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Energy 76 (2014) 66e72

Contents lists avai

Energy

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

Latent heat storage with tubular-encapsulated phase change materials(PCMs)

H.L. Zhang a,*, J. Baeyens b, J. Degrève a, G. Cáceres c, R. Segal c, F. Pitié d

aDepartment of Chemical Engineering, Chemical and Biochemical Process Technology and Control Section, Katholieke Universiteit Leuven, Heverlee,Belgiumb School of Engineering, University of Warwick, Coventry, United KingdomcUniversidad Adolfo Ibáñez, Faculty of Engineering and Science, Peñalolén, Santiago, ChiledWhittaker Engineering Ltd., Stonehaven, Scotland, United Kingdom

a r t i c l e i n f o

Article history:Received 20 November 2013Received in revised form13 March 2014Accepted 16 March 2014Available online 14 April 2014

Keywords:Heat storageLatent heatPhase change materialsNitrate-PCMTube-encapsulationExperiments

* Corresponding author. Tel.: þ32 16 322367; fax:E-mail addresses: Huili.Zhang@cit.kuleuven.be,

L. Zhang).

http://dx.doi.org/10.1016/j.energy.2014.03.0670360-5442/� 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

Heat capture and storage is important in both solar energy projects and in the recovery of waste heatfrom industrial processes. Whereas heat capture will mostly rely on the use of a heat carrier, the highefficiency heat storage needs to combine sensible and latent heat storage with phase change materials(PCMs) to provide a high energy density storage. The present paper briefly reviews energy developmentsand storage techniques, with special emphasis on thermal energy storage and the use of PCM. Itthereafter illustrates first results obtained when encapsulating NaNO3/KNO3-PCM in an AISI 321 tube, asexample of a storage application using a multi-tubular exchanger filled with PCM. To increase theeffective thermal conductivity of the PCM, 2 inserts i.e. metallic foam and metallic sponge are also tested.Experimental discharging (cooling) rates are interpreted by both solving the unsteady-state conductionequation, and by using Comsol Multiphysics. Predictions and experimental temperature evolutions are infair agreement, and the effect of the inserts is clearly reflected by the increased effective thermal con-ductivity of the insert-PCM composite. Application of Comsol to predict the mechanical behavior of thesystem, when melting and associated expansion increase the internal pressure, demonstrates that thepressure build-up is far below the Young’s modulus of the AISI 321 encapsulation and that this shell willnot crack.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction (HTTES) are crucial concepts to implement such solutions, and even

1.1. Energy development and storage techniques

Both theexpected increaseof energyconsumption from148�109

(2008) to 181 � 109 MWh in 2020 [1] and the depleting reserves offossil fuels with their increasing prices, foster the need to recover/capture and store energy, thereby calling upon the development andnew usage of existing and/or new materials. There is still a consid-erable scope for improving industrial energy efficiency, by reducingthermal energy losses (e.g. compressors, evaporators, furnaces, kilns,boilers, etc.), by energy-pinch measures, by process intensificationand by reducing the number of operation units. Co-generation,thermal waste heat recovery and stacked energy use moreoverseem to be key topics in a strategy to improve energy efficiency.Waste heat recovery and high temperature thermal energy storage

þ32 16 322991.zhanghl.lily@gmail.com (H.

traditional or sustainable power plants can use HTTES to improvetheir energy balance, since HTTES increases the flexibility andavailability of heat and electricity.

Besides industrial processes, the sustainable energy sectors(solar, wind, biomass, biogas) also look towards novel energystorage facilities. We need energy e electrical or thermal e but inmost cases where and when it is not available: energy storagetechnologies are essential to efficiently efficient use the fluctuatingenergy sources by matching the energy supply with demand, asrequested by the Alternating Current (A.C.) electricity grid. Thetraditional electricity market is therefore largely based on fuels soldand traded as commodities, and used to generate electricity toinstantaneously match supply with demand. A future electricitysystem predominantly or solely supplied by renewable energysources will therefore find it difficult to meet the fundamentalstability requirement of AC networks unless specific actions, e.g.storage, are taken from Ref. [2]. Within HTTES targets, there is apressing need to develop adequate technologies according to threepriorities (i) the development and use of low-cost materials with a

H.L. Zhang et al. / Energy 76 (2014) 66e72 67

long lifespan and thermo-chemical stability; (ii) the design ofefficient heat exchanger and storage architectures; (iii) the devel-opment of strategies, easily adapted to industrial settings.

