Compressible gas-droplet flow and heat transfer behind a condensation shock in an expanding channel

Abstract

A two-fluid mathematical model of a supersonic gas-droplet mixture flow with account of droplet growth due to vapor condensation behind a condensation shock in a plane expanding channel is constructed. The flow structure in both the inviscid core and the two-phase boundary layer assumed to be laminar is studied numerically. The range of flow parameters is considered in which the spontaneous condensation zone (“condensation shock”) is fairly narrow, and just behind this shock thermal parameters of the phases almost reach thermodynamic equilibrium. Downstream, the droplet radius continues to grow due to the flow expansion and further vapor condensation. Of primary concern is the flow region where the droplets become sufficiently inertial to travel with a velocity slip, and hence to model adequately the velocity and temperature fields in both phases a two-fluid model is required. In addition to the Stokes drag, the Saffman lifting force exerted on the droplets in the boundary layer is taken into account. The Saffman force results in droplet deposition and the formation of a thin liquid film on the channel walls. A parametric numerical analysis of the two-phase flow structure in the inviscid flow region and in the near-wall boundary layer is performed, and the effects of phase transitions (droplet condensation and evaporation, as well as the film formation) on the reduction of the adiabatic channel wall temperature are analyzed.