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Solar Energy 102 (2014) 212–222

CFD modeling of the impact of solar radiation in a tridimensionalurban canyon at different wind conditions

S. Bottillo ⇑, A. De Lieto Vollaro, G. Galli, A. Vallati

Sapienza University of Rome, DIAEE, Via Eudossiana 18, 00184 Rome, Italy

Received 13 November 2013; received in revised form 22 January 2014; accepted 24 January 2014Available online 12 February 2014

Communicated by: Associate Editor Matheos Santamouris

Abstract

In this study, the interaction between a tridimensional flow field and an urban street canyon, has been analyzed. Considering differentambient wind velocity intensities and directions, several numerical simulations have been performed. The aim of this study is to inves-tigate the effect of solar radiation, within a street canyon, for various characteristics of the ambient flow field. In the first part, the buoy-ancy effects have been excluded and the impact of tridimensional effects on the flow field has been evaluated. In the second part, thenatural convection effects on the flow structures and the heat processes have been analyzed. Through the evaluation of the Richardsonnumber an analysis of the convective heat transfer coefficient has been performed. The results show the importance of considering a tri-dimensional model and the impact of the longitudinal velocity component on the heat transfer processes along the street canyon.� 2014 Elsevier Ltd. All rights reserved.

Keywords: Urban canyon; CFD; Heat transfer coefficient; Solar radiation

1. Introduction

Thermal conditions in street canyons are importanttopics of urban microclimate, that influences the buildingsenergy demand and has a large impact on the thermal com-fort and health of the people (Moonen et al., 2012). Surfacetemperature distribution and air circulation play an impor-tant role on heat exchanges between the building and can-yon air, that in turn influence pedestrian comfort and theenergy demand of buildings. It is obvious that buildingsplaced in thermally critical positions, use more energy forair cooling in summer. The buildings energy demand repre-sents 70% of the residential energy in consumption, whichis 15% of the final energy consumption in EU (EuropeanCommission Energy, 2009), so that there is a great energy

http://dx.doi.org/10.1016/j.solener.2014.01.029

0038-092X/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +39 06 44 58 56 64; fax: +39 06 48 80 120.E-mail address: simone.bottillo@uniroma1.it (S. Bottillo).

saving potential by minimizing the energy for space coolingof the buildings. Furthermore, high external temperaturescause discomfort and inconvenience to the urban popula-tion. In the last decades, several studies have been per-formed on urban street canyons. Through numericalsimulations (Lei et al., 2012; Xie et al., 2007), wind tunnelexperiments (Uehara et al., 2000) and measurement cam-paigns (Offerle et al., 2007; Louka et al., 2002), the impactof surface heating on the flow field and on heat exchangehas been analyzed. Xie et al. (2007) pointed out that theits effect can be expressed through the Richardson dimen-sionless number and they studied the influence of groundheating on the thermo fluid-dynamic parameters within a2D canyon. Lei et al. (2012), studied the impact of ambientwind speed and ground heating on the flow field within acanyon, in particular they studied thermal effects and theformation of thermal-induced vortices. Allegrini et al.(2012a), analyzed the importance of buoyancy in

S. Bottillo et al. / Solar Energy 102 (2014) 212–222 213

two-dimensional models of urban canyons with differentaspect ratio, concluding that buoyancy has to be taken intoaccount for the calculation of the heat transfer coefficient.Using the adaptive wall function approach developed byDefraeye et al. (2011) and Allegrini et al. (2012b), they con-cluded that the AWF provides more accurate heat transferanalysis in urban CFD studies. Since it has been demon-strated that 3D effects have a remarkable impact on theflow field within a street canyon (Bottillo et al., 2013), inthis study, using a commercial CFD code (Ansys Fluent),several 3D numerical tests have been performed on an iso-lated street canyon, to evaluate how the flow field changeswithin the canyon at different ambient wind conditions andto highlight the importance of considering tridimensionaleffects. The dynamic field has been studied through twowind intensities and three wind directions, instead the ther-mal field is induced by setting up the solar radiation mod-ule, the ambient conditions and thermo physical propertiesvalues of the buildings and the ground. In the first part,excluding the natural convection effects, three simulationscharacterized by different ambient wind directions havebeen analyzed. Through the analysis of velocity vectors dis-tribution on several planes of interest within the canyon,the evaluation of tridimensional effects on the flow fieldhas been carried out. In the second part have been analyzedthe effects obtained by activating the natural convectionmodule, through a comparison of velocity vectors distribu-tion. In order to evaluate the importance the natural con-vection effects on the dynamic field and heat exchangeprocesses, two different ambient wind intensities and threewind directions have been analyzed. An analysis of the heattransfer coefficient correlated to the Richardson numberhas been performed, both as average values on the wind-ward and leeward fac�ade and as local values, consideringthree different vertical planes of interest within the canyon.

