# CFD simulation report
## 1. Project information
| Field | Value |
|---------------------|--------------------------------------|
| Project title | Benchmark circular cylinder |
| Project description | Reference: Henderson (1995) |
| Simulation ID | 80d0ef8e-f887-40ad-ab95-abb94a180926 |
| Report generated | 2026-07-07 15:29 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 ..... | 4. |
| 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 ..... | 5. |
| 4.1.4. Boundary $C_p$ , body_1 ..... | 5. |
| 4.2. Vortex shedding ..... | 5. |
| 4.2.1. Across-wind force spectrum ..... | 6. |
| 5. Annex: full-domain flow fields ..... | 7. |
| 5.0.1. Pressure coefficient ( $C_p$ ) (full domain) ..... | 7. |
| 5.0.2. Velocity magnitude (full domain) ..... | 8. |
| 5.0.3. Vorticity (full domain) ..... | 9. |
| 6. References ..... | 10. |
## 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 | $1792 \times 1472$ |
| Timesteps | 200000 |
| Blockage ratio | 3.4% |
### 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 ( $X \times Y$ ) | $36.5 \times 30$ m |
| Lattice spacing $\Delta x$ | 0.02038 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 circular body labeled 'body\_1' centered at approximately (10.5, 15.0). The body is enclosed within a dashed blue square bounding box with corners at (10.0, 14.5), (11.0, 14.5), (11.0, 15.5), and (10.0, 15.5). The x-axis is labeled 'x (flow ->)' and ranges from 9.8 to 11.2. The y-axis is labeled 'y' and ranges from 14.2 to 15.8. A light gray grid is visible in the background.
Figure 1: Source geometry with bounding boxes and body indices.
**Coefficient selection (EN 1991-1-4).** Open-flow / elevated geometry: use momentum-exchange $C_{D,S}$ and $C_{L,S}$ for overall section forces and vortex-shedding checks (EN1991-1-4:2005). Pressure-based coefficients are included for surface pressure mapping. Steps 1–25600 were omitted before the shedding FFT and the mean force coefficients. Mean $C_D$ and $C_L$ use steps 25601–199984. 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 | +0.21 | -0.85 | +1.06 |
### 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 | +1.382 | +0.002 |
#### 3.5.1. Streamwise shielding factors
Shielding factors compare time-mean MEA drag coefficients for geometrically identical obstacles at different streamwise positions: $S_i = \frac{C_{D,MEA,i}}{C_{D,MEA,baseline}}$ , 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 (Cp)
Figure 2: Gauge pressure coefficient near obstacles. A 2D contour plot showing the pressure coefficient (Cp) around a central black circular obstacle. The x-axis is labeled 'x (flow ->)' and ranges from 6 to 14. The y-axis is labeled 'y' and ranges from 13 to 17. A color bar on the right indicates Cp (gauge) values from -3 (blue) to 3 (red). The plot shows a high-pressure region (red/orange) on the left side of the obstacle and a low-pressure region (blue) on the right side, indicating flow separation and a wake.
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 contour plot showing the velocity magnitude (|u|) around a central black circular obstacle. The x-axis is labeled 'x (flow ->)' and ranges from 6 to 14. The y-axis is labeled 'y' and ranges from 13 to 17. A color bar on the right indicates |u| (m/s) values from 0.0 (dark purple) to 20.0 (yellow). Streamlines are shown as black lines flowing from left to right, curving around the obstacle. The velocity magnitude is highest (yellow) in the wake region and lowest (purple) 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. The plot shows streamlines and vorticity contours around a circular obstacle. The x-axis is labeled 'x (flow →)' and ranges from 6 to 14. The y-axis is labeled 'y' and ranges from 13 to 17. A color bar on the right indicates normalized vorticity values from -1.00 (blue) to 1.00 (red). The vorticity is concentrated in the wake of the obstacle, showing a vortex shedding pattern.
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. The plot shows the pressure coefficient (Cp) distribution around a circular obstacle. The x-axis is labeled 'x (flow →)' and ranges from 9.8 to 11.2. The y-axis is labeled 'y' and ranges from 14.2 to 15.8. The legend indicates: 'Obstacle' (black line), 'Cp > 0' (red line), and 'Cp < 0' (blue line). The Cp distribution is shown as a ribbon along the perimeter of the obstacle, with a localized pressure value of -0.55 indicated on the blue region.
