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Generalized rapid-distortion theory on transversely sheared mean flows with physically realizable upstream boundary conditions: application to trailing-edge problem

Published online by Cambridge University Press:  06 July 2017

M. E. Goldstein Open the ORCID record for M. E. Goldstein [Opens in a new window] ,
S. J. Leib  and
M. Z. Afsar
M. E. Goldstein*
Affiliation:
National Aeronautics and Space Administration, Glenn Research Center, Cleveland, OH 44135, USA
S. J. Leib
Affiliation:
Ohio Aerospace Institute, Cleveland, OH 44142, USA
M. Z. Afsar
Affiliation:
Department of Mechanical and Aerospace Engineering, Strathclyde University, 75 Montrose St., Glasgow GI 1XJ, UK
*
†Email address for correspondence: Marvin.E.Goldstein@nasa.gov
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Abstract

This paper is concerned with rapid-distortion theory on transversely sheared mean flows which (among other things) can be used to analyse the unsteady motion resulting from the interaction of a turbulent shear flow with a solid surface. It extends previous analyses of Goldstein et al. (J. Fluid Mech., vol. 736, 2013a, pp. 532–569; NASA/TM-2013-217862, 2013b) which showed that the unsteady motion is completely determined by specifying two arbitrary convected quantities. The present paper uses a pair of previously derived conservation laws to derive upstream boundary conditions that relate these quantities to experimentally measurable flow variables. The result is dependent on the imposition of causality on an intermediate variable that appears in the conservation laws. Goldstein et al. (2013a) related the convected quantities to the physical flow variables at the location of the interaction, but the results were not generic and hard to reconcile with experiment. That problem does not occur in the present formulation, which leads to a much simpler and more natural result than the one given in Goldstein et al. (2013a). We also show that the present formalism yields better predictions of the sound radiation produced by the interaction of a two-dimensional jet with the downstream edge of a flat plate than the Goldstein et al. (2013a) result. The role of causality is also discussed.

JFM classification

Acoustics: Aeroacoustics Mathematical Foundations: Mathematical Foundations Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 824 , 10 August 2017 , pp. 477 - 512
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Copyright
© Cambridge University Press 2017. This is a work of the U.S. Government and is not subject to copyright protection in the United States. 

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