# Study on Accuracy of CFD Simulations of Wind Environment around High-Rise Buildings: A Comparative Study of k-ε Turbulence Models Based on Polyhedral Meshes and Wind Tunnel Experiments

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## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. Outline of Wind Tunnel Experiment

#### 2.2. Numerical Simulations

#### 2.2.1. Model Building and Computational Domain

#### 2.2.2. Boundary Conditions

_{μ}is a constant with a value of 0.09; k(z) is the turbulent energy, which can be obtained from a wind tunnel experiment or an observation of corresponding surroundings; U(z) is the wind speed at any point in the computational domain; and z is the height of any point in the computational domain [43].

#### 2.2.3. Turbulence Model

#### 2.2.4. Convergence Conditions

#### 2.2.5. Meshing

#### 2.3. Mesh Sensitivity Analysis

_{0}is the value of the finest mesh (Case 4 in Table 2; base mesh size of 0.02 m), v

_{x}is the value of the other mesh (other cases in Table 2; base sizes of 0.1 m, 0.06 m, and 0.04 m), and n is the number of monitoring points.

## 3. Results

#### 3.1. Reattachment Length Comparison

_{R}) and behind the building (X

_{F}) are shown in Figure 8 [40]. Different CFD codes or different calculation conditions lead to different simulation results [55]. Table 3 lists the relative reattachment lengths on the top of the building (X

_{R}/b) and behind the building (X

_{F}/b) for eight turbulence models and the corresponding wind tunnel experiment. The SKE and SLRNKE models did not show a reattachment on the top of the building, which was inconsistent with the experiment. The X

_{F}/b-value for the V2FKE model was much higher than the value derived from the experiment. The simulation results of the STLKE model, the RTLKE model, the SLRNKE model, and the EBKE model are compared in this paper.

#### 3.2. Speed Comparison

#### 3.2.1. Comparison of Wind Speeds on the Vertical Plane at Y = 0

#### 3.2.2. Comparison of Wind Speeds on the Horizontal Plane

#### 3.3. Comparison of Turbulent Kinetic Energy

#### 3.3.1. Comparison of Turbulent Kinetic Energy at Y = 0

#### 3.3.2. Comparison of Turbulent Kinetic Energy at z/b = 0.125

#### 3.3.3. Comparison of Turbulent Kinetic Energy at z/b = 1.25

## 4. Discussion

- (a)
- In the low-wind-speed area, the STLKE model and the RTLKE model could predict turbulence kinetic energy in a more accurate way. The RTLKE model also performed well in predicting the wind speed on the vertical and horizontal planes. The RTLKE model could be used for simulations in research studies of low wind-speed areas to predict the size of the static-wind areas around high-rise buildings, the diffusion time of pollutants around buildings, etc.
- (b)
- In the high-wind-speed area, the STLKE model and the RTLKE model could accurately predict wind speed. Between them, the STLKE model performed better in simulating the turbulence kinetic energy. Therefore, the STLKE model is recommended to be used for simulations in research studies of high wind-speed areas (e.g., windward side) of high-rise buildings to predict the damage of high wind speed to the area around buildings during a typhoon, the maximum wind-speed area around high-rise buildings, etc.

## 5. Conclusions

- (1)
- Under polyhedral mesh conditions, the modified k-e models applied with the wall function and the damping function improved the accuracy of the simulations but could still not perfectly match the wind tunnel experiment results. The correction of the models (e.g., optimizing the closure coefficients of the RANS turbulence model) needs to be further studied in order to significantly improve the accuracy of CFD simulations.
- (2)
- In the low-wind-speed area, the simulation results of the RTLKE model were the closest to the experimental results of the wind tunnels. In the high-wind-speed area, the simulation results of the STLKE model were the closest to the experimental results of the wind tunnels. So, these two models are recommended to be used for the simulation of wind around high-rise buildings under different circumstances.
- (3)
- In practice, it is recommended to use the STLKE model to explore high-wind-speed areas around high-rise buildings (e.g., the high-wind-speed areas around buildings during a typhoon, the maximum wind speed area around high-rise buildings, etc.). It is recommended to use the RTLKE model to explore low-wind-speed areas around high-rise buildings (e.g., the size of the static-wind area around high-rise buildings, the diffusion time of pollutants around buildings, etc.).

