Study on the flow and thermal characteristics of a heat storage system

THE ASIAN SYMPOSIUM ON COMPUTATIONAL HEAT TRANSFER AND FLUID FLOW - 2011, 22 26 SEPTEMBER 2011, KYOTO, JAPAN Study on the flow and thermal characteristics of a heat storage system Chung-Jen Tseng, Tzu-Yu Kao, Chi-Fu Chen Department of Mechanical Engineering, National Central University, Chungli, Taiwan corresponding author, E-mail: cjtseng@cc.ncu.edu.tw Paper ID: 130 Abstract Solar power is a clean and sustainable energy. But the intensity of solar irradiation is unstable due to the change of season, weather, day and night. A heat storage system can be used as a buffer to mitigate the fluctuation of solar incidence. Phase change material (PCM) is the most feasible method of heat storage because of its high heat capacity and flexibility [1]. This study investigates the thermal and flow characteristics of an energy storage system using PCM. The governing dimensionless equations and boundary conditions of the problem are formulated and solved numerically by using the enthalpy-porosity method [2] with the control volume approach. The melting process, the total melting time, and the effects of several parameters are discussed. Results show that, for cases of high Peclet number, high Stefan number or high thermal conductivity ratio of the PCM to the heat transfer fluid, the melting time is reduced due to the enhancement of heat transfer and the circulation of the PCM. For intermediate and high temperature PCM energy storage systems, KF is the best material to use. Correlations between the dimensionless total melting time of the PCM and the Peclet number, Stefan number, aspect ratio and the thermal conductivity ratio are also derived for different conditions. 1. Introduction As the fossil fuel is running out, the development of alternative energies becomes more important. The alternative energy must be clean, cheap, and sustainable. Solar energy is one of the most suitable energy for these requirements. But the solar energy needs a heat storage system to be used as a buffer to mitigate the fluctuation of solar incidence. Phase change material (PCM) is the most feasible method of heat storage because of its high heat capacity and flexibility. The heat storage has three different types: sensible heat, latent heat, chemical heat. Sensible heat is simple, cheap and mature, but it has fluctuation of temperature and the quantity of heat storage is the least. Lorsch [3] used tubes passing through the solar collector in 1973. When the water flows in the tubes, heat is absorbed, then the hot water stores in a tank. Loef [4] used plate solar collector to receive the heat. The size of storage tank and collector are discussed. Dhifaoui et al. [5] filled the vertical pipe with small glass balls as porous media. The mechanism can keep the outlet temperature low, and increase the storage efficiency. Chemical energy has the largest quantity of heat storage, but the reaction is very slow and the reversibility is not good. Kanamori et al. [6] used the hydration and dehydration of Ca(OH) 2 / CaO as thermo chemical reaction. The temperature was above 400 o C. The heat storage efficiency was 77% for 120 minutes reaction. Latent heat has excellent flexibility, relatively good quantity of heat storage, and good stability of temperature. Fatih Demirbas [7] pointed out that the paraffin wax was a good PCM for low temperature. The heat storage density is around 200 kj/kg. But the conductivity of PCM is not good. In order to increase the heat transfer, several methods can be used, such as adding fins in PCM, adding high conductivity materials in PCM, changing the thickness of the shell, and changing the shape of tank [8-13]. 2. Theory and model description Melting and solidification problem includes two physical mechanisms phase change and heat transfer. This kind of problem has three features. (1) There is a moving boundary or zone between two phases to separate the different characteristic zones. (2) At the interface, the absorption and release of latent heat appears at the same time. This means the location of the interface is a function of time. For a melting process, the interface is moving toward the solid zone, until the melting process is finished. The interface can be seen as the moving boundary of solid zone or liquid zone. (3) The melting and solidification process is nonlinear; the boundary condition is determined by the absorption and release of latent heat. 2.1. Enthalpy-porosity method The enthalpy-porosity method is developed by Voller [2] at 1987. It is an enthalpy formulation based on fixed grid methodology. They used the variation in latent heat to represent the fraction of solid at the interface. Therefore, in the enthalpy-porosity method, a porosity of 0 represents solid, and 1 stands for liquid.

