The multiple source feedback of supersonic jet screech, I: Theory—frequency

Abstract

Screech sound, generated by the interaction of jet instability waves with the spatially periodic cell structure of choked or ‘‘off-design’’ supersonic jets, feeds back to initiate new instability waves at the nozzle. The interaction produces a phased array of effective point sources distance s apart, with a single equivalent (centroidal) source at distance n′s from the nozzle. The feedback criteria discussed at the last Meeting yield frequency f=fPRφ, where fPR=(U/s)⋅1/(1+M) for perfect reinforcement at the nozzle; U,M=instability wave velocity, Mach number; φ=(N+p+ν+I)/n′→1 with n′s≡(N+μ+ν)s, νs=distance of equivalent source from nearest cell end at (N+μ)s from the nozzle, N=integer, |μ|≤1/2, and I=−1, 0, or +1. Exact for any number of symmetrically disposed source strengths, numerical solutions show it to be a good approximation for arbitrary strengths and for inclusion of differing source distances (with weighted equivalent source). The mean s is appropriate for unequal source spacing; but then perfect reinforcement cannot occur. With perfect reinforcement unlikely, the 1953 hypothesis that f→fPR is confirmed as a simple and useful approximation.