Structure of Normal Shock Waves in Gas Mixtures

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Abstract
A theoretical analysis of steady, normal shock structure in binary gas mixtures of inert, monatomic gases is given. The analysis is based on the moment method of kinetic theory. The governing equations of this two-temperature-two-velocity model are in no way restricted by initial concentration of the species, mass ratio of the species, or Mach number. The system of equations which describes the structure includes the conservation of mass of each species, the conservation of momentum and energy of the mixture, the transfer of momentum and peculiar energy equations, the evolution of the stress moment of each species, and the heat flux moment of each species. The nondimensional parameters which characterize the phenomenon are identified as the number density ratio in the free stream η = (nj/ni)−∞, the mass ratio θ = mi/mj, and the mixture Mach number in the free stream M−∞. By choosing various combinations of these parameters, five different types of structures are proposed. By further restricting the light species and heavy species upstream Mach number, a given type of structure may be shown to require more than one scale for a complete transition. The anomalies resulting from some continuum theories and numerical calculations are investigated. The proper application of the Mott-Smith ansatz to normal shock waves in binary gas mixtures is clarified. Comparison with existing experimental and theoretical results is made.