# Turbulent Flows and Pollution Dispersion around Tall Buildings Using Adaptive Large Eddy Simulation (LES)

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{5}). The remaining two main contesting methodologies are the LES methodology, together with the hybrid RANS/LES approach, although this is only very rarely used in urban physics and wind engineering [8]. The importance of urban physics in addressing societal problems is also highlighted in the literature, with the strengths and limitations of CFD in the context of urban physics, and with suggestions/tips as to how to achieve good quality and accurate CFD simulation results for generic scenarios [9]. The challenges and applications, together with the complexities and difficulties in modelling accurately the dispersion of pollutants in the urban settings, are also reviewed by many authors who concluded that the LES methodology appears to be the most suitable numerical method for the purpose of numerical dispersion studies in urban areas, as opposed to RANS or DNS [10]. A similar review on the implementation of CFD for urban studies (modelling air flows and heat/thermal conditions) with 183 cases analysed, also reported that LES is found as superior to RANS simulations in terms of a more accurate representation of turbulence [11].

## 2. Methodology—Adaptive Large Eddy Simulation (LES)

#### 2.1. Theoretical Basis and Numerical Method

_{s}, with Q being the emission flow rate, the density and X

_{s}the volume of the source.

^{−12}and 10

^{−7}, respectively, for all variables (pressure velocity and tracer concentrations).

#### 2.2. Computational Set-Up

#### 2.3. Mesh Adaptivity

## 3. The LES Results

#### 3.1. The Initial Validation

_{ref}of 2.1 m/s, taken to be the air speed at the edge of the boundary layer. The simulated atmospheric boundary layer represented near-neutral atmospheric conditions and was initiated by a set of Irwin spires (vorticity-generators) at the inlet to the wind tunnel working section. The surface roughness condition was maintained by the roughness elements on the floor. The surface roughness length was 1.5 mm and the friction velocity 0.057Uref [37,38]. In these experiments, a passive tracer was released from the top left corner of the central building (Figure 1a), Building N, known as the Garden building), and measurements were taken for varying wind directions and model configurations. The source height was 0.1508 m, relative to the Garden building height of 0.143 m. Mean tracer concentrations were measured using Combustion Fast Flame Ionisation Detectors (FFIDs) carried on a three-dimensional traverse system. Our validation exercise was based on the comparison of the mean concentration data for one wind direction, with the LES simulation results with three different inlet boundary conditions. Differences ranged between 3% and 37%, with higher inconsistencies (>50%) exhibited in certain detector locations at low heights. More recently we implemented a data assimilation approach to investigate as to how the LES simulation results could be improved [39]. The implementation of the data assimilation method showed that the mean squared difference between the LES-FLUIDITY simulations and wind tunnel measurements can be reduced up to three order of magnitudes. In this current work, we utilise the seven buildings configuration and present an in-depth quantitative analysis of the effect of a tall building in their vicinity for tracer dispersion. The overall aim is to get a quantitative measure of how the presence of a tall building can affect the local mean flow and turbulence (turbulent fluctuations/Reynolds stresses) and their impact on the pollution dispersion. Two primary areas within the domain were chosen: (i) detectors within the building area and close to the source location, and (ii) detectors away from and downstream the building area, at a distance away and downstream the source. Distinct features are observed.

#### 3.2. Time-Series of Velocity Magnitudes

#### 3.3. Mean Velocities and Concentrations

^{−4}for the different configurations, clearly seeing the effect of the location of a tall building in the spread of pollution. We can clearly visually see the effect of each building configuration on the spread of the pollution and get an appreciation as to how the location of each tall building impacts the local environment. A more quantitative analysis is given in Section 3.5 further below.

#### 3.4. Mean Resolved Reynolds Stresses

#### 3.5. Turbulent Kinetic Energies (TKEs)

#### 3.6. Correlation Coefficients

## 4. Analysis and Discussion

#### 4.1. Mean Velocity Magnitudes, Concentration, Reynolds Stresses and TKEs

#### 4.1.1. Within the Building Area: (X = 0.119 m, Y = 0.0 m)

#### 4.1.2. Downstream the Building Area (X = 0.75 m, Y = 0.0 m, Tables 2 and 3)

#### 4.2. Correlation Coefficients

#### 4.2.1. Correlation Analysis at Z = 0.065 m (X = 0.119 m, Y = 0.0 m)

#### 4.2.2. Correlation Analysis at Z = 0.5 m (X = 0.119 m, Y = 0.0 m).

#### 4.2.3. Correlations between Tracer Concentrations at Different Locations

#### 4.3. Discussion

^{−4}and velocity streamlines are shown. Figure 9 shows clearly as to how the Tall3 and Tall4 configurations result in massive increases of the concentrations at higher levels; they also exhibit an overall smaller 3D extend of the tracer dispersion, with pollution somewhat being “trapped within the building area, and extending upwards, as opposed to what happens with the Tall1, Tall2 and even Tall6 configurations, where the tracers disperse further downstream of Tall6. For the downstream location, at the lower heights of Z = 0.065 m, interestingly configurations Tall2, Tall3 and Tall4 result in reducing the mean concentrations, whilst all configurations result in reducing the mean concentrations at the intermediate heights. However, at the higher levels (Z = 0.5 m) all configurations result in increased mean concentrations (Table 3).

