Etude de la convection mixte laminaire dans une cavité ventilée par la méthode de Boltzmann sur réseau

Abstract

Magister work exposed focuses on the numerical study of laminar mixed convection in a ventilated cavity. The geometry studied is a square cavity equipped with two openings: one is located in the lower left corner for the supply and the other located in the upper right corner, for evacuation. The bottom wall is subjected to a constant and uniform temperature, while the other walls are considered adiabatic. In this work, a detailed study on heat transfer by convection including mixed convection was presented. A literature review of the most important works found in the literature for the studied physical configuration has been exposed. The work continued with a presentation of the historical development of the new method of modeling and simulation used in this study, including the thermal lattice Boltzmann method with double population, as fundamental theoretical basis for its application. A computer code was developed and tested in this work with the MATLAB editor, using the thermal lattice Boltzmann method with the D2Q9 model for the dynamic field and D2Q5 for the thermal field. The calculation results were obtained for laminar flow and a Newtonian incompressible fluid with a Prandtl number Pr = 0,71. A typical configuration of a differentially heated square cavity was selected and used to validate the results obtained by the computer code. A first comparison of the results obtained by the LBM with those obtained by the fluent code (using the finite volume) and those in the literature is presented to the Richardson number Ri = 10. This allowed us to find a good agreement between the two methods. The rest of the analysis results of the CFD were presented by plotting the streamlines, the isotherms, velocity profiles and temperature in the middle of the cavity. This analysis is complemented by the quantification of heat transfer by studying the variation of the Nusselt number as a function of the variation of the Richardson number, the Reynolds number and Grashof number. This allowed us to assess the performance and capacity of the LBM to reproduce the phenomenon of mixed convection in a ventilated cavity.