Empirical validation and comparison of PCM modeling algorithms commonly used in building energy and hygrothermal software

Journal Pre-proof Empirical validation and comparison of PCM modeling algorithms commonly used in building energy and hygrothermal software Sajith Wijesuriya, Paulo Cesar Tabares-Velasco, Kaushik Biswas, Dariusz Heim PII:

S0360-1323(20)30108-6

DOI:

https://doi.org/10.1016/j.buildenv.2020.106750

Reference:

BAE 106750

To appear in:

Building and Environment

Received Date: 4 November 2019 Revised Date:

12 February 2020

Accepted Date: 14 February 2020

Please cite this article as: Wijesuriya S, Tabares-Velasco PC, Biswas K, Heim D, Empirical validation and comparison of PCM modeling algorithms commonly used in building energy and hygrothermal software, Building and Environment, https://doi.org/10.1016/j.buildenv.2020.106750. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.

1

Empirical validation and comparison of PCM modeling algorithms commonly used in

2

building energy and hygrothermal software.

3

Sajith Wijesuriya1, Paulo Cesar Tabares-Velasco2, Kaushik Biswas3, Dariusz Heim4

4

Key Words: Building Envelope, Thermal storage, PCM, Modeling, Validation

5

Highlights • • •

6 7 8 9 10 11

•

Validation study considered 6 PCM models in 5 software packages Two independent experimental studies provide the data Studies use Nano-PCM embedded in drywall and shape-stabilized PCM behind drywall Comparison of the modeled results demonstrate their ability to accurately model PCMs

12 13

Abstract

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Whole building energy modeling has become extremely important for designers, architects,

15

engineers, and researchers to predict energy performance of buildings. This is particularly

16

important for phase change materials (PCMs) due to their variable properties. For this reason,

17

building energy modeling tools have been developed and validated against different sources of

18

experimental data. However, an IEA Annex 23 surveyed over 250 research publications

19

concluding that the general confidence in currently used numerical models is still too low to use

20

them for designing and code purposes. The objective of this study is to assess the capability of

21

different simulation programs to model the PCMs in building envelope using data from two

22

independent studies using Nano-encapsulated PCMs (Nano-PCM) and shape-stabilized PCMs.

23

The study finds that the investigated PCM models accurately predict the PCM behavior in the

24

building envelope. 1

Department of Mechanical Engineering, Colorado School of Mines Department of Mechanical Engineering, Colorado School of Mines 3 Oak Ridge National Laboratory, TN, USA 4 Department of Environmental Engineering, Lodz University of Technology, Poland 2

Introduction

25

1

26

Buildings are responsible for nearly 40% of the total energy consumed in United States [1]. A

27

large portion of this energy consumption is used for space-conditioning, up to 50% during peak

28

time [2]. Therefore, there is an interest to increase the energy efficiency in buildings and energy

29

storage potential to reduce peak demand and potential energy use. Innovative sustainable design,

30

materials with improved thermal properties, and integration of thermal energy storage are some

31

of the methods used in the industry today.

32

Thermal energy storage (TES) is used in buildings due to its capacity to shift loads [3, 4]. TES

33

can make buildings more grid friendly and energy or cost efficient [5, 6]. TES can be either

34

sensible storage or a combination of latent and sensible storage. Interest and products using

35

latent heat storage in building envelopes has increased and have regained interest of researchers

36

during the last decades due their high capacity to store energy per mass [7]. In buildings, TES

37

can be applied in passive systems, which utilizes building envelope components to store and

38

release energy, or in active systems, which tend to be integrated with building heating,

39

ventilation, and air conditioning (HVAC) systems [8-10]. Passive PCM storage has become a

40

popular research topic due to building envelopes’ large surface area and the ability to add latent

41

heat storage into light mass buildings [9, 11-15] and is the focus on this study: PCMs uses in the

42

building envelope [16-18].

43

Due to their variable properties, design of PCM inclusions in buildings require careful and

44

accurate energy analysis as it is important to maximize the number of times PCMs cycle between

45

solid and liquid phases to utilize its latent heat. For this and other reasons, several PCM heat

46

transfer models have been implemented in different building energy modeling tools [19-25].

47

However, an IEA Annex 23 surveyed over 250 research publications concluding that the general

48

confidence in numerical models is still too low to use them for designing and code purposes [26].

49

Another article analyzes several modeling tools capable of simulating PCMs and supports the

50

need for extensive model validation and comparison of the different numerical tools available

51

today using a standardized procedure for PCM model validation [27]. These studies show

52

validation has an important role in model development but previous work has been limited in

53

range, applications, and conditions. For example: EnergyPlus PCM model was validated using

54

PCM shape-stabilized experimental data [28, 29], COMSOL 2D PCM model was validated

55

using PCM enhanced drywall with field data [30], ESP-r PCM model was validated for

56

microencapsulated PCM [31], and WUFI PCM model was validated with data from Dynamic

57

Heat Flux Meter Apparatus (DHFMA) [32]. These studies did not consider hysteresis in their

58

models. Recent studies have implemented different PCM models in EnergyPlus using Energy

59

Management System (EMS) and also as part of the source code with no clear validation with

60

hysteresis [32]. The thermal hysteresis in PCMs occur due to PCM characterization test method

61

and type of equipment used, and impaired PCM nucleation during the freezing process which is

62

also known as sub-cooling [7]. Thus, there is a need for a careful validation and comparison for

63

different PCM applications in the building envelope.

64

Additionally, it is important to consider the computational runtime and the performance

65

limitations of building energy modeling, PCM models included in whole building energy

66

modeling platforms tend to simplify the use of temperature dependent PCM properties like

67

specific heat, thermal conductivity, and melting point [33].

