- 學位論文
等速移動平板上非正交停滯點流的穩定性分析
Stability analysis of non-orthogonal stagnation point flow over a moving plate with constant velocity
摘要
流體流經過鈍形物體表面會因為黏滯力的影響產生上升力、阻力與渦流等，其中物體的形狀、物體本身的速度、流體的流速、流體溫度的高低等因素都對這個問題的影響有所不同，而這類停滯點問題在我們生活中隨處可見，也在工業中應用廣泛，因此是個非常值得研究的問題。 停滯點問題的穩定性分析發展的過程最早可以追朔到1976年的Wilson Gladwell一起提出理論，在他們的討論中簡化了許多這個問題所會遇到的難題，如:流體為穩態且不可壓縮流、基態解用最簡單的一維基態解、穩定性分析的維度也只有二維等。在本研究中改善了許多前人之假設，使其更加貼近現實之物理意義，如增加至三維分析、使用更加完善之基態解等。 本論文針對一均勻流以任意角度斜向打向一等速移動之無限長平板，造成非正交停滯點流場之穩定性分析，並深入去探討流體與平板之夾角α與壁面等速移動之速度U對此流場之影響與物理意義。引用前人之推導與函有物理意義之解說，得知主導此流場之不穩定性之因素為令流體轉向之離心力與流體本身之黏滯力。此流場之基態解是引用Cheng Chen(2020)[1]，而非前人所使用的Hiemenz flow solution。本文先由夾角α=π/2，壁面移動速度U=0開始出發，而結果總是穩定(always stable)，此結果與前人所作之結果是吻合的，而開始改變壁面移動速度，不穩定流場隨之發生，臨界速度(critical velocity)會隨著夾角α的減少而增加，此結果與前文所提到之物理意義是符合的，若是夾角減少，而隨之產生使的流體轉向的離心力也會減少，故使流場之穩定性增加，臨界速度自然提高。
並列摘要
The flow of fluid passing through the surface of a blunt object will cause rising force, resistance and vortex due to the effect of viscous force. Among them, the shape of the object, the speed of the object itself, the velocity of the fluid, the level of the fluid temperature and other factors all have an impact on this problem. The difference is that this kind of stagnation problem can be seen everywhere in our lives, and it is also widely used in industry, so it is a very worthy study. The development process of the stability analysis of the stagnation point problem can be traced back to 1976, when Wilson Gladwell put forward the theory together. In their discussion, they simplified many of the problems encountered in this problem, such as: the fluid is stable and not The simplest one-dimensional solution for compressed flow and ground state solution, and the dimension of stability analysis are only two-dimensional. In this study, many predecessors' assumptions have been improved to make them closer to the physical meaning of reality, such as adding to three-dimensional analysis and using more perfect ground state solutions. In this paper, the stability analysis of a non-orthogonal stagnation point flow field caused by a uniform flow obliquely moving to an equal velocity moving at an arbitrary angle, and in-depth discussion of the angle α between the fluid and the plate and the constant velocity of the wall surface The influence and physical significance of the velocity U of this flow field. Citing predecessors' derivations and physical explanations, it is known that the factors that dominate the instability of this flow field are the centrifugal force that turns the fluid and the viscosity of the fluid itself. The ground state solution of this flow field refers to Cheng Chen (2020) [1], not the Hiemenz flow solution used by predecessors. This article starts with the angle α=π/2 and the wall moving speed U=0, and the result is always stable. This result is consistent with the results made by the predecessors, and begins to change the wall moving speed, which is unstable The flow field will follow, and the critical velocity will increase with the decrease of the angle α. This result is consistent with the physical meaning mentioned above. If the angle is reduced, the centrifugal force that turns the fluid will be generated. It will also decrease, so the stability of the flow field increases and the critical speed naturally increases.
參考文獻
延伸閱讀
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