Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

On a response surface investigation of water transport in membrane humidifiers McCarthy, Edward James 2009

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

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
24-ubc_2009_fall_mccarthy_edward.pdf [ 4.3MB ]
Metadata
JSON: 24-1.0067751.json
JSON-LD: 24-1.0067751-ld.json
RDF/XML (Pretty): 24-1.0067751-rdf.xml
RDF/JSON: 24-1.0067751-rdf.json
Turtle: 24-1.0067751-turtle.txt
N-Triples: 24-1.0067751-rdf-ntriples.txt
Original Record: 24-1.0067751-source.json
Full Text
24-1.0067751-fulltext.txt
Citation
24-1.0067751.ris

Full Text

 ON A RESPONSE SURFACE INVESTIGATION OF WATER TRANSPORT IN MEMBRANE HUMIDIFIERS   by  EDWARD JAMES MCCARTHY B.Eng., Carleton University, 2007     A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in The Faculty of Graduate Studies (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  October 2009  © Edward James McCarthy, 2009  ii ABSTRACT  The design of experiments method was applied to create empirical models to evaluate performance of membrane humidifiers. Experiments were run and the results analyzed to develop a combined metric for humidifier performance, provide information regarding effects, and compare geometries and membranes.  A range of experimental designs were evaluated and a central composite design selected to produce a response surface model. The numeric factors chosen were wet and dry stream flow rates and temperatures and the categoric factor was pressure. Four humidifiers were tested with two distinct geometries and two membranes.  The experimental analysis provided factorial models for response surfaces in six performance metrics: water transfer rate; water recovery ratio; humidity ratio; relative humidity; dew point; and dew point approach temperature. All of these models displayed overall model significance and a high signal-to-noise ratio, but also an overall lack of fit to the second-order model. This demonstrated the suitability of the design of experiments approach but suggests the use of a higher-order model.  Based on these models and a priori information regarding performance metrics, a combined metric was proposed incorporating relative humidity, water recovery ratio, and water transport rate. Performance bounds are set using relative humidity, and water recovery ratios inside these bounds are plotted.  Dry side flow rate was found to have a positive effect on total water transport but a negative one on saturation-based metrics. Wet side flow rate had a positive effect on total water transport and a negative effect on relative transport metrics. Dry side  iii temperature had an overall negative effect. Wet side temperature had a similar effect to wet side flow rate. Low pressure had generally higher performance, but high pressure mitigated negative effects in dry side temperature and flow rate. The two geometries showed similar relative performance. The ionic membrane displayed consistently better water transport than the porous polymer membrane.  Based on these results simplified central composite designs for humidifier characterization are proposed, eliminating dry side temperature and pressure as a factor and allowing the possibility of varying flow rates in tandem. These tests have respectively 17 and 11 test runs for full humidifier characterization.  iv TABLE OF CONTENTS  ABSTRACT....................................................................................................................... ii TABLE OF CONTENTS ................................................................................................ iv LIST OF TABLES ......................................................................................................... viii LIST OF FIGURES .......................................................................................................... x LIST OF SYMBOLS AND ABBREVIATIONS ......................................................... xiv ACKNOWLEDGEMENTS .......................................................................................... xvi 1. INTRODUCTION....................................................................................................... 1 1.1. WATER MANAGEMENT IN FUEL CELLS ................................................................. 1 1.2. WATER MANAGEMENT SCHEMES ......................................................................... 4 1.2.1. Self-humidification ................................................................................. 4 1.2.2. Internal humidification............................................................................ 5 1.2.3. External humidification .......................................................................... 6 1.3. TECHNOLOGY CROSSOVER: ERVS ....................................................................... 8 1.4. HUMIDIFIER TERMINOLOGY ................................................................................. 9 1.5. HUMIDIFIER PERFORMANCE ............................................................................... 10 1.5.1. Water transfer rate................................................................................. 11 1.5.2. Water recovery ratio ............................................................................. 11 1.5.3. Humidity ratio....................................................................................... 12 1.5.4. Specific humidity .................................................................................. 12 1.5.5. Relative humidity.................................................................................. 13 1.5.6. Dew point temperature.......................................................................... 13 1.5.7. Dew point approach temperature .......................................................... 14 1.6. CONTROL VOLUME ANALYSIS ............................................................................ 15 1.7. PARAMETERS AFFECTING WATER TRANSPORT.................................................... 17 1.7.1. Geometric factors.................................................................................. 17 1.7.2. Flow parameters.................................................................................... 19 1.8. TESTING FOR PERFORMANCE DETERMINATION................................................... 21 1.9. DESIGN OF EXPERIMENTS METHOD..................................................................... 22 1.9.1. Design of experiments in fuel cell research.......................................... 23 1.9.2. Design of experiments for humidifier performance determination ...... 25 1.10. OVERVIEW OF THESIS......................................................................................... 25 2. DESIGN OF EXPERIMENTS ................................................................................ 27 2.1. FACTOR SELECTION............................................................................................ 27 2.2. FACTOR VALUES ................................................................................................ 28 2.3. CODED FACTORS ................................................................................................ 28 2.4. INTERACTIONS ................................................................................................... 30 2.5. EXPERIMENTAL DESIGNS.................................................................................... 31  v 2.5.1. Two-level factorial designs................................................................... 31 2.5.2. Three-level factorial designs................................................................. 34 2.5.3. Response surface methods .................................................................... 34 2.5.4. Taguchi methods................................................................................... 36 2.6. DESIGN SELECTION ............................................................................................ 37 2.6.1. Choice of alpha and center points......................................................... 39 2.7. FINAL DESIGN OF EXPERIMENTS ......................................................................... 40 3. EXPERIMENTAL APPARATUS........................................................................... 41 3.1. HUMIDIFIERS...................................................................................................... 41 3.1.1. Geometries ............................................................................................ 41 3.1.2. Membranes............................................................................................ 42 3.1.3. Rated flows for humidifiers .................................................................. 43 3.1.4. Humidifier orientation .......................................................................... 43 3.2. TEST STAND ....................................................................................................... 44 3.2.1. Convention for inlets and outlets .......................................................... 45 3.2.2. Air supply and control .......................................................................... 45 3.2.3. Water supply and humidification system.............................................. 46 3.2.4. Temperature sensing and control .......................................................... 47 3.2.5. Pressure sensing and control................................................................. 48 3.3. CONTROL SOFTWARE ......................................................................................... 49 3.4. WATER MEASUREMENT BALANCE ...................................................................... 49 3.5. EXPERIMENTAL PROTOCOL ................................................................................ 51 3.6. DESIGN EXPERT 7 .............................................................................................. 54 4. RESULTS AND STATISTICAL ANALYSES ...................................................... 55 4.1. STATISTICAL ANALYSIS TOOLS........................................................................... 56 4.1.1. ANOVA tables...................................................................................... 56 4.1.2. SSR-lambda plot ................................................................................... 57 4.1.3. Error plot ............................................................................................... 58 4.1.4. Normal plot of residuals........................................................................ 58 4.1.5. Residuals-predicted values plot ............................................................ 59 4.1.6. Predicted values vs actual values.......................................................... 59 4.2. WATER TRANSPORT RATE RESULTS.................................................................... 59 4.2.1. Model and ANOVA.............................................................................. 60 4.2.2. Error plot ............................................................................................... 61 4.2.3. Normal plot of residuals........................................................................ 62 4.2.4. Residuals-predicted values.................................................................... 63 4.2.5. Predicted values vs actual values.......................................................... 64 4.3. WATER RECOVERY RATIO RESULTS.................................................................... 65 4.3.1. Model and ANOVA.............................................................................. 65 4.3.2. Error plot ............................................................................................... 67 4.3.3. Normal plot of residuals........................................................................ 68 4.3.4. Residuals-predicted values.................................................................... 69 4.3.5. Predicted values vs actual values.......................................................... 70 4.4. STREAM 2 HUMIDITY RATIO RESULTS................................................................. 71 4.4.1. Model and ANOVA.............................................................................. 71  vi 4.4.2. Error plot ............................................................................................... 72 4.4.3. Normal plot of residuals........................................................................ 73 4.4.4. Residuals-predicted values.................................................................... 74 4.4.5. Predicted values vs actual values.......................................................... 75 4.5. STREAM 2 RELATIVE HUMIDITY RESULTS ........................................................... 75 4.5.1. Model and ANOVA.............................................................................. 76 4.5.2. Error plot ............................................................................................... 77 4.5.3. Normal plot of residuals........................................................................ 78 4.5.4. Residuals-predicted values.................................................................... 79 4.5.5. Predicted values vs actual values.......................................................... 80 4.6. STREAM 2 DEW POINT TEMPERATURE RESULTS .................................................. 81 4.6.1. Model and ANOVA.............................................................................. 81 4.6.2. Error plot ............................................................................................... 82 4.6.3. Normal plot of residuals........................................................................ 83 4.6.4. Residuals-predicted values.................................................................... 84 4.6.5. Predicted values vs actual values.......................................................... 85 4.7. DEW POINT APPROACH TEMPERATURE RESULTS................................................. 85 4.7.1. Model and ANOVA.............................................................................. 86 4.7.2. Error plot ............................................................................................... 87 4.7.3. Normal plot of residuals........................................................................ 88 4.7.4. Residuals-predicted values.................................................................... 89 4.7.5. Predicted values vs actual values.......................................................... 90 4.8. RESULTS SUMMARY ........................................................................................... 91 5. DISCUSSION ............................................................................................................ 92 5.1. THERMODYNAMIC CONSISTENCY ....................................................................... 92 5.2. READING RESPONSE SURFACE PLOTS.................................................................. 93 5.3. PERFORMANCE METRICS .................................................................................... 95 5.3.1. Defining “goodness”............................................................................. 95 5.4. ASSESSING “GOODNESS”.................................................................................... 96 5.4.2. Combined metrics ................................................................................. 99 5.5. MAIN EFFECTS ................................................................................................. 102 5.5.1. Stream 1 flow rate............................................................................... 102 5.5.2. Stream 3 flow rate............................................................................... 103 5.5.3. Stream 1 temperature .......................................................................... 104 5.5.4. Stream 3 temperature .......................................................................... 105 5.5.5. Pressure ............................................................................................... 107 5.6. FACTOR INTERACTIONS.................................................................................... 107 5.6.1. AC: Q1 and T1 ..................................................................................... 107 5.6.2. AE: Q1 and pressure............................................................................ 109 5.6.3. CE: T1 and pressure ............................................................................ 110 5.7. GEOMETRY ...................................................................................................... 110 5.8. MEMBRANE ..................................................................................................... 110 6. CONCLUSIONS ..................................................................................................... 112 6.1. DESIGN OF EXPERIMENTS IN HUMIDIFIER PERFORMANCE ................................. 112 6.2. PERFORMANCE OF TESTED HUMIDIFIERS .......................................................... 113  vii 6.3. CHARACTERIZING PERFORMANCE .................................................................... 114 6.4. FACTORS AFFECTING PERFORMANCE ............................................................... 114 6.5. HUMIDIFIER MODEL ......................................................................................... 115 6.6. FUTURE WORK ................................................................................................. 116 7. REFERENCES........................................................................................................ 117 APPENDIX A: RESULTS PLOTS ............................................................................. 120 APPENDIX B: ANOVA TABLES .............................................................................. 145 APPENDIX C: APPLYING A CCD TO ERVS......................................................... 152 APPENDIX D: A SIMPLIFIED CCD FOR HUMIDIFIERS .................................. 155   viii LIST OF TABLES  Table 1.1: Performance metrics for humidifiers........................................................................................... 15 Table 1.2: Geometric factors affecting humidifier performance .................................................................. 18 Table 1.3: Flow properties affecting humidifier performance...................................................................... 20 Table 1.4: Experimental protocols used in fuel cell humidifier literature .................................................... 22 Table 1.5: Experimental designs used in PEMFC literature......................................................................... 25 Table 2.1: Factor selections for design of experiments ................................................................................ 27 Table 2.2: Selection of factor values ............................................................................................................ 28 Table 2.3: 2k full factorial design in five factors including second-order effects ......................................... 32 Table 2.4: 2k-1 fractional factorial design in five factors aliased on interaction DE ..................................... 33 Table 2.5: Benefits and disadvantages of experimental designs considered ................................................ 39 Table 2.6: Final values for design of experiments........................................................................................ 40 Table 3.1: Flow rates for design of experiments .......................................................................................... 43 Table 4.1: Models for water transfer rate ..................................................................................................... 60 Table 4.2: Summary of statistical significance for water transport rate ....................................................... 60 Table 4.3: Models for water recovery ratio .................................................................................................. 65 Table 4.4: Summary of statistical significance for water recovery ratio ...................................................... 65 Table 4.5: Models for stream 2 humidity ratio ............................................................................................. 71 Table 4.6: Summary of statistical significance for stream 2 humidity ratio ................................................. 71 Table 4.7: Models for stream 2 relative humidity ........................................................................................ 76 Table 4.8: Summary of statistical significance for stream 2 relative humidity ............................................ 76 Table 4.9: Models for stream 2 dew point .................................................................................................... 81 Table 4.10: Summary of statistical significance for stream 2 dew point ...................................................... 81 Table 4.11: Models for dew point approach temperature ............................................................................. 86 Table 4.12: Summary of statistical significance for dew point approach temperature ................................. 86 Table 4.13: Summary of results with statistical significance across all tests................................................ 91 Table 5.1: Values of line plotted in Figure 5.1 ............................................................................................. 94  ix Table 5.2: Average of model F-values for metrics ....................................................................................... 98 Table B.1: ANOVA tables for water transport rate .................................................................................... 145 Table B.2: ANOVA tables for water recovery ratio ................................................................................... 146 Table B.3: ANOVA tables for stream 2 humidity ratio.............................................................................. 147 Table B.4: ANOVA tables for stream 2 relative humidity ......................................................................... 148 Table B.5: ANOVA tables for stream 2 dew point temperature................................................................. 149 Table B.6: ANOVA tables for dew point approach temperature................................................................ 150 Table C.1: Parameter values for a CCD for ERVs ..................................................................................... 153 Table D.1: Experimental table for CCD in Q1, Q3, and  T3 ........................................................................ 155 Table D.2: Experimental table for CCD in Q, T1, and T3 ........................................................................... 155 Table D.3: Experimental table for CCD in Q and T3.................................................................................. 156    x LIST OF FIGURES  Figure 1.1: Water production and flow in a fuel cell cathode humidification system .................................... 2 Figure 1.2: Optimal humidity range for a PEMFC stack with stoichiometry curves (from [2])..................... 4 Figure 1.3: Flow naming convention for humidifiers................................................................................... 10 Figure 2.1: Visualization of a central composite design in three factors ...................................................... 35 Figure 2.2: Visualization of a Box-Behnken design in three factors ............................................................ 36 Figure 3.1: Px1-32 plate geometry ............................................................................................................... 42 Figure 3.2: Px3-46 plate geometry ............................................................................................................... 42 Figure 3.3: Flow pattern and humidifier orientation used ............................................................................ 44 Figure 3.4: Schematic of test apparatus........................................................................................................ 45 Figure 3.5: Schematic of water balance measurement apparatus ................................................................. 51 Figure 3.6: Flowchart of experimental protocol ........................................................................................... 53 Figure 4.1: Pattern used for presenting diagnostics...................................................................................... 56 Figure 4.2: Example SSR-λ plot (Px1-32M, WRR) ..................................................................................... 58 Figure 4.3: Error plots for water transport rate............................................................................................. 61 Figure 4.4: Normal plots of residuals for water transfer rate........................................................................ 62 Figure 4.5: Residuals-predicted values plots for water transfer rate............................................................. 63 Figure 4.6: Predicted values vs. actual values for water transfer rate........................................................... 64 Figure 4.7: Error plots for water recovery ratio............................................................................................ 67 Figure 4.8: Normal plots of residuals for water recovery ratio..................................................................... 68 Figure 4.9: Residuals-predicted values plots for water recovery ratio ......................................................... 69 Figure 4.10: Predicted values vs. actual values for water recovery ratio...................................................... 70 Figure 4.11: Error plots for stream 2 humidity ratio..................................................................................... 72 Figure 4.12: Normal plots of residuals for stream 2 humidity ratio ............................................................. 73 Figure 4.13: Residuals-predicted values plots for stream 2 humidity ratio .................................................. 74 Figure 4.14: Predicted values vs. actual values for stream 2 humidity ratio ................................................ 75 Figure 4.15: Error plots for stream 2 relative humidity ................................................................................ 77   xi Figure 4.16: Normal plots of residuals for stream 2 relative humidity......................................................... 78 Figure 4.17: Residuals-predicted values plots for stream 2 relative humidity.............................................. 79 Figure 4.18: Predicted values vs. actual values for stream 2 relative humidity............................................ 80 Figure 4.19: Error plots for stream 2 dew point ........................................................................................... 82 Figure 4.20: Normal plots of residuals for stream 2 dew point temperature ................................................ 83 Figure 4.21: Residuals-predicted values plots for stream 2 dew point temperature ..................................... 84 Figure 4.22: Predicted values vs. actual values for stream 2 dew point ....................................................... 85 Figure 4.23: Error plots for dew point approach temperature ...................................................................... 87 Figure 4.24: Normal plots of residuals for dew point approach temperature ............................................... 88 Figure 4.25: Residuals-predicted values plots for dew point approach temperature .................................... 89 Figure 4.26: Predicted values vs. actual values for dew point approach temperature .................................. 90 Figure 5.1: Example for reading multiple axis plots .................................................................................... 94 Figure 5.2: Water recovery ratio plot within relative humidity bounds: Q1 vs Q3 for Px1-32M, with C=-1, D=0, E=-1 ............................................................................................................................. 100 Figure 5.3: Water recovery ratio plot within relative humidity bounds: T1 vs T3 for Px3-46N, with A=0, B=0, E=-1.............................................................................................................................. 101 Figure 5.4: Stream 2 relative humidity plot of Q1 vs Q3 for Px1-32N, with C=-1, D=0, E=-1................... 103 Figure 5.5: Water transfer rate plot of T1 vs Q3 for Px1-32M, with A=0, D=0, E=-1 ................................ 