Propagation of weak disturbances in a vibrationally relaxing gas

Abstract

One-dimensional nonsteady flows of an inviscid relaxing gas are treated by the method of integral relations. The flows are thought of as being produced in a semi-infinite cylindrical pipe terminated by a piston, when the piston begins to move into or out of the cylinder. The velocity of the piston has acceleration discontinuities. It is assumed that the piston speed up is small compared with the frozen speed of sound in an undisturbed gas Cf0, and all the dependent variables can be described in the form of perturbation expansions in powers of a small parameter e = up/Cf0. An approximate semi-analytical solution for the first-order problem is obtained by the method of integral relations and sample numerical calculations are systematically carried out for a vibrationally relaxing diatomic gas. Conflicting effects of convection and vibrational relaxation on the propagation of weak nonlinear waves are investigated in detail. NE of the simplest examples of an important class of one-dimensional nonsteady gas flow is given by the gas flow in a semi-infinite cylindrical pipe terminated by a piston, when the piston begins to move with nonzero acceleration. Although the piston problem can be solved exactly for many important cases in classical gasdynamics,1-2 the same cannot be said in the dynamics of real gases, where various thermodynamically irreversible processes are involved. The solution of this problem for the real gas is well-known only in the linear approximation (acoustic approximation).3 4 Several