Thermal performance simulations of a packed bed cool thermal energy storage system using n-tetradecane as phase change material

Thermal performance simulations of a packed bed cool thermal energy storage system using n-tetradecane as phase change material

International Journal of Thermal Sciences 49 (2010) 1752e1762 Contents lists available at ScienceDirect International Journal of Thermal Sciences jo...

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International Journal of Thermal Sciences 49 (2010) 1752e1762

Contents lists available at ScienceDirect

International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts

Thermal performance simulations of a packed bed cool thermal energy storage system using n-tetradecane as phase change material Shuangmao Wu, Guiyin Fang*, Xu Liu School of Physics, Nanjing University, Hankou Road 22, Nanjing 210093, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 21 May 2009 Received in revised form 25 March 2010 Accepted 26 March 2010 Available online 1 May 2010

The objective of this paper is to study the thermal performance of latent cool thermal energy storage system using packed bed containing spherical capsules filled with phase change material during charging and discharging process. According to the energy balance of the phase change material (PCM) and heat transfer fluid (HTF), a mathematical model of packed bed is conducted. n-tetradecane is taken as PCM and aqueous ethylene glycol solution of 40% volumetric concentration is considered as HTF. The temperatures of the PCM and HTF, solid and melt fraction and cool stored and released rate with time are simulated. The effects of the inlet temperature and flow rate of HTF, porosity of packed bed and diameter of capsules on the melting time, solidification time, cool stored and released rate during charging and discharging process are also discussed. Ó 2010 Elsevier Masson SAS. All rights reserved.

Keywords: Heat transfer Thermal performance Packed bed Cool storage n-Tetradecane Phase change material

1. Introduction Cool thermal energy storage (CTES) plays a significant role in conserving available energy, improving its utilization and correcting the mismatch that occurs between the supply and demand of energy. CTES is classified as sensible, latent heat and the combined storage systems. The advantages of the latent cool thermal energy storage system (LCTESS) in comparison with sensible storage are high heat storage density, small size of the system and a narrow temperature change during storing and releasing processes. Many applications have been used, such as cool storage systems for central air-conditioning, natural cooling of energy-efficient building. The LCTESS is employed as ice-on-coil, encapsulated phase change material, ice slurry and ice harvester [1,2]. The most attractive LCTESS is the encapsulated phase change materials (PCM) system, which uses cylindrical tank with or without fins, cans, plates or spherical capsules. Spherical capsule filling in packed bed seems to be the most effective and convenient method of encapsulation. Many materials were chosen as PCM for LCTESS. Water is widely used as PCM because of its high latent heat of freezing, low cost and no environmental pollution. However, the sub-cooling

* Corresponding author. Tel.: þ86 25 51788228; fax: þ86 25 83593707. E-mail address: [email protected] (G. Fang). 1290-0729/$ e see front matter Ó 2010 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ijthermalsci.2010.03.014

phenomenon occurs in solidification stage of water during the charging process and affects the performance of the systems. Bedecarrats et al. [3] presented a theoretical and experimental investigation of a phase change thermal energy storage system using spherical capsules. Sub-cooling was taken into account in the model. Cheralathan et al. [4] developed a simulation program to evaluate the temperature profiles of heat transfer fluid and phase change material at any axial location and studied the influence of the inlet temperature and porosity during the charging process. Ismail and Henriquez [5] also investigated the effect of inlet temperature and the mass flow rate of heat transfer fluid (HTF), and material of spherical capsule on the performance of the storage unit numerically and experimentally. Kousksou et al. [6] developed a two-dimensional model, taking sub-cooing phenomenon into consideration, to study the industrial process of energy storage and compared with experimental result for the tank in vertical and horizontal position. They found that the optimum running of the charge mode is obtained in the case of the vertical position. Seeniraj and Narasimhan [7] employed a LHTS unit for cold thermal storage in an air-conditioning plant, which has been numerically studied considering heat leak through sidewalls by convection. The influences of porosity, Stanton number, Stefan number and convective heat leak ratio on temperature, solidified fraction, energy storage and total charge fraction were investigated. Ismail and Stuginsky Jr [8] presented four basic groups of models, that is, the continuous solid phase models, Schumman’s model, the single phase models

