MRT-LBM simulation of natural convection in square annulus with a porous coating: route to chaos

Abstract

In this work, multiple-relaxation-time lattice Boltzmann method is applied for examining transient natural convection in a square annulus of circular interior cylinder. This duct is covered by a porous deposit on all interior walls. The Darcy-Brinkman-Forchheimer equation is implemented to model the momentum equations in the porous matrix and the Boussinesq approximation is assumed for buoyancy term. The impact of Darcy number (10−6 ≤ Da ≤ 10−2), Rayleigh number (Ra ≥ 101), radius ratio of the circular cylinder (0.05 ≤ R ≤ 0.40) and the thickness of the porous layer (0.05 ≤ δ ≤ 0.15) on natural convection are analysed. The outcomes are represented under the form of stream functions, isotherms and mean Nusselt number. In addition, temporal evolution and phase portrait are plotted to examine the unsteady flow at elevated Rayleigh numbers. The results are coherent and show that natural convection develops from stable state to chaotic flow via periodic and quasi-periodic oscillatory regimes as the Rayleigh number increases.