energies

Article Modeling PCM Phase Change Temperature and Hysteresis in Ventilation Cooling and Heating Applications

Yue Hu *, Rui Guo , Per Kvols Heiselberg and Hicham Johra

Division of Architectural Engineering, Department of the Built Environment, Aalborg University, Thomas Manns Vej 23, DK-9220 Aalborg Øst, Denmark; [email protected] (R.G.); [email protected] (P.K.H.); [email protected] (H.J.) * Correspondence: [email protected]



Received: 22 October 2020; Accepted: 1 December 2020; Published: 6 December 2020


Abstract: Applying phase change material (PCM) for latent heat storage in sustainable building systems has gained increasing attention. However, the nonlinear thermal properties of the material and the hysteresis between the two-phase change processes make the modelling of PCM challenging. Moreover, the influences of the PCM phase transition and hysteresis on the building thermal and energy performance have not been fully understood. This paper reviews the most commonly used modelling methods for PCM from the literature and discusses their advantages and disadvantages. A case study is carried out to examine the accuracy of those models in building simulation tools, including four methods to model the melting and freezing process of a PCM heat exchanger. These results are compared to experimental data of the heat transfer process in a PCM heat exchanger. That showed that the four modelling methods are all accurate for representing the thermal behavior of the PCM heat exchanger. The model with the DSC Cp method with hysteresis performs the best at predicting the heat transfer process in PCM in this case. The impacts of PCM phase change temperature and hysteresis on the building energy-saving potential and thermal comfort are analyzed in another case study, based on one modelling method from the first case study. The building in question is a three-room apartment with PCM-enhanced ventilated windows in Denmark. The study showed that the PCM hysteresis has a larger influence on the building energy consumption than the phase change temperature for both summer night cooling applications and for winter energy storage. However, it does not have a strong impact on the yearly total energy usage. For both summer and winter transition seasons, the PCM hysteresis has a larger influence on the predicted percentage of dissatisfied (PPD) than the phase change temperature, but not a strong impact on the transition season average PPD. It is therefore advised to choose the PCM hysteresis according to whether it is for a summer night cooling or a winter solar energy storage application, as this has a significant impact on the system’s overall efficiency.

Keywords: phase change material; temperature hysteresis; phase transition temperature; PCM modelling; building simulation

1. Introduction Buildings are intended to protect the occupants from the outdoor weather conditions and provide comfortable environments. Humans are especially sensitive to ambient temperature. They will easily experience thermal discomfort if the indoor temperature is not maintained within a narrow temperature range [1] and without rapid transient change to the operative temperature [2]. Besides, the building sector is the largest energy end-user in the world [3]. Therefore, diminishing indoor space heating

Energies 2020, 13, 6455; doi:10.3390/en13236455 www.mdpi.com/journal/energies Energies 2020, 13, 6455 2 of 21 and cooling needs have been identified as key targets for the reduction of global energy use and CO2 emissions [4]. Moreover, buildings can modulate their energy profiles to a certain extent by shifting their power load in time. The energy storage capacities of buildings or clusters of buildings can thus be employed to implement demand-side management and building energy flexibility strategies, which can greatly ease the management and improve the stability of smart energy grids with large shares of intermittent renewable energy sources [5]. With regard to the aforementioned matters, phase change materials (PCM) that change their phases near room temperatures (10 ◦C–30 ◦C) have drawn considerable attention over the last decade [6]. Unlike materials experiencing only sensible heat storage, a PCM has a phase transition (change in the microstructure of the material) at near ambient temperature. This phase transition requires a considerable amount of thermal energy (latent heat) but occurs with a very limited temperature variation. The latent heat thermal energy storage (LHTES) ability of the PCM is a great asset for high-density thermal storage at a constant temperature in building systems. PCM for building applications has volumetric heat storage capacities which are typically 5 to 14 times greater than sensible heat storage materials such as water or concrete [7]. However, the hysteresis, subcooling and other complex thermal properties of PCM greatly complicate the development of reliable LHTES models for building simulations. It is important to have a better understanding of the hysteresis and subcooling phenomena and the refinement of the numerical model dealing with these issues. There are mainly two reasons for the hysteresis phenomenon of PCM. One is the improper measurement methods employed to assess PCM properties. There are many well-developed measurement methods for PCM characteristics, including the inverse method, the DSC method and the T-history method. However, every measurement method has its limitations. Noticeable differences in the results can be observed when employing different methods or standards to measure PCM thermal properties [8]. An improper measurement method can lead to the observation of an “apparent hysteresis,” which in most cases, over-estimates the real hysteresis of the material. The differential scanning calorimetry (DSC) measurement is the standard method to test materials in small samples. It is done by measuring the differences of the heat flows between the reference sample with known thermal properties and the test sample under the same temperature change rate. The measurement results can be very different with different parameter settings. For example, with high heating and cooling heat rates or a large sample size, the inhomogeneity in the material will increase, especially for PCM with low thermal conductivity [8,9]. High heating and cooling heat rates can also increase the subcooling, hysteresis and phase transition temperature range [8,10,11]. However, low heating and cooling rates decrease the magnitude of the DSC signal, which makes it more sensitive to measurement noise [12]. On the other hand, a small sample size could increase the subcooling effect, and may not be representative of some nonhomogeneous materials. Some other more advanced measurement methods, such as the T-history method, are found to be more accurate than DSC for PCM with hysteresis and compound materials [9]. However, those methods are not commercially developed with standard guidance, which makes the comparison among measurements difficult. Arkar et al. [13–15] suggested that the properties of the PCM should be determined using similar heating and cooling rates to the actual temperature change rates of the real application. For PCM in the active building application systems, the thermal response of the PCM is usually 1–8 h for 20 K according to [16], which corresponds to a heating/cooling rate ranging from 0.04 to 0.33 K/min. For passive building applications, the thermal response time could be as long as 12 h, corresponding to a heating/cooling rate of 0.03 K/min. The other reason for the hysteresis phenomenon of PCM lies in its intrinsic material property. Decreasing the heating and cooling rates, sample size or temperature step can improve the measurement accuracy so that the measurement uncertainty decreases. However, the single enthalpy curve without hysteresis cannot be achieved even with infinitely slow measurement, because the existence of subcooling, incomplete crystallization or polymorphic crystal structures results in different shapes of Energies 2020, 13, 6455 3 of 21 heating and cooling curves [17]. In certain cases, even with the most accurate measurement method and with the smallest heating/cooling rates, the hysteresis phenomenon can still be observed. The large enthusiasm of the scientific community for PCM applications during the last few decades has led to the development of numerous numerical models for simulating the thermodynamics and heat storage in LHTES systems. The most commonly used methods to simulate the latent heat are the fixed grid methods [18], which solve phase change problems by accounting for the latent heat of the PCM into the governing energy equation. The latent heat of PCM is defined by either a function of heat capacity, a heat source or a function of enthalpy. Compared with the deformed grid method and the hybrid fixed/deformed method, which can also be used to solve a phase transition problem [19], the space grid is fixed throughout the whole calculation. It is thus simpler to implement the existing heat transfer numerical models and software. They include the heat capacity method and the enthalpy method. The heat capacity method can be further sorted as the square heat capacity method, the triangular heat capacity method or the DSC heat capacity method. However, the accuracy and reliability of PCM numerical models used for building applications are yet to be examined for proper design and simulation purposes [20]. Moreover, an increasing number of researchers are starting to realize the importance of modelling PCM hysteresis for building simulations. Dolado et al. [21] found the existence of temperature hysteresis while studying the thermal performance of a PCM heat exchanger and addressed the necessity of taking it into account in the numerical work. Kuznik et al. [13] applied a single melting/freezing curve of specific heat to their PCM wallboard model and compared it to the experimental data. They figured out that neither of the two methods can predict the temperature profile in the PCM wallboard. They thus suggested the importance of modelling PCM hysteresis in building simulations. Similarly, Barz et al. [22] compared a non-hysteresis model and a hysteresis model to the experimental data of the latent heat storage. The results show that the non-hysteresis model is of poor accuracy to represent the melting/solidification of the PCM storage. However, the sensitivity analyses of the PCM hysteresis are mostly about the PCM heat transfer process. The influences of the PCM phase transition and hysteresis on buildings’ thermal and energy performance have not been fully studied yet. There have only been a few studies about the sensitivity analysis of the PCM hysteresis on the energy performances of buildings, and those studies drew different conclusions. Ramprasad et al. [23] studied the hysteresis of the PCM on the building envelope and found out that hysteresis does not have a large influence on the annual building energy, but the influences on the surface temperature and zone temperature are considerable. Oppositely to Ramprasad et al., Moreles et al. [24] studied a building with PCM wall and found that an increase of PCM hysteresis temperature within the thermal comfort temperature can greatly decrease the building air-conditioning energy consumption. The discrepancy between the former studies about the influence of PCM hysteresis on the building energy indicates that more detailed and comprehensive studies have to be carried out. This article aims to examine the current PCM modelling methods and compare them against the experimental data of a PCM heat exchanger, and further study the influences of the PCM thermal properties on both building energy-saving potential and thermal comfort based on the PCM application in a ventilation system, including both a summer application and a winter application. Firstly, the paper reviews the most commonly used modelling methods for the nonlinear thermal properties of the PCM. To test their accuracy, a comparison is made with experimental data of a case study of a PCM heat exchanger with four modelling methods: the square heat capacity method, the triangular heat capacity method, the enthalpy method and the DSC heat capacity method. Finally, one modelling method is selected for another case study of an apartment with PCM-enhanced ventilated windows. The impacts of PCM phase change temperature and hysteresis on building energy-saving potential and thermal comfort are assessed. Energies 2020, 13, 6455 4 of 21

