On the propagation of decaying planar shock and blast waves through non-uniform channels

The propagation of planar decaying shock and blast waves in non-uniform channels is investigated with the use of a two-equation approximation of the generalized CCW theory. The effects of flow non-uniformity for the cases of an arbitrary strength decaying shock and blast wave in the strong shock limit are considered. Unlike the original CCW theory, the two-equation approximation takes into account the effects of initial temporal flow gradients in the flow properties behind the shock as the shock encounters an area change. A generalized order-of-magnitude analysis is carried out to analyze under which conditions the classical area–Mach (A–M) relation and two-equation approximation are valid given a time constant of decay for the flow properties behind the shock. It is shown that the two-equation approximation extends the applicability of the CCW theory to problems where flow non-uniformity behind the shock is orders of magnitude above that for appropriate use of the A–M relation. The behavior of the two-equation solution is presented for converging and diverging channels and compared against the A–M relation. It is shown that the second-order approximation and A–M relation have good agreement for converging geometries, such that the influence of flow non-uniformity behind the shock is negligible compared to the effects of changing area. Alternatively, the two-equation approximation is shown to be strongly dependent on the initial magnitude of flow non-uniformity in diverging geometries. Further, in diverging geometries, the inclusion of flow non-uniformity yields shock solutions that tend toward an acoustic wave faster than that predicted by the A–M relation.