## 5. Conclusions

- Within the building area: the presence of tall buildings led to enhanced TKEs for all configurations at the lower heights (Z = 0.065 m) but lowering of TKEs for some configurations at the intermediate and higher levels.
- Downstream the building area: the presence of tall buildings led to enhanced/increased Reynolds stresses and TKEs for all building configurations, for all heights.
- Both within and downstream the building area: Despite the increased TKEs at some higher levels, mean concentrations still increased at higher levels for all building configurations.
- Both within and downstream the building area: There is not always a definite reduction in the mean concentrations if the mean velocities or if the Reynolds stresses/TKEs increase, as one might naturally expect. Some of the configurations showed that even if there is an increase of the mean velocities, and an increase of the TKEs, the mean tracer concentrations also increased by many factors. This is particularly evident at the higher levels.
- Both within and downstream the building area: The reduction of the mean velocities seemed to have a greater impact on the mean concentrations as opposed to the enhanced TKEs, especially at the higher levels, for both locations within the building area and downstream the building area.
- Within the building area at lower level Z = 0.065 m. In the presence of tall buildings, at the lower height of Z = 0.065 m, the concentrations correlated strongest with the velocities at the same location. The Tall4 configuration exhibited the strongest correlations, whilst Tall3 the weakest, followed by the Tall2 configuration. It is worth noting that the normal configuration exhibited the strongest correlation (negative) with the horizontal Reynolds stresses.
- Within the building area at the higher level of Z = 0.5 m: The concentrations correlated the strongest with the velocities at the same location, for configurations Tall1, Tall2 and Tall3, whilst for configurations Tall4 and Tall6 it was the horizontal Reynolds stress $\overline{{\mathrm{u}}_{2}^{\prime}{\mathrm{u}}_{2}^{\prime}}$ that correlated the strongest with the concentrations. Contrary to the locations within the building area, it was the Tall6 configuration that exhibited the weakest correlations, followed by Tall4, whilst Tall1 exhibited the strongest correlations.
- Downstream the building area: In the presence of tall buildings, the tracer–tracer correlations showed how the downstream concentrations were affected by the upstream concentrations with varying magnitudes of the correlation coefficients. The Tall1 configuration resulted in positive correlations with the upstream concentrations at all heights, except for Z = 0.176 m. Tall2 has negative correlations for the lower/intermediate heights, whilst Tall3 is the only configuration with only positive correlations, i.e., as concentrations within the building area (upstream location) increase, so do the concentrations at the downstream location. For Tall4, exhibited mostly positive correlations, with the upstream concentrations at the higher levels having the greatest influence downstream, whilst the opposite seems to occur with the Tall6 configuration, in which the upstream concentrations at the lower levels have the greatest correlation (albeit negative) with the concentrations at the downstream location.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Available online: http://www.who.int/airpollution/ambient/health-impacts/en/ (accessed on 1 January 2019).
- The Lancet Report. Available online: https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(17)30505-6/fulltext (accessed on 1 January 2019).
- Santamouris, M.; Kolokotsa, D. (Eds.) Urban Climate Mitigation Techniques; Routledge: London, UK; New York, NY, USA, 2016. [Google Scholar]
- Hankey, S.; Marshall, J.D. Urban form, air pollution, and health. Curr. Environ. Health Rep.
