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

A single-phase, isothermal low-Reynolds k-epsilon model.

Single-phase Reynolds-Averaged Navier-Stokes flow For a detailed model description see freeflow/rans/model.hh.

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 ( $\varepsilon$). The model uses the one proposed by Chien [13]. A good overview and additional models are given in Patel et al. [51].

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

$$\frac{\partial \left( \varrho k \right)}{\partial t} + \nabla \cdot \left( \textbf{v} \varhho k \right) - \nabla \cdot \left( \left( \mu + \frac{\mu_\text{t}}{\sigma_\text{k}} \right) \nabla k \right) - 2 \mu_\text{t} \textbf{S} \cdot \textbf{S} + \varrho \tilde{\varepsilon} + D_\varepsilon \varrho = 0$$

.

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:

$$\frac{\partial \left( \varrho \tilde{\varepsilon} \right)}{\partial t} + \nabla \cdot \left( \textbf{v} \varrho \tilde{\varepsilon} \right) - \nabla \cdot \left( \left( \mu + \frac{\mu_\text{t}}{\sigma_{\varepsilon}} \right) \nabla \tilde{\varepsilon} \right) - C_{1\tilde{\varepsilon}} f_1 \frac{\tilde{\varepsilon}}{k} 2 \mu_\text{t} \textbf{S} \cdot \textbf{S} + C_{2\tilde{\varepsilon}} \varrho f_2 \frac{\tilde{\varepsilon}^2}{k} - E_\text{k} \varrho = 0$$

.

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

$$\mu_\text{t} = \varrho C_\mu f_\mu \frac{k^2}{\tilde{\varepsilon}}$$

.

The auxiliary and dampening functions are defined as:

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

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

$$f_1 = 1$$

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

$$f_\mu = 1 - \exp \left( -0.0115 y^+ \right)$$

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

.

Finally, the model is closed with the following constants:

$$\sigma_\text{k} = 1.00$$

$$\sigma_\varepsilon =1.30$$

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

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

$$C_\mu = 0.09$$

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

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