Smoothed particle hydrodynamics method for evaporating multiphase flows

The smoothed particle hydrodynamics (SPH) method has been increasingly used for simulating fluid flows; however, its ability to simulate evaporating flow requires significant improvements. This paper proposes an SPH method for evaporating multiphase flows. The present SPH method can simulate the heat and mass transfers across the liquid-gas interfaces. The conservation equations of mass, momentum, and energy were reformulated based on SPH, then were used to govern the fluid flow and heat transfer in both the liquid and gas phases. The continuity equation of the vapor species was employed to simulate the vapor mass fraction in the gas phase. The vapor mass fraction at the interface was predicted by the Clausius-Clapeyron correlation. An evaporation rate was derived to predict the mass transfer from the liquid phase to the gas phase at the interface. Because of the mass transfer across the liquid-gas interface, the mass of an SPH particle was allowed to change. Alternative particle splitting and merging techniques were developed to avoid large mass difference between SPH particles of the same phase. The proposed method was tested by simulating three problems, including the Stefan problem, evaporation of a static drop, and evaporation of a drop impacting a hot surface. For the Stefan problem, the SPH results of the evaporation rate at the interface agreed well with the analytical solution. For drop evaporation, the SPH result was compared with the result predicted by a level-set method from the literature. In the case of drop impact on a hot surface, the evolution of the shape of the drop, temperature, and vapor mass fraction were predicted.

Figure 1

Schematic of mass transfer from a liquid element to a gas element due to evaporation. Left: mass and vapor mass fraction of the gas element before evaporation. Right: increases in total mass and vapor mass fraction of the gas element.

Figure 2

Schematic of simulating particle splitting. Particle $a$ splits into two particles located on a line perpendicular to the line connecting particle $a$ and its nearest particle $b$.

Figure 3

Schematic of simulating particle merging. Particle $a$ merges into $b$ with the new particle located at the mass center of the two particles.

Figure 4

Schematic of the Stefan problem.

Figure 5

SPH prediction and analytical solution of evaporating mass flux as a function of vapor mass fraction at the interface.

Figure 6

Analytical solution and numerical prediction by considering only Eq. (24).

Figure 7

Initial SPH particle distribution of a static drop, and the computational domain. The drop is at the center and is surrounded by gas.

Figure 8

Snapshots of the evaporating drop at different times.

Figure 9

Normalized square of radius versus time.

Figure 10

Evolution of vapor mass fraction.

Figure 11

Evolution of temperature.

Figure 12

Schematic of drop impact on a surface.

Figure 13

Evolution of drop impact on a hot surface.

Figure 14

Evolution of temperature field of drop impact on a hot surface.

Figure 15

Evolution of the vapor mass fraction of drop impact on a hot surface.