等速移動平板上非正交停滯點流的二維分析

Two-dimensional analysis of non-orthogonal stagnation point flow over a moving plate with constant velocity

鄭盛尹(Sheng-Yin Cheng)

指導教授 ： 陳發林

國立臺灣大學/工學院/應用力學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201901671

摘要

流體流過物體表面會在表面產生摩擦力並對物體產生阻力及升力，除了物體的形狀，流體的速度快慢及溫度高低對問題的影響肯定也不同，而這類的問題在我們生活中隨處可見，因此是非常值得研究的。
前人研究流體垂直打向無限延伸的靜止平板、垂直打向等速移動平板、斜向打向靜止平板等問題，然而尚未有人進行流體斜向打向等速移動平板的研究，因此本論文參考前人研究的結果，同樣以相似解的技巧進行等速移動平板上非正交停滯點流的二維分析，研究中假設流體為穩態且不可壓縮流體，從Navier-Stokes方程式推導出微分方程式，並藉由流函數的設定及平板處的條件來取得邊界值問題的邊界條件，然而微分方程式為非線性，必須以數值方法來求解，論文中是以邊界值問題求解器bvp4c來解邊界值問題，除了以bvp4c解出的數值解以外，論文中也找出了近似解的函數。
第四章以找出的近似解畫出流場中不同位置的速度分布圖，探討角度及平板速度對流場中速度的影響，結果顯示在相同平板速度的情況下，角度越小時，流場中速度的變化越小。後來以平板處剪力為零的條件找出停滯點公式，停滯點將隨著平板速度的增加而右移，且角度越小右移的速度越快。最後畫出流線圖以了解不同角度及平板速度下的流場情形，從流線圖可以看出，當平板速度為零時，Ψ=0的流線會與平板交於停滯點的位置，然而平板速度不為零時，Ψ=0的流線會往左偏移，不會與平板有交點。

關鍵字：相似解、非正交停滯點流、移動平板、邊界值問題、數值方法

關鍵字

相似解 ； 非正交停滯點流 ； 移動平板 ； 邊界值問題 ； 數值方法

並列摘要

When fluid flows over an object, it will creates friction, resistance and lift on the object. In addition to the shape of the object, different fluid speed and temperature must have different effect on the problem. Many things in our life can be viewed as this problem. So it is worth to study.
The predecessors studied the fluid impinges vertically on a infinitely extending stationary plate, impinges vertically on a plate with constant velocity, and impinges obliquely on a stationary plate. However, no one studied the fluid obliquely impinges on a plate with constant velocity. Therefore, this paper refers to the predecessors, the two-dimensional analysis of non-orthogonal stagnation point flow over a moving plate with constant velocity is studied with the similar solution technique. The hypothesis is that the fluid is a steady-state and incompressible. The differential equation is derived from the Navier-Stokes equation. The boundary conditions of the boundary value problem are obtained by the setting of the stream function and the condition of the plate. However, the differential equation is nonlinear and must be solved by numerical method. In this paper, the boundary value problem solver bvp4c is used to solve the boundary value problem. In addition to the numerical solution solved by bvp4c, the paper also finds the function of the approximate solution.
Chapter four shows the velocity distribution of different positions in the flow field by the approximate solution and discusses the influence of the angle and the plate speed on the velocity in the flow field. The result shows that if the angle is small, the change of velocity in the flow field will be small. Later, the stagnation point formula is found under the condition that the shear stress at the plate is zero. The stagnation point will shift to right as the plate speed increases. If the angle is small, the shift will be faster. Finally, we plot the streamline to understand the flow field under different angle and plate speed. If the speed of the plate is zero, the streamline of Ψ=0 will intersect the plate at the position of the stagnation point. However, if the plate speed is not zero, the streamline of Ψ=0 will shift to left and will not intersect the plate.

Keywords: similarity solution, non-orthogonal stagnation point flow, moving plate, boundary value problem, numerical method

並列關鍵字

similarity solution ； non-orthogonal stagnation point flow ； moving plate ； boundary value problem ； numerical method

參考文獻

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