Li Xinfang Wang Xianju Zhu Dongsheng

(1Zhongshan Torch Polytechnic，Zhongshan 528436，China) (2College of Science，South China Agriculture University，Guangzhou 510642，China) (3Guangzhou Institute of Energy Conversion，Chinese Academy of Sciences，Guangzhou 510640，China)

Numerical analysis on cold storage characteristic of nanoparticle-enhanced phase change material for energy saving

Li Xinfang1Wang Xianju2Zhu Dongsheng3

(1Zhongshan Torch Polytechnic，Zhongshan 528436，China) (2College of Science，South China Agriculture University，Guangzhou 510642，China) (3Guangzhou Institute of Energy Conversion，Chinese Academy of Sciences，Guangzhou 510640，China)

The cold storage characteristic of nanoparticle-enhanced phase change material(NEPCM)was investigated by using numerical simulation method with Fluent software. The influence of Grashof number and particle concentration on the cold storage performance was discussed . The numerical results indicate that the cold storage characteristic of the NEPCM largely depends on the volume fraction of nanoparticles，while exhibits little sensitivity to Grashof number. As the volume fraction increases，the freezing time of the NEPCM is lowered for a given initial Grashof number. The total freezing time of the NEPCM can be lowered by 16.3% with Cu nanoparticles volume fraction is 1.0%. The reduction of the freezing time is attributed to the higher thermal conductivity of the NEPCM. At the same time，less energy per unit mass of the NEPCM is needed for freezing the NEPCM because of the lower latent heat of fusion.

nanoparticle-enhanced phase change material；cold storage；freezing time；numerical simulation

1 Introduction

Because the conventional energy sources are quickly depleted and the demand of energy is growing，more and more researchers pay attention to renewable energy sources and energy storage systems. Solid-liquid phase change provides considerable advantages such as high storage capacity and nearly isothermal behavior during the melting/freezing processes. During these years，researchers have tried to find new way to develop energy storage system. Using nano technology to enhance the heat transfer indicates great opportunity in storage system. Because the thermal conductivity of conventional heat transfer fluids is low，nanotechnology is considered to enhance thermal characteristics with substantially higher conductivities. The presence of the nanoparticles in the fluids increases appreciably the effective thermal conductivity of the fluid and consequently enhances the heat transfer characteristics. Masuda et al.[1]reported that the thermal conductivity was enhanced by dispersing ultra-fine(nanosize)particles in liquids. Soon thereafter，Choi[2]first designated the new fluids with higher thermal conductivity as "naofluids". Khanafer et al.[3]simulated heat transfer characteristic of the nanofluids in a two-dimensional enclosure for various pertinent parameters. Khodadadi et al.[4]were the first to report the improved functionality of phase change material (PCM) with nanoparticles. They found that the nanoparticle-enhanced phase change materials(NEPCM)exhibit higher thermal conductivity than the base fluids. Zhu et al.[5]simulated the thermal energy storage behavior of SiC-H2O nanofluids in a two-dimensional enclosure. Ranjbar et al.[6]studied the solidification behavior of the NEPCM and the relevant parameters . They found the nanofluid heat transfer rate increases with the increase in the nanoparticles volume fraction. Also，it was found that the temperature gradient in the liquid is too small to cause a significant natural convection in the liquid. Thus，heat conduction is dominant in heat transfer of both solid and liquid[7-8]. In this study the freezing of the NEPCM was studied.

2 Mathematical formulation

A physical model of two-dimensional enclosure is shown in Figure 1,in which the sideHis filled with nanofluid. The physical dimension of the enclosureHis chosen to be 10 mm. The horizontal walls are assumed to be adiabatic，not conductive，and impervious to mass transfer. The NEPCM in the enclosure is incompressible and the flow is laminar. The particle shape and particle size distribution are uniform，and both the nanoparticles and the base fluid are in a thermal equilibrium，which is consistent with the flow velocity The nanoparticles are assumed to have a uniform shape and size. Moreover，it is assumed that both the fluid phase and nanoparticles are in thermal equilibrium state and they flow at the same velocity. The left vertical wall is maintained at a high temperature(TH)，while the right vertical wall is kept at a low temperature(TC). The thermophysical properties of the NEPCM are assumed to be constant except for the density variation in the buoyancy force，which is based on the Boussinesq approximation.

Fig.1 Physical model of two-dimensional enclosure

Under these assumption，the governing equations are：

Continuity：

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(1)

X-momentum equation：

The instantaneous streamlines within the NEPCM for the initial 15s during the freezing of the NEPCM for an initialGr=104and a solid particle volume fraction of 1% are shown in Figure 4. The streamlines att=0 correspond to a similar case studied by Khanafer et al.[3]and Khodadadi et al[4]，and a CW rotating vortex is clearly observed. As a result of the sudden lowering of the temperatures of the two active walls att>0，the CW rotating vortex diminishes in strength and spatial coverage due to formation of a CCW rotating vortex next to the left wall. The creation of the dual-vortex flow pattern was examined in greater detail by lowering the time step to 0.1 s for this case. Note that the formation，growth and equilibration of the CCW vortex during the initial 15 s involves a dynamic interaction with the initially strong CW vortex. At thet=10-15 s instant，two vortices rotating in opposite directions and nearly equal in size are observed squeezed between the left wall and a thin frozen layer next to the right wall. For the remainder of the freezing process，the dual-vortex structure will persist however due to the leftward movement of the freezing front，the vortices will shrink in coverage space and their strength will decay. It should be noted that the actual Grashof number for this unsteady freezing problem decreases with time due to the continuous shrinking of the distance between the left wall and the liquid-solid interface.

