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

A single-phase, isothermal low-Reynolds 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

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:

$${\mu }_{\text{eff}}=\mu +{\mu }_{\text{t}}$$

.

The low-Reynolds k-epsilon models calculate the eddy viscosity with two additional PDEs, one for the turbulent kinetic energy (k) and for the dissipation ( $\epsilon$). The model uses the one proposed by Chien [21]. A good overview and additional models are given in Patel et al. [70].

The turbulent kinetic energy balance is identical with the one from the k-epsilon model, but the dissipation includes a dampening function ( $D_{\epsilon }$): $\epsilon =\tilde{\epsilon }+D_{\epsilon }$:

$$\frac{\partial \left(\varrho k\right)}{\partial t}+\mathrm{\nabla }\cdot \left(\mathbf{\text{v}}\text{varhho}k\right)-\mathrm{\nabla }\cdot \left((\mu +\frac{{\mu }_{\text{t}}}{{\sigma }_{\text{k}}})\mathrm{\nabla }k\right)-2{\mu }_{\text{t}}\mathbf{\text{S}}\cdot \mathbf{\text{S}}+\varrho \tilde{\epsilon }+D_{\epsilon }\varrho =0$$

.

The dissipation balance is changed by introducing additional functions ( $E_{\text{k}}$, $f_1$, and $f_2$) to account for a dampening towards the wall:

$$\frac{\partial \left(\varrho \tilde{\epsilon }\right)}{\partial t}+\mathrm{\nabla }\cdot \left(\mathbf{\text{v}}\varrho \tilde{\epsilon }\right)-\mathrm{\nabla }\cdot \left((\mu +\frac{{\mu }_{\text{t}}}{{\sigma }_{\epsilon }})\mathrm{\nabla }\tilde{\epsilon }\right)-C_{1\tilde{\epsilon }}{f}_1\frac{\tilde{\epsilon }}{k}2{\mu }_{\text{t}}\mathbf{\text{S}}\cdot \mathbf{\text{S}}+C_{2\tilde{\epsilon }}\varrho f_2\frac{{\tilde{\epsilon }}^2}{k}-E_{\text{k}}\varrho =0$$

.

The kinematic eddy viscosity ${\nu }_{\text{t}}$ is dampened by $f_{\mu }$:

$${\mu }_{\text{t}}=\varrho C_{\mu }{f}_{\mu }\frac{k^2}{\tilde{\epsilon }}$$

.

The auxiliary and dampening functions are defined as:

$$D_{\epsilon }=2\nu \frac{k}{y^2}$$

$$E_{\text{k}}=-2\nu \frac{\tilde{\epsilon }}{y^2}\exp (-0.5y^{+})$$

$$f_1=1$$

$$f_2=1-0.22\exp (-{\left(\frac{{\mathit{Re}}_{\text{t}}}{6}\right)}^2)$$

$$f_{\mu }=1-\exp (-0.0115y^{+})$$

$${\mathit{Re}}_{\text{t}}=\frac{k^2}{\nu \tilde{\epsilon }}$$

.

Finally, the model is closed with the following constants:

$${\sigma }_{\text{k}}=1.00$$

$${\sigma }_{\epsilon }=1.30$$

$$C_{1\tilde{\epsilon }}=1.35$$

$$C_{2\tilde{\epsilon }}=1.80$$

$$C_{\mu }=0.09$$

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