STUDIO logo STRUCTURAL ENGINEERING
# CFD simulation report
## 1. Project information
| Field | Value |
|---------------------|--------------------------------------|
| Project title | Demo project |
| Project description | Demo project description |
| Prepared by | Demo User (demo@formeo.ai) |
| Simulation ID | 2d5bce03-e933-4f66-a24d-12db0aeb0544 |
| Report generated | 2026-07-08 11:46 CEST |
## Contents
| | |
|-------------------------------------------------------------------------------|----|
| 1. Project information ..... | 1. |
| 2. Scope ..... | 2. |
| 3. Methodology ..... | 2. |
| 3.1. Simulation setup ..... | 2. |
| 3.2. Domain ..... | 2. |
| 3.3. Obstacle indexing ..... | 2. |
| 3.4. Zone-mean pressure coefficients ..... | 3. |
| 3.5. Momentum-exchange force coefficients ( $C_{D,MEA}$ , $C_{L,MEA}$ ) ..... | 3. |
| 3.5.1. Streamwise shielding factors ..... | 3. |
| 4. Flow fields ..... | 4. |
| 4.1. Figures ..... | 4. |
| 4.1.1. Pressure coefficient ( $C_p$ ) ..... | 4. |
| 4.1.2. Velocity magnitude ..... | 4. |
| 4.1.3. Vorticity ..... | 4. |
| 4.1.4. Boundary $C_p$ , body_1 ..... | 4. |
| 4.2. Vortex shedding ..... | 5. |
| 4.2.1. Across-wind force spectrum ..... | 5. |
| 5. Annex: full-domain flow fields ..... | 6. |
| 5.0.1. Pressure coefficient ( $C_p$ ) (full domain) ..... | 6. |
| 5.0.2. Velocity magnitude (full domain) ..... | 6. |
| 5.0.3. Vorticity (full domain) ..... | 7. |
| 6. References ..... | 8. |
## 2. Scope
Dimensionless aerodynamic fingerprint of the building geometry from a virtual digital wind tunnel.
This solver operates as a virtual digital wind tunnel, extracting the fundamental aerodynamic fingerprint of your building geometry. The report delivers pure, dimensionless aerodynamic coefficients ( $C_p$ , and where applicable $C_D$ , $C_L$ , and Strouhal numbers $n_s$ ) that integrate into any global design standard, whether ASCE 7, Eurocode 1, or local structural frameworks. We supply the exact geometric behaviour; you apply your local environmental safety factors.
## 3. Methodology
The simulation reproduces uniform approach flow past your geometry in a two-dimensional virtual wind tunnel. Reported $C_p$ , $C_D$ , $C_L$ , and $n_s$ are dimensionless coefficients extracted from the computed flow field. They describe the aerodynamic fingerprint of this section and are intended for use with your chosen design code and local safety factors. They are not tied to a prescribed wind speed or air density in this report.
**Applicability.** The model treats the geometry as an infinite prismatic strip (2D section normal to the span direction). This is appropriate when the along-span aspect ratio is large (typically $AR > 5$ ). For shorter bodies, three-dimensional tip and corner effects are not captured.
**Conservatism vs. 3D.** Sectional coefficients from a 2D strip study tend to be conservative for windward drag and peak suction on long facades, because tip relief and flow three-dimensionality are omitted. Where end effects or corner vortices govern the design, a dedicated 3D study is required.
### 3.1. Simulation setup
| Parameter | Value |
|-----------------|--------------------|
| Grid resolution | $2272 \times 1184$ |
| Timesteps | 259664 |
| Blockage ratio | 5.1% |
### 3.2. Domain
Geometry extent and lattice discretization in project length units. Spatial coordinates in field plots use the same unit system.
| Parameter | Value |
|--------------------------------|--------------------|
| Domain extent ( $X \times Y$ ) | $193 \times 101$ m |
| Lattice spacing $\Delta x$ | 0.08515 m |
### 3.3. Obstacle indexing
Connected obstacle components from the raster mask, ordered streamwise ( $+x$ ). Indices match the coefficient tables below and boundary $C_p$ figures in the flow-field section.
Figure 1: Source geometry with bounding boxes and body indices. The plot shows a cross-section of a body labeled 'body\_1' in blue text. The body is centered around x=55-60 and y=50. A dashed blue bounding box encloses the body, with x-coordinates from 50 to 65 and y-coordinates from 48 to 53. The x-axis is labeled 'x (flow ->)' and ranges from 50 to 70. The y-axis is labeled 'y' and ranges from 44 to 58.
Figure 1: Source geometry with bounding boxes and body indices.
**Coefficient selection (EN 1991-1-4).** Open-flow / elevated geometry: use momentum-exchange $\$C_{D,\$}$ and $\$C_{L,\$}$ for overall section forces and vortex-shedding checks (EN1991-1-4:2005). Pressure-based coefficients are included for surface pressure mapping. Steps 1–32458 were omitted before the shedding FFT and the mean force coefficients. Mean $C_D$ and $C_L$ use steps 32459–254268. Pressure $C_p$ is from the final timestep only.
