Etude de la convection naturelle dans une cavité carrée munie d’obstacles solides par la méthode de Boltzmann sur réseau

Abstract

The work focuses on the numerical simulation by the lattice Boltzmann method. Laminar natural convection is studied in a closed square cavity and differentially heated. The latter is provided with two solid obstacles placed inside on the horizontal walls. First, a detailed study of heat transfer by natural convection is exposed. A literature review and also presented on the most important works found in the configuration associated with this studied. The geometry chosen for this study is a square cavity formed by two horizontal adiabatic walls and two vertical walls, differentially heated. The cavity is completely filled with a Newtonian fluid. It is provided with two rectangular adiabatic obstacles interposed on the horizontal walls. The height of the two obstacles is varied from 10% to 40% H, while the width remains constant and equal to 10% of H. The calculation was performed for a laminar flow and an incompressible fluid with a Prandtl number Pr = 0.71. The calculations are performed by two different methods: the lattice Boltzmann method, with a double population where a program was developed under the MATLAB editor and tested during the work of this thesis. And the finite volume method using the Fluent commercial code. For the test case of a square cavity differentially heated, a validation of the results is presented for the two methods are compared with those in the literature. The results of the CFD analysis to the study geometric configuration are presented. The comparison between the two methods of calculation is displayed, by plotting the streamlines, the isotherms lines, the profiles of speed and temperature in the middle of the cavity. This analysis is complemented by a study of the influence of Rayleigh number and height of the obstacle on the Nusselt number. The results revealed that there's a good agreement between the two methods of calculation, and that the lattice Boltzmann can perfectly reproduce the phenomenon of natural convection in the configuration studied.