Energy Storage (ES) is the storage of some kind of energy thatcan be drawn upon at a later time and usefully re-applied in a givenoperation, thus having the energy production decoupled from itssupply and distribution, and to support the intermittent nature ofproducing alternative energy. An energy storage process is based onthree fundamental steps: charging (loading), storing and dis-charging (releasing) [3]. ES applications thus facilitate energymanagement, help to bridge power supply/needs and powerquality, and increase the system reliability [4]. Energy formsinclude mainly mechanical, chemical, electrical or thermal energy,each answering specific needs [4]. These different energy storageoptions, with their application characteristics, are summarized inFig. 1. They were assessed on their main characteristics by Pitié [5],and have been previously reviewed [4e6]. A novel approach forthermal energy storage uses powder circulation loops, combinedwith encapsulated PCMs [7e9].

In Thermal Energy Storage (TES), heat is transferred to storagemedia during the charging period, and released at a later stageduring the discharging step, to be usefully applied e.g. in generatinghigh pressure steam in solar power plants [10,11], or as heat carrierin high temperature industrial processes. In terms of storagemedia,a variety of choices exists depending on the storage systemselected, the temperature range and the specific application. Sen-sible heat storage has a lower storage capacity and efficiency thanPCMs. In most cases, storage is based on a solid/liquid phase changewith energy densities in the order of 100 kWh/m3. Thermo-chemical storage (TCS) systems can reach storage capacities ofw250 kWh/t, with efficiencies between 75% and nearly 100%.

Low temperature thermal energy storage (LTTES) (<200 �C) hasbeen extensively investigated and developed for cold applicationsin building cooling, or moderate temperature applications inbuilding heating, solar cooking, solar water boilers and air-heatingsystems, and in solar greenhouses. High temperature thermal en-ergy storage (HTTES) plays a vital role in renewable energy

Fig. 1. Energy storage techniques in terms of discharge rate and

technologies and waste heat recovery, with a wide range of in-dustrial applications where waste heat can be recovered, as in themanufacturing of construction materials (e.g. clay brick or cementkilns) and in the metallurgical industry [12]. Today, most HTTESapplications focus solar thermal energy [10,11,13e15] TES applica-tions are the subject of constant innovative research and designs asshown in the numerous reviews [e.g. 3,16,17]. HTTES is attractivefor improving the efficiency of industrial processes and solar en-gineering, provided they operate stably in a high range of tem-peratures, use storage media that are inexpensive, widely availableand compatible with a cost-effective system design [3]. Other re-quirements were presented by Zalba et al. [17]. Meeting all theserequirements needs innovative engineering approaches shaped bythe development and research into the fields of storage media.

Solid and liquid Sensible heat storage materials undergo nophase change within the temperature range [18,19]. It appears thatthe main candidates for liquid sensible heat storage are mineraloils or binary and ternary salt eutectics [20]. Disadvantages of saltsare their low solidification point (around 200 �C), whilst alsorequiring both more expensive piping materials and heat tracing.Furthermore, the sensible fraction of thermal energy is seldomfully recovered due to the required temperature difference as heattransfer driving force. The low energy storage density of sensibleheat materials moreover implies the use of large volumes orquantities in order to deliver the amount of energy storagenecessary for HTTES applications. Supercritical CO2 and H2O arestill in development, although results of the first s-CO2 applicationin Australia are very promising [21]. To replace the molten salt oroil circulation, powder circulation systems are proposed [7e9]since powders have virtually no lower and higher temperaturelimitation, have a specific heat comparable to molten salts, henceproviding a high storage capacity per unit weight due to thehigher operating DT, and finally a highly efficient boiler operation [w90%].

Despite its high energy density, Thermo-chemical heat storageis considered to be an expensive alternative and is, at the present, atearly stages of development [22].

system power rating (adapted from http://liquidair.org.uk).

