基于SPH方法的低韦伯数下三维液滴碰撞聚合与反弹数值模拟研究

SIMULATION OF COALESCENCE AND BOUNCING OF THREE-DIMENSIONAL DROPLET COLLISIONS WITH LOW WEBER NUMBERS BASED ON SPH METHOD

光滑粒子流体动力学方法(SPH方法)作为纯拉格朗日粒子方法,可以有效避免网格法在模拟大变形过程中带来的网格扭曲等缺陷,适合模拟含大变形的液滴碰撞聚合与反弹过程。该文基于Ott和Schnetter提出的修正SPH方法,利用有限差分与SPH一阶导数相结合的方法处理粘性项中的二阶导数问题,进行Couette流算例验证,数值解与理论解基本吻合;利用范德华模型中的分子内聚力项处理表面张力问题,进行初始方形液滴在表面张力作用下自然变化过程的算例验证,变化过程符合宏观实际;运用阐述的SPH方法模拟三维低韦伯数条件下相同尺寸的两个正十四烷液滴正碰与偏心碰撞动力学问题,同时对相同条件下的油与水等难溶液滴间正碰与偏心碰撞问题进行了模拟研究,仿真结果均与文献实验结果进行对比,两者非常吻合,表明该方法适合处理诸如液滴碰撞等大变形的问题。

As a Lagrangian particle method,Smoothed Particle Hydrodynamics（SPH） method can deal with a large deformation without mesh distortion effectively,which is different from traditional grid-based methods.So it is one of the most suitable methods to solve the problems such as coalescence and bouncing of colliding droplets.Based on the modified Ott-Schnetter SPH method,the solving equations are presented in this paper in which the second derivative item in viscosity is treated with combining a standard SPH first derivative with a finite difference approximation of a first derivative.The Couette flow is simulated and the numerical results by this method are in close agreement with the series results.Molecular cohesive pressure within a van der Waals（vdW） model is used to deal with the surface tension,which is validated via the evolution process of a liquid droplet from initial square shape under surface tension.Finally,three-dimensional problems of head-on and off-centre binary collision dynamics of two equal size tetradecane droplets are simulated.Meanwhile the collision of two immiscible droplets with a large surface tension difference,namely,a water droplet and a diesel oil droplet,is also investigated.The numerical results all show a good agreement with the experimental results.It indicates that this method is suitable to solve problems with large deformations such as collision of droplets.