Steady Gas-Droplet Flow Pattern and Heat Transfer Behind the Point of Incidence of a Shock Wave on a Flat Wall

Abstract

The structure of a steady 2D gas-droplet flow in the near-wall region behind the point of incidence of a normal or an oblique shock wave on a plane wall is investigated. In this case, the normal wave corresponds to the Mach stem in the Mach reflection mode, and the oblique wave corresponds to the regular reflection mode of the incident oblique wave. The main aim of the study is to evaluate the effect of small liquid droplets present in the free stream on the equilibrium temperature of the adiabatic wall behind the point of wave reflection. The question is investigated: to what extent the presence of an oblique shock wave incident on the wall can enhance the effect of reducing the equilibrium wall temperature by small droplets present in the flow. The flow region is split into the outer region of “effectively inviscid flow” and the region of an asymptotic laminar boundary layer. Flow calculations in each region are based on a two-fluid model of a gas-droplet mixture, taking into account the phase transition (evaporation) on the droplet surface. The most interesting wave configurations from the point of view of heat transfer, corresponding to “fully and partially dispersed waves” with incomplete evaporation of droplets behind the reflected wave, are studied. A simple limiting scheme of the formation of a liquid film by droplets deposited on the wall is adopted, with the effects of film instability and spattering being ignored. Based on numerical calculations, the estimates are obtained for the possible decrease in the equilibrium temperature of the adiabatic wall behind the point of incidence of a shock wave in a steady supersonic gas flow containing a low concentration of liquid droplets.