Non-linear wave propagation in a relaxing gas

An outline of the classical far-and near-field solutions for small-amplitude one-dimensional unsteady flows in a general inviscid relaxing gas is given. The structure of the complete flow field, including a non-linear near-frozen (high frequency) region at the front, is obtained by matching techniques when the relaxation time is ‘large’.If the energy in the relaxing mode is small compared with the total internal energy, the solution in the far field is, in general, more complex than that predicted by classical theory. In this case the rate process is not necessarily able to diffuse all convective steepening. An equation valid in this limit is derived and discussed. In particular, a sufficient condition for the flow to be shock-free is established. For an impulsively withdrawn piston it is shown that the solution is single-valued both within and downstream of the fan. Some useful similarity rules are pointed out.The corresponding formulation for two-dimensional steady flows is also noted in the small energy limit.