2.2. Model geometry The model considered in this study is shown in Fig.1. The inner cylinder is the channel which heat transfer fluid (HTF) flows through. The other zone is filled with PCM. Table 1: The properties of paraffin wax. Thermal conductivity k [W/ m-k] Specific heat Cp [J/ Kg-K] Density ρ [Kg/m 3 ] 0.2 1250 800 Dynamic Heat of Melting viscosity fusion point μ L f T m [Kg/m-s] [J/ Kg] [K] 8.00 10-3 1.25 10 5 303 Thermal expansion coefficient β [1/K] 2.00 10-3 Figure 1: The geometry of storage tank. Fig.2 is the 2-D axial symmetry scheme. The upper zone is PCM and lower zone is HTF. The bottom edge is the axis. For the base case, R 1 is 5 mm, R 2 is 15 mm, and l is 20 mm. The PCM is paraffin wax, and its physical properties are listed in Table 1. The HTF used is water. In the calculation, the HTF with high temperature flows from left side to right side. Heat is transported from HTF to PCM by conduction. Then the PCM is melted by absorbing the heat. Due to gravity, natural convection is observed in the melting PCM region. 2.3. Governing equation The assumptions used are summarized below. Axial symmetry PCM is uniform and isotropic The flow is Newtonian, incompressible, and laminar. Negligible viscous dissipation The Boussinesq approximation is employed The dimensionless parameters and governing equations in r- z cylindrical system are: r aor, z aoz, ao t U, U p p, u Uu, 2 a w, Uao Pe, Pr, k ) C Uw, T Tm ( Ta Tm) T ( a 0 R2 R1, Continuity equation: 1 w ( ru) 0 r r z p o B 2 2 a o (1) Figure 2: The 2-D axial symmetry scheme of storage tank. Momentum equation: Pe 2 u 2 u u u u Pr r z p 1 u u r r r r r Pe w 2 w w w w Pr r z ( S r 2 r BS 2 r u 1 1 z z Pe 2 2 C(1 f), C(1 f) S 3 z ) 3 ( f ) ( f ) 2 p w Ra T B S w 3 2 z (2) (3) Energy equation: 2

T 1 Pe f Pe r u T r w T L r r z Ste t 2 2 ( ) ( ) 2 2 2 T 2 1 T T 2 2 r r r z (4) correlation between the dimensionless total melting time of the PCM and the Peclet number is found to be 0.9556 6.79 Pe. total 2.4. Initial and boundary conditions There are seven boundaries include inlet, outlet, axis, and four walls. The velocity and temperature of inlet is fixed. Due to the fixed density of HTF, the velocity of outlet is the same value of inlet. The boundary condition of axis is axial symmetry for velocity and temperature. The walls are adiabatic and no-slip condition. The initial temperature of PCM is below the melting point. That means the PCM is solid at first. The dimensionless boundary conditions are shown below. Inlet ( z 0, 0r R1): T T in, min m out Outlet ( z H, 0 z H ): min m out Axis ( r 0 ): T 0 r Inner wall ( r R1, 0 z H ): T T k, r r u w 0 Outer wall ( r R2, 0 z H ): T 0, u w 0 r Left wall ( z 0, R1r R2): T 0, u w 0 z Right wall ( z H, R1r R2): T 0, u w 0 z Figure 3a: The temperature distribution for Pe =3.2 10 3. 2.5. Numerical method The numerical solutions are based on SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm which is implemented in commercial software ANSYS Fluent. A grid independence test was performed and a grid size of 500 x 150 was adopted. Figure 3b: The temperature distribution of Pe =6.4 10 2. 3. Results and discussion According to Eq. (4), the dimensionless total melting time (τ) of the PCM are functions of the Peclet number (Pe), Stefan number (Ste), aspect ratio (δ), and the thermal conductivity ratio (k ). Effects of these parameters are discussed in the following sections. 3.1. Effect of the Peclet number The value of Peclet number is determined by the velocity of HTF. For Ste = 0.1, 2, k =0.33, the Pe is varied from 3.2 10 3, 6.4 10 2, to 1.6 10 2. As shown in Figs. 3 and 4, the outlet temperature of HTF and the liquid fraction of PCM decrease as Pe is decreased. This is caused by the reduced inlet velocity. The natural logarithm relation between the total melting time and Pe is shown in Fig. 5. It can be seen that the scheme is an oblique line. The Figure 3c: The temperature distribution for Pe =1.6 10 2. 3

