A new formulation of a spray dispersion model for particle/droplet-laden flows subjected to shock waves

A new analytical model is derived based on physical concepts and conservation laws, in order to evaluate the post-shock gas velocity, the gas density and the spray dispersion topology during the interaction of a shock wave and a water spray in a one-dimensional configuration. The model is validated against numerical simulations over a wide range of incident Mach numbers $M_s$ and particle volume fractions $\tau _{v,0}$. Two regimes of shock reflection have been identified depending on $M_s$, where the reflected pressure expansion propagates either opposite to the incident shock-wave direction for weak incident Mach numbers or along with it for strong Mach numbers. The numerical simulations reveal the presence of a particle number-density peak for $M_s > 2$ and with particle diameters of the order of ${O}(10)\ \mathrm {\mu } \textrm {m}$. The formation of the number-density peak is discussed and a necessary condition for its existence is proposed for the first time.