105 Figure 5.6: Water transfer rate plot of T3 vs Q1 for Px1-32M, with B=0, C=-1, E=-1 ............................... 106 Figure 5.7: Stream 2 relative humidity plot of Q1 vs T1 for Px3-46N, with B=0, D=0, E=-1 .................... 108 Figure 5.8: Water transfer rate plot of Q1 vs T1 for Px3-46M, with B=0, D=0, E=-1 ................................ 109 Figure A.1: Plot for Px1-32M stream 2 DP low pressure........................................................................... 121 Figure A.2: Plot for Px1-32M DPAT low pressure .................................................................................... 121 Figure A.3: Plot for Px1-32M stream 2 HR low pressure .......................................................................... 122 Figure A.4: Plot for Px1-32M stream 2 RH low pressure .......................................................................... 122 Figure A.5: Plot for Px1-32M WRR low pressure ..................................................................................... 123 Figure A.6: Plot for Px1-32M stream 2 WTR low pressure ....................................................................... 123 Figure A.7: Plot for Px1-32N stream 2 DP low pressure ........................................................................... 124 Figure A.8: Plot for Px1-32N DPAT low pressure..................................................................................... 124 Figure A.9: Plot for Px1-32N stream 2 HR low pressure ........................................................................... 125   xii Figure A.10: Plot for Px1-32N stream 2 RH low pressure ......................................................................... 125 Figure A.11: Plot for Px1-32N WRR low pressure .................................................................................... 126 Figure A.12: Plot for Px1-32N WTR low pressure .................................................................................... 126 Figure A.13: Plot for Px3-46M stream 2 DP low pressure......................................................................... 127 Figure A.14: Plot for Px3-46M DPAT low pressure .................................................................................. 127 Figure A.15: Plot for Px3-46M stream 2 HR low pressure ........................................................................ 128 Figure A.16: Plot for Px3-46M stream 2 RH low pressure ........................................................................ 128 Figure A.17: Plot for Px3-46M WRR low pressure ................................................................................... 129 Figure A.18: Plot for Px3-46M WTR low pressure.................................................................................... 129 Figure A.19: Plot for Px3-46N 2 DP low pressure ..................................................................................... 130 Figure A.20: Plot for Px3-46N DPAT low pressure................................................................................... 130 Figure A.21: Plot for Px3-46N stream 2 HR low pressure ......................................................................... 131 Figure A.22: Plot for Px3-46N stream 2 RH low pressure ......................................................................... 131 Figure A.23: Plot for Px3-46N WRR low pressure .................................................................................... 132 Figure A.24: Plot for Px3-46N WTR low pressure .................................................................................... 132 Figure A.25: Plot for Px1-32M stream 2 DP high pressure........................................................................ 133 Figure A.26: Plot for Px1-32M DPAT high pressure ................................................................................. 133 Figure A.27: Plot for Px1-32M stream 2 HR high pressure ....................................................................... 134 Figure A.28: Plot for Px1-32M stream 2 RH high pressure ....................................................................... 134 Figure A.29: Plot for Px1-32M WRR high pressure .................................................................................. 135 Figure A.30: Plot for Px1-32M WTR high pressure .................................................................................. 135 Figure A.31: Plot for Px1-32N stream 2 DP high pressure ........................................................................ 136 Figure A.32: Plot for Px1-32N DPAT high pressure.................................................................................. 136 Figure A.33: Plot for Px1-32N stream 2 HR high pressure........................................................................ 137 Figure A.34: Plot for Px1-32N stream 2 RH high pressure........................................................................ 137 Figure A.35: Plot for Px1-32N WRR high pressure ................................................................................... 138 Figure A.36: Plot for Px1-32N WTR high pressure ................................................................................... 138 Figure A.37: Plot for Px3-46M stream 2 DP high pressure........................................................................ 139 Figure A.38: Plot for Px3-46M DPAT high pressure ................................................................................. 139   xiii Figure A.39: Plot for Px3-46M stream 2 HR high pressure ....................................................................... 140 Figure A.40: Plot for Px3-46M stream 2 RH high pressure ....................................................................... 140 Figure A.41: Plot for Px3-46M WRR high pressure .................................................................................. 141 Figure A.42: Plot for Px3-46M WTR high pressure .................................................................................. 141 Figure A.43: Plot for Px3-46N stream 2 DP high pressure ........................................................................ 142 Figure A.44: Plot for Px3-46N DPAT high pressure.................................................................................. 142 Figure A.45: Plot for Px3-46N stream 2 HR high pressure........................................................................ 143 Figure A.46: Plot for Px3-46N stream 2 RH high pressure........................................................................ 143 Figure A.47: Plot for Px3-46N WRR high pressure ................................................................................... 144 Figure A.48: Plot for Px3-46N WTR high pressure ................................................................................... 144  xiv LIST OF SYMBOLS AND ABBREVIATIONS  Symbol Description (units) A membrane area per layer in humidifier A coded level of stream 1 flow rate B coded level of stream 3 flow rate C coded level of stream 1 temperature D coded level of stream 3 temperature and dew point E coded level of pressure h enthalpy per unit mass (kJ kg-1) m&  mass flow rate (kg s-1) P pressure (Pa) Q volumetric flow rate (SLPM) Q&  heat transfer rate (kJ kg-1 s-1) T temperature (°C)  Greek symbols α coded value of extremes in central composite design λ model transformation ζ  specific humidity (kg water/kg mixture) φ relative humidity ω humidity ratio (kg water/kg dry air)  Subscripts and superscripts 1 stream 1 (dry inlet) 2 stream 2 (dry outlet) 3 stream 3 (wet inlet) 3→2 transfer from stream 3 to stream 2 4 stream 4 (wet outlet) air referring to dry air dp dew point layers layers of membrane in humidifier flow field stack liq refers to liquid water loss transfer or loss to humidifier surroundings max maximum min minimum ref reference state sat value at saturation total refers to total mixture w referring to water  Abbreviations BBD Box-Behnken Design CCD Central Composite Design DP Dew point DPAT Dew point Approach Temperature ERV Energy Recovery Ventilator HR Humidity Ratio   xv Symbol Description (units) HVAC Heating, Ventilating and Air Conditioning PEM Proton Exchange Membrane PEMFC Proton Exchange Membrane Fuel Cell RH Relative Humidity WRR Water Recovery Ratio WTR Water Transfer Rate    xvi ACKNOWLEDGEMENTS There are many people without whom I could not have produced this work. First I extend my gratitude to Dr. Walter Mérida, my supervisor, not only for his time and his valuable direction throughout this project, but also for his understanding and support of my various and time-consuming extracurricular activities involving snow and mountains.  dpoint technologies has been invaluable to me throughout my work, not only for their financial aid, along with NSERC and MITACS, but also for material and technical support. In particular at dpoint I would like to thank James Dean for accepting me as a student, sight unseen, and for continuing to support me throughout the past two years. I would also like to thank Chad Comeault for general encouragement and advice, technical discussions, and work on the test station; Chris Goodchild and Paulo Costa for testing support; Ryan Huizing for being a wealth of membrane information and for partially inspiring the basis of this project; and Kyuhyeon (Harris) Lee for building my test humidifiers and for general permanent cheeriness and inspiration.  I would like to thank Dr. Mérida’s group at UBC – Omar Herrera, Saul Pazos- Knoop, Amir Niroumand, and especially Tatiana Romero – for giving me a warm welcome and a firm but gentle shove up the fuel cell humidification learning curve and, in Tatiana’s case, proofreading services. I would like to extend my particular gratitude to David Kadylak from both dpoint and UBC for help with all technical sides of this work, for editing services, for patience with endless questions, and for being an all-around good guy.  Finally, I would like to thank my brother, Tom McCarthy, for all sorts of extracurricular support, and for making a mean bowl of chili. 1 1. INTRODUCTION  A 2005 analysis of a full polymer electrolyte membrane fuel cell (PEMFC) system for automotive applications, naming the cost of the fuel cell stack as 63% of an $8,640, 80 kW system, put the cost of reactant humidification systems at up to 7% of the total cost, approximately 20% of the cost of the total balance of plant [1]. This made reactant humidification the most expensive component in the system outside of the compressor-expander module and the stack itself. Humidification, therefore, is a promising area in which cost reductions for the overall system can be achieved. A practical understanding of the effects of changing operating conditions on overall humidifier performance is of great value in making changes to humidifiers in order to reduce these costs. 1.1. WATER MANAGEMENT IN FUEL CELLS  One of the major technical challenges in PEM fuel cell development is the management of water inside the fuel cell stack. The presence of water inside the fuel cell stack is inevitable; during operation, it is constantly produced at the fuel cell cathode by the cathode reaction. In addition, the characteristics of proton exchange membranes currently used in fuel cell stacks, such as DuPont’s Nafion membrane and other sulphonated fluoropolymers, and the mechanisms of proton transport across these membranes dictate the necessity of proper water management for effective operation of the fuel cell [2]. A simplified view of the production and movement of water within a cathode humidification system is presented in Figure 1.1.  2  Figure 1.1: Water production and flow in a fuel cell cathode humidification system   The proton conductivity of a sulphonated fluoropolymer depends on its water content. The sulphonated chains in the membranes create hydrophilic regions, which absorb large quantities of water. These regions of water allow the transport of H+ ions through the membrane. As the water content of the membrane decreases, the rate of conduction of protons through the membrane decreases along with it, limiting the rate of reaction and power produced by the fuel cell [3]. Water production in the stack is caused by this reaction, so the decrease in rate of reaction creates a feedback loop which dries out the membrane. A dry membrane not only poses issues for fuel cell performance, it also increases the chances of damage to the membrane itself, which can lead to long-term degradation in stack performance. The main cause of this degradation is the swelling that takes place in the membrane as it absorbs water, typically an increase of 10%-20% over the membrane’s dry volume [4,5]. Constant changes in volume as a membrane dries and rehydrates introduce mechanical stresses which may cause damage, such as so-called “pinholes”, to the membrane [6,7].  3  These dangers of a dehydrated membrane are counterbalanced by the need to avoid excess water accumulation on the surface of the membrane electrode assembly (MEA). Excess liquid water on either the anode or the cathode sides of the MEA will decrease the electrode area available for the fuel cell reaction to occur, increasing the mass transport losses associated with the reaction. This results in decreased power production from the stack.  It is therefore optimal to maintain the humidity through the fuel cell stack in a narrow band which causes neither dehydration nor flooding, as shown in Figure 1.2 [2]. This requires an equilibrium maintained between the two sources of water to the fuel cell stack: water created as a product of the cathode reaction; and water carried into the stack with either the oxidant or fuel streams [8]. The humidifiers discussed in this thesis are designed for cathode humidification in PEMFC systems.  4  Figure 1.2: Optimal humidity range for a PEMFC stack with stoichiometry curves (from [2])  1.2. WATER MANAGEMENT SCHEMES 1.2.1. SELF-HUMIDIFICATION  Numerous methods have been developed to deal with the problem of water management within the fuel cell stack [8-13]. The simplest of these is known as self- humidification. Self-humidification involves allowing the water produced at the cathode to provide all the water for the stack. Water is supplied to the anode entirely through back diffusion, and excess water is evaporated and pulled away by the cathode air stream. Self- humidification requires no additional parts or control systems in the balance of plant. This is only practical, however, in small, low-power applications. This is in part due to  5 the effect of the electro-osmotic drag; this movement of water in the direction of H+ ions means that the anode will always be drier than the cathode. In addition, when the air in the stack is not fully saturated, it will have a drying effect on the membrane. This effect is more pronounced as air temperature increases, as the saturation pressure for water in air increases with air temperature in a non-linear manner. 1.2.2. INTERNAL HUMIDIFICATION  An alternative humidification scheme is internal humidification, where water is supplied directly to the fuel cell stack as needed. There are a number of methods for accomplishing internal humidification [14-16]. The first is the injection of liquid water directly into the fuel cell. This poses issues for control to avoid the aforementioned problem of flooding the electrode surface. In a well-controlled situation, the flow of reactant gases would cause the injected water to be well distributed throughout the flow field on either side of the electrode [17].  Another form of internal humidification is the use of an internal membrane humidifier. In this case, a certain volume of the stack is dedicated to humidification. Liquid water flows on one side of a hygroscopic membrane positioned upstream of the stack with respect to the flow of reactants. The diffusion of the water through the membrane leads to humidification of reactant streams inside the stack. This method, like the former, requires a control system and supply of liquid water [18,19].  There is also research into another, more passive form of internal humidification. This method is the use of wicks or sponges between the flow field and the gas diffusion layer (GDL) [20,21]. These wicks promote the more even distribution of water throughout the stack by moving the excess water at the flow field outlet to areas of lower  6 humidity. An alternative use of these wicks moves water from a separate source to the membranes themselves. This avoids the problem of control, but still necessitates the maintenance of a separate water reservoir, and introduces a sealing problem to the stack design. 1.2.3. EXTERNAL HUMIDIFICATION  A further family of humidification schemes is external humidification. In this case the reactants are humidified before entering the stack. As with internal humidification, one method for accomplishing this is through direct injection of liquid water [22]. While moving this process outside the fuel cell stack simplifies its application, there is still a requirement for control systems and a liquid reservoir to supply the spray injection. Another direct humidification method, used mainly in laboratory settings, involves bubbling reactant gases through a heated reservoir to humidify them to saturation at the temperature of the reservoir. This process is known as “sparging”.  Another type of external humidification eliminates the need for a separate water reservoir. This is the use of so-called “enthalpy wheels”, rotating elements which absorb water from the stack exhaust and subsequently release it into the drier reactant streams. This technology is widely used in building heating, ventilating, and air conditioning (HVAC) systems for air humidity control. It requires additional moving components in the fuel cell system, however, introducing new sealing difficulties and possibilities for mechanical failure.  Finally, external humidification can be accomplished using passive membrane- based heat and humidity exchangers. These humidifiers use a hygroscopic membrane, commonly the same types of membranes used in MEAs, to separate exhaust and reactant  7 flows. The membrane allows the diffusion of water from exhaust to reactant, while preventing the crossover of gases. This allows an entirely passive humidification system, without the need for controls or an external reservoir, as long as the design of the humidifier is such that enough water is transferred to humidify the reactant streams. 1.2.3.1 Shell-and-tube humidifiers  Several designs have been developed for shell-and-tube humidifiers. One such common design is known as a shell-and-tube humidifier, which is similar to the shell- and-tube heat exchanger design. In the general case, exemplified by the product distributed by Perma Pure, the dry reactant stream flows inside cylindrical tubes of membrane, while the wet exhaust stream or coolant water flows in the opposite direction inside a shell surrounding these tubes. One advantage of this method is that it maximizes the use of membrane area for water transport; another is the increased pressure tolerance of the cylindrical geometry. There are, however, problems with even mixing of the wet stream, as gases may circumvent the tubes which are parallel to the direction of flow and tend to be concentrated in the center of the humidifier. In addition, production models of this type of humidifier are made from Nafion, the sulphonated fluoropolymer mentioned above and commonly used in fuel cell stacks. Nafion is a highly specialized material designed to optimize proton transport, and as a result is expensive. 1.2.3.2 Plate-and-frame humidifiers  An alternative design for membrane-based humidifiers is the plate-and-frame humidifier. Once again, the geometry is analogous to a common heat exchanger design, in this case the design of plate-and-frame heat exchangers. In such a humidifier, the exhaust and reactant gases enter the humidifier through separate manifolds which lead to  8 a planar flow field designed to allow for an evenly spread flow distribution. A number of these flow fields are stacked on top of one another, separated by hygroscopic membrane, and the exhaust and reactant are directed in their respective manifolds to alternating flow fields in a counter flow arrangement. When well designed, this allows an even distribution of humidity throughout humidified reactant. This can also be accomplished with much cheaper hygroscopic membranes than Nafion [23], resulting in increased cost savings. Humidifiers of this type are currently produced by DPoint Technologies, and are the primary focus of this thesis. 1.3. TECHNOLOGY CROSSOVER: ERVS  The enthalpy recovery ventilator (ERV) is another technology which operates on the same principles as fuel cell humidifiers. ERVs are also similar in construction to plate-and-frame design humidifiers. These devices are used in modern HVAC systems in buildings with low air leakage rates to save energy by pre-conditioning intake ventilation air. ERVs use a hygroscopic membrane, similar to those used in plate-and-frame humidifiers. The membranes separate alternating layers of building exhaust air and fresh ventilation air in a stacked planar arrangement. Winter – “heating” – ERV use is the most similar to fuel cell humidifiers. In this case, cold dry air is taken in from the environment and enters the ERV before any active building heating system. Stale air at building conditions, warm and humid relative to the intake air, is blown through the ERV before being finally exhausted to the environment. The ERV allows the passive transfer of heat and humidity from exhaust air to ventilation air, reducing the eventual load on the building air conditioning system. In summer – “cooling” – conditions, the situation is reversed, and hot humid ambient air is cooled and dried by building air in the ERV. This  9 can result in even more dramatic energy savings than the winter case, as a large portion of cooling load in warm climates is often related to the latent heat in humid air which is removed as water is “knocked out” of the intake air in the ERV.  The similarities in operation between planar ERVs and membrane humidifiers are clear. These similarities were used by Cave, and later Kadylak [24,25], to develop performance models for planar fuel cell humidification systems based on adaptations of earlier work by Zhang on ERVs [26-30]. While this thesis focuses primarily on testing humidifiers for fuel cell applications, the techniques described herein are equally applicable to testing ERVs. 1.4. HUMIDIFIER TERMINOLOGY  To simplify the discussion of humidifier flows, a certain common terminology is adopted to designate the flow at various points in the humidifier. This terminology will be used throughout this thesis. A typical fuel cell humidification system is shown schematically in Figure 1.3. Dry oxygen or atmospheric air, intended as the oxidant for the fuel cell, is blown into the humidifier dry side inlet (stream 1). At the same time, moist exhaust from the fuel cell cathode, depleted in oxidant, is returned to the humidifier wet side inlet (stream 3). A quantity of the moisture from stream 3 is transported through the humidifier membrane to the dry side, causing the flow at the humidifier dry side outlet (stream 2) to be humidified. Finally, the depleted oxidant and its remaining moisture flow out via the wet side outlet (stream 4).  10  Figure 1.3: Flow naming convention for humidifiers 1.5. HUMIDIFIER PERFORMANCE  In designing membrane humidifiers it is important to be able to measure and quantify performance. Humidifier performance can be defined in many ways. An increase in water transport at identical operating conditions is an objective increase in performance. The introduction to this chapter, however, laid out overall cost as a significant driver of fuel cell humidifier research. The membranes used in humidifiers are themselves the major cost driver of humidifiers. Taking this into consideration, improved performance can also be considered to be an increase in the water transport to membrane area ratio. The matter of quantifying performance, however, is further confused by the issue of defining performance under practical operating conditions. There are a number of methods of quantifying humidifier performance, and the selection of an appropriate performance metric is an essential tool in developing high performance humidifiers. These methods are summarized in Table 1.1.  11 1.5.1. WATER TRANSFER RATE  The most basic method for quantifying water transport in membrane humidifiers is the water transfer rate (WTR). This is the rate at which the mass of water is transported from the exhaust to the reactant stream. The water transfer rate has the benefit of being a direct measurement, being very easy to measure, and being an absolute metric of performance. It can be normalized by various factors, allowing the reporting of water transfer rate per volume of humidifier, per membrane area, or per dollar, for example. The performance of the fuel cell itself, however, is dependent on the relative humidity of the reactant streams, rather than the absolute mass of water contained within them. Under low flow conditions, a low water transfer rate can humidify the reactant streams to a satisfactory degree, while under high flow conditions a relatively higher water transfer rate may be inadequate to maintain stack performance. 1.5.2. WATER RECOVERY RATIO  Another humidifier performance metric is the water recovery ratio (WRR). This is based on the water transfer rate, but provides more generalized information about performance. The WRR, expressed as either a fraction or a percentage, is analogous to the effectiveness metric of a heat exchanger. The WRR is the ratio of the rate at which water is transported from exhaust to reactant, to the rate at which water is supplied to the humidifier in the exhaust stream, as demonstrated in equation 1.1.  2 1 3 w w w m mWRR m − = & & &  (1.1)  This metric allows a good side-by-side comparison of humidifiers and operating conditions. It does not provide a description of the condition of the reactant being  12 supplied to the fuel cell stack, and as such does not in isolation allow the estimation of whether the humidifier is operating at a satisfactory level in a fuel cell system. 1.5.3. HUMIDITY RATIO  One measurement commonly used in psychrometrics is the humidity ratio (HR). The humidity ratio is the ratio of the mass of water to the mass of dry air in a given sample of moist air, as demonstrated in equation 1.2.  w air m m ω =  (1.2)  This measurement is very convenient for the calculation of total water flux when the mass flow rate of dry air is known (as is the case for the experimental setup used in this thesis.) This calculation, used in the control volume analysis of the humidifier, is demonstrated in equation 1.3.  (1 )total airm m ω= +& &  (1.3)  As with mass transfer metrics, the humidity ratio does not provide enough information on its own to determine whether humidifier performance is adequate. 1.5.4. SPECIFIC HUMIDITY  The specific humidity is closely related to the humidity ratio. Its form is also a dimensionless mass ratio. The distinction between humidity ratio and specific humidity is that the specific humidity is a ratio of the mass of water to the total mass of humidified air in a given sample of moist air, as demonstrated in equation 1.4.  w total m m ζ =  (1.4)  13  This metric is useful for calculating water flux when the total mass flow rate of moist air is known, but its utility as a performance metric is subject to the same limitation as that of the humidity ratio. 1.5.5. RELATIVE HUMIDITY  Relative humidity (RH) may be the most widely known psychrometric measurement due to its daily usage in weather reportage. The relative humidity is the ratio of the vapour pressure of water in a medium to the saturation pressure of water at the conditions of the medium, as demonstrated in equation 1.5.  w sat w P P φ =  (1.5)  This is in fact a measure of how close the vapour is to saturation. Unlike any of the preceding metrics for reactant humidity, relative humidity takes into account the temperature of the reactant and the effect this has on the vapour saturation. The required level of reactant humidification has been described in terms of relative humidity, with the desirable reactant relative humidity being near to 100% [2,6]. The relative humidity of the humidified reactant is a good indication of the suitability of humidification in the system. This metric on its own, while indicating the adequacy of humidification, does not provide information regarding the level of performance of the humidifier in the same way as the WRR does. 1.5.6. DEW POINT TEMPERATURE  A measurement related to the relative humidity is the dew point temperature (DP). The dew point temperature is an expression of the temperature at which a given sample of moist air will reach saturation, if the humidity ratio is maintained at the same level. In  14 the example of humidification achieved using the sparging technique, the dew point temperature of the air is the temperature of the water bath through which the air is bubbled, independent of any subsequent heating steps. Partially because of this, and the widespread use of sparging as a laboratory humidification technique, dew point temperature of the reactants can be used as a specification for system humidification. On its own, however, dew point temperature provides little information regarding performance. 