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 $f$ | 1.69 Hz |
| Strouhal number $n_s$ | 0.172 |
| Characteristic dimension $b$ | 1.02 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 lift force (LU) on the y-axis (ranging from -0.04 to 0.04) against the sample index on the x-axis (ranging from 0 to 200,000). The plot shows an initial period of low-frequency, low-amplitude oscillations (up to sample index ~25,000) followed by a transition to high-frequency, high-amplitude periodic oscillations (from sample index ~25,000 to 200,000). Text in the top left corner of the plot area reads: "n = 174400 | Δt = 0.0001427 s" and "body\_1: Developed shedding (converged)". The bottom plot, titled "Across-wind force spectrum", shows the amplitude (LU) on the y-axis (ranging from 0.000 to 0.010) against the frequency (Hz) on the x-axis (ranging from 0 to 12). A solid blue line represents the magnitude of the Fast Fourier Transform (|FFT|), showing a very sharp peak at a frequency of approximately 1.69 Hz. A dashed red vertical line marks this peak, with a label "f = 1.69 Hz" in the legend.
Two plots showing cross-wind force fluctuation. The top plot is a time history of lift force (LU) vs sample index, showing a transition from low-frequency oscillations to high-frequency shedding. The bottom plot is the frequency spectrum (Amplitude LU vs Frequency Hz), showing a sharp peak at 1.69 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 plot is a square domain with a grid. The x-axis is labeled 'x (flow →)' and ranges from 0 to 35 with major ticks every 5 units. The y-axis is labeled 'y' and ranges from 0 to 30 with major ticks every 5 units. A black dot is located at approximately (10, 15). The color scale on the right, labeled ' $C_p$ (gauge)', ranges from -3 (dark blue) to 3 (dark red), with intermediate ticks at -2, -1, 0, 1, and 2. The plot shows a complex flow field with a high-pressure region (red/orange) near the black dot and a low-pressure region (blue) extending to the right and bottom.
Full-domain gauge pressure coefficient (Cp) plot at the final timestep.
Figure 7: Full-domain gauge pressure coefficient at the final timestep.
#### 5.0.2. Velocity magnitude (full domain)
The figure is a 2D contour plot representing a velocity magnitude field. The horizontal axis is labeled 'x (flow ->)' and has major tick marks at 0, 5, 10, 15, 20, 25, 30, and 35. The vertical axis is labeled 'y' and has major tick marks at 0, 5, 10, 15, 20, 25, and 30. A color bar on the right side of the plot indicates the velocity magnitude in m/s, with a scale from 0.0 (dark purple) to 20.0 (yellow), with intermediate labels at 2.5, 5.0, 7.5, 10.0, 12.5, 15.0, and 17.5. The plot shows a flow field with a central region of high velocity (yellow) and a wake region of low velocity (dark purple) behind a central obstacle. The streamlines are represented by black lines with arrows, showing the flow direction. The flow is generally from left to right, with a central region of high velocity (yellow) and a wake region of low velocity (dark purple) behind a central obstacle. The velocity magnitude is highest in the central region and decreases towards the boundaries and the wake.
A contour plot showing the velocity magnitude field with streamlines. The x-axis is labeled 'x (flow ->)' and ranges from 0 to 35. The y-axis is labeled 'y' and ranges from 0 to 30. A color bar on the right indicates velocity magnitude in m/s, ranging from 0.0 (dark purple) to 20.0 (yellow). The plot shows a flow field with a central region of high velocity (yellow) and a wake region of low velocity (dark purple) behind a central obstacle.
Figure 8: Full-domain speed field with streamlines.
#### 5.0.3. Vorticity (full domain)
The figure displays a 2D contour plot of normalized vorticity. The horizontal axis represents the flow direction $x$ (ranging from 0 to 35), and the vertical axis represents the transverse coordinate $y$ (ranging from 0 to 30). The vorticity is concentrated in a horizontal band around $y \approx 15$ , showing a series of alternating positive (red) and negative (blue) regions. A color bar on the right side of the plot provides a scale for the normalized vorticity, ranging from -1.00 (dark blue) to 1.00 (dark red), with intermediate values at -0.75, -0.50, -0.25, 0.00, 0.25, 0.50, and 0.75.
A contour plot of normalized vorticity in a rectangular domain. The x-axis is labeled 'x (flow ->)' and ranges from 0 to 35. The y-axis is labeled 'y' and ranges from 0 to 30. The plot shows a series of alternating positive (red) and negative (blue) vorticity regions along the centerline (y ≈ 15). A color bar on the right indicates the normalized vorticity values from -1.00 to 1.00.
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.