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

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

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

\[ \mu_\textrm{eff} = \mu + \mu_\textrm{t} \]

.

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 [53].

Turbulent Kinetic Energy balance:

\[ \frac{\partial \varrho k}{\partial t} + \nabla \cdot \left( \varrho \boldsymbol{u} k \right) - 2\mu_t \boldsymbol{S}\cdot\boldsymbol{S} + \beta^* \varrho\omega k - \nabla\cdot \left[ \left( \mu + \sigma_k \mu_t \right)\nabla k\right] = 0 \]

and \( S_{ij} = \frac{1}{2} \left[ \frac{\partial}{\partial x_i} u_j + \frac{\partial}{\partial x_j} u_i \right] \) based on \( a_{ij} \cdot b_{ij} = \sum_{i,j} a_{ij} b_{ij} \).

Dissipation(rate) balance:

\[ \frac{\partial \varrho \omega}{\partial t} + \nabla \cdot \left( \varrho \boldsymbol{u} \omega \right) - \frac{\gamma}{\nu_t}\left(2\mu_t \boldsymbol{S}\cdot\boldsymbol{S}\right) + \beta^* \varrho\omega^2 - \nabla\cdot \left[ \left( \mu + \sigma_k \mu_t \right)\nabla \omega\right] - 2\varrho\left( 1-F_1\right) \sigma_{\omega 2} \frac{1}{\omega}\nabla k \nabla \omega = 0 \]

The dynamic eddy viscosity \( \mu_\textrm{t} \) is calculated as follows:

\[ \mu_t = \varrho \frac{a_1 k}{max\left( a_1 \omega; \Omega F_2\right)} \]

and \( a_1 = 0.31 \) and \( \Omega = \sqrt{2\boldsymbol{\Omega}\cdot\boldsymbol{\Omega}} \text{ with } \boldsymbol{\Omega} = \frac{1}{2} \left( \nabla\boldsymbol{u} - \nabla^T\boldsymbol{u}\right) \) and \( F_2 = tanh\left( arg_2^2\right) \) and \( arg_2 = max\left( 2\frac{\sqrt{k}}{0.09\omega y}; \frac{500\nu}{y^2\omega} \right) \) 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