### 3.4. Zone-mean pressure coefficients
External pressure coefficients on windward and leeward facets (EN 1991-1-4 external pressures).
| Location | Obstacle ind. | $C_{p,\text{front}}$ | $C_{p,\text{rear}}$ | $C_{p,\text{net}}$ |
|----------|---------------|----------------------|---------------------|--------------------|
| Obstacle | body_1 | +0.622 | -0.623 | +1.245 |
### 3.5. Momentum-exchange force coefficients ( $C_{D,\text{MEA}}$ , $C_{L,\text{MEA}}$ )
Time-averaged momentum exchange on obstacle links; same $D$ and $A_{\text{ref}}$ as pressure integration. **Recommended for this open-flow / elevated geometry (EN1991-1-4:2005).**
| Object | Obstacle ind. | $C_{D,\text{MEA}}$ | $C_{L,\text{MEA}}$ |
|----------|---------------|--------------------|--------------------|
| Obstacle | body_1 | +1.127 | +1.704 |
#### 3.5.1. Streamwise shielding factors
Shielding factors compare time-mean MEA drag coefficients for geometrically identical obstacles at different streamwise positions: $S_i = \frac{C_{D,\text{MEA},i}}{C_{D,\text{MEA},\text{baseline}}}$ , where the baseline is the upstream-most duplicate (smallest $x$ ). Values below 1.0 indicate reduced drag from wake shielding (e.g. stacked solar panels or cylinder rows). No repeating obstacle shapes were detected at different streamwise positions; shielding factors require at least two geometrically identical bodies.
| Object | Obstacle ind. | Baseline | Shielding factor $S$ |
|----------|---------------|----------|----------------------|
| Obstacle | body_1 | — | N/A |
## 4. Flow fields
### 4.1. Figures
#### 4.1.1. Pressure coefficient ( $C_p$ )
Figure 2: Gauge pressure coefficient near obstacles. A 2D contour plot showing the distribution of the pressure coefficient (Cp) around a central obstacle. The x-axis represents the flow direction from 0 to 120, and the y-axis represents the vertical position from 40 to 60. A color bar on the right indicates Cp values from -3 (blue) to 3 (red). The obstacle is a dark shape in the center, with higher pressure (red/orange) on its windward side and lower pressure (blue) on its leeward side.
Figure 2: Gauge pressure coefficient near obstacles (5× streamwise, 2× vertical padding).
#### 4.1.2. Velocity magnitude
Figure 3: Speed field with streamlines near obstacles. A 2D plot showing velocity magnitude (|u| in m/s) and streamlines around a central obstacle. The x-axis ranges from 0 to 120, and the y-axis from 40 to 60. A color bar on the right indicates velocity magnitude from 0 (blue) to 20 (red). Streamlines show the flow path around the obstacle, with higher velocity (red) in the wake and lower velocity (blue) near the obstacle.
Figure 3: Speed field with streamlines near obstacles (5× streamwise, 2× vertical padding).
#### 4.1.3. Vorticity
Figure 4: Normalized vorticity near obstacles. A 2D plot showing normalized vorticity (omega) around a central obstacle. The x-axis ranges from 0 to 120, and the y-axis from 40 to 60. A color bar on the right indicates vorticity values from -1.0 (blue) to 1.0 (red). The plot shows regions of high vorticity (red and blue) in the wake of the obstacle.
Figure 4: Normalized vorticity near obstacles (5× streamwise, 2× vertical padding).
#### 4.1.4. Boundary $C_p$ , body\_1
Figure 5: Cp ribbon along obstacle perimeter. A 2D plot showing the pressure coefficient (Cp) distribution along the perimeter of a complex obstacle. The x-axis represents the flow direction from 50 to 70, and the y-axis represents the vertical position from 44 to 58. The plot shows the obstacle's boundary with Cp values labeled at various points: +0.91, -0.79, -0.56, -0.59, -0.84, and +0.72. A legend indicates: black line for the obstacle, red for Cp > 0, and blue for Cp < 0.
Figure 5: $C_p$ ribbon along obstacle perimeter. Map localized pressures to cladding and facade design.
### 4.2. Vortex shedding
Cross-wind vortex shedding per EN1991-1-4:2005. Peak shedding frequency $f$ and Strouhal number $n_s = f \frac{b}{U}$ from the across-wind force fluctuation spectrum. Characteristic dimension $b$ is the structure extent perpendicular to the wind direction (+x).