68

properties of PCMs are obtained from characterization methods [7], but often it is not possible to

69

use properties obtained from small samples (such from differential scanning calorimetry, DSC).

70

The sample size of the PCM used in the characterization influences the measured values of the

71

thermal properties and may not reflect the thermal behavior for different encapsulation methods

72

accurately [34, 35]. Finally, materials that exhibit two or three-dimensional behavior, hysteresis,

73

and subcooling [32, 36-39], have been difficult to incorporate into the PCM models without

74

compromising the computational runtime. Therefore, assessment and comparison of the different

75

PCM modeling software is required. There are studies comparing modeling capabilities of

76

different building energy modeling programs (BEMPs) using ASHRAE Standard 140 tests [40]

77

or doing broad simulation engine comparison [41]. However, there are no previous efforts

78

comparing specifically PCMs models using laboratory and field data to understand and quantify

79

the limitations of modeling techniques used in each numerical tool for a specific application (e.g.

80

PCMs micro/nano encapsulated in drywall). Given the need for validated models that can

81

accurately model PCMs, this study compares and validates PCM models that are part of popular

82

building energy and hygrothermal software commonly used in building industry [42-53]:

83

EnergyPlus, ESP-r, and WUFI. WUFI is compared here since building designers and modelers

The temperature dependent

84

commonly use it for energy and hygrothermal performance assessments. This study also

85

compares 1-dimensional (1D) and 2-dimensional models done in COMSOL, a specialized

86

numerical modeling software, using a more detailed model and finally a PCM modeling

87

algorithm developed with MATLAB. PCM applications analyzed are Nano-PCM in drywall and

88

shape-stabilized PCM layer behind the drywall.

89

2

90

Validation data used in this study uses experimental data from two independent PCM studies and

91

compares PCM models implemented in different energy modeling software. The analyzed PCM

92

heat and mass transfer models in this study are part of the following software:

93

(i) ESP-r: Building energy simulation tool commonly used in Europe that has two PCM models

94

introduced as special material (PCM_Cap, model no. 53) and defined as an active building

95

elements with variable thermo-physical properties (spmatl subroutine) [54, 55]. The latent heat

96

is calculated based on effective heat capacity, which is a linear function of temperature.

97

Temperature dependence conductivity (linearly) can be also taken into account during

98

simulation. ESP-r has developed sub-routines to model hysteresis in PCMs.

99

(ii) WUFI v6.1: Heat and mass transfer (HAMT) software for building structures [56-60]. WUFI

100

has the ability to define temperature dependent input functions via ‘Hygrothermal Functions’

101

object set and ‘Enthalpy, temperature dependent’ object [61]. WUFI also has the ability to define

102

temperature dependent conductivity via ‘Thermal Conductivity, temperature-dependent’ object.

103

This study uses these two objects to define the temperature dependent functions of PCM

104

properties. WUFI uses coupled heat and mass transfer equations to model heat and moisture

105

transfer. The moisture transfer modeling component of this program is turned off in the current

106

study to just model just the heat transfer as rest of the considered models only capture heat

107

transfer phenomena.

108

(iii)

109

(iv)

110

(https://www.comsol.com/heat-transfer-module) is used for the simulations presented here.

Methodology

COMSOL:

The

heat

transfer

module

of

COMSOL

Multiphysics®

111

Temperature-dependent material properties are incorporated in COMSOL using the

112

‘interpolation’ function. For PCMs, the measured enthalpy as a function of temperature is

113

provided as input and the specific heat is defined as the slope of the enthalpy vs. temperature

114

curve, the latter is calculated as part of the solution routine [30] [62]. Biswas et al. [63]

115

developed an algorithm using the ‘previous solution’ operator of COMSOL to capture the

116

hysteresis in PCM and evaluated the differences in energy saving estimates with and without

117

considering the impacts of hysteresis.

118

(v) This study also includes a PCM modeling algorithm written in MATLAB inspired by the

119

EnergyPlus PCM model. This algorithm is referred to as the “CSMPCM” model for

120

identification purposes from this point onwards as it is written for the research purposes at

121

Colorado School of Mines (CSM). This PCM model has been analytically verified using Stefan

122

problem, and numerically verified with the PCM model in EnergyPlus. This model used in this

123

validation study to give the authors more flexibility to further evaluate the model performance.

124

Table 1 compares the above PCM models based on numerical formulation (numerical methods),

125

solver type, method of latent heat input, and the input parameters to define the latent heat in the

126

“mushy” region. All models assume one-dimensional (1D) conduction heat transfer with

127

exception of COMSOL that uses 2D conduction heat transfer for ORNL Nano-PCM case. This

128

also allows the authors to compare the additional accuracy gain when going from 1D to 2D heat

129

transfer in building assemblies. These characteristics of PCM models in building energy

130

modeling software are discussed in detail in recent literature [7, 33].

131

Table 1: Numerical modeling methods used in PCM models Model

COMSOL

Numerical formulation

Finite element method [70, 71]

Solution schemes

Latent heat algorithm

Direct solver Enthalpy PARDISO based on method lower-upper decomposition [72] (matrix form of Gaussian

Latent heat data incorporation from the curves Interpolated h-T curves

Elimination) ESP-r

Finite Volume Method, Implicit, Explicit and Crank Nicholson. [53]

Direct solution method, semiimplicit scheme, iteration employed for the case of nonlinearity [73]

Effective heat capacity method

Linear function of effective heat capacity versus temperature

EnergyPlus PCM model

Finite Difference Method: Fully Implicit and Crank Nicholson [22]

Gauss–Seidel iterative scheme

Heat capacity method/ Enthalpy Method

Enthalpy curve with maximum of 16 temperature-enthalpy data points.

