# Ventilation and Air Quality in City Blocks Using Large-Eddy Simulation—Urban Planning Perspective

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Model Description

#### 2.2. Model Construction

#### 2.2.1. Modelling Area

#### 2.2.2. Urban Surface Data

#### 2.2.3. Tree Canopy Model

#### 2.2.4. Lagrangian Stochastic Particle Model (LPM)

#### 2.3. Computational Set-Up

#### 2.4. Simulations and Data Output

#### 2.5. Ventilation and Dispersion Measures

## 3. Results

#### 3.1. Particle Concentration pc

#### 3.2. Turbulent Particle Flux ${F}_{p}$

#### 3.3. Particle Dilution Rate D

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

ABL | Atmospheric boundary layer |

CFD | Computational fluid dynamics |

LAD | Leaf area density |

LES | Large-eddy simulaion |

LPM | Lagrangian stochastic particle model |

MOST | Monin-Obukhov similarity theory |

PAD | Plant area density |

PALM | Parallelized Large-Eddy Simulation Model |

par | parallel |

parJJ | paraller with Jin-Jang shape variation |

per | perpendicular |

perHV | perpendicular with height variation |

RANS | Reynolds-averaged Navier-Stokes equations |

## Appendix A. Technical Specifications

V${}_{\mathbf{type}}$ | Characteristics |
---|---|

Programming language | Fortran 95/2003 |

Discretization | Arakawa staggered C-grid [77,78] |

Parallelization | Two-dimensional domain decomposition (e.g., [36]). Communication between processors realized using Message Passing Interface (MPI). |

Sub-grid closure | 1.5-order scheme based on Deardorff [79] |

Advection scheme | 5th-order advection scheme by Wicker and Skamarock [80] |

Pressure solver | Iterative multigrid scheme (e.g., [81]) |

Time step closure | 3rd-order Runge-Kutta approximation [82] |

Boundary condition between the surface and the first grid level | Monin-Obukhov similarity theory [83] |

## Appendix B. Particle Concentration pc for the Supportive Simulations

**Figure A1.**40-min horizontal mean particle concentrations $pc$ (${\mathrm{m}}^{-3}$) for the (

**a**) neutral run with an easterly wind and (

**b**) stable run with a southwesterly wind separately above the boulevard, other street canyons, courtyards and surroundings at height z = 4 m (bars with solid lines) and z = 10 m (bar with dashed lines) for all runs. 90th percentile values are given with errorbars. The mean difference to the values in V${}_{\mathrm{par}}$ is given in percentages ($\Delta $V${}_{\mathrm{par}}$).

## Appendix C. 5-Minute Mean High-Frequency Vertical Turbulent Particle Flux Density F_{p,HF}

**Figure A2.**5-min mean high-frequency vertical turbulent particle flux density ${F}_{p,HF}$ (m

^{−2}s

^{−1}) at z = 20 m under the (

**a**) general and (

**b**) wintry inflow conditions. The analysis area is marked in Figure 2 with a black solid line.

## Appendix D. Low-Frequency Vertical Turbulent Particle Flux Density F_{p,HF} for the Supportive Simulations

**Figure A3.**Horizontal mean of the low-frequency vertical turbulent particle flux density ${F}_{p,LF}$ (m

^{−2}s

^{−1}) for the (

**a**) neutral and (

**b**) stable runs separately for the boulevard, other street canyons, courtyards and surroundings at z = 20 m for all runs. The difference to the value in V${}_{\mathrm{par}}$ is given in percentages ($\Delta $V${}_{\mathrm{par}}$).

## Appendix E. Column-Averaged Dilution Rate 〈D(x,y)〉_{t,z} for the Supportive Simulations

**Figure A4.**Mean ${\langle D(x,y)\rangle}_{t,z}$ (×10

^{−3}m

^{−3}s

^{−1}) for the (

**a**) neutral run with an easterly wind and (

**b**) stable run with a southwesterly wind separately for the boulevard, other street canyons, courtyards and surroundings between z = 1–20 m for all runs. D is calculated using data from the first 50 s after the particle source has been switched off. The difference to the value in V${}_{\mathrm{par}}$ is given in percentages ($\Delta $V${}_{\mathrm{par}}$).

