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3.1-git
DUNE for Multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media
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3.1-git
DUNE for Multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media
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Low-Re k-epsilon model. More...
Low-Re k-epsilon model.
Single-phase Reynolds-Averaged Navier-Stokes flow.
This model implements a single-phase, isothermal Reynolds-Averaged Navier-Stokes model, solving the momentum balance equation
\[ \frac{\partial (\varrho \textbf{v})}{\partial t} + \nabla \cdot (\varrho \textbf{v} \textbf{v}^{\textup{T}}) = \nabla \cdot (\mu_\textrm{eff} (\nabla \textbf{v} + \nabla \textbf{v}^{\textup{T}})) - \nabla p + \varrho \textbf{g} - \textbf{f} \]
The effective viscosity is composed of the fluid and the eddy viscosity:
\[ \mu_\textrm{eff} = \mu + \mu_\textrm{t} \]
.
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. [54].
The turbulent kinetic energy balance is identical with the one from the k-epsilon model, but the dissipation includes a dampening function ( \( D_\varepsilon \)): \( \varepsilon = \tilde{\varepsilon} + D_\varepsilon \):
\[ \frac{\partial \left( k \right)}{\partial t} + \nabla \cdot \left( \textbf{v} k \right) - \nabla \cdot \left( \left( \nu + \frac{\nu_\text{t}}{\sigma_\text{k}} \right) \nabla k \right) - 2 \nu_\text{t} \textbf{S} \cdot \textbf{S} + \tilde{\varepsilon} + D_\varepsilon = 0 \]
.
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:
\[ \frac{\partial \left( \tilde{\varepsilon} \right)}{\partial t} + \nabla \cdot \left( \textbf{v} \tilde{\varepsilon} \right) - \nabla \cdot \left( \left( \nu + \frac{\nu_\text{t}}{\sigma_{\varepsilon}} \right) \nabla \tilde{\varepsilon} \right) - C_{1\tilde{\varepsilon}} f_1 \frac{\tilde{\varepsilon}}{k} 2 \nu_\text{t} \textbf{S} \cdot \textbf{S} + C_{2\tilde{\varepsilon}} f_2 \frac{\tilde{\varepsilon}^2}{k} - E_\text{k} = 0 \]
.
The kinematic eddy viscosity \( \nu_\text{t} \) is dampened by \( f_\mu \):
\[ \nu_\text{t} = C_\mu f_\mu \frac{k^2}{\tilde{\varepsilon}} \]
.
The auxiliary and dampening functions are defined as:
\[ D_\varepsilon = 2 \nu \nicefrac{k}{y^2} \]
\[ E_\text{k} = -2 \nu \frac{\tilde{\varepsilon}}{y^2} \exp \left( -0.5 y^+ \right) \]
\[ f_1 = 1 \]
\[ f_2 = 1 - 0.22 \exp \left( - \left( \frac{\mathit{Re}_\text{t}}{6} \right)^2 \right) \]
\[ f_\mu = 1 - \exp \left( -0.0115 y^+ \right) \]
\[ \mathit{Re}_\text{t} = \frac{k^2}{\nu \tilde{\varepsilon}} \]
.
Finally, the model is closed with the following constants:
\[ \sigma_\text{k} = 1.00 \]
\[ \sigma_\varepsilon =1.30 \]
\[ C_{1\tilde{\varepsilon}} = 1.35 \]
\[ C_{2\tilde{\varepsilon}} = 1.80 \]
\[ C_\mu = 0.09 \]
Files | |
| file | freeflow/rans/twoeq/lowrekepsilon/fluxvariables.hh |
| file | dumux/freeflow/rans/twoeq/lowrekepsilon/iofields.hh |
| file | freeflow/rans/twoeq/lowrekepsilon/localresidual.hh |
| file | freeflow/rans/twoeq/lowrekepsilon/model.hh |
| A single-phase, isothermal low-Reynolds k-epsilon model. | |
| file | dumux/freeflow/rans/twoeq/lowrekepsilon/problem.hh |
| Low-Re k-epsilon turbulence problem base class. | |
| file | freeflow/rans/twoeq/lowrekepsilon/staggered/fluxvariables.hh |
| file | freeflow/rans/twoeq/lowrekepsilon/staggered/localresidual.hh |
| file | freeflow/rans/twoeq/lowrekepsilon/volumevariables.hh |
Classes | |
| struct | Dumux::LowReKEpsilonIOFields |
| Adds I/O fields for the low-Re k-epsilon turbulence model. More... | |
| struct | Dumux::Properties::LowReKEpsilonModelTraits< dimension > |
| Traits for the low-Reynolds k-epsilon model. More... | |
| class | Dumux::RANSProblemImpl< TypeTag, TurbulenceModel::lowrekepsilon > |
| Low-Re k-epsilon turbulence problem base class. More... | |
| class | Dumux::LowReKEpsilonFluxVariablesImpl< TypeTag, BaseFluxVariables, DiscretizationMethod::staggered > |
| The flux variables class for the low-Reynolds k-epsilon model using the staggered grid discretization. More... | |
| class | Dumux::LowReKEpsilonResidualImpl< TypeTag, BaseLocalResidual, DiscretizationMethod::staggered > |
| Element-wise calculation of the residual for low-Reynolds k-epsilon models using the staggered discretization. More... | |
| class | Dumux::LowReKEpsilonVolumeVariables< Traits, NSVolumeVariables > |
| Volume variables for the isothermal single-phase low-Re k-epsilons model. More... | |
Typedefs | |
| template<class TypeTag , class BaseFluxVariables > | |
| using | Dumux::LowReKEpsilonFluxVariables = LowReKEpsilonFluxVariablesImpl< TypeTag, BaseFluxVariables, GetPropType< TypeTag, Properties::GridGeometry >::discMethod > |
| The flux variables class for the low-Reynolds k-epsilon model. This is a convenience alias for that actual, discretization-specific flux variables. More... | |
| template<class TypeTag , class BaseLocalResidual > | |
| using | Dumux::LowReKEpsilonResidual = LowReKEpsilonResidualImpl< TypeTag, BaseLocalResidual, GetPropType< TypeTag, Properties::GridGeometry >::discMethod > |
| The local residual class for the low-Reynolds k-epsilon model. This is a convenience alias for the actual, discretization-specific local residual. More... | |
| using Dumux::LowReKEpsilonFluxVariables = typedef LowReKEpsilonFluxVariablesImpl<TypeTag, BaseFluxVariables, GetPropType<TypeTag, Properties::GridGeometry>::discMethod> |
The flux variables class for the low-Reynolds k-epsilon model. This is a convenience alias for that actual, discretization-specific flux variables.
| using Dumux::LowReKEpsilonResidual = typedef LowReKEpsilonResidualImpl<TypeTag, BaseLocalResidual, GetPropType<TypeTag, Properties::GridGeometry>::discMethod> |
The local residual class for the low-Reynolds k-epsilon model. This is a convenience alias for the actual, discretization-specific local residual.
1.9.3