#
Properties

- The
`nutUBlendedWallFunction`

boundary condition provides a wall constraint on the turbulent viscosity, i.e. `nut`

, based on velocity, i.e. `U`

using a binomial-function wall-function blending method between the viscous and inertial sublayer predictions of `nut`

for low- and high-Reynolds number turbulence models.
- The
`nutUBlendedWallFunction`

condition inherits some of the traits of the nutWallFunction boundary condition.

Required fields:

nut | Turbulent viscosity [m2/s]

#
Model equations

The model expressions ([52]):

\[
\nu_t = \max(0, \frac{u_{\tau^*}^2}{|\grad{\u}| + \zeta} -\nu_w)
\]

with

\[
u_{\tau^*} = \left( u_{\tau_{vis}}^n + u_{\tau_{log}}^n \right)^{1/n}
\]

\[
u_{\tau_{vis}} = \frac{u_p}{y^+}
\]

\[
u_{\tau_{log}} = \kappa \frac{u_p}{\ln(E y^+)}
\]

where

\( \nu_t \) | = | Turbulent viscosity [m2/s] |

\( u_{\tau^*} \) | = | Friction velocity estimation obtained by iterative means [m/s] |

\( u_{\tau_{vis}} \) | = | \(u_\tau\) computed by the viscous sublayer assumptions [m2/s] |

\( u_{\tau_{log}} \) | = | \(u_\tau\) computed by the inertial sublayer assumptions [m2/s] |

\( \nu_w \) | = | Kinematic viscosity of fluid near wall [m2/s] |

\( y^+ \) | = | Estimated wall-normal height of the cell centre in wall units |

\( \kappa \) | = | von Kármán constant [-] |

\( E \) | = | Wall roughness parameter [-] |

\( u_p \) | = | Magnitude of near wall velocity [m/s] |

\( \u \) | = | Velocity [m/s] |

\( n \) | = | Blending exponent [-] |

\( \zeta \) | = | Small value to prevent floating point exceptions |

#
Usage

Example of the boundary condition specification:

<patchName>
{
// Mandatory entries (unmodifiable)
type nutUBlendedWallFunction;
// Optional entries (unmodifiable)
n 4.0;
// Optional (inherited) entries
...
}

where the entries mean:

Property | Description | Type | Required | Default |

type | Type name: nutUBlendedWallFunction | word | yes | - |

n | Blending factor | scalar | no | 4.0 |

The inherited entries are elaborated in:

##
Notes on entries

- The full 'automatic wall treatment' description also requires use of the omegaWallFunction with the
`blending`

option `binomial`

or with the deprecated `blended`

flag set to `on`

.
- Suffers from non-exact restart since
`correctNut()`

(called through `turbulence->validate`

) returns a slightly different value every time it is called. See nutUSpaldingWallFunction.
- The inherited wall-function blending methods are not available for this wall function.

#
Further information

Tutorial

Source code