freeflow/rans/oneeq/model.hh File Reference

A single-phase, isothermal one-equation turbulence model by Spalart-Allmaras. More...

#include <dumux/common/properties.hh>
#include <dumux/freeflow/properties.hh>
#include <dumux/freeflow/turbulencemodel.hh>
#include <dumux/freeflow/rans/model.hh>
#include <dumux/freeflow/nonisothermal/iofields.hh>
#include "fluxvariables.hh"
#include "indices.hh"
#include "localresidual.hh"
#include "problem.hh"
#include "volumevariables.hh"
#include "iofields.hh"

Go to the source code of this file.

Description

A single-phase, isothermal one-equation turbulence model by Spalart-Allmaras.

Single-phase Reynolds-Averaged Navier-Stokes flow.

For a detailed model description see freeflow/rans/model.hh

This model, published by Spalart and Allmaras 1992 [65], uses one additional PDE for a working variable $\tilde{\nu}$. This variable has the units of a viscosity and can be converted to the eddy viscosity via a model function~( $f_\text{v1}$):

$$\nu_\text{t} = \tilde{\nu} f_\text{v1}$$

Here, as proposed by Wilcox [78] and Versteeg [75], the correction term which account for the transition or trip, is dropped from the original equations, such that the balance equation simplifies to:

$$\frac{\partial \tilde{\nu}\varrho}{\partial t} + \nabla \cdot \left( \tilde{\nu} \varrho \textbf{v} \right) - c_\text{b1} \tilde{S} \tilde{\nu} \varrho - \frac{1}{\sigma_{\tilde{\nu}}} \nabla \cdot \left( \left[ \mu + \tilde{\nu} \varrho \right] \nabla \tilde{\nu} \right) - \frac{c_\text{b2}}{\sigma_{\tilde{\nu}}} \varrho \left| \nabla \tilde{\nu} \right|^2 + c_\text{w1} f_\text{w} \varrho \frac{\tilde{\nu}^2}{y^2} = 0$$

Here, a modified mean effective strain rate ( $\tilde{S}$) based on the mean rotation rate tensor ( $\mathbf{\Omega}$) is used:

$$\tilde{S} = \sqrt{2 \mathbf{\Omega} \cdot \mathbf{\Omega}} + \frac{\tilde{\nu}}{\kappa^2 y^2} f_\text{v2}$$

$$\mathbf{\Omega} = \frac{1}{2} \left( \nabla \textbf{v}_\text{g} - \nabla \textbf{v}_\text{g}^{T} \right)$$

This balance equation is linked to the flow geometry by the distance to the closest wall ($y$). Further, the model uses the following functions and expressions:

$$\chi = \frac{\tilde{\nu}}{\nu}$$

$$f_\text{v1} = \frac{\chi^3}{\chi^3+c_\text{v1}^3}$$

$$f_\text{v2} = 1 - \frac{\chi}{1+f_\text{v1}\chi}$$

$$f_\text{w} = g_\text{w} \left( \frac{1+c_\text{w3}^6}{g^6_\text{w}+c_\text{w3}^6} \right)^\frac{1}{6}$$

$$g_\text{w} = r_\text{w} + c_\text{w2} (r_\text{w}^6 - r_\text{w})$$

$$r_\text{w} = \min \left[ \frac{\tilde{\nu}}{\tilde{S}\kappa^2 y^2},10\right]$$

$$\sigma_{\tilde{\nu}} = \frac{2}{3}$$

$$c_\text{b1} = 0.1355$$

$$c_\text{b2} = 0.622$$

$$c_\text{v1} = 7.1$$

$$c_\text{w1} = \frac{c_\text{b1}}{\kappa^2} + \frac{1+c_\text{b2}}{\sigma_{\tilde{\nu}}}$$

$$c_\text{w2} = 0.3$$

$$c_\text{w3} = 2$$

$$\kappa = 0.41$$

$$\sigma_{\tilde{\nu}} = 2/3$$

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

Namespaces
namespace	Dumux
	Adaption of the non-isothermal two-phase two-component flow model to problems with CO2.
namespace	Dumux::Properties
namespace	Dumux::Properties::TTag
	Type tag for numeric models.

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