Renewable Energy 34 (2009) Contents lists available at ScienceDirect. Renewable Energy. journal homepage:

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1 Renewable Energy 34 (29) Contents lists available at ScienceDirect Renewable Energy journal homepage: An analysis o a packed bed latent heat thermal energy storage system using PCM capsules: Numerical investigation A. Felix Regin *, S.C. Solanki, J.S. Saini Mechanical & Industrial Engineering Department, Indian Institute o Technology Roorkee, Roorkee , UA, India article ino abstract Article history: Received 26 January 28 Accepted 9 December 28 Keywords: PCM capsule Phase change material Parain wax Latent heat thermal energy storage Solidiication Melting This paper is aimed at analyzing the behavior o a packed bed latent heat thermal energy storage system. The packed bed is composed o spherical capsules illed with parain wax as PCM usable with a solar water heating system. The model developed in this study uses the undamental equations similar to those o Schumann, except that the phase change phenomena o PCM inside the capsules are analyzed by using enthalpy method. The equations are numerically solved, and the results obtained are used or the thermal perormance analysis o both charging and discharging processes. The eects o the inlet heat transer luid temperature (Stean number), mass low rate and phase change temperature range on the thermal perormance o the capsules o various radii have been investigated. The results indicate that or the proper modeling o perormance o the system the phase change temperature range o the PCM must be accurately known, and should be taken into account. Ó 28 Elsevier Ltd. All rights reserved.. Introduction Even though the problem o thermal energy storage within a capsule has been extensively studied, very little inormation is available on its perormance in the case o latent heat thermal energy storage packed bed systems consisting o such capsules. The packed bed latent heat thermal energy storage systems have been used or applications such as, solar thermal energy storage, low temperature storage systems or central air conditioning, energy eicient buildings and waste heat recovery systems []. Such systems have the advantage o large surace to volume ratio o the packed beds and o higher storage density or the phase change materials compared to conventional bulk storage in tank heat exchangers and sensible heat storage systems. A storage system operates in three modes as ollows... Charging mode The charging mode starts with circulation o the heat transer luid heated in the collection system at a temperature higher than the PCM melting temperature. This mode occurs during day time when solar energy collection takes place and terminates with * Corresponding author. Tel.: þ ; ax: þ addresses: elixregin@gmail.com, elixregin@redimail.com (A. Felix Regin). complete melting o the PCM, charging o the store does not terminate with complete melting o the PCM i the inlet luid temperature is above the melt temperature, charging o sensible heat continues..2. Discharging mode The discharging mode is started by circulation o the cold heat transer luid having inlet temperature lower than the PCM melting temperature. The heat transer luid exit temperature is time dependent because the rate o solidiication o the PCM varies with time. This mode terminates with complete solidiication o the PCM..3. Stand by mode This mode occurs when there is no urther storage o energy occurring because o decreasing heat transer luid temperature or the storage tank is completely charged or the energy is directly ed to the utility without using storage and/or no heating rom the bed is required. This is the transition period between the charge and discharge modes. The major actors to be considered in the design o a storage unit containing a PCM include: () temperature limits within which the unit is to operate; (2) the thermophysical properties o the PCM; (3) the storage capacity o the tank; (4) the coniguration o the storage 9-48/$ see ront matter Ó 28 Elsevier Ltd. All rights reserved. doi:.6/j.renene

