nutUBlendedWallFunction

Table of Contents

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