Propagation of Weak Shock Waves in a Vibrational Nonequilibrium, Nonuniform Gas

Problems concerned with the propagation of weak planar shock waves in a nonuniform, nonequilibrium gas is theoretically investigated. The medium under consideration is a diatomic thermally perfect gas with excited vibrational energy and is initially inhomogeneous with exponential density and temperature distributions. The systematic characteristic perturbation scheme is employed to render a first-order frozen shock expression. It is shown quantitatively that combined effects of nonequilibrium, nonlinearity, and stratification govern the nature of the shock wave propagation. The uniform gas limit of present theory agrees with previously known results of shock wave propagation in a general relaxing fluid. Numerical examples illustrate the variation of frozen shock strength and speed due to different magnitudes of relaxation rates and inhomogeneity. The interesting competition phenomenon between nonequilibrium effects and nonuniform effects on shock wave propagation is examined.