2. PCM Modelling Methods in Building Simulations The challenge of modelling PCM in building simulations lies in dealing with nonlinear thermal properties of the PCM and temperature hysteresis. This section summarizes and compares some of the modelling methods. Section 2.1 introduces the different PCM modelling methods regarding the latent heat of PCM; Section 2.2 discusses the modelling methods of PCM hysteresis; Section 2.3 compares different modelling methods against experimental data.

2.1. PCM Latent Heat Modeling Methods The most commonly used methods for PCM latent heat modelling are fixed grid methods, including the heat capacity method and the enthalpy method. The heat capacity method can be further sorted into the square heat capacity method, the triangular heat capacity method and the DSC heat capacity method. The square heat capacity curve method is easy to implement numerically. It is, therefore, the most commonly used method in numerical simulation tools and research studies. Besides, it is fast to compute, which is beneficial for certain applications where the calculation speed is important. Moreover, for many building material manufacturers, only some key parameters of the PCM properties are provided because of the lack of standards. The key parameters are normally the melting/freezing temperature range, melting/freezing temperature peak, specific heat capacity without phase change and total latent heat. A simple heat capacity curve can be easily deducted from those key parameters. The basic equations used for shape-stable PCM in building simulations are the Navier–Stokes momentum equation, the continuity equation and the energy equation, as shown in Equations (1)–(3).

∂u ρ + ρ(u )u = p + µ 2u + ρgβ∆T (1) ∂t · ∇ −∇ ∇ u = 0 (2) ∇ · ! ∂T ρCp(T) + u T = (λ T) (3) ∂t · ∇ ∇ ∇ where ρ is the density of the material (kg/m3); u is the velocity (m/s); t is the time (s); µ is the dynamic viscosity (Pa s); β is the thermal expansion coefficient (1/K); T is the temperature of the domain ( C); · ◦ λ is the thermal conductivity (W/m K). · With this limited data provided by the manufacturers, the heat capacity can be calculated with a simple piece-wise square function, as shown in Equation (4) [25].   C , T < T  s s  Cs+Cl L Cp(T) = + , Ts T Tl (4)  2 Tl Ts  − ≤ ≤  Cl, T > Tl where C is the specific heat capacity of PCM in liquid phase (J/kg K);Cs is the specific heat capacity of l · PCM in solid phase (J/kg K); L is the latent heat (J/kg); T is the PCM melting temperature ( C); Ts is the · l ◦ PCM freezing temperature (◦C). The limitation of this method is that when using it to solve Equation (3), the solver may not converge if the time step is too large or the phase change range is too small. There is a risk of missing the phase transition if the time step is too large and the temperature range of phase change is skipped, which is usually called a step-jump [26,27]. A solution to this problem is to use an approximated approach to redefine the heat capacity by a triangular function from [28,29]. Equations (5) and (6) show the corresponding equations for this triangular heat capacity curve. Alvaro et al. [30] have built a numerical model for the PCM ventilation system which considered hysteresis. The simplified equivalent heat capacity (heat capacity curve has a Energies 2020, 13, 6455 5 of 21 triangle shape centered on phase transition temperature) is used as the input of the model. The results show that the model is in good agreement with experimental data.   Cs, T < Ts and T > T    l  2M Ts+Tl Ts+Tl ( ) =  Cs + M + T , Ts T Cp T  Tl Ts 2 2 (5)  −  − +  +≤ ≤  C + M 2M T Ts Tl , Ts Tl T T s T Ts 2 2 l − l− − ≤ ≤ where M is the melting peak factor (J/kg K)), which can be calculated with the equation below: · 2L M = (6) (T Ts) l − The DSC heat capacity method uses the heat capacity curve determined by DSC method as the material input of the model. Hu et al. [31] used this model to simulate a PCM heat exchanger. The model results are in good agreement with the experimental data. Another model used the same approach to simulate the wallboard [13]. The DSC heating and cooling rate was set to 0.05 K/min to approach the real heat exchange rate of the wallboard exposed to summer conditions. It was found that it is essential to use the correct melting/freezing curves when simulating the heating and freezing processes of the wallboard. Eyres et al. [32] first proposed the enthalpy method to solve the heat flow in bodies under non-steady state conditions. The idea is to consider enthalpy as a function of phase fraction and temperature. It was then adopted by [25,33–37]. The Navier–Stokes equation and the continuity equation are the same as Equations (1) and (2). Equations (7)–(9) show the energy equations.

∂H ρ = (λ T) (7) ∂t ∇ ∇   CpT, T < T  s  L(T Ts) H = CpT + − , Ts T Tl (8)  Tl Ts  − ≤ ≤  CpT + L, T > Tl Z T H(T) = Cp(T)dT (9) Tre f where Tref is the reference temperature (◦C); H is the enthalpy of the PCM (J/kg). The enthalpy method has been applied in the work of Takeda et al. [38]. The enthalpy curves for melting and freezing processes were measured with the DSC method at 1 ◦C/min heating and cooling rate. Then an enthalpy function was made by taking a middle path between the melting enthalpy curve and the freezing enthalpy curve. The results from the model reveal similar variations as in the experiment.

2.2. Modeling of PCM Hysteresis Some researchers try to model the transition between freezing and melting processes within the phase change range. There are mainly two approaches currently. Bony et al. [39] proposed one approach in which the enthalpy transition line between the melting and freezing processes is a straight line that parallels to the sensible enthalpy curve, as shown in Figure1a. Another approach is used in the models of Kaushik et al. [40]. It suggests that there is no hysteresis shown until the PCM completely solidifies or melts. Then the enthalpy curve changes to another one, as seen in Figure1b. Ramprasad et al. [23] compared the two approaches with EnergyPlus simulations, and found out that hysteresis does not have a large influence on the annual building energy use, but the influence on the surface temperature and zone temperature is considerable. Energies 2020, 13, x FOR PEER REVIEW 6 of 21 completely solidifies or melts. Then the enthalpy curve changes to another one, as seen in Figure 1b. Ramprasad et al. [23] compared the two approaches with EnergyPlus simulations, and found out that hysteresisEnergies 2020 does, 13, 6455 not have a large influence on the annual building energy use, but the influence on6 ofthe 21 surface temperature and zone temperature is considerable.

FigureFigure 1. 1. TwoTwo approaches approaches to to model model the the transition transition between between melting melting and and freezing freezing processes: processes: ( (aa)) Straight Straight transitiontransition line line model; model; ( (bb)) One One curve curve model. model.

SomeSome more more complex complex models models are are al alsoso available available for for modelling modelling PCM PCM hysteresis, hysteresis, including including the the static static hysteresishysteresis model model [41], [41], which which directly directly implements implements data data from from DSC DSC measurements; measurements; and and the the kinetic kinetic modelmodel [42,43], [42,43], in in which which the the melting melting and and freezing freezing are are considered considered as as intrinsic intrinsic dynamic dynamic variables variables as as functionsfunctions of of temperature temperature and and time, time, and and the the parame parametersters are are generated generated by by fitting fitting the the macro macro kinetic kinetic modelsmodels to to experimental experimental data data [22]. [22 Barz]. Barz et al. et [22] al. [ compared22] compared the aforementioned the aforementioned models models by using by usingthem forthem latent for latentheat storage heat storage and comparing and comparing them to them the toexperimental the experimental data. The data. results The results show that show the that static the hysteresisstatic hysteresis model model has similar has similar accuracy accuracy to the to thekineti kineticc model, model, and and is iseasier easier to to implement implement by by direct direct parametrizationparametrization from from DSC DSC measurements. measurements. That That method method has has been been chosen chosen for for modelling modelling hysteresis hysteresis in in thisthis paper. paper.

