Extended lattice Boltzmann method for numerical simulation of thermal phase change in two-phase fluid flow

Abstract

In this article, a method based on the multiphase lattice Boltzmann framework is presented which is applicable to liquid-vapor phase-change phenomena. Both liquid and vapor phases are assumed to be incompressible. For phase changes occurring at the phase interface, the divergence-free condition of the velocity field is no longer satisfied due to the gas volume generated by vaporization or fluid volume generated by condensation. Thus, we extend a previous model by a suitable equation to account for the finite divergence of the velocity field within the interface region. Furthermore, the convective Cahn-Hilliard equation is extended to take into account vaporization effects. In a first step, a D1Q3 LB model is constructed and validated against the analytical solution of a one-dimensional Stefan problem for different density ratios. Finally the model is extended to two dimensions (D2Q9) to simulate droplet evaporation. We demonstrate that the results obtained by this approach are in good agreement with theory.

Investigation of vapor condensation on a flat plate and horizontal cryogenic tube using lattice Boltzmann method

“…Safari et al [26] extended the model of Lee to simulate thermal phase-change phenomena in two-phase fluid flows. Both liquid and gas phases were considered to be incompressible.…”

“…In this article, the phase-change model of Safari et al [26] is extended to investigate the vapor condensation, liquid film formation, and dew drop sprinkling from cryogenic horizontal tube. In the present simulation, the modified curved boundary treatment of Filippova and Hanel (FH) is used, which enable curved solid walls to be treated with second order accuracy.…”

“…The developed model was successfully validated for a one-dimensional Stephan problem with different density ratio up to 1:1000, and the ability of the model to simulate two-dimensional droplet evaporation was tested. Begmohammadi et al [27] employed the phase-change model of Safari et al [26] to simulate nucleate pool boiling. Bubble growth on and departure from superheated surface was simulated.…”

A Non-Isothermal Chemical Lattice Boltzmann Model Incorporating Thermal Reaction Kinetics and Enthalpy Changes

“…As with the single-phase system, this model has been validated over many years by repeated analyses and comparisons with analytical and experimental results [14,16,18,44,45]. It has been successfully applied to a variety of thermal flow problems including natural convection [14,18,44,[46][47][48][49][50], turbulent convection [51][52][53][54], thermal channel flows [14,40,55,56] and more complex systems involving multiple phases and phase change [57][58][59][60][61][62][63][64][65].…”

Numerical Simulation of Melting with Natural Convection Based on Lattice Boltzmann Method and Performed with CUDA Enabled GPU

“…All of those advantages make LBM a promising complementary approach to the direct solution of the Navier-Stokes (NS) equations [26]. In relatively recent studies, some researchers have begun to choose LBM to simulate phase change [10][11][12][13][14].…”