K-epsilon model

K-epsilon model. More...

Description

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

$$\frac{\partial (\varrho \mathbf{\text{v}})}{\partial t}+\mathrm{\nabla }\cdot (\varrho \mathbf{\text{v}}{\mathbf{\text{v}}}^{\text{T}})=\mathrm{\nabla }\cdot ({\mu }_{\text{eff}}(\mathrm{\nabla }\mathbf{\text{v}}+\mathrm{\nabla }{\mathbf{\text{v}}}^{\text{T}}))-\mathrm{\nabla }p+\varrho \mathbf{\text{g}}-\mathbf{\text{f}}$$

The effective viscosity is composed of the fluid and the eddy viscosity:

$${\mu }_{\text{eff}}=\mu +{\mu }_{\text{t}}$$

.

The k-epsilon models calculate the eddy viscosity with two additional PDEs, one for the turbulent kinetic energy (k) and for the dissipation ( $\epsilon$). The model uses the one proposed by Launder and Sharma [52] https://doi.org/10.1016/0094-4548(74)90150-7.

The turbulent kinetic energy balance is:

$$\frac{\partial \left(\varrho k\right)}{\partial t}+\mathrm{\nabla }\cdot \left(\mathbf{\text{v}}\text{varhho}k\right)-\mathrm{\nabla }\cdot \left((\mu +\frac{{\mu }_{\text{t}}}{{\sigma }_{\text{k}}})\mathrm{\nabla }k\right)-2{\mu }_{\text{t}}\mathbf{\text{S}}\cdot \mathbf{\text{S}}+\varrho \epsilon =0$$

.

The dissipation balance is:

$$\frac{\partial \left(\varrho \epsilon \right)}{\partial t}+\mathrm{\nabla }\cdot \left(\mathbf{\text{v}}\varrho \epsilon \right)-\mathrm{\nabla }\cdot \left((\mu +\frac{{\mu }_{\text{t}}}{{\sigma }_{\epsilon }})\mathrm{\nabla }\epsilon \right)-C_{1\epsilon }\frac{\epsilon }{k}2{\mu }_{\text{t}}\mathbf{\text{S}}\cdot \mathbf{\text{S}}+C_{2\epsilon }\varrho \frac{{\epsilon }^2}{k}=0$$

.

The dynamic eddy viscosity ${\mu }_{\text{t}}$ is:

$${\mu }_{\text{t}}=\varrho C_{\mu }\frac{k^2}{\tilde{\epsilon }}$$

.

Finally, the model is closed with the following constants:

$${\sigma }_{\text{k}}=1.00$$

$${\sigma }_{\epsilon }=1.30$$

$$C_{1\epsilon }=1.44$$

$$C_{2\epsilon }=1.92$$

$$C_{\mu }=0.09$$

Files
file	freeflow/rans/twoeq/kepsilon/fluxvariables.hh
file	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	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/staggered/localresidual.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 >
	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. More...
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. More...

Typedef Documentation

KEpsilonFluxVariables

template<class TypeTag , class BaseFluxVariables >

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

Note

Not all specializations are currently implemented

KEpsilonResidual

template<class TypeTag , class BaseLocalResidual >

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

Note

Not all specializations are currently implemented