# Numerical Simulation on Wind Speed Amplification of High-Rise Buildings with Openings

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## Abstract

**:**

## 1. Introduction

_{0}/d) and the fillet radius of the duct entrance and exit (r/d

_{0}), Ruiz et al. [21] evaluated the performance on the basis of average wind speed (U/U

_{0}) and turbulent kinetic energy (k/k

_{0}) ratios using the 3D steady RANS method, adding to the knowledge on wind energy harvesting of high-rise buildings.

## 2. CFD Verification and Validation

#### 2.1. Numerical Setups

_{H}at z = H, was 7.4 × 10

^{4}. The size of the computational domain was 94D(flow direction x) × 36D(spanwise direction y) × 36D(vertical direction z), as shown in Figure 2a. A structured grid was adopted for grid discretization, and the near-wall grid was appropriately encrypted, as shown in Figure 2b. Figure 2c shows a schematic diagram of the corresponding local encrypted area of the grid. Furthermore, to verify the effectiveness of the numerical simulation method and parameter settings, a square cylinder without opening measures was simulated via LES under different grid sizes, and the numerical simulation results were compared with those of the wind tunnel tests [25]. The three square cylinders with openings were named Case 1 (openings in X-direction), Case 2 (openings in Y-direction) and Case 3 (openings in both X-and Y-directions). The center of the opening hole was 5.45D away from the ground, as shown in Figure 3. Furthermore, Figure 4 illustrates the longitudinal section of the three models with openings. To study the effect of grid resolution, three different kinds of mesh schemes were arranged in the models, as shown in Table 1. The first grid point near the building model surface and the grid point near the ground were set to be different from each other. The grid stretch ratio was set to be less than 1.2, and the numbers of mesh schemes were about 8.96 × 10

^{5}and 1.508 × 10

^{6}, respectively.

#### 2.2. Boundary Conditions

_{0}is 2.25 × 10

^{−4}m, and the friction velocity u* is 0.557 m/s. The turbulent kinetic energy k(z) and dissipation rate ε(z) are determined as follows:

_{μ}is a model constant, whose value is 0.09.

_{S}is the subgrid-scale mixing length, and $\left|\overline{S}\right|=\sqrt{2{\overline{S}}_{ij}{\overline{S}}_{ij}}$. The subgrid mixing scale is defined as follows:

_{S}is the Smagorinsky constant, with its value varying according to the different properties of the flow field.

## 3. Results and Discussions

_{H}at z = H, are shown in Table 1.

_{i}is the wind pressure at the measurement point i of the model; ρ = 1.225 kg/m

^{3}is the air density; and U

_{H}is the incoming wind speed at the model height. For convenience of analysis, in the following analysis, C

_{pi,mean}and C

_{pi,rms}represent the mean and RMS wind pressure coefficients at the measurement point i, respectively.

#### 3.1. Effect of Openings on Wind Speed Amplification of High-Rise Buildings

_{i}is the mean wind speed at a measuring point in the openings, as shown in Figure 4, and U

_{r}is the mean wind speed of the approaching location at the same height. Equation (11) reflects the variation in mean wind speed. To analyze the influence on the pulsating wind speed in the flow direction, the amplification of pulsating wind speed is defined by referring to the above equation:

_{i,rms}is the RMS wind speed of the measuring point obtained via LES, as shown in Figure 4. From an observation of Table 2, it can be seen that after placing openings in the X-direction in the high-rise building, the mean and RMS wind speed in the openings both increased obviously compared to the wind speed of incoming flow at the same height (from A1 to A5). The wind speed amplification R

_{i}in the openings presented a trend of first increasing and then decreasing, reaching a peak at the center of the cylinder. In Case 1, the mean wind speed amplification R

_{i}of the monitoring points was basically the same as that for the RMS wind speed, which proves that in the case of along-wind openings in high-rise buildings, both the mean and RMS wind speed can increase in the openings, and the amplification amplitude R

_{i}is relatively close. This is because the narrow tube effect caused by the along-wind openings causes an acceleration in the mean and RMS wind speed in the openings.

