流體與多孔介質雙層流域中Couette-Poiseuille流場的穩定性分析

張庭岳

doi:10.6342/NTU201701277

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流體與多孔介質雙層流域中Couette-Poiseuille流場的穩定性分析

Stability of Couette-Poiseuille flow in superimposed fluid-porous domain

張庭岳 , Masters　　Advisor：陳發林　　

繁體中文 DOI： 10.6342/NTU201701277

流體穩定學；線性穩定性分析； Couette ； Poiseuille ；多孔介質； stability ； linear analysis ； Couette ； Poiseuille ； porous medium

Abstract │ Reference (17) │ Altmetrics

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This paper performs a linear stability analysis to investigate the stability of plane Couette-Poiseuille flow in a two-layer system. There is fluid layer overlying a porous layer saturated with the same fluid. The effect of superimposed Couette flow on the associated Poiseuille flow in such a two-layer system is explored carefully. The result shows that the presence of Couette flow would destabilize the Poiseuille flow with a small value of depth ratio, which is defined by the ratio of the depth of fluid layer to the depth of porous layer, and induce a tri-modal neutral curves. At moderate value of depth ratio, the Couette component generally produces a stabilization effect on the flow. When the velocity of the upper moving wall is large enough, a bi-modal neutral curve appears and a shift of instability mode occurs from the long-wave fluid-layer mode to the porous-layer mode with higher wavenumber. These stability characteristics are remarkably different from those of the plane Couette-Poiseuille flow in a single fluid layer that the flow becomes absolutely stable when the wall velocity is over 70% of the maximum velocity of the Poiseuille component of flow. The stability of pure Couette flow in such a two-layer system is also studied. It is found that the flow is still absolutely stable with respect to infinitesimal disturbances, which is as same as the stability characteristic of single fluid layer plane Couette flow.

Reference ( 17 ) 〈TOP〉

[1] A. E. Scheidegger, The Physics of Flow Through Porous Media, 3rd ed. Toronto: University of Toronto Press, 1974.
連結：
[2] M. C. Potter, “Stability of plane Couette-Poiseuille flow,” J. Fluid Mech., vol. 24, pp. 609-619, 1966.
連結：
[3] W. C. Reynolds & M. C. Potter, “Finite-amplitude instability of parallel shear flows,” J. Fluid Mech., vol. 27, pp. 465-492, 1967.
連結：
[4] F. D. Hains, “Stability of Plane Couette-Poiseuille Flow,” Phys. Fluids, 10, 2079, 1967.
連結：
[5] M.-H. Chang, F. Chen & B. Straughan, “Instability of Poiseuille flow in a fluid overlying a porous layer,” J. Fluid Mech., vol. 564, pp. 287-303, 2006.
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