Compressibility Effects in High-speed Droplet Impact

The role of compressibility on impacts produced by high-speed (supersonic/hypersonic) liquid droplets is not well understood. The development of hypersonic projectiles requires a better understanding of the forces imparted on the object and the consequences of impact. Droplet impact may create a water hammer effect that can lead to damage and alter the flow around the high-speed object. In this work, the impact of a 2D circular water droplet at Mach numbers greater than 2 on a rigid wall is investigated through numerical simulations. The simulations are compared against theory and approximation equations that account for compressibility. Numerical simulations are performed using a high-order accurate, shock- and interface-capturing, solution-adaptive discontinuous Galerkin method with the five-equations compressible multiphase model. As the speed of the droplet increases, the role of compressibility becomes increasingly important. The relationship between pressure and initial velocity is determined and compared to water hammer theory.