Passage of Shock Waves Through Ducts of Variable Cross Section

Abstract

If shock waves strong enough to produce supersonic flow pass through a duct of variable cross section, the shape of which is approximated by a single discontinuous area change, a variety of wave patterns may be found. These are unique for particular conditions except for a range of area convergence for which it was recently shown that three solutions exist. Examination of the transient processes that precede the establishment of the final flow suggests, and a general proof confirms, that only one of these solutions can actually be realized if the duct converges monotonically. For more general duct configurations, the other solutions may also be found, but the correct wave pattern may have to be established with the aid of a wave diagram in which area changes are properly taken into account. For configurations with a throat, additional wave patterns may appear both within and outside of the region of ambiguity which then loses its significance.