High-fidelity simulation of drop collision and vapor-liquid equilibrium of van der Waals fluids

The availability of a method to accurately predict the interaction of fuel drops and vapor-liquid equilibrium is crucial to the development of a predictive spray combustion model. The objective of this paper is to present such a method. A numerical method, based on the smoothed particle hydrodynamics (SPH), was coupled with a cubic equation of state for simulating the fuel drop dynamics and liquid-vapor distributions at various temperatures in the present study. SPH is a Lagrangian particle-based method, which is useful to simulate the dynamics of fluids with large deformations without the need for a transport equation to track the interface. The present study, furthermore, coupled SPH with van der Waals equation of state to simulate the phenomena of liquid oscillation, drop collisions at high velocity and characteristics of vapor-liquid equilibrium. This approach was found to offer the convenience of using a single set of equations, without the need for submodels, to predict drop breakup or vaporization. A hyperbolic spline kernel function was employed to eliminate the tensile instability that often has been reported in the literature. The numerical method presented here was found to successfully model the merging, stretching separation, fragmentation, and generation of secondary droplets in high-velocity collisions. In predicting vapor-liquid equilibrium, a variable-smoothing-length function was implemented to better facilitate the evaluation of vapor density at low temperatures. Finally, the results of this study indicate that, as the critical temperature was approached, no clear distinction was observed between the liquid and gas phases.