2 766 A. Felix Regin et al. / Renewable Energy 34 (29) Nomenclature A surace area o capsule, m 2 C p speciic heat, J/kg K D diameter o the bed, m D c diameter o the capsule, m (DT) m solid liquid phase change range, C (DT) p solid solid phase change range, C Dx element thickness, m H speciic enthalpy, J/kg h outer convective heat transer coeicient, W/m 2 K k thermal conductivity o PCM, W/m K k c thermal conductivity o capsule material, W/m K L latent heat o melting, J/kg l length o the bed, m L p latent heat o solid solid phase change, J/kg m mass o PCM, kg _m mass low rate o heat transer luid m total mass o heat transer luid in the bed, kg N number o elements in the bed Nu Nusselt number Q ch charged energy o the tank, kj Q dis discharged energy o the tank, kj Q total total energy storage capacity o the tank, kj Re Reynolds number R ext thermal resistance due to convection on the external surace o the capsule shell R c thermal resistance due to conduction through the capsule wall R in (t) resistance due to the solidiied/melt PCM layer inside the capsule Ste Stean number, C pl (T T m )/L T b bed temperature, C T b average temperature o the bed, C T c average temperature o capsules in the bed, C T heat transer luid temperature, C T average heat transer luid temperature o the bed, C T m melting temperature, C T p solid solid phase change temperature, C T w capsule wall temperature, C T inal inal temperature o the bed, C T initial initial temperature o the bed, C T N environment temperature, C t time, s U o overall heat transer coeicient o capsule, W/m 2 K U s overall heat transer coeicient o storage tank outer wall, W/m 2 K U v overall volumetric heat transer coeicient, W/m 3 K u supericial velocity in the bed, m/s X l melt raction o the bed, % X s solid raction o the bed, % X t total melt or solidiied raction o the bed, % r b density o bed, kg/m 3 r density o heat transer luid, kg/m 3 3 porosity Subscripts B bed heat transer luid l liquid PCM s solid PCM unit; (5) the type o heat transer luid and (6) pressure drop and pumping power. It is generally reported in the literature that the irst analytical study on modeling o the packed bed was conducted by Schumann [2] and most o the work reported till date has been ocused on Schumann s model. Laybourn [3] predicted the heat transer rates o cold storage tank during charging and discharging or building cooling applications with rectangular capsules using the concept o thermal resistance, which comprised o the convective resistance, wall resistance and ice layer resistance. Ismail and Henriquez [4] presented a mathematical model or predicting the thermal perormance o the cylindrical storage tank containing spherical capsules illed with water as PCM. The model was used to investigate the inluence o the working luid entry temperature, the low rate o the working luid and material o the spherical capsule o 77 mm diameter during the solidiication process. Arnold [5] has investigated the melting and reezing process o water as PCM within spherical capsules at macro- (storage tank) and micro- (single capsule) levels, separately and linking them by the heat transer across the capsule wall. Bedecarrets et al. [6,7] have investigated the ice storage tank using spherical capsules. They took into account the supercooling phenomenon during solidiication o water. The low pattern inside the tank and the eects o the position o the tank, coolant low rate and inlet temperature on the perormance o cold storage have been discussed. Jotshi et al. [8] studied the thermophysical properties o Alum/Ammonium Nitrate Eutectic or solar space heating applications and investigated the perormance o a packed bed system when the eutectic is encapsulated in.254 m diameter high density polyethylene balls and concluded that the Stanton number empirical equation or a typical packed bed thermal system ails i there is a phase change in the bed material. Chen et al. [9 ] developed a one dimensional porous medium model and a lump model assuming temperature uniormity in packed capsules to determine the thermal perormance o a low temperature storage system during the solidiication process. Recently, Cho and Choi [2] and Goncalves and Probert [3] conducted experiments on the reezing and the melting o parain and MgCl 2 $6H 2 O respectively. Most o the aorementioned investigations do not consider the non-isothermal behavior o the phase change process. The major objective o the present study is to investigate the eect o phase change temperature range on the perormance o the packed bed latent heat thermal energy storage system consisting o spherical capsules or solar water heating applications. The eects o size o the capsules, inlet heat transer luid temperature and luid low rate have been discussed or charging and discharging processes. 2. Numerical analysis Fig. shows the layout o the physical system that has been investigated. Assumptions involved in the present study are:. The tank is insulated and vertical with low rom the top when charging and low rom the bottom when discharging. 2. The low in the tank is axial and incompressible. 3. The thermophysical properties o the heat transer luid are invariant with temperature. 4. The porosity o the bed, which is deined as the ratio o the void volume to the total volume o the packed bed, is.4 [4].

