Relating street canyon vertical mass-exchange to upstream flow regime and canyon geometry

Sustainable Cities and Society 30 (2017) 49–57

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Relating street canyon vertical mass-exchange to upstream flow regime and canyon geometry Laurent Perret a,b,∗ , Karin Blackman a , Royston Fernandes a , Eric Savory c a b c

LHEEA UMR 6598 CNRS, Ecole Centrale de Nantes, 1, rue de la Noë, BP 92101, 44321 Nantes Cedex 3, France IRSTV, FR CNRS 2488, Nantes, France Department of Mechanical & Materials Engineering, Univ of Western Ontario, London, ON N6A5B9, Canada

a r t i c l e

i n f o

Article history: Received 14 November 2016 Accepted 2 January 2017 Available online 10 January 2017 Keywords: Boundary layer Street canyon Exchange velocity Particle image velocimetry Wind tunnel

a b s t r a c t Understanding and management of air quality is important to the sustainability of the urban environment and pedestrian level air quality is strongly influenced by the vertical airflow and consequent pollutant mass transfer that takes place at the roof level of street canyons. Using data from a scaled wind tunnel street canyon flow, the present work shows how a simple, first order “dead-zone” model may be successfully applied to provide a link between the vertical velocities at roof level and the magnitude of the mass-exchange. In addition, it is shown how the model may be modified to provide a prediction that takes into account both the geometry of the canyon as well as the canyon flow characteristics and those of the upstream roughness. The mass-exchange is also shown to be linked to the largest scales in the boundary layer passing over the canyon. Finally, it has also been demonstrated that, for the six configurations investigated here (two canyon geometries immersed in three different types of upstream roughness), the probability distribution function of the exchange velocity agrees very well with a log-normal distribution, thus allowing derivation of a simplified model of the instantaneous exchange velocity using a random number generator. © 2017 Elsevier Ltd. All rights reserved.

1. Introduction When considering the overall climate of a city, researchers have focussed on the urban heat island, in particular its effects on overall urban ventilation, building occupant and pedestrian comfort/health and building energy demand (Mirzaei, 2015). Although building-scale, micro-scale and city-scale models have been developed (Mirzaei, 2015), that link wind and thermal climate data to building energy models for example (Allegrini, Dorer, & Carmeliet, 2015), the wind flow prediction tends to be implemented via Computational Fluid Dynamics (CFD) models that consider only the time-averaged flow, despite the fact that the dynamic nature of the wind in the urban environment has yet to be elucidated, let alone quantified. Indeed, crucially, within a city there is an intermittent interaction between the atmospheric boundary layer flow and that within the individual street canyons, which governs the exchange processes of momentum, heat and pollutants, thus playing a critical

∗ Corresponding author at: LHEEA UMR 6598 CNRS, Ecole Centrale de Nantes, 1, rue de la Noë, BP 92101, 44321 Nantes Cedex 3, France. E-mail address: [email protected] (L. Perret). http://dx.doi.org/10.1016/j.scs.2017.01.001 2210-6707/© 2017 Elsevier Ltd. All rights reserved.

role in the quality of the urban atmosphere and the sustainability of human life. Although simple from a geometrical point of view, the idealized two-dimensional (2-D) street canyon model reproduces the main features of most common street configurations, notably the case for which the upstream wind is perpendicular to the street axis where the ventilation is largely driven by vertical exchanges between the canyon and the flow above. This configuration has been well-studied, with the time-averaged (steady) flow regimes being first identified by Hussain and Lee (1980) and then defined and illustrated by Oke (1988) as a function of the canyon streamwise width (W) to height (h) ratio. The three regimes − “skimming flow” when W/h < 1.5, “wake-interference flow” when 1.5 < W/h < 3 and “isolated roughness flow” when W/h > 3 – have since been much-quoted in the literature even though, at the time he made these definitions, Oke (1988) noted that this classification ignored turbulence, that is any unsteady flow dynamics. The standard practical model that has been used for the past two decades to predict street canyon dispersion, the Operational Street Pollution Model (OSPM) (Berkowicz, 2000 and subject to numerous validation studies, Kakosimos, Hertel, Ketzel, & Berkowicz, 2011) considers the canyon flow to be a steady vortex with dispersion computed by a plume model. Although traffic produced turbu-

