UNSTEADY START OF THE LAVAL NOZZLE

In the approximation of a two-dimensional flow of an ideal (inviscid and non-conducting) gas, the problem of a non-stationary launch of a Laval nozzle by an instantaneous rupture of the membrane at its exit is numerically solved for different ratios n > 1 of the pressures of the motionless gas inside and outside the nozzle. In the one-dimensional approximation, the stationary flow regime in a Laval nozzle changes from an unlocked subsonic flow (for 1 < n < n _*) to a locked sonic flow in the minimum nozzle cross-section (for n > n _*) with an easily determined value of n _*. The two-dimensionality of the flow complicates both stationary and non-stationary flow regimes in nozzles. In the two-dimensional stationary approximation, when n _* < n < n _**, the unlocked Taylor (Taylor G.) mode is realized, with supersonic zones near the walls of the minimum cross-sections of the nozzles, which is different from the locked Meyer (Meyer T.) mode. In the Meyer mode, when n > n _**, the supersonic flow covers the entire minimum cross-section, and in the vicinity of the "center" of the nozzle (the point where the sonic line meets the plane or the axis of symmetry), the flow is designed analytically. The numerically calculated non-stationary solutions did not confirm the known self-similar solutions of inverse problems about the launch of two-dimensional Laval nozzles.

“numerical” start of a Laval nozzle, membrane rupture, the role of non-stationarity of the flow, and the difference from self-similar solutions of inverse problems