3 A. Felix Regin et al. / Renewable Energy 34 (29) T iþ T bi T i T bi or T i T iþ T i T bi NTU ¼ exp N NTU ¼ exp N (5) (6) The outlet temperature o heat transer luid or ith element is: NTU T iþ ¼ T i T i T bi exp (7) N 5. Variation o temperature is only along the axial direction, i.e. the temperature is independent o radial position. 6. The tank o length l has been divided into N elements o suiciently small length l/n so that the element can be assumed to be at a single temperature. 7. Radiant heat transer between the capsules is negligible. 8. There is no internal heat generation in the bed. The packed bed column is divided into N elements, each containing PCM capsules surrounded by heat transer luid. The energy balance on an element o volume ADx having PCM at a temperature T b and the heat transer luid lowing at the rate o _m and entering at a temperature T can be written as _mcp T _mc p þ U s pddx T þ vt vx Dx T T N ¼ U v ADx T T b þ r ðadxþ3c p; vt vt The let hand side o Eq. () represents heat low by the movement o heat transer luid. The irst and second terms on the right hand side represent the heat exchange between the capsule and heat transer luid and heat loss to the environment respectively. The last term o Eq. () represents the rate o stored energy o the heat transer luid in the control volume. In case, the heat losses can be neglected (the storage tank is considered to be well insulated) and the energy stored in the heat transer luid is negligibly small, the energy balance at an instance o time becomes. _mcp T _mc p T þ vt vx Dx U v ADx T T b ¼ (2) or vt vx ¼ U va T T b _mcp On simpliication vt. ¼NTU T T b v x l Fig.. Layout and details o the storage system. where NTU½¼ ðu v AlÞ=ðð _mc p Þ ÞŠ is the number o transer units. Integration yields ðþ (3) (4) where T i is the heat transer luid temperature at inlet to the element, T iþ is the heat transer luid temperature at outlet rom the element, T bi represents the bed temperature o the element and N ¼ =Dx is the number o elements in the packed bed. Eq. (7) can be written or each control volume orming a system o N simultaneous equations. The NTU value and bed temperature o the element (T bi ) can be determined by knowing the volumetric heat transer coeicient and the energy transerred into the PCM capsules. This can be explained as ollows: The volumetric heat transer coeicient or thermal storage system can be written as [5]: U v ¼ 6U o ð 3Þ=D c (8) For the capsule, the outer surace overall heat transer coeicient, U o Eq. (8), is a unction o the mode (either charging or discharging), the state o the PCM capsule in the control volume (ully liquid, ully solid, or phase change processes) and the mechanism o heat transer (conduction, convection or combined conduction and convection). During the ully liquid or ully solid stages, the overall heat transer coeicient can be calculated by using thermal resistance concept or each capsule as given below: U o ¼ð=AÞðR ext þ R c Þ (9) where R ext is the convective thermal resistance on the external surace o the capsule shell and R c is the conductive thermal resistance through the capsule wall. During the phase change process the outer surace overall heat transer coeicient can be calculated by using thermal resistance concept or each capsule as given below: U o ¼ð=AÞðR ext þ R c þ R in ðtþþ () where R ext is the thermal resistance due to convection on the external surace o the capsule shell, R c is the thermal resistance due to conduction through the capsule wall and R in (t) is the resistance due to the solidiied/melt PCM layer inside the capsule. It is a unction o time. The external resistance R ext between the capsule wall and the heat transer luid depends on the porosity o the bed, heat transer luid properties and the Reynolds number o the heat transer luid low and can be determined rom the Nusselt number correlation proposed by Wekaeo et al. [6] as Nu Dc ¼ 2: þ :½6ð 3ÞŠ :6 ReD :6 c Pr =3 () The Reynolds number Re Dc can be obtained rom the relation Re Dc ¼ rud c =m where D c is the capsule diameter and u is the supericial velocity in the bed. The internal resistance o the capsule R in (t) depends on the solid liquid interace position which can be calculated by using one dimensional heat conduction model with phase change as derived by the authors in reerences [7,8] or the solidiication and

