Performance enhancement of a latent heat thermal energy storage system using curved-slab containers

Performance enhancement of a latent heat thermal energy storage system using curved-slab containers

Applied Thermal Engineering 37 (2012) 145e153 Contents lists available at SciVerse ScienceDirect Applied Thermal Engineering journal homepage: www.e...

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Applied Thermal Engineering 37 (2012) 145e153

Contents lists available at SciVerse ScienceDirect

Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Performance enhancement of a latent heat thermal energy storage system using curved-slab containers Hiroyoshi Koizumi*, Yunhai Jin 1 Department of Mechanical Engineering and Intelligent Systems, The University of Electro-Communications, Chofu, Tokyo 182-8585, Japan

a r t i c l e i n f o

a b s t r a c t

Article history: Received 9 August 2011 Accepted 4 November 2011 Available online 17 November 2011

In order to realize an inexpensive and high capacity thermal energy storage (TES) system, we propose a new compact slab type container which has an arc outer configuration for promoting the appearance of close contact melting. Transient 2D numerical melting simulation of a solid phase change material (PCM) in a container is performed by the enthalpy-porosity approach. The simulated result quantitatively elucidated the experimental melting process from the beginning to the end. The TES system is composed of curved-slab containers filled with PCM subjected to convective boundary conditions where heat transfer fluid flows between the containers. The performance enhancement of the latent heat TES system was analyzed, and this system shows a large amount of storage capacity with higher efficiency. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: Phase change material (PCM) Thermal energy storage (TES) system Close contact melting Curved-slab container Performance enhancement

1. Introduction Phase change problems are encountered extensively in nature and in a wide variety of technologically important processes. Such processes include thermal energy storage, melting of ice, crystal growth, and thermal control of electronic equipment using PCMs. Thermal energy storage (TES) has recently attracted increased interest in relation to thermal applications, such as water heating, waste heat utilization, cooling and air-conditioning. In particular, TES systems play an important role in providing enormous potential for facilitating energy savings and reducing environmental impact. Indeed, TES appears to provide one of the most advantageous solutions for correcting the gap that often occurs between the supply and demand of energy. TES is a term widely used to describe the storage used for both the heating and cooling of energy. It deals with the storing of energy by cooling, heating, melting, and solidifying a substance, and the energy becomes available as heat when the process is reversed [1]. Recently, Regin et al. [2] reviewed the development of available latent heat thermal energy storage technologies. Different aspects of storage such as material, encapsulation, heat transfer, applications and new PCM technology innovation have been examined. High storage density of PCM such as paraffin wax at small

* Corresponding author. Tel./fax: þ81 424 43 5395. E-mail address: [email protected] (H. Koizumi). 1 Graduate student at the University of Electro-Communications. 1359-4311/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2011.11.009

temperature changes (50e100  C) can be a significant advantage in solar applications and utilization of waste heat. In spite of these desirable properties of paraffin, its low thermal conductivity (z0.2 W/(m K)) is its major drawback, which decreases the rates of heat stored and released during melting and crystallization processes. In the TES system, both heat charging and discharging processes using spherical capsules have been investigated for enhancement of large latent heat storage due to its low volume to heat transfer surface area ratio and easy packing into the storage system [2e6]. Assis et al. [6] explored numerically and experimentally the melting of a solid PCM in spherical capsules. The solid PCM would sink to the bottom of sphere due to gravity during melting. The enthalpy-porosity method clarifies the sedimentation of a solid PCM, and the appearance of close motion of the solid PCM is accompanied by generation of liquid at the melting interface. This liquid is squeezed through a narrow gap between the melting surface and the capsule wall to the space above the solid PCM. Until now, a large number of papers have pointed out that the effect of solid phase sedimentation and appearance of close contact melting are significant for melting the solid PCM [7]. Koizumi [8] showed the limited results of an experimental study of constrained melting of PCM (three thin copper plates inserted at right angles in a spherical capsule) and unconstrained melting of PCM within a spherical capsule placed in an upwardly directed heated flow. But it is difficult for a spherical capsule to be subjected to close contact melting from the beginning to the end, and furthermore it is expensive for a large number of capsules to be filled with PCM.

