The lattice Boltzmann method is adopted to solve the liquid-vapor phase change problems in this article. By modifying the collision term for the temperature evolution equation, a new thermal lattice Boltzmann model is constructed. As compared with previous studies, the most striking feature of the present approach is that it could avoid the calculations of both the Laplacian term of temperature [∇ • (κ∇T )] and the gradient term of heat capacitance [∇ (ρc v )]. In addition, since the present approach adopts a simple linear equilibrium distribution function, it is possible to use the D2Q5 lattice for the two dimensional cases consided here, making it is more efficiency than previous works in which the lattice is usually limited to the D2Q9. This approach is firstly validated by the problems of droplet evaporation in open space and adroplet evaporation on heated surface, and the numerical results show good agreement with the analytical results and the finite difference method. Then it is used to model nucleate boiling problem, and the relationship between detachment bubble diameter and gravity acceleration obtained with the present approach fits well with the reported works.

In this paper, natural convection melting in a square cavity with gradient porous media is numerically studied at pore-scale level by adopting the lattice Boltzmann method. To generate the gradient porous media, a Monte Carlo technique based on the random sampling principle is used. The effects of several factors, such as Rayleigh number, gradient porosity structure, gradient direction, and particle diameters on natural convection melting are investigated in detail. Based on the numerical data, it is observed that the thermal performance of the gradient porous media always depends on the Rayleigh number and, specifically, as the Rayleigh number is set to 106, the total melting time obtained for the case of the negative gradient porous media is always shorter than the cases of positive gradient and uniform porous media. However, if the Rayleigh number is equal to 104, at which the heat transfer is dominated by the heat conduction, it is noted that the performance of the positive gradient porous media is better than the other cases. To have a better understand on this point, various simulations are also performed and we found that there usually exists a critical value of Rayleigh number to determine the thermal performance of the gradient porous media. Moreover, our numerical results also show that the influence of the particle diameter on the liquid fraction is insignificant as Rayleigh number is set to 104, while it has a great impact on the liquid fraction when Rayleigh number equals 106.

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Phase change material (PCM) has received significant attention due to its great potential for thermal energy storage. However, the major undesirable property of PCM is related to its low thermal conductivity. In this work, the electrohydrodynamic (EHD) enhancement of PCM melting in circular-elliptical annuli is investigated numerically by using the lattice Boltzmann method (LBM). The key motivation for our choice of the elliptical shape is due to the fact that the more curved elliptical surface corresponds to stronger charge injection strength, which may lead to stronger flow field, and the consequent increase of heat transfer rate. The influences of several non-dimensional parameters, including electric Rayleigh number T, thermal Rayleigh number (Ra) and the aspect ratio (AR) of the inner ellipse are investigated in detail. Based on the numerical results, it is found that the radial electro-convective flow induced by the external electric field makes a significant contribution to the enhancement of melting heat transfer, and specially, the maximum time saving in some cases is more than 85%. Moreover, we observe that when the Coulomb force is dominant over the buoyancy force, no matter the inner elliptical tube is oriented horizontally or vertically, the total melting times in these two cases are nearly the same, and the melting performance obtained for the circular electrode is usually better than the other cases. However, when the flow regime is dominated by the buoyancy force, the use of a slender vertical-oriented elliptical electrode instead of the circular one is more efficient.