study on a pcm heat storage system for rapid heat supply · 2011-11-16 · study on a pcm heat...

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Applied Thermal Engineering 25 (2005) 2903–2920

Study on a PCM heat storage system for rapid heat supply

Jinjia Wei, Yasuo Kawaguchi *, Satoshi Hirano, Hiromi Takeuchi

Energy Technology Research Institute, National Institute of Advanced Industrial Science and Technology,

Tsukuba 305-8564, Japan

Received 20 December 2004; accepted 25 February 2005

Available online 17 May 2005

Abstract

A thermal energy storage system employing phase change material (PCM) FNP-0090 (product of Nip-pon Seiro Co. Ltd.) for rapid heat discharge was studied numerically and experimentally. In the numerical

studies, the PCM was encapsulated in four different capsules (sphere, cylinder, plate and tube) for investi-

gating the effects of geometrical configurations. The effects of the capsule diameter and shell thickness and

the void fraction on the performance of the heat storage system were also investigated. The experiment was

conducted by using a commercial plate heat exchanger as the heat storage tank. It was found that the

spherical capsule showed the best heat release performance among the four types of investigated capsules,

whereas the tubular capsule with low void fraction was not ideal for rapid heat release of the thermal energy

stored in the PCM. The heat release performance decreased in the order of sphere, cylinder, plate and tube.The numerical results and the experimental data agreed within 10%.

� 2005 Elsevier Ltd. All rights reserved.

Keywords: Phase change material; Thermal energy storage; Rapid heat supply

1. Introduction

Thermal energy storage systems have a variety of applications such as thermal protection and
control of electronic components [1], heating and cooling of buildings (HVAC applications) and
1359-4311/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.applthermaleng.2005.02.014

* Corresponding author. Tel.: +81 29 8617257; fax: +81 29 8617275.

E-mail address: [email protected] (Y. Kawaguchi).

转载

mailto:[email protected]

Nomenclature

A surface area (m2)Bi Biot number Bi = hRp/klcp specific heat (kJ kg�1 K�1)d diameter (m)Fo Fourier numberh convective heat transfer coefficient (W m�2 K�1)H tank height (m)k thermal conductivity (W m�1 K�1)N row number of PCMPr Prandtl numberQ volumetric flow rate (m3 s�1) or heat flux (W m�2)r coordinate as shown in Fig. 3R radius (m)Re Reynolds number Re = Udo/mfS liquid–solid PCM interfaceSL longitudinal pitch (m), Fig. 1ST transverse pitch (m), Fig. 1Ste Stefan number Ste = cpl(Tm � Tin)/DHm

t time (s)T temperature (�C)U average fluid velocity before entering the heat storage tank U = w/qfAt (m s�1)u average fluid velocity in the heat storage tank u = w/qfeAt (m s�1)u* dimensionless average fluid velocity in the heat storage tank u* = uRp/alV volume (m3)w fluid mass flow rate (kg s�1)z coordinate as shown in Fig. 1

Greek symbols

a thermal diffusivity (m2 s�1)d capsule shell thickness (m)DHm latent heat of fusion (kJ kg�1)D average width of the space between two plates (m), Fig. 5e void fractionm kinematic viscosity (m2 s�1)q density (kg m�3)h dimensionless temperature

Subscriptsc capsule shellf fluid

2904 J. Wei et al. / Applied Thermal Engineering 25 (2005) 2903–2920

中国科技论文在线 http://www.paper.edu.cn

h initial state of charged heat storage tanki innerin inletl liquid PCMm melto outer surfaceout outletp PCMr ratios solid PCMsol solidificationt tankw wall; water

J. Wei et al. / Applied Thermal Engineering 25 (2005) 2903–2920 2905


hot water preparation [2]. By utilizing waste heat, thermal energy storage systems can reduce theconsumption of limited fossil fuel reserves and restrain output of CO2 to preserve the environ-ment. Phase change materials (PCMs) are promising candidates for consideration as heat storagemedia due to their large energy storage capacity [3], and the use of PCMs in energy storage hasbeen widely studied numerically and experimentally [4–7]. In these studies, the characteristiclength of the PCM was in an order of magnitude of 10 mm, requiring a long time to chargeand discharge the PCM. In some practical applications, an object requires to receive as much heatas possible within the first ten seconds. A PCM thermal storage system with small PCM size canbe used for rapidly supplying a large amount of heat to the object, but the performance of thiskind of thermal storage system has not been investigated yet. In the present study, a thermalenergy storage system employing PCM having a characteristic length of 2–5 mm for rapid heatdischarge was studied numerically and experimentally.

