Study of Rayleigh Benard Convection by LatticeBoltzman Method

Kheireddine Zehouani, and A. Boukhari
Department of Physics and Process Control, Szent Istvàn University, Hungary

Abstract: The lattice Boltzmann method (LBM and its schema D2Q9 and D2Q5) is applied for the numerical study of hydrodynamic and thermal instability during confinement of air or water in rectangular cavities with aspect ratios A = L/H varying in the range (0.5, 1, 2, 3, 5), The lattice Boltzmann method (LBM) was used to discretize the steady-state and transient flow equations. The cavity is differentially heated on the horizontal walls. The study is carried out for a Prandtl number of Pr = 0.71 (air), and for Pr = 7.01 (water). The Rayleigh number values change between (6×103)-(130×103). We have discussed and analyzed the influence of Rayleigh number on the dynamic and thermal fields as well as on the average Nusselt number of the flow. In addition, critical frequencies dominating the oscillatory flow have been determined. The results show the frequency dependence with the aspect ratio and the critical Rayleigh number. Although our study is two-dimensional, it is expected that the results of a three-dimensional numerical simulation, focusing on the possible obstacles or structure in the flow, as well as the possible presence of the instabilities due to the double diffusion, confirm the qualitative results obtained in this work.

Key words: Lattice Boltzmann method, Rayleigh-Bénard convection, rectangular cavity, instability