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**Distribution of wind-speed test points: (

**a**) distribution on the xz-plane (y = 0), (

**b**) distribution on the xy-plane (z = 0.125b and z = 1.25b).

Length (m) | Width (m) | Height (m) | Block Mesh Size/Base Mesh Size | |
---|---|---|---|---|

Block 1 | 0.16 | 0.16 | 0.2 | 10% |

Block 2 | 0.64 | 0.24 | 0.26 | 15% |

Block 3 | 0.72 | 0.4 | 0.32 | 20% |

Base Mesh Size (m) | Architectural Mesh Size (m) | Mesh Numbers of Building Surface | Calculation Time (s) | |
---|---|---|---|---|

Case 1 | 0.10 | 0.01 | 977 | 152 |

Case 2 | 0.06 | 0.006 | 2869 | 865 |

Case 3 | 0.04 | 0.004 | 5944 | 6235 |

Case 4 | 0.02 | 0.002 | 23,386 | 81,154 |

SKE | STLKE | SLRNKE | RKE | RTLKE | AKNKE | EBKE | V2FKE | Wind Tunnel Experiment | |
---|---|---|---|---|---|---|---|---|---|

X_{R}/b | — | 0.33 | — | 0.38 | 0.32 | 0.89 | 0.37 | 0.85 | 0.52 |

X_{F}/b | 2.63 | 2.38 | 2.53 | 3.05 | 2.65 | 3.55 | 3.20 | 4.35 | 1.42 |

AKNKE | EBKE | RKE | STLKE | RTLKE | Wind Tunnel Experiment | |
---|---|---|---|---|---|---|

Location of contour line of 0 m/s in X-direction (low-wind-speed area) | >3.5 | >3.5 | >3.5 | 2.90 | 3.15 | 1.85 |

Location of contour line of 5 m/s in Z-direction (high-wind-speed area) | 2.65 | 2.72 | 2.78 | 2.83 | 2.80 | 2.90 |

AKNKE | EBKE | RKE | STLKE | RTLKE | Wind Tunnel Experiment | |
---|---|---|---|---|---|---|

Location of the contour line of −0.25 m/s in Z-direction (low-wind-speed area) | 0.45 | 0.45 | 0.45 | 0.75 | 0.65 | 1.05 |

Location of the contour line of 0.5 m/s in Z-direction (high-wind-speed area) | 2.80 | 2.70 | 2.75 | 2.75 | 2.75 | 2.70 |

AKNKE | EBKE | RKE | STLKE | RTLKE | Wind Tunnel Experiment | |
---|---|---|---|---|---|---|

Location of the contour line of −0.5 m/s in X-direction (low-wind-speed area) | >3.5 | 2.90 | 2.94 | 1.98 | 2.25 | 1.40 |

Location of the contour line of 3 m/s in Y-direction (high-wind-speed area) | −1.23 | −1.35 | −1.35 | −1.45 | −1.35 | −1.65 |

AKNKE | EBKE | RKE | STLKE | RTLKE | Wind Tunnel Experiment | |
---|---|---|---|---|---|---|

Location of the contour line of 0 m/s in X-direction (low-wind-speed area) | 1.55 | 1.55 | 1.50 | 1.00 | 1.26 | 1.30 |

Location of the contour line of −0.5 m/s in X-direction (high-wind-speed area) | 0.55 | 0.30 | 0.33 | 0.04 | −0.10 | −0.02 |

AKNKE | EBKE | RKE | STLKE | RTLKE | Wind Tunnel Experiment | |
---|---|---|---|---|---|---|

Location of the contour line of 0 m/s in X-direction (low-wind-speed area) | 2.15 | 1.57 | 1.80 | 1.46 | 1.63 | 1.45 |

Location of the contour line of 4.25 m/s in Y-direction (high-wind-speed area) | −1.48 | −1.65 | −1.80 | −1.84 | −1.83 | −1.80 |

AKNKE | EBKE | RKE | STLKE | RTLKE | Wind Tunnel Experiment | |
---|---|---|---|---|---|---|

Location of the contour line of 0 m/s in X-direction (low-wind-speed area) | 1.62 | 1.07 | 1.00 | 0.92 | 0.92 | 1.60 |

Location of the contour line of −0.25 m/s in X-direction (high-wind-speed area) | 0.35 | 0.10 | 0.19 | 0.15 | 0.03 | −0.07 |

Location | Recommended Models | Not-Recommended Models (Much Different from the Experiment) |
---|---|---|

