Effect of non-parallel mean flow on the acoustic spectrum of heated supersonic jets: explanation of `jet quietening'

TL;DR

This paper extends non-parallel flow asymptotic theory to better predict the acoustic spectrum of heated supersonic jets, explaining the spectral quietening effect observed experimentally and computationally, with improved accuracy over parallel flow assumptions.

Contribution

It develops a non-parallel flow acoustic analogy model for heated jets, improving prediction accuracy of jet noise and explaining the quietening phenomenon.

Findings

Coupling term propagator is positive-definite at low frequencies.

Non-parallel effects reduce the coupling term's influence.

Predictions agree well with experimental data beyond peak frequency.

Abstract

Noise measurements of heated axisymmetric jets at fixed supersonic acoustic Mach number indicate that the acoustic spectrum reduces when the temperature ratio increases. The `spectral quietening' effect has been observed both experimentally and computationally using Large Eddy Simulations (LES). It was explained by Afsar {\it et al}. (M. Z. Afsar and M. E. Goldstein $\&$ A. M. Fagan AIAAJ., Vol. 49, p. 2522, 2011) through the cancellation introduced by enthalpy flux/momentum flux coupling term using the generalized acoustic analogy formulation. But the parallel flow assumption is known to give inaccurate predictions at high jet speeds. In this paper we therefore extend the non-parallel flow asymptotic theory of Goldstein {\it et al}. (M. E. Goldstein, A. Sescu $\&$ M. Z. Afsar, J. Fluid Mech., Vol. 695, p. 199, 2012) for the vector Green's function of the adjoint linearized Euler equations (ALEE) in the analogy. Using a steady Reynolds Averaged Navier Stokes (RANS) calculation for the jet mean flow, we find that the coupling term propagator is positive-definite and asymptotically sub-dominant at low frequencies corresponding to the peak jet noise when non-parallel flow effects are taken into account and self-consistent approximations for the turbulence structure are made. The validity of the non-parallel flow-based acoustic analogy model is assessed at various observation angles by computing the overall sound pressure level (OASPL) and use this to suggest a more rational explanation of the quietening effect. In general, our noise predictions are in very good agreement with acoustic data beyond the peak frequency.