# Wind Pressure Coefficient on a Multi-Storey Building with External Shading Louvers

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## Abstract

**:**

## 1. Introduction

## 2. Wind Tunnel Experiment

_{ref}and the reference height h

_{0}are equal to those experimental parameters, set by Jiang et al. [44] to establish the wind environment in the computational domain. The reference velocity U

_{ref}was 3.41 m/s at h

_{0}from the measurement result. The reference height h

_{0}is the building height. α is the coefficient for power-law profile to describe the characteristics of surface roughness considering terrain category and was set as 0.27 for suburban terrain. Figure 4 shows the turbulent intensity I and the wind velocity U profiles of airflow on the inlet of experiments and simulation.

## 3. CFD Simulation

#### 3.1. Reference Case

#### 3.1.1. Geometric Model

#### 3.1.2. Turbulence Model

#### 3.1.3. Computational Domain and Grid Resolution

_{0}). Note that the near-wall grids are just the wall-adjacent grids closed to the solids, rather than all grids between two adjacent louvers. In near-wall boundary layers on these surfaces, enhanced wall treatment is applied for y+ < 5 and y+ ≈ 1 [51]. Figure 7 shows the grid resolution in computational domain and around the cubic building. Compared with published research of a building with louvered windows [12], we had much higher grid density along louver length but lower grid density along louver width, because in our pre-simulation, it was found that in the study of wind pressure coefficient, the deviations were mainly caused by the grid density along louver length, rather than that along louver width. Based on the grid resolution, a coarser mesh and a finer mesh were created to ensure grid accuracy. The Grid Convergence Index (GCI) [52,53] was calculated to show the deviation between different mesh sizes. For the reference case, GCI of normalized velocity and wind pressure coefficient are 0.37% and 1.8%, which are small enough to ensure grid accuracy, as recommended by Vinchurkar and Longest [54].

#### 3.1.4. Boundary Conditions

_{μ}is set as 0.09 [47].

#### 3.1.5. Solver Settings

^{−6}for x, y, z momentum and 10

^{−4}for continuity, k and ε, the convergence of the simulation was considered to be achieved. The monitors were also set at some points in the measurement lines in the simulation to verify the convergence. Oscillatory convergence was observed for the scaled residuals. As recommended by Ref [34] and [55], the results were monitored for more than 10,000 iterations. There were no significant oscillations in measurement lines of velocity and pressure, the average values over the last iterations were unnecessary and not calculated.

#### 3.1.6. Calculation of Wind Pressure Coefficient

_{p}is calculated from the pressure difference between static pressure P on the building surfaces and static pressure P

_{ref}at the reference point, as provided in Equation (5):

_{0}and had the same distance from the inlet to the windward facade. ρ is the air density and taken as 1.225 kg/m

^{3}.

#### 3.2. Result Validation

_{n}as shown in Equation (6) is to demonstrate the airflow velocity distribution:

_{ref}distribution of the simulation data and the experimental results on vertical measurement locations. The average absolute deviation is 0.068 between simulation data and experimental data. Figure 9 shows C

_{p}distribution for comparison of the data from the reference case and the data from Jiang et al. [44] along measurement lines on the windward, roof and leeward surfaces. The average absolute deviation is 0.046 between the two cases for wind pressure coefficient. The average values of U/U

_{ref}and C

_{p}, as long as their deviation on each line, are shown in Table 1. The comparison results show that U and C

_{p}in the reference case are in good agreement with results from the previous study. The U and C

_{p}tendencies on these locations can be reproduced well by CFD technology. The maximum deviations occur beyond the roof for both, U and C

_{p}distributions. This phenomenon seems to be that the realizable k-ε model with default parameters may provide airflow characteristics with overestimated reattachment lengths on the roof, and in the recirculating region at the corner between the ground and the leeward facade [32,56,57]. This over-estimation leads to the U near the roof and leeward facade and the smaller gradient for C

_{p}along the roof line. Although, there are higher distortions in the reattachment region for the realizable k-ε model, the simulation accuracy is considered to be suitable enough to perform CFD simulations.

## 4. Results and Discussion

_{p}on shaded building surfaces is critical for exploring the potential ventilation capacity. For a sealed building, orifice equation assumes that the pressure distribution is independent to the presence of openings [13]. In orifice equation, C

_{p}is applied to calculate wind-induced airflow rate Q of natural ventilation in buildings [14,15], as shown in Equations (7) and (8),

_{d}is the discharge coefficient. P

_{i}is the pressure inside the building.