2.3.2.3. Comparison Comparison of of the the D Diifferentfferent PCM PCM Modelling Modelling Methods Methods ThisThis section section analyzes analyzes and and compares compares the the aforem aforementionedentioned most most commonly commonly used used PCM PCM modelling modelling methodsmethods in in the the building building simulation simulation tools. tools. The The comparison comparison study study case case is is an an air–PCM air–PCM heat heat exchanger exchanger mademade by by shape shape steady steady PCM PCM plates. plates. The The PCM PCM is is encaps encapsulatedulated by by the the fiber fiber board; board; thus, thus, the the convection convection inin the the liquid liquid PCM PCM is is not not simulated. simulated. In In this this case, case, the the finite finite element element numerical numerical model model for for a a PCM PCM heat heat exchangerexchanger is is based based on on the the conjunction conjunction of of heat heat tran transfersfer and and laminar laminar flow flow physics. physics. The The heat heat exchanger exchanger consistsconsists ofof 12.512.5 mm mm PCM PCM plates plates spaced spaced by 6by mm 6 airmm gaps. air Thegaps. test The scenario test scenario includes aincludes night ventilation a night ventilationmode and amode ventilation and a ventilation pre-cooling pre-cooling mode. In night mode. ventilation In night ventilation mode, the low-temperaturemode, the low-temperature ambient air ambientis supplied air is into supplied the heat into exchanger the heat toexchanger discharge to the discharge PCM during the PCM nighttime. during Innighttime. ventilation In ventilation pre-cooling pre-coolingmode, the PCM mode, is usedthe PCM to cool is downused theto cool high-temperature down the high-temperature ambient air ventilated ambient through air ventilated the heat throughexchanger the during heat exchanger the daytime during when the cooling daytime is needed. when cooling The influences is needed. of the The PCM influences modelling of the methods PCM modellingon the model’s methods accuracy on the are model’s evaluated accuracy based onare comparisonsevaluated based with on experimental comparisons data. with The experimental PCM in the data.system The is PCM para ffiinn the wax system 22. Its is propertiesparaffin wax are 22. listed Its pr inoperties Table1. are The listed hysteresis in Table of the1. The PCM hysteresis is around of the1 ◦ CPCM according is around to the 1 °C DSC according test with to a the heating DSC/cooling test with rate a ofheating/cooling 0.5 ◦C/min. The rate experiment of 0.5 °C/min. is set The up experimentin a climate is chamber set up in witha climate a hot chamber zone and with a cold a hot zone, zone whichand a cold are bothzone, conditioned which are both by aconditioned heater and cooler. The air temperature in the hot zone is 29 1 C, and the air temperature in the cold zone is by a heater and cooler. The air temperature in the ho± t zone◦ is 29 ± 1 °C, and the air temperature in the 9 1 C. During the night ventilation mode, the cold air in the cold zone is directed to the PCM heat cold± zone◦ is 9 ± 1 °C. During the night ventilation mode, the cold air in the cold zone is directed to theexchanger PCM heat bottom exchanger inlet. Afterbottom the inlet. PCM After is totally the PCM cooled is downtotally (solidified), cooled down the (solidified), hot air in from the hot the hotair inzone from is directedthe hot zone into theis directed PCM heat into exchanger the PCM top heat inlet. exchanger The PCM top temperatures inlet. The PCM is monitored temperatures at four is different heights inside the heat exchanger, as shown in Figure2. More details about the model and experimental case can be found in [31]. Energies 2020, 13, x FOR PEER REVIEW 7 of 21

monitored at four different heights inside the heat exchanger, as shown in Figure 2. More details Energiesabout2020 the, 13model, 6455 and experimental case can be found in [31]. 7 of 21

Table 1. The thermal properties of the PCM in the experimental setup [31]. Table 1. The thermal properties of the PCM in the experimental setup [31]. Name Paraffin Wax 22 Name Paraffin Wax 22 Density 820 kg/m3 3 Specific heatDensity capacity 820 kg2.3/m kJ/kg/°C ThermalSpecific conductivity heat capacity 2.3 kJ 0.18/kg/ ◦W/m/°CC Thermal conductivity 0.18 W/m/◦C LatentLatent heat heat 117 kJ 117/kg kJ/kg MeltingMelting range range 16–23 16–23◦C °C FreezingFreezing range range 14–21.5 14–21.5◦C °C MeltingMelting peak peak 21.5 ◦ 21.5C °C Freezing peak 20.7 C Freezing peak ◦ 20.7 °C

FigureFigure 2. Locations2. Locations of theof sensorsthe sensors for the for monitoring the monitoring of the PCM of the air temperaturesPCM air temperatures in the heat exchangerin the heat forexchanger experimental for experimental and simulation and cases simulation [31]: (a )cases front [31]: view; (a) ( bfront) side view; view; (b (c) )side top view; view. (c) top view.

FigureFigure3 shows 3 shows the averagethe average PCM temperaturePCM temperature profiles profiles at a height at ofa height 510 mm of in 510 the heatmm exchangerin the heat predictedexchanger by dipredictedfferent PCM by modelsdifferent and PCM measured models during and themeasured experiments. during The the temperature experiments. profiles The oftemperature all the models profiles show of trends all the that models are similar showto trends the experimental that are similar data. to The the curveexperimental of the DSC data. heat The capacitycurve of method the DSC with heat a 1 ◦capacityC temperature method hysteresis with a 1 has °C the temperature best fit to the hysteresis experiment, has especiallythe best fit during to the theexperiment, phase transition especially periods during (0.7–2.4 the phase h and tr 6.7–10ansition h). periods (0.7–2.4 h and 6.7–10 h). Figure4 shows the temperature deviation between model results and experimental data. The minimum model deviation comes from the DSC heat capacity method with a 1 ◦C temperature hysteresis. All the models show acceptable accuracy. The model deviations are always less than 1 ◦C. The model with the DSC heat capacity method and 1 ◦C temperature hysteresis has the lowest deviation from the experiment, with 0.6 ◦C of average deviation and 2.2 ◦C of maximum deviation.

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Energies 2020, 13, 6455 8 of 21 Energies 2020, 13, x FOR PEER REVIEW 8 of 21

Figure 3. The temperature of PCM at a height of 510 mm in the heat exchanger as a function of time.

Figure 4 shows the temperature deviation between model results and experimental data. The minimum model deviation comes from the DSC heat capacity method with a 1 °C temperature hysteresis. All the models show acceptable accuracy. The model deviations are always less than 1 °C. The model with the DSC heat capacity method and 1 °C temperature hysteresis has the lowest Figure 3. The temperature of PCM at a height of 510 mm in the heat exchanger as a function of time. deviationFigure from 3. The the temperature experiment, of PCMwith at0.6 a °Cheight of av oferage 510 mm deviation in the heat and exchanger 2.2 °C of as maximum a function ofdeviation. time.

Figure 4 shows the temperature deviation between model results and experimental data. The minimum model deviation comes from the DSC heat capacity method with a 1 °C temperature hysteresis. All the models show acceptable accuracy. The model deviations are always less than 1 °C. The model with the DSC heat capacity method and 1 °C temperature hysteresis has the lowest deviation from the experiment, with 0.6 °C of average deviation and 2.2 °C of maximum deviation.

