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

A single-phase, isothermal k-epsilon 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 "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 k-epsilon model.

Single-phase Reynolds-Averaged Navier-Stokes flow.

This model implements a single-phase, isothermal Reynolds-Averaged Navier-Stokes model, solving the momentum balance equation

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

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

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

.

The k-epsilon models calculate the eddy viscosity with two additional PDEs, one for the turbulent kinetic energy (k) and for the dissipation ( \( \varepsilon \)). The model uses the one proposed by Launder and Sharma [41] https://doi.org/10.1016/0094-4548(74)90150-7.

The turbulent kinetic energy balance is:

\[ \frac{\partial \left( k \right)}{\partial t} + \nabla \cdot \left( \textbf{v} k \right) - \nabla \cdot \left( \left( \nu + \frac{\nu_\text{t}}{\sigma_\text{k}} \right) \nabla k \right) - 2 \nu_\text{t} \textbf{S} \cdot \textbf{S} + \varepsilon = 0 \]

.

The dissipation balance is:

\[ \frac{\partial \left( \varepsilon \right)}{\partial t} + \nabla \cdot \left( \textbf{v} \varepsilon \right) - \nabla \cdot \left( \left( \nu + \frac{\nu_\text{t}}{\sigma_{\varepsilon}} \right) \nabla \varepsilon \right) - C_{1\varepsilon} \frac{\varepsilon}{k} 2 \nu_\text{t} \textbf{S} \cdot \textbf{S} + C_{2\varepsilon} \frac{\varepsilon^2}{k} = 0 \]

.

The kinematic eddy viscosity \( \nu_\text{t} \) is:

\[ \nu_\text{t} = C_\mu \frac{k^2}{\tilde{\varepsilon}} \]

.

Finally, the model is closed with the following constants:

\[ \sigma_\text{k} = 1.00 \]

\[ \sigma_\varepsilon =1.30 \]

\[ C_{1\varepsilon} = 1.44 \]

\[ C_{2\varepsilon} = 1.92 \]

\[ C_\mu = 0.09 \]

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

Namespaces
namespace	Dumux
	make the local view function available whenever we use the grid geometry
namespace	Dumux::Properties
namespace	Dumux::Properties::TTag
	Type tag for numeric models.

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