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Nomenclature cp [J/(kg d [mm] D [mm] Fo [-] GrH [-]

K)] specific heat at constant pressure thickness of the PCM container wall duct height for heat transfer fluid (seeFig. 5(b)) Fourier number, at/H2 Grashof number based on the PCM container height, gbDTH3/n2 GrW [-] Grashof number based on the PCM container width, gbDTW3/n2 h [W/(m2 K)] heat transfer coefficient H [mm] height of the PCM container k [W/(m K)] thermal conductivity L [mm or m] length of the PCM container Lm [J/kg] latent heat of melting n[-] total number of container layers stacked vertically in the TES system MF [%] melt volume fraction, molten volume/total molten volume, (MF ¼ 1 corresponds to the complete melting.) qup [W/m2] heat flux from the upper of the heat transfer fluid layer qdown [W/m2] heat flux from the bottom of the heat transfer fluid layer Qtotal [m3/hr] total volume flow rate of the heat transfer fluid Qv [m3/s] volume flow rate of the heat transfer fluid in one duct, Qtotal/n/3600 There are also alternative storage devices such as rectangular and cylindrical shapes with or without fins [9e12]. Shatikian et al. [12] explored numerically the process of melting of a PCM in a heat storage unit with internal fins open to air at its top for promoting the appearance of close contact melting. But an inexpensive and high capacity TES system with high efficiency has not been realized up to now. We thus propose a new compact slab type container with an outer arc configuration for prompting the direct contact melting. This TES system, which consists of curved-slab containers where heat transfer fluid flows between the containers, has another advantage which is allowing it to follow flexibly the flow amount of heat exchanging water by adjusting the number of stacked layers and the duct height for heat transfer fluid. Therefore, there will be a great demand for solar water heating systems with various heating capacities operating at a low-temperature heat exchange between PCM and water. At first, in order to clarify the melting process of a solid PCM in the curved-slab container numerically and experimentally, transient 2D numerical melting simulation was performed using Fluent 6.3 software [13], which incorporates such phenomena as convection in the liquid phase, volume expansion due to melting, sedimentation of the solid in the liquid, and close contact melting. Next, the performance enhancement of a latent heat TES system, which is composed of curved-slab containers where heat transfer fluid flows between containers, was analyzed. 2. Experiment 2.1. Determination of container configuration In order to realize the appearance of the close contact melting throughout the melting process, we first determined the container configuration filled with solid PCM. Fig. 1 shows two different configurations of container. Fig. 1(a) is the flat-slab container and Fig. 1(b) is the curved-slab container which is described in detail in the following subsection of 2.2. The two containers had a height of

r [-] radial coordinate along R R [mm] radius of the inner wall of the PCM container Rt [K/W] total thermal resistance S(r, z, t) [mm] position of the melting phase front (see Fig. 5(a)) Ste [-] Stefan number, cp DT/Lm t [s] time T [K] temperature melting temperature of the solid PCM Tm [K] pffiffiffi W [mm or m] width of the PCM container, 3R z[-] coordinate along the length of the PCM container, and also the flow direction of the heat transfer fluid in the TES system Greek symbols

a [m2/s] thermal diffusivity b [1/K] coefficient of thermal expansion at constant pressure DT [K] temperature difference, Tw  Tm n [m2/s] kinetic viscosity r [kg/m3] density Subscripts f heat transfer fluid l liquid PCM s solid PCM w wall

