atmAlphatkWallFunction
boundary condition provides a wall constraint on the kinematic turbulent thermal conductivity, i.e. alphat
, for atmospheric boundary layer modelling.atmAlphatkWallFunction
condition inherits the traits of the fixedValue boundary condition.Required fields:
alphat | Kinematic turbulent thermal conductivity [m2/s]
The boundary condition expression is:
\[ \alpha_t = max (\alpha_t^\prime, 0.01) \]
with
\[ \alpha_t^\prime = \frac{u^* \kappa y}{{Pr}_t \ln \left(max(E^\prime, 1 + 10^{-4} )\right)} + \frac{\nu_w}{Pr} \]
\[ u^* = C_\mu^{1/4} \sqrt{k} \]
\[ E^\prime = \frac{y + z_0}{z_0 + 10^{-4}} \]
where
\( \alpha_t \) | = | Kinematic turbulent thermal conductivity [m2/s] |
\( u^* \) | = | Friction velocity [m/s] |
\( \kappa \) | = | von Kármán constant [-] |
\( y \) | = | Ground-normal height [m] |
\( Pr \) | = | Molecular Prandtl number [-] |
\( {Pr}_t \) | = | Turbulent Prandtl number [-] |
\( \nu_w \) | = | Kinematic viscosity of fluid in the wall cell [m2/s] |
\( C_\mu \) | = | Empirical model constant [-] |
\( k \) | = | Turbulent kinetic energy [m2/s2] |
\( z_0 \) | = | Surface roughness length [m] |
Example of the boundary condition specification:
<patchName> { // Mandatory entries (unmodifiable) type atmAlphatkWallFunction; // Mandatory entries (runtime modifiable) Pr 0.90; Prt uniform 0.85; z0 uniform 0.001; // Optional entries (unmodifiable) Cmu 0.09; kappa 0.41; // Optional (inherited) entries value uniform 0; }
where the entries mean:
Property | Description | Type | Required | Default |
---|---|---|---|---|
type | Type name: atmAlphatkWallFunction | word | yes | - |
Pr | Molecular Prandtl number | TimeFunction1<scalar> | yes | - |
Prt | Turbulent Prandtl number | PatchFunction1<scalar> | yes | - |
z0 | Surface roughness length [m] | PatchFunction1<scalar> | yes | - |
Cmu | Empirical model constant | scalar | no | 0.09 |
kappa | von Kármán constant | scalar | no | 0.41 |
The inherited entries are elaborated in:
Tutorial:
Source code
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