EnergyPlus hysteresis PCM model

Finite Difference Method: Fully Implicit and Crank Nicholson

Gauss–Seidel iterative scheme

Enthalpy Method

Enthalpy curves approximated based on the heating and cooling curves by curve fitting (inputs: peak phase change temperature, lower and higher temperature ranges of phase change for melting and freezing)

CSMPCM model (written in MATLAB)

WUFI

Finite Difference Method: Fully Implicit (current study)

Gauss–Seidel iterative scheme

Enthalpy Method

Simplified PCM curve with maximum 16 data points

Finite Volume Method: Implicit

Matrix solver: Thomas-algorithm in (1D) [74], or ADI in (2D) simulations [75].

Enthalpy Method

Simplified temperatureenthalpy curve with 32 points (higher number of points is possible)

132 133

The two main PCM models used by energy software in Table 1 are the enthalpy method and the

134

heat capacity method. Enthalpy method considers the total amount of energy, which includes

135

both sensible and latent heat. This method presents heat capacity in terms of its integral form,

136

H(T). The effective specific heat capacity ( ) is obtained as the gradient (dh/dT) of the enthalpy

137

curves. Heat capacity method deals with heat capacity as a function of temperature within the

138

temperature range of the phase transition. It numerically imitates the effect of enthalpy by

139

controlling the heat capacity value during the phase change.

140

latent heat and the sensible heat. Equations 1 to 3 show the mathematical formulation for

141

enthalpy method, definition of the effective specific heat capacity, and heat capacity method. ∂h = ∂t

= ∗

ℎ



∂T = ∂t

ℎ

value considers both the

(1)

(2)

(3)

142

Among analyzed models, Finite difference method is the most common heat transfer algorithm

143

due to its simplicity to code [7], followed by finite volume and finite element numerical

144

schemes. EnergyPlus has the simplest (to code) but slowest solution scheme (Gauss-Seidel)

145

while WUFI and ESP-r has more complex and faster schemes.

146

enthalpy-temperature data or heat capacity- temperature data to include phase change effects.

147

2.1

148

Verification and validation (V&V) are important steps in numerical model development to

149

ensure desired performance and accuracy [76]. ASHRAE standard 140 defines three main

150

approaches for V&V: (1) analytical verification, (2) empirical validation, and (3) comparative

151

testing [77]. Verification of the analyzed PCM models have been partially documented in

152

literature, some have use analytical solution of Stefan Problem or lab data [29, 78, 79]. However,

153

these studies have not followed the same protocols or boundary conditions, making it impossible

154

to compare. This study uses Root Mean Square Error (RMSE) calculated in Equation 4,

155

Coefficient of Variation of the Root Mean Square Error (CV (RMSE)) and Normalized Mean

All models require either

Validation

156

Biased Error (NMBE) as the statistical indices to compare the data, which is suggested by

157

different validation guidelines and previous studies [80-85]. NMBE and CV (RMSE) have been

158

specifically used together to compare simulated and measured temperature data in previous

159

studies [86, 87]. Here,

160

average of the errors of a sample space divided by the mean of measured values

161

the global difference between the real values and the predicted ones as shown in the Equation 5.

162

NMBE is subjected to the cancellation errors and therefore, not recommended to be used alone

163

[84]. Hence, the current study also uses CV (RMSE). CV (RMSE) is the average of the square of

164

the errors of a sample space divided by the mean of measured values as shown in the Equation 6.

165

ASHRAE Guideline 14 considers NMBE ± 10% and CV (RMSE) ± 30% as the acceptable

166

calibration criteria for the hourly data.

is the actual measured value,

= ! + , = 34

1

is the predicted value. NMBE is the

& ∑' $() #$ %#$

*

∑*/0

+

0 = # ! 5

−

. It indicates

(4)

× 100

& ∑' $() #$ %#$ × *

100

(5)

(6)

167

Guideline 14 was developed for measurements of actual buildings where there are uncertainties

168

in occupancy, internal loads, and materials properties. Since the two validation cases have well-

169

defined boundary conditions and many properties are known, one should expect high accuracy or

170

use a higher standard. Thus, this study uses higher standard using NMBE ± 5% and CV (RMSE)

171

± 15%. In addition, this study uses RMSE to provide an absolute measure of the accuracy.

172

Future work should (beyond the scope of this study) scale up ramifications at building scale.

173

This validation study uses experimental data from two experiments: laboratory data from

174

Norwegian University of Science and Technology (NTNU) which used Hot-Box tests [88], and

175

field test data from ORNL’s Natural Exposure Test (NET) facility at, Charleston, South

176

Carolina, USA [30]. NTNU study uses shape-stabilize (DupontTM Energain®) PCM that has been

177

characterized with the temperature-enthalpy curve [89]. DupontTM Energain® PCM panel is a

178

mixture of ethylene based polymer and paraffin wax laminated on both sides with an aluminum

179

sheet [90]. The ORNL field study uses a paraffin based Nano-PCM and performed field

180

measurements over several months using this PCM with the goal to evaluate the performance of

181

Nano-PCM enhanced gypsum board [30].

182

Table 2 compares the two analyzed PCMs. The enthalpy curves for both studies are determined

183

using Differential Scanning Calorimetry (DSC). It should be noted that the temperature gradient

184

used in the DSC method can influence the enthalpy curve results [68]. Both PCMs were tested

185

using a slow heating rate (low temperature gradient) to minimize any measurement error/noise.

186

In addition, PCM percentage, distribution, and Nano capsule material can also affect the thermal

187

properties. Shape-stabilized PCM has a greater storage capacity since it is not mixed with

188

drywall. However, both products suffer from low thermal conductivity.

