流過一對並列雙橢圓柱渦旋逸出流場之數值研究

Numerical study on vortex shedding flows past a pair of two elliptic cylinders

廖梅娟(Mei-Chuan Liao)

指導教授 ： 彭逸凡

國立暨南國際大學/科技學院/土木工程學系/碩士(2012年)

https://doi.org/10.6837/NCNU.2012.00188

摘要

本論文以數值解析方法，研究流過一對橢圓流場之轉變過程。流場藉由 Navier-Stokes 方程及連續方程求解，離散數值方法中，以具二階精準度之中央插分法離散 Navier-Stokes 方程之空間項，時間項方面則利用 Adams-Bashforth 法處理對流項，以 Crank-Nicolson 法處理擴散項。解答邏輯過程採用分步法(Fractional step method)，含複雜邊界之障礙物則以內嵌法(Embedding method)處理之，網格系統採用正交、結構化，具局部加密效果之巢狀卡式網格(Nested grid)系統。本論文首先將系統化解析此流過一對並排橢圓流場，含雷諾數(Re)介於40~100 之間，及間距比(G)介於0.2~3.0 間之所有流場。預計含似單一柱體、雙柱體流場，對稱、偏斜流場，翻拍(flip-flopping)渦旋逸出流場，同相位、異相位渦旋逸出流場等多樣化渦旋逸出流場結構，將於本論文之結果中呈現。這些有趣、多樣化流場之演化、轉變過程將一併研究。

關鍵字

巢狀卡氏網格 ； 內嵌法 ； 分步法

並列摘要

In this paper, low Reynolds number (Re) flows past a pair of elliptic cylinders in a side-by-side arrangement are solved by numerical simulations and transitions of the flows are investigated. Numerical methods in solving the 2-D Navier-Stokes and continuity equations is a two-step fractional step method, for the numerical simulations of flows past bluff bodies an Immersed Boundary (IB) method has been implemented where local grid refinement procedure is adopted by using a nested grid formulation. Flows with Re ranges between 40~100 and Gap ratio (G) ranges between 0.2~3.0 are solved. From a global point of view, there are a variety of flow patterns. Including steady and vortex shedding flows, semi-single and twin vortex streets, symmetry and deflected flows, biased flip-flopping and stationary flip-flopping vortex shedding flows, in-phase and in anti-phase vortex shedding flows are founded. We numerically solve the variety of flows by tuning Re quasi-stationary and investigate the transition of various flow patterns by nonlinear analysis. Transition diagram of flows past a pair of elliptic cylinders at various Gs are proposed to be presented.

並列關鍵字

a pair of ellipses ； side-by-side arrangement ； nested grid method ； immersed boundary method

參考文獻

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