# A New Hypothesis on the Anisotropic Reynolds Stress Tensor for Turbulent FlowsThe k-ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document} Shear-Stress Transport (SST) Turbulence Model

A New Hypothesis on the Anisotropic Reynolds Stress Tensor for Turbulent Flows: The... [This chapter focuses on the mathematical formulations of the turbulent kinetic energy k and specific dissipation rate ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document} Shear-Stress Transport (SST) turbulence model proposed by Menter [3, 4] to provide a closure model to the Boussinesq-type counterparts of the new hypothesis on the anisotropic Reynolds stress tensor discussed in Chap. 5. The k-ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document} SST closure model of Menter [3, 4] is relying on the generalised Boussinesq hypothesis on the Reynolds stress tensor (1.113) with a modification to the definition of the scalar eddy viscosity coefficient. In other words, the k-ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document} SST turbulence model assumes that the Reynolds stress tensor (1.54) is related to the mean rate-of-strain (deformation) tensor (1.114) and the turbulent kinetic energy k defined by Eq. (1.63). The reason for the choice of the k-ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document} SST model as a baseline closure model is that it is a well-known fact that the k-ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document} SST formulation of Menter [3, 4] is validated against many industrially relevant turbulent flow problems with great success . It is also assumed that the k-ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document} SST turbulence model can capture the shear stress distribution correctly in the boundary layer and it is applicable to adverse pressure gradient flows . However, it is important to highlight from theoretical and practical aspects that any other existing eddy viscosity closure model can be employed in conjunction with the Boussinesq-type counterparts of the new hypothesis on the anisotropic Reynolds stress tensor proposed in Chap. 5.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# A New Hypothesis on the Anisotropic Reynolds Stress Tensor for Turbulent FlowsThe k-ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document} Shear-Stress Transport (SST) Turbulence Model

Part of the Fluid Mechanics and Its Applications Book Series (volume 120)
Springer Journals — Feb 27, 2019
9 pages      /lp/springer-journals/a-new-hypothesis-on-the-anisotropic-reynolds-stress-tensor-for-P0sVAq0bZB
Publisher
Springer International Publishing
© Springer Nature Switzerland AG 2019
ISBN
978-3-030-13542-3
Pages
57 –66
DOI
10.1007/978-3-030-13543-0_3
Publisher site
See Chapter on Publisher Site

### Abstract

[This chapter focuses on the mathematical formulations of the turbulent kinetic energy k and specific dissipation rate ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document} Shear-Stress Transport (SST) turbulence model proposed by Menter [3, 4] to provide a closure model to the Boussinesq-type counterparts of the new hypothesis on the anisotropic Reynolds stress tensor discussed in Chap. 5. The k-ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document} SST closure model of Menter [3, 4] is relying on the generalised Boussinesq hypothesis on the Reynolds stress tensor (1.113) with a modification to the definition of the scalar eddy viscosity coefficient. In other words, the k-ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document} SST turbulence model assumes that the Reynolds stress tensor (1.54) is related to the mean rate-of-strain (deformation) tensor (1.114) and the turbulent kinetic energy k defined by Eq. (1.63). The reason for the choice of the k-ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document} SST model as a baseline closure model is that it is a well-known fact that the k-ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document} SST formulation of Menter [3, 4] is validated against many industrially relevant turbulent flow problems with great success . It is also assumed that the k-ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document} SST turbulence model can capture the shear stress distribution correctly in the boundary layer and it is applicable to adverse pressure gradient flows . However, it is important to highlight from theoretical and practical aspects that any other existing eddy viscosity closure model can be employed in conjunction with the Boussinesq-type counterparts of the new hypothesis on the anisotropic Reynolds stress tensor proposed in Chap. 5.]

Published: Feb 27, 2019

Keywords: Two-equation engineering turbulence models; k - ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document} Shear-Stress Transport (SST) closure model; Mathematical derivations; Turbulent kinetic energy transport equation; Specific dissipation rate equation