atmLengthScaleTurbSource

Properties

• The atmLengthScaleTurbSource applies sources on either epsilon or omega to correct mixing-length scale estimations for atmospheric boundary layer modelling.
• The atmLengthScaleTurbSource can be applied on epsilon or omega based RAS turbulence models.
• The atmLengthScaleTurbSource inherits the traits of the fvOption, and cellSetOption.

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, either of the below:

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 expression for epsilon:

$$S_p = \alpha \rho C_1^* \frac{G_o}{\nu} C_\mu k_o$$

with (4, Eq. 16 wherein the exponentiation n is not present. n is an ad-hoc implementation):

$$C_1^* = (C_2 - C_1) \left( \frac{L}{L_{max}} \right)^n$$

Mixing-length scale estimation (59, Eq. 10.37 & p. 374):

$$L = C_\mu^{3/4} \frac{k_o^{3/2}}{\epsilon_o}$$

Specific dissipation rate

The model expression for omega:

$$S_p = \alpha \rho \gamma^* \frac{G_o}{\nu}$$

with (33, Eq. 3.34):

$$\gamma^* = \left( \gamma - \beta \right) \left( \frac{L}{L_{max}} \right)^n$$

Mixing-length scale estimation (33, Eq. 3.20):

$$L = \frac{\sqrt{k}}{C_\mu^{1/4} \omega_o}$$

Where:

$S_p$ : Source term without boundary conditions

$\epsilon_o$ : Previous-iteration epsilon [m2/s3]

$\omega_o$ : Previous-iteration omega [1/s]

$k_o$ : Previous-iteration k [m2/s2]

$G_o$ : Previous-iteration k-production contribution [m2/s3]

$C_1$ : Model constant (epsilon-based models) [-]

$C_2$ : Model constant (epsilon-based models) [-]

$C_1^*$ : Modified model constant field (epsilon-based models) [-]

$C_\mu$ : Empirical model constant [-]

$\gamma$ : Model constant (omega-based models) [-]

$\beta$ : Model constant (omega-based models) [-]

$\gamma^*$ : Modified model constant field (omega-based models) [-]

$\nu$ : Kinematic viscosity of fluid [m2/s]

$L$ : Mixing-length scale [m]

$L_{max}$ : Maximum mixing-length scale [m]

$\alpha$ : Phase fraction in multiphase computations, otherwise equals to 1

$\rho$ : Fluid density in compressible computations, otherwise equals to 1

Usage

Example of the fvOptions specification using constant/fvOptions file:

atmLengthScaleTurbSource1
{
    // Mandatory entries (unmodifiable)
    type                  atmLengthScaleTurbSource;

    atmLengthScaleTurbSourceCoeffs
    {
        // Mandatory (inherited) entries (unmodifiable)
        selectionMode    all;

        // Optional entries (unmodifiable)
        rho              rho;
        Lmax             41.575;
        n                3.0;
    }

    // Optional (inherited) entries
    ...
}

where the entries mean:

Property	Description	Type	Required	Default
type	Type name: atmLengthScaleTurbSource	word	yes	-
rho	Name of density field	word	no	rho
Lmax	Maximum mixing-length scale	scalar	no	41.575
n	Mixing-length scale exponent	scalar	no	3.0

The inherited entries are elaborated in:

• fvOption
  • cellSetOption

Further information

Tutorials

• atmFlatTerrain
• atmForestStability

Source code

• atmLengthScaleTurbSource

History: Introduced in version v2006