# A Parametric Study of Wind Pressure Distribution on Façades Using Computational Fluid Dynamics

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## Abstract

**:**

## Featured Application

**Efficient design of façade elements for wind loading.**

## Abstract

## 1. Introduction

## 2. Description of the CFD Model

#### 2.1. Geometry

#### 2.2. Computational Domain

#### 2.3. Boundary Conditions

#### 2.4. Turbulence Model

^{−4}, as recommended by [6]. As the model encounters no issues satisfying this limit, over all time steps, the more accurate solution for pressure in the second order is justified. Finally, temporal discretization was calculated through the Bounded Second Order Implicit transient formulation.

#### 2.5. Mesh

^{3}and 1 × 10

^{4}for all models due to the constraints associated with spatial discretization [22].

## 3. Model Convergence

#### 3.1. Mesh Sensitivuty Study

^{+}), is an important measure of mesh quality at wall features within the computational domain. For values less than 5, modeling takes account of turbulence dampening at the viscous sub-layer [12]. However, with the application of WMLES, turbulence was resolved directly at wall regions where Y

^{+}< 300 [23,24]. The minimum cell sizes of 2 mm, 1 mm and 0.5 mm do not cause Y

^{+}to exceed 300, with peak values of 290.1, 157.2 and 78.8, respectively (Table 1). This means for these respective cell sizes involving the sub-grid scale, the WMLES model was within operating limits for each mesh.

^{−4}s, 4 × 10

^{−4}s and 2 × 10

^{−4}s, with respect to the 2 mm, 1 mm and 0.5 mm cases. There appeared to be little variation in Co between the meshes, as the ratio of time-step to cell size remained the same in each case. For completeness, the number of cells, ratio and refinement factors for each of the three mesh sizes are given in Table 2.

#### 3.2. Convergence of Peak Pressures

_{wind}≤ [P

_{av}+ 1.64 P

_{rms}]

_{wind}represent the wind pressures, P

_{av}is the time averaged pressure and P

_{rms}is the root mean square error of pressures. Figure 4 illustrates that peak pressures acting on the critical fin only vary slightly due to changes in mesh size. The root mean square error statistic acts as the sample standard deviation of the pressure in each of the simulations and was calculated as:

_{0}’ and a final time of ‘T’. The quantitative differences between each mesh were then examined to prove convergence with respect to the critical fin.

_{1}and y

_{2}are the quantity of interest for Mesh 1 and Mesh 2, respectively. In general, for a solution to converge, a value between meshes must have the relation:

_{12}) is 3.3%, and between Mesh 2 and Mesh 3 (e

_{23}) is 12.3%. This increase in error with mesh density establishes a lack of convergence. However, the problem is not limited to this windward case, and the complexity associated with maintaining the continuity of airflow means that leeward suction influences these values.

_{12}was 29.2% and e

_{23}was 13.8%. Therefore, peak suction pressures on the leeward face of the critical fin tended to converge, independent of mesh size.

_{12}is 18.9% while e

_{23}is 13.1%. Therefore, resultant peak net pressures on the critical fin tend to converge, independent of the mesh size.

_{12}was 19.9% while e

_{23}equaled 13.1%. This methodology was extended to investigate mean and min forces as well. An L-shaped bend is apparent in Figure 6a and therefore it was clear that peak net force converges independent of mesh resolution. Mean force was also seen to converge. Minimum values represent outlier readings where in only 5% of instances, a smaller value was reported. The moment generated from the net force onto the connection between the bottom of the bracket and the top of the fin (in plan-view) was then calculated. For this purpose, using the net pressure distribution, the lever arm, $\overline{x}$ was calculated as:

_{12}equal to 21.8%, there is an improvement in reducing to a 0.5 mm mesh at a value of 13.9% for e

_{23}(Table 4). By increasing mesh resolution, the net moment decreases between each change (0.233 kNm/m in Mesh 1, 0.182 kNm/m in Mesh 2 and 0.157 kNm/m in Mesh 3). The resultant L-shaped curve is apparent in Figure 6b. As is also the case for net forces, average and minimum net moment values do not converge in the manner highlighted for peak loading conditions. Minimum values represent outlier data necessary for statistical analysis but are not useful for design—so proof of convergence is not required.

