A new thermal lattice Boltzmann model for liquid-vapor phase change

Abstract

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.

An efficient thermal lattice Boltzmann method for simulating three-dimensional liquid-vapor phase change

“…To treat the liquid-vapor phase change problem, the above governing equation is usually rewritten as a standard convection-diffusion equation in previous LB models [21,22,32], such that a discrete source term related to ∇ (ρc v ) was also needed to be added into the temperature evolution, which may affect the numerical stability and accuracy when the fluid properties change significantly across the liquid-vapor interface [24,25]. In this setting, recently we proposed a 2D MRT thermal LB model for liquid-vapor phase change [33], and in contrast to previous LB models, the calculation of ∇ (ρc v ) is eliminated in the proposed model. In this work, considering the significant differences in the development and implementation of 3D MRT model, we extend this 2D model to 3D situation, and the evolution equation for the temperature T distribution function g i (x, t) can be expressed as…”

“…In this section, we intend to validate the proposed thermal LB model by simulating the droplet evaporation in an open space. For this problem, it turns out that the square of the droplet diameter tends to evolve linearly in time (also called d 2 law) [33],…”

“…To address the above problems, in the current work, we target to construct an efficient thermal LB model for simulating 3D liquid-vapor phase change, and it can be viewed as an extension of our recent 2D LB approach for non-ideal fluids [33]. As shown later, the aforementioned defects do not exist for the present model such that it holds the major advantages of the LB method.…”

Droplet impact dynamics on Janus-textured heated substrates

“…The new thermal LB model proposed by Wang et al [29] is adopted to solve the liquid-vapor phase change problem, and the most significant feature of this model compared with the previous models is that the Laplace term of the calculated temperature [∇ • (κ∇T )] and the gradient term of the thermal capacitance ∇ (ρc v ) can be avoided. The evolution equation of the temperature distribution function can be described as…”