Applied Energy 142 (2015) 328–336

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Applied Energy

journal homepage: www.elsevier .com/ locate/apenergy

Thermal energy charging behaviour of a heat exchange device with azigzag plate configuration containing multi-phase-change-materials(m-PCMs)

http://dx.doi.org/10.1016/j.apenergy.2014.12.0500306-2619/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding authors.E-mail addresses: pengzhijian@cugb.edu.cn (Z. Peng), y.ding@bham.ac.uk

(Y. Ding).

Peilun Wang a,b, Xiang Wang b, Yun Huang b, Chuan Li c, Zhijian Peng a,⇑, Yulong Ding c,⇑a School of Engineering and Technology, China University of Geosciences, Beijing 100083, Chinab State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, Chinac Birmingham Centre for Thermal Energy Storage, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK

h i g h l i g h t s

� Heat exchange device containing m-PCMs with a zigzag configurationconsidered.� Better charging dynamics observed

with m-PCMs compared with singlePCMs.� Highly enhanced charging process

with m-PCMs of large meltingtemperature difference.� Further intensified charging process

by using m-PCMs with unequal massratios.

g r a p h i c a l a b s t r a c t

Multi-phase change materials in a heat exchange device with a zigzag configuration for processintensification.

a r t i c l e i n f o

Article history:Received 17 February 2014Received in revised form 15 December 2014Accepted 24 December 2014Available online 19 January 2015

Keywords:Multi-phase change materials (m-PCMs)Heat exchangeZigzag configurationProcess intensificationNumerical modellingExperimental validation

a b s t r a c t

This paper concerns heat exchange devices with a zigzag configuration containing multi-phase changematerials (m-PCMs). A two dimensional mathematical model was established to model the chargingbehaviour. An experimental system was built to validate the model. The modelling results agree reason-ably well with the experimental data for a single PCM, establishing confidence in the model. Extensivemodelling was then carried out under different conditions. The results show that the use of m-PCMsintensifies the charging process in comparison with the use of a single PCM. Given other conditions, a lar-ger phase change temperature difference between the m-PCMs gives a more remarkable enhancement ofthe charging process, and the use of m-PCMs with an unequal mass ratio gives further intensification. Themodelling results also show that, for a given input power, an optimal fluid velocity exists for obtaining ahigh rate of the melting process.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

World primary energy consumption today is approximately 550Exajoules. Approximately 80% of this total is provided by burningfossil fuels, which emit a large amount of waste heat due to eitheror both of low efficiencies as a result of economic and

thermodynamic constrains and mismanagements. The waste heathas a wide range of temperatures from very low grade (e.g. 35–40 �C in power plants) to very high grade (e.g. 1600 �C in ironmak-ing and steelmaking plants) and is often unsteady and randomlydistributed. Effective and efficient utilisation of such heatresources requires thermal energy storage. On the other hand,environmental concerns including global warming call for theuse of sustainable and renewable energy resources. Among suchresources, solar energy is regarded as one of the most promisingresources. There are two ways to harvest solar energy, solar

Nomenclature

A mushy zone constantAa cross-sectional areacp specific heat, (J/(kg K))Cs Smagorinsky constantDH hydraulic diameter, (m)Gðx; x0Þ filtering functionh sensitive heat, (J)H enthalpy, (J)L latent heat of the material, (J/kg)Lz mixing length for subgrid scalesPin inlet power, (W)QL latent heat, (J)Qtolat total heat, (J)Re Reynolds numberSb buoyancy source termSh energy source termSi momentum sink in i directionSt turbulence source termSte Stefan numbert time, (s)T temperature, (K)To initial temperature, (K)TPCM-1 phase change temperature of PCM-1, (K)TPCM-2 phase change temperature of PCM-2, (K)TPCM-3 phase change temperature of PCM-3, (K)ut turbulent viscosity, (kg/(m s))~v velocity vector, (m/s)

V space geometry of control volumew width of the inlet, (m)Yðx0Þ instantaneous quantityYðxÞ filtering quantity

Greek symbolsa thermal conductivity, (W/(m K))b liquid fraction or porosityq density, (kg/m3)l viscosity, (kg/(m s))e small numberD local grid scalej Karman constantDT temperature difference between TPCM-1and TPCM-3, (K)x mass fractionsij subgrid-scale stress(SGS)U turbulence parameters dimensionless timesjj isotropic part of the subgrid-scale stresses

Subscriptave average valueb base value or buoyancyin inlet valuel/s liquid/solid phaseref reference valuet turbulence

P. Wang et al. / Applied Energy 142 (2015) 328–336 329

thermal and solar photovoltaic (PV), which use respectively theenergy over the long and short wavelengths of the spectrum. Ther-mal energy storage is essential for the solar thermal route due tothe intermittent nature of solar radiation. At the heart of thesethermal energy storage applications are cost-effective high perfor-mance storage materials and associated devices.

