Computation of Jet Noise Using Large-Eddy Simulation and Lighthill’s Analogy

Abstract

Computational aeroacoustics involves numerical study of the acoustic field generated by unsteady fluid motion. An area of significant interest is unsteady turbulent flow in free jets and resultant far field acoustic pressure fluctuations. Since Lighthill’s mathematical formulation for jet noise generation in the early 1960’s, a search has continued for a physical interpretation of his formal results and, in particular, the noise source term. Far field measurements have not provided a clear picture concerning the nature of the acoustic source. Therefore, industry standard procedures for prediction of far field noise from exhaust jets rely on semi-empirical methods to calculate mean sound pressure levels and directivity. Our objective is to contribute to a more thorough understanding of the acoustic source from a shear flow using Large-Eddy Simulation (LES) turbulence modeling. Published work for direct numerical simulation of these flows has been confined to low Reynolds number (< 3000) with Mach numbers up to 2.0, to study the physics of sound generation and test aeroacoustic prediction methods (Mitchell, et al, 1995). While furthering understanding of jet noise generation, these cases limit exhaust dimensions to millimeters and make it difficult to compare results to measured data. Here we address large Reynolds numbers and high subsonic Mach number (compressible) flow combined with realistic geometries more representative of aircraft engine exhausts. Standard turbulence models compute the average flow field, which cannot be used to calculate the aeroacoustic field. Temporal fluctuations are required and can be obtained using LES, with a spatial filtering operation applied to the equations of motion. The technique is based on computing only large scale motions directly subject to the problem’s boundary conditions, while small scale motions are assumed to be more universal and their statistics and effect upon large scales are predicted using a “subgrid-scale” model. The motivation for this approach is that experimental observations of turbulent flows show that large scale turbulent structures vary markedly from one flow situation to another, while small scales show less variation from case to case. The acoustic radiation calculation consists of three steps; 1) an approximate result for the mean flow field using a compressible flow code employing a k-ϵ turbulence model, 2) unsteady turbulent fluid field simulation using the CFD code appended with a LES turbulence model (the k-ϵ prediction serving as an initial guess) and 3) far field acoustics obtained using Lighthill’s analogy. Extensive far field noise data from ground static measurements of a WR19-4 mini-turbofan engine are being drawn from for comparisons between computed results and measurements.