Wijesuriya Mines 0052E 11907.Pdf

EXPERIMENTAL ANALYSIS AND VALIDATION OF A NUMERICAL PCM MODEL FOR BUILDING ENERGY PROGRAMS

Wijesuriya Arachchige Sajith Indika Wijesuriya

A thesis submitted to the Faculty and the Board of Trustees of the Colorado School of Mines in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Mechanical Engineering).

Golden, Colorado

Date ------

Signed: ------Wijesuriya Wijesuriya

Signed: ------Dr. Paulo Tabares-Velasco Thesis Advisor

Golden, Colorado

Date ------

Signed: ------Dr. John Berger Professor and Department Head Department of Mechanical Engineering

ABSTRACT

The increase in peak electricity demand in recent years has stressed the importance of peak electricity demand shifting technologies. Phase Change Materials (PCMs) have a potential to improve the building envelope by increasing the thermal mass as well as contribute to a significant peak shift in whole building power demand. Therefore, special attention is given to properly capture the thermal behavior of PCMs in advanced building energy modeling software. Design of effective PCM thermal storage systems requires accurate energy modeling. There are analytical and numerical models developed during last few decades for this purpose, many have not been fully validated. Based on the current status of literature, the study identifies the limitations and drawbacks of existing methods. A parametric study is conducted to identify the optimum PCM thermo-physical properties, PCM locations in building envelope, under forced convection and a 5 hour pre-cooling strategy. Furthermore, an improved advanced numerical building envelope model is created in MATLAB to simulate the PCM performance in building envelope and an experimental apparatus is constructed to obtain useful experimental data for PCM included wall assemblies for validation purposes. This thesis also uses two datasets from laboratory studies of shape-stabilized and field studies Nano-PCMs to validate and compare PCM modelling algorithms of 6 modules in 5 building energy modelling software. Finally, two macroencapsulated PCMs (Bio based PCM and hydrate salts) are tested using the experimental apparatus to obtain data for validation purposes. To approximate the heat transfer through a wall assembly with PCM pouches several techniques are investigated that can capture 3D heat transfer characteristics. Method with the highest agreement is used to validate and compare the developed MATLAB algorithm and different building energy modelling software.

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TABLE OF CONTENTS

LIST OF FIGURES ...... ix

LIST OF TABLES ...... xviii

LIST OF SYMBOLS ...... xxi

CHAPTER 1 INTRODUCTION ...... 1

CHAPTER 2 BACKGROUND AND SIGNIFICANCE ...... 5

2.1. Phenomena of Phase Change of PCMs ...... 6

2.2. PCM encapsulation methods ...... 7

2.3. Thermal characteristics and properties of PCMs ...... 10

“Mushy” region of Phase Change ...... 10

Phase separation of the material ...... 12

Subcooling/supercooling effect and Hysteresis ...... 12

PCM Thermal conductivity ...... 14

PCM phase-change temperature range ...... 14

2.4. Types of PCMs ...... 15

Analyzed PCMs ...... 16

CHAPTER 3 MODELING PCMS IN BUILDING ENVELOPE ...... 19

3.1. Analytical Models ...... 20

3.2. Numerical Models ...... 20

Numerical models: Simulation methods ...... 20

Numerical Models: Grid and boundary considerations...... 23

Numerical Models: Discrete forms and solution schemes ...... 23

Numerical Models: In building energy modeling platforms ...... 24

CHAPTER 4 EXPERIMENTAL STUDIES ON PCM INCLUSION IN BUILDING ENVELOPE ...... 26

4.1. Scale of experimental studies ...... 26

4.2. PCM characterization methods ...... 26

Differential Scanning Calorimetry (DSC) ...... 27

T-history method ...... 28

Thermogravimetric analyses (TG) ...... 29

Dynamic Hot Box Method ...... 29

Heat Flow Meter Apparatus (HFMA) methods ...... 30

Other methods ...... 32

4.3.Experimental studies on macroencapsulated and microencapsulated PCMs ...... 32

CHAPTER 5 PARAMETRIC ANALYSIS OF A RESIDENTIAL BUILDING WITH PHASE CHANGE MATERIAL (PCM)-ENHANCED DRYWALL, PRE-COOLING, AND VARIABLE ELECTRIC RATES IN A HOT AND DRY CLIMATE ...... 34 5.1. Approach ...... 36

Building Description ...... 37

Precooling Strategy ...... 42

Convection Heat Transfer ...... 43

Mechanical Ventilation and Fan Selection ...... 44

5.2. Results and Discussion ...... 45

Parametric analysis results ...... 45

Hourly Results ...... 48

5.3. Conclusions ...... 60

CHAPTER 6 NUMERICAL HEAT TRANSFER MODEL FOR OPAQUE WALLS AND DESCRIPTION OF LABORATORY FACILITY FOR EXPERIMENTAL ANALYSIS ...... 62 6.1. 1D heat transfer algorithm to model building walls with PCM ...... 63

6.2. Modeling of PCM inclusions in the thesis model ...... 66

Modeling hysteresis in the thesis model ...... 67

6.3. PCM modeling objects in building energy modeling software ...... 71

EnergyPlus PCM modules ...... 71

WUFI PCM module ...... 72

6.4. Numerical PCM building envelope model verification ...... 73

Analytical Verification ...... 73

Numerical Verification ...... 78

6.5. State-of-the-art Laboratory for full-scale experimental studies of PCMs ...... 81

Wall Assembly Tests ...... 81

Environmental Chamber and the HVAC System ...... 82

HVAC and Chamber Instrumentation System ...... 84

Control and Data Acquisition ...... 86

Construction of Building Envelope Assemblies within the Chamber ...... 91

CHAPTER 7 EMPIRICAL VALIDATION AND COMPARISON OF PCM MODELING ALGORITHEMS COMMONLY USED IN BUILDING ENERGY AND HYGROTHERMAL SOFTWARE ...... 93 7.1. Introduction ...... 93

7.2. Methodology ...... 95

Validation ...... 99

Enthalpy-temperature curves of PCMs ...... 102

Numerical modeling considerations ...... 103

Shape-stabilized PCM wall data ...... 106

Nano-encapsulated wallboard data ...... 107

7.3. Results and Discussion ...... 109

NTNU shape-stabilized PCM ...... 109

Nano-encapsulated PCM wall ...... 113

7.4. Conclusions ...... 118

CHAPTER 8 EMPIRICAL VALIDATION AND COMPARISON OF PCM ALGORITHMS MODELING MACRO-ENCAPSULATED PCMS IN THE BUILDING ENVELOPE ...... 119 8.1. Introduction ...... 119

8.2. Methodology ...... 122

Macroencapsulated Phase Change Materials ...... 122

Full scale testing environment ...... 127

Envelope assemblies ...... 129

Cooling and heating temperature set-points for full-cycle tests ...... 133

Heat transfer modeling of macroencapsulated PCMs...... 134

Using the simplified methods in the 1D thesis model ...... 142

PCM models used in Building energy and hygrothermal software ...... 144

Validation ...... 144

8.3. Results and Discussion ...... 145

Temperature variation on the surfaces of the panels ...... 145

Temperature variation of the PCMs behind drywall ...... 147

Comparison of heat transfer approaches for PCM macroencapsulation ...... 148

Comparison of EnergyPlus, thesis model, and WUFI software ...... 155

Validation study with hysteresis characteristic data ...... 158

8.4.Conclusions ...... 162

CHAPTER 9 CONCLUSIONS AND FUTURE WORK ...... 164

9.1. Summary of significant results ...... 164

9.2. Potential for Future Work ...... 166

Further development of the building envelope model ...... 166

Laboratory experiments of different PCMs ...... 166

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REFERENCES CITED ...... 168

APPENDIX A. DISCRETE FORMS PREVIOUSELY USED IN NUMERICALLY MODELLING PCMS ...... 199 APPENDIX B. SUMMERY OF WHERE WHOLE BUILDING ENERGY MODELING PLATFORMS WITH PCM MODELS ARE USED ...... 200 APPENDIX C. COST CALCULATION PROCEDURES OF BEOPT ...... 204

APPENDIX D. SENSOR INFORMATION OF THE CHAMBER, HVAC SYSTEM, AND OUTSIDE ...... 206 APPENDIX E. SENSOR INFORMATION OF THE CHAMBER, HVAC SYSTEM, AND OUTSIDE ...... 209

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LIST OF FIGURES

Figure 2-1 Different PCM encapsulation types: (a) microencapsulated PCMs embedded in drywall, (b) Shape-stabilized PCMs: thin PCM layers enclosed between aluminum foil sheets, and (c) Macroencapsulated PCMs: PCMs enclosed in pouches. Figure shows the dimensions of the single PCM included unit and the commercially available dimensions...... 9

Figure 2-2 Enthalpy variation across the mushy region and deviation observed in PCMs used in building applications (Real PCM) in contrast to an ideal PCM. Graph shows the melting temperature range, melting latent heat, and melting sensible heat of the PCM. Graph constructed based on the data provided by [14]...... 10

Figure 2-3 Sensible heat and latent heat in the enthalpy change during the melting process. Graph constructed based on the data provided by [14]...... 11

Figure 2-4 Enhanced view of different PCM enthalpy curve combinations showing hysteresis (a) Subcooling effect and freezing temperature curve comes back and overlay on the melting curve, (b) subcooling causing separate curves for melting and freezing (c) hysteresis due to slow latent heat release, (d) apparent hysteresis due to non-isothermal conditions in measurements (Enthalpy data available at [53] and the curve concept inspired by [54])...... 13

Figure 2-5 Melting enthalpy and melting temperature ( – for different PCMs, An important criterion in selecting PCMs for building envelope applications: ...... 15 푇푚) Figure 2-6 Visualization of PCM packing in pouches once heated to a temperature of ~90 ˚C. . 18

Figure 3-1 Different scales of building energy modeling considered in the current study are at building scale, envelope scale. The PCM modeling algorithm incorporates PCM characteristics in the envelope modeling algorithm...... 19

Figure 5-1 View of the simulated house, orientation and, and its neighboring buildings...... 37

Figure 5-2 Enthalpy curves showcasing 1) Real PCM data from BioPCMTM Q23º obtained from DSC test and 2) Ideal PCM curves with thermal properties similar to the real PCM...... 39

Figure 5-3 Multilayer envelope constructions of the evaluated home indicating the location of the PCM-drywall. The interior environment is on the right and the exterior environment is on the left for all cases (the layer thicknesses does not represent the actual scale)...... 41

Figure 5-4 Precooling strategy with 25.6 °C setback temperature. The peach-shaded rectangle indicates peak hours while the blue shaded-region indicates precooling...... 42

Figure 5-5 Heat transfer coefficient values used next to the ceiling and exterior wall within the living zone for, (i) forced convection model (FC), (ii) CeilingDiffuser convection model (CeilingDiffuser) and (iii) natural convection model (NC)...... 44

Figure 5-6 BEopt parametric results, where each point represents a simulated home with a different combination of PCM properties and locations. The point close to the upper right corner and in red color represents the home with no PCM or pre-cooling. Point closest to the lower left corner in black color represents a home with precooling but no PCMs...... 45

Figure 5-7 BEopt parametric results for the cases with lowest energy related costs, where each point represents a simulated home with a different combination of PCM properties and locations. The point close to the upper right corner represents the home with no PCM...... 46

Figure 5-8 Selection of optimum points for each PCM location and envelope condition: PCMs in all three locations (3 Different PCMs optimized), single/same type of PCMs in three locations (A single PCM) and PCMs only in the ceiling (PCMs in ceiling only). Each of these points are the lowest annualized energy related cost (AERC) points for each category above...... 47

Figure 5-9 Annual variation of temperatures for the forced convection mode for PCMsoptimized for all locations. 0 indicates the start of the month January and the time is shown for the calendar year of 12 months...... 48

Figure 5-10 Annual variation of temperatures for the natural convection mode for PCMs optimized for all locations. X-axis represent the months of the year. 0 indicates the start of the month January and the time is shown for the calendar year of 12 months...... 49

Figure 5-11 Average indoor air temperature within the living zone for forced convection model for all envelope types. Hour 0 represents midnight of the first day...... 50

Figure 5-12 Average indoor air temperature for the natural convection model for all envelope types. Hour 0 represents midnight of the first day...... 50

Figure 5-13 Average indoor air temperature for homes with pre-cooling only and forced convection mode, and three setback temperatures (Tr): 24.4, 25.5 and 26.7˚C. Hour 0 represents midnight of the first day...... 51

Figure 5-14 Averaged indoor air temperature for homes with PCMs optimized in each location, with forced convection mode, three setback temperatures (Tr): 24.4, 25.5 and 26.7˚C. Indoor air temperature for Tr: 25.5 ˚C and 26.7 ˚C perform the same. Hour 0 represents midnight of the first day...... 52

Figure 5-15 Averaged PCM-drywall temperature in external wall for homes with PCMs optimized in each location, with forced convection mode, three setback temperatures (Tr): 24.4, 25.56 and 26.67˚C. Average drywall temperature (at ceiling) for Tr: 25.5 ˚C and 26.7 ˚C. Hour 0 represents midnight of the first day...... 53

Figure 5-16 Averaged PCM-drywall temperature in the external wall for the PCM optimized and installed in all drywall (PCM optimized) case: A comparison between the forced convection model and natural convection models...... 53

Figure 5-17 Average drywall temperature of the exterior wall under forced convection (FC) and natural convection (NC) model for, PCM optimized and installed in all drywall (PCM optimized case) and regular drywall (No PCM case). Hour 0 represents midnight of the first day...... 54

Figure 5-18 Average drywall temperature of the ceiling under forced convection (FC) and natural convection (NC) models for, PCM optimized and installed in all drywall (PCM optimized case) and regular drywall (No PCM case). Hour 0 represents midnight of the first day...... 54

Figure 5-19 Heat gain rates per unit area of the ceiling drywall for forced and natural convection models for cases: (i) No-PCM and precooling only (ii) PCMs included in the ceiling only. Hour 0 represents midnight of the first day...... 55

Figure 5-20 Cooling electricity power consumption variations for all cases with the forced convection model for July 22. Hour 0 represents midnight of the first day...... 56

Figure 5-21 Cooling electricity power consumption for all analyzed cases with the natural convection mode for July 22...... 56

Figure 5-22 Cost variations through the day when TOU rates are applied during the peak time for July 22 for all analyzed cases and with the forced convection...... 57

Figure 5-23 Cost variations through the day when TOU rates are applied during the peak time for July 22 for all analyzed cases and with the natural convection...... 57

Figure 5-24 Aggregated cooling and ventilation related electricity consumption in the precooling months (May-Oct), assuming the fan power is 25W for each fan...... 58

Figure 5-25 Aggregated cooling and ventilation related electricity consumption in the precooling months (May-Oct), assuming the fan power is 2 W for each fan...... 58

Figure 5-26 Seasonal cooling electricity energy cost for May-Oct period for each analyzed case with natural and forced convection assuming the fan power is 25W for each fan...... 59

Figure 5-27 Seasonal cooling electricity energy cost for May-Oct period for each analyzed case with natural and forced convection assuming the fan power is 2W for

each fan...... 60

Figure 6-1 Structure of the full validation study includes analytical verification, comparative testing, and empirical validation...... 62

Figure 6-2 Structure of interior and interface nodes, space and time discretization of the 1D algorithm...... 64

Figure 6-3 Structure of the functions in the numerical envelope model...... 65

Figure 6-4 Manufacturer provided melting curve data and melting and freezing curves obtained from the Dynamic Heat Flux Meter Apparatus (DHFMA) method for the hydrate-salts PCM of InfiniteRTM (Nominal melting temperature =23 ºC). .. 68

Figure 6-5 Approximated melting curve for the PCM hydrate-salts from DSC data...... 69

Figure 6-6 Approximated melting curve for the PCM hydrate-salts from DHFMA data...... 69

Figure 6-7 Approximated freezing curve for the PCM hydrate-salts from DHFMA data...... 70

Figure 6-8 EnergyPlus original PCM model data input interface...... 71

Figure 6-9 EnergyPlus Hysteresis PCM model data input interface to define PCM properties for melting and freezing curves separately...... 72

Figure 6-10 WUFI PCM model data input interface indicating the enthalpy curve input...... 73

Figure 6-11 Cross section temperature variation of the semi-infinite material layer after 24h period for the PCM drywall case...... 77

Figure 6-12 Transient temperature variation at a location 0.021m in the material layer for (i) Analytical solution (ii) thesis model, and (iii) EnergyPlus solutions ( of 0.2 ºC is implemented in the numerical solutions)...... 77

Figure 6-13 Heat훥푇푃퐶 flux at the exterior surface of the PCM layer...... 78

Figure 6-14 West facing wall of the residential building evaluated for numerical verification. .. 80

Figure 6-15 External and internal surface temperatures of the examined exterior wall without PCM inclusions from the thesis model and EnergyPlus...... 80

Figure 6-16 Verification of temperature variations on the internal and external; surfaces of the wall examined...... 81

Figure 6-17 Overview of the air handling unit and the chamber, Section A: AHU Main Duct, Section B: AHU Return Duct, and Section C: Chamber ...... 82

Figure 6-18 Plan View of the Ceiling Setup of the Chamber including the inlet diffuser, lights, and exhaust diffuser...... 83

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Figure 6-19 SkylineTM Outdoor AHU by DAIKIN, Group: Applied Air systems, Part Number: IM 770 houses the heating and cooling elements, filters, humidifier to condition the air...... 84

Figure 6-20 Sensor locations in the AHU and other components of the HVAC system describes the sensors in each section, section A: Main AHU enclosure and the connection to the supply air duct and the return air duct, section B: Return air duct...... 85

Figure 6-21 The ABB control unit consists of a (i) C1867 - MODBUS TCP Interface, (ii) PM 851 Processor UNIT, (III) 3 Analog Input Units, (iv) 1 Analog Output Unit, (v) 1 Digital Input Unit, and (vi) 1 Digital Output Unit...... 86

Figure 6-22 Instrunet data acquisition unit with connections linked to the experimental apparatus sensors and some ABB main system sensors also linked to the Instrunet system to verify readings...... 87

Figure 6-23 Hydraulic radiant wall heating and cooling apparatus...... 87

Figure 6-24 Radiant wall flow control apparatus includes the primary flow sensor, 3 speed flow pump, temperature sensors to measure inlet and outlet temperatures of the fluid flow to the radiant wall heat exchanger...... 89

Figure 6-25 Flow control valve apparatus indicates the process of flow from the boiler and flow from the chiller is mixed. The flow measurements through the radiant wall heat exchanger are also taken using the unit...... 89

Figure 6-26 PLC Control flow chart for the radiant wall control PID settings for the mixing valve operation is indicated in the Figure 6-25...... 90

Figure 6-27 Current PID settings for the mixing valve for the setpoint of 120 ºF...... 90

Figure 6-28 Radiant wall location within the environmental chamber and the locations of wall assembly panels relative to the radiant wall...... 92

Figure 7-1 (a) Enthalpy-Temperature (h-T) curves for shape-stabilized PCM, (b) and nano-encapsulated PCM...... 102

Figure 7-2 Non-uniform finite volume mesh implemented in COMSOL simulate the Nano-PCM layer in ORNL field test data. Nano-PCM layer comprises of two elements...... 103

Figure 7-3 Non-uniform finite volume mesh implemented in WUFI to simulate the Nano-PCM layer in ORNL field test data. Nano-PCM layer comprises of 24 volumes...... 103

Figure 7-4 Uniform finite difference mesh implemented in thesis model to simulate the

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Nano-PCM layer in ORNL field test data. Nano-PCM layer comprises of 4 points...... 104

Figure 7-5 Analyzed wall assembly using shape-stabalize PCMs. Red dots represent temperature measurement points, while black hollow circles represent WUFI monitoring locations. PCMs are located in the white layer (between Point 2 and 3)...... 107

Figure 7-6 Analyzed wall assembly using nano-encapsulated PCMs. Red dots represent temperature measurement points, while black hollow circles represent WUFI monitoring locations. PCMs are located in the white layer (between Point 5 and 6)...... 108

Figure 7-7 Temperature at Point (2): between the gypsum and PCM wallboard, and measured temperature at the boundary: Point (1). Simulated data for COMSOL, ESP-r, EnergyPlus (2 modules), Thesis model, and WUFI is shown...... 109

Figure 7-8 Temperature at the Point (3): between the PCM wallboard and mineral wool insulation. Simulated data for COMSOL, ESP-r, EnergyPlus (2 modules), Thesis model, and WUFI is shown...... 110

Figure 7-9 Heat flux at the Point (1): Hot-side boundary surface. Simulated data for COMSOL, EnergyPlus (2 modules), Thesis model, and WUFI is shown...... 112

Figure 7-10 Heat flux at the Point (3): Interface of the PCM wallboard and mineral wool insulation. Simulated data for COMSOL, EnergyPlus (2 modules), Thesis model, and WUFI is shown...... 112

Figure 7-11 Temperature at the Point (2): interface of OSB and cellulose insulation Simulated data for COMSOL, ESP-r, EnergyPlus (2 modules), Thesis model, and WUFI is shown...... 114

Figure 7-12 Temperature at the Point (3): middle of cellulose insulation. Simulated data for COMSOL, ESP-r, EnergyPlus (2 modules), Thesis model, and WUFI is shown...... 115

Figure 7-13 Model results at the Point (4), Point (5): interface of the cellulose insulation and the PCM wallboard. Simulated data for ESP-r, EnergyPlus (2 modules), Thesis model, and WUFI is shown...... 115

Figure 7-14 Heat flux at the Point (5): interface of the cellulose cavity and the Nano PCM wallboard. Simulated data for COMSOL, EnergyPlus (2 modules), Thesis model, and WUFI is shown...... 117

Figure 8-1 Dimensions of analyzed PCM pouches: (a) BioPCM, (b) hydrate-salts...... 122

Figure 8-2 Enthalpy-temperature melting curves obtained using DSC characterization

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method for BioPCM...... 125

Figure 8-3 Enthalpy-temperature curves obtained using DSC and DHFMA characterization methods for PCM hydrate-salts...... 126

Figure 8-4 Schematic overview of, Section A: Air handling unit (AHU), Section B: return duct of the air to the AHU, Section C: Environmental chamber...... 127

Figure 8-5 Front view and the key dimensions of how the 4 panels constructed. The exposed radiant wall in the right end is insulated with 5.08 cm (2 in) of R-10 insulation. Panel 3 and 4 are shown here with the front drywall layer removed to showcase the PCM pouch mats arrangement...... 130

Figure 8-6 Front view of the PCM pouches and the sensor locations of the interface with the drywall layer removed...... 131

Figure 8-7 Top view of the core section with each material layers and the sensor locations (split view) (a) wall panels with just regular drywall (b) wall panels with PCM pouches and regular drywall...... 132

Figure 8-8 Radiant wall supply fluid temperature setpoint and chamber air temperature...... 133

Figure 8-9 PCM inclusion in pouches (BioPCM case is shown here) (a) front view of the uneven PCM distribution (BioPCM) (b) schematic of the side view when PCM mats are placed between plywood and the drywall...... 134

Figure 8-10 Considered heat transfer simplification methods: (a) PCM distributed as a thin continuous layer, (b) PCM layer as a parallel path heat transfer, and (c) PCM as a porous material and parallel path ...... 135

Figure 8-11 Parallel path heat transfer across the wall assemblies with PCM pouches. This method assumes two paths across the entire assembly and assumes surfaces parallel to the heat transfer process are adiabatic. Here temperature at surface 1 and 5/ 4 and 8 are different...... 136

Figure 8-12 Parallel path heat transfer across the wall assemblies with PCM pouches. This method assumes two paths across only the PCM layer and the nodes on the interfaces are isothermal (temperature at surface 1 and 5/ 4 and 8 are same)...... 137

Figure 8-13 Geometry based dimension reductions used in the study (a) actual view of the pouch with 3D characteristics, (b) adjusted 3D view based on PCM volume and geometry, (c) reduced 2D view with the parallel path methods, (d) using the thermal resistance values temperature dependent effective conductivity is calculated and applied for 1D thesis model...... 143

Figure 8-14 Boundary and interface temperatures of the wall assembly with BioPCM. Lines, 1. Exterior surface temperature, 2. Plywood-pouches interface temperature, 3. Pouches-drywall interface temperature, 4. Exterior surface temperature...... 146

Figure 8-15 Boundary and interface temperatures of the wall assembly with PCM hydrate salts. Lines, 1. Exterior surface temperature, 2. Plywood-pouches interface temperature, 3. Pouches-drywall interface temperature, 4. Exterior surface temperature...... 146

Figure 8-16 Surface temperature recorded and visualized through the Infrared Camera measured every 2 hour intervals after radiant wall setpoint is increase from 40 ºC to 140 ºC...... 147

Figure 8-17 Average core surface temperature (panel 3): The temperatures at every 2 hour period is mapped with the figure Figure 8-16...... 148

Figure 8-18 Temperature at the interface of plywood and PCM of BioPCM wall panel. Lines, 1. Experimental data. 5 simplification methods: 2. Effective thickness 3. Full parallel path, solid PCM, 4. Partial parallel path, solid PCM, 5. Full parallel path, porous PCM, 6. Partial parallel path, porous PCM, and 7. Partial parallel path, without PCM (no-latent heat)...... 149

Figure 8-19 Temperature at the interface of PCM and drywall of BioPCM wall panel. Lines, 1. Experimental data. 5 simplification methods: 2. Effective thickness 3. Full parallel path, solid PCM, 4. Partial parallel path, solid PCM, 5. Full parallel path, porous PCM, 6. Partial parallel path, porous PCM, and 7. Partial parallel path, without PCM (no-latent heat)...... 150

Figure 8-20 Heat-flux calculations of BioPCMs panel, 1. Using heat released or absorbed by the fluid, 2. Heat flux meter measurements, and 3. Using thesis model and partial parallel path, solid PCM method...... 151

Figure 8-21 Cross section temperature plot of the BioPCM panel comparing the experimental data at the beginning of the heating cycle (t=0h) and at the end of the heating cycle (t=16h) for the modeled data with the thesis model for c=1 and c=0.5 discretization constants...... 152

Figure 8-22 Temperature at the interface of plywood and pouches of hydrate-salt wall panel. Lines, 1. Experimental data. 5 simplification methods: 2. Effective thickness 3. Full parallel path, solid PCM, 4. Partial parallel path, solid PCM, 5. Full parallel path, porous PCM, 6. Partial parallel path, porous PCM, and 7. Partial parallel path, without PCM (no-latent heat)...... 153

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4. Partial parallel path, solid PCM, 5. Full parallel path, porous PCM, 6. Partial parallel path, porous PCM, and 7. Partial parallel path, without PCM (no-latent heat)...... 153

Figure 8-24 Plywood-pouches interface temperature compared with the E+ (two modules), thesis model, and WUFI for BioPCM...... 155

Figure 8-25 Pouches-drywall interface temperature compared with the E+ (two modules), thesis model, and WUFI for BioPCM...... 156

Figure 8-26 Plywood-pouches interface temperature compared with the E+ (two modules), thesis model, and WUFI for hydrate-salts...... 157

Figure 8-27 Pouches-drywall interface temperature compared with the E+ (two modules), thesis model, and WUFI for hydrate-salts...... 157

Figure 8-28 Graphical comparison of interface temperature with and without the consideration of hysteresis for BioPCM simulated in EnergyPlus (a) plywood-pouches interface and (b) pouches-drywall interface...... 159

Figure 8-29 Graphical comparison of interface temperature with and without the consideration of hysteresis for BioPCM simulated in the thesis model (a) plywood-pouches interface and (b) pouches-drywall interface. Hysteresis data show an improved graphical comparison...... 159

Figure 8-30 Graphical comparison of interface temperature with and without the consideration of hysteresis for PCM hydrate-salts simulated in EnergyPlus (a) plywood-pouches interface and (b) pouches-drywall interface...... 161

Figure 8-31 Graphical comparison of interface temperature with and without the consideration of hysteresis for PCM hydrate-salts simulated in thesis model (a) plywood-pouches interface and (b) pouches-drywall interface...... 161

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LIST OF TABLES

Table 2-1 Properties of the PCM products used in the building envelope testing ...... 17

Table 2-2 Physical properties of the National Gypsum ThermalCORE® gypsum board containing PCM ...... 17

Table 3-1 Coefficients of the mathematical formulation to capture the phase change effects in numerical models...... 22

Table 3-2 Latent heat methods, discretization and time integration computation methods used in this study with different PCM modelling software ...... 25

Table 4-1 PCM characterization methods for PCMs used in building envelope applications ...... 27

Table 5-1 Annualized TOU rate, E-21 Super Peak TOU Rate [216] ...... 38

Table 5-2 Range of analyzed theoretical PCM properties and locations in parametric study ...... 39

Table 5-3 Specific Latent Heat and Costs of PCM Enhanced Drywall ...... 40

Table 5-4 Economic factors used in the 30-year parametric analysis ...... 41

Table 5-5 Optimal PCM properties for each location of application: Ceiling, external wall, partition wall ...... 48

Table 6-1 Definitions of the exterior heat transfer for the numerical verification study using the thesis algorithm ...... 65

Table 6-2 Phase change characterization data approximated by the simplified curves to implement in the PCM modeling algorithms ...... 70

Table 6-3 Thermal conditions used in the analytical verification cases ...... 75

Table 6-4 Material properties for the analytical verification with PCM (inspired by [247]) ...... 76

Table 6-5 Material properties for the numerical verification with PCM ...... 79

Table 6-6 Dimensions of the environmental chamber, H= height, L= length, and W= width. ... 83

Table 6-7 Summary of radiant wall heating and cooling system apparatus ...... 88

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Table 7-1 Numerical modeling methods used in PCM models ...... 97

Table 7-2 Properties of Analyzed PCMs ...... 101

Table 7-3 Numerical discretization considered in modeling the material layers with PCM inclusions...... 104

Table 7-4 Material properties of the wall assembly used in the NTNU controlled hot-box experiments...... 106

Table 7-5 Material properties of the wall assembly used in Nano-encapsulated wallboard...... 108

Table 7-6 Calculated Temperature RMSE, CV (RMSE) and NMBE for all analyzed PCM models at material interfaces ...... 111

Table 7-7 Temperature RMSE, CV (RMSE) and NMBE at: (i) exterior surface of the hot-side (Point 1), (ii) Interface between the PCM wallboard and the mineral wool insulation (Point 5) ...... 113

Table 7-8 Surface temperature RMSE, CV(RMSE) and NMBE values at (i) Interface of OSB and the cellulose filled cavity (point 2), (ii) Middle of the cellulose filled cavity (point 3) ...... 116

Table 7-9 RMSE, CV (RMSE) and NMBE calculations of the heat flux variations at the interface of cellulose cavity and the Nano PCM wallboard ...... 117

Table 8-1 Thermo-physical properties of analyzed macroencapsulated PCMs...... 123

Table 8-2 Sensor type, purpose, uncertainty, and quantity of the sensors used in the experimental analysis...... 128

Table 8-3 Thermo-physical properties and dimensions of the material used in the wall panels...... 130

Table 8-4 Accuracy analysis for the comparison of two interface temperatures for BioPCM ...... 150

Table 8-5 RMSE, CV(RMSE), NMBE values for the comparison of two interface temperatures for hydrate-salts ...... 154

Table 8-6 RMSE, CV(RMSE), NMBE calculations of temperatures at each interface for EnergyPlus, thesis model, and WUFI for BioPCM...... 156

Table 8-7 RMSE, CV(RMSE), NMBE calculations comparisons of temperatures at each interface for EnergyPlus, thesis model, and WUFI for hydrate-salts panel ..... 158

Table 8-8 RMSE, CV(RMSE), NMBE calculations of temperatures at each interface for EnergyPlus, thesis model for the simulations applying thermal hysteresis xix

characteristics for BioPCM panel...... 160

Table 8-9 Accuracy analysis of comparisons of temperatures at each interface for EnergyPlus, and thesis model for the simulations applying thermal hysteresis characteristics for PCM hydrate-salts ...... 162

LIST OF SYMBOLS

Nomenclature Meaning

ΔTPC Phase Change Temperature Range ΔH Enthalpy Difference Δt Time step/ time discretization Δx Space step/ time discretization A Area A/C Air Conditioning AirDistSys Air Distribution Measuring System BioPCM TM Bio based PCM type c Discretization constant COMSOL Cross-platform finite element analysis, solver and Multiphysics simulation software Cost at the beginning of the evaluation period $ Cost within the year k 퐶푂푆푇푖푛푖푡푖푎푙 퐶푂푆푇푦푒푎푟=푘 Averaged heat capacity 퐶푎푣푔 Specific heat capacity Heat capacity term as a function of temperature 푐푃 DAQ퐴 Data Acquisition Unit 퐶 (푇) dh/dT Specific enthalpy change per unit temperature Real discount rate dw Drywall 푑푟푡 E+ EnergyPlus EnergyPlus Energy Plus whole building energy modeling platform ESP-r A whole-building energy simulation tool

F0 Grid Fourier number View factor from surface 1 to 2 FLIR ResearchIR Infrared camera data acquisition interface 퐹12 xxi

h Enthalpy (J/kg) Hydrate-salts PCM hydrate-salts i Inflation rate % L Thickness of layers m Mass N Number of mortgage years k Thermal conductivity

Leff Effective thickness ky kth year MATLAB A multi-paradigm numerical computing environment

N Number of data points t Time

t2 Time 2 (at end)

Tr Set Point Set Back/ Relaxation Temperature Subscripts hpc Higher phase change m Melting lpc Lower phase change PARDISO A software for solving large sparse symmetric and nonsymmetrical linear systems of equations PC Phase Change proto Protocol R Relaxation ref Reference Rt Rate Total resistance V&V Verification and validation 푅푡표푡 Measured data Predicted/simulated data 푦푖 Mean of measured data 푦̂푖 V PCM volume in a pouch 푦̅PCM̅푚̅̅

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ys Simulated data Acronyms ACH Air Changes per Hour ADI Alternating Direction Implicit AERC Annualized Energy Related Costs Annual Energy Use

Annual Energy Use (Reference) AEU 퐴퐸푈푟푒푓 Annual Energy Use (Protocol) 퐴퐸푈푝푟표푡표 Average Source Energy Savings ASHRAE American Society of Heating, Refrigerating and 퐴푆퐸푆 Air-Conditioning Engineers BEopt Building Energy Optimization CondFD Conduction Finite Difference CTF Conduction Transfer Function CV(RMSE) Coefficient of Variance of Root Mean Square Error DHFMA Dynamic Heat Flux Meter Apparatus DSC Differential Scanning Calorimetry dw Drywall EMS Energy Management System Energy use in the current year k FC Forced Convection 퐸푈푘 HAMT Heat and Mass Transfer HFT Heat Flux Transducers HFM Heat Flux Meter IEA International Energy Agency IBP Institute for Building Physics IECC International Energy Conservation Code InfiniteRTM PCM manufacturer LH Latent Heat NC Natural Convection NET Natural Exposure Test

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NMBE Normalized Mean Biased Error NTNU Norwegian University of Science and Technology ORNL Oak Ridge National Laboratory OSB Oriented Strand Board Out Opening of the mixing valve (%) PCM Phase Change Material pcm Phase Change Material PW Present Worth Pv Actual Temperature (˚F) RMSE Root Mean Square Error Sp Setpoint Temperature (˚F) TARP Thermal Analysis Research Program Total cost within the year k

푇퐶푂푆푇Td(S)푦푒푎푟=푘 Derivative Time TES Thermal Energy Storage Ti(S) Integrator Time TMY3 Typical Meteorological Year 3rd update TOU Time of Use USD United States Dollar WUFI "Wärme Und Feuchtetransport Instationär" ("Transient Heat and Moisture Transport"). Greek letters α Thermal diffusivity ρ Density

λcav, λpcm Area ratios for cavity path and pcm path Ԑ Emissivity Porosity

휙

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CHAPTER 1 INTRODUCTION

Buildings account for about 40% of the global energy consumption and contribute over

30% of the CO2 emissions and a considerable proportion of this energy is used for thermal comfort in buildings [1]. In the United States, buildings use about 41% of primary energy (manual electricity from nuclear, hydro, wind and geothermal sources). This energy consumption contributes to the peak energy demand and increases the need for more fossil fuel based peaking power plants [2]. Climate change, which in part is the result of increased energy related greenhouse gas (GHG) emissions, mostly from fossil fuels, has become a major environmental issue worldwide [3]. United Nations Environmental Program (UNEP) reports on the contribution that buildings have on energy use and greenhouse gas emissions [4].