Figure 4. The deviation between the models and the experimental data. Figure 4. The deviation between the models and the experimental data. 3. The Effect of Phase Transition Temperature and Hysteresis Degree on the Building Energy 3. The Effect of Phase Transition Temperature and Hysteresis Degree on the Building Energy This section looks into the influences of the PCM phase transition temperature and hysteresis degreeThis on section the building’s looks into energy the performance.influences of Thethe investigatedPCM phase modeltransition is the temperature DSC heat capacity and hysteresis method withdegree hysteresis, on the building’s as it gives theenergy best fitperformance. to experimental The data investigated (see Section model2). PCM is forthe summer DSC heat applications capacity methodand winter with applications hysteresis, as are it studiedgives the separately best fit to withexperimental two different data Energyplus(see Section models.2). PCM Thefor summer PCM is applicationsmodelled with and a 1D winterFigure heat conduction4.applications The deviation finite are between distudiedfference the separately models model inand Energyplus,with the experimentaltwo different which data. calculates Energyplus the models. average ThePCM PCM temperature is modelled of the with whole a PCM1D heat in theconduction PCM-enhanced finite difference ventilated windowsmodel in (PCMVW).Energyplus, which 3. The Effect of Phase Transition Temperature and Hysteresis Degree on the Building Energy calculatesTwo PCMVWsthe average are installedPCM temperature in the external of wallsthe whole of the southwestPCM in roomthe PCM-enhanced of a three-room apartmentventilated windowsin Denmark.This (PCMVW).section The PCMVWlooks into is the equipped influences with of the the PCM PCM heat phase exchanger transition presented temperature in Section and hysteresis2.3 with a ventilateddegreeTwo on windowPCMVWs the building’s mounted are installed energy on a top performance.in of the it. Theexternal operating The wa investigatedlls control of the strategy southwest model of theis PCMVWroomthe DSC of isaheat explainedthree-room capacity in apartmentFiguremethod5. with For in the Denmark.hysteresis, summer The as night it PCMVW gives cooling the is applications,best equipped fit to experimental with the the PCM PCM thermal data heat (see energyexchanger Section storage 2).presented PCM is discharged for in summer Section by 2.3theapplications with cold outdoora ventilated and airwinter atwindow nighttime. applications mounted It then are on pre-cools studied a top of separately the it. The supplied operating with fresh two control air different during strategy day Energyplus time of the (Figure PCMVW models.5a1). isThe explained PCMPCM thermalis in modelled Figure energy 5. withFor storage the a summer1D is heat fully nightconduction shaded cooling from finite applications, solar difference radiation, the model whilePCM thermal thein ventilatedEnergyplus, energy window storage which is discharged by the cold outdoor air at nighttime. It then pre-cools the supplied fresh air during day iscalculates shaded bythe external average shading PCM temperature when the indoor of th aire whole temperature PCM in is higherthe PCM-enhanced than 24 ◦C (Figure ventilated5a2). timeThewindows airflow (Figure (PCMVW). rate 5a1). through The PCM thePCMVW thermal isenergy based storage on thepeople is fully load shaded of the from room, solar which radiation, is 60 m 3while/h/person the ventilatedin summerTwo PCMVWswindow and 30 mis 3areshaded/h/ personinstalled by external in winter,in the shading external according when wa tolls the the of indoor optimizationthe southwest air temperature results room of isof the higher a airflowthree-room than rate 24 inapartment [44]. For in winter Denmark. solar The energy PCMVW storage is equipped applications, with the the PCM PCM accumulates heat exchanger solar presented energy during in Section the day2.3 with (Figure a ventilated5b1), and laterwindow releases mounted the it toon preheat a top of the it. inletThe operating fresh air (Figure control5b2). strategy There of is the no shadingPCMVW foris explained the PCM thermalin Figure energy 5. For storagethe summer and the night ventilated cooling window.applications, The airflowthe PCM rate thermal is the sameenergy as storage for the summeris discharged night by cooling the cold applications. outdoor air Theat nighttime. details of It the then PCMVW pre-cools model the supplied and model fresh validation air during can day be foundtime (Figure in [45]. 5a1). The PCM thermal energy storage is fully shaded from solar radiation, while the ventilated window is shaded by external shading when the indoor air temperature is higher than 24

Energies 2020, 13, x FOR PEER REVIEW 9 of 21 Energies 2020, 13, x FOR PEER REVIEW 9 of 21

°C°C (Figure(Figure 5a2).5a2). TheThe airflowairflow raterate throughthrough thethe PCMVWPCMVW isis basedbased onon thethe peoplepeople loadload ofof thethe room,room, whichwhich 3 3 isis 6060 mm3/h/person/h/person inin summersummer andand 3030 mm3/h/person/h/person inin winter,winter, accordingaccording toto thethe optimizationoptimization resultsresults ofof thethe airflowairflow raterate inin [44].[44]. ForFor winterwinter solarsolar enerenergy storage applications, the PCM accumulates solar energy during the day (Figure 5b1), and later releases thethe itit toto preheatpreheat thethe inletinlet freshfresh airair (Figure(Figure 5b2).5b2). There is no shading for the PCM thermal energy storage and the ventilated window. The airflow rate isis thethe samesame asas forfor thethe summersummer nightnight coolingcooling applications.applications. TheThe detailsdetails ofof thethe PCMVWPCMVW modelmodel andand Energies 2020, 13, 6455 9 of 21 model validation can be found in [45].

Figure 5. TheThe PCM-enhanced PCM-enhanced ventilated ventilated windows windows (PCMVW (PCMVW))) controlcontrol strategies strategies for for both both summer summer and and winter applications [[45].45]. This study is conducted for the Danish climate. The summer application operated from 1st May This study is conducted for the Danish climate. TheThe summersummer applicationapplication operatedoperated fromfrom 1st1st MayMay to 31st October, while the winter application operated from 1st November to 30th April. The heating, toto 31st31st October,October, whilewhile thethe winterwinter applicationapplication operatedoperated fromfrom 1st1st NovemberNovember toto 30th30th April.April. TheThe heating,heating, ventilation and air conditioning (HVAC) system only operated during severe summer and severe ventilation and air conditioning (HVAC) system only operated during severe summer and severe winter periods, in cases when the PCM thermal energy storage could not provide enough pre-heated winter periods, in cases when the PCM thermal energy storage could not provide enough pre-heated or pre-cooled air. The HVAC system is a packaged terminal heat pump system with a heating coil COP or pre-cooled air. The HVAC system is a packaged terminal heat pump system with a heating coil of 2.87 and cooling coil COP of 1.87. The room air temperature setpoint is 22–26 C. The period of COP of 2.87 and cooling coil COP of 1.87. The room air temperature setpoint is 22–26◦ °C. The period severe summer is from 1st June to 31st August. The period for severe winter is from 1st November of severe summer is from 1st June to 31st August. The period for severe winter is from 1st November to 29th February. The transition season is when there is no operating HVAC system. The summer toto 29th29th February.February. TheThe transitiontransition seasonseason isis whenwhen therethere isis nono operatingoperating HVACHVAC system.system. TheThe summersummer transition season is May, September and October, and the winter transition season is March and April. transitiontransition seasonseason isis May,May, SeptemberSeptember andand October,October, andand thethe winterwinter transitiontransition seasonseason isis MarchMarch andand The corresponding PCMVW and HVAC operation schedules can be found in Figure6. April. The corresponding PCMVW and HVAC operation schedules can be found in Figure 6.

Figure 6. The PCMVW and HVAC (heat pump) operation schedule. Figure 6. The PCMVW and HVAC (heat pump) operation schedule. A local sensitivity analysis is conducted to determine which parameters had significant influences A local sensitivity analysis is conducted to determine which parameters had significant oninfluences the system’s on the energy system’s demand energy during demand the severe duri summerng the andsevere winter summer periods. and The winter sensitivity periods. analysis The influencesis performed on by the the system’s methodology energy of demand [46,47]: during the severe summer and winter periods. The sensitivitysensitivity analysisanalysis isis performedperformed byby thethe methodologymethodology ofof [46,47]:[46,47]: • Define input variables with their variation ranges. • Define input variables with their variation ranges. • Set variation level mm forfor eacheach inputinput variablevariable inin aa discretediscrete distribution.distribution. • Set variation level m for each input variable in a discrete distribution. • Use a one-parameter-at-a-timeone-parameter-at-a-time (OAT) methodmethod toto generategenerate pp == mm×n observations, where n is the • Use a one-parameter-at-a-time (OAT) method to generate p = m×n observations, where n is the number of input variables.variables. • Obtain output variablesvariables byby conductingconducting nn simulations.simulations. • Obtain output variables by conducting n simulations. Visualize the output distribution. •

Assess the importance of each input parameter to the output by calculating the sensitivity index, which is calculated by the equation below:

Emax,i Emin,i SIi = − (10) Emax Energies 2020, 13, 6455 10 of 21

where SIi is the local sensitivity index; Emax,i and Emin,i are the maximum and minimum outputs corresponding to the ith input; Emax is the maximum global output among all the inputs of all the variables. In this case, the input parameters are the phase transition temperature and hysteresis degree, and the outputs are the summer cooling energy demand, winter heating energy demand and total heating + cooling energy demand of the room. For the transition seasons, the HVAC system is not operating. The PCMVW is supposed to cover the heating and cooling energy demands. The system’s performance is then evaluated with the predicted percentage of dissatisfied (PPD) proposed by Fanger [48]. The lower the PPD, the better the indoor environment quality. The range of the PCM phase transition temperature in this study is from 15 to 25 ◦C, and the range of the PCM hysteresis degree is from 0 to 6 ◦C. The values are chosen because the most commonly used PCM in building applications have hysteresis from 0 to 6 ◦C, as shown in AppendixA (Table A1), which is a literature review of the PCM in building applications.