S. Wu et al. / International Journal of Thermal Sciences 49 (2010) 1752e1762

Nomenclature ap C D d H h heff k L Mc

Ml

Nu Pr qv Re r rp T Tm

surface area of spherical capsules per volume, [m1] specific heat, [J/(kg K)] internal cylindrical tank diameter, [m] diameter of capsule, [m] height of packed bed, [m] coefficient of convective heat transfer, [W/(m2 K)] effective coefficient of convective heat transfer, [W/(m2 K)] thermal conductivity, [W/(m K)] latent heat of fusion, [J/kg] ratio of thermal resistance of capsule wall to the resistance due to convection on the external surface of capsule, [] ratio of thermal resistance of molten liquid PCM to the resistance due to convection on the external surface of capsule, [] Nusselt number, [] Prandtl number, [] flow rate of HTF, [L/min] Reynolds number, [] radius of capsule, [m] solid-liquid interface, [m] temperature, [K] melting temperature, [K]

and the thermal diffusion models or models with thermal gradient inside the particles. The dynamic behavior of a single spherical capsule used in packed bed was also investigated numerically and experimentally. Ismail et al. [9,10] presented a numerical study of PCM enclosed in a spherical capsule. The mathematical model was used to predict the effect of size of spherical capsule, shell thickness, material, initial temperature of PCM and the external wall temperature on the solidified mass fraction and the time for complete solidification. Eames and Adref [11] described the results of an experimental study aimed at the characterization of the freezing and melting processes for water contained in spherical elements and developed semi-empirical equations that allow the mass of ice within a sphere to be predicted at any time. Chan and Tan [12] developed the experimental investigation on the solidification of an n-hexadecane inside a spherical enclosure. Some paraffin was also employed as PCM in cooling thermal storage system. The liquidesolid phase equilibrium of binary mixture system of n-tetradedcane and n-hexadecane was studied by He et al. [13e15]. Chevalliera et al. [16] determined the structural and thermodynamic behavior of mixtures which consist of a multiCn wax and C14 normal tetradecane during the cooling from the liquid state to the solid state. Kalaiselvam et al. [17] studied the phase change behavior and heat transfer characteristics of PCM inside a spherical capsule used in tank and n-tetradecane was used as PCM. Cho and Choi [18] investigated the thermal characteristics of spherical capsules using n-tetradecane, mixture of n-tetradecane and n-hexadecane and water as PCM. Reynolds number and inlet temperature during the freezing process and initial temperature during the melting process were studied. Nallusamy et al. [19] investigated experimentally the thermal behavior of a packed bed of combined sensible and latent heat thermal energy storage (TES) unit. A TES unit is designed, constructed and integrated with constant temperature bath/solar collector to study the performance of the storage unit, which contains paraffin as phase change

Ts u x

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solidification temperature, [K] velocity of the fluid flow,[m/s] location of the flow direction, [m]

Greek letters density, [kg/m3] porosity of packed bed, [] viscosity, [kg/(ms)] melt and solid fraction, [] time, [s]

r 3 m b s

Abbreviations PCM phase change material HTF heat transfer fluid LCTES latent cool thermal energy storage Subscripts c cover of capsules f heat transfer fluid i inner radius or initial temperature in inlet position l liquid phase o outer radius p phase change material s solid phase sur surrounding

material (PCM). It is found from the discharging experiments that the combined storage system employing batchwise discharging of hot water from the TES tank is best suited for applications where the requirement is intermittent. Even though the problem of packed bed containing spherical capsules has been extensively studied, the numerical study on packed bed using n-tetradecane as PCM is absent. Fig. 1 presents the melting and solidifying DSC curves of n-tetradecane, which was obtained using a differential scanning calorimeter (Pyris 1 DSC, PerkineElmer) at 5  C/min under a constant stream of argon at a flow rate of 20 ml/min. The accuracy of enthalpy was 5% and the accuracy of temperature was 0.2  C. It is known that n-tetradecane has a relatively high latent heat, high solidifying temperature

Fig. 1. Melting and solidifying DSC curves of n-tetradecane.

