# K-epsilon models

(Difference between revisions)
 Revision as of 07:40, 4 October 2006 (view source)← Older edit Latest revision as of 16:03, 18 June 2011 (view source) (→References) (8 intermediate revisions not shown) Line 1: Line 1: + {{Turbulence modeling}} == Introduction == == Introduction == - The K-epsilon model is one of the most common [[Turbulence modeling|turbulence models]]. 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 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]], $k$.  The second transported variable in this case is the turbulent [[dissipation]], $\epsilon$. It is the variable that determines the scale of the turbulence, whereas the first variable, $k$, determines the energy in the turbulence. + + The first transported variable is turbulent kinetic energy, $k$.  The second transported variable in this case is the turbulent dissipation, $\epsilon$. It is the variable that determines the scale of the turbulence, whereas the first variable, $k$, 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 == == Usual K-epsilon models == Line 11: Line 19: == Miscellaneous == == Miscellaneous == # [[Near-wall treatment for k-epsilon models]] # [[Near-wall treatment for k-epsilon models]] + + ==References== +  {{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}} + +  {{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}} + +  {{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}} + +  '''Wilcox, David C (1998)'''. "Turbulence Modeling for CFD". Second edition. Anaheim: DCW Industries, 1998. pp. 174. [[Category:Turbulence models]] [[Category:Turbulence models]] + + {{stub}}

## Latest revision as of 16:03, 18 June 2011

 Turbulence RANS-based turbulence models Linear eddy viscosity models Nonlinear eddy viscosity models Explicit nonlinear constitutive relation v2-f models $\overline{\upsilon^2}-f$ model $\zeta-f$ model Reynolds stress model (RSM) Large eddy simulation (LES) Detached eddy simulation (DES) Direct numerical simulation (DNS) Turbulence near-wall modeling Turbulence free-stream boundary conditions

## Introduction

The K-epsilon model is one of the most common turbulence models, although it just doesn't perform well in cases of large adverse pressure gradients (Reference 4). It is a 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, $k$. The second transported variable in this case is the turbulent dissipation, $\epsilon$. It is the variable that determines the scale of the turbulence, whereas the first variable, $k$, determines the energy in the turbulence.

There are two major formulations of K-epsilon models (see References 2 and 3). That of Launder and Sharma is typically called the "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 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.

## Miscellaneous

1. Near-wall treatment for k-epsilon models