Paraffin wax FNP-0090 was used as the PCM and was packed in four different capsules (sphere,cylinder, plate and tube) for investigating the effects of geometrical configurations. The capsulesfilled with PCM were placed in a rectangular tank. Water was used as the working fluid in thecirculation system to discharge the storage tank.

A one-dimensional model was used for solving the water temperature distribution along theflow direction in the tank, and a conductive one-dimensional phase change model was used forsimulating the solidification process of the PCM inside the capsules due to the neglected naturalconvection heat transfer inside the PCM. A moving liquid–solid unknown a priori interface com-plicates the numerical solution of heat transfer with phase change. There are mainly five methodsfor solving the problem: (1) to obtain the position of the interface by interpolation for a fixed gridand time step case [8]; (2) to use a variable time step obtained by iteration to prompt the interfaceto move just one grid so that it can always be superposed on the grid in the solution [9]; (3) to usea moving variable grid scheme to make the interface position always coincide with a discrete gridnode, which requires the interpolation of the local temperature-time histories within the solution
domain [4,5,8]; (4) to use the technique of coordinate transformation to immobilize the movinginterface, resulting in a complicated control equation [10]; and (5) to use the enthalpy as a

dsstsin

fiinc

2

2

cns

wfl

wt

a

w

2

S1as



ependent variable to write a unified single equation for the entire domain including liquid andolid whereby the interface can be determined from the enthalpy distribution [11]. In the presenttudy, the finite difference approximation and fixed grid and time step (method 1) were used forhe numerical solution of the PCM solidification process. The effects of the capsule diameter andhell thickness and the void fraction on the performance of the heat storage system were alsovestigated.A plate heat exchanger was used as a heat storage tank for experimental study. FNP-0090 waslled into the channels (the space between two plates) of one side of the heat exchanger and work-g fluid flowed in the channels of the other side of the heat exchanger. The numerical results were
ompared with the experimental data.
. Numerical analysis

.1. Heat transfer in the heat storage tank

Assuming one-dimensional heat transfer along the flow direction in the heat storage tank byonsidering that the tank is completely insulated and the natural convection in the tank is low,eglecting the heat diffusion due to the rapid water flow, and introducing the following dimen-
ionle
h

c

uid a

empe

nd u

ules t

ss variables

� ¼ ðT � T inÞ=ðT h � T inÞ; z� ¼ z=Rp; t� ¼ alt=R2p ¼ Fo; qr ¼ ql=qf ;

¼ c =c ; V ¼ A R =V ð1Þ
pr pl pf r o p f
here Ao is the external surface of the capsules. We can write the dimensionless equation for the
s
� � � � � �
ohf =ot þ u ohf =oz ¼ Q qrcprV r ð2Þ
here Q* is the heat flux from the PCM to the fluid and is proportional to the difference of the
rature between the outer surface of the capsule and the fluid
� � �
Q ¼ Biðho � hf Þ ð3Þ * is the dimensionless average velocity of the fluid in the tank and is expressed as� u ¼ uRp=al; u ¼ w=qfeAt ð4Þ
here At is the cross-sectional area of the tank.

.2. Heat transfer in the PCM

Four types of capsules (sphere, cylinder, plate and tube) were investigated in the present study.tainless steel was selected as the capsule material, which has a thermal conductivity of6.0 W m�1 K, a density of 7920 kg m�3 and a specific heat of 499 J/kg K. For the sphericalnd cylindrical capsules, the fluid flow is an external flow, while for the planar and tubular cap-

he fluid flow is an internal flow, as shown in Fig. 1.

Fig. 1. Arrangement of PCM in the heat storage tank. (a) Sphere, (b) cylinder, (c) plate and (d) tube.



The heat transfer coefficient h for sphere capsules in the heat storage tank can be obtained fromthe f

Foa cor

obvioclose

ollowing equations [12]:

jH ¼ 0.763=Re0.472e1.19 ð5Þ

h ¼ jHqfucpf=Pr2=3f ð6Þ

where jH is Colburn jH factor.
r the heat transfer to or from a bundle of cylinders in a cross flow, Zhukauskas [13] proposed relation in the form
Nu ¼ CRemmaxPr0.36f ðPrf=PrfwÞ0.25 ð7Þ

where Remax is the Reynolds number based on the maximum fluid velocity occurring withinthe cylinder bank, and the constants C and m are dependent on the configuration of the cylinderbundle and Remax, which can be found in [13].

For the heat transfer from the inner wall of the tube to the fluid flow, the Nusselt number was3.66 [14] since the Reynolds numbers in the present study were in the range of a laminar flow. Forthe heat transfer from the plate to the fluid flow in the channel between the two plates, the Nusseltnumber was obtained from the experimental value in a plate heat exchanger (PHE).

