An acoustic analogy is developed to predict the noise from jet flows. It contains two source models that independently predict the noise from turbulence and shock wave shear layer interactions. The acoustic analogy is based on the Euler equations and separates the sources from propagation. Propagation effects are taken into account by calculating the vector Green's function of the linearized Euler equations. The sources are modeled following the work of Tam and Auriault, Morris and Boluriaan, and Morris and Miller. A statistical model of the two-point cross-correlation of the velocity fluctuations is used to describe the turbulence. The acoustic analogy attempts to take into account the correct scaling of the sources for a wide range of nozzle pressure and temperature ratios. It does not make assumptions regarding fine-or large-scale turbulent noise sources, selfor shear-noise, or convective amplification. The acoustic analogy is partially informed by three-dimensional steady Reynolds-Averaged Navier-Stokes solutions that include the nozzle geometry. The predictions are compared with experiments of jets operating subsonically through supersonically and at unheated and heated temperatures. Predictions generally capture the scaling of both mixing noise and BBSAN for the conditions examined, but some discrepancies remain that are due to the accuracy of the steady RANS turbulence model closure, the equivalent sources, and the use of a simplified vector Green's function solver of the linearized Euler equations.
Nomenclature
AsConstant associated with the dilatation term
IntroductionThis paper presents an acoustic analogy for jet noise that is based on the Euler equations. The model contains equivalent sources for the turbulent mixing noise and the broadband shock-associated noise (BB-SAN). The comprehensive model development is based on two separate acoustic analogies, one for the mixing noise and the other for the BBSAN. The evaluation of the comprehensive analogy or the summation of the spectral density of the two independent analogies results in a prediction for total jet noise. These models are designed for a wide range of Mach numbers and temperature ratios. In the context of this theory there are no assumptions of shear-, self-, large-scale, or fine-scale noise sources or spectra.The acoustic analogy for turbulent mixing noise is inspired by the work of Morris and Farassat, 1 Morris and Boluriaan, 2 Tam and Auriault, 3 and physical measurements. The equivalent sources of the acoustic analogy consist of the dilatation and unsteady forces per unit mass. The dilatation term is consistent with that of Tam and Auriault 3 and the unsteady forces per unit mass are equivalent to those of Morris and Boluriaan.2 These choices of terms allow for the acoustic intensity to scale with increasing jet Mach number and temperature. The acoustic analogy for BBSAN is the model of Morris and Miller. 4 A statistical model of the two-point cross-correlation of the turbulent velocity fluctuations describes the properties of the tur...