以數值模式驗證含自由液面圓筒中之渦漩迸裂

Verification of Axisymmetric Vortex Breakdown in an Open Cylinder by Direct Numerical Simulation

鄭文雅(W. Y. Jang) ； 楊德良(D. L. Young) ； 廖清標(C. B. Liao)

《中國航空太空學會學刊》 28卷3期 (1996/09) Pp. 255-264

https://doi.org/10.6124/TAASRC.199609_28(3).10

摘要

本研究所探討的對象是含有自由液面的圓筒中的流場之渦漩迸裂與自由液面之變化。由實驗結果我們可以知道，當圓筒中的流體隨著底盤而開始轉動之後，其流場行爲將隨著底盤轉速；流體黏滯性甚至圓筒的幾何形狀……等條件而將會有很大的差異。於是，我們定義出雷諾數；福祿數以及細長比三個變數來加以探討。
前人對此等流場所進行的研究多著重於雷諾數與細長比兩個變數。本文試著加入福祿數這個變數，而結果發現其對於整個流場的行爲實有其舉足輕重的地位。首先，我們以數值模擬所得的結果與前人所做過的實驗加以比較，以驗證此數值模式的正確性，並進一步藉此數值模式來預測其他不同條件下的流場。結果顯示數值模式之模擬結果，在中低雷諾數下所得到之渦漩迸裂與自由液面之物理機制，均與實驗的結果相互吻合。對於更復雜的流場，數值計算結果可以提供數值流場顯影，轉換成錄影帶之用。

關鍵字

自由液面 ； 渦漩迸裂 ； 雷諾數 ； 福祿數 ； 細長比

並列摘要

The object concerned in this paper is the flow field in a cylindrical container with free surface. When the fluids in a cylindrical container start to rotate with the bottom disk, from the experimental results, we can see that the flow behaviors will differ greatly with the conditions, such as the rotational speed of bottom disk, the, fluid viscosity, and even the geometric shape of the cylindrical container. As a result, we define three variables, Reynolds Number, Froude Number and Aspect Ratio to explore the flow characteristics.
Researches of such flow fields conducted by predecessors emphasize on the variables of Reynolds Number and Aspect Ratio. We tried to consider the effect of Froude Number in this paper and found out that this parameter plays a vital role in the behavior of the entire flow field. The numerical model developed by Liao and Young was adopted here. First, we compared the results of our numerical simulation with those from the experiments conducted by predecessors to confirm the correctness of this numerical model. Furthermore, by this numerical model, we predict the flow fields under other different conditions. Besides, the numerical data sets produced by numerical models can be rendered as a video tape by means of numerical flow visualization in the future, especially for highly complicated flow fields.

並列關鍵字

Free Surface ； Vortex Breakdown ； Reynolds Number ； Froude Number ； Aspect Ratio