nutWallFunction is a base class that parents the derived boundary conditions which provide a wall constraint on various fields, such as turbulent viscosity, i.e. nut, or turbulent kinetic energy dissipation rate, i.e. epsilon, for low- and high-Reynolds number turbulence models.nutWallFunction condition inherits the traits of the fixedValue boundary condition.The nut 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)
The viscous and inertial sublayer estimations of nut are switched between each other depending on the \(y^+\) value of the point of interrogation.
\[ \nu_t = \nu_{t_{vis}} \qquad if \quad y^+ <= y^+_{lam} \]
\[ \nu_t = \nu_{t_{log}} \qquad if \quad y^+ > y^+_{lam} \]
where
| \( \nu_t \) | = | Turbulent viscosity at \(y^+\) [m2/s] |
| \( \nu_{t_{vis}} \) | = | \(\nu_t\) computed by the viscous sublayer assumptions [m2/s] |
| \( \nu_{t_{log}} \) | = | \(\nu_t\) computed by the viscous sublayer assumptions [m2/s] |
| \( y^+ \) | = | 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 nut is set as the nut estimation at \(y^+\) ([62], Eq. 27).
\[ \nu_t = \max( \nu_{t_{vis}}, \nu_{t_{log}} ) \]
The nut estimation at \(y^+\) is blended between the viscous and intertial sublayer estimations by using a binomial function ([51], Eqs. 15-16).
\[ \nu_t = ( (\nu_{t_{vis}} )^n + (\nu_{t_{log}} )^n)^{1/n} \]
where
| \( n \) | = | Binomial blending exponent |
The nut estimation at \(y^+\) is blended between the viscous and intertial sublayer estimations by using an exponential function ([62], Eq. 32).
\[ \nu_t = \nu_{t_{vis}} \exp[-\Gamma] + \nu_{t_{log}} \exp[-1/\Gamma] \]
where ([62], Eq. 31)
| \( \Gamma \) | = | Blending expression |
| \( \Gamma \) | = | \(0.01 (y^+)^4 / (1.0 + 5.0 y^+)\) |
Example of the boundary condition specification:
<patchName>
{
// Mandatory and other optional entries
...
// Optional (inherited) entries
Cmu 0.09;
kappa 0.41;
E 9.8;
blending stepwise;
n 4.0;
U U;
// Optional (inherited) entries
...
}
where the entries mean:
| Property | Description | Type | Required | Default |
|---|---|---|---|---|
| Cmu | Empirical model coefficient | scalar | no | 0.09 |
| kappa | von Kármán constant | scalar | no | 0.41 |
| E | Wall roughness parameter | scalar | no | 9.8 |
| blending | Viscous/inertial sublayer blending | word | no | stepwise |
| n | Binomial blending exponent | scalar | no | 2.0 |
| U | Name of the velocity field | word | no | U |
The inherited entries are elaborated in:
Options for the blending entry:
stepwise | Stepwise switch (discontinuous) max | Maximum value switch (discontinuous) binomial | Binomial blending (smooth) exponential | Exponential blending (smooth)
Source code
1.9.5