K-epsilon model. More...
A single-phase, isothermal k-epsilon model.
Single-phase Reynolds-Averaged Navier-Stokes flow.
A single-phase, isothermal Reynolds-Averaged Navier-Stokes model.
This model implements a single-phase, isothermal Reynolds-Averaged Navier-Stokes model, solving the momentum balance equation
\[\frac{\partial (\varrho \textbf{v})}{\partial t} + \nabla \cdot (\varrho \textbf{v} \textbf{v}^{\text{T}}) = \nabla \cdot (\mu_\textrm{eff} (\nabla \textbf{v} + \nabla \textbf{v}^{\text{T}})) - \nabla p + \varrho \textbf{g} - \textbf{f} \]
The effective viscosity is composed of the fluid and the eddy viscosity:
\[ \mu_\textrm{eff} = \mu + \mu_\textrm{t} \]
.
The k-epsilon models calculate the eddy viscosity with two additional PDEs, one for the turbulent kinetic energy (k) and for the dissipation ( \( \varepsilon \)). The model uses the one proposed by Launder and Sharma [launder1974a] https://doi.org/10.1016/0094-4548(74)90150-7.
The turbulent kinetic energy balance is:
\[ \frac{\partial \left( \varrho k \right)}{\partial t} + \nabla \cdot \left( \textbf{v} \varhho k \right) - \nabla \cdot \left( \left( \mu + \frac{\mu_\text{t}}{\sigma_\text{k}} \right) \nabla k \right) - 2 \mu_\text{t} \textbf{S} \cdot \textbf{S} + \varrho \varepsilon = 0 \]
.
The dissipation balance is:
\[ \frac{\partial \left( \varrho \varepsilon \right)}{\partial t} + \nabla \cdot \left( \textbf{v} \varrho \varepsilon \right) - \nabla \cdot \left( \left( \mu + \frac{\mu_\text{t}}{\sigma_{\varepsilon}} \right) \nabla \varepsilon \right) - C_{1\varepsilon} \frac{\varepsilon}{k} 2 \mu_\text{t} \textbf{S} \cdot \textbf{S} + C_{2\varepsilon} \varrho \frac{\varepsilon^2}{k} = 0 \]
.
The dynamic eddy viscosity \( \mu_\text{t} \) is:
\[\mu_\text{t} = \varrho C_\mu \frac{k^2}{\tilde{\varepsilon}} \]
.
Finally, the model is closed with the following constants:
\[ \sigma_\text{k} = 1.00 \]
\[ \sigma_\varepsilon =1.30 \]
\[ C_{1\varepsilon} = 1.44 \]
\[ C_{2\varepsilon} = 1.92 \]
\[ C_\mu = 0.09 \]
| Files | |
| file | fluxvariables.hh | 
| The flux variables class for the k-epsilon model. This is a convenience alias for that actual, discretization-specific flux variables. | |
| file | iofields.hh | 
| Adds I/O fields for the k-epsilon turbulence model. | |
| file | localresidual.hh | 
| The local residual class for the k-epsilon model. This is a convenience alias for the actual, discretization-specific local residual. | |
| file | model.hh | 
| A single-phase, isothermal k-epsilon model. | |
| file | problem.hh | 
| K-epsilon turbulence problem base class. | |
| file | fluxvariables.hh | 
| The flux variables class for the k-epsilon model using the staggered grid discretization. | |
| file | localresidual.hh | 
| Element-wise calculation of the residual for k-epsilon models using the staggered discretization. | |
| file | volumevariables.hh | 
| Volume variables for the isothermal single-phase k-epsilon model. | |
| Classes | |
| struct | Dumux::KEpsilonIOFields | 
| Adds I/O fields for the k-epsilon turbulence model.  More... | |
| struct | Dumux::Properties::KEpsilonModelTraits< dimension > | 
| Traits for the k-epsilon model.  More... | |
| class | Dumux::RANSProblemImpl< TypeTag, TurbulenceModel::kepsilon > | 
| K-epsilon turbulence problem base class.  More... | |
| class | Dumux::KEpsilonFluxVariablesImpl< TypeTag, BaseFluxVariables, DiscretizationMethod > | 
| The flux variables class for the k-epsilon model using the staggered grid discretization.  More... | |
| class | Dumux::KEpsilonResidualImpl< TypeTag, BaseLocalResidual, DiscretizationMethod > | 
| Element-wise calculation of the residual for k-epsilon models using the staggered discretization.  More... | |
| class | Dumux::KEpsilonVolumeVariables< Traits, NSVolumeVariables > | 
| Volume variables for the isothermal single-phase k-epsilon model.  More... | |
| Typedefs | |
| template<class TypeTag, class BaseFluxVariables> | |
| using | Dumux::KEpsilonFluxVariables = KEpsilonFluxVariablesImpl<TypeTag, BaseFluxVariables, typename GetPropType<TypeTag, Properties::GridGeometry>::DiscretizationMethod> | 
| The flux variables class for the k-epsilon model. This is a convenience alias for that actual, discretization-specific flux variables. | |
| template<class TypeTag, class BaseLocalResidual> | |
| using | Dumux::KEpsilonResidual = KEpsilonResidualImpl<TypeTag, BaseLocalResidual, typename GetPropType<TypeTag, Properties::GridGeometry>::DiscretizationMethod> | 
| The local residual class for the k-epsilon model. This is a convenience alias for the actual, discretization-specific local residual. | |
| using Dumux::KEpsilonFluxVariables = KEpsilonFluxVariablesImpl<TypeTag, BaseFluxVariables, typename GetPropType<TypeTag, Properties::GridGeometry>::DiscretizationMethod> | 
| using Dumux::KEpsilonResidual = KEpsilonResidualImpl<TypeTag, BaseLocalResidual, typename GetPropType<TypeTag, Properties::GridGeometry>::DiscretizationMethod> |