# Modeling and prediction of the peak radiated sound in sub-sonic axisymmetric air jets using acoustic analogy based asymptotic analysis

## TL;DR

This paper develops a novel asymptotic analysis-based noise prediction model for subsonic axisymmetric jets, accurately estimating peak sound levels by combining acoustic analogy, Green's functions, and turbulence modeling.

## Contribution

It introduces a new asymptotic approach within the acoustic analogy framework to predict jet noise, incorporating mean flow non-parallelism and turbulence source structure.

## Key findings

- Accurately predicts peak noise at Mach 0.9 for Strouhal numbers up to 0.6.
- Extends prediction range beyond unity Strouhal number using approximate Green's function.
- Shows reasonable agreement with experimental data for subsonic jet noise.

## Abstract

This paper uses asymptotic analysis within the generalized acoustic analogy formulation (Goldstein. J. Fluid Mech 488, pp. 315-333, 2003) to develop a noise prediction model for the peak sound of axisymmetric round jets at subsonic acoustic Mach numbers ($Ma$). The analogy shows that the exact formula for the acoustic pressure is given by a convolution product of a propagator tensor (determined by the vector Green's function of the adjoint linearized Euler equations for a given jet mean flow) and a generalized source term representing the jet turbulence field. Using a low frequency/small spread rate asymptotic expansion of the propagator, mean flow non-parallelism enters the lowest order Green's function solution via the streamwise component of the mean flow advection vector in a hyperbolic partial differential equation (PDE). We then address the predictive capability of the solution to this PDE when used in the analogy through first-of-its-kind numerical calculations when an experimentally-verified model of the turbulence source structure is used together with Reynolds-averaged Navier Stokes solutions for the jet mean flow. Our noise predictions show a reasonable level of accuracy in the peak noise direction at $Ma=0.9$, for Strouhal number up to about $0.6$, and at $Ma=0.5$ using modified source coefficients. Possible reasons for this are discussed. Moreover, the prediction range can be extended beyond unity Strouhal number by using an approximate composite asymptotic formula for the vector Green's function that reduces to the locally parallel flow limit at high frequencies.