**2017**, 4, 491–503. [Google Scholar] [CrossRef] [PubMed] - Hanna, S.; White, J.; Zhou, Y. Observed winds, turbulence, and dispersion in built-up downtown areas of Oklahoma City and Manhattan. Bound. Layer Meteorol.
**2007**, 125, 441–468. [Google Scholar] [CrossRef] - Solazzo, E.; Britter, R.E. Transfer processes in a simulated urban street canyon. Bound. Layer Meteorol.
**2007**, 124, 43–60. [Google Scholar] [CrossRef] - Odman, M.T.; Mathur, R.; Alapathy, K.; Srivastava, R.K. Multiscale Air Quality Modelling. In Next Generation Environmental Models and Computational Methods; SIAM: Philadelphia, PA, USA, 1997; pp. 58–69. [Google Scholar]
- Ramponi, R.; Blocken, B.; Laura, B.; Janssen, W.D. CFD simulation of outdoor ventilation of generic urban configurations with different urban densities and equal and unequal street widths. Build. Environ.
**2015**, 92, 152–166. [Google Scholar] [CrossRef][Green Version] - Blocken, B. Computational Fluid Dynamics for urban physics: Importance, scales, possibilities, limitations and ten tips and tricks towards accurate and reliable simulations. Build. Environ.
**2015**, 91, 219–245. [Google Scholar] [CrossRef][Green Version] - Lateb, M.; Meroney, R.N.; Yataghene, M.; Fellouah, H.; Saleh, F.; Boufadel, M.C. On the use of numerical modelling for near-field pollutant dispersion in urban environments—A review. Environ. Pollut.
**2016**, 208, 271–283. [Google Scholar] [CrossRef][Green Version] - Toparlar, Y.; Blocken, B.; Maiheu, B.; Van Heijst, G.J. A review on the CFD analysis of urban microclimate. Renew. Sustain. Energy Rev.
**2017**, 80, 1613–1640. [Google Scholar] [CrossRef] - Sagaut, P. Large Eddy Simulation for Incompressible Flows; Springer Science: Berlin/Heidelberg, Germany; New York, NY, USA, 1998. [Google Scholar]
- Pope, S.B. Ten questions concerning the large-eddy simulation of turbulent flows. New J. Phys.
**2004**, 6, 35. [Google Scholar] [CrossRef][Green Version] - Benson, R.A.; McRae, D.S. A Solution-Adaptive Mesh Algorithm for Dynamic/Static Refinement of Two and Three Dimensional Grids. In Proceedings of the International Conference on Numerical Grid Generation in Computational Fluid Dynamics and Related Fields, Barcelona, Spain, 3–7 June 1991. [Google Scholar]
- Tomlin, A.; Berzins, M.; Ware, J.; Smith, J.; Pilling, M.J. On the use of adaptive gridding methods for modelling chemical transport from multi-scale sources. Atmos. Environ.
**1997**, 31, 2945–2959. [Google Scholar] [CrossRef] - Srivastava, R.K.; McRae, D.S.; Odman, M.T. An adaptive grid algorithm for air-quality modeling. J. Comput. Phys.
**2000**, 165, 437–472. [Google Scholar] [CrossRef][Green Version] - FLUIDITY Software and Manual. Available online: http://fluidityproject.github.io/ (accessed on 1 January 2019).
- Pain, C.C.; Umpleby, A.P.; De Oliveira, C.R.; Goddard, A.J. Tetrahedral mesh optimisation and adaptivity for steady-state and transient finite element calculations. Comput. Methods Appl. Mech. Eng.
**2001**, 190, 3771–3796. [Google Scholar] [CrossRef] - Bentham, J.H.T. Microscale Modelling of Air Flow and Pollutant Dispersion in the Urban Environment. Doctoral Dissertation, Imperial College London, London, UK, 2004. [Google Scholar]
- Pavlidis, D.; Gorman, G.J.; Gomes, J.L.; Pain, C.C.; ApSimon, H. Synthetic-eddy method for urban atmospheric flow modelling. Bound. Layer Meteorol.
**2010**, 136, 285–299. [Google Scholar] [CrossRef] - Aristodemou, E.; Bentham, T.; Pain, C.; Colvile, R.; Robins, A.; ApSimon, H. A comparison of mesh adaptive LES with wind tunnel data for flow past buildings: Mean flows and velocity fluctuations. Atmos. Environ.
**2009**, 43, 6238–6253. [Google Scholar] [CrossRef] - Constantinescu, E.M.; Sandu, A.; Carmichael, G.R. Modeling atmospheric chemistry and transport with dynamic adaptive resolution. Comput. Geosci.
**2008**, 12, 133–151. [Google Scholar] [CrossRef] - Xu, X.; Yang, Q.; Yoshida, A.; Tamura, Y. Characteristics of pedestrian-level wind around super-tall buildings with various configurations. J. Wind Eng. Ind. Aerodyn.
