Abstract
This chapter addresses some of the challenges that arise when solving turbulent flow problems. It is not intended to provide a comprehensive account on turbulence modeling, rather, the intention is simply to introduce the subject and focus on the implementation details of some of the most popular turbulence models. The presentation is limited to incompressible turbulent fluid flow and begins with a general introduction to turbulence modeling. Then the Reynolds stress tensor that originates from the adopted averaging procedure and the Boussinesq hypothesis used in modeling the Reynolds stresses are presented. This is followed by a review of the k − ε and k − ω two-equation models. These are the most popular of the high Reynolds number and low Reynolds number turbulence models, respectively. The BSL and SST models are then introduced, both are derived by combining the k − ε and k − ω models so as to address their respective weaknesses. Finally the treatment of the near wall region is presented in detail.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Tennekes H, Lumley JL (1972) A first course in turbulence. MIT Press, Cambridge. ISBN 978-0-262-20019-6
Kolmogorov AN (1941) The local structure of turbulence in incompressible viscous fluids at very large Reynolds numbers. Doklady AN SSSR 30:299–303
Kolmogorov AN (1941) Dissipation of energy in isotropic turbulence. Dokl Akad Nauk SSSR 32:19–21.é
Moser RD, Kim J, Mansour NN (1999) Direct numerical simulation of turbulent channel flow up to Re τ = 590. Phys Fluids 11(4):943–945
Scardovelli R, Zaleski S (1999) Direct numerical simulation of free-surface and interfacial flow. Ann Rev Fluid Mech. 31:567–603
Le H, Moin P, Kim J (1997) Direct numerical simulation of turbulent flow over a backward-facing step. J Fluid Mech 330:349–374
Choi H, Moin P, Kim J (1993) Direct numerical simulation of turbulent flow over Riblets. J Fluid Mech 255:503–539
Leonard A (1974) Energy cascade in large-eddy simulations of turbulent fluid flows. Adv Geophys A 18:237–248
Sagaut P (2006) Large eddy simulation for incompressible flows-an introduction. Springer, Berlin
Ferziger JH (1995) Large eddy simulation. In: Hussaini MY, Gatski T (eds) Simulation and modeling of turbulent flows. Cambridge University Press, New York
Nieuwstadt FTM, Mason PJ, Moeng C-H, Schuman U (1991) Large eddy simulation of the convective boundary layer: a comparison of four computer codes. In: Durst F et al (eds) Turbulent shear flows, 8th edn. Springer, Berlin
Reynolds O (1895) On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Philos Trans Royal Soc London A 186:123–164
Favre A (1965) Equations des Gas Turbulents Compressibles. Journal de Mecanique 4(3):361–390
Boussinesq J (1877) Essai sur la théorie des eaux courantes. Mémoires présentés par divers savants à l’Académie des Sciences 23(1):1–680
Schlichting H (1968) Boundary-layer theory, 6th edn. Chapter XIX. McGraw Hill
Schmitt FG (2007) About Boussinesq’s turbulent viscosity hypothesis: historical remarks and a direct evaluation of its validity. Comptes Rendus Mécanique 335(9 and 10):617–627
Prandtl L (1925) Uber die ausgebildete Turbulenz. ZAMM 5:136–139
Baldwin BS, Lomax H (1978) Thin-Layer approximation and algebraic model for separated turbulent flows. AIAA Paper, Huntsville, pp 78–257
Cebeci T, Smith AMO (1974) Analysis of turbulent boundary layers. Ser Appl Math Mech, vol XV, Academic Press, Waltham
Baldwin BS, Barth TJ (1990) A one-equation turbulence transport model for high reynolds number wall-bounded flows. NASA TM-102847
Goldberg UC (1991) Derivation and testing of a one-equation model based on two time scales. AIAA J 29(8):1337–1340
Spalart PR, Allmaras SR (1992) A one-equation turbulence model for aerodynamic flows. AIAA Paper, Reno, pp 92–439
Jones WP, Launder BE (1972) The prediction of laminarization with a two-equation model of turbulence. Int J Heat Mass Transf 15:301–314
Launder BE, Sharma BI (1974) Application of the energy dissipation model of turbulence to the calculation of flow near a spinning disk. Lett Heat Mass Transfer 1(2):131–138
Chien K-Y (1982) Predictions of channel and boundary-layer flows with a low-reynolds-number turbulence model. AIAA J 20(1):33–38
Myong HK, Kasagi N (1990) A new approach to the improvement of k-ε turbulence model for wall-bounded shear flows. JSME Int J 33:63–72
