水利工程之一些高雷諾數流之解析研究

Analytical studies of some high Reynolds number flows in hydraulic engineering

余偉榤(Wei-Chieh Yu)

指導教授 ： 黃良雄

國立臺灣大學/工學院/土木工程學研究所/碩士(2017年)

https://doi.org/10.6342/NTU201703190

摘要

水利工程中由於流場中的初始速度、壓力梯度或外在加速等原因，流體時常具有一定的能量，因此在水利上探討的議題中，高雷諾數流占有一定的比重，如在流變儀的相關討論中，則要避免用低雷諾數流來求解其解析的物理性質表示式，本研究將就高雷諾數流進行討論。
高雷諾數流的分析可以分為低剪力與高剪力層不同流況的組合，這個部分在1967年時Batchelor在其著作中的邊界層流章節裡大致就有提到。然而雖然使用一強剪層與一弱剪層來分解高雷諾數流，由於弱剪力層中其黏滯性的影響非常之小，因此本研究直接將此區假設為無黏性流體並使用邊界層方程式來求解高剪力區域來繼續往後相關解析之推導。
雖然邊界層自提出迄今已經有了百年的發展，圓柱座標系中邊界層主要卻都是在探討外流場對圓柱所造成的影響，圓柱內部邊界層相關之速度分佈則是從1965年M. Holt推導後便較少有深入的應用研究，本研究接續M. Holt推導的邊界層方程式並應用於求解圓柱座標下高雷諾數流的完整流場。
本研究直接假設流場中存在邊界層，並以高雷諾數流來求解各題型，將完整流況分為兩區，非黏性流體及黏性流體區，尋求邊界條件以及應用控制體積正向力平衡與角動量守恆方程式來推求出邊界層之厚度與特定係數，組合而成完整流況以模擬高雷諾數流，以探討整體流場的相關物理性質。

關鍵字

圓柱 ； 剪應力 ； 邊界層理論 ； 高雷諾數流 ； 控制體積 ； M.Holt

並列摘要

In hydraulic engineering, the flow fluid usually has enough energy because of the effect from the initial velocity, pressure gradient and the force outside. Therefore, it is easy to find high-Reynold numbers flow in the most study of hydraulic research. For instance, it should get avoid to solve the physical solution in the case of the rheometer. This study is going to discuss in high-Reynold numbers flow.
The analysis of high-Reynold numbers flow makes up with low shear stress flow and high shear stress flow. It has mentioned in the boundary layer chapter of Batchelor’s literary work since 1967. However, the viscosity is not obvious in the low shear stress flow. Therefore, this study use inviscid flow to analyze the part of low shear stress flow, and use boundary layer equation to analyze the high shear stress flow.
Although boundary layer theory has developed for more than one hundred years, cylindrical boundary layer is dominant in discussing the effect of the situation when flow pass outside. There are few research studying in the boundary layer theory inside the cylinder since the boundary layer equations are derived by M. Holt. This study is going to continue the research of M. Holt, and apply to solve the full distribution of velocity in high-Reynold numbers flow.
This study directly make assumption of exist of boundary layer, and solve all type of equations in high-Reynold numbers flow. By dividing the whole flow field into two parts, for one named inviscid part and the other called viscous part. Finding the boundary conditions, using angular momentum equation and making use of the balance in direct force to deal with the particular parameters and thickness of boundary layer. Combine the velocity distribution of the two parts in order to simulate the high-Reynold numbers flow and study the physical properties of whole flow field.

並列關鍵字

cylindrical ； shear stress ； boundary layer theory ； high-Reynold numbers flow ； control volume ； M. Holt

參考文獻

13. 張哲維. (2008). “應用垂直旋轉式流變儀搭配理論發展求取流變參數”

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