**2017**, 166, 61–73. [Google Scholar] [CrossRef] - Stathopoulos, T. Wind environmental conditions around tall buildings with chamfered corners. J. Wind Eng. Ind. Aerodyn.
**1985**, 21, 71–87. [Google Scholar] [CrossRef] - Stathopoulos, T. Pedestrian level winds and outdoor human comfort. J. Wind Eng. Ind. Aerodyn.
**2006**, 94, 769–780. [Google Scholar] [CrossRef] - Blocken, B.; Stathopoulos, T.; Van Beeck, J.P.A.J. Pedestrian-level wind conditions around buildings: Review of wind-tunnel and CFD techniques and their accuracy for wind comfort assessment. Build. Environ.
**2016**, 100, 50–81. [Google Scholar] [CrossRef] - Zheng, C.; Li, Y.; Wu, Y. Pedestrian-level wind environment on outdoor platforms of a thousand-meter-scale megatall building: Sub-configuration experiment and wind comfort assessment. Build. Environ.
**2016**, 106, 313–326. [Google Scholar] [CrossRef] - Song, J.; Fan, S.; Lin, W.; Mottet, L.; Woodward, H.; Davies Wykes, M.; Arcucci, R.; Xiao, D.; Debay, J.E.; ApSimon, H.; et al. Natural ventilation in cities: The implications of fluid mechanics. Build. Res. Inf.
**2018**, 46, 809–828. [Google Scholar] [CrossRef] - Iqbal, Q.M.Z.; Chan, A.L.S. Pedestrian level wind environment assessment around group of high-rise cross-shaped buildings: Effect of building shape, separation and orientation. Build. Environ.
**2016**, 101, 45–63. [Google Scholar] [CrossRef] [PubMed] - Mao, J.; Gao, N. The airborne transmission of infection between flats in high-rise residential buildings: A review. Build. Environ.
**2015**, 94, 516–531. [Google Scholar] [CrossRef] [PubMed] - Burman, J.; Jonsson, L.; Rutgersson, A. On possibilities to estimate local concentration variations with CFD-LES in real urban environments. Environ. Fluid Mech.
**2019**, 19, 719–750. [Google Scholar] [CrossRef][Green Version] - Aristodemou, E.; Boganegra, L.M.; Mottet, L.; Pavlidis, D.; Constantinou, A.; Pain, C.; Robins, A.; ApSimon, H. How tall buildings affect turbulent air flows and dispersion of pollution within a neighbourhood. Environ. Pollut.
**2018**, 233, 782–796. [Google Scholar] [CrossRef] [PubMed] - Coirier, W.J.; Kim, S. CFD modelling for urban area contaminant transport and dispersion: Model description and data requirements. In Proceedings of the Sixth Symposium on the Urban Environment, The 86th AMS Annual Meeting, Atlanta, GA, USA, 1 February 2006. [Google Scholar]
- Franke, J.; Hellsten, A.; Schlnzen, H.; Carissimo, B. Best Practice Guideline for the CFD Simulation of Flows in the Urban Environment; COST Action 732; COST Office: Hamburg, Germany, 2007. [Google Scholar]
- Jarrin, N.; Benhamadouche, S.; Laurence, D.; Prosser, R. A synthetic-eddy-method for generating inflow conditions for large-eddy simulations. Int. J. Heat Fluid Flow
**2006**, 27, 585–593. [Google Scholar] [CrossRef][Green Version] - Robins, A.; University of Surrey, Guildford, UK. Personal communication, 2016.
- Robins, A.; Castro, I.; Hayden, P.; Steggel, N.; Contini, D.; Heist, D. A wind tunnel study of dense gas dispersion in a neutral boundary layer over a rough surface. Atmos. Environ.
**2001**, 35, 2243–2252. [Google Scholar] [CrossRef] - Robins, A.G. The Development and Structure of Simulated Neutrally Stable Atmospheric Boundary Layers. J. Ind. Aerodyn.
**1979**, 4, 71–100. [Google Scholar] [CrossRef] - Aristodemou, E.; Arcucci, R.; Mottet, L.; Robins, A.; Pain, C.; Guo, Y.K. Enhancing CFD-LES air pollution prediction accuracy using data assimilation. Build. Environ.
**2019**, 165, 106383. [Google Scholar] [CrossRef] - Chen, L.; Hang, J.; Sandberg, M.; Claesson, L.; Di Sabatino, S.; Wigo, H. The impacts of building height variations and building packing densities on flow adjustment and city breathability in idealized urban models. Build. Environ.
**2017**, 118, 344–361. [Google Scholar] [CrossRef] - The IBM Statistical Software SPSS. Available online: https://www.ibm.com/analytics/spss-statistics-software (accessed on 1 October 2019).