H ¼ 25 mm, a width of W ¼ 100 mm (R ¼ 58 mm), a length of L ¼ 180 mm, and their net PCM volumes were almost the same. The used PCM is n-Octadecane, and the material properties are presented in Table 1. The melting experiment was performed by bathing a container wholly into a transparent plastic tank filled with stagnant water at 45  C (Ste ¼ 0.15) whose temperature was 16.9  C above the melting temperature of n-Octadecane at 28.1  C. The PCM container was placed in the center part of the water tank made of transparent plastic with dimensions of 1 (height)  1.5 (width)  0.5 (depth) m3 as shown in Fig. 1(c). In order to maintain the water temperature at a certain level, an electric heater was used and its power was adjusted. 2.2. Melting performance of a curved-slab container Fig. 2 shows the configuration of the curved-slab container filled with solid PCM. The PCM used in the container is n-Octadecane. The container configuration was used in the one third part of the cylindrical shell perimeter with an inner radius of R. The width of pffiffiffiffiffi ffi the container was W ¼ 3 R, and the height was H. In order to stack the containers vertically in the TES system, both end side walls in the horizontal direction were set similarly at the center of the container of H. Therefore, the height of the container near both side walls became more slender than H. The melting experiment was also performed by bathing a container wholly in a transparent plastic tank filled with water at various temperatures from 30  C (Ste ¼ 0.017, DT ¼ 2  C) to 50  C (Ste ¼ 0.20, DT ¼ 22  C) as shown in Fig. 1(c). The container was made of aluminium with a wall thickness of d ¼ 1 mm, a height of H ¼ 25 mm, a width of W ¼ 200 mm (R ¼ 115 mm) and a length of L ¼ 100 mm, respectively. Only both end walls in the longitudinal z-direction were made of transparent acrylic plate with a wall thickness of 1 mm for visualization. At first, the container was filled with liquid PCM, and then the container was maintained at a constant temperature in order to set the constant and uniform temperature of PCM at about 25  C, which was the sub-cooling temperature of 3.1  C below the melting

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Fig. 1. Two different configurations of containers filled with PCM. (a) Flat-slab container. (b) Curved-slab container. (c) Transparent water tank with constant temperature.

Table 1 Material properties of n-octadecane. n-CH3(CH2)16CH3 Tm ¼ 28.1  C Lm ¼ 244 kJ/kg rs ¼ 890 kg/m3 ks ¼ 0.35 W/(m$K) cps ¼ 1.80 kJ/(kg$K)

Formula Melting point Latent heat of melting Density Thermal conductivity Specific heat

rl ¼ 773 kg/m3

kl ¼ 0.15 W/(m$K) cpl ¼ 2.18 kJ/(kg$K)

temperature at 28.1  C. That is, the solid PCM initially occupied 85% of the enclosed space, having a flat top near both the upper side walls. The melting process was monitored by video-camera. 3. Numerical simulation We tried to clarify the melting process numerically in a curvedslab container filled with solid PCM. Fig. 3 shows the schematic drawing of the 2D calculation model. Among various methods, the

enthalpy-porosity method [14] is the most suitable for solving the phase change problems in which the phase change takes place in a range of temperature. When a phase boundary is present, it is necessary to change the formulation somewhat to account for it. For liquidesolid systems there is a relatively simple method, which is based on tracking the enthalpy change at the liquidesolid interface. The advantage of this method is that no explicit velocity or thermal conditions are to be satisfied at the solideliquid interface [6] [9e14],. Transient 2D numerical melting simulation is performed using Fluent 6.3 software [13]. The simulation shows the melting process from the beginning to the end, and it incorporates such phenomena as convection in the liquid PCM, volumetric expansion due to melting, sedimentation of the solid PCM in the liquid PCM, and close contact. For the phase change region inside the PCM, the enthalpyporosity approach was used, by which the porosity in each cell is set to be equal to the liquid fraction in that cell. Accordingly, the porosity is zero inside fully solid regions. In order to describe the

2D numerical simulation

PCM: n-Octadecane Container wall thickness: d=1mm

Boundary-fitted grid, PCM: n-Octadecane

g 120

R

Enthalpy-Porosity method Air

Air

Mushy region

H

H

Liquid PCM

L

Solid PCM

PCM-air system

VOF method

Solid PCM

W

=

Conduction equation 3 R

Fig. 2. Configuration of curved-slab container filled with PCM.

Wall thickness: 1 mm Fig. 3. Schematic drawing of the 2D calculation model.