189

Table 2. Properties of Analyzed PCMs Laboratory work with shapestabilize PCM PCM type

Field experiments with Nano-PCM wallboard

Paraffin n-heptadecane (C17H36)

Encapsulation

laminated by aluminum sheets

included in graphite Nanosheets

PCM percentage in the wallboard by weight (%)

60

20

Wall type

Flexible sheet

Gypsum board

(5.26mm)

(13 mm)

Latent heat (kJ/kg)

>70.1

26.2

Total heat storage capacity (kJ/kg)

>170 (14°C - 30°C)

50 (15°C - 25°C)

Peak melting temperature (ºC)

21.7

21.4

Thermal conductivity in liquid phase (W/m-K)

0.22

0.43

Thermal conductivity in solid phase (W/m-K)

0.18

0.41

Specific heat capacity in liquid phase (kJ/kg-K)

3.00

2.24

Specific heat capacity in in solid phase (kJ/kg-K)

4.50

2.31

Characterization method and heating rate

DSC, 0.05 ºC/min

DSC, 1.0 °C/min

Latent storage capacity (kJ/m2)

428

770

190 191

2.2

Enthalpy-temperature curves of PCMs

192

Figure 1 shows the DSC enthalpy curves for the analyzed PCMs: shape-stabilized PCMs (Figure

193

1(a)) and Nano-PCM (Figure 1(b)). Figure 1(a) shows a slow enthalpy increase in the “mushy”

194

region (or wide melting range), while Figure 1(b) with the Nano-PCMs shows a prominent

195

enthalpy gradient (or short melting temperature range).

196

As shown in Table 1, COMSOL uses an enthalpy-temperature (h-T) curve that interpolates

197

within the available enthalpy-temperature values. CSMPCM model uses 4 points, EnergyPlus

198

(No hysteresis model) uses up to 16 discreet points, and WUFI uses 32 discrete points to

199

approximate the entire curve within the temperature range of the curve (the number of discrete

200

points can be further increased in WUFI). EnergyPlus hysteresis model requires, (i) peak phase

201

change temperature, (ii) low temperature difference of phase change, and (iii) high temperature

202

difference of melting/freezing curves to fit curves within the phase change region (in this study

203

only melting curve data is available and therefore a single curve is used for melting and

204

freezing). ESP-r uses linear function that relates effective heat capacity with temperature. These

205

specific input data is obtained from Figure 1. The shape-stabilized PCM melting temperature

206

ranges from 18.6 ºC to 25 ºC with the peak melting temperature at 21.7 ºC, while the Nano-PCM

207

phase change ranges from 20.4 ºC to 21.8 ºC, with the peak melting temperature at 21.4 ºC.

208 209

Figure 1: (a) Enthalpy-Temperature (h-T) curves for shape-stabilized PCM, (b) and Nano-PCM.

210

2.3

211

Table 3 shows how each model discretizes the analyzed PCM layer. COMSOL model uses a 2D

212

model with a mesh made using the ‘physics-controlled’ option of COMSOL and element size set

213

to “Normal” to model the Nano-PCM. This created a non-uniform mesh. The number of

214

discretized elements in the PCM-gypsum board are determined by the physics controlled mesh

215

algorithm and are about 2-6 with the highest count in drywall section closest to the stud and only

216

2 across the thickness of the PCM-gypsum board in most places along the drywall (see Figure

217

2). The calculated values are obtained at the middle of the cavity section as shown in the Figure

Numerical modeling considerations

218

2. A 1D COMSOL model is used to simulate shape-stabilized PCM. This too considered a non-

219

uniform mesh.

220 221 222

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

223

WUFI model uses Fine grid with Automatic (II) option for the discretization. Figure 3 shows the

224

non-uniform finite volume mesh created through this method for ORNL field study Nano-PCM

225

layer. Same approach was used in modelling the shape-stabilized PCM.

226 227 228

Figure 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.

229

For the CSMPCM model and EnergyPlus models, the grid size is uniform for each layer but each

230

layer has a different grid size, which depends on the thermal properties. Grid Fourier number of

231

1 was used for all calculations of special discretization (6 . Equation 7 shows the spacial

232

discretization is a function of thermal diffusivity, grid Fourier number, and the timestep. Inverse

233

of the grid Fourier number is termed the discretization constant and is denoted by ‘c’. Cases c=

234

2, 1, 0.5 were investigated to ensure the grid independency. All CSMPCM model and

235

EnergyPlus simulations use a timestep 67 equal to 1 minute. 6 = √ 9 67 = :

967 ;<

(7)

236

Based on the above calculations, Nano-PCM layer has four nodes uniformly across the layer for

237

CSMPCM model and EnergyPlus simulations (see Figure 4). Same approach was used in

238

modelling the shape-stabilized PCM.

239 240 241

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

242

The number of discretized cells is actually an input as shown in Table 3. For all the models, the

243

case indicating the grid independence was considered given the value displayed in Table 3.

244 245

Table 3: Numerical discretization considered in modeling the material layers with PCM inclusions. Spatial Discretization settings discretization method

Number of discretized cells in PCM layer in this study Shapestabilized PCM

Nano-PCM

COMSOL

EnergyPlus PCM model EnergyPlus hysteresis PCM model ESP-r

CSMPCM model

WUFI

Finite element method

Finite difference method Finite element method Control volume method Finite difference method Finite Volume Method

Maximum element size specification (1D) Physics controlled mesh, normal element size (2D) Space discretization constant=1 Relaxation factor = 1 Space discretization constant=1 Relaxation factor = 1 -

11 elements

3 nodes

2 elements along cross section 4 nodes

3 nodes

4 nodes

3 nodes

3 nodes

Space discretization constant=1

3 nodes

4 nodes

Fine (with Automatic (II) option enabled)

14 volumes

24 volumes

246

*nodes were increased from 4-8 with no significant difference in results

247

For EnergyPlus hysteresis PCM and the CSMPCM models that are based on the enthalpy method

248

and solid and liquid state cp values were used outside the phase change interval. For both

249

datasets, temperature dependent thermal conductivity information was available and used in this

250

study. For the PCM mixed or embedded in construction materials such as drywall (Nano-PCM

251

case), this study assumes PCMs are evenly distributed across the layer and therefore, uses

252

equivalent physical and thermal properties across the material layer (e.g. drywall). Although both

253

PCMs exhibit little hysteresis, this is not modeled since the NTNU shape-stabilized PCM only

254

contained melting curve and the hysteresis information was not available.