X-velocity (Y = 0) | STLKE, RTLKE | RKE, EBKE, AKNKE |

Z-velocity (Y = 0) | STLKE, RTLKE | RKE, EBKE, AKNKE |

X-velocity at z/b = 0.125 | STLKE, RTLKE | RKE, EBKE, AKNKE |

Y-velocity at z/b = 0.125 | RTLKE | STLKE, RKE, EBKE, AKNKE |

X-velocity at z/b = 1.25; | STLKE, RKE, RTLKE, EBKE | AKNKE |

Y-velocity at z/b = 1.25 | AKNKE | RKE, STLKE, RTLKE, EBKE |

Total | RTLKE |

Location | Recommended Models | Not-Recommended Models (Much Different from the Experiment) |
---|---|---|

X-velocity (Y = 0) | All | |

Z-velocity (Y = 0) | All | |

X-velocity at z/b = 0.125 | STLKE, EBKE, RKE, RTLKE, | AKNKE |

Y-velocity at z/b = 0.125 | STLKE, RTLKE | RKE, EBKE, AKNKE |

X-velocity at z/b = 1.25; | STLKE, RTLKE, RKE, EBKE | AKNKE |

Y-velocity at z/b = 1.25 | STLKE, RTLKE, EBKE, RKE | AKNKE |

Total | STLKE, RTLKE | EBKE, RKE, AKNKE |

AKNKE | EBKE | RKE | STLKE | RTLKE | Wind Tunnel Experiment | |
---|---|---|---|---|---|---|

Location of the contour line of 0.5 in X-direction (low-wind-speed area) | 0.90 | 2.05 | >3.5 | 0.65 | 1.60 | 0.77 |

Location of the contour line of 1 in Z-direction (high-wind-speed area) | _ | _ | _ | 2.25 | _ | 2.30 |

AKNKE | EBKE | RKE | STLKE | RTLKE | Wind Tunnel Experiment | |
---|---|---|---|---|---|---|

Location of the contour line of 0.5 in X-direction (low-wind-speed area) | 1.75 | 1.50 | - | 0.55 | 1.47 | 0.70 |

Location of the contour line of 1 in Y-direction (high-wind-speed area) | - | −0.54 | - | −0.65 | −0.48 | −1.02 |

AKNKE | EBKE | RKE | STLKE | RTLKE | Wind Tunnel Experiment | |
---|---|---|---|---|---|---|

Location of the contour line of 0.75 in X-direction (low-wind-speed area) | 2.61 | 1.74 | 2.10 | 0.88 | 1.70 | 0.87 |

Location of the contour line of 1 in Y-direction (high-wind-speed area) | −0.75 | −0.70 | −0.70 | −0.90 | - | −1.22 |

Location | Recommended Models | Not-Recommended Models (Much Different from the Experiment) |
---|---|---|

Y = 0 | STLKE, AKNKE, RTLKE | RKE, EBKE, |

z/b = 0.125 | STLKE, AKNKE, RTLKE | EBKE, RKE |

z/b = 1.25 | STLKE, RTLKE, EBKE | RKE, AKNKE |

Total | STLKE, RTLKE | RKE, EBKE, AKNKE |

Location | Recommended Models | Not-Recommended Models (Much Different from the Experiment) |
---|---|---|

Y = 0 | STLKE | RTLKE, RKE, AKNKE, EBKE |

z/b = 0.125 | STLKE, EBKE, RTLKE | RKE, AKNKE |

z/b = 1.25 | STLKE, EBKE, RKE | RTLKE, AKNKE |

STLKE | RTLKE, RKE, AKNKE, EBKE |

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**MDPI and ACS Style**

Xiong, M.; Chen, B.; Zhang, H.; Qian, Y.
Study on Accuracy of CFD Simulations of Wind Environment around High-Rise Buildings: A Comparative Study of k-ε Turbulence Models Based on Polyhedral Meshes and Wind Tunnel Experiments. *Appl. Sci.* **2022**, *12*, 7105.
https://doi.org/10.3390/app12147105

**AMA Style**

Xiong M, Chen B, Zhang H, Qian Y.
Study on Accuracy of CFD Simulations of Wind Environment around High-Rise Buildings: A Comparative Study of k-ε Turbulence Models Based on Polyhedral Meshes and Wind Tunnel Experiments. *Applied Sciences*. 2022; 12(14):7105.
https://doi.org/10.3390/app12147105

**Chicago/Turabian Style**

Xiong, Minghui, Bing Chen, Hua Zhang, and Yao Qian.
2022. "Study on Accuracy of CFD Simulations of Wind Environment around High-Rise Buildings: A Comparative Study of k-ε Turbulence Models Based on Polyhedral Meshes and Wind Tunnel Experiments" *Applied Sciences* 12, no. 14: 7105.
https://doi.org/10.3390/app12147105