k–ε and Other Two Equations Models

  • Anupam DewanEmail author


This chapter presents features of the standard k–ε model and some other two equation models. We first start with the steps for the derivations of the exact transport equations for k and ε and subsequently proceed to propose the modeled forms of these transport equations. We also suggest ways to handle walls and some other flow complexities using the k–ε model. We close this chapter by presenting the major potentials of the two equation models. We also present some examples where the k–ε model fails to accurately predict the flow behavior and needs to be modified.


Transport Equation Turbulence Kinetic Energy Eddy Viscosity Wall Function Viscous Sublayer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Cebeci T, Smith AMO (1974) Analysis of turbulent boundary layers. In: Series of Applied Mathematics and Mechanics, vol XV. Academic Press, LondonGoogle Scholar
  2. Chien KY (1982) Predictions of channel and boundary layer flows with a low-Reynolds number turbulence model. AIAA J 20:33–38zbMATHCrossRefGoogle Scholar
  3. Cho JR, Chung MK (1992) A k–ε–γ equation turbulence model. J Fluid Mech 237:301–322zbMATHCrossRefGoogle Scholar
  4. Chow WK, Li J (2007) Numerical simulations on thermal plumes with k–ε types of turbulence models. Build Environ 42:2819–2828CrossRefGoogle Scholar
  5. Craft TJ, Launder BE, Suga K (1996) Development and application of a cubic eddy viscosity model of turbulence. Int J Heat Fluid Flow 17(2):108–115CrossRefGoogle Scholar
  6. Dewan A, Arakeri JH (1996) Comparison of four turbulence models for wall-bounded flows affected by transverse curvature. AIAA J 34:842–844CrossRefGoogle Scholar
  7. Dewan A, Arakeri JH (2000) Use of k–ε–γ model to predict intermittency in turbulent boundary-layers. ASME J Fluids Eng 122(3):542–546CrossRefGoogle Scholar
  8. Dewan A, Arakeri JH, Srinivasan J (1996) A new turbulence model for the axisymmetric plume. Appl Math Model 21:709–719CrossRefGoogle Scholar
  9. Durbin PA (1991) Near wall turbulence closure modeling without damping functions. Theor Comput Fluid Dyn 3(1):1–13MathSciNetzbMATHGoogle Scholar
  10. Durbin PA, Petterson RBA (2001) Statistical theory and modeling for turbulent flows. Wiley, New YorkzbMATHGoogle Scholar
  11. Durbin PA, Reif BAP (2001) Statistical theory and modelling for turbulent flows. Wiley, USAGoogle Scholar
  12. Fernández JA, Elicer-Cortés JC, Valencia A, Pavageau M, Gupta S (2007) Application of linear and non-linear low-Re k–ε models in two-dimensional predictions of convective heat transfer in passages with sudden contractions. Int J Heat Fluid Flow 28:429–440CrossRefGoogle Scholar
  13. Jones WP, Launder BE (1972) The prediction of laminarization with a two equation model of turbulence. Int J Heat Mass Transf 15:301–314Google Scholar
  14. Karcz M, Badur J (2005) An alternative two-equation turbulent heat diffusivity closure. Int J Heat Mass Transf 48:2013–2022zbMATHCrossRefGoogle Scholar
  15. Kazerooni RB, Hannani SK (2009) Simulation of turbulent flow through porous media employing a v2f model. Sci Iran Trans B Mech Eng 16(2):159–167zbMATHGoogle Scholar
  16. Kolmogorov AN (1942) Equations of turbulent motion of an incompressible fluid. Izvestia Acad Sci USSR 6 (1&2):56–58Google Scholar
  17. 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 Transf 1(1):131–138CrossRefGoogle Scholar
  18. Launder BE, Spalding DB (1974) The numerical computation of turbulent flow. Comput Methods Appl Mech Eng 3:269–289zbMATHCrossRefGoogle Scholar
  19. Luo J, Rajinsky EH (2007) Conjugate heat transfer analysis of a cooled turbine vane using the v2f turbulence model. ASME J Turbomach 129:773–781CrossRefGoogle Scholar
  20. Menter FR (1994) Two equation eddy viscosity turbulence models for engineering applications. AIAA J 32(8):1598–1605CrossRefGoogle Scholar
  21. Michelassi V, Rodi W, Zhu J (1993) Testing a low Reynolds number k–ε turbulence model based on direct simulation data. AIAA J 31(9):1720–1723CrossRefGoogle Scholar
  22. Myong HK, Kasagi N (1990) A new approach to the improvement of k–e turbulence model for wall-bounded shear flows. JSME Int J Ser II 33(1):63–72Google Scholar
  23. Nagano Y, Tagawa M (1990) An improved k–e model for boundary layer flows. Trans ASME J Fluids Eng 112:33–39CrossRefGoogle Scholar
  24. Patel VC, Rodi W, Scheuerer G (1985) Turbulence models for near wall and low Reynolds number flows: a review. AIAA J 23(9):1308–1318MathSciNetCrossRefGoogle Scholar
  25. Pathak M, Dewan A, Dass AK (2007) Effect of streamline curvature on flow field of a turbulent plane jet in crossflow. Mech Res Commun 34(3):241–248zbMATHCrossRefGoogle Scholar
  26. Rodi W, Mansour NN, Michelassi W (1993) One equation near wall turbulence modeling with the aid of direct simulation data. Trans ASME J Fluids Eng 115(2):196–205CrossRefGoogle Scholar
  27. Rotta JC (1951) Statistiche Theorie nichthomogener Turbulenz. Z Phys 129:547–572MathSciNetzbMATHCrossRefGoogle Scholar
  28. Saffman PG (1970) A model for inhomogoneous turbulent flow. Proc R Soc Lond A317:417–433Google Scholar
  29. Sana A, Ghumman AR, Tanaka H (2007) Modification of the damping function in the k–ε model to analyse oscillatory boundary-layers. Ocean Eng 34:320–326CrossRefGoogle Scholar
  30. Shih T-H, Liou WW, Shabbir A, Zhu J (1995) A new k-ε eddy-viscosity model for high Reynolds number turbulent flows—model development and validation. Comput Fluids 24(3):227–238zbMATHCrossRefGoogle Scholar
  31. Wilcox DC (1988) Reassessment of the scale determining equation for advanced turbulence models. AIAA J 19(2):248–251CrossRefGoogle Scholar
  32. Wilcox DC (2006) Turbulence modeling for CFD, 3rd edn. DCW Industries, CaliforniaGoogle Scholar
  33. Wolfstein M (1969) The velocity and temperature distribution of one-dimensional flow with turbulence augmentation and pressure gradient. Int J Heat Mass Transf 12:301–318CrossRefGoogle Scholar
  34. Yakhot V, Orszag SA (1986) Renormalization group analysis of turbulence: I basic theory. J Sci Comput 1(1):1–51MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of Applied MechanicsIndian Institute of Technology, DelhiHauz KhasIndia

Personalised recommendations