2. CFD numerical model

The simulations have been performed with the commer-cial CFD code Ansys Fluent 14.0, 3D double precision,pressure based version and the steady RANS equationshave been solved in combination with the standard k–emodel.

The governing equations can be expressed as follows.Momentum equation:

�u|@�uı

@xj¼ � 1

q@�p@xiþ l

q@2�uı

@xi@xj� @

@xju0ıu0|

� �þ fi ð1Þ

Continuity equation:

@�uı

@xi¼ 0 ð2Þ

Heat conservation equation:

�uı

@T@xiþ @

@xiKT

@T@xi

� �¼ 0 ð3Þ

where �uı is the average speed of air flow; u0ıu0| is the Reynolds

stress; q is the air density; l is the molecular viscosity; fi is thethermal-induced buoyant force; T is the potential tempera-ture; KT is the thermal turbulent diffusivity. The standardk–e model has been used to solve the turbulence problem.The turbulence kinetic energy, k, and its rate of dissipation,e, are obtained from the following transport equations:

@

@tðqkÞ þ @

@xiðqkuiÞ ¼

@

@xjlþ lt

rk

� �@k@xj

� �þ Gk þ Gb � qe

ð4Þand

@

@tðqeÞ þ @

@xiðqeuiÞ ¼

@

@xjlþ lt

re

� �@e@xj

� �þ C1e

ekðGk

þ C3eGbÞ � C2eqe2

kð5Þ

where Gk is the generation of turbulence kinetic energy dueto the mean velocity gradients; Gb is the generation of tur-bulence kinetic energy due to buoyancy; C1e, C2e constantsare reported in the standard k–e model of Ansys Fluent14.0, 2011; rk and re are the turbulent Prandtl numbersfor k and e, respectively.

The turbulent viscosity lt is computed as follows:

lt ¼ qClk2

eð6Þ

where Cl = 0.09.The thermal turbulent diffusivity is related to the turbu-

lent viscosity through the turbulent Prandtl number (PrT):

KT ¼lt=qPrT

ð7Þ

where PrT = 0.85.The degree to which e is affected by the buoyancy is

determined by the constant C3e. In Ansys Fluent, C3e isnot specified, but is instead calculated according to the fol-lowing relation:

C3e ¼ tanhvu

��� ��� ð8Þ

where m is the component of the flow velocity parallel tothe gravitational vector and u is the component of the flowvelocity perpendicular to the gravitational vector. In thisway, C3e will become 1 for buoyant shear layers for whichthe main flow direction is aligned with the direction ofgravity. For buoyant shear layers that are perpendicularto the gravitational vector, C3e will become zero (AnsysFluent version 14.0.0, 2011). To evaluate the impact ofthermal effects, the natural convection module has beenactivated by setting incompressible ideal gas model forair density. The radiation exchanges has been evaluatedsetting up the S2S radiation model, in which the energyexchange parameters are accounted for by a geometricfunction called a “view factor”, and activating the SolarRay Tracing in the Solar Load Model, provided in AnsysFluent version 14.0.0. The simulated urban canyon has the

214 S. Bottillo et al. / Solar Energy 102 (2014) 212–222

following characteristics: it is placed in Milan, Italy(longitude: 9.18, latitude: 45.47, UTC:+1), it has an aspectratio H/W = 1 and L/W = 5, the orientation is N–S, thebuildings width and height are 20 m, the street width is20 m and the street length is 100 m. A steady state simula-tion has been carried out with the ambient temperatureand solar radiation at 11.00 a.m. 26 June in Milan, as givenby the software meteorological file. A comparison betweenthe values of surfaces temperature in a steady simulationand in a transient one (Bottillo et al., 2013), allows us toperform simulations in stationary case. As to the inner lay-ers of the ground and of the building walls and the heatfluxes a transient solution is different from a steady one,but the external surface temperature calculated in the stea-dy simulation is representative of the value calculated inthe transient one. That is due to the external thermal resis-tance which is much smaller than the total thermal resis-tance, so that the difference between the outer surfacetemperature and the sol–air temperature is much smallerthan the total temperature difference across the wall. Basedon the best practice guidelines by Franke et al. (2007) andTominaga et al. (2008), the extension of computational do-main is: 23H � 15H � 6H. These dimensions values havebeen chosen to take into account of the blockage ratioand to ensure the flow re-development behind the buildingregion. The temperature of surfaces has been obtained asresult of the heat transfer calculations, setting up: the solarload module (longitude: 9.18, latitude: 45.47, UTC:+1),the temperature of undisturbed air (303 K), the tempera-ture of the internal air of the buildings (299 K). To simu-late the ground influence, the computational domain hasbeen extended 5 m below the ground level. The groundhas been simulated setting the following parameters: den-sity = 1000 kg/m3; specific heat = 1000 J/kg K; thermalconductivity = 2 W/mK; temperature at �5 m = 288 K;emissivity = 0.9; solar radiation absorptivity (direct visibleand infrared) = 0.8 (Bottillo et al., 2013). Furthermore, thematerials characteristics have been reported in Bottilloet al. (2013): i.e. the building walls have: density =1000 kg/m3; specific heat = 1000 J/kg K; thermal conduc-tivity = 0.15 W/mK; thickness = 0.30 m; internal airtemperature = 299 K; emissivity = 0.9; solar radiationabsorptivity (direct visible and near infrared) = 0.8. Toensure an high quality of the computational grid, it is fullystructured and the shape of the cells has been chosen hexa-hedral. According to the study of Ramponi and Blocken(2012), the velocity profile has been set giving a uniformvelocity magnitude at the velocity inlet boundary, the tur-bulence intensity at 10% and the roughness lengthz0 ¼ 0:05 m. As the flow approaches the built area thevelocity inlet profile is fully-developed before reachingthe buildings (Bottillo et al., 2013).

