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

M. E. Goldstein, S. J. Leib, M. Z. Afsar

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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 analyze the unsteady motion resulting from the interaction of a turbulent shear flow with a solid surface. It extends previous analyses of Goldstein, Afsar & Leib (2013 a, b) 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.
LanguageEnglish
Pages477-512
Number of pages26
JournalJournal of Fluid Mechanics
Volume824
Early online date1 Jul 2017
DOIs
Publication statusPublished - 30 Aug 2017

Fingerprint

trailing edges
upstream
Conservation
Boundary conditions
boundary conditions
conservation laws
Shear flow
two dimensional jets
Acoustic waves
interactions
flat plates
Radiation
shear flow
solid surfaces
formalism
formulations
acoustics
Experiments
radiation
predictions

Keywords

  • rapid distortion theory
  • turbulence
  • aero-acoustics

Cite this

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title = "Generalized rapid-distortion theory on transversely sheared mean flows with physically realizable upstream boundary conditions: application to trailing edge problem",
abstract = "This paper is concerned with rapid distortion theory on transversely sheared mean flows which (among other things) can be used to analyze the unsteady motion resulting from the interaction of a turbulent shear flow with a solid surface. It extends previous analyses of Goldstein, Afsar & Leib (2013 a, b) 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.",
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AU - Leib, S. J.

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N2 - This paper is concerned with rapid distortion theory on transversely sheared mean flows which (among other things) can be used to analyze the unsteady motion resulting from the interaction of a turbulent shear flow with a solid surface. It extends previous analyses of Goldstein, Afsar & Leib (2013 a, b) 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.

AB - This paper is concerned with rapid distortion theory on transversely sheared mean flows which (among other things) can be used to analyze the unsteady motion resulting from the interaction of a turbulent shear flow with a solid surface. It extends previous analyses of Goldstein, Afsar & Leib (2013 a, b) 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.

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