geometric dependence of the scalar transfer efﬁciency

Boundary-Layer Meteorol (2012) 143:357–377DOI 10.1007/s10546-012-9698-5

ARTICLE

Geometric Dependence of the Scalar Transfer Efficiencyover Rough Surfaces

Naoki Ikegaya · Aya Hagishima · Jun Tanimoto ·Yudai Tanaka · Ken-ichi Narita · Sheikh Ahmad Zaki

Received: 31 May 2011 / Accepted: 11 January 2012 / Published online: 2 February 2012© Springer Science+Business Media B.V. 2012

Abstract We performed a series of wind-tunnel experiments under neutral conditions inorder to create a comprehensive database of scalar transfer coefficients for street surfacesusing regular block arrays representing an urban environment. The objective is to clarifythe geometric dependence of scalar transfer phenomena on rough surfaces. In addition, thedatasets we have obtained are necessary to improve the modelling of scalar transfer usedfor computational simulations of urban environments; further, we can validate the resultsobtained by numerical simulations. We estimated the scalar transfer coefficients using thesalinity method. The various configurations of the block arrays were designed to be similarto those used in a previous experiment to determine the total drag force acting on arrays. Ourresults are summarized as follows: first, the results for cubical arrays showed that the transfercoefficients for staggered and square layouts varied with the roughness packing density. Theresults for the staggered layout showed the possibility that the mixing effect of air can beenhanced for the mid-range values of the packing density. Secondly, the transfer coefficientsfor arrays with blocks of non-uniform heights were smaller than those for arrays with blocksof uniform height under conditions of low packing density; however, as the packing densityincreased, the opposite tendency was observed. Thirdly, the randomness of rotation anglesof the blocks in the array led to increasing values of the transfer coefficients under sparsepacking density conditions when compared with those for cubical arrays.

N. Ikegaya (B) · A. Hagishima · J. Tanimoto · Y. TanakaInterdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasuga-koen,Kasuga-shi, Fukuoka 816-8580, Japane-mail: [email protected]

K. NaritaDepartment of Engineering, Nippon Institute of Technology, 4-1 Gakuen-dai, Miyashiro, Saitama345-8501, Japan

S. A. ZakiRazak School of Engineering and Advanced Technology, University of Technology Malaysia,International Campus, Jalan Semarak, 54100 Kuala Lumpur, Malaysia

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358 N. Ikegaya et al.

Keywords Salinity methodology · Scalar transfer coefficient · Urban building arrays ·Wind-tunnel experiment

1 Introduction

Momentum, heat and scalar transfer processes in the atmosphere above urban rough surfacesare closely related to the urban atmospheric environment near the ground. It is well knownthat the scalar dispersion over urban areas is strongly affected by two different processes: thefirst involves the weakened horizontal advection effects induced by the reduced mean flow;the mean flow is reduced due to drag forces on the roughness elements. The other processis the vertical exchange of air caused by strong vertical flows along roughness elements; thevertical flows enhance the vertical mixing of the scalar. Hence, incorporative measurementsof both momentum and scalar transfer processes are important to gain a better understandingof the scalar dispersion in urban areas.

With regard to momentum transport phenomena in urban areas, several studies over thepast decades have used wind-tunnel experiments on urban-like block arrays and field mea-surements for various urban geometries. In these studies, aerodynamic parameters such asthe roughness length z0, the zero-plane displacement d and the drag coefficient Cd have beenexperimentally determined in order to describe the spatio-temporal-averaged features of theurban wind field. These experimental approaches have revealed two important features withrespect to Cd and z0 for three-dimensional (3-D) arrays. First, the values of Cd and z0 showpeaks against varying roughness packing density, λp (Counihan 1971; Wooding et al. 1973;Raupach et al. 1980; Farell and Iyenger 1999; Iyenger and Farell 2011). Second, if the arrayshave height variability, the values of Cd and z0 become larger than those for arrays withblocks of uniform height (Cheng and Castro 2002) and the peak shifts to larger values ofλp (Hagishima et al. 2009; Zaki et al. 2011) due to the large deficit of momentum inducedby tall blocks (Xie et al. 2008). Recently, Zaki et al. (2011) have extended a previous study(Hagishima et al. 2009) by considering the effects of both horizontal and vertical randomnessof array geometry.