Fig. 2. Schematic of the experimental rig. ①: PCM container, AISI 321, wall thickness1.5 mm, H/D w1; ②: Lid, AISI 321, wall thickness 1.5 mm; ③: Molten PCM, with orwithout inserts; ④: Picolog temperature logger to PC ⑤; ⑥: Inlet cooling fluidium; ⑦:Outlet cooling fluidium; ⑧: Concentric cooling vessel, with thermal insulation; T:Thermocouples; F: Flowmeter.

Fig. 3. Temperature at the axis of the cylinder (r ¼ 0) versus time cooling of the E-PCM(nitrates).

H.L. Zhang et al. / Energy 76 (2014) 66e7268

Latent heat storage is based on the heat absorption or heatrelease that occurs when a storage material undergoes a phasechange. Solideliquid transition is considered to be more efficientthan liquidevapour and solidesolid transitions. The main charac-teristics required for PCMs are a combination of thermal, physical,chemical and economic factors [23,24], PCMs include both organic(low Tapplications) and inorganic (moderate to high Tapplications)substances. Most of PCMs have a low thermal conductivity, leadingto low charging and discharging rates. In addition to adaptingPCM’s melting points to a high temperature range, the efficiency ofthe charging and discharging processes needs to be improved, withseveral heat transfer enhancement techniques previously proposed[25e28], such as: (i) the use of metal carrier structures made ofsteel or stainless steel; (ii) a dispersion of high conductivity ma-terial i.e. copper, silver or aluminium particles, within the PCM; (iii)the impregnation of high conductivity porous materials, either as ametal foam (copper, steel or aluminium), or as porous material likegraphite; (iv) the use of high conductivity, low density materialssuch as carbon fibres and paraffin composites; and (v) the micro-encapsulation of PCMs using graphite or polymers, or nickelcoating of PCM copper spheres for high T applications [29-31].Although the micro-encapsulation of PCM has been used to pro-duce slurries or for building applications, e.g. Refs. [32,33], it hasnot been used yet for high T purposes. Nano-composites haverecently been added in the research topics [34e37].

1.2. Objectives of the research

A 2012 paper [16] assessed the state-of-the-art in high tem-perature energy storage and established the needs for futuredevelopment to assure a breakthrough. These needs include thedevelopment of high capacity storage systems, using sensible andlatent heat storage media. Phase changes in solids (meltingeso-lidification) involve a major heat of transformation, and proposedPCM storage facilities have been reviewed by e.g. Zalba et al. [17].The encapsulation of PCMs in a tubular heat exchanger appears tooffer a straightforward solution, with the design of heat exchangerswell-known to engineers. The present paper considers the onthermal energy storage by using of a PCM. It will illustrate firstresults obtained when encapsulating NaNO3/KNO3-PCM in an AISI321 tube, as example of a heat storage application using a PCMtubular heat exchanger, and will discuss the results in terms ofachieved discharging (cooling) rates.

2. Experimental investigation of an encapsulated PCM

The experimental set-up to determine the heat transfer char-acteristics of a PCM, encapsulated in an AISI 321 tube, is illustratedin Fig. 2.

A closed cylindrical vessel, containing the PCM, is preheated inan electric furnace to a pre-defined temperature whereby the PCMis completely molten. The cylinder is then introduced into an openconcentric vessel having connections for cooling air, water or even athermal fluid (oil). The continuous and monitored flow of thecooling medium in the concentric space guarantees an efficient E-PCM cooling. Thermocoax thermocouples (0.5 mm O.D.) areinserted into the PCM at fixed positions, i.e. in the centre and/or at a1/2-distance from the central axis. The decrease in temperature infunction of time is recorded (Picolog and PC).

The accuracy on the time measurement is 1 s. The thermocou-ples were calibrated at 0 �C and 100 �C, and the uncertainty is 0.1 �C.The relative errors on both temperature (>160 �C) and time (up to3600 s), as illustrated in Fig. 3 are hence negligible.