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lence (Di Sabatino, Kastner-Klein, Berkowicz, Britter, & Fedorovich, 2003; Kastner-Klein, Fedorovich, Ketzel, Berkowicz, & Britter, 2003) and meandering of the incident wind direction are considered, the unsteady canyon flow dynamics are not. Hence, in terms of urban air quality assessment, street canyon flows are conventionally considered to comprise one or more large-scale mean vortices, or flow recirculation regions, upon which relatively small-scale turbulence is superimposed. However, even on a time-averaged basis, there is no sharp demarcation of the regimes defined by Oke (1988), as illustrated from the Unsteady Reynolds-Averaged Navier-Stokes (URANS) CFD numerical model study of Sini et al. (1996), where the flow and pollutant concentrations were predicted for several canyon widths from W/h = 0.33 to 14.82, with the results showing continuous, though mostly gradual, changes in parameters such as canyon wall pressure coefficients, in-canyon wind speeds, dosing rate by an external source and the decay rate of pollutant from the street. The high degree of variability in basic aerodynamic parameters, such as roughness length, z0 /h, and zero plane displacement, d/h, for different planform geometries (2-D parallel streets, 3-D block regular arrays and real urban regions) having the same plan area packing density, ␭p , was highlighted by Grimmond and Oke (1999), where they also attempted to relate those parameters to the three flow regimes. Recently, the present authors conducted an approximately 1:250 scale wind tunnel study in which long canyons (L/h = 30) of two different widths W/h = 1 and 3 were placed normal to the oncoming flow in three different roughness arrays formed from; (1) cubes of height h with ␭p = 25%, (2) 2-D square section bars of height h spaced 3 h apart giving ␭p = 25% and (3) the same 2-D bars spaced 1 h apart giving ␭p = 50% (Blackman, Perret, & Savory, 2015a). Instantaneous velocity vector fields were measured within and above the canyons for these six configurations, using Particle Image Velocimetry (PIV), from which mean and turbulence statistics were computed. For a given canyon width the flow was, indeed, dependent on the nature of the upstream roughness (2-D or 3-D) for the same plan area density. The streamwise velocities produced by the 3-D array were higher than for the equivalent 2-D array whilst the integral scales of turbulence were lower (although they increased with increasing 2-D roughness spacing, that is, the aspect ratio). In agreement with other published data, the relative contributions of the three orthogonal components to the total turbulent kinetic energy (TKE) showed that staggered and aligned arrays or 2-D and 3-D arrays of equal p do not generate the same profiles of TKE (Rotach, 1995; Macdonald, Carter Schofield, & Slawson, 2002). Other workers have also shown that roughness type is important in determining the magnitude and distribution of the Reynolds stresses and the length scales in the roughness sub-layer (Volino, Schultz, & Flack, 2009; Lee, Sung, & Krogstad, 2011). The ventilation rate of the canyon (important for local air quality), estimated via the computation of positive and negative (vertical) flow rate across the canyon opening, was also found to be influenced by the upstream flow regime, even with the narrow canyon of W/h = 1 (Blackman et al., 2015a). An upstream wake-interference flow regime (obstacle spacing of 3 h) led to stronger exchanges between the canyon and the flow above. For a given upstream roughness, changing from a skimming canyon flow (W/h = 1) to the wake interference flow regime (W/h = 3) increased the magnitude of the total positive and negative ventilation flow rates (i.e. the w’ velocity fluctuations). This trend with canyon width was consistent with that found by Ho and Liu (2013), although the magnitudes of the non-dimensional ventilation flow rates, Q/(Ue W L) (where Ue is the freestream velocity) were different in the two studies. All these findings emphasize that upstream roughness type and density play a significant role in determining the mean flow in a canyon of given aspect ratio, thus demonstrating the importance of carefully choosing the simulation method when car-