#### 4.1. General Features of Airflow Pattern

_{0}, the upward flow near the roof and the downward vortex near the ground. The streamlines were smooth above the small reverse flow on the roof. The larger reverse flow and the recirculating zone were generated on the lateral façade, and the leeward facade, respectively. In Figure 10b, the airflow streamlines towards the side rows were smoother than that towards the central rows, which demonstrates that the airflow pattern was almost not affected by the detailed geometry of the shaded building.

#### 4.2. Features of Local Wind Pressure Coefficient along Measurement Lines

_{p}at a specific point is evaluated by the range R as shown in Equation (9).

_{p}at a specific point on a measurement line for different shaded conditions. C

_{p-max}and C

_{p-min}are the maximum and minimum C

_{p}at that point in these shaded conditions. Note that C

_{p-max}and C

_{p-min}only represent the local values of a special point on a line in all shaded cases, which are different from the maximum and minimum C

_{p}on a whole line.

#### 4.2.1. Local Wind Pressure Coefficient on W-R-L Lines

_{p}on the central lines of R1 and R7 along the windward, roof and leeward surfaces under different shaded conditions. Generally speaking, the roof suffers the largest fluctuation of C

_{p}, while the leeward surface has the smallest difference of the local C

_{p}and R along the lines. The maximum and minimum value of C

_{p}are 0.86 and −1.08, respectively. The C

_{p-max}line and C

_{p-min}line have the similar shape and tendency except near the edge of the roof for around 1–1.4h

_{0}where has a flow separation. On the line of the windward facade, the maximum R is at about 0.8–0.9h

_{0}on the stagnation zone and the minimum R is near the edge between the windward and the roof surfaces. The R along these lines increases along 0–0.1h

_{0}, but the local C

_{p}decreases. From 0.1h

_{0}to 0.7h

_{0}, the local C

_{p}and the R both increase. After 0.7h

_{0}, the local C

_{p}in some cases begins to decrease but the R still grows up until around 0.9h

_{0}. These results indicate that near the maximum positive C

_{p}on the stagnation zone, the C

_{p}is strongly sensitive to the rotation angle θ of shading louvers. For the area near the vortex at the corner of the windward facade and the ground, the C

_{p}is not sensitive to different shaded conditions. On the lines of the roof, the C

_{p}suffers a sharp decrease near the edge, which is the continuation of the windward surface. Then the R increases to the widest at 1.05h

_{0}. In this area, the blocking effect of shading louvers makes the C

_{p}tendency smoother along the roof line. On the leeward line, the local C

_{p}just changes slightly at different points due to the leeward recirculation.

_{p}on the central lines of R2 and R6 along the windward, roof and leeward surfaces. Generally speaking, the tendencies of the C

_{p-max}line and the C

_{p-min}line along the lines in Figure 12d are similar to those in Figure 12b. The R along the central lines of R2 and R6 is smaller than that along the central lines of R1 and R7. However, there are also some significant differences between the two locations. On the windward surface, the R along the central lines of R2 is always larger. Even if the maximum C

_{p}on two locations are almost the same, the local C

_{p-min}near the ground is obviously different between two locations. the C

_{p-max}along the central lines of R1 is over 0.5 within 0–0.9h

_{0}, but the C

_{p-max}along the central lines of R2 is below 0.5 within 0–0.3h

_{0}. The shape difference on the C

_{p-min}line is not as obvious as that on the C

_{p-max}line. The C

_{p-min}along the central lines of R2 is about 0.2 smaller. These differences mean that on the lines of R2, the windward surface tends to suffer a larger fluctuation of positive wind pressure. On the roof, the shape and tendency of the C

_{p-max}and C

_{p-min}on the central lines of R2 and R6 are almost the same as those on the central lines of R1 and R7, and only the R is a little smaller for most locations than the central line. On the leeward, the gradient and the maximum value of C

_{p}along the central lines of R6 are slightly lower than those along the central lines of R7.

#### 4.2.2. Local Wind Pressure Coefficient on W-S-L Lines

_{p}on the central lines of the first floor along the windward, the lateral and the leeward surfaces. The windward surface suffers the largest fluctuation of C

_{p}, while the lateral wall has the smallest fluctuation of C

_{p}. Generally speaking, the windward surface has the widest R and the largest difference of the local C

_{p}along the central line. The leeward surface has the smallest R along the central lines. The C

_{p-max}line and the C

_{p-min}line have the similar shape and tendency. The maximum value and the C

_{p-min}are 0.55, and −0.44, respectively. On the windward surface, the largest R locates at 0.38h

_{0}and the smaller R locates on the edge between the windward and the lateral surfaces. On the lateral surface, the R increases slightly along 0.5–0.8h

_{0}, then within 0.8–1.2h

_{0}the R are almost the same. From 1.2h

_{0}to 1.4h

_{0}, the R increases obviously, then it decreases again near the edge between the lateral surface and the leeward surface. On the leeward surface, the local C

_{p}increases obviously but the R just increases slightly.