body\_1 — Developed shedding (converged)
| Quantity | Value |
|------------------------------|----------------|
| Peak shedding frequency $f$ | 0.31 Hz |
| Strouhal number $n_s$ | 0.158 |
| Characteristic dimension $b$ | 5.11 m |
#### 4.2.1. Across-wind force spectrum
The figure consists of two vertically stacked plots. The top plot, titled "Across-wind force fluctuation (lattice units)", shows the time history of lift force. The y-axis is labeled "Lift (LU)" and ranges from -0.50 to 0.25. The x-axis is labeled "Sample index" and ranges from 0 to 250,000. A blue line represents the fluctuation, which starts with a sharp negative peak around sample 10,000 and then settles into a high-frequency oscillation around zero. Text in the top left corner of the plot area reads: "n = 227206 | Δt = 0.000596 s" and "body\_1: Developed shedding (converged)". The bottom plot, titled "Across-wind force spectrum", shows the frequency spectrum of the lift force. The y-axis is labeled "Amplitude (LU)" and ranges from 0.000 to 0.006. The x-axis is labeled "Frequency (Hz)" and ranges from 0.0 to 2.0. A blue line represents the magnitude of the Fast Fourier Transform (|FFT|), showing a very sharp peak at approximately 0.31 Hz and several smaller peaks at higher frequencies. A red dashed vertical line is drawn at f = 0.31 Hz, as indicated by the legend.
Two plots showing cross-wind force fluctuation. The top plot is 'Across-wind force fluctuation (lattice units)' showing Lift (LU) vs Sample index. The bottom plot is 'Across-wind force spectrum' showing Amplitude (LU) vs Frequency (Hz).
Figure 6: Cross-wind force fluctuation time history and frequency spectrum (EN1991-1-4:2005).
## 5. Annex: full-domain flow fields
Full computational-domain views of the field plots shown zoomed in the flow-field section. Use these figures to inspect the complete wind-tunnel extent and far-field behaviour.
#### 5.0.1. Pressure coefficient ( $C_p$ ) (full domain)
A contour plot showing the full-domain gauge pressure coefficient ( $C_p$ ) at the final timestep. The x-axis represents the flow direction from 0 to 175, and the y-axis represents the vertical distance from 0 to 100. A small black airfoil model is positioned at approximately x=55 and y=50. The color scale on the right ranges from -3 (blue) to 3 (red), with 0 being white. The plot shows a high-pressure region (red/orange) on the upper surface of the airfoil and a low-pressure region (blue) on the lower surface, with the pressure field extending throughout the domain.
Figure 7: Full-domain gauge pressure coefficient at the final timestep.
Figure 7: Full-domain gauge pressure coefficient at the final timestep.
#### 5.0.2. Velocity magnitude (full domain)
A contour plot showing the full-domain velocity magnitude field with streamlines. The x-axis represents the flow direction from 0 to 175, and the y-axis represents the vertical distance from 0 to 100. A small black airfoil model is positioned at approximately x=55 and y=50. The color scale on the right ranges from 0.0 (dark purple) to 20.0 (yellow), with intermediate values at 2.5, 5.0, 7.5, 10.0, 12.5, 15.0, and 17.5. The plot shows the velocity magnitude field around the airfoil, with streamlines indicating the flow direction. The velocity is highest (yellow) in the wake of the airfoil and lowest (purple) in the far-field.
Figure 8: Full-domain speed field with streamlines.
Figure 8: Full-domain speed field with streamlines.
#### 5.0.3. Vorticity (full domain)
The figure displays a 2D flow field with normalized vorticity. The horizontal axis represents the flow direction $x$ (from 0 to 175), and the vertical axis represents the transverse direction $y$ (from 0 to 100). Streamlines are shown as black lines with arrows indicating the flow direction. A central vortex core is visible, characterized by a region of high vorticity (red/orange) surrounded by a region of low vorticity (blue). The color scale on the right indicates the normalized vorticity $\frac{\omega}{\omega_0}$ , ranging from -1.00 (blue) to 1.00 (red).
A contour plot of normalized vorticity in a 2D flow domain. The x-axis is labeled 'x (flow ->)' and ranges from 0 to 175. The y-axis is labeled 'y' and ranges from 0 to 100. The plot shows a series of horizontal streamlines with a central vortex core. The vorticity is represented by a color scale from -1.00 (blue) to 1.00 (red). The vortex core is located around x=75, y=50. The color scale is labeled with the symbol \frac{\omega}{\omega\_0}.
Figure 9: Full-domain normalized vorticity.
## 6. References
- [1] Krüger, T., Kusumaatmaja, H., Kuzmin, A., Shardt, O., Silva, G., & Viggen, J. R. (2017). **The Lattice Boltzmann Method: Principles and Practice**. Springer. ISBN 978-3-319-44647-9.
- [2] Henderson, R. (1995). Details of the drag curve near the onset of vortex shedding. **Physics of Fluids**, 7(9), 2102–2104.
- [3] Sohankar, A., Norberg, C., & Davidson, L. (1998). Low-Reynolds-number flow around a square cylinder at incidence: study of blockage, onset of vortex shedding and outlet boundary condition. **International Journal for Numerical Methods in Fluids**, 26(1), 39–56.
- [4] Franke, J., Hellsten, A., Schlünzen, H., & Carissimo, B. (2007). Best practice guideline for the CFD simulation of flows in the urban environment. COST Action 732.
- [5] Roshko, A. (1961). Experiments on the flow past a circular cylinder at very high Reynolds number. **Journal of Fluid Mechanics**, 10(3), 345–356.