energy conversion and management - · pdf file3. the model 3.1. basis of the model a pcm plate...

Energy Conversion and Management 52 (2011) 1890–1907

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Energy Conversion and Management

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Characterization of melting and solidification in a real scale PCM-air heatexchanger: Numerical model and experimental validation

Pablo Dolado ⇑, Ana Lazaro, Jose M. Marin, Belen ZalbaAragón Institute for Engineering Research (I3A), Thermal Engineering and Energy Systems Group, University of Zaragoza, Torres Quevedo Building,C/Maria de Luna 3, 50018 Zaragoza, Spain

a r t i c l e i n f o

Article history:Received 11 February 2010Received in revised form 29 October 2010Accepted 7 November 2010Available online 7 January 2011

Keywords:Thermal energy storage, TESPhase change material, PCMHeat transferModelSimulationValidation

0196-8904/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.enconman.2010.11.017

⇑ Corresponding author. Tel.: +34 976761000x5258E-mail address: [email protected] (P. Dolado).

a b s t r a c t

This paper describes the models developed to simulate the performance of a thermal energy storage (TES)unit in a real scale PCM-air heat exchanger, analyzing the heat transfer between the air and a commer-cially available and slab macroencapsulated phase change material (PCM). The models are based on one-dimensional conduction analysis, utilizing finite differences method, and implicit formulation, using thethermo-physical data of the PCM measured in the laboratory: enthalpy and thermal conductivity as func-tions of temperature. The models can take into account the hysteresis of the enthalpy curve and the con-vection inside the PCM, using effective conductivity when necessary. Two main paths are followed toaccomplish the modeling: the thermal analysis of a single plate, and the thermal behavior of the entireTES unit. Comparisons between measurements and simulations are undertaken to evaluate the models.Average errors of less than 12% on thermal power are obtained for the entire cycle. Once the model isvalidated, a series of parameters and variables is studied to verify their influence on the behavior anddesign of the TES unit.

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1. Introduction analysis of the phase change, the modeling of latent heat thermal

Modeling is a useful tool in a viability analysis of applicationsthat involve thermal energy storage by solid–liquid phase changematerials. Therefore, there is a necessity to develop experimentallyvalidated models that are rigorous and flexible to simulate heatexchangers of air and phase change materials (from here onPCM). When developing a model, the tradeoff between rigourand computational cost is crucial. There are many options reportedin scientific literature to face the mathematical problem of phasechange as well as to solve specific particularities such as hysteresis[1] phenomena or sub-cooling [2].

In the review by Zalba et al. [3], the authors present a compre-hensive compilation of thermal energy storage (from here on TES)with PCM. One of the sections presented by the authors deals spe-cifically with the heat transfer problem of the phase change. Theauthors gathered information from 1970 till 2003 and classifiedthe analysis of the heat transfer problem under four differentapproaches: moving boundary problems, numerical solutionconsidering only conduction, numerical solution considering alsoconvection, and numerical simulation in different heat exchangergeometries. The authors remarked that although there is a hugeamount of published articles dealing with the heat transfer

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energy storage systems still remains a challenging task.Later, Verma et al. [4] published a review on mathematical

modeling of TES systems with PCM. The authors classified themodels into two types on the basis of the corresponding law ofthermodynamics under they were analyzed (first or second law).In the review, the authors pointed out the specific utility of allthe models that have been experimentally validated. However, intheir paper showed that only 8 of the 17 compiled models pre-sented experimental validation, and they highlight that in orderto accept any model such an experimental analysis should be done.

Regarding PCM-air heat exchangers especially interesting is thework carried out by Vakilaltojjar and Saman [5]. They proposed aphase change TES for air conditioning applications. Through theirnumerical studies they concluded that the air velocity profile atthe entrance does not affect the heat-transfer characteristics andthe outlet air temperature considerably. They pointed out also thatbetter performance can be obtained by using smaller air gaps andthinner PCM slabs. However, the authors considered constant ther-mo-physical properties of the PCM and pointed out that the exper-imental validation was necessary.

Later, Halawa et al. [6] presented an improved model of the onedeveloped by Vakilaltojjar and Saman [5]. The improvement con-sists of taking into account the sensible heat, but the model onlyconsiders constant thermo-physical properties, and it is limitedto pure PCM as it considers single phase change temperature.The authors carried out the corresponding experiments to validate

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Nomenclature

Cair ¼ qair �_Vair

2�Nwalls� Cpair heat capacity

cp effective specific heat [J/(kg�K)]e thickness [m]h convection coefficient [W/(m2 K)]H height [m]L length [m]_m air mass flow [kg/s]

N number of elementsNTUair ¼ ðh � Dx �wÞ=Cair number of transfer units_Q thermal power [W]T temperature [K, �C]t time [s]v velocity [m/s]_V volumetric flow [m3/h]w depth [m]_W electrical power consumption [W]

yexp, ysim experimental or simulated value, respectivelyx Cartesian coordinate [m]

