Numerical simulation of aerosound from airfoils and exhaust jets using Lighthill theory with k -ε turbulence model and large eddy simulation

Far-field noise from turbulence near an NACA 0012 airfoil and potential core of a high-speed (subsonic) jet engine exhaust have been computed using the ANSWER computational fluid dynamics code of Runchal and Caretto [Intl. J. Num. Methods Eng. 24 (1990)] and Lighthill’s acoustic analogy. The k-ε turbulence model which is part of ANSWER is used to compute Reynolds stress from two ‘‘side’’ equations in addition to continuity, Navier–Stokes, and for high-speed flow, the energy equation. Three-dimensional turbulence intensities are obtained from the stress. Fluctuations are needed to calculate aerosound, while k-ε only produces averages. Thus the time derivative form of Lighthill’s analogy is used to calculate the sound. Time derivatives must be estimated; the characteristic time L/u′, as calculated by k-ε, is used. ANSWER modified to perform Large Eddy Simulation is used for the free jet, employing a hybrid subgrid scale model previously developed for application to a low-speed jet by Lee [UCLA dissertation (1992)] which combines the conventional Smagorinsky formulation with a deductive model formed by taking a Taylor series expansion of the flow field and using the first terms to give the fluctuations. Preliminary results are compared with jet noise measurements.