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PCM-air system with a moving internal interface but without interpenetration of the two media, a so-called “volume-of-fluid” (VOF) model [15] was used. The temperature distribution in the PCM container wall which was made by the aluminium with a thickness of 1 mm, was solved by the heat conduction equation. The temperature around the outside wall was set to be uniform and constant at Tw. Accordingly, the governing equations used here for the PCM-air and container wall system are as follows: continuity of void fraction, momentum equations, energy equations and conduction equation of the container wall. The boundary-fitted grid was used, and the basic equations were obtained using a control-volume based finite difference procedure. The convective terms were discretized using a first order accurate upwind difference scheme because the order of the convection velocity in the liquid PCM is extremely small within several mm/s. All calculations were carried out with double precision, and the real time step was set to 0.001 s. The initial temperature of the solid PCM was set to 25  C, which was the same temperature as that of the experiment. An almost uniform cell size was used, and the number of cells were between 4593 and 6025 in the case of the container size for H ¼ 15 mm and W ¼ 200 mm, and over 30 cells always existed between the container heights. Independent grid and time step results were obtained by several runs. 4. Total performance analysis of the TES system

a

S(t)

up

qup down

d

Liquid PCM

H qdown

Model

=

up +

down

q = qup + qdown S(t) d Liquid PCM

H

b

Solid PCM

n -Layers

Water

4.1. TES system composed of curved-slab containers Fig. 4 shows the schematic layout of the investigated TES system. The TES system is composed of n curved-slab containers which were stacked in a single slab container as shown in Fig. 2. This figure also shows the location of the heat transfer fluid flows between the slabs. The heat transfer fluid flows in the longitudinal z-direction between the slab containers, and water is used as a heat transfer fluid via a solar water heating system operating under a low-temperature heat exchange between PCM and water. Thermal performance of the TES system as shown in Fig. 4, whose outer size is ~1 (height)  1 (width)  1 (length) m3, was estimated. The PCM container wall was made of aluminium with a wall

Solid PCM

i-1

i

PCM

qdown

Ti-1

Water H

d D

PCM

i+1

Ti

Ti+1

qup qdown

d Container wall

z

z-direction PCM: n-Octadecane Fig. 5. Schematic drawing of the sedimentation model. (a) Sedimentation model. (b) Enlargement of one part of the TES system along the streamwise z-direction.

R 120

Water Exit

thickness of 1 mm, a width of W ¼ 1 m, and a length of L ¼ 1 m whose sizes coincide with the outer size of this TES system. The duct height for heat transfer fluid is D, and the container height of H assumes three different values of 15 mm (number of containers: n ¼ 50), 30 mm (n ¼ 28) and 45 mm (n ¼ 20), respectively.

PCM PCM

4.2. Sedimentation model of solid PCM in a curved-slab container

PCM

For unconstrained melting, the solid PCM exists near the thin molten layer along the bottom wall in a container due to gravity throughout the melting process. The position of the melting phase front, S(r, z, t), changes spatially both radial (r: radial coordinate along the radius of the inner wall of the PCM container) and longitudinal z-directions with time. The length of the PCM container, L, was divided into 500 elements of a sufficiently small length, L/500 ¼ Dz, so that the element could be assumed to be a single thickness of the solid PCM which changes along the longitudinal z-direction. That is, the melting phase front is uniform in the radial r-direction within the small length of Dz, but the melting front in the longitudinal z-direction is changing discretely along each small length of Dz during melting.

PCM PCM PCM

z-direction

Outer size of the TES system:

1 (height)

1 (width)

1 (length) m3

Fig. 4. Schematic layout of a TES system composed of curved-slab containers.

