The open source CFD toolbox
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 [m2/s3]
omega     | Specific dissipation rate                 [1/s]


epsilon   | Turbulent kinetic energy dissipation rate [m2/s3]
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 ([3], 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 ([61], 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 ([36], Eq. 3.34):

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

Mixing-length scale estimation ([36], 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:

# Further information

Tutorials

Source code

History

• Introduced in version v2006