Three-dimensional effects induced by depth variation in a differentially heated cavity

Abstract

This work investigates a natural convection flow occurring in a differentially heated cavity. The main purpose of this paper is to analyze the influence of the cavity depth variation on heat transfers and flow dynamics. Three-dimensional numerical simulations are conducted. The working fluid is air, the vertical aspect ratio (cavity height over width) is equal to 4, and the Rayleigh Number is equal to 108. The impact of the rear and front boundary conditions on the flow topology is highlighted. When the cavity depth increases, three-dimensional effects are encountered that enhance local heat transfer at the isothermal walls. In particular, for horizontal aspect ratio (cavity depth over width) greater than 1, an alternation of local maximum and minimum Nusselt numbers can be observed along the y-direction toward the center of the wall in the lower half part of the isothermal wall, which are similar to a wave-like behavior. It is shown that they are due to vortex structures generated by a Görtler instability. The depth variation increases the emergence of those structures, but paradoxically several characteristics of both flow and heat transfer, such as the depth-averaged shear stress or the Nusselt numbers, tend to the two-dimensional case value as the cavity gets deeper.