# CFD simulation report
## 1. Project information
| Field | Value |
|---------------------|--------------------------------------|
| Project title | Bechmark rectangular cylinder (1:1) |
| Project description | Reference: Sohankar et al., (1998) |
| Simulation ID | 50c08774-e495-4c98-86c8-add9422fd739 |
| Report generated | 2026-07-07 15:23 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: A 2D plot showing the source geometry of a rectangular 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. A blue dashed rectangle represents the obstacle, with its center labeled 'body\_1'. The rectangle's bounding box is approximately from x=10.0 to x=11.0 and y=14.5 to y=15.5.
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 1–38400 were omitted before the shedding FFT and the mean force coefficients. Mean $C_D$ and $C_L$ use steps 38401–195249. 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 | +0.71 | -0.70 | +1.41 |
### 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 | +1.510 | +0.000 |
#### 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 square 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 values from -3 (blue) to 3 (red). The plot shows a high-pressure region (red/orange) directly behind the obstacle and lower pressure regions (blue) further downstream and to the sides.
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 square 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| values from 0.0 (dark purple) to 20.0 (yellow). Streamlines are overlaid on the color field, showing the flow being deflected around the obstacle. The velocity magnitude is highest (yellow) in the wake of 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 a rectangular obstacle at x=10, y=15. Streamlines flow from left to right. A color bar on the right indicates normalized vorticity values from -1.00 (blue) to 1.00 (red). High positive vorticity (red) is concentrated in the wake of the obstacle, while negative vorticity (blue) is seen further downstream.
Figure 4: Normalized vorticity near obstacles (5× streamwise, 2× vertical padding).
#### 4.1.4. Boundary Cp, body\_1
Figure 5: Cp ribbon along obstacle perimeter. The plot shows a square obstacle with x from 10.0 to 11.0 and y from 14.5 to 15.5. A legend indicates: black line for 'Obstacle', red for 'Cp > 0', and blue for 'Cp < 0'. The Cp values are labeled on the perimeter: +0.70 on the left face, -0.99 on the top face, -0.70 on the right face, and -1.13 on the bottom face.
Figure 5: Cp 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 $f$ | 1.47 Hz |
| Strouhal number $n_s$ | 0.15 |
| 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 time history of lift force. The y-axis is labeled "Lift (LU)" and ranges from -0.02 to 0.02. The x-axis is labeled "Sample index" and ranges from 0 to 200,000. The plot shows a blue line representing the lift force, which starts with a transient period and then settles into a steady-state oscillation. A text box in the upper left corner of the plot area contains the text: "n = 161600 | Δt = 0.0001427 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 to 10. The plot shows a blue line representing the magnitude of the Fast Fourier Transform (|FFT|), which has a sharp peak at a frequency of 1.47 Hz. A red dashed vertical line marks this peak, with a legend entry "f = 1.47 Hz".
Figure 6: Cross-wind force fluctuation time history and frequency spectrum. The top plot shows 'Across-wind force fluctuation (lattice units)' with Lift (LU) vs Sample index. The bottom plot shows 'Across-wind force spectrum' with 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)
The figure is a contour plot of the pressure coefficient ( $C_p$ ) over a full computational domain. 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 color bar on the right side of the plot indicates the values of $C_p$ (gauge), ranging from -3 (dark blue) to 3 (dark red), with intermediate ticks at -2, -1, 0, and 1. The plot shows a complex flow field with high pressure (red) near the black square and low pressure (blue) in the far field.
A contour plot showing the full-domain gauge pressure coefficient (Cp) at the final timestep. The plot is a square domain with x and y axes ranging from 0 to 35. A color bar on the right indicates Cp values from -3 (blue) to 3 (red). A small black square is located at approximately (10, 15). The plot shows a complex flow field with high pressure (red) near the black square and low pressure (blue) in the far field.
Figure 7: Full-domain gauge pressure coefficient at the final timestep.
#### 5.0.2. Velocity magnitude (full domain)
A contour plot of velocity magnitude 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. 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 obstacle (a black square) and a wake region. The velocity magnitude is highest (yellow) in the wake and lowest (purple) near the obstacle. Streamlines are overlaid on the contour plot, showing the flow path around the obstacle.
A contour plot showing the velocity magnitude field 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. 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 obstacle (a black square) and a wake region. The velocity magnitude is highest (yellow) in the wake and lowest (purple) near the obstacle. Streamlines are overlaid on the contour plot, showing the flow path around the obstacle.
Figure 8: Full-domain speed field with streamlines.
#### 5.0.3. Vorticity (full domain)
The figure is a contour plot representing the full-domain normalized vorticity. 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. The plot area is filled with a color map where red indicates positive vorticity and blue indicates negative vorticity. A series of alternating red and blue regions are visible, primarily concentrated between y=10 and y=20, and extending along the x-axis from approximately x=10 to x=35. These regions are separated by thin, wavy lines. A color bar on the right side of the plot provides a scale for the vorticity values, 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. The label
$\frac{\omega}{\omega_0}$
is positioned next to the color bar.
A contour plot of full-domain normalized vorticity. 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 x-axis, with a color bar on the right indicating 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.