Peak electricity energy demand consists of several elements such as energy demand for industrial operations, energy demand of electric appliances including lighting and energy demand for space conditioning. In the research discussed here, the main focus is energy demanded for space conditioning i.e. heating and cooling of living spaces. In USA, around 32 % of the building energy in the commercial sector is consumed for space conditioning, and 53.1% for space conditioning in residential sector [5]. Air conditioning is an important component of this consumption, as more than 95% of the space cooling is generated using site electricity therefore increasing the electricity demand significantly during the peak. During the summer the building cooling related non coincident peak demand can be as high as 50%.

There are different strategies to reduce peak building power demand and overall reduction of building space conditioning energy such as: on site generation [6], smart controls [7] and distributed energy storage [8]. Many studies have been conducted in incorporating renewable energy sources through demand response (DR) and smart grid strategies as discussed by Aghaei and Alizadeh [9]. Sun et al. [10] defines and compares different conclude that PCMs require sophisticated control strategies to achieve maximum cost saving.

Nowadays, there are several advanced TES systems integrated into the building envelope. These materials need to store and release energy within desired time periods for demand response purposes. However, this requires adequate design and controls to optimal dispatch. The application of PCMs in building applications depends on the ability to accurately predict the heat transfer characteristics of the improved envelope. Therefore, PCM modeling techniques have become a critical component within the building energy modeling platforms and it is the focus on this Thesis.

Al-Saadi and Zhai [11] in their review of PCM modeling techniques, show many modeling approaches that attempt to recognize the PCM behavior in building envelope applications. However, these models fail to capture advanced thermal characteristics of PCMs that contribute to successful predictions of PCM included building envelope heat transfer. Therefore, the overall goals of the proposed research is to: (1) identify important variables and find optimal PCM properties (2) test different PCMs encapsulation types (3) develop, verify, and validate a heat transfer PCM model that can simulate different PCMs applications in the building envelope. This is done through investigation and comparison of different whole building energy modeling software that can model PCMs, experimental investigations using a state-of-the art experimental chamber, development of a numerical model which includes a numerical solution to represent advanced thermal behaviors of PCM like hysteresis and sub-cooling observed in PCM applications.

The overall objectives of this research are to, i. Identify important variables and find optimal PCM properties for building envelope applications. ii. Develop a numerical model which utilizes effective numerical techniques to solve a building envelope assembly with PCM inclusions. iii. Design and build experimental apparatus inside controlled environment to test different PCMs. iv. Conduct laboratory research to validate the numerical model and identify PCMs characteristics that could further improve the numerical solution. v. Verify and validate different PCM models in software like EnergyPlus and WUFI.

The following steps summarize the technical approach of the proposed project:

I. Parametric analysis of a residential building with phase change material (PCM)- enhanced drywall, precooling, and variable electric rates in a hot and dry climate to investigate potential cost savings and energy savings for the consumer.

II. Verification and validation of different PCM models available in whole building energy models such as, EnergyPlus, ESP-r, MATLAB (Thesis model), and WUFI.

III. Laboratory experiments to test different PCMs and develop data to validate the building envelope studies.

This thesis is divided in the following chapters:

 Chapter 2 reviews the characteristics and thermo-physical properties of PCMs to gain knowledge on thermal characteristics and influence of properties associated with phase change phenomena. This chapter also highlights the significance of the PCMs and lays a background on why further research is required.

 Chapter 3 evaluates the existing analytical solutions and numerical modeling techniques used to model PCMs in building applications. The analysis of numerical studies includes, methods used to capture the thermal characteristics, grid considerations for numerical PCM models, and properties of existing numerical PCM models. The most suitable numerical techniques for the current research are established using this evaluation.

 Chapter 4 looks into current state of experimental studies which uses the PCM types used in the experimental and numerical analysis in different scales of experiments. It also discusses the PCM characterization methods.

 Chapter 5 conducts a parametric study using an existing whole building energy modeling platform to identify the optimum PCM properties to shift and reduce peak cooling power demand with pre-cooling, ToU electricity rates, and different convection modes. Mr. Matthew Brandt at Colorado School of Mines has contributed to the research discussed in this chapter to construct EnergyPlus input files used in the parametric analysis. This work has been published in the journal of Applied Energy [12].

 Chapter 6 describes the multilayer building envelope algorithm and also discusses the experimental facility located at the Department of Mechanical Engineering of Colorado School of Mines which facilitates system scale experiments of wall assemblies.

 Chapter 7 conducts validation study using data obtained from laboratory studies and field experiments. Data for the validation study on shape-stabilized PCMs is granted from Norwegian University of Science and Technology (NTNU) [13]. The experimental data for the validation studies on Nano-PCMs comes from the Oak Ridge National Laboratory [14]. Dr. Kaushik Biswas provided latent heat curve for the analyzed PCM hydrate salts using Dynamic Heat Flux Meter Apparatus (DHFMA) method and also developed a 2D model of a wood stud wall with the Nano-PCMs and the 1D model for shape-stabilized PCM wall in COMSOL used in chapter 7. ESP-r simulations presented in this thesis were done by Dr. Dariuz Heim from Lodz University of Technology in Poland.

 Chapter 8 conducts a validation study using in-house experiments of two macroencapsulated PCMs in full-scale. These experimental are conducted at the environmental chamber discussed in the chapter 8. It also introduces 5 simplified techniques to calculate heat transfer through pouched PCMs.

 Finally, chapter 9 discusses the summary of significant results and the future research based on this work.

Chapters 5, 7 and 8 include the introduction, methodology, results, and conclusions of each step.

CHAPTER 2 BACKGROUND AND SIGNIFICANCE

PCMs can store energy in two forms, latent heat and sensible heat. The magnitude and the rate of latent heat absorbed and released depends on material properties [15]. Therefore, the advantage of using PCMs lies in the amount of latent heat a small amount of PCM can store under different storage techniques compared to that in a sensible heat storage material of the same volume. For an instance, a 25 mm thick PCM layer can hold same amount of energy as a 420 mm concrete wall as long as the PCM layer changes phase [11]. Therefore, PCMs can shift peak time periods based on the latent heat capacity, and other physical parameters related to the application of PCMs [10].

PCMs can also reduce or delay external fluctuations in temperatures, solar load, and heating or cooling needs. There are several modeling methods that are used to simulate the PCM behavior in building envelope applications [11, 16]. More detailed evaluation of available numerical models indicates both advantages and disadvantages of these modeling approaches [17]. The main concern highlighted in the above work is that these models fail to capture advanced thermal characteristics of PCMs which is essential for successful predictions of PCM included building envelope heat transfer. PCMs used in building applications deviate from the ideal behavior displaying these advanced thermal characteristics. One way of mitigating these behaviors is by reducing hysteresis effects, increasing latent capacity by increasing the density of the PCMs within the PCM product [18], improving conduction properties to increase the rate of heat storage and release [19, 20], chemical construction by including additives [21], and encapsulation methods like shape stabilization and microencapsulation [22, 23]. However, it is important to note that these methods should be employed without increasing the building mass because the current construction market prefer lightweight structures while improving the energy usage characteristics within the structure (wallboard types instead of masonry or concrete).

Heat transfer through many PCMs is complex because of the nonlinear behavior of thermal characteristics. Kosny [15] explains how the solid phase and the liquid phase of a PCM has

5 different thermo-physical characteristics while they co-exist within the enclosure. Enclosure/encapsulation is how the PCM is packed in the particular application. During the phase transition of the PCMs, the liquid state and the solid state are separated by a moving interface. Considering the basic physics, the energy and mass balances should be satisfied in either side of this moving boundary which makes it difficult to model. Either side of this moving boundary is also called two phase/ “mushy” region. The enthalpy change which occurs across this region is quite complex and dependent upon the material properties of the PCMs such as the latent heat, expansion coefficient, melting range and rate of heat transfer [17].

Latent heat of the PCMs defines the heat storage capability of the PCMs. When compared with other building envelope materials like stone, wood, brick and gypsum, PCMs present more attractive thermal storage characteristics. To indicate the importance of the latent heat, Zhang et al. [24] discuss how in order to keep the indoor air in the comfort range for a longer period without heating or cooling load, the heat of fusion of a PCM should be high enough to keep the inner surface of the wall at the melting temperature. This refers to having high latent heat next to the inner surface of the wall so the PCM are not fully melted nor frozen. Furthermore, the latent heat capacity of the material determines the weight/volume fraction of the PCMs required for the optimum performance of the building envelope.

Melting temperature of the PCM is another important property. Melting temperature is usually selected to fall within the comfort range of the occupants and are researched in the existing standards [25]. The exact value of the optimum melting temperature required depends on the building, climate, and the application [24]. Furthermore, a study of a PCM wall in a passive solar house indicates that heat storage occurs with a melting temperature of 1-3 ˚C above the average room temperature [26]. This section discusses these attractive characteristics of PCM in detail.

2.1. Phenomena of Phase Change of PCMs

Generally, phase change/ phase transition happens from solid to solid, solid to liquid, from solid to air, liquid to vapor and even solid to solid (restructuring of bonds at atomic level). In building applications mostly Solid-Liquid [27, 28], and Solid-Solid phase change [29, 30] is used. The material can be a pure substance, eutectic mixture, or non-eutectic mixture. Eutectic mixtures

6 change the phase at a constant temperature but, non-eutectic mixtures change the phase during a temperature interval.

PCMs used in real world applications are not usually pure substances and therefore, temperature interval in which the phase change becomes an important factor [31]. This temperature interval is called the melting range. Kuznik et al. [27] review the phase change process in a multi component mixture of PCMs in great detail. This study indicates that behavior of the system becomes more complex with the presence of multiple melting points from eutectic to non-eutectic mixtures.

Using the phase change behavior, PCM-enhanced building envelopes gain the ability to manipulate the thermal response. They can delay the effects of external thermal excitations reaching the interior of the building [15]. At a warmer exterior weather the interior is kept cooler and at cooler exterior weather the interior is kept relatively warmer. A high thermal conductivity is not required for these applications because the design expectations of the thermal system are peak load reduction and time shift of thermal response. But, there can be other building applications where the enhanced envelope is required to absorb and release heat faster. When fast absorption and release of latent heat is required, PCM properties need to be enhanced. Kosny [15] highlights that, most of the applications seem to use low conductive organic PCMs. Due to thermal comfort considerations the operating temperature of these PCMs are low. Kosny [15] further suggests switching from organic PCMs inorganic PCMs that have 4-5 times higher thermal conductivities would be advisable. This research therefore investigates hydrate-salt inorganic PCMs and is discussed in the later sections.

It is evident that the exact thermal performances expected need to be achieved by carefully managing the contributing characteristics. Parametric and optimization studies help determine these optimum combination of characteristics and properties.

2.2. PCM encapsulation methods

Encapsulation contains the PCM inside a coating or shell material to hold the PCM and to keep it separated from the surrounding material. Separation of PCMs helps to monitor the composition of liquid/solid phases as well as avoids reactions with surroundings. The encapsulation method,

 Offer corrosion resistance, thermal stability, strength, and flexibility.

 Offer an adequate heat transfer surface.

Ensure structural stability and offer easy handling.

Encapsulation methods may change with the PCM based on the chemical characteristics. PCM applications in building envelope commonly uses shape stabilization, nano/microencapsulation, and macroencapsulation [32]:

• Shape stabilization: Shape-stabilized PCMs (also referred to as ss-PCMs), are prepared by impregnating the PCMs within a supporting material. The PCM takes the form or the shape of the enclosure. They can be composites and microencapsulated [33]. Shape-stabilized PCMs are also available in larger areas like thin sheets/plates [34-36]. • Microencapsulation: Microencapsulation is a type of shape-stabilization. It is generally a polymer/inorganic shell [37], having a diameter in the range of 1μm–1000μm. Microencapsulation assists adding organic PCMs safely in to the building envelope layers. Micro-PCMs have a core-shell structure that can prevent the interior PCMs from leaking during its solid–liquid phase change procedure. Qiu et al. [38] indicates the ability to withstand volume change during phase transition and significant increase of heat transfer area as featured advantages of microencapsulated PCMs. Improvements in heat transfer results from the latent heat absorption by the PCM in the suspended MEPCM (Micro Encapsulated Phase Change Material) particles during the melting process. Karkri al. [39] highlights the importance of microencapsulation in widening the scope of PCM applications for instance, by preventing leakage of molding paraffin during phase transition. Microencapsulated PCMs have been applied in concrete/mortar [40-42], wall boards, and gypsum plaster or implemented as sandwich panels or slabs [43]. Konuklu et al. [44] discusses the mechanical and thermal improvements in the material due to the addition of microencapsulated PCMs. Micro encapsulation can help increase the latent capacity of gypsum dry wall around 10 times [45]. However, microencapsulation is the more expensive than macroencapsulation and microencapsulation of salt hydrates is a difficult task due to their hydrophilic nature. Figure 2-1a shows a microencapsulated PCM embedded gypsum wallboard. Figure 2-1(c) shows the panel is used in the wall construction.

• Macroencapsulation: A common way of encapsulating the PCM in a spherical, tubular, cylindrical or rectangular container having milliliters to several liters of PCM and t serving directly as heat exchangers (usually 1-10 cm in size). Wei et al. [46] investigates several types of encapsulation shapes and indicate that, from the heat release point of view, spherical PCM capsules show the highest thermal performance. The skin of the container acts as a self – supporting structure isolating PCM from the surrounding environment. For building envelope applications, plastics (polyethylene [47], formed white poly-film and heavy-duty nylon [48]) films are commonly used as the container materials. Metallic encapsulates can increase the heat transfer due to the high conductivity. However, metal vessels are not suitable to encapsulate PCM hydrate-salts due to corrosion and degradation [49]. PCM leakage can be a challenge in macroencapsulation in pouches and to prevent that techniques like improved formed poly-film for encapsulation and mixing PCMs with thickening agents are used [50]. Macroencapsulation is the least complex encapsulation method due to simplicity of containers and the low production costs of the containers.

Figure 2-1a shows microencapsulated PCMs embedded in drywall. This drywall is available in 1.2m x 1.2 m (4ft x 4ft) PCM panels. Figure 2-1b shows the shape stabilized PCMs in thin aluminum foil. This product is further discussed in the validation study in chapter 7. Figure 2-1c shows the macroencapsulated BioPCM mats used in the experimental analysis of this research and described further in the chapter 8.

2.3. Thermal characteristics and properties of PCMs

Phase change phenomena and heat transfer characteristics discussed in the previous section is highly influenced by complex behavior observed in PCMs used in building applications. These characteristics are observed in experimental PCM studies and have presented problems in attempts to model PCMs. Therefore, this section looks into these complex characteristics.

“Mushy” region of Phase Change

Figure 2-2 shows the temperature-enthalpy curve of a Bio based PCM comprising of fatty acids, fatty alcohols, esters, emulsifiers, and thickening/ gelling agents. PCMs used in building applications are usually not pure substances and therefore indicate a melting temperature range. The red shaded area shows the melting temperature range of the material approximated by the author using the starting point and the end point of the melting. This temperature interval is also referred to as the “mushy” region of melting.

The total enthalpy difference during the phase change comprises of the sensible heat and the latent heat. The sensible heat calculation for each phase is defined in the equation 2-1. Tm,low is low bound of the melting temperature range and then Tm,high is the higher bound of the melting temperature range.

푞 = 푐푠,푃퐶푀훥푇, 푇 ≤ 푇푚,푙표푤 (2-1) 푐푠,푃퐶푀 + 푐푙,푃퐶푀 푞푠푒푛푠푖푏푙푒,푃퐶푀 = { 푞 = 훥푇, 푇푚,푙표푤 < 푇 < 푇푚,ℎ푖푔ℎ 2 푞 = 푐푙,푃퐶푀훥푇, 푇 ≥ 푇푚,ℎ푖푔ℎ Figure 2-3 shows the sensible heat and latent heat contributions to the enthalpy change during the melting process for the Bio-based PCM in Figure 2-2. The cream color shared enthalpy difference is the melting latent heat and green color shaded enthalpy difference is the sensible heat.

Figure 2-3 Sensible heat and latent heat in the enthalpy change during the melting process. Graph constructed based on the data provided by [14].

There are many complex thermal behaviors observed for PCMs within the “mushy” region and are discussed in the next sections.

Phase separation of the material

Phase separation of the material takes place within this “mushy” region of phase change. This phenomenon usually occurs when there is more than one constituent in the substance, which is common practice in commercial PCMs. Kosny [15] discusses how the melting/solidifying temperature of each component might also be influenced by the composition of each constituent of the mixture.

Subcooling/supercooling effect and Hysteresis

Hysteresis PCMs are categorized as real hysteresis and apparent hysteresis. Real hysteresis occurs due to material properties and apparent hysteresis is independent of the material properties. The most common form of real hysteresis is Subcooling. Many PCMs do not freeze at the melting temperature and start crystallization only after a temperature below the nominal melting temperature [31]. Solidification/ freezing of the PCM happens where the solid phase grows with the liquid layer at the interface. As the temperature decreases this interface should occur at a certain point. At the initiation, there is no or only a small solid particle. This solid particle is also called the nucleus. At the surface of the nucleus there occurs an instance where energy released by crystallization at the surface is lesser than that of surface energy gained. This energy flow barrier exists until the nucleus grow satisfactorily. If this nucleation is delayed to occur with the temperature decreases below the melting point the Subcooling occurs. Due to this the freezing curve indicates a delay in initiation of solidification. This is shown in the figures Figure 2-4a and Figure 2-4b by the blue line continuing towards the left showing decrease of temperature and again turning towards increasing temperature in the figures [31]. Subcooling is more visible in hydrate salts but can be reduced using additives [15]. A recent study by Li et al. [51] discusses the subcooling effects of PCMs and how the effect can vary with different additives.

Real hysteresis can occur as a result of slow latent heat release. Mehling and Cabeza [31] discusses the reason for the slow heat release being slow formation of the crystal lattice or diffusion processes are necessary to homogenize the sample. The temperature of the sample then drops below the cooling heating temperature. This is not observed in the melting process since the kinetics process occurs much faster [52]. These conditions can separate melting and freezing curve and is shown in Figure 2-4c.

Apparent hysteresis occurs due to non-isothermal conditions at measurement for the characterization. This can be caused by the heating rates used in the characterization in melting if high heating rates. If the heating rates are high thermal equilibrium of the specimen could not be reached and the melting curve could be pushed further right in the graph and fro freezing curve it could be pushed to further left. This could cause curves shown in Figure 2-4d. Careful calibration of the instrumentation can minimize the effects of the apparent hysteresis which occurs due to the instrumentation in methods of characterization. The magnitude of the separation of the curves can depend on the heating rates used, sample size used in the tests, and the data acquisition steps used. All four curves in Figure 2-4 shows effects of hysteresis while only Figure 2-4a and Figure 2-4b showing Subcooling effect.

There are several methods used to characterize PCM: Differential Scanning Calorimetry (DSC), Twin bath method, T-history, Dynamic Hot-Box method, Heat Flow Meter Apparatus (HFMA) methods are some of these tests. These are discussed in detail in chapter 4.

PCM Thermal conductivity

PCM thermal conductivity can differ between liquid and solid phases [55]. Low conductivity is typically undesirable and is observed in PCMs like Paraffins [15]. Thus, there are efforts to increase the thermal conductivity of PCMs using composites, graphite, aluminum powder, copper, and microencapsulation techniques [56-59] [15].

Thermal conductivity of PCMs also has an impact on the PCM characterization results. High temperature gradients created within the PCM samples due to low conductivity can cause inaccuracies in estimations of the heat storage capacity with respect to temperature when using PCM characterization methods.

PCM phase-change temperature range

Selection of a particular PCM depends on the application (envelope, HVAC), location inside the building envelope (exterior/interior, wall, ceiling, floor) and the geographical location (weather data) of the implementation. Because PCMs have a melting/freezing temperature range, many studies have optimized this temperature range for the particular application.

For: different PCM products [60], for different locations in the residential buildings [61], related to layer thicknesses [62], and PCM use in different climates/climate zone classifications [63, 64]. The objective of some of these optimizations are either, cooling/heating load reduction, energy savings, comfort, cost savings, or a combination of these objectives.

Once a suitable phase-change temperature and the phase-change temperature range is selected for the application, further selections can be carried out for other important properties like, conductivity, durability, melting and freezing behaviors, energy density (important factor when designing lightweight structures).

Figure 2-5 Melting enthalpy and melting temperature ( – for different PCMs, An important criterion in selecting PCMs for building envelope applications 푇푚)

2.4. Types of PCMs

Identifying suitable material and thermal characteristics of PCMs is a priority of this project. The first criteria to consider in selecting a material is the melting temperature range. Each selection must have a melting temperature range falling within the temperature variation of the environment they are used in. Several PCM types are explored in this section.

• Paraffinic organic PCMs

Organic PCMs are primarily categorized as paraffins and non-paraffins [65]. Organic PCMs crystallize with little or no subcooling [66]. Paraffins consist of chain n-alkanes. The crystallization of the –CH3 chain releases a high amount of latent heat [67]. However, Paraffins have low thermal conductivity, relatively high flammability, and might generate toxic smoke and fumes when wet burning [68]. Paraffin PCMs are studied in the validation study in chapter 7 of this thesis.

• Non-Paraffinic Bio-based organic PCMs

Non-Paraffinic organic PCMs include a highly diversified group of chemical compounds [15]. Unlike Paraffins, each of these bio-based compounds display their own unique physical characteristics. This category of PCMs include the largest collection of potential future PCMs. Bio-based PCMs are obtained from animal fat and vegetation such as beef tallow, lard, palm,

15 coconut, and soybean. The fatty acids, esters and fatty alcohols also belongs to non-paraffinic PCMs family has a wide range of properties as described by Tyagi and Buddhi [69] and therefore, fatty acids have high heat of fusion and also a reliable melting and solidifying behavior with no subcooling. Sugar acids are not useful in building envelope applications as they have high melting points in the range of 90-200 ˚C [15].

• Inorganic Phase Change Materials

Inorganic PCMs can be either salt hydrates or metallics [69]. Metallics have very high melting temperatures and therefore, are not suitable for building envelope applications. Salts however, have suitable melting ranges for building PCM applications with latent heat around 200 kJ/kg and a thermal conductivity around 0.5 W/m-K [15] [70]. Salt hydrates are alloys of inorganic salts and water combined to form crystalline solids and are non-toxic, non-flammable, and moderately corrosive properties, low environmental impact, and possibility of recycling is another advantage of inorganic PCMs [71]. However, inorganic PCMs undergo Subcooling during the solidification process and might exhibit phase segregation during transition irritancy, variable chemical stability, non-stability upon cycling [72]. Abhat [73] indicates that there instability upon cycling due the separation of water and salt can cause decrease latent heat with time.

• Eutectics and PCM Mixtures

Eutectic PCMs are a mixture of two or more chemical components that solidify simultaneously at a minimum freezing point and when melting, the components liquefy simultaneously [15, 74, 75]. Eutectics are known for their sharp melting temperature and high volumetric thermal storage density [71, 75]. Mixtures of fatty acids and fatty-acid esters have shown suitable thermal characteristics for building envelope applications [15]. Eutectic mixtures of capric acid and lauric acid applied in the wall-board applications are suitable for applications in the building envelopes [76]. The BiPCM PCM used in this research is an example of a PCM mixture of bio-based PCMs and used experimental analysis in chapter 3.

Analyzed PCMs

This study tests two PCM encapsulation types: macro and microencapsulated PCMs. Microencapsulated PCM are integrated in drywall and macroencapsulated PCM pouches comes

16 from two manufacturers. Table 2-1 lists the PCM products used in this research and they are of three brand types and acquired from ENRG BlanketTM, ThermalCORETM, and INSOLCORP.

Table 2-1 Properties of the PCM products used in the building envelope testing Manufacturer Product Types Encapsulation Peak melting Nominal trade name/s temperature latent heat ( capacity (kJ/kg) 푇푚) Phase Change BioPCM TM Organi Macro 23 ˚C/73˚F ~230 Energy c Solutions ThermalCORE Micronal® Organi Micro 23 ˚C/73 ˚F ~110 c INSOLCORP Infinite RTM Inorga Macro 23˚C/73 ˚F ~200 nic

• ThermalCORETM

National Gypsum was the first company to introduce the PCM-enhanced gypsum boards to the North American construction material market in 2009. ThermalCORETM PCM drywall has the same appearance as regular drywall using PCM with melting pint of 23 ºC. Table 2-2 shows the physical properties of the ThermalCORETM PCM product in detail.

Table 2-2 Physical properties of the National Gypsum ThermalCORE® gypsum board containing PCM Property Value

Specific heat 1.2 kJ/kg K Board density 800 kg/m3 Enthalpy of fusion of the PCM ~110 J/g Latent heat capacity (ΔH) 251 kJ/m2

• BioPCMTM

BioPCMTM is a macroencapsulated that transition from solid gel to a softened gel. The product is includes a mixture of fatty acids [77], fatty alcohols [78], esters [79], emulsifiers, and thickening/ gelling agents [80]. The exact fractions of the additives are not known. This PCM product is biodegradable and has a neutral carbon footprint [81]. Manufactures produces multiples melting temperatures and heat capacities: M27 (307kJ/m2), M51 (580 kJ/m2), and M91 (1033 kJ/m2) and the current research uses M51. Figure shows the how the PCM in pouches are observed once BioPCMs are heated to ~90 ºC.

Figure 2-6 Visualization of PCM packing in pouches once heated to a temperature of ~90 ˚C.

• Infinite RTM

Macroencapsulated PCM based on hydrate salts developed by Applied Innovation Group available from the melting temperatures between 18ºC-28ºC. This PCM is encapsulated in pouches in multilayer, heavy-duty nylon/PE foil [15].

All the PCM products discussed above are recommended for residential and industrial applications in building walls. The products are already implemented in real life applications in field studies.

CHAPTER 3 MODELING PCMS IN BUILDING ENVELOPE

Energy consumption estimation is highly important when designing sustainable and high efficiency buildings. Therefore, engineers, architects, and researchers seek robust, fast, and accurate whole building modeling techniques that can simulate state-of-the art technologies. Hence, this chapter looks into existing PCM modeling techniques and software.

Building energy modeling is conducted in district, building, and envelope scale. The current research focuses on the building scale, and the envelope scale heat transfer modeling. Figure 3-1 shows different scales of heat transfer modeling considered in this work and where PCM modeling algorithms apply.

3.1. Analytical Models

Stefan problem defines the temperature distribution u (x, t) that yields an explicit type solution for freezing/melting of a semi-infinite PCM- layer initially at a constant temperature in a homogenous phase, with a constant temperature at the surface [82]. The analytical solution for the case of heat transfer in a PCM in a 1-dimensional semi-infinite layer is used for our baseline verification purposes and has been used in previous research [83, 84]. Furthermore, recent studies discuss analytical solutions for solid-liquid phase transition of pure PCMs [85-87]. However, most PCMs do not demonstrate isothermal phase change process and the complex behavior of PCMs have led to more advanced analytical methods. Generally, analytical solutions have drawbacks when capturing dynamic behavior of PCMs with their complex thermal characteristics. For that reason, whole building energy modeling platforms use comprehensive numerical methods.

3.2. Numerical Models

Approximate numerical models constructed during last several decades use many mathematical methods to recognize PCM behavior. ANSYS Fluent, BSim, COMSOL, DeST, EnergyPlus, HEATING, IDA ICE, , PCMexpress, PowerDomus, RADCOOL, SUNREL, and WUFI are software are capable of modeling PCMs [15]. Among these software, EnergyPlus, ESP- r, and WUFI are considered in this study based on their popularity, key recent applications in literature, and the potential for future research. In addition, an additional model is developed in MATLAB some results are compared to a 2-Dimensional model in COMSOL. This section discusses how these methods are integrated to modeling PCMs and specifically in building applications.

Numerical models: Simulation methods

Heat Source Method

Heat source method splits the enthalpy in to sensible heat and latent heat. Latent heat portion is defined as the heat source [88]. This has been used for different PCM applications designed to take advantage of the off-peak electrical energy for space heating [89-91].

Heat capacity method

The heat capacity method describes the temperature change T(x, t) using the heat capacity cp(T). Within the temperature range of a phase transition, this method deals with heat capacity as a function of temperature. Heat capacity method has been used to evaluate phase change in liquid metals in recent studies [92, 93]. Most of the modelling algorithms using heat capacity method are built for 1D heat transfer studies [83]. A 3D study by Sa et al. [94] numerically compares two PCM-enhanced wallboards with heat capacity defined to vary with the temperature and a Gaussian-type equation and expresses the capacitance-temperature relationship. Heat capacity method shows low accuracy with high temperature gradients in the mushy region [95]. It is suggested in literature that application of heat capacity method in numerical solutions for real PCMs needs further evaluation. TRNSYS software uses heat capacity method to model PCMs in building applications.

Enthalpy Method

Eyres et al. [96] introduces enthalpy method, and uses this technique to demonstrate the variations of thermal properties with time (enthalpy change with time). The enthalpy method deals with a total amount of energy required during the phase-change. This includes both sensible and latent heat. It is one of the most commonly used fixed-domain methods for solving the moving boundary problem, Voller and Swaminathan [97] Studies a general implicit source based enthalpy model. The consistent linearization of the discretized source is a highlighted feature in this study. In using enthalpy method the conductivity and the density is considered to be temperature dependent. The key feature of the outcomes of the above studies is eliminating the need of accurately track the phase change boundary.

The enthalpy method used in this study includes subsets of both apparent heat capacity and source based methods. TRNSYS Type-241 [98], PCM Express – ESP-r [99], and EnergyPlus [100] utilizes different versions of the enthalpy method. These applications indicate the applicability of the enthalpy model to approximate PCM behavior. Günther et al. [101] discusses the ability of enthalpy method to correctly account for the subcooling effect.

Apparent heat capacity and combined methods

Apparent heat capacity method increases the heat capacity at the mushy region directly proportional to the latent heat and inversely proportional to the temperature difference. This method is also one of the extensively studied method alongside enthalpy method says Kuznik. et al. [55], but when the phase change happens without the mushy region, the solutions of this method may not be accurate as shown by Tenchev, R. and P. Purnell [102] or produces an error with large time steps [103, 104].

A recent study incorporates a similar enthalpy method implemented by Swaminathan, C. and V. Voller [105] where the PCM model is represented by a nonlinear source term in the governing equation [106]. Within the source term the authors take into account the liquid phase fraction and it is set to vary with the temperature. Therefore, this approach is called a quasi- enthalpy method. TRNSYS Type-204 and TRANSYS Type-260 uses effective heat capacity method [55].