Paraffin wax FNP-0090, donated by Nippon Seiro Co., Ltd., was selected as the PCM, thethermal properties of which are shown in Table 1. The melting and solidification characteristicsof the wax supplied by the manufacturer were measured by use of DSC (differential scanningcalorimeter). Following the experiments, the DSC curve of the wax in the thermal storage system,which experienced a series of melting and solidification processes, were also checked, and no

us changes were observed. For the DSC measurements, a 3.6-mg sample was placed in ad aluminum pan and heated from 0 to 100 �C and then cooled from 100 to 0 �C at 5 �C/min.

0

10

20

30

40

0 40 60 80 100

Hea

t Flo

w (

mW

)

T (˚C)

20

Heating process

Cooling process

Table 1

Thermal properties of FNP-0090

Tm (�C) DHm (kJ kg�1) kl (W m�1 K) ks (W m�1 K) ql (kg m�3) qs (kg m�3) cpl (kJ kg

�1 K) cps (kJ kg�1 K)

81.3 216.7 0.26 0.42 764 900 2.12 1.60



Fig. 2 shows the DSC measurement of heat flow versus temperature for paraffin wax FNP-0090following the experiments. The peak in the heating process (the upper curve) marks the meltingpoint and that in the cooling process (the lower curve) marks the nucleation temperature. Wecan see that the wax actually melts and solidifies within a broad temperature range, not at a singlepoint. The latent heat of fusion at a melting point can be obtained by calculating the area underthe DSC curve and then dividing the area by the heating rate, 5 �C/min. The measured Tsol is88.0 �C, only slightly lower than the temperature corresponding to the peak in the melting pro-cess. The measured latent heat is 216.7 kJ kg�1. The merits of large latent heat of fusion, smallsupercooling for nucleation and being less harmful make paraffin wax FNP-0090 a good candi-date for PCM for rapid release of a large amount of heat.

A conductive one-dimensional phase change model was used for simulating the solidificationprocess of the PCM inside the capsule. Due to the small size of the PCM (the maximum diameteris 5 mm) and small superheat of the liquid PCM above the melting temperature (the maximumsuperheat is less than 20 K) in the present study, the Rayleigh number was estimated to be lessthan 200. Thus, the natural convection in the liquid PCM could not occur [15], making theone-dimensional phase change model reasonable. In reality, PCM has a solidification temperaturerange as shown in Fig. 2. For simplicity, the solidification temperature Tsol was assumed to

Fig. 2. DSC curve of paraffin wax FNP-0090.

be coand p

nstant here. One-dimensional heat transfer equations in spherical, cylindrical (tubular)lanar capsules filled with PCM are as follows:

Sphere : ðqcpÞroh�

ot�¼ 1

r�2o

or�krr�2

oh�

or�

� �r� 6¼ S�ðt�Þ ð8Þ

oh� 1 o oh��

Cylinder or tube : ðqcpÞr ot� ¼r� or�

krr�or�

r� 6¼ S�ðt�Þ ð9Þ

Byheat

to beFo

Fo

Fo

Thanaly

Fig. 3

(b) cy


oh� o oh��


Plate : ðqcpÞr ot� ¼or�

kror�

r� 6¼ S�ðt�Þ ð10Þ

where r* = r/Rp and S* = S/Rp.
assuming that the liquid–solid interface moves only one-dimensionally in the r-direction, thebalance at the liquid–solid interface in PCM is expressed as
� � � �
krohsor�
� ohlor�

¼ 1

StedS ðt Þdt�

r� ¼ S�ðt�Þ ð11Þ

Three regions, the liquid PCM region, solid PCM region and capsule shell, may exist in thePCM capsule. Fig. 3(a) shows the three regions for the spherical, cylindrical and planar capsules,and Fig. 3(b) shows the three regions for the tubular capsule. In Fig. 3(b), R�

o is the outer radius ofa computational cell for tube. The thermal properties of the material in each region are assumed

constant. In Eqs. (8)–(11), (qcp)r and kr differ among the three regions.
r the capsule shell region:
1 < r� 6 R�o for sphere; cylinder and plate

ðqcpÞr ¼ qccpc=qlcpl; kr ¼ kc=kr R�i 6 r� < R�

p for tubeð12Þ

r the solid PCM region:

S�ðt�Þ 6 r� < 1 for sphere; cylinder and plate
ðqcpÞr ¼ qscps=qlcpl; kr ¼ ks=kl R�
p < r� < S�ðt�Þ for tubeð13Þ

r the liquid PCM region:

0 < r� < S�ðt�Þ for sphere; cylinder and plate
ðqcpÞr ¼ 1; kr ¼ 1
S�ðt�Þ < r� < R�o for tube

ð14Þ

e vacancy in a capsule caused by the change of densities by solidification is neglected in thesis, and the density of solid PCM is assumed to equal to that of liquid PCM.