Greek symbolsk thermal conductivity [W/(m K)]

q density [kg/m3]g fan isentropic performanceDp pressure difference [Pa]DT temperature difference [K, �C]Dt time step [s]Dx, Dy node length and height respectively [m]

Subscripts and superscriptsair related to the air; current position in the air stream

air, inlet air at the inlet of the TES unitair � 1 previous position in the air streamambientTES ambienteff effectiveenc encapsulationfanTES fan of the TES unitin TES unit air inletout TES unit outletpc phase changePCM related to the phase change materialPCM � 1; PCM + 1 previous and next PCM node in position,

respectivelypump pumping requirementst � 1 previous instantTES thermal energy storage unitwalls set of slabs that constitute a wall

AcronymsBi Biot numberFo Fourier numberFoenc ¼ kenc �Dt

qenc �Cpenc �e2FoPCM ¼ kPCMðTÞ�DtqPCMðTÞ�CpPCMðTÞ�Dy2-

Foenc—PCM ¼ kenc �Dtðqenc �Cpenc �eþqPCM �CpPCM �DyÞ�eBienc ¼ hair �e

kenc

PCM phase change materialRE relative errorRME relative maximum errorTES thermal energy storage1D, 2D, 3D one-, two-, three-dimensional respectively

P. Dolado et al. / Energy Conversion and Management 52 (2011) 1890–1907 1891

the model [7] and concluded that the design of a thermal storageappropriate for air systems entails the careful consideration ofsome factors such as PCM with appropriate melting point, rangeof outlet and inlet temperature, and air flow rates.

Hed and Bellander [8] developed a mathematical model of aPCM-air heat exchanger. The authors highlighted the importanceof the thermo-physical properties of the PCM as there is a com-pletely different behavior between an ideal PCM (with phase tran-sition at a given temperature) and a commercially available PCM.Although they analyzed specifically the thermal behavior of thePCM system under different shapes of the PCM cp(T) curve (the restof the properties remain constant), the authors pointed out that thetwo central properties in such equipment are both, PCM heat con-ductivity and its variation with temperature, and heat capacity andits variation with temperature. The validation of the model withmeasurements on a prototype was carried out. In spite of havinga good agreement in general, they remark that differences obtainedfor certain temperatures are due to difficulties in air flow measure-ments. The authors presented interesting results finding out thatthe heat-transfer coefficient between the airflow and PCM in-creases significantly when the surface is rough as compared tosmooth surface. They also pointed out that in any design withPCM considerably attention needs to be taken to the time depen-dent behavior of the equipment.

When working with commercially available PCM (or mixturesor impure materials), the phase change takes place over a temper-ature range and therefore a two-phase zone (mushy region) ap-pears between the solid and liquid phases. In these cases, it isappropriate to consider the energy equation in terms of enthalpy[9]. When the advective movements within the liquid are negligi-ble, the energy equation is expressed as follows:

q@h@t¼ ~rð~kr~TÞ ð1Þ

The solution of this equation requires knowledge of theenthalpy–temperature functional dependency and the thermal con-ductivity–temperature curve. The advantage of this methodology isthat the equation is applicable to every phase; the temperature isdetermined at each point and the value of the thermo-physical prop-erties can then be evaluated. In thermal simulations of PCM, the accu-racy of the model’s results relies on the material properties’ data [10].In the geometry studied in this work, the main properties were enthal-py and thermal conductivity, but notice that the rate of melting/solid-ification can also depend on other material properties such as viscosityor density [11]. In the models developed here the variation of thermo-physical properties with temperature in all phases was considered.

The main objective of this work was to develop and experimen-tally validate a model that simulated the transient response of activesystems of PCM-air heat exchangers. The model considered thepoints reported previously (kPCM(T), hPCM(T),qPCM(T), hysteresis, nat-ural convection, surface friction factor. . .) and also fit to the particu-larities of the application, such as thermal interaction between theTES unit and the ambient or internal fan dissipation. Two modelswere developed in the numerical computing environment Matlab(R2008b version) [31]. They were based on the analysis of the heattransfer in the PCM itself by the finite differences method, withimplicit formulation. This methodology has been widely used toanalyze the heat transfer problem of the phase change as the workcarried out by Goodrich [12], and it exponentially increased fromthe works done by Voller [13] up to date [14]. Due to the specificgeometry and working conditions of the study system, only one-dimensional conduction was considered. Previously other models

1892 P. Dolado et al. / Energy Conversion and Management 52 (2011) 1890–1907

were presented by Dolado et al. (discretized semi-analytic model,bidimensional conduction model, and fluid-dynamic model)[15,16] and a comparison showed that the models here presenteda good balance between precision and computational cost whenanalyzing this type of heat exchanger. The PCM utilized was a com-mercially available organic type, melting at approximately 27 �C.The PCM was presented macroencapsulated in aluminum rigid slabs,not flat but with bulges to enhance the heat transfer and to allow thePCM volume expansion. To validate and estimate the accuracy of themodels, experimental data presented previously [17] were com-pared with the results of the simulations. In order to obtain designconclusions, a series of parameters and variables was studied toverify their influence on the thermal performance of the TES unit.