There are numerous thermal energy storage materials, whichcan be broadly classified into three types of sensible, latent and(chemical) reaction heat. These materials have different character-istics and hence require the use of different thermal energy storagedevices and systems. This work concerns mainly a novel thermalenergy storage device containing the latent heat based storagematerials termed as phase change materials (PCMs) and the phasechange occurs between liquid and solid states. The most salientfeatures of the PCMs are high energy storage density and isother-mal process during the phase change process [1,2]. PCMs also havedisadvantages with low thermal conductivity being one of them,which limits the charge and discharge rates and gives a low powerdensity. Several methods have been proposed and investigated toresolve this issue, which can be divided into two categories ofthermo-physical property enhancement of PCMs [3–9] and struc-tural improvement of heat exchange devices [10–13].

The use of m-PCMs to enhance heat transfer has attracted someattention over the past two decades. These studies investigated m-PCMs in shell-and-tube and slab configurations with either con-stant wall temperature or heat flux conditions. Adebiyi et al. [1]studied a packed bed containing m-PCMs by using mathematicalmodelling. They showed that the use of 5 PCMs gave 13–26%enhancement in heat transfer in comparison with the use of a sin-gle PCM. Gong and Mujumdar [14] showed significant enhance-ment of charge–discharge rates of a slab [14] and a tube [15] ofm-PCMs in comparison with that of a single PCM. Wang et al.[16] analysed the charge process of a cylindrical heat storagecapsule and found that the melting process of the capsule contain-

ing m-PCMs was 15–25% faster than that containing a single PCM.Shaikh and Lafdi [17] studied numerically a combined convection–diffusion phase change heat transfer process in a compositem-PCMs slab of various configurations. They showed that a signif-icant enhancement of heat transfer could be obtained through dif-ferent arrangements of the m-PCMs, which could not be achievedby using single PCMs. Fang and Chen [18] studied a shell and tubeunit containing m-PCMs and the results indicated the existence ofan optimal combination of m-PCMs to give a maximum thermalenergy charge rate. Rady [19] studied a packed bed of granularcomposites of m-PCMs and found that different combinations ofthe m-PCMs in the composite bed had a significant impact onthe overall storage unit performance.

This work investigates into the use of m-PCMs in a heatexchange device with a zigzag configuration for which, to the bestof our knowledge, little has been done. No studies have been foundin the literature on the effects of inlet temperature and velocity fora given input power on the heat transfer process. Due to highdemanding on computing resources, the zigzag configuration wasassumed to be a two-dimensional problem and the focus is onthe melting process. The model was solved numerically in theFLUENT environment. An experimental system was designedaccordingly to validate the model.

2. Numerical modelling

2.1. The physical model

Fig. 1 shows the physical model for the numerical work, whichhas a zigzag plate configuration containing m-PCMs. This configu-ration gives a corrugated surface, which offers several advantagesincluding increased surface area and disturbed flow for heat trans-fer intensification and has been used in plate heat exchangers [20].A heat transfer fluid (HTF) flows between the two sets of m-PCM-

Fig. 1. A schematic diagram of the zigzag configuration containing m-PCMs.

Fig. 2. Meshing of the computational domain.

Table 1Thermophysical properties of the NaCl–MgCl2 salt for the validation experiments.

Density(kg/m3)

Thermalconductivity (W/m K)

Specific heat(kJ/kg K)

Meltingpoint (K)

Latent heat(kJ/kg)

2200 0.6 0.93 713.15 280

330 P. Wang et al. / Applied Energy 142 (2015) 328–336

plates, leading to melting or solidification of the PCMs uponabsorbing or releasing heat from the HTF. To make the demandof computational resources at a manageable level, the plate isassumed to be sufficiently wide so that the problem can be simpli-fied to be 2-dimensional. As the configuration has a periodic fea-ture, only one segment is simulated; see Fig. 2. With reference toFig. 1, the geometries of the zigzag plate are given as:H1 = H2 = 2 mm; H3 = H4 = 4 mm; H5 = 2 mm; and the thickness ofthe plate is 1 mm. The PCMs considered in this work are sodiumchloride and magnesium chloride. The physical properties of thePCMs are tabulated in Table 1.

