Nonlinear stability of mixed convection flow under non-Boussinesq conditions. Part 2. Mean flow characteristics

Based on amplitude expansions developed in Part 1 (Suslov & Paolucci 1999), we examine the mean flow characteristics of non-Boussinesq mixed convection flow of air in a vertical channel in the vicinity of bifurcation points for a wide range of temperature differences between the walls, and Grashof and Reynolds numbers. The constant mass flux and constant pressure gradient formulations are shown to lead to qualitatively similar, but quantitatively different, results. The physical nature of the distinct shear and buoyancy disturbances is investigated, and detailed mean flow and energy analyses are presented. The variation of the total mass of fluid in a flow domain as disturbances develop is discussed. The average Nusselt number and mass flux are estimated for supercritical regimes for a wide range of governing parameters.

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Nonlinear stability of mixed convection flow under non-Boussinesq conditions. Part 1. Analysis and bifurcations

Journal of Fluid Mechanics ◽

10.1017/s0022112099006217 ◽

1999 ◽

Vol 398 ◽

pp. 61-85 ◽

Cited By ~ 13

Author(s):

S. A. SUSLOV ◽

S. PAOLUCCI

Keyword(s):

Mixed Convection ◽

Open Systems ◽

Landau Equation ◽

Vertical Channel ◽

Variable Density ◽

Special Treatment ◽

Convection Flow ◽

Mixed Convection Flow ◽

Weakly Nonlinear ◽

Wide Range

The weakly nonlinear theory for modelling flows away from the bifurcation point developed by the authors in their previous work (Suslov & Paolucci 1997) is generalized for flows of variable-density fluids in open systems. It is shown that special treatment of the continuity equation is necessary to perform the analysis of such flows and to account for the potential total fluid mass variation in the domain. The stability analysis of non-Boussinesq mixed convection flow of air in a vertical channel is then performed for a wide range of temperature differences between the walls, and Grashof and Reynolds numbers. A cubic Landau equation, which governs the evolution of a disturbance amplitude, is derived and used to identify regions of subcritical and supercritical bifurcations to periodic flows. Equilibrium disturbance amplitudes are computed for regions of supercritical bifurcations.

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Stability of mixed-convection flow in a tall vertical channel under non-boussinesq conditions

Journal of Fluid Mechanics ◽

10.1017/s0022112095004022 ◽

1995 ◽

Vol 302 ◽

pp. 91-115 ◽

Cited By ~ 29

Author(s):

Sergey A. Suslov ◽

Samuel Paolucci

Keyword(s):

Mixed Convection ◽

Three Dimensional ◽

Vertical Channel ◽

Reynolds Numbers ◽

Convection Flow ◽

Two Dimensional ◽

Mixed Convection Flow ◽

The Stability ◽

Pseudo Spectral Method ◽

Pseudo Spectral

We have examined the linear stability of the fully developed mixed-convection flow in a differentially heated tall vertical channel under non-Boussinesq conditions. The Three-dimensional analysis of the stability problem was reduced to an equivalent two-dimensional one by the use of Squire's transformation. The resulting eigenvalue problem was solved using an integral Chebyshev pseudo-spectral method. Although Squire's theorem cannot be proved analytically, two-dimensional disturbances are found to be the most unstable in all cases. The influence of the non-Boussinesq effects on the stability was studied. We have investigated the dependence of the critical Grashof and Reynolds numbers on the temperature difference. The results show that four different modes of instability are possible, two of which are new and due entirely to non-Boussinesq effects.

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