CFD Analysis of Urban Canopy Flows Employing the V 2 F Model : Impact of Different Aspect Ratios and Relative Heights

Computational fluid dynamics (CFD) is currently used in the environmental field to simulate flow and dispersion of pollutants around buildings. However, the closure assumptions of the turbulence usually employed in CFD codes are not always physically based and adequate for all the flow regimes relating to practical applications. )e starting point of this work is the performance assessment of the V2F (i.e., v2 − f ) model implemented in Ansys Fluent for simulating the flow field in an idealized array of twodimensional canyons.)e V2Fmodel has been used in the past to predict low-speed and wall-bounded flows, but it has never been used to simulate airflows in urban street canyons. )e numerical results are validated against experimental data collected in the water channel and compared with other turbulence models incorporated in Ansys Fluent (i.e., variations of both k-ε and k-ω models and the Reynolds stress model). )e results show that the V2F model provides the best prediction of the flow field for two flow regimes commonly found in urban canopies. )e V2F model is also employed to quantify the air-exchange rate (ACH) for a series of two-dimensional building arrangements, such as step-up and step-down configurations, having different aspect ratios and relative heights of the buildings. )e results show a clear dependence of the ACH on the latter two parameters and highlight the role played by the turbulence in the exchange of air mass, particularly important for the step-down configurations, when the ventilation associated with the mean flow is generally poor.