**Figure 1.**The computational domain, with the initial unstructured, tetrahedral mesh, based on a wind tunnel configuration of seven buildings. The scaled dimensions of the computational domain are shown: 5 m in the x-direction, 4 m in the y-direction and 3 m in the z-direction. Based on the 1:200 scale, these dimensions correspond to 1 km length (x-direction); 800 m breadth (y-direction) and 600 m height. The seven buildings are circled in red.

**Figure 2.**The seven buildings’ configuration in the Large Eddy Simulation (LES) simulations. (

**a**) All buildings as in the wind tunnel. The normal, N-configuration, with dimensions as in the wind tunnel; (

**b**–

**f**): Tall1 to Tall6 configurations. Here, the height of each tall building is 0.6 m as opposed to their original height. Note: All heights given in Table 1, with dimensions in metres. The red dot shows the tracer emission at the top of building N. The inflow in all configurations was from left to right (west to east) as shown. The black dots denote the location where data are analysed in this paper.

**Figure 3.**(

**a**) The mean velocity profile and (

**b**) the diagonal components of the Reynolds stresses as measured in the wind tunnel and as represented in the computational simulations.

**Figure 4.**Examples of the anisotropic mesh adaptivity for the instantaneous LES results for (

**a**) the velocity magnitude field (m/s) in the vertical (X–Z) plane for Tall6 configuration; and (

**b**) the tracer field concentrations (parts per million) in the vertical (Y–Z) plane for the Tall3 configuration.

**Figure 5.**Variation of velocity magnitude at three different heights (

**a**) within the building area (X = 0.119 m, Y = 0.0 m) and (

**b**) downstream the building area (X = 0.75 m, Y = 0.0 m).

**Figure 6.**Variation of mean velocities and mean concentrations at different heights for all building configurations: (

**a**,

**b**) within the building area, X = 0.119 m and (

**c**,

**d**) downstream the building area, X = 0.75 m. The dotted black lines indicate the three different levels (heights) at which distinct variations are observed.

**Figure 7.**Variation of velocity magnitudes (left column) and tracer concentrations (right column) for the different tall building configurations in a horizontal plane at height Z = 0.065 m. The two sensor locations, at x = 0.119 m and x = 0.75 m, are indicated with the two black asterisks. In each configuration, the tall building is highlighted in purple.

**Figure 8.**Variation of velocity magnitudes (left column) and tracer concentrations (right column) for the different tall building configurations in a horizontal plane at height Z = 0.176 m. The two sensor locations, at x = 0.119 m and x = 0.75 m, are indicated with the two black asterisks. In each configuration, the tall building is highlighted by its number, the tall building is the only building to be seen at this height.

**Figure 9.**Velocity streamlines and Tracer isosurfaces equal to 1 × 10

**(in purple) for all building configurations, showing the dispersion of the tracer in the local environment of the tall building. The effect of the location of the tall building on the tracer concentrations at the higher levels is clearly seen, especially in the Tall3, Tall4 and Tall6 configurations.**

^{−4}**Figure 10.**Vertical variation of the nondiagonal and diagonal components of the Reynolds stress tensor, for all building configurations within the building area, i.e., at X = 0.119 m, Y = 0.0 m. (

**a**) The left column shows the nondiagonal components: (i) $\overline{\mathrm{u}{}^{\prime}\mathrm{v}{}^{\prime}}$, (ii) $\overline{\mathrm{u}{}^{\prime}\mathrm{w}{}^{\prime}}$ and (iii) $\overline{\mathrm{v}{}^{\prime}\mathrm{w}{}^{\prime}}$, whilst (

**b**) the right column shows the diagonal components: (i) $\overline{\mathrm{u}{}^{\prime}\mathrm{u}{}^{\prime}}$, (ii) $\overline{\mathrm{v}{}^{\prime}\mathrm{v}{}^{\prime}}$ and (ii) $\overline{\mathrm{w}{}^{\prime}\mathrm{w}{}^{\prime}}$.

**Figure 11.**Vertical variation of the nondiagonal and diagonal components of the Reynolds stress tensor, for all building configurations within the building area, i.e., at X = 0.75 m, Y = 0.0 m. (a) The left column shows the nondiagonal components: (i) $\overline{\mathrm{u}{}^{\prime}\mathrm{v}{}^{\prime}}$, (ii) $\overline{\mathrm{u}{}^{\prime}\mathrm{w}{}^{\prime}}$ and (iii) $\overline{\mathrm{v}{}^{\prime}\mathrm{w}{}^{\prime}}$, whilst (b) the right column shows the diagonal components: (i) $\overline{\mathrm{u}{}^{\prime}\mathrm{u}{}^{\prime}}$, (ii) $\overline{\mathrm{v}{}^{\prime}\mathrm{v}{}^{\prime}}$ and (ii) $\overline{\mathrm{w}{}^{\prime}\mathrm{w}{}^{\prime}}$.

Building | Wind Tunnel (Normal) | Tall1 | Tall2 | Tall3 | Tall4 | Tall6 |
---|---|---|---|---|---|---|

N | 0.1428 | 0.1428 | 0.1428 | 0.1428 | 0.1428 | 0.1428 |

1 | 0.1315 | 0.6 | 0.1315 | 0.1315 | 0.1315 | 0.1315 |

2 | 0.1238 | 0.1238 | 0.6 | 0.1238 | 0.1238 | 0.1238 |

3 | 0.1152 | 0.1152 | 0.1152 | 0.6 | 0.1152 | 0.1152 |

4 | 0.0315 | 0.0315 | 0.0315 | 0.0315 | 0.6 | 0.0315 |

6 | 0.1228 | 0.1228 | 0.1228 | 0.1228 | 0.1228 | 0.6 |

Within the Building Area (X = 0.119 m, Y = 0.0 m) | ||||||
---|---|---|---|---|---|---|

