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]

Required fields:

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 ([1], Eq. 5, rhs-term:3):

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

with (([70], Eq. 18, rhs-term:3), ([1], Eq. 5, rhs-term:3 has a typo)):

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

and ([1], 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 ([61], 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 ([1], Eq. 4):

\[ R = - \frac{B}{G_o + \zeta} \]

Buoyancy production term ([1], Eq. 7):

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

Specific dissipation rate

The model expression for omega (([36]) ([1], Eq. 5, rhs-term:3)):

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

with (([70], Eq. 19, rhs-term:3), ([1], Eq. 5, rhs-term:3 has a typo)):

\[ C_3 = (\gamma - \beta) \alpha_B; \]

and ([1], 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 ([36] 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 ([1], Eq. 4):

\[ R = - \frac{B}{G_o + \zeta} \]

Buoyancy production term ([1], 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