epsilonWallFunction
boundary condition provides a wall constraint on the turbulent kinetic energy dissipation rate, i.e. epsilon
, and the turbulent kinetic energy production contribution, i.e. G
, for low- and high-Reynolds number turbulence models.epsilonWallFunction
condition inherits the traits of the fixedValue boundary condition.Required fields:
epsilon | Turbulent kinetic energy dissipation rate [m2/s3]
The model expressions:
\[ \epsilon_{vis} = 2 w k \frac{\nu_w}{y^2} \]
\[ \epsilon_{log} = w C_\mu \frac{k^{3/2}}{\nu_{t_w} y} \]
\[ G = w (\nu_{t_w} + \nu_w) |\vec{n} \cdot (\grad{\u})_f | C_\mu^{1/4} \frac{\sqrt{k}}{\kappa y} \qquad if \quad y^+ >= y^+_{lam} \]
where
\( \epsilon \) | = | Turbulent kinetic energy dissipation rate [m2/s3] |
\( \epsilon_{vis} \) | = | \(\epsilon\) computed by the viscous sublayer assumptions [m2/s3] |
\( \epsilon_{log} \) | = | \(\epsilon\) computed by the inertial sublayer assumptions [m2/s3] |
\( w \) | = | Cell-corner weights [-] |
\( k \) | = | Turbulent kinetic energy [m2/s2] |
\( \nu_w \) | = | Kinematic viscosity of fluid near wall [m2/s] |
\( y \) | = | Wall-normal distance [m] |
\( C_\mu \) | = | Empirical model constant [-] |
\( \nu_{t_w} \) | = | Turbulent viscosity near wall [m2/s] |
\( \vec{n} \) | = | Face unit normal vector [-] |
\( \u \) | = | Velocity [m/s] |
\( \kappa \) | = | von Kármán constant [-] |
The epsilon
predictions for the viscous and inertial sublayers can be blended by four different methods:
stepwise | Stepwise switch (discontinuous) max | Maximum value switch (discontinuous) binomial | Binomial blending (smooth) exponential | Exponential 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 epsilon
are switched between each other depending on the \(y^+\) value of the point of interrogation.
\[ \epsilon = \epsilon_{vis} \qquad if \quad y^+ < y^+_{lam} \]
\[ \epsilon = \epsilon_{log} \qquad if \quad y^+ >= y^+_{lam} \]
where
\( \epsilon \) | = | \(\epsilon\) 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 epsilon
is set as the epsilon
estimation at \(y^+\) ([62], Eq. 27).
\[ \epsilon = \max(\epsilon_{vis}, \epsilon_{log}) \]
The epsilon
estimation at \(y^+\) is blended between the viscous and intertial sublayer estimations by using a binomial function ([51], Eqs. 15-16).
\[ \epsilon = ((\epsilon_{vis})^n + (\epsilon_{log})^n)^{1/n} \]
where
\( n \) | = | Binomial blending exponent |
The epsilon
estimation at \(y^+\) is blended between the viscous and intertial sublayer estimations by using an exponential function ([62], Eq. 32).
\[ \epsilon = \epsilon_{vis} \exp[-\Gamma] +\epsilon_{log} \exp[-1/\Gamma] \]
where ([62], p. 193)
\( \Gamma_\epsilon \) | = | \(\Gamma = 0.001 (y^+)^4 / (1.0 + y^+)\) |
\( \Gamma_G \) | = | \(\Gamma = 0.01 (y^+)^4 / (1.0 + 5.0 y^+)\) |
\( \Gamma_\epsilon \) | = | Blending expression for \(\epsilon\) |
\( \Gamma_G \) | = | Blending expression for \(G\) |
Example of the boundary condition specification:
<patchName> { // Mandatory entries (unmodifiable) type epsilonWallFunction; // Optional entries (unmodifiable) lowReCorrection false; blending stepwise; n 2.0; // Optional (inherited) entries ... }
where the entries mean:
Property | Description | Type | Required | Default |
---|---|---|---|---|
type | Type name: epsilonWallFunction | word | yes | - |
lowReCorrection | Flag: apply low-Re correction | bool | no | false |
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) binomial | Binomial blending (smooth) exponential | Exponential 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.lowReCorrection
operates with only stepwise
blending treatment to ensure the backward compatibility.lowReCorrection
is on
, stepwise
blending treatment is fully active.lowReCorrection
is off
, only the inertial sublayer prediction is used in the wall function, hence high-Re mode operation.Tutorial
Source code
History