2.2. Mathematical formulation and numerical modelling

The mathematical formulation of the phase change problemincludes mass, momentum and energy balance equations, whichcan be solvable with initial and boundary conditions [21]. Theenergy equation takes the following form:

@

@tqHð Þ þ r � ðq~vHÞ ¼ r � ðkrTÞ þ Sh ð1Þ

where H, q, ~v , k, T and Sh are respectively the enthalpy, density,velocity vector, thermal conductivity, temperature and energysource term. The enthalpy, H, includes both sensible enthalpy (h)and latent enthalpy (DH):

H ¼ hþ DH ð2Þ

with the sensible enthalpy given by:

h ¼ href þZ T

Tref

cp dT ð3Þ

where href, Tref, and cp stand for the enthalpy at a reference temper-ature, the reference temperature and the specific heat at a constantpressure, respectively. The latent enthalpy in Eq. (2) is related to thefraction of liquid phase (b) during phase change and the specificlatent heat of the PCM (L) as:

DH ¼ bL ð4Þ

with b given by the following equation:

b ¼0 T < TsT�TsTl�Ts

Ts < T < Tl

1 T > Tl

8><>: ð5Þ

where Ts and Tl stand for respectively the freezing point and themelting point. The above method is known as the enthalpy–poros-ity model, which treats the phase-changing region (mushy region)as porous with porosity equal to the liquid fraction. The source termof the energy equation is given as:

Sh ¼@ðqDHÞ@t

þr � ðq~vDHÞ ð6Þ

Due to the formation of liquid during phase change, fluid flowoccurs in the liquid phase and the mushy zones, which are gov-erned by the following set of momentum equations:

@ðquÞ@tþr � ðq~vuÞ ¼ r � ðlruÞ � @P

@xþ Sx ð7Þ

@ðqvÞ@t

þr � ðq~vvÞ ¼ r � ðlrvÞ � @P@yþ Sy þ Sb ð8Þ

where u and v are respectively the x- and y-direction velocity, P isthe pressure, l is the viscosity, and Sx, Sy and Sb stand for respec-tively the source terms of phase change zone in the x-direction,y-direction and that due to the gravitational acceleration(y-direction) and are given in the following [22]:

Sx ¼ �Að1� b2Þ

b3 þ eu ð9Þ

Sy ¼ �Að1� b2Þ

b3 þ ev ð10Þ

Sb ¼ �qgbðh� href Þ

cpð11Þ

where g is the gravitational acceleration, e is a small number (e.g.0.001) to prevent division by zero, and A is the mushy zone constantwith a value depending on the structure of the porous mushy zonebut normally taken as 10�5 [23]. The phase change can induce tur-bulent flows and as a result the following turbulent sink term needsto be considered:

St ¼ �Að1� b2Þ

b3 þ eU ð12Þ

where U stands for the turbulence parameter obtained from theturbulent flow model. Because the zigzag configuration makes theflow field complex, the Large Eddy Simulation (LES) model is used.In LES, the contribution of the large scales of turbulence to momen-tum and energy transfer is computed exactly, and only the effect ofthe small scales of the turbulence is modeled. Decomposition into alarge scale component and a small subgrid scale is done by applyinga filtering operation:

YðxÞ ¼Z

DYðx0ÞGðx; x0Þdx0 ð13Þ

where Y(x0) is the instantaneous parameter and G(x, x0) is the filter-ing function given as follows:

Fig. 3. Experimental system.

P. Wang et al. / Applied Energy 142 (2015) 328–336 331

Gðx; x0Þ ¼1=V ; x0 2 V0; x0 R V

�ð14Þ

where V is taken as the grid cell volume. In the Navier–Stokes equa-tions, the subgrid-scale stress (SGS), sij, takes the following form:

sij ¼ quiuj � q�ui�uj ð15Þ

where q�ui�uj and quiuj are affected by the filtering function. The sub-grid-scale stresses turbulence models employ the Boussinesqhypothesis, computing the subgrid-scale turbulence stresses by:

sij �13sjjdij ¼ �2utSij ð16Þ

where Sij is the rate-of-strain tensor, and ut is the turbulent viscositygiven by:

ut ¼ qL2s jSj ð17Þ

in which, Ls is the mixing length at the subgrid scales, which can beexpressed by:

Ls ¼minðjd;CsDÞ ð18Þ

where j, d and Cs are respectively the Karman constant, the dis-tance to the closest wall and the Smagorinsky constant (taken as0.1 in this work [24]), and D is the local grid scale, which is relatedto the computational cell volume by D = V1/3; and jSj is the secondinvariant of the shear rate tensor, which can be calculated by:

jSj ¼ffiffiffiffiffiffiffiffiffiffiffiffi2SijSij

qð19Þ

The above equations, together with the following mass balanceequation, constitute the full set of models for the phase changeproblem.

