| It exists extensively in nature for free surface flow, such as dam-break in hydraulic engineering, overflow in free surface and flow in open channels, which influences widely to the survival and development of mankind, so it's of great significance to study free surface flow problem. A liquid droplet impacting on a solid surface is a classic free surface flow problem. The phenomenon of diffusion, rebound and broken of a droplet when it impacts on a solid surface exists extensively in chemical industry and metallurgical industry. It's a good way to study free surface flow by studying the phenomenon of a droplet impacting on a solid surface.The Smoothed Particle Hydrodynamics (SPH) method is applied in the numerical simulation of a droplet impacting on a solid surface which is a Lagrangian meshfree particle method. The SPH equations and the key technology which are suitable to generalized hydrokinetics are studied, and the SPH fluid equations are derived from Lagrangian fluid equations. Artificial Compression is applied to calculate the time derivative of stress considering incompressible fluid as compressible fluid. Artificial viscosity is applied to eliminate unphysical oscillation in results. The treatment method of boundary conditions including rigid boundary and free surface boundary is studied, and so do the search of free surface particles, the choice of time steps and the searching method among neighboring particles.SPH method is applied to establish 2-Dimensional model to simulate a liquid droplet impacting on a solid surface. The comparison between the simulated results and experimental results is done, and the flow field, the pressure, the speed and displacement of the representative particles are all studied. The spreading factor is studied by changing the related parameters, such as initial velocity and initial radius of the droplet. Based on above analysis the 3-Dimensional model is established to study the motion of the droplet when it impacts on a solid surface.The theoretical model of a droplet impacting on a solid surface is established to study the relationship between spreading factor and contact angel, the relationship between impacting velocity of the droplet and contact angel, so the relationship between spreading factor and impacting velocity of the droplet can be got, which can be compared with numerical simulated results. |