Near-frozen quasi-one-dimensional flow I. The reservoir problem

Abstract
Non-equilibrium quasi-one-dimensional nozzle flows are considered in the limit when the relaxation time is large compared with some characteristic flow time. Non-uniformities which arise in the reservoir region, for convergent-divergent nozzles, are treated by the method of matched asymptotic expansions (see, for example, Van Dyke 1964). It is shown that even away from this stagnation zone the solution does not proceed simply in integral powers of the rate parameter. The correct solution is deduced for a vibrationally relaxing gas. It is noted, however, that this near-frozen solution does not necessarily remain valid at downstream infinity where the overall entropy production may become important. Solutions valid in this region are presented in part II of this paper.