3.1. Severe Summer and Winter Conditions The study starts with the PCM phase change temperature and hysteresis degrees and their influences on the room energy demand for severe summer (1st June–31th August) and winter (1st November–29th February) conditions, when the HVAC is used to guarantee good quality of the indoor environment. For summer night cooling applications during the severe summer conditions, 11 PCM with different phase transition temperatures (no hysteresis) are firstly studied. For those PCM, the melting temperature equals freezing temperature. Their latent heat, thermal conductivity and other properties are all the same. Figure7 shows some of the PCM temperatures from those cases. There are large differences in the PCM temperature profiles for PCM with different phase transition temperatures. For the days with low average daily outdoor air temperature, the PCM with low phase transition temperature has a more stable temperature profile and a relatively low temperature during the daytime. For the days with high average daily outdoor air temperature, the PCM with high phase transition temperature has a more stable temperature profile and a relatively low temperature during the daytime. For PCM with a 21 ◦C phase transition temperature, the PCM temperature is more stable than the PCM with 25 ◦C for most days. That is because the average outdoor air temperature is much closer to 21 ◦C, so that the PCM with a 21 ◦C phase transition temperature is more activated than the one with a 25 ◦C phase transition temperature. The relations between the PCM phase change temperature and the PCM temperature profiles are quite different from day to day due to the differences in the daily outdoor airEnergies temperature. 2020, 13, x FOR PEER REVIEW 11 of 21

Figure 7. The PCM temperature profiles for models with different phase change temperatures for Figure 7. The PCM temperature profiles for models with different phase change temperatures for summer night cooling application. summer night cooling application.

The study is carried out with seven PCM with different hysteresis degrees during severe summer. For those PCM, hysteresis degree is the difference between the melting peak and the freezing peak; melting peak = 21 °C + hysteresis/2; freezing peak = 21 °C − hysteresis/2. Figure 8 shows some of the PCM temperatures. It shows that PCM with no hysteresis has the most stable temperature profile and lowest temperature during the daytime for most of the days when the ventilation pre- cooling is needed, and the PCM with 5 °C hysteresis has the highest temperature during the daytime for most of the days when the ventilation pre-cooling is needed. When outdoor air temperature is relatively low, the PCM with no hysteresis has the lowest temperature during both daytime and nighttime. It indicates that PCM with no hysteresis can benefit the building’s energy-saving the most during severe summer.

Figure 8. The PCM temperature profiles for models using PCM with different hysteresis degrees for summer night cooling application.

For winter solar energy storage applications during the severe winter condition, the study compares the models using the same 11 PCM with different phase transition temperatures (no hysteresis), and 7 PCM with different hysteresis degrees. Figure 9 shows the influences of the PCM phase change temperature on the PCM temperature profiles. For the days with high solar radiation, the PCM with a higher phase transition temperature has a higher temperature during the day; during the night time (when the ventilation pre-heating is mostly needed), the PCM with a 25 °C transition temperature cools down the fastest. There is no significant difference regarding the PCM temperature when solar radiation is low. In general, it is hard to tell from the PCM temperature profile whether the PCM phase change temperature has a positive or a negative influence on the energy-saving potential.

Energies 2020, 13, x FOR PEER REVIEW 11 of 21

Figure 7. The PCM temperature profiles for models with different phase change temperatures for Energiessummer2020, 13 ,night 6455 cooling application. 11 of 21

The study is carried out with seven PCM with different hysteresis degrees during severe summer.The studyFor those is carried PCM, out hysteresis with seven degree PCM withis th die ffdifferenceerent hysteresis between degrees the duringmelting severe peak summer.and the Forfreezing those peak; PCM, melting hysteresis peak degree = 21 °C is + thehysteresis/2; difference freezing between peak the melting= 21 °C − peakhysteresis/2. and the Figure freezing 8 shows peak; melting peak = 21 C + hysteresis/2; freezing peak = 21 C hysteresis/2. Figure8 shows some of the some of the PCM temperatures.◦ It shows that PCM with◦ no− hysteresis has the most stable temperature PCMprofile temperatures. and lowest temperature It shows that during PCM with the nodaytime hysteresis for most has the of mostthe days stable when temperature the ventilation profile andpre- lowestcooling temperature is needed, and during the thePCM daytime with 5 for°C mosthysteres of theis has days the when highest the ventilationtemperature pre-cooling during the is daytime needed, andfor most the PCM of the with days 5 ◦ Cwhen hysteresis the ventilation has the highest pre-c temperatureooling is needed. during When the daytime outdoor for air most temperature of the days is whenrelatively the ventilationlow, the PCM pre-cooling with no is hysteresis needed. When has the outdoor lowest air temperature temperature during is relatively both low,daytime the PCM and withnighttime. no hysteresis It indicates has that the lowestPCM with temperature no hysteresis during can both benefit daytime the building’s and nighttime. energy-saving It indicates the most that PCMduring with severe no hysteresis summer. can benefit the building’s energy-saving the most during severe summer.

FigureFigure 8.8. TheThe PCMPCM temperaturetemperature profilesprofiles forfor modelsmodels usingusing PCMPCM withwith didifferentfferent hysteresishysteresis degreesdegrees forfor summersummer nightnight coolingcooling application.application.

ForFor winterwinter solar solar energy energy storage storage applications applications during du thering severe the wintersevere condition,winter condition, the study the compares study thecompares models the using models the sameusing 11 the PCM same with 11 diPCMfferent with phase different transition phase temperatures transition temperatures (no hysteresis), (no andhysteresis), 7 PCM withand 7 di PCMfferent with hysteresis different degrees. hysteresis Figure degrees.9 shows Figure the influences 9 shows ofthe the influences PCM phase of the change PCM temperaturephase change on temperature the PCM temperature on the PCM profiles. temperature For the pr daysofiles. with For high the solardays radiation,with high thesolar PCM radiation, with a higherthe PCM phase with transition a higher phase temperature transition has temperature a higher temperature has a higher during temperature the day; during during the the day; night during time (whenthe night the time ventilation (when the pre-heating ventilation is mostlypre-heating needed), is mostly the PCM needed), with the a 25 PCM◦C transitionwith a 25 temperature°C transition coolstemperature down the cools fastest. down There the fastest. is no significant There is no di significantfference regarding difference the regarding PCM temperature the PCM temperature when solar radiationwhen solar is low.radiation In general, is low. it In is hardgeneral, to tell it fromis hard the to PCM tell from temperature the PCM profile temperature whether profile the PCM whether phase changeEnergiesthe PCM 2020 temperature phase, 13, x FOR change PEER has aREVIEWtemperature positive or a has negative a positive influence or a on negative the energy-saving influence on potential. the energy-saving12 of 21 potential.

FigureFigure 9.9.The The PCM PCM temperature temperature profiles profiles for models for models using PCM using with PCM different with phase different change phase temperatures change fortemperatures winter energy for winter storage energy application. storage application.

Subsequently,Subsequently, FigureFigure 10 10 shows shows thethe influencesinfluences ofof PCMPCM hysteresishysteresis degreedegree onon thethe PCMPCM temperature profilesprofiles forfor winter winter solar solar energy energy storage storage applications. applicatio Itns. shows It shows that for that the daysfor the with days high with solar high radiation, solar radiation, PCM with larger hysteresis has a higher temperature during most of the nighttime when the ventilation pre-heating is needed, for example, 5th and 6th of February. For the days with low solar radiation, no significant difference is found among the models with different hysteresis, as the case of 8th February shows.

Figure 10. The PCM temperature profiles for models using PCM with different hysteresis degrees for winter energy storage application.