(2)

Y-momentum equation：

(3)

Energy equation：

(4)

In addition，the thermal conductivity of the NEPCM was measured by a Hot Disk Thermal Constants Anlyser，and the viscosity of the NEPCM was measured using capillary viscometers.

(7)

3 Khanafer K，Vafai K，Lightstone M L. Buoyancy-driven heat transfer enhancement in a two-dimentional enclosure utilizing nanofluids[J]. Int. J. Heat Mass Transfer，2003，19：3639-3653.

(8)

Whereas the heat capacitance，latent heat of fusion for the NEPCM and part of the Boussinesq term are：

(9)

(10)

(11)

Withφis the volume fraction of the nanoparticles and subscripts f，nf and p stand for base fluid，NEPCM and nanoparticles，respectively.

4 Khodadadi J，Hosseinizadeh S F. Nanoparticle-enhanced phase change materials(NEPCM)with great potential for improved thermal energy storage[J]. Int. J. Comm Heat Mass Transfer，2007，34：534-543.

The above equations can be cast in non-dimensional form by incorporating the following dimensionless parameters：

The pertinent thermophysical properties are given in Table 1. The present processing method can be found elsewhere[3-4].

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Table 1 Thermophysical properties of the nanoparticle，water and NEPCM

The initial and boundary conditions for the present investigation are presented as Table 2.

Table 2 Initial and boundary conditions

3 Numerical methods

Starting at timet=0，the temperatures of both active left and right walls were lowered by the same amount such that the cold right wall was held 10 ℃ below the freezing temperature of the base fluid(TH=273.15 andTC=263.15 K). Consequently，the NEPCM will start freezing on the right wall and the solid front travels to the left. The remaining boundary conditions were unchanged in comparison to the conditions prior tot=0.

Starting with steady natural convection within the Cu-H2O NEPCM that is inside a differentially-heated square cavity，freezing of the Cu-H2O NEPCM was investigated. The temperatures of the left and right walls were lowered by 10 ℃. In effect，the cold right wall was held 10℃ lower than the freezing temperature of the base fluid(273.15 K). Consequently，the NEPCM will start freezing on the right wall and the solid front travels to the left. The other boundary conditions remained unchanged. Solid particle volume fractions of 0，0.1%，1.0% and 5.0% were considered for two initial Grashof numbers of 104and 105. The pertinent properties are given in Table 1. Contours of the volume fraction of the NEPCM during freezing at various time instants are shown in Figure 2 and Figure 3 for an initial Grashof number of 104. The time instants in Figure 2 are 100 and 600 s，the time instants in Figure 3 are 1 200 and 2 400 s. Color gray is used to identify the liquid phase，whereas color black is indicative of the frozen solid phase. In general，the sharp liquid-solid interface is nearly vertical with a mild misalignment toward the colder wall early on，thus favoring a longer wetted length on the top insulated wall. This can be attributed to the buoyancy-driven convection in the cavity that was already at full strength att=0 in the form of a clockwise(CW)rotating vortex. Fort>0，the strength of this vortex diminishes whereas a second counter-clockwise(CCW)rotating vortex is created next to the left wall(see Figure 4).

In order to verify the numerical code，comparison of the average Nusselt number along the hot wall with previous works[9-11]for different Rayleigh numbers is shown in Table 3. This table shows an excellent agreement between our results and those of other benchmark solutions，which suggests that our calculation method is adequate to describe the phase change process of the NEPCM correctly.

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Table 3 Comparison of present numerical simulation with previous works

4 Results and Discussion

The SIMPLE method within version 6.2 of the commercial code Fluent was utilized to solve the governing equations. For all the cases reported here，uniform grid spacings for bothxandydirections were utilized. The calculating time step was 1s. The Quick differential algorithm was used to deal with the momentum and energy equations，whereas the PRESTO algorithm was used to deal with the pressure correction equation. The under-relaxation factors for the velocity components，pressure correction，thermal energy and liquid fraction were 0.5，0.3，1 and 0.9 respectively. In order to satisfy convergence criteria(10-7for continuity and momentum，and 10-9for thermal energy)，the number of iterations for every time step was set to 1 000.

For this Grashof number(Gr=104)，it is observed that as the solid particle volume fraction is raised，the Cu-H2O NEPCM will freeze more rapidly. There are two possible reasons to explain the behavior of the quicker freezing rate. One is the higher thermal conductivity for the NEPCM，because the crystal growth mainly depends on heat transfer. At the process of freezing，a large amount of heat will be discharged. If the heat can’t be released in time，the freezing process will be hindered. After adding the nanoparticles to the base fluid，the fluid has higher thermal conductivity. Therefore，the freezing speed of the NEPCM is able to be accelerated. Another reason may be the Cu nanoparticles acting as a nucleating agent. It is known that the freezing process of pure water has a supercooling degree about 4 ℃. When the nanoparticles are added into water，the supercooling degree of water is decreased according to the mechanism of heterogeneous nucleation. The beginning of freezing time is ahead. This is also helpful to save the freezing time.

2.2.2 Decomposition of vanillin to small carboxylic acids

Fig.2 Contours of volume fraction of NEPCM at various time instants during freezing course(Gr=104)

Fig.3 Contours of volume fraction of NEPCM at various time instants during freezing course(Gr=104)

Fig.4 Streamline patterns of Cu-H2O NEPCM at various time instants for initial 15 s during freezing course(Gr=104，φ=1.0%)

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