Abstract
The constitutive equations used in the Reynolds-averaged Navier–Stokes (RANS) equations are referred to as turbulence models. Although a large number of studies have been performed on the development of turbulence models, there has not been a universal turbulence model that is applicable to all turbulent flows. However, we in general suggest the use of the k-\(\varepsilon \) model for “simple” flows and the Large-Eddy Simulation (LES) for more complex flows (Chap. 8) found in many practical engineering applications. In this book, we refer to “simple flows” as stationary flows that have average streamlines that are relatively straight on the absolute coordinate system with low level of acceleration. Flows that impinge on walls, separate from corners, pass through a curved channel, and is in a rotational field would not be considered simple. In this and the next chapters, discussions on the strengths and limitations of these methods are offered. Since our objective is not to introduce all turbulence models available, we ask readers to refer to [3, 6, 28] for comprehensive reviews on RANS.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
There are also different Boussinesq approximations that appear in the analysis of flows with buoyancy and water waves.
- 2.
- 3.
References
Abe, K., Nagano, Y., Kondoh, T.: An improved \(k\)-\(\epsilon \) model for preduction of turbulent flows with separation and reattachment. Trans. Jpan. Soc. Mech. Eng. B 58(554), 3003–3010 (1992)
Baldwin, B.S., Lomax, H.: Thin layer approximation and algebraic model for separated turbulent flows. AIAA Paper 78–257 (1978)
Cebeci, T.: Analysis of Turbulent Flows with Computer Programs, 3rd edn. Butterworth-Heinemann (2013)
Daiguji, H., Miyake, Y., Yoshizawa, A. (eds.): Computational Fluid Dynamics of Turbulent Flow: Models and Numerical Methods. Univ. Tokyo Press (1998)
Daly, B.J., Harlow, F.H.: Transport equations in turbulence. Phys. Fluids 13(11), 2634–2649 (1970)
Durbin, P.A., Reif, B.A.P.: Statistical Theory and Modeling for Turbulent Flows, 2nd edn. Wiley (2011)
Hanjalić, K., Launder, B.E.: Contribution towards a Reynolds-stress closure for low-Reynolds-number turbulence. J. Fluid Mech. 74(4), 593–610 (1976)
Hinze, J.O.: Turbulence. McGraw-Hill, New York (1975)
Jones, W.P., Launder, B.E.: The prediction of laminarization with a two-equation model of turbulence. Int. J. Heat Mass Trans. 15(2), 301–314 (1972)
Kajishima, T., Miyake, Y.: A discussion on eddy viscosity models on the basis of the large eddy simulation of turbulent flow in a square duct. Comput. Fluids 21(2), 151–161 (1992)
Launder, B.E., Reece, G.J., Rodi, W.: Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 68(3), 537–566 (1975)
Launder, B.E., Spalding, D.B.: The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Engrg. 3(2), 269–289 (1974)
Launder, B.E., Tselepidakis, D.P., Younis, B.A.: A second-moment closure study of rotating channel flow. J. Fluid Mech. 183, 63–75 (1987)
Lumley, J.L., Newman, G.R.: The return to isotropy of homogeneous turbulence. J. Fluid Mech. 82(1), 161–178 (1977)
Mansour, N.N., Kim, J., Moin, P.: Reynolds-stress and dissipation-rate budgets in a turbulent channel flow. J. Fluid Mech. 194, 15–44 (1988)
Menter, F.R.: Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32(8), 1598–1605 (1994)
Miyata, H. (ed.): Analysis of turbulent flows. In: Computational Fluid Dynamics Series, vol. 3. Univ. Tokyo Press (1995)
Myong, H.K., Kasagi, N.: A new approach to the improvement of \(k\)-\(\epsilon \) turbulence model for wall-bounded shear flows. JSME Int. J. 33(1), 63–72 (1990)
Nagano, Y., Tagawa, M., Niimi, M.: An improvement of the \(k\)-\(\epsilon \) turbulence model (the limiting behavior of wall and free turbulence, and the effect of adverse pressure gradient). Trans. Jpn. Soc. Mech. Eng. B 55(512), 1008–1015 (1989)
Patankar, S.: Numerical Heat Transfer and Fluid Flow. Hemisphere, Washington (1980)
Patel, V.C., Rodi, W., Scheuerer, G.: Turbulence models for near-wall and low Reynolds number flows - A review. AIAA J. 23(9), 1308–1319 (1985)
Rotta, J.C.: Statistische theorie nichthomogener turbulenz. Zeitschrift für physik 129(6), 547–572 (1951)
Shima, N.: Prediction of turbulent boundary layers with a second-moment closure. Parts I and II. J. Fluids Eng. 115(1), 56–69 (1993)
So, R.M.C., Lai, Y.G., Hwang, B.C., Yoo, G.J.: Low-Reynolds-number modelling of flows over a backward-facing step. ZAMP 39(1), 13–27 (1988)
Spalart, P.R., Allmaras, S.R.: A one-equation turbulence model for aerodynamic forces. AIAA Paper 92–439 (1992)
Speziale, C.G.: Analytical methods for the development of Reynolds-stress closures in turbulence. Annu. Rev. Fluid Mech. 23, 107–157 (1991)
Suga, K.: Near-wall grid dependency of low-Reynolds-number eddy viscosity turbulence models. Trans. Jpn. Soc. Mech. Eng. B 64(626), 3315–3322 (1998)
Wilcox, D.C.: Turbulence Modeling for CFD, 3rd edn. DCW Industries (2006)
Yamamoto, M.: Time average turbulent flow model. Stress equation model (RSM). Turbomachinery 24(4), 240–247 (1996)
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Kajishima, T., Taira, K. (2017). Reynolds-Averaged Navier–Stokes Equations. In: Computational Fluid Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-319-45304-0_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-45304-0_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-45302-6
Online ISBN: 978-3-319-45304-0
eBook Packages: EngineeringEngineering (R0)