BuildingConfiguration | Z = 0.065 m | Z = 0.12 m | Z = 0.148 m | Z = 0.176 m | Z = 0.3 m | Z = 0.5 m |

Tall 1 | −29 | −20 | 329 | 130 | −2 | −5 |

Tall 2 | −58 | −21 | 11 | 16 | 8 | 5 |

Tall 3 | 184 | 154 | 77 | −37 | −68 | −76 |

Tall 4 | 232 | 462 | 108 | 0.11 | −80 | −84 |

Tall 6 | 528 | 125 | 138 | 27 | −20 | −22 |

Downstream area (X = 0.75 m, Y = 0.0 m) | ||||||

Tall 1 | 451 | 400 | 124 | 40 | −46 | −34 |

Tall 2 | 109 | 68 | −20 | −29 | 3 | −3 |

Tall 3 | 189 | 111 | −3 | −35 | −35 | −46 |

Tall 4 | 209 | 101 | −16 | −46 | −42 | −46 |

Tall 6 | 340 | 175 | 9 | −22 | −51 | −65 |

Within the Building Area (X = 0.119 m, Y = 0.0 m) | ||||||
---|---|---|---|---|---|---|

BuildingConfiguration | Z = 0.065 m | Z = 0.12 m | Z = 0.148 m | Z = 0.176 m | Z = 0.3 m | Z = 0.5 m |

Tall 1 | 59 | 5 | 73 | −41 | 2173 | 1,117,771 |

Tall 2 | 15 | −38 | 15 | 53 | 329 | 992 |

Tall 3 | −53 | −77 | −83 | −81 | 151,927 | 37,218,926 |

Tall 4 | −99 | −97 | −82 | −65 | 281,719 | 69,114,350 |

Tall 6 | 339 | −56 | 47 | −70 | 432 | 2086 |

Downstream the building area (X = 0.75 m, Y = 0.0 m) | ||||||

Tall 1 | 43 | −1 | −22 | −35 | 448 | 11,032 |

Tall 2 | −31 | −63 | −65 | −61 | 123 | 488 |

Tall 3 | −77 | −89 | −90 | −89 | 180 | 25,936 |

Tall 4 | −89 | −94 | −94 | −94 | 150 | 21,367 |

Tall 6 | 60 | −58 | −70 | −74 | 75 | 13,695 |

Within the Building Area (X = 0.119 m, Y = 0.0 m) | ||||||
---|---|---|---|---|---|---|

BuildingConfiguration | Z = 0.065 m | Z = 0.12 m | Z = 0.148 m | Z = 0.176 m | Z = 0.3 m | Z = 0.5 m |