Introduction
e continuous growth of large cities occurred in the last decades has prompted the scientific community towards the understanding of the urban environment [1,2].Great attention has been paid especially in predicting the flow field within and outside the urban street canyon, which is the space delimited by the street and the facades of the surrounding buildings.Knowledge on wind and temperature distributions within the street canyon is crucial, for example, in the design of the urban geometry with the aim of achieving an energy-optimized architecture of the city [3][4][5] as well as determining the concentration of pollutants emitted at the street level by vehicular traffic [6][7][8].
One of the parameters that mostly influence the gross features of the flow over urban canopies is the aspect ratio, AR, which is defined as the ratio between the average height of the buildings, H, and the spacing, W, between two consecutive buildings.Oke [3] introduced three kinds of flow regimes as a function of AR: isolated obstacle, wake interference, and skimming flow.In the isolated-obstacle regime (AR < 0.4), the flow around each building is not affected by disturbances coming from other obstacles.In the wake-interference flow (0.4 < AR < 0.67), two counterrotating vortices form within the canyon, and the wake of each building interacts with the subsequent building.e skimming flow (AR > 0.67) corresponds to narrow urban canyons, where the wind circulation is characterized by a vortex that occupies a large part of the canyon.Besides the three flow regimes defined by Oke, there is a fourth flow pattern, the multivortex flow regime (AR > 1.54), which is a variant of the skimming flow [9].Another important parameter influencing the street canyon is the relative height of the buildings, H 2 /H 1 , where H 1 and H 2 are the heights of the leeward and the windward buildings, respectively.
anks to the increasing computational power of computers, computational fluid dynamics (CFD) has recently supported laboratory and field experiments, improving the knowledge of street-canyon flows.Much effort has been done in recent years to analyze urban canopy flows by means of CFD, often using Reynolds-averaged Navier-Stokes (RANS) simulations of two-dimensional (2D) arrays of buildings.e interest of the scientific community for such a simplified building arrangement is justified by the fact that the 2D array can be considered as an archetype for more complex geometries [10][11][12][13].Huang et al. [14] carried out 2D simulations to investigate the effect of wedge-shaped roofs on the flow in an urban street canyon and found that they have significant influence on the vortex structure and pollutant distribution pattern.Memon et al. [15] analyzed heating in 2D isolated street canyons applying the RNG k-ε model (here, k is the turbulent kinetic energy, while ε is its rate of dissipation).ose authors compared their results with wind-tunnel data and showed that the nighttime and daytime air temperature difference between urban and rural areas closely resembles each other.Murena and Mele [16] analyzed an ideal deep street canyon with 2D unsteady RANS simulations using the shear stress transport (SST) k-ω model.ey observed that short-time variations of wind velocity can greatly influence the mass transfer rate between the canyon and the overlying boundary layer.Allegrini et al. [17] carried out 2D steady RANS simulations with different near-wall treatments in order to validate numerical results for buoyant flows in urban street canyons by comparison with wind-tunnel measurements.ey compared the results of different turbulence models (STD k-ε, realizable k-ε, k-ω, Spalart-Allmaras, and Reynolds stress model (RSM)), showing a better agreement of the STD k-ε model with the NEWFs (nonequilibrium wall functions) than the LRNM (low-Reynolds number modeling).Ho et al. [18] studied idealized 2D urban street canyons of different ARs and urban boundary-layer depths using the RNG k-ε model.ey found that the atmospheric turbulence contributes most to street-level ventilation because the turbulent component of the air-exchange rate (ACH) dominates the transport process.Xie et al. [19] investigated the impact of the urban street layout on the local atmospheric environment through numerical simulation and wind-tunnel experiments.e authors found that the vortex structure in the canyon and, consequently, the street layout strongly influence the wind field and the pollutant dispersion in the canopy.
A well-known CFD approach alternative to RANS simulation is the large eddy simulation (LES), which explicitly resolves the larger structures of the turbulence, while it models the finer ones by adopting suitable closure assumptions [20][21][22].It is believed that the RANS approach provides reasonable accurate predictions of mean flow quantities and that it is still an appropriate methodology considering the low CPU cost.However, in some applications such as the analysis of transient features of the flow like vortex shedding in the wake, LES performs generally better than RANS simulation [6].In any case, LES resolves the large-scale turbulent eddies, which are 3D by nature.erefore, since in this work a 2D simulation has been used, the most suitable CFD approach is the RANS one.
Based on the previous literature, the k-ε turbulence model appears to be the most widely employed one in CFD simulations of urban canopy flows.However, uncertainties still exist regarding the capability of CFD codes in simulating velocity and turbulence fields in different flow regimes.For this reason, a comparison between numerical results obtained through Ansys Fluent v.14.5 [23] and experimental data taken in the water channel has been carried out in this work.In addition to the most known turbulence models, the comparison has also taken into account the V2F model, based on the k − ε − v 2 closure developed by Durbin [24].e V2F model is similar to the STD k-ε model but includes an additional transport equation that models the velocity scale, v 2 , and its source term, f [25].Since the V2F model incorporates both near-wall turbulence anisotropies and nonlocal pressure-strain effects, it is usually employed for low-speed and wall-bounded flows. is implies that wall functions are not required, and consequently, lower computational costs are needed.e V2F model has been developed for attached or mildly separated boundary layers and used mainly for studying three-dimensional (3D) boundary layers [26,27] and heat transfer problems in jet impingement [28][29][30] and in ribbed-channel flows [31,32], subsonic and transonic flows for aerospace applications [33,34], and flow physical phenomena in enclosed environments [35][36][37].To the best of our knowledge, this paper is the first one to deal with numerical simulations of 2D street canyons by means of the V2F model.Here, the effectiveness of the V2F model in predicting the flow field for two typical building arrangements (AR � 0.5 and 1) has been investigated.e V2F model is also employed to analyze the air-exchange rate (ACH) for a series of two-dimensional building arrangements, such as step-up and step-down configurations, having different aspect ratios and relative heights of the buildings, a design quite underexplored in the literature.
is paper is organized as follows: firstly, the experimental setup used in the water channel and the numerical approach followed in the simulation are described.Secondly, tests of the V2F model through comparisons with the experimental data and results obtained employing other turbulence models are presented and discussed together with the analyses of several flow regimes referred to several ARs and H 2 /H 1 .Particular attention is also paid to the analysis of canyon ventilation as well as to its dependence on the canyon geometry.is paper concludes with a summary of the main results.e water channel allows the reproduction of the atmospheric boundary layer with several advantages [38][39][40][41].One of them is that image analysis techniques, such as particle tracking velocimetry, can be easily employed.ese permit accurate spatial measurements, which generally allow a clearer understanding of complex ows such as the one under investigation.

