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nutUBlendedWallFunction

# 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.

nut  | Turbulent viscosity         [m2/s]


# Model equations

The model expressions ():

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

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.

Tutorial

Source code