Initial investigations used a 60 wt% NaNO3, 40 wt% KNO3eutectic PCM mixture (Tm ¼ 230 �C), with air and water cooling. To

study heat transfer enhancement, metallic foam and metallicsponge were inserted in the PCM. Three E-PCM cylinders (AISI 321)were used, 27.3, 75 and 39 mm O.D., with respective height 27.7, 77and 37 mm. With this geometry (H/D w 1) the mathematicaltreatment as equivalent sphere (having the same ratio of externalsurface to volume) is widely applied and acceptable, since thesphericity of such a cylinder, defined as the ratio of the surface areaof the equivalent volume sphere and the surface area of the particle,is about 0.9 [38,39]. Ongoing investigations deal with additionalPCM, such as Sb2O3 (Tm ¼ 655 �C), NaOH/NaCl/Na2CO3(Tm ¼ 318 �C), and others. For the Na/K-nitrates, the cylinder of75 mm O.D. was mostly used. The properties of the investigatednitrate-system are listed in Table 1.

Fig. 4. Geometry of an E-PCM sphere of PCM and AISI coating (R0, R, respectively outerand inner diameter of the inert shell).

H.L. Zhang et al. / Energy 76 (2014) 66e72 69

The experiments were repeated 5 times for each sub-system.Deviations of T versus t between the 5 repeat experiments wereoverall within 3%. Average results are presented in Fig. 3.

The experimental results illustrate the effect of different pa-rameters. The temperature of phase change is not a constant 230 �C,as obtained when a substance that solidifies is pure. With mixtures,the solidification takes place over a range of temperatures, andthere appears a two-phase zone, sometimes referred to as the“mushy region” [17], between the solid and liquid zones.

The effect of inserts, metallic foam or metallic sponge is evident,with a clear shorter discharge rate as a result. The cooling curvewith forced water cooling (hence with a far higher external heattransfer coefficient) is very steep, and the temperature decreasesfrom 270 �C to 160 �C in less than 700 s (against 2500e3700 s whenair cooling is applied). This external heat transfer coefficient is animportant parameter of the Biot-number: as will be shown below,the inverse Biot-number is an important dimensionless group thatfixes the rate of cooling.

3. Data treatment

3.1. Fundamental hypotheses

Fig. 4 represents the geometry of an E-PCM sphere, with anitrate-PCM and AISI coating (R0, R, respectively, outer and innerdiameter of the inert shell). The inner radius (r) represents thedecreasing radius as the PCM melts, and hence delineates the solidpart of the salt.

Within the temperature range under consideration (see Fig. 3,i.e. 270e230 �C for the PCM as liquid, and 230-160 �C for the solidPCM), it is assumed that the salts have a constant density r, specificheat cp and thermal conductivity k, independent of pressure andtemperature. The liquid pressure within the shell is uniform. Thesalt in its solid state can be considered as homogeneous, withconstant values of density r, and being non-deformable.

The shell wall (AISI 321) is considered to be homogeneous,isotropic and present at a known and uniform temperature. At theinterfaces, an equality of phase temperature and heat flux conti-nuity at the melting front, and an equality of temperature andpressure at the shell/salt interface are accepted. It is moreoverassumed that the corrosion between the shell and salts is negli-gible. This assumption is not trivial since chemical reactions occurbetween metals and salts (in different degrees depending on the

Table 1Properties of the nitrate-system.

Property System compound

Na/KeNO3

Liquid SolidCp (kJ/kg K) 1.11 0.93m (kg/ms) 0.003[f(T)] e

k (W/mK) 0.45 0.78r (kg/m3) 2096 2192

Encapsulating cylinder AISI321

O.D. (mm) 75Wall thickness (mm) 1.5Height (mm) 77k (W/mK) 17Cp (kJ/kg K) 0.51Equivalent sphere diameter (mm) 75.7

Metallic foamPPI 50Porosity 0.95k (W/mK) 17

Metallic spongePorosity 0.9k (W/mK) 17

metal), and high temperatures and pressures affecting the mate-rials could alter the material’s properties. This is currently exam-ined by submitting the E-PCM to up to 5000 heating and coolingcycles, whilst defining the mechanical properties by destructivetesting of the shell at set intervals (every 500 cycles).