4 768 A. Felix Regin et al. / Renewable Energy 34 (29) reerences [9,2] or melting o PCM inside cylindrical and spherical capsules respectively. The bed temperature is calculated by using the energy balance between the heat transer luid and the bed. The energy transerred to the bed, U v ADxðT T b Þ, results in raising the bed temperature at the rate o dt b =dt written as dt U v ADx T T b ¼ r b ðadxþð 3ÞC b p;b dt For simpliication, multiply by ððalþ=ð _mc p Þ Þ on both sides U v T T b Al _mcp! ¼ rc p b ð 3ÞdT b dt Al _mcp! (2) (3) Since NTU½¼ ðu v AlÞ=ðð _mc p Þ ÞŠ, this equation can be written as rcp ð 3ÞAl b _mcp dt b dt ¼ NTU T T b (4) Eq. (4) can be discretized or ith element by using simple explicit and irst order inite dierence ormulation [2], and can be written as rcp ð 3ÞAl b _mcp T nþ bi T n bi T nþ bi Tbi n Dt ¼ NTU Ti n Tn bi rcp b ð 3ÞAl ¼ _mc p Dt$NTU Ti n Tn bi (5) (6) This energy balance equation can be applicable only to the sensible heat storage materials and can be converted to enthalpy equation that can be applicable to the phase change storage bed material as H nþ bi H n bi rb ð 3ÞAl ¼ _mc p Dt$NTU Ti n Tn bi (7) Heat low, W L p = 3 kj/kg (solid - solid) T p = 43.9 C (smaller peak) T (m-e) = 52.9 C (solidus point) T m = 59.9 C (larger peak) Fig. 2. DSC signal or the parain wax used. (ii) When PCM is in solid solid phase: As the phase change occurs over a range o temperature T ðpaþ to T ðpþa2þ the enthalpy or the phase change is calculated by dividing the latent heat L p or complete solid solid phase change by the range o temperature and multiplied by the actual temperature change, i.e. ððl p Þ=ða þ a 2 ÞÞðT T ðpaþþ L p H ¼ C ps T þ T T ða þ a 2 Þ ðpaþ T (m+e2) = 6.6 C (liquidus point) L = 9 kj/kg (solid - liquid) T ðpaþ < T < T ðpþa2þ (2) (iii) When PCM is in the above solid phase change temperature range but below the melting temperature range: H nþ bi ¼ _mcp r b ð 3ÞAl Dt$NTU Ti n Tn bi þ Hbi n (8) H ¼ C ps T þ L p T ðpþa2þ T T ðmeþ (2) Using this equation, enthalpy o bed in the element at particular time can be determined by using the known enthalpy values in the previous time period. This equation is valid at all elements at a particular time. The phase change material used in this study is a technical grade Parain wax o congealing point 58 C with a purity o 99%. For determining the behavior o the PCM during melting process the measurements have been perormed with TA Instruments Dierential Scanning Calorimeter (DSC) 29 module with a liquid nitrogen cooling system. The DSC curve or melting o the parain wax is shown in Fig. 2. It is seen that there exist two peaks, the larger peak is due to solid liquid phase change and the smaller peak due to solid solid phase transition at about C below the main melting temperature range. The phase change process o parain wax can be divided into ive sub-processes, i.e. solid phase, solid solid phase change in temperature range, above the solid phase change temperature range but below the melting temperature range, solid liquid phase change in temperature range and the liquid phase. The corresponding enthalpy temperature (H T) relations are: (i) When PCM is in solid phase: H ¼ C ps T T T ðpaþ (9) (iv) When PCM is in the solid liquid phase: This occurs in a temperature range T ðmeþ to T ðmþe2þ, the latent heat L is similarly assumed to be supplied over this range and enthalpy is accordingly written as: L H ¼ C ps T þ L p þ T T ðe þ e 2 Þ ðmeþ (v) When PCM is in the liquid phase: T ðmeþ < T < T ðmþe2þ (22) H ¼ C ps ðt m T initial ÞþC pl T inal T m þl p þl TT ðmþe2þ (23) The bed temperature T b can be evaluated as a unction o H b, i.e. by employing the enthalpy as the dependent variable and temperature as the independent variable. The temperature distribution o all the elements in the bed is predicted at an instant o time by knowing the enthalpy values in each element. Temperature distribution o the bed as unction o location o the storage tank

5 A. Felix Regin et al. / Renewable Energy 34 (29) and time can indicate the amount o energy stored as well as the stratiication in the bed. The melt/solidiied raction o an element can be calculated based on the temperature o bed at a particular time. The total melt raction or solidiied raction in a storage tank represented by integrating the melt/solidiied raction distribution in all the elements in the bed using the ollowing equation: X t ¼ XN i ¼ X i N (24) where X t is the total melt or solidiied raction o the bed, X i is the melt or solidiied raction o an element i and N is the total number o elements in the bed. The total energy stored in the ith element can then