_{p}on the central lines of the F2–F5 along the windward, the lateral and the leeward surfaces. Generally speaking, the tendencies of the C

_{p-max}and C

_{p-min}along the central lines on different floors are similar to those on F1. The maximum value on the C

_{p-max}line is larger when the floor is higher, except for F5, on which the maximum value on the C

_{p-max}line is a little smaller than those on F4. The minimum value on the C

_{p-min}line is lower when the floor is higher. The locations of the minimum value on the C

_{p-min}lines are on the lateral surface for all floors. However, for F1 and F2, the locations are near edge of the windward surface at around 1.4h

_{0}, while for the higher floors, C

_{p}near the edge of the leeward surface at around 0.55h

_{0}is the minimum value on the C

_{p-min}lines. On the windward surface, the R along the central lines is wider for the higher floors. The absolute gradient of the C

_{p-max}line becomes lower near the central vertical lines but becomes higher near the edge of the lateral surface. On the lateral surface, the R becomes wider at around 0.55h

_{0}for the higher floors because of the lower C

_{p-min}. Along the lines on the lateral surface, the location of the minimum R becomes closer to the windward surface, as the floor becomes higher. The fluctuation of R near the edge of the leeward surface becomes smooth. This phenomenon means that as the floor gets higher, the wind suction effect of reverse flow becomes greater than the effect of the backward recirculation, but the negative pressure area, caused by the reverse flow, seems to be smaller than the negative pressure area caused by recirculation. On the leeward surface, the R along the central lines are similar for F1, F2 and F3, while the R are a little wider for F4 and F5. The absolute gradient of C

_{p}becomes lower for the higher floors, which means that higher floors are prone to have smoother C

_{p}distribution along these lines.

#### 4.2.3. Local Wind Pressure Coefficient on R-S Lines

_{p}, on the central lines of R3–R5, along the roof and leeward surfaces. The C

_{p}distributions along R-S lines are obviously smoother than C

_{p}along W-R-L and W-S-L lines, because only the windward surface undergoes positive wind pressure. Generally, The R has the largest value on the central lines of R3, while R has the smallest value on the central lines of R4. The result indicates that R4 on the lateral surface seems to be the transitional zone, where the impact of reverse flow becomes weaker, so the presence of shading louvers cannot change C

_{p}greatly. On the three lines, most local R on the roof is larger than those on the lateral surface. The maximum C

_{p}locates on the lateral surface near the ground for the central lines of R3 but on the roof for the central lines of R4 and R5. The minimum C

_{p}locates on the roof for the central lines of R3 and R4 and on the lateral surface for the central lines of R5. The largest R locates at 0h

_{0}for the central lines of R3 and R5 and at around 0.48h

_{0}near the edge between the roof and lateral surfaces for the central lines of R4. The R changes strongly along the central lines of R3 but more slightly along other two lines. The result of R3 means that the reverse flow near the roof and the lateral surface are both sensitive to the shaded conditions.

#### 4.3. Impact of Shading Louvers on Average Wind Pressure Coefficient

_{p}on outside surfaces of rooms. $\overline{{C}_{\mathrm{p}}}$ is the average C

_{p}on outside surface of a room belongs to the intersection of one floor and one row, as given by Equation (10). $\Delta \overline{{C}_{\mathrm{p}}}$ is the difference of $\overline{{C}_{\mathrm{p}}}$ between a shaded condition and the non-shaded condition, as given by Equation (11). $\overline{\Delta {C}_{\mathrm{p}\text{-}\mathrm{R}}}$ is the average difference of $\overline{{C}_{\mathrm{p}}}$ for all shaded conditions, compared with the non-shaded condition in a special row, as given by Equation (12). $\overline{\Delta {C}_{\mathrm{p}\text{-}\mathsf{\theta}}}$ is the average difference of $\overline{{C}_{\mathrm{p}}}$ between a specific shaded condition and the non-shaded condition in a whole row, as given by Equation (13),

_{R}is the area of the outside surface of a room. In all simulation cases, the rooms in different floors and rows are assumed to have the same A

_{R}. Considering the usage of the symmetry model and symmetry domain in simulations, A

_{R}in R1 and R7 are set as the half value of the real area. ∆S

_{R}is the area of a grid on the outside surface. $\overline{{C}_{\mathrm{p}\text{-}\mathsf{\theta}\text{-}i}}$ is the $\overline{{C}_{\mathrm{p}}}$ for the shaded condition with a specific rotation angle θ, and i is set as 1–6 to represent θ = 0°, 15°, 30°, 45°, 60° and 75°. $\overline{{C}_{\mathrm{p}\text{-}\mathrm{n}}}$ is the $\overline{{C}_{\mathrm{p}}}$ in the non-shaded condition. $\overline{{C}_{\mathrm{p}\text{-}\mathrm{R}\text{-}j}}$ is the $\overline{{C}_{\mathrm{p}}}$ in a specific row, and j is set as 1–7 to represent R1–R7.

