Discrete tone emission from high-pressure ratio supersonic jets fromconvergent-divergent nozzles

Abstract

The results of a test program to investigate the discrete tone generation from free axisymmetric supersonic jets issuing from convergent-divergent conical nozzles of different sizes and expansion ratios in a range of stagnation pressure ratio never reported before are presented. In both highly overexpanded and underexpanded jet conditions, the second shock-cell length was found to be in good agreement with Pack's modified theoretical formula for the first shock-cell length of slightly incorrectly expanded supersonic jets, when the nozzle diameter was replaced by the jet diameter dj corresponding to the fully expanded jet Mach number M-. The use of dj in normalizing shock-associated noise data was first proposed by Tarn and Tanna. To a good approximation, the second shock-cell length displayed a linear dependence on the parameter p2 = M.J — rather than on (J. The apparent length of the first shock cell was also found to display linear dependence on P 2 but only in the overexpanded jet condition. The linear variation of the second shock-cell length with p2 was found to be invariant for all the nozzles tested, but in the case of the first shock cell, the proportionality constant varied with the nozzle expansion ratio. The discrete tone fundamental frequency was found not to depend on the nozzle exit diameter but to be inversely proportional to the nozzle throat diameter. With a constant ratio between the disturbance convection velocity and the fully expanded jet velocity, the combination of Powell's simplified feedback loop equation with the shock-cell length obtained from the modified theoretical formula predicted to a good practical accuracy the discrete tone fundamental frequency.