SST model

SST model. More...

Description

A single-phase, isothermal SST (Shear Stress Transport) -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 Menter, 1994 [56].

Turbulent Kinetic Energy balance:

$$\frac{\partial \varrho k}{\partial t}+\mathrm{\nabla }\cdot \left(\varrho \mathit{u}k\right)-2{\mu }_t\mathit{S}\cdot \mathit{S}+{\beta }^{\ast }\varrho \omega k-\mathrm{\nabla }\cdot \left[(\mu +{\sigma }_k{\mu }_t)\mathrm{\nabla }k\right]=0$$

and $S_{ij}=\frac{1}{2}[\frac{\partial }{\partial x_i}{u}_j+\frac{\partial }{\partial x_j}{u}_i]$ based on $a_{ij}\cdot b_{ij}=\sum _{i,j}{a}_{ij}{b}_{ij}$.

Dissipation(rate) balance:

$$\frac{\partial \varrho \omega }{\partial t}+\mathrm{\nabla }\cdot \left(\varrho \mathit{u}\omega \right)-\frac{\gamma }{{\nu }_t}(2{\mu }_t\mathit{S}\cdot \mathit{S})+{\beta }^{\ast }\varrho {\omega }^2-\mathrm{\nabla }\cdot \left[(\mu +{\sigma }_k{\mu }_t)\mathrm{\nabla }\omega \right]-2\varrho (1-F_1){\sigma }_{\omega 2}\frac{1}{\omega }\mathrm{\nabla }k\mathrm{\nabla }\omega =0$$

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

$${\mu }_t=\varrho \frac{a_{1}k}{max(a_1\omega ;\mathrm{\Omega }{F}_2)}$$

and $a_1=0.31$ and $\mathrm{\Omega }=\sqrt{2\mathbf{\Omega }\cdot \mathbf{\Omega }}\text{ with }\mathbf{\Omega }=\frac{1}{2}(\mathrm{\nabla }\mathit{u}-{\mathrm{\nabla }}^T\mathit{u})$ and $F_2=tanh\left(ar{g}_2^2\right)$ and $ar{g}_2=max(2\frac{\sqrt{k}}{0.09\omega y};\frac{500\nu }{y^2\omega })$ where y is the distance to the closest wall and $\nu$ is the kinematic viscosity.

Files
file	freeflow/rans/twoeq/sst/fluxvariables.hh
file	freeflow/rans/twoeq/sst/iofields.hh
file	freeflow/rans/twoeq/sst/localresidual.hh
file	freeflow/rans/twoeq/sst/model.hh
	A single-phase, isothermal SST (Shear Stress Transport) -Eq. model.
file	freeflow/rans/twoeq/sst/problem.hh
	SST turbulence model problem base class.
file	freeflow/rans/twoeq/sst/staggered/fluxvariables.hh
file	freeflow/rans/twoeq/sst/staggered/localresidual.hh
file	freeflow/rans/twoeq/sst/volumevariables.hh

Classes
struct	Dumux::SSTIOFields
	Adds I/O fields for the Reynolds-Averaged Navier-Stokes model. More...
struct	Dumux::Properties::SSTModelTraits< dimension >
	Traits for the sst model. More...
class	Dumux::RANSProblemImpl< TypeTag, TurbulenceModel::sst >
	SST turbulence model problem base class. More...
class	Dumux::SSTFluxVariablesImpl< TypeTag, BaseFluxVariables, DiscretizationMethod >
	The flux variables class for the SST model using the staggered grid discretization. More...
class	Dumux::SSTResidualImpl< TypeTag, BaseLocalResidual, DiscretizationMethod >
	Element-wise calculation of the residual for SST models using the staggered discretization. More...
class	Dumux::SSTVolumeVariables< Traits, NSVolumeVariables >
	Volume variables for the isothermal single-phase SST 2-Eq model. More...

Typedefs
template<class TypeTag , class BaseFluxVariables >
using	Dumux::SSTFluxVariables = SSTFluxVariablesImpl< TypeTag, BaseFluxVariables, typename GetPropType< TypeTag, Properties::GridGeometry >::DiscretizationMethod >
	The flux variables class for the SST model. This is a convenience alias for that actual, discretization-specific flux variables. More...
template<class TypeTag , class BaseLocalResidual >
using	Dumux::SSTResidual = SSTResidualImpl< TypeTag, BaseLocalResidual, typename GetPropType< TypeTag, Properties::GridGeometry >::DiscretizationMethod >
	The local residual class for the SST model. This is a convenience alias for the actual, discretization-specific local residual. More...

Enumerations
enum class	Dumux::SSTModel { Dumux::SSTModel::BSL , Dumux::SSTModel::SST }
	The available variations of the SST Turbulence Model. More...

Typedef Documentation

SSTFluxVariables

template<class TypeTag , class BaseFluxVariables >

using Dumux::SSTFluxVariables = typedef SSTFluxVariablesImpl<TypeTag, BaseFluxVariables, typename GetPropType<TypeTag, Properties::GridGeometry>::DiscretizationMethod>

Note

Not all specializations are currently implemented

SSTResidual

template<class TypeTag , class BaseLocalResidual >

using Dumux::SSTResidual = typedef SSTResidualImpl<TypeTag, BaseLocalResidual, typename GetPropType<TypeTag, Properties::GridGeometry>::DiscretizationMethod>

Note

Not all specializations are currently implemented

Enumeration Type Documentation

SSTModel

enum class Dumux::SSTModel

strong

Enumerator
BSL
SST