^{−4}s is revised down to 2.5 × 10

^{−4}s, to account for increased wind speed in subsequent models. This adjustment is made to maintain Courant Number (Co) values less than the upper limit of 40 for solution stability. As a result of this change, the solutions were found to have sufficient stability. Solution data were acquired every 160 time-steps, or 0.04 s, to maintain the frequency of the previous studies.

## 4. Results

#### 4.1. Results for Geometry No. 1 (g = 80 mm d = 400 mm)

#### 4.2. Results for Geometry No. 5 (g = 160 mm d = 560 mm)

#### 4.3. Results for Geometry No. 11 (g = 0 mm d = 800 mm)

#### 4.4. Results for Geometry No. 13 (g = 400 mm d = 800 mm)

#### 4.5. Results for Geometry No. 14 (g = 80 mm d = 400 mm)

#### 4.6. Results for Geometry No. 15 (g = 0 mm d = 800 mm)

## 5. Discussion and Interpretation

#### 5.1. Sheltered Case

#### 5.2. Unsheltered Case

## 6. Conclusions

- The Venturi Effect tends to reduce the magnitude of pressures at the end of the fin nearest the building. The narrower the gap for airflow, the smaller the net pressure at this location.
- The more the flow is constricted towards the building, the greater the suction on the leeward side of the critical fin.
- Increasing the bracket length for a given fin length, achieves efficient distribution of load.
- Wind load is spread more evenly in cases where fin length is aerodynamically more efficient by utilizing the benefits of the Venturi Effect without the relative impact on continuity of the flow that occurs for less efficient fins.
- Reducing both fin length and bracket length tends to reduce moments.
- With these effects taken into account, the most efficient fin, as a combination of forces and moments has a length of 560 mm due to its ability to distribute stress through its aerodynamic efficiency, with a bracket of 80 mm recommended to minimize moments.
- The least efficient design is where the fins are directly attached to the building and with the longest fin length (800 mm).

