omegaWallFunction
boundary condition provides a wall constraint on the specific dissipation rate, i.e. omega
, and the turbulent kinetic energy production contribution, i.e. G
, for low- and high-Reynolds number turbulence models.omegaWallFunction
condition inherits the traits of the fixedValue boundary condition.Required fields:
omega | Specific dissipation rate [1/s]
The model expressions:
\[ \omega_{vis} = \frac{6 \nu_w}{\beta_1 y^2} \]
\[ \omega_{log} = \frac{\sqrt{k}}{C_\mu \kappa y} \]
\[ G = w (\nu_{t_w} + \nu_w) |\vec{n} \cdot (\grad{\u})_f | C_\mu^{1/4} \frac{\sqrt{k}}{\kappa y} \qquad if \quad y^+ > y^+_{lam} \]
where
\( \omega \) | = | Specific dissipation rate [1/s] |
\( \omega_{vis} \) | = | \(\omega\) computed by the viscous sublayer assumptions [1/s] |
\( \omega_{log} \) | = | \(\omega\) computed by the inertial sublayer assumptions [1/s] |
\( w \) | = | Cell-corner weights [-] |
\( k \) | = | Turbulent kinetic energy [m2/s2] |
\( y \) | = | Wall-normal distance [m] |
\( C_\mu \) | = | Empirical model constant [-] |
\( \nu_w \) | = | Kinematic viscosity of fluid near wall [m2/s] |
\( \nu_{t_w} \) | = | Turbulent viscosity near wall [m2/s] |
\( \vec{n} \) | = | Face unit normal vector [-] |
\( \u \) | = | Velocity [m/s] |
\( \kappa \) | = | von Kármán constant [-] |
The omega
predictions for the viscous and inertial sublayers can be blended by six different methods:
stepwise | Stepwise switch (discontinuous) max | Maximum value switch (discontinuous) binomial2 | Binomial blending (smooth) n = 2 binomial | Binomial blending (smooth) exponential | Exponential blending (smooth) tanh | Tanh blending (smooth)
G
predictions for the viscous and inertial sublayers are always blended in a stepwise manner, and G
below \(y^+_{lam}\) (i.e. in the viscous sublayer) is presumed to be zero.
The viscous and inertial sublayer estimations of omega
are switched between each other depending on the \(y^+\) value of the point of interrogation.
\[ \omega = \omega_{vis} \qquad if \quad y^+ <= y^+_{lam} \]
\[ \omega = \omega_{log} \qquad if \quad y^+ > y^+_{lam} \]
where
\( \omega \) | = | \(\omega\) at \(y^+\) |
\( y^+ \) | = | Estimated wall-normal distance of the cell centre in wall units |
\( y^+_{lam} \) | = | Estimated intersection of the viscous and inertial sublayers in wall units |
The maximum value of the viscous and inertial sublayer estimations of omega
is set as the omega
estimation at \(y^+\) ([62], Eq. 27).
\[ \omega = \max(\omega_{vis}, \omega_{log}) \]
The omega
estimation at \(y^+\) is blended between the viscous and intertial sublayer estimations by using a binomial function ([51], Eq. 15). This method is a special case of the following binomial
method in order to ensure bitwise regression.
\[ \omega = ((\omega_{vis})^2 + (\omega_{log})^2)^{1/2} \]
The omega
estimation at \(y^+\) is blended between the viscous and intertial sublayer estimations by using a binomial function ([51], Eqs. 15-16).
\[ \omega = ((\omega_{vis})^n + (\omega_{log})^n)^{1/n} \]
where
\( n \) | = | Binomial blending exponent |
The omega
estimation at \(y^+\) is blended between the viscous and intertial sublayer estimations by using an exponential function ([62], Eq. 32).
\[ \omega = \omega_{vis} \exp[-\Gamma] +\omega_{log} \exp[-1/\Gamma] \]
where ([62], Eq. 31)
\( \Gamma \) | = | Blending expression |
\( \Gamma \) | = | \(0.01 (y^+)^4 / (1.0 + 5.0 y^+)\) |
The omega
estimation at \(y^+\) is blended between the viscous and intertial sublayer estimations by using a tanh function ([33], Eqs. 33-34).
\[ \omega = \phi \omega_1 + (1 - \phi) \omega_2 \]
with
\[ \phi = tanh \left( \left(\frac{y^+}{10}\right)^4 \right) \]
\[ \omega_1 = \omega_{vis} + \omega_{log} \]
\[ \omega_2 = \left( (\omega_{vis})^{1.2} + (\omega_{log})^{1.2} \right)^{1/1.2} \]
Example of the boundary condition specification:
<patchName> { // Mandatory entries (unmodifiable) type omegaWallFunction; // Optional entries (unmodifiable) beta1 0.075; blending binomial2; n 2.0; // Optional (inherited) entries ... }
where the entries mean:
Property | Description | Type | Required | Default |
---|---|---|---|---|
type | Type name: omegaWallFunction | word | yes | - |
beta1 | Model coefficient | scalar | no | 0.075 |
blending | Viscous/inertial sublayer blending method | word | no | stepwise |
n | Binomial blending exponent | scalar | no | 2.0 |
The inherited entries are elaborated in:
fixedValueFvPatchField
nutWallFunctionFvPatchScalarField
Options for the blending
entry:
stepwise | Stepwise switch (discontinuous) max | Maximum value switch (discontinuous) binomial2 | Binomial blending (smooth) n = 2 binomial | Binomial blending (smooth) exponential | Exponential blending (smooth) tanh | Tanh blending (smooth)
Cmu
, kappa
, and E
are obtained from the specified nutWallFunction
in order to ensure that each patch possesses the same set of values for these coefficients.binomial2
and binomial
blending methods exist at the same time is to ensure the bitwise regression with the previous versions since binomial2
and binomial
with n=2
will yield slightly different output due to the miniscule differences in the implementation of the basic functions (i.e. pow
, sqrt
, sqr
).Tutorial
Source code