$\left(i\right)\overline{{u}^{\prime}{u}^{\prime}}$ | ||||||

Tall 1 | −41 | −19 | 326 | −92 | 1101 | 1377 |

Tall 2 | −46 | −50 | 185 | 76 | 107 | 230 |

Tall 3 | 5564 | 1350 | 885 | 396 | 6743 | 3904 |

Tall 4 | 2642 | 1048 | 1986 | −23 | 3977 | 1254 |

Tall 6 | −17 | −85 | −47 | −95 | −8 | −46 |

$\left(ii\right)\overline{{v}^{\prime}{v}^{\prime}}$ | ||||||

Tall 1 | 136 | 298 | 156 | −65 | −44 | 10 |

Tall 2 | 4034 | 1040 | 7110 | 5894 | 1391 | 4498 |

Tall 3 | 6825 | 3119 | 5699 | 6344 | 16,007 | 2906 |

Tall 4 | 3487 | 1494 | 1957 | 145 | 3237 | 1102 |

Tall 6 | −25 | −4 | −60 | −87 | −36 | −63 |

$\left(iii\right)\overline{{w}^{\prime}{w}^{\prime}}$ | ||||||

Tall 1 | 414 | 163 | 196 | 185 | 243 | 72 |

Tall 2 | 142 | 140 | 130 | 384 | 121 | −0.33 |

Tall 3 | 14,492 | 15,580 | 14,244 | 22,072 | 19,389 | 6205 |

Tall 4 | 5817 | 5983 | 3499 | 4441 | 15,721 | 5083 |

Tall 6 | 504 | 1367 | 38 | −57 | −33 | −53 |

$\left(iv\right)\overline{{u}^{\prime}{v}^{\prime}}$ | ||||||

Tall 1 | −99 | 269 | −19,292 | 75 | 3755 | 88,009 |

Tall 2 | −175 | −112 | 28,594 | 1370 | −683 | 10,987 |

Tall 3 | 2091 | 2813 | 64,533 | 9526 | 256,272 | 50,885 |

Tall 4 | 2896 | −377 | 9504 | −79 | 19,210 | −64,635 |

Tall 6 | −59 | −92 | 541 | 85 | −498 | 1908 |

$\left(v\right)\left(i\right)\overline{{u}^{\prime}{w}^{\prime}}$ | ||||||

Tall 1 | 79 | 174 | −311 | 90 | 4053 | 617 |

Tall 2 | 594 | 188 | 130 | −102 | 2864 | 66 |

Tall 3 | 75,910 | 971 | 715 | 445 | 59,255 | −1775 |

Tall 4 | −33,815 | 1721 | −1369 | 467 | 62,277 | 684 |

Tall 6 | 162 | 267 | −7 | 93 | −1299 | 64 |

$\left(vi\right)\overline{{v}^{\prime}{w}^{\prime}}$ | ||||||

Tall 1 | −984 | 486 | 1266 | 2733 | 99 | 664 |

Tall 2 | −248 | 95 | 253 | 6288 | 2108 | −824 |

Tall 3 | 20,355 | 132 | −18,835 | −34,960 | 4977 | 3053 |

Tall 4 | −17,606 | 4291 | −5978 | 15,664 | 110,571 | 15,657 |

Tall 6 | 486 | 1607 | −175 | −51 | 197 | −112 |

Downstream the Building Area (X = 0.75m, Y = 0.0 m) | ||||||
---|---|---|---|---|---|---|

BuildingConfiguration | Z = 0.065 m | Z = 0.12 m | Z = 0.148 m | Z = 0.176 m | Z = 0.3 m | Z = 0.5 m |

$\left(i\right)\overline{{u}^{\prime}{v}^{\prime}}$ | ||||||

Tall 1 | −1798 | 2384 | 3623 | 1567 | 65,784 | 1,477,173 |

Tall 2 | −609 | −1621 | −2517 | −565 | 905 | 253,283 |

Tall 3 | 196 | −1199 | −3647 | −1000 | 8209 | −125,944 |

Tall 4 | −1815 | −889 | 627 | −144 | −24,425 | −1,251,768 |

Tall 6 | −6752 | −4886 | −2341 | 561 | 25,347 | 277,463 |

$\left(ii\right)\overline{{u}^{\prime}{w}^{\prime}}$ | ||||||

Tall 1 | −10,124 | −1114 | 148 | 587 | 32,106 | −26,815 |

Tall 2 | 374 | −816 | −602 | −841 | 2136 | 131 |

Tall 3 | −3783 | −1455 | −874 | −987 | −408 | −5430 |

Tall 4 | 125 | −293 | −540 | −825 | −36,087 | −11,894 |

Tall 6 | 13,069 | 2631 | 515 | 391 | 37,967 | −5948 |

$\left(iii\right)\overline{{v}^{\prime}{w}^{\prime}}$ | ||||||

Tall 1 | 1636 | 2288 | 366 | −5212 | −6031 | −34,895 |

Tall 2 | −1533 | 209 | 209 | 236 | 478 | 1695 |

Tall 3 | −2419 | 68 | 579 | 1006 | 4668 | 12,363 |

Tall 4 | −93 | −320 | −140 | −465 | 4021 | 819 |

Tall 6 | −5112 | −2123 | −1679 | −6197 | −3521 | −71,739 |

**Table 6.**Percentage (%) change of mean turbulent kinetic energies (TKEs) relative to the normal case.

Location | X = 0.119 m, Y = 0.0 m | X = 0.75 m, Y = 0.0 m | ||||
---|---|---|---|---|---|---|

BuildingConfiguration | Z = 0.065 m | Z = 0.176 m | Z = 0.5 m | Z = 0.065 m | Z = 0.176 m | Z = 0.5 m |

Tall 1 | 79 | −84 | 630 | 2521 | 1943 | 23,905 |

Tall 2 | 118 | 132 | 250 | 650 | 939 | 3824 |

Tall 3 | 7234 | 1375 | 4105 | 1530 | 1296 | 12,237 |

Tall 4 | 3357 | 74 | 2082 | 1425 | 937 | 25,447 |

Tall 6 | 42 | −94 | −53 | 4392 | 1144 | 19,944 |

**Table 7.**Pearson correlation coefficients between tracer concentrations and velocities, Reynolds stresses and TKEs at: X = 0.119 m, Y = 0 m, Z = 0.065 m.