rying out wind tunnel studies of canyon flows, as noted previously by Savory et al. (2013). Indeed, when considering the classification of canyon regimes described here, based on the time-averaged flow, such a definition is made very unclear if the geometry of the canyon under consideration implies one kind of flow regime whilst the upstream roughness is defined as giving a different regime (Blackman et al., 2015a). When such considerations are taken into account alongside the fact that time-averaged canyon flow fields look very different from any instantaneous realization of the flow, one may reasonably question the practical value of this type of classification, especially when it comes to understanding the dynamics that actually govern canyon flow and dispersion. Hence, the present research has been motivated by a desire to seek a new classification of canyon regimes that incorporates the time-varying nature of the flow and its effects on canyon ventilation. Urban canyon flows are dominated by vortical structures (“eddies”) both within the oncoming boundary layer and generated locally by the flow around the canyon buildings and many researchers, for example Barlow and Leitl (2007), Coceal et al. (2007) and Perret and Savory (2013), have highlighted the strong unsteadiness of the flow developing at the building roof and its role in generating intermittent coherent turbulent structures which penetrate downwards, causing mixing of air in the street. The coupling between the large scale coherent structures in the boundary layer (associated with low and high momentum regions) and the smaller scales in the shear layer at the top of the canopy was observed by Takimoto et al. (2011) and Inagaki et al. (2012). In a PIV study of a W/h = 1 canyon the present authors used twopoint spatial correlations, Proper Orthogonal Decomposition (POD) and spatial averaging to elucidate some of the aspects of the flow dynamics (Perret & Savory 2013). Strong ejection (Q2) and penetration (Q4) events were observed above the canyon up to a height of z/h = 2 and a non-linear coupling between the large-scales (identified through the first POD mode) and the smaller scales (other modes) was quantified. The experimental setup comprised a skimming flow regime canyon immersed in a roughness array formed from cubes of the same height as the canyon but with a plan area density corresponding to the wake interference. Thus, there was strong flow separation at the upstream edge of the upstream canyon obstacle that gave rise to a significant vertical “flapping” motion and a shear layer of thickness O(h) in contrast to previous studies of similar canyons immersed in a skimming flow roughness where the shear layer was thinner, O(0.2 h), for example Salizzoni et al. (2011) and Kellnerová et al. (2012), because of separation occurring at the downstream edge of the upstream building in those cases. Hence, it is clear that any canyon classification model based on dynamics will have to consider both the local canyon geometry and the upstream roughness geometry. The present work is a wind tunnel study at approximately 1:250 scale of two different canyons (aspect ratio W/h = 1 and 3) immersed in the same upstream roughness in which flow field measurements have been undertaken using PIV together with two reference hotwire anemometers. The authors have already shown that the street canyon flow in this wind tunnel is well-scaled to published reference data for the same roughness (Blackman et al., 2015a) as well as to data from a field study of a similar type of idealized street canyon formed from shipping containers (Blackman, Perret, & Savory, 2015b; Perret, Blackman, & Savory, 2016). This prior work gives confidence that the wind tunnel experiment captures very well the dynamics of the full-scale case. The questions to be addressed in the present paper are:

(1) Can the vertical mass-exchange between the canyon and the boundary layer above be described by a relatively simple firstorder “dead-zone” model and