. Definitions of the regions of liquid PCM, solid PCM and capsule shell, and the coordinate system. (a) Sphere,

linder, (c) plate and (d) tube.



Th

for bschem

cooleLtd.,

e boundary conditions can be expressed as follows:

t� ¼ 0; h� ¼ 1.0 ð15Þ

t� > 0; oh�=or� ¼ 0r� ¼ 0 for sphere; cylinder and plate

r� ¼ R�o for tube

ð16Þ

kroh�=or� ¼ �Biðh� � h�f Þ

r� ¼ R�o for sphere; cylinder and plate

r� ¼ R�i for tube

ð17Þ

h� ¼ h� ¼ h� ; r� ¼ S�ðt�Þ ð18Þ
s l sol
2.3. Numerical simulation

It should be noted that for the present very small PCM size, the capsule number in the heat stor-age tank is very large (more than 360000 for 2-mm-diameter spherical capsules), and it is inefficientand not necessary to make a full 3-D computation of the water flow and heat transfer in the heatstorage tank because each capsule is located in the identical condition. If the outside of the heat stor-age tank is well adiabatic and large numbers of PCM capsules are uniformly distributed in the tank,a one-dimensional model described in Section 2.1 appears to be a preferred suitable choice.

Eq. (2) describes the heat transfer of the working fluid in the tank and Eqs. (8)–(11) describe theheat transfer of the PCM inside the capsules. The numerical solution of the heat transfer problemin the thermal storage system composed of the tank packed with PCM-filled capsules was realizedby using a marching technique in which the PCM heat transfer inside the capsule was coupledwith the energy balance equation (Eq. (3)) between the outside of the capsule and the workingfluid. The equations were discretized in space with second-order accuracy by use of a control vol-ume method and in time with first-order accuracy by use of an implicit backward differencescheme. The tank height was evenly divided into N layers each containing one layer of PCM cap-sule. The solidification process in the numerical simulations was treated in a quasi-static manner.The temperature field in each phase was solved with a fixed interface during a short time step andthe amount of heat transferred across the interface within this time interval was then used todetermine the progression of the solidification front. The temperature slopes at the interface

oth the solid and liquid regions were approximated by use of a second-order differencee. The Gauss–Seidel iteration method was used for the numerical solution.

3. Experimental setup and procedure

The thermal energy storage system used in the experimental study is shown in Fig. 4. The sys-tem mainly consisted of a plate heat exchanger (PHE), two thermostatic baths of hot and coldfluids, an electromagnetic flowmeter having a resolution of 0.01 m3/h, a cascade boiling-pointpump that permitted us to control the variation of flow rate in the loop from 0.3 to 1.2 m3/h, a

r and a collection tank. The plate heat exchanger was a commercial model (Hisaka works,BXC-214-PO-60) having a capacity of 3 L and was used as the PCM heat storage tank here.

∆P

1211

12 3

T

TT

T

4 5

6

913

14

17

1015

8

716

Fig. 4. Schematic of the experimental apparatus. 1. Plate heat exchanger; 2–5. Solenoid valve; 6. Thermostatic bath of

hot fluid; 7. Valve; 8. Collection tank; 9. Electromagnetic flowmeter; 10, 11. Solenoid valve; 12. Cascade boiling-point

pump; 13. Cooler; 14–16. Valve; 17. Thermostatic bath of cold fluid.

W

∆T

L

T2i T1o

Secondary side flow

Primary side flow

T1iT2o



The schematic diagram of the plate heat exchanger is shown in Fig. 5. The dimensions of the plateof the PHE were 303 mm in length, 103 mm in width, and 175 mm in thickness. The number ofplates in the PHE was 60 and the width of the flow passage between two plates was not uniform

Fig. 5. Schematic diagram of plate heat exchanger.