3. Results

In a previous work (Bottillo et al., 2013), our numericalmodel has been validated by comparison with experimental

and numerical results (Uehara et al., 2000 and Xie et al.,2007) for a fixed wind direction and canyon geometry. Inthis study, considering different ambient wind conditions,several simulations have been performed on an isolatedurban canyon, in order evaluate the effects on the flow fieldand heat exchange processes within the canyon. Since wehave chosen to study the importance of considering a 3Dmodel, we have performed some simulations with naturalconvection module deactivated, changing the ambient windspeed main direction, just to analyze the buildings impacton the flow field and how it changes along the street can-yon. Afterwards, the natural convection module has beenactivated, to evaluate how the flow field changes consider-ing thermal effects, at different ambient wind directions andmagnitude. In Table 1 is shown the list of the simulationsperformed and their differences of settings (ambient windvelocity intensities, activation of natural convection mod-ule and ambient wind direction). The windward fac�ade istotally heated by the direct solar radiation, while the lee-ward fac�ade is in shadow and it receives the diffuse solarradiation and exchanges longwave radiation with the othersurfaces; the wind direction has been expressed through theangle formed by an undisturbed wind velocity vector andthe North direction, assuming positive degrees clockwisefrom the North (20�N, 45�N and 70�N).

3.1. Three-dimensional effects

Three simulations have been performed (SIM.A, D andG), with natural convection deactivated, to evaluate the tri-dimensional effects on the flow field within a street canyon;these simulations have been characterized by three differentwind directions (20�N, 45�N and 70�N respectively) and awind velocity magnitude over the building u0 of 2 m/s. InFig. 1 are shown the XZ velocity vectors for SIM.A(u0 = 2 m/s, 20�N, natural convection off) on the three ver-tical planes considered within the canyon (North and Southplane, placed at 10 m from the relative opening and Centralplane in the middle of the canyon). Even if this simulation ischaracterized by a strong longitudinal velocity component(average Y velocity at North Plane = 1.48 m/s, at Centralplane = 1.22 m/s, at South Plane = 1.34 m/s), the flow fieldchanges significantly as the air passes through the canyon,from the North plane to the South one. Similar values ofaverage Y velocity component are found also for the otherwind directions. The Fig. 1 shows an aerodynamic vortexcoming from the roof in each plane of interest (the skim-ming flow). In the North and Central planes, it can benoticed a weak vortex in the left lower corner of the canyon,that tends to disappear as the air moves to the south open-ing. At the South plane, the main vortex from the roof occu-pies all the area between the buildings. As the wind speedbecomes transverse to the canyon direction (SIM.D andSIM.G) the skimming flow occupies a larger area betweenthe buildings in the North and Central plane; in the Southplane (Fig. 4(a1), (b1) and (c1)) it can be noticed that whenthe wind speed direction is 70�N the skimming flow

Table 1List and specifications of the CFD simulations performed.

Simulation Wind speed (u0)(m/s)

Nat. conv.mod.

Wind direction(�N)

SIM.A 2 – 20SIM.B

p

SIM.C 4p

SIM.D 2 – 45SIM.E

p

SIM.F 4p

SIM.G 2 – 70SIM.H

p

SIM.I 4p

SIM.L –

Fig. 1. SIM.A (u0 = 2 m/s, 20�N, natural convection off), XZ velocityvectors on the North (a), Central (b) and South plane (c).

Fig. 2. SIM.D (u0 = 2 m/s, 45�N, natural convection off), XY velocityvectors on a plane placed at z = 10 m.

