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

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.

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
	The energy balance equation for a porous solid.
namespace	Dumux::Properties::TTag
	Type tag for numeric models.

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