In addition to these investigations on aerodynamic parameters, the estimation of heat ormass transfer coefficients over urban-like arrays have been performed over the last decade.For example, Barlow and Belcher (2002) adopted the naphthalene sublimation method for themeasurement of mass transfer coefficients of the street surface of a two-dimensional (2-D)canyon. Further, the study discusses the effects of the street aspect ratio, H/W , (here, Hand W denote the block height and width of the street, respectively) on the transfer coeffi-cients. Barlow et al. (2004) also investigated the transfer coefficients of each facet of severaltypes of 2-D canyons using the same method, and discussed the effects of source location,source size and the aspect ratio H/W on the transfer coefficients. Pascheke et al. (2008)performed an experiment using this technique to estimate the transfer coefficients of twotypes of 3-D arrays—an array with cubical blocks and an array with blocks of non-uniformheights for λp = 25%. The geometry of the arrays is identical to that of the arrays adoptedin the experimental work on airflow by Cheng and Castro (2002). Therefore, in the study ofPascheke et al. (2008), the effects of horizontal advection and vertical mixing on the transferefficiency could be separately evaluated. Further, the study pointed out that the height varia-tions in the blocks cause larger turbulence exchange of the scalar but reduce scalar transportby advection. Narita (2007) determined the transfer coefficients for surfaces of both 2-D and3-D canopies based on the water evaporation method. Hagishima et al. (2005) compared thetransfer coefficients of heat and mass for surfaces of urban roughness elements obtained by

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Geometric Dependence of the Scalar Transfer Efficiency 359

previous wind-tunnel experiments and outdoor field observations of building surfaces. Therelations between scalar transfer coefficients and geometrical parameters have been inves-tigated for several arrays based on these previous studies; however, a comprehensive andsystematic database on the transfer coefficients (particularly for 3-D arrays) is an importantrequirement.

The experimental data on scalar transfer processes are significant for the validation andimprovement of not only urban canopy models but also computational fluid dynamical (CFD)approaches used for resolving explicitly fluid flow for urban buildings. There are several CFDstudies dealing with the dispersion of scalars constantly emitted from scalar sources locatedwithin urban canopies (Li et al. 2008, 2010; Michioka et al. 2010; Bransford et al. 2011). Incontrast to studies that consider constant fluxes on the scalar surface, the Dirichlet boundarycondition for scalars is debatable in urban canopy simulations. Studies applying this type ofcondition can be classified into two groups—one assumes a wall function between a scalarsurface and the first layer and the other resolves the thin sub-layer adjacent to the surface.For example, Cai et al. (2008) performed large-eddy simulations (LES) on the detailed air-flow and distributions of scalar concentration over a 2-D roughness, thereby reproducing theexperiment of Barlow et al. (2004), and compared the results of the two experiments. Theyreported that similar results for transfer coefficients with respect to the W/H ratio could beobtained based on a wall function assuming a logarithmic profile above a surface with a scalarsource. Recently, Cheng and Liu (2011) performed a LES that reproduced the experiments ofBarlow et al. (2004) in order to examine scalar dispersion under the condition of skimmingflow. They calculated the surface scalar flux by means of molecular diffusion between thesurface and the first scalar layer. However, the difference in the transfer coefficients obtainedfrom their results and those of Barlow’s experiment is approximately 20%. Therefore, theyconcluded that the use of a wall function can possibly estimate surface fluxes in a more accu-rate manner. This increase in accuracy by the use of a wall function is supported by the resultsof Cai et al. (2008). In contrast, the results of Boppana et al. (2010) were in good agreementwith those of Pascheke et al. (2008) in terms of scalar fluxes obtained by LES; further, thestudy emphasized the necessity of a fine grid adjacent to a scalar source in order to resolvethe thin sub-layer dominated by molecular diffusion. Despite the significant advancementsprovided by these studies, the question of how a surface scalar boundary condition shouldbe considered remains ambiguous because of the limited experimental data that are availablefor use in order to validate and improve scalar transfer modelling.

In order to better understand the scalar transfer process above an urban surface, the fol-lowing aspects need to be investigated. Firstly, the currently available experimental dataon scalar transfer coefficients are insufficient for understanding scalar transfer phenomena.A variety of roughness configurations are required to be examined to improve scalar transfermodelling; these configurations can elucidate the geometric dependence of scalar transfer.Secondly, experimental investigations on both scalar transfer processes and the momentumdeficit over an array are essential in order to analyze the structure of the geometric dependenceof the scalar transfer process.