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(2) Can that model be modified to encompass the influence of both the canyon geometry and the upstream roughness? Hence, using a relatively idealized building configuration, the present study is the first step towards quantifying the unsteady behaviour of the flow and its implication in terms of canyon ventilation for different canyon flow regimes. The focus is on the large-scale unsteadiness of the shear layer separating from an upstream canyon edge, its impact on the instantaneous flow field within the canyon and its link with the oncoming boundary layer. Although the geometry studied here is simple compared to any real urban environment, as noted by Savory et al. (2013) it is only by first examining and quantifying the flow dynamics for such well-defined cases that one will eventually be able to apply those findings to the interpretation of the flow regimes for more complex cases. The next section of this paper discusses the experimental setup, measurement approach and data analysis methods. This is followed by a discussion of the results and then the conclusions. 2. Experimental details and analysis methods 2.1. Wind tunnel setup The experiments were conducted in the low-speed, suck-down boundary layer wind tunnel in the LHEEA at Ecole Centrale de Nantes (Fig. 1), which has working section dimensions of 2 m (width) × 2 m (height) × 24 m length and a 5:1 ratio inlet contraction. The empty-tunnel has a free-stream turbulence intensity of 0.5% over a wind speed range of 3–10 m/s with good spanwise uniformity to within ±5%, Savory et al. (2013). Full details of the experiment may be found in Blackman et al. (2015a) but the main points will be summarized here. The experiments used five 800 mm high vertical tapered spires located immediately downstream of the contraction and a 200 mm high solid fence across the working section 750 mm downstream of the spires to initiate the boundary layer development. These were followed by an initial 13 m fetch of 50 mm staggered cube roughness elements with a plan area density of 25% to initiate boundary layer development. The canyon flow measurement tests were taken 5.5 m downstream of this initial development region whilst the roughness arrays over this last portion of the wind tunnel floor were either 50 mm cubes arranged in a staggered array with p = 25% or 50 mm square section, twodimensional bars that spanned the width of the tunnel, with an element spacing of either 1 or 3 h (Fig. 1 top row and bottom left). Blackman et al. (2015a) showed that the effects of the roughness transition from the initial development region were negligible. Six flow configurations were investigated: two canyon widths of W/h = 1 or 3, with 3 different types of upstream roughness elements. The measurement canyons are defined as “cnh” with n = 1 or 3, and the upstream roughness is staggered cubes (denoted as “cub”) or 2D bars (denoted as “b1h” or “b3h”). The canyon building length was L = 30 h, with the canyon height h = 50 mm. The velocity fields were measured in a vertical plane in the centre of the canyon aligned with the free stream flow direction (Fig. 1, bottom right). A Dantec particle image velocimetry (PIV) system set up in stereoscopic configuration was used to measure the three velocity components. A commercially available smoke generator was used to seed the flow with water-glycol droplets (mean diameter = 1 ␮m) which were illuminated using a light sheet generated by a Litron double cavity Nd-YAG laser (2 × 200 mJ). A frequency of 7 Hz was used between pairs of pulses and two CCD cameras with a 60 mm objective lens were used to record 5000 pairs of images in each experiment. A time-step of 400 ␮s was set between two images of the same pair and multi-pass cross-correlation PIV processing resulted in a final interrogation

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Table 1 Main characteristics (friction velocity u∗ , displacement height d and roughness length z0 ) of the three upstream flow configurations. Upstream roughness

Notation

u∗ /Ue

d/h

z0 /h

Staggered cubes 2D bars, 1 h spacing 2D bars, 3 h spacing

cub b1h b3h

0.066 0.047 0.072

0.892 0.980 0.552

0.061 0.008 0.143

(adapted from Blackman et al., 2015a).

window size of 16 × 16 pixels with an overlap of 50%. The final spatial resolution was 0.83 and 1.68 mm in the longitudinal and vertical directions, respectively. Two single hot-wire anemometer probes (HWA) were used to measure, at 10 kHz and in synchronization with the PIV, the streamwise velocity component above the downstream canyon block at heights of 1.2 and 4 h. The maximum standard deviations of the main PIV statistics due to statistical error were estimated (assuming Gaussian velocity distributions) to be 0.0041, 0.0029 and 0.0002 for the mean velocity, velocity standard deviation and turbulent shear stress normalized by the freestream velocity, respectively. All the experiments were performed with the same free-stream velocity Ue = 5.9 m/s measured with a pitot-static tube located at x = 15 m, y = 0 m and z = 1.5 m, giving a Reynolds number, based on canyon height, of Reh = 1.9 × 104 . The spanwise homogeneity was investigated by Rivet (2014) over the cube array (Rcu) for z/h > 2 and he determined that the turbulence statistics taken at three spanwise measurement locations were in agreement to within 5%. In addition, Savory et al. (2013) showed that the centre-line mean flow profiles were independent of canyon length when L/h > 9 and the canyon length in the present work (L/h = 30) greatly exceeds that value. The main characteristics of the three upstream flow configurations are summarized in Table 1. 2.2. Analysis method In this section, we show how the concept of the first-order deadzone model is employed in the present study to investigate the influence of both the canyon geometry and the upstream roughness configuration on the mass exchange between the canyon and the above flow. This approach was originally developed to model accidental pollutant spills in rivers to take into account the influence of the main channel geometry heterogeneities on dispersion phenomena. The focus was on bank heterogeneities such as groyne fields, side arms or harbours, which can be considered as dead zones, i.e zones where flow velocity is very slow compared to the main stream river. The contact regions between the main channel and these lateral dead zones, where exchange of mass and momentum take place, are characterized by strong velocity shear favouring the formation of mixing-layer-like coherent structures. These are very similar to what happens at the roof level when considering the interaction between streets and the above boundary layer flow in cities. For a detailed review of the mass-exchange between channel lateral heterogeneity and the main stream in rivers, the reader is referred to the study of Weitbrecht et al. (2008). It must be noted here that the same concept of a first-order model has also been used to model the mass-exchange between the river main flow and a submerged aquatic vegetation canopy (Ghisalberti and Nepf, 2005). The classical first-order model derived for the mass-exchange between the main stream and a dead zone is here employed to model the mass-exchange between a canyon of height h, width W and lateral extension L. When considering the timeevolution of M the mass of a tracer dispersed within the canyon, the dead-zone model reads as: dM = −ELW (Cc − Cabl ) dt