1.5.7. DEW POINT APPROACH TEMPERATURE  The dew point approach temperature (DPAT) is another measurement often used in humidification system specifications. Once again, this is a metric which has an analogy in heat exchanger design, in this case the “pinch temperature”. The DPAT is expressed as the difference between the dew point temperature of the moist exhaust air entering the humidifier from the stack and the dew point temperature of the humidified reactant leaving the humidifier to enter the stack.  3 2dp dpDPAT T T= −  (1.6)  In the idealized case for a humidifier system the DPAT approaches a value of 0; higher DPATs indicate decreased performance. The analogy to the pinch temperature is not a complete one. As with the dew point temperature, the DPAT does not explicitly take into account the effects of temperature, and a humidifier operating with a high DPAT at a high temperature may be performing much better in terms of total water transport and water recovery ratio than a similar humidifier operating with a lower DPAT at a lower temperature. This is because the saturation curve of water increases non- linearly in such a way that vapour at a higher temperature will have a much higher  15 saturation pressure than at a lower temperature. As such, the DPAT, while appropriate as a performance specification for a fuel cell system when the other system parameters are specified, on its own provides no practical information regarding humidifier performance. Table 1.1: Performance metrics for humidifiers Performance metric Advantages Disadvantages Water transfer rate - Unambiguous - Directly measured - No relative performance information Water recovery ratio - Generalized - Similar to heat exchanger analysis - Good for comparisons - No saturation state information - Dependent on inlet conditions Humidity ratio - Convenient for water flux calculations - No saturation state or relative performance information Relative humidity - Good indicator for system performance - No relative performance information - Outlet temperature dependent Dew point temperature - Commonly used to specify system requirements - Temperature independent - No relative performance information Dew point approach temperature - Commonly used to specify humidifier performance - Difficult to understand - Temperature dependent  1.6. CONTROL VOLUME ANALYSIS  The thermodynamic models of planar humidifiers mentioned above provide detailed descriptions of heat and mass transfer in humidifier channels. These and other models are outlined in section 1.8. All are subject to limitations that this work is intended to circumvent by using a statistical approach rather than a thermodynamic one. Overall performance of full humidifiers is the focus of this work, rather than the transport phenomena involved. It is essential, however, to understand the mass and heat transfer taking place within the humidifier, so a control volume analysis is presented here. For a sign convention this control volume uses the directions for streams from Figure 1.3; assumes that heat exchange with the surroundings goes from the humidifier to the  16 surroundings; and assumes that heat and mass transfer between wet and dry sides is from the wet to the dry side.  Each humidifier is tested before use to ensure the absence of internal and external leaks. This means that for the full humidifier, considering the possibility of condensation on wet and dry sides,  2 2 2 4 4 4 1 1 3 3(1 ) (1 ) (1 ) (1 )air liq air liq air airm m m m m mω ω ω ω+ + + + + = + + +& & & & & &  (1.7)  For a control volume encompassing only the dry side or the wet side, the water transport across the membrane must be considered, resulting in  2 2 2 1 1 3 2(1 ) (1 )air liq air wm m m mω ω →+ + = + +& & & &  (1.8) for the dry side and, for the wet side,  4 4 4 3 3 3 2(1 ) (1 )air liq air wm m m mω ω →+ + = + −& & & &  (1.9)  The absence of leaks does not prevent heat loss to the humidifier’s surroundings. An energy balance for the full humidifier results in  2 2 2 2 2 2 4 4 4 4 4 4 1 1 1 1 3 3 3 3 ( ) ( ) ( ) ( ) air air w liq liq air air w liq liq loss air air w air air w m h h m h m h h m h Q m h h m h h ω ω ω ω + + + + + + = + + + && & & & & &  (1.10)  A control volume including only the dry side must consider both the sensible and latent heat transfer from the wet side, resulting in  2 2 2 2 2 2 12 1 1 1 1 3 2 3 2 ( ) ( ) air air w liq liq loss air air w w w layers A m h h m h Q m h h m h dA ω ω → → + + + = + + ∑ ∫ && & & &  (1.11)  The final term in equation 1.11 reflects the variation in water transport between wet and dry sides at various points and layers in the humidifier. This term causes modeling difficulties in full humidifiers; nothing found in the literature has a model for  17 this transport in a full humidifier. This modeling difficulty is an inspiration for the experimental approach taken in this work. 1.7. PARAMETERS AFFECTING WATER TRANSPORT  The complexity of modeling water transport in membrane humidifiers is exacerbated by the number of factors outside of the membrane itself which affect the rate of water transport. These factors can be divided into two groups: first, geometric factors related to the construction, design, and topology of the humidifier and the humidifier flow field plate; and second, flow parameters, related to the conditions of the exhaust and reactant streams entering the humidifier during operation. 1.7.1. GEOMETRIC FACTORS  Plate-and-frame type humidifiers can be made with any number of designs for topology and overall size. This thesis focuses primarily on the testing of two humidifiers with set geometries produced by DPoint technologies, and as such has little emphasis on the contributions of individual geometric factors. Reasons for this are the conflation of various geometric factors with one another and the difficulty of selecting an appropriate basis for normalization of geometry, whether humidifier volume, total membrane area, active membrane area, or another basis. Regardless, a brief review of these geometric factors is essential to the discussion of humidifier performance. They are summarized in Table 1.2.  The flow field plate in the plate-and-frame humidifier, discussed further in section 3.1, is designed to guide flow from the intake manifolds through a series of channels that spread it across the membrane and return it to the outlet manifolds. The geometry and  18 topology of these channels is a major driver of performance in the humidifier. This channel geometry includes overall channel shape; channel height; channel length; and channel width. Each of these has a separate effect on the performance. An increase in channel width, while the width of the lands separating channels remains the same, leads to an increase in the active membrane area used for water transport. An increase in channel length increases, in turn, the residence time of air in the humidifier, improving the potential for water transport. An increase in channel height leads to an increase in the theoretical time for a representative water molecule in the center of the channel to diffuse to the membrane, where it can be transported to the dry side [31].  Other geometric factors relate more to the total volume of the humidifier assembly. The overall width of the flow field plate, as distinct from the width of the channels themselves, has an effect on the number of channels across the plate and in turn the distribution of the flow throughout the channels. Likewise, the number of flow field plates used affects the distribution of flow in each plate and the flow rate through each plate; a higher flow design requires more plates. Increasing either of these factors also increases membrane usage, thus increasing cost. Table 1.2: Geometric factors affecting humidifier performance Geometric factor Effect Channel shape Can change flow Reynolds number and active membrane area. Channel height Increasing height increases diffusion time and decreases friction. Channel length Increasing length increases residence time and pressure drop. Channel width Increasing width increases active membrane area and decreases friction.   19 1.7.2. FLOW PARAMETERS  This thesis is more concerned with the properties of the gas streams entering the humidifier than with the geometric factors. During fuel cell operation, these flows will vary as power demands on the stack vary. Understanding the effects of these parameters on the performance of the humidifier is important in identifying an ideal operating range for the humidifier. These flow parameters are summarized in Table 1.3. 1.7.2.1 Flow rate  An important flow property affecting the humidifier performance is the flow rate of gas into the humidifier. This, in particular, varies as the power demand on the stack changes. The flow rate leaving the stack is, during operation, similar to the flow rate entering the stack, though a certain quantity of oxygen has been consumed to become water in the cathode reaction. There remains, however, the possibility of controlling the flow in the humidifier independently of the flow to or from the stack by use of a gate or other valve. Flow rate affects the quantity of water entering the humidifier; the rate at which water can be convected from the surface of the membrane; and the residence time of air and water inside the humidifier channels [31]. 1.7.2.2 Temperature  Temperature has a significant effect on water transport through membranes. The role of temperature in saturation pressure of water was mentioned earlier. A hotter stream has may contain significantly more water than a cooler stream. Temperature also appears to have a significant effect in a more direct way on the behaviour of water diffusion through membranes; this effect will be explored in this thesis. Depending on the membrane used in the humidifier, the actual effect of temperature on water transport may  20 vary greatly. The temperature of gas flows entering fuel cell humidifiers has a very wide range depending on the system design and make-up. 1.7.2.3 Relative humidity  The relative humidity of gas streams entering the humidifier, coupled with the temperature, determines the mass of water entering the humidifier. In addition, a reactant stream which is already somewhat humidified will behave differently regarding water transport than a totally dry reactant stream. 1.7.2.4 Pressure  Fuel cell humidifiers may be operated at a wide range of pressures. As a general rule, the pressure of the reactant entering the stack will be higher than that of the exhaust, as there are pressure losses through the stack and, where the humidifier is used, through the humidifier. In the types of hygroscopic membranes used, the effect of changing pressure differential has been demonstrated small compared to the effect of changing temperature [25]. Absolute pressure does, however, have an effect on the total water transport through the membrane, and must be considered as a flow parameter. Depending on the system application, PEMFCs can operate at pressures from close to ambient to absolute pressures more than twice that. Table 1.3: Flow properties affecting humidifier performance Flow property Effect Flow rate Affects rate at which water is supplied to humidifier and desorbed from membrane. Temperature Affects saturation pressure of water in air stream and transport behaviour of membrane. Relative humidity Affects water supplied to humidifiers. Pressure Affects transport behaviour of membrane.   21 1.8. TESTING FOR PERFORMANCE DETERMINATION  Cave developed a thermodynamic model based on ERV methods for predicting performance in membrane humidifiers, while Kadylak used a different approach to develop a model based on an effective mass transfer coefficient. [24,25,32]. These models are limited in terms of their application to practical humidifier operating conditions by various phenomena which occur in real operation, particularly condensation and the presence of a temperature gradient causing two-phase flow. For modeling purposes, validation experiments for these had to be run at conditions where condensation on the membrane was carefully avoided, and to avoid heat transfer to surroundings an isothermal condition had to be maintained. In the interests of providing information of practical value in humidifier design and operation, however, it is important to have a model which will consider all of the flow parameters outlined above at the levels in which they will be present during fuel cell operation. Given the difficulty of analytical modeling, there is potential in the development of a consistent method for empirical modeling of fuel cell humidifiers.  A number of other researchers have also published investigations into the performance of membrane humidifiers; a summary is presented in Table 1.4. Huizing et al studied geometric factors and some flow factors in a one-factor-at-a-time style experiment, using the same type of plate-and-frame humidifiers used in this thesis [31]. This research was focused on selecting an appropriate ratio of residence time to diffusion time for humidifier design. Se-Kyu Park et al tested a single-plate version of a similar membrane humidifier, using Nafion as the membrane, and varying temperature and gas flow rates in a one-factor-at-a-time experiment, where levels of all factors except the one  22 under experimentation remain constant [19,33]. They also proved the concept of membrane humidification by running a single-cell test stack with this humidifier and comparing its performance to the same stack run with sparging. Sang-Kyun Park et al developed a model for a shell-and-tube humidifier [34]. Their experimental validation included dynamic behaviour, but depended only on changing the air flow rates. Chen and Peng conducted more in-depth studies of the behaviour of similar shell-and-tube humidifiers, focusing on the liquid-to-gas case, where the wet side uses liquid coolant water rather than cathode exhaust gases [35-37]. Their model includes a more complete static and dynamic experimental validation, as they change air flow rate, air temperature, water temperature, and pressure, but it remains a one-factor-at-a-time experiment. Table 1.4: Experimental protocols used in fuel cell humidifier literature Researcher Humidifier type Experimental protocol Cave Planar gas-to-gas, single-cell Two-level factorial (DoE method) Huizing Planar gas-to-gas One-factor-at-a-time, geometric and flow properties Kadylak Single-cell gas-to-gas One-factor-at-a-time, multiple factors Se-Kyu Park Single-plate gas-to-gas One-factor-at-a-time, temperature and flow rates Sang-Kyun Park Shell-and-tube liquid-to-gas One-factor-at-a-time, only flow rate Chen & Peng Shell-and-tube liquid-to-gas One-factor-at-a-time, multiple factors McCarthy Planar gas-to-gas Central composite design (response surface DoE method)  1.9. DESIGN OF EXPERIMENTS METHOD  A reliable approach for developing an empirical model of humidifier performance is provided within the framework of the design of experiments (DoE) methods. These methods were pioneered by Fisher during the early 20th century, and further developed by various researchers including Box and Taguchi throughout the following sixty years [38- 41]. While DoE methods span a wide range of types of experiments and topics, they have  23 at their core the same goal and general approach. The goal of DoE approaches is to maximize the efficiency of the experimental process, particularly through maximizing the accuracy of information obtained through testing while minimizing the number of test runs necessary. Depending on the effects investigated, the possible inputs, and the type and accuracy of information desired, a number of “off-the-shelf” methods have been developed that can be used. Underpinning all of these techniques are the ideas of coded parameters, where each parameter and the outcomes are transformed to a normalized form, often between -1 and 1, and of randomization, where tests are run in a random order for the purpose of avoiding bias. The DoE methods provide a stark contrast to one- variable-at-a-time methods, with their ability to cover a full range of operating conditions and assess the effects of interactions between parameters. 1.9.1. DESIGN OF EXPERIMENTS IN FUEL CELL RESEARCH  Fuel cell stacks, like humidifiers, are complex systems affected by numerous input parameters. These parameters include reactant flows, stoichiometries, temperatures, relative humidities, and pressures. This results in significant modeling difficulties for entire stacks. This fact has led a number of researchers to begin characterizing fuel cell stack performance with DoE methods over the last several years, as a surfeit of test runs for fuel cell stacks can be costly and time consuming [42]. A summary is presented in Table 1.5.  In 2003, Dante et al [43] began the trend by using a fractional factorial technique to investigate effects and interactions in a PEM fuel cell for the purpose of performance improvement. This design allowed them to investigate the interactions of four factors at  24 two levels each, provided the desired results regarding methods for stabilizing output power of the stack, and validated the use of DoE methods for fuel cell applications.  Wu, Yu, and Shiah investigated the use of the Taguchi method for fuel cell performance optimization [44], and later the use of this method in tandem with a neural network method to allow progressive optimization of the system [45]. The Taguchi method is an optimization method developed particularly for use by businesses, which is limited by its lack of information across a range of values, but is particularly efficient. The use of a neural network allows progressive steps to improve on the limitations of the Taguchi method.  The most prolific researchers of DoE methods for evaluating fuel cell performance are Wahdame et al at France’s FCLAB. Their work relies heavily on the Taguchi method and the use of analysis of variance (ANOVA) statistical sensitivity methods to determine optimal operating points for fuel cell stacks of a range of operating powers, from single cell to 500 W to 5 kW [46,47]. Wahdame et al have also been the only fuel cell researchers to use a response surface DoE methodology to characterize the response of their subject fuel cell continuously across its operating range [48].  Finally, Meiler et al published a brief discussion of the use of the Box-Behnken response surface for restricted areas, but focused on a sequential optimization method [49]. This method uses a sequential search through three experimental parameters to find a local optimum point for performance. The researchers admit that a shortcoming of this method is that it has no way of testing whether the optimum discovered is a global optimum or simply local.   25 Table 1.5: Experimental designs used in PEMFC literature Experimental design PEMFC researchers using design Fractional factorial Dante et al. Taguchi methods Wu, Yu, Shiah; Wahdame et al. Advanced sequential optimization Wu, Yu, Shiah; Meiler et al Response surface methods Wahdame et al.; McCarthy  1.9.2. DESIGN OF EXPERIMENTS FOR HUMIDIFIER PERFORMANCE DETERMINATION  In a similar manner to its use in fuel cell performance evaluation, DoE can be used to evaluate humidifier performance. This allows the inclusion of a wide variety of flow parameters and considers the interactions between these parameters, all using standard fuel cell humidifier operating conditions. It is the development and application of just such a DoE system to fuel cell humidifiers that is the topic of this thesis, and will be discussed in upcoming chapters. Cave, in his work, used a full factorial experimental design to characterize the effects of flow rates on performance [24,50] 1.10. OVERVIEW OF THESIS  The preceding introduction lays out a basic understanding of the humidifiers being investigated and the methods by which they are currently evaluated. This overview is preceded by a background in design of experiments methods and a literature review of their application to fuel cell research. The literature contains only one use of basic DoE methods in reactant humidification research.  Chapter 2 of this thesis describes the choice and development of a design of experiments method for evaluating fuel cell humidifiers. This includes a discussion of relevant parameters and reasonable ranges of these parameters to investigate, followed by an overview of available DoE methods and their benefits and shortcomings. Finally it lays out the development of the particular method used for these humidifiers.  26  Chapter 3 outlines the experimental set-up and experimental method used to apply the DoE method developed in chapter 2, including equipment used, humidity measurement, and limitations of the experimental method used.  Chapter 4 lays out the data acquired through the experimental method and the initial analysis of this data using statistical techniques.  Chapter 5 discusses the relevance and significance of this data. This discussion focuses particularly on the optimization of humidifier performance and on the development of an effective metric for measuring and communicating humidifier performance, based on the results found through testing and analysis.  Chapter 6 restates the main conclusions gained through this analysis and discussion, and lays out a basis for future work in this field of study.  Also included are four appendices. Appendix A contains Plots of the models produced, to allow a visual interpretation of humidifier performance. Appendix B contains the ANOVA tables from the data analysis. Appendix C contains a method for applying the experimental principles described in this work to ERVs. Appendix D contains the experimental tables for a proposed simplified experimental protocol for humidifier characterization.    27 2. DESIGN OF EXPERIMENTS  Upon consideration of the large number of factors affecting the performance of membrane humidifiers, the design of experiments method was chosen as an alternative to thermodynamic models for providing a complete and reliable understanding of the effects and interactions of these parameters. This chapter lays out the process and rationale for the experimental design used in this thesis. This includes the consideration of all flow parameters in the humidifier system and the selection of factors used; decision and rationale for levels of these factors in the experimental runs; presentation and discussion of various designs of experiments of potential utility for humidifier characterization; selection of a central composite design as the design used in the current work; and presentation of the final design of experiments used in the current work. 2.1. FACTOR SELECTION  The parameters considered in the factor selection for the experimental design are chosen from the flow parameters outlined in the introduction. Each of these four parameters – humidity, temperature, flow rate, and pressure – can take a distinct value in stream 1 and stream 3 at each inlet. This means that there are eight distinct parameters in humidifier operation. These are outlined in Table 2.1. Table 2.1: Factor selections for design of experiments Parameter Stream 1 Stream 3 Humidity Eliminated as having small variation; φ1 = 0% at T1 Eliminated as having small variation; φ 3 = 100% at T3 Temperature Depending on system manufacturer and application, can range from atmospheric to a higher temperature than the stack itself during steady operation. Factor; T1min = 25°C and T1max = 110°C Variation in T3 at φ 3 = 100% will have a significant effect on ω3. Factor; T3min = 60°C and T3max = 80°C Flow rate Set by the fuel cell stoichiometry and power demand, can be varied independently [24,50]. Factor; Q1min and Set by the fuel cell stoichiometry and power demand, can be varied independently [24,50]. Factor; Q3min and  28 Parameter Stream 1 Stream 3 Q1max set by the rated flows of the humidifier to be tested Q3max set by the rated flows of the humidifier to be tested Pressure Low or high pressure; P1 is treated as a categoric factor with two levels: P1low corresponds to a level slightly above atmospheric, and P1high to the outlet of a compressor in the desired application There is some pressure drop through the cathode, but otherwise no independent control of P3 in a passive humidifier system; P3 is set by the same two-level categoric factor as P1, with P3 < P1 2.2. FACTOR VALUES  Considering the above, the factors to be used in this study, and their levels in terms of real values, are presented in Table 2.2. Convention in design of experiments is to assign a separate factor name to the coded level of each factor, while the usual nomenclature refers to the real value, rather than the coded level, of the factor, as discussed below. This table also presents the names used for each of these factors in the experimental design. Table 2.2: Selection of factor values Factor Factor Name Range of values Q1 A Range of rated flows for subject humidifier dry side Q3 B Range of rated flows for subject humidifier wet side T1 C 25°C ≤ T1 ≤ 110°C Φ1 = 0% T3 D 60°C ≤ T3 ≤ 80°C Φ3 = 100% Pressure E Categoric Level 1 “Low”: P1 > P3 and P3 ≈ Patm Chosen: P1 = 20 kPa; P3 = 10 kPa Level 2 “High”: P1 > P3 and P3 >> Patm Chosen: P1 = 170 kPa; P3 = 140 kPa 2.3. CODED FACTORS  While the factors above are presented with their real values, much of the remainder of this work will use coded values for factors. These coded factors are normalized values universally used within the field of design of experiments, and serve to generalize designs and factor combinations [38].  29  For designs using two levels of a numeric factor, the coded factor takes on two values, -1 and +1, usually represented simply as - and +. In these cases, - represents the lower of the two real values taken by the factor, while + represents the higher. - and + may represent values at the very extremes of the possible ranges of the factor in question, depending on the choice of experimental design, but may also be closer to the center of the range, depending on the information desired from the experiments.  When further levels of a factor are to be used, the coded values for factors are essentially based off the same normalizing scale as these - and + values. The central point of the factor range is given the value of 0, and the main factor levels equidistant from this central point are given the values -1 and +1. Other factor levels, generally also placed equidistant from the center point, are given values equal to their distance from the center point as a fraction of the distance of the -1 and +1 points. As such, a point higher than and twice as far from the center point as the +1 value takes a value of +2, while one lower than and half as far from the center point takes a value of -0.5. An example of the calculation of this coded value is shown in equation 2.1. The expression inside the brackets normalizes the coded value to a range from -1 to +1. The α is a value which may be set arbitrarily for some experimental designs.  1 1max 1min 1 2 QA Q Q α     = − ⋅  −     (2.1)  Categoric factors may use a similar system of coded factors. In this case, given two levels of a categoric factor, one may be designated “low” and the other “high”; they are then assigned values of -1 and +1 respectively. Alternatively, particularly in the event  30 that the categoric factor has a broader range, it may simply be designated by integers from 1 to the total number of cases for the categoric factor.  Each test point within the design of experiments is thus designated by the combination of coded factors that define it. These coded factors are used to make up tables of values for design of experiments, as laid out later in this chapter. 2.4. INTERACTIONS  Identifying important interactions between factors was one of the major goals of this work. Interactions are effects caused by the combined levels of two or more factors, rather than simply by the level of one factor. For example, the effect of flow rate in stream 3 could also depend on the temperature and the water content of stream 3. The order of an interaction is the number of factors involved.  