一結合VOF介面追蹤法及等位函數於兩相流模擬

Abstract

本研究主要基於VOF法中的CISIT法，並引入等位函數以改善兩相流中表面張力計算的準確性，以此方法模擬各種兩相流場以驗證本方法的適用性。在一般VOF法計算界面曲率時，須先將流體體積分率平滑化，在原始的CISIT中，採用平均平滑化的處理方式，而此方式所得之表面張力準確度較低，故本文引入等位函數法的方式以改善其準確性，此稱之為結合等位函數之VOF介面追蹤法(CLSVOF)。在本方法中，定義介面位置在體積分率為0.5與等位函數為零之處，計算等位函數時其初始分布會由體積分率轉換，再由重新初始化方程式計算其分布，並配合CSF模型計算表面張力，而流場中速度與壓力的耦合使用PISO法處理，最後以CISIT預測流體介面的運動。本文將測試二維流場中表面張力的準確性並模擬單一氣泡上升的問題，再推展至三維流場，包括單一氣泡上升、雙氣泡融合與兩液滴碰撞的問題。測試結果顯示，相較於CISIT，以CLSVOF模擬的表面張力更準確，且所產生的spurious currents較弱(spurious currents是由於使用CSF模型所造成的)，而在三維流場的模擬中，相較於CISIT法，使用CLSVOF可在網格數較少時，呈現較接近實驗的結果。

This study is based on a VOF method, is called CISIT, and introduces of the level-set function to improve computation accuracy of surface tension and then simulated different two-phase flows to confirm the applicability of this method. When general VOF method to calculate the curvature of the interface, volume fraction must first be smoothed, in the original CISIT, adopting a treatment of averaging smoother, but in this way that obtained a not accurate surface tension, so we introduced the level-set function to improve its accuracy, this method is called a coupled level-set function and VOF interface tracking method (CLSVOF). In this method, position of interface is defined in volume fraction of 0.5 and level-set of zero, when calculating the level-set function its initial distribution will be converted by volume fraction, and solved re-initialization equation to obtain the distribution, and with the CSF model to calculate the surface tension, coupled velocity and pressure in the flow field is using PISO, finally CISIT is used to predict the motion of the interface. In the two-dimensional flow field, this article tested the accuracy of surface tension and simulated a problem of single bubbles rising in a stationary liquid, and then extended to the three-dimensional flow field, including single bubble rise and two bubble coalescence and droplet collision. Test results show that, compared with CISIT, the result simulated by the CLSVOF, surface tension is more accurately and spurious currents are smaller (a numerical error, spurious currents are caused by CSF model), and in the three-dimensional flow field, the CLSVOF method can present the results closer to the experiments when using coarser grid.