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Fig. 1. Investigated canyon and upstream roughness configurations (c1hb1h and c3hb1h: top left, c1hb3h and c3hb3h: top right and c1hcub and c3hcub: bottom left) and employed PIV setup (bottom right).

where E is the exchange velocity into the main stream averaged over the canyon width and Cc and Cabl are the concentrations in the canyon and atmospheric boundary layer, respectively. The tracer mass in the canyon is given by M = Cc LWh. The above equation for dM/dt therefore reads as E dCc = − (Cc − Cabl ) dt h In the case of a constant exchange velocity E, the time-evolution of the concentration within the cavity corresponds to an exponential decay with time, with a characteristic time Tc = h/E. This time-scale, also called mean residence time (Weitbrecht, Socolofsky, & Jirka, 2008) can be seen as the time required to transport across the interface between canyon and the flow above main stream a volume of fluid corresponding to the cavity volume (Tuna, Tinar, & Rockwell, 2013). As noted by Weitbrecht et al. (2008), the characteristic time Tc can be evaluated from direct measurement of the concentration response of the canyon configuration (with the above equation) or by using the indirect method proposed by Weitbrecht et al. (2008) and Tuna et al. (2013), as described below. In their study of mass-exchange between groyne fields and a main river, Weitbrecht et al. (2008), proposed to estimate the instantaneous exchange velocity E (t) by:



W/2

E (t) =

1 W

|w(x, z = h, t)|dx −W/2

where w (x, z = h, t) is the instantaneous vertical velocity at roof level. It must be noted here that, following Tuna et al. (2013), the factor 1/2 included by Weitbrecht et al. (2008) is omitted. Moreover, Weitbrecht’s definition of the exchange velocity is different from that used by Neophytou et al. (2014) in their study of street canyon flows as the latter is based on the absolute value of the average vertical velocity, therefore does not account for the influence of the turbulent fluctuations in the exchange process. The two definitions being not equivalent, Neophytou et al’s results are therefore

not reported in the present study. Using this approach, it becomes obvious that the mass-exchange between the canyon and the above flow is driven by the characteristics of the vertical component w (t) at roof level. In the following, given the similarity between the present configuration and those investigated in the framework of tracer dispersion between bank heterogeneity and the main river, the validity of the first-order dead-zone model and the above definition of the exchange velocity based on the vertical component at roof level are assumed. The exchange velocity E (t) is, therefore, employed to investigate the influence of the canyon configuration on mass-exchange with the atmospheric boundary layer. In the following sections, the characteristics of the exchange velocity are presented as well as its link with the flow characteristics. An attempt to link the average exchange velocity E and both the characteristics of the oncoming boundary layer flow and the geometry of the studied canyon is also presented.

3. Results and discussion 3.1. Statistics of the instantaneous exchange velocity In this section, the one-point statistics of the exchange velocity are examined as a function of both the canyon width and the upstream roughness configuration. Probability density functions (pdf) of E(t) for the six investigated configurations are given in Fig. 2. As expected, their shapes and characteristics vary: the most expected value (or peak value) of the pdf increases with canyon width and their width, directly related to the standard deviation of the variable E(t) increases with varying upstream roughness. The narrowest distribution is obtained for the 1 h bar roughness, the 25% cube array provides an intermediate value whereas the widest pdf is obtained for the 3 h bar upstream terrain. This trend is valid for both canyon widths. Besides these conclusions, the most striking feature all the computed pdf share is the excellent fit of a log-normal law to the data. It, therefore, means that, given the values of the mean and the standard deviation, one can generate

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Fig. 2. Probability density functions (pdf) of E(t) for the six flow configurations separated in two sets for clarity. Left: W/h = 1, right: W/h = 3. Upstream roughness: 1 h bars (red squares), 3 h bars (blue circles) and 25% cubes (purple triangles). Symbols: data, lines: theoretical log-normal distribution.