be expressed as the sum o the heat storage o capsules and the heat transer luid: q total;i ¼ q PCM;i þ q HTF;i (25) The energy stored in the capsules contained in the bed element i is given by q PCM;i ¼ Z Tpa T initial Z Tmþe2 þ T me Z Tpþa2 mc ps dt þ mc ps dt þ ml p T pa Z Tinal mc pl dt þ ml þ mc pl dt (26) T mþe2 The energy stored in the heat transer luid is given by q HTF;i ¼ m C p; T initial T inal (27) where T initial denotes the initial temperature, T inal the inal temperature o the process and m is the mass o the heat transer luid in the element. The energy stored in the storage comprising o N such elements can then be written as: Q storage ¼ XN i ¼ q total;i (28) Alternatively, the stored energy o the system while charging, Q ch may be computed using the molten raction o the PCM, temperature o the PCM and that o the heat transer luid inside the tank. Similarly the discharged energy o the system Q dis may be computed using the solidiied raction o the PCM, temperature o PCM and that o the heat transer luid. These quantities can be written respectively, as: Q ch ¼ X m L þ mc ps ðt m T initial ÞþmC pl ðt c T m Þ þ m C p; T T initial Q dis ¼ X s L þ mc pl T inal T m þ mc ps ðt m T c Þ þ m C p; T inal T c ð29þ ð3þ 3. Results and discussion Key parameters o the analysis are the heat transer luid inlet temperature, mass low rate, phase change temperature range and the radius o the capsule. In the present work a cylindrical storage tank o m diameter and.5 m length (length to diameter ratio.5) completely illed with PCM capsules has been considered or the storage o energy collected by a solar collector system or a period o 6 h per day. The storage system contains parain wax as phase change material in HDPE spherical capsule, having the storage capacity o 85.5 MJ o thermal energy when considering only the latent heat o the storage material. The total storage capacity o the tank increases to 43.7 MJ when considering the latent heat and sensible heat o the parain wax along with the sensible heat o the heat transer luid (water) over the temperature range o 2 C. Numerical calculations were made with various element and time step sizes and it was ound that the results are independent o element and time step size below respective sizes o mm and s. Consequently, these values were used in all numerical simulations. Table summarizes the range o operating parameters o this investigation. The results obtained rom the analysis are presented and discussed below. 3.. Temperature distribution o the bed The temperature distribution o the bed was predicted with various values o Stean number, mass low rate, capsule diameter and PCM melting temperature range both or melting and solidiication process. Fig. 3 shows typical temperature distribution o bed at dierent axial positions or various values o instant o time rom start o the charging mode o 4 mm capsules. The low rate is.796 kg/s (w. mm/s), and the initial temperature o the storage and the inlet temperature o heat transer luid are 5 C and 7 C respectively. During initial heating period, the capsules near the entrance are charged while those near the exit are very close to the initial bed temperature. As time elapses the bed temperature rises. During the melting process there are three stages namely; solid heating, phase change and liquid heating as indicated in Fig. 3. The parain wax used in this experiment is characterized by melting in a range o temperature; the melting starts at a temperature o 52.9 C (T (me) in Fig. 3) and is completed at 6.6 C (T (mþe2) in Fig. 3). The solid heating takes place up to the temperature T (me) (stage in Fig. 3), the phase change is between the range T (me) to T (mþe2) (stage 2 in Fig. 3) and the liquid heating takes place above the temperature T (mþe2) (stage 3 in Fig. 3). Fig. 4 shows the temperature distribution during solidiication mode or a 4 mm capsule. These distributions also show characteristics similar to those o melting, i.e. liquid cooling (stage in Fig. 4), solid cooling (stage 3 in Fig. 4) and solidiication (stage 2 in Fig. 4). It can be observed that the bed is not completely solidiied even at the end o h where as almost the entire bed had melted in a much shorter period. This is due to the very low heat transer coeicient during solidiication process as compared to that o the melting process. It is because o high resistance o solidiied layer ormed in the inner wall o the capsule during solidiication process, which reduces the heat transer rate between the bed and the heat transer luid where as during melting process, the melted Table Range o operating parameters. Problem Initial temperature, C Stean number, Ste (T HTF, C) Mass low rate, kg/s Capsule radii, mm Melting (7 82 C) Solidiication (5 35 C) Phase change temperature range, C