H. Koizumi, Y. Jin / Applied Thermal Engineering 37 (2012) 145e153

In order to realize the sedimentation of a solid PCM in the liquid phase, we used the following simplified model. Fig. 5 shows the schematic drawing of the sedimentation model. The upper part of Fig. 5(a) shows the real melting phenomenon from both the upper and lower sides of the solid PCM by adding the heat fluxes through the upper and the lower sides of the container. Both amounts of melting for dup and ddown are uniform throughout each sedimentation process in the radial r-direction. On the other hand, the lower part of Fig. 5(a) shows the proposed melting model, in which the thickness of the solid PCM is forced to reduce the small amount of dup þ ddown by adding the heat fluxes qup þ qdown through the upper liquid PCM in a short period. The solid PCM stays along the container bottom wall across the thin molten layer due to gravity throughout the melting process. The proposed model aims to be advantageous for calculating just the melting process. That is, the melting thickness within a short period corresponds to the amount of dup þ ddown is decreasing from S(r, t) in each longitudinal element of Dz by adding the heat fluxes qup þ qdown. The melting calculation is repeated until the melting is complete, that is, S(r, t) becomes zero in all longitudinal elements. Fig. 5(b) shows the schematic drawing of the heat transfer fluid flows between containers and the heat fluxes to the PCM. The following assumptions are introduced in this melting performance analysis (i) The PCM is homogeneous and isotropic. (ii) Since only a small Stefan number is considered, a sensible amount of heat is completely ignored. (iii) The melting process is quasi-static phase change. (iv) Convection in the liquid PCM is ignored. (v) Conduction of the PCM in the longitudinal z-direction is ignored, because the conduction of PCM in the spanwise direction will be comparably small. (vi) The temperature of the solid PCM is kept constant at melting temperature, Tm.

149



Rtup ¼

3 1 1 r þ d 1 r1 þ d þ H  S½t þ ln 1 þ ln 2p,Dz h r1 kAl r1 kl r1 þ d

Rtdown ¼

  3 1 1 r þd 1 r2 ln 2 þ ln þ 2p,Dz h ðr2 þ dÞ kAl r2 kl r2  Th



(3)

where h is the heat transfer coefficient, Dz is the length of one element in the longitudinal z-direction. d is the wall thickness and r1 and r2 are the inner and outer radii of the composite cylinder, respectively. kAl is the thermal conductivity of aluminium container wall. In this analysis, h uses the value of the fully developed channel flow. The third term on the right side in Rtdown corresponds to the thin molten layer thickness, Th, between the melting bottom surface of solid PCM and the container bottom wall. For simplicity, Th is the estimate of the analytical result of the spherical capsule by Fomin and Saitoh [16], and it is a constant value of 1 mm throughout the melting. The temperature of the inlet heat transfer fluid was set at various uniform temperatures (various inlet Stefan numbers). The program was made by C code. The phase change material is n-Hexacosane which was usually used in the case of water as a heat transfer fluid, and the material properties are presented in Table 2. n-Hexacosane is safe and shows high heats of fusion, and it is compatible with all metal containers and easily incorporated into heat storage systems.

4.4. Basic equation for heat transfer fluid The heat transfer water flows parallel in the longitudinal zdirection of the curved-slab, and it is assumed that the variation of temperature is only along the longitudinal direction, i.e., the temperature is independent of the perimeter of the cylindrical shell. For each layer, the variation of the internal energy of the heat transfer fluid per unit time is due to energy fluxes exchanged at the bottom and the top of the layer, and with the nodules is given as:

  dT ¼ rf cPf Qv ðTi  Ti1 Þ  qup þ qdown A dt

4.3. Determination of an interface position of solid PCM

rf cPf V

The total energy, E(t), in each longitudinal element of Dz during the phase change process is given as

where i denotes the node’s position along the longitudinal zdirection as shown in Fig. 5(b), (i ¼ 1/inlet, i ¼ l/outlet). Here V is the cell volume occupied by the fluid in the layer, and Qv is the volume flow rate of fluid per unit time through each duct, respectively. The length of the PCM container, L, was divided into 500 elements of a sufficiently small length, L/500 ¼ Dz, so that the element could be assumed to be a single temperature which decreases along the streamwise z-direction.