Fig. 1. Experime

Fig. 2. Compact storage module panels by

2. Experimental setup

The experimental setup consisted of a closed loop as shown inFig. 1.

The total amount of PCM in the TES unit was approximately135 kg. The organic PCM utilized was macroencapsulated in alumi-num rigid slabs (see Fig. 2). The slabs were located parallel to theair flow in the TES unit.

Not only the main variables that characterize the thermalbehavior of the TES unit were measured, but also a single PCMplate was monitored. In this way, two different sets of data werecollected: data for the entire unit performance and detailed datafor a single plate.

ntal setup.

Rubitherm [32]: photo and 3D sketch.

Fig. 4. PCM panel and air flow system.


3. The model

3.1. Basis of the model

A PCM plate model was developed with finite differences,one-dimensional, implicit formulation. Implicit formulation wasselected because of its unconditional stability. The basis model as-sumed only conduction heat transfer inside the PCM plate, in anormal direction to the air flow. The model analyzed the tempera-ture of the airflow in a one-dimensional way. Due to its symmetry,the analyzed system was a division of the prototype.

In the present work, the model was implemented in MatlabR2008b [31]. The software implements direct methods (variantsof Gaussian elimination [18]) through the matrix divisionoperators, which can be used to solve linear systems.

3.2. Study system

Fig. 3 shows the study system: the PCM-air TES unit. The airinlet was located on the upper side of the TES unit. The air floweddownwards in the TES unit, circulating parallel to the PCM slabs,exchanging energy with the PCM, and eventually was blownoutside the TES unit by a centrifugal fan.

The system was studied from the point of view of a single slab.As the PCM zone of the TES unit was insulated as well as due to thedistribution of the slabs inside the TES unit, some symmetry rela-tionships could be considered so only the dotted domain in Fig. 4was modeled.

The nodal distribution of the mathematical model is shown inFig. 5. Depending on whether the encapsulation is considered,two more nodes have to be included between the PCM surfaceand the airflow.

In the experimental study, the heat transfer processes that takeplace inside the TES unit between the air flowing through the slabsand the PCM inside the slabs were: forced convection in the air,conduction in the shell of the aluminum slab, and conductionand natural convection in the PCM itself.

The order of magnitude of the resistances was obtained asfollows:

1hair¼ from

110

to1

40¼ 0:1—0:025

m2 KW

� �ð2Þ

Fig. 3. Air flow through

eencap

kencap¼ from

0:001300

to0:001200

¼ 3:33� 10�6 to 5� 10�6 m2 KW

� �ð3Þ

ePCM

kPCM¼ from

0:0050:2

to0:0050:16

¼ 0:025—0:031m2 K

W

� �ð4Þ

1hnatural conv

¼ from1

74to

147¼ 0:014� 0:021

m2 KW

� �; ½19� ð5Þ

The air convection coefficient was estimated in the range offorced convection for gases. According to this preliminary analysisand comparing equations, it can be stated that within the workingconditions of the experiments, the thermal resistance of the encap-sulation was negligible. The dominant resistance of the processcould be convection on the air side and not always conduction–convection in the PCM.

In this case the thermal resistance of the encapsulation wasvery low, and therefore it was not necessary to consider encapsu-lation in the node system, as the heat transfer process was con-trolled by the convection on the air side and/or by theconduction–natural convection in the PCM. However, in othercases it is not always possible to disregard the thermal influence

the storage unit.

Fig. 5. Nodal distribution in the 1D plate system.


of the encapsulation, and therefore two models were developed:the first model did not take into account the thermal behavior ofthe encapsulation and the second model did, and it was developedin order to be used for general purposes.

The node equations of the two models are summarized inTables 1 and 2.

3.3. Air convection coefficient calculation

In order to obtain an accurate value for the convection coeffi-cient of the air flowing through the PCM slabs, certain consider-ations were required.

3.3.1. Air propertiesDensity, thermal conductivity, and dynamic viscosity were ex-

pressed as functions of temperature for the working temperaturerange (0–50 �C) [20].

Table 1Node temperature equations not considering encapsulation.

Nodes Equations

Air flow Tair ¼ Tair�1 � NTUairðTair�1 � TsurfaceÞPCM surface Tsurface ¼ Tt�1

PCM þ FoTPCMþ1 þ FoBiTair

� �=ð1þ Foþ FoBiÞ

PCM inner TPCM ¼ ½Tt�1PCM þ FoðTPCM�1 þ TPCMþ1Þ�=ð1þ 2FoÞ

PCM central TPCM ¼ ðTt�1PCM þ 2FoTPCM�1Þ=ð1þ 2FoÞ

Table 2Node temperature equations considering encapsulation.