3.2. Application of the unsteady-state conduction approach

The unsteady-state conduction involves a material temperatureto be dependent on both time and spacial coordinates. The corre-sponding differential equation in spherical coordinates takes theform of:

vTvt

¼ a

r2v

vr

�r2vTvr

�(1)

with temperature T, time t, radial position r, and thermal diffusivitya (m2/s) ¼ k/rcp.k ¼ thermal conductivity of the PCM (W/mK)r ¼ density of the PCM (kg/m3)cp ¼ specific heat capacity of thePCM (J/kg K)

The analytical solution of Eq. (1) is given by numerous articlesand textbooks, e.g. Carslaw and Jaeger [40] and Smith [41] forconstant physical properties. The solution results in the predictionof the temperature at a given point in the body at time t, measuredfrom the start of the cooling or heating operations, ad including 3dimensionless parameters, being:

s ¼ ktrcpR2

¼ atR2

ðFourier-numberÞ (2)

1Bi

¼ khR

ðInverse Biot-numberÞ (3)

h ¼ external heat transfer coefficient (W/m2K)

n ¼ rR

dimensionless distance in the direction of

the heat conduction:(4)

3.3. The use of Comsol Multiphysics

Differentmodels havemoreover been used, andwere previouslyreviewed by Quintard andWhitaker [42e44] and by Ahmadia et al.[45]: these treatments dealwith heterogeneous porousmedia usingthe volume averaging method in the transport equations of mo-mentum, mass and energy. In this context, heat storage models are

Table 3Calculated effective thermal conductivity (W/m K) of the PCM-insert composite.

System N� . 1 N� . 2 N� . 3 N� . 4 Average

Nitrate melt þ foam 0.565 0.496 0.485 0.522 0.517Nitrate solid þ foam 0.965 0.869 0.851 0.914 0.900Nitrate melt þ sponge 0.710 0.547 0.532 0.602 0.598Nitrate solid þ sponge 1178 0.955 0.932 1050 1.029

H.L. Zhang et al. / Energy 76 (2014) 66e7270

trying to improve the efficiency of a PCMassessment, by simulationswith specific boundary conditions. Such models were developed byLopez et al. [46,47] and later extended by Pitié et al. [48], presentingthe confined melting in composite materials made of graphite-nitrates and ceramic-nitrates respectively. These authors includedphase change models accounting for the pressure effects of themolten salt within the thermo-mechanical matrix. In this context,an AISI 321 steel and nitrates composite is used in the present paper,considering the better mechanical strength in comparison withpreviously studied graphite composites. As performed within thecited papers, a first attempt is made to understand the salt meltingwithin the AISI 321 steel sphere, by providing an appropriatethermo-mechanical treatment using Comsol Multiphysics (2013)software, offering additional calculationprocedures such as internalpressure build-up due to the thermal expansion of the PCM. ComsolMultiphysicswas used to assess the behavior through the procedureof “Thermal Stress contains Heat Transfer and Solid Mechanicsphenomena”, necessary to obtain values to validate the model. Inorder to provide results with a minimum error range, it uses anextra-finemesh of 6046, will be presented hereafter. Both analyticaland Comsol predictions will be illustrated in the following section.

3.4. The effect of inserts to enhance the heat transfer: the effectivethermal conductivity

In order to predict the effective thermal conductivities of thePCM when inserts (foam, sponge) were present, a series of empir-ical correlations was used, as listed in Table 2. The symbols keff, kPCMand kin represent, respectively, the effective thermal conductivity ofthe composite mix, the thermal conductivity of the PCM itself, andthe thermal conductivity of the insert. The porosity, 3, representsthe void space (PCM-filled) of the composites.

Predicted values for the composite systems are given in Table 3.The deviations of the different predicted values and the averagevalue are within �10%. The inserts clearly increase the thermalconductivity of the composite, with sponge (porosity 0.9) having aslightly higher effect that the metallic foam. Thermal conductivitiesof the nitrate as melt or solids were given in Table 1 as respectively0.45 and 0.78 W/m K.

