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version 3.8
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A single-phase, isothermal SST (Shear Stress Transport) -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 <dumux/freeflow/rans/problem.hh>#include "fluxvariables.hh"#include "localresidual.hh"#include "volumevariables.hh"#include "iofields.hh"Go to the source code of this file.
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
\[ \frac{\partial (\varrho \textbf{v})}{\partial t} + \nabla \cdot (\varrho \textbf{v} \textbf{v}^{\text{T}}) = \nabla \cdot (\mu_\textrm{eff} (\nabla \textbf{v} + \nabla \textbf{v}^{\text{T}})) - \nabla p + \varrho \textbf{g} - \textbf{f} \]
The effective viscosity is composed of the fluid and the eddy viscosity:
\[ \mu_\textrm{eff} = \mu + \mu_\textrm{t} \]
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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 Menter, 1994 [51].
Turbulent Kinetic Energy balance:
\[ \frac{\partial \varrho k}{\partial t} + \nabla \cdot \left( \varrho \boldsymbol{u} k \right) - 2\mu_t \boldsymbol{S}\cdot\boldsymbol{S} + \beta^* \varrho\omega k - \nabla\cdot \left[ \left( \mu + \sigma_k \mu_t \right)\nabla k\right] = 0 \]
and \( S_{ij} = \frac{1}{2} \left[ \frac{\partial}{\partial x_i} u_j + \frac{\partial}{\partial x_j} u_i \right] \) based on \( a_{ij} \cdot b_{ij} = \sum_{i,j} a_{ij} b_{ij} \).
Dissipation(rate) balance:
\[ \frac{\partial \varrho \omega}{\partial t} + \nabla \cdot \left( \varrho \boldsymbol{u} \omega \right) - \frac{\gamma}{\nu_t}\left(2\mu_t \boldsymbol{S}\cdot\boldsymbol{S}\right) + \beta^* \varrho\omega^2 - \nabla\cdot \left[ \left( \mu + \sigma_k \mu_t \right)\nabla \omega\right] - 2\varrho\left( 1-F_1\right) \sigma_{\omega 2} \frac{1}{\omega}\nabla k \nabla \omega = 0 \]
The dynamic eddy viscosity \( \mu_\textrm{t} \) is calculated as follows:
\[ \mu_t = \varrho \frac{a_1 k}{max\left( a_1 \omega; \Omega F_2\right)} \]
and \( a_1 = 0.31 \) and \( \Omega = \sqrt{2\boldsymbol{\Omega}\cdot\boldsymbol{\Omega}} \text{ with } \boldsymbol{\Omega} = \frac{1}{2} \left( \nabla\boldsymbol{u} - \nabla^T\boldsymbol{u}\right) \) and \( F_2 = tanh\left( arg_2^2\right) \) and \( arg_2 = max\left( 2\frac{\sqrt{k}}{0.09\omega y}; \frac{500\nu}{y^2\omega} \right) \) where y is the distance to the closest wall and \( \nu \) is the kinematic viscosity.
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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