Nodes Equations

Air flow Tair ¼ Tair�1 � NTUairðAir surface Tsurface ¼ Tt�1

surface þ 2ðh

Surface encapsulation Tenc ¼ Tt�1enc þ 2ðFoenc—

hEncapsulation PCM TPCM ¼ Tt�1

PCM þ FoPCM

hPCM inner TPCM ¼ Tt�1

PCM þ FoðTPC

hPCM central TPCM ¼ Tt�1

PCM þ 2FoTP

�

3.3.2. Friction factor: rugosity of the encapsulation surfaceAs the PCM slabs manufactured by Rubitherm [32] have a spe-

cial shape, rugosity had to be estimated carefully. As can be ob-served in Figs. 2 and 6, PCM panels were not flat but presenteduniformly spread bulges over the panel surface.

In order to obtain a rugosity value, calculations were required[21]. From Fig. 6:

Unit total surface = 15.2 � 15.2 = 231.04 mm2.Bulge surface = 10.6 � 10.6 = 112.36 mm2 (48.63% over unittotal surface).Bulge high � 0.6 mm.

Therefore depending on the shape of the bulge, the rugosity val-ues were as follows:

Maximum rugosity = 0.6 � 0.4863 = 0.292 mm ? bulge shape:_Q

_Q

_Q

_.Medium rugosity = 0.6 � (0.4863–0.2432) = 0.292–0.145 mm ? bulge shape: _\_\_\_.Minimum rugosity = 0.6 � 0.4863/2 = 0.145 mm ? bulgeshape: _K_K_K_.

In this specific study case, rugosity was estimated to be0.25 mm, with rounded-edge bulges.

Tair�1 � TsurfaceÞFoencTenc þ FoencBiencTairÞ

i.½1þ 2ðFoencBienc þ FoencÞ�

PCMTsurface þ 2FoPCM—encTencÞi.½1þ 2ðFoenc—PCM þ 2FoPCM—encÞ�

ð2Tenc þ TPCMþ1Þi.ð1þ 3FoPCMÞ

M�1 þ TPCMþ1Þi.ð1þ 2FoÞ

CM�1

�.ð1þ 2FoÞ

Fig. 6. Rugosity estimation.


3.3.3. Convection coefficientThe study of the thermal boundary layer showed that there was

no free development of the layer between the plates, thereforeinternal forced convection correlations had to be used. The Nusseltnumber can be calculated depending on the Reynolds numberusing the Gnielinski correlation for transition and turbulent flow[22], or using straight section ducts and isothermal surface rela-tions for laminar flow [23,24].

3.4. PCM properties data: thermo-physical properties

The main input data of the model were material properties: en-thalpy and thermal conductivity. As the simulation analyzed thetransitory response of the PCM-air TES unit, a temperature-depen-dence of the properties was required.

3.4.1. Enthalpy–temperature curveThe storage capacity of the PCM is usually given by its latent

heat value, but the PCM used here was a commercial type, not apure substance, and therefore, the PCM melts and solidifies in atemperature range instead of in a set temperature; PCM also havehysteresis and some present sub-cooling phenomena. In thesecases, latent heat and cp values were not sufficient to define thestorage capacity at each temperature. Nevertheless, the enthalpyvs. temperature curve of the PCM provided such information. Inthis work the curves were obtained utilizing the T-history method[25] by means of its improved version [26], obtaining typicalcurves as shown in Fig. 7, and then incorporated into the model.

Fig. 7. PCM enthalpy–t

From Fig. 7 an average phase change temperature for the PCMcould be established at 26.5 �C.

3.4.2. HysteresisDepending on the stage of the process (heating or cooling, see

Fig. 7) the models selected the appropriate enthalpy–temperaturecurve to be used in the simulation.

To solve the discontinuity that occurred when switching fromone curve to the other (related to changing from heating to cooling,or vice versa within the phase change), transition functions wererequired. According to Bony and Citherlet [1], during a heating stepinside the phase change zone, the slope of the transition line wasthe same as the solid phase slope in the inferior part of the phasechange; and during a cooling step it was identical to the slope ofthe liquid phase at the superior part of the phase change.

3.4.3. Thermal conductivity curveExperimental results of thermal conductivity obtained by the

laboratory of the Netzsch company utilizing laserflash methodol-ogy [33] for the solid and liquid states of the PCM were incorpo-rated into the model. Thermal diffusivity was measured using aNETZSCH model 457 MicroFlashTM laser flash diffusivity appara-tus. To estimate the thermal conductivity within the phase change,the methodology proposed by Lazaro [27] was used: a proportionalmass rule based on enthalpy–temperature curve.

3.4.4. Natural convection inside the PCMTo obtain a good agreement between experimental results and

simulations, it is not always sufficient to assume only conductioninside the PCM. To address this issue, effective thermal conductiv-ity was implemented and therefore convection in the PCM liquidphase could be taken into account when necessary. Natural con-vection was studied in a rectangular enclosure for the geometryutilized in this work [28].

