K-epsilon models

From CFD-Wiki

Turbulence modeling

Turbulence

RANS-based turbulence models Linear eddy viscosity models Algebraic models Cebeci-Smith model Baldwin-Lomax model Johnson-King model A roughness-dependent model One equation models Prandtl's one-equation model Baldwin-Barth model Spalart-Allmaras model Two equation models k-epsilon models Standard k-epsilon model Realisable k-epsilon model RNG k-epsilon model Near-wall treatment k-omega models Wilcox's k-omega model Wilcox's modified k-omega model SST k-omega model Near-wall treatment Realisability issues Kato-Launder modification Durbin's realizability constraint Yap correction Realisability and Schwarz' inequality Nonlinear eddy viscosity models Explicit nonlinear constitutive relation Cubic k-epsilon EARSM v2-f models model model Reynolds stress model (RSM)

Large eddy simulation (LES) Smagorinsky-Lilly model Dynamic subgrid-scale model RNG-LES model Wall-adapting local eddy-viscosity (WALE) model Kinetic energy subgrid-scale model Near-wall treatment for LES models

Detached eddy simulation (DES)

Direct numerical simulation (DNS)

Turbulence near-wall modeling

Turbulence free-stream boundary conditions Turbulence intensity Turbulence length scale

Contents 1 Introduction 2 Usual K-epsilon models 3 Miscellaneous 4 References

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, . The second transported variable in this case is the turbulent dissipation, . It is the variable that determines the scale of the turbulence, whereas the first variable, , 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.

Usual K-epsilon models

1. Standard k-epsilon model
2. Realisable k-epsilon model
3. RNG k-epsilon model

Miscellaneous

1. Near-wall treatment for k-epsilon models

References

[1] Bardina, J.E., Huang, P.G., Coakley, T.J. (1997), "Turbulence Modeling Validation, Testing, and Development", NASA Technical Memorandum 110446.

[2] Jones, W. P., and Launder, B. E. (1972), "The Prediction of Laminarization with a Two-Equation Model of Turbulence", International Journal of Heat and Mass Transfer, vol. 15, 1972, pp. 301-314.

[3] Launder, B. E., and Sharma, B. I. (1974), "Application of the Energy Dissipation Model of Turbulence to the Calculation of Flow Near a Spinning Disc", Letters in Heat and Mass Transfer, vol. 1, no. 2, pp. 131-138.

[4] Wilcox, David C (1998). "Turbulence Modeling for CFD". Second edition. Anaheim: DCW Industries, 1998. pp. 174.