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Costola, D.; Blocken, B.; Hensen, J.L.M. Overview of pressure coefficient data in building energy simulation and airflow network programs. Build. Environ.
**2009**, 44, 2027–2036. [Google Scholar] [CrossRef] [Green Version] - Aylanc, N.; Kasperski, M. Design wind loads for cladding elements, in 5th European and African Conference on Wind Engineering. In Proceedings of the 5th European and African Conference on Wind Engineering, Florence, Italy, 19–23 July 2009; Firenze University Press: Florence, Italy, 2009; pp. 379–391. [Google Scholar]
- Blocken, B. 50 years of computational wind engineering: Past, present and future. J. Wind Eng. Ind. Aerodyn.
**2014**, 129, 69–102. [Google Scholar] [CrossRef] - Montazeri, H.; Blocken, B. CFD simulation of wind-induced pressure coefficients on buildings with and without balconies: Validation and sensitivity analysis. Build. Environ.
**2013**, 60, 137–149. [Google Scholar] [CrossRef] - Casey, M.; Wintergerste, T. Best Practice Guidelines, ERCOFTAC Special Interest Group on “Quality and Trust in Industrial CFD”; European Research Community on Flow; Turbulence and Combustion: London, UK, 2000. [Google Scholar]
- Franke, J.; Baklanov, A. Best Practice Guideline for the CFD Simulation of Flows in the Urban Environment: COST Action 732 Quality Assurance and Improvement of Microscale Meteorological Models; Meteorological Inst: Hamburg, Germany, 2007. [Google Scholar]
- Tominaga, Y.; Mochida, A.; Yoshie, R.; Kataoka, H.; Nozu, T.; Yoshikawa, M.; Shirasawa, T. AIJ guidelines for practical applications of CFD to pedestrian wind environment around buildings. J. Wind Eng. Ind. Aerodyn.
**2008**, 96, 1749–1761. [Google Scholar] [CrossRef] - Blocken, B.B.; Carmeliet, J.J. Pedestrian Wind Environment around Buildings: Literature Review and Practical Examples. J. Therm. Envel. Build. Sci.
**2004**, 28, 107–159. [Google Scholar] [CrossRef] - Delaunay, D.; Lakehal, D.; Pierrat, D. Numerical approach for wind loads prediction on buildings and structures. J. Wind Eng. Ind. Aerodyn.
**1995**, 57, 307–321. [Google Scholar] [CrossRef] - Selvam, R.P. Computation of pressures on Texas Tech University building using large eddy simulation. J. Wind Eng. Ind. Aerodyn.
**1997**, 67, 647–657. [Google Scholar] [CrossRef] - Cochran, L.; Derickson, R. A physical modeler’s view of computational wind engineering. J. Wind Eng. Ind. Aerodyn.
**2011**, 99, 139–153. [Google Scholar] [CrossRef] - Haque, N.; Katsuchi, H.; Yamada, H.; Nishio, M. Strategy to develop efficient grid system for flow analysis around two-dimensional bluff bodies. KSCE J. Civ. Eng.
**2015**, 20, 1913–1924. [Google Scholar] [CrossRef] - Liu, J.; Niu, J.; Du, Y.; Mak, C. Large Eddy Simulation on the Pedestrian Level Wind around a Building Community: Evaluation of Influencing Factors. In Proceedings of the 4th International Conference on Building Energy, Environment, Melbourne, Australia, 5–9 February 2018; pp. 390–395. [Google Scholar]
- Li, W.-W.; Meroney, R.N. Gas dispersion near a cubical model building. Part I. Mean concentration measurements. J. Wind Eng. Ind. Aerodyn.
**1983**, 12, 15–33. [Google Scholar] [CrossRef] - Gousseau, P.; Blocken, B.B.; Van Heijst, G.J.F. Quality assessment of Large-Eddy Simulation of wind flow around a high-rise building: Validation and solution verification. Comput. Fluids
**2013**, 79, 120–133. [Google Scholar] [CrossRef] - Tominaga, Y.; Mochida, A.; Murakami, S.; Sawaki, S. Comparison of various revised k-ε models and LES applied to flow around a high-rise building model with 1:1:2 shape placed within the surface boundary layer. J. Wind Eng. Ind. Aerodyn.
**2008**, 96, 389–411. [Google Scholar] [CrossRef] - O’Rourke, M. Fundamental Concepts, Fluid Properties, Inviscid Flow, Internal Flow [Lecture to BE and BSc Engineering], (MEEN20010: Mechanis of Fluids I); University College Dublin: Belfield, Dublin, 2011. [Google Scholar]
- Versteeg, H.K.; Malalasekera, W. An Introduction to Computational Fluid Dynamics: The Finite Volume Method; Pearson Education: London, UK, 2007. [Google Scholar]
- Argyropoulos, C.D.; Markatos, N.C. Recent advances on the numerical modelling of turbulent flows. Appl. Math. Model.
**2015**, 39, 693–732. [Google Scholar] [CrossRef] - Piomelli, U.; Balaras, E. Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech.
**2002**, 34, 349–374. [Google Scholar] [CrossRef] [Green Version] - Tamura, T.; Nozawa, K.; Kondo, K. AIJ guide for numerical prediction of wind loads on buildings. J. Wind Eng. Ind. Aerodyn.
**2008**, 96, 1974–1984. [Google Scholar] [CrossRef] - Syrakos, A.; Varchanis, S.; Dimakopoulos, Y.; Goulas, A.; Fraggedakis, D. A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods. Phys. Fluids
**2017**, 29, 127103. [Google Scholar] [CrossRef] - Cardiff, P. Lecture 5–7: Finite Volume Method and Fluid Dynamics with Ansys Fluent [Lecture to Mechanical Engineering Stage 4], (MEEN40150: Computational Continuum Mechanics II); University College Dublin: Belfield, Dublin, Ireland, 2016. [Google Scholar]
- Fluent, A. Ansys Fluent Theory Guide; ANSYS Inc.: Canonsburg, PA, USA, 2011; Volume 15317, pp. 724–746. [Google Scholar]

**Figure 3.**Detail of structured mesh (

**a**) around the building (

**b**) around the leading fin (

**c**) around the lower edge of the leading fin for a mesh with cell size of 2 mm.

**Figure 4.**Peak wind pressures (

**a**) Mesh 1 (2 mm), (

**b**) Mesh 2 (1 mm), (

**c**) Mesh 3 (0.5 mm). In each figure, the left-hand portion of the image illustrates results for the entire building and the right-hand portion of the image is zoomed in on the critical fin.

