Effect of non-parallel mean flow on the acoustic spectrum of heated supersonic jets: Explanation of “jet quietening”

Abstract

Noise measurements of heated axisymmetric jets at a 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. It was explained by Afsar, Goldstein, and Fagan [AIAA J. 49, 2522 (2011)] through the cancellation introduced by the 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 nonparallel flow asymptotic theory of Goldstein, Sescu, and Afsar [J. Fluid Mech. 695, 199 (2012)] for the vector Green’s function of the adjoint linearized Euler equations in the analogy. Using the steady Reynolds averaged Navier Stokes calculation for the jet mean flow, we find that the coupling term propagator is positive-definite and asymptotically subdominant at low frequencies corresponding to the peak jet noise when nonparallel flow effects are taken into account and self-consistent approximations for the turbulence structure are made. We then assess the validity of the non-parallel flow-based acoustic analogy model by computing the overall sound pressure level (OASPL) at various observation angles. Interpretation of the latter allows 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.