應用移動粒子流體力學於液滴入水中之模擬

Numerical Simulation of Water Splash by Applying Moving Particle Semi-Implicit Method

自由液面行為是自然界中常見的一種現象，它包含了碎波的生成、變形以及分離，由於其計算邊界不固定，邊界位置需要作為計算結果的一部份進行求解，因此自由液面的數值模擬一直是計算流體力學的挑戰，近年來在計算流體力學技術的發展上，一種新的數值方法即無網格法，得到了關注。在目前學術研究領域已有十餘種無網格法，本文對其中一類移動粒子半隱式（MPS）法進行研究，根據移動粒子半隱式法的基本思想，從無網格法建立近似函數對控制方程式的等效變換，進行了算法推導並編譯程式，針對液滴入水產生的潑濺現象進行數值模擬，發現潑濺現象的產生取決於液膜的厚度以及液滴的初始速度，可見移動粒子半隱式法在模擬流體自由液面中所具有的優勢。 Water splash can be observed obviously in the case of the droplet impact into a liquid surface. It is important to clarify the surface tension effect in order to understand splash phenomena absolutely. Analytical and numerical approaches have been carried out to investigate these phenomena. The recent interests are concerned about the mesh free methods. More than ten mesh free methods have been developed so far. These methods are superior to the conventional grid methods in simulating free surface, breaking waves, droplet breakup and multiphase flow. In this research, a mesh free method, moving particle semi-implicit method (MPS), is conducted and applied to analyze the incompressible flows with the surface tension effect. A surface tension model is adopted to analyze splash behavior. The amount of water splashed by such an impact is examined. The simulation results show that the splash phenomena are sensitive to the liquid pool depth and the initial drop velocity.