具小曲率半徑的矩形彎管內流場分歧研究

Flow Bifurcations in a Square Curved Tube for Small Curvature Ratio

駱文傑(Win-Jet Luo)

《中國航空太空學會學刊》 36卷2期 (2004/06) Pp. 163-169

https://doi.org/10.6124/TAASRC.200406_36(2).06

摘要

本文主要針對矩形彎管內因不同的驅動壓力梯度與彎管的曲率半徑所產生流場分歧現象進行探討。由於彎管的幾何形狀以及離心力的作用使得流體在彎管的橫截面上產生渦漩運動。在不同的驅動壓力及不同的彎管的曲率半徑等設計參數下，在彎管的橫截面上會產生不同的流場狀態。本文採用連續法以分別針對長寬比爲1及曲率半徑β=50、β=1.5等曲率半徑下的流場狀態進行探討。藉由連續法可找到各個例子的定常解，及造成流場產生不穩定狀態變化的分歧點；再藉由線性穩定度的分析方法來判定各個定常解的穩定度，以建構出隨外加壓力與曲率半徑轉變的分歧圖。對於長寬比爲1及曲率半徑β=1.5的例子，可找到在過去研究上未曾找到的2-cell、4-cell、6-cell及不對稱等四種流場狀態。此外本文藉由橫截面上軸向速度的分佈以瞭解各個流場狀態形成的緣由。所得的結果亦可提供工業管路設計與生理上血管流分析的參考。

關鍵字

分歧 ； 定常解 ； 穩定度 ； 連續法

並列摘要

This study investigates the bifurcation phenomena caused by different driving pressure gradient and curvature radius. The curvature geometry and the centrifugal force result in the appearance of vortices in the transverse of the curved tube. Different driving pressure and curvature radius may lead to different flow states. A continuation method with the pressure gradient as continuation parameter is used to find multiple steady-states caused by nonlinear effect. This study investigates the flow bifurcations in the cases of curvature radius β=50 and β=1.5. Four types of steady flow states, which were not reported in the literature are calculated and the corresponding bifurcation diagram is constructed for the cases of aspect ratio=1 and curvature radius=1.5. Linear stability analysis is used to check the stability of these steady states and locate the bifurcation points exactly. The genetic of the states can be derived from the distribution of axial velocity. The related calculated results are useful for the design of industrial duct assembly and analysis of physiological blood flow.

並列關鍵字

Bifurcation ； Stability ； Continuation method