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:

fixedValue

Options for the blending entry:

stepwise    | Stepwise switch (discontinuous)
max         | Maximum value switch (discontinuous)
binomial    | Binomial blending (smooth)
exponential | Exponential blending (smooth)

Further information

Source code

Foam::nutWallFunctionFvPatchScalarField

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