Table 3-1 compares the analyzed methods in terms of how they solve transient heat transfer equation. Each of these methods are solved using different numerical solvers such as G-S (Gauss Seidel) or TDMA (Tri-Diagonal Matrix Algorithm) [17]. Equation 3-1 shows the generalized form of the heat equation. In summary, (i) heat source method: latent heat is treated as a source term (ii) heat capacity method: heat capacity term accounts for both sensible and latent heat (iii) enthalpy method: enthalpy term accounts for sensible and latent heat.

(3-1) ∂ϕ ∂ ∂ϕ A = (Γϕ ) + R ∂t ∂x ∂x Table 3-1 Coefficients of the mathematical formulation to capture the phase change effects in numerical models. Mathematical Values of the coefficients in the order as they appear in method the formulation

Heat source method T k ρ 휙 - ρL A 휙 Γ 휕푓푅푙 Heat capacity ρ 푎푣푔 T k 0 퐶 휕푡 method 퐴 Enthalpy method Ρ퐶 (푇) h k/ 0

퐶푃 22

Here,

퐶푎푣푔 = averaged heat capacity 퐶푃 = specific heat capacity 퐴 퐶 (푇) = heat capacity term as a function of temperature h = enthalpy ρ = density

푘 = thermal conductivity 푇 = temperature

퐿 = latent heat

푡 = time 휕푓푙 = liquid fraction gradient Numerical휕t Models: Grid and boundary considerations.

PCM modeling must solve the moving boundary problem because, in addition to the fixed boundaries which define the computational domain, there is a boundary across which the phase change takes place (the “mushy” region). Thermodynamic equilibrium conditions should be satisfied on this time dependent moving boundary. Literature looks into several grid methods for numerical solutions. There are three main methods: fixed grid method [105], front tracking method [107], and hybrid method [108]. Fixed grid method is commonly used in building envelope problems with PCMs due to the complex nature of implementing a moving grid method. The complexities of front tracking and moving mesh methods can lead to significantly increased computational time [11]. All PCM algorithms used in this research use fixed grid methods.

Numerical Models: Discrete forms and solution schemes

Finite element method, finite difference method and finite volume method are frequently used modeling formulations used in PCM modeling. Discrete forms used in literature when numerically modeling PCMs are shown in detail in Appendix A.

Numerical Models: In building energy modeling platforms

Building energy modeling programs include numerical solutions for building envelope with PCMs. However, most of these programs consider convenience over accuracy and therefore, make assumptions to simplify the algorithm when implemented in the models [17]. A PCM study which uses COMSOL to simulate PCMs and discusses how the 3D/2D models [109]. Several studies use in-house whole building energy models implementing numerical solutions for PCM inclusions which are verified with existing numerical solutions or validated with experimental data [103, 110, 111]. However, the commercial whole building energy modeling platforms are more comprehensive and are updated frequently with more effective PCM models. Therefore, the PCMs modeling algorithms require frequent validation.

Commercially available building simulation platforms are useful in evaluating annual energy simulations for PCM included building models [112]. The following software is among mostly referenced and have some type of PCM mod

 ESP-r: Tool developed by University of Strathclyde and commonly used in Europe that has couple of PCM models [113-115]. PCMs are introduced as special materials and defined as active building elements that have the ability to change their thermo-physical properties. Fallahi et al. [116] Proposes a numerical solution for ESP-r. The solution is based on a finite difference method. The program simulates and predicts temperature profiles and heat fluxes for different configurations of PCM inclusion. ESP-r is used by Kośny et al. [117] due to its built in ability to model PCM sub-cooling effect.  TRNSYS: Tool Developed by University of Wisconsin-Madison. Earlier TRNSYS models use enthalpy method and solved using explicit schemes [118, 119]. However, later TRNSYS models do not use enthalpy method and use heat capacity/ heat source methods [120]. Castellón, et al.[121] compares, but does not offer proper validation results. There are other TRNSYS PCM models for building wall PCM applications [55, 122]. Implements TRNSYS Type-1270 PCM model which assumes that the PCM undergoes its phase transition at a constant temperature and the specific heat capacity of the two phases are constant. TRNSYS Type-285 uses the boundary temperature concept through a massless dummy layer with a small resistance [16]. Validation is done in small scale tests [55].

 EnergyPlus: Tool developed by Department of Energy [123] that has a finite difference algorithm (CondFD) method coupled with an enthalpy temperature function to simulate PCM that has been verified and validated [100] [124, 125].  WUFI: Tool developed by the Fraunhofer IBP, Holzkirc.hen, Germany [126] presents numerical tools for modeling the heat and moisture transfer within building structures. WUFI, which in German stands for “Wärme und Feuchte instationär”. WUFI can perform coupled transient heat and moisture transport simulations user-defined time steps using Finite-volume method and is able to simulate PCMs as illustrated by previous studies [127-129].

Table 3-2 summarizes Latent heat methods, discretization and time integration computation methods used in this study with different PCM modelling software. PCM modeling modules used in whole building energy modeling software and studies which have added corrections to the existing methods and added techniques to address the complex PCM behaviors are shown in Appendix B. Based on this analysis we select the enthalpy method to model latent heat, finite difference method for discretization, and fully implicit method for time integral computations in the 1D heat transfer modelling algorithm to model building walls with PCM presented in this thesis. This heat transfer modelling algorithm is modeled using MATLAB modelling language.

Table 3-2 Latent heat methods, discretization and time integration computation methods used in this study with different PCM modelling software Software Latent heat method Discretization Time integration computations

COMSOL Enthalpy Finite element Implicit

ESP-r Effective heat capacity Finite volume Explicit

EnergyPlus Enthalpy Finite difference Implicit

TRNSYS Effective heat capacity Finite difference Implicit: Crank–Nicholson or Enthalpy /Finite element

WUFI Enthalpy Finite volume Implicit

CHAPTER 4 EXPERIMENTAL STUDIES ON PCM INCLUSION IN BUILDING ENVELOPE

Laboratory studies are used to characterize PCMs and to collect data for validating different numerical PCM models. This chapter discusses the literature of experimental PCM characterization, PCM inclusion methods, and the experimental methods to improve the numerical solutions.

4.1. Scale of experimental studies

PCM are characterized by thermal properties (density, thermal conductivity, specific heat) that might change in liquid phase and solid phase. Additional properties are latent heat and melting temperature Tm. Latent heat is typically represented by the temperature dependent enthalpy curve h(T). PCM calorimetric measurement are used to determine h(T) curve for PCMs. Kosny [15] indicates that theoretical and experimental analyses of building technologies is performed at three levels.

• Material scale • System scale • Whole building scale

Material scale occurs when only the PCMs performance is examined. System scale relates to are applications in exterior/interior wall, ceiling, and floor envelope assemblies. PCM characterization studies are conducted in material scale.

4.2. PCM characterization methods

PCM characterization methods quantify the phase melting and freezing enthalpy of PCMs as well as its melting and crystallization behaviour. The sample sizes used and the final output of the thermal property after processing the data from some commonly used methods are shown in Table 4-1. These methods are discussed in detail in the following section.

Table 4-1 PCM characterization methods for PCMs used in building envelope applications Method Sample size Thermo-physical (mass or area) Property output calculated

Differential Scanning Calorimetry (DSC) 0.5-100 mg [31] cp f(T)

T-history method 10-15 g [15] cp f(T)

Heat Flow Meter Apparatus (HFMA) 0.25 m × 0.25 m [130] h f(T)

Dynamic Hot Box Method 2.4 m × 2.4 m [15] h f(T)

Differential Scanning Calorimetry (DSC)

DSC is a standard tool for the measurement of latent heat of PCMs and, is widely used, accessible and versatile [131]. DSC detects difference in the thermal response that a reference and evaluated sample indicate when simultaneously subjected to a temperature program [132]. Outputs of the tests are calculations of thermo-physical properties like Cp(T), H(T), melting temperature

(Tm), freezing temperature (Tf).

There are two methods of DSC used in characterizing PCMs used in building applications, heat-flux DSC and power compensation DSC. Heat-flux DSC method is used in the data obtained for validation studies in this research. This apparatus is a heat-exchanging calorimeter where measurement of the heat flow rate between test sample and surroundings is conducted. Heart with the environment takes place via a well-defined heat conduction path with known thermal resistance.

This method measures the difference of temperature between the reference material and the PCM sample tested with equal heat input. The heat flux is measured indirectly in this method.

The test obtains cp(T) function of temperature. The enthalpy or the storage capacity Δh is then calculated by integration over temperature. This is shown in equation 4-1. The start point of integration is usually chosen by the researcher conducting the tests observing the output data.

(τ) d τ (4-1) T h(T) = ∫T0 cp

Here, the rate of heat-flux (dH/dt) is proportional the specific heat capacity (cp) of the sample. Therefore cp can be calculated via equation 4-2. Here the m is the mass of the sample.

(4-2)

1 푑퐻 푑푇 ℎ(푇) = ( ):( ): Furthermore, DSC tests are conducted푚 푑푡 in isothermal푑푡 step-testing mode, or dynamic ramp mode and discussed by Kosny [15]. Dynamic ramp mode is used for the data obtained in the current research.

DSC uses a small PCM sample size in the range of 10-100 mg. Lázaro et al. [132] highlight how the small sample size may not be a representative of the subcooling effects of the larger PCM storage. Another drawback of this method is the variation of the results with sample sizes tested under same heating rates as most PCMs have poor thermal conductivities. Therefore, in a large sample of PCM, the temperature gradients observed are steeper than that for a smaller sample tested with the same heating rate. There are studies that looks into using different experimental apparatus to minimize the inaccuracies observed in DSC measures [133]. However, many studies use DSC method to characterize PCMs used in wall assembly applications [134]. Therefore, a conventional measurement method with the use of DSC as specified in ASTM E793 Standard [135] is used by the manufacturers for the PCM products used in this study. The DSC characterization data used in the validation studies are obtained from the experimental studies conducted by Cao et al. [136] for the shape-stabilized PCM and conducted by Biswas et al.[14] for the Nano-PCM used in the chapter 7 of this research. For the shape-stabilized PCM heating rate of 0.05 ºC/min and for Nano-PCM heating rate of 1.0 ºC/min was used. DSC data is provided by the manufacturers for BioPCM (the heating rate was not available), and PCM hydrate-salts (1.0 ºC/min rate) [48] used in the validation studies in chapter 8 this research.

T-history method

T-history method records temperature changes of the specimen during the time of phase transition. The experimental device usually consists of the heating equipment that provides a constant temperature water bath to absorb heat from, or release heat to the test PCM samples.

Tested materials are placed in laboratory glass tubes. At least one glass test tube is filled with tested PCM, while a second one contains a reference material (distilled water is commonly used as a reference material). Temperature of the PCM) is suddenly exposed to an atmosphere whose temperature is T∞, the temperature versus time curve of the PCM, the T -history curve is then obtained. This method is mainly used to determine the PCM freezing point, specific heat, latent heat, thermal conductivity, and heat diffusion coefficient. More information about the T-history method and the improved T-history method approaches re found in the literature [31, 137, 138].

Advantages of this method can be listed as follows,

 Uses a simple experimental setup  Facilitates testing of larger samples than DSC  Measures heat of fusion, specific heat and thermal conductivity of several samples PCMs simultaneously  Accepts PCM hydrate-salts, paraffins and custom made PCM blends.  Facilitates exploration of new PCM types

However the uneven temperature distribution and temperature stratification across the material sample could still restrict the T-history method results [15].

Thermogravimetric analyses (TG)

Thermogravimetric analysis measures the thermal stability of PCM products [139]. This technique monitors the mass of a substance as a function of temperature or time as the sample specimen is subjected to a controlled temperature program in a controlled atmosphere. The TGA curve therefore, expresses time or temperature on the x-axis and weight or weight percent (%) in the y axis. Literature discusses this method in detail [15].

Dynamic Hot Box Method

Dynamic hot-box method facilitates the full scale building envelope experimental analysis. PCM characterization via Dynamic hot-box method is defined in ASTM C1363: hot-box apparatus to generate dynamic thermal characterization of full size building envelope assemblies [140]. Hot- box methods can be guarded hot-box method or calibrated hot-box. Guarded hot-box method is discussed here and used in generation of experimental data discussed in chapter 7.

The test apparatus of the hot–box method includes two compartments: box 1 and box 2. The test specimen is placed between the surfaces of the two boxes (vertical or horizontal apparatus is used) [15]. Box 2 is referred to as the Cold box or the climatic chamber and has cooling systems connected and additional with fans to provide the low temperature setpoint. During the testing, the temperature in the cold box is kept at a constant value. The Hot box (Box 1) includes a metering box and a thermal guard. Main test chamber of the hot side is the metering box. This chamber is also equipped with heaters and fans. Measures are taken to maintain the temperatures of the metering box above a defined temperature. Additional electrical heater provides heating power to heat up the chamber beyond the controlled value.

The thermal guard surrounds the metering box and the temperature in the thermal guard is also controlled by the heating elements. This guard is applied to no or limited heat flux occurs from the metering box towards the thermal guard. Therefore, the heat generated within the metering box is made sure to flow through the test specimen. Hot-box measurements can be used to measure the thermal performance of opaque and transparent building envelope elements (walls, roofs, and windows). Specimen sizes can be ~ 2.4 m x 2.4 m in size. This method is used to measure either U-value (the overall heat transfer through the tested structure) or the thermal resistance to heat flux within the structure. Kosny et al. [141] uses the heat flows measured on the PCM and non-PCM sides of the wood-framed test wall of dynamic hot-box testing to evaluate the performance of the PCMs.

Heat Flow Meter Apparatus (HFMA) methods

Kosny et al. [142] introduces this HFMA test method. This test is done utilizing temperature and heat flux instrumentation. There are commercial HFMA apparatus available in the market today. Conventional HFMA instrument measures temperature and heat flux at a specified time interval, and uses the data to determine steady state and thermal transmission properties of a test specimen. ASTM C518 Standard Test Method for Steady-State Thermal Transmission Properties specifications are used in this test method. This method is further discussed in recent studies by Kośny et al. [143].

DHFMA method uses similar step-method as in DSC that can be applied to larger scale specimens (~0.25 m x 0.25 m). DHFMA uses the HFMA instruments for its measurements. The apparatus consists of two isothermal plates with heat-flux transducers (one or more) attached to

30 each plate. The plate temperatures are controlled by using electric heating elements and water based chillers. The top and bottom plates are set to different temperatures to apply a temperature gradient on the sample. Then, the temperature of a PCM included specimen is changed by a small step. The resulting heat flow in or out of the specimen is measured during this process. The heat capacity of the specimen is then determined at the mean temperature. This is described in the equation 4-3. Here, Cp is heat capacity, H is enthalpy, T is temperature, Q is the heat flow out or heat flow in from the specimen. This method assumes a linear relationship between enthalpy and temperature for small temperature increments used.

(4-3)

푑퐻 ∆퐻 ∆푄 퐶푝 = ≈ = 푑푇 ∆푇 ∆푇 To describe the apparatus, there is a heat flow sensor on each of the upper and lower isothermal plates. The specimen is placed between these plates. The sides are designed to be adiabatic. The upper and lower isothermal plate assemblies are kept at the same temperature to impose a uniform temperature across the specimen. Following this, a temperature change is then introduced on both plates. Heat flows through the plates are measured until equilibrium is reached. Equilibrium is assumed when the heat flow values become negligible. The enthalpy per unit surface area for each step temperature change of the specimen is calculated by integrating the heat flow rate measurements over time. This data is used to construct the temperature-enthalpy curve for the PCM specimen tested.

The characterization data used for PCM salt-hydrates in the validation study of macroencapsulated PCMs in this research uses DHFMA characterization data and is measured and processed by Dr. Kaushik Biswas at the Oak Ridge National Laboratory. Enthalpy (kJ/kg)- Temperature (ºC) data gathered in ~1 ºC intervals are provided for the analysis in current research. Biswas et al. [144] states that HFMA instruments have poor accuracy for temperature steps smaller than 1ºC. Detailed experimental approach of this characterization method is described by Shukla and Kosny [145].

Other methods

In addition to above characterization methods, DSC Step-Testing method and DSC Dynamic Ramp Mode [146], Differential Thermal Analysis (DTA) [147] are some methods that have been used to characterize PCMs in material scale. These methods are mostly examines to improve the results of DSC method.

There are some studies which compare different characterization methods. A recent study compares DSC and improved DHFMA methods and concludes that at very low heating rates for DSC method both methods showed same sub-cooling effects therefore, indicating that DHFMA method is effective to test PCM wallboards [148].

4.3. Experimental studies on macroencapsulated and microencapsulated PCMs

This research focuses on the use of PCMs in the whole building scale and system scale applications. System scale tests are conducted in test huts designed to conduct field studies, envelope of existing buildings, or specialized chambers constructed for the testing of wall assemblies.

PCM wall assemblies are tested in dynamic hot-box apparatus to examine shape-stabilized PCM behind drywall to gather experimental data to investigate the impact of PCMs in reducing temperature fluctuation [136]. PCM-enhanced foams are tested at the Oak Ridge National Laboratory using a hot-box apparatus [15]. Same facility is used to test wood-framed wall containing blown PCM-enhanced fiberglass insulation [149].

Test cubicles are used to examine macro encapsulated PCMs in free-floating conditions in a recent study with the PCM containers are attached to polyurethane foam wall [150]. System scale tests are conducted at Oak Ridge National Laboratory to analyze Nano-PCMs and a wall of existing building was used to construct the experimental apparatus [14]. Wall structures are made of OSB, cellulose insulation in addition to the Nano-PCM embedded gypsum and the heat transfer study using this assembly is used to gather data for validation purposes. Kosny et al. [151] tested a retrofit strategy for masonry walls using inorganic PCM-enhanced foam insulation using the walls and roof of an existing building. Another study conducted field testing of walls side-by-side to evaluate Phase Change Frame Wall (PCFW)s and examined lower peak heat transfer rates across the walls and gathered data for validation purposes [152]. Muruganantham et al. [153] tested

32 macroencapsulated PCM pouches arrays covering the ceiling to investigate cooling load reductions of the interior environment. Allqallaf et al. [154] tested a concrete slab with vertical cylindrical holes to examine the effect of the geometry of macroencapsulation for PCM use in roofs.

Whole building scale tests apply PCMs in multiple components like exterior/interior walls, slabs, ceilings, and floors. An 82-m2 single-family home is used in a study at the university campus in Nottingham, England to implement PCM wallboards with microencapsulated PCM. A commercial building at Charles Sturt University (CSU) located in New South Wales, Victoria, Australia is used to implement microencapsulated PCM in floors and ceilings. This building has 880-m2 floor area and was constructed using lightweight steel framing technology [15]. A two story PCM house is constructed at Oak Ridge National Laboratory [155]. This construction had a with total floor area of 253-m2. Then floor of this house is insulated with 10.2-cm-thick layer of PCM-enhanced cellulose insulation and 9 cm of PCM-enhanced cellulose insulation is installed on the attic gable walls. Furthermore, A 20 % by weight of microencapsulated bio-based PCM is also added to blown cellulose fibers in the exterior framed cavity of this house enabling a whole building PCM application. All the above whole building level studies are used to assess the impact of PCMs on the interior temperature profiles and heat transfer across the envelope.

To date, there has not been a study that investigates multiple wall panels in parallel in a controlled environment. The experimental facility discussed in this study facilitates experimental investigation multiple wall panels with PCMs.

CHAPTER 5 PARAMETRIC ANALYSIS OF A RESIDENTIAL BUILDING WITH PHASE CHANGE MATERIAL (PCM)-ENHANCED DRYWALL, PRE-COOLING, AND VARIABLE ELECTRIC RATES IN A HOT AND DRY CLIMATE

This section contributes to the fulfillment of the following objectives of this research: (i) identify important variables and find optimal PCM properties for building envelope applications. This study was published in the journal of Applied Energy, 15 July 2018: 497-514 [12].

Buildings account for about 75% of U.S. electricity consumption and 40% of total U.S. energy consumption [156]. Nearly 15% of U.S. electricity use comes from building cooling systems, and it can be as high as 50% in summer when considering non-coincident peak demand [157]. Peak loads can cause difficulties for electric companies because the power generation capacity must be equal to peak demand [158], which may result in electric companies significantly increasing their production rates during peak hours. Shifting demand away from peak hours (i.e., reducing the total peak demand) is therefore a viable solution for utilities as well as building owners. Therefore, many potential technologies, such as batteries and thermal storage, are being considered to help reduce peak demand and also improve thermal comfort [159-161].

Building thermal storage has the potential to rely on the innate building mass; however, U.S. homes typically have low thermal mass [162, 163], thus one option is to use phase change materials (PCMs) to increase homes’ thermal mass. PCMs may be combined with precooling, where smart programmable thermostats cool the house during off-peak time and increase the set point at peak time [164-167]. Although the overall benefits of PCMs and precooling are well known from several decades of research [69, 168-170], few studies examine the process of optimizing various PCM properties and concentrations with specific precooling strategies.

Previous PCM studies have analyzed different applications, encapsulation techniques, and locations within buildings. The location of PCMs in buildings varies widely in the literature, including micro- and macro-encapsulation in or behind drywall [69, 171-176], concrete [177, 178], fiber insulation [141, 179], or other systems, such as hot water systems, floor heating systems [25,

69, 180] and storage tanks [181, 182]. Wallboard applications have been studied extensively [69, 168-170, 183-185]. Early studies focused primarily on drywall impregnated with PCMs [186, 187] and later on micro- and macro-encapsulation of PCMs [172, 173, 185]. Studies indicate that PCM- enhanced drywall can improve thermal comfort by reducing thermal stratification due to natural convective air mixing [184], and can help mitigate effects of extreme events like heat waves [188].

PCM performance in different applications heavily depends on proper PCM selection based on their properties: melting temperature, melting temperature range, latent heat, thermal conductivity, and others. However, few studies have looked into different combinations of PCM inclusion [189-195]; some optimized the PCM thickness [196] or examined the effects of PCMs on interior partition walls [183], ceilings, and exterior walls [197]. Others looked at increasing heat transfer between the indoor environment and the walls [198, 199] or explored the optimum PCM melting temperature in different cities [200] according to the outdoor boundary conditions, which showed that the use of passive PCM systems in the building envelope with optimized peak melting temperature for each climate zone can yield energy savings [201]. However, no study has analyzed synergies between PCMs with programmable thermostats and variable electric rates (Time-Of-Use Rates or TOU), as precooling has been used previously to reduce peak demand.

When PCMs are embedded in the drywall or behind the drywall, effective heat transfer depends on several parameters, one of which is the convection heat transfer between the indoor air and the interior wall surfaces. Under regular indoor conditions, natural convection is present, resulting in low heat transfer coefficients between the indoor air and inside wall surfaces of the building envelope (1-6 W/m2-K). A couple of studies suggest that natural convection cannot adequately transfer heat towards the envelope to store a high amount of thermal energy in the PCM wallboard [198, 202]. Thus, this study addresses the current gaps on PCM performance when combined with precooling in a home subjected to TOU pricing and with a variable set point. It also addresses the gaps on the role convection has on PCM performance by focusing on optimizing PCM embedded in drywall using parametric analysis. The contributions of this study are: (1) to analyze the impact indoor natural and forced convection have on the effectiveness to reduce peak demand in a home with a precooling schedule with and without PCMs and (2) to inform engineers, architects, and PCM’s manufacturers about the optimal PCM properties used when PCMs are embedded in drywall. No previous study has analyzed this important issue in residential buildings.

In addition, one interest in this study is to look further than annualized energy related costs and investigate the cooling related costs.

5.1. Approach

This study uses Building Energy Optimization (BEopt) Version 2.3 and EnergyPlus Version 8.1 to perform all energy and cost analysis associated in the parametric analysis. BEopt performs annual building energy simulations using EnergyPlus as the background simulation engine. BEopt can perform parametric or optimization analyses based on monetary savings, energy savings, or a combination of both using a sequential search optimization technique to find different energy packages [203]. BEopt optimization algorithm identifies the least-cost approach to achieve minimal whole-house energy use involving different combinations of discrete residential system equipment and material options. BEopt can find intermediate optimal points all along the least- cost curve minimum-cost building designs at different target energy savings levels [203]. However, BEopt’s sequential optimization algorithm has the objective function to minimize energy use and the optimization mode only keeps the most cost effective points and few near optimum points which eliminates the combinations that are required to the next stage of the study. Therefore, all cases are evaluated using parametric analysis, where every single combination is analyzed, allowing us to study how all the different PCM combinations (cost, location, and PCM concentration) perform. After analysis of the entire results, subsequent post-processing finds optimal solutions, as the study focuses on the cases with lowest energy cost and perform hourly comparisons.

EnergyPlus is a whole building energy simulation program, which uses an integrated, simultaneous solution approach to solve for different heat transfers processed in and out of the built environment. Both BEopt and EnergyPlus have been validated for residential peak reduction using the building envelope and electric bill calibration [204-206]. The default conduction heat transfer algorithm in EnergyPlus is Conduction Transfer Function (CTF). This method is efficient because it calculates the current surface temperature and heat fluxes with a limited number of previous surface temperatures and fluxes [207]. However, BEopt uses a hybrid approach in PCM modeling: SurfaceProperty:HeatTransferAlgorithm. Any construction assembly with PCMs is modeled with the conduction finite difference (CondFD) algorithm while all others surfaces use

CTF to reduce simulation runtime. Both algorithms have been verified or validated previously and used in different PCM studies [208, 209].

Building Description

The analyzed house represents a relatively new home located in Phoenix, Arizona, USA. The view of the house and the neighboring buildings are shown in the Figure 5-1. Phoenix is located in climate region Hot-Dry (2B), according to Building America [210]; IECC Zone 2 in [211]; and BWk (Arid, desert hot arid) according to the Köppen-Geiger climate classification [212]. This study uses typical meteorological year (TMY3) weather data for Phoenix. The house has a conditioned area of 231 m2, a garage, slab-on-grade, and an unconditioned attic [213]. It follows the 2014 House Simulation Protocols [214], except for: a variable cooling set point schedule (compared with the prescribed flat setpoint of 24.4 °C); more frequent natural ventilation, when weather allows it; and drywall with micro-encapsulated PCMs.

Figure 5-1 View of the simulated house, orientation and, and its neighboring buildings.

The parametric analysis uses a project analysis period of 30 years and 3% inflation rate. Electric rates are defined by the Salt River Project E-21 Super Peak Time-Of-Use (TOU) Rates with a fixed service cost of USD 17/month and electric rates shown in Table 5-1. Other energy

37 costs, such as natural gas, oil, and propane use state averages. Table 5-1 indicates peak rates are about 4 times higher than off-peak during the summer and about 60% higher in winter. Thus, this study only uses precooling from May to October. Using these rates, the baseline home has an annual cooling energy cost of about USD 480.

Table 5-1 Annualized TOU rate, E-21 Super Peak TOU Rate [215]. Peak Rate Regular Rate Months (3:00 6:00 P.M.) (USD/kWh) – (USD/kWh) Jan-April 0.075 0.123 May-June 0.082 0.297 July-Aug 0.084 0.350 Sept-Oct 0.082 0.297 Nov-Dec 0.075 0.123

• PCM Parametric Analysis

The goal of this study is to find the optimal PCMs that minimize cooling electricity energy costs for the analyzed home. The choice of PCM properties defined in BEopt are based on simplified latent heat profiles. Real PCMs generally have a non-linear enthalpy-temperature curve [216], and will have hysteresis and sub-cooling effects. In this study, simplifications include assuming a linear behavior during phase change and neglecting the effects of hysteresis and subcooling. Although the PCMs in this study do not reflect any PCM on the market, the simplified PCM model has similar characteristics to actual PCMs. For example, Figure 5-2 shows the latent heat curve of an existing PCM (BioPCMTM Q23) [217].

This particular PCM has a melting/freezing temperature around 23 ˚C. Table 5-2 also shows the linearized latent heat profiles used in this study with the same melting temperature of 23 ˚C. Each of the three ideal PCM curves represents properties of an ideal PCM with the same melting temperature and latent heat, but with a different melting temperature range. This approach simplifies the analysis and provides an appropriate approximation as validated in previous studies [213, 218].

Figure 5-2 Enthalpy curves showcasing 1) Real PCM data from BioPCMTM Q23º obtained from DSC test and 2) Ideal PCM curves with thermal properties similar to the real PCM.

The analyzed PCM properties are: (1) latent heat of PCM-enhanced drywall, (2) melting temperature, and (3) melting temperature range. Other drywall/PCM properties such as density, specific heat, thickness, and thermal conductivity are kept constant for all analyzed PCMs, based on previous work by the author [213]. For example, previous work shows increasing the thermal conductivity of the PMC-drywall did not affect the performance of the drywall, thus this study does not optimize thermal conductivity.

Table 5-2 provides a summary of all properties, and the number of properties considered for this study. Note that this study focuses on reduction of energy costs using PCM in drywall in three main locations in homes: exterior walls (walls exposed to the outdoor environment), partition walls (walls between zones), and ceilings. In all cases, the PCM-enhanced drywall is in direct contact with the indoor environment.

Table 5-2 Range of analyzed theoretical PCM properties and locations in parametric study. Number Property Values Analyzed Latent Heat of PCM embedded in 4 0, 23, 47, 70 drywall (kJ/kg) Melting Temperature (°C) 4 22.2, 23.3, 24.4, 25.5 Melting Temperature Range (°C) 3 1.11, 3.33, 5.55 Density (kg/m3) 1 801

Table 5-2 continued Specific Heat (kJ/kg-K) 1 0.837 Thickness (m) 1 0.0127 Thermal Conductivity (W/m-K) 1 0.157 Locations 3 Exterior Wall, Partition Walls Ceilings

Early analysis showed that using the actual current cost for micro-encapsulated PCMs produce no savings over a 30-year period, as the current PCM price is considerably high. Thus, this study uses a PCM-drywall cost of USD 1.76/ft2 or USD18.9/m2 (by comparison, the total cost of regular drywall is about USD 7.0/m2, on average). This price assumes the future price of PCMs will decrease as manufacturing technology improves with increased adoption. This estimation is based on the actual cost of paraffin wax (about USD 1.8 – 2.0/kg as raw materials), with an additional cost of ~50% for the micro-encapsulation process [219], labor, and future reductions due to manufacturing improvements. Therefore, this study uses a USD 2.0/kg rate for cost calculations. The analyzed PCM has a specific latent heat of 115 kJ/kg (pure PCM) with concentration varying from 20-60% that results in drywall with a latent heat of 23-70 kJ/kg (assuming a thickness of 0.0127 m). Although 60% PCMs by weight is unrealistic for commercialized products [124], a similar total latent heat for the drywall with concentrations lower than ~30% can be achieved with PCMs having a latent heat around 200 kJ/kg. Table 5-3 shows the specific latent heat of PCMs, cost by mass of PCMs, concentration by percent weight, resulting total latent heat, and total cost of the enhanced drywall (including installation costs).

Table 5-3 Specific Latent Heat and Costs of PCM Enhanced Drywall. Type of Drywall Normal PCM-Enhanced Specific Latent Heat of pure PCM (kJ/kg) -- 115 115 115 Cost of PCM (USD/kg) -- 2 2 2 Amount of PCM in Drywall (Weight %) 0 20 40 60 Total Latent Heat of PCM/Drywall (kJ/kg) 0 23 47 70 Total Latent Storage PCM/Drywall (kJ/m2) 0 237 473 710 Total Cost (USD/m2) 7.00 11.00 15.00 19.00

These multilayer envelope constructions used in the current study are shown in the Figure 5-3.

After adjusting for the PCM costs and PCM application options in the drywall the study seeks the most cost-effective PCM combination from the values shown in Table 5-2. Table 5-4 shows some of the economic assumptions used in the current 30-year parametric analysis.

Table 5-4 Economic factors used in the 30-year parametric analysis. Down Payment 4% Mortgage interest rate 5% Mortgage period 30 Project analysis period 30 Inflation rate 3% Discount rate (dr) 3% Marginal and Labor Costs 1 Multiplier Marginal Income Tax Rate Federal 28% Marginal Income Tax Rate State 0% Natural Gas USD 1.3314 /therm (Utility)

Precooling Strategy

Studies have explored the possibility of electric load shifting with precooling of both commercial and residential buildings [164, 220, 221] [222]. This study uses a cooling set point schedule based on previous work which concluded that precooling strategies for a new Phoenix home with PCMs require at least 5 hours of precooling [164, 223, 224]. Therefore, this study analyzes a set point schedule with five hours of precooling at 20 °C with different setback (or relaxation) temperatures: 24.4 °C (76 ºF), 25.5 °C (78 ºF), and 26.6 °C (80 º F). Cost savings are calculated based on a reference home using a constant set point (24.4 °C). Figure 5-4 indicates the precooling strategy with a setback temperature of 25.6 °C. The precooling and relaxation schedule is not used on weekends as most TOU rates apply only on weekdays (i.e., the home has a constant set point of 24.4 °C on weekends). The peach-shaded rectangle indicates peak hours, while the blue-shaded region is the precooling period. Recall that the annualized TOU rates are provided in Table 1.

Figure 5-4 Precooling strategy with 25.6 °C setback temperature. The peach-shaded rectangle indicates peak hours while the blue shaded-region indicates precooling.

