Résumé:
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.