The model calculated the effective thermal conductivity askeff = c � kPCM, utilizing the expressions proposed by MacGregorand Emery [19] for large rectangular enclosures. The correlationproposed by MacGregor was not strictly valid for this case (ratioH/e out of range; enclosed fluid changing phase in a temperaturerange, which meant a change in temperature and in PCM proper-ties; and temperatures varying with time), but it served a firstestimation.

emperature curve.


Theoretically, in this specific study case, the effect of naturalconvection was not crucial as the c values are generally very closeto 1 and always in the range 1 < c < 2.

3.5. Thermal losses/gains of the TES unit

Also taken into account were the aspects of dissipation of theinternal fan of the TES unit and ambient temperature effect overthe unit. The TES unit electrical consumption was measured andthe ambient temperature was monitored for each experiment.

4. Validation results

To verify the numerical models developed, a series of experi-ments in different working conditions were carried out. The aim

Fig. 8. Experimental results and simulation for a 48

Fig. 9. Experimental results and simulation for a 45

was to compare simulations and experiments in the widest work-ing range available with the experimental setup.

4.1. TES unit

The next Figs. 8–10 show how the simulations fit the experi-mental results for three different constant inlet air temperaturecurves in the melting stage.

The graphics plotted show the degree of agreement betweenexperimental results and simulations. To quantify the differencebetween experimental data and simulated results, the relativemaximum error (from here on RME) [9] and an average error wereused as indicated in Eqs. (6) and (7):

RME ð%Þ ¼ max1;2;...;N

yexp � ysim

yexp

�� 100

( )ð6Þ

�C air inlet temperature setpoint, melting stage.

�C air inlet temperature setpoint, melting stage.

Fig. 10. Experimental results and simulation for a 40 �C air inlet temperature setpoint, melting stage.


Average error ð%Þ ¼X

1;2;...;N

yexp � ysim

yexp

�� 100

( ),N ð7Þ

The RME was always less than 15% for the 40 �C case. For the othertwo cases, specific errors of up to 30% could be found when the PCMin the TES unit was almost melted at low power rates. However, theaverage error for the melting process was less than 12% in all cases;furthermore, for the 40 �C case the average error was less than 4%.

A full cycle experiment and its corresponding simulation areshown in Fig. 11.

The average difference between measurements and simulationswas 160 W, although differences of up to 400 W were found in spe-cific locations of the curve.

Fig. 11. Full cycle comparison results be

The differences between the power curves could possiblyexist due to the air inlet temperature input data used in themodel:

� The experimental power values were obtained by the tem-perature difference measured with the thermopile [17,27]which takes into account the temperature distribution inthe section of the duct.

� The model used as input the air temperature measured by asingle Platinum resistance temperature detector PT100located in the middle of the inlet section, which did not takeinto account that temperature distribution, so thermalpower is calculated with slightly greater imprecision.

tween experiment and simulation.


4.2. Single plate

To compare simulation results with the single plate experi-ments, encapsulation thermal equations were considered in themodel. The location of the temperature sensors over and insidethe single plate is shown in Fig. 12.

Fig. 13 shows the experimental measurements and the simula-tion results.

The differences in temperatures between the measured dataand the simulated results are shown in Table 3.

Although there was an acceptable agreement between mea-surements and simulations for the entire heat transfer process(average differences of less than 1 �C), it could be observed thatat the end of the melting stage, experimental temperature dataevolved smoother than in the simulations. Some of the differencesbetween experimental data and simulations were due to the non-exact matching of the location of the temperature sensors andmonitored positions in the simulations. The temperature sensorsof the PCM also might not be exactly in the middle of the PCMthickness and could make contact with the encapsulation.

5. Model sensitivity

Different situations were simulated by varying PCM propertiesand operating conditions to analyze the sensitivity of the model.All simulation results plotted here used the same experimentalair inlet temperature curve, fan dissipation, and ambient tempera-ture evolution.

The power curve plotted in the next figures corresponds to _QTES,detailed in:

_Q TES ¼ _QPCM þ _W fanTES þ _Q ambient;TES ¼ _m � cp � ðTout � T inÞ ð8Þ

5.1. PCM properties input data

As the calculation results relied on the precision of the inputdata, the effect of a series of variations in the PCM thermo-physicalproperties was analyzed.

Fig. 12. Temperature sensors distribution over and inside the plate.

5.1.1. PCM enthalpy–temperature curveThe main input data of the model was the enthalpy–tempera-

ture curve of the PCM. The effects of varying the enthalpy valuesand the average phase change temperature were studied in thissection.

For the experimental data used as reference, the temperaturedifference between the inlet air and the average phase change ofthe PCM had two different values according to the thermal cyclestage: it was 5 �C until complete melting, and 9.5 �C until completesolidification.

