# FAQ 004391 EN

26 March 2020

004391

## Does RWIND Simulation apply a boundary layer model?

In RWIND Simulation, each model surface in the wind flow is treated as a "smooth" wall. This definition results in a boundary layer in the areas around the flow close to the walls, which has an influence on the velocity profile perpendicular to the wall depending on the air viscosity. This boundary layer is created in RWIND Simulation according to the so-called "wall law." This law describes the velocity profile perpendicular to the wall and can be represented by the dimensionless variables u+ and y+.

Dimensionless variable u+:
$\mathrm u^+=\frac{\mathrm U}{{\mathrm u}_{\mathrm\tau}}$
where
U is the velocity on the wall,
uτ is the frictional velocity.

Dimensionless variable y+:
$\mathrm y^+=\frac{{\mathrm u}_{\mathrm\tau}\cdot\mathrm y}{\mathrm\nu}$
where
y is the wall distance,
uτ is the frictional velocity,
ν is the kinematic viscosity of the air.

Using the friction velocity uτ:
${\mathrm u}_{\mathrm\tau}=\sqrt{\frac{{\mathrm\tau}_{\mathrm w}}{\mathrm\rho}}$
where
τw is the shear stress,
ρ is the air density.

By describing the boundary layer model in the viscous partial layer directly next to the wall
$\mathrm u^+=\mathrm y^+$

and in the subsequent logarithmic layer
$\mathrm u^+=\frac1{\mathrm\kappa}\cdot\ln\;\mathrm y^++\mathrm C$

you obtain the following velocity distribution,

where
κ is the Kármán constant (κ = 0.41 for the simulation of a smooth wall),
C is the constant (C = 5 for the simulation of a smooth wall).

To ensure that the solution process is relatively fast and robust, the program specifies the corresponding boundary layer model directly in the first cell next to the model surface. The remaining part of the boundary layer results from the solution of the globally applied Navier-Stokes equations.

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• Updated 5 April 2021

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