The PCM temperature profiles depend on the outdoor weather conditions, e.g., outdoor air temperature for summer and outside surface received solar radiation for winter, which makes it hard to predict the building’s energy performance based on the analysis of several days. Figure 11 summarizes the heat pump’s energy demands for the room with different PCM phase change temperatures during the whole severe summer and winter seasons, and compares them to the model with no PCM and only ventilated window with same ventilation strategy and airflow rate. Figure 11a shows that compared with the model without PCM, the models with PCM which have different phase transition temperatures all have lower energy demands. With the increase of the PCM phase change temperature, the energy demands of the room for both summer and winter tend to increase slightly. Figure 11b indicates that for severe summer, the energy savings increase and then decrease along with the increase of the PCM phase change temperature. For severe winter, the energy savings decrease along with the increase of the PCM phase change temperature. As a result, the total energy savings in severe seasons increase and then decrease along with the increase of the PCM phase change temperature. However, the change is quite small compared to the total energy demand. Energies 2020, 13, x FOR PEER REVIEW 12 of 21

Figure 9. The PCM temperature profiles for models using PCM with different phase change temperatures for winter energy storage application.

Energies 2020, 13, 6455 12 of 21 Subsequently, Figure 10 shows the influences of PCM hysteresis degree on the PCM temperature profiles for winter solar energy storage applications. It shows that for the days with high solar PCMradiation, with largerPCM with hysteresis larger has hysteresis a higher has temperature a higher duringtemperature most of during the nighttime most of whenthe nighttime the ventilation when pre-heatingthe ventilation is needed, pre-heating for example, is needed, 5th for and example, 6th of February. 5th and 6th For of the February. days with For low the solar daysradiation, with low nosolar significant radiation, di nofference significant is found difference among is thefound models among with the dimodelsfferent with hysteresis, different as hysteresis, the case ofas 8ththe Februarycase of 8th shows. February shows.

FigureFigure 10.10. The PCM temperature profilesprofiles forfor models using PCM with didifferentfferent hysteresishysteresis degrees degrees forfor winterwinter energyenergy storagestorage application.application.

TheThe PCMPCM temperaturetemperature profilesprofiles dependdepend onon thethe outdooroutdoor weatherweather conditions,conditions, e.g.,e.g., outdooroutdoor airair temperaturetemperature for for summer summer and and outside outside surface surface received received solar solar radiation radiation for for winter, winter, which which makes makes it hard it hard to predictto predict the building’sthe building’s energy energy performance performance basedon ba thesed analysis on the ofanalysis several days.of several Figure days. 11 summarizes Figure 11 thesummarizes heat pump’s the energy heat pump’s demands energy for the demands room with fo dir fftheerent room PCM with phase different change temperaturesPCM phase duringchange thetemperatures whole severe during summer the whole and winter severe seasons, summer and and compares winter seasons, them to theand model compares with them no PCM to the and model only ventilatedwith no PCM window and withonly sameventilated ventilation window strategy with same and airflow ventilation rate. strategy Figure 11 anda shows airflow that rate. compared Figure with11a shows the model that without compared PCM, with the the models model with without PCM whichPCM, the have models different with phase PCM transition which have temperatures different allphase have transition lower energy temperatures demands. all With have the lower increase energy of thedemands. PCM phase With change the increase temperature, of the PCM the energy phase demandschange temperature, of the room the for bothenergy summer demands and of winter the room tend for to increaseboth summer slightly. and Figure winter 11 tendb indicates to increase that forslightly. severe Figure summer, 11b the indicates energy that savings for severe increase summe and thenr, the decrease energy alongsavings with increase the increase and then of thedecrease PCM phasealong changewith the temperature. increase of the For PCM severe phase winter, change the energytemperature. savings For decrease severe winter, along with the energy the increase savings of thedecrease PCM phasealong with change the temperature. increase of the As PCM a result, phase the change total energy temperature. savings As in a severe result, seasons the total increase energy andsavings then in decrease severealong seasons with increase the increase and ofthen the decr PCMease phase along change with temperature. the increase However, of the PCM the change phase isEnergieschange quite 2020 smalltemperature., 13, comparedx FOR PEER However, toREVIEW the total the energychange demand.is quite small compared to the total energy demand.13 of 21

Figure 11.11. TheThe influenceinfluence of of PCM PCM phase phase change change temperature temperature on on building building energy energy for severefor severe summer summer and winterand winter seasons: seasons: (a) the (a) heatthe heat pump’s pump’s energy energy demand; demand; (b) the(b) energythe energy savings savings compared compared to no to PCM.no PCM.

The influenceinfluence of of the the PCM PCM hysteresis hysteresis on on the the room’s room energy’s energy demand demand is shown is shown in Figure in Figure 12a. It shows12a. It that,shows compared that, compared with the with model the withoutmodel without PCM, the PCM, models the models with PCM with and PCM diff erentand different hysteresis hysteresis degrees alldegrees have lowerall have energy lower demands energy fordemands summer, for winter summer, and totalwinter periods. and total Along periods. with the Along increase with of the PCMincrease hysteresis, of the PCM the summer hysteresis, energy the demandsummerincreases, energy demand while the increases, winter energy while demandthe winter decreases. energy demand decreases. The decreasing energy demand in winter is higher than the increasing energy demand in summer. As a result, the total heat pump energy demand decreases along with the increase of the PCM hysteresis degree. Figure 12b shows that along with the increase of the PCM hysteresis, the energy savings in summer decrease, while the energy savings in winter increase. The total energy saving in severe seasons increases along with the increase of the hysteresis, due to more energy savings during winter.

Figure 12. The influence of PCM hysteresis on the building’s energy for severe summer and winter seasons: (a) the heat pump’s energy demand; (b) the energy savings compared to no PCM.

The sensitivity analysis determines which variable has a higher impact on the model’s energy demand during severe summer and winter seasons. Figure 13 shows the local sensitivity indexes of the PCM phase change temperature and hysteresis on the building’s energy demand. For both summer and winter, the PCM hysteresis degree has a much bigger sensitivity index than the phase change temperature —0.253 and 0.207, respectively. However, for the yearly total energy demand, both phase transition temperature and hysteresis degree have small sensitivity indexes. That indicates that the PCM hysteresis degree has large influences on the summer and winter energy demands, but not a large influence on the annual total energy demand. The phase change temperature has a high impact on the summer energy demand, but not so high of an impact on the winter energy demand and annual total energy demand.

Energies 2020, 13, x FOR PEER REVIEW 13 of 21

Figure 11. The influence of PCM phase change temperature on building energy for severe summer and winter seasons: (a) the heat pump’s energy demand; (b) the energy savings compared to no PCM.

The influence of the PCM hysteresis on the room’s energy demand is shown in Figure 12a. It shows that, compared with the model without PCM, the models with PCM and different hysteresis degrees all have lower energy demands for summer, winter and total periods. Along with the Energies 2020, 13, 6455 13 of 21 increase of the PCM hysteresis, the summer energy demand increases, while the winter energy demand decreases. The decreasing energy demand in winter is higher than the increasing energy Thedemand decreasing in summer. energy As demand a result, in winter the total is higher heat thanpump the energy increasing demand energy decreases demand inalong summer. with Asthe a result,increase the of total the PCM heatpump hysteresis energy degree. demand Figure decreases 12b shows along that with along theincrease with the of increase the PCM of hysteresis the PCM degree.hysteresis, Figure the energy 12b shows savings that in along summer with decrease the increase, while of the the energy PCM savings hysteresis, in winter the energy increase. savings The intotal summer energy decrease, saving in while severe the seasons energy increases savings alon in winterg with increase. the increase The of total the energyhysteresis, saving due in to severe more seasonsenergy savings increases during along winter. with the increase of the hysteresis, due to more energy savings during winter.

Figure 12. The influenceinfluence of PCM hysteresishysteresis on the building’s energy for severe summer and winter seasons: ( a) the heat pump’s energy demand; (b) the energy savingssavings comparedcompared toto nono PCM.PCM.

The sensitivity analysis determines which variable has a higher impact on the model’s energy The sensitivity analysis determines which variable has a higher impact on the model’s energy demand during severe summer and winter seasons. Figure 13 shows the local sensitivity indexes of the demand during severe summer and winter seasons. Figure 13 shows the local sensitivity indexes of PCM phase change temperature and hysteresis on the building’s energy demand. For both summer the PCM phase change temperature and hysteresis on the building’s energy demand. For both andsummer winter, and the winter, PCM the hysteresis PCM hysteresis degree has degree a much has biggera much sensitivity bigger sensitivity index than index the than phase the change phase temperaturechange temperature —0.253 and—0.253 0.207, and respectively. 0.207, respectively However,. However, for the yearly for the total yearly energy total demand, energy both demand, phase transitionboth phase temperature transition andtemperature hysteresis and degree hysteresis have small degree sensitivity have small indexes. sensitivity That indicates indexes. that That the PCMindicates hysteresis that the degree PCM hashysteresis large influences degree has on la therge summer influences and on winter the summer energy demands,and winter but energy not a largedemands, influence but onnot the a annuallarge influence total energy on demand. the annual The phasetotal changeenergy temperaturedemand. The has phase a high change impact ontemperature the summer has energy a high demand, impact on but the not summer so high ofenergy an impact demand, on the but winter not so energy high demandof an impact and annualon the Energiestotalwinter energy 2020energy, 13 demand., x demand FOR PEER and REVIEW annual total energy demand. 14 of 21

Figure 13. TheThe sensitivity sensitivity index index of of phase phase change change temper temperatureature and and hysteresis hysteresis degree degree on on the the HVAC energy demand: ( (aa)) the the summer summer energy energy demand; demand; ( (bb)) the the winter energy demand; ( c)) the yearly total energy demand.

