Numerical simulation of conduction problem with evaporation based on a SPH model improved by a fractional order convection-diffusion equation

Abstract

Smoothed particle hydrodynamics (SPH) simulations of phase transitions are not accurate because of the decrease in liquid particles at the end of the evaporation phase transition. In this paper, we establish a numerical model of droplet evaporation suitable for SPH by introducing a time fractional-order convection–diffusion equation. This model was used to study the evaporation process of droplets under different environments, and the stationary evaporation of droplets was simulated by combining convection–diffusion equations of different orders to determine the optimal order. The results conformed to the “D2 Law,” confirming the effectiveness and accuracy of our method. The model was then used to study the phase transition process of droplets impacting flat and curved surfaces. Among the tested equations, the 0.1-order convection–diffusion equation had the best correction effect on the evaporation model. This equation improved the accuracy of the calculation and had a good corrective effect for both static evaporation and the evaporation of droplets impacting flat and curved surfaces.