5.1.1.1. Enthalpy. The effect on the TES unit power curve of an en-ergy variation from �30% to +30% on the enthalpy values of the en-thalpy–temperature curve, was studied (Fig. 14).

The simulations showed an expected result: as the PCM enthal-py values increased, the energy delivered increased, also increasingthe power peak and the duration of the process. It was also ob-served that in the melting stage there was a change in the shapeof the curve as the enthalpy values increase, but this change inshape did not occur in the solidification stage. This behavior de-pended on the temperature difference between the inlet air andthe average phase change of the PCM: greater the difference, fasterthe process.

Within the working range, a 10% increment in the value of thePCM enthalpy from its measured value led to differences in thesimulation results: of 250 W in the high temperature plateau inmelting, and of 100 W in the high temperature plateau in solidifi-cation. The time elapsed until full melting extended by 20 min andthe time elapsed to fully solidify extended by 15 min.

5.1.1.2. Average phase change temperature. Another study analyzedthe effect of moving the average temperature phase change of thePCM in the enthalpy–temperature curve (Fig. 15). This variationcould be related to the imprecision regarding the association ofthe enthalpy–temperature data pairs of the PCM input curve.

The effect of decreasing the average phase change temperaturedepended on the ongoing stage:

� In the melting stage it led to higher power peaks and shortertimes till full melting; there was a change in the shape of thepower curve: as the average phase change temperature waslower, the energy could be absorbed faster at high powervalues.

� In the solidification stage, decreasing the average phasechange temperature had the opposite effect. As this temper-ature moved to lower values it made the solidification of thePCM more difficult, thereby requiring more time to accom-plish full solidification and lowering the power delivered.

Table 4 summarizes the relative errors obtained in the powercurve for different imprecisions in the enthalpy–temperatureassociation.

The table showed that a mismatching in temperature of only1 �C in the PCM enthalpy–temperature values could lead to relativeerrors of up to 20% in the power curve of the TES unit and up to 14%in elapsed times till full melting. This point highlighted not onlythe importance of the accuracy in the measurements of input databut also of selecting the proper phase change temperature of thePCM according to the operating conditions of the TES application.Choosing a good performance in only one of the stages, avoidingthe analysis of the full cycle, could lead to important drawbacksin the performance of the entire TES unit.

5.1.2. PCM effective thermal conductivityNatural convection can be studied by means of the effective

thermal conductivity. As stated previously, in this specific study

Fig. 13. Experimental data (a) and simulation results (b).

Table 3Differences in temperatures between measurements and simulations.

Tmeasured � Tsimulated (�C)

Position Outlet air PCMdown PCMmid PCMup Encdown Encmid Encup

Average �0.3 0.1 �0.7 �0.7 0.5 �0.2 �0.4Maximum �0.9 1.7 �1.9 3.5 1.3 �2.1 �1.6


case the effect of natural convection in the PCM itself was negligi-ble in the entire thermal process, although it is interesting to studythe effect of the PCM thermal conductivity on the TES unit thermalperformance.

In Fig. 16 power curve evolution was compared for a set of dif-ferent fixed PCM thermal conductivity values and for the real ther-

mal conductivity (as a function of temperature). An increment inthe PCM thermal conductivity led to a higher power peak and toa faster process. However, while decreasing thermal conductivity,for very low values a different shape of the power curve could beobtained as the process controlling the heat transfer began to beconduction in the PCM.

Fig. 14. Simulations for different PCM enthalpy–temperature curves.

Fig. 15. Simulations for different PCM average phase change temperature.

Table 4Relative errors (RE) between measurements and simulations.

Tpc (�C) +5 +2 +1 Ref. �1 �2 �5

Relative error range in power (%) 22–78 6–37 3–20 0–7 5–10 8–18 41–79RE in time till full melting (%) �38 �21 �14 4 14 24 57RE in time till full solidification (%) 24 10 7 5 �2 �5 �14


Fig. 16. Simulations for different PCM thermal conductivity set values.

Fig. 17. Simulations for different air flows.


The same effect was reported when simulating the PCM withthermal conductivity as a function of temperature.

No significant difference was appreciated while increasing thePCM thermal conductivity from its real value, as in this case thelimiting resistance was not the conduction in the PCM but the con-vection in the air flow. However, when decreasing the PCM thermal

conductivity, the simulated power curve changed its shape clearlydue to the fact that the new resistance controlling the heat transferprocess was the conduction in the PCM.

For design purposes, within the working conditions, using a fixedthermal conductivity value in the range of 0.1–1 W/(m K) led to nosignificant differences in the performance of the TES unit.


5.2. Geometrical issues and operating conditions

There are two main paths to improve the performance of thePCM-air heat exchangers: enhance the PCM properties or optimizethe heat exchanger design [29]. The latter is generally cheaper thanthe first option, and therefore it is interesting to study the effect ofa series of operating conditions and geometrical parameters on theTES unit.

