Species separation in a curved shock wave in supersonic flow of a gas mixture

This paper describes an extension and a synthesis of existing theoretical models of non-planar shock waves in gas mixtures. A means of predicting the modified Rankine-Hugoniot conditions and the species separation in gas mixtures in supersonic flow through curved, two-dimensional shock waves is presented. The results reported here are consistent with the structure of the shock being governed by the Navier-Stokes equations. The prediction algorithm is not limited by the mole fraction of the species in the gas mixture. The species are assumed to be non-reacting. The effects of mixture initial Mach number, initial mole fraction, free stream Reynolds number, component mass ratio, and shock standoff distance are described. Numerical results indicate that the species separation: (1) decreases with increasing polar angle; (2) increases with increasing mixture initial Mach number; (3) decreases with increasing shock standoff distance; and (4) decreases with increasing free stream Reynolds number. Consistent modified Rankine-Hugoniot conditions are also obtained. The analysis requires that the ratio of shock thickness to shock radius be of the order unity or less. An upper limit with regard to mixture initial Mach number and species mass ratio, beyond which the analysis is invalid, is described. (U.S.)