晶格波茲曼法於障礙物強制振盪運動之數值探討

Abstract

在流體問題的探討之中，當使用計算流體力學方法來模擬流場時，首先必須將所要探討的流場區域切割成若干個網格後，再進行Navier-Stokes方程式的離散計算。當遭遇到具有移動物體的流場問題時，傳統計算流體力學方法如有限體積法等，在進行此類移動邊界問題之模擬時，常受到網格必須排除移動固體障礙物的限制，因此在障礙物附近的網格必須隨計算時間不斷地重新切割與調整，使得整體計算處理的複雜程度增加。所以，找尋更有效率處理移動邊界的計算方法一直是目前計算流體力學所努力的目標。在本研究中，我們以新概念計算流體力學的數值方法¬—晶格波茲曼法(lattice Boltzmann method)為基礎，配合上Lallemand及Luo(2003)所提出處理移動邊界問題的數值模式，以該模式中固體邊牆的反彈機制(bounce back)與二次內插法(quadratic interpolation)，來模擬具有移動邊界之流場。本研究中利用晶格波茲曼法中不需要將流場進行重新切割變形之優點，來解決以往傳統計算流體力學方法處理移動邊界時，必須要將網格隨計算時間不斷進行更動變形或是重新切割之缺點。 在本研究中，首先我們以二維度層流流況下具外部移動邊界的簡單剪力流(Couette flow)作為模擬目標，配合上傳統有限體積法的運用，藉此比較晶格波茲曼法與有限體積法兩者間的計算效率以及精確度。由結果可以看出晶格波茲曼法有著與有限體積法相近的精確度，而其計算效率則優於有限體積法，因此可認定晶格波茲曼法確實為一有效率且具精確度的計算流體力學方法。 接著本研究使用晶格波茲曼法，配合當中移動邊界之數值模式去模擬一個有障礙物振盪運動的長直渠道。當該障礙物以不同倍數關係的渦街頻率進行振盪運動時，計算其後方尾流區域的速度剖面，並與Dutta等人(2007)以顆粒顯影流速儀所測得之實驗值相互比對，其模擬驗證結果相當不錯。此結果顯示出晶格波茲曼法除了具有效率這項優勢外，亦能夠對於移動邊界的問題，進行有效的處理。

In fluid dynamics, numerical approaches are one of the powerful methods to analyze fluid fields. When traditional numerical methods are used to simulate a flow field, the first step is to divide the flow field into many discrete grids. The discrete Navier-Stokes equation of each grid is next computed. If there exists moving boundaries in the fluid field, these grids need to be re-computed or transformed in each time step. Thus, the traditional computational fluid dynamics (CFD) methods such as finite volume method (FVM) are computationally intensive, if there are moving boundaries in the fluid field. Therefore, the abatement of the computational complexities in numerical methods for processing the moving boundaries in fluid fields is the major issue of present study. In this thesis, a new numerical method, the Lattice Boltzmann Method (LBM), is introduced. LBM is combined with a numerical technique for solving the moving boundary given by Lallemand and Luo (2003), who proposed a simple bounceback scheme and a quadratic interpolation method. LBM does not need to perform the same re-computed or transformed works used in the traditional CFD, thus the performance of LBM is much better than the traditional CFD methods. Firstly, we use LBM to simulate the 2-D Couette flow and compare the efficiency and accuracy with each other. The results of the simulations show that the efficiency of LBM is better than FVM and the accuracy remains the same as FVM. We also use LBM to simulate a channel flow over a forced oscillating obstacle. In this simulation, we analyze the wake areas of the forced obstacle in several oscillating frequencies. These results are compared with the experiment of the particle image velocimetry conducted by Dutta et al. (2007). The numerical results are found to be in good agreement with the experimental data. Thus, it is concluded that LBM is efficient in processing moving boundary flow problems.