6 77 A. Felix Regin et al. / Renewable Energy 34 (29) T (m+e2) T = 7 C (Ste =.43) T initial = 5 C 3 42 Stage 3 Stage Time in min Melt raction, % T = 7 C (Ste =.43) T initial = 5 C Time in min 54 T (m-e) 5 Stage Fig. 3. Temperature proiles o melting o spherical capsules in the bed Fig. 5. Melt raction distribution o the spherical capsule bed as unction o time. layer ormed near the inner wall o the capsule increases the heat transer rate by natural convection mode Melt/solid raction distribution o the bed Fig. 5 shows the melt raction distribution o the bed as unction o time and axial position during the charging mode o 4 mm capsules. It is observed high energy transer in the inlet region leads to higher melt raction there and the heat transer luid leaving the bed almost at the initial bed temperature leading to almost zero melt raction. Fig. 6 shows the solid raction distribution o the bed during the discharging mode Eect o heat transer luid temperature (or Stean number) Fig. 7 shows the total melt raction o the PCM in the bed or various values o Stean number (heat transer luid temperatures). The time to reach the complete melting o bed (melt raction o 75 7 Solidiication problem T = 5 C (Ste=.42) T = 7 C initial m =.796 kg/s Solidiication problem T = 5 C (Ste =.42) T initial = 7 C 65 3 Stage 8 T (m+e2) 55 T (m-e) Time in min Stage 2 Solid raction, % Time in min 5 Stage Fig. 4. Temperature proiles o solidiication o spherical capsules in the bed Fig. 6. Solid raction distribution o the spherical capsule bed as a unction o time.

7 A. Felix Regin et al. / Renewable Energy 34 (29) T initial = 5 C The curves rise to the complete melting position early with the increase in the mass low rate. Higher the mass low rate, the shorter the time interval needed or complete charging Eect o capsule size Melt raction, % () T = 7 C (Ste=.43) 2 (2) T = 75 C (Ste=.79) (3) T = 78 C (Ste=.248) (4) T = 82 C (Ste=.25) Fig. 9 shows the total melt raction o PCM as a unction o capsule radius and time indicating the complete charging time o the bed is 48, 5, 54, 57, and 63 min or 2, 25, 3, 4, 5 and mm capsule radii respectively; the bed with smaller capsules taking less time or charging. It can be seen that at the end o 6 h o charging, the total melt raction or 2 mm capsule is 8.2% and or mm capsule is 73%. For the capsule o 2 mm radius it took shorter time by 24% to reach the melt raction o % than that or the mm capsule during the melting process. Fig. shows the total solidiied raction o PCM as a unction o capsule radii. It can be observed that at the end o 6 h o discharging process the solidiied raction or 2 mm capsule is 5% while or mm capsule is 26%; a reduction in solidiication raction o about 49%. For melting process, the eect o radius o capsule is much weaker, or example there is reduction o only 9% as the capsule radius changes rom mm to 2 mm. It means it is better to select a capsule o smaller radius to get higher storage rate in the bed. %) decreases as the inlet temperature o heat transer luid is increased. For the Stean number o.25 (T in ¼ 82 C), the time was shorter by about 42% to reach the melt raction o % than that or the Stean number o.43 (T in ¼ 7 C). This shows the melt raction and the complete charging time are strongly aected by the inlet temperature o heat transer luid (Stean number). Higher Stean number (i.e. higher inlet heat transer luid temperature), the shorter the time interval or complete charging Eect o mass low rate o heat transer luid Fig. 8 shows the variation o total melt raction o PCM as a unction o time or dierent heat transer luid mass low rates. Melt raction,% Fig. 7. Eect o Stean number on melt raction o the bed T = 7 C (Ste =.43) T initial = 5 C () m =.398 kg/s (2) (3) m =.94 kg/s (4) m =.592 kg/s Fig. 8. Melt raction vs time or various mass low rate Eect o melting temperature range on the perormance o the system Fig. shows the temperature distribution in the storage tank or the melting o PCM at constant temperature process (T m ¼ 59.9 C). In the beginning, the PCM in the capsules near the entrance is heated and melted but the PCM in the capsules near the exit remains unaected and the temperature is equal to the initial bed temperature. It requires a large amount o energy in terms o latent heat at a particular temperature or phase change process. The temperature o the bed is equal to the melting temperature o the PCM or longer period in this ideal case. A very high slope o temperature distribution is observed near the melting temperature Melt raction, % 8 T = 7 C (Ste=.43) T initial = 5 C Capsule radius () r = 2 mm (2) r = 25 mm 2 (3) r = 3 mm (4) r = 4 mm (5) r = 5 mm 6 th (6) r = mm hour Fig. 9. Melt raction o the spherical capsule bed or various capsule radii. 4