## 5. Conclusions

- The validation of the studied building shows a small deviation between the numerical data and the data from the previous study. The average absolute deviation is 0.046 for wind pressure coefficient C
_{p}and 0.068 for normalized velocity U/U_{ref}. The Grid Convergence Index of U/U_{ref}and C_{p}for the reference case is 0.37%, and 1.8%, respectively. Therefore, the parameters of the simulation cases are feasible for the shaded building, and the computational settings is useful for further case studies of shaded buildings. - In general, the fluctuations of C
_{p}on the windward and roof surfaces are mostly stronger than those on the lateral and leeward surfaces along the measurement lines. These results indicate that when the ventilation openings located on the roof and windward facade with louvers, the ventilation routes can lead to larger fluctuations of ventilation rate. In building design, it is important to diagnose the risks of inadequate ventilation for shaded buildings, especially those with roof ventilation systems. - The stagnation zone of the windward surface has the highest average wind pressure coefficient $\overline{{C}_{\mathrm{p}}}$. For most floors and rows, $\overline{{C}_{\mathrm{p}}}$ decreases with a higher rotation angle θ. And $\overline{{C}_{\mathrm{p}}}$ has the greatest reduction for all floors when θ turns from 60° to 75°. These results indicate that ventilation openings on the stagnation zone contribute to higher ventilation rate for the windward facade with louvers. When the rotation angle is taken for more than 60°, it is essential to avoid bad indoor wind environment for rooms with ventilation openings located on the shaded facade.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

A | opening area |

A_{R} | area of the outside surface of a room |

B | louver width |

C_{d} | discharge coefficient |

C_{p} | wind pressure coefficient |

C_{p-max} | maximum wind pressure coefficient |

C_{p-min} | minimum wind pressure coefficient |

C_{μ} | empirical constant |

F1, F2, F3, F4, F5 | labels for different floors |

h_{0} | reference height (m) |

i | shaded condition |

I | turbulent intensity |

j | building row |

k | turbulent kinetic energy (m^{2}/s^{2}) |

P | static pressure |

P_{i} | indoor pressure |

P_{ref} | static pressure at the reference point |

Q | wind-induced airflow rate (m^{3}/s) |

R | range of wind pressure coefficient |

R1, R2, R3, R4, R5, R6, R7 | labels for different rows |

U | wind velocity (m/s) |

U(z) | wind velocity at the height z (m/s) |

U_{n} | normalized velocity |

U_{ref} | reference velocity |

W | distance between louvers and the windward facade |

x, y, z | coordinates |

y+ | dimensionless wall distance |

α | coefficient for power-law profile of wind velocity |

ε | turbulence dissipation rate (m^{2}/s^{3}) |

θ | rotation angle of external shading louvers (°) |

ρ | air density |

∆S_{R} | area of a grid on the outside surface |

$\overline{{C}_{\mathrm{p}}}$ | average wind pressure coefficient |

$\Delta \overline{{C}_{\mathrm{p}}}$ | difference of average wind pressure coefficient between a shaded condition and the non-shaded condition |

$\overline{\Delta {C}_{\mathrm{p}\text{-}\mathrm{R}}}$ | average difference of wind pressure coefficient for all shaded conditions compared with the non-shaded condition in a special row |

$\overline{\Delta {C}_{\mathrm{p}\text{-}\mathsf{\theta}}}$ | average difference of wind pressure coefficient between a specific shaded condition and the non-shaded condition in a whole row |

$\overline{{C}_{\mathrm{p}\text{-}\mathrm{n}}}$ | average wind pressure coefficient in the non-shaded condition |

$\overline{{C}_{\mathrm{p}\text{-}\mathrm{R}\text{-}j}}$ | average wind pressure coefficient in a specific row j |

$\overline{{C}_{\mathrm{p}\text{-}\mathsf{\theta}\text{-}i}}$ | average value of wind pressure coefficient for the shaded condition i with a specific rotation angle θ |

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**Figure 3.**Measurement lines on the central plane of the studied building for (

**a**) velocity U; and (

**b**) wind pressure coefficient C

_{p}.

