Calculation of hysteresis and flow-rate oscillations of base pressure in supersonic annular nozzles

Abstract

The interaction of the turbulent axisymmetric near wake behind the face of the central body of an annular nozzle with the supersonic annular jet discharging from this nozzle is analyzed. The flow in the monoparametric near wake is calculated by the integral method [1] while the flow in the nonviscous jet is calculated by the method of through calculation using a monotonic explicit difference system of the first order of accuracy [2]. The interaction between the nonviscous and turbulent streams is determined by the displacement thickness of the wake. The initial conditions of the wake are determined from the integral conditions of attachment with the mixing flow in the isobaric base region. The interaction flow is described by the particular solution of the equations which passes through the singular saddle point — the throat of the wake. The near wake and base pressure in different modes of discharge from an annular nozzle at the exit cross section of which the ratio of outer and inner radii is y₂/y₁ = 1.3 and the Mach number is M = 2.54 are calculated as an example. The region of hysteresis of the base pressure, connected with the ambiguity of the interaction flow owing to the formation of the throat of the wake within the first or second barrel of the jet, and the parameters of the low-frequency flow-rate oscillations of base pressure in this region are determined. The results of the calculations are in satisfactory agreement with experimental data.