atmBuoyancyTurbSource
applies sources on k
and either epsilon
or omega
to incorporate effects of buoyancy for atmospheric boundary layer modelling.atmBuoyancyTurbSource
can be applied on epsilon
or omega
based RAS turbulence models.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]
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):
\[ B = \beta_B \alpha_{t_o} (\grad{T_o} \cdot \vec{g}) \]
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):
\[ B = \beta_B \alpha_{t_o} (\grad{T_o} \cdot \vec{g}) \]
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 [-] |
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:
cellSetOption
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