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

A single-phase, isothermal k-omega 2-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 "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 Wilcox, 2008 [95].

Turbulent Kinetic Energy balance:

$$\frac{\partial \left(\varrho k\right)}{\partial t}+\mathrm{\nabla }\cdot \left(\mathbf{v}\varrho k\right)-\mathrm{\nabla }\cdot \left[(\mu +{\sigma }_{\text{k}}{\mu }_{\text{t}})\mathrm{\nabla }k\right]-P+{\beta }_k^{\ast }k\varrho \omega =0$$

with $P=2{\mu }_{\text{t}}\mathbf{S}\cdot \mathbf{S}$ and $S_{ij}=\frac{1}{2}[\frac{\partial }{\partial x_i}{v}_j+\frac{\partial }{\partial x_j}{v}_i]$ based on $a_{ij}\cdot b_{ij}=\sum _{i,j}{a}_{ij}{b}_{ij}$.

Dissipation balance:

$$\frac{\partial \left(\varrho \omega \right)}{\partial t}+\mathrm{\nabla }\cdot \left(\mathbf{v}\varrho \omega \right)-\mathrm{\nabla }\cdot \left[(\mu +{\sigma }_{\omega }{\mu }_{\text{t}})\mathrm{\nabla }\omega \right]-\alpha \frac{\omega }{k}P+{\beta }_{\omega }{\omega }^2-\varrho \frac{{\sigma }_d}{\omega }\mathrm{\nabla }k\mathrm{\nabla }\omega =0$$

The dynamic eddy viscosity ${\mu }_{\text{t}}$ is calculated as follows:

$${\mu }_{\text{t}}=\varrho \frac{k}{\tilde{\omega }}$$

With a limited dissipation:

$$\tilde{\omega }=\text{max}\{\omega ,0.875\sqrt{\frac{P}{{\mu }_{\text{t}}{\beta }_{\text{k}}}}\}$$

And a cross-diffusion coefficient ${\sigma }_{\text{d}}$

$${\sigma }_{\text{d}}=\{\begin{array}{ll}0& \text{, if }\mathrm{\nabla }k\cdot \mathrm{\nabla }\omega \le 0\\ 0.125& \text{, if }\mathrm{\nabla }k\cdot \mathrm{\nabla }\omega >0\end{array}.$$

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