K-epsilon models

{{Turbulence modeling}}
== Introduction ==

The K-epsilon model is one of the most common [[Turbulence modeling|turbulence models]], although it just doesn't perform well in cases of large adverse pressure gradients (Reference 4). It is a [[Two equation models|two equation model]], that means, it includes two extra transport equations to represent the turbulent properties of the flow. This allows a two equation model to account for history effects like convection and diffusion of turbulent energy.

The first transported variable is turbulent kinetic energy, <math>k</math>.  The second transported variable in this case is the turbulent dissipation, <math>\epsilon</math>. It is the variable that determines the scale of the turbulence, whereas the first variable, <math>k</math>, determines the energy in the turbulence.

There are two major formulations of K-epsilon models (see [[#References|References]] 2 and 3).  That of Launder and Sharma is typically called the [[Standard k-epsilon model | "Standard" K-epsilon Model]].  The original impetus for the K-epsilon model was to improve the mixing-length model, as well as to find an alternative to algebraically prescribing turbulent length scales in moderate to high complexity flows.

As described in [[#References|Reference]] 1, the K-epsilon model has been shown to be useful for free-shear layer flows with relatively small pressure gradients.  Similarly, for wall-bounded and internal flows, the model gives good results only in cases where mean pressure gradients are small; accuracy has been shown experimentally to be reduced for flows containing large adverse pressure gradients.  One might infer then, that the K-epsilon model would be an inappropriate choice for problems such as inlets and compressors. 

To calculate boundary conditions for these models see [[Turbulence free-stream boundary conditions|turbulence free-stream boundary conditions]].

== Usual K-epsilon models ==
# [[Standard k-epsilon model]]
# [[Realisable k-epsilon model]]
# [[RNG k-epsilon model]]

== Miscellaneous ==
# [[Near-wall treatment for k-epsilon models]]

==References==
[1] {{reference-paper|author=Bardina, J.E., Huang, P.G., Coakley, T.J.|year=1997|title=Turbulence Modeling Validation, Testing, and Development|rest=NASA Technical Memorandum 110446}}

[2] {{reference-paper|author=Jones, W. P., and Launder, B. E.|year=1972|title=The Prediction of Laminarization with a Two-Equation Model of 
Turbulence|rest= International Journal of Heat and Mass Transfer, vol. 15, 1972, pp. 301-314}}

[3] {{reference-paper|author=Launder, B. E., and Sharma, B. I.|year=1974|title=Application of the Energy Dissipation Model of Turbulence to 
the Calculation of Flow Near a Spinning Disc|rest=Letters in Heat and Mass Transfer, vol. 1, no. 2, pp. 131-138}} 
 


[[Category:Turbulence models]]

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