S. Bottillo et al. / Solar Energy 102 (2014) 212–222 215

disappears and the flow field is characterized by an upwardmotion. The analysis shows that, the composition of thetransversal and longitudinal velocity components,

determines the formation of a spiral vortex, that grows upas the air passes through the canyon and as the wind direc-tion becomes transverse. In Fig. 2 is shown the flow field ofSIM.D (u0 = 2 m/s, 45�N, natural convection off) on an XYplane placed at z = 10 m. As it can been seen, the flow fieldis characterized by an aerodynamic vortex, due to geomet-rical discontinuities. It occupies a large area within the can-yon, on the easterly side, from the northerly opening to 2Hdistance from the opening itself. When the wind direction is20�N (SIM.A) this area is smaller, instead when the winddirection is 70�N (SIM.G), it is wider, but the flow field isbasically the same. In Fig. 3 the velocity vectors compo-nents on three YZ vertical planes within the canyon forSIM.G (u0 = 2 m/s, 70�N, natural convection off), parallelsto the building fac�ades, are shown. These planes are placedat 0.40 m from the fac�ades and in the middle of the canyon.As it can be seen, the flow pattern changes significantly fromthe windward fac�ade to the leeward one and from the northopening to the south one. In the YZ plane near the wind-ward fac�ade, the velocity vectors have a downward Z com-ponent from the north opening to the Central plane. Insteadfrom the Central plane to the South one, the velocity isweak and the air flows mainly along the ground. In the Cen-tral YZ plane it can be noticed a waveform flow, from thenorth opening to the south one. Instead in the YZ plane,near the leeward fac�ade, the velocity vectors are character-ized basically by an upward Z component. Furthermore,there is an area near the north opening, affected by anaerodynamic vortex with vertical axis, in which the vectorshave an Y component opposite to the main wind direction.

Fig. 3. SIM.G (u0 = 2 m/s, 70�N, natural convection off), YZ velocity vectors on: a plane placed at 0.40 m from the WW fac�ade (a), a plane in the middleof the canyon (b) and a plane place at 0.40 m from the LW fac�ade (c).

Fig. 4. Effects of natural convection on the flow field, when u0 = 2 m/s, on the South plane between SIM.A and SIM.B (20�N), (a1) and (a2), SIM.D andSIM.E (45�N) (b1) and (b2), SIM.G and SIM.H (70�N) (c1) and (c2).

216 S. Bottillo et al. / Solar Energy 102 (2014) 212–222

Fig. 5. XZ velocity vectors on South plane, when u0 = 4 m/s, for SIM.C(a) (20�N, no natural convection), SIM.F (b) (45�N, no natural convec-tion) and SIM.I (c) and SIM.L (d) (70�N, with natural convection moduleon and off, respectively).

S. Bottillo et al. / Solar Energy 102 (2014) 212–222 217

As the wind direction becomes longitudinal to the canyon,the flow field is similar, but the above mentioned effectsare less marked. Another simulation, characterized by winddirection of 80�N has been performed; it has been noticedthat even if the flow is strongly transversal to the canyondirection, the longitudinal effects are remarkable and theresults are very similar to the 70�N simulation.

3.2. Natural convection effects on flow fields

To evaluate the impact of thermal effects on the flowfield within the canyon, a comparison between simulations,respectively with natural convection module activated anddeactivated, has been carried out. The simulations resultsshow that the thermal effects on the flow field becomestronger as the air passes through the canyon from thenorth opening to the south one, so it has been chosen tostudy the natural convection effects on the south XZ plane.In Fig. 4 are shown a comparison of XZ velocity vectorsbetween SIM.A and SIM.B, SIM.D and SIM.E, SIM.Gand SIM.H, characterized by an ambient velocity intensityu0 = 2 m/s. When the wind direction is 20�N (SIM.A) andthe natural convection module is deactivated, the flow fieldis characterized only by the aerodynamic vortex, instead,when the natural convection is activated (SIM.B), a ther-mal induced vortex can be observed, near the sun exposedfac�ade (Fig. 4(a1) and (a2)). The same results can beobserved (Fig. 4(b1) and (b2)) when the ambient winddirection is 45�N (SIM.D, E), even if the thermal inducedvortex occupies a smaller area than the one seen in SIM.B.When the wind direction is 70�N and the natural convec-tion is deactivated (SIM.G), the XZ velocity vectors onthe South plane, are all upward; this motion is due to tridi-mensional effects, and it is stronger near the fac�ade in sha-dow (Fig. 4(c1)). When natural convection is activated(SIM.H), the upward motion is on both fac�ades and itdetermines two weak vortices, characterized by differentrotation direction (Fig. 4(c2)). Xie et al. (2007) andAllegrini et al. (2012a) performed 2D simulations of urbancanyon characterized by an aspect ratio H/W = 1. Theyfound that, when the surfaces are heated, the single pri-mary vortex (in isothermal conditions) was broken downinto two counter-rotating vortices whose magnitude wasdetermined by the surface-heating configurations. Wefound that the formation of thermal induced vortex,depends by the ambient wind direction and the flow fieldwithin the canyon of SIM.B and SIM.D, can be relatedto the ones obtained in 2D simulations only in the regionbetween the Central plane and the south canyon opening.In Fig. 5 are shown the XZ velocity vectors on the Southplane for SIM.C, F, I and L characterized by an ambientvelocity intensity u0 = 4 m/s. As it can be seen, the naturalconvection effects are weak for these simulations. When thewind direction is 20�N (SIM.C), a small thermal inducedvortex can be observed near the lower corner of the sunexposed fac�ade (Fig. 5(a)). This vortex is almost missingwhen the wind direction is 45�N (SIM.F), as it can be seen

