臺灣博碩士論文加值系統

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。

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.

致謝 i
摘要 ii
Abstract iii
目錄 iv
圖目錄 vi
表目錄 viii
符號說明 ix
第一章　緒論 1
1.1 研究背景 1
1.2 文獻回顧 2
1.3 研究動機 4
1.4 研究方法 5
第二章　線性穩定性分析 6
2.1 問題描述 6
2.2 統御方程式 6
2.3 邊界條件 7
2.4 穩定基態解 7
2.5 無因次化之統御方程式 10
2.6 線性擾動方程式 10
2.7 正規模態展開 11
2.8 Squire’s theorem 12
2.9 特徵函數 13
2.10 純Couette流場之推導 14
第三章　數值方法 18
3.1 Chebyshev tau數值方法 18
3.2 數值方法的收斂性 21
3.3 中性穩定曲線 21
3.4 驗證程式 22
第四章　結果與討論 26
4.1 厚度比與速度比對穩定基態解之影響 26
4.2 厚度比與速度比對中性穩定曲線之影響 27
4.3 不穩定發生時的流動特徵 32
4.4 純Couette流場的穩定性分析 36
第五章　結論與未來展望 38
5.1 結論 38
5.2 未來展望 39
參考文獻 40

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