The Water-Channel Experiments
e water channel has a rectangular cross section of 0.35 m height and 0.25 m width and 7.4 m length (Figure 1).e ow rate is set by a oodgate placed at the closing section of the channel, and the water depth, h 0.16 m, is maintained constant throughout the experiments (more information about the facility can be found in [42]).e reference frame has been de ned with the x-axis aligned with the streamwise velocity and the z-axis vertical.e water is seeded with nonbuoyant particles (2 μm in diameter), which were assumed to be passively transported by the ow.Upwind of the buildings, the channel bottom is covered by unevenly spaced, roughness elements (pebbles with an average diameter of 5 mm) in order to reproduce the logarithmic vertical pro le of the undisturbed streamwise velocity as well as the (nearly) constant Reynolds stress pro le typically observed in the atmospheric boundary layer.e roughness Reynolds number, Re τ u * H/] (here, u * −u ′ w ′ is the friction velocity, v 10 −6 •m 2 •s −1 is the kinematic viscosity of water, and H is the obstacle height), ranges from 340 up to 470; that is, it is well above the critical value of 70 given by Snyder [43], which guarantees the independence of the investigated large-scale structures and the mean ow of Reynolds number e ects [44].erefore, in our experiments, Re τ is large enough to ensure both the conditions of full turbulence of the simulated boundary layer and the dynamic similarity between experiments and real conditions.e urban canopy is composed of a 2D regular array of urban-like obstacles with square sections of B H 20 mm and length 25 cm glued onto the channel bottom (Figure 2).Two geometrical con gurations have been investigated, one referred to the skimming ow (AR 1) and one to the wakeinterference regime (AR 0.5).To this end, the distance between the obstacles, W, has been varied from 20 mm to 40 mm.e framed area is 99 mm long (x-axis) and 72 mm high (z-axis) and is located in correspondence with the 20th canyon, where the ow can be considered fully developed.
e velocity components along the x-and z-axes, respectively, u and w, have been measured using the feature tracking (FT), a technique based on the image analysis [45].A high-speed camera (CMOS with a resolution of 1280 × 1024 pixels) acquires images at 250 frames per second for 40 s during each experiment, while a green laser light sheet (wavelength of 532 nm) illuminates the acquisition area.Velocities have been determined by the FT algorithm from the displacements of the seeding particles between successive frames.A Gaussian interpolation algorithm [46] was applied to the scattered velocity samples to obtain a twodimensional, Eulerian description of the motion on the x-z plane.After this procedure, 10000 instantaneous ow elds (each 1/250 s) with a spatial resolution of 1 mm have been obtained.Details of the undisturbed approaching ow are given in [47].

Mathematical Formulation.
In the case of incompressible, turbulent ows, Ansys Fluent solves the balance equations of mass and momentum and additional transport equations related to closure assumptions.In particular, the rst two equations can be expressed as follows (Einstein summation rule applies): where g i is the acceleration due to gravity, p the pressure, μ the viscosity, and ρ the density.e Reynolds stress tensor u i ′ u j ′ (here, prime indicates uctuation around the mean) is usually modeled using a linear proportionality to the rate of strain (Boussinesq eddy-viscosity model):

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where δ ij is the Kronecker delta.e turbulent kinetic energy k and the eddy viscosity μ t are determined by adding to ( 1) and ( 2) two or more additional equations [48].Since the three k-ε models, the two k-ω models and the RSM, implemented in Ansys Fluent are well known and widely employed in the literature, only the V2F model is briefly described below.

e V2F Model.
Standard eddy-viscosity models use specific damping functions to simulate the region close to the solid boundary.is is because the k-ε closure for μ t is isotropic, while near-wall turbulence is strongly anisotropic [49].
e V2F model was developed to avoid the use of damping functions and correctly reproduce the attenuation of the turbulence near solid boundaries [25,31]. is model solves an elliptic relaxation function, f, and three transport equations, respectively, for k, ε, and v 2 , where the latter is the velocity scale.e V2F model is based on a turbulent viscosity hypothesis proposed by Durbin for the region close to the solid boundary [49]: where T � k/ε and C μ is a constant.Information on the anisotropy of the flow in the near-wall region is taken through the transport equation of v 2 , which, in turn, is derived from the transport equation of the Reynolds stress normal to the wall.Summarizing, the transport equations for k, ε, and v 2 are, respectively, read as follows: where S k , S ε , and S v 2 are source terms, while e function f, included to take into account the anisotropic wall effects, is modeled by solving an elliptic Helmholtz-type equation: where L is a length scale, C 1 and C 2 are constants, and S f is a source term.More information on the V2F model can be found in [48].

