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  • 學位論文

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

指導教授 : 陳發林

摘要


本論文將對流體層-多孔介質層所組成的雙層流域中的Couette-Poiseuille流場進行線性穩定性分析,並深入討論多孔介質層的厚度與Couette流場對此系統所造成的影響。研究結果顯示,此系統之不穩定性與厚度比有極高度的相關,其中厚度比的定義為:流體層厚度與多孔介質層厚度的比值。厚度比較小時,如0.1,當有Couette流場的存在時,相較於只有Poiseuille流場時還要來得不穩定,Couette流場的加入會使中性穩定曲線的最低點愈來愈低,且會產生不穩定模態的轉換;厚度比具有一定大小時,如1.0,當Couette流場所帶來的效應不強時,會使系統變穩定,但當Couette流場的效應夠強時,多孔介質層的存在使系統發生模態的轉換,從「流體層模態」轉變成「多孔層模態」,令系統成為有條件穩定的狀態;厚度比夠大時,如10,雙層系統可以近似為單層流體層的情形,多孔介質層所造成的影響可忽略不計,Couette流場的加入會給予Poiseuille流場很強烈的穩定效果,而當上邊界移動速度大於Poiseuille流場的最大速度的70%時,會使系統成為無條件穩定的狀態。以上所觀察到的現象有別於以往對於Couette-Poiseuille流場的文獻結果,是個嶄新的發現。另外,本論文亦有針對流體層-多孔層雙層流域中的純Couette流場進行線性穩定性分析,研究結果指出,雙層流域中的純Couette流場是無條件穩定的,我們沒有在給定的參數條件下找到中性穩定曲線,此結果與單層流體層流域中的純Couette流場的線性穩定性分析結果相同。

並列摘要


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.

並列關鍵字

stability linear analysis Couette Poiseuille porous medium

參考文獻


[14] P. G. Drazin & W. H. Reid, Hydrodynamic Stability, 2nd ed. Cambridge University Press, 1981.
[1] A. E. Scheidegger, The Physics of Flow Through Porous Media, 3rd ed. Toronto: University of Toronto Press, 1974.
[2] M. C. Potter, “Stability of plane Couette-Poiseuille flow,” J. Fluid Mech., vol. 24, pp. 609-619, 1966.
[3] W. C. Reynolds & M. C. Potter, “Finite-amplitude instability of parallel shear flows,” J. Fluid Mech., vol. 27, pp. 465-492, 1967.
[4] F. D. Hains, “Stability of Plane Couette-Poiseuille Flow,” Phys. Fluids, 10, 2079, 1967.

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