Fig. 3. Mean (top left), standard deviation (top right), skewness SkE (bottom left) and flatness FE (bottom right) of the exchange velocity at roof level for the six configurations. Solid bars: 1 h wide canyon, hatched bars: 3 h wide canyon. Upstream roughness: 1 h bars (red), 3 h bars (blue) and 25% cubes (purple).

a set of random data having the same statistical characteristics of the instantaneous exchange velocity of a given configuration. For the sake of completeness, the characteristics of the pdf, up to the fourth order moment, are presented in Fig. 3, confirming the above conclusion: the wider the canyon and the rougher the upstream terrain (i.e the lower d/h, or the higher friction velocity or the higher roughness length z0 /h), the higher the exchange.

Finally, the link between the mass-exchange velocity and the upstream flow characteristics shown previously is investigated further here via computation of the temporal correlation coefficient of the instantaneous exchange velocity E (t), which reads as: CEE () =

E’ (t) E’ (t + ) E2

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by the shear-layer dynamics, which has been shown, in the case of street canyon flows, to be composed of a strong flapping motion and the presence of vortical coherent structures (Perret and Savory, 2013). In agreement with previous studies of cavity-river interaction and with what one would expect, the stronger the shear-stress, the larger the exchange velocity. This also translates into; the wider the canyon, the stronger the exchange and the more the flow regime tends to a wake interference regime (i.e largest displacement height d/h and friction velocity u∗ /Ue ). In order to take into account the influence of the dead-zone cavity on the mass-exchange characteristics, Weitbrecht et al. (2008) have proposed using a length scale similar to a hydraulic radius defined as the ratio between the cavity cross-section area W.h divided by its lateral boundary W + 2h. They showed that the factor two in the denominator had no dynamic role in the physical problem and could be omitted. The resulting length scale they used was, therefore, defined as: Fig. 4. Variation of the temporal correlation coefficient of the instantaneous exchange velocity. Closed symbols: W/h = 1, open symbols: W/h = 3. Upstream roughness: 1 h bars (red squares), 3 h bars (blue circles) and 25% cubes (purple triangles).

where E’ (t) is the temporal fluctuation of E (t) around its mean and E its standard deviation. The resulting temporal correlation coefficients for the six configurations investigated in the present study are presented in Fig. 4. Despite the low temporal resolution of the employed PIV setup which cannot record the time-history of the velocity signal with a high data rate (acquisition frequency of 7 Hz), the six configurations show non-negligible correlation levels, with a time-scale corresponding to the integral time-scale of the oncoming boundary-layer flow (Blackman et al., 2015a). It confirms that, if the mass-exchange between the canyon and the above flow is primarily driven by the shear-layer dynamics, it is also strongly influenced by the large-scales of the atmospheric boundary-layer, possibly through an amplitude modulation mechanism as found by Blackman and Perret (2016) in the case of the small-scale turbulence within an urban canopy immersed in an atmospheric boundary layer. 3.2. Link between the mean exchange velocity E and the flow main characteristics The definition of the exchange velocity E (t) being based on the absolute value of the vertical velocity w (t) along a horizontal line at roof level, its main characteristics must be linked not only to those of the shear-layer developing from the upstream building and across the canyon but also to the canyon geometry, in particular its aspect ratio W/h. In terms of the mass-exchange between the main river and lateral dead zones, both aspects have been investigated. Based on laboratory experiments, Sanjou and Nezu (2013) have shown the link between the average exchange velocity E (t) and the velocity scale us defined from the Reynolds shear-stress u’w’ spatially averaged over a horizontal line at z = h, namely:



W/2 1/2

us = < |u’w’|

1 >= W

1/2

|u’w’|

dx

−W/2

where <·> is the spatial averaging operation along the horizontal line across the canyon at z = h. They found a linear relationship between the two quantities. The same approach has been tested in the present study and it is shown in Fig. 5, left, that, despite the difference between the flow configurations, the same conclusion can be drawn. As concluded by Sanjou and Nezu (2013), the massexchange between the canyon and the above flow is mainly driven

