Spatio-temporal instabilities in mixed convection of air subject to large temperature gradient

Abstract

The problem of stability of mixed convection flow in an air-filled tall vertical differentially heated channel is considered when the cross-channel temperature difference is of the order of a hundred degrees Kelvin. It is shown that the realistic nonlinear fluid properties variation associated with large temperature gradient leads to significant deviations from the flow scenarios predicted using conventional constant-property Boussinesq approximation. In the Boussinesq limit of small temperature gradients the conduction state becomes unstable with respect to shear-driven disturbances of a primary flow. In contrast, when the fluid properties are allowed to vary, a new buoyancy-driven instability may arise. These two physically distinct instabilities can co-exist and compete over a wide range of parameters (such as the Grashof and Reynolds numbers and non-dimensional temperature difference between the channel walls) governing the problem. This enables a rich diversity of resulting flow patterns that evolve both in space and time. In nearly natural convection regimes (with a cubic primary velocity profile) the shear-driven instability is found to be absolute (convection cells occupy the full channel volume), while in predominantly forced convection regimes with relatively large pressure gradient along the channel (Poiseuille-type flows) the shear-driven instability is known to be convective with convection cells carried away by the primary flow. In contrast, for small to moderate values of the Reynolds number, the buoyancy instability reveals its convective nature with disturbances propagating downwards regardless of the direction of the applied external pressure gradient. The goal of this study is twofold: first, to provide an insight into the physics of various instabilities arising in mixed convection channel flows and, second, to determine the accurate boundary separating regions of absolute and convective instabilities in the multi-parameter space of the mixed convection problem. Analytical results are confirmed by direct numerical integration of the disturbance equations and resulting flow fields are presented for both shear- and buoyancy-driven instabilities.