freeflow/rans/twoeq/sst/model.hh File Reference

A single-phase, isothermal SST (Shear Stress Transport) -Eq. model. More...

#include <dumux/common/properties.hh>
#include <dumux/freeflow/properties.hh>
#include <dumux/freeflow/rans/model.hh>
#include <dumux/freeflow/rans/twoeq/indices.hh>
#include <dumux/freeflow/turbulencemodel.hh>
#include <dumux/freeflow/rans/problem.hh>
#include "fluxvariables.hh"
#include "localresidual.hh"
#include "volumevariables.hh"
#include "iofields.hh"

Go to the source code of this file.

Description

A single-phase, isothermal SST (Shear Stress Transport) -Eq. model.

Single-phase Reynolds-Averaged Navier-Stokes flow.

For a detailed model description see freeflow/rans/model.hh

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 [41].

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.

Classes
struct	Dumux::Properties::SSTModelTraits< dimension >
	Traits for the sst model. More...
struct	Dumux::Properties::TTag::SST
	The type tag for the single-phase, isothermal SST model. More...
struct	Dumux::Properties::ModelTraits< TypeTag, TTag::SST >
	states some specifics of the isothermal SST model More...
struct	Dumux::Properties::FluxVariables< TypeTag, TTag::SST >
	The flux variables. More...
struct	Dumux::Properties::LocalResidual< TypeTag, TTag::SST >
	The local residual. More...
struct	Dumux::Properties::VolumeVariables< TypeTag, TTag::SST >
	Set the volume variables property. More...
struct	Dumux::Properties::IOFields< TypeTag, TTag::SST >
	The specific I/O fields. More...
struct	Dumux::Properties::TTag::SSTNI
	The type tag for the single-phase, non-isothermal SST 2-Eq. model. More...
struct	Dumux::Properties::ModelTraits< TypeTag, TTag::SSTNI >
	The model traits of the non-isothermal model. More...
struct	Dumux::Properties::VolumeVariables< TypeTag, TTag::SSTNI >
	Set the volume variables property. More...
struct	Dumux::Properties::IOFields< TypeTag, TTag::SSTNI >
	The specific non-isothermal I/O fields. More...

Namespaces
namespace	Dumux
namespace	Dumux::Properties
namespace	Dumux::Properties::TTag
	Type tag for numeric models.

Include dependency graph for freeflow/rans/twoeq/sst/model.hh: