Simulations of the shock waves and cavitation bubbles during a three-dimensional high-speed droplet impingement based on a two-fluid model

• A two-fluid model is first sued to simulate high-speed droplet impingements.
• Numerical cavitation like behavior is simulated under the two-fluid approach.
• The growth rate of cavitation bubble is not related to the impact velocity.
• The minor cavitation bubble is caused by the eruption of the main cavitation bubble.

In this paper, we investigate the aerodynamic characteristics inside a droplet impingement using a compressible two-fluid model. A hybrid type Riemann solver is proposed to compute numerical fluxes across the interfaces of gas–gas, liquid–liquid and gas-liquid flows in the considered flow-fields. Here, the compressible liquid flows with high Reynolds number value allow us to use an inviscid approach and neglect the surface tension effect under the assumption of high Weber number. Numerical results demonstrate the evolution of shock-front, rarefaction, cavitation inside the droplet and the contact periphery expands very quickly and liquid compressibility plays an important role in the initial formation of flow physics inside the liquid droplet. Grid independence study is performed. A secondary cavitation zone is simulated to appear near the wall due to the expansion wave propagating downward caused by the eruption of the main cavitation bubble near the top of the liquid droplet. We also found that the growth rate of the cavitation zone is independent of the impact flow velocity. The estimated maximum wall pressure against the incoming Mach number is shown to be closer to the theoretical data than any other previous analysis.