255

Both lab and field studies measure wall inner and outer surface temperature and this is used as

256

the boundary conditions: surface temperature (Dirichlet Boundary Condition). However, this

257

boundary condition is implemented differently using workarounds in each modeling software, as

258

most cannot accommodate fixing a surface temperature:

259

•

In COMSOL, either inner or outer surface temperatures directly or heat flux boundary

260

conditions can be assigned at the inner and outer surfaces. Biswas et al. [30, 62] utilized

261

both temperature and heat flux boundary conditions. Biswas et al. used heat flux

262

boundary conditions for annual performance evaluations of PCMs using typical weather

263

data and used temperature boundary conditions for model validation using measured

264

temperature data. Thus, this study also uses temperature boundary conditions for both

265

analyzed cases in COMSOL.

266

•

In

EnergyPlus,

exterior

surface

temperature

is

set

using

‘SurfaceProperty

267

OtherSideCoefficients’ that allows users to specify a surface temperature. This can only

268

be used on one side of a wall, so the interior surface temperature is set by increasing

269

convection

270

ConvectionCoefficients’) and setting the indoor air temperature to the actual surface

271

temperature.

272

•

273 274

transfer

coefficient

to

1,000

W/m2-K

(‘SurfaceProperty

In CSMPCM model, the interior and exterior temperature values are directly assigned to the surface nodes.

•

In WUFI, the interior and exterior temperature values were assigned, and a convective heat resistance of 0.001 m2-K/W was used on the both surfaces.

275 276

heat

•

In ESP-r, the interior and exterior temperature values were assigned using temporal

277

entities ("model context" menu and "use observed/temporal data" option). The convection

278

heat transfer coefficient was set to 100 W/ (m2-K).

279

Timestep used in all simulation programs is one minute but the experimental data from NTNU

280

experiments was recorded every 10 minute and the ORNL field study data every hour. Therefore,

281

the boundary condition data is interpolated to 1 minute from the recorded data for both cases.

282

Moreover, moisture transfer is not considered in the PCM models (including EnergyPlus, WUFI)

283

to ensure only the heat transfer phenomena is captured throughout all programs for the validation

284

purposes. Moisture transport is analyzed in more detail in a subsequent publication [91].

285

2.4

286

Table 4 shows material used and their properties for the NTNU wall assembly. PCM panels used

287

in the study have 1000 mm width and 1198 mm length [88]. These PCM panels are tested with a

288

wood frame wall construction.

289 290

Shape-stabilized PCM wall data

Table 4: Material properties of the wall assembly used in the NTNU controlled hot-box experiments Layer

Conductivity (W/m-K)

Density (kg/m3)

Specific heat capacity (J/kg-K)

Thickness (m)

0.21

700

1000

0.013

PCM DuPont

0.22 (solid)

855

3250 (solid)

0.0053

(Shape-stabilized PCM)

0.18 (liquid)

3

Mineral wool insulation

0.033

29

1030

0.296

4 (interior BC)

Gypsum

0.21

700

1000

0.009

1 (exterior BC) 2

Gypsum wallboard

2250 (liquid)

wallboard

291 292

Figure 5 indicates the layer structure of the wall assembly for this dataset. The thermocouples

293

used in the study are type T30/2/506 made by Gordon with an accuracy of ±0.1 K and the heat

294

flux meters are type PU_43T made by Hukseflux with an accuracy of ±5%. The tests were

295

performed in a hot box apparatus, where initially the cold box side was kept at −20 °C and the

296

hot side was kept at 20 °C. At t = 0, a heater in the hot box started heating the air temperature

297

inside the hot box for 7 hours (heating stage). The final inside wall temperature reached an upper

298

limit of ~24 °C [92]. This indicates that the PCMs within the panels would not have fully melted.

299

After that, the heater was turned off and the hot box slowly cooled to the initial temperature, 20

300

°C (cooling stage). Temperature is measured at either side of the PCM layer (point 2 and point 3)

301

while heat flux is measured only at behind the PCM layer (point 3).

302 303 304 305

Figure 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 colored layer (between Point 2 and 3).

306

2.5

307

Table 5 shows material properties used by Biswas et al. [30] to model the test wall with the

308

Nano-PCM wallboard. The test wall was built and monitored in a natural exposure test facility,

309

which is a conditioned building in Charleston, SC. The test wall was constructed using typical

310

wood framing, with oriented strand board (OSB) on the outside and the Nano-PCM wallboard on

311

the inside, and cellulose insulation in the cavities created by the wood framing.

Nano-encapsulated wallboard data

312

Table 5: Material properties of the wall assembly used in Nano-PCM wallboard Layer

Material

Thermal Conductivity

Density (kg/m3)

Specific heat capacity

Thickness (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 wallboard

0.427 (liquid)

658

2240 (liquid)

0.013

0.41 (solid)

2310 (solid)

313 314

The test wall was instrumented with an array of thermistors and relative humidity (RH) sensors

315

across the cross-section of the wall, at the different interfaces and in the center of the cavity. A

316

heat flux sensor was installed at the interface of the cellulose insulation and the Nano-PCM

317

wallboard. The data from the sensors was recorded on an hourly basis. The overall testing and

318

monitoring were performed for 12+ months, to capture the performance under different weather

319

conditions. Table 6 shows the installed sensor accuracies.