ZH EðtÞ ¼ rs Lm A,SðtÞ þ

rl cPl A,ðTw  qðr; tÞÞ dr

(1)

S

where S(t) is the position of the solideliquid interface, Lm is the latent heat of fusion, and A is the cross sectional area related to the heat transfer, respectively. The two terms on the right side represent, in order, the latent heat and the sensible heat, respectively. q(r, t) is the temperature of liquid PCM, and r is the radial direction of the PCM container. Since considering only the small Stefan number, the sensible heat is completely ignored in this analysis. Then, the change of the interface position with time is given from the energy balance between the solid PCM and heat fluxes added from the upper and lower container walls to the solid PCM as:

  dE dSðtÞ ¼ rs Lm A ¼ A qup þ qdown dt dt TðtÞ  Tm TðtÞ  Tm ¼ þ Rtup Rtdown

(4)

4.5. Calculation procedure The time derivative, dS(t)/dt, in Equation (2) was discretized using a first order accurate forward-difference scheme. On carrying out a grid and time step independent test, it was found that the results were free from grid size of Dz ¼ L/500 ¼ 2 mm, and time interval at Dt ¼ 0.001 s. Table 2 Material properties of n-hexacosane.

(2)

where Rtup and Rtdown are the thermal resistances through each container wall. These values with convective heat transfer in a fully composite cylinder were used:

Formula Melting point Latent heat of melting Density Thermal conductivity

n-C26H54 Tm ¼ 56  C Lm ¼ 256 kJ/kg rs ¼ 800 kg/m3 ks ¼ 0.21 W/(m$K)

rl ¼ 770 kg/m3

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A calculation is performed following the procedure described below: Step 1: calculate the heat flux of qup þ qdown by Equations (2) and (3). Step 2: calculate the new heat transfer fluid temperature distribution of Ti (i ¼ 1, ..., l) in the longitudinal z-direction by Equation (4). Here, the inlet heat transfer fluid temperatures are changed from 58  C (Ste ¼ 0.02, DT ¼ 2.5  C) to 71  C (Ste ¼ 0.12, DT ¼ 15  C). Step 3: determine the new interface position of S(t) in each longitudinal grid using the new temperature Ti (i ¼ 1, ..., l) and Equation (2), and then calculate the amount of E(t) by using S(t). Step 4: calculate the new melt volume fraction in each grid of Dz, and then obtain the averaged melt volume fraction, MF, along the longitudinal grid. Then, the processes from Step 1 to Step 4 are repeated until the complete melting of the solid PCM, that is MF ¼ 1. 5. Results and discussion 5.1. Effect of container configuration on the melting process At first, the preliminary experiment was performed to clarify the effect of container configurations on the melting process. Fig. 6 shows the visualization photographs in the cross section of the melting solid PCM for two different type containers as shown in Fig. 1(a) and (b), and the materials appear to be as white as the solid PCM. Fig. 6(a) shows the result of flat-slab container, and the lower part of the figure shows the local visualization photograph from the reverse side of the container which was made of the transparent acrylic plate. Fig. 6(b) is the result of the curved-slab container. A remarkable difference of the melting process between the two container geometries is that the solid and liquid PCMs exist upside down. In the case of a flat-type container, liquid PCM stayed near the bottom container wall and, its thickness became thicker with time during melting process, and thus it is impossible to promote the melting of the solid PCM due to its small conductivity and thick molten layer. On the contrary, for the curved-slab container the solid PCM always exists near the bottom wall across the thin molten layer along the inner container wall due to gravity throughout the melting process. Therefore, it is necessary to continue the close contact melting which is important to promote the melting of the solid PCM from the beginning to the end [8]. Complete melting took 27 min for the flat-slab container and 17 min for the curved-slab container, respectively. In the case of the flat-slab container, the stagnant thick molten layer including a large number of small air-bubbles as shown in the lower part of Fig. 6(a), which was produced between the bottom of the solid PCM and the lower surface of the container plate, appeared from the early stage of the melting process. Air-bubbles were regenerated in the melting process which was included in the solidification of liquid PCM. Furthermore, the molten layer was forced to remain between the bottom of the solid PCM and the lower surface of the flat container plate because the outflow of the liquid PCM in the molten layer was prevented due to the next upper large flat solid PCM. And then, the molten layer thickness increased rapidly with time as shown in the upper part of Fig. 6(a). On the contrary, the solid PCM in the curved-slab container as shown in Fig. 6(b) always remained near the bottom of the container wall. Along the contact area, a very thin molten PCM (liquid layer with velocity) exists which is apparently not visible in the photograph. Within this gap the molten material flows to both the edges of the contact area, and consequently, the highest