#### 3.2. Distribution of Mean Wind Pressure Coefficients

#### 3.3. Analysis of Time-Averaged Flow Field

- (1)
- In general, one large-size separation vortex and two small-size separation vortices are formed on each side of the standard square cylinder close to the sidewall, and a pair of symmetric vortices of equal size and in opposite direction also exist on the leeward side. The large-size separation vortices and the small-size separation vortices at the upstream corner are connected with the leeward separation vortices. In the longitudinal section, the top of the windward side and the top of the leeward side of the square cylinder are separation points, and flow separation occurs when the air flows through this region. The top of the standard square cylinder and the top of the leeward surface each form a separate vortex, and the two separate vortices exist independently of each other. Due to the shielding effect of the structure, the incoming flow directly acts on the windward side of the structure, and then flow separation occurs at the top and two sides of the windward surface. Therefore, the side face and the top of the structure are in the separation zone. The suction effect is generated by the existence of the separation vortex, resulting in negative pressure on the side face and the top of the structure. The leeward side of the structure is subjected to the mixed effect of the separation vortex on the side face of the structure and the shedding vortex on the top, which produces wind suction, so it is also represented as negative pressure.
- (2)
- When compared with the standard square cylinder, the overall wind pressure distribution on the surface of the three opening models is consistent with the standard square cylinder, showing positive pressure on the windward side and negative pressure on the top, side face and leeward side. However, the wind pressure coefficient at the same position is different. For instance, the flow field around Case 1 changes significantly due to the aerodynamic measures of the X-direction openings. The wind pressure on the windward side is lower and the separation vortices behind the sidewalls of the cylinder are reattached on the flow field of the cross section. Symmetric vortices no longer appear on the leeward side. The incoming flow flows along with the openings, dividing the section into two rectangular sections with a large side ratio. The incoming flow in the openings disperses the large-scale separation vortices on the leeward side, and the generated separation vortices form vortices on the leeward side at the top of the tunnel. The scale of the generated separation vortices is lower than that of the standard square cylinder. The height of the vortex core is equal to the height of the tunnel, which reduces the negative pressure on the leeward side. Therefore, according to the cloud chart of wind pressure coefficient, the wind pressure difference between this area and the entrance of the opening on the windward side forms a narrow tube effect, which leads to a sharp increase in incoming wind speed in the opening due to the opening measure in the X-direction.
- (3)
- Similar to Case 1, the surrounding flow field and wind pressure distribution of Case 2 and Case 3 are clearly different from those of the standard square cylinder due to the opening measures. Under the opening measure in the Y-direction, due to the shielding effect of the windward side, the incoming flow in these openings basically has a lateral effect, and there is no large pressure difference due to the symmetrical distribution of wind pressure at both ends of the openings. As a result, although there is also a large negative pressure in the transverse openings, the X-direction wind speed in this area is significantly lower than that in the X-direction openings at the same height. After the measures for openings in both the X- and Y-directions are taken, the flow field and surface wind pressure distribution around Case 3 are close to those of Case 1. The wind speed under the influence of the measures of openings in both the X- and Y-directions presents an amplification compared to the wind speed of incoming flow at the same height (See Table 4). The wind speed amplification degree is slightly lower than that of Case 1, which also proves that the measure of X-direction openings plays a more important role in the incoming wind speed than that in the Y-direction.