in Fig. 5(b). Observing the velocity vectors of SIM.I(u0 = 4 m/s, 70�N, natural convection on, Fig. 5(c)), itcan be noticed an upward motion near the sun exposed fac�-ade weaker than the one of SIM.H (u0 = 2 m/s, 70�N, nat-ural convection on, Fig. 4(c2)). To evaluate better the

218 S. Bottillo et al. / Solar Energy 102 (2014) 212–222

buoyancy force effects in SIM.I, a comparison with SIM.L(u0 = 4 m/s, 70�N, natural convection off) has been per-formed; as it can be seen in Fig. 5(c) and (d), the upwardmotion near the fac�ades on XZ south plane is weaker whennatural convection module is deactivated.

3.3. Natural convection effects on heat exchanges

To quantify the effects of natural convection on the flowfield within an urban canyon, the Richardson number hasbeen evaluated for each simulation studied, with naturalconvection module activated. The Richardson number isdefined by:

Ri ¼ g � ðT w � T aÞ � HT a � u2

ð9Þ

where Tw is the average temperature of the considered fac�-ade, Ta is the ambient air temperature, H is the maindimension of the street canyon (H = 20 m) and u is theambient wind speed (u0). For very low Richardson num-bers (forced convection) the buoyancy forces can be ne-glected. For Ri around 1 (mixed convection) themechanical and the buoyancy forces are both important.For very high Richardson numbers (natural convection)the mechanical forces can be neglected (Allegrini et al.,2012b). The resulting Richardson numbers on the wind-ward fac�ade (WW) and on the leeward one (LW), for eachsimulations with natural convection module activated, arereported in Table 2.

As it can be seen in Table 2 the highest values ofRichardson number are reached when the ambient windspeed (u0) is 2 m/s (SIM.B, E and H), near the windwardfac�ade, which is exposed to solar radiation. These valuesare three times higher than the ones reached near the lee-ward fac�ade, which is in shadow. When the ambient windspeed (u0) is 4 m/s (SIM.C, F and I) the Richardson num-ber is always lower than 1, which means that the buoyancyforce has a weak effect on the flow field (especially near theleeward fac�ade). Table 3 shows the average values ofconvective heat transfer coefficient (hc), on the windwardfac�ade (WW) and on the leeward one (LW); as it can beseen the heat transfer coefficient increases by approxi-mately 50% when the natural convection module isactivated and the ambient wind speed (u0) is 2 m/s: SIM.A,B, D, E, G, H. The analysis of Tables 2 and 3, shows thatRi is not fully-representative of hc; for example, when the

Table 2Richardson numbers, calculated with the average values of fac�adestemperatures and the ambient velocity values of u0 = 2 m/s (SIM.A, E, H)and 4 m/s (SIM.C, F, I).

Ri SIM.B SIM.E SIM.H SIM.C SIM.F SIM.I

u0 2 m/s 2 m/s 2 m/s 4 m/s 4 m/s 4 m/sDirection 20�N 45�N 70�N 20�N 45�N 70�N

WW 3.3 2.9 3.1 0.7 0.6 0.6LW 1.1 1.0 1.1 0.2 0.2 0.2

ambient wind speed (u0) is 2 m/s, the average Ri on theLW is around 1 and the increase of hc is around 50%, thatis the same result on WW where Ri is three times higher.When the ambient wind speed (u0) is 4 m/s and the direc-tion is 70�N (SIM.I and SIM.L), the increase of hc, dueto natural convection effects, is not negligible, even if theaverage Richardson number is low. The comparisonbetween SIM.I and SIM.L shows that the natural convec-tion effect, on heat exchanges, determines an increase of theheat transfer coefficient ranging from 10% on WW fac�adeto 14% on the LW one.

