中雷諾數流場移動物體之數值計算

Abstract

本論文主旨擬利用一套數值模式來模擬移動邊界問題，此模式是利用有限差分法結合混合卡式沉浸邊界模式，來求解含有移動物體的黏性不可壓縮流問題，其控制方程為奈維爾-史托克斯方程式。首先，將此模式分別應用在固定以及移動邊界的二維問題，其中用來驗證固定邊界的問題是模擬均勻流體流經無窮域的靜止圓柱，然而驗證移動邊界的問題則是利用圓柱在靜止流場中來回移動，並將其數值結果與文獻相比，藉此來驗證此套模式的正確性和可靠性。最後，將此模式應用在三維流場的移動邊界問題，而此問題主要是模擬圓球於流體中等速落下之三維流場，並且將結果與實驗數據相比。由此可得到在雷諾數大於500之後，流場已開始產生不對稱之現象，而當雷諾數等於800時，於三維渦度圖當中可觀察到球在撞擊牆之後，複合的渦環捲上原始的渦環並做三維的運動。由此可知，此數值模式的結果提供了在實驗上無法直接觀察到的三維運動現象。

In this thesis, the numerical model which is the finite-difference model with hybrid Cartesian/immersed boundary method is applied for solving the 2D and 3D Navier-Stokes equations with immersed and moving boundary on a fixed Cartesian grid. There are two studies in 2D which are carried out to verify the robustness of the present model with reference data from uniform flow past a stationary circular cylinder, and in-line oscillating circular cylinder in a fluid at rest. However, the numerical model is applied to simulate a moving boundary problem which is dropping sphere with constant velocity in 3D flow field. Therefore, the flow field is asymmetric at Reynolds numbers above 500 from both experimental and numerical results. Moreover, the flow field after impact at Reynolds number equals to 800, the combined vortex ring rolls upward to contact the primary vortex ring and acts as a 3D motion in all directions. Therefore, the numerical simulations can fill up the lack of the results in experiment within 3D visualization.