UNSTEADY TRANSONIC NOZZLE-FLOW OF DENSE GASES

Vapours of retrograde fluids, i.e. media with large values of the spec ific heats, may have the remarkable property that sonic conditions are reached three times rather than once during isentropic expansion or c ompression. As a result, the acceleration of such a fluid through a co nverging-diverging Laval nozzle under steady flow conditions may lead to the occurrence of an expansion shock discontinuity. Theoretical con siderations then suggest that nozzles with two throats should be desig ned to achieve a full shock-free subsonic-supersonic expansion. In thi s study the unsteady flow of a dense, retrograde gas through slender n ozzles (with one and two throats) is considered. The combination of th e Navier-Stokes equations supplemented with a non-classical equation o f state for the fluid yields a generalized wave equation, with its val idity restricted to flow conditions near the critical value M = 1. Thi s equation is used to study the transition process which sets in if a steady subsonic solution is perturbed by lowering the pressure at the end of the nozzle.