# Two equation turbulence models

(Difference between revisions)
 Revision as of 22:59, 8 May 2006 (view source)Jola (Talk | contribs) (more content, not by far finished yet, will write more)← Older edit Revision as of 20:37, 9 May 2006 (view source)Jola (Talk | contribs) m (small improvements)Newer edit → Line 1: Line 1: - Two-equation turbulence models are one of the most common type of turbulence models. Models like the $k-\epsilon$ 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. + 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]], $\omega$. In any case the second variable should be thought of as the variable that transports and determines the scale of the turbulence (length-scale or time-scale), whereas the first variable, $k$, determines the strength or energy in the turbulence. + 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. - The basis for all two-equation models is the [[Boussinesq eddy viscosity assumption]], which postulates that the [[Reynolds stress tensor]] is proportional to the strain rate tensor: + 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: :$\tau_{ij} = 2 \, \mu_t \, S_{ij}$ :$\tau_{ij} = 2 \, \mu_t \, S_{ij}$ - Or the same equation written out more explicitly: + Or the same equation written more explicitly: :$-\overline{\rho u'_i u'_j} = \mu_t \, \left( \frac{\partial U_i}{\partial x_j} + \frac{\partial U_j}{\partial x_i} \right)$ :$-\overline{\rho u'_i u'_j} = \mu_t \, \left( \frac{\partial U_i}{\partial x_j} + \frac{\partial U_j}{\partial x_i} \right)$ {{stub}} {{stub}}

## Revision as of 20:37, 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 have two extra transport equations to represent the turbulent properties of the flow. Most often one of the transported variables is the 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, $\epsilon$ 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 is proportional to the mean strain rate tensor:

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

Or the same equation written more explicitly:

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