Convection Heat Transfer

A previous study analyzing the same house showed that PCMs in the drywall cannot fully freeze after 5 hours of precooling. This is potentially due to weak heat transfer between the inside wall surface and the indoor air, with natural convection coefficients of about 1 - 6 W/m2-K [198, 213]. This study implements a forced convection mode with up to four ceiling fans in the living space operating during the entire period of precooling and peak hours (from 10 A.M. to 6 P.M.). The fans are implemented in EnergyPlus by adding (1) additional electric loads from each fan, (2) additional internal gains that represent the heat generated by the fan motors, and (3) by using a forced convection algorithm when the fans are on.

EnergyPlus has a natural and forced convection model, TARP and CeilingDiffuser, respectively. TARP is the default model. In this study, we implemented a schedule that turns the fan on/off at the appropriate time and switches the model to use convection coefficients from natural to forced convection in the same period. The CeilingDiffuser model deviates from the actual expected performance of a ceiling fan because the CeilingDiffuser model in EnergyPlus is defined using empirical studies which used diffuser types other than typical ceiling fans [225]. However, it is the closest built-in model we can use to interpolate for coefficient values for a fan- based forced convection regime.

The CeilingDiffuser convection model calculates the convection coefficients at walls, ceilings, and floors based on Air Changes per Hour (ACH) [226] and has actual room convection coefficients up to 20 times higher than natural convection coefficients [226, 227]. Thus, this study implements average values from these two models (CeilingDiffuser and TARP) as shown in Figure 5-5 which are similar to another study looking at forced convection [198]. These are implemented in EnergyPlus using a schedule and the SurfaceConvectionAlgortihm:Inside:UserCurve object. An assumption in this study is that ceiling fans would provide similar air mixing as the A/C system.

The studies indicate that radial ceiling diffusers used for the empirical studies in [225] are of practical importance with better mixing due to use of radial ceiling diffusers [228]. This study assumes the convection coefficients are constant for the forced convection condition during the fan operation. Here the combined TARP and CeilingDiffuser coefficient are referred to as forced convection. The study assumes that the convection coefficient is constant for the forced convection case.

Mechanical Ventilation and Fan Selection

The use of mechanical ventilation adds additional cooling electricity use which can potentially decrease the cost savings. Fan costs range from lower than USD 100/unit to USD 1,000/unit with an expected lifetime of 11 years. Fan electric energy use ranges from 2-100W in current products in demand. For example, Big Ass Fans has ultra-energy efficient fans [229] with power ratings between 2-30 W [230], [231]. Energy Star rated fans generally have power consumption range of 20-100 W with an average of 65 W [232]. Therefore, the parametric analysis uses a value of USD 400/unit and a default fan energy use of 25 W.

An ultra-energy efficient fan with 2 W electricity use is also included in the simulations to demonstrate the impact of fan efficiency in the performance of the PCMs. When on, the fan motors generate heat with a sensible radiant fraction of 0.7. Overall, the baseline home has the natural convection model (TARP) and no fans operating. The forced convection cases use the custom model described above, in which a natural convection model is used when the fans are off and a forced convection model is used when the fans are on; it also takes into account the thermal load added by the fan and motor electricity consumption.

5.2. Results and Discussion

Parametric analysis results

In total, more than 20,000 simulated homes are simulated in the parametric analysis and included in Figure 5-6. Close evaluation of Figure 5-6 indicates that sections with higher annualized energy related costs are formed due to the high percentage of PCMs included in the drywall. Since higher cost cases are undesirable for further evaluation, the next step of the parametric study only includes the 0 kJ/kg and 23 kJ/kg PCM drywall configurations and Figure 5-7 shows the values from this step Figure 5-7 shows the output from a subset of the total parametric results. Each point represents a simulated home with a combination of PCM properties. The y-axis shows the Annualized Energy Related Costs (AERC). The x-axis shows Average Source Energy Savings (ASES) considering default energy conversions from BEopt to compare site electric and gas savings [203]. Appendix 3 explains the costing procedure in detail.

Interestingly, there are three main clusters and two points that stand apart. The two points away from the clusters are (i) the reference case with no PCMs and no precooling and (ii) the case with precooling only and no PCM inclusions. The reference corresponds to the maximum AERC, while the case with precooling only has the highest energy use (lowest ASES).

In all cases, precooling decreases energy costs, but increases energy use (negative energy savings) as also shown in the literature [213]. The clustering of other points relates to the location of PCMs and the latent heat. Cases with 60% and 40% PCM inclusion still show high cost, thus are not shown in Figure 5-7. The lower cost points indicated above have a 20% PCM inclusion corresponding to an effective latent heat of 23 kJ/kg. PCMs included in the ceiling-only cases have a higher energy penalty and lower AERC. PCMs installed in all three locations (ceilings, exterior walls, interior walls) tend to have lower energy penalties but higher annualized energy related costs due to the greater quantity of PCMs in use (higher initial costs).

For each of these option classes (PCMs in all three locations, PCMs in two locations, PCMs in ceilings only), there is a case with the lowest annualized energy cost. For further analysis, these optimum points are considered in greater detail. Table 5-5 shows the optimal PCM properties for each case as indicated also in Figure 5-8, where the rest of the simulated homes are removed. One interest in this study is to look further than annualized energy related costs and investigate the cooling related costs.

The five selected cases are:

 Baseline: Includes no precooling and no PCMs  Precooling, no PCMs: Includes five-hour precooling strategy indicated in Figure 5-4 and no PCMs  Precooling, PCMs in ceilings only: Includes five-hour precooling strategy indicated in Figure 5-4 and PCMs only in the ceilings  Precooling, different PCMs: Includes five-hour precooling strategy indicated in Figure 5-4 and the most optimal PCMs of any properties in all three locations (exterior walls, internal walls, and ceilings)  Precooling, same PCM: Includes five-hour precooling strategy indicated in Figure 5-4 and a same type of PCM of one set of properties in all three locations (exterior walls, internal walls, and ceilings)

Table 5-5 shows the optimal PCM properties for each location selected from the parametric analysis. The same PCM types are observed as the optimum (lowest energy costs) under the two convection models. In all cases, the parametric study output selections show the lowest latent heat

(23 kJ/kg) to minimize the costs. This is mainly due to the ability to fully utilize the latent heat during the pre-cooling time interval.

Table 5-5 Optimal PCM properties for each location of application: Ceiling, external wall, partition wall Ceiling Melting Melting Latent temperature temperature Heat(kJ/ (ºC) range(ºC) kg) Ceiling 24.4 1.11 23 External Wall 25.5 1.11 23 Partition wall 22.2 5.55 23

Hourly Results

• Indoor Air Temperature

Figure 5-9 and Figure 5-10 show hourly temperature values for the exterior wall inside surface, ceiling inside surface, and indoor air temperature for the entire year with forced and natural convection, respectively. The PCM application depicted here is the case which has the most optimal PCMs of any properties in all three locations.

Figure 5-9 Annual variation of temperatures for the forced convection mode for PCMs optimized for all locations. 0 indicates the start of the month January and the time is shown for the calendar year of 12 months.

The cream-colored region represents the melting region of the PCM included in the ceiling and external walls selected as one of the optimal properties obtained from the parametric analysis. In all cases with forced convection, the inside surface and indoor air temperatures oscillate less and remain closer to the PCM melting range during the May-October period. All else being equal, the same case with the natural convection model shows significantly higher fluctuations of ceiling inside surface and exterior wall inside surface temperatures. This is an indication that the PCM is experiencing a more complete phase change with the forced convection model.

Figure 5-11 and Figure 5-12 focus on two arbitrary, typical summer days (July 21st and 22nd), showing the indoor air temperature for all the analyzed cases with forced and natural convection and a setback temperature (Tr) of 25.6 ºC during the peak hours. All cases with natural convection show the room air temperature rapidly reaching the setback set point as the PCMs do not store enough energy to meet the cooling demand during on-peak hours.

In contrast, all cases with PCM inclusions with forced convection show reduced indoor air temperature fluctuations, and the time required for the temperature to reach the setback temperature is delayed. This indicates that enhancing the convective heat transfer increases the

49 rate of heat exchange between the indoor air and the PCMs, thus effectively storing and releasing more thermal energy.

Figure 5-11 Average indoor air temperature within the living zone for forced convection model for all envelope types. Hour 0 represents midnight of the first day.

Figure 5-12 Average indoor air temperature for the natural convection model for all envelope types. Hour 0 represents midnight of the first day.

• Setpoint Setback (Tr)

Set point setback, or relaxation temperature, plays a role in reducing on-peak energy use. Figure 5-13 shows hourly results for indoor air temperature with three different setbacks—24.4 ˚C, 25.5 ˚C, and 26.7 ˚C—for the precooling only case. Figure 5-14 shows same setback temperatures used when PCMs are optimized for each location. When the temperature is relaxed to 24.4 ˚C all homes (even with PCMs) require additional cooling.

However, if the set point is increased to 25.5 ˚C the homes with PCMs optimized for each location can last the entire three-hour peak period without any cooling. This increase of relaxation temperature is acceptable assuming the ceiling fans will improve air motion, thus increasing the temperature range which is expected to be reasonably comfortable for the occupants.

• Average Drywall Temperature

The average drywall temperature is the average temperature of the two nodes that discretized the drywall at the interior living zone surface. Average drywall temperature analysis in this subsection is done for ceiling, external wall or partition wall. Figure 5-15 shows the average PCM-drywall temperature in an external wall for the case with PCMs included and optimized for all three locations (PCM optimized case), forced convection, and with the same three setback temperatures.

Although a setback of 24.4 ºC shows a closer fit to the PCM melting temperature range, it requires cooling during the peak time for all three PCM inclusion cases. Therefore, our analysis focuses on the setback temperature of 25.6 ºC and the results below are presented relative to the selected setpoint. Setback temperatures 25.6 ºC (black line) and 26.7 ºC perform the same. Therefore, further increase of the setback temperature would not affect the temperature variation.

Figure 5-16 shows the average PCM-drywall temperature in the external wall for the PCMs optimized in all locations with either natural or forced convection. The house with forced convection can freeze the PCMs during the precooling period and almost melt the PCMs during the setback period. In contrast, the house with natural convection does not freeze/melt the PCMs during the precooling/setback periods, while suffering from higher temperature variations.

Figure 5-17 shows the average PCM-drywall temperature in the external wall for the case with optimized PCMs in all three locations (Table 5-5). Furthermore, all cases use the fan/forced convection model. The wall with lowest temperature oscillations has optimal PCM with forced convection. This indicates the positive effect of PCMs being optimized for each location in the envelope.

Figure 5-18 shows the average PCM-drywall temperature in the ceiling for case with PCMs installed only on the ceiling with the forced convection and natural convection models. As with Figure 5-17, the lowest temperature fluctuation is observed for the case with PCM and forced convection.

• Heat Transfer across the Building Envelope

Figure 5-19 shows heat fluxes at the ceiling surface for the two cases: (i) with PCMs in the ceiling only and (ii) with precooling and no PCMs. These cases are assessed for both natural convection and forced convection modes. Negative values indicate heat flux leaving the ceiling to the indoor air (freezing the PCM) and positive values indicate heat flux going from the indoor air into the ceiling (melting the PCM).

Implementing forced convection increases heat transfer by at least 40% during the precooling period and even higher in the setback period. The case with PCMs and forced convection has significant positive heat flux during on-peak hours. This indicates that the PCM melts during the peak time by absorbing heat within the living zone, which keeps the living zone temperature at or below the setback temperature.

• Energy and Cost Savings

Cooling energy consumption shifted away from peak hours drives the cooling electricity cost savings. Therefore, Figure 5-20 and Figure 5-21 show cooling power consumption for all analyzed cases in one day, July 22 with natural and forced convection. The baseline home without precooling and no PCMs consumes the largest amount of electric energy during the peak time.

Figure 5-21 also shows that cooling energy is not zero during on-peak hours since the fans still operate during this period.

Figure 5-20 Cooling electricity power consumption variations for all cases with the forced convection model for July 22. Hour 0 represents midnight of the first day.

Figure 5-21 Cooling electricity power consumption for all analyzed cases with the natural convection mode for July 22.

Figure 5-22 and Figure 5-23 show hourly cooling electricity cost variation during a day for all cases with forced and natural convection. As observed from previous figures, the baseline house uses the highest energy during the peak time, thus having higher energy costs. All cases with PCMs

56 and forced convection have the lowest energy cost, and only the case with PCMs optimized for all locations fully shifts cooling electric energy (not considering fan motor electricity) out of the peak time when the setback is at 25.6 ºC.

Figure 5-22 Cost variations through the day when TOU rates are applied during the peak time for July 22 for all analyzed cases and with the forced convection.

Figure 5-23 Cost variations through the day when TOU rates are applied during the peak time for July 22 for all analyzed cases and with the natural convection.

Seasonal Cooling Electricity Consumption and Cost

Figure 5-24 and Figure 5-25 show the aggregated cooling electricity consumption over the cooling season (May-October). Note that these graphs show only energy use above 4600 kWh to highlight the differences between cases. All cases with precooling have an energy penalty of about 4% or 6.0% when forced convection is present.

Figure 5-24 Aggregated cooling and ventilation related electricity consumption in the precooling months (May-Oct), assuming the fan power is 25W for each fan.

This is an expected result as additional electricity is used to precool the home as well as to operate ceiling fans in the forced convection cases. Interestingly, when precooling is used with forced convection but without PCMs, the energy penalty is the highest. Therefore, PCMs improve the performance of precooling.

Figure 5-25 Aggregated cooling and ventilation related electricity consumption in the precooling months (May-Oct), assuming the fan power is 2 W for each fan. 58

Besides comfort, energy cost saving is also an important factor to consider. The maximum cost savings possible with any energy storage system (with regards to peak electric costs) is calculated by assuming all energy use during on-peak hours is shifted without energy penalties. These results assume three hours of peak cooling energy are evenly shifted to the rest of the day resulting in the maximum cooling energy cost savings of USD 190, or a reduction of 39.5%. This defines the upper limit of savings for the current study. All cases analyzed in this study have energy cost savings that range from 21.9% to 29.4%.

Figure 5-26 shows the aggregated energy costs for the May-October period for all five envelope conditions with natural and forced convection assuming the fan energy use is 25 W. Fan energy use increases the cooling electricity energy cost by 2-5%. The aggregated costs are higher for each case than with natural convection. Hence, the fan power and efficiency plays a role in determining the cost effectiveness of the proposed system.

Figure 5-26 Seasonal cooling electricity energy cost for May-Oct period for each analyzed case with natural and forced convection assuming the fan power is 25W for each fan.

Figure 5-27 shows the same case assuming four fans with a rated energy use of 2 W. Due to the high efficient fans, differences in energy use between forced and natural convection are minimal. Hence, the fan power and efficiency plays a role in determining the cost effectiveness of the proposed system.

Figure 5-27 Seasonal cooling electricity energy cost for May-Oct period for each analyzed case with natural and forced convection assuming the fan power is 2W for each fan.

5.3. Conclusions

This study uses parametric analysis to study and optimizes PCM properties and location for a new home in Phoenix with time-of-use electric rates and two different interior convection modes. Annual building energy simulations are conducted using EnergyPlus and BEopt with an emphasis on summer precooling to evaluate the thermal behaviors, energy consumption patterns, and cost savings. The selection of the right PCM properties, PCM location, and proper convection mode is important to achieve the optimal PCM performance in different locations in the building envelope. Therefore, forced convection and a natural convection models are used in the current study.

Based on the analyzed home and climatic region, this study shows forced convection improves the heat transfer between the walls and indoor air, keeping the living zones cooler and with less temperature fluctuations during the precooling stage and the peak time, although there is an energy penalty associated with precooling. However, shifting the electricity consumption from the peak time through precooling causes a prominent reduction of cooling electricity costs. When the PCMs are used in the envelope, the costs are reduced and with the use of forced convection mode this improves further based on the fan efficiency. The highest cost savings are observed when the PCMs are optimized for all locations under the forced convection mode using high- efficiency fans; the maximum cost savings observed are 29.4%. Other scenarios yield around 25%

60 savings. Under these conditions, cooling-related energy can be shifted up to 99.98% for a design day. These potential savings, along with the increased thermal comfort while precooling, will be beneficial to the homeowner and provide relief to the electric grid during peak hours. The results in this section sets-up important inputs for the work described in the next 2 chapters.

CHAPTER 6 NUMERICAL HEAT TRANSFER MODEL FOR OPAQUE WALLS AND DESCRIPTION OF LABORATORY FACILITY FOR EXPERIMENTAL ANALYSIS

This section contributes to the fulfillment of the following objectives of this research: (ii) develop a numerical model which utilizes effective numerical techniques to solve a building envelope assembly with PCM inclusions and (iii) design and build experimental apparatus and a suitable controlled environment to test different PCMs. Verification and validation (V&V) are important steps in any model development to ensure desired and accurate performance [233]. ASHRAE standard 140 defines three main approaches for V&V: (1) analytical verification, (2) empirical validation and (3) comparative testing [234]. There have been attempts to verify and validate numerical building envelope models, Appendix E summarizes studies in recent literature and their key findings. This research conducts a full validation study of a building envelope model with the ability to model PCMs. Figure 6-1 shows a flow chart of the verification and validation studies conducted in this study. It conducts analytical verification, numerical comparison, and finally empirical validation using data from laboratory experiments, field-experiments, and experimental tests conducted in-house controlled environmental chamber.

Figure 6-1 Structure of the full validation study includes analytical verification, comparative testing, and empirical validation.

This research uses MATLAB as its numerical modeling language to build a heat transfer algorithm for building walls. MATLAB has been used for building modeling in several prior studies [235-238]. MATLAB has also been the modeling platform for other parallel published work in the research group of the author [239]. Analytical verification and the comparative testing of this algorithm is discussed in this chapter. Empirical validation of the algorithm is discussed in chapter 7 and 8.

6.1. 1D heat transfer algorithm to model building walls with PCM

The developed mathematical algorithm is a finite difference numerical model inspired by the EnergyPlus Conduction Finite Difference (CondFD) model that can simulate PCMs [103]. The numerical solution uses Gauss-Seidel scheme as its solver. The discretized 1D heat transfer equation is shown in equation 6-1.

(6-1) 푗+1 푗 푗+1 푗+1 푗+1 푗+1 푇푖 − 푇푖 (푇푖+1 − 푇푖 ) (푇푖−1 − 푇푖 ) 퐶푃 ∗ 휌 ∗ 훥푥 = 푘푊 ∗ + 푘퐸 ∗ 훥푡 훥푥 훥푥 Where,

푖 푇푗+1 = Temperature of node i being modeled at new time step (푗 + 1) 푖 푇푗 = Temperature of node i being modeled at previous time step 푗 푖+1 푇 = Temperature of adjacent node (푖 + 1) to interior of construction 푖−1 푇 = Temperature of adjacent node (푖 − 1) 훥푡 = Timestep

훥푥 = Finite difference space discretization 푝 퐶 = Specific heat of material

휌 = Density of material 푗+1 푘푖 =Equation Thermal 6.1conductivity is defined of for node four I beingdifferent modelled node types,at new time step 푗 + 1

i. Exterior surface node exposed to the outdoor conditions (half-node) ii. Internal nodes within same layer/material iii. Interface nodes at the interface between two different layers/materials (half-node)

iv. Interior surface node exposed to the interior conditions (half-node)

Nodes (i) and (iv) considers the convection and radiation heat transfer while node type (iii) uses averages thermo-physical properties conductivity, specific heat, and density from materials either side of the node and calculates the node temperature. Therefore, these nodes are modeled as half-nodes. The algorithm then solves the equations at each node while iterating through each material layer of the wall. The structure of interface nodes and interior nodes are shown in Figure

6-2. Uniform mesh size is used for each layer in the algorithm. x1, x2, x3 are three interior nodes of the current layer and Δx is the space discretization based on the equation 6-2. Δt is the time discretization.

Figure 6-2 Structure of interior and interface nodes, space and time discretization of the 1D algorithm.

Figure 6-3 is a flow chart of the functions contributing to the main function of the thesis algorithm: (i) material properties and PCMs recognition function includes the logical flow of reading the material and PCM properties and defining the discretization used in the finite difference algorithm. Furthermore, this function reads the PCM enthalpy curve data inputs and defines the enthalpy function that includes the PCM properties in the building envelope simulation; (ii) weather information and temporal information function reads the TMY3 weather file and calculates the external convection and radiation heat-fluxes. It also assists running the model for

64 the defined number of time steps or the time period of the year. If the boundaries are defined by the boundary temperature for validation purposes, the exterior and interior node temperatures are read from files through this module; (iii) coefficient function calculates the convection and radiation heat transfer coefficients. Main function houses the finite difference algorithm described above.

Figure 6-3 Structure of the functions in the numerical envelope model.

Exterior surface node interacts with the outside air by convection the sky and sun by radiation heat transfer. Similarly, the interior surface node interacts with the inside air and the radiation effects from within the zone. For the verification purposes, the developed (thesis) algorithm, uses the convection and radiation models from EnergyPlus as shown in Table 6-1.

Table 6-1 Definitions of the exterior heat transfer for the numerical verification study using the thesis algorithm Boundary Mechanism Model Exterior Convection DOE-2 [240, 241] Longwave Radiation EnergyPlus documentation [242] Shortwave radiation EnergyPlus documentation [243, 244] Interior Convection TARP model [245] Longwave Radiation EnergyPlus documentation [243] Shortwave radiation EnergyPlus documentation [243]

6.2. Modeling of PCM inclusions in the thesis model

When the thesis algorithm identifies the material layer and the thermos-physical properties, the space discretization for each layer is calculated using equation 6.2. Space discretization is a function of the thermal diffusivity of the material ( ), a space discretization constant ( ), and the time step ( ). The user inputs the space discretization훼 constant, with a default value of푐 1. This is F the same asΔ푡 the inverse of Fourier number ( 0). The time step used in all simulations using the algorithm is 1 minute. Thesis model uses fully implicit time integration scheme that is unconditionally stable and does not have a stability criterion.

Therefore, the Fourier number is defined arbitrarily. The variable c is the inverse of the grid Fourier number. Cases c=0.5, 1, 2, were investigated to find changes in results less than 0.1%.

Therefore, a grid Fourier number (F0) of 1 used in this thesis. After calculating the Δx, the number of nodes for each layer was calculated by dividing the layer thickness by Δx and rounding up the resultant value. The thickness of the layer is then divided again with this rounded up number of nodes to find the final Δx used in the algorithm. The timestep and special discretization considerations of 1D heat transfer in opaque building walls with PCMs are further discussed in detail by Tabares-Velasco and Griffith [233] and taken into consideration in the simulations used in the chapter 7 and chapter 8.

(6-2) 훼훥푡 훥푥 = √푐훼 훥푡 = √ 퐹표 PCMs are included in the finite difference approach by coupling it with a single enthalpy- temperature function (equation 6-3) and is used to calculate an equivalent specific heat ∗ at each time ℎstep(푇) (equation 6-4). This enthalpy function accounts for both the latent heat and 퐶푝 (the푇) sensible heat. Enthalpy curve is defined by using the total enthalpy and the melting/ freezing temperature range.

(6-3)

ℎ = ℎ(푇)

푗 푗−1 (6-4) ∗ ℎ푖 − ℎ푖 퐶푝(푇) = 푗 푗−1 푇푖 − 푇푖 For the simulation of PCMs, this algorithm uses the enthalpy method implemented with a fixed uniform grid. Furthermore, finite difference discretization technique is implicitly solved using fully implicit method.

Modeling hysteresis in the thesis model

The thesis model does not simulate the subcooling characteristics discussed in the chapter 2 (section 2.3.3). It simulates the real and apparent hysteresis when two curve data is available. The simplification methods used in modelling enthalpy curves is discussed in this section. The thesis algorithm has a built in function to recognize the PCM included layer. Once the PCM layer is recognized the algorithm needs effective heat capacity and conductivity values to dynamically implement at each time step through the phase change temperature range.

Figure 6-4 shows all available PCM curves for the InfiniteRTM hydrate-salt PCM with nominal melting temperature of 23 ºC based on the commercial rating by the manufacturer. The manufacturer has provided PCM characteristics data and has only the melting curve. This is shown in black color. The hysteresis curves were provided for this PCM by Dr. Kaushik Biswas from the Oak Ridge National Laboratory who used DHFMA tests. There are two distinct curves in this data for melting and freezing and shown in yellow and blue.

The circles in the curves represent discrete data points provided. Note that within the temperature range the phase change occurs the data is recorded every 1 ºC and outside this range the points temperature is recorded are more relaxed. The frequency of reporting data is determined by the researcher who conducts the characterization study. The curves are drawn linking these data points. The peak melting/ freezing temperature for each curve is suggested by the manufacturer/researchers who provided the data. Based on this information further approximations are made to obtain the enthalpy data to include in the algorithms.

To include latent heat and the sensible heat in the algorithm the temperature enthalpy curves are approximated with straight lines. The lower and higher limits of phase change are determined by the author by observing the graph. This may lead to some inaccuracies and should be taken into account. These approximations assist to include enthalpy data of the PCMs to the different PCM modelling algorithms investigated in this research such as; (i) melting temperature range of the PCM (ii) freezing temperature range (iii) peak melting temperature, (iv) peak freezing temperature (v) latent heat during the phase change (vi) sensible heat during the phase change.

Approximated melting curve for the PCM hydrate-salts for the DSC data is shown in the Figure 6-5. The peak melting temperature is 23 ºC. Lower bound of melting temperature range is 20 ºC, and upper bound of melting temperature range is 25 ºC. Latent heat of melting is ~190 kJ/kg. Sensible heat of melting is ~15 kJ/kg.

Figure 6-5 Approximated melting curve for the PCM hydrate-salts from DSC data.

Approximated melting curve for the PCM hydrate-salts for the DHFMA data is shown in the Figure 6-6. The peak melting temperature is 26 ºC. Lower bound of melting temperature range is 20 ºC, and upper bound of melting temperature range is 28 ºC. Latent heat of melting is ~150 kJ/kg. Sensible heat of melting is ~24 kJ/kg.

Figure 6-6 Approximated melting curve for the PCM hydrate-salts from DHFMA data.

Approximated freezing curve for the PCM hydrate-salts for the DHFMA data is shown in the Figure 6-7. The peak freezing temperature is 25 ºC. Lower bound of freezing temperature range is 18 ºC, and upper bound of freezing temperature range is 26 ºC. Latent heat of freezing is ~150 kJ/kg. Sensible heat of freezing is ~24 kJ/kg.

Figure 6-7 Approximated freezing curve for the PCM hydrate-salts from DHFMA data.

The summary of the phase change characterization data approximated by the simplified curves to implement in the PCM modeling algorithms are shown in the Table 6-2.

Table 6-2 Phase change characterization data approximated by the simplified curves to implement in the PCM modeling algorithms Curve Peak phase Phase change Latent heat Sensible change temperature (kJ/kg) heat temperature range(ºC) (kJ/kg) (ºC) Melting (DSC) 23 5 190 15 Melting (DHFMA) 26 8 150 24 Freezing (DHFMA) 25 8 150 24

The approximated curve data is used for the PCM simulations of heat transfer across building envelopes modeled in this research in chapter 7 and chapter 8. To include the hysteresis characteristics observed in the PCMs the melting and freezing status should be recognized in the algorithm. A variable is defined (a marker) which can have ‘0’or ‘1’ discrete values based on the freezing or melting curve applies in relevant cycle. If the marker values is ‘1’ the melting curve data is considered. If the marker is ‘0’ freezing curve data is considered.

6.3. PCM modeling objects in building energy modeling software

Verification and validation studies in this research uses several building energy modeling software with PCM computational models. This section describes how the PCM characteristics and thermo-physical properties are included in these modules.

EnergyPlus PCM modules

EnergyPlus has two PCM numerical models. The original PCM model which is still available in the platform uses the above mentioned enthalpy function method where enthalpy- temperature data is input for discrete points within the melting temperature range. This is shown in the Figure 6-8. Temperature Coefficient for Thermal Conductivity is 0. Corresponding enthalpy (Enthalpy 1, 2…) value for a selected temperature (Temperature 1, 2…) value of the curve is entered in the table 16 discrete entries can be used in this module. If the enthalpy change in the melting/ freezing temperature range is simplified with a straight line the curve can be defined with 4 points.

Figure 6-8 EnergyPlus original PCM model data input interface.

A recent update of the software includes a PCM model which can simulate hysteresis effects of the PCMs. This new module addresses the asymmetry observed in the PCM melting and solidifying and therefore, introduces separate data entries to define melting and freezing processes. This is reflected in the data inputs required for the melting curve and the freezing curve as indicated in Figure 6-9. The liquid and solid state thermo-physical properties are input separately. The latent heat and specific heat are separately input. Low and high temperature differences based on the phase change temperature interval and peak phase change temperatures discussed in the section 6.2.1 are used as inputs for this module.

Figure 6-9 EnergyPlus Hysteresis PCM model data input interface to define PCM properties for melting and freezing curves separately.

WUFI PCM module

Verification and validation studies also consider the techniques used in WUFI hygrothermal numerical modeling software discussed in the chapter 3. The interface of hygrothermal functions object in WUFI to input PCM characteristics and thermo-physical data is shown in Figure 6-10. The enthalpy function is defined same as in original PCM model discussed above in section 6.3.1. This interface facilitates the input of the enthalpy curve data using the hygrothermal functions object. The enthalpy-temperature data is input in the yellow shaded area.

Figure 6-10 WUFI PCM model data input interface indicating the enthalpy curve input.

6.4. Numerical PCM building envelope model verification

This section uses analytical and numerical solvers to verify the numerical envelop model. These steps assure that the model: (i) is able to solve analytical problems correctly, (ii) is able to solve simple tests that allow to identify potential bugs in the code and (iii) is stable.

Analytical Verification

Analytical verification is conducted a PCM included envelope. For this the study assumes a single layer of material. This method that considers a front tracking method is considered only for the verification purposes of the thesis model.

Analysis of PCM envelope using Stefan problem:

The Stefan problem introduced in the analytical models in chapter 3 is used for the analytical verification. using the following assumptions: [82].

1. Heat is stored only as latent heat. The sensible heat stored is negligible compared to the phase change enthalpy and therefore only latent heat at the phase change temperature is considered in heat transfer. 2. Heat transfer is only by conduction (no convection). Then, the temperature profiles are linear and the heat flux is proportional to the temperature gradient.

3. At the beginning, at t = 0, the PCM is liquid and its temperature is the phase change

temperature Tm [246].

4. Temperature at x = 0 is changed to T0= 0 and kept constant at that level for the simulation time.

Equation 6-5 describes the analytical solution for the 1D heat equation [247]. The author defines a parameter M to determine the position of the phase change front. Each elements of the equation 6-5 is described below.

2 푠 (6-5) 0.5 2 푙 푠 푂 푚 훼 푘 √훼 (푇 − 푇 )exp (−휆 푙 ) 푓푔 푝푖 exp (−휆 ) 훼 휆푖 = − 푠 0.5 푠 푚 푠 푙 푚 훼 퐶푝 푇 퐸푟푓(휆) 푘 √훼 푇 퐸푟푓푐 (휆( 푙 ) ) 훼

훼푠 = thermal diffusivity of the solid 훼푙 = thermal diffusivity of the solid 푘푠 = thermal conductivity of the solid 푘푙 = thermal conductivity of the liquid 푇푚 = melting temperature of the PCM 푇푂 = initial homogenous temperature across the layer 휆 = the root of the transcendental equation 푖푓푔 = latent heat 푡 = time 푠 퐶푝 = specificHere, heatthe Stefan of the solid Number phase ( St) is defined in equation 6-6. The position of the phase change front at time t is described in equation 6-7.

(6-6) 푐푝(푇표 − 푇푚) 푆푡 = 푖푓푔

(6-7)

푀(푡) = 2휆√훼푙푡

Based on the value of M, and relationships can be defined for each x location. The

푠 푙 T equation 6.8 and equation 6.9 define푇 the temperature푇 distribution. s is the solid state temperature and Tl is the liquid state temperature.

(6-8) 푇푚 푥 푇푠 = 0.5 퐸푟푓(휆) 2(훼푠푡)

(6-9) 표 푚 푙 푇 − 푇 푥 푠 0.5 푇 = 훼 퐸푟푓 푐 ( 푙 ) 퐸푟푓푐 (휆)( 푙 ) 2√훼 푡 훼 Table 6-3 shows the initial conditions used in this study. Initial homogenous temperature across the layer is the initial temperature across the entire material layer.

Table 6-3 Thermal conditions used in the analytical verification cases Condition Value Initial homogenous temperature across the layer ) 50 ºC

Exterior surface temperature (푇0 0 ºC Tm 29.5 ºC

ΔTpc 0ºC

Table 6-4 describes the inputs to the thesis model and EnergyPlus models to create the same problem in each platform. A single material layer is considered for the thesis model. For EnergyPlus a zone with one wall was used. The walls were initially at a homogenous temperature of 50 °C and had a melting temperature range of 29.4–29.6 °C (this approximates the fixed melting temperature assumption in the Stefan Problem.). A semi-infinite wall was simulated by a thick wall in both software.

For EnergyPlus, the “OtherSideCoefficient” feature; the indoor air temperature was set to the desired temperature and the inside convective heat coefficient was set to 1000 W/m2-˚C to assign the temperature to the boundary node. Same was done for the thesis model. These

75 techniques are discussed in a study that discusses diagnostic test cases to verify heat transfer algorithms in building energy simulation programs [233].

