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2025-06-03

VE0310 | Atmospheric Boundary Layer Test with Rough Surface

Description

This example is based on the Atmospheric Boundary Layer (ABL) test from the document of the German WTG: Fact Sheet of Committee 3 - Numerical Simulation of Wind Flows, Chapter 9.1 (see references). It is an extension of VE0309 - Atmospheric Boundary Layer Test.

VE0309 | Test of Atmospheric Boundary Layer

In this case the rough surface boundary condition is used on the bottom wall and the results are compared with the smooth surface. In the following article, the development of a velocity, turbulence kinetic energy, and turbulence dissipation rate are shown for Terrain Category 0 defined in EN 1991-1-4. A vertically anisotropic turbulence acc. to Chapter 6.3.1 and RANS k-ω SST turbulence model is used.

Fluid Properties	Kinematic Viscosity	ν	1.500e-5	m²/s
Fluid Properties	Density	ρ	1.250	kg/m³
Wind Tunnel	Length	D_x	800.000	m
	Width	D_y	80.000	m
	Height	D_z	300.000	m
Calculation Parameters	Reference Velocity	u_ref	20.000	m/s
	Reference Height	z_ref	10.000	m
	von Kármán Constant	κ	0.410
	Turbulence Viscosity Constant	C_μ	0.090
Roughness Parameters	Aerodynamic Surface Rougness Length	z₀	0.003	m
Roughness Parameters	Roughness Constant	C_s	0.500

Testing of the atmospheric boundary layer conducted in a wind tunnel without any obstructions. Focus on airflow examination.

Atmospheric Boundary Layer Test

Analytical Solution

An analytical solution is not available. The example provides an overview of the chosen quantity field development in an empty wind tunnel with rough surface on the bottom wall.

The wind speed profile is calculated from the following equation:

u (z) = \frac{u_{*}}{κ} \ln (\frac{z + z_{0}}{z_{0}})

z₀	Roughness length

Wind Speed Profile

where u_* is the friction velocity, defined as:

u_{*} = \frac{u_{ref} κ}{\ln (\frac{z_{ref} + z_{0}}{z_{0}})}

Friction Velocity

The turbulence k profile is defined according to the following equation:

k (z) = \frac{u_{*}^{2}}{\sqrt{C_{μ}}}

C_μ	Parameter of the turbulence model

Turbulence k Profile

The turbulence ω profile is calculated according to the following equation:

ω (z) = \frac{u_{*}}{κ \sqrt{C_{μ}}} \frac{1}{z + z_{0}}

Turbulence Omega Profile

For the rough surface equivalent, the sand-grain roughness height has to be calculated according to the following formula:

k_{s} = \frac{9.793 z_{0}}{C_{s}}

Equivalent Sand-Grain Roughness Height

RWIND Simulation Settings

Modeled in RWIND 3.03.0220
Steady flow simulation type
Mesh density is 28%: 2,482,465 cells
Number of tunnel boundary layers is 10
The height of the first cell at the bottom is 0.046 m
y+ ranges from 800 to 1000
RANS k-ω SST turbulence model
Inlet boundary condition - ABL v, k, ω; zero pressure gradient
Tunnel bottom - no-slip boundary condition with wall function for wall constraint on the turbulent viscosity (sand-grain roughness) - nutkRoughWallFunction in OpenFOAM
Tunnel walls and top - slip boundary condition
Outlet boundary condition - zero pressure; zero velocity gradient

Results

The comparison of the air flow behavior (development of the velocity, turbulence kinetic energy and turbulence dissipation rate) with rough and smooth surfaces is shown in the following plot.

Analysis comparing wind flow over a rough and smooth bottom surface using terrain flow techniques in a wind tunnel.

Terrain Flow Analysis – Wind Tunnel Comparison for Rough and Smooth Bottom Surface

RWIND 3 results - Velocity field (terrain category I)

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Verification Example 0310 | 01

References

Windtechnological Society WTG eV (2023). WTG Code of Practice M3 - Numerical Simulation of Wind Flows. Aachen: Sgt.
OpenFOAM, "nutkRoughWallFunction," OpenFOAM User Guide, [online].

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