A Sonic Condition Model for Pseudo-Shock in Divergent Ducts

Abstract

A newly constructed model calculates the starting position of the pseudo-shock, or shock train, in the divergent ducts. The model is based on the conservation laws of mass, energy and momentum of the inflow and outflow into/from the pseudo-shock region, and further uses a sonic condition in the core flow of the pseudo-shock. The model adopts an empirical growth rate of the low-velocity region, and the divergent angle of the nozzles becomes a design parameter. The lengths of the pseudo-shocks calculated show reasonable agreement with the experimental results. Pressure distribution with quick increase near the starting position is simulated. The supersonic core flow cross-section becomes smaller than that at the starting position of the pseudo-shock. The pressure at the sonic point rises to 0.7 of that at the duct exit. The length of the quick pressure-increase region becomes longer as the Mach number increases at the starting position.