Effect of de-correlating turbulence on the low frequency decay of jet-surface interaction noise in sub-sonic unheated air jets using a CFD-based approach

In this paper we extend the Rapid-distortion theory (RDT)-based model derived by Goldstein, Afsar & Leib (J. Fluid Mech., vol. 736, pp. 532-569, 2013) for the sound generated by the interaction of a large-aspect-ratio rectangular jet with the trailing edge of a flat plate to include a more realistic upstream turbulence spectrum that possess a de-correlation (i.e. negative dip) in its space-time structure and use results from three-dimensional Reynolds-Averaged Navier-Stokes (RANS) solutions to determine the mean flow, turbulent kinetic energy and turbulence length & time scales. Since the interaction noise dominates the low-frequency portion of the spectrum, we use an appropriate asymptotic approximation for the Rayleigh equation Green’s function, which enters the analysis, based on a two-dimensional mean flow representation for the jet. We use the model to predict jet-surface interaction noise for a range of subsonic acoustic Mach number jets, nozzle aspect ratios, streamwise and transverse trailing-edge locations and compare them with experimental data. The RANS meanflow computations are also compared with flow data for selected cases to assess their validity. We find that finite de-correlation in the turbulence spectrum increases the low-frequency algebraic decay (the low-frequency “roll-off”) of the acoustic spectrum with angular frequency to give a model that has a pure dipole frequency scaling. This gives better agreement with noise data compared to Goldstein et al. (2013) for Strouhal numbers less than the peak jet-surface interaction noise. For example, through sensitivity analysis we find that there is a difference of 10 dB at the lowest frequency for which data exists (relative to a model without de-correlation effects included) for the highest acoustic Mach number case. Secondly, our results for the planar flow theory provide a first estimate of the low-frequency amplification due to the jet-surface interaction for moderate aspect ratio nozzles when RANS meanflow quantities are used appropriately. This work will hopefully add to noise prediction efforts for aircraft configurations in which the exhaust systems are tightly integrated with the airframe.