Numerical Study of Time-dependent Buoyancy-induced Cavity Flows

A 2D square cavity with isothermal horizontal sides and vertical adiabatic sides, is considered, containing a 'virtual' heat source, i.e a heat generating element with permeable boundaries. The horizontal sides of the enclosure are isothermal, and the vertical sides are adiabatic. The source is also square, its size being 1/100 of the cavity side, and is centred in the cavity.The problem is worked out numerically. The solution method is based on control-volume discretizations of the transport equations and a 2nd order projection scheme for time integration.The analysis is directed to demonstrate the potential of the method in the detection of critical values of the leading parameter, the Grashof number, at which some dramatic change in the flow structure occur. The first critical Gr-value, marking the onset of a time-dependent behaviour, is primarily investigated. Air (Pr = 0.71) is considered as the working fluid. The analysis is performed using 31x31, 61x61, and 121x121 grids.The sensitivity of the solution to 'minor' details is also investigated, by treating the same case, but for a 'real' (i.e. with impermeable walls) heat source.