Geometry and Numerical Domain.
e building array described in Section 2 has been numerically modeled by considering a 3D domain (Figure 3).It is composed of twelve buildings and, consequently, eleven street canyons.According to [50], the computational domain has been extended in the streamwise direction to 10H between the inflow boundary and the first building and to 20H between the last building and the outflow boundary.Its height has been set equal to 10H. e numerical runs have also been conducted considering a 2D computational domain corresponding to the vertical section passing through the channel axis (Figure 4 and the grey plane in Figure 3). is procedure has been followed since the investigated domain is symmetric along the y-axis.

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In order to test the e ectiveness of this choice, both the 3D and 2D models have been run and compared with the experimental data.
e results of this test will be shown below.In addition to the cases AR 0.5 and 1 with buildings of equal height used to test the model capability, other geometries have been taken into account.In particular, ve arrays of buildings with di erent ARs (0.5, 1, 1.33, 2, and 4) have also been investigated varying H 2 /H 1 (0.4, 0.5, 0.7, 1.5, 2, and 2.5) for each of the ve ARs.

Boundary Conditions and Simulation Settings.
e vertical pro le of the magnitude of the undisturbed mean velocity, V, measured in the water channel upwind of the building array (interpolated by using a tting function implemented in Ansys Fluent) has been set as the velocity inlet boundary condition at the in ow.Here, V assumes the meaning of time average of the 10000 instantaneous velocity magnitudes collected during the experiment.e ow has been considered not a ected by any obstacle at its boundary since the inlet velocity pro le is fully developed.For this reason, a free-slip condition has been applied to the bottom surface before and after the building array.A zero (relative) pressure has been imposed as the outlet boundary condition.It is used to force the ow in the direction normal to the outlet without any back ow.A free-slip condition has been imposed at the water-air boundary, while a no-slip condition has been applied at the surfaces of the buildings and at the bottom of the canyon as well. is choice is justi ed on the basis of several tests we conducted, which showed a better agreement between measured and simulated ows inside the canyon.
e numerical solver has employed a structured, nonorthogonal, fully collocated, cell-centered, nite-volume approach for the discretization of the computational domain, and the velocity vector has been decomposed into its Cartesian components.Physical di usive cell uxes have been approximated using a conventional second-order central di erencing scheme, and the SIMPLE algorithm [51] has been used for pressure correction.
e convergence target based on the root mean square has been set to 10 −7 .
e quantities of interest, such as velocity and turbulent kinetic energy, have been monitored at several grid Advances in Meteorology points during the solving process to check whether stable levels before convergence were met or not.
3.5.Mesh and Grid Independence Test.Both the 3D and 2D domains have been discretized by using orthogonal grids (Figure 5).Since the geometry is relatively simple, a blockbased hexahedral mesh has been used to enhance the quality of the mesh.e grid lines have been re ned near the solid surfaces (bottom, rooftops, and building walls).e choice of the most suitable mesh spacing is not a trivial task since the use of a too coarse mesh can give rise to considerable errors, while an excessively ne mesh costs in terms of computing time. is is the reason why any CFD simulation should be preceded by a series of grid independence tests.e velocity magnitude V computed at z/H 7.5 in correspondence with the vertical pro les passing through the center of the ninth canyon (the reason for this choice is clari ed in the next section) has been analyzed as a function of four grid meshes of di erent densities (Table 1).Assuming Mesh A (interval size equal to 0.001 m) as the pivot case, the percentage di erence Δ (%) between Mesh A and the nest of the four (Mesh D) is only 0.08%.erefore, in the remainder of this work, Mesh A is used for all the CFD analyses.e same interval size of the mesh has been employed for the 3D model, for a total amount of nearly 1.2 million cells.
e vertical pro les of the nondimensional velocity, V/u ref , passing through the center of the ninth canyon are given in Figure 6 for the case AR 1. e results show an overall good agreement between the experiment and simulations.e percentage di erence between the 2D and 3D cases is nearly 5.30% for the entire pro le.erefore, it is possible to assume that the 2D model describes the ow eld with the same accuracy as the 3D model.

