Shock-induced cavitation and wavefront analysis inside a water droplet

The objective of the present study is to develop a basic understanding interaction shock waves with density inhomogeneities. We consider here particular instance planar air impinging on spherical water-droplet and discuss what extent this can lead inception cavitation inside droplet. effort centers early phases process during which geometry amplitude propagating wavefront modified by refraction subsequent internal reflections at droplet interface. problem analysed using both simple ray theory 2-D multiphase, compressible hydrodynamic code (ECOGEN). Within context theory, occurrence focusing examined in details parametric equations are derived for transmitted its multiple reflections. It found that wave patterns predicted calculations compare extremely well more accurate numerical solutions from simulations. In particular, it shown assumes complex time-dependent shape whose dominant feature existence cusp singularities. These singular points trace out surfaces caustics associated system rays. From singularities energy flux refracted wave, caustic surface $k$-th reflected deduced. As consequence process, simulations show formation negative-pressure regions flow field. low-pressure zones identified as possible spots where may occur, depending magnitude pressure reached. Finally, results provide quantitative information dependence negative peak upon incident-shock-wave strength.