Navier-Stokes Equations based Acoustic Analogy with Shock-Noise Prediction Example*

We propose a new acoustic analogy that retains the Navier-Stokes equations as both the propagator and source terms. This approach relies on a new decomposition involving the base flow, aerodynamic fluctuations, and acoustic fluctuations. The aerodynamic fluctuating quantities are further decomposed into large-scale highly spatially coherent turbulence and fine-scale spatially incoherent turbulence. The resultant sources of sound are written as two-point cross-correlations involving each term of the Navier-Stokes equations. The linearized Navier-Stokes equations are solved for the vector Green’s function for the purpose of predicting the acoustic propagation. A closed-form equation for the spectral density of the fluctuating acoustic quantities is derived by a convolution integral involving the vector Green’s function and the two-point cross-correlation source term from Navier-Stokes equations. The closed-form equation is valid for acoustic fluctuations. We model the source terms using a combination of experimental data, source term analysis, and numerical simulation. We show a sample prediction for shock-associated noise using the dominant term in the source model for an off-design supersonic jet flow.