RH =

W.h W +h

In their experimental study of the mass-exchange between groyne fields and main stream in rivers, these authors showed that, when normalized by the main stream velocity, the mean exchange velocity E (t)/Ue scaled linearly with the normalized hydraulic radius RH /h. This scaling was shown to hold quite well when various geometries of groynes were considered (including groynes with backward or forward slope). Fig. 5, right, shows the same scaling applied to the present data. It can be seen that, even if the values of the normalized exchange velocity E (t)/Ue of each of the two investigated canyon geometries (i.e W/h = 1 and W/h = 3) are grouped together with similar values, a scatter still exists, showing that, in the present case, the geometry of the cavity is not the sole factor governing the dynamics of the shear-layer where the massexchange takes place. It must be noted however that, in spite of the differences between the present flow configurations and those investigated by Weitbrecht et al. (2008), the values of E (t)/Ue found here (taking into account the factor 1/2) are in good agreement with those predicted by the scaling derived by those authors. However, a major difference exists between the flow configurations investigated by Weitbrecht et al. (2008) and street canyon flows immersed in atmospheric boundary layers: groynes are very similar to fences, the thickness of the obstacle being small when compared to its height, therefore clearly defining the location of the flow separation over the obstacle, whereas in the case of buildings whose width can be of the same order of their height (or equal, as in the present case), the location of the flow separation depends on the regime of the upstream flow. As shown by Grimmond and Oke (1999), the latter ranges from skimming flow, for which the flow separation is located at the downstream corner of the upstream building of the canyon, to wake interference regime in which the flow separation occurs at the upstream corner of the upstream building. The location of the separation point affects the dynamics of the shearlayer and, therefore, the mass-exchange between the canyon and the above flow (Blackman et al., 2015a). Here, an attempt to improve the parametrizations presented in the literature is proposed by including characteristics of the upstream boundary layer. Changing the flow regime from skimming to wake interference has a direct impact on the friction velocity u∗ and the displacement height d of the oncoming boundary layer. Fig. 6, left, shows how incorporating the normalized friction velocity u∗ /Ue in Weitbrecht et al’s scaling improves the prediction. The flow configurations are no longer grouped solely based on the canyon geometry as both the canyon geometry and the upstream flow characteristics are now included. A linear rela-

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Fig. 5. Evolution of the exchange velocity as a function of (left) the shear stress velocity scale us and (right) the canyon hydraulic radius RH .Closed symbols: W/h = 1, open symbols: W/h = 3. Upstream roughness: 1 h bars (red squares), 3 h bars (blue circles) and 25% cubes (purple triangles). Data for river groynes of Weitbrecht et al. (2008) (brown plus signs) and canonical cavities of Chang et al. (2006) (orange stars) are also shown when possible.

Fig. 6. Variation of normalized exchange rate with two different normalized length scales. Closed symbols: W/h = 1, open symbols: W/h = 3. Upstream roughness: 1 h bars (red squares), 3 h bars (blue circles) and 25% cubes (purple triangles). Data of Chang et al. (2006) (orange stars) are also shown.

tionship between the average exchange velocity E (t)/Ue and the new parameter u∗ /Ue .RH /h is found to agree quite well with the present data. The second scaling proposed here attempts to include only length scales, namely the canyon geometry and the displacement height of the oncoming boundary layer, in a modified hydraulic radius R˜H defined as: (h + h − d) .W R˜H = (h + h − d) + W When compared to the original definition provided by Weitbrecht et al. (2008), the quantity h − d is added to the vertical dimension of the canyon to take into account the fact that, when the flow regime shifts toward a wake interference regime (i.e decreasing d/h), the flow separation location shifts to the upstream corner of the upstream building, inducing a thicker shear-layer with a stronger flapping motion, regardless of the canyon geometry (Blackman et al., 2015a). Using this modified length scale R˜H , the different flow configurations, depending on its canyon geometry and upstream boundary layer characteristics, are now clearly differentiated (Fig. 6, right). Again, this modified scaling results in a linear relationship between the average exchange velocity E (t)/Ue and the modified hydraulic radius. Both scalings also lead to the same conclusion regarding the link between the intensity

