Operation of Laval nozzles in undesigned modes

Abstract

WHEN designing the gas flow conditions for Laval nozzles it is usually stipulated that the velocity should change from subsonic at the input to supersonic at the output. The transonic flow and passage through the critical velocity occur close to the minimal channel cross-section. If the pressure-difference between the two ends does not reach the design figure, however, the nozzle operates in modes in which the velocity field is primarily subsonic, though supersonic regions may occur. The latter are either adjacent to the channel walls, while the flow remains purely subsonic close to the axis of symmetry; or else they occupy all the central part of the pipe, in which case their forward boundary is a sonic surface, and their rear boundary a density jump, from which a second surface can depart with the critical velocity. The first mode, with local supersonic zones at the channel walls, was first studied by Taylor, then later by many other authors; a detailed history of the topic will be found in [1], where the relevant solutions of the differential equations of gas dynamics are given. The aim of the present paper is to examine the second type of undesigned operating mode, when the supersonic velocity region in the central part includes a density jump cutting the axis of symmetry at right angles.