Three-dimensional numerical simulation of free convection in a plane-parallel flow

Abstract

The results are given of numerical simulation of convection in Couette and Poiseuille flow for stationary (∂T*/∂t = 0) and uniformly increasing (∂T*/∂t = η = const) mean temperature of the convective layer. Numerical experiments were made for air (Prandtl number Pr = 0.7) in the range of Rayleigh numbers 2 000 ⩽ Ra ⩽ 44 000. The results confirm the conclusion drawn in earlier studies that at slightly supercritical Ra the dominant forms in the convection are cylindrical rolls with helical circulation. The rolls are oriented along the direction of the flow and are stationary formations. When a certain value of Ra, which depends on the vertical distribution of the temperature and velocity, is reached, the roll structure is deformed by transverse perturbations. All the considered flow forms have a stabilizing influence on the transverse modes, occurring at larger Rayleigh numbers than is the case for convection in a fluid at rest. The perturbations are displaced at a phase velocity close to the mean velocity of the undisturbed flow. In the considered range of Rayleigh numbers, a shear flow does not have an appreciable influence on the heat transfer, although there is a certain tendency for the Nusselt number to be larger in a shear flow.