#### 3.4. Analysis of Instantaneous Flow Field

- (1)
- A large number of vortex structures of different sizes and shapes are distributed around the structures. With a change in height, the vortex structures are also distributed differently, showing obvious three-dimensional characteristics. In the top region of the square cylinder, as the strip vortex separates at around the top separation point of the windward side of the upstream square cylinder, it mixes with the separation vortexes on both sides of the top, forming three-dimensional separation shear vortexes on the top of the square cylinder. With the continuous evolution of the vortex structure, the separation vortexes gradually move from the separation region to the downstream region. The measure of openings in the X-direction causes the flow separation point at the edge of the windward side to move down and the vortices at the top of the square cylinder to decrease. After establishing the openings in the X-direction, the narrow tube effect is formed, which not only accelerates the air flow through the entrance but also disorganizes the large-scale vortices on the leeward side. It forms several small-scale vortices near the entrance and on the leeward side, which disperses energy more. However, the measure of openings in the Y-direction leads to the lateral flow of separation vortices on both sides into the openings, which weakens the energy distribution on both sides. As a result, the lateral shear vortices of Case 2 are smaller than those of Case 1 and Case 3 and closer to the wall, which is determined by the variation in the aerodynamic configuration of the building caused by the opening measures.
- (2)
- Due to the friction effect on the ground, curved banded boundary-layer vortexes of different scales are generated in the near-ground region in front of the windward side for the three types of square cylinders with openings. The friction effect of the ground also causes the formation of spiral separation vortices on the side of the square cylinders, which is an embodiment of the turbulence pulsation of the incoming flow. Combined with the horizontal vortex diagrams in Figure 11, Figure 12 and Figure 13, the flow field morphology of Case 1, Case 2 and Case 3 is different after adopting openings in the X-direction, Y-direction and both X- and Y-directions, respectively. The side separation vortices of Case 2 are closer to the wall, and there are abundant small-scale vortices. In addition, three-dimensional strip separation vortices are also formed on the side of the square cylinder. The strip vortices of Case 1 and Case 3 have a larger scale and more concentrated vortex structure, while the strip vortices on the side of the square cylinder of Case 2 have a more dispersed scale. It can also be seen that the wind speed in the X-direction openings of Case 1 and Case 3 is significantly higher than that on the windward side of these square cylinders at the same height, while the windward side of Case 2 presents a lower wind speed as a whole due to the shielding effect. For vortices of various forms around the square cylinder, the larger these vortices are, the more energy they carry, the slower they move, and the smaller the wind pressure pulsation they generate. Conversely, the smaller the scale of the vortices, the more obvious the wind pressure pulsation. It is precisely because the opening measures change the aerodynamic configuration of the square cylinder that Case 1 and Case 3 gather small-scale vortex structures in the X-direction openings, which enhances the wind pressure pulsation and increases the mean and RMS wind speed in the openings, thus affecting the wind load on the surface of the square cylinder.

## 4. Conclusions

- (1)
- The parameter settings and inflow turbulence based on self-sustaining boundary conditions and generated via LES were adopted. The simulated mean wind profiles and wind velocity spectra are basically consistent with the related wind tunnel test results and can well predict the wind loads of the square cylinders.
- (2)
- Under the effect of the opening measures, the aerodynamic configuration of the square cylinders is changed, and the wind load and incoming wind speed also vary. By adopting the X-direction opening measure, the pressure on the windward side of the square cylinders decreases. Part of the air flow in the square cylinders flows through the tunnel into the wake negative pressure area, which affects the flow separation point location, shear flow diffusion angle and flow reattachment phenomenon. Meanwhile, the wind speed in the openings increases significantly due to the narrow tube effect, which blows away the large-scale vortices on the leeward side, leading to energy dispersion and weakening the wind pressure on the structural surface. In contrast, the wind speed in the openings decreases significantly due to the shielding effect, and the wind load and the wind-induced response on the surface of the square cylinder are not significantly improved.
- (3)
- Under the measure of openings in both the X- and Y-directions, the vortex structures in the openings are more complex, the vortex departure frequency components are more complex, and the energy distribution is more dispersed. The wind speed in the X-direction openings still increases sharply, but the wind speed reduction in the Y-direction openings is weaker than that of Case 2. The wind speed in the central monitoring point still increases significantly under the influence of opening measures in both the X- and Y-directions, which proves that the X-direction openings play a more important role than the openings in the Y-direction.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Overview of the Pearl River Tower [18].