320

Table 6: Installed sensor accuracy Sensor

Accuracy

Sensitivity

Repeatability

Supply Voltage

10K ohm thermistor

± 0.2ºC

-

± 0.2%

2.5Vdc

Humidity Sensor

± 3.5%

-

± 0.5%

5Vdc

Heat Flux Transducer

± 5%

(5.7 W/m2)/mV

-

-

321 322

The conductivities of the cellulose insulation and Nano-PCM wallboard were measured in a heat

323

flow meter following standard ASTM C518 [93]. The density of cellulose was based on the

324

volume of the test wall cavity and mass of insulation added, and the conductivity of cellulose

325

was measured at the same density as the test wall cavity insulation. The specific heats of the

326

Nano-PCM wallboard were based on the DSC data provided by the manufacturer, as the slopes

327

of the temperature-dependent enthalpy function in the fully-frozen and fully-molten regimes.

328

Remaining material properties were obtained from published literature.

329

These PCM panels are tested using a wood frame stud and cavity wall construction. Figure 6

330

shows the 2D arrangement of the experimental apparatus. The construction has the cavity section

331

and the stud section. Considering the stud section helps observe if there are 2D effects of heat

332

transfer that influence the modeling approach considered. The measurements used for the

333

validation study here are across the cavity section.

334 335

Figure 6 2D arrangement of the experimental apparatus to test the Nano-PCM wallboard

336

Figure 7 further shows the layer structure of the wall assembly used in the experiments and

337

location of the heat flux and temperature sensors. Surface temperature data at the exterior and

338

interior surfaces and three locations within the wall panel were monitored in this study. Although

339

the heat flux transducer was placed at the interface of the cellulose insulation and the PCM

340

wallboard (point 5), the temperature sensor was located at point 4 in the cellulose insulation layer

341

but its exact location is not reported. Thus, point 4 is not used for validation. 10 K ohm

342

thermistor used in the study had an accuracy of ±0.2 °C and the heat flux transducer had an

343

accuracy of ±5%.

344 345 346 347

Figure 7 Analyzed wall assembly using Nano-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).

Results and Discussion

348

3

349

3.1

350

Figure 8 and Figure 9 show temperature at the interface between the gypsum and PCM

351

wallboard (point 2 in Figure 5) and between the PCM wallboard and mineral wool insulation for

352

(point 3 in Figure 5) respectively. Both figures show results from: experimental data, COMSOL,

353

ESP-r, E+ (no hysteresis model), E+ (hysteresis model with just the melting curve), CSMPCM

354

model, and WUFI. The horizontal dashed line shows the peak melting temperature of the PCM

355

and the horizontal shaded area indicates the melting temperature range. The peak melting

356

temperature of the PCM is 21.7 ºC and the highest and lowest temperatures observed at the point

357

2 is 22.7 ºC and 19.4 ºC. The highest and lowest temperatures observed at the point 3 is 22.6 ºC

358

and 19.3 ºC. Therefore, the PCM did not transition fully from melting to freezing. However, the

359

results are important as the PCM is still transitioning from one solid phase to liquid and then

360

transitions back to solid in a partial cycle. In fact, it also helps to test ability of models to

361

simulate partial phase change, which it has been shown to be challenging to simulate [94].

362

Figure 8 also includes the line showing the temperature variation at the hot side boundary (point

363

1) to see maximum and minimum temperatures observed at the hot surface for this experiment.

NTNU shape-stabilized PCM

364 365 366

Figure 8 Temperature at Point (2): between the gypsum and shape-stabilized PCM. Outer boundary condition, Point (1) is also shown as a reference.

367 368 369

Figure 9 Temperature at the Point (3): between the shape-stabilized PCM and mineral wool insulation

370

For both figures above COMSOL, ESP-r, E+ (no hysteresis model), E+ (hysteresis model with

371

just the melting curve), CSMPCM model, and WUFI lie close together. Table 7 summarizes the

372

performance of all PCM models based on RMSE, CV (RMSE) and NMBE values. RMSE values

373

are similar for all models. All values fall well within the accepted tolerances for the NMBE and

374

CV (RMSE). Although not shown in Figure 8, modeling the walls without PCMs gives a

375

CV(RMSE) value of 0.92 % at the interface between gypsum and PCM wallboard (point 2) and

376

1.03 % at the interface of PCM wallboard and mineral wool insulation (point 3) which indicates

377

the deviation from the PCM cases. All values are well below the recommended ranges of 5%

378

(NMBE) and 15% (CV(RMSE)).

379 380

Table 7: Calculated Temperature RMSE, CV (RMSE) and NMBE for all analyzed PCM models at material interfaces Point 2 of Figure 5 Software

Point 3 of Figure 5

RMSE (ºC)

CV (RMSE) (%)

NMBE (%)

RMSE (ºC)

CV(RMSE) (%)

NMBE (%)

COMSOL

0.08

0.37

0.19

0.12

0.56

0.34

ESP-r

0.08

0.62

-0.16

0.13

0.67

0.03

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

CSMPCM 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

381 382

Figure 10 shows the heat flux measured at the surface of the high temperature side of the

383

envelope assembly (point 1 in Figure 5).

384

processes, differences are observed between modeled heat fluxes and the experimental data.

385

These differences are potentially caused by the actual heat flux meter, as measuring surface heat

386

flux is challenging, prone to errors, and has higher uncertainty (±5%) than temperature

387

measurements. For the experimental measurements, heat flux meters had an accuracy of ±

388

5%.This uncertainty level is displayed with the experimental data lines in Figure 10 and Figure

389

11.