@q@tþr � ðq~vÞ ¼ 0 ð20Þ

They were solved in the FLUENT environment. The Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithmwas used for velocity–pressure coupling. The PREssure StaggeringOption (PRESTO) scheme was used for pressure spatial discretisa-tion, whereas the Bounded Central Differencing (BCD) schemewas used for the discretisation of the momentum terms.

2.3. Boundary and initial conditions

Fig. 2 shows schematically the meshing of the computationaldomain, generated by the Gambit software. It should be noted thatthe mesh geometry in this figure is inconsistent with that as pre-sented in Fig. 1 because the mesh here covers different numberof zigzag peaks from those as shown in Fig. 1. The entire calcula-tion domain was set initially at a zero velocity and a temperatureof To (which was lower than the lowest melting point of m-PCMs).

At the inlet, both fluid velocity and temperature were givenwith the fluid temperature higher than the highest melting pointof m-PCMs. At the outlet, fully developed flow condition isassumed (l > 116DH, where DH is the hydraulic diameter). Periodicboundary conditions were assumed for both the upper and lowerplates. Adiabatic boundary conditions were applied to the frontand back walls. No-slip boundary conditions were applied to theinterior zigzag tooth-like wall surfaces.

3. Experimental verification

3.1. Experimental system and procedure

The experimental work was carried out to verify the model.Fig. 3 shows a schematic diagram of the experimental system used

in the work, which consists mainly of an electric heating furnace, ahigh temperature blower, and one phase change heat exchanger.Various temperature, flow and pressure transducers were installedand linked to a data acquisition unit. The phase change heatexchangers contained 23 pairs of parallel zigzag plates (1 mmthick) with phase change materials sealed between each pair ofthe zigzag plates. Flow of heat transfer fluid was through channelsof adjacent pairs of the zigzag plates. Temperature of the phasechange materials was measured using thermocouples; see Fig. 4for the thermocouple arrangement. Air was used as the heat trans-fer fluid due to high melting points of phase change materials con-sidered in this work. The two heat exchangers could be charged atthe same time. It was also possible, through the use of a combina-tion of valves, to charge one of the heat exchangers whereas theother was discharged. In this work, only one of the phase changeheat exchangers was used and the charge–discharge processesoccurred cyclically.

In a typical charge process, air was heated to a preset tempera-ture by the electric heating furnace and driven to circulate in theloop by the high temperature blower. The heated air flowedthrough either one of the phase changer heat exchangers whereheat was transferred to and stored within the phase change mate-rial. Upon fully charged (judged from the temperature measure-ments of the outlet air temperature), the electric furnace and thehigh temperature blower were switched off to end the chargingstep. In the discharge step, the ambient air blower was switchedon to deliver a preset rate of air flow to the charged phase changeheat exchanger.

3.2. Verification and validation of simulation models

The computational domain was represented by a 2-dimensionalbase grid, which had 49,163 mesh cells with 19,560 cells in thePCM domain and 13,770 cells in HTF domain. A finer grid was cre-ated through increasing the mesh density near the plate walls. Gridindependence was studied using grid sizes of 0.3, 0.4 and 0.5 mm,which gave a total number of cells of 84,932, 63,410 and 49,163,respectively. Fig. 5 shows the results. One can see that there is littleeffect of grid size on the time evolution of liquid fraction. It wastherefore decided to use the grid size of 0.5 mm with 49,163 cellsin all subsequent simulations.

A NaCl–MgCl2 salt with a 4:6 mass ratio was used in the valida-tion experiments, which had a phase change temperature of713.15 K. Other thermophysical properties of the salt are given inTable 1. The specific heat (cp) and thermal conductivity (k) of theheat transfer fluid (air) for a temperature range of 200–1000 Kare given in the following:

Fig. 4. Arrangement of thermocouples within the phase change heat exchanger and the position of the central thermocouple.

Fig. 5. Grid independence investigation.