Stabilization Analysis.
Since the interrogation area adopted during the experiments is located far enough from the inlet to assure the ow independence along the streamwise direction, before starting the comparisons, it is essential to verify whether the same condition holds for the CFD simulations or not. is test has been conducted for AR 1 by analyzing the V/u ref vertical pro les passing through the center of each of the 11 canyons.e percentage di erences between the velocity magnitudes calculated for two contiguous canyons have been evaluated within the canyon (0 < z/H ≤ 1) and in the boundary layer above (z/H > 1) (Table 2).Such di erences become small from the fourth building onward, after which a well-de ned trend towards the equilibrium occurs.is trend stabilizes after the ninth canyon, where Δ is almost constant (≈0.35%).For this reason, from now on, it is implicit that the vertical pro le considered for comparisons is the one passing through the center of the ninth canyon.

Turbulence Model Evaluation.
In this section, the average velocities calculated by means of numerical simulations conducted using seven turbulence models implemented in Ansys   6: Vertical pro les, passing through the center of the ninth canyon, of the nondimensional velocity magnitude calculated using the 2D (blue circles) and the 3D (red diamonds) models for AR 1.
e continuous line refers to the experimental data.e height is normalized by the building height, H.

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Fluent are compared with those measured in the water channel.e turbulence models employed in the analysis are the standard (STD) k-ε model [52], renormalization group (RNG) k-ε model [53], realizable k-ε model [54], standard (STD) k-ω model [55], shear stress transport (SST) k-ω model [56], Reynolds stress model (RSM) [57], and v 2 − f (V2F) model [24].e aim is to assess the accuracy of the V2F model in estimating the velocity pro les and the ow eld within the canyon for both the skimming ow (AR 1) and the wakeinterference regime (AR 0.5).
Figure 7 shows the comparisons between the observed (line) and simulated (symbols) vertical pro les of V/u ref for AR 1 (Figure 7(a)) and 0.5 (Figure 7(b)).Overall, the velocity above the canyon is lower for AR 0.5, that is, for the wake-interference regime, in agreement with the eld campaign measurements [54].e simulated pro les do not di er considerably, and the di erences with the measured pro les are reasonably small, even though a general underestimation occurs within the canyon.In contrast, the model generally overestimates the velocity above the canyons.However, the V2F model gives velocity pro les closer to those observed in both the analyzed ow regimes (see the percentage di erences listed in Tables 3 and 4 among the seven turbulence models obtained for the two ARs).e V2F model results have been compared with the experimental data also to assess its capability to capture global ow characteristics such as the number and location of the vortex structures formed within the canyon.
e correct simulation of the vortex topology is of great importance [58], for example, for the determination of the concentration of  Table 3: Percentage di erences between measured and modeled velocities within and above the canyon (AR 1).Advances in Meteorology pollutants emitted within the canyon [59,60], particularly when the source is located at the street level.e three k-ε models results also show a good agreement with the experiments, especially for AR 1, while the two kω models and the RSM, in particular, always show the larger di erences.
is is understandable in that the Reynolds number within the canyon is not large and the k-ε models are more accurate in these conditions [55].In contrast, the V2F models are recognized as giving better performance for both low-Reynolds number and wall-bounded ows.Overall, it is possible to conclude that the V2F model reproduces the velocity pro les inside the canyon better than the other turbulence models.
Figure 8 shows the maps for the two ARs of the streamlines associated with the measured (Figures 8(a) and 8(b)) and simulated (Figures 8(c) and 8(d)) velocities.All of them conform to the canonical con guration of the canopy ow, that is, a current nearly parallel to the streamwise direction above the canopy and a main vortex within the canyon, characterized by lower velocity.For AR 1, the CFD simulates also a counterclockwise recirculating region located in the upper part of the facet of the leeward building and other two smaller vortices, located at the bottom corners.ese data also match other results reported in the literature [60][61][62][63][64].Both measurements and simulations show that the size of the secondary vortex located at the bottom of the leeward building grows with AR.At AR 0.5, indeed, it shows two adjacent vortices: the downstream one is by far the larger and rotates clockwise, while the upstream one is smaller, occupying nearly 1/4 of the canyon and rotates counterclockwise. is pattern is in agreement with experimental data and numerical simulations performed in [9,60,61,[63][64][65].
In conclusion, among the seven turbulence models considered here, the model V2F shows the best agreement with the experimental data, particularly within the canyon.Furthermore, it requires the shortest calculation time.

