/dx  =  O)  283  c  c  i n t e r i o r  87  nodes  (M  =  INSD  IF(N  .EO.  1)GOTO  IF(N  .EO.  NXJGOTO  T K M . N ) GOTO  =  TO  M  =  NYM1)  85 86  SOIL( 1 . 1 . 1 . 1 .  FUW.M.N)  70  C C  boundary  c  nodes  T K M . N )  88  »  IF(N  .EO.  GOTO  70  (AT  M =  INSD,  SOILA( 1 ,0, 1)  N=1  1 . 1 .  TI(M.N)  =  TO  N-INX)  FUW.FUD.M.N)  S0ILA(O.0.2.1.  FUW.FUD.M.N)  C C  bottom  boundary  nodes  (dT/dy  M=NY)  C 89  IF(N  .EO.  1)GOTO  IF(N  .EO.  NX)GOTO  T K M . N ) GOTO  '  91 92  SOIL( 1 .2.  1.0.  FUW.M.N)  70  C  c c  "bottom  91  ( l e f t  T K M . N ) GOTO GOTO  70 60 C C  right  corner  nodes)  => S U I U 0 . 2 . 2 . 0 .  FUW.M.N)  -  FUW,M.N)  70  TI(M.N)  92  and  S0IL(2,2.0.0.  70  CONTINUE CONTINUE Modify  T1(M,N)  for  nodes  adjacent  to  Pipes  C NI»2+INX DO  190 K<J= 1 , LAYER K= 1 M » MP(KJ) DO 160 K • 1, 4 LC(K)»NI + ( K - 1 ) M X LCM(K) •= L C ( K ) 1 LCP(K) = LC(K) + 1 DO 1 8 0 N-INX. NX IF (K . G T . 41G0TO 190 IF(N EO. LC(K))GOTO 3 GOTO 180  s i d e  nodes  in  the  order  T1(M,N)=TPIPE T K M . N - 1 )=PIPE( T K M , N + 1 ) =PIPE( T1(M-1.N)=PIPE TKM+1 ,N)»PIPE( TAOO  »  TOIF  »  TRANS 1 corner  of  1 . .2. . 1 . 2 . . (1..2.. 1 . .2.  ML.  MR.  2.1, 0.1, 1.2, 1.0. 1.0. 1 2.  UM.  BM  TPIPE,BIP.M.N-1) TPIPE,8IP.M.N+1) TPIPE.BIP,M-1,N) TPIPE,BIP,M*1,N)  T1(M.N-1)+T1(M-1,N)+T1(M.N+1)+T1(M+1.N) 4.•TPIPE  -  TAOD  -  TRANS 1  +  TDIF  in  order  nodes  the  of  T1(M-1,N-1)=PIPE(0.667, T K M + 1 ,N+1 ) = P I P E ( 0 . 6 6 7 . TKM+1,N-1)=PIPE(0.667.  UL,  BR,  1.333, 1.333, 1.333.  BL,  UR  2 . 2 . 1 . 1 . 1.1,2.2, 2 , 1 . 1 . 2 .  TPIPE,BIP,M-1,N-1) T P I P E . B I P . M+1 . N + 1 ) TPIPE,BIP, M+1.N-1)  T 1 < M - 1 , N+ 1 ) = P I P E ( 0 . 6 6 7 , K  =  K  +  LC(K)  180  t.333.  1,2,2,1.  TP I P E . B I P , M - 1 . N + 1 )  1  «  NI  +  (K-I)*IX  LCM(K)  =  LC(K)  -  1  LCP(K)  =  LC(K)  +  1  CONTINUE  160  CONTINUE  190  CONTINUE IF  (LC(K)  GT.  NX)IP  =  K  IF  (LC(K)  . L E .  NX)IP  «  K  -  1  C C  C a l c u l a t e  amount  of *  heat  t r a n s f e r r e d  during  dt  C TRANS 1  *  TRANS 1  TRANS2  -  Ul  TRAN  =  ICALL  TRAN =  UP  *  DIA  *  (NX-INX)»DX  +  TRANS 1  +  • •  OT  *  (TIN  N P / O . D 6 -  *  T1(1.NM))  4.  »  *  LAYER)  0T/1.D6  TRANS2  1  C C  Increment  time  IF(TIME  GE.  u n t i l  s p e f l f i e d  time  l i m i t  Is  reached  (36CO  sec)  C TF)GOTO  1  TIME"TIME+DT 00  80  M»1,NY  00  90  N*1,NX  T(M.N)*T1(M.N) 90  CONTINUE  80  CONTINUE GOTO  99  C C  o u t p u t s  at  tlme=TF  (end  of  f i n a l  time  step  In  an  hour)  C C  -  s o i l  temperatures  (15  C  -  Heat  t r a n s f e r r e d ,  OTRAN  C  -  Pipe  a i r  o u t l e t  s p e c i f i e d  columns  [C])  [Md/hr]  temperature.  TPOUT  [Cj  C 1  OTRAN  »  IF((J  . L E .  T5  -  TRAN  «  (GHL  IRISE  -  1.)  .OR.  J  .GE.  ISET)  .AND.  OTRAN  .GT.  0.)  OTRAN  DABS(0TRAN*1.D6)/(CPA'TRATE*360O.)  IF(d  . L E .  IRISE  .OR.  IF(d  GT.  IRISE  .AND.  d  .GE. d  ISET)  .LT.  TPOUT  ISET)TPOUT  *  TPIPE  •  T5  -  TPIPE  -  T5  C 2  RETURN END  C C  FUNCTION  C  for  SUBPROGRAM  c o r n e r  and  'PIPE*  s i d e  to  nodes  compute in  the  nodal  v i c i n i t y  temperature of  a  at  T+DT  pipe  C FUNCTION  PIPE(A1,A2,  IMPLICIT  REAL*8(A-H.  IC 1 . I C 2 . I C 3 . I C 4 .  TE.BI.M.N)  0-2)  COMMON/TEMP/T(100,350) COMMON/PAR/FUW,  HP.  UP.  U l ,  PIPE'A1*FUW*(IC1*T(M,N-1) ft  •T(M-M.N)  +2*BI*TE)  +  (1  BII  +IC2*T(M-I.N) -  4*FUW  -  +IC3*T(M.N*1)  A2«FUW«BI  +IC4  )*T(M.N)  RETURN END C C  FUNCTION  SUBPROGRAM  FUNCTION IMPLICIT  SURF(IC1.IC2.IC3,IC4. REAL *8 ( A - H . 0-Z)  *SURF*  for  surface  convective  C TE.BI.FU.M.N)  nodes  285  COMMON/TEMP/T(100.350) SURF=FU*( IC1'"i ( M . N - 1 ) &  +  (  1  -  4.*FU  -  +  IC2*T(M-1.N)  +  IC3*T(M.N+1)  +  IC4»T(M+1,N)  +  2.