Analysis and extension of the quadratic constitutive relation for RANS methods

The quadratic constitutive relation was proposed as an extension of minimal complexity to linear eddy-viscosity models in order to improve mean flow predictions by better estimating turbulent stress distributions. However, the successes of this modification have been relatively modest and are limite...

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Bibliographic Details
Published inAeronautical journal Vol. 125; no. 1292; pp. 1746 - 1767
Main Authors Sabnis, K., Babinsky, H., Spalart, P.R., Galbraith, D.S., Benek, J.A.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.10.2021
Subjects
Boundary layers
Channel flow
Constitutive relationships
Corner flow
Energy
Fluid flow
Friction
Investigations
Pipe flow
Reynolds number
Simulation
Turbulence models
Turbulent flow
Velocity
Viscosity
Vortices
Vorticity equations
eddy-viscosity model
square duct
corner flow
turbulent stress distribution
quadratic constitutive relation
corner vortices
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Summary:The quadratic constitutive relation was proposed as an extension of minimal complexity to linear eddy-viscosity models in order to improve mean flow predictions by better estimating turbulent stress distributions. However, the successes of this modification have been relatively modest and are limited to improved calculations of flow along streamwise corners, which are influenced by weak secondary vortices. This paper revisits the quadratic constitutive relation in an attempt to explain its capabilities and deficiencies. The success in streamwise corner flows cannot be entirely explained by significant improvements in turbulent stress estimates in general, but is instead due to better prediction of the particular turbulent stress combinations which appear in the mean streamwise vorticity equation. As a consequence of this investigation, a new formulation of turbulent stress modification is proposed, which appears to better predict the turbulent stress distributions for a variety of flows: channel flow, equilibrium boundary layers, pipe flow, separated boundary layers and square duct flow.
ISSN:0001-9240
2059-6464
DOI:10.1017/aer.2021.42