## Appendix F. Column-Averaged Dilution Rate 〈D(x,y)〉_{t,z} with Different Averaging Periods

**Figure A5.**Mean ${\langle D(x,y)\rangle}_{t,z}$ (×10

^{−3}m

^{−3}s

^{−1}) under the general (

**left**) and wintry (

**right**) inflow conditions separately for the boulevard, other street canyons, courtyards and surroundings between z = 1–20 m for all runs. D is calculated for different averaging periods: (

**a**) 30 s; (

**b**) 40 s; (

**c**) 50 s; (

**d**) 60 s and (

**e**) 70 s. The difference to the value in V${}_{\mathrm{par}}$ is given in percentages ($\Delta $V${}_{\mathrm{par}}$).

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**Figure 1.**The city-block-design alternatives. From left to right: V${}_{\mathrm{par}}$ (the longer sides of buildings parallel to the boulevard), V${}_{\mathrm{per}}$ (the longer sides perpendicular to the boulevard), V${}_{\mathrm{perHV}}$ (similar to V${}_{\mathrm{per}}$ but the building height varies) and V${}_{\mathrm{parJJ}}$ (similar to V${}_{\mathrm{par}}$ but with Jing-Jang building structure variation). The boulevard is marked in red and the major junction with a black dot.

**Figure 2.**The computational domain for southwesterly ($WD$ = 225${}^{\circ}$) inflow conditions and V${}_{\mathrm{par}}$ where the longer sides of building blocks are parallel to the boulevard. The domain is separated into child (

**B**) and parent (

**A**) domains, where the white colour stands for the topography elevation Z = 0 m. The data output domains are marked with rectangles: the small domain with a solid black and the large domain with a black dashed line. The boulevard is marked in red.

**Figure 3.**A map of the tree canopy height ${Z}_{\mathrm{canopy}}$ (m) for the whole computational domain. Orientation as in Figure 2.

**Figure 4.**The vertical profile of $PAD$ (m${}^{2}$ m${}^{-3}$) for the street along the boulevard (blue dashed line with dots). Example profiles for smaller and taller trees outside of the boulevard plotted in green (dashed line with stars) and red (dashed line with triangles), respectively. Additionally, the winter time $PAD$ profile for the street trees is given in black (solid line).

**Figure 5.**The particle source area (in colours) in the block-design alternatives V${}_{\mathrm{par}}$ and V${}_{\mathrm{parJJ}}$. Source areas are divided into groups 1, 2 and 3 based on the estimated mean traffic rates in year 2025 (see legends). Street surfaces below trees (white dots) are omitted as source areas. Orientation as in Figure 2.

**Figure 6.**The vertical profile of (

**a**) streamwise velocity u (m s${}^{-1}$), (

**b**) Reynolds stress $\overline{{u}^{\prime}{w}^{\prime}}$ (m${}^{2}$ s${}^{-2}$), and (

**c**) potential temperature $\theta $ (K) at the inflow boundary for the general (solid line) and wintry (dashed line) inflow conditions. The top x-axis for $\theta $ is for the wintry conditions.

**Figure 7.**40-min horizontal mean particle concentrations $pc$ (m${}^{-3}$) under the (

**a**) general and (

**b**) wintry inflow conditions separately above the boulevard, other street canyons, courtyards and surroundings at height z = 4 m (bars with solid lines) and z = 10 m (bar with dashed lines) for all runs. 90th percentile values are given with errorbars. The mean difference to the values in V${}_{\mathrm{par}}$ is given in percentages ($\Delta $V${}_{\mathrm{par}}$).

**Figure 8.**40-min temporal mean of particle concentration $pc$ (m${}^{-3}$) at height z = 4 m under the (

**a**) general and (

**b**) wintry inflow conditions. Notice the orientation of the mean wind and different scales of $pc$. Cross sections in Figure 8 are marked with white lines.

