# CFD Analysis of Wind Distribution around Buildings in Low-Density Urban Community

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## Abstract

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## 1. Introduction

## 2. Mathematical Formulation

#### 2.1. Real View of the Studied Area

^{2}. The four orientations are presented in Figure 1.

#### 2.2. Hypothesis

- Flow with three-dimensional (3D) aspect in steady state.
- Air is considered as the work fluid with constant physical and thermal properties.
- Flow with turbulent and fully developed aspect.
- Thermal effects due to the thermal gradient between the ground and the ambient air are neglected.

#### 2.3. Geometric Configuration and Numerical Model

#### 2.4. Governing Equations

_{k}and G${}_{\omega}$ represent, respectively, the generation of k and ω due to the mean velocity gradient. ${\mathrm{\Gamma}}_{k}$ and ${\mathrm{\Gamma}}_{\omega}$ are, respectively, the effective diffusivity for k and ω. Y

_{k}and Y${}_{\omega}$ are the dissipation of k and ω, respectively, due to the turbulence. S

_{k}and S${}_{\omega}$ are the source terms for turbulent kinetic energy and its source dissipation ratio (considered to be zero in the present simulation), respectively. The default value of the turbulent Prandtl number Pr

_{t}is 0.85. The effective diffusivity for the k-ω model is given by the following expression:

_{D}is the drag coefficient

_{f}is the friction drag coefficients and C

_{p}is the pressure drag coefficients.

#### 2.5. Grid Distribution and Boundary Conditions

_{a}) and $\frac{\partial u}{\partial y}=\frac{\partial v}{\partial y}=\frac{\partial k}{\partial y}=\frac{\partial \omega}{\partial y}=0$.

_{0}is the average value of the inlet velocity (in the present study u

_{0}= 2, 4, 6, and 8 m/s), C

_{μ}is a constant value equal to 0.09, and d is the hydraulic diameter d = 457 m. Based on the different considered inlet velocity, we obtained the following values of k

_{0}and ω

_{0}. The imposed values of k

_{0}and ω

_{0}imposed at the inlet boundary are presented in Table 2.

#### 2.6. Numerical Method

^{−4}. We have verified that decreasing this convergence criterion has practically no effect on the results.

#### 2.7. Validation Test

_{p}(Figure 4b). As shown in Figure 4, our chosen model uses the simple algorithm (semi-implicit method for pressure-linked equations) with the k-ω turbulence model and for three different mesh sizes, i.e., 128 × 10

^{3}cells, 400 × 10

^{3}cells, and 600 × 10

^{3}cells. Figure 4a clearly shows a noticeable difference between the plot using 128 × 10

^{3}and 400 × 10

^{3}cells, whereas no significant difference is observed between plots with 400 × 10

^{3}and 600 × 10

^{3}cells. So, the grid-size convergence is reached for the 400 × 10

^{3}cells, which allows reduced calculation times and delivers results in agreement with Ramponi et al. [13], with an error rate of less than 2.5%.

## 3. Results

_{d}(Figure 11a), the friction coefficient C

_{f}(Figure 11b), and the turbulent kinetic energy k (Figure 11c).

_{d}, C

_{f}, and k remain constant when varying z and increasing amplitude for large values of the wind velocity. Along the third zone (z = 40 up to z = 67 m), the growth rate of the different curves is strongly influenced by the wind speed. We can clearly observe that the slope of the P

_{d}, C

_{f}, and k as a function of z increases with wind velocity, which shows the intensification of the height effect on the turbulence level as the wind speed increases. Thus, the top of the tower has a high turbulence zone when the air speed exceeds 4 m/s. It is therefore strongly discouraged to install a landing zone for helicopters, for example, or to plan any human activity in the open air.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Wind speed and pressure coefficient validation (

**a**) Vertical profile of stream-wise wind speed (

**b**) Pressure coefficient.

**Figure 5.**Comparison of the pressure coefficient profiles for different wind angles with Glumac et al. [10].

**Figure 8.**Streamlines and X velocity contours on the plane Z = 1.5 m: V = 4 m/s for the EST direction inlet (

**a**), the WEST direction inlet (

**b**), the SOUTH direction inlet (

**c**), and the NORTH direction inlet (

**d**).

**Figure 9.**Zoomed view streamlines and X velocity contours: V = 4 m/s, SOUTH direction inlet (

**a**) Hail’s tower, (

**b**) Mosque, (

**c**) Dates Market, (

**d**) Semah Center Hail.

**Figure 11.**Dynamic pressure (

**a**), friction coefficient (

**b**), and the turbulent kinetic energy (

**c**) as function of altitude z.

${\mathit{\alpha}}_{\mathit{\infty}}^{*}$ | ${\mathit{\alpha}}_{\mathit{\infty}}$ | ${\mathit{\alpha}}_{\mathbf{0}}$ | ${\mathit{\beta}}_{\mathit{\infty}}^{*}$ | ${\mathit{\beta}}_{\mathit{i}}$ | ${\mathit{R}}_{\mathit{\beta}}$ | ${\mathit{R}}_{\mathit{k}}$ | ${\mathit{R}}_{\mathit{w}}$ | ${\mathit{\zeta}}^{*}$ | ${\mathit{M}}_{\mathit{t}\mathbf{0}}$ | ${\mathit{\sigma}}_{\mathit{k}}$ | ${\mathit{\sigma}}_{\mathit{w}}$ |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0.52 | 1/9 | 0.09 | 0.072 | 8 | 6 | 2.95 | 1.5 | 0.25 | 2 | 2 |

u_{0} (m/s) | k_{0} (m²/s) | ω_{0} (1/s) |
---|---|---|

2 | 0.015 | 0.007 |

4 | 0.06 | 0.014 |

6 | 0.135 | 0.021 |

8 | 0.24 | 0.028 |

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**MDPI and ACS Style**

Hnaien, N.; Hassen, W.; Kolsi, L.; Mesloub, A.; Alghaseb, M.A.; Elkhayat, K.; Abdelhafez, M.H.H.
CFD Analysis of Wind Distribution around Buildings in Low-Density Urban Community. *Mathematics* **2022**, *10*, 1118.
https://doi.org/10.3390/math10071118

**AMA Style**

Hnaien N, Hassen W, Kolsi L, Mesloub A, Alghaseb MA, Elkhayat K, Abdelhafez MHH.
CFD Analysis of Wind Distribution around Buildings in Low-Density Urban Community. *Mathematics*. 2022; 10(7):1118.
https://doi.org/10.3390/math10071118

**Chicago/Turabian Style**

Hnaien, Nidhal, Walid Hassen, Lioua Kolsi, Abdelhakim Mesloub, Mohammed A. Alghaseb, Khaled Elkhayat, and Mohamed Hssan Hassan Abdelhafez.
2022. "CFD Analysis of Wind Distribution around Buildings in Low-Density Urban Community" *Mathematics* 10, no. 7: 1118.
https://doi.org/10.3390/math10071118