*BI*TE)  2.*FU«BI)*T(M.N)  RETURN END C C  FUNCTION  SUBPROGRAM  *SOIL*  for  no-flow  boundary  nodes  and  Interior  nodes  C FUNCTION  SOIL!IC1.IC2,IC3,IC4.  IMPLICIT  REAL *8(A-H,  FU.M.N)  0-2)  COMMON/TEMP/T(100.350) S 0 I L » F U * ( I C 1 * T ( M . N - 1 ) &  (1  -  4 . « F U )  *  +  IC2*T(M-1.N)  +  IC3*T(M.N+1)  for  nodes  +  IC4*T(M+1.N))  •  T(M.N)  RETURN END C C  FUNCTION  C  SUBPGM  *SOILA*  boundary  along  depth  of  I n s u l a t i o n  C FUNCTION  S0ILA(IC1,IC2.IC3,IC4.  IMPLICIT  REAL * 8 ( A - H ,  COMMON/INDEX/I,  FUW.FUD.M.N)  0-Z)  J  COMMON/SOILV/TS(G),TSOUT(12).VMC.C1.C2.DIA.DPIPE.DINS.VSEP,RAREA.  TRATE.DT,TF.LAYER.NL.NP  COMMON/TEMP/T(100.350) SOILA «  »  (1  -  3.*FUW  (IC1*T(M.N-1)  +  -  FUD)*T(M.N)  IC2«T(M-1.N)  +  +  (FUD  •  TSOUT(I))  IC3*T(M.N+1)  +  +  FUW  IC4»T(M+1.  * N))  RETURN END C C  c a l c u l a t e  C  t r a n s f e r  mass  flow  rate  per  pipe  and  convective  heat  c o e f f i c i e n t  C SUBROUTINE IMPLICIT  TXPIPE  REAL*8  (A-H.  COMMON/AIR/CPA.  0-2)  RHOA.  FRMASS  COMMON/GEOM/GHL.GHW.BH.WH. COMMON/MAT/THCRC. COMMON/PAR/FUW.  RKCRC.  HP.  UP,  RTILT1.RTILT2.S1.S3. RKP,  U l .  GVOL  THPIPE  BII  COMMON/SOILV/TS(6).TSOUT(12).VMC,C1,C2,DIA.DPIPE.DINS,VSEP.RAREA. P I » 3 . 1 4 1 5 9 VIS PR  •  RKA EX  18.5D-6  •  0.71 »  0.0254  0.3  =  REY  »  FRMASS/IVIS  RNU  •  0.023 •  •  HP  -  RNU  UP  *  1 . / ( 1 . / H P  *  DIA)  (REY**0.8)  *  (PR*«EX)  RKA/DIA +  THPIPE/RKP)  RETURN END C C  SUBROUTINE  'ERROR*  to  p r i n t  error  messages  C  1  C  SUBROUTINE ERROR(ICODE, A. IMPLICIT REAL*8(A-H, 0-Z) WRITE(5,DICODE. ICODE. A FORMAT('Stabi1ity c r i t e r i o n RETURN 2 END  •)  #'.11.'  v i o l a t e d .  C R ' , 1 1 . '  F10.2)  TRATE.DT,TF.LAYER.NL,NP  286  C  SUBROUTINE  C  rockbed  *LTROCK* thermal  to  compute  the  amount  of  heat  t r a n s f e r r e d  to/from  storage  C SUBROUTINE IMPLICIT  LTROCK  REAL*8  ( A - H ,O - Z )  COMMON/AIR/CPA,  RHOA.  COMMON/AREAS/AB,  FRMASS  A P . A C 1,  A C 3 , A G . APFACT  COMMON/GEOM/GHL.GHW.BH.WH, C0MM0N/EQN/C4.C5.C6, COMMON/INDEX/I,  RT1LT 1 . R T I L T 2 , S 1 . S 3 ,  TPIN,  GVOL  IMODE  <J  COMMON/OCCUR/ICALL.  ICAL  COMMON/RKOUT/ICOUT COMMON/PSYC/TDP,  TC.TP,  COMMON/ROCK/STCAP,  RH.WA,  FRATE,  WCSAT,WPSAT,WOUT,  TINIT,  TIN  RHOR  COMMON/SOILV/TS(6),TSOUT(12).VMC,C1,C2,DIA.DPIPE,DINS.VSEP,RAREA.TRATE.DT,TF.LAYER.NL.NP COMMON/SUN/SR.SS, DIMENSION  D A , WS,  UZ(1,31),  ICOUT  *  1  IMODE  =  0  IRISE.  XM(31),  I SET  MORD(1,3).  TOUT(2),  A(31)  C IF  ( T I N  IF  ( J  TPIN  . G T . 22.  .AND.  . L E . IRISE '  .OR.  TIN d  . L E .40.)  . G E . ISET)  IMODE  IMODE  »  -  1  2  TIN  C IF  (I CALL  RKR  =  CPR  = *  VOID  =  US  0.4  0 . 0 3 15 0.3  BEDH  «  BEDW  =  AP  GHL'GHW  =  ASVR  1  880.  RDIA -  N E . O)G0T0  0.93  1. GHW  =  ' 0 . 8  190.5  C ROCKWT VOLRK STAP  =• 0 . 5 »  =  2.  VOLBED ACS  »  •  STCAP  *  AP  «  *  BEDH  »  -  VOID)  BEDW  •  T1  -  FRATE*0.5/(ACS*R0IA)  HV  =  HS  VOLBEO/ACS  G50. •  =  BIR  1000./CPR  VOLRK/AP  V0LRK/(1.  BEDL  RNTU  *  ROCKWT/RHOR  *  ( T 1 « « 0 . 7 )  HV*VOLBED/(FRATE'O.5*CPA)  HV/ASVR »  HS  RNTUC  >  *  (RDIA«0.5)/RKR  RNTU/(1.  •  0.2*BIR)  AS  »  2.*(BEDW*BEDH)  UA  =  US  *  +  2.*(BEDL*BEDH)  •  (BEDL'BEDW)  AS  T3  •  RHOR  C4  =  3.603  • •  CPR ' A C S *  C5  •  3.603  •  C6  =  3.6D3  •  FRATE*0.5  (1. *  -  VOID)  CPA/T3  UA/(BEDL*T3) RKR •  ACS/T3  C WRITE(5,65) 65  FORMAT ( / '  MCr/Ap  WRITE(5,151STCAP, 15  FORMAT(3F8.O.  C 1  NPDE  •  1  RNTU RNTU.  10F8.2)  HV. HS.  HV RHOR,  HS BEDW,  RHOR BEDL,  BEDW STAP  BEDL  m3RK/m2AP'/>  287  NPTS  •  KEON  •  KBC  2  =  METH EPS  31 2 O  < =  0.0O01 MORDC 1 , 1 ) - 2 MORD(1.2)  =  4  MORD(1.3)  =  0  TINT  »  TLAST MOUT  O. =  =  1. O  TOUT(1) KMOL IF  *  =  TLAST  O  (ICALL  . E O . 