and the average value was D = 2 mm. The material of the plate was stainless steel and the thick-ness was 0.4 mm. The PCM was filled into the channels of the secondary side of the PHE. Two


type-T thermocouples were located at the inlet and outlet of the primary side of the PHE forrecording the working fluid temperature, and two platinum resistance thermometer probes wereinserted into the midpoints of the PHE from the inlet and outlet of the secondary side for moni-toring the PCM temperature. The thermocouples were connected to a PC-based temperature dataacquisition system. The pressure drop in the PHE was measured using static pressure taps havinga pressure transducer resolution of 0.1 Pa. A 4-kW heater was installed in the thermostatic bath ofhot fluid for supplying a high fluid temperature up to 110 �C. The chilling fluid was regulated bythe cooler that had a capacity of 470 W, and the cold fluid temperature could be controlled in therange of �20 to 40 �C. In the experiments, paraffin wax FNP-0090 was used as the PCM. The hotfluid used for heating the PCM was a mixture of 50% water and 50% ethylene glycol whereas thecold fluid used for cooling the PCM was tap water. The temperature in the thermostatic bath ofhot fluid was set at a constant of Th and the temperature in the thermostatic bath of cold fluid wasset at a constant of Tin. A series of values of Th ranging from 40 to 105 �C and Tin ranging from 15to 35 �C were set in the experiments for investigating the initial storage tank temperature and inletfluid temperature effects. Corrugated steel pipes with an outer diameter of 20 mm were used in thecirculation system. The outside of the PHE and the pipes were attached with a 9-mm thick ther-mal insulation layer, the material of which was Armaflex F-020 (product of Armacell LLC) hav-ing a thermal conductivity of 0.04 W m�1 K�1.

The experimental procedure included three stages: (1) heating process to charge the PCM, (2)stand-by and (3) cooling process to discharge the PCM. Each stage had a different fluid circulatingroute that could be switched quickly by use of solenoid valves. Six solenoid valves were installed inthe circulation system as shown in Fig. 4.

At first, the hot EG (ethylene glycol) mixed water having a temperature of Th was circulated bythe cascade boiling-point pump from the thermostatic bath of hot fluid to the heat storage tank tocharge the PCM. The circulating route of the heating process was 6–10–12–9–5–1–3–6.

After the PCM temperatures, monitored by the two platinum resistance thermometer probes,reached the set temperature Th, the cold water in the thermostatic bath of cold fluid was circulatedthrough a 17–11–12–9–4–17 route and the system entered a stand-by stage.

When the cold-water temperature reached the set one, Tin, the discharge process began. Thecold water in the thermostatic bath of cold fluid was pumped into the heat storage tank to removethe heat from the PCM. The circulating route of the cooling process was 17–11–12–9–5–1–2–8 inwhich the chilling water flowed through the PHE from the bottom to the top to avoid natural con-


vection. The time period lasted 30–120 s according to the flow rate. The temperatures of the inletand outlet of the heat storage tank were recorded at time intervals of 0.1 s.

4. Results and discussion

In the experiment, the average thickness of the PCM was dp = D = 2.0 mm, and the capsulethickness (plate thickness in the PHE) was d = 0.4 mm. Since the inner volume of the PHE was3.0 L, the inner volume of the PHE plus the plate volume was 3.6 L. The void fraction, whichis defined as the fraction of the inner volume of the tank taken up by the fluid, was 0.42.

Fig. 6 shows the measured outlet fluid temperature at different initial storage temperature Th

with flow rate fixed at 20 L/min. For Th greater than 90 �C at which the PCM melted completely

0 5 10 15 20 25 30 35 4020

30

40

50

60

70

80

90

100

110

Tfo

ut (

˚C)

t (s)

Th = 105˚CTh = 100˚CTh = 95˚CTh = 90˚CTh = 85˚CTh = 80˚CTh = 70˚CTh = 60˚CTh = 50˚CTin = 40˚C

Fig. 6. Measured outlet fluid temperatures.



in the heating process of DSC measurement as shown in Fig. 2, the curves begin to collapse ontoone after 4.5 s when the initially stored hot fluid flows out of the tank. This is due to the meltingprocess with latent heat release that dominates the heat exchange process. For Th < 90 �C, thecurves generally shift down with decreasing Th.

Fig. 7(a) and (b) respectively show the effect of flow rate and inlet fluid temperature on the out-let fluid temperature distribution. It can be seen that the outlet fluid temperature curve graduallybecomes more and more decreased with time as the flow rate is decreased or the inlet fluid tem-perature is increased. This means that the duration of heat discharge increases with decreasingflow rate or increasing inlet fluid temperature. For comparison, the numerical results are alsoshown in Fig. 7(a) and (b). In the numerical simulation, the tank wall effect on the heat transferwas considered by evenly distributing the heat received from the wall over the fluid. The heattransfer interaction between the wall and the fluid was simulated by use of a one-dimensionalmodel of adiabatic channel flow. The numerical results agree with the measurements to within10%.

