A statistical jet-noise model based on the acoustic analogy and a RANS solution

Abstract

We introduce a hybrid model for the evaluation of jet noise. The model uses the information from a solution of the Reynolds-averaged Navier-Stokes equations (RANS). It evaluates the jet-noise power spectral density (PSD) in the quiescent region outside the turbulent jet. It includes the following components:1. A propagation model based on the high- and low-frequency approximations of the Lilley analogy Green's function. The high-frequency approximation is determined by combining a moving-medium Lighthill analogy and ray acoustics. The low-frequency model is made by using a flow-factor approach on each component of the source two-point CPSD. Weuse available analytical expressions of flow factors evaluated in the low-frequency limit.2. A fixed-frame source model based on the source terms of the Goldstein (2001) expression for the Lilley analogy. Both the applied-stress and applied-force equivalent acoustic sources are retained. The used acoustic analogy allows for expressing the 2-point covariance of the applied-stress source by using 2-point velocimetry measurements in a turbulent jet. Specifically the applied-stress source can be put in correspondence to the unit-density Reynolds-stress statistics. Available measurements of the unit-density Reynolds-stress 2-point statistics are here used to derive an analytical model for the applied-stress 2-point correlation coefficient. Also the applied-force 2-point statistics, required for modelling noise source mechanisms at the presence of density inhomogeneities in the flow, is expressed on the basis of the unit-density Reynolds-stress 2-point statistics. Numerical methods are used to derive the frequency-wavenumber expression for a volumetric source-strength tensor.3. A jet-flow prediction by using a commercial RANS solver and a set of connection relations expressing source-model parameters starting from the RANS solution. The RANS system includes Reynolds Stress modelling (RSM) closure equations. Turbulence anisotropy is then incorporated in the flow-statistics estimation. The proposed connection relations introduce a set of empirical parameters which are evaluated by matching model components to both velocimetry and acoustics measurements. Modelled far-field jet-noise 1/3-octave spectra are compared to corresponding measurements for isothermal, unheated and hot jets.

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