0)  BACKSPACE REA0(2,11) 11  GOTO  3  2 ( A ( I K ) ,  FORMAT(31F  I K » 1 . 3 1 )  7.0)  C  3  OX  =  DO  10  BEDL/INPTS IK  XM(IK)  » '  1.  -  1)  NPTS  DFLOAT(IK-1)  » DX  IF  (ICALL  . E O . O)  UZ(I.IK)  =  IF  (ICALL  . N E . 0)  UZ(I.IK)  =• A ( I K )  TINIT  CONTINUE  10  CALL •  MOL ID ( N P D E . N P T S , K E O N , K B C . M E T H , E P S . M O R D . T I N T . T L A S T , M O U T , T O U T , U Z ,  XM. KMOL) 1  ICALL » RETURN END  SUBROUTINE  PDE(UT.  IMPLICIT  U.  REAL*8(A-H,  DIMENSION  U ( 1 , 3 1 ) .  COMMON/AIR/CPA.  UX.  UT(1,31),  RHOA,  COMMON/E0N/C4,C5,CG, COMMON/INDEX/I,  FX,  UXX,  T,  XM, IX,  NPDE)  O-Z) UX(1.31).  UXX(1,31).  FX(1.31).  XM(31).  TPIN.  IMODE  d  COMMON/OUT/RHINS,  TRPN.  COMMON/ROCK/STCAP,  TRSP.  FRATE.  SUMQU.  TINIT.  TPOUT,  OTRAN,  PN1  RHOR  COMMON/SOILV/TS(G),TSOUT(12).VMC.C1,C2.DIA,DPIPE,DINS,VSEP,RAREA COMMON/SUN/S R . S S.  DA.  WS.  IRISE.  ,  TRATE.DT.TF,LAY  ISET  COMMON/RKOUT/ICOUT IF  (IMODE  . E O . 0)FDIR  »  IF  (IMODE  . E O .  OFDIR  »  -1.  IF  (IMODE  . E O . 2)FDIR  =  1.  DO  20  Id  »  U T ( I . I d ) 20  O.  1.31 =  F D I R * C 4 « U X ( 1 . I J )  +  C 5 » ( T S O U T ( I ) - U ( 1 , Id))  +  CONTINUE IX  »  IF  (T  31 . G E .  1.  .AND.  ICOUT  1)GOTO  . E O .  1  RETURN 1  WRITE(2.10)  10  FORMAT(31F7.2) IF  (IMODE  OTRAN IF  =  (U(1.K), EO  FRATE  (OTRAN  O) *  . L E . IRISE  IF(d  . G T . »  2  IRISE  K=1,31)  GOTO  5 ( U ( 1 , 1) O. QTRAN  CPA *  . L T . O . )  IF(d ICOUT  A(31)  FRMASS  OR.  J  . G E .  .AND. d . L T .  -  U(1.31))  ISET)  TPOUT  ISET)TPOUT  • =  3600./1.DG U ( 1, 1 ) U(  1,31)  CG*UXX(1.Id)  ER,NL.NP  288  RETURN 5  OTRAN  =  TPOUT  =  O. 99.  RETURN END C SUBROUTINE IMPLICIT  FUNC(F.  U,  UX.  REAL*8(A-H.  DIMENSION  F(1).  UXX,  T.  X.  IX,  NPDE)  O-Z)  U(1),  UX(1).  UXX(1)  RETURN END C SUBROUTINE IMPLICIT  BNDRY(T.  UL.  REAL*8(A-H,  C0MM0N/EQN/C4.C5.C6, DIMENSION  1  UR(  AL(1)  •  BL(1)  »  0.  CL(1)  »  O.  1 ),  AL.  BL.  CL.  UR,  AR,  BR.  CR.  NPDE)  O-Z) TPIN.  AR(1).  IMODE  BR(1).  CR(1),  UL(1).  AL(1),  BL(1),  CL(1)  0.  IF(IMODE  .EO.  IF(IMODE  .EO.  DGOTO  1  IF(IMOOE  .EO.  2)G0T0  2  AL(1)  •  BL(1)  =  0.  CL(1)  »  TPIN  0)RETURN  1 .  RETURN 2  AR(1)  =  1.  BR(1)  «  0.  CR(1)  *  TPIN  RETURN  END C C  SUBROUTINE  C  m o d i f i e d  *NTLOAD* Parton  to  and  compute  Logan's  outside  equation,  temperatures and  thus  using  hourly  Kimball  heat  and  Bellamy's  load  C SUBROUTINE IMPLICIT  NTLOAD  REAL*8  (JA)  (A-H.  COMMON/AREAS/AB,  O-Z)  AP,  A C 1.  ACS,  AG,  APFACT  COMMON/COVER/NNC COMMON/CONV/CW1,  CW2.  COMMON/DATA/TOUT.  CW3.  HW.  RHT(24).  VW.  COMMON/GEOM/GHL.GHW.BH.WH. COMMON/HEAT/TMAX(12). COMMON/OCCUR/ICALL. COMMON/PROP/RHOP,  DA,  COMMON/SYSTEM/INSN. LOGICAL  HBA  RTILT1.RTILT2,S1.S3. HEATLD,  OSUP.  GVOL  QPASS  ICAL RHOG,  COMMON/RADI A N / P S I , R D E L C (  COMMON/INDEX/J.  HPA,  RHSET  TMIN(12).  ALPP,  COMMON/SUN/SR.SS.  HCA.  RKG,  THG,  TAULW,  EPC,  EPP  12),RLAT,RWI(24).RBDN.RGAM(6),RBETA( 6 )  WS,  IRISE,  ISET  ISTDEV  J  INSN  C IF  (ICAL  A  •  B  =  C  «  PI TIN  .NE.  0)  GOTO  3  1.86 2.2 -0.17 '  3. =>  14159 17.  C C C  o v e r a l l  heat  transfer  c o e f f i c i e n t s  of  g l a z i n g .  Insulated  wall  and  perimeter  289  IF  (NNC  1)  RHRHC  = O.  IF  (NNC . E O . 2)  EO.  RHRHC  =  RGLAZE  = 0.12063  UGLAZE  »  -  0.12063  UNW  »  1./RNW  NAEV  =  •  0.166667  NNC*THG/RKG  +  RHRHC  + 1./HW  1./RGLAZE  RNW  UPERIM  •  +  2.8148  +  0.4587  + 1./HW  1.39  1.0  C IF  (.NOT.  AC  «  AW  *  WH *  ANW  =•  2  •  WH/DSIN(RTILT2))  * GHL  2  AC -  AC1 + AC3  AW  2.  •  ANW  1  GHL  (S3  GOTO 1  (INSN))GOTO  AC 1  «  •  (WH *  GHL)  *  GVOL/GHL  0.  AGB =  2.  PERIM  =  (GHW+GHL)  UA  »  UGLAZE*(AGB  IR  «  IRISE  IS  =  ISET  * +  2. AC •  AW) +  UNW*ANW +  C  3  IHRMIN  »  PI  +  1 1  DINT(IRISE  T1  •  •  T6  <= D A +  T2  =  (ISET  =  -  TMIN(I)  01  *  TSET  02  »  DEXP(B)  DISP  +  C)  IHRMIN)  2. ' A  (TMAX(I)  TSET  -  -  TMIN(I)) +  •  DSIN(T1/T6)  T2  TMIN(I) -  1.  =• D 1 / D 2  C  5  IF  (OA  T3  -  -B  T4  »  TSET  -  T5  »  T4  DEXP(T3)  TOUT  «  GOTO  6  *  (JA  •  -  (TMIN(I)  (TMIN(i) (JA  -  -  -  DISP)  •  -  PI  -  IHRMIN)  =•  (TMAXfl)  -  TMIN(I))  TMIN(I)  +  T19  *  IF  (JA  . G T . ISET)  TIN •  17.  <J A  . L T  ISET)  TIN *  22.  HEATLD  •  »  ICAL  1  RETURN ENO  UA  ( T I N -  C)  T5  IF  -  DA +  DISP)  T19  »  *  5  ISET)/(24.  T18 TOUT  6  . L T . ISET)G0T0  TOUT)  DSIN(T18/T6)  •  36O0./1.D6  UPERIM'PERIM  +  0.373«GV0L*NAEV  290  Appendix  A  291  Direct radiation interception factor and diffuse radiation view factor  The expressions for P j and F j are derived, or otherwise extracted from the literature. k  k  tp = solar azimuth angle 7 = surface azimuth angle 6 = xjj — 7 a = solar elevation angle f = surface tilt angle L = length of the greenhouse W — width of the greenhouse h = distance from plant canopy (gutter height) level to ridge If 6 = 90°, then direct radiation from the sun is at grazing incidence to the receiving surface. If \6\ > 9 0 ° , then direct radiation does not impinge onto the receiving surface in sucrra way as to transmit into the house. For the situation \0\ < 90°, then there are a few possible situations. For an east-west oriented greenhouse I. South Roof Fig. A 1.1 shows the projection onto the plant canopy level of a gableroof type greenhouse, as direct sunlight enters through the south roof. A l ternative configurations are shown in Fig. A 1.2, where plans of the horizontal surface area covered by the direct radiation are indicated. In each of the cases, the total area of the ground covered by direct radiation entering through the south roof is equal to area AXYB. Case 1.  \AP\ > W \PX\ < L where AP  =  W + h cot x  PX  a cos  6  = /icot a s i n f l  292  note: for C V house, W = W/2, and for SS and BS, x  Pk  P  areaANFB  =  area AXYB  LeiAE  = W, EF = L  since: areaANFB  = areaAEFB  areaAEFB  =  areaAEN  =  EN IPX  =  areaAEN  AE.EF  2  area^Xytf =  -  -AE.EN AP.EF AE/AP,  hence: EN =  AE.PX/AP  areaAEN  =  \AE .PX/AP 2  from which:  WT  Pkp —  —- (  W 2 F L C O T A S I N 6  2 VWi +  \  fccotacos^y  L(W + h cot a cos 9) X  Special case: at noon, tp = 0, therefore 9 = 0 CV: P  -  2 k  =  1 + tan £ cot a  SS, BS: Pikp  1 1 + tan £ cot a  WW l=  The interception factor, P , for the SS vertical absorber plate acting the receiving surface may be derived in a similar manner, thus kq  hi - \ (f^T " \\ a  p  m  2 V h + n , tan a cos t> J •  L(h ~ Wi tan a cos 8)  k q  Case 2.  PX\ > L  k p  _  a.Te&ANB  ~  areaAXYB  since: BN/QX  =  AB/AQ,  AB = EF, QX = AP, AQ = PX, are&ANB =  2  -AB.BN  hence: BN =  AB.QX/AQ  zre&ANB =  l  -AB\QXjAQ  from which:  p  — k p  L 2h cot a sin 0  Similarly L 2Wi tan a sin 6  294  C a s e 3.  \AP\ < W \PX\ < L  The situation of \AP\ < W would not occur in a the SS type house. For other house types,  k p  _  area.AXNB  ~  areaJXYB  since: a r e a ^ X J V B = JLTZ&APNB area^PiVB =  areav4PX =  2  AB.AP  -AP.PX  hence:  D  k = 1 - — cot a sin 0 P  - areavlPX  Direct sunlight through south roof above: CV shaped greenhouse below: SS shaped greenhouse  296  Fig. A1.2  Intersection of d i r e c t sunlight through roof surface facing the sun (south roof) and the plane at the gutter height (plant canopy) l e v e l . Alternative configurations.  297  298  II. North Roof This only applies to the C V house. Referring to Fig. A l . 