E ects of Aspect Ratio and Building Height Variations on the Canyon Ventilation.
Once the V2F model performance has been veri ed against experimental data, the same model has been used to investigate urban street canyons characterized by variants of the skimming ow for narrow canyons (AR > 1) and for variations of the relative height of the buildings H 2 /H 1 ≠ 1. e goal is to quantify the air ventilation properties of the canyon making use of the airexchange rate (ACH).e latter is a measure of the rate of air removal from the street canyon [66]: where the subscript "+" indicates positive (upward) vertical velocity, while W is the canyon length.Since RANS models do not calculate the instantaneous velocity components, according to [67], ACH has been estimated as the sum of its average and uctuating parts: where the contribution w ′ is obtained from μ t and k by using (3) and assuming isotropic conditions.e computational parameters and settings adopted in the previous section have also been employed for these additional analyses.

E ect of Aspect Ratio
Variations.Street canyons with AR > 1.54 are characterized by the multivortex ow regime.Compared to AR 1, this variant of the skimming ow involves a higher reduction of the wind speed within the canyon and lower vertical di usion of pollutants emitted within the cavity [9].ree narrower street canyons with AR > 1 (AR 1.33, AR 2, and AR 4) have therefore been investigated to analyze their ventilation properties.e multivortex con gurations in the skimming ow have rstly been analyzed in terms of streamlines (Figure 9).e results show the transition from the one-vortex regime to the multivortex regime as AR increases.
e case AR 1.33 (Figure 9(a)) still shows the main clockwise vortex as seen for AR 1 (Figure 8(c)), but the two recirculation zones at the canyon bottom are more noticeable.For AR 2, these two vortices merge to form a larger counterclockwise structure (Figure 9(b)).e canyon is therefore divided into two regions, one lying above the other, where the upper recirculation is stronger and drives the lower vortex.e upper recirculation is still shifted downstream (x 0.26H, z 0.71H), according to AR 1, while the lower, atter vortex is centered in the cavity (x 0.26H, z 0.22H).ese results agree reasonably well with the water-channel experiments performed by Baik et al. [68] for AR 2, which showed (x 0.32H, z 0.75H) and (x 0.29H, z 0.17H) as the locations of the centers of the upper and lower recirculation regions, respectively.
Further increases in AR lead to the formation of additional vortices within the cavity.For example, for AR 4, three vertically aligned vortices are formed (Figure 9(c)), with increasing dimensions upwards.e con guration of narrow buildings is particularly interesting for the investigation of dispersion phenomena.In fact, pollutants typically emitted by vehicular tra c at the canyon bottom through linear sources are trapped in the lower part of the canyon, where strong values of mean and standard deviation of concentration occur near the sidewalks [7,69], directly a ecting the nal receptor.Furthermore, the external wind ows above the canopy almost parallel to the roofs, resulting in a poor canyon ventilation process, are strongly hampered by the structure of the vortices.is corroborates the idea that, for the skimming ow, the uid has di culty in penetrating the interelement spaces, and therefore it skims, remaining nearly parallel to the roofs [68,70].For this reason, it is fundamental to consider a correct urban planning to minimize unwanted e ects of pollutant accumulation.
By comparing the vertical pro le of V/u ref calculated for all the ARs (Figure 10), it can be seen that, above the canyon, it depends appreciably on AR.On the contrary, V/u ref changes considerably with AR within the canyon, especially going from the standard skimming ow to the multivortex regime.While the velocity magnitude for AR 1.33 is similar to that seen for AR 1, it drastically drops for AR 2 and 4, indicating that the multivortex ow is characterized by very poor ventilation, particularly at the street level.e results presented above conform to those presented in [9,58,61,[65][66][67]71], which simulated canopy ows through CFD, employing di erent turbulence models.
e nondimensional air ventilation components for the ve ARs are shown in Figure 13 (see data points referring to H 2 /H 1 1).While the mean contribution ACH/(u ref W) does not change appreciably with AR, the lower the aspect ratio, the higher the ACH ′ /(u ref W). is suggests that turbulence plays a major role in air exchanges between the canyon and the overlying layer. is is particularly true for the wake-interference regime, where

