# Advances in CFD Modeling of Urban Wind Applied to Aerial Mobility

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## Abstract

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## 1. Introduction

## 2. Turbulence Models

- MITRAS [34], defined by authors as a “microscale obstacle-resolving model”, computes the wind components, temperature, humidity, and precipitation fields, explicitly resolving obstacles, such as buildings, which are represented by impermeable grid cells at the building positions so that the wind speed vanishes in these grid cells.
- PALM [35], which is an abbreviation for “Parallelized Large-Eddy Simulation Model”, has been widely used to model the atmospheric layer both in the ocean and on land. It uses an LES turbulence model and is especially focused on parallelization. PALM has been used to study ventilation at the pedestrian level, to study wind in street canyons, and even to simulate entire cities. In this regard, the simulation of the city of Macau stands out [36]. The simulation domain has an extension of 30 km
^{2}and a spatial resolution of 1 m. The simulation time was about one hour, while the results required 128 CPUs in parallel, running for 1.5 h. - ASMUS [37] has been specifically designed to simulate wind and temperature distribution in cities. The turbulence model is RANS and employs the Prandtl–Kolmogorov relation to fulfill the kinetic energy of turbulence modeling. They achieved mesh resolutions of 2 m and were able to simulate more than 44 h. However, the total CPU time is not included in the original paper and it appears that no other studies since 2014 have used this software.
- ENVI-met [38] is built on RANS equations using a 1.5 order turbulence closure model. Some studies [39] mentioned that this closure model tends to overestimate the turbulent production in areas with high acceleration or deceleration, such as the flow around a building. ENVI-met is the detailed vegetation model, in which plants are not only symbolized as a porous media to solar insolation and wind flow, but could actually interact with the surrounding environment by evapotranspiration [40] It has been used to study the wind pattern in cities such as Bilbao [39]. Unlike the other options, it is a paid software.

## 3. Meshing

## 4. Boundary Conditions

- One of the most common options is known as extrapolation [54]. In this method, only one of the mesoscale model profiles is imposed on an entire inlet face of the CFD domain, while the mesoscale wind data are extrapolated in the grid points outside that profile. This method is the easiest to implement; however, the distributions of the wind velocity on the boundary is uniform in the horizontal direction and, as a consequence, extrapolation is not capable of appropriately coupling the mesoscale and CDF solvers over complex terrains.
- Imposing the zero-gradient boundary conditions at the outflow boundaries and a space-varying inlet condition is another solution [55]. The problem with this solution is in determining which boundary is an inlet and which one is outlet, and how that configuration can change from one day to another.
- The side and top surfaces are modeled as spatially and time-varying velocity inflow and outflow conditions, and the data are extracted from the mesoscale model solutions using interpolation [56]. This solution is the most robust while it comes at the price of implementation complexity.

- Baik, Park, and Kim [64], using the turbulence model RNG $k-\u03f5$, estimated the viscosity dissipation using following the equation:$$\u03f5\left(z\right)=\frac{{C}_{\mu}^{\frac{3}{4}}{k}^{\frac{3}{2}}}{\kappa z},$$
- Mochida et al. [65] calculated the viscous dissipation based on the length scale of the precedent mesoscale domain. In order to do it, they used the following equation:$$\u03f5\left(z\right)=2\sqrt{\frac{2{k}^{3/2}}{{B}_{1}l}},$$
- Another method is considered by Tewari et al. [63]. They used the definition of the viscous dissipation:$$\u03f5\left(z\right)=\frac{\rho {C}_{\mu}{k}^{2}}{{\mu}_{t}},$$

## 5. Dimensionality Reduction Methods

## 6. Data Assimilation and Validation

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${B}_{1}$ | Closure constant |

${C}_{\mu}$ | Mathematical constant |

DF | Darcy–Forchheimer model |

DNS | Direct numerical simulation |

DMD | Dynamic mode decomposition |

DTM | Digital terrain model |

IDW | Inverse distance weighting interpolation |

G | Filtering kernel |

GIS | Geographic information system |

$k$ | Turbulence kinetic energy |

LES | Large-eddy simulation |

$\tilde{p}$ | Static pressure |

P | Mean component of the pressure |

POD | Proper orthogonal decomposition |

p | Fluctuating component of the pressure |

RANS | Reynolds-averaged Navier–Stokes equations |

UAV | Unmanned aerial vehicle |

${\tilde{u}}_{i}$ | i-the component of the fluid velocity |

${\mathrm{U}}_{\mathrm{i}}$ | Mean component of the velocity |

${\mathrm{u}}_{\mathrm{i}}$ | Fluctuating component of the velocity |

${u}_{*}$ | Shear velocity |

${T}_{ij}$ | Viscous stresses |

$\u03f5$ | Turbulence dissipation |

$\kappa $ | von Kárman constant |

$\tilde{\rho}$ | fluid density |

$\omega $ | Specific rate of dissipation of turbulence kinetic energy |

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**Figure 3.**Diagram showing the relationship between the different components of the proposed solution.

**Figure 6.**Numerical predictions of the flow field at University of León campus showing the different flow patterns for two different wind directions.

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**MDPI and ACS Style**

García-Gutiérrez, A.; Gonzalo, J.; López, D.; Delgado, A.
Advances in CFD Modeling of Urban Wind Applied to Aerial Mobility. *Fluids* **2022**, *7*, 246.
https://doi.org/10.3390/fluids7070246

**AMA Style**

García-Gutiérrez A, Gonzalo J, López D, Delgado A.
Advances in CFD Modeling of Urban Wind Applied to Aerial Mobility. *Fluids*. 2022; 7(7):246.
https://doi.org/10.3390/fluids7070246

**Chicago/Turabian Style**

García-Gutiérrez, Adrián, Jesús Gonzalo, Deibi López, and Adrián Delgado.
2022. "Advances in CFD Modeling of Urban Wind Applied to Aerial Mobility" *Fluids* 7, no. 7: 246.
https://doi.org/10.3390/fluids7070246