Table 6-4 Material properties for the analytical verification with PCM (inspired by [246]) Property Units PCM inclusion 1 Material /Equivalent Application - PCM-drywall Thermal Conductivity kl and ks W/m-˚C 0.23 Specific Heat Capacity (Cpl and Cps) J/kg- ˚C 1400 Density kg/m3 1000 Evaluated thickness m 0.020 Simulated thickness (semi-infinite consideration) m 0.3 % PCM in the layer - 30% Equivalent Latent heat in the layer based on the above f. Kg/kg 33 (To approximate the Stefan problem) ºC 0.2

훥푇푃퐶

Same material properties, boundary and initial conditions indicated here are applied in the thesis model for the verification purposes. For each PCM inclusion cases,

1. Distributed PCM in drywall represents a 0.02 m layer. A 0.3 m layer is evaluated to meet the semi-infinite condition was implemented in the analytical solution. Therefore, the first 0.02m is considered when comparing results to best represent the PCM enhanced thickness.

Results of the Analysis of PCM envelope using Stefan problem:

Figure 6-11 shows the temperature distribution along the cross section of the material layer for the PCM drywall which also demonstrates the position of the phase change front. Shaded darker is the solidified region and the lighter shade is the liquid region. The first ~ 0.02m distance from the left edge is evaluated. This figure shows a snapshot where the melting front is at x=0.107 m and after and evaluation time of 24h.

Figure 6-11 Cross section temperature variation of the semi-infinite material layer after 24h period for the PCM drywall case.

Figure 6-12 compares the thesis model results with the Stefan Problem solution and showcases the transient temperature of the sixth node into the material layer to represent 0.02 m length. Results from the same problem simulated in EnergyPlus platform is also included here. The two simulations of EnergyPlus and thesis model behaves the same in graphical comparison and RMSE values show agreement for both.

Figure 6-13 compares the transient heat flux at the exterior surface. Results from the same problem simulated in EnergyPlus platform is also included here.

Figure 6-13 Heat flux at the exterior surface of the PCM layer.

After the analytical verification, the author conducts the numerical verification of the thesis model.

Numerical Verification

This section discusses the verification of the numerical algorithm with EnergyPlus version 8.4. A series of diagnostic test cases for verification of conductive heat transfer algorithms and boundary conditions in building energy simulation programs are introduced in ASHRAE 1052-RP [248] and used for EnergyPlus model verification in [233] [246].

First, a multilayer assembly with the same properties as in the exterior wall described in the chapter 6 is verified using the diagnostic test cases. The multilayer tests help verify the behavior of the intermediate nodes of the layers and response from materials with different properties. The layer properties are listed in the Table 6-5.

Table 6-5 Material properties for the numerical verification with PCM Property Units Layer 1 Layer 2 Layer 3

a. Material - Plywood Stud and Gypsum Cavity b. Thermal W/m-˚C 0.115 0.054 0.1603 Conductivity c. Density Kg/m^3 512.64 162.40 801 d. Specific Heat J/k-ºC 1214.23 1178.9 837.4 Capacity e. Thickness m 0.0127 0.0889 0.0127

Numerical verification using a previously evaluated envelope assembly:

This section looks at a more comprehensive verification with the residential home discussed in chapter 5. After considering several key assumptions, temperature and heat flux from exterior wall described in the study is compared with the thesis model.

Assumptions:

a. Only the object “Wall 13” is considered (west facing exterior wall attached to the living zone as indicated in the Figure 6-14) for the analysis. b. Internal loads contributions from people, lights, and other equipment are not included considered in the EnergyPlus model. c. For the PCM inclusion case, only the evaluated wall includes PCMs and the other walls remain without TES. d. Solar and wind exposure on the other exterior walls are made negligible.

Same weather file and other simulation conditions used in the chapter 6 are used here except for the above mentioned assumptions. The current work evaluates the envelope assembly for (i) non-PCM and (ii) PCM included cases. Simulations are conducted for the month of July.

Figure 6-14 West facing wall of the residential building evaluated for numerical verification.

• Results: Numerical Verification:

This section presents the results from the comparison of the single-wall study extended from the case discussed in the Figure 6-15 shows the graphical comparison of the external and internal surface temperatures of the examined exterior wall without PCM inclusions.

Figure 6-15 External and internal surface temperatures of the examined exterior wall without PCM inclusions from the thesis model and EnergyPlus.

Numerical envelope model agree with the RMSE for the external surface temperature is 0.0096 ºC and RMSE for internal surface temperature is 0.0127 ºC.

Figure 6-16 shows graphical comparison for the external and internal boundary surface temperatures for 5 days in the month of July. Numerical envelope model with the PCM model agree with RMSE for the external surface temperature is 0.6562 ºC and RMSE for internal surface temperature is 0.5236 ºC.

Figure 6-16 Verification of temperature variations on the internal and external; surfaces of the wall examined.

6.5. State-of-the-art Laboratory for full-scale experimental studies of PCMs

After the analytical and numerical verification of the thesis model, the author conducts laboratory tests of wall assemblies with PCMs to: (i) create experimental data collected under different environmental conditions to validate the PCM models (ii) compare performance of PCM models with different PCMs (iii) understand and quantify the current differences between building envelope PCM modeling tools and actual field data from PCMs customers. The proposed experimental work of the current research is conducted in a 27.8m2 (300ft2) state-of-the-art environmental chamber.

Wall Assembly Tests

Wall assembly tests investigate the thermal behaviors of the PCM inclusions in different building envelope assemblies. These experiments bring together several facilities to establish the

81 expected enclosure and the environmental conditions. This section describes the organization of facilities, test procedures so far carried out, and experimental plan for the proposed research.

Environmental Chamber and the HVAC System

Full scale experience will be performance in an enclosure with a carefully controlled environment. Overview of the AHU and the environmental chamber is shown in the Figure 6-17. Figure 6-18 shows a sketch of the top view of the chamber that has dimensions of 5.38m (length) X 4.46m (width) X 2.67m (height) and can accommodate full size drywall panels vertically. The environmental chamber used in the current study has the ability to control: (i) supply and return air flow rate (ii) supply and return relative humidity, (iii) supply and return dry bulb temperature and (iv) outmost of outdoor air supply to chamber. It has a dedicated air handling unit (AHU) located on the roof of Mechanical Engineering Department building of the Colorado School of Mines.

Figure 6-17 Overview of the air handling unit and the chamber, Section A: AHU Main Duct, Section B: AHU Return Duct, and Section C: Chamber.

Table 6-6 shows the dimensions of different components in the environmental chamber. Ventilation system of the chamber is such that both supply and return air ducts are connected to the movable ceiling. Room and the diffuser dimensions are showcased in the Table 6-6.

Table 6-6 Dimensions of the environmental chamber, H= height, L= length, and W= width. Part Dimensions (m) Room 5.38(L) X 4.46(W) X 2.67(H) Door 1.5(W) X 2.12(H) Inlet Diffusers 0.58(L) X 0.58(W) Exhaust Diffusers 1.17(L) X 0.58(W) Light 1.17(L) X 0.55(W)

Lights and supply ducts, and the return vents are arranged symmetrically. The return duct is located near south-west corner of the chamber. Lights, diffuser locations are shown in the Figure 6-18.

Figure 6-18 Plan View of the Ceiling Setup of the Chamber including the inlet diffuser, lights, and exhaust diffuser.

Sensors placed inside the chamber monitor temperature, humidity, CO2, VOC, particulate, and static pressure. Appendix 4 describes all sensors used, their functions, and locations. Sensors, their locations in the AHU, chamber, and outside are described in detail in the Figure 6-20.

Chamber is also equipped with a hydronic radiant wall that has the ability to maintain a constant and variable surface temperature independent of the indoor air temperature to mimic external boundary conditions such as an exterior wall subject to solar radiation. Radiant wall setup will be discussed in detail in later sections.

HVAC and Chamber Instrumentation System

The AHU shown in Figure 6-20, consists of:

 Outdoor AHU shell: unit encloses the air conditioning elements (Figure 6-19)  Filter bank: two air filters that removes the particles in air to maintain clean heating and cooling coils and improve indoor air quality  Pre-heat coil: heat coil after mixing chamber that makes sure the mixed air temperature is always higher than 45 ˚F to avoid risk of freezing during winter.  Chilled water coil: 10-row cooling coil  Re- heating coil: re-heats the air if needed when dehumidification is needed  Supply and return side fans: fans with variable frequency drives that allow flow rate to go from 1-20ACH. Regulates the airflow speeds within the AHU  Steam humidifier: Humidifies supply air

Figure 6-19 SkylineTM Outdoor AHU by DAIKIN, Group: Applied Air systems, Part Number: IM 770 houses the heating and cooling elements, filters, humidifier to condition the air.

Control and Data Acquisition

Data acquisition (DAQ) system collects data to facilitate the systematic changes of set points required for the experiments. There are two main DAQ units which the sensors communicate with in the current experimental set up, (i) ABB control unit (ii) InstrunetTM DAQ apparatus.

 ABB main control unit monitors information related to the chamber control system and the air handling unit (AHU). It receives information from temperature, humidity, and flow sensors located within AHU and the ducts and sends information back to different actuators. Figure 6-21 shows the hardware components of the ABB DAQ unit. This unit consists of a (i) C1867 - MODBUS TCP Interface, (ii) PM 851 Processor UNIT, (III) 3 Analog Input Units, (iv) 1 Analog Output Unit, (v) 1 Digital Input Unit, and (vi) 1 Digital Output Unit.  Instrunet DAQ (captures data from all sensors needed for heat transfer experiments. It communicates with the sensors used in experiments and also monitor few of the main system sensor inputs to assure smooth and accurate control. Figure 6-22 shows the hardware components of the Instrunet DAQ unit.

The next section looks closely into the both DAQ components and related control mechanisms.

Figure 6-22 Instrunet data acquisition unit with connections linked to the experimental apparatus sensors and some ABB main system sensors also linked to the Instrunet system to verify readings.

• Hydronic Radiant Wall Temperature Control

The hydronic radiant wall is used to set-up the outside boundary conditions in the chamber. The system consists of a three-speed pump, a mini boiler, control valve and chiller located outside of the chamber as shown in Figure 6-23. Table 6-7 shows the heating and cooling apparatus of the radiant wall system.

Figure 6-23 Hydraulic radiant wall heating and cooling apparatus.

Table 6-7 Summary of radiant wall heating and cooling system apparatus Unit Performance indicators Notes

Mini Boiler Volts: 120, Make: Electro Industries Power: 2.5 kW Model: EMB-S-2 Set Temp.: 150 ºF Expected flow: 0.11 m3/h (1.89 L/min) Chiller Volts:115 Make: Perlick Corporation Refrigerant: 134a Model: 4414QC

Max. Fluid Temp.: 230 ºF Motor: 1/3 HP Split-Phase Max. Fluid Supply: Carbonator Pump Motor 0.2916 m3/h (4.86 L/min) Heat Exchanger Operating pressure: 150 psig Make: TriangleTube Max. operating temp: 365 ºF 3 speed pump Volts:115 v Make: Groundfos Frequency: 60 Hz Model: UPS26-99FC Max. Flow(designed): 7.5 m³/h Flow at max. speed(observed): 0.29 m3/h

Figure 6-24 shows the flow and temperature monitoring devices which assist to regulate the temperature setpoint to the radiant wall. The temperatures are monitored at the supply and return lines. Radiant wall temperature control is achieved by a three-way mixing valve and a pressure independent control valve as shown in Figure 6-25.

Figure 6-24 Radiant wall flow control apparatus includes the primary flow sensor, e speed flow pump, temperature sensors to measure inlet and outlet temperatures of the fluid flow to the radiant wall heat exchanger.

• PLC Control and PID setup

This subsection looks into the radiant wall controller program and the PID parameters. PID control flow chart is shown in the Figure 6-26.

Figure 6-26 PLC Control flow chart for the radiant wall control PID settings for the mixing valve operation is indicated in the Figure 6-25.

Figure 6-27 Current PID settings for the mixing valve for the setpoint of 120 ºF.

Here,

푆푝 = Setpoint Temperature (˚F )

푃푣 = Actual Temperature (˚F)

푂푢푡 = Opening of the mixing valve (%)

퐺푎푖푛 = Proportional Gain

푇푖(푆) = Integrator Time

푇푑(푆) = Derivative Time 90

PID control parameter values are first set using a trial and error method under the original system (where the boiler was activated upon meeting the setpoint and vice versa). This was due to the fact that the temperature response from the chiller was slow. However, after implementing the mixing valve, the auto tuning for the PID control was used which gave highly improved control over the setpoint. Here we use the Relay-based auto tuning. Relay-based auto tuning is a simple way to tune PID controllers [249]. The method includes temporarily swapping a simple relay for the PID controller in the feedback loop [250].

• Chamber Environment Control

Approach for the chamber control is similar to the above. However, due to the significant volume of the chamber and the different thermal properties to be controlled, the calibration takes more effort. Chamber has three main control modes, (i) Supply Air Temperature based (DAT), (ii) Room Air Temperature based (RAT), (iii) Multi-Variable based (VAV). Each of the modes have PID controller units.

Construction of Building Envelope Assemblies within the Chamber

The structure of the multilayer panels in the proposed research are different from an actual residential building envelope. Actual envelope consists of a 2x4’’ stud and cavity as discussed in chapter 5. The analyzed structures do not have studs, water retardant layers, and the finishing coatings. There are few reasons for this:

 One of the main objectives of the study is to validate a numerical model and therefore, to reduce the possible 2D/3D effects of the heat of heat transfer.  Current research plans to switch the panels to test different combinations and therefore, to efficiently move the apparatus.

Test surface area for the current research is approximately 1.2 m x 2.4 m (4 ft. x 8 ft.) per panel and therefore, facilitates tests in the system scale. First stage of the experimental studies implements an experimental method inspired by DHFMA and Dynamic Hot-Box methods discussed above. The sample sizes used in the DHFMA method is usually of ~ 0.3 m x 0.3 m (2 ft. x 2 ft.) for ambient conditions of 10°C – 40 °C [145]. In contrast, Dynamic Hot-Box method uses larger samples of around 2 m x 2 m. Approximately 2.4 m x 2.4 m (8 ft. x 8 ft.) or larger cross section of the clear wall area of the enclosure is used to determine its thermal performance by

Fazio et al.[251]. Martin et al.[252] used a frame of 2.0 m x 2.0 m (8 ft. x 8 ft.) for their specimens in a dynamic hot-box apparatus. The current experimental setup can test multiple panels across the radiant wall surface as shown in Figure 6-28. Therefore, the experimental apparatus and the sensor system for the apparatus is inspired by these studies and will be discussed in detail in chapter 8.

Figure 6-28 Radiant wall location within the environmental chamber and the locations of wall assembly panels relative to the radiant wall.

CHAPTER 7 EMPIRICAL VALIDATION AND COMPARISON OF PCM MODELING ALGORITHEMS COMMONLY USED IN BUILDING ENERGY AND HYGROTHERMAL SOFTWARE

This section contributes to the fulfillment of the following objectives of this research: (v) Verify (using the numerical model) and validate (using the experimental data from laboratory experiments and field experiments) different PCM models in software platforms like EnergyPlus and WUFI. This study is under review in the journal of Building and Environment. Dr. Kaushik Biswas of Oak Ridge National Laboratory conducted the COMSOL simulations and the PCM characterization for the Nano-PCMs. Dr. Dariuz Heim at Lodz University of Technology conducted the ESP-r simulations of this study.

7.1. Introduction

Buildings are responsible for nearly 40% of the total energy consumed in United States [253]. A large portion of this energy consumption is used for space-conditioning, up to 50% during peak time [254]. Therefore, there is an interest to increase the energy efficiency in buildings and energy storage potential to reduce peak demand and potential energy use. Innovative sustainable design, materials with improved thermal properties, and integration of thermal energy storage are some of the methods used in the industry today.

Thermal energy storage (TES) is used in buildings due to its capacity to shift loads [255, 256]. TES can make buildings more grid friendly and energy or cost efficient [257, 258]. TES can be either sensible storage or a combination of latent and sensible storage. Interest and products using latent heat storage in building envelopes has increased and have regained interest of researchers during the last decades due its high capacity to store energy per mas [15]. In buildings TES can be applied in passive systems, which utilizes building envelope components to store and release energy, or in active systems, which tend to be integrated with building heating, ventilation, and air conditioning (HVAC) systems [259]. Passive PCM storage has become a popular research topic due to building envelope large surface area and the ability to add latent heat storage into light

93 mass buildings [260-263] and is also the focus on this study: PCMs uses in the building envelope [264, 265].

Due to their variable properties, design of PCM inclusions in buildings require careful and accurate energy analysis as it is important to maximize the number of times PCMs cycle between solid and liquid phases to utilize its latent heat. For this and other reasons, several PCM heat transfer models have been implemented in different building energy modeling tools [266-272]. However, an IEA Annex 23 surveyed over 250 research publications concluding that the general confidence in currently used numerical models is still too low to use them for designing and code purposes [266, 273]. Another article analyzes several modeling tools capable of simulating PCMs and supports the need for extensive model validation and comparison of the different numerical tools available today using a standardized procedure for PCM model validation [274]. These studies show validation has an important role in model development but previous work has been limited in range, applications, and conditions. For example: EnergyPlus PCM model was validated using PCM shape-stabilized experimental data [246, 275], COMSOL 2D PCM model was validated using PCM enhanced drywall with field data [14], ESP-r PCM model was validated for microencapsulated PCM [276], and WUFI PCM model was validated with data from Dynamic Heat Flux Meter Apparatus (DHFMA) [277]. These studies did not consider hysteresis in their models. Recent studies have implemented different PCM models in EnergyPlus using Energy Management System (EMS) and also as part of the source code with no clear validation with hysteresis [277]. The thermal hysteresis in PCMs occur due to PCM characterization test method and type of equipment used, and impaired PCM nucleation during the freezing process which is also known as sub-cooling [15]. Thus, there is a need for a careful validation and comparison for different PCM applications in the building envelope.

Additionally, it is important to consider the computational runtime and the performance limitations of building energy modeling, PCM models included in whole building energy modeling platforms tend to simplify the use of temperature dependent PCM properties like specific heat, thermal conductivity, and melting points [120]. The temperature dependent properties of PCMs should be obtained from characterization methods [15], but often it is not possible to use properties obtained from small samples (such from differential scanning calorimetry, DSC). The sample size of the PCM used in the characterization influences the measured values of the thermal properties and may not reflect the thermal behavior for different encapsulation methods accurately [278, 279].

Finally, materials that exhibit two or three dimensional behavior, hysteresis, and subcooling [277, 280-283], have been difficult to incorporate into the PCM models without compromising the computational runtime. Therefore, assessment and comparison of the different PCM modeling software is required.

While there has been studies comparing the thermal load modeling capabilities of different building energy modeling programs (BEMPs) using ASHRAE Standard 140 tests [284] or doing broad simulation engine comparison [285], there are no previous efforts comparing specifically PCMs models using laboratory and field data to understand and quantify the limitations of modeling techniques used in each numerical tool for an specific application (e.g. PCMs micro/nano encapsulated in drywall). Given the need for validated models that can accurately model PCMs, this study compares and validates PCM models that are part of popular building energy and hygrothermal software commonly used in building industry [286-297]: EnergyPlus, ESP-r, and WUFI. WUFI is compared here since building designers and modelers commonly use it for energy and hygrothermal performance assessments. It also compares COMSOL, a specialized numerical modeling software, using a more detailed two-dimensional heat transfer model and finally an algorithm developed in MATLAB (Thesis algorithm). PCM applications analyzed are Nano-PCM in drywall and shape-stabilized PCM layer behind drywall.

7.2. Methodology

Validation data used in this study uses experimental data from two independent PCM studies and compares PCM models implemented in different energy modeling software. The analyzed PCM heat and mass transfer models in this study are part of the following software:

(i) ESP-r: Building energy simulation tool commonly used in Europe that has two PCM models introduced as special material (PCM_Cap, model no. 53) and defined as an active building elements with variable thermo-physical properties (spmatl subroutine) [113, 298]. The latent heat is calculated based on effective heat capacity which is a linear function of temperature. Temperature dependence conductivity (linearly) can be also taken into account during simulation. ESP-r has developed sub-routines to model hysteresis in PCMs.

(ii) WUFI v6.1: Heat and mass transfer (HAMT) software for building structures [127, 129, 299- 301]. WUFI has the ability to define temperature dependent input functions via ‘Hygrothermal

Functions’ object set and ‘Enthalpy, temperature dependent’ object [302]. WUFI also has the ability to define temperature dependent conductivity via ‘Thermal Conductivity, temperature- dependent’ object. This study uses these two objects to define the temperature dependent functions of PCM properties. WUFI uses coupled heat and mass transfer equations to model heat and moisture transfer. The moisture transfer modeling component of this program is turned off in the current study to exclusively model just the heat transfer as rest of considered models only capture heat transfer phenomena.

(iii) COMSOL: The heat transfer module of COMSOL Multiphysics® (https://www.comsol.com/heat-transfer-module) is used for the simulations presented here. Temperature-dependent material properties are incorporated in COMSOL using the ‘interpolation’ function. For PCMs, the measured enthalpy as a function of temperature is provided as input and the specific heat is defined as the slope of the enthalpy vs. temperature curve, the latter is calculated as part of the solution routine [14] [144]. Biswas et al. [130] developed an algorithm using the ‘previous solution’ operator of COMSOL to capture the hysteresis in PCM and evaluated the differences in energy saving estimates with and without considering the impacts of hysteresis.

(iv) EnergyPlus v9.0: Building energy simulation software that models PCMs with a finite difference algorithm (CondFD) coupled with an enthalpy temperature function [100, 123, 246, 289]. EnergyPlus has two PCM models: with and without hysteresis. Hysteresis model uses polynomial fitting curves to describe the properties of PCM adapted from the Ginzburg-Landau theory of phase transitions [277]. EnergyPlus’ original PCM model object is MaterialProperty:PhaseChange. The object requests the inputs, (i) temperature dependent coefficient for thermal conductivity, and (ii) temperature-enthalpy data points to define the enthalpy curve. The recently introduced PCM model object named is MaterialProperty: PhaseChangeHysteresis. For both EnergyPlus PCM models, temperature dependent thermal conductivity is defined with the MaterialProperty: VariableThermalConductivity object.

(v) MATLAB: A multi-paradigm numerical computing environment and proprietary programming language [303]. MATLAB is used to model PCM inclusions in the building envelope in literature [111, 216, 297, 304]. Thesis model (in MATLAB) has been analytically verified using Stefan problem, and numerically verified with the PCM model in EnergyPlus in the

96 chapter 6. This model is used in this validation study to give the author more flexibility to further evaluate the model performance

Table 7-1 compares the above PCM models based on numerical formulation (numerical methods), solver type, method of latent heat input, and the input parameters to define the latent heat in the “mushy” region. All models assume one-dimensional (1D) conduction heat transfer with exception of COMSOL that uses 2D conduction heat transfer for ORNL Nano-PCM case. This also compares the additional accuracy gain when going from 1D to 2D heat transfer in building assemblies. These characteristics of PCM models in building energy modeling software are discussed in detail in recent literature [15, 120].

Table 7-1 Numerical modeling methods used in PCM models Model Numerical Solution schemes Latent Latent heat data formulation heat incorporation from the algorithm curves COMSOL Finite element Direct solver Enthalpy Interpolated h-T method [305, PARDISO based on method curves 306] lower-upper decomposition [307]: (matrix form of Gaussian Elimination) ESP-r Finite Volume Direct solution Effective Linear function of Method, method, semi- heat effective heat capacity Implicit, Explicit implicit scheme, capacity versus temperature and Crank iteration employed method Nicholson. [297] for the case of non- linearity [308] EnergyPlu Finite Difference Gauss–Seidel Heat Enthalpy curve with s PCM Method: Fully iterative scheme capacity maximum of 16 model Implicit and method/ temperature-enthalpy Crank Nicholson Enthalpy data points. [269] Method

Table 7-1 continued EnergyPlus Finite Gauss–Seidel Enthalpy Enthalpy curves hysteresis Difference iterative scheme Method approximated based PCM model Method: Fully on the heating and Implicit and cooling curves by Crank curve fitting Nicholson (inputs: peak phase change temperature, lower and higher temperature ranges of phase change for melting and freezing) Thesis Finite Gauss–Seidel Enthalpy Simplified PCM curve algorithm Difference iterative scheme Method with maximum 16 Method: Fully data points Implicit (current study)

WUFI Finite Volume Matrix solver: Enthalpy Simplified Method: Thomas-algorithm Method temperature-enthalpy Implicit in (1D) [309], or curve with 32 points ADI in (2D) (higher number of simulations [310]. points is possible)

The two main PCM models shown in Table 7-1 are the enthalpy method and the heat capacity method. Enthalpy method considers the total amount of energy, which includes both sensible and latent heat. This method presents heat capacity in terms of its integral form, H (T). The effective specific heat capacity ( ) is obtained as the gradient (dh/dT) of the enthalpy curves.

Heat capacity method deals with heat푐 푝capacity as a function of temperature within the temperature range of the phase transition. It numerically imitates the effect of enthalpy by controlling the heat capacity value during the phase change. Value considers both the latent heat and the sensible heat. Equations 7-1 to 7-3 show the퐴 mathematical formulation for enthalpy method, 퐶 (푇) effective specific heat capacity, and heat capacity method.

(7-1) ∂h 휕 푘 휕ℎ 휌 = ( ) ∂t 휕푥 푐푝 휕푥

(7-2) 푑ℎ 푐푝 = 푑푇 (7-3) 퐴 ∂T 휕 휕푇 휌 ∗ 푐 (푇) = (푘 ) ∂t 휕푥 휕푥 Among analyzed models, Finite difference method is the most common heat transfer algorithm due to its simplicity to code [15], followed by finite volume and finite volume numerical schemes. EnergyPlus has the simplest (to code) but slowest solution scheme (Gauss-Seidel) while WUFI and ESP-r has more complex and faster schemes. All models require either enthalpy- temperature data or heat capacity- temperature data to include phase change effects.

Validation

Verification and validation (V&V) are important steps in numerical model development to ensure desired performance and accuracy [311]. ASHRAE standard 140 defines three main approaches for V&V: (1) analytical verification, (2) empirical validation, and (3) comparative testing [312]. Verification of the analyzed PCM models have been partially documented in literature, some have use analytical solution of Stefan Problem or lab data [233, 246, 313]. However, these studies have not followed the same protocols or boundary conditions, making it impossible to compare. This study uses Root Mean Square Error (RMSE) calculated in equation 7-4, Coefficient of Variation of the Root Mean Square Error (CV (RMSE)) and Normalized Mean Biased Error (NMBE) as the accuracy analysis indices to compare the data, which is suggested by different validation guidelines and studies [314-319].

NMBE and CV (RMSE) have been specifically used together to compare simulated and measured temperature data in previous studies [173, 320]. Here, is the actual measured value,

is the predicted value. NMBE is the average of the errors of a 푦sample푖 space divided 푦̂by푖 the mean of measured values . It indicates the global difference between the(푦 푖real− 푦̂values푖) and the predicted ones as shown in the푦̅̅푚 ̅equation̅ 7-5. NMBE is subjected to the cancellation errors and therefore not recommended to be used alone [318]. Therefore, the current study also uses CV (RMSE). CV (RMSE) is the average of the square of the errors of a sample space divided by the mean of measured values as shown in the equation 7-6. ASHRAE 2 (푦푖 − 푦̂푖) ̅푦̅푚̅̅ 99

Guideline 14 considers NMBE ± 10 % and CV (RMSE) ± 30 % as the acceptable calibration criteria for the hourly data (ASHRAE guideline 14).

Guideline 14 was developed for measurements of actual buildings where there are uncertainties in occupancy, internal loads, and materials properties. Since the two validation cases have well-defined boundary conditions and many properties are known, one should expect high accuracy or use a higher standards. Thus, this study uses higher standard using NMBE ± 5% and CV (RMSE) ± 15%. In addition, the use of RMSE provides an absolute measure that is also accessed.

(7-4)

푁 2 ∑푖=1(푦푖 − 푦̂푖) 푅푀푆퐸 = √ 푁

(7-5) 푁 1 ∑푖=1(푦̂푖 − 푦푖) 푁푀퐵퐸 = ( ) × 100 푦̅̅푚̅̅ 푁

× 100 (7-6) 푁 2 1 ∑푖=1(푦푖−푦̂푖) 퐶푉 (푅푀푆퐸) = 푦̅̅̅푚̅̅ √ 푁 This validation study uses experimental data from two experiments: laboratory data from Norwegian University of Science and Technology (NTNU) using Hot-Box tests [13], and field test data from ORNL’s Natural Exposure Test (NET) facility at, Charleston, South Carolina, USA [14]. NTNU study uses shape-stabilize (DupontTM Energain®) PCM that has been well characterized enthalpy curve [321]. DupontTM Energain® PCM panel is a mixture of ethylene based polymer and paraffin wax laminated on both sides with an aluminum sheet [322]. The ORNL field study uses a paraffin based nano-PCM and characterized the PCM and performed field measurements over several months with the goal to evaluate the performance of nano-PCM enhanced gypsum board [14]. Thesis model was also verified using the same methodology as for the EnergyPlus model [246].

Table 7-2 compares the two analyzed PCMs. The enthalpy curves are determined using Differential Scanning Calorimetry (DSC). Temperature gradient used in the DSC method can influence the enthalpy curve results [216]. Both PCMs are tested using a slow heating rate (low 100 temperature gradient) to minimize any measurement error/noise. In addition, PCM percentage, distribution, and nano capsule material can also affect the thermal properties. Shape-stabilized PCM has a greater storage capacity since it is not mixed with drywall. However, both products suffer from low thermal conductivity.

Table 7-2 Properties of Analyzed PCMs Laboratory work with shape- Field experiments with stabilize PCM Nano-PCM wallboard PCM type Paraffin

n-heptadecane (C17H36) Encapsulation laminated by aluminum sheets included in graphite nano- sheets PCM percentage in the 60 20 wallboard by weight (%) Wall type Flexible sheet Gypsum board (5.26mm/0.2 inch) (13 mm/0.5 inch) Latent heat (kJ/kg) >70.1 26.2 Total heat storage capacity >170 (14°C - 30°C) 50 (15°C - 25°C) (kJ/kg) Peak melting temperature (ºC) 21.7 21.4 Thermal conductivity in 0.22 0.43 liquid phase (W/m-K) Thermal conductivity in solid 0.18 0.41 phase (W/m-K) Specific heat capacity in 3.00 2.24 liquid phase (kJ/kg-K) Specific heat capacity in in 4.50 2.31 solid phase (kJ/kg-K) Characterization method and DSC, 0.05 ºC/min DSC, 1.0 °C/min heating rate Latent storage capacity 428 770 (kJ/m2)

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Enthalpy-temperature curves of PCMs

Figure 7-1 shows the enthalpy curve for the analyzed PCMs: shape-stabilized PCMs (Figure 7-1a) and Nano-PCM (Figure 7-1b). Figure 7-1a shows a slow enthalpy increase in the “mushy” region (or wide melting range), while Figure 7-1b with the Nano-PCMs shows a prominent enthalpy gradient (or short melting temperature range).

As shown in Table 7-1, COMSOL uses an enthalpy-temperature (h-T) curve that interpolates within the available enthalpy-temperature values. Thesis algorithm uses 4 points, EnergyPlus (No hysteresis model) uses up to 16 discreet points, and WUFI uses 32 discrete points to approximate the entire curve within the temperature range of the curve. EnergyPlus hysteresis model requires, (i) peak phase change temperature, (ii) low temperature difference, and (iii) high temperature difference of phase change curves to fit curves within the phase change region. ESP- r uses linear function that relates effective heat capacity with temperature. These specific input data is obtained from Figure 7-1. The shape-stabilized PCM melting temperature ranges from 18.6 ºC to 25 ºC with the peak melting temperature at 21.7 ºC, while the Nano-PCM phase change ranges from 20.4 ºC to 21.8 ºC, with the peak melting temperature at 21.4 ºC.

Figure 7-1 (a) Enthalpy-Temperature (h-T) curves for shape-stabilized PCM, (b) and nano- encapsulated PCM.

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Numerical modeling considerations

Table 7-3 shows how each model discretizes the analyzed PCM layer. COMSOL model uses a 2D model with a mesh made using the ‘physics-controlled’ option of COMSOL and element size set to “Normal” to model the Nano-PCM. This created a non-uniform mesh. The number of discretized elements in the PCM-gypsum board are determined by the physics controlled mesh algorithm and are about 2-6 with the highest count in drywall section closest to the stud and only 2 across the thickness of the PCM-gypsum board in most places along the drywall. This is shown in the Figure 7-2. A 1D COMSOL model is used to simulate shape-stabilized PCM. This too considered a non-uniform mesh.

Figure 7-2 Non-uniform finite volume mesh implemented in COMSOL simulate the Nano-PCM layer in ORNL field test data. Nano-PCM layer comprises of two elements.

For WUFI, Fine grid with Automatic (II) option is used for the discretization. The non- uniform finite volume mesh created through this method is shown in Figure 7-3 for ORNL field study Nano-PCM layer.

Figure 7-3 Non-uniform finite volume mesh implemented in WUFI to simulate the Nano-PCM layer in ORNL field test data. Nano-PCM layer comprises of 24 volumes.

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For thesis model and EnergyPlus the grid size is uniform for each layer but each layer has different grid size which depends on the thermal properties as defined in equation 6.2. Nano-PCM layer has 4 nodes uniformly across the layer. This is shown in Figure 7-4.

Figure 7-4 Uniform finite difference mesh implemented in thesis model to simulate the Nano- PCM layer in ORNL field test data. Nano-PCM layer comprises of 4 points.