Fig. 6. Comparison between experimental and modelling results for thermocouple1 and the outlet as shown in Fig. 4.

332 P. Wang et al. / Applied Energy 142 (2015) 328–336

� Specific heat in J/(kg K)

cp ¼ 1043:96081� 0:327T þ 7:79328� 10�4T2

� 3:5606� 10�7T3 ð21Þ

� Thermal conductivity in W/m K

k ¼ 0:0096þ 5:975� 10�5T ð22Þ

Fig. 6 compares the measured and calculated time evolutions ofthe PCM temperature at position 1 and outlet (as indicated inFig. 4). It can be seen that a reasonably good agreement has beenachieved, thus establishing confidence in the model. The deviationof thermocouple 1 at the initial stage is likely to be associated withthe existence of pores in the PCM as the material was loaded intothe plate heat exchangers in the form of compacted powder. Otherreasons may include temperature dependence of the PCM proper-ties and uneven distribution of the heat transfer fluid flow acrossall the plates, which were not considered in the modelling.

4. Modelling results and discussion

This work considers m-PCMs with different phase change tem-peratures, which, as indicated in the Introduction, has not beenstudied in the literature. Numerical simulations are done on 3PCMs contained between zigzag plates as shown in Fig. 7. The 3PCMs are arranged in the order of PCM-1, PCM-2 and PCM-3 inthe flow direction of the heat transfer fluid with the phase changetemperatures of PCM-1 (TPCM-1) > PCM-2 (TPCM-2) > PCM-3 (TPCM-3).It is also assumed that TPCM-1 � TPCM-2 = TPCM-2 � TPCM-3 = DT/2,where TPCM-2 = (TPCM-1 + TPCM-3)/2 = 713.15 K and DT = TPCM-1

� TPCM-3. Six sets of m-PCMs with different melting temperaturesare selected for the modelling study with DT = 20, 40, 60, 80, 90,and 100 K. The results are compared with DT = 0 K (a single PCMonly). Unless otherwise indicated, the inlet velocity and tempera-ture of the heat transfer fluid are fixed at 6 m/s and 873.15 K,and the mass ratio of m-PCMs is taken as unity.

Fig. 7. Arrangement of an m-PCMs unit.

Fig. 8. Liquid fractions of the three PCMs as a function of dimensionless time atdifferent DT values (empty, half-filled and filled symbols stand for liquid fractionsof PCM-1, PCM-2 and PCM-3, respectively).

Fig. 9. Time evolution of dimensionless outlet temperature.

P. Wang et al. / Applied Energy 142 (2015) 328–336 333

4.1. PCMs with equal mass ratio

In order to conveniently discuss the simulation results, the tem-perature and time were defined in dimensionless forms as follows:

Dimensionless time : s ¼ cpðTin � TaveÞL

at

H2 ¼ Ste� Fo ð23Þ

where Ste and Fo are respectively the Stefan and Fourier numbers, ais the PCM thermal diffusivity given by a = k/(qcp) with k the PCMthermal conductivity, t is the time elapsed and Tave is the averagephase change temperature of m-PCMs calculated by:

Tave ¼ TPCM-1 �x1 þ TPCM-2 �x2 þ TPCM-3 �x3 ð24Þ

where x1, x2 and x3 are respectively the mass fractions of thePCM-1, PCM-2 and PCM-3.

Dimensionless temperature : h ¼ T � To

Tin � Toð25Þ

where Tin is the inlet temperature of the heat transfer fluid, and To isthe initial temperature.

Fig. 8 shows the liquid fractions of the three PCMs with equalmass ratio as a function of time for 7 different combinations ofmelting temperatures. One can see that, although the melting tem-perature of PCM-3 is the lowest, it takes the longest time to com-plete the melting process in all cases and hence forms the rate-limiting factor of the whole melting process. The main reasonsfor this lie in the arrangement of the three PCMs and the locationof the PCM-3. During charge, the heat transfer fluid carries heatin and transfers the heat to the PCM-1 first, then the PCM-2 andfinally the PCM-3. The temperature of the heat transfer fluiddecreases during this process. As a result, before the PCM-1 andPCM-2 are fully charged, the temperature of heat transfer fluid atthe inlet to the PCM-3 part is always lower than those to thePCM-1 and PCM-2 parts. Fig. 8 also shows that the larger the DT,the longer the melting time of PCM-1 as more energy is neededfor the PCM-1 to melt. However, the effect of DT on the meltingtimes of PCM-2 and PCM-3 are opposite to that of PCM-1 with ahigher DT leading to a shorter melting time. This is because a

higher DT gives a larger temperature difference and hence a largerdriving force for transferring heat to the PCM-2 and PCM-3.

