Constitutive Relations and Realizability of Single-Point Turbulence Closures

Shih, Tsan‐Hsing

doi:10.1007/978-94-015-8666-5_4

Cited by 20 publications

(7 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A term S m Ω n is then said to be of power m + n and extension 2, etc. Shih & Lumley (1993) (see also Shih 1996) also include a term of power 6 and extension 4. They use a notation with the mean velocity gradient tensor and its transpose, but with the present notation such a term can be written as…”

Section: Appendix a Summary Of The Proposed Modelmentioning

confidence: 99%

An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows

2000

View full text Add to dashboard Cite

Some new developments of explicit algebraic Reynolds stress turbulence models (EARSM) are presented. The new developments include a new near-wall treatment ensuring realizability for the individual stress components, a formulation for compressible flows, and a suggestion for a possible approximation of diffusion terms in the anisotropy transport equation. Recent developments in this area are assessed and collected into a model for both incompressible and compressible three-dimensional wall-bounded turbulent flows. This model represents a solution of the implicit ARSM equations, where the production to dissipation ratio is obtained as a solution to a nonlinear algebraic relation. Three-dimensionality is fully accounted for in the mean flow description of the stress anisotropy. The resulting EARSM has been found to be well suited to integration to the wall and all individual Reynolds stresses can be well predicted by introducing wall damping functions derived from the van Driest damping function. The platform for the model consists of the transport equations for the kinetic energy and an auxiliary quantity. The proposed model can be used with any such platform, and examples are shown for two different choices of the auxiliary quantity.

show abstract

Section: Appendix a Summary Of The Proposed Modelmentioning

confidence: 99%

An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows

2000

View full text Add to dashboard Cite

show abstract

“…This model as mentioned is not extended to scalars effects, it will be coupled respectively to the classic Launder, Reece and Rodi (LRR) model (Launder et al (1975), Cadiou (1996b)), the Craft and Launder (CL) model (Craft el al. (1989), Launder et al (1996) and Launder (1999)) and the Shih and Lumley (SL) model (Shih et al (1989) and Shih (1996)). This coupling will be noted respectively model 1, model 2 and model 3.…”

Section: The Speziale Sarkar and Gatski (Ssg) Modelmentioning

confidence: 99%

A Study of the Asymptotic Equilibrium Behavior in Stratified Turbulence Submitted to Horizontal Shear

2014

JAFM

View full text Add to dashboard Cite

In this work, the asymptotic equilibrium behaviour of dimensionless parameters in stably stratified turbulence submitted to a horizontal shear is studied using two different methods. The first one is an analytic method and is based on linear solutions obtained when non linear effects of pressure and viscosity are neglected. The Laplace Transform is used for integrating differential system. The principal result of this first part of our work is the existence of asymptotic equilibrium states at high shear for all non dimensionless parameters. The second method is a numerical one and is based on a second-order modeling of equations. The Speziale Sarkar and Gatski (SSG) model is retained for pressure-strain correlation and dissipation time evolution equation, whereas, three of the most known second-order models are retained for the scalar field. The principal result of this second part is the big contribution of the SSG models for predicting asymptotic equilibrium states of non dimensional parameters.

show abstract

“…A similar procedure can be followed for the heat flux vector in order to identify a proper normalization. The approach commonly followed was proposed by Shih andLumley (1993, 1996) and has been used in previous algebraic representations of scaled heat flux models by Abe et al (1996) and Wikström et al (2000).…”

Section: Velocity Second-moment and Scalar Flux Transport Equationsmentioning

confidence: 99%

Second-moment and scalar flux representations in engineering and geophysical flows

Gatski¹

2009

Fluid Dyn. Res.

View full text Add to dashboard Cite

Tensor and vector representations of velocity second-moments and the scalar fluxes have long been used in the closure of the transport equations describing the motion of turbulent flows. These representations are the turbulent models or parameterizations that have been the basis for extensive research in the Reynolds-averaged Navier-Stokes approach as well as other formulations resulting in transport equations for averaged flow variables. They have led to the development of improved nonlinear eddy viscosity, algebraic Reynolds stress models and algebraic scalar flux models. Over the last two decades, the process used in developing such closures has been formalized, and this has led to models and parameterizations capable of replicating more complex flow dynamics. The intent here is to provide the reader with a summary description of a procedure that can be followed to rationally construct such explicit representations from the full transport equations for both tensor and vector quantities in general, and the velocity second-moments and the heat fluxes in particular, applicable to both engineering and geophysical flows.

show abstract

Constitutive Relations and Realizability of Single-Point Turbulence Closures

Cited by 20 publications

References 18 publications

An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows

An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows

A Study of the Asymptotic Equilibrium Behavior in Stratified Turbulence Submitted to Horizontal Shear

Second-moment and scalar flux representations in engineering and geophysical flows

Contact Info

Product

Resources

About