The method for characterizing interactions is one of the strengths of using coded factors. Interactions are modeled as a multiplication of the factor levels involved, as demonstrated in equations 2.2 and 2.3. The values of these interactions are tabulated along with the coded factors in the design of experiments, as demonstrated later in this chapter.  AB A B= ⋅  (2.2)   ABC A B C= ⋅ ⋅  (2.3)  The orthogonal contrasts of the main effects are shown in some cases. These use the standard notation of a superscripted 2.  31  These orthogonal contrasts are included only when some show statistical significance. Otherwise, all factors and interactions are included in the models, with the less significant ones carrying negligible weight. 2.5. EXPERIMENTAL DESIGNS  Design of experiments and statistical theory present numerous possibilities for experimental designs to investigate humidifier performance. Some of these designs were mentioned in the literature review as designs that have been used in some PEMFC testing and characterization research. These designs are reviewed for their benefits and shortcomings in order to decide on a design with which to go forward for humidifier characterization. The experimental designs discussed in this chapter can be broadly split into four families; two-level factorial designs, three-level factorial designs, response surface methods, and Taguchi methods. 2.5.1. TWO-LEVEL FACTORIAL DESIGNS  Two-level factorial designs, as a group, are experimental designs that test combinations of the low and the high levels of factors to draw conclusions about their effects. These designs can be an efficient way of identifying and quantifying interactions and important factors. They do not provide the ability to create non-linear response models. 2.5.1.1 Full factorial designs  The basic two-level factorial design is the 2k full factorial design. In this design, every combination of low and high value of factors is tested together. This results in a design of experiments requiring 2k runs to complete, where k is the number of factors  32 used in the experiment. This design provides a good estimate for all factor effects and interactions, with no confounding between factors and interactions at any level. It is, however, a comparatively inefficient design, requiring a relatively large number of test runs; in the event that the high resolution it provides is not necessary, the full factorial design can be unnecessarily expensive. A full factorial design for the factors chosen above and their second-order interactions, omitting higher-order interactions, is shown in Table 2.3. Table 2.3: 2k full factorial design in five factors including second-order effects Run  A B C D E AB AC AD AE BC BD BE CD CE DE 1 - - - - - + + + + + + + + + + 2 + - - - - - - - - + + + + + + 3 - + - - - - + + + - - - + + + 4 + + - - - + - - - - - - + + + 5 - - + - - + - + + - + + - - + 6 + - + - - - + - - - + + - - + 7 - + + - - - - + + + - - - - + 8 + + + - - + + - - + - - - - + 9 - - - + - + + - + + - + - + - 10 + - - + - - - + - + - + - + - 11 - + - + - - + - + - + - - + - 12 + + - + - + - + - - + - - + - 13 - - + + - + - - + - - + + - - 14 + - + + - - + + - - - + + - - 15 - + + + - - - - + + + - + - - 16 + + + + - + + + - + + - + - - 17 - - - - + + + + - + + - + - - 18 + - - - + - - - + + + - + - - 19 - + - - + - + + - - - + + - - 20 + + - - + + - - + - - + + - - 21 - - + - + + - + - - + - - + - 22 + - + - + - + - + - + - - + - 23 - + + - + - - + - + - + - + - 24 + + + - + + + - + + - + - + - 25 - - - + + + + - - + - - - - + 26 + - - + + - - + + + - - - - + 27 - + - + + - + - - - + + - - + 28 + + - + + + - + + - + + - - + 29 - - + + + + - - - - - - + + + 30 + - + + + - + + + - - - + + + 31 - + + + + - - - - + + + + + +  33 Run  A B C D E AB AC AD AE BC BD BE CD CE DE 32 + + + + + + + + + + + + + + + 2.5.1.2 Fractional factorial designs  Fractional factorial designs are a class of experimental designs closely related to full factorial designs which are used when a full factorial design is too expensive, in terms of cost, resources, or time. To clarify the concept of fractional factorial designs, it is instructive to introduce the idea of design resolution. The resolution, R, of a design is a characteristic such that no interaction of order s is confounded with any interaction of order lower than R – s [38,51]. While full factorial designs avoid confounding altogether, fractional factorial designs are intended to have a lower resolution, confounding effects caused by higher order interactions. The benefit to using fractional factorial designs is the lower cost and increased efficiency achieved by decreasing the number of runs used. Fractional factorial designs are most useful either when it can be safely assumed that high order effects are negligible, which is true for many cases, or when previous testing has revealed that certain main effects or low-order interactions are negligible. In this case, these negligible factors can be confounded with factors of interest. Table 2.4 shows a 2k-1 factorial design aliased on the DE interaction, for the purpose of comparison with the 2k factorial design above. Table 2.4: 2k-1 fractional factorial design in five factors aliased on interaction DE Run  A B C D E AB AC AD AE BC BD BE CD CE DE 1 - - - - - + + + + + + + + + + 2 + - - - - - - - - + + + + + + 3 - + - - - - + + + - - - + + + 4 + + - - - + - - - - - - + + + 5 - - + - - + - + + - + + - - + 6 + - + - - - + - - - + + - - + 7 - + + - - - - + + + - - - - + 8 + + + - - + + - - + - - - - + 9 - - - + + + + - - + - - - - + 10 + - - + + - - + + + - - - - +  34 Run  A B C D E AB AC AD AE BC BD BE CD CE DE 11 - + - + + - + - - - + + - - + 12 + + - + + + - + + - + + - - + 13 - - + + + + - - - - - - + + + 14 + - + + + - + + + - - - + + + 15 - + + + + - - - - + + + + + + 16 + + + + + + + + + + + + + + + 2.5.2. THREE-LEVEL FACTORIAL DESIGNS  Three-level factorial designs, also designated as 3k designs, are similar to 2k designs, with the addition of a third point for testing. This third point tends to be the center point. 3k designs provide a quadratic estimate of response across the factor range. They are very inefficient compared to the response surface methods discussed below, and will receive no further attention here. 2.5.3. RESPONSE SURFACE METHODS  Response surface methodology (RSM) is a class of designs of experiments intended to provide a continuous estimate of the measured response across the range of possible factor combinations. The graphical result of an RSM experiment is a surface in (n + 1)-dimensional space that describes the response in terms of n considered factors and interactions. An estimate of variance across the response surface is also provided through RSM techniques. These response surface methods have resolution RV. 2.5.3.1 Central composite designs  The central composite design (CCD) is a common design which can be built using sequential experimentation from a full factorial design. It uses all of the same factor level combinations as a full factorial design; a certain number of center runs; and “star points” at an arbitrary ±α value from the center for one factor at a time while the other factors are kept at 0. A CCD can also be built from a fractional factorial design. The choice of α is  35 dependent on the properties desired of the response surface. For a CCD built from a full factorial design, the choice of kα =  makes the design rotatable, meaning that the estimated variance is constant along the surface of any circle, sphere, or hypershere, depending on the number of factors used, centered on 0. Another common value for α is 1, creating a rectangular CCD, with good estimate of variance near the center and largely eliminating the need for center points [38].  One benefit of the CCD, excepting the rectangular design, is that it avoids continued experimentation at the extreme values being tested. This can be of significant benefit because testing these points may be problematic or undesirable. These points may be difficult to reach, maintain, or control; they may increase the potential for equipment damage; or they may simply not be common operating conditions. A visualization of a CCD for three factors is given in Figure 2.1.  Figure 2.1: Visualization of a central composite design in three factors   36 2.5.3.2 Box-Behnken designs  An alternative to the CCD is the Box-Behnken design (BBD). The BBD is built using sequential design from an incomplete block design, another class of design. The resulting design, like a rectangular CCD, uses only three levels of factor combinations, including center points, but uses a small number fewer runs than are necessary in a rectangular CCD. It is also, unlike a rectangular CCD, rotatable. There are also no runs at the corners of the test area, where there are combinations of all factors high or low. These runs, as discussed for CCDs, can be prohibitive in some instances. A visualization of a Box-Behnken design for three factors is given in Figure 2.2.  Figure 2.2: Visualization of a Box-Behnken design in three factors 2.5.4. TAGUCHI METHODS  Taguchi methods are a class of designs developed relatively recently by Genichi Taguchi, primarily for use in optimization [40,41]. While not used in this work, these designs have significant potential for humidifier optimization and are used extensively in  37 the PEMFC DoE applications described in the literature review. For these reasons, Taguchi methods warrant a brief mention.  Being concerned largely with optimization rather than broad modeling, the thrust of Taguchi techniques is generally to find the best operating point within a given range. Given a good selection of a range, these techniques often provide the most efficient and effective method of reaching a solution which, while not guaranteed to be the best, is always close to the best. Once a general understanding of the governing relations for membrane humidifiers is achieved, these methods can be of significant value in approximating the ideal operating points for any individual model of humidifier. 2.6. DESIGN SELECTION  For selection of the design used in this work, in addition to standard considerations of maximizing efficiency and the presence of four numeric factors and one categoric factor, the following were considered: 1) The nature of the system and the non-linear curve for water vapour saturated in air made a linear response unlikely; 2) The nature of the system and previous work suggested the existence of some second-order interactions [50]; 3) The existence of significant third-order interactions was unlikely; 4) The purpose of this work was to model interactions and response across humidifier operating range; 5) The purpose of this work was also to study and compare numerous metrics for humidifier performance;  38 6) Humidifiers are designed to operate more within their operating range than at the edges; and 7) An excess of tests on the experimental setup used are time-consuming.  Considerations 1 and 4 suggest the adoption of an RSM design, rather than a two- level factorial design, for the ability to produce a second-order fit to the data and the unlikelihood of a good linear fit to the data. There remains value in the use of a two-level factorial test as a screening test in order to identify significant effects, and perhaps provide information to increase the efficiency of further response surface testing; however, consideration 5 allows the possibility, due to the differences in calculation of water recovery metrics, that the important interactions differ between metrics. A preliminary screening with a two-level factorial, however, remains of value in testing the assumption behind consideration 3.  While a three-level full factorial test provides the same quadratic response surface fit as RSM methods and removes any aliasing effects, consideration 7 rejects these tests on the basis of experimental inefficiency. Three-level factorials providing a comparable amount of information to RSM methods in five factors require significantly more runs and are significantly more expensive.  Taguchi methods have been used in optimization of similar systems [44,46,47], and remain candidates for further optimization of humidifier systems. Basing optimization of humidifiers on flow parameters is difficult since flows can change with stack operating demands, however, and this study did not consider the range of geometric factors. Taguchi methods, while efficient for optimization, are so at the expense of providing continuous information throughout the test region, which is more useful when  39 humidifiers may operate at many points in this region. For this reason Taguchi methods are not used in this work.  Within the umbrella of RSM designs, CCD and BBD have been introduced. BBDs have the benefit of slightly increased efficiency over CCDs and are all rotatable. In this case the increase in efficiency is small compared to other arguments in favour of using a CCD. These include: • A basis of a 2k factorial design allowing a test for higher-order interactions; • The opportunity to place the majority of test points away from the edges of the humidifier operating range; • The presence of test points at five levels on each factor allowing a good estimate of fit for model curvature; and • The relative insignificance of rotatability as a design criterion in this application.  This comparison process is summarized in Table 2.5. Table 2.5: Benefits and disadvantages of experimental designs considered Design Benefits Disadvantages Full factorial No aliasing Expensive; low-order 2 k  Fractional factorial Efficient Aliasing; low-order 3 k  Higher-order; controlled aliasing Very expensive Central composite Higher-order; relatively efficient Some aliasing Response surface Box-Behnken Higher-order; efficient; rotatable Some aliasing Taguchi Efficient; information for optimization No general information  2.6.1. CHOICE OF ALPHA AND CENTER POINTS  With the choice of a CCD, the remaining design choices are the coded value of α to be used and the number of center points. As the real levels of α are fixed at the edges of the operational range, the choice of value for α in fact affects the real level of the  40 values at ±1. Common values of α, discussed above, are k±  and ±1. The former, in this case ±2, provides rotatability, while the latter provides a rectangular CCD. In this work, the rectangular CCD is undesirable, as it tests exclusively at the edges of the operating range, which are not common operating values. In a similar way, the choice of ±2 as values for α bring the majority of test points too close to the center in this application, where humidifiers, while not operating mainly at the extreme ends of their ranges, may see a significant variation in operating conditions as system demands change. To move the values of ±1 farther from the center, a value of 2α = ± , commonly used for rotatability in smaller CCD designs, is chosen as an intermediate value [38,51].  For a CCD of this design, six center points are generally recommended to provide a good estimate of variance [38,51]. There is no reason to modify this, so six center points are used. 2.7. FINAL DESIGN OF EXPERIMENTS  The preceding parts of this chapter have specified the design of experiments used in this work. This will be a central composite design, consisting of six center points, star points at 2α = , and a two-level full factorial design. The design uses four numeric factors and one categoric factor. The salient points of the experimental table are tabulated here in Table 2.6. Table 2.6: Final values for design of experiments Numeric factors Factor values Coded values -α -1 0 1 α A: Q1, SLPM Humidifier dependent; discussed in following chapter B: Q3, SLPM Humidifier dependent; discussed in following chapter C: T1, °C 25 37.3 67.5 97.7 110 D: T3, °C 60 62.9 70 77.1 80 Categoric factor Level 1, low Level 2, high E: Pressure, kPa P1 = 20, P3 = 10 P1 = 170, P3 = 140  41 3. EXPERIMENTAL APPARATUS  While the preceding chapter outlines the theoretical design of experiments used in this work, it leaves aside the question of the physical arrangement of the experiments. The following chapter addresses the apparatus used to conduct the experiments. The major elements of this experimental apparatus are the humidifiers tested, the test stand used to run and control the experiments, the apparatus for measuring water transport, the test protocol followed, and the software used. 3.1. HUMIDIFIERS  In order to obtain some generalized conclusions from this work, it was necessary to test a number of humidifiers. DPoint Technologies provided four of their humidifiers for this test. All of these humidifiers were planar with hygroscopic membrane separating the flow field plates. These plates were made of injection moulded polypropylene. 3.1.1. GEOMETRIES  Of the four humidifiers used, there were two different geometries. Two of the humidifiers were DPoint’s Px1-32 type and two were DPoint’s Px3-46 type.  The Px1-32 humidifier plate is 153 mm long, 29.25 mm wide, and has a depth of 0.85 mm, as shown in Figure 3.1. A Px1-32 is built such that the total height of plates and membrane is 32 mm. A survey of DPoint customer requirements, testing conditions, and DPoint’s specifications revealed use of the Px1-32 at flow rates ranging from 5 SLPM to 100 SLPM.  42  Figure 3.1: Px1-32 plate geometry   The Px3-46 humidifier plate is 160 mm long, 55.7 mm wide, and has a depth of 0.85 mm, as shown in Figure 3.2. A Px3-46 is built such that the total height of plates and membrane is 46 mm. A survey of DPoint customer requirements, testing conditions, and DPoint’s specifications revealed use of the Px3-46 at flow rates ranging from 50 SLPM to 250 SLPM.  Figure 3.2: Px3-46 plate geometry 3.1.2. MEMBRANES  In the four humidifiers tested, there were two different membranes, designated here as membranes M and N. Membrane M is a porous polymer membrane, while membrane N is an ionic perfluorinated composite membrane. Humidifiers with  43 membrane N also used a porous woven support layer against the membrane on the wet, lower pressure side. One each of the Px1-32s and the Px3-46s were made with membrane M, while one of each was made with membrane N. The four humidifiers thus represented all possible combinations of the two geometries and two membranes used. 3.1.3. RATED FLOWS FOR HUMIDIFIERS  As factors Q1 and Q3 are dependent on the humidifier tested, it is necessary to determine a range of flows to test for each humidifier. As these humidifiers are produced by DPoint Technologies, these values were determined through a combination of DPoint materials, customer requirements and information, consultation, and the limitations of the experimental setup used. The values of the flows for each humidifier are outlined above. The limitations of the apparatus made the low end of the flow range for the Px1-32 inaccurate for testing, so it was avoided. The final tested range is shown in Table 3.1. Table 3.1: Flow rates for design of experiments Geometry -1 level of flow (SLPM) +1 level of flow (SLPM) Px1-32 20 100 Px3-46 50 250 3.1.4. HUMIDIFIER ORIENTATION  The humidifiers were held in the same orientation for all tests, consistent with the recommended orientation for their use in fuel cell systems. In this orientation, all flow is in a vertical plane. Stream 1 enters at the bottom of the humidifier, and stream 2 exits at the top. Stream 3 enters at the top of the humidifier, and stream 4 exits at the bottom. This is shown in Figure 3.3.  44  Figure 3.3: Flow pattern and humidifier orientation used 3.2. TEST STAND  All testing for this work was carried out on a modified Greenlight GenIV FCTS (Fuel Cell Test Station). This test station and its packaged software were originally designed to deliver and control cathode and anode gases and humidification to a fuel cell mounted on the test bench. In addition to modifications associated with this work, this test stand has also been previously modified by both Greenlight and DPoint personnel in order to provide a platform designed for the delivery and control of humidified air to membrane humidifiers. These changes have entailed the removal or isolation of all systems designed for handling gases other than air, and the redesign of the compressed air supply system to provide flow to the anode side as well as the cathode. The coolant cart has been dismantled. A schematic of the apparatus described below is given in Figure 3.4.  45 Figure 3.4: Schematic of test apparatus 3.2.1. CONVENTION FOR INLETS AND OUTLETS  Subsequent to the test stand’s conversion to a humidifier test station, a consistent convention has been observed regarding the flow pattern used. The former cathode side of the test stand is used as the wet side, and the anode side as the dry side. Thus, on the test station, the anode inlet supplies stream 1, the anode outlet accepts air from stream 2, the cathode inlet supplies stream 3, and the cathode outlet accepts air from stream 4. This convention is maintained throughout the experiments and throughout the rest of this work. 3.2.2. AIR SUPPLY AND CONTROL  The air supply used was compressed air. The flow rate of this air was controlled by a Teledyne HFC-303 mass flow controller calibrated for air on each of the anode and cathode sides. The rated range of these controllers is 0 SLPM to 520 SLPM, with ±1% full scale (F.S) accuracy. At low flow in the Px1-32, this is a significant percentage of desired flow, but it does not cause any possible overlap between flow setpoints.  46  The air supply from the test stand ports to the humidifiers and return to the ports was carried by means of silicon heater hoses: 1” ID for the Px3-46 and ½” ID for the Px1-32s. Hose clamps attached these hoses to the test stand ports and to the humidifier ports.  The building compressed air, supplied by a central air compressor unit, was assumed to be close to 0% RH, particularly as it was heated at every test point used. 3.2.2.1 Air filtration  The presence of compressor oil in the test system has the potential of contaminating the membranes in the humidifiers, causing a decrease in performance unrelated to test conditions and biasing the test as duration increases. In response to this, a pair of coalescing filters was added to the air intake in a series configuration. These filters are microfiber coalescing elements from United Filtration, with the first one being grade 70C and the second grade 50C. These have efficiency ratings of 95% and 99.99% respectively against 0.01 micron particles and aerosols, and were considered to adequately protect the test humidifiers from oil in the air lines. These filters are in addition to the smaller 50C coalescing filters already installed on both anode and cathode sides of the air supply system upstream of the MFCs. 3.2.3. WATER SUPPLY AND HUMIDIFICATION SYSTEM  The main water supply is also from the building. This water is filtered through a CSP-DI four-stage reverse osmosis/deionization filter from Spectrapure and stored in a pressurized tank in the range of 30 psi to 40 psi. As the tank provides water directly to the test stand, it is not necessary to constantly supply water to the tank from the building  47 system, but efforts were made to ensure that the water pressure in the tank remained above 30 psi.  Humidification was only used on the cathode side of the test stand, though both anode and cathode sides retain the same system described here and the same humidification apparatus. For humidification, air from the MFCs is sent through a spray injector by means of a bypass valve directly controlled by the test stand software. The water heater in this spray injector is controlled by the desired dew point temperature specified by the user. Air exits this humidification system fully saturated and at the specified dew point temperature. The spray injector apparatus are custom-built for this test stand.  The humidification system was calibrated prior to performing tests by running a humidified air stream directly into the water measurement system. This calibration demonstrated accurate dew point control by the system across the range of dew point temperatures and cathode flow rates used in this experiment. 3.2.4. TEMPERATURE SENSING AND CONTROL  All temperature sensors in the test stand were K-type thermocouples, and have been regularly calibrated with the test stand to ensure accurate temperature measurement. These include thermocouples used primarily as feedback for the test stand control and thermocouples used primarily for experimental data acquisition.  Air temperature control is achieved using heater blocks integrated with the spray injectors, but downstream relative to air flow, for humidification. Supply air will either be directed directly to these heaters from the MFCs via the bypass valve or will enter the heaters after humidification. On the anode inlet side, this heater was the sole element  48 used for temperature control, and depending on flow rate tended to operate between 20% and 80% duty cycle within the test range. On the cathode inlet side this heater functioned as a reheater after the humidification process, and was always maintained at the same temperature as the spray injector, thus generally running significantly below 20% duty cycle.  Thermocouples for temperature control were located directly at the anode and cathode inlet ports. Preliminary testing revealed significant heat loss from the anode inlet port to the humidifier inlet port as the stream 1 temperature diverged from atmospheric. In order to counter this heat loss, two measures were taken. First, insulation was added to the hose in order to minimize heat loss to the atmosphere. Second, and more importantly, the control was set to heat stream 1 above the desired temperature at the anode inlet control point such that at the humidifier inlet it was at the desired temperature. Subsequent testing proved this to be a consistent and effective method of maintaining the correct test conditions at the humidifier inlets. Due to the added thermal inertia of the humidified stream, stream 3 did not display this temperature loss throughout the experiment.  In addition to control thermocouples at the anode and cathode inlet ports, control thermocouples were located at each spray injector and in the water measurement balance. Additional thermocouples for data acquisition were located at all four humidifier ports. 3.2.5. PRESSURE SENSING AND CONTROL  Pressure taps for sensing and control are located directly at the inlets to the humidifier, beside the thermocouples. There are also differential pressure transmitters located on the outlet sides of the humidifier to measure pressure drop across the  49 humidifier on both wet and dry sides. The pressure taps are WIKA S-10 pressure transmitters with a range of 0-60 psi and an accuracy of ±0.25% F.S. Differential pressure transmitters are Winters PTD differential pressure transmitters with a range of 0- 50 psi and an accuracy of ±0.25% F.S. This range is very close to the absolute value of differential pressures expected across the humidifier in some flow conditions. In this study, pressure drop through the humidifier is not considered. Pressure is regulated through a Fairchild Model 1000 pressure regulator, controlled through an SMC ISE40 pressure switch. 3.3. CONTROL SOFTWARE  The software used for test stand control was Greenlight’s FCAnalytics software, modified sequentially by Greenlight personnel, DPoint personnel, and this researcher for humidifier testing. This software allows manual specification of the desired flow-rates, temperatures, and pressures in the test stand system. It includes a module for automation; this module, however, is without a feedback option. For this reason, all control of test conditions was accomplished manually by the experimenter. 3.4. WATER MEASUREMENT BALANCE  For the purpose of measuring water transferred across the humidifier, a condensing water balance was used. Since this work did not involve any transient testing, and the water balance allows a good time- and space-averaged measurement, it was chosen as a simple and robust method of measuring moisture content.  