# Two equation turbulence models

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 Revision as of 20:37, 9 May 2006 (view source)Jola (Talk | contribs)m (small improvements)← Older edit Revision as of 20:50, 9 May 2006 (view source)Jola (Talk | contribs) Newer edit → Line 1: Line 1: Two-equation turbulence models are one of the most common type of turbulence models. Models like the [[K-epsilon models|k-epsilon model]] and the [[K-omega models|k-omega model]] have become industry standard models and are commonly used for most type of engineering problems. Two-equation turbulence models are also very much still an active area of research and new refined two-equation models are still being developed. Two-equation turbulence models are one of the most common type of turbulence models. Models like the [[K-epsilon models|k-epsilon model]] and the [[K-omega models|k-omega model]] have become industry standard models and are commonly used for most type of engineering problems. Two-equation turbulence models are also very much still an active area of research and new refined two-equation models are still being developed. - By definition, two-equation models have two extra transport equations to represent the turbulent properties of the flow. Most often one of the transported variables is the [[Turbulent energy|turbulent energy]], $k$. The second transported variable can vary depending on what type of two-equation model it is. Common choices are the turbulent [[Dissipation|dissipation]], $\epsilon$ or the [[Specific dissipation|specific dissipation]], $\omega$. The second variable can be thought of as the variable that determines the scale of the turbulence (length-scale or time-scale), whereas the first variable, $k$, determines the energy in the turbulence. + By definition, two-equation models include two extra transport equations to represent the turbulent properties of the flow. Most often one of the transported variables is the [[Turbulent kinetic energy|turbulent kinetic energy]], $k$. The second transported variable varies depending on what type of two-equation model it is. Common choices are the turbulent [[Dissipation|dissipation]], $\epsilon$, or the [[Specific dissipation|specific dissipation]], $\omega$. The second variable can be thought of as the variable that determines the scale of the turbulence (length-scale or time-scale), whereas the first variable, $k$, determines the energy in the turbulence. - The basis for all two-equation models is the [[Boussinesq eddy viscosity assumption]], which postulates that the [[Reynolds stress tensor]] is proportional to the mean strain rate tensor: + The basis for all two-equation models is the [[Boussinesq eddy viscosity assumption]], which postulates that the [[Reynolds stress tensor]], $\tau_{ij}$, is proportional to the mean strain rate tensor, $S_{ij}$, and can be written in the following way: :$\tau_{ij} = 2 \, \mu_t \, S_{ij}$ :$\tau_{ij} = 2 \, \mu_t \, S_{ij}$ - Or the same equation written more explicitly: + Where $\mu_t$ is a scalar property called the [[Eddy viscosity|eddy viscosity]]. The same equation can be written more explicitly as: :$-\overline{\rho u'_i u'_j} = \mu_t \, \left( \frac{\partial U_i}{\partial x_j} + \frac{\partial U_j}{\partial x_i} \right)$ :$-\overline{\rho u'_i u'_j} = \mu_t \, \left( \frac{\partial U_i}{\partial x_j} + \frac{\partial U_j}{\partial x_i} \right)$ {{stub}} {{stub}}

## Revision as of 20:50, 9 May 2006

Two-equation turbulence models are one of the most common type of turbulence models. Models like the k-epsilon model and the k-omega model have become industry standard models and are commonly used for most type of engineering problems. Two-equation turbulence models are also very much still an active area of research and new refined two-equation models are still being developed.

By definition, two-equation models include two extra transport equations to represent the turbulent properties of the flow. Most often one of the transported variables is the turbulent kinetic energy, $k$. The second transported variable varies depending on what type of two-equation model it is. Common choices are the turbulent dissipation, $\epsilon$, or the specific dissipation, $\omega$. The second variable can be thought of as the variable that determines the scale of the turbulence (length-scale or time-scale), whereas the first variable, $k$, determines the energy in the turbulence.

The basis for all two-equation models is the Boussinesq eddy viscosity assumption, which postulates that the Reynolds stress tensor, $\tau_{ij}$, is proportional to the mean strain rate tensor, $S_{ij}$, and can be written in the following way:

$\tau_{ij} = 2 \, \mu_t \, S_{ij}$

Where $\mu_t$ is a scalar property called the eddy viscosity. The same equation can be written more explicitly as:

$-\overline{\rho u'_i u'_j} = \mu_t \, \left( \frac{\partial U_i}{\partial x_j} + \frac{\partial U_j}{\partial x_i} \right)$