Fig. 8 shows the variation of heat release as a function of the initial storage temperature Th. Wecan see that the heat release increases significantly with increasing Th for Th < 90 �C, and thenincreases gradually when Th exceeds 90 �C. The theoretical sensible heat storage and total heatstorage curves are also shown, and the experimental data agree well with the theoretical curve.From 60 �C, the wax starts to melt partly and the latent heat increases with increasing Th upto the temperature of 90 �C. The effect of the flow rate on the heat release at Th = 90 �C is notobvious.

In the following numerical simulated results, the inner volume of the tank was Vt = 3 L, and theinlet water temperature was Tin = 25 �C with a flow rate of 20 L/min. The initial storage tank tem-perature was set at Th = 90 �C. For this temperature, the maximum Raleigh number in the PCM isless than 20, ensuring that the natural convection heat transfer could not occur in the phasechange procedure of PCM. Four different sizes of capsules (do or di = 2.0, 3.0, 4.0 and5.0 mm), two different void fractions (e = 0.25 and 0.5), and two different capsule thicknesses
(d = 0.2 and 0.4 mm) were investigated. The tank wall was assumed to be very thin and adiabaticso that the heat stored in the wall was not considered in the calculation.

40 50 60 70 80 90 100 1100

200

400

600

800

1000Experimental heat release, Q = 20 l/minExperimental heat release, Q = 15 l/minExperimental heat release, Q = 10 l/minExperimental heat release, Q = 5 l/min

Th (˚C)

Hea

t (kJ

)

Theoretical total heat storage Theoretical sensible heat storage

0 20 40 60 8020

40

60

80

100

Tfo

ut (

˚C)

t (s)

Flow rate Experiment Calculation(L/min)

20 15 10 5

t = 4.5 s

0 10 20 30 400

20

40

60

80

100

Tfo

ut (

˚C)

t (s)

Tin (˚C) Experiment Calculation

15 25 35

t = 4.5 s

(a)

(b)

Fig. 7. Measured and calculated outlet fluid temperature. (a) Effect of flow rate and (b) effect of inlet fluid temperature.



Fig. 8. Effect of initial temperature on heat release.

Fig. 9(a)–(d) respectively show the fluid temperature at the outlet of the heat storage tank forspherical, cylindrical, planar and tubular capsules. The discharge of the heat storage system is

0 5.0 10.0 15.0 20.020

40

60

80

100

t (s)

Tfo

ut(o C

)

do (mm) ε = 0.5 ε = 0.25

Sphere (δ = 0.4 mm)

2345

0 5.0 10.0 15.0 20.020

40

60

80

100

t (s)

Tfo

ut (

o C)

do (mm) ε = 0.5 ε = 0.25

Sphere (δ = 0.2 mm)

2345

0 5.0 10.0 15.0 20.020

40

60

80

100

t (s)

Tfo

ut (

o C)

do (mm) ε = 0.5 ε = 0.25

Cylinder (δ = 0.4 mm)

2345

0 5.0 10.0 15.0 20.020

40

60

80

100

t (s)

Tfo

ut(o C

)

d (mm) ε = 0.5 ε = 0.25

Cylinder (δ = 0.2 mm)

2345

0 5.0 10.0 15.0 20.020

40

60

80

100

t (s)

Tfo

ut(o C

)

do (mm) ε = 0.5 ε = 0.25

Plate( δ = 0.4 mm)

2345

0 5.0 10.0 15.0 20.020

40

60

80

100

t (s)

Tfo

ut(o C

)

do (mm) ε = 0.5 ε = 0.25

Plate (δ = 0.2 mm)

2345

0 5.0 10.0 15.0 20.020

40

60

80

100

t (s)

Tfo

ut(o C

)

di (mm) ε = 0.5 ε = 0.25

Tube (δ = 0.4 mm)

345

0 5.0 10.0 15.0 20.020

40

60

80

100

t (s)

Tfo

ut(o C

)

di (mm) ε = 0.5 ε = 0.25

Tube (δ = 0.2 mm)

2345

(a)

(b)

(c)

(d)

Fig. 9. Numerical fluid temperature at the outlet of the heat storage tank. (a) Sphere, (b) cylinder, (c) plate and (d) tube.



