The open source CFD toolbox
kLowReWallFunction

Note
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# Properties

• The kLowReWallFunction boundary condition provides a wall constraint on the turbulent kinetic energy, i.e. k, for low- and high-Reynolds number turbulence models.
• The kLowReWallFunction condition inherits the traits of the fixedValue boundary condition.

k    | Turbulent kinetic energy    [m2/s2]


# Model equations

The model expressions for k for viscous and inertial sublayers are switched in a stepwise manner:

$k = \max(k_{log} u_\tau^2, \zeta) \qquad if \quad y^+ > y^+_{lam}$

$k = \max(k_{vis} u_\tau^2, \zeta) \qquad if \quad y^+ <= y^+_{lam}$

with

$k_{log} = \frac{\ln (y^+) C_k}{\kappa} + B_k$

$k = \frac{2400 C_f}{C_{eps2}^2}$

$y^+ = \frac{u_\tau y}{\nu_w}$

$u_\tau = C_\mu^{1/4} \sqrt{k}$

$C_f = \frac{1}{(y^+ + C)^2} + \frac{2 y^+}{C^3} - \frac{1}{C^2}$

where

 $$k$$ = Turbulent kinetic energy [m2/s2] $$k_{vis}$$ = k prediction in the viscous sublayer $$k_{log}$$ = k prediction in the inertial sublayer $$y$$ = Wall-normal height [m] $$y^+$$ = Estimated wall-normal height of the cell centre in wall units $$y^+_{lam}$$ = Estimated intersection of the viscous and inertial sublayers in wall units $$u_\tau$$ = Friction velocity [m/s] $$\zeta$$ = Small value to prevent floating point exceptions $$C_\mu$$ = Empirical model constant [-] $$\nu_w$$ = Kinematic viscosity of fluid near wall [m2/s]

# Usage

Example of the boundary condition specification:

<patchName>
{
// Mandatory entries (unmodifiable)
type            kLowReWallFunction;

// Optional entries (unmodifiable)
Ceps2           1.9;
Ck              -0.416;
Bk              8.366;
C               11.0;

// Optional (inherited) entries
...
}


where the entries mean:

Property Description Type Required Default
type Type name: kLowReWallFunction word yes -
Ceps2 Model coefficient scalar no 1.9
Ck Model coefficient scalar no -0.416
Bk Model coefficient scalar no 8.366
C Model coefficient scalar no 11.0

The inherited entries are elaborated in:

• fixedValueFvPatchField
• nutWallFunctionFvPatchScalarField

## Notes on entries

• The coefficients Cmu, kappa, and E are obtained from the specified nutWallFunction in order to ensure that each patch possesses the same set of values for these coefficients.

Source code