The number of discretized cells is actually an input as shown in Table 7-3. For all the models, the case indicating the grid independence was considered to show the data below.

Table 7-3 Numerical discretization considered in modeling the material layers with PCM inclusions. Spatial Discretization settings PCM layer discretized discretization SS PCM NE-PCM method Finite Element Maximum element size 11 elements COMSOL Method specification (1D) Physics controlled mesh, 2 elements normal element size (2D) EnergyPlus PCM Finite Difference Space discretization 3 nodes 4 nodes model Method constant (c)=1 Relaxation factor = 1 EnergyPlus Finite Element c=1 3 nodes 4 nodes hysteresis model Method Relaxation factor =1 ESP-r Control Volume 3 nodes 3 nodes* Method Thesis model Finite Difference c=1 3 nodes 4 nodes Method WUFI Finite Volume Fine (with Automatic 14 volumes 24 volumes Method (II) option enabled) *nodes were increased from 4-8 with no significant difference in results

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For EnergyPlus hysteresis PCM model and the thesis model that are based on the enthalpy method, solid and liquid state cp values are used outside the phase change interval. For both datasets, temperature dependent thermal conductivity information is available and used in this study. For the PCM mixed or embedded in construction materials such as drywall (Nano-PCM), this study assumes PCMs are evenly distributed across the layer and therefore, uses equivalent physical and thermal properties across the material layer (e.g. drywall). Although both PCMs exhibit little hysteresis, this is not modeled since the NTNU shape-stabilized PCM only contained melting curve and the hysteresis information was not available.

Both lab and field studies measure wall inner and outer surface temperature and this is used as the boundary conditions: surface temperature (Dirichlet boundary condition). However, this boundary condition is implemented differently using workarounds in each modeling software as most cannot accommodate fixing a surface temperature:

 COMSOL: either inner or outer surface temperatures directly or heat flux boundary conditions can be assigned at the inner and outer surfaces. Biswas et al. [14, 144] utilized both temperature and heat flux boundary conditions. Biswas et al. used heat flux boundary conditions for annual performance evaluations of PCMs using typical weather data and used temperature boundary conditions for model validation using measured temperature data. Thus, this study also uses temperature boundary conditions for both analyzed cases in COMSOL.  EnergyPlus: exterior surface temperature is set using ‘SurfaceProperty OtherSideCoefficients’ that allows users to specify a surface temperature. This can only be used on one side of a wall, so the interior surface temperature is set by increasing convection heat transfer coefficient to 1,000 W/m2-K (‘SurfaceProperty ConvectionCoefficients’) and setting the indoor air temperature to the actual surface temperature.  ESP-r: the ideal control of temperature on both sides of the test sample was assumed and convection heat transfer coefficient was set to 500 W/ (m2-K).  Thesis model: boundary temperature values are directly assigned.  WUFI: the interior and exterior temperature values are assigned, and a convective heat resistance of 0.001 m2-K/W was used on the both surfaces.

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Timestep used in all simulation programs is one minute but the experimental data from NTNU experiments was recorded every 10 minute and the ORNL field study data every hour. Therefore, the boundary condition data is interpolated to 1 minute from the recorded data. Moreover, moisture transfer is not considered in the PCM models (including WUFI and EnergyPlus) to ensure only the heat transfer phenomena is captured throughout all programs for the validation purposes. Moisture transport is analyzed in more detail in a subsequent publication [323].

Shape-stabilized PCM wall data

Table 7-4 shows material used and their properties for the NTNU wall assembly. PCM panels used in the study have 1000 mm width and 1198 mm length [13]. These PCM panels are tested with a wood frame wall construction.

Table 7-4 Material properties of the wall assembly used in the NTNU controlled hot-box experiments Layer Material Conductivity Density Specific heat Thickness (m) (W/m-K) (kg/m3) capacity (J/kg-K) 1 (exterior Gypsum 0.21 700 1000 0.013 BC) wallboard 2 PCM DuPont 0.22 (liquid) 855 2250 (liquid) 0.0053 0.18 (solid) 3250 (solid) 3 Mineral wool 0.033 29 1030 0.296 insulation 4 (interior Gypsum 0.21 700 1000 0.009 BC) wallboard

Figure 7-5 indicates the layer structure of the wall assembly for this dataset. The thermocouples used in the study are type T30/2/506 made by Gordon with an accuracy of ±0.1 K and the heat flux meters are type PU_43T made by Hukseflux with an accuracy of ±5%. The tests are performed in a hot box apparatus, where initially the cold box side was kept at −20 °C and the hot side was kept at 20 °C. At t = 0, a heater in the hot box started heating the air temperature inside the hot box for 7 hours (heating stage). The final inside wall temperature reached an upper

106 limit of ~24 °C [324]. This indicates that the PCMs within the panels would not have fully melted. After that, the heater was turned off and the hot box slowly cooled to initial temperature, 20 °C (cooling stage).

Nano-encapsulated wallboard data

Table 7-5 shows material properties used by Biswas et al. [14] to model the test wall with the Nano-PCM wallboard. The conductivities of the cellulose insulation and Nano-PCM wallboard are measured in a heat flow meter following ASTM C518.1 The density of cellulose was based on the volume of the test wall cavity and mass of insulation added, and the conductivity of cellulose was measured at the same density as the test wall cavity insulation. The specific heats of the Nano- PCM wallboard are based on the DSC data provided by the manufacturer, as the slopes of the temperature-dependent enthalpy function in the fully-frozen and fully-molten regimes. Remaining material properties are obtained from published literature. These PCM panels are also tested with a wood frame wall construction.

1 ASTM C518-17, Standard Test Method for Steady-State Thermal Transmission Properties by Means of the Heat Flow Meter Apparatus, ASTM International, West Conshohocken, PA, 2017, www.astm.org

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Table 7-5 Material properties of the wall assembly used in Nano-encapsulated wallboard Layer Material Thermal Density Specific heat Thickness 3 Conductivity (kg/m ) capacity (m) (kJ/kg-K) (W/m-K) 1 OSB 0.13 650 1410 0.013 2 Cellulose cavity 0.042 40.8 1420 0.14 3 Nano-PCM 0.427 (liquid) 658 2240 (liquid) 0.013 wallboard 0.41 (solid) 2310 (solid)

Figure 7-6 shows the layer structure of the wall assembly used in the experiments and location of the heat flux and temperature sensors. Surface temperature data at the exterior and interior surfaces and three locations within the wall panel was monitored in this study. Although the heat flux transducer was placed at the interface of the cellulose insulation and the PCM wallboard (point 5), the temperature sensor was located at point 4 in the cellulose insulation layer but its exact location is not reported. Thus, point 4 is not used for validation. 10 K ohm thermistor used in the study had an accuracy of ±0.2 °C and the heat flux transducer had an accuracy of ±5%.

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7.3. Results and Discussion

NTNU shape-stabilized PCM

Figure 7-7 and Figure 7-8 show temperature at the interface between the gypsum and PCM wallboard (point 2 in Figure 7-5) and between the PCM wallboard and mineral wool insulation for (point 3 in Figure 7-5) respectively. Both figures show results from: experimental data, COMSOL, ESP-r, E+ (no hysteresis model), E+ (hysteresis model with just the melting curve), Thesis model, and WUFI. The horizontal line in yellow shows the peak melting temperature of the PCM and the horizontal shaded area indicates the melting temperature range. The peak melting temperature of the PCM is 21.7 ºC and the highest and lowest temperatures observed at the point 2 is 22.7 ºC and 19.4 ºC. The highest and lowest temperatures observed at the point 3 is 22.6 ºC and 19.3 ºC.

Figure 7-7 shows the temperature at the point 1 to indicate the maximum temperature of the heated boundary surface. Therefore, the PCM did not transition fully from melting to freezing. However, the results are important as the PCM is still changing phase, not fully, but going from almost frozen to almost melt. In fact, it also helps to test ability of models to simulate partial phase change, which it has been shown to be challenging to simulate [325].

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Figure 7-8 also includes the line showing the temperature variation at the hot side boundary to see maximum and minimum temperatures observed at the hot-surface for this experiment. All results from the analyzed software are within the uncertainty of the measurements and follow the same trend indicating the models ability to capture partial phase change.

Figure 7-8 Temperature at the Point (3): between the PCM wallboard and mineral wool insulation. Simulated data for COMSOL, ESP-r, EnergyPlus (2 modules), Thesis model, and WUFI is shown.

Table 7-6 summarizes the performance of all PCM models based on RMSE, CV (RMSE) and NMBE values. RMSE values show agreement of all models. All values fall well within the accepted tolerances for the NMBE and CV (RMSE).

Although not shown in Figure 4 modeling the walls without PCMs gives a CV(RMSE) value of 0.92 % at the interface between gypsum and PCM wallboard and 1.03 % at the interface of PCM wallboard and mineral wool insulation which indicates the deviation from the PCM cases. All values are well below the recommended ranges of 5% (NMBE) and 15% (CV(RMSE)).

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Table 7-6 Calculated Temperature RMSE, CV (RMSE) and NMBE for all analyzed PCM models at material interfaces Point 2 of Figure 2 Point 3 of Figure 2

Model RMSE CV(RMSE) NMBE RMSE CV(RMSE) NMBE (ºC) (%) (%) (ºC) (%) (%) COMSOL 0.08 0.37 0.19 0.12 0.56 0.34 ESP-r 0.14 0.64 -0.38 0.11 0.52 -0.19 E+ PCM model 0.08 0.39 0.17 0.13 0.64 0.37 E+ hysteresis PCM model 0.08 0.58 0.17 0.13 0.61 0.37 Thesis model 0.07 0.34 0.15 0.12 0.58 0.34 WUFI 0.08 0.39 0.06 0.12 0.56 0.32 No-PCM - 0.92 0.17 - 1.03 0.38

Figure 7-9 shows the heat flux measured at the surface of the high temperature side of the envelope assembly (point 1 in Figure 7-5). During both the heating up and cooling down processes differences are observed between modeled heat fluxes and the experimental data. These differences are potentially caused by the method of setting the exterior boundary condition and how the heat flux is calculated in the software. The boundaries are defined as temperature boundary conditions in the software.

The heat fluxes calculated from simulations relate to the heat flux in the material layer which is subjected to the thermal properties of the material whereas the heat flux meter captures the heat flux at the surface which is subjected to the uncertainty of the sensors and measurement errors related to sensor placement. Note that ESP-r heat-flux results are not shown as they are not typically reported from the software. For the experimental measurements, heat flux meters had an accuracy of ±5%. This uncertainty level is displayed with the experimental data lines in Figure 7-9 and Figure 7-10.

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Figure 7-9 Heat flux at the Point (1): Hot-side boundary surface. Simulated data for COMSOL, EnergyPlus (2 modules), Thesis model, and WUFI is shown.

Figure 7-10 shows the heat flux measured at the interface between the shape-stabilized PCM layer and the mineral wool insulation layer. Interior heat fluxes (Point 3 in figure 2) are calculated using the temperature gradient between the interface node and the immediate node to the left. Modeled results are within ±10% of each other.

Figure 7-10 Heat flux at the Point (3): Interface of the PCM wallboard and mineral wool insulation. Simulated data for COMSOL, EnergyPlus (2 modules), Thesis model, and WUFI is shown.

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Both EnergyPlus models produce very close values since no hysteresis is modeled. The finite volume model of WUFI, and finite element model of COMSOL are observed together. Thesis model stands below both these sets of data. All models follow the same trend but with different slopes with thesis model having the closest agreement with the experimental data.

Table 7-7 shows the RMSE, CV (RMSE) and NMBE values for the heat flux. At the exterior surface (Point 1 in Figure 7-5) RMSE values are all above ± 1.5 tolerance and all CV (RMSE) values are above 40%. Surface heat flux is challenging to measure and typically heat flux is accurately recorded in between layers. The heat fluxes at the interface of the PCM wallboard and mineral wool insulation (point 3) show RMSE values below ± 1.0 and CV (RMSE) values between 5.5 - 12.2 % and fall within the acceptable tolerances. All models over-estimate the heat flux values based on the NMBE calculations, but are still within the recommended ranges of 15% (CV(RMSE)).

Table 7-7 Temperature RMSE, CV (RMSE) and NMBE at: (i) exterior surface of the hot-side (Point 1), (ii) Interface between the PCM wallboard and the mineral wool insulation (Point 5) Point 2 of Figure 2 Point 3 of Figure 2

Software RMSE CV(RMSE) NMBE RMSE CV(RMSE) NMBE (W/m2) (%) (%) (W/m2) (%) (%) COMSOL 1.92 43.4 0.85 0.48 12.1 11.3 E+ PCM model 1.79 45.6 0.86 0.33 8.4 7.1 E+ hysteresis PCM model 1.82 41.3 0.96 0.33 8.4 7.1 Thesis model 1.59 36.1 1.13 0.22 5.5 3.1 WUFI 1.96 44.5 0.97 0.48 12.2 11.5

Nano-encapsulated PCM wall

Figure 7-11 shows the temperature at the interface between the OSB layer and the cellulose cavity layer (point 2 in Figure 7-6) for all analyzed software. Three summer days, July 20-22 are selected to display the results. The temperature variations observed in this field study represent realistic boundary conditions in contrast with the laboratory study. The horizontal dash-line

113 represents the peak melting temperature of the PCM and the horizontal shaded gray area indicates the melting temperature range.

All models follow the same trend except for ESP-r because of the different boundary condition implemented. In ESP-r, it is not possible to just assign a surface temperature because this is a state variable as well as air temperature inside any thermal zone. The only possibility is to define the control function for heating/cooling to maintain indoor air temperature as close as possible to assumed surface temperature changes. Additionally, the heat transfer coefficient should be maximized to decrease internal surface resistance. ESP-r, the model author used had the maximum number of 12 periods for 24 hours to control indoor air temperature and assumed convection heat transfer coefficient equal to 500 W/m2-K. Even then the temperature profiles differ between models with direct surface temperature definition (1-minute frequency) and ESP-r model.

Figure 7-11 Temperature at the Point (2): interface of OSB and cellulose insulation Simulated data for COMSOL, ESP-r, EnergyPlus (2 modules), Thesis model, and WUFI is shown.

Figure 7-12 shows the temperature at the middle of the cavity. Temperature fluctuations are reduced compared to Figure 7-11 due to the insulation. All models predict the PCM behavior very closely. In both Figure 7-11 and Figure 7-12 COMSOL, two E+ models, Thesis model, and WUFI lines are together hence might not be visible separately.

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Figure 7-12 Temperature at the Point (3): middle of cellulose insulation. Simulated data for COMSOL, ESP-r, EnergyPlus (2 modules), Thesis model, and WUFI is shown.

Figure 7-13 shows the experimental temperature at point 4 and point 6. However, point 6 is the boundary condition and point 4 location was not exactly measured. Thus, we show simulated values at point 5 (between point 4 and point 6). As expected from the results from Figure 7-9 to Figure 7-13, all models obtain similar temperature values with ESP-r having lower surface temperature. Considering the second day of the displayed results, the highest and lowest temperatures measured at the left to the interface of cellulose cavity and the PCM wallboard (point 4 of Figure 7-6) are 23 ºC and 20.6 ºC. The highest and lowest temperatures observed at the interior surface (point 6 of Figure 7-6) are 21.5 ºC and 20.2 ºC. The peak melting temperature of the PCM is 21.4 ºC. Therefore, the PCM does not fully change phase from melting to freezing and vice versa in the analyzed period of time.

Figure 7-13 Model results at the Point (4), Point (5): interface of the cellulose insulation and the PCM wallboard. Simulated data for ESP-r, EnergyPlus (2 modules), Thesis model, and WUFI is shown.

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RMSE, CV (RMSE) and NMBE calculations related to comparisons in Figure 7-11 and Figure 7-12 are indicated in Table 7-8. All models show RMSE values below 1 except for ESP-r. All models also show NMBE and CV (RMSE) values below the recommended ranges with exception of ESP-r as explained previously. NMBE values give a sense of the total difference between models predicted. The negative values are an indication that models show less values in magnitude and therefore under-predicted.

Table 7-8 Surface temperature RMSE, CV(RMSE) and NMBE values at (i) Interface of OSB and the cellulose filled cavity (point 2), (ii) Middle of the cellulose filled cavity (point 3) Point 2 of Figure 3 Point 3 of Figure 3

Software RMSE CV NMBE RMSE CV(RMSE) NMBE (ºC) (RMSE) (%) (ºC) (%) (%) (%) COMSOL 0.30 1.04 -0.58 0.12 0.97 -0.85 ESP-r 2.91 9.97 -7.77 0.11 6.06 -5.45 E+ PCM model 0.03 1.02 -0.59 0.13 0.93 -0.81 E+ hysteresis PCM model 0.03 1.02 -0.59 0.13 0.93 -0.81 Thesis model 0.28 0.98 -0.58 0.12 0.95 -0.81 WUFI 0.30 1.02 -0.60 0.12 0.94 -0.83

Figure 7-14 shows the heat fluxes at the interface of the cellulose cavity and Nano-PCM wallboard (point 5 of Figure 7-6). For the modeled results, the heat flux is calculated using the temperature gradient between the interface node of the cellulose cavity and the Nano-PCM wallboard and the immediate next node modeled in the cellulose cavity.

The heat flux meters used in this experiment also had an accuracy tolerance of ±5% and this uncertainty is shown in the experimental data line of the Figure 7-14.

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Figure 7-14 Heat flux at the Point (5): interface of the cellulose cavity and the Nano PCM wallboard. Simulated data for COMSOL, EnergyPlus (2 modules), Thesis model, and WUFI is shown.

RMSE, CV (RMSE) and NMBE values for heat fluxes in Figure 7-14 are given in Table 7-9. All RMSE values are below 1 and show agreement. All values fall within the accepted tolerances for the NMBE and CV (RMSE). All models produce very similar results CV (RMSE) values between 16.27 - 17.55 %, and under-estimate heat flux peak by about 20 %.

Table 7-9 RMSE, CV (RMSE) and NMBE calculations of the heat flux variations at the interface of cellulose cavity and the Nano PCM wallboard Point 2 of Figure 3 Software RMSE CV(RMSE) NMBE (W/m2) (%) (%) COMSOL 0.42 17.55 0.07 E+ PCM model 0.41 17.27 -0.20 E+ hysteresis PCM model 0.41 17.27 -0.20 Thesis model 0.41 17.33 -0.16 WUFI 0.39 16.27 -0.13

In all the temperature comparisons, the differences between the measured and modelled values are within the uncertainty range for all cases. Differences could be due to the positioning of sensors, hygrothermal effects, and hysteresis. This indicates confidence that the models can

117 predict temperature values along similar walls. In contrast, there is greater disagreement with heat flux data, as this is typically harder to measure and compute. Interestingly, COMSOL 2D model show similar results to rest of the PCM models that used 1D heat transfer models. Therefore, for the measured locations, 2D calculation did not produce more accurate results.

7.4. Conclusions

This study empirically validates and compares 6 PCM models implemented in different building energy (EnergyPlus, ESP-r), hygrothermal (WUFI) and heat transfer (COMSOL) software, and mathematical programming language (MATLAB)/ Thesis model using data from two independent experimental studies with Nano-PCM embedded in drywall and shape-stabilized PCM behind the drywall construction material. This is a unique study that compares several up to date PCM numerical modeling software commonly used in the field with two different PCM types commonly used. The author conducts an extensive accuracy analysis of the compared results using RMSE, CV (RMSE) and NMBE calculations. Based on the analyzed PCMs, all the evaluated software tools demonstrate their ability to accurately model shape-stabilized PCM behind drywall. However, heat flux predictions show greater deviation from than surface measurements. All models agree also with the Nano-PCM experiments but ESP-r has the lowest convergence due to less precise definition of boundary conditions. Interestingly, this study shows no additional gains in accuracy when comparing a 2D heat transfer model with 1D modeling for Nano-PCM and shape-stabilized PCMs. Study affirms that this numerical modeling software can be used to model PCMs and extend the studies to evaluate unique behaviors like hygrothermal performance (WUFI, EnergyPlus). However, more work is needed to evaluate PCM in macroencapsulated applications when 2D/3D heat transfer hysteresis can have stronger effects.

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CHAPTER 8 EMPIRICAL VALIDATION AND COMPARISON OF PCM ALGORITHMS MODELING MACRO-ENCAPSULATED PCMS IN THE BUILDING ENVELOPE

This section contributes to the fulfillment of the following objectives of this research: (iii) Design and build experimental apparatus and a suitable controlled environment to test different PCMs, (iv) Conduct laboratory research to validate the numerical model and identify PCMs characteristics that could further improve the numerical solution, (v) Verify (using the numerical model) and validate (using data from laboratory experiments, field experiments, and experimental data from the in-house test apparatus) different PCM models in software platforms like EnergyPlus and WUFI. The Dynamic Heat Flux Meter Apparatus characterization of PCM hydrate salts in this study is conducted by Dr. Kaushik Biswas at the Oak Ridge National Laboratory.

8.1. Introduction

Reducing electricity demand during peak period decreases the stress on the electricity grid [326]. Specifically, electricity used for space cooling has a significant contribution to peak electricity demand as residential cooling drives electric peak demand in summer [327, 328]. Energy storage is one of the potential solutions to shave and shift building energy demand [329, 330]. Building thermal mass can be used as thermal energy storage (TES) due to the variability of heating and cooling energy demand of the buildings [15, 331]. However, most residential buildings in the U.S. tend to have low thermal mass [135], thus PCMs used in building envelope can increase the thermal mass of the building envelope, shift peak demand of HVAC system, and improve thermal comfort [332, 333]. In current research projects performed in the United States, PCMs are often used as an integral part of the building thermal envelope [219].

Due to its variable thermal properties, PCM heat transfer modeling requires algorithms that allow for variable properties, such as finite different approach. Although there are studies proposing conduction transfer function (CTF), this approach has some limitations and has not been adopted in any building energy simulation programs [334]. Most PCMs models used in building energy simulation tools use either finite different of finite volume method [15]. The design and

119 operation of PCMs requires accurate energy modeling, which in turn requires validation of these modeling approaches.

A recent IEA survey that looked into 250 publications states that the general confidence in currently used numerical models is still too low to use them for designing and code purposes [266]. A recent study validated and compared 6 PCM models used in 5 energy modeling software [335]. However, this study is focused only on Paraffins PCMs nano-encapsulated and shape-stabilized behind the drywall, but there are no current efforts for validating other PCMs or encapsulation types. Recent reviews of PCMs show that solid phase and the liquid phase of a PCM has different thermo-physical characteristics while they co-exist within the inclusion [15, 336]. PCM encapsulation also influences heat transfer as macroencapsulated applications might be subject to 2D or 3D heat transfer phenomena and movement inside PCM encapsulation.

PCMs can be either organic, inorganic, or eutectic compounds [73, 219]. Organic PCMs consist of fatty acids, fatty alcohols, esters, emulsifiers, and thickening agents [278, 337]. Inorganic PCMs are mostly made of hydrate-salts or metallics [338]. Both organic and inorganic PCMs have been used in building applications [136, 137, 337, 339-343]. PCMs are typically encapsulated either at micro or macro scale to contain PCM to hold the PCM and keep it separated from the surrounding material [15, 344, 345]. Macroencapsulated PCMs avoid additional costs related to microencapsulation [346]. There are few studies in literature which implements macroencapsulated PCM pouches in the building envelope [153, 347-351]. Macroencapsulated PCM implementation in the wall are passive or active [265, 352-354], static or dynamic [355]. Most popular PCM application is to use macro-encapsulated PCM in pouches behind drywall or above false ceiling [136, 342, 343, 356-360]. PCMs have low thermal conductivity [361], [362], with the container/pouch material can be selected to enhance the thermal conductivity [363]. This study focuses on macroencapsulated PCMs in pouches placed behind drywall.

Macroencapsulated PCMs experimental studies are done at material scale [364], system scale [365], and whole building scale [366]. Previous studies with macroencapsulated Bio-based PCM (BioPCM) at system scale level investigate the impact of the PCMs on the temperature oscillations in the building [340, 341], and the impact PCMs have on the operative temperature and cooling power demand of an office cubicle in a full-scale test room [337]. These studies conclude that macroencapsulated PCMs have greater ability to reduce indoor air temperature

120 oscillations compared with a non-PCM envelope. Another study compares field indoor air temperature against EnergyPlus with macroencapsulated PCMs to find PCM in wall and ceiling is shown to be the most suitable options in terms of increased thermal comfort and peak daytime temperature reduction [197] and with no complete validation. Biswas [367] performs a partial validation of EnergyPlus using data from BioPCM applications in a metal roof but only focusing on the attic with no clear description on how to simulate plastic pouches in a 1D model. Another study implements BioPCM behind the drywall in the exterior walls of a test hut to record PCM performance data to apply in a numerical PCM algorithm and used the inverse method to analyze PCM performance but did not conduct a validation study [80]. Muruganantham [356] implemented BioPCMs as a retrofitted mock up building and simulated the PCM as thin layer in EnergPlus to conduct a whole building energy analysis but did not validate their approach. PCM salts (calcium chloride hydrate) pouches have been implemented in a metal roof in a study to quantify the residential attic performance but does not validate the approach [340]. Therefore, these studies do not conduct validation and comparison of the heat transfer across the building envelope and also do not consider hysteresis effects.

Literature shows that macroencapsulated PCMs show 2D heat transfer effects due to the pouches or containing devices [368]. However, since most building energy modeling software assumes 1D heat transfer, it is important to develop, validate, and document a methodology to simplify this complex heat transfer and include the challenging thermal behaviors of macroencapsulated PCMs into these models.

Thus, this study validates and compares PCM algorithms in energy modeling software such as EnergyPlus, thesis model and WUFI to quantify their accuracy when modeling PCMs in building envelopes. No previous study has validated this software with different macroencapsulated PCMs. Thus, the objectives and contributions of this study are: (1) show full- scale wall experimental data from two walls with macroencapsulated PCMs, (2) validate and compare different PCM models used in building simulation programs and (3) develop a methodology to simplify 2D/3D heat transfer from the macroencapsulated system to a 1D heat transfer.

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8.2. Methodology

This study validates and compares 4 PCM models using in-house laboratory data from two macroencapsulated PCMs: a BioPCM in plastic foil/white plastic sheeting pouches and PCM hydrate–salts (hydrate-salts) encapsulated in thermoplastic foil/ multilayer white polyfilm pouches. As a reference an additional wall is also tested without PCMs. The analyzed PCMs models are EnergyPlus hysteresis PCM model [369], EnergyPlus regular (without hysteresis) PCM model [233], thesis model, and WUFI. These computational approach of these PCM models are compared and fully described in a previous publication [335](chapter 7 of the thesis). The experimental work in this study is conducted in a state-of-the-art experimental chamber located at the Department of Mechanical Engineering at Colorado School of Mines that facilitates testing of full scale wall panels under controlled conditions. Wall panels are constructed inside the chamber and placed against a radiant wall to control the exterior boundary conditions and conduct full cycle melting and freezing tests of the PCM products. Collected data is then used to validate and compare PCM modeling software.

Macroencapsulated Phase Change Materials

Figure 8-1 shows the analyzed PCMs which are commercially available and contained in pouches [370]. Figure 8-1a shows BioPCM contained in pouches made of plastic foil /white plastic sheeting. These sheets are available in 0.42 m wide mats that come in lengths of 1.22 m or 2.44 m. Figure 8-1b shows hydrate-salts contained in heavy-duty nylon/PE foil sheets. The average thickness of the pouches is 6.4 mm for the BioPCM and 6.0 mm for the hydrate-salts. The pouch thickness is not consistent over the surface area as the PCM is loosely packed.

Figure 8-1 Dimensions of analyzed PCM pouches: (a) BioPCM, (b) hydrate-salts.

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As shown in the figure, these sheets are not uniform since there is 6-21 mm gap between pouches. Therefore, extra attention is given to evaluate the impact of the presence of air with the PCM layer

Table 8-1 shows thermo-physical properties of the analyzed PCMs. Typical PCM melting temperatures used in the envelope applications are 19-27 ºC [353]. All PCMs used in the current study have a nominal melting point of 23 ºC. Hydrate-salts have higher density and thermal conductivity than the BioPCM. Therefore, for a given storage capacity, hydrate-salts add more weight to the building. Hydrate-salts are also about 4 times more conductive than the BioPCM.

Table 8-1 Thermo-physical properties of analyzed macroencapsulated PCMs. BioPCM Hydrate-salts

Product name M-51 BioPCM TM InfiniteRTM Peak nominal melting temperature 23˚C/73˚F 23˚C/73˚F Latent heat capacity (kJ/kg) ~230 ~200 Specific heat capacity (J/kg-K) 1,970 3,140 Thermal conductivity (W/m-K) Liquid: ~ 0.15 Liquid: ~0.54 Solid: ~ 0.25 Solid: ~1.09 Density (kg/m3) 860 3,420

Average thickness of the pouch – L 0.0064 0.0060 pouch (m) Latent heat (kJ/m2) ~580 ~684 Pouch material Plastic foil / white Thermos-plastic foil/ plastic sheeting. multilayer white heavy- duty nylon/PE foil bags Pouch material thickness between 0.508 1.118 the pouches (mm)

• Characterization curves of PCMs

Material characterization method is important in determining the thermal characteristics of the PCMs. There are several methods used in literature and the accuracy of the characteristic data depends on the method used [15, 278, 371]. Commonly used methods of characterization are:

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Differential Scanning Calorimetry (DSC) [372], T-history [137], guarded Hot-Box [339], and Heat Flow Meter Apparatus (HFMA) methods [130, 373]. Among these methods, Dynamic HFMA method is the more suitable method to characterize PCMs in full scale as it is used to characterize PCMs in conditions closer to the actual use of the product in buildings [80, 374]. However, manufacturers usually used DSC to characterize PCMs. The reported latent heat of the BioPCM is ~230 kJ/kg and. ~200 kJ/kg for hydrate-salts.

Recent experimental work on macroencapsulated PCMs has shown complex PCM behaviors like hysteresis and sub-cooling [340, 341, 359, 375]. The sub-cooling/ supercooling and slow heat release can cause real hysteresis. Non-isothermal conditions of the measurements can cause apparent hysteresis [278]. Sub-cooling effects are commonly seen in the hydrate-salts [376]. To obtain more reliable information on the complex behaviors of PCMs like hysteresis, author has obtained DHFMA tests to characterize the PCMs latent heat curve.

Figure 8-2 shows enthalpy curves for BioPCM obtained from DSC method and provided by the manufacturer. Melting starts at 20 ºC and finishes at 26 ºC. Freezing starts at 25 ºC and finishes at 19 ºC. Therefore, melting and freezing temperature range of ~6 ºC is observed. Peak melting temperature of 23 ºC (the rated melting temperature for the product), peak freezing temperature of 22 ºC, latent heat of 220 kJ/kg, and sensible heat of 12 kJ/kg are considered. The enthalpy change for two curves show same values. Hysteresis is defined considering the difference between the peak melting and freezing temperatures and observed a difference of 1 ºC (23 ºC peak melting temperature and 22 ºC peak freezing temperature). How these values are used to determine the simplified curves to implement in PCM modelling software is discussed in detail in chapter 6 (section 6.21). No Subcooling is observed for the BioPCM.

The source of the hysteresis of DSC characterization results could be the non-homogenous nature of the material as BioPCM product used in this study is a mixture of multiple organic materials, emulsifiers, and thickening/ gelling agents and apparent hysteresis driven by the testing method.

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Figure 8-2 Enthalpy-temperature melting curves obtained using DSC characterization method for BioPCM.

Figure 8-3 shows the hydrate salt enthalpy curve obtained from the DSC and DHFMA. DSC results shows a peak melting temperature of 23 ºC (rated melting temperature for the product), melting temperature range of ~5 ºC, latent heat of 190 kJ/kg and sensible heat of 15 kJ/kg. Compared to DSC, DHFMA shows that peak melting temperature shifts from 23 ºC to 26 ºC. Peak temperature of freezing is around 25 ºC. Melting starts at 20 ºC and finishes at 28 ºC. Freezing starts at 27 ºC and finishes at 19 ºC. Therefore, melting and freezing temperature range of ~8 ºC is measured. DHFMA results showed latent heat of 150 kJ/kg, and sensible heat of 24 kJ/kg for both melting and heating, hysteresis is defined considering the difference between the peak melting and freezing temperatures and observed a difference of 1 ºC (26 ºC peak melting temperature and 25 ºC peak freezing temperature), minimal subcooling. How these values are used to determine the simplified curves to implement in PCM modelling software is discussed in detail in chapter 6 (section 6.21). These characteristics data is used with the hysteresis PCM algorithms in EnergyPlus and thesis model.

The difference between the DSC and DHFMA results could be attributed to the test method. DSC test uses a dynamic ramp method of 1.0 ºC/min of heating rate and the DHFMA method uses a step method of heating and cooling. The step method allows for the specimen to come to the equilibrium state whereas the dynamic ramp method yield more uncertainties of the thermal equilibrium of the specimen relative to the step method. The length of the timestep is

125 determined by the signal generated after the temperature increment is taken [146]. After the temperature step (increment/decrement) is taken, time is allowed until the detected signal to come back to zero and then the next step is taken. For DHFMA method used in this study timestep is 60 minutes and temperature increment is ~1 ºC. DSC method uses a test sample of mass ~10-30 mg whereas the DHFMA method uses ~ 25 cm x 25 cm pouched PCM sample for the tests and the data is area-averaged over several pouches and could lead to difference against DSC data. This also relates to reason for reduced latent heat observed in the DHFMA results compared to the DSC data. Furthermore, achieving the thermal equilibrium for non-uniform large samples can be difficult and should be considered. The differences of DSC and DHFMA test methods used are further discussed in detail in the chapter 4 (section 4.2). The source of the hysteresis of DHFMA characterization results could be the non-homogenous nature of the material as salt-hydrate product used in this study is a mixture of salts and thickening/ gelling agents. The errors attributing to the measuring process can also further contribute to the differences observed.