**Figure 2.**Computational situations: (

**a**) computational domain and boundary conditions; (

**b**) meshes for the whole domain; and (

**c**) local meshes.

**Figure 3.**Geometries and computational grids for three models with openings: (

**a**) model without openings; (

**b**) Case 1; (

**c**) Case 2; and (

**d**) Case 3.

**Figure 4.**Longitudinal section of three models with openings: (

**a**) Case 1; (

**b**) Case 2; and (

**c**) Case 3.

**Figure 5.**Histograms of the range of CFL number of three mesh schemes: (

**a**) Mesh 1; (

**b**) Mesh 2; and (

**c**) Mesh 3.

**Figure 6.**Comparison of wind tunnel tests and numerical simulations: (

**a**) mean wind velocity profile; (

**b**) turbulence intensity profile and velocity spectrum at (

**c**) z = 0.5H and (

**d**) z = H; (

**e**) mean wind pressure coefficients; and (

**f**) RMS wind pressure coefficients.

**Figure 7.**Mean wind pressure coefficients for standard cylinder: (

**a**) windward; (

**b**) leeward; (

**c**) leftward; and (

**d**) rightward.

**Figure 8.**Comparison of mean pressure coefficients for three cases (from left to right: Case 1, Case 2 and Case 3): (

**a**) windward; (

**b**) leeward; (

**c**) leftward; and (

**d**) rightward.

**Figure 9.**Comparison of time-averaged streamlines around the cylinder: (

**a**) standard; (

**b**) Case 1; (

**c**) Case 2; and (

**d**) Case 3.

**Figure 14.**Comparisons of the structure of transient vortices around the building model (from left to right: top view, overall view and partial enlarged view of top position): (

**a**) standard; (

**b**) Case 1; (

**c**) Case 2; and (

**d**) Case 3.

Case | Minimum Grid Size | Stretch Ratio | Number of Cells | y^{+} | S_{t} |
---|---|---|---|---|---|

Standard_Mesh 1 | 0.005D | 1.15 | 896,000 | <30 | 0.098 |

Standard_Mesh 2 | 0.001D | 1.15 | 896,000 | <15 | 0.096 |

Standard_Mesh 3 | 0.0005D | 1.10 | 1,508,000 | <5 | 0.098 |

Case 1 | 0.0005D | 1.10 | 1,540,000 | <5 | 0.092 |

Case 2 | 0.0005D | 1.10 | 1,540,000 | <5 | 0.09 |

Case 3 | 0.0005D | 1.10 | 1,400,000 | <5 | 0.092 |

A1 | A2 | A3 | A4 | A5 | |
---|---|---|---|---|---|

R_{i} | 1.024 | 1.36 | 1.30 | 1.27 | 1.10 |

R_{i,rms} | 1.025 | 1.36 | 1.31 | 1.28 | 1.11 |

B1 | B2 | B3 | B4 | B5 | |
---|---|---|---|---|---|

R_{i} | 0.0055 | −0.001 | 0.00129 | 0.00255 | 0.0001 |

R_{i,rms} | 0.077 | 0.049 | 0.049 | 0.052 | 0.093 |

C1 | C2 | C3 | C4 | C5 | |

R_{i} | 1.06 | 1.41 | 1.26 | 1.28 | 1.24 |

R_{i,rms} | 1.07 | 1.41 | 1.26 | 1.28 | 1.25 |

C6 | C7 | C8 | C9 | ||

R_{i} | −0.022 | −0.00363 | 0.00248 | 0.028 | |

R_{i,rms} | 0.07 | 0.075 | 0.075 | 0.078 |

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**MDPI and ACS Style**

Gu, Z.; Chen, F.; Zhu, Y.; Mei, Y.; Wang, Z.; Xu, L.; Li, Y.
Numerical Simulation on Wind Speed Amplification of High-Rise Buildings with Openings. *Atmosphere* **2023**, *14*, 1687.
https://doi.org/10.3390/atmos14111687

**AMA Style**

Gu Z, Chen F, Zhu Y, Mei Y, Wang Z, Xu L, Li Y.
Numerical Simulation on Wind Speed Amplification of High-Rise Buildings with Openings. *Atmosphere*. 2023; 14(11):1687.
https://doi.org/10.3390/atmos14111687

**Chicago/Turabian Style**

Gu, Ziqi, Fubin Chen, Yuzhe Zhu, Yu Mei, Zhanli Wang, Linfeng Xu, and Yi Li.
2023. "Numerical Simulation on Wind Speed Amplification of High-Rise Buildings with Openings" *Atmosphere* 14, no. 11: 1687.
https://doi.org/10.3390/atmos14111687