An inspection of Fig. 8 also indicates that the effect of DT on themelting time of the PCM-2 changes with time, significant in the ini-tial stage of melting, decreases with time and finally diminishes.An explanation to this observation could be as follows. In the initialstage, PCM-1 stores heat in a sensible form. When the temperatureof PCM-1 increases to above its melting temperature, latent heatstorage starts and becomes dominant. During this process, thehigher the DT, the higher the TPCM-1, and hence more time delayoccurs to the change from the sensible heat dominant to the latentheat dominant storage. This in turn leads to the increase in theinlet temperature of the heat transfer fluid to the PCM-2 partand hence the significant difference. When the melting process ofthe PCM-1 is close to completion, the sensible heat storagebecomes dominant and the effect of PCM-1 melting temperatureon the heat transfer fluid temperature enters the PCM-2 part,and hence the effect of DT on the melting of the PCM-2 becomesmall.

The effect of DT on the melting process of the PCM-3 differs sig-nificantly from that on the PCM-2. This can be explained as follows.In the initial stage of melting, energy storage occurs in the form ofsensible heat. Due to the buffering effect of the PCM-2, the heattransfer fluid temperature entering the PCM-3 part does notchange much with time. As a result, a higher DT (meaning a lowerTPCM-3) gives a quicker melting process for the PCM-3. With theprogress of the melting, the heat transfer fluid temperatureincreases, making the PCM-3 start to melt even at high DT values.

Fig. 9 plots the dimensionless outlet temperature of the heatexchanger with equal mass ratio as a function of time. For a givenDT, there is a period within which the dimensionless temperatureis zero (the outlet temperature is equal to the initial temperature).The duration of the period depends on DT; the larger the DT, thelonger the duration. The reason for this is that all the thermalenergy that enters the phase change heat exchanger has beentransferred to the phase change material and stored within thematerial. After the zero dimensionless temperature period, thetime-dependence of the dimensionless outlet temperature is afunction of DT. At lower values of DT, the time dependence ofthe outlet dimensionless temperature (h) shows a clear 3-stageprocess with h increasing with time first, then no effect of timeon h, and finally h increasing with time again. The three stage pro-cess corresponds nicely to the sensible heat storage, latent heatstorage and sensible heat storage as discussed before. The secondstage of the process becomes obscure with increasing DT and even-tually more or less disappears at the highest DT considered in thiswork. Fig. 9 also suggests that the outlet temperature of the secondstage be closely related to the melting temperature of the PCM-3

Fig. 10. Dimensionless time evolution of the liquid fraction of all PCMs.

Fig. 11. Dimensionless time evolution of the outlet dimensionless temperaturesand liquid fractions of PCM-1, PCM-2 and PCM-3 for a mass ratio of 16:6:8.

Fig. 12. Dimensionless time dependence of the m-PCMs effectiveness: gi (i = 1–6)corresponding to DT = 20, 40, 60, 80, 90, and 100. The inset is the average g overall sby integrating over the distribution.

334 P. Wang et al. / Applied Energy 142 (2015) 328–336

(TPCM-3); the higher the DT, the lower the outlet temperature. Thisagrees with the above analyses that the overall melting timedepends on the TPCM-3.

Fig. 10 shows the overall liquid fraction of the 3 PCMs withequal mass ratio as a function of the dimensionless time. Thedimensionless times to completely melt all the PCMs at DT = 0,20, 40, 60, 80, 90, and 100 K are 136, 132, 128, 120, 112, 109 and105, respectively. This results reveal it takes longer time for theheat exchanger with only one PCM (DT = 0 K) to complete themelting process than that with m-PCMs (DT – 0 K), indicating thatthe use of m-PCMs could give considerable intensification of thecharging process.

4.2. Effect of mass ratio of m-PCMs

Fig. 11 shows the dependence of the total liquid fraction and thedimensionless outlet temperature for a combination of PCM-1,PCM-2 and PCM-3 with a mass ratio of 16:6:8 at DT = 80 K. Onecan see that the PCMs melt completely within s = 100 (correspond-ing to approximately 2750 s) simultaneously. The correspondingdimensionless outlet temperature is about h = 0.15. A prolongedperiod on stream to s = 125 (corresponding to approximately3400 s) gives h � 0.31 (730 K). A comparison of these data withthat shown in Fig. 10 indicates that a longer duration of s = 115(�3200 s) is needed for complete melting of the three PCMs withequal mass ratio at DT = 80 K. Besides, when DT = 80 K, the corre-sponding outlet temperatures are considerably higher withh = 0.4 (see Fig. 9) and 0.25 (see Fig. 11), respectively, at s = 115.These results suggest the enhancement of the charging process

could be achieved through manipulating the mass ratio of thePCMs.