3.2. Transition Seasons 3.2. Transition Seasons For the transition seasons, the HVAC system does not operate. It is thus the PCMVW that solely For the transition seasons, the HVAC system does not operate. It is thus the PCMVW that solely regulates the indoor thermal comfort. The PPD is used to examine the thermal comfort of the study regulates the indoor thermal comfort. The PPD is used to examine the thermal comfort of the study cases. The lower the PPD, the better the indoor thermal comfort. Figure 14 shows the influence of cases. The lower the PPD, the better the indoor thermal comfort. Figure 14 shows the influence of the the PCM phase change temperature on the PPD during transition seasons. Compared to the model PCM phase change temperature on the PPD during transition seasons. Compared to the model without PCM, the models with PCM all have lower PPD. For the summer transition season, the PPD without PCM, the models with PCM all have lower PPD. For the summer transition season, the PPD decreases along with the increase of the phase change temperature. For the winter transition season, the PPD increases along with the increase of the PCM phase change temperature, except for 17 °C. Consequently, the average PPD during the transition season remains the same along with the increase of the PCM phase transition temperature, except for 17 °C, which is slightly higher.

Figure 14. The predicted percentage of dissatisfied (PPD) of the models with different PCM phase change temperatures in transition seasons.

Similarly, the influence of the PCM hysteresis on the PPD is shown in Figure 15. Compared to the model without PCM, the models with PCM all have lower PPD. For the summer transition season, the PPD increases along with the increase of the PCM hysteresis. For the winter transition season, the PPD decreases along with the increase of the PCM hysteresis degree. Consequently, the average PPD during the transition season remains the same along with the increase of the PCM hysteresis degree.

Energies 2020, 13, x FOR PEER REVIEW 14 of 21

Figure 13. The sensitivity index of phase change temperature and hysteresis degree on the HVAC energy demand: (a) the summer energy demand; (b) the winter energy demand; (c) the yearly total energy demand.

3.2. Transition Seasons For the transition seasons, the HVAC system does not operate. It is thus the PCMVW that solely regulates the indoor thermal comfort. The PPD is used to examine the thermal comfort of the study

Energiescases. The2020, lower13, 6455 the PPD, the better the indoor thermal comfort. Figure 14 shows the influence14 of of the 21 PCM phase change temperature on the PPD during transition seasons. Compared to the model without PCM, the models with PCM all have lower PPD. For the summer transition season, the PPD decreasesdecreases alongalong withwith thethe increaseincrease ofof thethe phasephase changechange temperature.temperature. For the winter transition season, thethe PPDPPD increasesincreases alongalong withwith thethe increaseincrease ofof thethe PCMPCM phasephase changechange temperature, except for 17 ◦°C.C. Consequently,Consequently, the the average average PPD PPD duringduring thethe transitiontransition seasonseason remainsremains thethe samesame alongalong withwith thethe increaseincrease ofof thethe PCMPCM phasephase transitiontransition temperature,temperature, exceptexcept forfor 1717◦ °C,C, whichwhich isis slightlyslightly higher.higher.

Figure 14. The predicted percentage of dissatisfied (PPD) of the models with different PCM phase Figure 14. The predicted percentage of dissatisfied (PPD) of the models with different PCM phase change temperatures in transition seasons. change temperatures in transition seasons. Similarly, the influence of the PCM hysteresis on the PPD is shown in Figure 15. Compared to the Similarly, the influence of the PCM hysteresis on the PPD is shown in Figure 15. Compared to model without PCM, the models with PCM all have lower PPD. For the summer transition season, the model without PCM, the models with PCM all have lower PPD. For the summer transition season, the PPD increases along with the increase of the PCM hysteresis. For the winter transition season, the PPD increases along with the increase of the PCM hysteresis. For the winter transition season, the the PPD decreases along with the increase of the PCM hysteresis degree. Consequently, the average PPD PPD decreases along with the increase of the PCM hysteresis degree. Consequently, the average PPD during the transition season remains the same along with the increase of the PCM hysteresis degree. Energiesduring 2020 the, 13transition, x FOR PEER season REVIEW remains the same along with the increase of the PCM hysteresis degree.15 of 21

Figure 15. TheThe predicted predicted percentage percentage of of dissatisfied dissatisfied (P (PPD)PD) of of the cases using PCM with didifferentfferent hysteresis degrees in transition seasons.seasons.

Another sensitivity analysis is conducted to study which parameter has a higher impact on indoor thermal comfort duringduring transitiontransition seasons.seasons. Th Thee results are presented in Figure 1616.. It is shown that the hysteresis degree has a largerlarger sensitivitysensitivity indexindex thanthan thethe phasephase changechange temperaturetemperature for both summer and winter transition seasons—0.088 and 0.082, respectively. However, the transition season average sensitivitysensitivity indexesindexes of of both both hysteresis hysteresis degree degree and and phase phase transition transition temperature temperature are not are so not high, so high, which indicates that the PCM has a large influence on the thermal comfort in summer transition and winter transition seasons, but not a large influence on the annually average thermal comfort during transition seasons. The phase change temperature does not have great influence on the thermal comfort in transition seasons.

Figure 16. The sensitivity indexes of phase change temperature and hysteresis degree on the PPD: (a) the summer transition season; (b) the winter transition season; (c) the transition season average.

In general, the phase change transition temperature and hysteresis have higher impacts on the severe summer and winter seasons than the transition seasons, for both summer and winter applications. The reason could be that for transition seasons, the building needs less regulation and energy input to achieve good thermal comfort.

4. Discussion The modelling of PCM is more complicated than other building materials due to its nonlinear thermal properties. Moreover, the phase change occurs over a temperature range and presents temperature hysteresis between the melting and the freezing processes, which makes the modelling of PCM challenging. This paper studied the different modelling methods of PCM used in building simulations regarding their accuracies compared to an air–PCM heat exchanger, and the influences

Energies 2020, 13, x FOR PEER REVIEW 15 of 21

Figure 15. The predicted percentage of dissatisfied (PPD) of the cases using PCM with different hysteresis degrees in transition seasons.

Another sensitivity analysis is conducted to study which parameter has a higher impact on indoor thermal comfort during transition seasons. The results are presented in Figure 16. It is shown that the hysteresis degree has a larger sensitivity index than the phase change temperature for both Energiessummer2020 and, 13 ,winter 6455 transition seasons—0.088 and 0.082, respectively. However, the transition season15 of 21 average sensitivity indexes of both hysteresis degree and phase transition temperature are not so whichhigh, which indicates indicates that the that PCM the PCM has a has large a large influence influence on the on thermal the thermal comfort comfort in summer in summer transition transition and winterand winter transition transition seasons, seasons, but not but a largenot a influencelarge influence on the on annually the annually average average thermal thermal comfort comfort during transitionduring transition seasons. seasons. The phase The change phase temperature change te doesmperature not have does great not influence have great on the influence thermal comforton the inthermal transition comfort seasons. in transition seasons.