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of 2.73  C and melting temperature of 7.79  C. Compared to water, n-tetradecane has little supercooling temperature and relatively higher phase change temperature. Hence, n-tetradecane is a promising phase change material for cool thermal energy storage. The present paper presents a mathematical model and studies the dynamic performance of packed bed using n-tetradecane as PCM during charging and discharging process. Numerical simulations are carried out to discuss the effects of inlet temperature of HTF, porosity of packed bed, flow rate of HTF and size of the capsules on the thermal performances of packed bed CTESS. 2. Mathematical model Fig. 2 shows the schematic diagram of packed bed CTESS. This system consists of three main parts, a cylindrical tank (called packed bed), a refrigeration system and an outdoor unit. The packed bed is a cylindrical tank with height of H and diameter of D containing spherical capsules filled with PCM. In this study, both charging and discharging process are studied numerically. In order to simplify the mathematical model, the following assumptions are considered: (1) the tank is insulated; (2) temperatures of PCM and HTF only vary along the axial direction; (3) solidification and melt latent heat of PCM, specific heat and thermal conductivity of PCM and HTF are constant; (4) the PCM has a constant solidifying and melting temperature; (5) the velocity profile is regards as fully developed flow in axial direction, (6) effect of PCM volume change was neglected due to its change is less than 5%. In this model, the PCM capsules behave as a continuous medium and not as a medium comprised of individual particles. So, we used a continuous phase model. With the foregoing assumption, the conservation equation for PCM and HTF are stated. 2.1. Charging process

 vTf vTf v2 Tf þ rf Cf 3u ¼ kf 3 2 þ heff ap Tp  Tf vs vx v x

 vTp ¼ heff ap Tf  Tp vs

rl Cl ð1  3Þ

(1)

where Tf denotes the temperature of HTF, Tp is the temperature of PCM, u is the mean velocity of HTF, 3 is the porosity of bed, ap is the

(2)

The Eq. (2) represents the internal energy change of PCM is equal to the heat transfers by convection from HTF to PCM capsules. Solidification stage (second stage):

rs Lð1  3Þ

 vb ¼ heff ap Tm  Tf vs

(3)

where L, b, Tm denote latent heat of freezing, solid fraction and freezing temperature, respectively. The Eq. (3) represents the latent heat removed from PCM is equal to the energy transfer to the HTF by convection during the solidification process. Solid phase stage (last stage):

rs Cs ð1  3Þ

In the charging process, the cool heat transfer fluid (HTF) flows over the spherical capsules in packed bed. PCM in the spherical capsules undergoes sensible cooling of liquid phase, solidification, sensible sub-cooling of solid phase. The energy balance equation on PCM and HTF can be written as:

rf Cf 3

surface area of spherical capsules per volume, heff is the effective coefficient of heat transfer between PCM and HTF. The first term of the left hand side of Eq. (1) represents the rate change of interval energy of HTF, while the second term accounts for energy change due to the HTF flow. The two terms on the right hand represent the heat change by conduction and the energy transfer by convection between the HTF and the capsules, respectively. In the solidification stage, the PCM temperature Tp should be equal to freezing point Tm. Initially, temperature of the liquid PCM is equal to the surrounding temperature. With the time undergoing, the temperature gradually decreases to the phase change temperature, and the solidification stage takes place. Then the temperature of solid PCM decreases to inlet temperature of HTF and the charging process terminates. The PCM temperature is also calculated by using energy balance on PCM and HTF. Liquid phase stage (first stage):

 vTp ¼ heff ap Tf  Tp vs

(4)

The initial and boundary conditions of the above equations are stated in the following. At the beginning of the charging process, the temperature of HTF and PCM is considered to be the same value. So,

Tf ðt ¼ 0Þ ¼ Ti

(5)

Tp ðt ¼ 0Þ ¼ Ti

(6)

At the inlet position of packed bed, the fluid is assigned to be constant. Therefore,

Tf ðx ¼ 0Þ ¼ Tin

(7)

The temperature for HTF at the bed outlet position, for x > H is assigned constant. Therefore,

vTf ðx ¼ HÞ ¼ 0 vx

(8)

where Ti and Tin denote the initial temperature of PCM/HTF and inlet temperature of HTF. In the present study, the form of correlation used for the heat transfer coefficient of the spherical capsules and HTF was developed by Beek [20] for the case of capsules arranged in a random form.