considered to be finished when the outlet temperature has reached the temperature at the inlet.During the first lapse of time of 4.5 s for e = 0.5 or 2.25 s for e = 0.25, the outlet temperature re-mains constant since the hot fluid stored in the tank in the initial condition is flowing out, and
then the temperature decreases. For smaller PCM diameters, the decrease of temperature can



be divided into three phases: to decrease gradually firstly due to the large amount of sensible andlatent heat released from PCM, and to decrease rapidly after the heat from PCM is almost com-pletely released, and then to decrease gradually again to the inlet fluid temperature. For the largerdiameters, however, the heat transfer surface is not large enough for the rapid release of the heat,and hence the heat is released over a long period of time. Therefore, the temperature decrease be-comes gradual on the whole compared to that of the smaller diameters. Generally, the duration ofheat discharge increases with PCM diameter. The diameter effect increases in the order of sphere,cylinder, plate and tube. For the tubular capsule case, the outlet temperature drops suddenly afterthe hot fluid stored initially in the heat storage tank flows out of the tank. This is because the heattransfer coefficient is much smaller than that of the other three cases. For the tubular case, thevoid fraction effect on the outlet temperature is large, whereas for the other three cases the voidfraction takes apparent effect only for larger diameters. For the spherical and cylindrical capsules,the heat release performance are almost independent of void fractions, whereas for the planar andtubular capsules, the heat release velocity for the smaller void fraction was lower than the largerone. The outlet fluid temperature is mainly determined by the heat transfer coefficient (Bi num-ber), heat transfer surface area, the heat exchange time (Fo number) between fluid and PCM,and the heat amount stored in the tank. For the sphere and tube case, the heat transfer coefficientand surface area are large enough, and thus the heat stored in the PCM will be almost completelyreleased very quickly even for a short heat exchange time at the smaller void fraction, resulting ina sharp slope of the outlet fluid temperature curve following a flat part for both the larger andsmaller void fractions, as shown in Fig. 9(a) and (b). Actually, the amount of the PCM increaseswith decreasing void fraction. However, the amount of hot fluid initially stored in the heat storagetank decreases correspondingly due to the fixed tank volume. In the present study, the heat stor-age amount in the tank (including hot fluid, sensible and latent heat of the PCM) for e = 0.5 and0.25 are almost the same. Therefore, the large heat transfer coefficient, heat transfer surface areaand the same heat amount stored in the tank result in almost the same outlet fluid temperaturecurves for e = 0.5 and 0.25. For the plate and tube cases, the heat storage amount for e = 0.5and 0.25 are almost the same, but the heat transfer coefficient and surface area are not largeenough. Therefore, the heat release velocity at the small void fraction is lower than that at largevoid fraction due to a short heat exchange time. Comparison of the figures for the effect of thecapsule shell thickness shows that the larger shell thickness of 0.4 mm has slightly more improve-ment in rapid heat release than the smaller one of 0.2 mm. However, larger shell thickness leads toa decrease in the amount of PCM filled into the capsule for the same void fraction and hence thethermal energy storage is reduced. An optimum can be obtained by considering the balance of theheat release velocity requirement and the total energy requirement.

Fig. 10(a)–(d) show the distribution of the amount of heat release of the heat storage systemalong the tank from the inlet (z/H = 0) to the outlet (z/H = 1) at t = 10 s. The void faction is0.5 and the shell thickness is 0.2 mm. The heat is normalized by the sensible heat, Q0, stored inthe PCM and capsule at the beginning. Generally speaking, the amount of heat release decreaseswith increasing distance of the PCM from the inlet. Small diameters show a large amount of heatrelease compared to the larger ones, and a flat distribution of the heat release near the inlet forsmaller diameters indicates that all energy has been released in these PCM layers. The amountof heat release decreases in the order of sphere, cylinder, tube and plate. These curves provide
us with the information about the PCM state at different positions along the tank at 10 s.

0 0.2 0.4 0.6 0.8 1.00

0.5

1.0

1.5

2.0

2.5

3.0

Q/Q

0

z/H

do =2 .0 mmdo =3 .0 mmdo =4 .0 mmdo =5 .0 mm

Sphereδ = 0.2 mmε = 0.5

0 0.2 0.4 0.6 0.8 1.00

0.5

1.0

1.5

2.0

2.5

3.0

Q/Q

0

z/H

do = 2.0 mmdo = 3.0 mmdo = 4.0 mmdo = 5.0 mm

Cylinderδ = 0.2 mmε = 0.5

(a) (b)

0 0.2 0.4 0.6 0.8 1.00

0.5

1.0

1.5

2.0

2.5

3.0

Q/Q

0

z/H

do = 2.0 mmdo = 3.0 mmdo = 4.0 mmdo = 5.0 mm

Plateδ = 0.2 mmε = 0.5

0 0.2 0.4 0.6 0.8 1.00

0.5

1.0

1.5

2.0

2.5

3.0

Q/Q

0

z/H

di = 2.0 mmdi = 3.0 mmdi = 4.0 mmdi = 5.0 mm

Tubeδ = 0.2 mmε = 0.5

(c) (d)

Fig. 10. Numerical heat release of the thermal storage system at t = 10 s. (a) Sphere, (b) cylinder, (c) plate and (d) tube.

