Building Wind Load Analysis
Building Wind Load: Theoretical Foundations
Overview
Professor, what exactly are we trying to determine with wind analysis around buildings?
There are three main objectives. (1) Determining wind loads for structural design, (2) Evaluating wind environment at pedestrian level (pedestrian comfort), and (3) Planning for natural ventilation.
For super high-rise buildings, wind loads become the governing factor in structural design. The Building Standards Act uses wind force coefficients to calculate design wind pressure, but CFD analysis is required for complex building shapes or when interference with surrounding buildings is a factor.
Cases where CFD is used instead of wind tunnel tests are increasing, right?
Exactly. However, in the architectural field, CFD is not a complete replacement for wind tunnel tests; they have a complementary relationship. The Architectural Institute of Japan's "Recommendations for Loads on Buildings" also provides guidelines for CFD analysis.
Governing Equations
What equations describe the wind around buildings?
The incompressible Navier-Stokes equations are fundamental. Since wind speeds around buildings are M < 0.3, compressibility can be ignored.
The wind pressure coefficient is defined as follows.
Here, $p$ is the local pressure, $p_\infty$ is the reference pressure, and $V_H$ is the reference wind speed at the building height.
The wind speed profile in the atmospheric boundary layer is often expressed by a power law.
Here, $\alpha$ is the power exponent dependent on surface roughness. It is approximately $\alpha \approx 0.25$--$0.35$ in urban areas and $\alpha \approx 0.10$--$0.15$ over the sea.
I see. So we give the atmospheric boundary layer profile as the inlet boundary condition.
Turbulence Models
Let's organize the turbulence models used in architectural CFD.
| Model | Characteristics | Suitability for Building Wind Analysis |
|---|---|---|
| Standard k-epsilon | Isotropic turbulence. Low computational cost. | Tends to underpredict separation for bluff bodies. |
| RNG k-epsilon | Vorticity-dependent viscosity. Improved separation prediction. | Effective for flow around square cylinders. |
| SST k-omega | Good accuracy near walls. | Recommended for wind pressure distribution on building surfaces. |
| LES (Smagorinsky) | Directly solves large-scale eddies. | Essential for peak and fluctuating wind pressures. |
| DES/DDES | RANS+LES hybrid. | Predicts fluctuating wind pressure at practical computational cost. |
Does k-epsilon fail to correctly predict separation around buildings?
The standard k-epsilon model tends to underpredict the wake vortices behind bluff bodies (like square cylinders or rectangular prisms). The reattachment length at the roof corner of a building often doesn't match experiments. While RNG k-epsilon or Realizable k-epsilon improve this, LES is desirable for predicting peak wind pressures.
Pedestrian Level Wind Environment
What are the evaluation criteria for building wind?
The Architectural Institute of Japan defines wind environment evaluation scales. The target is wind speed at pedestrian height (1.5 m above ground).
| Rank | Annual Cumulative Exceedance Probability | Environmental Guideline |
|---|---|---|
| 1 (Good) | Exceeding 10 m/s less than 1% | Residential areas, parks |
| 2 (Acceptable) | Exceeding 10 m/s less than 5% | General urban areas |
| 3 (Slightly Poor) | Exceeding 10 m/s less than 10% | Commercial districts |
| 4 (Poor) | Exceeding 10 m/s 10% or more | Countermeasures required |
For wind environment evaluation, the annual wind direction frequency distribution is also considered, right?
Exactly. The standard method is to conduct CFD for 16 wind directions (22.5-degree increments), then combine it with the wind direction frequency data from AMeDAS at the target location to calculate the annual exceedance probability.
The Aerodynamic Reason Why Tokyo Skytree "Rotates a Triangle with Height"
The cross-section of Tokyo Skytree is an equilateral triangle at the base, but the design gradually rotates the cross-section with height, approaching a circular shape near the top. This is not just a design feature but an aerodynamic design to suppress resonance (swaying due to building wind) caused by Kรกrmรกn vortices. Cylindrical or simple triangular cross-sections can cause Kรกrmรกn vortices to synchronize at specific wind speeds, leading to large vibrations. By varying the cross-section with height, vortices find it difficult to synchronize across the entire height. This ingenious solution, validated through a combination of CFD and wind tunnel experiments, supports the safety of the world's tallest self-supporting radio tower.
Computational Methods for Building Wind Load
Computational Domain and Mesh
For CFD around buildings, how large should the computational domain be?
There are recommended values based on the AIJ (Architectural Institute of Japan) Guidelines.
| Parameter | Recommended Value | Remarks |
|---|---|---|
| Inlet to building | 5H or more | H is building height |
| Building to outlet | 15H or more | For wake development |
| To side boundaries | 5H or more | Blockage ratio 5% or less |
| To top boundary | 5H or more | Blockage ratio 5% or less |
| Blockage ratio | 3% or less recommended | Building cross-section / Domain cross-section |
So the blockage ratio needs to be kept low.
Yes. A high blockage ratio creates an artificial acceleration effect, leading to overestimation of wind pressure. Below 3% is ideal, and it should not exceed 5% at maximum.
Inlet Boundary Conditions
How do we set the inlet condition for the atmospheric boundary layer?
Provide a profile based on the power law or log law. Turbulence quantities also need to be specified simultaneously.
Velocity profile (log law):
Turbulent kinetic energy:
Here, $u_*$ is the friction velocity, $\kappa = 0.41$ is the von Kรกrmรกn constant, $z_0$ is the roughness length, and $C_\mu = 0.09$.
How is $z_0$ (roughness length) determined?
Use values corresponding to surface roughness categories.
| Surface Category | $z_0$ [m] | Power Exponent $\alpha$ | Example |
|---|---|---|---|
| I (Sea) | 0.0002--0.005 | 0.10 | Coast, airport |
| II (Open country) | 0.01--0.05 | 0.15 | Farmland, low-rise housing |
| III (Suburban) | 0.1--0.5 | 0.20 | Medium-density urban area |
| IV (Urban) | 0.5--2.0 | 0.27 | High-rise building clusters |
Mesh Strategy
Let's organize the key points for mesh generation around buildings.
- On building surfaces: Minimum 10 divisions per edge (refine at corners).
- Near ground surface: $y^+ < 1$ (to ensure accuracy of wall shear stress).
- Refinement around building: Refine area within 2 times building height.
- Wake region: Do not coarsen too much up to 10H behind the building.
- Cell growth rate: 1.2 or less.
snappyHexMesh is often used to create meshes around buildings, right?
OpenFOAM's snappyHexMesh is widely used in architectural CFD. It reads building geometry in STL format and automatically performs local refinement and prism layer addition. STAR-CCM+'s trim mesh follows a similar efficient approach.
When to Use Steady RANS vs. LES
In what cases is LES necessary?
Here are guidelines for selection.
| Objective | Recommended Method | Reason |
|---|---|---|
| Mean wind pressure distribution | Steady RANS | Sufficient accuracy for practical work. |
| Peak wind pressure | LES/DES | Prediction of fluctuating component is needed. |
| Pedestrian wind environment (mean) | Steady RANS | Efficient calculation for 16 wind directions. |
| Vortex-induced vibration evaluation | LES | Prediction of vortex shedding frequency. |
| Natural ventilation | Unsteady RANS/LES | Fluctuating wind pressure at openings is important. |
Got it. Thank you for the detailed explanation.