The open source CFD toolbox
nutWallFunction

# Properties

• 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.

# Model equations

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 stepwise switch (discontinuous) method

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 switch (discontinuous) method

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 binomial blending (continuous) method

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 exponential blending (continuous) method

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 $$\Gamma$$ = $$0.01 (y^+)^4 / (1.0 + 5.0 y^+)$$

# Usage

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