Prediction of Noise from High Speed Subsonic Jets Using an Acoustic Analogy

A prediction of the noise radiated by a jet flow, based on a steady Reynolds Averaged Navier-Stokes simulation of the jet flow field, requires the solution to two problems. The first is the modeling of the source statistics, using the output of a two-equation turbulence model to define the amplitude, length and time scales of the sources. The second is the calculation of the propagation of the generated noise to the far field observer. This paper focuses on the second of these problems, though noise prediction formulas are developed and radiated noise predictions are made. First, the mean flow is estimated using a k-epsilon or k-omega turbulence model. Then Lilley’s equation in adjoint form is solved numerically. The problem formulation and the numerical solution are described. In addition, high and low frequency asymptotic solutions to Lilleys equation are described, and these solutions are compared with the numerical solutions. The acoustic analogy used for the noise predictions is based on the linearized Euler equations, so the Greens function to Lilleys equation must be transformed to obtain the Greens functions to the linearized Euler equations. This transformation is performed numerically for the adjoint solutions and analytically for the asymptotic solutions. It is shown that, although the high frequency solutions agree well with the numerical solutions, the transformed low frequency asymptotic solutions are not in such good agreement with the numerical solutions. Finally, noise predictions are made for the radiated noise at dierent observer angles to the jet axis. Though the agreement is found to be good at large angles to the jet downstream axis, the agreement is less satisfactory in the peak noise direction, particularly at low frequencies. This suggests that an additional noise source mechanism is responsible for radiation in the peak noise direction. he prediction of noise radiated by a jet using a steady Reynolds Averaged Navier-Stokes (RANS) solution is an attractive alternative to a large scale computation of the instantaneous flow field. It is certainly computationally less expensive, though the RANS solution itself can take appreciable time, particularly for three-dimensional jets. In this paper a methodology is described that uses a hybrid approach. First the average jet flow field is predicted using a two-equation turbulence model. Then an acoustic analogy is used to relate properties of the mean flow to the radiated noise. This involves two steps. First, the statistical properties of the turbulence are modeled. Secondly, the propagation of sound through the jet mean flow is determined. In this paper, the statistical properties of the noise sources are represented by their cross spectral density rather than their two-point cross correlation. The sound propagation is calculated by a solution of Lilley’s equation based on a locally parallel mean flow approximation. Both numerical and analytic solutions are obtained. Finally comparisons are made with experimental measurements of jet noise. The original acoustic analogy was developed by Lighthill. 1 Though he did not refer to his method as an acoustic analogy he did describe his method as an “analogy approach to the problem of aerodynamic sound production.” By basing his acoustic analogy on an inhomogeneous wave equation Lighthill chose explicitly to include all convection and propagation eects in the “equivalent forcing terms” as otherwise “it would be necessary to consider the modifications” to the sound “due to its convection with the turbulent flow