8 772 A. Felix Regin et al. / Renewable Energy 34 (29) Solid raction, % Solidiication problem T = 5 C (Ste=.42) T initial = 7 C Melting at various phase change temperature range rd hour T m 6 th hour T = 7 C (Ste=.43) T initial = 5 C 3 55 Capsule radius 2 () r = 2 mm (2) r = 25 mm (3) r = 3 mm (4) r = 4 mm (5) r = 5 mm 6 th hour (6) r = mm Fig.. Solid raction o the spherical capsule bed or various capsule radii. (T m ¼ 59.9 C) when melting is complete again a very high slope o temperature occurs near the inlet temperature o heat transer luid line. The charging o the capsule takes place by sensible heating o the solid and sensible heating o the liquid in the stage and stage 2 o Fig. respectively. For example, at o.5, the bed takes 5 min to reach the melting temperature (solid heating), the bed is at the same temperature till 4 min during this period o 35 min the melting takes place at the melting temperature and inally the 5 () (ΔT) m = C (ideal case) (2) (ΔT) m = 8.7 C (actual) Fig. 2. Bed temperature proile at the end o 3rd and 6th hours o melting o spherical capsule at phase change temperature ranges o and 8.7 C. bed took min to reach the temperature o 7 C (liquid heating). The eect o phase change temperature range on the charging process is shown in Fig. 2 where the bed temperature proile at the end o 2nd, 4th and 6th hours o melting is shown or the case o PCM melting at ixed temperature o 59.9 C and that melting in the temperature range T ðmeþ to T ðmþe2þ. Higher stratiication is observed or the PCM melting in the range o phase change (i.e. 8.7 C) compared to that melting at a ixed temperature. This is because o higher heat transer rate, since the PCM starts to melt at 52 C which is much lower temperature as compared to 59.9 C Melting at constant phase change temperature T m Stage 2 Melt raction, % 8 Capsule radius= 4 mm T = 7 C (Ste=.43) T initial = 5 C 2 55 Stage 4 5 T h,in = 7 C (Ste =.43) T initial = 5 C Fig.. Temperature distribution o melting o spherical capsule bed (melting at constant phase change temperature, T m ¼ 59.9 C). 2 Phase change temperature range () (ΔT) m = 8.7 C (actual) (2) (ΔT) m = (ideal) Fig. 3. Eect o phase change temperature range on melt raction o the spherical capsule bed.

9 A. Felix Regin et al. / Renewable Energy 34 (29) Even though the heat transer coeicient is same in both the cases, the varying temperature dierence between the PCM and heat transer luid, a dierent heat transer rate is obtained. As a result, the bed having PCM melting in a temperature range reaches the complete melting earlier than the PCM with ixed melting temperature as can be seen in Fig. 3, which shows the total melt raction as unction o time or these time cases. A dierence o 3.6% in the complete melting time or PCM with ixed phase change temperature and that with phase change in a temperature range ((DT) m ¼ 8.7 C) is observed. 4. Conclusions A model or a packed bed latent heat thermal energy storage using spherical capsules is developed in the present study to predict the thermal behavior o the system. This study investigates the eects o heat transer luid inlet temperature, mass low rate, phase change temperature range and the radius o the capsule on the dynamic response o a packed bed latent heat thermal energy storage system using spherical capsules or both charging and discharging modes. The ollowing conclusions can be drawn:. The complete solidiication time is too longer compared to the melting time. This is due to the very low heat transer coeicient during solidiication. 2. Higher the Stean number (i.e. higher inlet heat transer luid temperature) the shorter is the time or complete charging. Similarly or higher the mass low rate o heat transer luid shorter is the time or complete charging. 3. The charging and discharging rate are signiicantly higher or the capsule o smaller radius compared those o larger radius. 4. 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