2.0 3.0 4.0 5.00.0

0.2

0.4

0.6

0.8

1.0

d (mm)

Q/Q

w

ε = 0.5 ε = 0.25

SphereCylinderPlateTube



Fig. 11 shows the total heat release amount of the PCM at t = 10 s and d = 0.2 mm. We can seefrom this figure that the heat release decreases with increasing diameter. For e = 0.5 and

Fig. 11. Numerical heat release of the PCM at t = 10 s.

d < 4 mm, Q/Qw increases in the order of plate, tube, cylinder and sphere, whereas for e = 0.25or d > 4 mm, Q/Qw increases in the order of tube, plate, cylinder and sphere. The smaller e shows

Fig. 12. Numerical temperature distribution of the PCM at t = 10 s. (a) Sphere, (b) cylinder, (c) plate and (d) tube.





a smaller Q/Qw, especially for large diameters and the tube case. The value of Q/Qw for all thecases is lower than unity, which means that the amount of heat release is smaller than that of asensible heat storage system of hot water. In the present study, the inlet fluid temperature is con-sidered to be a constant. In an actual case, the hot fluid would be used for heating an object andthen would return to the heat storage system, and thus the inlet fluid temperature would be a func-tion of the fluid temperature at the outlet of the tank and the thermal properties of the object.After a certain period of heat exchange between the working fluid and the object, the latent heatstored in the PCM is fully released and only sensible heat remains in the tank, which becomesmuch smaller than that of pure water for the same temperature due to the small density andspecific heat of the PCM compared to that of water. Therefore, we would expect that the objectreceive more heat for the PCM case compared with the pure water heat storage case.

Fig. 12(a)–(d) show the radial temperature distribution of the PCM at four different positionsalong the tank from the inlet (z/H = 0) to the outlet (z/H = 1) at t = 10 s. The regions of the PCMare shown by dot patterns, and the capsule shell is in the region of r* < 1 for the tube case and theregion of r* > 1 for the other cases, in which the temperature shows a nearly flat distribution dueto the high thermal conductivity of the shell compared to that of the PCM. These figures provideus with the information of the state of the solidification process at 10 s. The position of the liquid–solid interface indicated in the temperature distribution curve is the position beyond which thetemperature drops rapidly. We can clearly see the existence of the liquid–solid interface positionfor the larger diameter of 5 mm except in the sphere case at z/H = 0, which shows that the PCMhas not completely solidified yet. Comparison of the interface position for the sphere, cylinder andplate cases further shows that the heat release decreases in the order of sphere, cylinder and plate,which is in accordance with the conclusion obtained from Fig. 11. For a smaller diameter of2 mm, almost all of the PCM in the tank is completely solidified, and some PCM layers nearthe inlet release all of their heat storage to the circulating fluid and the temperature drops to a
uniform value close to the inlet temperature.
5. Conclusions

A PCM thermal energy storage system with small PCM diameters for rapid heat release wasstudied numerically and experimentally. In the experimental study, the effects of initial storagetank temperature, flow rate and inlet fluid temperature on the heat discharge of PCM encapsu-lated in a plate envelope were investigated. In the numerical analyses, four different capsule shapes(sphere, cylinder, plate and tube), four different capsule diameters (2, 3, 4 and 5 mm), two differentcapsule shell thicknesses (0.2 and 0.4 mm), and two different void fractions (0.25 and 0.5) wereinvestigated. The main conclusions may be summarized as follows:

(1) The discharge of the thermal energy storage system was faster with increasing fluid flow rateor decreasing inlet fluid temperature, and the variation of the flow rate was effective inchanging the discharging time.

(2) For the initial temperature Th greater than 90 �C, the effect of Th was small on the heatrelease process, whereas for Th lower than 90 �C, the heat release increased significantly with
Th.



(3) The spherical capsule showed the best heat release performance among the four types ofinvestigated capsules, whereas the tubular capsule with low void fraction was not ideal forrapid heat release of the thermal energy stored in the PCM.

(4) The duration of heat discharge increased with increasing PCM diameter and the shortesttime occurred for the small spherical capsule. The diameter effect increased in the order ofspherical, cylindrical, planar and tubular capsules.

(5) The capsule shell thickness of 0.4 mm showed a slight improvement in rapid heat release overthat of 0.2 mm, but the total thermal storage energy was reduced due to the decreasedamount of PCM.

(6) For the spherical and cylindrical capsules, the heat release performance are almost indepen-dent of void fractions, whereas for the planar and tubular capsules, the heat release velocityfor the smaller void fraction was lower than the larger one.

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