Simulation of phase separation in a Van der Waals fluid under gravitational force with Lattice Boltzmann method

Abstract

Purpose – This paper aims to assess the accuracy of Lattice Boltzmann method (LBM) for numerical simulation of the stratification of a Van der Waals (VdW) fluid subjected to a gravity field and non-uniform temperature distribution. A sensitivity analysis of the influence of the pseudopotential parameters and the grid resolution is presented. The effect of gravity force on interface densities, density profiles and liquid volume fraction is studied. Design/methodology/approach – The D2Q9 multiple-relaxation-time pseudopotential LBM for two-phase flow is proposed to simulate the phase separation. The analytical solution for density profiles in a one-dimensional problem is derived and used as a benchmark case to validate the numerical results. Findings – The numerical results reproduce the analytical density profiles with great accuracy over a wide range of simulation conditions, including variations of the gravity and temperature fields. Particularly, the numerical simulations are able to represent the effect of gravity on the existence and position of the liquid– vapor boundary of an ideal pure substance in thermodynamic equilibrium. The sensitivity of the results to variations of the calibration parameters of the VdW pseudopotential was assessed. Research limitations/implications – The numerical simulations were performed assuming a VdW fluid in a 2-D cavity with one periodic direction for which analytical solutions for benchmarking purposes are possible to obtain. Originality/value – The following fundamental question is addressed: Is the pseudopotential LBM capable of simulating accurately the liquid–vapor equilibrium under gravity forces and temperature gradients? Moreover, regarding that the pseudopotential model requires the calibration of several internal parameters to achieve thermodynamic consistency, the sensitivity of the results to variations of these parameters is assessed.