3 which shows the projection of direct radiation onto the plant canopy level as it enters through the north roof, P = 0 if kp  \MP\  >  W  \PX\  > L  x  or  Since the projection of the end point of the ridge lies outside the floor area in these situations, only one principal case shall be considered:  k p  \MP\  < W  \PX\  < L  x  _  BLTe&XEFP  ~  xre&XEFY  Again, \etAE  = W, EF = L  since: = cXve&XEFY  are&XEFP  areaX£Fy FN  = W  FPY  =  PY  x  - areaFPF  EF.FP  - h cot a cos 9 -FP.PY  2 = h cot a sin 9  hence: a r e a F P y = -{Wi2  hcot a cos 6){h cot asm 6)  from which: Pk  P  h.  — 1 — TT cot a sin 9 2L  A1.3  Intersection of d i r e c t sunlight through roof surface facing away from the sun (north roof) and the plane at the gutter height l e v e l .  300  III. East and West Gable Ends The development of criteria for the alternative situations where direct sunlight enters through the end walls follows in a similar manner. As Smith and Kingham (1971) did in their analyses, it was assumed that an end wall might be regarded as being of rectangular dimensions W and h/2 for the portion above the gutter height level. Case 1. \AP\ < W  x  \PY\ < L where AP - hi + h cot a sin 0 PY  = hi cot a cos 0  hi = h/2 For the C V house, this situation implies the entire projection of direct sunlight lies within the greenhouse floor area, hence P = 1.0 kp  Otherwise k p  _  area,4£JVy  ~  zrezAEXY  since: areaA^JVY = K<Z<LAEXY areaA£XY = zrezENX NX  AE.EN  =  = AP,EN  zreaENX  -EN.NX  l  = PY  hence: are&ENX =-(hi 2  cot a cos 0) (hi cot a sin 0)  from which: Pkp — 1 — T^JT" cot a sin 0  301  Similarly, r  k.  q  1 - —— tan a sin 0  —  Case 2.  \AP\ > W\ \PY\ < L  SS: a.rea.AEN zrezAEXY since: a r e a A £ X Y = AE.EY ZTeaAEN =  2  =  -AE.EN  . 4 £ = W , , i S / V = AE cold hence: 1Witan a 2 /lysine?  Similarly, P '  kk q  1 /i< cot a =  2 H ! sin 0 7  CV: area.AEQNY /"fen — k p  areaA£XF  cot a cos 0)  since: - areaQTVX  cXTeaAEQNY = are&AEXY areaQNX QN =  = - (h cot a sin 6 - W )  2  x  2  x  cot 6  PXcotO  PX = /i-cotasinfl - IV, hence: areaQTVX =  -QN.NX  2  from which: areaQNX  Pt» = 1 t p  _  j  areaAEXy  _  (hi  cot  a a i n l - W i )  2  2 W j / i i cot a sintf  Case 3.  jpyj > L  SS:  ^  areaA^FN *"  areayl^Xy  since: areaAEFN  = areaAEFB  areaAEFB  = AE.AB  -  areaANB  = WL  a r e a A £ X y = A £ . P y = W ^ cot Q cos 6 7  areaANB BN =  =  2  ABianO  -AB.BN  303  hence: = -Z, 2 tan0 2  areaANB from which: WL-  iLHanO  Wh cot a cos 0  k p  x  CV: P k p  _  ^eaAEQNR  ~  areaAEXY  since: aieaAEQNR  = are&ACNB - areaECQ -  areaACNB  = WL  areaECQ  =  ^EC.CQ  areaABR  =  ^£2tan0 ml  CQ = EC cot 9 BR = AB tan 0 hence: area£CQ = areaABR  =  -£C2cot0 2 ^AB.BR  and p  =  |(H / 1 2 cotfl + .L2tanfl) Wi/ii cot a cos 0  areaABR  304  L CV s h a p e Case  1  £  W w ,  X 4 '  Case 2  Case 3  Fig.  A1.4  C  £  I n t e r s e c t i o n of d i r e c t s u n l i g h t through e i t h e r g a b l e end and t h e p l a n e a t the gutter height l e v e l  x \--\  \  \  K  \  !  SS  shape  \  Case  e  1  w  Case 2  Case 3  L = dbj N = ajb.  nL  - i sin 20 (l+A")(l-rZ )  2  s  2  -A™'*1 +  l Y + iA"-sin*<DIn [( ',f ) (, . . . l * ^ * * [\A- + L -2AIcos<t>/ \l+xV--}-Z,--2Aicos t>/ I  4- A tan- (i) - V(A*- + r  1  J  (  - 2A I cosfl>)cot" '(A - + L* - 2NL cos O) r  1  r  v  + cos 0 f* v d + --«.in»*) I t a n - ( f " * ° ° J C  8  :cos O  + tan-  Feingold,  1966)  /(H-s siii*<^) a  N  (source:  n  L-( 1 + A" + L-- 2NL cos <P) (1 - r I ) (A'- + 1 - 2NL cos <t>)  3  + \ sin <> t In  ^  7 L  307  Appendix  B  Psvchrometrics:The following equations are used in the calculation of psychrometric properties that are carried out at various parts of the simulation. 1. saturation vapor pressure for -40°C  < t  dh  < 0°C  / V , = exp[89.63121 - 7511.52/7 + 0.023998977/ - 1 . 