**Figure 5.**Peak Pressure Distributions for 3 mesh resolutions with respect to distance along the fin from its top edge (

**a**) windward side (

**b**) leeward side (

**c**) net pressures. Peak pressures have a 95% confidence interval of not being exceeded within the simulation.

**Figure 6.**(

**a**) Differences in peak net force (per meter fin-height) due to changes in mesh resolution, (

**b**) Differences in peak net moment (per meter fin-height) due to changes in mesh resolution. Peak net force has a 95% confidence interval of not being exceeded within the experiment.

**Figure 7.**(

**a**) Mean net pressures distributions for 3 mesh resolutions with respect to the distance along the fin from its top edge, (

**b**) Minimum leeward pressure distributions for 3 mesh resolutions with respect to the distance along the fin from its top edge. Minimum pressures have a 5% confidence interval of not being exceeded within the experiment.

**Figure 8.**Façade geometry types for sample numbers 1–13. Bracket Length ‘g’ is defined on the horizontal axis. Fin length in millimeters is defined on the vertical axis.

**Figure 9.**Results for Building with g = 80 mm, d = 400 mm (

**a**) Time-averaged velocity (vector arrows) and pressures (contours) (

**b**) Time-averaged pressures (

**c**) Peak pressures (

**d**) Peak and time-averaged net pressures (kPa) versus position from top of fin in meters.

**Figure 10.**Results for Building with g = 160 mm, d = 560 mm (

**a**) Time-averaged velocity (vector arrows) and pressures (contours) (

**b**) Time-averaged pressures (

**c**) Peak pressures (

**d**) Peak and time-averaged net pressures (kPa) versus position from top of fin in meters.

**Figure 11.**Results for Building with g = 0 mm, d = 800 mm (

**a**) Time-averaged velocity (vector arrows) and pressures (contours) (

**b**) Time-averaged pressures (

**c**) Peak pressures (

**d**) Peak and time-averaged net pressures (kPa) versus the position from the top of the fin in meters.

**Figure 12.**Results for a building with g = 400 mm, d = 800 mm (

**a**) Time-averaged velocity (vector arrows) and pressures (contours) (

**b**) Time-averaged pressures (

**c**) Peak pressures (

**d**) Peak and time-averaged net pressures (kPa) versus position from top of fin in meters.

**Figure 13.**Results for Building with g = 80 mm, d = 400 mm (

**a**) Time-averaged velocity (vector arrows) and pressures (contours) (

**b**) Time-averaged pressures (

**c**) Peak pressures (

**d**) Peak and time-averaged net pressures (kPa) versus the position from the top of the fin in meters.

**Figure 14.**Results for a building with g = 0 mm, d = 800 mm (

**a**) Time-averaged velocity (vector arrows) and pressures (contours) (

**b**) Time-averaged pressures (

**c**) Peak pressures (

**d**) Peak and time-averaged net pressures (kPa) versus the position from the top of the fin in meters.

**Figure 15.**Peak net pressures for models ‘1’, ‘5’, ‘11’ and ‘13’ versus distance from the top of the fin as a percentage of total fin length.

**Figure 16.**Contour plot of peak net force in terms of normalized fin length, for a given façade element.

**Figure 19.**Combined scores from Figure 18 that are normalized in terms of relative efficiency.

**Figure 20.**Peak net pressures for model numbers ‘1’, ‘11’, ‘14’ and ‘15’ versus distance from the top of the fin as a percentage of the total fin length.

