Numerical Simulation of the Convection in a Non-Homogenous Lid-Driven Square Cavity Subjected to a Gravitational Stable Condition
Authors: Poletto Vinícius G. , De Lai Fernando C. , Franco Admilson T. , Junqueira Silvio L. M. 
Published: November 2016

The lid-driven flow inside a porous square cavity is numerically simulated. The porous media is modelled on the microscopic scale (heterogeneous porous medium) with a square heat conductive single block representing the solid constituent. Conversely, the fluid relies between the block and the cavity surfaces. A vertical positive thermal gradient, obtained by keeping the sliding-lid temperature TH higher than the base one TC, aligned with the gravity force enables a gravitational stable condition where the buoyant-induced flow does not occurs spontaneously. Instead, the flow comes about as the cavity top surface slides with constant velocity. Conservation equations are applied separately for each constituent and are coupled by boundary conditions at the fluid to solid interface (block surface). The Boussinesq-Oberbeck approximation accounts for the buoyant effects. The equations are solved via the finite volume method with the use of the SIMPLE algorithm for the pressure-velocity coupling and QUICK interpolation scheme for the treatment of the advection terms. The aim of the present work is to investigate how variations on the flow parameters and the block size affect the thermal process throughout the cavity. A top lid velocity based Reynolds number evaluates the intensity of the forced convection process while the Grashof number is associated with the intensity of buoyancy. The flow parameters cover only the laminar regime, such as 102≤Re≤103 and 103≤Gr≤107. The Re and the Gr numbers are also analyzed by the means of the Richardson number, Ri, which accounts the relative predominance of buoyancy over the inertia effects. Moreover, a clear fluid cavity and enclosure configurations with three different block dimensions, namely B = 0.3, 0.6 and 0.9, are simulated. The heat transfer across the cavity can be characterized as a competitive effect, since the flow is hindered as the buoyancy effect rises. Results show that an increase in Re, or decrease in Gr, enhances the heat transfer, revealing a convection dominant regime. Alternatively, an increase in Gr, or a decrease in Re, leads the fluid to a stagnant-prone condition where a conduction dominant regime is verified. Thus, the surface-average Nusselt number, Nuav, tends to unity as the flow is confined to the adjacency of the sliding-lid. The placement of the single block in the cavity can enhance or hinder the heat transferred, depending on the flow regime. For instance, if a B = 0.6 block is inserted in the presence of a convection dominant regime, the Nuav is increased. Conversely, if the fluid is quiescent, a B = 0.6 block alters the flow path and the Nuav decreases. Intense blockage effects are observed for larger values of B since the block interferes on the flow more significantly. For a convection dominant regime, for instance, a B = 0.9 block causes the Nuav to drop. However, in the presence of stagnant fluid, the same obstacle forces the flow to circumvent it. Thus, the Nuav number increases, indicating that heat transfer mode returns to a convective pattern.