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題名 | Effects of Crispation and Gravity Field on the Onset of Oscillatory B'enard-Marangoni Convection in a Horizontal Fluid Layer=流體層中表面變形與重力場效應對振動模式貝納-馬瑞勾尼對流起始時之影響 |
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作者姓名(中文) | 張福平; 江可達; | 書刊名 | 樹德學報 |
卷期 | 19 1997.03[民86.03] |
頁次 | 頁59-80 |
分類號 | 444.1 |
關鍵詞 | 振動模式; 不穩定性; 貝納-馬瑞勾尼對流; 重力場效應; 模式的轉換; |
語文 | 英文(English) |
中文摘要 | 本文探討表面變形與重力場效應對一具有可變形自由上表面之水平流體層中貝納- 馬瑞勾尼對流起始時振動模式不穩定性現象之影響。本文中穩定性分析是以線性穩定理論為 基礎, 所獲得 Sturm-Liouville 特徵值問題的統制方程式將藉由四階郎奇 - 庫塔 - 基爾 方法與布登方法來求解。 其結果顯示:Crispation 值會產生較強的不穩定效果,而遞減重 力場效應卻是一穩定性因素。對流不穩定性出現的模式由穩態模式轉換振動模式時,其關係 參數值 T 值隨著 Crispation 值增加而減少,隨著重力場效應數ε值的增大而增加。 振動 模式貝納 - 馬瑞勾尼對流起始時,在普郎特數 Pr 值小於 1, 其臨界雷利數 Rc 隨著 T 值 增大而提昇,而卻隨著 Bo 值增大而適當地增大。在普郎特數 Pr 值小時,對流不穩定性出 現的模式以振動模式先出現。 |
英文摘要 | The effects of crispation and gravity field on the oscillatory instability of B'enard-Marangoni convection in a horizontal fluid layer with a deformable upper free surface is investigated. The governing equations of the Sturm-Liouville's problem based on the linear stability theory are numerically solved, using the fourth order Runge-Kutta-Gill's method and making use of the Broyden's method. The results show that the effect of the Crispation numer C is strongly destabilizing, while that of a reduced gravity field is stabilizing. At the transition, a jump from a stationary mode to an oscillatory one does occur and the parameter T is found to decrease with the Crispation number C and increases with the parameter ε. The critical Rayleigh number Rc of oscillatory modes of B'enard-Marangoni convection decreases significantly as the parameter T decreases and increases moderately as the Bond number Bo increases, provided the Prandtl number Pr < 1. Additionally, the oscillatory modes become prevailing at small values of the Prandtl number Pr. |
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