Y^{+}(Max) | Y^{+}(Mean) | Y^{+}(Variance) | Co (Max) | Co (Mean) | Co (Variance) | |
---|---|---|---|---|---|---|

Mesh 1 (2 mm) | 290.1 | 212.3 | 830.6 | 38.1 | 27.7 | 12.4 |

Mesh 2 (1 mm) | 157.2 | 112.0 | 276.6 | 38.4 | 19.2 | 12.8 |

Mesh 3 (0.5 mm) | 78.8 | 58.3 | 63.1 | 33.4 | 24.2 | 8.1 |

Cells | Ratio | Refinement (r) | |||
---|---|---|---|---|---|

Mesh 1 (2 mm) | 78,962 | Mesh_{1–2} | 1.414 | Mesh_{1–2} | 1.189 |

Mesh 2 (1 mm) | 111,688 | Mesh_{2–3} | 1.376 | Mesh_{2–3} | 1.173 |

Mesh 3 (0.5 mm) | 153,652 | -- | -- | -- | -- |

Peak (m) | Mean (m) | Min (m) | |
---|---|---|---|

Mesh 1 (2 mm) | 0.250 | 0.239 | 0.347 |

Mesh 2 (1 mm) | 0.244 | 0.237 | 0.286 |

Mesh 3 (0.5 mm) | 0.242 | 0.239 | 0.225 |

Net Forces | Lever Arm Lengths | Net Moments | |||||||
---|---|---|---|---|---|---|---|---|---|

Peak | Mean | Min | Peak | Mean | Min | Peak | Mean | Min | |

e_{12} | 19.9% | 22.8% | 5.1% | 2.4% | 0.9% | 17.5% | 21.8% | 23.4% | 13.3% |

e_{23} | 13.1% | 2.7% | 133.5% | 0.9% | 1.2% | 21.4% | 13.9% | 3.9% | 123.6% |

Model No | g (mm) | d (mm) | D (m) | 5D (m) | 10D (m) | 6D (m) | Domain Length (m) | Domain Height (m) |
---|---|---|---|---|---|---|---|---|

1/14 | 80 | 400 | 1.28 | 6.4 | 12.8 | 7.68 | 20.88 | 16.64 |

2 | 320 | 400 | 1.52 | 7.6 | 15.2 | 9.12 | 24.48 | 19.76 |

3 | 0 | 480 | 1.28 | 6.4 | 12.8 | 7.68 | 20.88 | 16.64 |

4 | 240 | 480 | 1.52 | 7.6 | 15.2 | 9.12 | 24.48 | 19.76 |

5 | 160 | 560 | 1.52 | 7.6 | 15.2 | 9.12 | 24.48 | 19.76 |

6 | 400 | 560 | 1.76 | 8.8 | 17.6 | 10.56 | 28.08 | 22.88 |

7 | 0 | 640 | 1.44 | 7.2 | 14.4 | 8.64 | 23.28 | 18.72 |

8 | 240 | 640 | 1.68 | 8.4 | 16.8 | 10.08 | 26.88 | 21.84 |

9 | 80 | 720 | 1.60 | 8.0 | 16.0 | 9.6 | 25.68 | 20.8 |

10 | 320 | 720 | 1.84 | 9.2 | 18.4 | 11.04 | 29.28 | 23.92 |

11/15 | 0 | 800 | 1.60 | 8.0 | 16.0 | 9.6 | 25.68 | 20.8 |

12 | 160 | 800 | 1.76 | 8.8 | 17.6 | 10.56 | 28.08 | 22.88 |

13 | 400 | 800 | 2.00 | 10.0 | 20.0 | 12.0 | 31.68 | 26.00 |

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**MDPI and ACS Style**

McGuill, C.; Keenahan, J.
A Parametric Study of Wind Pressure Distribution on Façades Using Computational Fluid Dynamics. *Appl. Sci.* **2020**, *10*, 8627.
https://doi.org/10.3390/app10238627

**AMA Style**

McGuill C, Keenahan J.
A Parametric Study of Wind Pressure Distribution on Façades Using Computational Fluid Dynamics. *Applied Sciences*. 2020; 10(23):8627.
https://doi.org/10.3390/app10238627

**Chicago/Turabian Style**

McGuill, Christopher, and Jennifer Keenahan.
2020. "A Parametric Study of Wind Pressure Distribution on Façades Using Computational Fluid Dynamics" *Applied Sciences* 10, no. 23: 8627.
https://doi.org/10.3390/app10238627