nutWallFunction

- The class
`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. - The class is not an executable itself, yet a provider for common entries to its derived boundary conditions.
- The
`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