Nu ¼ 3:22 Re1=3 Pr1=3 þ 0:117 Re0:8 Pr0:4

(9)

Finally, the heat transfer coefficient is determined from

Fig. 2. Schematic diagram of the packed bed CTESS.

h ¼

kf Nu d

(10)

S. Wu et al. / International Journal of Thermal Sciences 49 (2010) 1752e1762

where Nu, Re, Pr are Nusselt number, Reynolds number and Prandtl number of HTF, respectively. In the charging process, the latent heat transfer to the HTF must pass through the solidified PCM and the cover of the spherical capsule. In order to calculate the heat transfer between the HTF and PCM, we must take the thermal resistance of solidified PCM and the cover into account. So, the effective coefficient is presented,

heff

h ¼ 1 þ Mc þ Ms

(11)

Mc ¼ Rc =Rh

(13)

Ms and Mc are the ratio of the thermal resistance of solidified PCM and the cover of capsules to the thermal resistance due to convection on the external surface of the capsules. 2.2. Discharging process

3. Numerical solution Equations (Eqs. (1)e(13)) governing the HTF and PCM temperature are discretized using implicit finite difference approach and central difference approximation. The packed bed is divided into M layers along the axial direction. The space step and time step are Dx and Ds. The discretized equation of Eqs. (1)e(4) can be written as following, respectively.

 n nþ1 nþ1 ða  bÞTiþ1 þ 1 þ 2b þ cni Tinþ1 þ ða  bÞTi1 ¼ Tin þ cni qi (14)

qni þ uni DsTinþ1 1 þ uni Ds 

n bnþ1 ¼ bi þ uni Ds qm  Tinþ1 i

qni þ uni DsTinþ1 1 þ uni Ds

(15) 

(16)

(17)

where

a ¼

uDs 2Dx

uf ni ¼

heff ni ap rf Cf 3

(18)

(19)

(20)

In liquid phase stage,

uni ¼ cni ¼

heff ni ap

(21)

uf ni Ds

(22)

rl Cl ð1  3Þ 1 þ uni Ds

In phase change stage,

uni ¼

heff ni ap rs Lð1  3Þ

cni ¼ uf ni Ds

During discharging process, HTF flows over the capsules, PCM releases the stored cool thermal energy to the HTF and the HTF temperature decreases gradually to inlet temperature. Discharging process terminates when the outlet temperature reaches the inlet temperature. PCM undergoes sensible heating of solid PCM (first stage), melting (second stage) and sensible heating of liquid PCM (last stage). The equations of energy balance between PCM and HTF are similar to the equations of charging process. From Eq. (11), we know that the solidified PCM will decrease the heat transfer coefficient, while the melted PCM layer in capsules will increase the heat transfer rate by natural convection during the second stage of discharging process. In order to calculate the effect of natural convection on the heat transfer, we induce effective thermal conductivity of melted phase change material keff [21].

qnþ1 ¼ i

kf

Dx2 rf Cf

(12)

Ms ¼ Rs =Rh

qnþ1 ¼ i

b ¼

1755

(23) (24)

In solid phase stage,

uni ¼

heff ni ap rs Cs ð1  3Þ

(25)

cni ¼

uf ni Ds 1 þ uni Ds

(26)

