 The open source CFD toolbox
nutUWallFunction

# Properties

• The nutUWallFunction boundary condition provides a wall constraint on the turbulent viscosity, i.e. nut, based on velocity, i.e. U, for low- and high-Reynolds number turbulence models.
• The nutUWallFunction condition inherits the traits of the nutWallFunction boundary condition.

nut  | Turbulent viscosity         [m2/s]


# Model equations

The model expressions:

$\nu_t = f_{blend}(\nu_{t_{vis}}, \nu_{t_{log}})$

with

$\nu_{t_{vis}} = 0$

$\nu_{t_{log}} = \nu_w \left( \frac{y^+ \kappa}{\ln(E y^+)} - 1 \right)$

$y^+ = \max \left( 0, \frac{\kappa_{Re} y^+_{lam}}{1 + \ln(E y^+_{lam}) } \right)$

$\kappa_{Re} = \frac{\kappa u_p y}{\nu_w}$

where

 $$\nu_t$$ = Turbulent viscosity [m2/s] $$\nu_{t_{vis}}$$ = $$\nu_t$$ computed by the viscous sublayer assumptions [m2/s] $$\nu_{t_{log}}$$ = $$\nu_t$$ 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 [-] $$C_\mu$$ = Empirical model constant [-] $$y$$ = Wall-normal height [m] $$f_{blend}$$ = Wall-function blending operator between the viscous and inertial sublayer contributions

# Usage

Example of the boundary condition specification:

<patchName>
{
// Mandatory entries (unmodifiable)
type            nutUWallFunction;

// Optional (inherited) entries
...
}


where the entries mean:

Property Description Type Required Default
type Type name: nutUWallFunction word yes -

The inherited entries are elaborated in:

## Notes on entries

• Suffers from non-exact restart since correctNut() (called through turbulence->validate) returns a slightly different value every time it is called. See nutUSpaldingWallFunction.
• Please refer to Foam::nutUWallFunctionFvPatchScalarField::calcYPlus function for the details on how $$y^+$$ is computed.
• See nutWallFunction for the wall function blending treatments.

Tutorial

Source code