ρ-VOF: a Method for Simulating Sharp Free Interface in Gas-Liquid Flow

A new density based numerical simulation method, named ρ-VOF, was developed for gas-liquid flow. The governing equation originated from the simplified EFM (effective field modeling)model, in which, the items of nonconservation and nonhyperbolicity in the original equation were removed. The free interface in the control volume was reconstructed, according to the volume fraction field. Also, the spatial distribution of the fluids in the control volume was achieved. AUSM⁺-up scheme was applied to calculate the convective fluxes and pressure fluxes, taking consideration of the contact discontinuity of the free interface. The new method is capable of simulating the interaction between shock discontinuity and contact discontinuity uniformly and maintaining the sharpness of the free interface. Also, the cost in calculation is independent of the complexity of the free interface. At the last part, typical examples of gas-liquid flow were simulated, such as shock in liquid tube problem, shock in gas-liquid tube problem and shock passing by a two-dimensional droplet problem. Comparing the current results with the published data, the validity of ρ-VOF was confirmed.