Figure 4a: The liquid fraction distribution for Pe =3.2 10 3. Figure 5: The total melting time versus Pe. Figure 4b: The liquid fraction distribution for Pe =6.4 10 2. 3.2. Effect of the Stefan number The Stefan number represents the ratio of sensible heat to latent heat. The larger Ste means the larger sensible heat. For Pe = 3.2 10 3, 2, k =0.33, Ste is varied from 0.1, 0.5, to 1.0. As shown in Figs. 6 and 7, the temperature and the liquid fraction of PCM increases as Ste is increased. This is because of the sensible heat from HTF is increased when Ste is increased. The relation between the total melting time and Ste is shown in Fig. 8. The dash line is the curve fitting. The correlations between the dimensionless total melting time of the PCM and the Stefan number are found to be ln( ) 0.8982ln( Ste) 7.7002 (0.001 ste 0.05) ln( ) 1.0598ln( Ste) 7.1682 (0.05 ste 1) Figure 6a: The temperature distribution for Ste =0.1. Figure 4c: The liquid fraction distribution for Pe =1.6 10 2. 4

Figure 6b: The temperature distribution for Ste =0.5. Figure 7b: The liquid fraction distribution for Ste =0.5. Figure 6c: The temperature distribution for Ste =1.0. Figure 7c: The liquid fraction distribution for Ste =1.0. Figure 7a: The liquid fraction distribution for Ste =0.1. Figure 8: The total melting time versus Ste. 5

3.3. Effect of the aspect ratio For Pe = 1.6 10 4, Ste = 0.17, k =0.33, the aspect ratio δ of the length to the thickness of the PCM is varied from 2, 3, to 6. As shown in Figs. 9 and 10, the temperature and the liquid fraction of PCM decrease as δ is increased. The length of PCM increases with the δ for the same thickness. With the length getting longer, heat is more difficult to transfer to the outlet. The relation between the total melting time and δ is shown in Fig. 11. The correlation between the dimensionless total melting time of the PCM and the aspect ratio is found to be 3 2 43.678 23.68 260.103 333.597. total Figure 9c: The temperature distribution for δ = 6. Figure 9a: The temperature distribution for δ = 2. Figure 10a: The liquid fraction distribution for δ = 2. Figure 9b: The temperature distribution for δ = 3. Figure 10b: The liquid fraction distribution for δ = 3. 6

Figure 10c: The liquid fraction distribution for δ = 6. Figure 12a: The temperature distribution for k = 0.001. Figure 12b: The temperature distribution for k = 0.01. Figure 11: The total melting time versus δ. 3.4. Effect of the thermal conductivity ratio The thermal conductivity ratio is the ratio of the thermal conductivity of PCM to that of HTF. For Pe = 3.2 10 3, Ste = 0.1, δ = 2, k is varied from 0.001, 0.01, to 0.1. As shown in Figs. 12 and 13, the temperature and the liquid fraction of the PCM increase as k is increased. The relation between the total melting time and k is shown in Fig. 14. The correlation between the dimensionless total melting time of the PCM and the thermal conductivity ratio is found to be 3 2 ln( ) 0.0031(ln k ) 0.0303(ln k ) 0.6524(ln k ) 8.8035. Figure 12c: The temperature distribution for k = 0.1. 7

Figure 13a: The liquid fraction distribution for k = 0.001. Figure 14: The total melting time versus k. 3.5. Selection of intermediate and high temperature PCM Besides the safety and stability, the two most important features of PCM are the heat storage capacity and the melting time. Larger heat storage capacity and faster melting are desired. According to Table 2, KF has the largest heat storage capacity and relative shorter melting time. Therefore KF may be considered as the best candidate among the materials compared in Table 2. Figure 13b: The liquid fraction distribution for k = 0.01. Table 2: The total melting time and the heat storage capacity for several PCMs. PCM Total melting time [s] Heat storage [kj] KNO 3 -NaNO 3 2764 2.51 LiBr 12424 6.45 NaCl 8014 9.44 Na 2 CO 3 5000 6.94 MgCl 2 8352 9.55 K 2 CO 3 3422 4.76 KF 6370 12.16 Figure 13c: The liquid fraction distribution for k = 0.1. 4. Conclusions This study numerically investigated the melting and heat transfer characteristics of a cylindrical heat storage tank. Effects of Pe, Ste, δ, k on the melting of PCMs are discussed. The results are summarized below: Pe, Ste, and k are inversely proportional to the total melting time; δ is proportional to the total melting time. For intermediate and high temperature PCM energy storage systems, KF may be considered as the best material to use. 8

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