 The open source CFD toolbox
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                  [m2/s2]


Corrections applied to either of the below, if exist:

epsilon   | Turbulent kinetic energy dissipation rate [m2/s3]
omega     | Specific dissipation rate                 [1/s]


k             | Turbulent kinetic energy                   [m2/s2]
epsilon/omega | Dissipation rate OR Specific dissipation rate [m2/s3]/[1/s]
T             | Temperature                                [K]
alphat        | Kinematic turbulent thermal conductivity   [m2/s]


# Model equations

## Turbulent kinetic energy dissipation rate

The model expressions for epsilon (, Eq. 5, rhs-term:3):

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

with ((, Eq. 18, rhs-term:3), (, Eq. 5, rhs-term:3 has a typo)):

$C_3 = (C_1 - C_2) \alpha_B + 1.0;$

and (, 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 (, 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 (, Eq. 4):

$R = - \frac{B}{G_o + \zeta}$

Buoyancy production term (, Eq. 7):

$B = \beta_B \alpha_{t_o} (\grad{T_o} \cdot \vec{g})$

## Specific dissipation rate

The model expression for omega (() (, Eq. 5, rhs-term:3)):

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

with ((, Eq. 19, rhs-term:3), (, Eq. 5, rhs-term:3 has a typo)):

$C_3 = (\gamma - \beta) \alpha_B;$

and (, 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 ( 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 (, Eq. 4):

$R = - \frac{B}{G_o + \zeta}$

Buoyancy production term (, 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:

# Further information

Tutorials

Source code

History

• Introduced in version v2006