4.3. Effectiveness of the use of m-PCMs

To quantitatively compare charging performance enhancementthrough the use of m-PCMs, the following ratio is introduced:

g ¼ QDT–0K

QDT¼0Kð26Þ

where Q refers to the total amount of thermal energy stored and g isthe ratio of the total heat stored in m-PCMs to that in a single PCM.The g can therefore be regarded as the m-PCMs effectiveness.Fig. 12 shows the change of g as a function of time for differentDT values. For a given DT, g decreases first with time, reaches aminimum s = smin, then increases with time, peaks at s = smax, andfinally decreases to zero. Both the smin and smax are functions ofDT; the higher the DT, the greater the smin and the shorter the smax.The smin lies in the range of 6–12, whereas the smax is between 85and 95. The time duration with DT larger than 1 is far longer thanthat with DT smaller than 1. The m-PCMs effectiveness at smin

and smax are also a function of DT; a larger DT gives a lower g atthe smin but a higher g at the smax. For a given DT, the largest valueof g is around 1.2 at smax, which is much higher than the smallest gof 0.85 at smin. These observations indicate that g is higher than 1for most part of the charging process, leading to an overall processintensification through the use of m-PCMs, and as shown in Fig. 12,the average g over all s by integrating over the distributionincreases with the value of DT, meaning that a higher DT gives a lar-ger extent of overall process enhancement.

4.4. Effects of inlet temperature and velocity

The effects of inlet temperature and velocity are considered fora given input power where the input power is expressed as:

Pin ¼ cp � qv inAa � ðTin � TbÞ ð27Þ

where Aa is the cross-sectional area, v is the inlet velocity of the heattransfer fluid and Tb is the base temperature defined as Tb = 1/2(Tin + To). The base case of this set of modelling work was underthe conditions of v = 6 m/s, Tin = 873.15 K, To = 663.15 K, m-PCMsmass ratio of 16:6:8 and DT = 80 K. Different conditions are realisedthrough changing the inlet temperature and the inlet velocity of theheat transfer fluid. For doing this systematically and efficiently, twodimensionless parameters, average Stefan number, Ste(ave), and

Table 2Simulation conditions for the given input power and initial temperature.

Cases Average Ste Re

1 0.53 972 0.57 823 0.62 764 0.68 655 0.75 556 0.85 45

Fig. 13. Time evolution of liquid fraction at different Reynolds/Stefan numbers (thenumber in the legend corresponds to the cases listed in Table 2).

Fig. 14. Time evolution of the outlet temperature at different Reynolds/Stefannumbers (the number in the legend corresponds to the cases listed in Table 2).

Fig. 15. Time evolution of the ratio of the latent heat to the total stored heat atdifferent Reynolds/Stefan numbers (the number in the legend corresponds to thecases listed in Table 2).

P. Wang et al. / Applied Energy 142 (2015) 328–336 335

Reynolds number, Re, are used. The following equations reflect thechanges of the two parameters:

SteðaveÞ ¼ Ste1 �x1 þ Ste2 �x2 þ Ste3 �x3 ð28Þ

where Ste1, Ste2, and Ste3 are respectively the Ste numbers of PCM-1,PCM-2 and PCM-3.

Re ¼ qvDH

lð29Þ

where DH is the hydraulic diameter of the zigzag channels [25].Table 2 presents the modelling conditions according to Re andSte(ave) for fixed Pin and To.

Fig. 13 shows the liquid fraction as a function of time. The melt-ing rate (the slope of the curve) is seen to increase with increasingRe number or decreasing Ste(ave) number. Such an increase in themelting rate does not seem to be associated with the overall heattransfer driving force (the temperature difference). This is because,for a given input power, an increase in the Reynolds numberimplies an overall decrease in the difference of the inlet tempera-ture and the initial temperature according to Eqs. (27) and (29).It is plausible that an increase in the Reynolds number gives anenhancement of the overall heat transfer between the heat transferfluid and the m-PCMs and hence an overall increase in the meltingrate. Interpretation of the observations from Fig. 13 could also bedone from a different angle as follows. For a given power input, adecrease in the inlet velocity of the heat transfer fluid (Re number)means an increase in the inlet temperature of the fluid (Ste(ave)).This implies that the temperature difference between the heattransfer fluid and the PCM at the inlet region remains at a highlevel even after complete melting of the PCM in the inlet region,leading to more heat stored in the inlet region as the sensible heatand less heat flowing to the downstream region for melting thePCMs there and hence the observed low melting rate.