Therefore, this study uses the enthalpy curve from DSC method for both PCMs when comparing the simplified heat transfer methods using the thesis model and to compare between other modelling software like EnergyPlus, and WUFI. DHFMA hysteresis results are only used in final analysis with EnergyPlus hysteresis model and the thesis model in the section 8.35.

Figure 8-3 Enthalpy-temperature curves obtained using DSC and DHFMA characterization methods for PCM hydrate-salts.

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Full scale testing environment

The laboratory consists of an environmental chamber made of stainless steel walls, a dedicated air handling unit (AHU), and a radiant wall. Figure 8-4 shows a sketch of the top view of the chamber and the dedicated heating, ventilation and air conditioning (HVAC) system. Cooling is provided by a 5 Ton chiller and a 10 row deep cooling coil. Heating is provided through the campus heating system. The chamber interior dimensions are 5.38 m (17.65 ft.) length ×4.46 m (14.63 ft.) width × 2.67 m (8.76 ft.). Ceiling height is variable from 2.67 to 3m and is able to accommodate full scale wall assemblies vertically. Chamber has the ability to control: (i) supply and return air flow rate, (ii) supply and return air relative humidity, (iii) supply and return dry bulb temperature, and (iv) the percentage of outdoor air.

The north-west wall is equipped with a hydronic radiant wall that can simulate an exterior wall subjected to solar radiation and/or drive heat transfer by applying a temperature difference across a wall assembly as it has its dedicated water (water and 30% glycol mixture) heater and chiller. The radiant wall has a surface temperature range of 4 - 60 ºC (40 - 140 ºF)

Figure 8-4 Schematic overview of, Section A: Air handling unit (AHU), Section B: return duct of the air to the AHU, Section C: Environmental chamber.

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Instrumentation and system control is done using multiple sensors and four main data acquisition (DAQ) units are used,

1. ABB PLC system (Custom interface): This system is dedicated to control purposes HVAC system and to measure supply and return air temperature, humidity, air flow rate, VOC and CO2. 2. Instrunet: This DAQ logs main experimental data such as wall surface and interface temperatures, heat flux, VOC and CO2 in the supply and return ducts, flow temperature sensors of the radiant wall. 3. Air Distribution Measuring System (AirDistSys 5000): This DAQ collects air temperature and air velocity at different locations inside the chamber. 4. FLIR T630 Infrared Camera (FLIR ResearchIR): Infrared camera to measure average interior wall surface temperature.

Table 8-2 shows instrumentation (and its uncertainty) used in this study. Thermistors are used to measure all surface temperatures all surface. Interior wall surface temperature is additionally measured by infrared thermal camera and values. Radiant wall water supply and return temperature is measured using two sets of sensors in (and on) the pipes.

Table 8-2 Sensor type, purpose, uncertainty, and quantity of the sensors used in the experimental analysis. Sensor type Purpose Uncertainty Number of sensors Heat flux meters Measure heat flux ±3% 1 per measuring between PCM and area adjacent external layer. (each panel) Thermistors/ Measure surface ±0.1ºC 1/5/7 per Surface temperature at all measuring area Thermistors surfaces Omni-directional Measure air speed near ±2% 3/4 per measuring hot-sphere wall or above PCM area Anemometers FLIR T630s Measure the surface ±2ºC Covers area of the Infrared Camera temperatures of the wall panels 3 and 4

BELIMO LRX24- Measure radiant wall ± 2% 1 unit leading the EP flow meter water flow rate flow pump.

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Inside air temperature and air speed is measured with omni-directional hot-sphere anemometers at different locations near the walls. Heat fluxes through the wall panels are measured/calculated using two methods for redundancy purposes: (i) using heat flux meters located behind the PCM layer (interface between PCM and plywood) and (ii) measuring the water flow rate and supply and return air temperature.

Envelope assemblies

Multilayer 1D walls are constructed without a stud in order to: (i) eliminate the 2D/3D effects around studs and cavities since the study is focused on validating the 1D PCM models, and (ii) focus on macroencapsulated PCM heat transfer rather than whole wall with 2D/3D phenomena. Each wall is 2.44 m x 1.22 m (8 ft. x 4 ft.) and the size is selected to: eliminate any edge effects, select the typical wall size, and cover complete radiant wall. The wall panels however does not cover the entire chamber wall. Any remaining exposed surfaces of the heat exchanger surface and the north-west wall is insulated using R-10 XPS insulation panels to minimize heat losses. Figure 8-5 shows the walls analyzed and installed against the on the radiant wall (north-west wall).

Panel 1 is the reference panel with no PCMs. PCM pouch mats are fastened to the plywood in the panels 3 and 4. Panel 3 and 4 are shown here without drywall layer to show the pouches. Each 1.22 m x 2.44 m /1.22 m x 2.44 m (4 ft. x 4 ft. / 4 ft. x 8 ft.) drywall panels are fastened with stainless steel fasteners from ~10 cm from the edge of the panels to minimize thermal bridging effects. Finally, two bars across all walls horizontally are installed to avoid bending of the panels to increase surface contact and reduce constant resistance. However, there was a slight bending mostly on the drywall, which does not affect the PCMs surfaces.

Each PCM pouch panel has 4 mats. To avoid edges or overlaps within the center of panel area a single mat is first placed in the center and the other 3 mats are cut in half and fastened around the central PCM mat. In addition, the 0.4 m x 0.4 m core area considered to place sensors are shown for both panel 3 (green) and panel 4 (orange). All wall assemblies have: (1) 0.019 m (0.75 inch) plywood as the layer exposed to the radiant wall, (2) a thin copper layer to improve the heat transfer and fire safety at the interface of plywood and drywall, and (3) 0.0127 m (0.5 inch) drywall layer exposed to the interior of the chamber. Panel 3 includes the BioPCMs and the Panel 4 includes the Hydrate-salts.

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Table 8-3 indicates the thermo-physical properties and dimensions of the materials used to construct the wall assemblies. These property values are obtained from the ASHRAE handbook of fundamentals and the manufacturers [377].

Table 8-3 Thermo-physical properties and dimensions of the material used in the wall panels. Material ρ Conductivity Specific Heat Effective Effective (kg/m3) (W/m-K) Capacity Latent Heat Thickness (J/kg-K) (kJ/kg) (m) Plywood (5-ply) 470 0.10 1880 0 0.0191 Regular drywall 800 0.16 1200 0 0.0127 PCM drywall 800 0.16 1200 110 0.0127 BioPCM pouch 850 0.25 1500 0 0.000508 material (pm) hydrate-salt pm 925 0.50 1500 0 0.001118 Air 1.225 0.0248 1005 0 N/A

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Figure 8-6 shows the front-view of the PCM mats behind the drywall. Large surface areas (compared to wall thickness) produce a one-dimensional heat flux (ASTM C 1363-97 [378], ASTM C 177-97 [379]). In addition, only the center part of the walls (shaded region) is used for thermal measurements as the outer part is used as a buffer zone where 1-dimensional flux cannot be safely assumed. All sensors are placed within this shaded core area of 0.4m×0.4m. The seven thermistors are placed to obtain average surface temperature from each interface.

Heat flux meter has an area of 0.1m×0.1m and is placed at the center of the core area to capture maximum pouch area. Four Thermistors are placed aligned the middle of the pouch on the plywood surface (T1, T3, T4, T5) and the drywall surface (two sensors either side of the pouch).

Two Thermistors are placed aligning the top and the bottom of the pouch (T2, T7). One thermistor is placed aligning the gap in between the pouches T6. The sensors are placed in this order on both side of the pouches. Given similar dimensions of both PCM macroencapsulation systems, both walls have the same sensor arrangement.

Figure 8-6 Front view of the PCM pouches and the sensor locations of the interface with the drywall layer removed.

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Figure 8-7 shows the top view of each assembly layers of the core area wall panels investigated. For the regular drywall at each interface 5 thermistors are used. There are two interfaces, behind the pouches and in front of the pouches for macroencapsulated PCM cases. Each interface has 7 thermistors and the heat flux meter is placed behind the PCM layer in parallel to the copper layer. Thermistors in the plywood-pouches interface are placed on the plywood surface slightly carved in (shown here in the plywood layer). Similarly, thermistors in the pouches-drywall interface are placed on the drywall surface slightly carved in (shown here in the drywall layer).

When averaging the temperature measured at interface sensors later in the study, the T2 and T6 are assumed to be located across the air cavity and other thermistors to be located either side of PCMs.

A surface thermistor is placed on the interior surface TS(in) and the exterior surface TS(ext) to measure surface temperatures. Two thermistors are placed on the hydronic wall fluid pipes where the flow enters the panel area Trw,inl and flow exits the panel area, Trw,oul. The interface temperature sensors (T1-T7) as seen from above is also shown here.

Figure 8-7 Top view of the core section with each material layers and the sensor locations (split view) (a) wall panels with just regular drywall (b) wall panels with PCM pouches and regular drywall.

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Cooling and heating temperature set-points for full-cycle tests

Figure 8-8 shows the radiant wall supply fluid temperature and chamber supply air temperature setpoints. These are selected not to represent actual wall temperatures but to allow the PCMs to fully cycle from solid to liquid and vice-versa with semi-realistic temperature rates: heat up rate of about 0.35 ºC/min. Literature shows temperature gradients in the range of 0.05 ºC/min [136] to 10.0 ºC/min [380] are used in characterizing PCMs in building envelope applications. Usually slower heating rates can capture the characteristics better as they allow test sample more time to reach thermal equilibrium [381].

The radiant wall supply temperature cycles from 5 ºC to 60 ºC while the chamber supply air temperature setpoint is maintained at 12.8 ºC. Chamber interior air temperature is allowed to float by 4-7 ºC. These experiments are repeated 5 times for repeatability purposes. The time interval between the setpoint changes are determined based on (ii) when the interface temperatures come to a steady state, (ii) and both sides of the PCM layer reach beyond the phase change temperature interval. A range of 12-24 hour time intervals are examined to find cycling period that allows for PCM to fully change phase. It is determined to cycle 16 hours to allow temperatures to get to steady state at each cycle and shown in blue shaded range in Figure 8-8. Data is obtained for 100 hours allowing for 3 full cycles of phase change for the analysis purposes.

Figure 8-8 Radiant wall supply fluid temperature setpoint and chamber air temperature.

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Heat transfer modeling of macroencapsulated PCMs

PCM encapsulation influences the PCM melting and freezing processes. PCM pouches in the building envelope create air voids due to the gaps between the pouches as well as the uneven distribution of the PCMs in the pouches. PCMs in the pouches are concentrated towards the middle/lower of the pouch due to gravity effects and melting. These voids can hinder the heat transfer across the PCM layer. Figure 8-9a shows the gaps between the pouches on the vertical direction and horizontal direction Furthermore, it shows how the distribution within the

BioPCM leading to empty pockets within(퐴1). the pouch as well as air gaps due to the uneven thickness of the pouch. Figure 8-9b shows a schematic of the cross section of macroencapsulation to visualize the airgaps and PCM distribution. The rated average thickness of the PCM pouch layer is 6.4mm for the BioPCM and 6 mm for hydrate salts. To find the average PCM volume of a pouch a fluid displacement test is used by removing the PCMs from the pouches and completely submerging the PCM in olive oil (hydrate-salts has a water content) and the volumes for 5 pouches are averaged for each pouch type. The measuring devices has a ± 5% uncertainty. BioPCM measured average value is 19.6 cm3 and PCM-salts is 14.5 cm3 of PCM per pouch.

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To simplify heat transfer process through the pouches with minimal accuracy losses, three methods are considered and are summarized in Figure 8-10. Figure 8-10a shows an effective thickness approach, Figure 8-10 b considers parallel path heat transfer approach and Figure 8-10 c also considers parallel path heat transfer and treats the PCMs as a porous media. For these calculations the reference cross sectional area A is the aggregate of A1 and A2 indicated in the above. PCM pouch layer comprises of repetition of ‘A’ units across the surface. For BioPCM A=77.2 cm2 and for hydrate-salts A=54, 0 cm2.

1. Effective thickness approach: This method defines an effective thickness assuming PCM is evenly distributed as a thin layer as shown in Figure 8-10a [153]. It ignores the void section between (or inside) pouches, and assumes nominal PCM density, specific heat capacity, and latent heat of PCM. Equation 8-1 and Equation 8-2 shows the calculation of the effective thickness Leff.

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(8-1)

퐴 = 퐴1 + 퐴2

(8-2) 푉푃퐶푀 퐿푒푓푓 = 퐴 2. Parallel path with continuous PCM: This method simulates PCM pouches using parallel path thermal network to calculate an effective thermal conductivity that includes PCM and void spaces. This is done in two approaches as discussed by Bergman et al. [382] to model heat transfer across a composite wall.

2(a): The parallel network analysis considers also the drywall and plywood (Figure 8-11).Therefore, is termed “full” parallel path. Thus, one serial network consist of plywood-air-pouch-air-drywall (network cavity) and another serial network consist of

plywood-pouch material-PCM-pouch-drywall (network pcm). Acav and Apcm are cavity path area and PCM path area.

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2(b): The parallel network analysis considers only the PCM layer (Figure 8-12). Therefore, a single node temperature is implemented with the assumption of interfaces (surfaces normal to the heat transfer direction) are isothermal. This is termed “partial” parallel path moving forward.

Equation 8-3 shows the total thermal resistance (Rtot) for parallel heat transfer, this equation is the same for 2(a) and 2(b).

(8-3) 푅푐푎푣 ∗ 푅푝푐푚 푅푡표푡 = 푅푐푎푣 + 푅푝푐푚

For 2(a), resistances through first serial path (Rcav) includes resistances of drywall, air, pouch material air, drywall as shown in equations 8-4 and 8-5. Pouch thickness value values (Lpm) for the pouch gaps are given by the manufacturer (Lpm).

(8-4)

푅푐푎푣 = 푅푐푎푣,푑푤 + 푅푐푎푣,푎푖푟1 + 푅푐푎푣,푝푚 + 푅푐푎푣, 푎푖푟2+ 푅푐푎푣,푝푙푦

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퐿푎푖푟 1 퐿푎푖푟 1 (8-5) 푑푤 푎푖푟 ∗ 푟푎푑 1−2 푝푚 푎푖푟 ∗ 푟푎푑 3−4 푝푙푦 1 퐿 푘 ℎ 퐿 푘 ℎ 퐿 푅푐푎푣 = ( + + + + ) 퐴푐푎푣 푘푑푤 퐿푎푖푟 1 푘푝푚 퐿푎푖푟 1 푘푝푙푦 ( 푎푖푟 + 푟푎푑 1−2) ( 푎푖푟 + 푟푎푑 3−4) 푘 ℎ 푘 ℎ Resistances through second serial path (Rpcm), through plywood, pouch material, PCM, pouch material, drywall is shown in equation 8-6.

(8-6)

푅푝푐푚 = 푅푝푐푚,푑푤 + 푅푝푐푚,푝푚1 + 푅푝푐푚,푃퐶푀 + 푅푝푐푚,푝푚2+ 푅푝푐푚,푝푙푦

(8-7) 퐿푝푚 퐿푝푚 1 퐿푑푤 ⁄ 퐿푃퐶푀 ⁄ 퐿푝푙푦 푅푝푐푚 = ( + 2 + + 2 + ) 퐴푝푐푚 푘푑푤 푘푝푚 푘푃퐶푀(푇) 푘푝푚 푘푝푙푦

The effective area of PCM serial network (Apcm) is based on the PCM occupied volume

(VPCM) and thickness LPCM as shown equation 8-8. Pouch material thickness Lpm and the average pouch thickness Lpouch is used to calculate the PCM thickness LPCM (equation 8-9). Ap2 and Ap1 are determined as shown in equation 8-10 and the area ratios (λcav, λpcm) for parallel heat transfer are defined in equation 8-11 and equation 8-12.

(8-8) 푉푃퐶푀 퐴푝푐푚 = 퐿푃퐶푀

(8-9)

퐿 푃퐶푀 = 퐿푝표푢푐ℎ−퐿푝푚

(8-10)

퐴푐푎푣 = 퐴 − 퐴푝2

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(8-11) 퐴푐푎푣 휆푐푎푣 = 퐴

(8-12) 퐴푝푐푚 휆푝푐푚 = 퐴 Heat transfer through the pouches is only due to conduction and radiation heat transfer as the PCM pouches are very thin, and are actually in a gel state due to gelling agents added to PCMs. The gel state was also confirmed by visual inspection. Recent analysis of PCMs in pouches has also confirms these assumptions [80]. Therefore, conduction and radiation heat transfer resistances are used to calculate the total resistance through the air gaps and shown in equation 8-13 and equation 8-14.

(8-13)

푅푐푎푣, 푎푖푟1(푐표푛푑) ∗ 푅푐푎푣,푎푖푟 (푟푎푑1−2 ) 푅푐푎푣,푎푖푟1 = 푅푐푎푣, 푎푖푟1(푐표푛푑) + 푅푐푎푣,푎푖푟 (푟푎푑1−2 )

(8-14) 푅푐푎푣, 푎푖푟1(푐표푛푑) ∗ 푅푐푎푣,푎푖푟 (푟푎푑 3−4 ) 푅푐푎푣,푎푖푟2 = 푅푐푎푣, 푎푖푟1(푐표푛푑) + 푅푐푎푣,푎푖푟 (푟푎푑 3−4 ) The radiative heat transfer between surface 1-2 and 3-4 (Figure 8-11) are shown in equation

8-15 and equation 8-16. Here, Tave (1, 4) is the average temperature is calculated using temperatures of surface 1 and 4 (equation 8-17). In calculating the radiation heat transfer coefficient Tave (1, 4) is used in place for T2 and T3 because the simulations showed these values showed less than 0.10 RMSE when comparing due to the high relative conductivity of the pouch material to air. The view factors between the surfaces, F12 and F34 are calculated using the radiation exchange equation for two rectangular plates and are 0.85 for each surface [383]. Emissivity of each surface is obtained through ASHRAE handbook of fundamentals and published databases (Ԑplywood=0.95,

Ԑcopper=0.07, Ԑdrywall=0.85, BioPCM pouches (cream surface plastic pouches) ԐBioPCM,pm =0.8,

Hydrate salt pouches (nylon foil with painting coat): Ԑsalts,pm=0.80)[377, 384]. For the plywood layer surface the emissivity of the copper is assumed when calculating radiative heat transfer even

139 if the copper layer is not modelled as a separate layer. Thermal conductivity resistance in all opaque layers is calculated using equation 8-18.

(8-15) 1 − 휀1 1 1 − 휀2 (( 1 ) + ( 12) + ( 2 )) 휀 퐹 휀 푅푐푎푣,푎푖푟 (푟푎푑1−2 ) = 2 2 퐴푐푎푣(푇1 + 푇푎푣푒(1,4))(푇1 + 푇푎푣푒(1,4))

(8-16) 1 − 휀3 1 1 − 휀4 (( 3 ) + ( 34) + ( 4 )) 휀 퐹 휀 푅푐푎푣,푎푖푟 (푟푎푑 3−4 ) = 2 2 퐴푐푎푣(푇푎푣푒(1,4) + 푇4 )(푇푎푣푒(1,4) + 푇4)

(8-17) 푇1 + 푇4 푇푎푣푒(1,4) = 2

(8-18) 퐿푙푎푦푒푟 푅푐표푛푑 = 퐴푝푎푡ℎ ∗ 푘푙푎푦푒푟 Thermal conductivity of the PCM layer is defined in three stages of phase change, solid, liquid and the “mushy region”. The mushy region considers the temperature dependent conductivity show in equation 8-19. Tm, low is low bound of the melting temperature range and then Tm, high is the higher bound of the melting temperature range. ks, PCM is solid state PCM thermal conductivity and kl, PCM is liquid state PCM thermal conductivity.

푘푠,푃퐶푀, 푇 ≤ 푇푚,푙표푤 (8-19)

푠,푃퐶푀 푙,푃퐶푀 푃퐶푀 푙,푃퐶푀 (푘 − 푘 ) 푚,푙표푤 푚,푙표푤 푚,ℎ푖푔ℎ 푘 = 푘 + ( 푚,ℎ푖푔ℎ 푚,푙표푤 (푇 − 푇 ) ) 푇 < 푇 < 푇 푇 − 푇 푙,푃퐶푀 푚,ℎ푖푔ℎ { 푘 , 푇 ≥ 푇 The effective density (ρ), specific heat (cp), and latent heat (LH) are calculated based on mass basis following equations 8-20 to 8-22 [375].

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(8-20)

푚푃퐶푀 휌푚,푃퐶푀 = 휌푃퐶푀 ∗ ( ) 푚푃퐶푀 + 푚푝푚+ 푚푎푖푟

(8-21) 푚푃퐶푀 푐푝푚,푃퐶푀 = 푐푝푃퐶푀 ∗ ( ) 푚푃퐶푀 + 푚푝푚+ 푚푎푖푟

(8-22) 푚푃퐶푀 퐿퐻푚,푃퐶푀 = 퐿퐻푃퐶푀 ∗ ( ) 푚푃퐶푀 + 푚푝푚+ 푚푎푖푟 3. Parallel path method assuming PCMs are porous: Same as 2 (“full” parallel path and “partial” parallel path) but considers the PCMs as a soft porous permeable solid matrix, [385-388]. The effective conductivity kPCM, porous is calculated using equation 8-23 [389-391] for heat transfer through porous media, where kPCM is the PCM conductivity in continuous media and kair is the thermal conductivity of air surrounding the PCM. Conductive heat transfer is assumed through the pore structure within the PCMs due to thin layers considered. Ԑ is the porosity and defined in equation 8-24. The inter-particle porosity data is not available for the PCMs investigated. Porosities are therefore approximated by values obtained from literature for the components that PCMs comprises of, =0.3 for BioPCM (esters, fatty acids, fatty alcohols) [392], and =0.1 for

PCM hydrate-salts [386,휙 393]). After the conductivity is calculated, the resistance of휙 the PCM layer is defined in equation 8-25.

(8-23) 푘푎푖푟 푘푃퐶푀,푝표푟표푢푠 = 푘푃퐶푀 ∗ (1 + (휙 ∗ ( − 1))) 푘푃퐶푀 (8-24) 푉푣표푖푑 휙 = 푉푃퐶푀 (8-25) 퐿푃퐶푀 푅푐표푛푑,푝표푟표푢푠 = 퐴푝2 ∗ 푘푃퐶푀,푝표푟표푢푠

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Using the simplified methods in the 1D thesis model

Thesis model is a 1D heat transfer model. Therefore, above discussed parallel path resistor methods should be implemented to calculate the temperatures at each node to compare with the experimental data for the validation study. Parallel path thermal resistance values are used to calculate the effective conductivity of the layer nodes.

For full parallel path method, the heat transfer is calculated for the cavity path and pcm path using the thesis model separately since the exterior and interior boundary temperatures are the same for the two paths. Effective conductivity is calculated through the air layer of the cavity path since both conduction and radiative heat transfer is considered. The resultant heat fluxes are then averaged weighted based on the area of each path. This helps to calculate the node temperature values for drywall-pouches and pouches-plywood interfaces.

For the partial parallel path method, the effective conductivity values are dynamically calculated since the interface temperatures are assumed the same for the both paths. Area weight is also used in this method to calculate total resistance value. keff, pouch values are calculated for the

PCM pouch layer using the equation 8-26. Reff, pouch is the total R value across the PCM pouches layer. The keff, pouch values are calculated for each timestep and are dependent on the temperature since the conductivity of the PCM (kPCM) is temperature dependent.

(8-26)

퐿푝표푢푐ℎ 푘푒푓푓,푝표푢푐ℎ = 퐴 ∗ 푅푒푓푓,푝표푢푐ℎ Figure 8-13 summarizes how the heat transfer across pouches with 3D heat transfer characteristics is simplified using the geometry of the pouches and parallel path thermal resistance methods. Figure 8-13a shows the actual pouch indicating non-homogenous PCM distribution. Figure 8-13b shows the reduced 3D view based on PCM distribution and geometry. Figure 8-13c shows the 2D view of the parallel path method applied to calculate the heat transfer and Figure

8-13d shows how the current timestep keff values calculated using resistor methods are used in the 1D heat transfer thesis model using the current timestep temperatures.

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For the thesis model, a uniform mesh size is used across the PCM pouches layer. Average of the effective conductivities of the liquid phase and the solid phase is used to set the space discretization Δx using the equation 6-2. Δt used throughout this study is 1 minute.

These simplifications and assumptions are built and compared validated the thesis model due to programming flexibility. After this, the simplification with the closest agreement is implement in EnergyPlus, thesis model and WUFI.

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PCM models used in Building energy and hygrothermal software

This study compares PCM models from EnergyPlus (2 modules), and WUFI in addition to a customized validated PCM model in thesis model previously validated with analytical and empirical data. A detailed description and comparison between these models is described in a recent study [335]. The comparison of the different heat transfer methods and validation study of EnergyPlus, thesis model and WUFI are conducted without hysteresis data. Hysteresis data of PCMs are used in the final section of the study to compare the simulations of EnergyPlus and thesis model with and without hysteresis.

Validation

ASHRAE standard 140 defines three main approaches for V&V: (1) analytical verification, (2) empirical validation, and (3) comparative testing [394]. Verification and validation (V&V) are important steps in numerical model development to ensure desired performance and accuracy [233]. Tabares et al. discusses an approach to validate PCM models with experimental data. The empirical validation of the PCM modeling software has not been done for PCM pouches using the system scale implementation.

RMSE, NMBE and CV (RMSE) are recommended for error evaluation of energy, heat- flux and temperature [317]. This study uses graphical comparison, Root Mean Square Error (RMSE), Coefficient of Variation of the Root Mean Square Error (CV (RMSE)), and Normalized Mean Biased Error (NMBE) as the indices to validate the models and are used together in several recent studies [320, 395]. The recommended ranges of (NMBE) and (CV (RMSE)) are ± 10% and 30% according to the ASHRAE guideline14.

The thesis tolerances considered are NMBE of ± 5% and CV(RMSE) of ± 15%. These measures are calculated using equations 8-27 to 8-29. Here, represents measured values and represents simulated values. N is number of data points. is푦푖 the mean of the measured values.푦̂ 푖 푦̅̅푚̅̅ (8-27)

푁 2 ∑푖=1(푦푖 − 푦̂푖) 푅푀푆퐸 = √ 푁

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(8-28) 푁 1 ∑푖=1(푦̂푖−푦푖) 푁푀퐵퐸 = ( ) × 100 ̅푦̅푚̅̅ 푁

× 100 (8-29) 푁 2 1 ∑푖=1(푦푖−푦̂푖) 퐶푉 (푅푀푆퐸) = 푦̅̅̅푚̅̅ √ 푁 As similar temperature variations are observed in the 3 melting and freezing cycles in the considered time interval, the author zoomed into of 32-hour window for the graphical comparison and the accuracy analysis. Differences due to the positioning of sensors, hygrothermal effects are not taken into account in this analysis.

8.3. Results and Discussion

Temperature variation on the surfaces of the panels

Figure 8-14 and Figure 8-15 show the surface temperatures for all the panels investigated for a 4-day (96 hour) test. Blue shaded area indicates allowed half-cycle time of 16 hours. The dashed horizontal line shows the nominal PCM melting temperature of the PCM of 23 ºC. Cream color shaded area indicates the phase change interval obtained from the manufacturer provided PCM data. For BioPCM the value is 6 ºC and for the PCM hydrate-salts the value is 5 ºC. Both figures show the exterior (Exterior surface) temperature and interior (Interior surface) temperature measurements. These temperatures are input as temperature boundary condition for the thesis model and other software used in the validation study.

Average interface temperatures between plywood and pouches interface (Experimental (ply-pou)) and average temperature at the across pouches and the drywall (Experimental (pou- dry)) are also shown for both panels. These averaged values are calculated by taking the location of each interface thermistor in the interface and are described above. Actual heating rates observed across the PCM pouches are 0.11 ºC/min at the interface of plywood-pouches pouches and 0.05 ºC /min at the interface of PCM pouches-drywall for both heating and cooling for both BioPCMs and Hydrate-salts.

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6 ºC

5 ºC

Figure 8-15 Boundary and interface temperatures of the wall assembly with PCM hydrate salts. Lines, 1. Exterior surface temperature, 2. Plywood-pouches interface temperature, 3. Pouches- drywall interface temperature, 4. Exterior surface temperature.

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Temperature variation of the PCMs behind drywall

Figure 8-16 shows the temperature variations observed on the surface of the drywall exposed to the interior of the chamber. The core area is represented by the box, and the surface temperature sensor is located at the “curser”. The figure also shows that the temperature distribution is influenced by the PCM pouch mats. Maximum temperature differences observed across the core measuring area is ~1.2 ºC. This is less than the rated uncertainty of the IR camera surface temperature measurements.

Figure 8-16 Surface temperature recorded and visualized through the Infrared Camera measured every 2 hour intervals after radiant wall setpoint is increase from 40 ºC to 140 ºC. 147

Figure 8-17 maps the discrete temperature measurements shown in the above Figure 8-16 to the temperatures measured from the in surface thermistor at the surface of the BioPCM panel.

Figure 8-17 Average core surface temperature (panel 3): The temperatures at every 2 hour period is mapped with the figure Figure 8-16.

Comparison of heat transfer approaches for PCM macroencapsulation

This section conducts a graphical comparison and accuracy analysis of interface temperatures to select a method that shows the closest agreement with the experimental data.

• BioPCM

Figure 8-18 graphically compares temperature at the plywood-pouches interface for BioPCM. Averaged temperature of the 7 interface sensors are used for experimental temperature. The average temperature is calculated taking into consideration the location of the temperature sensors on the pouch mat. The sensors at the top of the pouch and the gap in-between pouches are considered to be placed at air-pouch material-air path of heat transfer, and the sensors at the middle of the pouch and bottom of the pouch are considered to be placed at pouch material-PCM-pouch material path of the heat transfer.

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Data is shown for 32 hours (the second full cycle of melting and freezing of the data shown above). The average temperatures for plywood-pouches interface and pouches-drywall interface for the full parallel path method are calculated using the weights of the areas Acav and Apcm of each path. The interface temperatures for the partial parallel path are directly output in the thesis model. Blue shaded area shows the cooling cycle of 16 hours. Methods (i) effective thickness, (ii) full parallel path, solid PCM, (iii) partial parallel path, solid PCM, (iv) full parallel path, porous PCM, and (v) partial parallel path, porous PCM are compared with the experimental data. Lines 4 (partial parallel path, solid PCM and line 6 (partial parallel path, porous PCM show closest agreement in graphical comparison. Full parallel path method with no latent heat is also shown in figure to indicate the influence of the latent heat on the curves.

Figure 8-19 shows the graphical comparison of temperature at the pouches-drywall interface for BioPCM. Methods, (i) effective thickness, (ii) full parallel path, solid PCM, (iii) partial parallel path, solid PCM, (iv) full parallel path, porous PCM, and (v) partial parallel path, porous PCM are compared with the experimental data.

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Area averaged temperature of the 7 interface sensors are used for experimental temperature.

Table 8-4 shows the accuracy analysis related to the above comparisons. While CV(RMSE) values and NMBE values fall within the guideline the RMSE values are lowest for partial parallel path, solid PCM method. From the graphical comparison and the accuracy analysis, the partial parallel path, solid PCM method is the method with least disagreement for the BioPCM simulation.

Table 8-4 Accuracy analysis for the comparison of two interface temperatures for BioPCM. Software Interface: plywood-pouches Interface: pouches-drywall RMSE CV (RMSE) NMBE RMSE CV (RMSE) NMBE (ºC) (%) (%) (ºC) (%) (%) Effective 1.31 5.0 -3.5 2.57 9.8 3.2 thickness

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Table 8-4 continued Full parallel path, 3.11 11.9 5.3 2.52 9.7 4.3 solid PCM Partial parallel 0.97 3.7 -0.02 1.76 6.7 2.6 path, solid PCM Full parallel path, 2.94 11.2 5.4 2.34 8.9 4.3 porous PCM Partial parallel 1.14 4.4 1.1 1.67 6.9 2.2 path, porous PCM

Figure 8-20 shows the heat flux through the wall assembly with BioPCM. The line 1 represents heat flux calculated the heat flux at the radiant wall based on inlet and outlet fluid temperatures. The line 2 represents heat flux calculated using Heat Flux Meter data. The line 3 represents heat flux at the plywood-pouches interface calculated using thesis model, partial parallel path solid PCM above.

Figure 8-21 shows the temperature plot through the cross section of the wall panel using the partial parallel path, solid PCM method for BioPCM. Temperatures are plotted at two times. t=0h corresponds to the starting point of heating cycle in Figure 8-18. t=16h corresponds to the

151 end point of heating cycle in Figure 8-18. The simulations are done for c=1 and c=0.5 discretization constants for the PCM pouches layer for the equation 6.2 which models 5 nodes and 7 nodes. Plywood-pouches interface temperature shows that model overestimates temperature at the end of the heating cycle.

