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Convective instabilities in concurrent two-phase flow: Part II. Global stability

Authors

  • Raymond J. Gumerman,

    1. Deptrtment of Chemical Engineering, Stanford University, Stanford, California 94305
    Current affiliation:
    1. Chevon Research Corporation, Richmond, California
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  • George M. Homsy

    Corresponding author
    1. Deptrtment of Chemical Engineering, Stanford University, Stanford, California 94305
    • Deptrtment of Chemical Engineering Stanford University Stanford, California 94305
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Abstract

The method of energy is used to determine global stability limits for thermally stratified two-phase plane Couette flow. Instabilities due to surface tension variations, buoyancy effects, and shear are allowed for, but surface waves are specifically excluded from consideration. Under these assumptions, the Marangoni, Rayleigh, and Reynolds numbers completely describe the system. Stability plots, valid for disturbances of any magnitude, are presented for both streamwise oriented roll vortices and two-dimensional transversely oriented disturbances. It is shown that rolls are the most dangerous disturbances in the sense that they cannot be shown to be stable relative to transverse disturbances at any nonzero Reynolds numbers. Comparisons are made with existing linear limits, and these are seen to be close only for moderate Reynolds numbers.

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