Properties🔗
- The
atmBuoyancyTurbSource
applies sources onk
and eitherepsilon
oromega
to incorporate effects of buoyancy for atmospheric boundary layer modelling. - The
atmBuoyancyTurbSource
can be applied onepsilon
oromega
based RAS turbulence models. - The
atmBuoyancyTurbSource
inherits the traits of the fvOption, andcellSetOption
.
Corrections applied to:
k
- Turbulent kinetic energy [m\(^2\)/s\(^2\)]
Corrections applied to either of the below, if exist:
epsilon
- Turbulent kinetic energy dissipation rate [m\(^2\)/s\(^3\)]
omega
- Specific dissipation rate [1/s]
Required fields:
k
- Turbulent kinetic energy [m\(^2\)/s\(^2\)]
alphat
- Kinematic turbulent thermal conductivity [m\(^2\)/s]
and either of:
epsilon
- Turbulent kinetic energy dissipation rate [m\(^2\)/s\(^3\)]
omega
- Specific dissipation rate [1/s]
Model equations🔗
Turbulent kinetic energy dissipation rate🔗
The model expressions for epsilon
([2], Eq. 5, rhs-term:3):
with (([66], Eq. 18, rhs-term:3), ([2], Eq. 5, rhs-term:3 has a typo)):
\[C_3 = (C_1 - C_2) \alpha_B + 1.0;\]and ([2], Eq. 10, with a typo of \(C_2\) instead of using \((C_2 - 1.0)\)):
\[\alpha_B = {neg}_0 (R) (1.0 - (1.0 + \frac{C_2 - 1.0}{C_2 - C_1}) L ) + pos(R) (1.0 - L)\]Mixing-length scale estimation ([59], Eq. 10.37 & p. 374) normalised by \(L_{max}\):
\[L = \frac{C_\mu^{3/4}}{L_{max}} \frac{k_o^{3/2}}{\epsilon_o}\]Gradient Richardson number ([2], Eq. 4):
\[R = - \frac{B}{G_o + \zeta}\]Buoyancy production term ([2], Eq. 7):
\[B = \beta_B \alpha_{t_o} (\grad{T_o} \cdot \vec{g})\]Specific dissipation rate🔗
The model expression for omega
(([33]) ([2], Eq. 5, rhs-term:3)):
with (([66], Eq. 19, rhs-term:3), ([2], Eq. 5, rhs-term:3 has a typo)):
\[C_3 = (\gamma - \beta) \alpha_B;\]and ([2], Eq. 10):
\[\alpha_B = {neg}_0 (R) (1.0 - (1.0 + \frac{\beta}{\beta - \gamma}) L ) + pos(R) (1.0 - L)\]Mixing-length scale estimation ([33] Eq. 3.20) normalised by \(L_{max}\):
\[L = \frac{1}{C_\mu^{1/4} L_{max}} \frac{\sqrt{k_o}}{\omega_o}\]Gradient Richardson number ([2], Eq. 4):
\[R = - \frac{B}{G_o + \zeta}\]Buoyancy production term ([2], Eq. 7):
\[B = \beta_B \alpha_{t_o} (\grad{T_o} \cdot \vec{g})\]Turbulent kinetic energy🔗
The model expression for k:
Where:
- \(S_p\)
- Source term without boundary conditions
- \(\epsilon\)
- Turbulent kinetic energy dissipation rate (Current iteration) [m2/s3]
- \(\omega\)
- Specific dissipation rate (Current iteration) [1/s]
- \(k\)
- Turbulent kinetic energy (Current iteration) [m2/s2]
- \(\epsilon_o\)
- Previous-iteration epsilon [m2/s3]
- \(\omega_o\)
- Previous-iteration omega [1/s]
- \(k_o\)
- Previous-iteration k [m2/s2]
- \(C_1\)
- Model constant (epsilon-based models) [-]
- \(C_2\)
- Model constant (epsilon-based models) [-]
- \(\beta\)
- Model constant (omega-based models) [-]
- \(\gamma\)
- Model constant (omega-based models) [-]
- \(C_3\)
- Modified model constant field [-]
- \(L\)
- Normalised mixing-length scale [-]
- \(L_{max}\)
- Maximum mixing-length scale [m]
- \(B\)
- Buoyancy production term [m2/s3]
- \(T_o\)
- Previous-iteration temperature [K]
- \(\alpha_{t_o}\)
- Previous-iteration kinematic turbulent thermal conductivity [m2/s]
- \(G_o\)
- Previous-iteration turbulent kinetic energy production contribution [m2/s2]
- \(\vec{g}\)
- Gravitational field [m/s2]
- \(C_\mu\)
- Empirical model constant [-]
- \(R\)
- Gradient Richardson number [-]
- \(\beta_B\)
- Thermal expansion coefficient [-]
- \(\alpha\)
- Phase fraction in multiphase computations, otherwise equals to 1
- \(\rho\)
- Fluid density in compressible computations, otherwise equals to 1
- \(\zeta\)
- Small value to prevent floating-point exceptions [-]
Usage🔗
Example of the fvOptions specification using constant/fvOptions
file:
atmBuoyancyTurbSource1
{
// Mandatory entries (unmodifiable)
type atmBuoyancyTurbSource;
atmBuoyancyTurbSourceCoeffs
{
// Mandatory (inherited) entries (unmodifiable)
selectionMode all;
// Optional (unmodifiable)
rho rho;
Lmax 41.575;
beta 3.3e-03;
}
// Optional (inherited) entries
...
}
where the entries mean:
Property | Description | Type | Required | Default |
---|---|---|---|---|
type | Type name: atmBuoyancyTurbSource | word | yes | - |
kAmb | Ambient value for k
|
scalar | yes | - |
rho | Name of density field | word | no | rho |
Lmax | Maximum mixing-length scale | scalar | no | 41.575 |
beta | Thermal expansion coefficient | scalar | no | 3.3e-03 |
The inherited entries are elaborated in:
-
fvOption
cellSetOption
Further information🔗
Tutorials
- $FOAM_TUTORIALS/verificationAndValidation/atmosphericModels/atmFlatTerrain
- $FOAM_TUTORIALS/verificationAndValidation/atmosphericModels/atmForestStability
Source code
History:
- Introduced in version v2006