The effective conductivity when foam is present is w15% higherfor both molten and solid PCM. When metallic sponge is present,the effective thermal conductivity increases by 32%.

4. Discussion

4.1. Discharging rate (temperature in function of time)

Fig. 3 illustrates that the discharging rate of both liquid and solidPCM is a function of two main parameters:

- the presence of inserts (metallic foam or metallic sponge) has alimited effect on the cooling rate of the liquid salt. It, however,significantly reduces the time associated with the phase change(at temperature of 230 �C) which is associated with the action of

Table 2Equations for the effective conductivity of the PCM and insert-composites.

N� . Ref. Equation (keff)

1 [49] k 3PCM � kð1� 3Þ

INS2 [50,51] kPCM

hkINSþ2kPCM�ð1� 3Þ�ðkPCM�kINSÞkINSþ2kPCMþð1� 3Þ�ðkPCM�kINSÞ

i3 [52]

kPCM

"1�

ffiffiffiffiffiffiffiffiffiffið1� 3Þ3

pþð1� 3ÞþkPCM

kINS�½

ffiffiffiffiffiffiffiffiffiffið1� 3Þ3

p�ð1� 3Þ�

1�ffiffiffiffiffiffiffiffiffiffið1� 3Þ3

pþkPCM

kINS�

ffiffiffiffiffiffiffiffiffiffið1� 3Þ3

p#

4 [53]kPCM

�kINSþ

�3j�1

�kINS�

�3j�1

�ð1� 3ÞðkPCM�kINSÞ

kINSþ�3j�1

�kINSþð1� 3ÞðkPCM�kINSÞ

�

the inserts as nuclei for crystal formation. Once the phasechange is completed, temperature reduction rates of all exper-imental results with air cooling are nearly parallel.

- the difference in air and water cooling is outspoken. This is re-flected in the external heat transfer coefficient being onlyw30 W/m2 K for air cooling, and w1000 W/m2 K in the case ofwater cooling. This reflects itself in a significant reduction of theinverse Biot-number, and according to the solution of the un-steady-state conduction equation, in significantly shorter cool-ing times. The period of phase change is moreover not at alloutspoken and short in comparison with the air-cooled results.

- within the temperature range under consideration, cooling ratescan be fairly well represented by a linear temperature versustime approximation. This results in an expression of therespective cooling rates as DT/Dt (�C/s), which provides atentative method of comparison as presented in Fig. 5.

The effect of the metallic inserts is clearly demonstrated bycomparing the values of DT/Dt, which approximately increaseproportionally with the increased thermal conductivity of thecomposite system, metallic sponge being more efficient thanmetallic foam.

4.2. Comparison of experimental (T, t) results with theoreticalpredictions

Although the theoretical treatment of the different systemstested is ongoing, Fig. 6 illustrates the preliminary comparison ofthe data for the PCM without inserts and being air-cooled, withpredictions by both the unsteady state conduction and Comsolapproaches.

In the simulation approach, the main uncertainty is due to therelative errors associated with the physical and geometrical prop-erties used.

Fig. 5. Comparison of the DT/Dt (�C/s) for the various set-ups. Air cooling of liquid PCM(1) no inserts; (2) metallic sponge; (3) metallic foam. Air cooling of solid PCM (4) noinserts; (5) metallic sponge; (6) metallic foam. Water cooling of (7) liquid PCM þ foam;and (8) solid PCM þ foam.

Fig. 6. Comparison of experimental temperature vs. time curves and predictions bysolving the unsteady-state conduction equation, and as predicted by ComsolMultiphysics.

Fig. 7. Pressure versus fraction of liquid phase.

H.L. Zhang et al. / Energy 76 (2014) 66e72 71

The calculated T versus t profiles are obtained from solving Eq.(1), providing a relationship between:

(i) a dimensionless temperature, Y, being equal to (T � Tx)/(T0 � Tx) with T the varying temperature at time t and radialposition r, and T0 and Tx being two selected reference tem-peratures (at t ¼ 0, and r ¼ R, respectively). Y can vary from0 to 1;

(ii) a dimensionless time, X, expressed by Eq. (2) as X ¼ (kt)/(rCpR2). X can vary from 0 to N.