To evaluate how the buoyancy effect changes the flowfield within our street canyon, it has been chosen to calcu-late the Richardson number for each of the three XZ planesof interest (North, Central and South plane), according tothe recommendation of Allegrini et al. (2012b). In Tables 4and 5 are shown, for each simulation, the average values oftemperature and heat transfer coefficient on vertical lines,built as intersections of the planes of interest and the build-ing fac�ades. Furthermore, the table shows the average val-ues of velocity magnitude and turbulent kinetic energycalculated at 0.40 m from the above-mentioned lines. Atlast the Richardson local values have been calculated, usingthe average values of wall temperature and velocity magni-tude on each vertical line. As it can be seen, on the wind-ward fac�ade (Table 4), the local Richardson values, atthe North plane, are similar to the average Richardson val-ues, both when the ambient wind speed (u0) is 2 m/s, andwhen it is 4 m/s. Instead, as the air passes through the can-yon, the local Richardson number increases; that meansthat the buoyancy force becomes stronger. The trend oflocal Richardson values is due to the increase of wall tem-perature and a decrease of velocity, as the air moves fromthe North plane to the South one. The highest local Rich-ardson value (local Ri = 16.7), on the windward fac�ade, isreached in SIM.H (u0 = 2 m/s, 70�N, natural convectionon) at the South plane, where the comparison betweenthe velocity vectors with SIM.G (u0 = 2 m/s, 70�N, naturalconvection off) has shown a strong rising air motion, whennatural convection model is activated (Fig. 4(c1) and (c2)).On the leeward fac�ade (Table 5), at the North plane, thelocal Richardson numbers are strongly higher than theaverage values; that is due to the aerodynamic vortex atthe northern opening, that determines a region of weakvelocity magnitude. At the Central and South plane thelocal Richardson numbers are lower than the ones at Northplane, but they are greater than 1 and greater than the aver-age Richardson values; which means that the buoyancyforce affects the flow field also near the fac�ade in shadow.The results show that natural convection strongly affectsthe flow field and the values of the heat transfer coefficient.The analysis of heat transfer coefficient on each planes ofinterest (Tables 4 and 5) shows that at the North plane,hc is always higher than the average value for each simula-tions. Instead, the highest difference between hc values,when natural convection module is respectively activatedand excluded, is reached on Central and South planes,

Table 3Average values of heat transfer coefficient on both fac�ades, for each simulation performed.

hc (W/m2 K) SIM.A SIM.B SIM.C SIM.D SIM.E SIM.F SIM.G SIM.H SIM.I SIM.L

Nat. convection –p p

–p p

–p p

–u0 2 m/s 4 m/s 2 m/s 4 m/s 2 m/s 4 m/sDirection 20�N 20�N 45�N 45�N 70�N 70�N

WW 7.0 10.5 13.7 8.2 12.1 16.9 7.2 11.1 14.4 13.1LW 6.4 9.2 13.0 7.1 10.5 15.7 6.4 9.9 13.5 11.7

Table 4Thermo fluid-dynamic parameters of the windward fac�ade on each plane of interest.

WINDWARD FACADE (natural convection on)

SIM.B SIM.E SIM.H SIM.C SIM.F SIM.Iu0 = 2 m/s u0 = 2 m/s u0 = 2 m/s u0 = 4 m/s u0 = 4 m/s u0 = 4 m/s20�N 45�N 70�N 20�N 45�N 70�N

T wall (K) North 322.8 319.1 320.6 321.7 315.1 316.1Central 325.8 323.3 324.1 317.8 318.7 320.7South 327.1 325.7 328.2 323.0 321.3 324.6

Ri local North 3.3 2.1 3.8 0.9 0.4 0.9Central 4.3 3.7 5.9 0.7 0.8 2.5South 5.5 5.4 16.7 1.2 1.3 20.6

k (m2/s2) North 0.41 0.86 0.67 0.79 1.73 1.35Central 0.29 0.45 0.36 0.39 0.92 0.55South 0.31 0.32 0.29 0.40 0.52 0.47

u (m/s) North 1.97 2.25 1.74 3.76 4.27 3.07Central 1.86 1.89 1.52 3.61 3.64 2.16South 1.69 1.66 0.99 3.25 3.07 0.83

hc (W/m2K) North 11.96 16.51 14.94 17.16 23.48 21.20Central 9.92 11.95 11.28 12.79 17.36 13.84South 9.76 10.38 9.19 12.64 14.06 11.36

Windward fac�ade (natural convection off)

SIM.A SIM.D SIM.G – – SIM.Lu0 = 2 m/s u0 = 2 m/s u0 = 2 m/s – – u0 = 4 m/s20�N 45�N 70�N – – 70�N

T wall (K) North 326.5 324.9 324.4 – – 316.1Central 331.5 328.1 330.6 – – 321.4South 333.6 331.7 336.8 – – 326.8

k (m2/s2) North 0.17 0.28 0.29 – – 1.1Central 0.07 0.19 0.11 – – 0.4South 0.07 0.10 0.08 – – 0.3

u (m/s) North 1.86 1.96 1.50 – – 3.0Central 1.80 1.69 0.99 – – 1.9South 1.63 1.30 0.31 – – 0.7

hc (W/m2K) North 8.75 10.57 10.72 – – 19.8Central 6.57 8.84 6.82 – – 12.2South 6.34 6.88 5.28 – – 9.5

