K-epsilon model

K-epsilon model. More...

Description

K-epsilon model.

Single-phase Reynolds-Averaged Navier-Stokes flow.

This model implements a single-phase, isothermal Reynolds-Averaged Navier-Stokes model, solving the momentum balance equation

\[ \frac{\partial (\varrho \textbf{v})}{\partial t} + \nabla \cdot (\varrho \textbf{v} \textbf{v}^{\textup{T}}) = \nabla \cdot (\mu_\textrm{eff} (\nabla \textbf{v} + \nabla \textbf{v}^{\textup{T}})) - \nabla p + \varrho \textbf{g} - \textbf{f} \]

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 [41] https://doi.org/10.1016/0094-4548(74)90150-7.

The turbulent kinetic energy balance is:

\[ \frac{\partial \left( k \right)}{\partial t} + \nabla \cdot \left( \textbf{v} k \right) - \nabla \cdot \left( \left( \nu + \frac{\nu_\text{t}}{\sigma_\text{k}} \right) \nabla k \right) - 2 \nu_\text{t} \textbf{S} \cdot \textbf{S} + \varepsilon = 0 \]

.

The dissipation balance is:

\[ \frac{\partial \left( \varepsilon \right)}{\partial t} + \nabla \cdot \left( \textbf{v} \varepsilon \right) - \nabla \cdot \left( \left( \nu + \frac{\nu_\text{t}}{\sigma_{\varepsilon}} \right) \nabla \varepsilon \right) - C_{1\varepsilon} \frac{\varepsilon}{k} 2 \nu_\text{t} \textbf{S} \cdot \textbf{S} + C_{2\varepsilon} \frac{\varepsilon^2}{k} = 0 \]

.

The kinematic eddy viscosity \( \nu_\text{t} \) is:

\[ \nu_\text{t} = C_\mu \frac{k^2}{\tilde{\varepsilon}} \]

.

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	freeflow/rans/twoeq/kepsilon/fluxvariables.hh
file	dumux/freeflow/rans/twoeq/kepsilon/iofields.hh
file	freeflow/rans/twoeq/kepsilon/localresidual.hh
file	freeflow/rans/twoeq/kepsilon/model.hh
	A single-phase, isothermal k-epsilon model.
file	dumux/freeflow/rans/twoeq/kepsilon/problem.hh
	K-epsilon turbulence problem base class.
file	freeflow/rans/twoeq/kepsilon/staggered/fluxvariables.hh
file	freeflow/rans/twoeq/kepsilon/volumevariables.hh

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::staggered >
	The flux variables class for the k-epsilon model using the staggered grid discretization. More...
class	Dumux::KEpsilonResidualImpl< TypeTag, BaseLocalResidual, DiscretizationMethod::staggered >
	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, GetPropType< TypeTag, Properties::GridGeometry >::discMethod >
	The flux variables class for the k-epsilon model. This is a convenience alias for that actual, discretization-specific flux variables. More...
template<class TypeTag , class BaseLocalResidual >
using	Dumux::KEpsilonResidual = KEpsilonResidualImpl< TypeTag, BaseLocalResidual, GetPropType< TypeTag, Properties::GridGeometry >::discMethod >
	The local residual class for the k-epsilon model. This is a convenience alias for the actual, discretization-specific local residual. More...

Typedef Documentation

KEpsilonFluxVariables

template<class TypeTag , class BaseFluxVariables >

using Dumux::KEpsilonFluxVariables = typedef KEpsilonFluxVariablesImpl<TypeTag, BaseFluxVariables, GetPropType<TypeTag, Properties::GridGeometry>::discMethod>

The flux variables class for the k-epsilon model. This is a convenience alias for that actual, discretization-specific flux variables.

Note

Not all specializations are currently implemented

KEpsilonResidual

template<class TypeTag , class BaseLocalResidual >

using Dumux::KEpsilonResidual = typedef KEpsilonResidualImpl<TypeTag, BaseLocalResidual, GetPropType<TypeTag, Properties::GridGeometry>::discMethod>

The local residual class for the k-epsilon model. This is a convenience alias for the actual, discretization-specific local residual.

Note

Not all specializations are currently implemented