Fig. 6. Visualization of the melting solid PCM for two different types of containers. (a) Flat-slab container. (b) Curved-slab container.

melting rate is attained at the contact area. Therefore realization of the close contact melting throughout the melting process is clarified. That is, it is found that the curved bottom wall of a slab type container was very important for realization of the close contact melting. At the same time, we confirmed that the container length of L ¼ 100 mm was of sufficient size to grasp the 2D melting phenomena by another visualization experiment. 5.2. Melting performance of a curved-slab container Fig. 7 shows the melting performances for Ste ¼ 0.15 (Tw ¼ 45  C) which were obtained numerically and experimentally. Fig. 7(a) shows the relationship between the melt volume fraction, MF, and melting time in the case of the container height of H ¼ 25 mm, width of W ¼ 200 mm and length of L ¼ 100 mm. The solid line shows the calculated result, and the dotted line shows the experimental result. MF is defined as liquid PCM volume/total PCM volume, and MF ¼ 1 corresponds to the complete melting, and therefore, MF indicates the heat accumulated by the PCM through the process of phase change. Fig. 7(b) shows the instantaneous visualizations which correspond to the three different representative melting instances as shown by the marks [ in Fig. 7(a), but the container size ratios of width and height are not to scale. Fig. 7(bei) shows these visualizations at 4 min and MF ¼ 0.45 after the initiation of melting, Fig. 7(b-ii) shows them at 7 min and MF ¼ 0.65,

H. Koizumi, Y. Jin / Applied Thermal Engineering 37 (2012) 145e153

151

Fig. 7. Melting performance. (a) Melt volume fraction versus time. (b) Visualization photographs (experiment), and temperature and velocity contours (calculation).

and Fig. 7(b-iii) shows them at 11 min and MF ¼ 0.80, respectively. The photos on the left side of the container were obtained by the experiment, and the two on the right hand side were obtained by the numerical simulation, that is, the simulated temperature and velocity contours, respectively. The complete melting time by the experiment was 16 min, and the corresponding melting time by the simulation was 17.5 min, respectively. Qualitative agreement is obtained, but the deviation between experimental and simulated results increases slightly with time. Judging from the discrepancy between the experimental and simulated melting shape of the solid PCM as shown in Fig. 7 (biii) which corresponds to 11 min and MF ¼ 0.80, it seems that the numerical simulation could not correctly obtain the thickness of the thin molten layer along the inner bottom container wall when the solid PCM becomes small and thin, especially in the later melting period. The local velocity in the liquid phase was below about 1 mm/s near the narrow region between the solid PCM and the upper container wall even in the final stage of the melting due to its stable narrow liquid layer. Additionally, the local velocities

were comparatively faster from 1 mm/s to 5 mm/s near both side walls due to the large room for the liquid phase. Dimensional analysis applied herein in general follows the approach suggested in Shatikian et al. [12] [17],. Fig. 8 shows the melt fraction versus an appropriate combination of the Fourier, 1/3 Stefan, and Grashof numbers, namely Fo$Ste2/3$Gr1/6 W $GrH , for all cases which maintain a constant length of L ¼ 100 mm considered in the present simulation. The product of the Fourier and Stefan numbers, Fo$Ste2/3, takes into account the transient heat conduction and phase change. This product cannot account for the effects of heat convection in the liquid PCM. It is possible that a higher heat input leads to a more intensive motion in the liquid phase, and that the convective effect plays an important role in these situations. Then, two Grashof numbers are included in the study, one is the GrW based on the PCM container width and the other is the GrH based on the PCM container height. One can see that all curves almost merge 1/3 4 2 into a single curve, Fo$Ste2/3$Gr1/6 W $GrH ¼ 8  10 $MF , which is shown by the bold-type solid line in the figure. This indicates that the container height-related convection indeed plays an important

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Fig. 8. Generalized results for all simulated cases: Melt fractions. Fig. 9. Complete melting time versus total volume flow rate of the heat transfer fluid.

