長球體流場在不同攻角與高雷諾數下RANS計算解析

A COMPUTATIONAL STUDY OF HIGH-REYNOLDS-NUMBER FLOWS PAST A PROLATE SPHEROID AT NON-ZERO ANGLES OF INCIDENCE BY RANS EQUATIONS

長球體可視為理想化的潛艦外殼形狀，值此我國正全力發展潛艦國造之際，相關的水動力學分析不僅具有學術研究的價值，同時也具有先導性國防應用的意義。本研究旨在使用雷諾平均方程式（Reynolds-averaged Navier- Stokes equations，以下簡稱RANS方程式），模擬穩態(steady)的流場且採用標準k-ω紊流模型與SST transition兩種紊流模型求解，來探討長軸與直徑比為6:1之橢球體在不同入流攻角下之流場特性，而為國內大型空蝕水槽之實驗作預備，本研究也將探討有限空間實驗條件下的水槽槽壁效應，而我們所採用的水槽尺寸為國立台灣海洋大學的大型空蝕水槽。
我們探討兩種不同入流速度所造成的流場現象，若以橢球長軸作為特徵長度，其雷諾數分別為4.2x106和107，本研究並未設置激紊器與激紊位置。對於每一種入流速度，我們又變化入流攻角，範圍介於0°至40°間，以探討不同條件下的流場特性。相關計算結果顯示，在橢球背風處皆會產生一對穩定的渦漩，且攻角較大時，橢球體表面會出現兩次剝離現象，首先在橢球前中段第一次剝離後，此剝離流會在背風處再附著(reattach)於橢球表面，然後再次發展出第二次剝離，而攻角較小時，則只會在橢球後段產生一次剝離。另外，標準k-ω模型的結果與實驗數據較相近，能較準確地捕捉渦漩，並預測物體的受力，而SST transition模型則有考慮過渡的狀態，因此在尚未過渡的區域上表面壓力有較好的表現。至於槽壁效應的議題，我們發現只有在高入流攻角下，才會有相對顯著的影響。

A prolate spheroid is an idealized submarine in shape. The flow around it characterizes hydrodynamic features of a submarine. In the present study, we employed the Reynolds-averaged Navier-Stokes (RANS) equations to investigate the flow around a 6:1 prolate spheroid at different angles of attack with two different turbulence models, namely, the standard - kwturbulence model and the SST transition model. In addition, to understand the blockage effect for future experiments conducted in the NTOU cavitation tunnel, we also studied the same flow in a confined flow region defined by the tunnel. Two different inflow speeds were selected for the present study. The Reynolds numbers corresponding to the two speeds are 6 4.2 10´and 710 , respectively, if the characteristic length is twice the polar radius of the prolate spheroid. In addition, we assumed that no turbulence stimulators were employed. For each Reynolds number, we varied the angle of attacks from 0 to 40 in the series of computations. The results show that a twin vortex is formed on the leeward side for all flow at a non-zero angle of attack. Furthermore, when the angle of attack is not small, the flow around the prolate spheroid separates twice. The second separation takes place after the furst-separated flow reattaches to the surface of spheroid. In addition, compared to the experimental data, the results obtained with the standard - kwmodel better capture the flow physics such as the vortex system and the force acting on the prolate spheroid. The SST transition model, on the other hand, can better predict the surface pressure distribution in the transition region as it takes the flow transition into consideration. Finally, the blockage effect is prominent only when the angle of attack is big enough.