A General One-Dimensional Theory of Compressible Inviscid Swirling Flows in Nozzles

Abstract

SummaryAn approximate analytical method is presented for determining the swirling compressible flow through a nozzle. The method is developed from the techniques introduced by Carpenter and Johannesen. It is perfectly general in that the swirl distribution need not be specified a priori but the radial gradients of the stagnation enthalpy and entropy are assumed to be small. The principal assumption is that changes in the nozzle cross-sectional area are sufficiently gradual and smooth for the radial velocity component to be neglected at each section, i e the usual assumption of one-dimensional compressible flow theory. Analytical expressions are derived for various flow characteristics, e g mass-flux coefficient, impulse function and back-pressure ratio required for choking. The analytical results are compared to numerical results for two main classes of swirling flows. On the whole the analytical results are found to be good approximations for moderate swirl levels. The approximate numerical method is found to be reasonably successful at predicting flow reversal at the nozzle wall. The main result is that a swirl parameter is found such that, with the sole exception of the free-vortex case, the mass-flux-coefficient data for all swirling flows investigated collapse onto a single curve.