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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.

Contact:Dr Sergey Karabasov…