1 6 5 4 5 5 l ( l 0 " ) r - 1.2810336(10 )r 5  -2.0998405(10 for 0°C < t  _11  _8  3  ) T - 12.150799 In T) 4  < 120 C L1  dh  P  2  = eip[24.2779 - 6238.64/7 - 0.344438 In T)  w<f  where T = t + 273.16 2. actual vapor pressure P = {RH){P )f w  Wi!  100  note: long-term U . S . weather data gives t rather than RH. In this case, P is solved as a root of the quadratic shown in item 5 below. dp  w  3. humidity ratio W = 0.622P /(P tu  W  atm  -  = 0.622P„J{P  atm  -  P) w  P ) w<!  4. enthalpy h - 1.006f for -b0°C  < t  dt  + 1^(2501 +  l.nbt ) dh  < 110 C P  db  5. dew-point temperature for - 5 0 ° C < t t for 0°C < t  db  db  dp  < 0°C = 5.994 + 12.41 In P + 0.4273(/n w  Pf w  < 50° C t  dp  = 6.983 + 14.38 In P + 1.079(/n w  P) w  2  309  Appendix  D  310  Appendix D - Data acquisition equipment Solar radiation - sensor locations are shown in Fig. A4.1 device  model  outside global radiation  silicon photodiode pyranometer  Li-Cor LI-200SB  outside diffuse radiauon  ditto, with shadow band  2010 S  transmitted radiauon  photovoltaic pyranometer  Rho-Sigma RS-1008  inside PAR  photosynthetic irradiance sensor  Li-Cor LI-190SEB  variable  Temperature - sensor locations are shown in Figs. A4:2, A4.3 greenhouse air temperature  thermistors or T-type thermocouples  absorber plate temperature storage inlet and outlet temperatures rockbed temperatures soil storage temperatures plant canopy temperature greenhouse cover temperature  Infrared thermometer  FenwaJ UUA-33J1 or Omega PR- T- 24  311  Others - sensor locations are shown in Fig , A<fr2 charging and discharging air flow rates  hot wire anemometer  Flowtronic 55B1 (AC-powered)  energy consumption  hot water flow meters  A.B. Svensk Varmematning SVMK-241-047-3  relative humidity  wet and dry bulb thermometers  312  EARTH THERMAL  • CXS  £.6A£i£  HEADER HOUSE  SS w.6"8l£  • CM W. GABLE.  SOLA/? SHED  CONTROL HOUSE  CH £.  GAbLL  NOT 70 SCALE.  TOTAL OUTSIOC SOLAR RADIATION AHD Diffuse RADIAflOH Si SS  S. ROOF  5  S.WAU-  S  V£?^  O-r/RA NO METERS  Fig. A4.1 Layout of research greenhouses at Agriculture Canada Saanichton Station and locations of solar radiation sensors  P  313  sensor 1-6 7-12  rockbed temperatures (east storage chamber) rockbed temperatures (west storage chamber) 1,4,5; 8,9,12: at a depth of 0.56 m 2,3,6; 7,10,ll:at a depth of 0.76 m  13,14 15 16 17 18 19-21 22  storage outlet air temperature storage inlet (central plenum) temperature peak collecting duct air temperature heating duct outlet temperature greenhouse air temperature at gutter height level absorber plate temperatures relative humidity at plant canopy level  sensor 1-7  s o i l temperatures near edge region  8-14  s o i l temperatures near center region  15-18  s o i l temperatures along the p i p e ' s longitudinal axis  19,20  pipe i n l e t a i r temperature  21  pipe outlet a i r temperature  22-25  pipe a i r temperature  26  greenhouse a i r temperature at gutter height l e v e l  27  r e l a t i v e humidity at plant canopy l e v e l  315  insulated north wall  a: ci: co: f: p: q:  inside a i r i n s i d e s u r f a c e of greenhouse cover o u t s i d e s u r f a c e o f greenhouse cover greenhouse f l o o r p l a n t canopy v e r t i c a l absorber plate  F i g . A6.1 -  G r e e n h o u s e t h e r m a l e n v i r o n m e n t model t e m p e r a t u r e s and h u m i d i t y r a t i o  316  Appendix  E  317  'DESIGN*  to  h e a t i n g by  generate  f r a c t i o n  Anthony  K.  inputs:  annual  u s i n g  s o l a r  the  c o n t r i b u t i o n  s i m p l i f i e d  design  and  s o l a r  procedure  ( L a u ,  1987)  roof  t i l t s ,  Lau  l a t i t u d e monthly  d e c l i n a t i o n  d a i l y  outside  g l o b a l  s o l a r  r a d i a t i o n  mean  d a i l y  maximum  o u t s i d e  a i r  temperature  mean  d a i l y  miminum  o u t s i d e  a i r  temperature  greenhouse o v e r a l l  f l o o r  heat  conventional thermal IMPLICIT  angle  mean  a r e a ,  loss  r a t i o ,  wall  c o e f f i c i e n t  greenhouse  storage  l e n g t h - t o - w i d t h  device  design  a l t e r n a t i v e s  REAL*8  ( A - H .  (1,  (CV) (1  c o l l e c t i o n  for  2,  3,  rockbed, 4  for  method 2  each  for  (T  or  F)  s o i l )  storage  d e v i c e )  0-Z)  COMMON/CALL/ICAL COMMON/INDEX/I.J COMMON/HEAT/TMAX(12), COMMON/SUN/SR.SS.  TMIN(12).  DA(12),  DTD(12),  IRISE(12),  DTN(12).  T0UT(2O,3O)  ISET(12)  COMMON/RADIAN/RDELC(12).RLAT DIMENSION  DELC(12) .  DIMENSION  H ( 1 2 ) . S ( 1 2 ) , S P ( 1 2 ) , T A U E ( 1 2 ) . T A U ( 1 2 ) .  DIMENSION  ODY(12).  LOGICAL  IR(12).  IS(12),  0NT(12).  QTL(12),  TMX(12), QL(12).  TMN(12) S L R ( 1 2 ) , F S ( 1 2 ) , F M ( 1 2 )  QDL(12).  0NL(12)  CV  READ(4  16)  DL AT  R E A 0 ( 4 , 16) R E A D ( 4 , 16) R E A D ( 4 , 16)  (OELC(I).  READ(4  (TMIN(I).  1 = 1 , WH.  .  16)  READ(4  16)  (TAUE(I  ) .  I = 1 ,  12)  (TMAX(I ) .  1 = 1 ,  12)  16)  AP,  17)  CV  READ(4  15)  ISTDEV  ,  15  , 15) F O R M A T ( I 1)  16  FORMAT(15F8  17  FORMAT(L1)  12)  1= 1 . 1 2 )  REA0(4 , READ(4 , READ(4  1 = 1 .  ( H ( I ) .  RLWR,  12) TILT1,  TILT2.  UGLAZE  ICASE O)  C GHW  =  DSORT(AP/RLWR)  GHL  =  AP/GHW  PI  =  3.14159  RLAT  =  DLAT  PI/180.  *  TILT1  *  PI/180.  RTILT2  =  TILT2  •  PI/180.  DO  90  1=1.12  RDELC(l) 90  *  RTILT1  =  DELC(I)  *  PI/180.  CONTINUE  C IF(TILT1  . E O .  90.)T21  IF(TILT2  . E O .  90.)T21  ./DTAN(RTILT1)  IF(TILT2  NE.  90.)T21  ./DTAN(RTILT1)  8H  =  S1  =  S3  =  GHW/T21 BH/DSIN(RTILT1) BH/DSIN(RTILT2)  AC 1  =  AC3  »  AG  =  S1*GHL S3*GHL BH  *  GHW *  0.5  /DTAN(RTIL T2) +  1./DTAN(RTILT2)  height  318  GVOL  =  UNW  =  (AG +  UPERIM NAEV  WH'GHW)  * GHL  0.29 =  =  1.39  1.0  C IF  ( C V ) GOTO  AC  =  AW  =  ANW 3  5  WH * G H L =  (S3  GOTO  5  AC =  AC 1  AW  2.  =  ANW  3  AC 1  »  AGB =  WH/DSIN(RTILT2) )  + AC3 »  (WH * G H L )  2. =  *  GVOL/GHL  *  AC +  AW + A G B  (GHW+GHL)  UGLAZE'AGLAZE  *  2.  UA  =  +  UNW'ANW  IF  (ISTDEV  .EO  1)  GOTO  I F  (ISTDEV  .EO  2)  GOTO  IF  (ICASE  EO.  1)  GOTO  81  I F  (ICASE  EO.  2)  GOTO  82  IF  (ICASE  EO.  3)  GOTO  83  I F  (ICASE  EO.  4)  GOTO  84  IF  (ICASE  EO.  1)  GOTO  91  IF  (ICASE  EO  2)  GOTO  92  IF  (ICASE  EO.  3)  GOTO  93  I F  (ICASE  EO.  4)  GOTO  94  C  8  9  \*  81  AO A 1  =  = 1 .03  A2  =  0.  B1  =  - 1.9G  B2  =  GOTO 82  AO  0.  =1.15  A1  =  -0.89  A2  =  -0.35  B1  =  -0.82  B2  =  -9.18  AO  6 =1.13  Al  =  -0.71  A2  »  -0.44  BI  =  -0.G1  B2  =  GOTO 84  -1.00  e  GOTO 83  AO  -3.24 6  "0.80  A1  «  -0.44  A2  '  -0.39  B1  -  -0.73  B2  »  -6.38  GOTO  6  C 91  AO  =0.87335  A1  =  -2151.4783  A2  >  2150.6968  B1  =  -0.83676  B2  =  -0.83657  GOTO  6  * GHL  0.  AGLAZE PERIM  +  8 9  +  UPERIM'PERIM  +  0.373'GVOL  *NAEV  319  92  AO  =0.854  A1  =  -0.759  A2  =  0.055  B1  =  -1.19  B2  =  -9.762  GOTO 93  AO  6 =0.791  A1  =  A2  =  B1  =  B2  '  -0.588 -0.752 -  GOTO 94  1.002 -22.4  6  -0.771  AO Al  =  -0.574  A2  =  -1.185  BI  »  -0.976  B2  =  -27.64  DO  10  C 6  IK  ICAL  *  -  9,  17  O  DTD(I)  =  0.  DTN(I)  •  O.  IF  (IK  . G T . 12)  I  =  IK  IF  (IK  . L E . 12)  I  =  IK  +  24  -  12  C CALL  RISET  C IR1 = I R I S E ( I ) IR24 DO  =  20  JA  1  =  IR1.  IR24  IF  (JA  . L E . 24)  J  = JA  IF  (JA  . G T . 24)  J  =  CALL 20  +  IRISE(I)  NTLOAD  JA  -  24  (JA)  CONTINUE  C OOL(I)  «  OTD(I)  •  UA  •  36OO./1.06  QNL(I)  «  DTN(I)  •  UA •  36OO./1.06  OL(I) 10  =  ODL(I)  +  ONL(I)  CONTINUE  C DO  40  IF IJ I  IK •  =  I J I  2  9.  17  G T .  