EXACT-SOLUTIONS FOR TRANSONIC-FLOWS OF DENSE GASES IN 2-DIMENSIONAL AND AXISYMMETRICAL NOZZLES

Flows of dense gases in two-dimensional and axisymmetric nozzles are c onsidered. If during an isentropic expansion the fundamental derivativ e changes the sign within the flow region, nozzles with two throats an d one antithroat are necessary for a shock-free acceleration to supers onic conditions. Exact solutions to the transonic inviscid small-distu rbance equation for flows of dense gases in plane and axisymmetric noz zles are obtained. The exact nozzle shapes have only one throat, one a ntithroat, and an inflection point. In the latter, the minimum or maxi mum of the Mach number is attained. The flow in a throat-antithroat-th roat configuration may be constructed by solving the small-disturbance equation locally for a sequence of points along the isentrope.