5.2.1. Air flowFive airflows were simulated. Fig. 17 shows a clear difference

behavior depending on the heat transfer phenomenon controllingthe process:

Fig. 18. Calculated pumpi

Fig. 19. Simulations for different shape

� With low airflows, convection on the air side controlled andthe process presented lower power peaks, required longertimes to reach full melting or solidification, and the TES unitcould release almost constant power for several hours.

� With high airflows, the bottleneck of the heat transfer pro-cess was due to the conduction within the PCM: the powercurve had higher power peaks and the process requiredshorter times to fully melt or solidify.

The drawback of increasing the airflow was the electrical con-sumption and dissipation that originated from its correspondingfan. The pumping power of the simulated cases was calculatedaccording to:

ng power vs. air flow.

s of bulges over the plate surface.


Wpump ¼_V � Dp

gð9Þ

The pressure drop of the TES unit was first estimated in accor-dance to the expressions proposed by Idel’cik [30] for tubes of rect-angular cross section, rectangular section elbows with sharp

Fig. 20. Simulations for different thermal condu

Fig. 21. Simulations for dif

corners, and discharge from straight walled elbow with sharp cor-ner in the turn. The expression was then corrected by means of amultiplication factor to fit the experimental data gathered inprevious works. Fig. 18 shows the pumping power potentialdependence on the air flow, assuming a performance of 80%.Experimental data for pressure drop fitted to a second order

ctivity values of the encapsulation material.

ferent PCM thickness.


polynomial equation so an expected third order polynomial depen-dence was obtained for the pumping power as turbulence is fa-vored by higher airflows and by the plate bulges.

5.2.2. Encapsulation rugosity (bulge shape)Due to the shape of the plate and the existence of bulges over its

surface, there was an important effect on heat transfer. See Section3.3.2 for the calculation of rugosity. In Fig. 19 the rugosity is ar-ranged from a maximum value (square bulge shape) to a minimumvalue (no bulges).

As shown in the figure, bulges can significantly enhance heattransfer as they are related to the improvement of the convectioncoefficient value: the higher the encapsulation rugosity, the higher

Fig. 22. Simulations for different

Fig. 23. Calculated pumping pow

the power peak and the shorter the melting and solidificationtimes.

5.2.3. Encapsulation thermal conductivityIn Fig. 20 the simulations considered a set of different thermal

conductivity values for the encapsulation material.Depending on the nature of the encapsulation material, the

thermal resistance of the encapsulation was negligible comparedto those of convection on the air side or conduction within thePCM: if kenc was in the range of kPCM or higher, the power curvewas in all cases the same. If kenc was inferior to kPCM, then thepower peak was lower and the time required to fully melt orsolidify extended.

lengths of the PCM system.

er vs. PCM system length.


No compatibility issues between the PCM and the encapsulationmaterial were considered; only thermal phenomena were takeninto account.

5.2.4. PCM thicknessIn Fig. 21, simulations with different PCM thickness values are

reported.The total mass of PCM in the TES unit was maintained constant

(135 kg), but the width of the system had to fit the volume: as thePCM thickness increased, the width of the system decreased. Twoopposite consequences then appeared: firstly, the heat transfer

Fig. 24. Simulations for different

Fig. 25. Calculated pumpi

surface of the TES unit decreased as the slabs’ volume enlarged;and secondly, the air velocity increased as the slabs’ volume en-larged, which was linked to an increase of the air convection coef-ficient values.

When the thickness of the PCM slab increased, the power peakdecreased and the time elapsed for the process to complete themelting or the solidification increased.

When the thickness decreased, the absorption/release of heatwas faster, which meant that the effect of increasing the heattransfer surface was greater than the effect of the reduction of theair convection coefficient values due to the air velocity decrease.

air gaps between the slabs.

ng power vs. air gap.


5.2.5. PCM system lengthThe next simulations were carried out maintaining both the to-

tal mass of PCM and its thickness constant. The heat transfer sur-face was maintained constant: an increment in length wascompensated by a reduction in width.

In Fig. 22 it is observed that as the length increases, the powerpeak raises and the process requires shorter times to completemelting or solidification. This increment in length meant higherair velocities, as the width was reduced and the airflow was main-tained constant and thereby the convection coefficient increased.

Again, as the length increases there is a drawback in the pres-sure drop and so in the electrical consumption of the fan.

Fig. 23 shows the pumping power dependence on the PCM sys-tem length, assuming a performance of 80%.

5.2.6. Air gapThe air gap is related to the Reynolds number and to the air con-

vection coefficient.From Fig. 24 it can be observed that as this gap narrowed, the

power peaks increased and times till full melting or solidificationdecreased. If the gap widened, power peaks diminished and melt-ing or solidification times extended: this was due to the fact thatthe bottleneck of the heat transfer process was on the air side.

In Fig. 25 the pumping power dependence on the air gap is plot-ted, showing that air gaps of less than 10 mm quickly led to highpumping powers.