**Figure 9.**40-min mean particle concentration $pc$ (m${}^{-3}$) across the boulevard. (Cross Section 1 and Section 2, which are marked in Figure 8, are shown in (

**a**,

**b**) under the general inflow conditions, and in (

**c**,

**d**) under the wintry inflow conditions, respectively. Cross sections are viewed from the south. Lengths of the wind arrows are relative to the wind speeds normal to the cross section. Height in m a.g.l. are given in the left. Notice the different scales of $pc$.)

**Figure 10.**Horizontal mean of the low-frequency vertical turbulent particle flux density ${F}_{p,LF}$ (m${}^{-2}$ s${}^{-1}$) under the (

**a**) general and (

**b**) wintry inflow conditions separately for the boulevard, other street canyons, courtyards and surroundings at z = 20 m for all runs. The difference to the value in V${}_{\mathrm{par}}$ is given in percentages ($\Delta $V${}_{\mathrm{par}}$).

**Figure 11.**40-min mean low-frequency vertical turbulent particle flux density ${F}_{p,LF}$ (m${}^{-2}$ s${}^{-1}$) at z = 20 m under the (

**a**) general and (

**b**) wintry inflow conditions. Positive values indicate upward flux.

**Figure 12.**The volume averaged particle dilution rate ${\langle D\left(t\right)\rangle}_{V}$ (m${}^{-3}$ s${}^{-1}$) between z = 1–20 m under the (

**a**) general and (

**b**) wintry inflow conditions. Results are represented relative to V${}_{\mathrm{par}}$ (${\langle D\left(t\right)\rangle}_{V,{\mathrm{V}}_{\mathrm{par}}}$).

**Figure 13.**Mean ${\langle D(x,y)\rangle}_{t,z}$ (×10${}^{-3}$ m${}^{-3}$ s${}^{-1}$) under the (

**a**) general and (

**b**) wintry inflow conditions separately for the boulevard, other street canyons, courtyards and surroundings between z = 1–20 m for all runs. D is calculated using data from the first 50 s after the particle source has been switched off. The difference to the value in V${}_{\mathrm{par}}$ is given in percentages ($\Delta $V${}_{\mathrm{par}}$).

**Figure 14.**The temporal mean particle dilution rate ${\langle D(x,y)\rangle}_{t,z}$ (m${}^{-3}$ s${}^{-1}$) between z = 1–20 m for the first 60 s after the particle has been switched off: (

**a**) general and (

**b**) wintry inflow conditions.

**Table 1.**The boundary conditions of the model runs. Details of the conditions can be found in Maronga et al. [35].

Boundary | Domain | |
---|---|---|

Parent | Child | |

Bottom and solid walls | No-slip condition for the horizontal wind components u and v (i.e., $u=v=w=$ 0 m s${}^{-1}$). For potential temperature $\theta $, the vertical gradient $\partial \theta /\partial z$ = 0 K m${}^{-1}$. Monin-Obukhov similarity theory (MOST) is applied between any solid-wall boundary and the first grid level normal to the respective boundary surface. | Same as for the parent. |

Top | Dirichlet condition, i.e., $u={U}_{g}$ (geostrophic wind speed) and $v=w=0$ m s${}^{-1}$. $\theta $ is extrapolated using the initial gradient of $\theta $ from a precursor run. | Two-way nesting. Boundary conditions obtained from the parent domain. |

Horizontal: Lateral | Cyclic boundary conditions | Two-way nesting. Boundary conditions obtained from the parent domain. |

Horizontal: streamwise | Non-cyclic. A time-dependent turbulent inflow is produced by a turbulence recycling method [43]. Requires a precursor run that is carried out over a domain of the same vertical extent as the parent domain and 1/16 in area. | Two-way nesting. Boundary conditions obtained from the parent domain. |

V${}_{\mathbf{type}}$ | Characteristics |
---|---|

V${}_{\mathrm{par}}$ | Building blocks by the boulevard are oriented so that the longest side is parallel to the boulevard. Building heights are fixed to 30 m. |

V${}_{\mathrm{per}}$ | Building block by the boulevard are oriented so that the longest side is perpendicular to the boulevard. Building heights are fixed to 30 m. |

