nutUSpaldingWallFunction

Description

The nutUSpaldingWallFunction is boundary condition that provides a wall function for the turbulent viscosity (i.e. nut) based on velocity (i.e. U). Using Spalding's law gives a continuous nut profile to the wall.

$$y^+ = u^+ + \frac{1}{E} \left[exp(\kappa u^+) - 1 - \kappa u^+\, - 0.5 (\kappa u^+)^2 - \frac{1}{6} (\kappa u^+)^3\right]$$

where:

Property	Description
$y^+$	Wall-normal height of a cell centre in wall units
$u^+$	Velocity at \f$y^+\f$ in wall units
$\kappa$	von Karman constant

Usage

The condition requires entries in both the boundary and field files.

Boundary file

<patchName>
{
    type            wall;
    ...
}

Field file

<patchName>
{
    // Mandatory entries
    type            nutUSpaldingWallFunction;

    // Optional entries
    maxIter         <label>;
    tolerance       <scalar>;

    // Inherited entries
    ...
}

where:

Property	Description	Type	Required	Default
type	Type name: nutUSpaldingWallFunction	word	yes	-
maxIter	Number of Newton-Raphson iterations	label	no	10
tolerance	Convergence tolerance	scalar	no	0.0001

The inherited entries are elaborated in:

• nutWallFunctionFvPatchScalarField.H

• Suffers from non-exact restart since correctNut() (called through turbulence->validate) returns a slightly different value every time it is called. This is since the seed for the Newton-Raphson iteration uses the current value of *this (\c =nut ).
• This can be avoided by overriding the tolerance. This also switches on a pre-detection whether the current nut already satisfies the turbulence conditions and if so does not change it at all. This means that the nut only changes if it 'has really changed'. This probably should be used with a tight tolerance, to make sure to kick every iteration, e.g.

maxIter     100;
tolerance   1e-7;

Further information

Tutorial:

• airFoil2D

Source code:

• nutUSpaldingWallFunction

API:

• Foam::nutUSpaldingWallFunctionFvPatchScalarField

History: Introduced in version 2.4.0