6. Computational issues: time step

Computational cost and precision are two important issues inPCM modeling for TES systems and its integration in building sim-ulation tools (such as the tool Trnsys [34] used to simulate thetransient performance of thermal energy systems). This sectionstudied the time step and its effect on the accuracy of the results.

Fig. 26 shows the effect of time step size on the power curve.Results showed that typical time steps (of 1 h) in building sim-

ulation tools led to inaccurate power curves. Adequate resultscould be obtained using time steps up to almost 5 min, and there-fore it is recommended to solve 1 h time-step simulations bymeans of, at the most, 5 min time-step loops if using this model.

Fig. 26. Simulations for

7. Conclusions

A model was developed and experimentally validated to testthe thermal behavior of a TES unit consisting of a PCM-air heatexchanger.

The model was based on one-dimensional conduction analysis,utilizing finite differences method, and implicit formulation. Thephase change process was described by means of the hPCM(T) curve.

As the effect of hysteresis phenomenon on the TES unit thermalperformance can be substantial, it has been included in the modeland considered for the PCM enthalpy–temperature curve.

Natural convection within the liquid PCM has been consideredin the model by means of the effective thermal conductivity.

The model is theoretically valid for every air flow under internalforced convection and it was experimentally validated for an airvelocity range from 0.7 to 2.1 m/s and for an inlet air temperaturerange from 8 to 45 �C. As the model is one-dimensional, the length/thickness ratio in each plate must be over 10 to ensure a negligible2D conduction.

From the comparison between simulations and experimentalresults it was concluded that to determine the thermal behaviorof the TES unit, thermal simulation of the PCM encapsulationwas not necessary. This happened in this specific study case dueto the relationship between the main thermal resistances in theprocess. However, it is mandatory to take into account the rugosityof the encapsulation, as rugosity is related to the calculation of heattransfer between the air and the PCM slabs.

From these comparisons it could also be concluded that a 1Dmodel was suitable to achieve good results of the thermal behaviorof this type of TES unit. Average errors of less than 12% on thermalpower were obtained for the entire cycle.

The analyses carried out to study the influence of the PCM ther-mal properties used as inputs showed that:

� A 10% increment in the value of the PCM enthalpy from itsmeasured value led to differences in the simulation resultsof 6% of thermal power in the high temperature plateau inmelting and of 2.5% in the high temperature plateau in solid-ification. It also meant that times elapsed until full meltingextended by 11% and times to fully solidify extended by 10%.

different time steps.


� A drop of the average phase change temperature in the melt-ing stage led to higher power peaks and shorter times untilfull melting. In the solidification stage, decreasing the aver-age phase change temperature had the opposite effect: asthis temperature moved to lower values it made the solidifi-cation of the PCM more difficult, requiring more time toaccomplish full solidification and lowering the powerdelivered.

� A mismatching in temperature of only 1 �C in the PCMenthalpy–temperature values could lead to relative errorsof up to 20% in the power curve of the TES unit and up to14% in elapsed times till full melting.

� An enhancement of the PCM thermal conductivity led tominor improvements on the TES unit thermal performance,as in many cases the bottleneck of the heat transfer processwas on the air side.

� The hysteresis phenomenon in the enthalpy–temperaturecurve of the PCM was a point to consider as the thermal per-formance of the TES unit is greatly affected by thisphenomenon.

The previous aspects stress the significance of selecting ade-quate PCM for the desired application and also emphasize theimportance of the accuracy of the material properties’ data usedas inputs of the model, as the simulations could return completelydifferent results.

From the analyses of the influence of a series of geometricalparameters and operating conditions (airflow, encapsulation rug-osity, encapsulation thermal conductivity, PCM slab thickness,PCM system length, air gap) it was concluded that the thermalpower curve of the TES unit could be adapted to the correspondingapplication requirements without modifying the PCM propertiesbut by modifying the heat exchanger design. For example, higherpower peaks and shorter melting/solidification times could bereached by means of: increasing the air flow rate (although thedrawback is in the fan’s electrical consumption), increasing therugosity of the slab surface, reducing the PCM slab thickness,increasing the PCM system length or by reducing the air gap be-tween the PCM slabs.

Finally, to integrate this model in building simulation tools suchas Trnsys [34], which typically use time steps of 1 h, in order to ob-tain sufficiently accurate results, it is recommended to solve 1 htime steps of the model by means of calculation-loops of 5 minor less.

Acknowledgments

The authors would like to thank the Spanish government for thepartial funding of this work within the framework of the researchProjects ENE2005-08256-C02-02 and ENE2008-06687-C02-02.Pablo Dolado is especially grateful to the former Ministry of Educa-tion and Science of the Spanish government by his grant (ReferenceCode BES-2006-12468). The authors wish to thank the companyCIATESA for the support given in the early stages of the experimen-tal work. Special thanks are given to Mr. Miguel Zamora, CIATESAR&D Manager, for his collaboration.

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