Application of Non-homogeneous Rapid-distortion theory to the trailing edge noise problem by Dr Mohammed Afsar
Date: Wed 10 Feb 2016, 14:00 - 15:00
Location: Room 2.20, Geography Building, Mile End
Goldstein, Afsar & Leib (J. Fluid Mech., vol. 736, pp. 532-?569, 2013) showed that the hydrodynamic component of the small amplitude unsteady motion on a transversely sheared flow is determined by two arbitrary convected quantities in the absence of solid surfaces and hydrodynamic instabilities. Since these quantites are arbitrary functions of their arguments, they can be used to specify appropriate upstream boundary conditions for unsteady surface interaction problems. In this talk we address the trailing edge noise problem by developing a first-principles model based on this theory.
To fix ideas, we consider a trailing edge of an infinitesimally thin flat plate lying parallel to the level curves of a two-dimensional mean flow. The arbitrary convected quantity remaining in the analysis is then related to the upstream turbulence correlation function by inverting the appropriate Fourier transform. Our latest results indicate that physically realizable upstream turbulence that possesses a finite de-correlation region (i.e. negative) in its space-time structure actually increases the low-frequency algebraic decay of the acoustic spectrum with angular frequency. The algebraic decay is known as the low frequency ‘roll-off’ and we show by accurately predicting it, our results are in much closer agreement with noise data for Strouhal numbers less than the peak noise.
Finally, we compare our numerical predictions of the sound field with experimental data (Bridges, AIAA Paper 2014-?0876) using three-dimensional Reynolds-Averaged Navier- Stokes (RANS) solutions to determine the mean flow, turbulent kinetic energy and turbulence length & time scales for a range of subsonic acoustic Mach number jets, nozzle aspect ratios & streamwise and transverse trailing-edge locations. Here, our results show that the RDT-based model, coupled with a RANS meanflow, is able to predict the low-frequency amplification due to the jet-surface interaction reasonably well for a variety of nozzle operating conditions.
Key words: Rapid-distortion theory (RDT); realizable turbulence; trailing-edge noise.
Short Bio: M.Z. Afsar holds a First Class Honors degree in Aeronautical Engineering from the University of Bristol and a Ph. D. in Engineering from the University of Cambridge. He has worked with colleagues at NASA Glenn Research Center under various Post-doctoral Fellowships during 2008 - 2013. In July 2013, he took up the Chapman Fellowship & Laminar Flow Control Research Associateship at the Department of Mathematics at Imperial College London where, currently, he is a visiting Post-doc.