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ACH is nearly an order of magnitude greater than ACH ′ .However, a question here arises regarding the signi cance of the air-exchange rate for the multivortex ow.In fact, since ACH depends only on the ow kinematics around the upper part of the canyon, it cannot provide any information on the actual air exchange occurring at the cavity bottom, where the second (or third) vortex is located.erefore, the use of ACH for evaluating the ventilation performance of a street canyon and its relation with pollutant removal mechanisms must be considered with circumspection for multivortex regimes.

E ect of Building Height Variations.
Another geometrical factor that considerably in uences the ventilation in the urban street canyon is the relative height of the buildings, H 2 /H 1 .is parameter has already been investigated in other works [62,[72][73][74][75][76][77] for 2D ows, while useful insights into the e ects of building height variations for arrays of 3D buildings have recently been reported in [78][79][80].e additional analysis we provide here focuses on the combined e ect of the variability of both building heights and AR.Six H 2 /H 1 have been considered for each of the ve ARs, in particular the step-up con gurations, where the leeward building (H 1 ) is shorter than the windward building (H 2 /H 1 1.5, 2, and 2.5), and the step-down con gurations, where the leeward building is taller than the windward building (H 2 /H 1 0.4, 0.5, and 0.7).
Figure 11 shows the streamlines obtained for the stepup geometry (H 2 /H 1 > 1).For AR 0.5 and H 2 /H 1 1.5 (Figure 11(a)), the ow eld does not depart signi cantly from that observed for H 2 /H 1 1 (Figure 9(a)), in agreement with the numerical results in [64].e size of the main vortex increases as H 2 /H 1 increases (Figures 11(f) and 11(k)), and its center does not move appreciably along the x-axis, while it moves upward, reaching about the height of the leeward building.At the bottom of the canyon, the recirculation zone at the corner of the leeward building becomes smaller as H 2 /H 1 increases, while the anticlockwise vortex at the corner with the windward building progressively increases in size.A similar behavior occurs for AR 1 (Figures 11(b), 11(g), and 11(l)).
Regarding the other skimming ows, their dependence on H 2 /H 1 is somehow greater.e progressive ejection of the upper vortex from the canyon into the overlying layer observed for AR 1.33 (Figures 11(c 11(d)) and it progressively moves upward as H 2 /H 1 grows, and for H 2 /H 1 2.5, the vortex is practically outside of the canyon.Similar considerations can be drawn for the case AR 1.33, which shows the transition from the standard skimming ow when H 2 /H 1 1 (Figure 9(a)) to the multivortex regime for H 2 /H 1 > 1 (Figures 11(c), 11(h), and 11(m)).e recirculation zones at the bottom of the canyon are combined together, and two counterrotating vortices occupy the canyon.
In terms of air ventilation, ACH ′ /(u ref W) always exceeds its average counterpart, ACH/(u ref W), even though not to a large extent as for H 2 /H 1 1.Furthermore, ACH does not depend signi cantly on H 2 /H 1 when AR 1 and 2, while a clear decrease in ACH for increasing H 2 /H 1 takes place for the other aspect ratios.In particular, taller windward buildings allow lower vertical mass transfer between the canyon and the overlying region.
Finally, Figure 12 shows the ow patterns for the stepdown con gurations (H 2 /H 1 < 1).ey are characterized by a wide clockwise vortex placed over the canyon and the top of the windward building.Overall, the lower the H 2 /H 1 , the smaller the ACH (Figure 13(c)), with the exception of the case (AR 2, H 2 /H 1 0.67), when there is only a large vertical structure occupying both the canyon and the overlying region up to z ≈ H 1 (Figure 12(a)).e latter con guration corresponds with the largest ACH calculated in the present analysis and is mainly associated with large ACH.In contrast, for all the other step-down con gurations investigated here, the main vortex (or the two or more vortices, when AR ≥ 1.33) remains con ned within the canyon.e latter represents the main di erence between step-up and step-down con gurations, and it might have great in uence on the concentration of pollutants emitted within the canyon, particularly at the street level.
Lastly, we note that, from the point of view of air quality analysis, the development of secondary vortices in the lower corners of the canyon for AR 0.5 and 1 should determine an accumulation of pollutants near the sidewalks in the case of vehicular tra c emissions, whatever be the value of the height ratio.For AR 1.33 and 2, the presence of the two  Advances in Meteorology 11  12 Advances in Meteorology counterrotating vortices further limits the ventilation in the canyon, especially in the portion closest to the ground.For AR 4, the vertically aligned multiple vortices con guration strongly inhibits the exchange of air with the higher levels and paves the way to the stagnation of pollutants at the pedestrian level.

