基于表面力模型的液滴冲击弹性基底SPH模拟

SPH simulation of liquid drops impact on elastic substrates based on a surface force model

采用光滑粒子动力学SPH方法建立液滴冲击弹性基底的流固耦合数值模型,给出描述粘性流体和弹性固体运动的SPH离散方程和数值处理格式,引入人工耗散项来抑制标准SPH方法的数值震荡。为模拟液滴的表面张力效应,通过精确检测边界粒子,采用拉格朗日插值方法计算表面法向量和曲率,结合界面理论中的连续表面力CSF方法,建立了适用于自由表面液滴的表面力模型,方形液滴变形的模拟结果与拉普拉斯理论解吻合较好。随后,采用SPH流固耦合模型模拟1.0 mm直径水滴以不同速度(0.2 m/s^3.0 m/s)冲击两种薄板型基底,分析了基底弹性变形对液滴铺展、收缩以及回弹行为的影响。

A fluid-solid interaction model for the simulation of liquid drops impinging on elastic substrates was established by using the smoothed particle hydrodynamics(SPH)method.The SPH discrete equations for describing the motion of viscous fluids and elastic solids were introduced,and corresponding numerical schemes were given.The artificial diffusion terms were introduced to deal with the numerical oscillation in the standard SPH.To simulate the surface tension effect on liquid drops,by accurately detecting the boundary particles,the parameters including surface normal and curvature were calculated through the Lagrange interpolation.Combined with the continuous surface force(CSF)method in the interface theory,the surface force model for free surface droplets was proposed.The simulation result of square droplet deformation was consistent with the Laplace equation.Subsequently,the model was used to simulate the impact of 1.0 mm-diameter water drops on two types of thin-plate substrates.The effect of substrate deformation on droplet behaviors,including spreading,recoiling,and bouncing,were analyzed.