**Figure 4.**Wind characteristics of approaching flow for computational fluid dynamics CFD simulation: (

**a**) velocity U; and (

**b**) turbulent intensity I distributions.

**Figure 7.**Grid resolution for the reference case: (

**a**) global grid resolution; (

**b**) grid resolution around the building and louvers.

**Figure 8.**Comparison of normalized velocity U/U

_{ref}distribution around the building on the measurement line: (

**a**) 2.5h

_{0}, (

**b**) 1.5h

_{0}, (

**c**) 0.5h

_{0}and (

**d**) −0.5h

_{0}.

**Figure 10.**Airflow pattern and wind pressure distribution. (

**a**) Airflow towards the central rows; (

**b**) Airflow towards the side rows.

**Figure 11.**Arrangement of rooms and measurement lines. (

**a**) Locations of seven rows and five floors, (

**b**) W-R-L lines along windward, roof and leeward surfaces; (

**c**) W-S-L lines along windward, lateral and leeward surfaces; and (

**d**) R-S lines along roof and lateral surfaces.

**Figure 12.**Local range R, local and average value of wind pressure coefficient C

_{p}for different shaded conditions on the central lines of different rows along the windward, roof and leeward surfaces. (

**a**) Local value along R1 and R7; (

**b**) Local range R and average value along R1 and R7; (

**c**) Local value along R2 and R6; (

**d**) Local range R and average value along R2 and R6.

**Figure 13.**Local range R, local and average value of wind pressure coefficient C

_{p}for different shaded conditions on the central lines of different floors along the windward, lateral and leeward surfaces. (

**a**) Local value along F1; (

**b**) Local range R and average value along F1; (

**c**) Local value along F2; (

**d**) Local range R and average value along F2; (

**e**) Local value along F3; (

**f**) Local range R and average value along F3; (

**g**) Local value along F4; (

**h**) Local range R and average value along F4; (

**i**) Local value along F5; (

**j**) Local range R and average value along F5.

**Figure 14.**Local range R, local and average value of wind pressure coefficient C

_{p}for different shaded conditions on the central lines of different rows along the roof and lateral surfaces. (

**a**) Local value along R3; (

**b**) Local range R and average value along R3; (

**c**) Local value along R4; (

**d**) Local range R and average value along R4; (

**e**) Local value along R5; (

**f**) Local range R and average value along R5.

**Figure 15.**Average wind pressure coefficient $\overline{{C}_{\mathrm{p}}}$ on outside surfaces of rooms under different shaded conditions for (

**a**) R1; (

**b**) R2; (

**c**) R3; (

**d**) R4; (

**e**) R5; (

**f**) R6; (

**g**) R7.

**Figure 16.**Difference $\Delta \overline{{C}_{\mathrm{p}}}$ of average wind pressure coefficient $\overline{{C}_{\mathrm{p}}}$ between different shaded conditions and the non-shaded condition for (

**a**) F5; (

**b**) F4; (

**c**) F3; (

**d**) F2; (

**e**) F1.

**Table 1.**Comparison of average value of normalized velocity U/U

_{ref}and wind pressure coefficient C

_{p}on measurement lines.

Value Type | U/U_{ref} | C_{p} | |||||
---|---|---|---|---|---|---|---|

−0.5h_{0} | 0.5h_{0} | 1.5h_{0} | 2.5h_{0} | Windward | Roof | Leeward | |

Average value (reference case) | 1.21 | 0.94 | 1.03 | 0.72 | 0.62 | −0.45 | −0.19 |

Average value (Jiang et al.) | 1.22 | 0.97 | 1.05 | 0.74 | 0.6 | −0.45 | −0.18 |

Absolute deviation | 0.08 | 0.05 | 0.04 | 0.1 | 0.03 | 0.09 | 0.02 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zheng, J.; Tao, Q.; Li, L. Wind Pressure Coefficient on a Multi-Storey Building with External Shading Louvers. *Appl. Sci.* **2020**, *10*, 1128.
https://doi.org/10.3390/app10031128

**AMA Style**

Zheng J, Tao Q, Li L. Wind Pressure Coefficient on a Multi-Storey Building with External Shading Louvers. *Applied Sciences*. 2020; 10(3):1128.
https://doi.org/10.3390/app10031128

**Chicago/Turabian Style**

Zheng, Jianwen, Qiuhua Tao, and Li Li. 2020. "Wind Pressure Coefficient on a Multi-Storey Building with External Shading Louvers" *Applied Sciences* 10, no. 3: 1128.
https://doi.org/10.3390/app10031128