In the above equations, subscript i denotes axial location of the packed bed and n denotes the present moment. For example, Tni and qni denote the temperature of HTF and PCM on the position of iDx at the time of nDs. The program flowchart of the model is given in Fig. 3. 4. Results and discussion The packed bed is in vertical position and heat transfer fluid flows from the top to the bottom. Packed bed, which is insulated with polyurethane foams, has an inner diameter of 100 cm, a wall thickness of 5 cm, and a height of 150 cm. Spherical capsule, made of high-density polyethylene, has an inner diameter of 98 mm and a thickness of 1 mm. The heat transfer fluid is aqueous ethylene glycol solution of 40% volumetric concentration and n-tetradecane is used as PCM filled in the capsules. The thermal properties of PCM and HTF are given in Table 1. In this work, the thermal behaviors of packed bed during the charging and discharging process are studied. The numerical simulations are conducted at various inlet temperatures (7 to 2  C of cool storage process and 8e19  C of cool release process), various flow rates (10e50 L/min), various porosity of packed bed (0.37e0.55) and various diameter of capsules (6e15 cm), which is shown in Table 2. 4.1. Charging process of packed bed 4.1.1. Thermal behavior of charging process In order to investigate the thermal behavior of charging process, the average porosity of packed bed, flow rate of HTF, the inlet temperature of HTF, and initial temperatures of PCM and HTF are assumed to be 0.45, 30 L/min, 4  C and 13  C, respectively. The temperature histories of HTF and PCM at middle and outlet positions of packed bed are shown in Fig. 4. As shown in Fig. 4, there are three stages namely, liquid cooling, phase change (freezing) and

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Fig. 3. Program flowchart of the model.

solid sub-cooling during the charging process. The liquid cooling takes place up to the freezing temperature Ts, the freezing keeps on Ts and the solid sub-cooling takes place below the temperature Ts. It is also observed from Fig. 4 that the HTF temperature decreases rapidly until it reaches the freezing temperature. During the freezing process, the HTF temperature is nearly constant at the forepart of freezing, and then it decreases slowly to the inlet temperature. The time for complete freezing at the middle location is about 130 min and at the outlet is about 210 min. This is due to the fact that heat transfer rate decreases as the temperature difference between PCM and HTF decreases along the flow direction of HTF. So, it is clearly seen that the closer to the outlet position, the longer time for complete solidification and charging process. Fig. 5 presents temperature profiles of PCM at different time. During initial cooling period, the capsules near the inlet position are charged while those near the outlet position are very close to

Table 1 Thermalephysical property of PCM and HTF. Properties

PCM Solid

Solidifying point,  C Solidifying latent heat, kJ/kg Melting point,  C Melting latent heat, kJ/kg Specific heat, kJ/(kg K) Thermal conductivity, W/(m K) Density, kg/m3

2.73 213.83 7.79 218.56 2.00 0.273 803

HTF Liquid e e e e 2.55 0.211 765

3.45 0.44 1070

the initial temperature (see t ¼ 10 min in Fig. 5). As time elapse, the PCM temperature decreases and the freezing stage near the outlet occurs. From the Fig. 5, we can see that all capsules are on the period of freezing at the time of 40 min, while PCM temperatures of all capsules are almost below freezing point Ts and the freezing stage of all capsules finishes at the time of 200 min. Fig. 6 shows variation of cool stored rate and solidified fraction with time. Freezing does not occur during the first 10 min and the PCM stores cool energy only in the sensible form. When the temperature of PCM reaches the freezing temperature, that freezing stage starts and the cool storage capacity increases with

Table 2 The parameters used in the study. The effect parameters

Flow rate (L/min)

Inlet temperature ( C)

Porosity

Diameter of capsules (cm)

Cool stored process Case 1 30 Case 2 10e50 Case 3 30 Case 4 30 Case 5 30

4 4 7 to 2 4 4

0.45 0.45 0.45 0.37e0.55 0.45

10 10 10 10 6e15

Cool released process Case 6 30 Case 7 10e50 Case 8 30 Case 9 30 Case 10 30

13 13 8e19 13 13

0.45 0.45 0.45 0.37e0.55 0.45

10 10 10 10 6e15

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Fig. 4. Variation of temperatures of PCM and HTF at different positions with time during charging process.