During both the heating up and cooling down

390 391

Figure 10 Heat flux at the Point (1): Hot-side boundary surface

392

Figure 11 shows the heat flux measured at the interface between the shape-stabilized PCM layer

393

and the mineral wool insulation layer. Interior heat fluxes (Point 3 in Figure 5) are calculated

394

using the temperature gradient between the interface node and the immediate node to the left.

395

Modeled results are within ±10% of each other. Both EnergyPlus models produce very close

396

values since no hysteresis is modeled. WUFI and COMSOL heat flux results are similar.

397

CSMPCM model stands below both these sets of data with the closer agreement to the

398

experimental data. All models follow the same trend but with different slopes with CSMPCM

399

model having the closest agreement with the experimental data. Heat-flux measurements could

400

not be directly obtained for ESP-r at the interface nodes.

401 402 403

Figure 11 Heat flux at the Point (3): Interface of the shape-stabilized PCM and mineral wool insulation

404

Table 8 shows RMSE, CV (RMSE) and NMBE values for the heat flux. At the exterior surface

405

(point 1 in Figure 5), all CV (RMSE) values are above 40%, missing the 20% threshold and

406

ESP-r has higher bias error than the other models. Surface heat flux is challenging to measure

407

and typically heat flux is accurately recorded in between layers. The heat fluxes at the interface

408

of the PCM wallboard and mineral wool insulation (point 3 in Figure 5) show RMSE values

409

below ±1.0 W/m2 and CV (RMSE) values between 5.5 - 12.2 %, falling within the defined

410

tolerances. However, all models over-estimate the heat flux values and have a NMBE larger

411

than the 5% threshold except for CSMPCM model..

412 413

Table 8: 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 1 of Figure 5 Software

Point 3 of Figure 5 NMBE (%)

RMSE (W/m2)

CV(RMSE) (%)

NMBE (%)

RMSE (W/m2)

CV(RMSE)

COMSOL

1.92

43.4

0.85

0.48

12.1

11.3

ESP-r

2.09

47.4

10.7

-

-

-

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

CSMPCM 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

(%)

414 415

3.2

Nano-PCM wall

416

Figure 12 shows the temperature at the interface between the OSB layer and the cellulose cavity

417

layer (point 2 in Figure 7) for all analyzed software. Three summer days, July 20-22 are selected

418

to display the results. Hour 1 is 1 a.m. on the first day (July 20). The temperature variations

419

observed for the field study represent realistic boundary conditions for building envelope

420

applications in contrast with the laboratory study. The horizontal dash line represents the peak

421

melting temperature of the PCM and the horizontal shaded cream colored area indicates the

422

melting temperature range. Temperature variations show models follow the same trend. The

423

modeled values seem to be under predicted at the peaks. In Figure 12 COMSOL, two E+

424

models, ESP-r, CSMPCM model, and WUFI lines are together hence might not be visible

425

separately.

426 427

Figure 12 Temperature at the Point (2): interface of OSB and cellulose insulation.

428

Figure 13 shows the temperature at the middle of the cavity. Temperature fluctuations are

429

reduced compared to Figure 12 due to the insulation. All models predict the experimental

430

temperature very closely. In both Figure 12 and Figure 13 Experimental, COMSOL, two E+

431

models, ESP-r, CSMPCM model, and WUFI lines are together hence might not be visible

432

separately.

433 434

Figure 13 Temperature at the Point (3): middle of cellulose insulation.

435

Figure 14 shows the experimental temperature at point 4 and point 6. However, point 6 is the

436

boundary condition and point 4 location was not exactly measured. Thus, the authors show

437

simulated values at point 5 (between point 4 and point 6 of Figure 7). As expected from the

438

results from Figure 9 to Figure 13 all models obtain similar temperature values.

439

For the simulated data at point 5, two E+ models, ESP-r, CSMPCM model, and WUFI lines are

440

together hence might not be visible separately. Considering the second day of the displayed

441

results, the highest and lowest temperatures measured at the left to the interface of cellulose

442

cavity and the PCM wallboard (point 4 of Figure 7) are 23 ºC and 20.6 ºC. The highest and

443

lowest temperatures observed at the interior surface (point 6 of Figure 7) are 21.5 ºC and 20.2

444

ºC. The peak melting temperature of the PCM is 21.4 ºC. Therefore, the PCM does not fully

445

change phase from melting to freezing and vice versa in the analyzed period of time. COMSOL

446

results were not available for this point. However, two E+ models, ESP-r, CSMPCM model, and

447

WUFI lines are observed together for the temperature at point 5.

448 449 450

Figure 14 Model results at the Point (4), Point (5): interface of the cellulose insulation and the PCM wallboard.

451

Table 9 shows RMSE, CV (RMSE) and NMBE calculations for Figure 12 and Figure 13. All

452

models show RMSE values below 1 ºC and have NMBE and CV (RMSE) values below the

453

recommended ranges. The negative values are an indication that models show less values in

454

magnitude and therefore, under-predicted the surface temperatures.

455 456

Table 9: 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 7 Software

Point 3 of Figure 7 NMBE (%)

RMSE (ºC)

CV(RMSE) (%)

NMBE (%)

RMSE (ºC)

CV(RMSE)

COMSOL

0.30

1.04

-0.58

0.12

0.97

-0.85

ESP-r

0.33

1.15

0.67

0.22

0.91

0.79

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

CSMPCM 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

(%)

457

Figure 15

458

wallboard (point 5). Results are zoomed in to the middle day of the results shown above. 0h and

459

24h indicates the midnight. For the modeled results, the calculated heat flux uses the temperature

460

gradient between the interface node of the cellulose cavity and the Nano-PCM wallboard and the

461

immediate next node modeled in the cellulose cavity. Heat flux meters used in this experiment

462

also had an accuracy tolerance of ±5% and this uncertainty is shown in the experimental data of

463

the Figure 15.