S. Bottillo et al. / Solar Energy 102 (2014) 212–222 219

when the ambient wind speed is 2 m/s and the direction is70�N. These variations of the heat transfer coefficientdetermine a decrease of 3.8–8.6 K on the WW fac�ade tem-perature when natural convection module is activated; theLW fac�ade temperature, instead, is 2.0–5.1 K lower whennatural convection is on. The temperature of the LW fac�-ade, in shadow, is several degrees higher than the air tem-perature, for all the simulations performed; that is due to

the longwave radiation from the opposite fac�ade (exposedto sun radiation) and to the shortwave diffuse radiation.Since the air temperature near the fac�ade does not changesignificantly among the simulations, the wall temperaturedecrease determines a lower thermal load of buildings.Saneinejad et al. (2011) conducted a 2D study on the heattransfer coefficient on the vertical walls of a street canyon,and they reported the hc values in relation to the ambient

Table 5Thermo fluid-dynamic parameters of the leeward fac�ade on each plane of interest.

LEEWARD FACADE (natural convection on)

SIM.B SIM.E SIM.H SIM.C SIM.F SIM.Iu0 = 2 m/s u0 = 2 m/s u0 = 2 m/s u0 = 4 m/s u0 = 4 m/s u0 = 4 m/s20�N 45�N 70�N 20�N 45�N 70�N

T wall (K) North 309.1 308.5 309.0 306.8 306.6 307.1Central 310.8 309.6 310.1 308.4 307.2 308.1South 311.1 310.6 311.7 309.1 308.2 309.6

Ri local North 54.8 12.6 11.0 4.9 1.6 1.6Central 4.8 3.6 2.3 2.3 0.9 0.6South 2.3 2.2 3.1 0.9 0.5 1.0

k (m2/s2) North 0.39 0.38 0.35 1.00 0.91 0.85Central 0.22 0.35 0.30 0.46 0.82 0.51South 0.21 0.25 0.18 0.35 0.54 0.29

u (m/s) North 0.26 0.51 0.57 0.68 1.17 1.24Central 0.98 1.05 1.36 1.16 1.62 2.19South 1.45 1.42 1.29 2.03 2.58 2.02

hc (W/m2K) North 10.68 10.73 10.56 16.07 15.97 15.64Central 8.20 9.99 9.86 11.39 14.94 13.19South 8.19 8.82 7.60 10.41 13.18 9.96

LEEWARD FACADE (natural convection off)

SIM.A SIM.D SIM.G – – SIM.Lu0 = 2 m/s u0 = 2 m/s u0 = 2 m/s – – u0 = 4 m/s20�N 45�N 70�N – – 70�N

T wall (K) North 311.1 311.2 311.5 – – 307.3Central 314.4 313.3 313.8 – – 308.5South 315.8 315.0 316.8 – – 310.7

k (m2/s2) North 0.23 0.18 0.17 – – 0.7Central 0.10 0.13 0.09 – – 0.4South 0.07 0.07 0.05 – – 0.2

u (m/s) North 0.36 0.60 0.64 – – 1.3Central 0.49 0.72 1.01 – – 2.0South 0.87 1.08 0.90 – – 1.7

hc (W/m2K) North 8.31 7.85 7.68 – – 14.1Central 5.69 6.50 6.24 – – 11.3South 5.01 5.62 4.73 – – 8.4

220 S. Bottillo et al. / Solar Energy 102 (2014) 212–222

wind speed and to the local wind speed, taken as anaverage value on a vertical line in the middle of the canyon.They found that when the ambient wind speed is 2 m/s, hc

is 3.08 W/m2 K and 2.22 W/m2 K, respectively on thewindward fac�ade and the leeward one. Instead, whenthe ambient wind speed is 3.5 m/s, these values are4.8 W/m2 K and 3.62 W/m2 K. The simulations performedin this paper that approximate better the two-dimensional-ity conditions, are SIM.G (u0 = 2 m/s, 70�N, natural con-vection off) and SIM.L (u0 = 4 m/s, 70�N, naturalconvection off). A comparison of heat transfer coefficient,shows that our values are more than two times higher thanthe ones of Saneinejad et al. (2011). The main reason of thisdifference is that, in our simulations, even if the ambientwind speed has a strong component transversal to the can-yon direction, the tridimensional effects cannot beneglected. As it can be seen in Tables 4 and 5, the meanvelocity values for wind direction 70�N (SIM.G, L), both

on WW and LW fac�ades, are higher than the local velocityvalues reported by Saneinejad et al. (2011), in almost theentire length of the canyon. Indeed, the average velocityvalue on a YZ plane in the middle of the canyon is greaterthan 1.5 m/s for both simulations. Allegrini et al. (2012a)analyzed the convective heat transfer coefficient in severalurban configurations, through CFD simulations. As wehave done, they studied the importance of buoyancy, butthey performed 2D simulations on urban canyons. Theyfound that natural convection effects have a relevant influ-ence only when the ambient wind speed is below 1 m/s. Ourhc values are more than two times higher and they are com-parable to ASHRAE values (ASHRAE, 2009), probablybecause of the higher values of the velocity magnitude inthe canyon in our simulations induced by the 3D character-istics of the flow field. Our results show that the heat trans-fer coefficient (hc) seems to have strong dependence fromthe value of velocity (u) and turbulent kinetic energy (k)