Configuration | Vel | $\overline{{\mathit{u}}^{\prime}{\mathit{u}}^{\prime}}$ | $\overline{{\mathit{v}}^{\prime}{\mathit{v}}^{\prime}}$ | $\overline{{\mathit{w}}^{\prime}{\mathit{w}}^{\prime}}$ | $\overline{{\mathit{u}}^{\prime}{\mathit{v}}^{\prime}}$ | $\overline{{\mathit{u}}^{\prime}{\mathit{w}}^{\prime}}$ | $\overline{{\mathit{v}}^{\prime}{\mathit{w}}^{\prime}}$ | TKE |
---|---|---|---|---|---|---|---|---|

Normal | −0.041 | −0.340 | −0.074 | 0.002 | −0.295 | −0.118 | −0.282 | −0.307 |

Tall1 | 0.294 | −0.265 | 0.044 | 0.119 | 0.200 | −0.231 | 0.085 | 0.009 |

Tall2 | −0.369 | −0.183 | −0.253 | −0.049 | 0.231 | 0.080 | 0.212 | −0.260 |

Tall3 | −0.243 | −0.001 | −0.079 | −0.066 | −0.029 | −0.074 | −0.036 | −0.069 |

Tall4 | −0.537 | 0.101 | 0.199 | 0.262 | 0.299 | −0.225 | −0.133 | 0.256 |

Tall6 | 0.337 | −0.198 | 0.050 | −0.126 | −0.250 | −0.180 | −0.205 | −0.182 |

**Table 8.**Pearson correlation coefficients between tracer concentrations and velocities, Reynolds stresses and TKEs at: X = 0.119 m, Y = 0 m, Z = 0.5 m.

Configuration | Vel | $\overline{{\mathit{u}}^{\prime}{\mathit{u}}^{\prime}}$ | $\overline{{\mathit{v}}^{\prime}{\mathit{v}}^{\prime}}$ | $\overline{{\mathit{w}}^{\prime}{\mathit{w}}^{\prime}}$ | $\overline{{\mathit{u}}^{\prime}{\mathit{v}}^{\prime}}\prime $ | $\overline{{\mathit{u}}^{\prime}{\mathit{w}}^{\prime}}$ | $\overline{{\mathit{v}}^{\prime}{\mathit{w}}^{\prime}}$ | TKE |
---|---|---|---|---|---|---|---|---|

Normal | −0.198 | 0.003 | −0.103 | 0.026 | 0.144 | −0.041 | −0.016 | −0.043 |

Tall1 | −0.875 | 0.371 | 0.116 | 0.372 | 0.026 | 0.372 | 0.145 | 0.388 |

Tall2 | 0.414 | 0.088 | 0.273 | 0.008 | −0.220 | −0.117 | 0.127 | 0.218 |

Tall3 | −0.214 | 0.125 | 0.055 | 0.047 | 0.174 | 0.015 | 0.060 | 0.172 |

Tall4 | 0.228 | 0.030 | 0.228 | 0.174 | 0.084 | −0.053 | 0.284 | 0.212 |

Tall6 | 0.011 | 0.011 | 0.079 | −0.018 | 0.013 | −0.064 | −0.078 | 0.038 |

**Table 9.**Pearson correlation coefficients between tracer concentrations at the downstream location: X = 0.75 m, Y = 0.0 m, Z = 0.065 m, with tracer concentrations at the within the building area location: X = 0.119 m, Y = 0.0 m, at different heights.

Building Configuration | Z = 0.065 m | Z = 0.12 m | Z = 0.148 m | Z = 0.176 m | Z = 0.3 m | Z = 0.5 m |
---|---|---|---|---|---|---|

Normal | 0.048 | 0.53 | −0.184 | −0.095 | −0.071 | n/a |

Tall1 | 0.066 | 0.103 | 0.118 | −0.029 | 0.01 | 0.036 |

Tall2 | 0.041 | −0.326 | −0.272 | −0.231 | 0.077 | −0.032 |

Tall3 | 0.008 | 0.038 | 0.1 | 0.124 | 0.199 | 0.067 |

Tall4 | 0.054 | −0.057 | 0.149 | −0.026 | 0.221 | 0.283 |

Tall6 | −0.215 | −0.294 | 0.077 | −0.137 | 0.0318 | 0.075 |

© 2020 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**

Aristodemou, E.; Mottet, L.; Constantinou, A.; Pain, C.
Turbulent Flows and Pollution Dispersion around Tall Buildings Using Adaptive Large Eddy Simulation (LES). *Buildings* **2020**, *10*, 127.
https://doi.org/10.3390/buildings10070127

**AMA Style**

Aristodemou E, Mottet L, Constantinou A, Pain C.
Turbulent Flows and Pollution Dispersion around Tall Buildings Using Adaptive Large Eddy Simulation (LES). *Buildings*. 2020; 10(7):127.
https://doi.org/10.3390/buildings10070127

**Chicago/Turabian Style**

Aristodemou, Elsa, Letitia Mottet, Achilleas Constantinou, and Christopher Pain.
2020. "Turbulent Flows and Pollution Dispersion around Tall Buildings Using Adaptive Large Eddy Simulation (LES)" *Buildings* 10, no. 7: 127.
https://doi.org/10.3390/buildings10070127