Therefore, in our study, we performed a series of wind-tunnel experiments under neu-tral conditions in order to create a comprehensive database of scalar transfer coefficientsfor various types of regular block arrays. The geometry of the arrays used for measurementwas designed to capture the effects of the layout, the aspect ratio of the blocks and heightvariability and rotation angle of the blocks under different conditions of λp. In Sect. 2, wedescribe the details of the salinity methodology used in order to quantify the scalar transferfrom the floor of a block array. Subsequently, in Sect. 3, we present the results for severalarrays under different conditions of λp. The configuration of arrays, fetches and scalar source

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sizes used for our measurements were designed to be similar to those used in the studies ofHagishima et al. (2009) and Zaki et al. (2011); these studies estimated the values of Cd, z0

and d . Thus, we combine our present data on the transfer coefficients with data from theirstudies to explain the dependency of the transfer efficiency on the geometric configurationof the arrays.

2 Experimental Details

2.1 Measurement Principle of the Salinity Method

We estimated the scalar transfer coefficient CE using the salinity method. In this method, saltwater is the scalar source used for measurement, and the amount of evaporation from the saltwater surface is calculated based on the measured increase in salinity over a fixed period oftime under a constant flow condition. The relation between salinity and water mass can beexpressed by

WWater =(

1 − c

c

)WSod, (1)

where c denotes the salinity of the salt water, and WSod and WWater represent the massesof sodium chloride and water, respectively. In addition, WSod and WWater are defined by thevolume V and density of water ρwater as follows:

WWater = ρwaterV, (2)

WSod =(

c

1 − c

)ρwaterV . (3)

If the salinity of the salt water changes during a period Δt from time tb to ta, the amount ofevaporation per unit surface area per unit of time (surface scalar flux) E , can be expressedby

E = ρwaterV

A�t

(1 −

(1 − ca

ca

) (cb

1 − cb

)). (4)

Here, A denotes the area of the salt water surface and subscripts a and b denote the valuesof time, ta and tb, i.e. ca and cb denote the salinity at these time instants. In the followingsections, we discuss the geometric dependence of the scalar transfer coefficient CE, whichis defined as follows:

CE(z) = E

ρairUref (z) (qsurf − qref ), (5)

where qsurf and qref refer to the specific humidity at the salt water surface and of air, respec-tively. The term ρair denotes the density of air and Uref (z) denotes the flow speed at a referenceheight z. The scalar transfer coefficient CE can be written,

CE(z) = k

ρairUref (z), (6)

where k denotes the mass transfer coefficient (kg m−2 s−1).

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Fig. 1 Schematic figures ofarray layouts; a square and bstaggered. Cubical blocks arearranged for SQ1 and ST1.Rectangular blocks of1.5L × L × L are arranged forSQ1.5 and ST1.5

(a) (b)

Airflow

(a) (c)

(d) (e)

Airflow

L L LH=3L H=2L L L L

(b)

Fig. 2 Schematic figures for non-uniform arrays a SQ1.5-sq, b SQ1.5-st, c SQ1.5-st*, d ST1.5-sq, e ST1.5-st.The colours of the blocks (white, charcoal and black) refer to the block heights (L , 2L and 3L , respectively)

2.2 Configuration of the Arrays

The rough surfaces used for the measurements were regular arrays comprising rectangularblocks, where all blocks had a uniform base of dimensions 25 mm ×25 mm with L = 25 mmbeing used as the basic length scale. Moreover, we adopted several types of configurationsused for the measurement of the drag coefficient Cd (Hagishima et al. 2009; Zaki et al.2011). The configurations of the arrays are categorized into three types described below.First, we selected two types of array with uniform block heights—those of heights L and1.5L (referred to as a uniform array in the study). The plan layouts comprising lattice-typesquares and staggered patterns (shown in Fig. 1) were used for both arrays with heights Land 1.5L; these arrays are denoted as SQ1, SQ1.5, ST1 and ST1.5, respectively. Secondly,we used five types of arrays with non-uniform block heights (referred to as a non-uniformarray in the study). The schematic plan views of the arrays are shown in Fig. 2. Four arraysconsisted of a 1:3 combination of cubes (L × L × L) and tall blocks (3L × L × L); thesearrays are referred to as SQ1.5-sq, SQ1.5-st, ST1.5-sq and ST1.5-st. The prefixes SQ and STindicate square and staggered arrays, respectively, for all blocks; in addition, the suffixes sqand st refer to the layouts of the tall blocks. Moreover, we used another array configurationcomposed of a 1:1 combination of cubes (L × L × L) and tall blocks (2L × L × L); werefer to this array as SQ1.5-st*. The average block height Hav of these five arrays is 1.5L .The detailed configurations of these arrays are explained in Hagishima et al. (2009). Thirdly,we configured two types of arrays comprising repeating units of 64 blocks that are rotated

