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005985

Mahyar Kazemian, M.Sc.

2025-03-10

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Overview

A. General Information

B. Wind Flows, Wind Effects, and Numerical Simulation

C. WTG Guideline M3 for Numerical Simulation of Wind Flows

C1. Purpose and Content of the Guideline
C2. Task Assignment for Required CFD Modeling
- C2.1 Assignment of Calculation Methods to Investigation Requirements
- C2.2 Requirements for Numerical Investigations

D. Notes on CFD Modeling

E. Practical Use of Results of Computational Fluid Dynamics Simulation

F. Documentation

G. Quality Assurance

H. Examples

I. References

H1.4. Atmospheric Boundary Layer Test

Description

This example is based on the Atmospheric Boundary Layer (ABL) test from the document of German WTG: Fact Sheet of Committee 3 - Numerical Simulation of Wind Flows, Chapter 9.1 (see references). Before each numerical simulation, it should be checked whether the atmospheric boundary layer defined at the inflow reaches the structure by testing its development in an empty tunnel. This affects not only the distribution of the velocities, but also the turbulent quantities. The test must be carried out for both steady (RANS) and transient (URANS, LES) calculations. In the following article, the development of a velocity field, turbulence kinetic energy field, and turbulence dissipation rate field is shown for the four terrain categories I to IV defined in the EN 1991-1-4. A vertically anisotropic turbulence acc. to Chapter 6.3.1 and the 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

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.

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 friction velocity, defined as:

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

Friction Velocity

Turbulence k profile is defined according following equation:

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

C_μ	Parameter of the turbulence model

Turbulence k Profile

Turbulence ω profile is defined calculated according to the following equation:

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

Turbulence Omega Profile

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 1,000
RANS k-ω SST turbulence model
Inlet boundary condition - ABL v, k, ω zero pressure gradient
Tunnel bottom - no-slip boundary condition
Tunnel walls and top - slip boundary condition
Outlet boundary condition - zero pressure; zero velocity gradient

Results

The validation metric is calculated according to WTG: Fact Sheet of Committee 3 - Numerical Simulation of Wind Flows, Chapter 5.3.2 (see references). At first, the value of the hit rate parameter q for the mean value of the pressure coefficient is calculated. The relative deviation W_rel is considered.

\begin{matrix} q = \frac{n}{N} = \frac{1}{N} \cdot \sum_{i = 1}^{N} n_{i} \\ n_{i} = \{\begin{cases} 1, & if |\frac{P_{i} - O_{i}}{O_{i}}| \leq W_{rel} \\ 0, & else \end{cases} \end{matrix}

N	Total number of data points
n_i	Indicator function (1 if prediction is “correct”, 0 otherwise)
P_i	Predicted value
O_i	Reference value
W_rel	Allowed relative deviation

Validation Metric According to WTG

Alternatively, the relative mean square error e² can also be calculated according to the following formula.

e^{2} = \frac{\sum_{i = 1}^{N} {(P_{i} - O_{i})}^{2}}{\sum_{i = 1}^{N} O_{i}^{2}}

Deviation Form of the Mean Error

The desired values of the hit rate parameter q are more than 90% and the relative mean square error should be lower than 0.01. From the following table, it is clear that the comparison of the input velocity and the velocity in the tunnel (x = 0 m) meets the requirements.