12)  I J  1  -  8  2  = =  GOTO  IK  GOTO 1  =  (IK  IK IK  IR(I)  =  IS(I)  =  -  12 8  I R I S E U J ) ISET(IJ)  TMX(I)  «  TMAX(IJ)  TMN(I)  *  TMIN(IJ)  OOY(l)  =• O D L I I J )  QNT(I)  =  ONL(IJ)  QTL(I)  =  QL(IJ)  C TAU(I)  => T A U E ( I J )  S(I  H ( I J )  )  -  SP( I )  =  SLR(I) FS(I)  S( I ) »  *  AP AO +  • •  TAU( I ) S ( l )  •  TAU(I)/OTL(I)  A1*DEXP(B1*SLR(I))  •  A2*DEXP(B2*SLR(I  ))  IF  40  . LE  (SLR(I)  FM( I )  =  0.  - O .007  )  *  FS(I )  o.  =  0.03*FS<I)  IF  (FS(I )  . GT .  FS(I)  + 1 .  IF  (F5(I)  . LT .  FS(I)  0.  IF  (FM(I)  .GT .  FM(I)  1 .  IF  (FM(I)  . LT .  FM( I )  0.  SUMO  =  SUMO  OTL( I )  SUMS  =  SUMS  (FS(I)  OTL(I))  SUMM  =  SUMM  (FM(I)  OTL(I))  0.92*(FS(I  ) * *2 )  CONTINUE FSY  =  SUMS/SUMO  FMY  -  SUMM/SUMO  C WRITE(5.61) 61  OLAT  FORMAT(/'LATITUDE  • ' .  F 1 0 . 2 / )  WRITE(5.63) 63 29  FORMAT(/'GHL  GHW  AP  RLWR  GVOL  WRITE(5.29)GHL.GHW.AP.RLWR.GVOL.TILT1,TILT2. FORMAT(F5.1,  F 8 . 1 .  3 F 8 . 0 ,  2 F 8 . 1 .  F B . O , L 8 .  UA,  TILT 1 CV.  UA  TILT2  CV  ISTDEV  ICASE'/)  ISTDEV.ICASE  218)  WRITE(5.62) 62  FORMAT(/5X.'  Sep  WRITE(5.22)  ( ! R ( I ) .  WRITE(5.23) WRITE(5.24)  Oct 1-1,  9)  ( I S ( I ) ,  1=1,  9)  (TMX(l).  1-1,  9)  WRITE(5.25)  (TMN(I).  1=1,  9)  WRITE(5.26)  (ODY(I).  1=1.  9)  WRITE(5.27)  (ONT(I),  1=1,  9)  WRITE(5,28)  ( Q T L ( I ) ,  1=1,  WRITE(5.31)  ( S ( I ) .  WRITE(5.32)  (TAU(I).  WRITE!5.36)  ( S P ( I ) .  WRITE15.33)  (SLR(I),  WRITEI5.34)  ( F S ( I ) ,  1=1,  WRITE(5.38)  (FM(I).  WRITE(5.35)  F S Y . FMY  Feb  Mar  Apr  May')  9) 9)  1=1,  9) 9)  1=1,9)  FORMAT(15,  22  F O R M A T ( / ' I R I S E ' .  23  FORMAT('ISET  24  FORMAT(/'TMAX  25  FORMAT('TMIN  26  FORMAT(/'QDL  27  FORMA T( ' Q N L  ' .  9FB.O)  28  FORMAT('OL  ' ,  9F8  31  FORMAT(/'H8AR  32  FORMAT('TAU  ' ,  9F8.2)  36  FORMAT('HP  ,  9F8.2)  33  FORMAT(/'SLR  ' .  9F8.2)  34  FORMAT(/'F S  ' .  9F8.2)  38  FORMAT(/'FM  ' .  35  FORMAT(/'annua  1  END  Jan  9)  1=1,  21  STOP  Dec  9)  1=1. 1=1.  Nov  9 F b . 2 ) ' .  918) 918)  ' . ' ,  9F8.2) 9F8.2)  ' .  ' ,  9F8.0) O)  9F8.2)  9F8.2) fs.  fm  - ' ,  2F10.3)  to O  321  c C  SUBROUTINE  *RI SET *  to  compute  s u n r i s e  and  sunset  hours  C SUBROUTINE IMPLICIT  RISET  REAL*8(A-H,  COMMON/INOEX/I,  0-Z)  u  COMMON/SUN/SR.SS.  DA(12).  IRISE112),  ISET(12)  COMMON/RADIAN/RDELC(12).RLAT  PI  =  WS  »  DWS  3.14159 DARC0S(-DTAN(RLAT) -  WS  OA(I) SR  •  SS *  *  =  OWS  12.  -  SR  2 . / 1 5 .  DA(I) -  ISET(I)  *  DWS/15.  +  IRISE(I)  * DTAN(RDELC(1)))  180./PI  -  DINT(SR DINT(SS  +  0.5)  +  0.5)  RETURN END C C  SUBROUTINE  *NTL0AD*  to  compute  d a l l y  gross  h e a t i n g  load  C SUBROUTINE IMPLICIT  NTLOAD  REAL*8  (JA)  ( A - H .  0-Z)  COMMON/CALL/ICAL COMMON/INDEX/T. J COMMON/HEAT/TMAX(12), COMMON/SUN/SR.SS.  TMIN(12).  DA(12).  DTD(12),  IRISE(12),  DTN(12),  ISET(12)  C IF  (I  .GT.  5)  IJ  •  I  -  8  IF  (I  . L E .  5)  Id  '  I  +  4  A  •  1.86  B  -  2.2  C  -  PI  -O.17 =  3.14159  IHRMIN T1  =  DINT(IRISE(I)  *  PI  T6  -  DA( I )  T2  =  (TMAX(I)  TSET  =  *  (ISET(I) +  01  =  TSET  '  DEXP(B)  DISP IF  «  ( J  -  +  C)  IHRMIN)  2 . *A -  TMIN(I,  D2  -  TMIN(I)) +  *  DSIN(T1/T6)  T2  TMIN(I) -  1.  D1/D2 . G E .  IRISE(I) (dA  .AND.  d  . L T .  ISET(I))GOTO  C T3  »  -B  T4  «  TSET  *  T5  *  T4  •  TOUT(Id. TIN  *  DTN(  I )  GOTO 5  '  -  -  DA(I)  •  DISP)  (TMIN(I)  -  DISP)  +  T5  -  (TIN  -  T O U T d J .  d))  +  DTN(I )  6 -  PI  T19  =  (TMAX(I)  *  DTD ( I ) RETURN ENO  I S E T ( I ) ) / ( 2 4 .  17.  T18  TIN  -  (TMIN(I)  0EXP(T3) d)  TOUT(Id.  6  -  *  (J  d)  "  -  IHRMIN) -  TMIN(I))  TMIN(I)  +  *  DSIN(T18/T6)  T19  22. «  (TIN  -  T O U T d d ,  J))  +  DTD( I )  C)  5  T0UT(2O.3O)  

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