The principle of the water balance system used was to cool the exhaust stream 2 water vapour far below its saturation point, to the range of 12ºC ± 2ºC depending on its  50 flow rate and temperature, and to measure the liquid water produced. In order to accomplish this, the stream 2 air first entered an indirect heat exchanger, with building water at about 10°C providing the cold stream in the heat exchanger. This air, with the water vapour in it cooled below its saturation point, entered a large chamber filled with loose packing in order to cause the air flow to stagnate. In this chamber, any liquid water droplets in the air stream condensed and collected at the bottom of the chamber, where they were directed through an outlet nozzle to the water balance. The quantity of water in the balance was measured to produce an averaged steady state measurement of water flow. The remaining air from stream 2, assumed to contain saturated water vapour since it had been cooled below the saturation point, was exhausted at the top of the chamber. The temperature of the chamber and exhaust air were measured. Using the assumption of saturation to designate this temperature as the dew point temperature, the water content of the exhaust air was calculated and combined with the flow rate and the water collected in the water balance to produce a final time averaged measurement of the water content in stream 2. A schematic of this apparatus is shown in Figure 3.5.  51 Hot, humid air (40C-80°C) Cooled air, supersaturated water vapour (~12°C) Cold supply Water (~10°C) Cooling water drain Air, saturated water vapour exhaust (~12°C) Heat exchanger Condensation chamber Water balance Knockout water (~12°C)  Figure 3.5: Schematic of water balance measurement apparatus 3.5. EXPERIMENTAL PROTOCOL  In the interests of removing as much experimental bias as possible from the results, an experimental protocol was developed and adhered to for all experiments. All experiments were also run by the same researcher. All tests were conducted at steady state.  At the beginning of testing, the factor values for the first test to take place were specified in FCAnalytics. The flow rate and pressures were gradually brought to these levels, taking care that the pressure on the dry side remained higher than that on the wet side at all times and that until P3 reached 140 kPa in high pressure testing the pressure differential never exceeded 15 kPa. Once pressures and flow rates were at the correct levels, the temperatures and dew point temperatures were allowed to stabilize. In all cases, before the first test, the stand was run for at least 15 minutes at the first test case in  52 order to allow the water contents of the membrane and of the water balance chamber to reach a steady state.  Measurements were taken over 10 minute intervals, with the FCAnalytics software taking a log point of all data input at intervals of 10 seconds. This allowed the use of 600 data points for averaging the steady state conditions. After each test point, the factor values on the software were set to the following test point. This was in turn allowed to stabilize for at least 10 minutes before the next measurement was taken. A flowchart of the experimental protocol is shown in Figure 3.6.  53  Figure 3.6: Flowchart of experimental protocol   The nature of the test stand removed some of the possibility of complete randomization. The amount of time necessary to reach a high pressure state dictated that  54 the high pressure and low pressures be tested independently. In addition, the thermal inertia of the heater block required that testing be done from low stream 1 temperatures to high stream 1 temperatures. The spray injector used for stream 3 temperature and dew point control allowed randomization on stream 3 temperature. The amount of time taken for testing and the varied time taken to reach steady state conditions at varied factor-level combinations removed the ability for the experimental design to include blocking on days tested; however, all tests were performed within a 3-week period where atmospheric conditions within the laboratory remained substantially the same. 3.6. DESIGN EXPERT 7  The experimental matrix was produced with the aid of Design Expert 7 software (DX7). This software allows specification of experimental design, experimental parameters such as the value for α, factor names, factor levels, factor types, number of factors, responses, and type of responses, and produces a matrix for the desired experiments. For post-experimental analysis, it allows a broad range of statistical analysis and model production. Analysis of variance (ANOVA) tables, factorial models, analyses of residuals, and other statistical results presented throughout this work have been produced with the aid of Design Expert 7.       55 4. RESULTS AND STATISTICAL ANALYSES  All data collected from the water balance were recorded in terms of g/min. The Goff-Gratch equation for calculating saturation pressures was used to convert this measurement in terms of WTR to WRR, DPAT, and stream 2 DP, RH, and HR for each test point. These six responses were each analyzed separately for each humidifier, using the DX-7 software. This analysis results in the generation of 48 separate response surfaces, as each categoric factor for pressure has a separate surface. DX-7 is used to produce quadratic fits, residual plots, and ANOVA tables for each of these surfaces. The sum of squares of residuals vs. lambda (SSR-λ) plots are used to determine values of λ for transforms to minimize the sums of squares of the residuals, and fit visualizations of the residuals are used to determine whether these are acceptable transformations [52]. These statistical analyses are presented in this chapter, while comparisons between the responses are presented in the next.  Results of the models are plotted in Appendix A using a multiple axis format to show all of the interactions. A consistent scaling for each metric is used throughout these plots, outlined at the beginning of the appendix.  Diagnostics in this chapter are presented together, grouped by performance metric. This is done to facilitate comparison between humidifier geometries and membrane types. All diagnostics are presented in a 2x2 pattern, arranged as shown in Figure 4.1. These are inspected in a qualitative way to provide further insight into the validity of the model than that gained from the ANOVA tables [52].  56 Px1-32 M Px1-32 N Px3-46 M Px3-46 N  Figure 4.1: Pattern used for presenting diagnostics 4.1. STATISTICAL ANALYSIS TOOLS 4.1.1. ANOVA TABLES  Analysis of variance tables, commonly known as ANOVA tables, are a standard tool in statistical analysis. The tables in this thesis contain five columns of data: the sum of squares; degrees of freedom; the mean square; the F-value; and the p-value.  The sum of squares measures the contribution of each main effect or interaction to the total model sum of squares. Also included is the error sum of squares, which measures the differences between the individual responses at factor-level combinations and the averages for these combinations.  The degrees of freedom show how many statistically independent contributions there are to each sum of squares. In the case of this model, the degrees of freedom for each of the main effects and each of the interactions are 1; the degrees of freedom for an interaction is the product of the main effects it includes.  Mean squares is the sum of squares divided by the degrees of freedom.  The F-values are obtained by dividing the mean square by the error mean square. This value gives an idea of the importance of the corresponding effect or interaction. A  57 value close to 1 indicates a lack of significance to the effect, as its mean sum of squares and the error mean sum of squares are in effect measuring the same thing.  Finally, the p-value is a value used to estimate whether the corresponding effect or interaction is statistically significant. This definition of statistical significance is based on an arbitrary cut-off at a percentage level. In this research, statistical significance at the 95% level is considered, meaning that p-values of 0.05 and below are considered statistically significant. This statistical significance must, however, be considered in tandem with other measurements of meaning, such as fit tests and visual assessment of the data and residuals.  The ANOVA tables themselves are included in Appendix B. A summary of results is presented here. 4.1.2. SSR-LAMBDA PLOT  When evaluating the data, one technique that can be used to obtain a better fit is the power transform. In this case, a value for λ is chosen, and the effects are graphed raised to the power of λ, with a value of 0 indicating the use of a logarithm. In general, a good choice of λ minimizes the value of the sum of squares. In order to visualize this a plot known as a Box-Cox plot is used which plots the sums of squares corresponding to values of λ. This facilitates selection of λ, though the choice of transforms should still be checked with graphical methods. As the selection of λ is the only information from the SSR-λ plot used in this thesis, rather than reproducing all of the plots, an example is shown here in Figure 4.2.  58 Lambda Ln (R e si du a lS S) Box-Cox Plot for Power Transforms -1.85 0.07 1.99 3.90 5.82 -3 -2 -1 0 1 2 3  Figure 4.2: Example SSR-λ plot (Px1-32M, WRR) 4.1.3. ERROR PLOT  The error plot plots the results of the response surface model against the experimental results at each of the experimental points. This allows an initial assessment of the suitability of the model to the data. The data should be close to a linear diagonal plot, representing the line where the model exactly replicates the experimental data. The farther away a point is from this diagonal, the less accurate the model prediction of that experimental point is. This plot shows the experimental error in the model and illuminates any major deficiencies in the model. 4.1.4. NORMAL PLOT OF RESIDUALS  The normal plot of the residuals plots the studentized residuals (the residuals divided by an estimate of their standard deviation) against their quantiles, allowing a comparison to the normal distribution. This visualization allows a judgment of the validity of standard statistical methods in evaluating the data obtained, as most methods  59 are based on an assumption of close relation to the normal distribution. This plot is checked for the similarity between the studentized residuals and the normal distribution, and for any consistent departures from this distribution. This most often takes the form of leptokurtosis, where the tails of the distribution contain relatively more data than the center as compared with the normal distribution. The opposite behaviour is referred to as platykurtosis. When the points at the top of the distribution are above the line of the normal, the distribution is leptokurtic. 4.1.5. RESIDUALS-PREDICTED VALUES PLOT  This plot graphs the value of the residuals for each test point against the predicted value of that point according the model generated. This is visually inspected to ensure that the variation in the residuals is evenly and randomly spread across the range of predicted values. The residuals-predicted values plot reveals problems with the model by revealing any areas with a consistent bias in one direction, or particularly large residuals at one end of the model. 4.1.6. PREDICTED VALUES VS ACTUAL VALUES  This plot allows a direct visualization of the accuracy of the model developed for each humidifier. It plots the actual values measured experimentally at each point against the values obtained through use of the response surface method. This provides a further method for judging the suitability of the model and whether it diverges from reality at any particular level. 4.2. WATER TRANSPORT RATE RESULTS  A square root transform was used for water transport rate.  60 4.2.1. MODEL AND ANOVA Table 4.1: Models for water transfer rate Px1-32M Px1-32N Px3-46M Px3-46N Sqrt(WTR)  = Sqrt(WTR)  = Sqrt(WTR)  = Sqrt(WTR)  = 1.83  1.94  2.75  2.9 0.36  * A 0.33  * A 0.42  * A 0.44  * A 0.16  * B 0.16  * B 0.18  * B 0.16  * B -0.29  * C -0.27  * C -0.58  * C -0.41  * C 0.29  * D 0.34  * D 0.5  * D 0.5  * D -0.38  * E -0.46  * E -0.5  * E -0.62  * E 0.056  * A * B 0.098  * A * B 0.066  * A * B 0.1  * A * B -0.064  * A * C -0.053  * A * C -0.17  * A * C -0.17  * A * C 0.06  * A * D 5.40E-03  * A * D 0.033  * A * D 0.049  * A * D 0.11  * A * E 0.08  * A * E 0.095  * A * E 0.035  * A * E -0.075  * B * C -0.055  * B * C -0.057  * B * C -0.034  * B * C 0.013  * B * D 0.041  * B * D 0.02  * B * D 0.014  * B * D 2.14E-03  * B * E 8.36E-03  * B * E 0.013  * B * E -3.15E-03  * B * E -0.12  * C * D -0.12  * C * D -0.13  * C * D -0.11  * C * D 0.19  * C * E 0.18  * C * E 0.29  * C * E 0.19  * C * E -0.19  * D * E -0.15  * D * E -0.13  * D * E -0.13  * D * E -0.13  * A^2 -0.13  * A^2 -0.16  * A^2 -0.14  * A^2 8.04E-03  * B^2 -0.025  * B^2 -0.038  * B^2 -0.054  * B^2 0.023  * C^2 3.33E-03  * C^2 0.23  * C^2 0.18  * C^2 0.086  * D^2 0.1  * D^2 0.12  * D^2 0.092  * D^2  Table 4.2: Summary of statistical significance for water transport rate Factor All Model Membrane All but Only A x B x C x D x E x AB   N AC  Px3-46 AD AE    Px3-46N BC     Px1-32M BD BE CD x CE x DE x A2 x B2 C2  Px3-46  61 Factor All Model Membrane All but Only D2    Px1-32M   As water transport rate is a direct measurement of water transport through the membrane, there is little need for interpretation. For each humidifier, all of the main effects are significant. Significant interactions are only those between temperatures and pressures. 4.2.2. ERROR PLOT 0 5 10 15 20 0 2 4 6 8 10 12 14 16 18 20 Experimental WTR (g/min) M od el  W TR  (g/ m in ) 0 5 10 15 20 0 2 4 6 8 10 12 14 16 18 20 Experimental WTR (g/min) M od el  W TR  (g/ m in ) 0 10 20 30 40 0 5 10 15 20 25 30 35 40 Experimental WTR (g/min) M od el  W TR  (g/ m in ) 0 10 20 30 40 0 5 10 15 20 25 30 35 40 Experimental WTR (g/min) M od el  W TR  (g/ m in )  Figure 4.3: Error plots for water transport rate   62  The error plots for the water transport rate are plotted on different axes for the Px1-32 and the Px3-46 humidifiers, reflecting the sizes of the humidifiers and the change in quantity of water transferred. Overall, the model follows the experimental points with no major outliers. The majority of points are clustered in the lower range of water transport. The residual sums of squares, seen in Appendix B, are all similarly low. 4.2.3. NORMAL PLOT OF RESIDUALS N o rm a l %  Pr o ba bi lit y Normal Plot of Residuals -2.74 -1.08 0.58 2.23 3.89 1 5 10 20 30 50 70 80 90 95 99 Normal Plot of Residuals -2.19 -1.10 -0.00 1.09 2.19 1 5 10 20 30 50 70 80 90 95 99 Internally Studentized Residuals N o rm a l %  Pr o ba bi lit y Normal Plot of Residuals -2.55 -1.27 0.01 1.28 2.56 1 5 10 20 30 50 70 80 90 95 99 Internally Studentized Residuals Normal Plot of Residuals -2.53 -1.36 -0.19 0.98 2.15 1 5 10 20 30 50 70 80 90 95 99 Membrane M Membrane N 99 1 5 10 20 30 50 70 80 90 95 99 1 5 10 20 30 50 70 80 90 95 99 1 5 10 20 30 50 70 80 90 95 99 1 5 10 20 30 50 70 80 90 95 -2 4 3. 92. 30.-1 8 -2. 9 2.1.00.-1 0 -2. 2.1.20.-1. -2. 3 2.10.9-0.-1.  Figure 4.4: Normal plots of residuals for water transfer rate   63  Figure 4.4 reveals a good fit for the normal distribution and for the transform used. There is a slight S pattern apparent in three of the humidifiers, but no great deviation from the normal. The exception to this is the resulting plot for the Px1-32M, which shows noticeable platykurtosis, particularly on the higher end. This suggests either the presence of outlier results or a lack of fit to the distribution. 4.2.4. RESIDUALS-PREDICTED VALUES In te rn a lly  St u de n tiz e d R e si du a ls Residuals vs. Predicted -3.00 -1.43 0.15 1.72 3.29 0.53 1.38 2.23 3.08 3.93 Residuals vs. Predicted -3.00 -1.50 0.00 1.50 3.00 0.63 1.49 2.35 3.21 4.07 Predicted In te rn a lly  St u de n tiz e d R e si du a ls Residuals vs. Predicted -3.00 -1.50 0.00 1.50 3.00 1.20 2.37 3.53 4.70 5.86 Predicted Residuals vs. Predicted -3.00 -1.50 0.00 1.50 3.00 1.33 2.46 3.60 4.74 5.87 P x 1 -3 2 P x 3 -4 6  Figure 4.5: Residuals-predicted values plots for water transfer rate   64  The possible outlier causing kurtosis seen in Figure 4.4 is seen repeated in Figure 4.5. Otherwise, Figure 4.5 suggests a generally even spread of residual values. The actual values are weighted towards the center and lower ends of the range. The few residuals at the top of the range have similar magnitudes to the rest, but tend to be positive, which may be cause for concern in the model, suggesting the possibility of underprediction. 4.2.5. PREDICTED VALUES VS ACTUAL VALUES Pr e di ct e d Predicted vs. Actual 0.53 1.40 2.27 3.14 4.01 0.63 1.47 2.32 3.16 4.01 Predicted vs. Actual 0.63 1.51 2.38 3.26 4.14 0.65 1.52 2.39 3.27 4.14 Actual Pr e di ct e d Predicted vs. Actual 1.02 2.30 3.59 4.87 6.15 1.02 2.30 3.59 4.87 6.15 Actual Predicted vs. Actual 1.33 2.51 3.70 4.88 6.07 1.35 2.53 3.71 4.89 6.07 P x 1 -3 2 P x 3 -4 6  Figure 4.6: Predicted values vs. actual values for water transfer rate   65  Figure 4.6 reconfirms the results of Figure 4.5. The model for water transfer rate appears to have a good fit, with the beginnings of a small underprediction of performance at higher values of water transfer. 4.3. WATER RECOVERY RATIO RESULTS  A square root transform was used for water recovery ratio. 4.3.1. MODEL AND ANOVA Table 4.3: Models for water recovery ratio Px1-32M Px1-32N Px3-46M Px3-46N Sqrt(WRR)  = Sqrt(WRR)  = Sqrt(WRR)  = Sqrt(WRR)  = 0.53  0.56  0.5  0.53 0.12  * A 0.1  * A 0.089  * A 0.086  * A -0.1  * B -0.095  * B -0.11  * B -0.12  * B -0.069  * C -0.074  * C -0.096  * C -0.069  * C -0.033  * D -9.80E-03  * D -0.015  * D -0.018  * D 0.025  * E -2.52E-03  * E 0.045  * E 0.024  * E -0.011  * A * B 9.33E-03  * A * B -9.43E-03  * A * B -3.70E-03  * A * B -0.022  * A * C -0.023  * A * C -0.027  * A * C -0.031  * A * C 1.33E-03  * A * D -6.08E-03  * A * D -0.01  * A * D -8.21E-03  * A * D 0.06  * A * E 0.042  * A * E 0.039  * A * E 0.029  * A * E -3.26E-04  * B * C 1.30E-02  * B * C 0.017  * B * C 0.014  * B * C 6.95E-03  * B * D -7.72E-03  * B * D 5.72E-04  * B * D 2.02E-03  * B * D 5.76E-03  * B * E 0.027  * B * E 3.63E-03  * B * E 5.65E-03  * B * E -0.014  * C * D -7.87E-03  * C * D -7.53E-04  * C * D -5.37E-03  * C * D 0.038  * C * E 0.03  * C * E 0.026  * C * E 0.018  * C * E -0.032  * D * E 1.24E-03  * D * E 2.47E-03  * D * E 5.92E-03  * D * E -0.044  * A^2 -0.046  * A^2 -0.037  * A^2 -0.031  * A^2 0.053  * B^2 0.043  * B^2 0.042  * B^2 0.04  * B^2 1.70E-04  * C^2 -9.89E-03  * C^2 0.032  * C^2 0.024  * C^2 6.37E-03  * D^2 0.011  * D^2 7.97E-03  * D^2 5.67E-03  * D^2  Table 4.4: Summary of statistical significance for water recovery ratio Factor All Model Membrane All but Only A x B x C x D    Px1-32N E    Px1-32N AB     Px1-32N  66 Factor All Model Membrane All but Only AC    Px1-32M AD AE x BC  Px3-46 BD BE     Px1-32N CD CE x DE     Px1-32M A2 x B2 x C2  Px3-46 D2                  67 4.3.2. ERROR PLOT 0 20 40 60 80 100 0 10 20 30 40 50 60 70 80 90 100 Experimental WRR (%) M od e l W RR  (% ) 0 20 40 60 80 100 0 10 20 30 40 50 60 70 80 90 100 Experimental WRR (%) M od e l W RR  (% ) 0 20 40 60 80 100 0 10 20 30 40 50 60 70 80 90 100 Experimental WRR (%) M o de l W RR  (% ) 0 20 40 60 80 100 0 10 20 30 40 50 60 70 80 90 100 Experimental WRR (%) M o de l W RR  (% )  Figure 4.7: Error plots for water recovery ratio   While there are no consistent variations from a linear trend of fit between the modeled and experimental water recovery ratios, the Px1-32 humidifiers display a greater range of scatter than the Px3-46s, with residual sums of squares an order of magnitude greater, as seen in Appendix B.    68 4.3.3. NORMAL PLOT OF RESIDUALS N o rm a l %  Pr o ba bi lit y Normal Plot of Residuals -2.88 -1.51 -0.14 1.24 2.61 1 5 10 20 30 50 70 80 90 95 99 Normal Plot of Residuals -2.37 -0.91 0.54 2.00 3.46 1 5 10 20 30 50 70 80 90 95 99 Internally Studentized Residuals N o rm a l %  Pr o ba bi lit y Normal Plot of Residuals -2.64 -1.36 -0.08 1.20 2.47 1 5 10 20 30 50 70 80 90 95 99 Internally Studentized Residuals Normal Plot of Residuals -2.59 -1.34 -0.08 1.17 2.43 1 5 10 20 30 50 70 80 90 95 99  Figure 4.8: Normal plots of residuals for water recovery ratio   Despite the clear indication from the Box-Cox plots that a square root transform was the best option for water recovery ratio, Figure 4.8 indicates a lack of fit due to changing curvature in the residuals. This lack of fit suggests the normal distribution may be a poor choice of model for water recovery ratio.  69 4.3.4. RESIDUALS-PREDICTED VALUES In te rn a lly  St u de n tiz e d R e si du a ls Residuals vs. Predicted -3.00 -1.50 0.00 1.50 3.00 0.21 0.40 0.59 0.78 0.97 Residuals vs. Predicted -3.00 -1.39 0.23 1.84 3.46 0.26 0.41 0.56 0.72 0.87 Predicted In te rn a lly  St u de n tiz e d R e si du a ls Residuals vs. Predicted -3.00 -1.50 0.00 1.50 3.00 0.26 0.44 0.62 0.80 0.98 Predicted Residuals vs. Predicted -3.00 -1.50 0.00 1.50 3.00 0.30 0.46 0.62 0.78 0.94  Figure 4.9: Residuals-predicted values plots for water recovery ratio   While Figure 4.8 shows a lack of fit to the normal distribution, Figure 4.9 shows that the residuals remain evenly spread throughout the range of values, showing equal predictive behaviour throughout the model.  70 4.3.5. PREDICTED VALUES VS ACTUAL VALUES Pr e di ct e d Predicted vs. Actual 0.20 0.39 0.58 0.77 0.97 0.20 0.38 0.57 0.75 0.93 Predicted vs. Actual 0.24 0.41 0.57 0.74 0.91 0.24 0.41 0.57 0.74 0.91 Actual Pr e di ct e d Predicted vs. Actual 0.24 0.43 0.61 0.79 0.98 0.24 0.42 0.60 0.78 0.96 Actual Predicted vs. Actual 0.30 0.46 0.62 0.78 0.94 0.30 0.46 0.62 0.78 0.94 Membrane M Membrane N P x 1 -3 2 P x 3 -4 6 0.97 0. 0. 70. 70.580. 9 .24 1.740 7.41 0.2 0. 80. 90. 10.43 .30 . 40. 80. 20. 6 0.2 0.39 0.58 0.77 0.98 0.24 0.43 0.61 0.79 0.91 0.24 0.41 0.57 0.74 0.94 0.30 0.46 0.62 0.78  Figure 4.10: Predicted values vs. actual values for water recovery ratio   Figure 4.10 demonstrates once again the even spread of predictive behaviour throughout the range of the model. The spread of values away from the central line, however, repeats the suggestion of Figure 4.8 that the method used here – CCD – may not produce the best model for this metric.  71 4.4. STREAM 2 HUMIDITY RATIO RESULTS  A natural logarithm transform was used for stream 2 humidity ratio. 4.4.1. MODEL AND ANOVA Table 4.5: Models for stream 2 humidity ratio Px1-32M Px1-32N Px3-46M Px3-46N Ln(Stream 2 HR)  = Ln(Stream 2 HR)  = Ln(Stream 2 HR)  = Ln(Stream 2 HR)  = -3.19  -3.1  -3.16  -3.26 -0.05  * A -0.11  * A -0.21  * A -0.19  * A 0.16  * B 0.17  * B 0.1  * B 0.13  * B -0.25  * C -0.23  * C -0.24  * C -0.36  * C 0.26  * D 0.33  * D 0.33  * D 0.34  * D -0.43  * E -0.5  * E -0.43  * E -0.35  * E 0.038  * A * B 0.061  * A * B 0.055  * A * B 0.021  * A * B -0.049  * A * C -0.019  * A * C -0.086  * A * C -0.065  * A * C 0.047  * A * D -0.045  * A * D -0.023  * A * D -0.029  * A * D 0.24  * A * E 0.19  * A * E 0.1  * A * E 0.15  * A * E -0.05  * B * C -0.039  * B * C 3.41E-03  * B * C -5.80E-03  * B * C 0.019  * B * D -5.17E-03  * B * D -3.02E-03  * B * D -9.65E-03  * B * D 0.019  * B * E 0.054  * B * E 0.014  * B * E 0.031  * B * E -0.084  * C * D -0.072  * C * D -0.038  * C * D -0.016  * C * D 0.16  * C * E 0.13  * C * E 0.078  * C * E 0.13  * C * E -0.16  * D * E -0.086  * D * E -0.013  * D * E -0.02  * D * E     1.03E-04  * A^2 -0.049  * A^2     -0.046  * B^2 -0.024  * B^2     0.084  * C^2 0.12  * C^2     0.035  * D^2 0.062  * D^2  Table 4.6: Summary of statistical significance for stream 2 humidity ratio Factor All Model Membrane All but Only A    Px1-32M B x C x D x E x AB     Px46-N AC  Px3-46 AD AE x BC BD BE CD   N  72 Factor All Model Membrane All but Only CE x DE  Px1-32  4.4.2. ERROR PLOT 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 Experimental stream 2 HR (g/g) M od e l s tre a m  2 HR  (g/ g) 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 Experimental stream 2 HR (g/g) M od e l s tre a m  2 HR  (g/ g) 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 Experimental stream 2 HR (g/g) M o de l s tre am  2 HR  (g/ g) 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 Experimental stream 2 HR (g/g) M o de l s tre am  2 HR  (g/ g)  Figure 4.11: Error plots for stream 2 humidity ratio   The error plots for stream 2 humidity ratio reveal the same clustering at the low end of results as for water transport rate. Some significant outliers can be seen at higher humidity ratios for the Px1-32M humidifier, reflected in the highest residual sum of squares of the four models.  73 4.4.3. NORMAL PLOT OF RESIDUALS N o rm a l %  Pr o ba bi lit y Normal Plot of Residuals -3.91 -2.28 -0.65 0.98 2.61 1 5 10 20 30 50 70 80 90 95 99 Normal Plot of Residuals -2.01 -0.89 0.22 1.34 2.45 1 5 10 20 30 50 70 80 90 95 99 Internally Studentized Residuals N o rm a l %  Pr o ba bi lit y Normal Plot of Residuals -3.86 -2.34 -0.82 0.70 2.22 1 5 10 20 30 50 70 80 90 95 99 Internally Studentized Residuals Normal Plot of Residuals -4.29 -2.58 -0.86 0.86 2.57 1 5 10 20 30 50 70 80 90 95 99 P x 1 -3 2 P x 3 -4 6  Figure 4.12: Normal plots of residuals for stream 2 humidity ratio   Figure 4.12 demonstrates a better fit to the normal for most humidifiers than for the water recovery ratio, but the presence of a slight S curvature remains. In addition, there appears to be a significant outlier, which is repeated in the same position for all except the Px1-32N. This outlier pulls the normal farther from the correct fit than it otherwise would be.  74 4.4.4. RESIDUALS-PREDICTED VALUES In te rn a lly  St u de n tiz e d R e si du a ls Residuals vs. Predicted -3.91 -2.18 -0.45 1.27 3.00 -4.08 -3.43 -2.78 -2.12 -1.47 Residuals vs. Predicted -3.00 -1.50 0.00 1.50 3.00 -4.16 -3.45 -2.75 -2.05 -1.34 Predicted In te rn a lly  St u de n tiz e d R e si du a ls Residuals vs. Predicted -3.86 -2.15 -0.43 1.28 3.00 -4.31 -3.62 -2.93 -2.24 -1.55 Predicted Residuals vs. Predicted -4.29 -2.47 -0.65 1.18 3.00 -4.30 -3.65 -2.99 -2.34 -1.68  Figure 4.13: Residuals-predicted values plots for stream 2 humidity ratio   Figure 4.13 suggests an even spread of positive and negative residuals at any given predicted value. It also displays a decrease in this spread at higher predicted values. This suggests that, while the proposed model tends neither to under- nor over-predict, its accuracy increases at higher predicted values. The outliers mentioned above are also present for the same three humidifiers.  75 4.4.5. PREDICTED VALUES VS ACTUAL VALUES Pr e di ct e d Predicted vs. Actual -4.53 -3.73 -2.93 -2.13 -1.33 -4.53 -3.73 -2.93 -2.13 -1.33 Predicted vs. Actual -4.41 -3.62 -2.83 -2.04 -1.25 -4.41 -3.62 -2.83 -2.04 -1.25 Actual Pr e di ct e d Predicted vs. Actual -4.32 -3.61 -2.90 -2.19 -1.48 -4.32 -3.61 -2.90 -2.19 -1.48 Actual Predicted vs. Actual -4.30 -3.65 -2.99 -2.34 -1.68 -4.29 -3.64 -2.99 -2.34 -1.69 Membrane M Membrane N P x 1 -3 2 P x 3 -4 6 -4. 3 -1. 3-2 3-2.-3 3 -4 1 -1 5- .04-2 3- .62 -4.3 -1. 8-2 9-2.-3.6 -4.30 -1. 8-2. 4-2. 9-3. 5 -1.33 -4.53 -3.73 -2.93 -2.13 -1.48 -4.32 -3.61 -2.90 -2.19 -1.25 -4. 1 -3.62 -2.83 -2.04 -1.68 -4.30 -3.65 -2.99 -2.34  Figure 4.14: Predicted values vs. actual values for stream 2 humidity ratio   Figure 4.14 confirms that the proposed CCD model gives good predictions at the tops of the range of values. There is some spread and outlying values in the lower half of the range for all humidifiers. 4.5. STREAM 2 RELATIVE HUMIDITY RESULTS  A natural logarithm transform was used for stream 2 relative humidity.  76 4.5.1. MODEL AND ANOVA Table 4.7: Models for stream 2 relative humidity Px1-32M Px1-32N Px3-46M Px3-46N Ln(Stream 2 RH)  = Ln(Stream 2 RH)  = Ln(Stream 2 RH)  = Ln(Stream 2 RH)  = -0.53  -3.20E-01  -0.71  -0.65 -0.064  * A -0.086  * A -0.21  * A -0.23  * A 0.062  * B 0.072  * B 0.11  * B 0.071  * B -0.39  * C -3.60E-01  * C -0.55  * C -0.49  * C -0.015  * D 0.034  * D 0.073  * D 0.069  * D 0.086  * E 2.22E-03  * E 0.1  * E 0.042  * E 0.052  * A * B 0.073  * A * B 0.018  * A * B 0.048  * A * B -0.26  * A * C -0.22  * A * C -0.28  * A * C -0.31  * A * C 0.096  * A * D -0.01  * A * D 4.34E-03  * A * D 0.017  * A * D 0.24  * A * E 0.19  * A * E 0.14  * A * E 0.082  * A * E 0.064  * B * C 0.061  * B * C 0.12  * B * C 0.14  * B * C 9.11E-03  * B * D -0.013  * B * D -0.03  * B * D -0.011  * B * D -0.018  * B * E 0.025  * B * E 7.93E-03  * B * E -0.01  * B * E -0.016  * C * D -6.60E-03  * C * D 0.055  * C * D 0.037  * C * D 0.17  * C * E 0.16  * C * E 0.11  * C * E 0.072  * C * E -0.15  * D * E -9.40E-02  * D * E -0.014  * D * E -3.49E-03  * D * E  Table 4.8: Summary of statistical significance for stream 2 relative humidity Factor All Model Membrane All but Only A  Px3-46 B    Px1-32M C x D  Px3-46 E    Px1-32N AB AC x AD AE x BC  Px3-46 BD BE CD CE x DE  Px1-32   77 4.5.2. ERROR PLOT 0 50 100 150 0 20 40 60 80 100 120 140 160 Experimental stream 2 RH (%) M od e l s tre am  2 RH  (% ) 0 50 100 150 0 20 40 60 80 100 120 140 160 Experimental stream 2 RH (%) M od e l s tre am  2 RH  (% ) 0 50 100 150 0 20 40 60 80 100 120 140 160 Experimental stream 2 RH (%) M od el  st re a m  2 RH  (% ) 0 50 100 150 0 20 40 60 80 100 120 140 160 Experimental stream 2 RH (%) M od el  st re a m  2 RH  (% )  Figure 4.15: Error plots for stream 2 relative humidity   The error plots for stream 2 humidity display a greater scatter than the previous plots, reflected in the largest sums of squares of residuals, seen in Appendix B. The error plots remain overall linear; some large outliers and scatter groups at higher ranges of relative humidity for the Px1-32s imply some underlying error in the model.  