User Story
In this example, we are going to calculate the averaged wind pressure coefficient (Cp), which belongs to Group 2, according to Figure 2.2 in WTG-Merkblatt-M3:
- G2: Absolute values with medium accuracy requirements. The area of application can include parameters or preliminary studies when later investigations with higher accuracy are planned (e.g., wind tunnel examination of class G3).
- R2: Solitary, all relevant wind directions with sufficiently fine directional resolution.
- Z2: Statistical mean values and standard deviations, provided they involve stationary flow processes, for which a statistical verification of fluctuations with a peak factor is sufficient.
- S1: Static effects. They are sufficient to represent the structural model with the necessary mechanical detail, but without mass and damping properties.
Description
This verification case, based on the document of the German WTG: Fact Sheet of Committee 3 - Numerical Simulation of Wind Flows, Chapter 9.2 (see references), compares computational fluid dynamics calculations of wind pressure coefficients to experimental data from Tokyo Polytechnic University's (TPU) aerodynamic database (see references). The analysis focuses on a high-rise building model (ratio 2:1:5). TPU's boundary layer wind tunnel data – rigorously validated through peer-reviewed studies and publicly accessible via their wind engineering portal – provides benchmark metrics for assessing turbulence modeling accuracy and grid sensitivity effects. Key comparison parameters include mean values of pressure coefficients at critical building zones (windward face, sidewalls, leeward separation regions).
| Fluid Properties | Kinematic Viscosity | ν | 1.500e-5 | m2/s |
| Density | ρ | 1.250 | kg/m3 | |
| Wind Tunnel | Length | Dx | 2720.000 | m |
| Width | Dy | 900.000 | m | |
| Height | Dz | 720.000 | m | |
| Building | Breadth | B | 80.000 | m |
| Depth | D | 40.000 | m | |
| Height | H | 200.000 | m | |
| Calculation Parameters | Reference Velocity | uref | 22.000 | m/s |
| Reference Height | zref | 10.000 | m | |
| von Kármán Constant | κ | 0.410 | ||
| Turbulence Viscosity Constant | Cμ | 0.090 | ||
| Aerodynamic Surface Roughness Length | z0 | 1.000 | m |
Analytical Solution
No analytical solution is available. The example provides a comparison of RWIND CFD simulation results and experimental data (TPU Aerodynamic Database).
The wind speed profile is calculated from the Power Law according to the following formula:
where profile exponent α is defined as
The turbulence intensity is taken from the TPU Aerodynamic Database according the following graph for α=0.25.
RWIND Simulation Settings
- Modeled in RWIND 3.04
- Transient flow simulation type
- Mesh density is 20% with refinements: 5,698,702 cells
- Spalart-Allmaras DDES model
- Inlet boundary condition - velocity profile and turbulence intensity profile
- Tunnel bottom - no-slip boundary condition
- Tunnel walls and top - slip boundary condition
- Outlet boundary condition - zero pressure; zero velocity gradient
WTG-Merkblatt M3 Accuracy Requirement
The WTG-Merkblatt M3 provides two key methods for validating simulation results. The Hit Rate (q) Method evaluates how many of the simulated values Pi correctly match the reference values Oi within a defined tolerance, using a binary classification approach (hit or miss). This approach assesses the reliability of the simulation by calculating a hit rate q, similar to confidence functions used in reliability theory. In contrast, the Normalized Mean Squared Error (e2) method offers a more detailed accuracy assessment by quantifying the average squared deviation between simulated and reference values, normalized to account for scale differences. Together, these methods provide both qualitative and quantitative measures for simulation validation.
Results
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 experimental data from TPU with the results of the flow simulation in RWIND does not meet the requirements.
| Surface | q [%] for Wrel = 10% | q [%] for Wrel = 20% | e2 [1] |
| Windward | 27.3 | 72.7 | 0.035 |
| Right Sideward | 0.0 | 9.1 | 0.114 |
| Left Sideward | 27.3 | 45.5 | 0.121 |
| Leeward | 0.0 | 0.0 | 0.118 |
In the following graphs, average wind pressure coefficients obtained by means of RWIND simulation are compared to the mean values from time series in the test points measured by means of the TPU Aerodynamic Database. The comparisons are carried out on the windward, right side, left side, and leeward surfaces of the building.
The graphs show very good agreement on the windward surface. Wind pressure coefficients are crucial for building loads, especially on this surface. In the case of other surfaces, good agreement is seen between the trend of the simulation results and the experiment.
Remark: The experimental data shown in the graphs are plotted on the basis of data files obtained from the TPU website. However, the graphs shown on the TPU website match the data files only in the case of the windward surface.