S. Bottillo et al. / Solar Energy 102 (2014) 212–222 221

in the proximity of the fac�ade. These values, in turn, arestrongly related to the effects of buoyancy forces, in partic-ular the turbulent kinetic energy. The effects of wind direc-tion on the flow fields and thermal processes are rathercomplex. The calculated values of velocity magnitudealong the building fac�ades are different from the longitudi-nal component of the external wind speed (u0): in particularat the North plane, near the windward fac�ade, the velocitymagnitude (u) is similar or even higher than the value ofundisturbed velocity (u0), while it is often lower near theleeward fac�ade. The average hc values, when the winddirection is 20�N and 70�N, are very similar, both onWW and LW fac�ade. That is due to a balance between u

and k: for example, considering u0 = 2 m/s, when the winddirection is 20�N, the velocity magnitude along the WW,is higher than 70�N, while the turbulent kinetic energy islower. Viceversa, along the LW, the velocity magnitudeis higher when the wind direction is 70�N, while the turbu-lent kinetic energy value is lower. When the wind directionis 45�N, the average hc value is higher than at 20�N and at70�N, because it is characterized by the highest combina-tion of velocity magnitude and turbulent kinetic energyalong the building fac�ades. Considering the effects of natu-ral convection, the average hc value when the wind direc-tion is 70�N is slightly higher than 20�N because thebuoyancy effects are more relevant. In order to evaluatethe heat transfer coefficient, the relations reported byHagashima and Tanimoto (2003), derived from Defraeyeet al. (2010) in which hc is expressed as function of u andk separately, seems useful. Our results show that the localRichardson number has a remarkable impact on the shapeof flow fields, as shown in Fig. 4, in particular on the valuesof upward velocity (Bottillo et al., 2013).

4. Conclusions

In this study several numerical simulations have beenperformed to investigate the physical phenomena thatcharacterize a street canyon with aspect ratio H/W = 1,N–S oriented, during a summer day. A fully 3D modelhas been simulated, considering different ambient windspeed conditions. The results show the importance of con-sidering the tridimensional effects on the flow field withinthe urban canyon; it has been shown, indeed, that, for eachambient wind condition, the vortex structure changessignificantly along the entire length of the canyon.Furthermore, introducing the natural convection effects,the flow field becomes more complex, and in several sectionof interest, the flow pattern is double-vortex in structure. Ithas been noticed that the average Richardson number isnot fully-representative of the effects of natural convection,while it is necessary to take into account the local values oftemperature and velocity (Allegrini et al., 2012b). TheRichardson number has been calculated at local scale inorder to evaluate the combination of tridimensional effectsand buoyancy forces. Our results show that for an externalvelocity magnitude of 2 m/s, the buoyancy effects are

important, while for 4 m/s the natural convection effect isless significant. The tridimensional structure of the flowaffects the values of the heat transfer coefficient; even ifthe ambient wind direction is almost transversal to the can-yon, there is always a remarkable longitudinal velocitycomponent, that in turn affects the heat transfer coefficientvalues. The average hc value depends strongly on the valueof ambient velocity u0 and less on the wind direction, whilethe hc values along the canyon can have strong variations.Furthermore, we have shown how, the buoyancy forceinfluences the heat exchange, causing a decrease of fac�adestemperature, that in turn reduce the cooling load of build-ings. It has been shown the importance of considering thesolar heating and the radiative exchanges, that producean increase of temperature also on the surfaces in shadow.Therefore, it has been pointed out that buoyancy affects theentire area within the canyon and not only the one in prox-imity of the surfaces exposed to the sun radiation. The con-vective heat transfer coefficient seems to be related to thelocal values of velocity magnitude and to the turbulentkinetic energy that increases several times under tridimen-sional and natural convection conditions. The values ofhc, reported in this paper, are higher than the ones calcu-lated in 2D models (Saneinejad et al., 2011 and Allegriniet al., 2012a) and they approximates better the traditionalvalues used to calculate the thermal loads of buildings(ASHRAE, 2009). Further analysis for various parameters,such as wind velocity and direction, canyon geometry, theflow field interaction with an urban boundary layer, and acomparison between results of the numerical model andexperimental measurements on hc,, will be object of futurework.

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