Résumé:
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.