time. Higher cool stored rate is observed at the initial time period, and thereafter it decreases rapidly. At the beginning, PCM has direct contact with the capsules, but later thermal resistance is formed in between the liquid PCM and capsule surface. Hence thermal energy has to travel through this solid layer before reaching the external surface. So, a sharp decrease in cool stored rate values is observed. Cool stored rate decreases slowly to zero at the time of 210 min, and the charging process terminates. The total heat storage capacity is about 154 MJ, while the latent heat storage capacity is 105 MJ. It is calculated that the latent cool energy storage capacity is only 68% of the total cool energy storage capacity, which is due to the sensible cooling of the HTF and PCM. Fig. 7 shows the effect of sub-cooling phenomena on the temperature of PCM and cool stored rate. The effect on the temperature of PCM is not obvious when the sub-cooling degree is 1 K. However, this effect is significant when the sub-cooling degree is 2 K, especially at the sensible cool storage stage. It is clearly seen that the larger sub-cooling of PCM, the longer time for complete charging process, and also the lower cool stored rate.

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Fig. 6. Variation of cool stored rate and solidified fraction with time.

cool stored rate at different flow rate, respectively. The flow rate of HTF is varied from 10 to 50 L/min, while other parameters are kept same. As seen in Fig. 8, the higher flow rate of HTF, the less time for complete solidification, and also the higher average cool stored rate. This is due to an increase in flow rate of HTF translates an increase in heat transfer coefficient between HTF and capsules. Higher increase in flow rate leads to a smaller change in complete solidification time. 4.1.3. Effect of inlet temperature of cool HTF Fig. 10 represents the effect of various inlet temperatures with the range 7 to 2  C on the total solidification time and average cool stored rate. It is found that the lower inlet temperature, the less time for complete solidification. This is due to the lower inlet temperature, the higher temperature difference between the HTF and PCM, and so the higher heat transfer rate. Compared to inlet temperature of 0  C, the time are shorter by about 30% and 46% to reach the complete solidification for inlet temperature of 2  C and 4  C. This shows that inlet temperature of HTF strongly affects the time for complete solidification. As shown in Fig. 10, for the high

4.1.2. Effect of flow rate of HTF Figs. 8 and 9 display the effect of flow rate of HTF on total solidification time and average cool stored rate and instantaneous

Fig. 5. Temperature profiles of PCM at different time during charging process.

Fig. 7. Effect of sub-cooling phenomena on the temperature of PCM and cool stored rate.

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Fig. 8. Effect of flow rate of HTF on total solidification time and average cool stored rate.

inlet temperature (Tin > 2  C), the solidification time increases rapidly with the increasing inlet temperature of HTF, while it has smaller influence on solidification time when it is lower than 4  C. The lower inlet temperature of HTF will increase the expense for refrigeration system to produce HTF. Fig. 11 shows variation of cool stored rate with time at different HTF inlet temperature. The cool storage capacity becomes smaller when the inlet temperature increases, which is because of the sensible cooling of the PCM and HTF. The cool stored rate decreases with the increasing inlet temperature.

Fig. 10. Effect of inlet temperature on total solidification time and average cool stored rate.

Fig. 13 represents variation of cool stored rate with time at different porosity of packed bed. As the porosity value increases, the time for completion of storage decreases due to the decrease in mass of PCM. The value of cool stored rate is smaller at lower porosity.

4.1.4. Effect of porosity of packed bed Fig. 12 shows effect of porosity (0.37e0.55) on total solidification time and average cool stored rate under the same diameter of capsules, inlet temperature and flow rate of HTF. It is observed that the time for complete solidification is 223 min, 175 min and 137 min for the porosity of 0.37, 0.45 and 0.53, respectively. So it is clearly known that lower porosity increases the solidification time. Lower porosity indicates higher cool storage capacity of packed bed, and hence longer time required for complete solidification.

