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

• atmFlatTerrain
• atmForestStability

Source code

• atmBuoyancyTurbSource

History: Introduced in version v2006