OpenFOAM Documentation - atmBuoyancyTurbSource

Properties🔗

The atmBuoyancyTurbSource applies sources on k and either epsilon or omega to incorporate effects of buoyancy for atmospheric boundary layer modelling.
The atmBuoyancyTurbSource can be applied on epsilon or omega based RAS turbulence models.
The atmBuoyancyTurbSource inherits the traits of the fvOption, and cellSetOption.

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):

\[S_p = \alpha \rho \frac{C_3 B}{k_o} \epsilon\]

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)):

\[S_p = \alpha \rho \frac{C_3 B}{k_o} \omega\]

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:

\[S_p = \alpha \rho \frac{B}{k_o} k\]

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

Source code

$FOAM_SRC/atmosphericModels/fvOptions/atmBuoyancyTurbSource

History:

Introduced in version v2006

Open∇FOAM

atmBuoyancyTurbSource