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Fig. 3 Distribution of blocks inthe horizontal random array forST1R* and ST1R configurations.The number on each block refersto its rotation angle in degrees.The term θ refers to the rotationangle of a block and theanticlockwise direction is definedas positive. a Schematic view ofST1R*, b schematic view ofST1R and c detailed diagramdefining rotation angle

Airflow

-21 -30 -29 -16 -10 20 -13-42

41

35

27

14 -10 -41 39 35 -3 -8 16

-35 3 -12 12 17 -9 0

-16 -22 8 -35 42 0 32 -45

10 18 42 30 -12 11 -39

-20 -5 -11 14 -8 -2 14 -11

40 -25 10 -2 -42 29 26

8 0 -4 4 21 -18 23 -15

1

1

5

1

1

5

-18.5 -1.5 2.5 13.5 -8.5 -13.5 -2.53.5

15.5

13.5

14.5

13.5 15.5 -13.5 10.5 4.5 16.5 3.5 1.5

-6.5 -19.5 5.5 -9.5 18.5 19.5 -18.5

9.5 -17.5 1.5 -9.5 9.5 -4.5 -1.5 6.5

-6.5 3.5 -15.5-19.5 18.5 -18.5 0.5

10.5 -20.5 16.5 -16.5 -7.5 11.5 -10.5 2.5

18.5 2.5 -17.5 9.5 -7.5 19.5 -11.5

-7.5 -20.5-14.5 -6.5 6.5 -5.5 17.5 -8.5

W

W

L

+θ

(a)

(b)

(c)

randomly in a staggered layout (referred to as a horizontal random array). The rotation anglefor each block is determined by a random variation within ranges of −22.5◦ to 22.4◦ or−45◦ to 44◦. We describe these two types of arrays as ST1R* and ST1R, respectively, withthe distributions of rotation angles shown in Fig. 3. The detailed configurations of ST1Rare described in Zaki et al. (2011). Table 1 lists all the arrays used in our experiments. Fourdifferent values of the roughness packing density, λp (7.7, 12.1, 17.4 and 30.9%) were usedfor the configuration ST1, with three values of λp (7.7, 17.4 and 30.9%) used for the otherarrays.

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Table 1 Details of the measured arrays—Hav denotes average height of blocks, σ denotes the standard devi-ation of the heights of blocks, θav denotes average rotation angle, and σθ denotes standard deviation of therotation angle

Arrays Layout Remarks

SQ1 Lattice-type square Cubical arrays(L × L × L), Hav/L = 1.0, σ/Hav = 0

ST1 Staggered

SQ1.5 Lattice-type square Uniform arrays with tall rectangular blocks(L × L ×1.5L), Hav/L = 1.5, σ/Hav = 0

ST1.5 Staggered

SQ1.5-st* Lattice-type square 1:1 combination of cubes (L × L × L) andtall rectangular blocks(L × L × 2L), Hav/L = 1.5, σ/Hav =0.33

SQ1.5-sq Lattice-type square 1:3 combination of cubes (L × L × L) andtall rectangular blocks(L × L × 3L), Hav/L = 1.5, σ/Hav =0.58

SQ1.5-st

ST1.5-sq Staggered

ST1.5-st

ST1R* Staggered with rotation angle range from−22.5◦ to 22.4◦

θav = −0.8, σθ = 12.4, Hav/L =1.0, σ/Hav = 0

ST1R Staggered with rotation angle range from−45◦ to 44◦

θav = 0.5, σθ = 23.6, Hav/L = 1.0,

σ/Hav = 0

Table 2 Comparison of mass transfer coefficients k and scalar transfer coefficients CE for a smooth surface,with the root-mean-squares (r.m.s.) indicated

Equation or method Uref k (r.m.s.) CE (r.m.s.) CE/CE(m s−1) (×103 kg m−2 s−1) (×103) (salinity method)

Equation 9 – 10.89 4.76 1.10

Water evaporationmethod

1.86 9.67 (0.30) 4.43 (0.03) 1.02

Salinity method 1.90 9.79 (0.35) 4.32 (0.13) 1.00

2.3 Instrumentation

Figure 4 shows the wind-tunnel arrangement used for the measurements. The device used wasan open-circuit wind tunnel with a test section of height 0.9 m, width 0.9 m and length 4.8 mand located in an indoor environment (room). The air temperature of the room was maintainedat a constant value (using air-conditioning) during the measurements. Four propeller fans witha propeller diameter of 350 mm and maximum rotational frequency of 1,550 rpm were setup at one end of the tunnel. A wire mesh was set up at a leeward position approximately 1 mfrom the fans in order to ensure a uniform cross-sectional airflow distribution.