78 4.5.3. NORMAL PLOT OF RESIDUALS N o rm a l %  Pr o ba bi lit y Normal Plot of Residuals -3.46 -1.89 -0.32 1.25 2.82 1 5 10 20 30 50 70 80 90 95 99 Normal Plot of Residuals -2.68 -1.41 -0.14 1.13 2.40 1 5 10 20 30 50 70 80 90 95 99 Internally Studentized Residuals N o rm a l %  Pr o ba bi lit y Normal Plot of Residuals -4.27 -2.61 -0.95 0.72 2.38 1 5 10 20 30 50 70 80 90 95 99 Internally Studentized Residuals Normal Plot of Residuals -2.93 -1.47 -0.01 1.45 2.92 1 5 10 20 30 50 70 80 90 95 99 P x 1 -3 2 P x 3 -4 6  Figure 4.16: Normal plots of residuals for stream 2 relative humidity   Figure 4.16 reveals some interesting behaviour not yet seen, and not evident from ANOVA tables. Both plots for membrane M display a similar lack of fit pattern, with more data in the upper tail pulling the model distribution away from the normal distribution. While there are some small outliers for the Px3-46N, this membrane otherwise seems to fit this transform significantly better than membrane M.  79 4.5.4. RESIDUALS-PREDICTED VALUES In te rn a lly  St u de n tiz e d R e si du a ls Residuals vs. Predicted -3.46 -1.85 -0.23 1.38 3.00 -2.14 -1.54 -0.93 -0.32 0.29 Residuals vs. Predicted -3.00 -1.50 0.00 1.50 3.00 -1.81 -1.27 -0.74 -0.20 0.33 Predicted In te rn a lly  St u de n tiz e d R e si du a ls Residuals vs. Predicted -4.27 -2.45 -0.64 1.18 3.00 -2.52 -1.86 -1.20 -0.54 0.12 Predicted Residuals vs. Predicted -3.00 -1.50 0.00 1.50 3.00 -2.28 -1.68 -1.09 -0.49 0.11  Figure 4.17: Residuals-predicted values plots for stream 2 relative humidity   The distinct behaviour of each membrane is repeated in Figure 4.17. Membrane N shows a relatively even spread throughout. Membrane M shows a noticeable increase in spread as the predicted values increase, and betrays the outliers causing the uneven distribution.  80 4.5.5. PREDICTED VALUES VS ACTUAL VALUES Pr e di ct e d Predicted vs. Actual -2.29 -1.63 -0.96 -0.29 0.38 -2.29 -1.63 -0.96 -0.29 0.38 Predicted vs. Actual -2.02 -1.41 -0.80 -0.19 0.42 -2.02 -1.41 -0.80 -0.19 0.42 Actual Pr e di ct e d Predicted vs. Actual -2.53 -1.87 -1.20 -0.54 0.12 -2.53 -1.87 -1.22 -0.56 0.09 Actual Predicted vs. Actual -2.38 -1.76 -1.14 -0.52 0.11 -2.38 -1.76 -1.15 -0.53 0.09 P x 1 -3 2 P x 3 -4 6  Figure 4.18: Predicted values vs. actual values for stream 2 relative humidity   Most tellingly for the RH metric, Figure 4.18 shows the paucity of results at the lowest end. The outliers seen in the earlier plots are visible near the center of the predicted range. The model shows significant spread from the center to the high end of its range.  81 4.6. STREAM 2 DEW POINT TEMPERATURE RESULTS  No transform was used for stream 2 dew point. 4.6.1. MODEL AND ANOVA Table 4.9: Models for stream 2 dew point Px1-32M Px1-32N Px3-46M Px3-46N Stream 2 DP  = Stream 2 DP  = Stream 2 DP  = Stream 2 DP  = 47.26  48.99  46.3  48.14 -0.9  * A -1.92  * A -3.43  * A -3.73  * A 2.99  * B 3.1  * B 2.46  * B 1.95  * B -4.6  * C -4.23  * C -6.67  * C -4.41  * C 4.76  * D 6.04  * D 6.27  * D 6.2  * D 0.47  * E -0.83  * E 1.71  * E 0.28  * E 0.71  * A * B 1.14  * A * B 0.38  * A * B 1  * A * B -0.91  * A * C -0.37  * A * C -1.12  * A * C -1.59  * A * C 0.92  * A * D -0.79  * A * D -0.68  * A * D -0.49  * A * D 4.51  * A * E 3.51  * A * E 2.56  * A * E 1.78  * A * E -0.96  * B * C -0.75  * B * C -0.15  * B * C 0.035  * B * C 0.42  * B * D -0.11  * B * D -0.17  * B * D -0.017  * B * D 0.51  * B * E 1.13  * B * E 0.7  * B * E 0.33  * B * E -1.59  * C * D -1.36  * C * D -0.39  * C * D -0.75  * C * D 2.77  * C * E 2.33  * C * E 2.03  * C * E 1.3  * C * E -2.7  * D * E -1.37  * D * E -0.066  * D * E 0.019  * D * E     -0.96  * A^2 9.30E-03  * A^2     -0.41  * B^2 -0.89  * B^2     2.22  * C^2 1.49  * C^2     1.25  * D^2 0.68  * D^2  Table 4.10: Summary of statistical significance for stream 2 dew point Factor All Model Membrane All but Only A    Px1-32M B x C x D x E     Px3-46M AB AC  Px3-46 AD AE x BC BD BE CD  Px1-32  82 Factor All Model Membrane All but Only CE x DE  Px1-32  4.6.2. ERROR PLOT 20 30 40 50 60 70 20 25 30 35 40 45 50 55 60 65 70 75 Experimental DP (degC) M od el  DP  (de gC ) 20 30 40 50 60 70 20 25 30 35 40 45 50 55 60 65 70 75 Experimental DP (degC) M od el  DP  (de gC ) 20 30 40 50 60 70 20 25 30 35 40 45 50 55 60 65 70 75 Experimental DP (degC) M od el  DP  (de gC ) 20 30 40 50 60 70 20 25 30 35 40 45 50 55 60 65 70 75 Experimental DP (degC) M od el  DP  (de gC )  Figure 4.19: Error plots for stream 2 dew point   The error plots for stream 2 dew point reveal a similar trend to the previous error plots with regards to the model fit between humidifier models. Sums of squares of  83 residuals four times larger for the Px1-32s imply residuals with twice the magnitude of those for the Px3-46s. 4.6.3. NORMAL PLOT OF RESIDUALS N o rm a l %  Pr o ba bi lit y Normal Plot of Residuals -3.89 -2.24 -0.58 1.08 2.74 1 5 10 20 30 50 70 80 90 95 99 Normal Plot of Residuals -1.96 -0.87 0.22 1.30 2.39 1 5 10 20 30 50 70 80 90 95 99 Internally Studentized Residuals N o rm a l %  Pr o ba bi lit y Normal Plot of Residuals -4.03 -2.49 -0.95 0.60 2.14 1 5 10 20 30 50 70 80 90 95 99 Internally Studentized Residuals Normal Plot of Residuals -4.46 -2.73 -1.00 0.73 2.47 1 5 10 20 30 50 70 80 90 95 99 Membrane M Membrane N P x 1 -3 2 P x 3 -4 6 99 1 5 10 20 30 50 70 80 90 95 9 1 5 10 20 30 50 70 80 90 95 99 1 5 10 20 30 50 70 80 90 95 99 1 5 10 20 30 50 70 80 90 95 -3. 9 2. 41.-0.-2. 4 -1. 6 2. 91.080.-0. 7 -4. 3 2. 40.-0. 5-2. 9 -4. 6 2.0.7-1. 0-2. 3  Figure 4.20: Normal plots of residuals for stream 2 dew point temperature   In keeping with the close relationship of dew point to humidity ratio, Figure 4.20 displays noticeable similarity to Figure 4.12, particularly the low outliers. Once again, Px1-32N displays a better fit than the other humidifiers  84 4.6.4. RESIDUALS-PREDICTED VALUES In te rn a lly  St u de n tiz e d R e si du a ls Residuals vs. Predicted -3.89 -2.17 -0.45 1.28 3.00 24.49 35.85 47.22 58.58 69.94 Residuals vs. Predicted -3.00 -1.50 0.00 1.50 3.00 29.73 40.42 51.11 61.80 72.49 Predicted In te rn a lly  St u de n tiz e d R e si du a ls Residuals vs. Predicted -4.03 -2.27 -0.52 1.24 3.00 23.44 34.84 46.23 57.63 69.03 Predicted Residuals vs. Predicted -4.46 -2.60 -0.73 1.13 3.00 28.71 38.22 47.74 57.25 66.76  Figure 4.21: Residuals-predicted values plots for stream 2 dew point temperature   The outliers in three plots are once again present in Figure 4.21. The other noticeable feature of this plot is the increase of spread for all humidifiers near the center of the range, with more accurate prediction near the ends of the range. The residuals show no obvious bias in the model.  85 4.6.5. PREDICTED VALUES VS ACTUAL VALUES Pr e di ct e d Predicted vs. Actual 24.49 36.44 48.39 60.33 72.28 25.49 37.19 48.88 60.58 72.28 Predicted vs. Actual 29.38 40.48 51.58 62.68 73.78 29.38 40.48 51.58 62.68 73.78 Actual Pr e di ct e d Predicted vs. Actual 23.44 35.11 46.79 58.46 70.13 24.31 35.77 47.22 58.68 70.13 Actual Predicted vs. Actual 28.51 38.08 47.64 57.20 66.76 28.51 38.01 47.50 57.00 66.49 P x 1 -3 2 P x 3 -4 6  Figure 4.22: Predicted values vs. actual values for stream 2 dew point   Figure 4.22 confirms the findings from Figure 4.21, providing no new information. The spread for the Px3-46 humidifiers is smaller than for the Px1-32s. 4.7. DEW POINT APPROACH TEMPERATURE RESULTS  No transform was used for dew point approach temperature.  86 4.7.1. MODEL AND ANOVA Table 4.11: Models for dew point approach temperature Px1-32M Px1-32N Px3-46M Px3-46N DPAT  = DPAT  = DPAT  = DPAT  = 22.7  21.02  21.91  23.66 0.94  * A 1.89  * A 3.74  * A 3.42  * A -3.02  * B -3.13  * B -1.99  * B -2.49  * B 4.61  * C 4.22  * C 4.42  * C 6.62  * C 2.35  * D 1.07  * D 0.9  * D 0.81  * D -0.47  * E 0.8  * E -0.29  * E -1.73  * E -0.7  * A * B -1.13  * A * B -0.98  * A * B -0.4  * A * B 0.92  * A * C 0.37  * A * C 1.61  * A * C 1.11  * A * C -0.93  * A * D 0.79  * A * D 0.5  * A * D 0.66  * A * D -4.53  * A * E -3.51  * A * E -1.79  * A * E -2.54  * A * E 0.94  * B * C 0.77  * B * C -0.033  * B * C 0.13  * B * C -0.42  * B * D 0.12  * B * D -9.38E-03  * B * D 0.14  * B * D -0.5  * B * E -1.12  * B * E -0.32  * B * E -0.73  * B * E 1.58  * C * D 1.4  * C * D 0.73  * C * D 0.4  * C * D -2.79  * C * E -2.31  * C * E -1.33  * C * E -2.02  * C * E 2.7  * D * E 1.33  * D * E -0.022  * D * E 0.092  * D * E     -0.029  * A^2 0.94  * A^2     0.89  * B^2 0.42  * B^2     -1.51  * C^2 -2.21  * C^2     -0.69  * D^2 -1.2  * D^2  Table 4.12: Summary of statistical significance for dew point approach temperature Factor All Model Membrane All but Only A    Px1-32M B x C x D x E  Px3-46 AB     Px3-46N AC  Px3-46 AD AE x BC BD BE CD   N CE x DE   M   87 4.7.2. ERROR PLOT 0 10 20 30 40 0 5 10 15 20 25 30 35 40 45 Experimental DPAT (degC) M od el  DP AT  (de gC ) 0 10 20 30 40 0 5 10 15 20 25 30 35 40 45 Experimental DPAT (degC) M od el  DP AT  (de gC ) 0 10 20 30 40 0 5 10 15 20 25 30 35 40 45 Experimental DPAT (degC) M od el  DP AT  (de gC ) 0 10 20 30 40 0 5 10 15 20 25 30 35 40 45 Experimental DPAT (degC) M od el  DP AT  (de gC )  Figure 4.23: Error plots for dew point approach temperature   The trends and the residuals for the dew point approach temperature are near identical to those for the stream 2 dew point. The overall trends show the model following the experimental data, but significant scatter is reflected in the values of the residuals.  88 4.7.3. NORMAL PLOT OF RESIDUALS No rm a l %  Pr o ba bi lit y Normal Plot of Residuals -2.50 -1.05 0.40 1.85 3.29 1 5 10 20 30 50 70 80 90 95 99 Normal Plot of Residuals -2.41 -1.33 -0.24 0.84 1.92 1 5 10 20 30 50 70 80 90 95 99 Internally Studentized Residuals N o rm a l %  Pr o ba bi lity Normal Plot of Residuals -2.13 -0.59 0.95 2.49 4.03 1 5 10 20 30 50 70 80 90 95 99 Internally Studentized Residuals Normal Plot of Residuals -2.47 -0.75 0.98 2.70 4.43 1 5 10 20 30 50 70 80 90 95 99 Membrane M Membrane N P x 1 -3 2 P x 3 -4 6 99 1 5 10 20 30 50 70 80 90 95 99 1 5 10 20 30 50 70 80 90 95 9 1 5 10 20 30 50 70 80 90 95 9 1 5 10 20 30 50 70 80 90 95 -2. 0 3.1.0.-1. 5 -2.4 1.90.84-0.2-1.3 -2.1 4.02.40.-0. -2.4 4. 32.700.98-0.7  Figure 4.24: Normal plots of residuals for dew point approach temperature   Figure 4.24 is very similar to Figure 4.20, but reversed, as higher DP tends to correspond with lower DPAT and vice versa. The same outliers and platykurtosis are seen at the top end of the plots. This is related to inverse quality of the DPAT, where for comparable conditions higher values indicate decreased performance.  89 4.7.4. RESIDUALS-PREDICTED VALUES In te rn a lly  St u de n tiz e d R e si du a ls Residuals vs. Predicted -3.00 -1.28 0.45 2.17 3.89 7.05 15.28 23.50 31.73 39.95 Residuals vs. Predicted -3.00 -1.50 0.00 1.50 3.00 4.69 12.69 20.69 28.68 36.68 2 Predicted In te rn a lly  St u de n tiz e d R e si du a ls Residuals vs. Predicted -3.00 -1.24 0.52 2.28 4.03 8.16 16.80 25.44 34.07 42.71 Predicted Residuals vs. Predicted -3.00 -1.14 0.71 2.57 4.43 10.20 17.30 24.40 31.50 38.60 P x 1 -3 2 P x 3 -4 6  Figure 4.25: Residuals-predicted values plots for dew point approach temperature   Despite the similarity of the normal plots for DPAT, Figure 4.25 reveals the differences between it and the stream 2 dew point. The spread, while showing some decrease in the Px3-46 at higher values, is generally even across the range of values. The outliers present here are more extreme than for any other metrics.  90 4.7.5. PREDICTED VALUES VS ACTUAL VALUES Pr e di ct e d Predicted vs. Actual 3.72 13.41 23.11 32.80 42.50 3.72 13.41 23.11 32.80 42.50 Predicted vs. Actual 3.38 11.75 20.12 28.49 36.86 3.38 11.75 20.12 28.49 36.86 2 Actual Pr e di ct e d Predicted vs. Actual 7.24 16.11 24.98 33.84 42.71 7.24 15.93 24.62 33.31 42.00 Actual Predicted vs. Actual 9.44 16.73 24.02 31.31 38.60 9.44 15.81 22.18 28.55 34.92 Membrane M Membrane N P x 1 -3 2 P x 3 -4 6 3. 2 42 03 .8023. 113 1 .38 3 .868.492 .12.75 7.2 42.713 8424.9816.11 9.44 38.6031.3124.0216.73 42.50 3.72 13.41 23.1 32.80 42.71 7.24 16. 24.98 33.84 36.86 3.38 11.75 20.12 28.49 38.60 9.44 16.73 24.02 31.31  Figure 4.26: Predicted values vs. actual values for dew point approach temperature   The even spread evident in Figure 4.25 is emphasized in Figure 4.26; at the same time, the magnitude of the spread, and the related inadequacy of the model for accurate prediction of DPAT, are particularly demonstrated for the Px1-32 humidifiers.    91 4.8. RESULTS SUMMARY Table 4.13: Summary of results with statistical significance across all tests Factor WTR WRR HR RH DP DPAT A x x B x x x  x x C x x x x x x D x  x  x x E x  x AB AC    x AD AE  x x x x x BC BD BE CD x CE x x x x x x DE x A2 x x B2  x C2 D2   Table 4.13 is used to identify effects of particular interest for investigation and system design. Each of the effects identified has statistical significance for all humidifiers tested; this is not to imply that they must necessarily be significant without further investigation of diagnostic plots, as throughout this chapter, and the effects themselves. This table is used as a guideline throughout the following chapter’s discussion to aid in evaluation of metrics and of important effects and interactions.     92 5. DISCUSSION 5.1. THERMODYNAMIC CONSISTENCY  The data used to produce the response surfaces for each of the metrics investigated here were all based on direct physical measurements of temperature and pressure and on the assumptions of mass conservation through the humidifier and of full saturation of the outlet stream of the water balance. The standard psychrometric relations outlined in Section 1.5 are used to calculate the set of data for the six metrics at each experimental point from these initial measurements. As such, the data used to produce the response surfaces are thermodynamically consistent between metrics. Each set of data, however, is subject to a separate statistical analysis to produce its response surface model. The relations used to produce the data are not linear; each metric uses a different transform, depending on its Box-Cox plot; and this transformed data is subjected to a least squares analysis. Following these operations, thermodynamic consistency is no longer maintained between the six response surfaces produced.  An example of this is found in comparing stream 2 dew points to stream 2 relative humidities; in the first experimental run, the model stream 2 dewpoint is 50.7°C for a 48.4°C stream 2 drybulb temperature. The model stream 2 relative humidity is 95.2%, rather than the supersaturated condition this dew point would translate to. These response surfaces are entirely independent of one another and any thermodynamic consistency is accidental.  93 5.2. READING RESPONSE SURFACE PLOTS  The fact of the response surfaces produced in this work being in five dimensions – four numeric factors and one response – means that the graphical representations of the results bear some explanation. The results presented in this section and in Appendix A are all presented in the form of two-dimensional contour plots. This allows a visualization of the change of the response, presented as the contour elevation, with the change in the two factors on the plot axes. To enable this visualization the two numeric factors not on the plot axes are held at a constant level for that plot, and each plot is for a unique level of pressure. The levels of the unplotted factors are indicated in the figure caption, and the legend for the contour shades given with each plot.  The full response surfaces in Appendix A are given a more involved graphical treatment. In order to allow a visualization of all four numeric factors and the response, each plot is made up of twelve contour subplots, each read as described in the preceding paragraph. One diagonal of the plot is taken up by subplotted boxes containing a factor name and scale. These scales are projected vertically and horizontally to provide the scales for each of the subplots. As with the single contour plots, in each two-dimensional contour plot the factors not involved are maintained at a constant level. It can be noted that the twelve subplots are in fact six pairs of identical plots, only with the axes reversed.  A simplified example of this type of plot is given in Figure 5.1: Example for reading multiple axis plots. In this case, the plot is a curved line in four dimensions, with the values given in Table 5.1: Values of line plotted in Figure 5.1. The plot shows six two-dimensional projections of this line in subplots A through F, and subplots G through L are A through F with reversed axes. Subplot D, for example, has Q1 on the x-axis and  94 T1 on the y-axis, while subplot K repeats the same information with T1 on the x-axis and Q1 on the y-axis. The values of Q1 do not vary; this is reflected in the straight lines in subplots A, D, F, J, K, and L. Q3 increases linearly; this can be seen looking at the y- direction in subplots F, H, and I, and in the x-direction in subplots B, E, and J. T1 increases in a quadratic manner; this can be seen by the non-linear spread of points and the curved lines in subplots C, D, E, G, H, and K. Finally, T3 decreases linearly; this is not visible in subplots A or L, but can be seen in subplots B, C, G, and I. Together, these subplots combine to give a full picture of the behaviour of the line. Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure 5.1: Example for reading multiple axis plots  Table 5.1: Values of line plotted in Figure 5.1 Factor Corresponding values Q1 150 150 150 150 150 150 Q3 50 90 130 170 210 250 T1 39 46 55 66 79 94  95 Factor Corresponding values T3 80 76 72 68 64 60  5.3. PERFORMANCE METRICS  A significant portion of this work has been dedicated to the investigation of the actual metrics used in measuring humidifiers performance. This has extended to the statistical analysis of the experimental results using all six proposed metrics, for the purpose of a direct and empirical comparison of these metrics that goes beyond a thought experiment. In order to discuss the results of this study in any meaningful manner, it is first necessary to use the results obtained from the statistical analysis, and prior knowledge, to decide on the best metric for use in assessing performance. The intent of this section of the discussion is to determine a performance metric for use in this thesis and to be proposed as a standard for humidifier performance determination. 5.3.1. DEFINING “GOODNESS”  In order to determine the best metric for use in humidifiers, it is first necessary to define what is meant by “best”. Every metric investigated here exists because it has a certain inherent “goodness”, whether that is a certain physical meaning, a demonstrated use in modeling, or something else. In this work, the following properties were considered desirable, in descending order of priority: 1) Performance in application: the information given directly by a metric regarding suitability of a humidifier in a PEMFC application; 2) Relative performance: the ease of use of a metric in cross-humidifier comparisons; 3) Absolute performance: the metric’s utility in assessing total water transport;  96 4) Statistical model: the suitability of a metric to the statistical methods proposed. 5.4. ASSESSING “GOODNESS” 5.4.1.1 Performance in application  The only metric which on its own gives any generalized information regarding potential performance in a fuel cell system is relative humidity. Of the others, dew point and dew point approach temperature are often used to specify desired performance, but in isolation cannot indicate a constant target for humidifier performance. Relative humidity, as demonstrated in Figure 1.2, is a consistent target for humidifier performance across a broad range of conditions. An ideal humidifier would be capable of performing within the acceptable band of humidities, regardless of flow conditions. Relative humidity is the only metric incorporating both the information of water content and saturation pressure. Because of this, relative humidity must be included in any humidifier performance assessment conducted for any general purposes. 5.4.1.2 Relative performance  Any metric can be used to compare similar humidifiers, but comparing dissimilar humidifiers becomes more complex. This comparison becomes meaningless if the humidifiers are tested at different conditions; however, for dissimilar humidifiers, flow rate design points will often be different. The WRR metric takes into account the effects of different flow rates at stream 3, though not that of differing flow rates at stream 1 as the water content of stream 1 approaches zero. Stream 1 flow rate, along with some of its interactions, has been shown to be a significant factor.  97  The other metric with normalization is the DPAT, which records the difference between dew points, rather than a ratio like the WRR. DPAT, however, is inherently weak in that it is dependent only on dew point. As discussed earlier, at a lower stream 3 temperature a “better” DPAT can still indicate decreased performance as compared to a humidifier at a higher temperature. Since this means that DPAT is only meaningful if compared at similar temperatures, it has no advantage over a simple stream 2 dew point measurement; the first term on the right side of equation 1.6 for DPAT must be the same for any meaningful comparisons, which reduces to a comparison of stream 2 dew points. 5.4.1.3 Absolute performance  The absolute performance of a humidifier is judged by the absolute quantity of water that it transfers. All metrics are based on the water transported, but all except for the water transfer rate are in fact based on the composition of the air-water vapour mixture exiting stream 2. The water transport rate is the only metric that gives water transport information unbiased by flow conditions or flow rates. It also has the advantage of being easy to normalize by various means, particularly by total membrane area in the humidifier, which allows a good estimation of the cost effectiveness of the humidifier in transferring water. 5.4.1.4 Use in statistical model  While the three points above have a clear “best” metric, it is more difficult to see which applies best to a statistical model. All of the metrics investigated here have demonstrated a statistical lack of fit to the quadratic or linear models, with high lack of fit F-values indicating that the lack of fit is very unlikely to be simply the product of noise. This implies that the inclusion of further terms, or the use of a higher-order model, would  98 give a better fit to variations within the design space. At the same time, the model F- values and the signal to noise ratios are both high, demonstrating that the model itself has significance and, statistically speaking, can be used to investigate trends within the design space. The implication of these numbers is that, while the variations from this model are not caused only by random error contained in the experimental data, the overall model follows the general shape of the response surface.  The model fit values vary from humidifier to humidifier. Both Px3-46 humidifiers demonstrate a better fit than the Px1-32 humidifiers. Likewise, membrane N demonstrates better fit than membrane M. There is, however, a difference in fit between metrics. Since the F-values vary between humidifiers, but vary in a similar manner, the average F-values for each humidifier are used to rate overall fit of the model to the metric. This is demonstrated in Table 5.2.  Table 5.2: Average of model F-values for metrics Metric Average of model F-values Water transport rate 73.07 Water recovery ratio 54.41 Stream 2 humidity ratio 55.73 Stream 2 relative humidity 32.69 Stream 2 dew point 28.70 Dew point approach temperature 18.16   All of these values, statistically speaking, suggest that there is less than a 0.01% chance of the model being insignificant. With this in mind, it is somewhat redundant to pick a metric on the basis of its being more significant than another, despite the difference in F-values. Regardless, these values provide a certain level of insurance when selecting metrics that the metric can be acceptably modeled using statistical methods. Of the three metrics mentioned as possible best metrics for each criterion so far in section  99 5.1: water transport rate displays the most significance; WRR is similar to stream 2 HR, and still a high value; and stream 2 RH, while lower, retains a higher F-value than the dew point measurements. The cause of these variations in fit from the same data is the transformations undergone by the data as it is translated into each metric. 5.4.2. COMBINED METRICS  The fact of three distinct metrics, each of which carries a vital piece of information regarding performance, suggests that the adoption of a single metric to characterize humidifier performance would result in poor information. The unique information provided by each metric leads to the use of different metrics to reach a combined solution.  Of first importance is the stream 2 RH. This allows an indication of the range inside which a humidifier is working as intended. A humidifier working outside this range is either performing insufficiently well to prevent drying, or is flooding the stack. The response surface model for stream 2 RH allows the specification for each humidifier tested of the range within the design space where performance is acceptable; according to Figure 1.2 [2], this is where 80% < RH < 100%, though the low range can vary depending on fuel cell conditions. The WRR and water transfer rates outside of this region are of less interest, as in operation the humidifier should be kept within the specified operating range. This optimization process may also allow for the diminution of the flows necessary in the humidifier to reach this performance level. These flows may be varied by use of a gate or valve in the balance of plant; a reduction of flow in the humidifier can reduce parasitic load on the blower system caused by humidifier pressure drop.  100  Once this area of effective performance has been established, it becomes meaningful to compare humidifier effectiveness. This meaning is achieved by comparing relative performance, as measured by WRR, within the bounds established by the optimization process. The highest value of the WRR within this range can be considered an optimal performance point of the humidifier for comparative purposes; however, for applications where the demand on the stack, and therefore humidifier, varies, it may be of more interest to consider the range or the mean of WRR within the optimization space. Plots of WRR bounded in this way are reproduced in Figure 5.2 and Figure 5.3. Stream 1 Flow Rate (SLPM) St re am  3 Fl ow  Ra te  (S LP M )   20 40 60 80 100 20 30 40 50 60 70 80 90 100 20 30 40 50 60 70  Figure 5.2: Water recovery ratio plot within relative humidity bounds: Q1 vs Q3 for Px1-32M, with C=-1, D=0, E=-1   101 Stream 1 Temperature (degC) St re am  3 Te m pe ra tu re  (de gC )   40 60 80 100 60 65 70 75 80 32 34 36 38 40 42 44 46  Figure 5.3: Water recovery ratio plot within relative humidity bounds: T1 vs T3 for Px3-46N, with A=0, B=0, E=-1   To convey absolute performance, a similar rationale is used. The maximum water transfer rate may not be at the same point as the maximum WRR; as the desirable traits of a performance metric outlined above make absolute performance subordinate to relative performance, a final performance metric would be the water transfer rate and the WRR at the point with the highest WRR within the region of acceptable stream 2 relative humidity. The following discussion of effects will focus mainly on the behaviour of these three metrics.  102 5.5. MAIN EFFECTS  The effects of all five main factors can be seen through inspection of the model equations for the response surfaces, found in Chapter 4. Their respective significance is also seen in Table 4.13 and in more detail in the previous ANOVA summaries. These effects are not given in terms of confidence intervals, as the changing variance throughout the model surface means that there is no unique confidence interval. The positive and negative effects referred to below are a repetition of the quantitative effects of the factors, the magnitude of which in the response surface models can be seen from the magnitude of the factors present in the equations presented in Chapter 4. 