اعمال خصوصيات جريانهاي آشفته در روش MPS چند فازي

Applying Turbulent Flow Characteristics to the Multi-Phase MPS Method

محاسبات مربوط به جريان با حل معادله‌هاي مومنتم و پيوستگي انجام مي‌شود. يكي از روش هاي حل اين معادله‌ها در مسايل با سطح آزاد متحرك به دليل شرايط پيچيده و امكان برخورد سطوح آزاد با يكديگر روش MPS چند فازي است. اين روش يك روش لاگرانژي است كه ابري از ذرات جايگزين شبكه محاسباتي مي شوند و در حالت چند فازي معادله‌هاي حاكم بر چند فاز گاز، مايع و جامد به صورت همزمان حل مي‌شوند. در اين مقاله اثر اعمال آشفتگي با مدل صفر معادله اي در روش MPS مطالعه شده است. نتايج حاصل از اين تحقيق حاكي از افزايش پايداري روش و بهبود برآورد سطح آزاد در مساله شكست سد در مقايسه با حالت غيرلزج و با لزجت گردابه اي ثابت است. همچنين ارتقاي مدل بوسيله اعمال مدل هاي آشفتگي در مدل چند فازي نشان دهنده عدم تاثير نوع تابع كرنل مورد استفاده در حل معادلات مومنتم و پيوستگي بر روي پايداري روش مي باشد.

The purpose of this paper is to put forward a new method of Multi-phase Moving Particle Semi-implicit (MP-MPS) for solving continuity and momentum equations of viscous fluid flow. MP-MPS is a Lagrangian meshless method that solves the governing differential equations of gas, fluid and solid phases, simultaneously. This method has many applications in problems of free surface flow which is due to their complex conditions and non-linear equations. Among these complexities is the need to consider the effect of turbulence. Until now, MPS method has been used widely for inviscid fluids or those with constant eddy viscosity. In this paper, the effect of turbulence closure model is investigated using Prandtl’s mixing-length theory. The enhancement of MPS model in estimating free surface flow considering the effect of turbulence is demonstrated through comparing its results with those of fluid with constant eddy viscosity and inviscid fluid for a typical dam break problem. The results obtained from the developed model show that determination of eddy viscosity of each particle in each time step based on their location and velocity is important and has a major effect on the final hydrodynamic parameters computations. In addition, results obtained through the improvement made in the numerical model have a good degree of similarity with those obtained through experiments. Also, the results indicate that applying the turbulence nature of the flow helps in obtaining a more stable solution and therefore in this case, the type of Kernel function used in MPS method has no significant effect on its stability.