Towards the prediction of supersonic jet noise predictions using a unified asymptotic approximation for the adjoint vector Green's function

Afsar, M. Z. and Sescu, A. and Sassanis, V. and Lele, S. K. (2017) Towards the prediction of supersonic jet noise predictions using a unified asymptotic approximation for the adjoint vector Green's function. In: 23rd AIAA/CEAS Aeroacoustics Conference, 2017-06-05 - 2017-06-09.

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    Abstract

    In this paper we continue efforts aimed at modeling jet noise using self-consistent analytical approaches within the generalized acoustic analogy (GAA) formulation. The GAA equations show that the far-field pressure fluctuation is given by a convolution product between a propagator tensor that depends on the (true) non-parallel jet mean flow and a generalized fluctuating stress tensor that is a stationary random function of time and includes the usual fluctuating Reynolds’ stress tensor as well as enthalpy fluctuation components. Here, we focus on approximating the propagator tensor by determining an appropriate asymptotic solution to the adjoint vector Green’s function that it depends on by using an asymptotic approach at all frequencies of interest for jet noise prediction. The Green’s function is then rationally approximated by a composite formula in which the GSA (Goldstein-Sescu-Afsar, J. Fluid Mech., vol. 695, pp. 199-234, 2012) non-parallel flow Green’s function asymptotic solution is used at low frequencies and the O(1) frequency parallel flow Green’s function is used for all frequencies thereafter. The former solution uses the fact that non-parallelism will have a leading order effect on the Green’s function everywhere in the jet under a distinguished scaling in which the jet spread rate is of the same order as the Strouhal number for a slowly-diverging mean flow expansion. Since this solution, however, is expected to apply up to the peak frequency, the latter O(1) frequency Green’s function in a parallel flow must be used at frequencies thereafter. We investigate the predictive capability of the composite Green’s function for the prediction of supersonic axi-symmetric round jets at fixed jet Mach number of 1.5 and two different temperature ratios (isothermal & heated) using Large-eddy simulation data. Our results show that, in the first instance, excellent jet noise predictions are obtained using the non-parallel flow asymptotic approach, remarkably, up to a Strouhal number of 0.5. This is true for both heated and un-heated jets. Furthermore, we develop the analytical approach required to extend this solution by appropriate asymptotic approximation to O(1) frequencies.