K-omega model

K-omega model. More...

Description

A single-phase, isothermal k-omega 2-Eq. 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:

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

.

Two additional PDEs, one for the turbulentKineticEnergy (k) and a second for the dissipation (omega) are used to calculate the eddy viscosity for this model. The model is taken from Wilcox, 2008 [95].

Turbulent Kinetic Energy balance:

$$\frac{\partial \left(\varrho k\right)}{\partial t}+\mathrm{\nabla }\cdot \left(\mathbf{v}\varrho k\right)-\mathrm{\nabla }\cdot \left[(\mu +{\sigma }_{\text{k}}{\mu }_{\text{t}})\mathrm{\nabla }k\right]-P+{\beta }_k^{\ast }k\varrho \omega =0$$

with $P=2{\mu }_{\text{t}}\mathbf{S}\cdot \mathbf{S}$ and $S_{ij}=\frac{1}{2}[\frac{\partial }{\partial x_i}{v}_j+\frac{\partial }{\partial x_j}{v}_i]$ based on $a_{ij}\cdot b_{ij}=\sum _{i,j}{a}_{ij}{b}_{ij}$.

Dissipation balance:

$$\frac{\partial \left(\varrho \omega \right)}{\partial t}+\mathrm{\nabla }\cdot \left(\mathbf{v}\varrho \omega \right)-\mathrm{\nabla }\cdot \left[(\mu +{\sigma }_{\omega }{\mu }_{\text{t}})\mathrm{\nabla }\omega \right]-\alpha \frac{\omega }{k}P+{\beta }_{\omega }{\omega }^2-\varrho \frac{{\sigma }_d}{\omega }\mathrm{\nabla }k\mathrm{\nabla }\omega =0$$

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

$${\mu }_{\text{t}}=\varrho \frac{k}{\tilde{\omega }}$$

With a limited dissipation:

$$\tilde{\omega }=\text{max}\{\omega ,0.875\sqrt{\frac{P}{{\mu }_{\text{t}}{\beta }_{\text{k}}}}\}$$

And a cross-diffusion coefficient ${\sigma }_{\text{d}}$

$${\sigma }_{\text{d}}=\{\begin{array}{ll}0& \text{, if }\mathrm{\nabla }k\cdot \mathrm{\nabla }\omega \le 0\\ 0.125& \text{, if }\mathrm{\nabla }k\cdot \mathrm{\nabla }\omega >0\end{array}.$$

Files
file	freeflow/rans/twoeq/komega/fluxvariables.hh
file	freeflow/rans/twoeq/komega/iofields.hh
file	freeflow/rans/twoeq/komega/localresidual.hh
file	freeflow/rans/twoeq/komega/model.hh
	A single-phase, isothermal k-omega 2-Eq. model.
file	freeflow/rans/twoeq/komega/problem.hh
	K-Omega turbulence model problem base class.
file	freeflow/rans/twoeq/komega/staggered/fluxvariables.hh
file	freeflow/rans/twoeq/komega/staggered/localresidual.hh
file	freeflow/rans/twoeq/komega/volumevariables.hh

Classes
struct	Dumux::KOmegaIOFields
	Adds I/O fields for the Reynolds-Averaged Navier-Stokes model. More...
struct	Dumux::Properties::KOmegaModelTraits< dimension >
	Traits for the k-omega model. More...
class	Dumux::RANSProblemImpl< TypeTag, TurbulenceModel::komega >
	K-Omega turbulence model problem base class. More...
class	Dumux::KOmegaFluxVariablesImpl< TypeTag, BaseFluxVariables, DiscretizationMethod >
	The flux variables class for the k-omega model using the staggered grid discretization. More...
class	Dumux::KOmegaResidualImpl< TypeTag, BaseLocalResidual, DiscretizationMethod >
	Element-wise calculation of the residual for k-omega models using the staggered discretization. More...
class	Dumux::KOmegaVolumeVariables< Traits, NSVolumeVariables >
	Volume variables for the isothermal single-phase k-omega 2-Eq model. More...

Typedefs
template<class TypeTag , class BaseFluxVariables >
using	Dumux::KOmegaFluxVariables = KOmegaFluxVariablesImpl< TypeTag, BaseFluxVariables, typename GetPropType< TypeTag, Properties::GridGeometry >::DiscretizationMethod >
	The flux variables class for the k-omega model. This is a convenience alias for that actual, discretization-specific flux variables. More...
template<class TypeTag , class BaseLocalResidual >
using	Dumux::KOmegaResidual = KOmegaResidualImpl< TypeTag, BaseLocalResidual, typename GetPropType< TypeTag, Properties::GridGeometry >::DiscretizationMethod >
	The local residual class for the k-omega model. This is a convenience alias for the actual, discretization-specific local residual. More...

Typedef Documentation

KOmegaFluxVariables

template<class TypeTag , class BaseFluxVariables >

using Dumux::KOmegaFluxVariables = typedef KOmegaFluxVariablesImpl<TypeTag, BaseFluxVariables, typename GetPropType<TypeTag, Properties::GridGeometry>::DiscretizationMethod>

Note

Not all specializations are currently implemented

KOmegaResidual

template<class TypeTag , class BaseLocalResidual >

using Dumux::KOmegaResidual = typedef KOmegaResidualImpl<TypeTag, BaseLocalResidual, typename GetPropType<TypeTag, Properties::GridGeometry>::DiscretizationMethod>

Note

Not all specializations are currently implemented