of the mass-exchange and both the characteristics of the canyon geometry and the upstream flow regime (i.e smallest exchange corresponding to the narrowest canyon and an upstream skimming flow regime, the strongest resulting from the combination of the widest canyon and greatest displacement height and friction velocity). The performance of the proposed scaling are also evaluated in terms of the prediction of the standard deviation of the exchange velocity E . Fig. 7 shows that a linear relationship between E /Ue and the scaling parameters holds reasonably well. Again, the best agreement is obtained for the scaling based on the modified hydraulic radius based on the displacement height and therefore taking into account the nature of the upstream flow regime (Fig. 7, right). Finally, to demonstrate the potential of the present results in terms of operational use, the present linear model for the exchange velocity has been combined with that of Macdonald et al. (1998) which predicts the displacement height d of the flow developing over an urban-like roughness array from the value of the plan area density p of the array by (with ˛ = 4.43):





d/h = 1 + ˛−p p − 1 . As shown in Fig. 8, it allows for the prediction for the magnitude of mass-transfer via that of the exchange velocity for both a given canyon geometry (W/h) and a given upstream terrain plan

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L. Perret et al. / Sustainable Cities and Society 30 (2017) 49–57

Fig. 7. Variation of normalized standard deviation of the exchange velocity with different normalized length scales. Closed symbols: W/h = 1, open symbols: W/h = 3. Upstream roughness: 1 h bars (red squares), 3 h bars (blue circles) and 25% cubes (purple triangles).

Fig. 8. Magnitude of the average exchange velocity E predicted using the present model and that from Macdonald et al. (1998) which relates the displacement height d to the plan area density p . Black circles represent the six configurations investigated in the present study; the black star is for the aerodynamic cavities of Chang et al. (2006). Dashed lines defining the plan area density range of real cities and the corresponding flow regimes are taken from Grimmond & Oke (1999).

area density p . It also confirms the importance of both parameters, representing local and more global effects, respectively, on the capacity of a city to ventilate its streets.

importance of the shear layer dynamics developing at roof level and across the canyon in driving the canyon mass-exchange. It has also been confirmed that the dynamics of this flow region are due to both the local effects (driven by the canyon geometry) and the upstream flow regime. Through the use of temporal correlation coefficients of the exchange velocity, the mass-exchange dynamics have also been linked to the largest scales of the atmospheric boundary layer flow in which the canyon is immersed, emphasizing the need to both properly model the upstream flow (in experiments or numerical simulation for instance) and account for its characteristics when deriving local models. A geometrical scaling parameter based on the canyon dimensions, adapted from the literature by taking into account the nature of the upstream flow regime via the use of its displacement height, has been shown to enable the derivation of a simple linear model for both the mean exchange velocity and its standard deviation. It has also been demonstrated that, for the six investigated configurations, the probability distribution function of the exchange velocity agrees very well with a log-normal distribution. Therefore, knowing the nature of the distribution (which depends only on two parameters: the mean and the standard deviation of the random variable) and having a simple model linking the mean and standard deviation of the exchange velocity to both the canyon geometry and the nature of the upstream flow regime allows for the derivation of a simplified model of the instantaneous exchange velocity using a random number generator.

4. Conclusions

Acknowledgements

The mass-exchange between a street canyon and the lower atmosphere has been investigated using data obtained from wind tunnel experiments for a set of six different flow configurations comprising two canyon widths and three different upstream flows. Based on available results from the literature for similar configurations, such as river groynes, aerodynamic cavities or aquatic vegetation canopies, the validity of a dead-zone model to represent the global time-evolution of the concentration of a tracer contained in the canyon has been postulated here. This model, based on the use of a characteristic exchange velocity, allows for a direct link between the dynamics of the vertical velocity measured at rooflevel across the canyon and the magnitude of the mass-exchange between the canyon and the flow above. Analysis of different scaling laws to link the mean exchange velocity to characteristics of both the canyon and the upstream flows, as well as to the canyon dimensions, have confirmed the

The authors should like to thank Mr Thibaut Piquet for technical support during the experimental program and the Ontario Graduate Scholarship Program for providing funding. The first author also acknowledges financial support from the French National Research Agency through research grant URBANTURB no. ANR-14-CE220012-01.

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