• PCM hydrate salts

Figure 8-22 shows the graphical comparison of temperature at the plywood-pouches interface for hydrate-salts. Similar to the BioPCM case, average temperature is calculated taking into consideration the location of the temperature sensors on the pouch mat. Data is shown for 32 hours (for the same time period used for the BioPCM). Methods (i) effective thickness, (ii) full parallel path, solid PCM, (iii) partial parallel path, solid PCM, (iv) full parallel path, porous PCM, and (v) partial parallel path, porous PCM are compared with the experimental data. Lines 4 (full parallel path, solid PCM) and line 6 (full parallel path, porous PCM) show closest agreement in graphical comparison. Averaged temperature of the 7 interface sensors are used for experimental temperature. Full parallel path method with no latent heat is also shown in figure to indicate the influence of the latent heat on the curves.

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Figure 8-23 shows the graphical comparison of temperature at the Pouches-drywall interface for Hydrate-salts. Methods i) effective thickness, (ii) full parallel path, solid PCM, (iii) partial parallel path, solid PCM, (iv) full parallel path, porous PCM, and (v) partial parallel path, porous PCM are compared with the experimental data.

Figure 8-23 Temperature at the interface of pouches and drywall of hydrate-salt wall panel Lines, 1. Experimental data. 5 simplification methods: 2. Effective thickness 3. Full parallel path, solid PCM, 4. Partial parallel path, solid PCM, 5. Full parallel path, porous PCM, 6. Partial parallel path, porous PCM, and 7. Partial parallel path, without PCM (no-latent heat).

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Lines 4 (full parallel path, solid PCM) and line 6 (full parallel path, porous PCM) show closest agreement in graphical comparison. Averaged temperature of the 7 interface sensors are used for experimental temperature.

Table 8-5 shows the accuracy analysis for the above comparisons. While CV(RMSE) values and NMBE values fall within the guideline the RMSE values are lowest for method full parallel path porous PCM. From the graphical comparison and the accuracy analysis, the full parallel path, porous PCM method is the method with the least disagreement for the hydrate-salts PCM simulation.

Table 8-5 RMSE, CV(RMSE), NMBE values for the comparison of two interface temperatures for hydrate-salts.

Interface: plywood-pouches Interface: pouches-drywall Software RMSE CV (RMSE) NMBE RMSE CV (RMSE) NMB (ºC) (%) (%) (ºC) (%) E (%) Effective thickness 2.30 8.9 -5.9 2.85 11.1 3.5 Full parallel path, 1.47 5.7 3.6 1.46 5.7 4.1 solid PCM Partial parallel 4.06 15.6 -2.7 2.5 9.6 4.7 path, solid PCM Full parallel path, 1.44 5.6 3.5 1.43 5.3 4.0 porous PCM Partial parallel 3.90 15.0 -2.4 2.47 9.5 4.5 path, porous PCM

Based on this analysis, method 2(b) for the BioPCM and method 3(a) for the Hydrate-salts are selected for further analysis. Adjusted porosity value for BioPCM yielded no improved results and adjusted porosity for Hydrate-salts yielded improved results. The approaches full parallel path and partial parallel path showed contrasting results for the two PCMs. The contrasting thermal resistances through the PCM layer due to 4 times higher conductivity of PCM-hydrate salts can be a cause of two different approaches of thermal networks used resulting in the choices with least

154 disagreement for BioPCM and hydrate-salts. The increasing difference between effective conductivity values across the PCM pouches layer can lead to different resistance.

Comparison of EnergyPlus, thesis model, and WUFI software

After selecting the methods with lowest RSME and NMBE (partial parallel path, solid PCM for the BioPCM and full parallel path porous PCM, for the hydrate-salts) from the above comparisons, the thermo-physical properties and dimensions considered in the selected method are implemented in the EnergyPlus and WUFI software. Both modules (with and without the ability to model hysteresis are used for EnergyPlus). Total thermal resistance (R value) across the PCM layer obtained from the thesis model simulations are used to determine the effective conductivity across PCM layer and implemented for both selected methods. Simulated data is then compared with the experimental data at the each interface. For EnergyPlus hysteresis model and the thesis model, only the melting curve obtained from DSC characterization considered at this stage of the analysis for both PCMs.

• BioPCM

Figure 8-24 shows the plywood-pouches interface temperature for E+ (two modules), thesis model, and WUFI simulated data compared with the experimental data. Graphical comparison shows agreement of the simulated curves with the experimental data.

Figure 8-24 Plywood-pouches interface temperature compared with the E+ (two modules), thesis model, and WUFI for BioPCM.

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Figure 8-25 shows the pouches-drywall interface temperature for E+ (two modules), thesis model, and WUFI simulated data compared with the experimental data. All the models overestimate the temperatures after the PCMs.

Figure 8-25 Pouches-drywall interface temperature compared with the E+ (two modules), thesis model, and WUFI for BioPCM.

Table 8-6 shows the accuracy analysis of the above graphical comparisons. CV(RMSE) values and NMBE values fall within the guideline. All models show agreement with tolerances of ± 1.79 ºC for the plywood- pouches interface and ± 1.63 ºC for Pouches-drywall interface.

Table 8-6 RMSE, CV(RMSE), NMBE calculations of temperatures at each interface for EnergyPlus, thesis model, and WUFI for BioPCM. Interface: plywood- pouches Interface: Pouches-drywall Software RMSE CV (RMSE) NMBE RMSE CV(RMSE) NMBE (ºC) (%) (%) (ºC) (%) (%) E+ PCM model 1.66 6.4 1.7 1.63 6.2 2.9 E+ Hysteresis 1.57 6.0 0.5 1.61 6.1 3.0 model Thesis model 0.97 3.7 -0.02 1.76 6.7 2.6 WUFI 1.79 5.1 3.0 1.57 6.0 2.9

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• PCM hydrate-salts

Figure 8-26 shows the graphical comparison of plywood-pouches interface temperature for E+ (two modules), thesis model, and WUFI.

Figure 8-26 Plywood-pouches interface temperature compared with the E+ (two modules), thesis model, and WUFI for hydrate-salts.

Figure 8-27 shows graphical comparison of the plywood-pouches interface temperature for E+ (two modules), thesis model, and WUFI for hydrate-salts.

Figure 8-27 Pouches-drywall interface temperature compared with the E+ (two modules), thesis model, and WUFI for hydrate-salts.

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Table 8-7 shows the accuracy analysis for the above comparisons. CV(RMSE) values and NMBE values fall within the guideline. All models show agreement with tolerances of ± 1.47 ºC for the plywood-pouches interface and ± 1.49 ºC for Pouches-drywall interface.

Table 8-7 RMSE, CV(RMSE), NMBE calculations comparisons of temperatures at each interface for EnergyPlus, thesis model, and WUFI for hydrate-salts panel

Interface: plywood-pouches Interface: Pouches-drywall Software RMSE CV (RMSE) NMBE RMSE CV (RMSE) NMBE (ºC) (%) (%) (ºC) (%) (%) E+ PCM model 1.32 5.1 3.0 1.37 5.3 3.7 E+ Hysteresis 1.47 5.7 3.5 1.49 5.7 4.0 model Thesis model 1.43 5.6 3.5 1.43 5.5 4.0 WUFI 1.34 5.2 3.0 1.36 5.3 3.7

Validation study with hysteresis characteristic data

Up to this point of the analysis, the hysteresis data was not implemented in the algorithms. This section compares the EnergyPlus and thesis model simulations including the hysteresis characteristics discussed in the section 8.21. For all figures showing results in this section peak temperature of the melting is shown in light blue dashed lines and peak temperature of the freezing is shown in dark blue dotted lines. The blue shaded area indicates the freezing cycle time interval of 16 hours.

• BioPCM

Figure 8-28 shows the interface temperature of the BioPCM panel simulated in EnergyPlus hysteresis model with and without hysteresis data. Figure 8-28a shows the plywood and pouches interface temperature and Figure 8-28b shows the pouches and drywall interface temperature. No hysteresis data means that the single DSC curve data is used and with hysteresis means that 2 curves for melting and freezing are used. The graphical comparison shows that during the phase change, the curves are relatively closer to the experimental data curve when the hysteresis is considered.

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Figure 8-29 shows the interface temperature of the BioPCM panel simulated in thesis model with hysteresis and without hysteresis data. Graphical comparison shows that during phase change the curve with hysteresis moves further leftward.

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Table 8-8 shows the accuracy analysis for the above comparisons for the cases graphically compared in the Figure 8-28 and Figure 8-29. CV(RMSE) values and NMBE values fall within the thesis guideline. EnergyPlus and the thesis model show improved biased error when the hysteresis data is considered.

Table 8-8 RMSE, CV(RMSE), NMBE calculations of temperatures at each interface for EnergyPlus, thesis model for the simulations applying thermal hysteresis characteristics for BioPCM panel.

Interface: plywood-pouches Interface: Pouches-drywall Software RMSE CV (RMSE) NMBE RMSE CV (RMSE) NMBE (ºC) (%) (%) (ºC) (%) (%) E+ Hysteresis melting curve 1.57 6.0 0.5 1.61 6.1 3.0 only E+ Hysteresis 1.17 4.5 0.5 1.55 6.0 2.9 both curves Thesis model melting curve 0.97 3.7 0.02 1.76 6.7 2.6 only Thesis model Hysteresis both 1.24 4.7 0.5 1.56 6.0 2.9 curves

• Hydrate-salts

Figure 8-30 shows the interface temperature of the PCM hydrate-salts panel simulated in EnergyPlus hysteresis model with and without hysteresis data. The graphical comparison shows similar to the BioPCMs, that during the phase change the curves are relatively closer to the experimental results when the hysteresis is considered. This is observed more during the freezing process. Figure 8-31 shows the interface temperature of the PCM hydrate-salts panel simulated in thesis model with and without hysteresis data.

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Table 8-9 shows the accuracy analysis for the cases graphically compared in the Figure 8-30 and Figure 8-31. CV(RMSE) values and NMBE values fall within the thesis guideline. Similar to the BioPCM case, EnergyPlus and the thesis model show improved biased error when the hysteresis data is considered.

Table 8-9 Accuracy analysis of comparisons of temperatures at each interface for EnergyPlus, and thesis model for the simulations applying thermal hysteresis characteristics for PCM hydrate-salts

Interface: plywood-pouches Interface: Pouches-drywall Software RMSE CV (RMSE) NMBE RMSE CV (RMSE) NMBE (ºC) (%) (%) (ºC) (%) (%) E+ Hysteresis melting curve 1.47 5.7 -3.5 1.49 5.7 -4.0 only E+ Hysteresis 1.41 5.5 -0.5 1.55 5.9 -2.9 both curves Thesis model melting curve 1.43 5.6 -3.5 1.43 5.5 -4.0 only Thesis model Hysteresis both 1.24 4.7 -0.4 1.56 6.0 -2.9 curves

Consideration of hysteresis in PCM modelling showed impact in graphical comparison and accuracy analysis of the results, specifically the biased error is improved.

8.4. Conclusions

This study conducted experimental analysis of macroencapsulated PCMs (encapsulated in pouches) with a nominal melting temperature of 23 ºC. Two PCMs (BioPCM and PCM hydrate- salts) are tested in full scale (2.4m × 1.2 m (8ft×4ft)) wall assemblies inside an environmental chamber. Data from 3 full melting and freezing cycles gathered across 100 hours are used for the validation study.

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Several heat transfer methods are proposed to simplify 3D heat transfer into a 2D model in PCM algorithm developed in MATLAB (thesis model) which was previously verified and validated. These methods capture 2D heat transfer effects due to the presence of different materials, voids between material interfaces, uneven and lose packaging of the PCMs in pouches. In total, 5 different methods are compared using laboratory data and the methods with lowest disagreement are implemented in the two wall panels with EnergyPlus (2 PCM modules), and WUFI. The comparison of the different software shows agreement for temperature comparisons of the both interfaces for both PCMs with. Temperature tolerances of ± 1.79 ºC for the plywood-pouches interface and ± 1.63 ºC for Pouches-drywall interface are observed for BioPCM and tolerances of ± 1.47 ºC for the plywood-pouches interface and ± 1.49 ºC for pouches-drywall interface are observed for the hydrate-salts. Application of hysteresis data showed improvements in the comparison of EnergyPlus and thesis model simulation results. However, heat flux predictions showed greater deviation from than surface measurements indicating additional measures must be taken to implement further instrumentation for reliable heat flux measurements.

In conclusion, EnergyPlus, thesis model, and WUFI software show capability of simulating the heat transfer across the wall assemblies with macroencapsulated PCMs in pouches with additional simplifications and assumptions discussed in this research. Engineers and researchers can adopt the simplification approaches of heat transfer across the PCM pouches (Partial parallel path, solid PCM for BioPCM pouches and Full parallel path, porous PCM for PCM hydrate-salt pouches) to improve the heat transfer predictions of building walls of whole building energy modeling software. These methods can be included in the PCM modeling algorithms with the modules to enter thermo-physical and dimensions data of the PCM pouches.

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CHAPTER 9 CONCLUSIONS AND FUTURE WORK

The research conducted in this thesis has been motivated by the need to (i) investigate optimum PCM properties and application types in building envelopes, (ii) verify and validate PCM modeling algorithms with experimental data with different PCM encapsulations, (iii) generate experimental data for validation purposes of different PCM encapsulations, and (iv) develop accurate numerical algorithms to simulate the heat transfer process associated with phase change for building envelope applications.

The main tasks of this research has been to (i) conduct a parametric analysis of a residential building with phase change material (PCM)-enhanced drywall, pre-cooling, and variable electric rates in a hot and dry climate to investigate potential cost savings and energy savings for the consumer, (ii) conduct verification and validation of different PCM models available in whole building energy modeling software like EnergyPlus, ESP-r and WUFI, (iii) design, implement, and conduct laboratory experiments to test different PCM products and develop data to validate the PCM modeling algorithms of building energy modeling software.

The research presented in this thesis the author constructed a numerical algorithm in MATLAB (thesis model) to simulate opaque building envelope with passive PCM applications. Furthermore, a state of the art environmental chamber is used to construct and implement experimental apparatus to test the heat transfer across multilayer wall assemblies with microencapsulated and macroencapsulated PCM.

The following section summarizes the significant results from this research work.

9.1. Summary of significant results

 A parametric study of a residential building located in hot-and dry climate was conducted using a pre-cooling of 5 hours, with different PCM latent heats, melting temperatures, melting temperature ranges, PCM conductivities, and locations of application and the author found the optimum PCM applications can shift the

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cooling electricity demand ~99.9% from the peak time with forced convection during precooling using high-efficiency fans.

 When the Time of Use (ToU) electricity rates are implemented (Arizona Salt River project), highest cost savings are observed when the PCMs are optimized for all locations of the envelope (ceiling, exterior opaque walls, and interior partition walls) under the forced convection mode using high-efficiency fans; the maximum cost savings observed are 29.4%. Other scenarios yield around 25% savings.

 6 PCM modeling algorithms implemented in different building energy and hygrothermal modeling software (EnergyPlus, ESP-r, and WUFI) and heat transfer (COMSOL) software, and math thesis model are validated and compared using data from two independent experimental studies with and shape-stabilized PCM behind the drywall and Nano-PCM embedded in gypsum wallboards. Based on the analyzed PCMs, all the evaluated software tools demonstrate their ability to accurately model shape-stabilized PCM behind drywall. All modeling software agreed with the Nano-PCM experiments but ESP-r had the lowest convergence due to less precise definition of boundary conditions. Interestingly, this study showed no additional gains in accuracy when comparing a 2D heat transfer model with 1D modeling for Nano-PCM and shape-stabilized PCMs.

 An experimental analysis of macroencapsulated PCMs encapsulated in pouches with a nominal phase change temperature of 23 ºC is conducted. Two PCMs (BioPCM and PCM hydrate-salts) are tested in full scale: 2.4m × 1.2 m (8ft × 4ft) wall assemblies in a controlled environment. Five simplification steps are evaluated using the thesis model to simulate the heat transfer across the PCM pouches layer. These methods showed improved accuracy.

 After the comparison, the methods with closest accuracy agreement are implemented in E+ (2 PCM modules), thesis model, and WUFI. Temperature tolerances of ± 1.79 ºC for the plywood-pouches interface and ± 1.63 ºC for Pouches-drywall interface are observed for BioPCM and tolerances of ± 1.47 ºC for the plywood-pouches interface and ± 1.49 ºC for pouches-drywall interface are observed for the hydrate-salts for this validation study.

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 Application of hysteresis data obtained from the manufacturer (for BioPCM) and Dynamic Heat Flux Meter Apparatus (DHFMA) tests (for hydrate-salts) improved the bias error of EnergyPlus and thesis model results.

 EnergyPlus, thesis model, and WUFI show capability of simulating the heat transfer across the wall assemblies with pouched macro encapsulated PCMs with additional simplifications and assumptions discussed in this research.

9.2. Potential for Future Work

Future work of this research falls into two sections: (i) further development of the building envelope model and (ii) laboratory experiments on different PCMs for validation purposes.

Further development of the building envelope model

 Thesis model developed here to evaluate PCMs in building envelope can be implemented in a whole building energy modeling platform like EnergyPlus to conduct whole building energy analysis and the simplification methods used can be used in modelling PCM pouches in future research.

 There are several parameters considered in modeling PCM pouches. Dimensions like thickness of the air layer, PCM volume, thermo-physical properties like variable conductivity of the PCMs, approximated PCM enthalpy data are a few. Therefore, this research can be extended to conduct sensitivity analysis of these parameters and how they influence the accuracy of the model.

 This research did not analyze the efficiency of the methods used to evaluate heat transfer across PCM pouches layer. Therefore, the current model can be made faster solving and more robust by

Laboratory experiments of different PCMs

 Macroencapsulated PCM products vary with the material type, pouch sizes, pouch material. There are products with increased PCM mass (2x mass BioPCM inside pouches), increased conductivity (3x conductivity BioPCM). Therefore, the current

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facility will be used to test these PCMs in parallel and create data for validation purposes.

 Full scale apparatus discussed here can be improved to quick switching of PCM mats. This would enable the researchers to test multiple PCMs parallel and quickly and create experimental databases for validation purposes of PCM modelling algorithms.

 Hygrothermal effects can also influence the heat transfer across the building envelope in realistic applications. Using the ability of the chamber to control interior relative humidity, the experimental hygrothermal analysis of PCM included building envelopes can be conducted.

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198

APPENDIX A. DISCRETE FORMS PREVIOUSELY USED IN NUMERICALLY MODELLING PCMS

Table A-1 Discrete forms previously used in numerically modelling PCMs Discrete form Study Time integration Modeled object and the platform Finite [396] Implicit Multi-layer window shutter with PCM in Element CFD Method [397] Implicit PCM wallboard in CFD [398] Implicit PCMs in pipes (mathematical theory) [399] Implicit and Evaluation of a moving boundary problem Explicit solving (mathematical theory) [400] Implicit PCM inclusions in walls in CFD implicitly. [401] - Lightweight concrete and gypsum walls with PCM in ABAQUS [402] - Wall thermal mass in HWC and LWC external wall types Finite Volume [403] - PCM composite wallboard in an in-house Method model

[90] 2-D PCM wall building model in an in- house model [404] Implicit Mortar wall containing a microencapsulated (PCM) Finite [405] Implicit PCM included external building walls in Difference an in-house model Method [406] Fully Implicit PCM included gypsum board in an in- house model [80] Implicit and Uses a Forward Time and Central Space Explicit (FTCS) [382] [407] Explicit PCM-composite layers built in multilayer constructions

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APPENDIX B. SUMMERY OF WHERE WHOLE BUILDING ENERGY MODELING PLATFORMS WITH PCM MODELS ARE USED

Table B-1 Summary of where whole building energy modeling platforms with PCM models are used in field studies and studies to upgrade/improve them Software Tool or [408] Simulatio Recognition, and Observations, sub function n methods remedial work applications and routine Identified on the complex references to (if named) in section PCM behavior additional case 3.2.1. Discussed in studies chapter 2. [114, 407] Effective Includes an Conducts floating Introduction heat additional heat temperature of a PCM capacity source to the applications model to ESP- method + latent heat [121] r Heat method source method ESP-r [103] Effective Introduces a Compares the heat temperature BESTEST Case Overcome the capacity correction 600 model results Limitations in method scheme to the with ESP-r ESP-r's PCM latent heat simulation [409] Solution method Algorithm Type 204 [410] Effective - Evaluated indoor heat comfort with capacity PCM applications method in envelope [411] TRNSYS Type-222 [412] Effective - Simulate heat characteristics capacity of a wall with method PCM as a standard active wall

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Table B-1 continued Type-232 [412] - - Studies the Models the influence of solar collector sorption isotherm field PCM hysteresis effect applications on indoor climate and energy demand for heating [413] Type-240 [98] Enthalpy Recognizes Model for Method Subcooling and storage tanks implements switching and experiments. method of the curves. (two different material data files) Type-241 [98] Enthalpy Removes the Conducts Model for Method Subcooling comparative PCM walls analysis in simulation of the and TRNSYS, Type- operative room experiments 240 (storage tank temperature for a TRNSYS application) reference room using gypsum and PCM plasters Type-285 [16] Enthalpy Recognizes Conducts Model for Method hysteresis and building level PCM walls considers tests and melting and [55] experiments solidification curves separately in validation. Conducts wall level tests [17]

Type-399 [354] Effective Implements PCM-Type heat different capacity (Type 399) Curves to model푝 method 퐶 (푇) and the hysteresis building Type (Type 56) models

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Table B-1 continued [412] - - Studies the Models the influence of solar collector sorption isotherm field PCM hysteresis effect applications on indoor climate and energy demand for heating [413] Type-240 [98] Enthalpy Recognizes Model for Method Subcooling and storage tanks implements switching and experiments. method of the curves. (two different material data files) Type-241 [98] Enthalpy Removes the Conducts Model for Method Subcooling comparative PCM walls analysis in simulation of the and TRNSYS, Type- operative room experiments 240 (storage tank temperature for a TRNSYS application) reference room using gypsum and PCM plasters Type-285 [16] Enthalpy Recognizes Conducts Model for Method hysteresis and building level PCM walls considers tests and melting and [55] experiments solidification curves separately in validation. Conducts wall level tests [17]

Type-399 [354] Effective Implements PCM-Type heat different capacity (Type 399) Curves to model푝 method 퐶 (푇) and the hysteresis building Type (Type 56) models

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Table B-1 continued Type - [292] Enthalpy Models Tests two 3258 Method hysteresis, identical full- Subcooling, and scale test- cells [80, 414]

푘(푇) CondFD [100] Enthalpy Implements a Development of Method single curve a thermal model method of building surfaces.

CondFD [415] Enthalpy - Conducts Further Method floating and simulations controlled temperature tests CondFD [416] Enthalpy Implements Tests using Method phase fraction as BESTEST an invertible building function of specifications temperature. CondFD [417] Enthalpy Conducts field E+ Method tests using a house and observes significant delays during cooling attributed to hysteresis.

CondFD [418] Enthalpy - Field tests using Method identical cabins CondFD [124] Enthalpy Studies Method hysteresis conditions CondFD [277] Enthalpy Integrates a Method hysteresis model to EnergyPlus using the EMS group

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APPENDIX C. COST CALCULATION PROCEDURES OF BEOPT

This section explains the cost calculations BEopt considers. AERC is calculated by taking into account the cash flows generated by the principal portion of loan payments that are made for the length of the loan period, loan interest, replacement costs (for the components that wear out), utility bills, loan tax deductions, residual values, rebates (PV and whole house efficiency), federal and non-federal tax credits, and the mortgage down payment. Equation 1 is used to inflate the sum of these cash flows.

(C-1) 푘 푦푒푎푟=푘 푖푛푖푡푖푎푙 퐶푂푆푇Here, the inflation= 퐶푂푆푇 rate is denoted(1 + 푖by) i. The initial cost is the cost at the beginning of the evaluation period, and represents the cost at the end of the year which is annualized. The method used퐶푂푆푇 here 푦푒푎푟=푘to annualize the composite cash flows is present worth푘 (PW) of the cash flow, as shown in equation 2.

(C-2) 푁 −푘 푘=0 푦푒푎푟=푘 푛 푃푊 = ∑ (−푇퐶푂푆푇 is the total cost) in(1 the + 푑year) while represents the nominal discount rate. Finally, the푇퐶푂푆푇 annualized푦푒푎푟=푘 energy related cost is determined 푑by푛 annualizing the present worth using the real discount rate, equation 3.

(C-3) −푃푊∗푑푟 1 푁 퐴퐸푅퐶 = 1−(1+푑푟) In a case where the real discount rate, is zero, BEopt uses equation 4 which approximates equation 3 for small values of , in order푑푟 to avoid a situation. 푟 푑 0/0 (C-4) −푃푊 푁 The퐴퐸푅퐶 x-axis = shows Average Source Energy Savings (ASES) considering default energy conversions from BEopt to compare site electric and gas savings [203] which is calculated using equation 5.

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(C-5) 퐴퐸푈푟푒푓∗퐴퐸푈푝푟표푡표∗100% 퐴푆퐸푆 = 퐴퐸푈푟푒푓 Here, the average of annual energy use is denoted by AEU. Equation 6 is used to calculate AEU, where the energy is use in year and is the mortgage period.

푘 퐸푈 푘 푁

(C-6) 푁 ∑푘=0 퐸푈푘 AEU = 푁

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APPENDIX D. SENSOR INFORMATION OF THE CHAMBER, HVAC SYSTEM, AND OUTSIDE

Table D-1 Sensors implemented in the Air Handling Unit and the Chamber Unit at the Department of Mechanical Engineering at Colorado School of Mines. Physical Model number Tag Description about the sensor location(inside/outside) Immersion Temperature Sensor (RTD Class A Pt1000), Nylon BA/T1K(20 TO 120F)-I-2"-BB2 Fitting (2 sensors): 2’’ length and ¼’’ diameter, stainless steel Cooling coil supply line TS-4JXX-1 probe (outside) Immersion Temperature Sensor (RTD Class A Pt1000), Nylon BA/T1K(20 TO 120F)-I-2"-BB2 Fitting (2 sensors): 2’’ length and ¼’’ diameter, stainless steel Cooling coil return TS-4JXX-2 probe line(outside) TS4X-WEL- Immersion well, Machined 304 Cool Coil supply BA/2"M304 1 Stainless Steel: BA/2’’M304 line(outside) TS4X-WEL- Immersion well, Machined 304 Cool Coil return BA/2"M304 2 Stainless Steel: BA/2’’M304 line(outside) Duct Averaging Temp Sensor BA/T1K(-30 TO )(RTD Class A Pt1000), Before first HC 130F)-A-8'-BB2 TS-2.8 JX-1 Flexible, 8’ J-Box (upstream)(outside) Duct Averaging Temp Sensor BA/T1K(-30 TO )(RTD Class A Pt1000), After first 130F)-A-8'-BB2 TS-2.8 JX-2 Flexible, 8’ J-Box HC(downstream)(outside) Duct Temp Sensor(RTD Class BA/1K(A)-D-8"- BB2 A Pt1000): 8’’ length, ¼’’ TS-1.8 JX-1 diameter, BAPi Box 2 not included Duct Temp Sensor(RTD Class BA/1K(A)-D-8"- BB2 A Pt1000): 8’’ length, ¼’’ TS-1.8 JX-2 diameter, BAPi Box 2 not included Duct Temp Sensor(RTD Class BA/1K(A)-D-8"- BB2 A Pt1000): 8’’ length, ¼’’ TS-1.8 JX-3 diameter, BAPi Box 2 not included Outside Air Pressure Pickup ZPS-ACC10 Port ZPS —ACC10, roof top OAP3 mount Roof(outside)

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Table D-1 continued OA Temp/Hum Sensor (1 BA/T1K(-30 T0 sensor): H200 humidity Roof/AHU 130F)-H200-O-BB OATS-TO transmitter, weather proof box /shaded(outside) BA/T1K(-30 T0 Duct Hum Transmitter with 130F)-H200-O-BB- Temp Sensor (2 sensors): H200 2 DHTS-TS humidity transmitter, BAPI-box Supply duct (inside) BA/T1K(-30 T0 Duct Hum Transmitter with 130F)-H200-O-BB- Temp Sensor (2 sensors): H200 2 DHTS-TR humidity transmitter, BAPI-box Return duct(inside) BAPI-Stat 2 Room Hum BA/BS4XC-F-2- – Transmitter/Temp Sensor (1 10G16-20M16-Z- sensor): (H205) humidity Chamber Inside WMW RHTS-TRM transmitter, LCD Display Wall(inside) Chamber outside ZPS-SW1,2,3 Differential Pressure Switch DP-SW1,2,3 wall(inside) Room CO2 Transmitter in BA/BS3F-DCD05- BAPI-Stat 3 enclosure (1 Chamber Inside Z-LED CD-TRM sensor) Wall(inside) BA/DCD05-D-BB- Duct Service CO2 Transmitter, LED CD-TS Periodic Occupancy (1 sensor) Supply duct(inside) Room VOC Transmitter in BA/BS3F-VOC05- BAPI-Stat 3 enclosure (1 Chamber Inside Z-LED VOC-TRM sensor) Wall(inside) VOC Duct Service VOC BA/VOC05-D-BB – VOC-TS Transmitter (1 sensor) Supply duct(inside) Ebtron SA Flow GP-P1 Flow rate sensor for supply air Supply duct(inside) Supply duct Ebtron SA Flow Flow rate sensor for supply air GP-P2 (Perpendicular) Ebtron RA Flow GP-P3 Flow rate sensor for return air Return duct Return duct Ebtron RA Flow Flow rate sensor for return air GP-P4 (Perpendicular) Ebtron OA Flow GP-P5 Flow rate sensor for outdoor air Outside: OA intake Ebtron SA Chamber external wall Transmitter Transmitter GP-P1T (already installed) Ebtron RA Chamber external wall Transmitter Transmitter GP-P2T (already installed)

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Table D-1 continued Ebtron OA Chamber external wall Transmitter Transmitter GP-P3T (already installed) Pressure pick up port for ZPS-ACC-06 SPP-RM chamber Chamber false ceiling ZPS-ACC-07 SPP-1 Pressure pick up port Supply duct Main AHU Duct ZPS-ACC-07 SPP-2-4 Pressure pick up port downstream supply fan Main AHU Duct upstream ZPS-ACC-07 SPP-5 Pressure pick up port filters ZPS-ACC-07 SPP-6 Pressure pick up port Return duct

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APPENDIX E. SENSOR INFORMATION OF THE CHAMBER, HVAC SYSTEM, AND OUTSIDE

Table E-1 Verification and Validation studies of building envelope numerical models Study Model to Data Links/Highlights

[106]  Verifies simulation constructed on STAR program (Simplified Transient Analysis of Roofs) and compares to analytical solutions from [84].  Neglects super-cooling effects since their objective is to simplify their model. [419]  Uses an In-house numerical model and compares with Paraffin PCM (K18)- enhanced concrete sandwiched wallboards.  Concludes that peak temperature in the phase change test cell was up to 10 °C less than in the control test cell during sunny days. [397]  Compares the simulated thermal comfort in the two rooms at the attic house during the summer. [36]  Uses an in-house model developed in [183] and compares with a test cell, MICROBAT, to measure the temperatures and characterizes the phase change effects of a PCM composite.  Recommends investigation on hysteresis effects observed. [416]  Runs EnergyPlus PCM model and highlights the errors observed due to material thermal characteristics.  Takes phase transition occurring over a temperature range into account and introduces a phase fraction as an invertible function of temperature. [420]  Uses EcoIndicator 99 (EI99) and evaluates the environmental impact of including PCMs in a typical Mediterranean building (cubicles).  Discusses that PCMs must operate as long as possible during the year to reduce the operational impact [417]  Runs building simulations on EnergyPlus and compares the simulation results with a field measured data in a residential house. [418]  Runs building simulations on EnergyPlus and uses identical cabins built on the Tamaki Campus of the University of Auckland.  Focuses on the reduction of daily indoor temperature. [246]  Runs building simulations on EnergyPlus and compares the simulation results with an analytical solution in[82], and a numerical solution in[421] for verification and data from [275] for validation.  Uses an approach as dictated by ASHRAE Standard 140 to identify and resolve bugs in the EnergyPlus numerical model.

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Table E-1 continued [422]  Uses an in-house model to extrapolate the results for walls outfitted with Phase change frame walls (PCFW) located in coastal and transitional climates in the State of California.  Concludes that PCFWs would produce better results in energy savings as the outdoor air temperature increased [16]  Tests a numerical module for TRNSYS developed FORTRAN and uses data from [36] to address hysteresis with validation.  Recommends charging and discharging process of PCMs to be evaluated under dynamic environmental conditions. [423]  Models the thermal behaviors of multi-layer living wall in MATLAB/Simulink and experimental work from Sunliang [324] is used for validation.  Studies PCMs in different locations within the wall and the inclusion method and phase change properties which yield maximum savings. [40]  Uses a MATLAB/Simulink based model and tests a multi-layer heat exchanger in the laboratory prototype level. [406]  Investigates the load shifting capacity considering the thermal comfort and indoor air quality. [406]  Estimates the optimal location of a thin PCM layer in the frame wall. [292]  Uses a TRNSYS Type 3285 module as the numerical model and uses experimental data[414]  Uses variable phase change materials thermal capacity. [130]  Runs simulations on COMSOL Multiphysics® [424] for a wall model previously validated with [14], [144 683] and compares experimental data obtained from DHFMA method.  Assumes that PCM state remained on the same enthalpy curve even if the melting or freezing was interrupted

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