5.5.1. STREAM 1 FLOW RATE  Q1 is an important positive factor for both WTR and WRR. As the flow in the dry stream is increased, the rate at which moisture is convected away from the membrane surface increases commensurately. At high Q1, desorption is not limiting process in water transport across the humidifier membrane.  In the four composition-based metrics, however, Q1 has a negative effect. This is caused by the dilution of the air-water vapour mixture as dry air is introduced into the system at a higher rate. For stream 2 RH, the effect of Q1 is negative. Since Q1 is set by stack stoichiometry and power demand, however, it is difficult to optimize based on Q1. A plot of the effects of Q1 and Q3 on RH is shown in Figure 5.4.  103 Stream 1 Flow Rate (SLPM) St re am  3 Fl ow  Ra te  (S LP M )   20 40 60 80 100 20 30 40 50 60 70 80 90 100 0 50 100 150  Figure 5.4: Stream 2 relative humidity plot of Q1 vs Q3 for Px1-32N, with C=-1, D=0, E=-1  5.5.2. STREAM 3 FLOW RATE  Q3 has a small positive effect on WTR. This is because an increase in Q3 introduces more water into the humidifier system, increasing overall transport. At the same time, increased Q3 has a relatively large negative effect on the WRR. This increased flow rate also increases the value of the denominator in equation 1.1, and the increase in water transfer is not large enough to compensate for this increase in the denominator. This suggests that the transport processes across the membrane in the humidifier are rate limiting, rather than the rate at which water is supplied to the membrane. This is a strong argument for improved membrane technology. In addition, there is potential for system optimization in systems meeting performance requirements, by using bypass gates to vary  104 Q3 into the humidifier and reduce overall system drop while maintaining an acceptable level of performance. The positive effect of Q3 on stream 2 RH is of the same magnitude as other positive effects. 5.5.3. STREAM 1 TEMPERATURE  Increasing T1 has a strong negative effect on performance, as seen in Figure 5.5. This negative effect remains in the model produced for every metric, and is the most consistent result of this study. The reasons for this effect are discussed by Romero and Mérida in [53]. The high T1 initially increases the evaporation of water from the membrane surface, to the point that the rate of transport from the surface is higher than that at which water is conducted through the membrane. This causes a drying of the membrane layer adjacent to the dry stream. This dry membrane subsequently acts as a barrier to further water transport, resulting in the significant decrease in water transport observed with increases in T1. As this work provides only steady state measurements, the likely transient increase in water transport at the beginning of this process is not seen.  105 Stream 1 Temperature (degC) St re am  3 Fl ow  Ra te  (S LP M )   40 60 80 100 20 30 40 50 60 70 80 90 100 0 5 10 15 20 25 30 35  Figure 5.5: Water transfer rate plot of T1 vs Q3 for Px1-32M, with A=0, D=0, E=-1  5.5.4. STREAM 3 TEMPERATURE  The effect of T3 is combined with the effect of increasing water content in stream 3 as the dew point temperature is raised, since 3 100%φ = . This has a strong positive effect on absolute performance as judged by WTR caused by the effects of more water supplied to the wet side of the membrane. This positive effect is also noted in stream 2 HR and dew point measurements. This positive effect is shown with Q1 for water transport ratio in Figure 5.6.  106 Stream 1 Flow Rate (SLPM) St re am  3 Te m pe ra tu re  (de gC )   20 40 60 80 100 60 65 70 75 80 0 5 10 15 20 25 30 35  Figure 5.6: Water transfer rate plot of T3 vs Q1 for Px1-32M, with B=0, C=-1, E=-1   At the same time, increasing T3 has a negative, less significant, effect on WRR. The reasons for this are similar to the reasons for the same effect with increasing Q3, increasing the denominator in the Q3 calculation. This same effect is seen in the effect of T3 on DPAT, as it increases the first term in equation 1.6.  The effect on stream 2 RH is more mixed. The small values seen in the RH effect are caused by the dependence of the RH measurement on the dry bulb temperature of the stream as well as the wet bulb temperature. A higher value of T3 has a heating effect on stream 2, raising its saturation pressure and thereby creating a demand for greater water transport to increase the RH.  107 5.5.5. PRESSURE  While pressure is a statistically significant result in most of the models, the model values associated with it vary. From the results of the water transfer rate, it is clear that increased system pressure has the effect of depressing the absolute water transfer. This is also seen in stream 2 HR, the other metric with no normalizing based on saturation pressure. The effect on WRR and stream 2 RH, however, is mixed and small; this lends confidence to Kadylak’s assertion that pressure has a relatively insignificant effect on WRR [25]. This suggests that for tests where absolute performance is not required information, pressure may be left out, and that there is little to be gained in terms of suitability for the application through specifying pressure for humidification purposes. The effects of pressure are also highly influenced by other flow factors, as discussed below in section 5.6. 5.6. FACTOR INTERACTIONS  Due to the large number of factor interactions present in this system, only the most significant ones are discussed here. These are AC, AE, and CE. 5.6.1. AC: Q1 AND T1  The negative effect seen in an increase of T1 is seen repeated in this interaction. Of the three metrics of concern, the clearest result of this interaction is in stream 2 RH. The interaction of Q1 and T1 compounds the diffusion effect of the higher flow rate with the higher stream 2 saturation pressure caused by an increased T1. This is evident in the significant negative value associated with this interaction in the RH model as in Figure 5.7. The values associated with it in WRR and WTR are also negative, but much less so. In WTR, shown in Figure 5.8, this reflects the dominance of the negative effect of a high  108 T1 over the positive convective effect of a higher Q1. For WRR, the behaviour is similar; since this interaction includes neither Q3 nor T3, which make up the normalizing portion of the WRR metric, WRR for the AC interaction tracks with WTR. Stream 1 Flow Rate (SLPM) St re am  1 Te m pe ra tu re  (de gC )   50 100 150 200 250 30 40 50 60 70 80 90 100 110 0 50 100 150  Figure 5.7: Stream 2 relative humidity plot of Q1 vs T1 for Px3-46N, with B=0, D=0, E=-1   109 Stream 1 Flow Rate (SLPM) St re am  1 Te m pe ra tu re  (de gC )   50 100 150 200 250 30 40 50 60 70 80 90 100 110 0 5 10 15 20 25 30 35  Figure 5.8: Water transfer rate plot of Q1 vs T1 for Px3-46M, with B=0, D=0, E=-1  5.6.2. AE: Q1 AND PRESSURE  The interaction between Q1 and the categoric pressure factor has a positive result in all models. As discussed above, on its own, Q1 is positive for absolute water transport with a negative effect on WRR, while pressure has negative effects on WTR and mixed results otherwise. The implication of the positive result of this interaction is that the negative consequences of an increased overall pressure are mitigated at higher flow rates, suggesting that in terms of optimizing humidification, high pressure systems will perform comparatively better with a higher flow across the membrane.  110 5.6.3. CE: T1 AND PRESSURE  Once again, this interaction is an example of two factors with negative main effects combining in a positive interaction. The interaction between T1 and pressure is positive for all metrics. This suggests that the deleterious effect of T1 is mitigated at higher pressures. While it is still advisable to avoid high temperatures to optimize humidification performance, this result suggests that if these conditions are necessary they should only be used in with a high pressure system. 5.7. GEOMETRY  As the two geometries tested have different flow specifications, it is difficult to compare them directly without non-dimensional parameters. Their performance may, however, be inspected across the range of the response surface design space for comparison, as shown in the plots in Appendix A. Most notably, the form of performance variation between the two humidifier geometries is remarkably similar. Flow rates used to test the Px1-32s were comparably higher relative to the capacity of the humidifier than those used to test the Px1-46s, causing some differences in contour shapes, but the overall trends remain the same for both geometries. The similarities in shape are reassuring, giving confidence in making similar predictions for both humidifier types. 5.8. MEMBRANE  The comparisons between the membranes can be also seen in Appendix A. Between the two membranes, the shape of the response surface remains the same. Membrane N demonstrates slightly better performance for both humidifier geometries. This is in keeping with its being a prototype, specialized membrane intended for  111 humidification purposes, while membrane M is a more generally established membrane for a wider range of applications.   112 6. CONCLUSIONS 6.1. DESIGN OF EXPERIMENTS IN HUMIDIFIER PERFORMANCE  One of the major goals of this work was to apply a response surface method to evaluating membrane humidifier performance, as an alternative to the analytical modeling performed by previous researchers. The use such a method has to date been non-existent in membrane humidifier literature. The experimental design chosen was a central composite design in five factors. The five factors chosen were Q1, Q3, T1, T3, and pressure level. The resulting experimental design necessitated 60 test runs per humidifier tested; four humidifiers were tested, to compare the results and check for consistency.  The results of the analysis demonstrated this type of response surface model to be an adequate tool for evaluating and predicting humidifier performance. While the results produced were limited to quadratic models, and displayed a lack of fit on the small scale which was not attributable solely to noise, the overall models had a high level of significance and tracked the results. This response surface covered the entire range of the humidifier design space, including areas that are difficult to model due to heat transfer and condensation phenomena. The analysis also suggested the best choices of transforms for modeling in performance metrics, revisited in section 6.2.  In addition, inspection of the model results suggests a modified, less expensive, model that can be of practical use in humidifier evaluation. As the effect of pressure is small on the metrics of most concern, and most applications operate at stable pressure, this can be removed from the model as a factor. In addition, the model demonstrates that T1 has a very strong negative effect. In the event that a low temperature is used, or that the incoming stream 1 can be cooled, a low T1 can be specified. A response surface for  113 any humidifier can then be produced with a central composite design using only 17 tests, in Q1, Q3, and T3, including 3 center points. In the event that independent control of Q1 and Q3 is impossible, T1 can be reintroduced for a similar design using 17 tests, or a response surface model in the two factors Q1=3 and T3 can be produced with only 11 tests, including 3 center points.  These models can be used either to characterize prototypical humidifiers, or to provide system manufacturers with an improved modeling tool for overall system models in the form of a single set of equations for the humidifier module. 6.2. PERFORMANCE OF TESTED HUMIDIFIERS  Despite the differences in flow rates and sizes, both humidifier types yielded the same WRR (within the range of experimental error). The Px3-46s are a larger humidifier design than the Px1-32s, using in this work 2.5 times the flow. As such, in terms of absolute WTR, they transport in the range of two times as much water as the smaller humidifiers. The stream 2 RH metric, however, is an absolute indicator rather than one normalized based on membrane size. The smaller Px1-32 displayed improved water transport over the Px3-46. While the differences vary across the response surface range, the Px1-32M output an RH value on average 10%-15% higher, while that of the Px1-32N was 15%-20% higher than for the Px3-46s, which had statistically similar performance to one another. This higher performance could be due to the use of flow rates in the Px1-32 which are higher relative to the design flow condition than for the Px3-46.  114 6.3. CHARACTERIZING PERFORMANCE  This work also set out to suggest an improved system for characterizing humidifier performance based on an assessment and analysis of six common methods for reporting humidity and humidifier performance. Using a statistical analysis of these metrics and a prioritized list of desired properties from a performance measurement, a combined metric was proposed.  This metric consists of three parts. The first is to use the response surface of a humidifier to locate the bounds within which the humidifier performs to a satisfactory level; the most generalized metric for determining this is stream 2 relative humidity, and a proposed range is 80% < RH < 100%, though the low range may be varied depending on the application.. Within this range, the response surface for water recovery ratio is used to locate the highest peak. This is the optimal performance point from a standpoint of overall effectiveness. To determine absolute performance, the water transfer rate at this point may be used. 6.4. FACTORS AFFECTING PERFORMANCE  A further driving force of this work was the determination of the effects of each flow factor on humidifier performance. The use of a design of experiments with resolution RV also allowed the investigation of factor interactions.  Significant results were mostly as expected. An increase in Q1 increases overall water transfer, but the dilution introduced by an excess of dry air causes a drop in saturation-based performance metrics. An increase in Q3 also increases water transfer, but the commensurate decrease in relative performance demonstrates that water is beginning to be supplied to the membrane faster than it can be transported. Likewise an increase in  115 T3, which increases the water content of the wet stream, results in an increase of overall water transport but a decrease in relative performance.  An increase in T1 has a strong negative effect on humidifier performance as judged by all metrics. This is consistent with Romero and Mérida’s findings [53]. As a high T1 increases desorption from the membrane, the membrane adjacent to the dry stream becomes dehydrated and subsequently provides a barrier to water transport in the steady state case. This effect was compounded in the negative interaction between Q1 and T1.  Pressure has relatively small effects on its own, but is important in interaction with Q1 and T1. High pressure tends to somewhat depress water transport, but this effect is mitigated at high flows. In addition, the effect of high pressure mitigates the effect of high T1 discussed above. 6.5. HUMIDIFIER MODEL  The empirical nature of this makes it impossible to use it to produce a single, generalized model for humidifiers based on flow parameters. The general form of the response surfaces for all four humidifiers, however, is similar, suggesting that performance of other humidifiers based on the same technology will follow a similar shape. This graphical information mirrors the information on effects obtained through the statistical analysis. As discussed in section 6.1, a model is suggested here which can quickly produce an individual empirical model for any similar humidifier.  116 6.6. FUTURE WORK  The central composite design is an effective method for producing response surface models that can in turn be used to predict the performance of commercial products and to be integrated into overall system models. Simplified central composite designs, as discussed in section 6.1, can be used to generate response surface models for new humidifiers quickly and in an inexpensive manner. It would be beneficial to undertake a complete study of this type before using a simplified model to characterize humidifiers with significant differences from those presented here, such as shell-and-tube type humidifiers or liquid-to-gas humidifiers.  In addition, the model could be improved by the assessment of a higher-order response surface. In order to limit the expense of producing this model, the results of this study can be used to decrease the necessary number of factors to be tested, as suggested in the presentation of the proposed simplified central composite design. A higher order model may account for some of the fluctuations in the model, or allow a confident assessment of their significance. A further use of design of experiments related to this model would be the application of Taguchi’s methods of optimization to humidifier design. Alternatively, Taguchi methods based on the combined metric proposed here could be a less resource-intensive alternative for point optimization to the simplified CCD presented here.      117 7. REFERENCES    [1] E.J. Carlson, P. Kopf, J. Sinha, S. Sriramulu, Y. Yang, Cost Analysis of PEM Fuel Cell Systems for Transportation, National Renewable Energy Laboratory Report No. NREL/SR-560-39104(Golden, Colorado) (2005) 85-95. [2] J. Larminie, A. Dicks, Fuel Cell Systems Explained, second ed., John Wiley & Sons, West Sussex, England, 2003. [3] Spinolo, Chiodellu, Magistris, Tamburini. Data Weighting, J.Electrochem.Soc. 135 (1998) 1419. [4] M.B. Satterfield, J.B. Benziger. Non-Fickian water vapor sorption dynamics by Nafion membranes, J. Phys. Chem. B 112(12) (2008) 3693-3704. [5] M.B. Satterfield, P.W. Majsztrik, H. Ota, J.B. Benziger, A.B. Bocarsly. Mechanical properties of Nafion and titania/Nafion composite membranes for polymer electrolyte membrane fuel cells, J. Polym. Sci. B 44(16) (2006) 2327-2345. [6] W. Merida, Diagnosis of PEMFC stack failures via electrochemical impedance spectroscopy, Ph.D. Thesis (2002). [7] S.D. Knights, K.M. Colbow, J. St-Pierre, D.P. Wilkinson. Aging mechanisms and lifetime of PEFC and DMFC, J. Power Sources 127(1-2) (2004) 127-134. [8] M.V. Williams, H.R. Kunz, J.M. Fenton. Operation of Nafion®-based PEM fuel cells with no external humidification: influence of operating conditions and gas diffusion layers, J.Power Sources 135(1) (2004) 122-134. [9] M. Watanabe, H. Uchida, Y. Seki, M. Emori, P. Stonehart. Self-Humidifying Polymer Electrolyte Membranes for Fuel Cells, J.Electrochem.Soc. 143(12) (1996) 3847-3852. [10] H. Uchida, Y. Ueno, H. Hagihara, M. Watanabe. Self-Humidifying Electrolyte Membranes for Fuel Cells, J.Electrochem.Soc. 150(1) (2003) A57-A62. [11] F.N. Büchi, S. Srinivasan. Operating proton exchange membrane fuel cells without external humidification of the reactant gases, J. Electrochem. Soc. 144(8) (1997) 2767- 2772. [12] F. Liu, B. Yi, D. Xing, J. Yu, Z. Hou, Y. Fu. Development of novel self-humidifying composite membranes for fuel cells, J.Power Sources 124(1) (2003) 81-89. [13] M. Watanabe, H. Uchida, M. Emori. Polymer Electrolyte Membranes Incorporated with Nanometer-Size Particles of Pt and/or Metal-Oxides: Experimental Analysis of the Self-Humidification and Suppression of Gas-Crossover in Fuel Cells, J Phys Chem B 102(17) (1998) 3129-3137. [14] N.E. Vanderborgh, J.C. Hedstrom, Fuel cell water transport, (1990). [15] C.Y. Chow, B.M. Wozniczka, Electrochemical fuel cell stack with humidification section located upstream from the electrochemically active section, (1995). [16] D.S. Watkins, K.W. Dircks, D.G. Epp, R.D. Merritt, B.N. Gorbell, Integrated fuel cell power generation system, (1993). [17] D.L.I. Wood, J.S. Yi, T.V. Nguyen. Effect of direct liquid water injection and interdigitated flow field on the performance of proton exchange membrane fuel cells, Electrochim.Acta 43(24) (1998) 3795-3809.  118 [18] K.H. Choi, D.J. Park, Y.W. Rho, Y.T. Kho, T.H. Lee. A study of the internal humidification of an integrated PEMFC stack, J.Power Sources 74(1) (1998) 146-150. [19] S.-.K. Park, E.A. Cho, I.-.H. Oh. Characteristics of membrane humidifiers for polymer electrolyte membrane fuel cells, Korean J. Chem. Eng. 22(6) (2005) 877-881. [20] M. Watanabe, Y. Satoh, C. Shimura. Management of the Water Content in Polymer Electrolyte Membranes with Porous Fiber Wicks, J.Electrochem.Soc. 140(11) (1993) 3190-3193. [21] S. Ge, X. Li, I.-. Hsing. Internally humidified polymer electrolyte fuel cells using water absorbing sponge, Electrochim.Acta 50(9) (2005) 1909-1916. [22] S.H. Jung, S.L. Kim, M.S. Kim, Y. Park, T.W. Lim. Experimental study of gas humidification with injectors for automotive PEM fuel cell systems, J.Power Sources 170(2) (2007) 324-333. [23] R. Huizing, Design and membrane selection for gas to gas humidifiers for fuel cell applications, M.A.Sc. Thesis (2007). [24] P. Cave, Membrane moisture transfer in fuel cell humidifiers, M.A.Sc. Thesis (2007). [25] D. Kadylak, Effectiveness method for heat and mass transfer in membrane humidifiers, M.A.Sc. Thesis (2009). [26] J.L. Niu, L. Zhang. Membrane-based enthalpy exchanger: material considerations and clarification of moisture resistance, J. Membr. Sci. 189(2) (2001) 179-191. [27] L.Z. Zhang, D.S. Zhu, X.H. Deng, B. Hua. Thermodynamic modeling of a novel air dehumidification system, Energy Build. 37(3) (2005) 279-286. [28] L.Z. Zhang, Y. Jiang. Heat and mass transfer in a membrane-based energy recovery ventilator, J. Membr. Sci. 163(1) (1999) 29-38. [29] L. Zhang, Y. Jiang, Y.P. Zhang. Membrane-based humidity pump: performance and limitations, J.Membrane Science 171(2) (2000) 207-216. [30] L. Zhang, J.L. Niu. Effectiveness correlations for heat and moisture transfer processes in an enthalpy exchanger with membrane cores, J. Heat Transfer 124(5) (2002) 922-929. [31] R. Huizing, M. Fowler, W. Mérida, J. Dean. Design methodology for membrane- based plate-and-frame fuel cell humidifiers, J. Power Sources 180(1) (2008) 265-275. [32] D. Kadylak, P. Cave, W. Merida. Effectiveness correlations for heat and mass transfer in membrane humidifiers, Int. J. Heat Mass Transfer 52(5-6) (2009) 1504-1509. [33] S. Park, I.-.H. Oh. An analytical model of NafionTM membrane humidifier for proton exchange membrane fuel cells, J. Power Sources 188(2) (2009) 498-501. [34] S.-.K. Park, S.-.Y. Choe, S.-.H. Choi. Dynamic modeling and analysis of a shell- and-tube type gas-to-gas membrane humidifier for PEM fuel cell applications, Int. J. Hydrogen Energy 33(9) (2008) 2273-2282. [35] D. Chen, H. Peng. A thermodynamic model of membrane humidifiers for PEM fuel cell humidification control, J. Dyn. Sys., Meas., Control 127(3) (2005) 424-432. [36] D. Chen, W. Li, H. Peng. An experimental study and model validation of a membrane humidifier for PEM fuel cell humidification control, J. Power Sources 180(1) (2008) 461-467. [37] C. D, A Thermodynamic Model of Membrane Humidifiers for PEM Fuel Cell Humidification Control, Journal of dynamic systems, measurement, and control (2005).  119 [38] D.C. Montgomery, Design and Analysis of Experiments, 6th Ed. ed., John Wiley & Sons, Inc, Hoboken, NJ, 2005. [39] G. Taguchi, Introduction to Quality Engineering: Designing Quality Into Products and Processes, The Organization, Tokyo, 1986. [40] G. Taguchi, System of Experimental Design: Engineering Methods to Optimize Quality and Minimize Costs, UNIPUB/Kraus International Publications, White Plains, NY, 1987. [41] P.J. Ross, Taguchi Techniques for Quality Engineering, 1st Edition ed., McGraw- Hill, New York, NY, 1988. [42] B. Wahdame, D. Candusso, X. François, F. Harel, J. Kauffmann, G. Coquery. Design of experiment techniques for fuel cell characterisation and development, Int J Hydrogen Energy 34(2) (2009) 967-980. [43] R.C. Dante, J.L. Escamilla, V. Madrigal, T. Theuss, J. de Dios Calderón, O. Solorza, et al. Fractional factorial design of experiments for PEM fuel cell performances improvement, Int J Hydrogen Energy 28(3) (2003) 343-348. [44] W. Yu, S. Wu, S. Shiah. Parametric analysis of the proton exchange membrane fuel cell performance using design of experiments, Int J Hydrogen Energy 33(9) (2008) 2311- 2322. [45] S. Wu, S. Shiah, W. Yu. Parametric analysis of proton exchange membrane fuel cell performance by using the Taguchi method and a neural network, Renewable Energy 34(1) (2009) 135-144. [46] B. Wahdame, D. Candusso, J. Kauffmann. Study of gas pressure and flow rate influences on a 500 W PEM fuel cell, thanks to the experimental design methodology, J.Power Sources 156(1) (2006) 92-99. [47] B. Wahdame, D. Candusso, X. Francois, F. Harel, A. De Bernardinis, J.-. Kauffmann, et al. Study of a 5 kW PEMFC Using Experimental Design and Statistical Analysis Techniques, Fuel Cells 07(1) (2007) 47-62. [48] B. Wahdame, D. Candusso, X. François, F. Harel, M. Pera, D. Hissel, et al. Analysis of a Fuel Cell Durability Test Based on Design of Experiment Approach, IEEE Trans. on Energy Conversion 23(4) (2008) 1093-1104. [49] M. Meiler, D. Andre, Á. Pérez, O. Schmid, E.P. Hofer. Nonlinear D-optimal design of experiments for polymer–electrolyte–membrane fuel cells, J.Power Sources 190(1) (2009) 48-55. [50] P. Cave, W. Merida. Water flux in membrane fuel cell humidifiers: flow rate and channel location effects, J. Power Sources 175(1) (2008) 408-418. [51] R.L. Mason, R.F. Gunst, J.L. Hess, Statistical Design and Analysis of Experiments - With Applications to Engineering and Science, 2nd Edition ed., John Wiley & Sons, Hoboken, New Jersey, 2003. [52] W.S. Cleveland, Visualizing Data, Hobart Press, Summit, N.J., 1993. [53] T. Romero, W. Mérida. Water transport in liquid and vapour equilibrated Nafion™ membranes, J.Membr.Sci. 338(1-2) (2009) 135-144. [54] F.C. McQuiston, J.D. Parker, J.D. Spitler, Heating, Ventilating, and Air Conditioning: Analysis and Design, 6th Ed. ed., John Wiley & Sons, Hoboken, New Jersey, 2005.    120 APPENDIX A: RESULTS PLOTS  This appendix contains plots of the response surface models resulting from the analysis of the experimental results in this work. These results are primarily divided by low, then high pressure; within these, divided by humidifier; and the results of each humidifier are presented by performance metric.  In an effort to maintain consistency, each performance metric uses the same scale for contour shading throughout this appendix.  Stream 2 dew point ranges from 30°C to 70°C.  Dew point approach temperature ranges from 0°C to 40°C.  Stream 2 humidity ratio ranges from 0 kg/kg to 0.25 kg/kg.  Stream 2 relative humidity ranges from 0% to 150%.  Water recovery ratio ranges from 0% to 100%.  