Summary and Conclusions
Water-channel data have been used to diagnose the capability of the v 2 − f (V2F) turbulence model, implemented in Ansys Fluent, to reproduce the ow eld in a regular array of 2D buildings.e experiments refer to two very common geometrical con gurations, that is, the skimming ow (AR 1) and the wake-interference regime (AR 0.5).One of the strengths of the V2F model is the equation of the turbulent viscosity, which takes into account the anisotropy of the ow in the near-wall region through the modeling of a velocity scale.e performances of the V2F model have been compared with those of other six turbulence models implemented in Ansys Fluent.e results have shown that the V2F model gives the best results with shorter computational time.Further simulations conducted using the V2F model have made it possible to analyze canyon ventilation for a variety of aspect ratios and step-up and step-down congurations by calculating the air-exchange rate (ACH).For the step-up con gurations (H 2 /H 1 > 1), the increase of the relative height of the buildings does not appreciably change the total ACH for both the wake-interference and the skimming ows, while a certain decrease of ACH occurs for AR > 1.33.On the contrary, step-down con gurations (H 2 /H 1 < 1) appear to be in general less ventilated and therefore more prone to pollutant recirculation.For all the geometries investigated, the air ventilation is mainly determined by turbulent motions with the exception of the wake-interference regime for H 2 /H 1 0.67, the latter canyon geometry being characterized by the largest contribution of the mean ACH.
In conclusion, the V2F turbulence model has proved to be a useful tool for wind engineers as well as for investigations concerning air quality control and urban planning.

e
numerical simulations have been validated with a series of experiments conducted in the close-loop water channel located at the Laboratory of Hydraulics of the 2 Advances in Meteorology University of Rome "La Sapienza."

Figure 1 :
Figure 1: Side and top views of the experimental apparatus.e x-axis refers to the longitudinal axis of the channel (streamwise), while the z-axis is parallel to the vertical.

Figure 3 :Figure 4 :
Figure 3: e computational domain for the 3D simulation.H indicates the building height.

Figure 7 :
Figure 7: Comparison between simulated (symbols) and measured (line) vertical pro les of V/u ref passing through the center of the canyon for AR 1 (a) and AR 0.5 (b).

Figure 8 :
Figure 8: Streamlines of the mean velocity magnitude for AR 1 measured in the laboratory (a) and simulated (c) and for AR 0.5 measured in the laboratory (b) and simulated (d).

5 Figure 10 :Figure 11 :
Figure 10: Comparison among the simulated vertical pro les of V/u ref passing through the center of the canyon for AR 4, AR 2, AR 1.33, AR 1, and AR 0.5.

Figure 13 :
Figure 13: Nondimensional ACH components as a function of the relative building heights for ve aspect ratios: (a) mean component, (b) turbulent component, and (c) total ACH.

Table 1 :
Characteristics of the four meshes used for the grid independence test and corresponding percentage di erences Δ.

Table 2 :
Percentage di erences between the velocity magnitudes calculated along the vertical pro les passing through the center of two contiguous canyons.

Table 4 :
Percentage di erences between measured and modeled velocities within and above the canyon (AR 0.5).