464

shows the heat fluxes at the interface of the cellulose cavity and Nano-PCM

465 466

Figure 15 Heat flux at the Point (5): interface of the cellulose cavity and the Nano-PCM wallboard.

467

Table 10 shows RMSE, CV (RMSE) and NMBE values for heat fluxes in Figure 15. All RMSE

468

values are below 1 W/m2 and the NMBE results are within the defined 5% threshold. However,

469

CV (RMSE) are slightly higher than this study standards, producing very similar results CV

470

(RMSE) values between 16.27 - 17.55 %, and under-estimate heat flux peak by about 20 %.

471

These differences are potentially caused by the actual heat flux meter, as measuring surface heat

472

flux is challenging, prone to errors, and has higher uncertainty (±5%) than temperature

473

measurements As indicated with the shape-stabilized PCM case heat-flux measurements could

474

not be directly obtained for ESP-r at the interface nodes.

475 476

Table 10 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 7 Software

RMSE (W/m2)

CV(RMSE) (%)

NMBE (%)

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

CSMPCM model

0.41

17.33

-0.16

WUFI

0.39

16.27

-0.13

477 478

In all the temperature comparisons, the differences between the measured and modelled values

479

are within the uncertainty range for all cases. Differences could be due to the positioning of

480

sensors, hygrothermal effects, and thermal hysteresis of the PCM. This indicates confidence that

481

the models can predict temperature values along similar walls. In contrast, there is greater

482

disagreement with heat flux data, as this is typically harder to measure and compute.

483

Interestingly, COMSOL 2D model shows similar results to rest of the PCM models that used 1D

484

heat transfer models. Therefore, for the measured locations, 2D calculation did not produce

485

results that are more accurate.

486

4

487

This study empirically validates and compares 6 PCM models implemented in different building

488

energy and hygrothermal software (EnergyPlus, ESP-r and WUFI). In addition, a 2D model

489

developed in COMSOL and another PCM model developed in MATLAB (CSMPCM model) are

490

also validated and compared using data from two independent experimental studies with Nano-

491

PCM embedded in drywall and shape-stabilized PCM behind the drywall construction material.

492

This is a unique study that compares several up to date PCM numerical modeling software

493

commonly used in the field with two different PCM types commonly used. The authors conduct

494

an extensive accuracy analysis of the compared results using RMSE, CV (RMSE) and NMBE

495

calculations. Based on the analyzed PCMs, all the evaluated software tools demonstrate their

496

ability to accurately predict surface and nodal temperature. However, heat flux predictions show

497

greater deviation from actual heat flux surface measurements and in some occasions do not meet

498

the study threshold for CV (RSME) and NMBE.. Interestingly, this study shows no additional

499

gains in accuracy when comparing a 2D heat transfer model with 1D modeling for Nano-PCMs

500

embedded in drywall over a stud wall. . Study affirms that these numerical modeling software

501

can be used to model PCMs and extend the studies to evaluate unique behaviors like

502

hygrothermal performance (WUFI, EnergyPlus). However, more work is needed to evaluate

503

different types of PCM and macroencapsulated applications when 2D/3D heat transfer effects

504

and/or hysteresis can have stronger effects.

505

5

506

The authors would like to thank Matthias Pazold and Florian Antretter from Fraunhofer Institute

507

for Building Physics IBP for their help with WUFI, Joe Clarke and John Allison from Energy

508

Systems Research Unit, University of Strathclyde for their support in ESP-r and the reviewers

509

for their critical feedback especially ESP-r feedback.

510

Conclusions

Acknowledgements

511 512

6

Nomenclature Nomenclature COMSOL cA(T) cp dh/dT EnergyPlus E+ ESP-r

h k MATLAB N PARDISO V&V yi

Meaning Cross-platform finite element analysis, solver and Multiphysics simulation software Effective specific heat capacity term Specific heat capacity Specific enthalpy change per unit temperature Energy Plus whole building energy modeling platform EnergyPlus Environmental Systems Performance – Research https://www.strath.ac.uk/research/energysystemsresearchunit/ap plications/esp-r/ Specific enthalpy Thermal conductivity A multi-paradigm numerical computing environment Number of data points A software for solving large sparse symmetric and nonsymmetrical linear systems of equations. Verification and validation Measured data Mean of the measured data Simulated data

Acronyms ADI ASHRAE DHFMA DSC EMS HAMT HFT IBP NET NMBE NTNU ORNL

Alternating Direction Implicit American Society of Heating, Refrigerating Conditioning Engineers Dynamic Heat Flux Meter Apparatus Differential Scanning Calorimetry Energy Management System Heat and Mass Transfer Heat Flux Transducers Institute for Building Physics Natural Exposure Test Normalized Mean Biased Error Norwegian University of Science and Technology Oak Ridge National Laboratory

and

Air-

OSB PCM CV(RMSE) IEA TES WUFI 513 514

Oriented Strand Board Phase Change Material Coefficient of Variance of Root Mean Square Error International Energy Agency Thermal Energy Storage "Wärme Und Feuchtetransport Instationär" ("Transient Heat and Moisture Transport").

515

7

516

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Empirical validation and comparison of PCM modeling algorithms commonly used in building energy and hygrothermal software Highlights •

Validation study considered 6 PCM models in 5 software packages

•

Two independent experimental studies provide the data

•

Studies use Nano-PCM embedded in drywall and shape stabilized behind drywall

•

Comparison of the modeled results demonstrate their ability to accurately model PCMs