V${}_{\mathrm{perHV}}$ | The orientation of the building blocks is similar to V${}_{\mathrm{per}}$ but the building height varies. The highest buildings are situated at the nodal points of the public transport, whereas the lowest buildings as well as open urban spaces are situated between the nodal points. Buildings on the eastern side of the boulevard are generally higher. |

V${}_{\mathrm{parJJ}}$ | A so-called “Jin-Jang” block model, in which the buildings are similar to those in V${}_{\mathrm{par}}$ but the base height is lower and tower-like structures set above the base. Thus the building shape and height are very irregular. |

**Table 3.**Horizontal mean of the high-frequency vertical turbulent particle flux density ${F}_{p,HF}$ (m${}^{-2}$ s${}^{-1}$) separately for the boulevard, other street canyons, courtyards and surroundings at z = 20 m under both general and wintry inflow conditions. Horizontal mean of the low-frequency vertical turbulent particle flux density ${F}_{p,LF}$ over the same domain is given in brackets.

Inflow Conditions | V${}_{\mathbf{par}}$ | V${}_{\mathbf{per}}$ | V${}_{\mathbf{perHV}}$ | V${}_{\mathbf{parJJ}}$ |
---|---|---|---|---|

Boulevard | ||||

General | 0.193 | 0.162 | 0.169 | 0.213 |

(0.233) | (0.238) | (0.292) | (0.247) | |

Wintry | 0.221 | 0.168 | 0.159 | 0.178 |

(0.294) | (0.209) | (0.211) | (0.191) | |

Other street canyons | ||||

General | 0.085 | 0.078 | 0.247 | 0.117 |

(0.054) | (0.056) | (0.138) | (0.102) | |

Wintry | 0.115 | 0.141 | 0.180 | 0.102 |

(0.120) | (0.120) | (0.229) | (0.111) | |

Courtyards | ||||

General | 2.2$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$10${}^{-3}$ | $-3.5\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$10${}^{-3}$ | 1.1$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$10${}^{-3}$ | 17.1$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$10${}^{-3}$ |

($-4.5\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$10${}^{-3}$) | (0.8$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$10${}^{-3}$) | (1.2$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$10${}^{-3}$) | (16.7$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$10${}^{-3}$) | |

Wintry | $-0.0\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$10${}^{-3}$ | $-0.4\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$10${}^{-3}$ | 2.0$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$10${}^{-3}$ | $-5.6\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$10${}^{-3}$ |

(0.5$\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$10${}^{-3}$) | ($-2.0\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$10${}^{-3}$) | ($-4.3\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$10${}^{-3}$) | ($-7.7\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}$10${}^{-3}$) | |

Surroundings | ||||

General | 0.038 | 0.039 | 0.058 | 0.045 |

(0.026) | (0.040) | (0.071) | (0.047) | |

Wintry | 0.043 | 0.041 | 0.045 | 0.037 |

(0.085) | (0.059) | (0.057) | (0.074) |

© 2018 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**

Kurppa, M.; Hellsten, A.; Auvinen, M.; Raasch, S.; Vesala, T.; Järvi, L. Ventilation and Air Quality in City Blocks Using Large-Eddy Simulation—Urban Planning Perspective. *Atmosphere* **2018**, *9*, 65.
https://doi.org/10.3390/atmos9020065

**AMA Style**

Kurppa M, Hellsten A, Auvinen M, Raasch S, Vesala T, Järvi L. Ventilation and Air Quality in City Blocks Using Large-Eddy Simulation—Urban Planning Perspective. *Atmosphere*. 2018; 9(2):65.
https://doi.org/10.3390/atmos9020065

**Chicago/Turabian Style**

Kurppa, Mona, Antti Hellsten, Mikko Auvinen, Siegfried Raasch, Timo Vesala, and Leena Järvi. 2018. "Ventilation and Air Quality in City Blocks Using Large-Eddy Simulation—Urban Planning Perspective" *Atmosphere* 9, no. 2: 65.
https://doi.org/10.3390/atmos9020065