Numerical studies on droplet impact to wettable solid boundary based on SPH method

Abstract

Droplet impact on solid surface is a common natural phenomenon and industrial process which is also a complex polyphase conditions coupling process with gas, liquid and solid. And during the droplet’s deformation and movement, it is often affected by the wettability of solid wall. In this paper, a lagrange SPH numerical method, with the attraction of the van der Waals state equation added to simulate the surface tension of the droplet, is applicated to simulate the process of single droplet impact on wettable surface and investigate the influence mechanism of surface wettability to the droplet’s deformation and movement. Several improvements for traditional SPH methd are presented such as, a Lagrange wettable solid wall boundary condition of which solid wall pariticles’ hydrophilia and capillary action are unified supposed to be a adsorption force to the liquid particles of support domains. The force is deemed relevant to fluid pressure, saturation and solid wall’s hydrophilia. Then a stress correction method is proposed for the stress instability caused by the SPH kernel function. The method uses two different shapes of kernel functions to calculate the tensile and compressive stresses, respectively. After that, a SPH model compiled in Fortran language and based on the above two improved methods is established to simulate static and dynamic droplets’ deformation processes on different wettable wall. The following studies were carried out based on the simulation results. Firstly, the effect of stress correction method is investigated by the comparison between simulating results with the stress correction before and after used. Secondly, the validity of the wettable solid wall boundary condition is studied based on the simulation results of static droplet deformation. Finally, the influence of the wall wettability on the droplet movement process after the collision is analyzed. Researches show that, the stress correction method improves the stress instability problem in the traditional SPH method, even in the large deformation movement can still maintain a uniform particle distribution. In addition, the stress correction method can better simulate the surface tension of free surface flow, and can get a more smooth free surface. According to the change characteristics of droplet’s static contact angle, the mentioned wettable solid wall boundary condition can clearly reflect the wall’s wettability. Simulation of doplet impact on wettable wall shows good agreement with the experiment result. During rebound stage, a large enough wettability will induce droplet deforming into liquid column. The wettability have a little influence to droplet’s spreading stage, the wall friction force plays a major role. While during retraction and rebound stages, the influence of wettability is obvious. This study improves the theory of the interaction between free surface fluid and solid wall, and can provide a reference for further study of the effects between free surface fluids and wettable media or discrete particles.