非恆定史托克斯方程式基本解的推導與應用

The Derivations and Applications of Fundamental Solutions for Unsteady Stokes Equations

蕭健雄(Chien-Hsiung Hsiao)

指導教授 ： 楊德良

共同指導教授 ： 蔡丁貴

國立臺灣大學/工學院/土木工程學研究所/博士(2013年)

https://doi.org/10.6342/NTU.2013.01518

摘要

本研究架構分成二部份，第一部分內容主要是推導非恆定史托克斯流體的基本解，包含非恆定力源、非恆定力矩源、非恆定偶力源、非恆定應力源等四種基本解，物理意義分別代表瞬時點力、瞬時點力矩、瞬時點力偶和瞬時點應力等。利用已推導的各種基本解，再配合牛頓流體應力公式，計算包含各種點力源作用在球體控制體積表面力及力矩。
第二部份則是組合已推導出之各種不同基本解和使用摺積積分，獲得流場控制方程式，因為控制方程式為積分方程，我們利用拉普拉斯轉換方法求出各種組合力源之強度，再代入第一部分已推導各種點力源作用在球體控制體積其表面力及力矩公式，即可推導出一些在史托克斯流體或低雷諾數流體問題的正解。求得的正解包含球體在非恆定史托克斯流體的移動和轉動；剪力流流經球體所導致的力矩；拋物線流流經球體所導致的受力等。

關鍵字

奇異解法 ； 非恆定史托克斯流體 ； 點力源 ； 力矩源 ； 偶力源 ； 應力源 ； 剪力流 ； 拋物線流

並列摘要

There are two research themes in this thesis. The first active research theme is the derivations of fundamental solutions in the unsteady Stokes equations. We provide a complete, symmetrical and detailed derivation in explicit form for the fundamental solutions of the unsteady Stokes equations, including an unsteady Stokeslet, rotlet, Stokeslet doublet, stresslet and potential dipole. The forces and torques exerted on the fluid solid bodies due to the singularities are also calculated.
Our second issue of interest concerns with employing a combination of fundamental solutions, convolution integral and Laplace transform to investigate the physics of fluids, solids, and their applications in Stokes flow systems. Many exact solutions of hydrodynamic forces and torques in a time dependent shear flow and parabolic flow are obtained.

並列關鍵字

the Singularity method ； unsteady Stokes flows ； Stokeslet ； Stokeslet doublet ； rotlet ； stresslet ； shear flow ； parabolic flow.

參考文獻

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