4.1.5. Effect of diameter of capsules Effect of diameter of capsules on total solidification time and average cool stored rate is given in Fig. 14. The diameter of the capsules is varied from 6 to 15 cm. Capsules with 10 cm diameter freezes in 176 min, whereas PCM with 6 cm diameter freezes in 162 min. As expected, PCM in the smaller diameter capsules freezes faster than in the larger diameter capsules. A reduction of the capsule diameter induces an increase in the number of capsules and in the heat transfer area, and hence the heat transfer rate between the fluid and capsules increases. Fig. 15 displays variation of cool stored rate with time at different diameter of capsules. It is shown that diameter of capsules has no significant effect on the cool stored rate and complete charging time compared to the other parameters, such as flow rate and inlet temperature of HTF.

Fig. 9. Variation of cool stored rate with time at different HTF flow rates.

Fig. 11. Variation of cool stored rate with time at different HTF inlet temperature.

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Fig. 12. Effect of porosity on total solidification time and average cool stored rate.

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Fig. 14. Effect of diameter of capsules on total solidification time and average cool stored rate.

4.2. Discharging process of packed bed 4.2.1. Thermal behavior of discharging process In order to study the dynamic performances of discharging process, the average porosity of packed bed, flow rate of HTF, diameter of capsules, the inlet temperature of HTF, and initial temperatures of PCM and HTF are assumed to be 0.45, 30 L/min, 10 cm, 13  C and 4  C, respectively. Fig. 16 shows variations of temperatures of PCM and HTF at different positions with time during discharging process. During the first stage (solid heating), the PCM temperature increases rapidly due to great temperature difference between HTF and solid PCM. With time elapses, the PCM inside capsules reaches the melt temperature and the phase change stage commences. At the last stage (liquid heating), the PCM temperature increases until it reaches the inlet temperature. It is observed that the time for complete melting in the outlet position is longer than in the other positions. Fig. 17 presents temperature profiles of PCM at different time during discharging process. At the beginning, the capsules near the inlet position are melted while temperatures of those near the outlet position are very close to the initial temperature (see t ¼ 10 min and 20 min in Fig. 17). As time elapse, the PCM

Fig. 13. Variation of cool stored rate with time at different porosity of packed bed.

temperature increases and the melting stage near the outlet takes place. It is seen that all capsules are on the period of melting at the time of 40 min, while PCM temperatures of mostly capsules are below melting temperature Tm (see the time of 160 min in Fig. 17) because of the melting stage terminates. Fig. 18 displays variations of cool released rate and melt fraction with time during discharging process. Higher cool released rate is observed at the initial time period, and thereafter it decreases with time. At the beginning, PCM has direct contact with the capsules, but later a thermal resistance is formed in between the liquid PCM and capsule surface. Hence thermal energy has to travel through this liquid layer before reaching the external surface. So, a sharp decrease in cool released rate values is observed. Cool released rate decreases slowly to zero at the time of 270 min, and the discharging process terminates. When the value of melt fraction increases to 1, the melting stage finishes. 4.2.2. Effect of flow rate of HTF Figs. 19 and 20 display the effect of flow rate of HTF on total melting time, average cool released rate and instantaneous cool released rate, respectively. The flow rate of HTF is varied from 10 to 50 L/min. As seen in Fig. 19, the higher flow rate of HTF, the less time

Fig. 15. Variation of cool stored rate with time at different diameter of capsules.

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Fig. 16. Variations of temperatures of PCM and HTF at different positions with time during discharging process.

Fig. 19. Effect of flow rate of HTF on total melting time and average cool released rate.

Fig. 17. Temperature profiles of PCM at different time during discharging process.

Fig. 20. Variation of cool released rate with time at different HTF flow rate.

Fig. 18. Variation of cool released rate and melt fraction with time.

Fig. 21. Effect of inlet temperature on total melting time and average cool released rate.

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Fig. 24. Variation of cool released rate with time at different porosity of packed bed.

