Predictive capability of low frequency jet noise using an asymptotic theory for the adjoint vector Green’s function in non-parallel flow

Goldstein, Sescu & Afsar (J. Fluid Mech., vol. 695, pp. 199-234, 2012) formulated an asymptotic theory in non-parallel flows for the vector Green’s function that enters adjoint linearized Euler equations in the generalized acoustic analogy formulation (Goldstein. J. Fluid Mech. 488, pp. 315-333, 2003). The theory introduced a new distinguished scaling at low frequencies for a slowly-diverging mean flow that showed how the leading order non-parallel flow Green’s function solution would be (mathematically) different to the same parallel flow result at all points in the jet. The theory gave qualitative agreement with the full numerical calculation of the Linearized Euler Equations in Karabasov et al. (2011, AIAA-2929). The present paper follows on from this work and is concerned with assessing the predictive capability of the Goldstein et al. (2012) asymptotic theory for low frequency jet noise. Using Goldstein’s generalized acoustic analogy formulation we determine the propagator (that depends on the adjoint vector Green’s function) using a steady Reynolds-Averaged Navier-Stokes (RANS) calculation to obtain the mean flow field for the asymptotic theory. The jet is axi-symmetric and unheated with an acoustic Mach number of 0.9. We recover the basic structure of the Goldstein et al. (2012) qualitative analysis by showing the large increase in magnitude of the low frequency dominant propagator component when the true non-parallel flow is used. Our main result shows that this asymptotic solution can predict the jet noise spectrum at 30 degees to the jet axis remarkably well up to the peak noise when a suitably constructed axi-symmetric turbulence model is used within the acoustic analogy. Since the calculation time for this approach is considerably faster than solving the full Linearized Euler equations, the merits for doing this are immediately clear.