Water transport rate ranges from 0 g/min to 35 g/min.  121   30 40 50 60 70 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80 Figure A.1: Plot for Px1-32M stream 2 DP low pressure   0 10 20 30 40 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.2: Plot for Px1-32M DPAT low pressure  122   0 0.05 0.1 0.15 0.2 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.3: Plot for Px1-32M stream 2 HR low pressure   0 50 100 150 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.4: Plot for Px1-32M stream 2 RH low pressure  123   0 50 100 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.5: Plot for Px1-32M WRR low pressure   0 10 20 30 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.6: Plot for Px1-32M stream 2 WTR low pressure  124   30 40 50 60 70 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.7: Plot for Px1-32N stream 2 DP low pressure   0 10 20 30 40 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.8: Plot for Px1-32N DPAT low pressure  125   0 0.05 0.1 0.15 0.2 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.9: Plot for Px1-32N stream 2 HR low pressure   0 50 100 150 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.10: Plot for Px1-32N stream 2 RH low pressure  126   0 50 100 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.11: Plot for Px1-32N WRR low pressure   0 10 20 30 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.12: Plot for Px1-32N WTR low pressure  127   30 40 50 60 70 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.13: Plot for Px3-46M stream 2 DP low pressure   0 10 20 30 40 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.14: Plot for Px3-46M DPAT low pressure  128   0 0.05 0.1 0.15 0.2 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.15: Plot for Px3-46M stream 2 HR low pressure   0 50 100 150 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.16: Plot for Px3-46M stream 2 RH low pressure  129   0 50 100 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.17: Plot for Px3-46M WRR low pressure   0 10 20 30 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.18: Plot for Px3-46M WTR low pressure  130   30 40 50 60 70 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.19: Plot for Px3-46N 2 DP low pressure   0 10 20 30 40 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.20: Plot for Px3-46N DPAT low pressure  131   0 0.05 0.1 0.15 0.2 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.21: Plot for Px3-46N stream 2 HR low pressure   0 50 100 150 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.22: Plot for Px3-46N stream 2 RH low pressure  132   0 50 100 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.23: Plot for Px3-46N WRR low pressure   0 10 20 30 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.24: Plot for Px3-46N WTR low pressure  133   30 40 50 60 70 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.25: Plot for Px1-32M stream 2 DP high pressure   0 10 20 30 40 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.26: Plot for Px1-32M DPAT high pressure  134   0 0.05 0.1 0.15 0.2 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.27: Plot for Px1-32M stream 2 HR high pressure   0 50 100 150 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.28: Plot for Px1-32M stream 2 RH high pressure  135   0 50 100 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.29: Plot for Px1-32M WRR high pressure   0 10 20 30 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.30: Plot for Px1-32M WTR high pressure  136   30 40 50 60 70 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.31: Plot for Px1-32N stream 2 DP high pressure   0 10 20 30 40 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.32: Plot for Px1-32N DPAT high pressure  137   0 0.05 0.1 0.15 0.2 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.33: Plot for Px1-32N stream 2 HR high pressure   0 50 100 150 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.34: Plot for Px1-32N stream 2 RH high pressure  138   0 50 100 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.35: Plot for Px1-32N WRR high pressure   0 10 20 30 Q1 (SLPM) 40 60 80 100 20 40 60 80 Q3 (SLPM) 100/20 40 60 80 100 40 60 80 20 40 60 80 100/20 40 60 80 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.36: Plot for Px1-32N WTR high pressure  139   30 40 50 60 70 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.37: Plot for Px3-46M stream 2 DP high pressure   0 10 20 30 40 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.38: Plot for Px3-46M DPAT high pressure  140   0 0.05 0.1 0.15 0.2 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.39: Plot for Px3-46M stream 2 HR high pressure   0 50 100 150 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.40: Plot for Px3-46M stream 2 RH high pressure  141   0 50 100 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.41: Plot for Px3-46M WRR high pressure   0 10 20 30 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.42: Plot for Px3-46M WTR high pressure  142   30 40 50 60 70 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.43: Plot for Px3-46N stream 2 DP high pressure   0 10 20 30 40 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.44: Plot for Px3-46N DPAT high pressure  143   0 0.05 0.1 0.15 0.2 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.45: Plot for Px3-46N stream 2 HR high pressure   0 50 100 150 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.46: Plot for Px3-46N stream 2 RH high pressure  144   0 50 100 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.47: Plot for Px3-46N WRR high pressure   0 10 20 30 Q1 (SLPM) 100 150 200 250 50 100 150 200 Q3 (SLPM) 250/50 100 150 200 250 100 150 200 50 100 150 200250/50 100 150 200 T1 (degC) 110/25 46 68 89 110 46 68 89 25 46 68 89 110/25 46 68 89 T3 (degC) 60 65 70 75 65 70 75 80  Figure A.48: Plot for Px3-46N WTR high pressure  145 APPENDIX B: ANOVA TABLES Table B.1: ANOVA tables for water transport rate Px1-32M Sum of  Mean F p-value  Px1-32N Sum of  Mean F p-value Source Squares df Square Value Prob > F  Source Squares df Square Value Prob > F Model 26 19 1.37 33.07 < 0.0001  Model 29.7 19 1.56 48.86 < 0.0001   A 5.1 1 5.1 123.2 < 0.0001    A 4.43 1 4.43 138.5 < 0.0001   B 0.97 1 0.97 23.53 < 0.0001    B 1.02 1 1.02 31.75 < 0.0001   C 3.29 1 3.29 79.5 < 0.0001    C 2.85 1 2.85 88.94 < 0.0001   D 3.37 1 3.37 81.44 < 0.0001    D 4.61 1 4.61 144.17 < 0.0001   E 8.46 1 8.46 204.34 < 0.0001    E 12.76 1 12.76 399 < 0.0001   AB 0.099 1 0.099 2.39 0.1298    AB 0.3 1 0.3 9.53 0.0037   AC 0.13 1 0.13 3.2 0.0811    AC 0.09 1 0.09 2.83 0.1005   AD 0.12 1 0.12 2.81 0.1013    AD 9.34E-04 1 9.34E-04 0.029 0.8652   AE 0.51 1 0.51 12.39 0.0011    AE 0.25 1 0.25 7.93 0.0075   BC 0.18 1 0.18 4.32 0.0441    BC 0.098 1 0.098 3.05 0.0882   BD 5.33E-03 1 5.33E-03 0.13 0.7216    BD 0.055 1 0.055 1.71 0.1987   BE 1.83E-04 1 1.83E-04 4.42E-03 0.9474    BE 2.80E-03 1 2.80E-03 0.087 0.7691   CD 0.43 1 0.43 10.5 0.0024    CD 0.46 1 0.46 14.31 0.0005   CE 1.49 1 1.49 35.9 < 0.0001    CE 1.32 1 1.32 41.31 < 0.0001   DE 1.46 1 1.46 35.34 < 0.0001    DE 0.96 1 0.96 30 < 0.0001   A^2 0.3 1 0.3 7.3 0.0101    A^2 0.33 1 0.33 10.45 0.0025   B^2 1.21E-03 1 1.21E-03 0.029 0.8653    B^2 0.012 1 0.012 0.38 0.5414   C^2 9.63E-03 1 9.63E-03 0.23 0.6321    C^2 2.07E-04 1 2.07E-04 6.47E-03 0.9363   D^2 0.14 1 0.14 3.31 0.0763    D^2 0.2 1 0.2 6.3 0.0162 Residual 1.66 40 0.041    Residual 1.28 40 0.032 Lack of Fit 1.6 30 0.053 10.36 0.0002  Lack of Fit 1.1 30 0.037 2.05 0.1161 Pure Error 0.052 10 5.16E-03    Pure Error 0.18 10 0.018 Cor Total 27.66 59     Cor Total 30.98 59  Px3-46M Sum of  Mean F p-value  Px3-46N Sum of  Mean F p-value Source Squares df Square Value Prob > F  Source Squares df Square Value Prob > F Model 54.26 19 2.86 75.03 < 0.0001  Model 53.42 19 2.81 135.32 < 0.0001   A 7.22 1 7.22 189.57 < 0.0001    A 7.64 1 7.64 367.78 < 0.0001   B 1.37 1 1.37 35.88 < 0.0001    B 1 1 1 48.06 < 0.0001   C 13.42 1 13.42 352.54 < 0.0001    C 6.7 1 6.7 322.37 < 0.0001   D 9.88 1 9.88 259.58 < 0.0001    D 9.89 1 9.89 475.83 < 0.0001   E 14.71 1 14.71 386.53 < 0.0001    E 23.13 1 23.13 1113.14 < 0.0001   AB 0.14 1 0.14 3.67 0.0627    AB 0.34 1 0.34 16.25 0.0002   AC 0.91 1 0.91 23.82 < 0.0001    AC 0.96 1 0.96 46.13 < 0.0001   AD 0.034 1 0.034 0.89 0.3508    AD 0.077 1 0.077 3.72 0.0608   AE 0.36 1 0.36 9.55 0.0036    AE 0.048 1 0.048 2.3 0.1371   BC 0.1 1 0.1 2.7 0.108    BC 0.038 1 0.038 1.82 0.1849   BD 0.013 1 0.013 0.34 0.5653    BD 6.23E-03 1 6.23E-03 0.3 0.5872   BE 6.70E-03 1 6.70E-03 0.18 0.6771    BE 3.96E-04 1 3.96E-04 0.019 0.8909   CD 0.54 1 0.54 14.26 0.0005    CD 0.41 1 0.41 19.52 < 0.0001   CE 3.32 1 3.32 87.15 < 0.0001    CE 1.5 1 1.5 72.12 < 0.0001  146 Px3-46M Sum of  Mean F p-value  Px3-46N Sum of  Mean F p-value Source Squares df Square Value Prob > F  Source Squares df Square Value Prob > F   DE 0.66 1 0.66 17.36 0.0002    DE 0.67 1 0.67 32.11 < 0.0001   A^2 0.48 1 0.48 12.63 0.001    A^2 0.38 1 0.38 18.21 0.0001   B^2 0.027 1 0.027 0.72 0.4006    B^2 0.055 1 0.055 2.64 0.1122   C^2 0.95 1 0.95 24.85 < 0.0001    C^2 0.58 1 0.58 27.95 < 0.0001   D^2 0.26 1 0.26 6.94 0.0119    D^2 0.16 1 0.16 7.55 0.0089 Residual 1.52 40 0.038    Residual 0.83 40 0.021 Lack of Fit 1.47 30 0.049 8.73 0.0005  Lack of Fit 0.78 30 0.026 4.84 0.006 Pure Error 0.056 10 5.60E-03    Pure Error 0.054 10 5.35E-03 Cor Total 55.78 59     Cor Total 54.26 59  Table B.2: ANOVA tables for water recovery ratio Px1-32M Sum of  Mean F p-value  Px1-32N Sum of  Mean F p-value Source Squares df Square Value Prob > F  Source Squares df Square Value Prob > F Model 1.61 19 0.085 22.51 < 0.0001  Model 1.23 19 0.065 18.01 < 0.0001   A 0.57 1 0.57 152.03 < 0.0001    A-Stream 1 FR 0.41 1 0.41 113.02 < 0.0001   B 0.41 1 0.41 109.2 < 0.0001    B-Stream 3 FR 0.36 1 0.36 101.33 < 0.0001   C 0.19 1 0.19 51.38 < 0.0001    C-Stream 1 Temp 0.22 1 0.22 61.25 < 0.0001   D 0.042 1 0.042 11.3 0.0017    D-Stream 3 Temp 3.84E-03 1 3.84E-03 1.07 0.3077   E 0.039 1 0.039 10.33 0.0026    E-Pressure 3.81E-04 1 3.81E-04 0.11 0.7465   AB 3.97E-03 1 3.97E-03 1.06 0.3104    AB 2.78E-03 1 2.78E-03 0.77 0.3844   AC 0.015 1 0.015 4.01 0.0522    AC 0.018 1 0.018 4.88 0.033   AD 5.69E-05 1 5.69E-05 0.015 0.9027    AD 1.18E-03 1 1.18E-03 0.33 0.5695   AE 0.15 1 0.15 38.67 < 0.0001    AE 0.071 1 0.071 19.87 < 0.0001   BC 3.40E-06 1 3.40E-06 9.05E-04 0.9761    BC 5.59E-03 1 5.59E-03 1.55 0.2199   BD 1.55E-03 1 1.55E-03 0.41 0.5247    BD 1.91E-03 1 1.91E-03 0.53 0.4706   BE 1.33E-03 1 1.33E-03 0.35 0.5557    BE 0.03 1 0.03 8.36 0.0062   CD 6.32E-03 1 6.32E-03 1.68 0.2021    CD 1.98E-03 1 1.98E-03 0.55 0.4624   CE 0.059 1 0.059 15.75 0.0003    CE 0.035 1 0.035 9.69 0.0034   DE 0.04 1 0.04 10.69 0.0022    DE 6.17E-05 1 6.17E-05 0.017 0.8965   A^2 0.036 1 0.036 9.53 0.0037    A^2 0.04 1 0.04 11.04 0.0019   B^2 0.053 1 0.053 14.09 0.0006    B^2 0.035 1 0.035 9.74 0.0033   C^2 5.40E-07 1 5.40E-07 1.44E-04 0.9905    C^2 1.82E-03 1 1.82E-03 0.51 0.4805   D^2 7.57E-04 1 7.57E-04 0.2 0.656    D^2 2.45E-03 1 2.45E-03 0.68 0.4145 Residual 0.15 40 3.76E-03    Residual 0.14 40 3.60E-03 Lack of Fit 0.15 30 4.84E-03 9.4 0.0004  Lack of Fit 0.13 30 4.37E-03 3.42 0.0222 Pure Error 5.15E-03 10 5.15E-04    Pure Error 0.013 10 1.28E-03 Cor Total 1.76 59     Cor Total 1.37 59  Px3-46M Sum of  Mean F p-value  Px3-46N Sum of  Mean F p-value Source Squares df Square Value Prob > F  Source Squares df Square Value Prob > F Model 1.52 19 0.08 75.96 < 0.0001  Model 1.28 19 0.067 101.19 < 0.0001   A 0.32 1 0.32 299.58 < 0.0001    A 0.3 1 0.3 449.5 < 0.0001   B 0.49 1 0.49 467.43 < 0.0001    B 0.59 1 0.59 891.26 < 0.0001   C 0.37 1 0.37 352.82 < 0.0001    C 0.19 1 0.19 285.75 < 0.0001  147 Px3-46M Sum of  Mean F p-value  Px3-46N Sum of  Mean F p-value Source Squares df Square Value Prob > F  Source Squares df Square Value Prob > F   D 9.46E-03 1 9.46E-03 8.99 0.0046    D 0.013 1 0.013 19.92 < 0.0001   E 0.12 1 0.12 117.39 < 0.0001    E 0.036 1 0.036 53.7 < 0.0001   AB 2.85E-03 1 2.85E-03 2.71 0.1078    AB 4.39E-04 1 4.39E-04 0.66 0.4212   AC 0.024 1 0.024 22.66 < 0.0001    AC 0.031 1 0.031 46.78 < 0.0001   AD 3.45E-03 1 3.45E-03 3.28 0.0778    AD 2.16E-03 1 2.16E-03 3.25 0.0791   AE 0.062 1 0.062 58.88 < 0.0001    AE 0.033 1 0.033 50.17 < 0.0001   BC 8.75E-03 1 8.75E-03 8.31 0.0063    BC 6.30E-03 1 6.30E-03 9.49 0.0037   BD 1.05E-05 1 1.05E-05 9.97E-03 0.921    BD 1.30E-04 1 1.30E-04 0.2 0.6604   BE 5.27E-04 1 5.27E-04 0.5 0.483    BE 1.28E-03 1 1.28E-03 1.92 0.1733   CD 1.82E-05 1 1.82E-05 0.017 0.8962    CD 9.22E-04 1 9.22E-04 1.39 0.2455   CE 0.027 1 0.027 25.44 < 0.0001    CE 0.013 1 0.013 19.16 < 0.0001   DE 2.43E-04 1 2.43E-04 0.23 0.6333    DE 1.40E-03 1 1.40E-03 2.11 0.1542   A^2 0.026 1 0.026 24.46 < 0.0001    A^2 0.018 1 0.018 26.65 < 0.0001   B^2 0.033 1 0.033 31.61 < 0.0001    B^2 0.029 1 0.029 44.14 < 0.0001   C^2 0.019 1 0.019 18.25 0.0001    C^2 0.011 1 0.011 16.21 0.0002   D^2 1.19E-03 1 1.19E-03 1.13 0.295    D^2 6.01E-04 1 6.01E-04 0.9 0.3472 Residual 0.042 40 1.05E-03    Residual 0.027 40 6.64E-04 Lack of Fit 0.039 30 1.31E-03 4.57 0.0076  Lack of Fit 0.025 30 8.19E-04 4.09 0.0115 Pure Error 2.86E-03 10 2.86E-04    Pure Error 2.00E-03 10 2.00E-04 Cor Total 1.56 59     Cor Total 1.3 59  Table B.3: ANOVA tables for stream 2 humidity ratio Px1-32M Sum of  Mean F p-value  Px1-32N Sum of  Mean F p-value Source Squares df Square Value Prob > F  Source Squares df Square Value Prob > F Model 22.38 15 1.49 21.13 < 0.0001  Model 25.79 15 1.72 41.61 < 0.0001   A 0.1 1 0.1 1.43 0.2387    A 0.45 1 0.45 10.91 0.0019   B 1.02 1 1.02 14.48 0.0004    B 1.1 1 1.1 26.63 < 0.0001   C 2.56 1 2.56 36.29 < 0.0001    C 2.15 1 2.15 51.96 < 0.0001   D 2.73 1 2.73 38.62 < 0.0001    D 4.31 1 4.31 104.33 < 0.0001   E 11.09 1 11.09 157.07 < 0.0001    E 14.82 1 14.82 358.66 < 0.0001   AB 0.046 1 0.046 0.64 0.4263    AB 0.12 1 0.12 2.88 0.0968   AC 0.076 1 0.076 1.07 0.3065    AC 0.011 1 0.011 0.27 0.6042   AD 0.071 1 0.071 1.01 0.3209    AD 0.065 1 0.065 1.58 0.2158   AE 2.34 1 2.34 33.19 < 0.0001    AE 1.43 1 1.43 34.51 < 0.0001   BC 0.079 1 0.079 1.12 0.2962    BC 0.049 1 0.049 1.19 0.2808   BD 0.012 1 0.012 0.17 0.6808    BD 8.57E-04 1 8.57E-04 0.021 0.8862   BE 0.014 1 0.014 0.2 0.6568    BE 0.12 1 0.12 2.8 0.1013   CD 0.22 1 0.22 3.17 0.082    CD 0.17 1 0.17 4.02 0.0512   CE 1.04 1 1.04 14.79 0.0004    CE 0.72 1 0.72 17.35 0.0001   DE 0.97 1 0.97 13.73 0.0006    DE 0.29 1 0.29 7.09 0.0108 Residual 3.11 44 0.071    Residual 1.82 44 0.041 Lack of Fit 3.03 34 0.089 11.9 0.0001  Lack of Fit 1.64 34 0.048 2.76 0.0457 Pure Error 0.075 10 7.49E-03    Pure Error 0.18 10 0.018 Cor Total 25.48 59     Cor Total 27.6 59  148  Px3-46M Sum of  Mean F p-value  Px3-46N Sum of  Mean F p-value Source Squares df Square Value Prob > F  Source Squares df Square Value Prob > F Model 21.55 19 1.13 58.75 < 0.0001  Model 21.19 19 1.12 101.41 < 0.0001   A 1.52 1 1.52 78.66 < 0.0001    A 1.69 1 1.69 153.56 < 0.0001   B 0.69 1 0.69 35.59 < 0.0001    B 0.43 1 0.43 38.77 < 0.0001   C 5.31 1 5.31 275.24 < 0.0001    C 2.29 1 2.29 208.4 < 0.0001   D 4.64 1 4.64 240.29 < 0.0001    D 4.45 1 4.45 404.67 < 0.0001   E 7.24 1 7.24 374.89 < 0.0001    E 11.07 1 11.07 1006.2 < 0.0001   AB 0.013 1 0.013 0.7 0.4086    AB 0.096 1 0.096 8.71 0.0053   AC 0.13 1 0.13 6.92 0.012    AC 0.24 1 0.24 21.54 < 0.0001   AD 0.028 1 0.028 1.43 0.2383    AD 0.017 1 0.017 1.57 0.2169   AE 0.88 1 0.88 45.61 < 0.0001    AE 0.41 1 0.41 37.73 < 0.0001   BC 1.08E-03 1 1.08E-03 0.056 0.8144    BC 3.71E-04 1 3.71E-04 0.034 0.8551   BD 2.98E-03 1 2.98E-03 0.15 0.6964    BD 2.91E-04 1 2.91E-04 0.026 0.8716   BE 0.038 1 0.038 1.99 0.1666    BE 8.02E-03 1 8.02E-03 0.73 0.3983   CD 8.03E-03 1 8.03E-03 0.42 0.5226    CD 0.045 1 0.045 4.12 0.049   CE 0.63 1 0.63 32.81 < 0.0001    CE 0.25 1 0.25 22.31 < 0.0001   DE 0.016 1 0.016 0.81 0.3729    DE 6.76E-03 1 6.76E-03 0.61 0.4377   A^2 0.044 1 0.044 2.3 0.1375    A^2 1.97E-07 1 1.97E-07 1.79E-05 0.9966   B^2 0.011 1 0.011 0.58 0.4511    B^2 0.039 1 0.039 3.58 0.0658   C^2 0.27 1 0.27 13.8 0.0006    C^2 0.13 1 0.13 12.1 0.0012   D^2 0.072 1 0.072 3.75 0.06    D^2 0.023 1 0.023 2.07 0.1576 Residual 0.77 40 0.019    Residual 0.44 40 0.011 Lack of Fit 0.74 30 0.025 7.71 0.0009  Lack of Fit 0.41 30 0.014 4.48 0.0082 Pure Error 0.032 10 3.20E-03    Pure Error 0.03 10 3.05E-03 Cor Total 22.32 59     Cor Total 21.63 59  Table B.4: ANOVA tables for stream 2 relative humidity Px1-32M Sum of  Mean F p-value  Px1-32N Sum of  Mean F p-value Source Squares df Square Value Prob > F  Source Squares df Square Value Prob > F Model 14.01 15 0.93 11.24 < 0.0001  Model 11.03 19 0.58 11.96 < 0.0001   A 0.16 1 0.16 1.94 0.1702    A-Stream 1 FR 0.3 1 0.3 6.14 0.0175   B 0.15 1 0.15 1.84 0.1823    B-Stream 3 FR 0.21 1 0.21 4.31 0.0443   C 6.21 1 6.21 74.79 < 0.0001    C-Stream 1 Temp 5.09 1 5.09 104.84 < 0.0001   D 8.76E-03 1 8.76E-03 0.11 0.7469    D-Stream 3 Temp 4.50E-02 1 4.50E-02 0.93 0.3413   E 0.44 1 0.44 5.34 0.0256    E-Pressure 2.96E-04 1 2.96E-04 6.09E-03 0.9382   AB 0.085 1 0.085 1.02 0.3169    AB 0.17 1 0.17 3.51 0.0684   AC 2.16 1 2.16 25.97 < 0.0001    AC 1.59 1 1.59 32.76 < 0.0001   AD 0.3 1 0.3 3.59 0.0648    AD 3.35E-03 1 3.35E-03 0.069 0.7942   AE 2.32 1 2.32 27.87 < 0.0001    AE 1.47 1 1.47 30.34 < 0.0001   BC 0.13 1 0.13 1.57 0.2163    BC 0.12 1 0.12 2.47 0.1239   BD 2.65E-03 1 2.65E-03 0.032 0.859    BD 5.40E-03 1 5.40E-03 1.10E-01 0.7405   BE 0.013 1 0.013 0.15 0.6991    BE 0.024 1 0.024 0.5 0.4841   CD 8.02E-03 1 8.02E-03 0.097 0.7575    CD 1.40E-03 1 1.40E-03 0.029 0.8662   CE 1.18 1 1.18 14.15 0.0005    CE 1.04 1 1.04 21.48 < 0.0001  149 Px1-32M Sum of  Mean F p-value  Px1-32N Sum of  Mean F p-value Source Squares df Square Value Prob > F  Source Squares df Square Value Prob > F   DE 0.84 1 0.84 10.14 0.0027    DE 0.35 1 0.35 7.23 0.0104 Residual 3.65 44 0.083    Residual 1.94 40 0.049 Lack of Fit 3.59 34 0.11 15.84 < 0.0001  Lack of Fit 1.76 30 0.059 3.24 0.027 Pure Error 0.067 10 6.66E-03    Pure Error 0.18 10 0.018 Cor Total 17.66 59     Cor Total 12.97 59  Px3-46M Sum of  Mean F p-value  Px3-46N Sum of  Mean F p-value Source Squares df Square Value Prob > F  Source Squares df Square Value Prob > F Model 19.58 15 1.31 50.69 < 0.0001  Model 16.52 15 1.1 56.88 < 0.0001   A 1.8 1 1.8 69.96 < 0.0001    A 2.07 1 2.07 107.1 < 0.0001   B 0.44 1 0.44 17.16 0.0002    B 0.2 1 0.2 10.52 0.0023   C 12.07 1 12.07 468.62 < 0.0001    C 9.71 1 9.71 501.24 < 0.0001   D 0.21 1 0.21 8.35 0.006    D 0.19 1 0.19 9.87 0.003   E 0.62 1 0.62 23.97 < 0.0001    E 0.11 1 0.11 5.59 0.0225   AB 0.011 1 0.011 0.42 0.5218    AB 0.074 1 0.074 3.85 0.0562   AC 2.54 1 2.54 98.59 < 0.0001    AC 3.04 1 3.04 156.73 < 0.0001   AD 6.02E-04 1 6.02E-04 0.023 0.8792    AD 8.80E-03 1 8.80E-03 0.45 0.5038   AE 0.81 1 0.81 31.51 < 0.0001    AE 0.27 1 0.27 13.95 0.0005   BC 0.45 1 0.45 17.52 0.0001    BC 0.59 1 0.59 30.37 < 0.0001   BD 0.03 1 0.03 1.15 0.2898    BD 3.86E-03 1 3.86E-03 0.2 0.6574   BE 2.52E-03 1 2.52E-03 0.098 0.756    BE 4.19E-03 1 4.19E-03 0.22 0.6441   CD 0.096 1 0.096 3.74 0.0597    CD 0.043 1 0.043 2.22 0.143   CE 0.49 1 0.49 19 < 0.0001    CE 0.21 1 0.21 10.8 0.002   DE 8.00E-03 1 8.00E-03 0.31 0.58    DE 4.88E-04 1 4.88E-04 0.025 0.8746 Residual 1.13 44 0.026    Residual 0.85 44 0.019 Lack of Fit 1.04 34 0.031 3.25 0.0261  Lack of Fit 0.69 34 0.02 1.28 0.355 Pure Error 0.094 10 9.41E-03    Pure Error 0.16 10 0.016 Cor Total 20.71 59     Cor Total 17.37 59  Table B.5: ANOVA tables for stream 2 dew point temperature Px1-32M Sum of  Mean F p-value  Px1-32N Sum of  Mean F p-value Source Squares df Square Value Prob > F  Source Squares df Square Value Prob > F Model 3764.37 15 250.96 10.02 < 0.0001  Model 3731.28 15 248.75 16.89 < 0.0001   A 32.67 1 32.67 1.3 0.2596    A 146.75 1 146.75 9.97 0.0029   B 358.32 1 358.32 14.31 0.0005    B 384.82 1 384.82 26.13 < 0.0001   C 846 1 846 33.78 < 0.0001    C 717.28 1 717.28 48.71 < 0.0001   D 906.11 1 906.11 36.18 < 0.0001    D 1461.11 1 1461.11 99.23 < 0.0001   E 13.43 1 13.43 0.54 0.4678    E 41.17 1 41.17 2.8 0.1016   AB 16.21 1 16.21 0.65 0.4254    AB 41.57 1 41.57 2.82 0.1   AC 26.39 1 26.39 1.05 0.3103    AC 4.46 1 4.46 0.3 0.5847   AD 26.93 1 26.93 1.08 0.3054    AD 19.97 1 19.97 1.36 0.2505   AE 812.81 1 812.81 32.45 < 0.0001    AE 492.8 1 492.8 33.47 < 0.0001   BC 29.36 1 29.36 1.17 0.2848    BC 18.18 1 18.18 1.23 0.2726   BD 5.52 1 5.52 0.22 0.6409    BD 0.36 1 0.36 0.024 0.8768  150 Px1-32M Sum of  Mean F p-value  Px1-32N Sum of  Mean F p-value Source Squares df Square Value Prob > F  Source Squares df Square Value Prob > F   BE 10.35 1 10.35 0.41 0.5236    BE 50.8 1 50.8 3.45 0.07   CD 80.97 1 80.97 3.23 0.079    CD 59.24 1 59.24 4.02 0.0511   CE 307.85 1 307.85 12.29 0.0011    CE 218.01 1 218.01 14.81 0.0004   DE 291.42 1 291.42 11.64 0.0014    DE 74.77 1 74.77 5.08 0.0293 Residual 1101.96 44 25.04    Residual 647.9 44 14.72 Lack of Fit 1073.73 34 31.58 11.19 0.0002  Lack of Fit 585.54 34 17.22 2.76 0.0454 Pure Error 28.22 10 2.82    Pure Error 62.36 10 6.24 Cor Total 4866.32 59     Cor Total 4379.18 59  Px3-46M Sum of  Mean F p-value  Px3-46N Sum of  Mean F p-value Source Squares df Square Value Prob > F  Source Squares df Square Value Prob > F Model 4899.98 19 257.89 39.97 < 0.0001  Model 3430.05 19 180.53 47.91 < 0.0001   A 471.76 1 471.76 73.12 < 0.0001    A 557.83 1 557.83 148.05 < 0.0001   B 242.95 1 242.95 37.66 < 0.0001    B 152.22 1 152.22 40.4 < 0.0001   C 1777.38 1 1777.38 275.5 < 0.0001    C 777.08 1 777.08 206.24 < 0.0001   D 1574.46 1 1574.46 244.04 < 0.0001    D 1535.92 1 1535.92 407.63 < 0.0001   E 175.25 1 175.25 27.16 < 0.0001    E 4.68 1 4.68 1.24 0.2719   AB 4.6 1 4.6 0.71 0.4036    AB 32.29 1 32.29 8.57 0.0056   AC 40.45 1 40.45 6.27 0.0165    AC 81.08 1 81.08 21.52 < 0.0001   AD 14.96 1 14.96 2.32 0.1357    AD 7.83 1 7.83 2.08 0.1571   AE 262.6 1 262.6 40.7 < 0.0001    AE 127.09 1 127.09 33.73 < 0.0001   BC 0.7 1 0.7 0.11 0.7428    BC 0.039 1 0.039 0.01 0.9193   BD 0.9 1 0.9 0.14 0.7115    BD 9.31E-03 1 9.31E-03 2.47E-03 0.9606   BE 19.73 1 19.73 3.06 0.088    BE 4.27 1 4.27 1.13 0.2935   CD 4.83 1 4.83 0.75 0.392    CD 17.84 1 17.84 4.73 0.0355   CE 164.99 1 164.99 25.57 < 0.0001    CE 67.74 1 67.74 17.98 0.0001   DE 0.17 1 0.17 0.027 0.8707    DE 0.014 1 0.014 3.83E-03 0.951   A^2 17.3 1 17.3 2.68 0.1094    A^2 1.61E-03 1 1.61E-03 4.28E-04 0.9836   B^2 3.13 1 3.13 0.49 0.4898    B^2 14.74 1 14.74 3.91 0.0549   C^2 91.7 1 91.7 14.21 0.0005    C^2 41.26 1 41.26 10.95 0.002   D^2 28.98 1 28.98 4.49 0.0403    D^2 8.56 1 8.56 2.27 0.1397 Residual 258.06 40 6.45    Residual 150.72 40 3.77 Lack of Fit 246.81 30 8.23 7.31 0.0011  Lack of Fit 138.3 30 4.61 3.71 0.0166 Pure Error 11.25 10 1.13    Pure Error 12.42 10 1.24 Cor Total 5158.04 59     Cor Total 3580.76 59  Table B.6: ANOVA tables for dew point approach temperature Px1-32M Sum of  Mean F p-value  Px1-32N Sum of  Mean F p-value Source Squares df Square Value Prob > F  Source Squares df Square Value Prob > F Model 3101.15 15 206.74 8.27 < 0.0001  Model 2304.8 15 153.65 10.42 < 0.0001   A 35.32 1 35.32 1.41 0.241    A 142.36 1 142.36 9.65 0.0033   B 364.63 1 364.63 14.58 0.0004    B 392.64 1 392.64 26.62 < 0.0001   C 848.79 1 848.79 33.95 < 0.0001    C 710.76 1 710.76 48.2 < 0.0001   D 220.98 1 220.98 8.84 0.0048    D 46.03 1 46.03 3.12 0.0842  151 Px1-32M Sum of  Mean F p-value  Px1-32N Sum of  Mean F p-value Source Squares df Square Value Prob > F  Source Squares df Square Value Prob > F   E 13.37 1 13.37 0.53 0.4686    E 37.95 1 37.95 2.57 0.1158   AB 15.82 1 15.82 0.63 0.4306    AB 40.64 1 40.64 2.76 0.104   AC 26.9 1 26.9 1.08 0.3053    AC 4.37 1 4.37 0.3 0.5891   AD 27.94 1 27.94 1.12 0.2963    AD 19.75 1 19.75 1.34 0.2534   AE 821.32 1 821.32 32.85 < 0.0001    AE 493.42 1 493.42 33.46 < 0.0001   BC 28.31 1 28.31 1.13 0.2931    BC 19.07 1 19.07 1.29 0.2617   BD 5.59 1 5.59 0.22 0.6385    BD 0.47 1 0.47 0.032 0.8598   BE 9.87 1 9.87 0.39 0.5331    BE 50.6 1 50.6 3.43 0.0707   CD 80.07 1 80.07 3.2 0.0804    CD 62.89 1 62.89 4.26 0.0448   CE 310.56 1 310.56 12.42 0.001    CE 212.7 1 212.7 14.42 0.0004   DE 291.67 1 291.67 11.67 0.0014    DE 71.16 1 71.16 4.83 0.0334 Residual 1100.15 44 25    Residual 648.88 44 14.75 Lack of Fit 1072.76 34 31.55 11.52 0.0001  Lack of Fit 587.94 34 17.29 2.84 0.0414 Pure Error 27.4 10 2.74    Pure Error 60.93 10 6.09 Cor Total 4201.3 59     Cor Total 2953.67 59  Px3-46M Sum of  Mean F p-value  Px3-46N Sum of  Mean F p-value Source Squares df Square Value Prob > F  Source Squares df Square Value Prob > F Model 3323.68 19 174.93 27.7 < 0.0001  Model 1946.95 19 102.47 26.23 < 0.0001   A 467.52 1 467.52 74.04 < 0.0001    A-Stream 1 FR 5.61E+02 1 5.61E+02 143.53 < 0.0001   B 247.68 1 247.68 39.22 < 0.0001    B-Stream 3 FR 1.58E+02 1 1.58E+02 40.37 < 0.0001   C 1754.97 1 1754.97 277.92 < 0.0001    C-Stream 1 Temp 7.83E+02 1 7.83E+02 200.42 < 0.0001   D 26.28 1 26.28 4.16 0.048    D-Stream 3 Temp 3.23E+01 1 3.23E+01 8.26 0.0065   E 179.78 1 179.78 28.47 < 0.0001    E-Pressure 5.13 1 5.13 1.31 0.2587   AB 5.04 1 5.04 0.8 0.377    AB 30.46 1 30.46 7.8 0.008   AC 39.12 1 39.12 6.19 0.0171    AC 8.33E+01 1 8.33E+01 21.32 < 0.0001   AD 13.91 1 13.91 2.2 0.1456    AD 8.14E+00 1 8.14E+00 2.08 0.1566   AE 257.52 1 257.52 40.78 < 0.0001    AE 127.82 1 127.82 32.72 < 0.0001   BC 0.56 1 0.56 0.088 0.7681    BC 3.50E-02 1 3.50E-02 8.99E-03 0.9249   BD 0.66 1 0.66 0.1 0.749    BD 2.81E-03 1 2.81E-03 7.20E-04 0.9787   BE 21.33 1 21.33 3.38 0.0735    BE 4.19 1 4.19 1.07 0.3066   CD 5.2 1 5.2 0.82 0.3696    CD 17.26 1 17.26 4.42 0.0419   CE 163.26 1 163.26 25.85 < 0.0001    CE 70.92 1 70.92 18.16 0.0001   DE 0.34 1 0.34 0.054 0.8179    DE 1.90E-02 1 1.90E-02 4.87E-03 0.9447   A^2 16.48 1 16.48 2.61 0.1141    A^2 0.015 1 0.015 3.95E-03 0.9502   B^2 3.36 1 3.36 0.53 0.4698    B^2 14.66 1 14.66 3.75 0.0598   C^2 91.01 1 91.01 14.41 0.0005    C^2 42.49 1 42.49 10.88 0.002   D^2 27.02 1 27.02 4.28 0.0451    D^2 8.92 1 8.92 2.28 0.1386 Residual 252.58 40 6.31    Residual 156.24 40 3.91 Lack of Fit 241.37 30 8.05 7.17 0.0012  Lack of Fit 1.44E+02 30 4.79 3.81 0.015 Pure Error 11.22 10 1.12    Pure Error 1.26E+01 10 1.26 Cor Total 3576.26 59     Cor Total 2103.19 59   152 APPENDIX C: APPLYING A CCD TO ERVS  In a similar manner to how a CCD is evolved for fuel cell humidifiers, a CCD can be designed to characterize ERVs. To begin, consider each parameter for an ERV system: • P1 and P3: In ERV systems, air is supplied through a blower at near atmospheric pressure. P1 and P3 can be set to atmospheric or slightly above atmospheric to reflect the effect of the blowers. • Q1: Q1 may vary in an ERV at different times of day or times of year as demands on the overall HVAC system vary. The values of Q1min and Q1max are dictated by the rated flows of the ERV to be tested. • Q3: In ERV systems, Q1 ≈ Q3. Q3 is therefore eliminated as a parameter, and its value set to Q3 = Q1. • T1 and T3: The nature of ERV systems dictates that the treatment of T1 and T3 be different from in fuel cell systems. The drier and wetter sides of the ERV can be either indoor or outdoor, depending on the season. A two-level categoric factor is added to the experiment, with the levels being either “cooling” (summer) or “heating” (winter) conditions. Instead of using T1 and T3, it is simpler to use Tindoor and Tdiff. Tindoor is eliminated as an independent parameter and set by the seasonal factor, with the value determined by ASHRAE building standards. Based on ANSI/ASHRAE Standard 55-2004, Tindoorheating = 22°C and Tindoorcooling = 24°C. • Tdiff: Tdiff is the remaining temperature parameter after the modification of T1 and T3, where Tdiff = |Toutdoor – Tindoor|. The range of Tdiff is limited by system and environmental factors; Tdiffmin is the temperature differential at which the ERV system will come into use, while Tdiffmax is dictated by the normal extremes of  153 local conditions. Tdiffmax in heating conditions may be limited by the minimum operating temperature of the ERV. • Φindoor: Φindoor may be eliminated as a parameter along with Tindoor,, as it will also be dictated by ASHRAE building standards and set by the seasonal factor. A combination of standards and studies lead to the selection of Φindoorheating = 40% and Φindoorcooling = 50%. • Φoutdoor: Unlike with fuel cells humidifiers, Φoutdoor is a significant parameter. Atmospheric humidity in any region may vary on a daily basis, and Φoutdoor must reflect that variation. Fortunately for the experimental designer, using relative humidity as a parameter takes into account variations in temperature when calculating moisture content, so Φoutdoor has no need of taking different values across the set of heating versus cooling conditions. As such, the limits Φoutdoormin and Φoutdoormax are set by local atmospheric conditions; Φoutdoormin = 20% and Φoutdoormax = 100% are typical values [54].  The parameters for the design of experiments for ERVs are presented in Table C.1: Table C.1: Parameter values for a CCD for ERVs Parameter Range of values Q Range of rated flows for subject ERV Season Categoric Level 1 “cooling”: Tindoor = 24C and Φindoor = 50% Level 2 “heating”: Tindoor = 22C and Φindoor = 40% Tdiff Range of typical temperature differentials Φoutdoor Range of typical atmospheric humidities  The differences in performance between heating and cooling seasons are likely to lead to significant differences in effectiveness. Because of this, it may be more effective to run two separate CCD tests, one for each season, rather than to attempt to amalgamate  154 both seasons under the aegis of a single categoric factor. This experimental design requires 17 test runs.  155 APPENDIX D: A SIMPLIFIED CCD FOR HUMIDIFIERS  An outline for a simplified CCD for characterizing humidifiers was presented in 6.1. The experimental tables in terms of coded factors for these designs are presented here in Table D.1, Table D.2, and Table D.3. Table D.1: Experimental table for CCD in Q1, Q3, and  T3  Coded levels for factors Run Q1 Q3 T3 1 -1 -1 -1 2 -1 -1 1 3 -1 1 -1 4 1 -1 -1 5 -1 1 1 6 1 -1 1 7 1 1 -1 8 1 1 1 9 0 0 0 10 0 0 0 11 0 0 0 12 α 0 0 13 -α 0 0 14 0 α 0 15 0 -α 0 16 0 0 α 17 0 0 -α  Table D.2: Experimental table for CCD in Q, T1, and T3  Coded levels for factors Run Q T1 T3 1 -1 -1 -1 2 -1 -1 1 3 -1 1 -1 4 1 -1 -1 5 -1 1 1 6 1 -1 1 7 1 1 -1 8 1 1 1 9 0 0 0 10 0 0 0 11 0 0 0 12 α 0 0 13 -α 0 0 14 0 α 0 15 0 -α 0  156  Coded levels for factors Run Q T1 T3 16 0 0 -α 17 0 0 α  Table D.3: Experimental table for CCD in Q and T3  Coded levels for factors Run Q T3 1 -1 -1 2 -1 1 3 1 -1 4 1 1 5 0 0 6 0 0 7 0 0 8 α 0 9 -α 0 10 0 α 11 0 -α 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.24.1-0067751/manifest

Comment

Related Items