Lattice Boltzmann simulation of the two-dimensional Poiseuille-Rayleigh-Benard flows instability

Abstract

A numerical method based on the lattice Boltzmann equation (LBE) is developed in two dimensions to solve the equations of conservation of energy and momentum of a Poiseuille-Rayleigh-Benard (PRB) mixed-flow. The configuration considered in this work is a channel heated from below, cooled from the top and crossed by a fluid (Pr = 1). The study is conducted for a range of Rayleigh numbers (0 < Ra < 5000) and Reynolds (0 < Re < 500). For Re = 0 and Ra exceeds the critical value (1707.76), the Rayleigh-Benard (RB) mixed-flow appears. However, for Re values other than 0, the transition from Poiseuille flow in a cellular flow is obtained for the largest critical Ra (in limited area) and characteristics of cells depend on the intensity of the flow at the entrance of the channel. Key words: Poiseuille-Rayleigh-Benard flow, Lattice Boltzmann equation (LBE), horizontal rectangular channel.