Fig. 22. Variation of cool released rate with time at different HTF inlet temperature.

for complete melting time, but decreasing rate of complete melting time decreases with the increasing flow rate of HTF. Lower flow rate of HTF leads to smaller cool released rate. 4.2.3. Effect of inlet temperature of HTF Fig. 21 presents the effect of various inlet temperature of HTF on the total melting time and average cool released rate. The inlet temperature of HTF is varied from 8 to 19  C. It is found that higher inlet temperature results in rapid melting. This is due to the fact that the higher inlet temperature, the larger temperature difference between the HTF and PCM, and hence the higher heat transfer rate. Higher inlet temperatures lead to only a smaller change in complete melting time. The average cool released rate increases with the increasing inlet temperature of HTF. Fig. 22 shows variation of cool released rate with time at different inlet temperature of HTF. The time for complete discharging process decreases by 20% and 30% when the inlet temperature of HTF increases from 10  C to 13  C and 16  C, respectively. The cool released rate at higher inlet temperature is larger than at the lower inlet temperature.

Fig. 23. Effect of porosity on total melting time and average cool released rate.

4.2.4. Effect of porosity of packed bed Fig. 23 shows effect of porosity (0.37e0.55) on total melting time and average cool released rate under the same diameter of capsules, inlet temperature and flow rate of HTF. The time for complete melting decreases by 16% and 29% when porosity is 0.45 and 0.51, respectively. So it is clearly known that lower porosity increases the melting time, whereas lower porosity indicates higher cool storage capacity of packed bed. Fig. 24 presents variation of cool released rate with time at different porosity of packed bed. As the porosity value increases, the time for complete discharging decreases due to the decrease in mass of PCM. The value of cool released rate is much smaller at lower porosity. 4.2.5. Effect of diameter of capsules Fig. 25 illustrates the effect of diameter of capsules on total melting time and average cool released rate. The diameter of the capsules is varied from 6 to 15 cm. The complete melting time is 189, 195, 202, 212 and 212 min for 6, 8, 10, 12 and 14 cm of the capsule diameter. It is concluded that the packed bed with smaller diameter capsules takes less time for complete melting. Fig. 26 displays variation of cool released rate with time at different diameter of capsules. The effect of diameter of capsules on melting

Fig. 25. Effect of diameter of capsules on total melting time and average cool released rate.

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(5) Compared to other three varying parameters, the diameter of capsules has less significant effect on complete melting and solidification time. Acknowledgments The authors are grateful to the National Natural Science Foundation of China (No. 50776043) and the National High Technology Research and Development Program of China (No. 2006AA05Z222) for providing funds for this research. References

Fig. 26. Variation of cool released rate with time at different diameter of capsules.

and discharging time is less significant than that of porosity of packed bed, the inlet temperature and flow rate of HTF. 5. Conclusions This paper presents the mathematical model of the cool thermal energy storage system using packed bed containing spherical capsules filled with n-tetradecane to predict the thermal behavior of the this system. The effects of flow rate, inlet temperature of HTF, porosity of packed bed and the size of capsules on the dynamic performances of the system during charging and discharging process are investigated. Based on the parametric studies, the following conclusion can be drawn: (1) The PCM at outlet position takes more for complete solidification and melting. Higher cool stored and released rate are observed at the initial time period, and thereafter they decrease with time. The latent heat storage capacity is only about 70% of the total heat storage capacity, which is due to the sensible cooling of the PCM and HTF. (2) The time for complete solidification and melting decreases when the flow rate of HTF increases, but decreasing rate of complete solidification and melting time decreases with the increasing flow rate of HTF. Higher flow rate of HTF also results in higher cool stored and released rate. (3) The inlet temperature of HTF has strongly effect on the thermal performance of both charging and discharging process. The time for complete solidification increases as inlet temperature of HTF increases, whereas the complete melting time decreases with the increasing inlet temperature of HTF. Lower inlet temperature will increase the expense to produce cool HTF during the charging process. The cool stored rate is higher at lower inlet temperature during charging process, while cool released rate is lower at lower inlet temperature during discharging process. (4) Lower porosity indicates higher cool storage capacity of packed bed, and hence longer time required for complete solidification and melting. The value of cool stored and released rate is much smaller at lower porosity.

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