atmNutWallFunction

Description

The atmNutWallFunction is a boundary condition that provides a wall constraint on the turbulent viscosity (i.e. nut) based on the turbulent kinetic energy (i.e. k) and velocity (i.e. U) for atmospheric boundary layer modelling.

The governing equation of the boundary condition:

$$\tau_w = {U^*_u} {U^*_k}$$

with:

$${U^*_u} = \frac{\kappa U_w}{ln(z_p / z_0)}$$ $${U^*_k} = C_{\mu}^{1/4} \sqrt{k}$$

where:

Property	Description
$\tau_w$	Wall shear stress
$U^*_u$	Local friction velocity based on near-ground velocity
$U^*_k$	Local friction velocity based on near-ground k
$\kappa$	von Karman constant
$U_w$	Near-ground velocity
$z_p$	Vertical coordinate
$z_0$	Surface roughness length [m]
$C_mu$	Empirical model constant
$k$	Turbulent kinetic energy

References

• Theoretical expressions (tags:RH, SBJM, SM):

Richards, P. J., & Hoxey, R. P. (1993).
Appropriate boundary conditions for computational wind
engineering models using the k-ε turbulence model.
In Computational Wind Engineering 1 (pp. 145-153).
DOI:10.1016/B978-0-444-81688-7.50018-8

Sørensen, N. N., Bechmann, A., Johansen, J., Myllerup, L.,
Botha, P., Vinther, S., & Nielsen, B. S. (2007).
Identification of severe wind conditions using
a Reynolds Averaged Navier-Stokes solver.
In Journal of Physics: Conference
series (Vol. 75, No. 1, p. 012053).
DOI:10.1088/1742-6596/75/1/012053

Sumner, J., & Masson, C. (2012).
k−ε simulations of the neutral atmospheric boundary layer:
analysis and correction of discretization errors on practical grids.
International journal for numerical
methods in fluids, 70(6), 724-741.
DOI:10.1002/fld.2709

Usage

The condition requires entries in both the boundary and field files.

Boundary file

<patchName>
{
    type            patch;
    ...
}

Field file

<patchName>
{
    // Mandatory entries
    type            atmNutWallFunction;
    z0Min           <scalar>;
    z0              <PatchFunction1<scalar>>;

    // Inherited entries
    ...
}

where:

Property	Description	Type	Required	Default
type	Type name: atmNutWallFunction	word	yes	-
z0Min	Minimum surface roughness length [m]	scalar	yes	-
z0	Surface roughness length [m]	PatchFunction1<scalar>	yes	-

The inherited entries are elaborated in:

• nutkWallFunctionFvPatchScalarField.H
• PatchFunction1.H

Further information

Tutorial:

• N/A

Source code:

• atmNutWallFunction

API:

• Foam::atmNutWallFunctionFvPatchScalarField

History: Introduced in version v2006