Research On SPH Modeling Of Liquid-vapor Phase Transition Based On Van Der Waals Theory

Most matters in nature exist in forms of solid, liquid and gas. Phase change is an important research topic which is commonly seen in physics and chemistry from macro-scale to micro-scale. The van der Waals(vdW) equation describes the long-range attractive force and short-range repulsive force between particles. The vdW equation can not only explain the coexistence of liquid and vapor, and liquid-vapor phase transition, but also describe the surface tension between the two phases. Some of the results can be used to study the erosion of the hydraulic machinery surface from the liquid-gas two-phase flow, the phase change on the special material surfaces, and the multi-phase flow.Smoothed particle hydrodynamics(SPH) is a purly meshfree Lagrangian particle method. The feature that each SPH particle represents a certain volume in continue scale, which is similar to classical molecular dynamic methond and dissipative particle dynamics, makes it possible to use the inter-particle equation of state to do fluid mechanics calculation. The vdW equation of state is used in SPH method to study the liquid-vapor phase transition. In order to get stable and reasonable results, the smoothing length of the attractive force should be larger than that of the repulsive force. To avoid the stress instability which is inherent in SPH method, a core repulsive force and the artificial viscosity are used here.Combined with a potential function that describes the repulsive force between liquid and the surface, the van der Waals equation of state is used in the 2D SPH model as a surface tension model. The surface tension model is validated by simulating the coalescence of two equally sized static droplets in vacuum. The model is used in simulating the phenomenon of liquid droplet impact on hydrophobic surface, and the simulated results are in good agreement of the related experimental results, indicating that the scheme we treat the surface tension and the repulsive force of the hydrophobic surface is effective and applicable in droplet impact surface problems. The 2D model is also used in simulating the vaporization of two droplets on hot surface, and the condensation of vapor near the cold walls. The formation, growth and coalescence of the condensed droplet are captured in the simulation, which reveals that the model is able to do phase change simulations.The 3D SPH phase change model is parameterized for water. The model is first validated by forming a condensed liquid drop from a 3D 40-nanometer supercritical fluid system. The liquid density is close to the theoretical value after equilibrium. In order to get a liquid-vapor phase diagram, the densities of liquid and vapor at different temperatures are calculated, and the model reproduces a phase diagram which is consistent with the theoretical one. By heating a liquid drop to a coexistent temperature and cooling the supercritical gas to the same coexistence temperature, the effects of temperature change direction is compared and the comparison shows that for the same target temperature, different temperature change direction barely affect the simulated results. Also, within the threshold of the density, the model is able to get same liquid and vapor densities for different initial density conditions.