Kolmogorov AN (1942) Equations of turbulent motion of an incompressible fluid. Izvestia Acad Sci USSR Phys 6(1 and 2):56–58
Wilcox D (1988) Reassessment of the scale-determining equation for advanced turbulence models. AIAA J 26(11):1299–1310
Wilcox DC (1998) Turbulence modeling for CFD, 2nd edn. DCW Industries, US
Menter FR (1992) Influence of freestream values on k − ω turbulence model predictions. AIAA J 30(6):1657–1659
Menter FR (1993) Zonal two-equation k − ω turbulence model for aerodynamic flows. AIAA Paper, Orlando, pp 1993–2906
Menter F (1994) Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J 32(8):1598–1605
Menter FR, Kuntz M, Langtry R (2003) Ten years of industrial experience with the SST turbulence model, 4th edn. Turbulence, Heat and Mass Transfer, Antalya, pp 73–86
Menter FR, Carregal Ferreira J, Esch T, Konno B (2003) The SST turbulence model with improved wall treatment for heat transfer predictions in gas turbines. In: Proceedings of the international gas turbine congress, Tokyo, IGTC2003-TS-059
Menter FR (2009) Review of the shear-stress transport turbulence model experience from an industrial perspective. Int J Comput Fluid Dyn 23(4):305–316
Daky BJ, Harlow FH (1970) Transport equations in turbulence. Phys Fluids 13:2634–2649
Fu S, Launder BE, Tselepidakis DP (1987) Accommodating the effects of high strain rates in modelling the pressure-strain correlation. Report no. TFD/87/5, Mechanical Engineering Department, Manchester Institute of Science and Technology, England
Gibson MM, Launder BE (1986) Ground effects on pressure fluctuations in the atmospheric boundary layer. J Fluid Mech 86(Pt. 3):491–511
Gibson MM, Younis BA (1986) Calculation of swirling jets with a reynolds stress closure. Phys Fluids 29:38–48
Wilcox DC, Rubesin MW (1980) Progress in turbulence modeling for complex flow fields including effects of compressibility. NASA TP-1517
Wilcox DC (1988) Multiscale model for turbulent flows. AIAA J 26(11):1311–1320
Patel VC, Rodi W, Scheuerer G (1985) Turbulence models for near-wall and low reynolds number flows: a review. AIAA J 23(9):1308–1319
Medic G, Durbin PA (2002) Toward improved prediction of heat transfer on turbine blades. ASME J Turbomach 124(2):187–192
Sahay A, Sreenivasan KR (1999) The wall-normal position in pipe and channel flows at which viscous and turbulent shear stresses are equal. Phys Fluids 11(10):3186–3188
Bredberg J (2000) On the wall boundary condition for turbulence models. Department of Thermo and Fluid Dynamics, Chalmers University of Technology, Internal report 00/4, Goteborg
Launder BE, Spalding DB (1974) The numerical computation of turbulent flows. Comput Methods Appl Mech Eng 3:269–289
Grotjans H, Menter F(1998) Wall function for general application cfd codes. In: Computational fluid dynamics 1998, Proceedings fourth European CFD Conference ECCOMAS, Wiley, Chichester
Menter F, Esch T (2001) Elements of industrial heat transfer prediction. In: Proceedings 16th Brazilian congress of mechanical engineering (COBEM), pp 117–127
Kader BA (1981) Temperature and concentration profiles in fully turbulent boundary layers. Int J Heat Mass Transf 24:1541–1544
Tucker PG (2003) Differential equation-based wall distance computation for DES and RANS. J Comput Phys 190:229–248
Sethian JA (1999) Fast marching methods. SIAM Rev 41(2):199–235
Tucker PG, Rumsey CL, Spalart PR, Bartels RE, Biedron RT (2004) Computations of wall distances based on differential equations. AIAA Paper 2004–2232
Xu J-L, Yan C, Fan J-J (2011) Computations of wall distances by solving a transport equation. Appl Math Mech 32(2):141–150
OpenFOAM (2015) Version 2.3.x. http://www.openfoam.org
Hellsten A (1998) Some improvements in menter’s k-omega-SST turbulence model. In: 29th AIAA fluid dynamics conference, AIAA-98-2554
OpenFOAM Doxygen (2015) Version 2.3.x. http://www.openfoam.org/docs/cpp/
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Moukalled, F., Mangani, L., Darwish, M. (2016). Turbulence Modeling. In: The Finite Volume Method in Computational Fluid Dynamics. Fluid Mechanics and Its Applications, vol 113. Springer, Cham. https://doi.org/10.1007/978-3-319-16874-6_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-16874-6_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-16873-9
Online ISBN: 978-3-319-16874-6
eBook Packages: EngineeringEngineering (R0)