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

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

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.

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