role in the differences between high and narrow systems. This correlation, also shown in Fig. 8, is valid for the range of parameters explored in the present study, and in particular, for 0.02 < Ste<0.28 and Pr z 57. This MF dependence on Gr1/3 H is irrelevant to the Nusselt number (Nu) dependence of the stable infinite layer heated from the upper surface and cooled from the lower surface in the laminar free convection [18], which depends on the power law of 1/4: Nu ¼ 0.54 (Gr$Pr)1/4. Therefore, it seems that the MF dependence on both GrW and GrH comes from its own complex container configuration. 5.3. Thermal performance of TES system Thermal performance of the TES system, whose size is ~1 (height)  1 (width)  1 (length) m3, was estimated. When the total number of curved-slab containers is n in the TES system as shown in Fig. 4, the container number of n ¼ 50 corresponds approximately to the container height of H ¼ 15 mm, n ¼ 28 to H ¼ 30 mm and n ¼ 20 to H ¼ 45 mm, respectively. The duct height for heat transfer fluid, D, maintains a constant value of 5 mm throughout the analysis. The representative length scale of the duct flow Reynolds number (Re) is defined using the equivalent hydrodynamic diameter of 2  D. The heat transfer fluid is water, and the total volume flow rate, Qtotal, is changed between 0.9 m3/h and 5.4 m3/h. Then the maximum duct Re number is approximately 150 (average velocity in the duct: Um ¼ 14 mm/s) in the case of Qtotal ¼ 5.4 m3/h and n ¼ 20, and then the duct flows are always creeping ones. Fig. 9 shows the complete melting time versus total volume flow rate, Qtotal, for various Stefan numbers, Ste, and the container number, n (n depends only on the container height, H). When the Ste number increases from 0.02 (DT ¼ 2  C) to 0.12 (DT ¼ 15  C), the melting time rapidly decreases. In particular, it takes up to 2 h to obtain the complete melting for Ste ¼ 0.12 and Qtotal > 2 m3/h irrespective of the number of slab layers. Therefore, it is possible to use not only inexpensive electric power during the night-time for utilizing the air-conditioner during day-time hours but also solar energy for utilizing heat sources, such as a Stirling engine, with small temperature differences. Recently, Regin et al. [3] analyzed the behaviour of a packed bed latent heat TES system. The packed bed is composed of spherical capsules filled with paraffin wax as PCM used with a solar water heating system. The results obtained are used for the thermal performance analysis of both charging and discharging processes. The TES system composed of spherical capsules has an outer diameter of 1 m and a length of 1.5 m, and its capacity is 1.2 m3. The

Ste number is 0.1143 and Qtotal is 2.87 m3/h, and the porosity of the bed, which is defined as the ratio of the void volume to the total volume of the packed bed, is 0.4. That is, the net PCM volume of the TES system using spherical capsules [3] is about one-half of that of this curved-slab TES system in the case of the stacked layer numbers of n ¼ 20 (H ¼ 45 mm, and the curved-slab TES system has a capacity of about 1 m3 and the equivalent porosity of the layer is 0.88). It takes over 6 h for the melt fraction to reach 80%, irrespective of capsule diameters changing from 20 mm to 60 mm. Although it is difficult to compare directly the two results of the performance enhancement, it is clear that this TES feasibility study using curved-slab containers shows itself to be an inexpensive and high capacity latent heat TES system with higher efficiency.

6. Conclusions A feasibility study was performed to realize an inexpensive and high capacity latent thermal energy storage (TES) system. In this study, we propose a new compact slab type container which has an arc outer configuration for promoting the appearance of close contact melting. Transient 2D numerical melting simulation of solid phase change material (PCM) in a container was performed by an enthalpy-porosity approach. The simulated results quantitatively elucidated the experimental melting process from the beginning to the end. The TES system is composed of thin slab layers filled with PCM subjected to convective boundary conditions where heat transfer fluid flows between the slabs. The performance enhancement of the latent heat TES system using the curved-slab PCM containers was obtained analytically, which revealed that this TES system shows itself to have a large heat storage capacity with high efficiency.

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