Since T0 and Tx are selected, they are not subject to a mea-surement error. The relative error on Y is hence limited todY ¼ d(DT)/(T0 � Tx) ¼ dT/(T0 � Tx). With dT ¼ 0.1 K, and (T0 � Tx)w100 K, dY is below 0.1% meaning that the error on the T calcula-tions is negligible.

Towards the error on X, the sum of errors needs to be consid-ered, with to dX/X ¼ P

d(xi)/xi ¼ d(k)/k þ d(t)/t þ d(r)/r þ d(Cp)/Cp) þ 2d(R)/Ri

The uncertainties on the different properties are 0.01W/m K (k),2 kg/m3 (r), 0.01 kJ/kg K (Cp), 1 s (t) and 0.05 mm (R).

Using the average properties of Table 1, the relative error on Xvaries between 3.3 (liquid salt) and 2.6% solid salt) only.

The overall error on the calculated T versus t profile is thereforevery low, meaning that the measured and simulated results areconsidered to be in very good agreement.

The major observations provide some insight in the occurringphenomena:

- clearly, the theoretical calculation of the cooling rate of theliquid PCM underestimates the experimental temperaturegradient. This is due to the fact that only conduction is taken intoconsideration, whilst natural convectionwithin the liquid phasealso contributed to the heat transfer. When calculating theRayleigh-number within the salt, values exceeding 107 are ob-tained, significantly above the threshold 1700 normally given forthe onset of natural convection. This will be further investigatedby comparing buoyancy and drag forces within the melt. Since itis difficult to predict the contribution of the natural convection,a solution as proposed by Zalba et al. [17] might be appropriate:the melt is characterized by an effective thermal conductivity,exceeding the thermal conductivity as such. An expression of

this effective thermal conductivity could not be obtained yet,but it should indeed be expressed as

ktotal ¼ kmelt � f ðRayleigh numberÞ (5)

From the results, the value of the f(Rayleigh) is between 1.2 and1.4, but further refining is required.

- the Comsol predictions of the temperature evolution are verypromising, again with an underestimation of the cooling in theliquid phase, but a close prediction of the periods of phasetransformation and solid’s cooling.

4.3. Mechanical behavior of the system

During the heating cycle, the expansion during melting creates apressure within the encapsulating shell. Comsol enables the pre-dictionof this pressure.During thecoolingprocess,when the fractionof liquid phase gradually decreases from 1 (completely molten) to0 (completely solidified), the pressure decreases with time (andhencewith inherent temperature), as shown in Fig. 7. Themaximumpressure achieved, i.e. 0.85 GPa, is far below the Young’s modulus ofAISI 321 stainless steel (w10 GPa), being the transition to a plasticbehavior of the steel. At the tested temperatures, the steel is more-over far below itsmelting point. It is hence evident that the shell willnot crack during the heatingecooling cycles. This is currentlyinvestigated by cycling E-PCMs for up to 5000 heatingecooling cy-cles, followed by destructive testing at an interval of 500 cycles.

5. Conclusions

The thermo-mechanical model of a PCM coated in a sphericalstainless steel shell was experimentally and theoretically examinedduring the discharging cycles.

Theoretical predictions and experimental data are in fairagreement, although the addition of natural convection in the meltneeds further investigation.

The volume expansion upon melting and associated pressureincrease is significantly below the acceptable mechanical proper-ties of the shell and shell cracking is not expected to occur.

The novel encapsulated salt was proven to be an attractivematerial for heat storage. Ongoing studies will complete the

H.L. Zhang et al. / Energy 76 (2014) 66e7272

theoretical treatment, will assess the mechanical properties of theshell as a function of the number of hotecold cycles, and willinclude the effect of rising pressures on salt’s properties (assumedconstant in the present first approach).

Acknowledgement

This work was supported by the projects CONICYT/FONDAP/15110019 (SERC-CHILE), CONICYT/FONDECYT/1120490 and by theCenter for the Innovation in Energy of UAI. Authors moreoveracknowledge the European Commission for co-funding the “CSP2”Project e Concentrated Solar Power in Particles e (FP7, Project N�

282 932).

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