Etude numérique de la convection mixte turbulente dans des cavités ventilées

Abstract

In this study, we are interested by the two-dimensional numerical simulation of turbulent mixed convection in a ventilated square cavity. The cavity is equipped with a slot entrance located in the bottom left corner and a slot exit located at the upper left corner of the cavity. The width of the slot is 1/10 of the side of the cavity. The considered cavity walls are maintained adiabatic, except the vertical left wall which is heated to a higher temperature than the ambient temperature. The governing equations are discretized using the finite volume method. Turbulence is modelled by the LRN k-ε model of Launder and Sharma, and the line by line technique with the Thomas algorithm (TDMA) is employed for solving iteratively the discretized equations. The control parameters of our study are: the Grashof number based on the difference between the temperature of the hot wall and the temperature of the vertical air stream at the entrance hat is set to 109, Prandtl number of air taken equal to 0.71 and the Reynolds number which vary as the Richardson number takes the following values: 0.1, 0.5, 1, 2, 5, 10, 20 and 40. After running the calculation program developed under FORTRAN language, a steady state solution is obtained for all considered Richardson numbers. Streamlines show a flow characterized by the presence of two countra-rotating cells for 0.1 ≤ Ri ≤ 5, whose size and shape depend on the Richardson number. By increasing the Richardson number, more cells with irregular shapes are formed in the upper part of the cavity for Ri = 10, Ri = 20 and Ri = 40, where we found a stable thermal stratification. The variation of average Nusselt number as a function of Reynolds number, shows that the heat transfer drops sharply when the forced convection is dominant (0.1 ≤ Ri < 2). However, for lower Reynolds numbers (5 ≤ Ri ≤ 40), the heat transfer characteristics change, indicating an almost linear decrease of the average Nusselt number. The region adjacent to the heated wall is the place where thermal and dynamic boundary layers are developed, and as a consequence important values of temperature and velocity are detected, influenced the turbulent quantities profiles, as the Reynolds stresses, the production and the dissipation rate of the turbulent kinetic energy. The variation of the turbulence intensity at the entrance from: I0 = 1% to I0= 4% and I0= 8% did not have a large influence on the velocity and temperature fields; however, a small impact is reported on the turbulent quantities.