Fig. 14 shows the time evolution of the outlet temperatureunder different conditions for a fixed input power. One can see thatthe overall melting time decreases with increasing Re number(decreasing Ste number), which is consistent with the conclusionsdrawn from Fig. 13. However, Fig. 14 also indicates that theincrease in Re number to above 81.96 does not give much benefitin terms of the melting rate, an indication of existence of anoptimal Re number.

It is interesting to look at the time-evolution of the ratio of thelatent heat (QL) to the total stored heat (Qtotal) for a given inputpower. Fig. 15 shows the results. QL/Qtotal is seen to rise abruptlyafter an initial stage of �100 s when part of the m-PCMs is heatedup to the melting temperature. The ratio then peaks at �500 s afterwhich a small decrease in the ratio occurs with time, forming ashoulder-like curve before picking up to reach a second peak.The duration for reaching the second peak depends on the Re num-ber; the higher the Re number, the shorter the duration is neededto reach the second peak. The QL/Qtotal value of the second peak isfar higher than that of the first peak and the absolute peak valuesdepend on the Re number; and the peak value of the QL/Qtotal ratiodecreases with increasing Re number for the first peak whereas thereverse occurs for the second peak. The reasons for the observa-tions of the two peaks are explained as follows. At the beginning,the temperature difference between the PCM and the heat transferfluid is large and the PCM at the inlet of the channel (PCM-1)reaches the phase change temperature, leading to the rapid riseof QL/Qtotal and the formation of the first peak. As the meltingprocess proceeds, the temperature difference between the PCMand the heat transfer fluid reduces and hence the melting processslows down with more thermal energy stored in the sensible form,leading to the decrease in QL/Qtotal. With increasing temperature ofthe PCM-1 due to the increase in the sensible heat, the temperatureof the heat transfer fluid rises when it enters into the downstream

336 P. Wang et al. / Applied Energy 142 (2015) 328–336

parts, which facilitates the melting of the PCM-2 and PCM-3, lead-ing to the rise of QL/Qtotal and hence the formation of the secondpeak. After all the PCMs melt completely, heat is stored in the sen-sible form and hence the QL/Qtotal decreases in the final stage. Thereasons for the effect of Re/Ste(ave) on the peak QL/Qtotal values canbe explained as follows. For a given input power, a low Re impliesa high driving force for heat transfer, which, as mentioned above,gives a high melting rate of the PCM at the channel inlet partand hence the high peak QL/Qtotal at the first peak. At the same time,a low Re implies a low flow velocity. This also implies a low rate ofcarrying heat to the downstream PCM-2 and PCM-3 and a low heattransfer coefficient between the PCM and heat transfer fluid, andhence the long duration of the charging process.

5. Conclusions

A heat exchange device with a zigzag configuration containingmulti-phase change materials (m-PCMs) has been investigated inthis work. A two dimensional mathematical model was establishedto model the charging behaviour of the device. An experimentalsystem was built to validate the model. The following observationswere obtained under the conditions of this work:

� The modelling results agree reasonably well with the experi-mental data, indicating the validity of the model.� The use of m-PCMs intensifies the charging process in compar-

ison with the use of a single PCM.� A larger phase change temperature difference between the

m-PCMs gives a more remarkable enhancement of the chargingprocess.� The use of m-PCMs with unequal mass ratio gives further

intensification.� For a given input power, an optimal inlet velocity exists to give

a high rate of the melting process.

However, the current work only considers the charging process.Future work is needed on the discharging process.

Acknowledgments

The authors gratefully acknowledge financial supports fromChinese Academy of Sciences through its Focused DeploymentProject (KGZD-EW-302-1), China Ministry of Science & Technologythrough its Key Technologies R&D Program of China(2012BAA03B03), the National Natural Science Foundation ofChina (61274015), and the UK Engineering and Physical SciencesResearch Council (EPSRC) through its Energy Storage for Low Car-bon Grids Project (EP/K002252/1) and NexGen-TEST Project (EP/L014211/1).

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