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標題: 流經二維方形突柱與直流道之暫態流場數值模擬
Numerical Simulation of Transient Incompressible Flow Past a Surface-Mounted Square Cylinder in Channel and Straight Channel
作者: 汪坤宣
Wang, Kun-Hsuan
關鍵字: vorticity;渦度;stream function;surface-mounted square cylinder;circulation;PSOR;separation region;relaxation factor;adverse pressure gradient;流線函數;方形突柱流道;環流量;點迭代法;逆流區;加速因子;逆壓梯度
出版社: 機械工程學系
本研究係採用渦度、流線函數方程式的數值計算方法,模擬方形突柱流道與直流道暫態流場的流體行為。計算過程中,以環流量方式決定渦度邊界條件;藉由固體表面為渦流之源頭,並產生一定的渦度,以滿足流體於固體表面無滑動速度(no-slip)之邊界條件。對於流體的流線函數,以PSOR(Point Successive Over-Relaxation)迭代法求解流場的流線函數方程式;對於渦度於流場中之擴散與傳輸,則以渦度傳輸方程式來模擬暫態流場的變化。
本文選取四種不同的雷諾數1、10、100、200加以探討流道中速度隨時間、或隨位置的變化以及逆流區(Separation region)的發生、成長及穩態的尺寸大小,並檢視入口區域的變化。結果顯示:在方形突柱左側之逆流區的大小,隨著雷諾數的增加而變小,而在方形突柱右側之逆流區的大小,隨著雷諾數的增加而變大。

In this study, the vorticity-stream function formulations are used to simulate the transient flow past a surface-mounted square cylinder and straight channel. A Dirichlet- type vorticity boundary condition based on the circulation and Stoke theorem is proposed at the solid surface. The no-slip condition at the solid surface is satisfied by producing vorticity near it. The PSOR iteration method is used to solve stream function equation;The transport and diffusion of vorticity in the flow field is simulated by solving the vorticity transport equation.
One of the main purpose in this study is to observe the dynamical process of the vorticity and stream function in the flow field. Four Reynolds numbers are used in the simulation ,which are 1,10,100 and 200 . The results show that the dimension of the separation region at the leftside of the square cylinder decreases with Reynolds number,but the dimension of the separation region at the rightside of the square cylinder increases with Reynolds number.
The slope of pressure coefficient vs x-distance is -0.2399 in the straight channel calculation for Reynolds number 100,that is very close to the theoretical value —0.24.
The pressure-drop difference between the surface-mounted square cylinder and straight channel at the 14 diameter length is -1.27 .
On the other hand ,the flow behavior in the entrance zone are re-examined.
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