Figure 16. The sensitivity indexes of phase change temperature and hysteresis degree on the PPD: Figure 16. The sensitivity indexes of phase change temperature and hysteresis degree on the PPD: (a) (a) the summer transition season; (b) the winter transition season; (c) the transition season average. the summer transition season; (b) the winter transition season; (c) the transition season average. In general, the phase change transition temperature and hysteresis have higher impacts on In general, the phase change transition temperature and hysteresis have higher impacts on the the severe summer and winter seasons than the transition seasons, for both summer and winter severe summer and winter seasons than the transition seasons, for both summer and winter applications. The reason could be that for transition seasons, the building needs less regulation and applications. The reason could be that for transition seasons, the building needs less regulation and energy input to achieve good thermal comfort. energy input to achieve good thermal comfort. 4. Discussion 4. Discussion The modelling of PCM is more complicated than other building materials due to its nonlinear thermalThe properties.modelling of Moreover, PCM is more the phasecomplicated change than occurs other over building a temperature materials rangedue to andits nonlinear presents temperaturethermal properties. hysteresis Moreover, between the the meltingphase change and the occurs freezing over processes, a temperature which makesrange theand modelling presents oftemperature PCM challenging. hysteresis This between paper the studied melting the and diff erentthe freezing modelling processes, methods which of PCM makes used the in modelling building simulationsof PCM challenging. regarding This their paper accuracies studied compared the different to an modelling air–PCM heatmethods exchanger, of PCM and used the in influences building ofsimulations PCM phase regarding change their temperature accuracies and compared hysteresis to an on air–PCM a building’s heat exchanger, energy-saving and potentialthe influences and thermal comfort. The main reasons for PCM hysteresis identified in the literature are divided into two categories. One is due to the misconception of hysteresis because of improper measurement methods. This apparent hysteresis is avoidable if overall knowledge about the thermal properties of the PCM is obtained before a suitable measurement method is chosen, such as the homogenous and subcooling level of the material, the typical heat rate and the temperature range of the PCM application. The other one is due to the intrinsic material properties because of the existence of subcooling, incomplete crystallization or polymorphic crystal structures. The most commonly used PCM modelling methods found in the literature are introduced and categorized. A case study of the heating and cooling processes of a PCM heat exchanger is conducted with four selected modelling technics. The conclusion is that the four modelling methods (the square heat capacity method, the triangular heat capacity method, the enthalpy method and the differential scanning calorimetry (DSC) heat capacity method) are equally accurate at representing the thermal behavior of the PCM heat exchanger. The model with the DSC heat capacity method and a 1 ◦C hysteresis is, however, the most accurate in that case. A second case study with a southwest room in an apartment with two PCM-enhanced ventilated windows in Denmark is conducted. The PCM is modelled with the DSC heat capacity method and temperature hysteresis. It is shown that the PCM hysteresis has a larger influence on the heat pump energy consumption than the phase change temperature for both summer night cooling and winter energy storage. For summer night cooling, the room energy demand increases along with the increase Energies 2020, 13, 6455 16 of 21 of the hysteresis. For winter solar energy storage, the room energy demand decreases along with the increase of the hysteresis. As a result, the PCM hysteresis does not have a strong impact on the heat pump’s yearly total energy demand. For both summer and winter transition seasons, the PCM hysteresis has a larger influence on the PPD than the phase change temperature, but not a strong impact on the transition season average PPD. The findings of this work about the PCM hysteresis’s effect on the building energy are quite the opposite to those of Ramprasad et al. [23]. and Moreles et al. [24]. The reason is that, in this paper, the summer application, winter application and transition season application are studied separately. In contrast, the former studies are only based on one PCM application. Besides the hysteresis, this paper also took PCM phase change temperature into account. A suggestion for PCM modelling and experimental works is that one should be more considerate when choosing PCM modelling methods. Overall knowledge or some measurement of the PCM properties is necessary from the beginning of the investigations. The adequate modelling methods can be decided on based on the understanding of the material characteristics. Meanwhile, the choice of the PCM should fit the application, because a building’s energy demand changes differently as a function of the PCM hysteresis for summer night cooling and winter solar energy storage. Moreover, the boundary conditions should be carefully defined and chosen based on real building applications, such as the exposed temperature range, the heating/cooling rate and the phase transition range of the chosen PCM. The PCM properties should be characterized for the entire temperature range of the application, as the PCM properties might differ significantly from what one could expect. Finally, one should keep in mind that this paper presents a study based on the Danish climate, which has a fairly mild summer. Such study should be extended to other climates.

Author Contributions: Conceptualization, Y.H. and P.K.H.; methodology, Y.H.; software, R.G.; validation, Y.H.; data curation, Y.H.; writing—original draft preparation, Y.H., R.G. and H.J.; writing—review and editing, R.G., H.J. and P.K.H.; funding acquisition, P.K.H. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the EU Horizon 2020 research and innovation program (ReCO2ST), grant number 882901. Conflicts of Interest: The authors declare no conflict of interest. Energies 2020, 13, 6455 17 of 21

Appendix A

Table A1. The thermal properties of PCM found in the literature for building applications (the hysteresis degree is calculated as the difference between melting peak and freezing peak).

Melting Freezing Melting Freezing Hysteresis Latent Heat Measurement Type Reference Range (◦C) Range (◦C) Peak (◦C) Peak (◦C) Degree (◦C) (kJ/kg) Method

MePCM from PG8H2–E 23.9–26.9 18.4–23.1 25.54 20.21 5.33 - DSC 1 ◦C/min [49]

Dodecanol 23.8–27.1 18.3–23.2 25.22 20.11 5.11 - DSC 1 ◦C/min [49]

MePCM from PG8H2 23.7–27.2 18.1–22.9 25.14 20.07 5.07 - DSC 1 ◦C/min [49]

Paraffin 23–29 20–25 23 27.7 4.7 179 DSC 2 ◦C/min [50]

Paraffin within copolymer 15.1–28.2 9.6–24.5 22.2 17.8 4.4 107.5 DSC 0.05 ◦C/min [51]

Paraffin within copolymer 10–28 12–29 22.1 17.9 4.2 72.4/71.0 DSC 0.05 ◦C/min [13]

PCM–wallboard 16.8–19.35 16.9–22.1 21.05 16.98 4.07 35 DSC 0.2 ◦C/min [52] Q20 16–24 13–18 20 16 4 210–250 DSC [53] Paraffin PCM 6 0–7 5 3 0.5 3.5 178 DSC 1 C/min [54] − − ◦ C24 24–27 21–23 24 27 3 140 DSC [55] Q27 24–30 23–27 27 24 3 210–250 DSC [53] Q29 27–32 24–27 29 26 3 210–250 DSC [53]

Paraffin Microtek 37 D 32–37 29–35 36 33 3 220 DSC 0.15 ◦C/min [56]

Paraffin hydrocarbon 23–28.5 21–24.9 25.5 22.9 2.6 75 DSC 1 ◦C/min [38]

Paraffin PCM 28 15–28 15–22 23 20.5 2.5 161 DSC 1 ◦C/min [54] Gallium 29.5–30.5 26.9–29 30 27.5 2.5 80 T-history [9]

Fatty acid wall board 18.5–24.2 15.0–18.6 20.3 17.9 2.4 39.1 DSC 0.2 ◦C/min [57] Q23 20–26 18–24 23 21 2 210–250 DSC [53] Q25 23–28 22–25 25 23 2 210–250 DSC [53]

Paraffin in gypsum board 25–28.5 24–27.5 28 26.5 1.5 75 DSC 2 ◦C/min [58]

Gypsum–PCM compound 21–24 20–22.5 24 22.5 1.5 - DSC 0.05 ◦C/min [59] Energies 2020, 13, 6455 18 of 21

Table A1. Cont.

Melting Freezing Melting Freezing Hysteresis Latent Heat Measurement Type Reference Range (◦C) Range (◦C) Peak (◦C) Peak (◦C) Degree (◦C) (kJ/kg) Method C H 6.7–( 4.5) 6.3–( 7.9) 5.6 7.1 1.5 210 T-history [60] 13 28 − − − − − − PCM–plaster compound 24.1–28.5 23.2–27.1 28.12 26.8 1.32 16.5 DSC 1~2 ◦C/min [61] Hexadecane 16.5–19.5 16.2–17.2 18 16.7 1.3 236 T-history [9] RT27 24.5–28.2 25.0–26.9 27 25.9 1.1 180 T-history [9] HS22P (inorganic) 21–25 - 23 22 1 185 T-history [62]

RT27 (organic paraffin) 26.86–28.69 27.94–26.44 28.37 27.38 0.99 130.8 DSC 1 ◦C/min [63] Butyl stearate 16–20.9 16–20.8 20.9 20.4 0.5 30.7 DSC [64]

Emerest 2326 16.69–19.75 16.51–19.6 19.57 19.45 0.12 140 DSC 0.2 ◦C/min [52] C21 (salt hydrate) 21–26 18–22 21 21 0 134 DSC [55]

Paraffin RT 25 22–26 23–26 25 25 0 - DSC 0.2 ◦C/min [15] Energies 2020, 13, 6455 19 of 21

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