A square void in the floor of the wind tunnel (positioned at a leeward point approxi-mately 3 m from the wire mesh) was used as a water tank; the tank’s base dimensions were720 mm × 720 mm (28.8L × 28.8L) with a depth of 50 mm. The water surface and thesurrounding floor were at identical levels. The floor surrounding the water tank was covered

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fence tank or wet paper filter

fan

[mm]

regularly arrayed blocks

800720Fetch 32801200

720

900

dew point sensor

Fig. 4 Schematic plan view of the wind tunnel

Fetch 130L

Wind-tunnel

1L

Air temperature

20L

Wind speedSurface temperature

Tank filled with salt water

Same configurationairflow

Dew point(outside of wind tunnel)

L

Fig. 5 Diagrammatic elevation view of the wind tunnel

with a rectangular array made of wood; this floor housed the target array. We immersed arectangular array of blocks in the tank such that the height of these immersed blocks wasidentical to those of the array on the floor (ensuring a common “roof” level, as shown inFig. 5). For the condition with λp = 7.7%, a total of 64 blocks were arranged in the tank.In other words, the entire floor of the test section of the wind tunnel was covered with anidentical regular array, and a square-shaped scalar source was installed on the floor with afetch of 130L upwind of the scalar source to develop the momentum boundary layer. Thefetch and the area for measuring the flux were identical to those used for the surface-dragmeasurements in Hagishima et al. (2009). We compared the experimental conditions of thecurrent study with those for the previous surface-drag measurements of Hagishima et al.(2009); in our study, while a fetch of 130L was installed upwind of the measured area of dragforce, there was no corresponding fetch for the scalar source. Therefore, it is noteworthy thatthere are edge effects both at the windward and side edges, and the scalar transfer coeffi-cients obtained in the study were inevitably overestimated as compared with the equilibriumcoefficients.

The salinity of the salt water was measured with a salinometer (Guildline Instruments,Autosal 8400B) that had a measurement resolution better than 2 × 10−4%. It was calibrateddaily using IAPSO (International Association for the Physical Sciences of the Ocean) stan-dard seawater.

The mean flow speed was measured using a Pitot-static tube connected to a differentialpressure gauge (Sibata Scientific Technology, ISP-3-20DS). The Pitot-static tube was posi-tioned 500 mm (20L) above the leeward edge of the water tank. According to the resultsobtained by Hagishima et al. (2009), the boundary-layer thickness for momentum wasassumed to be within the range of 6L–12L(all experimental data are listed in Table 3);hence, the chosen height of 20L for the static tube is above the boundary layer. The velocityat 20L for all measurements of the scalar transfer coefficient is between 1.92 and 2.08 m s−1,and the maximum velocity difference in these measurements is less than 8.5%. This suggeststhat the velocity at 20L is slightly affected by the flow contraction due to a block array.

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Table 3 Estimated values of CE for all arrays; C∗E is defined by Uref (2L) for SQ1 and ST1 and Uref (3L) for

other arrays, C.V. denotes the coefficient of variation, δ/L denotes the boundary-layer height normalized byL and u∗/Uref (20L) denotes the friction velocity normalized by the reference wind speed Uref (20L)

Arrays λp CE (20L) × 103 C∗E × 103 C.V. (%) δ/La u∗/Uref (20L)a Uref (20L)

SQ1 7.7 5.14 7.38 0.93 7.00 0.0729 1.97

17.4 4.82 7.11 0.75 7.25 0.0736 1.98

30.9 4.53 6.87 2.38 6.50 0.0724 1.98

ST1 7.7 5.10 7.60 1.94 8.50 0.0789 1.99

12.7 5.29 − 0.39 − − 2.01

17.4 5.38 9.41 0.84 8.50 0.0804 2.02

30.9 4.94 7.43 0.89 7.50 0.0733 2.01

SQ1.5 7.7 5.03 − 1.81 8.38 0.0777 1.98

17.4 4.89 − 0.73 7.5 0.0797 2.06

30.9 3.73 − 2.68 8.25 0.0807 2.01

ST1.5 7.7 5.68 8.16 1.41 9.50 0.0848 1.95

17.4 5.23 7.93 0.64 9.75 0.0837 2.02

30.9 3.87 5.65 2.09 9.00 0.0764 2.01

SQ1.5-st* 7.7 4.89 − 1.00 − 0.0829 1.98

17.4 4.94 − 1.72 − 0.0844 1.99

30.9 4.46 − 0.71 − 0.0858 2.04

SQ1.5-sq 7.7 4.70 − 0.77 − 0.0857 1.99

17.4 4.40 − 2.60 − 0.0874 2.05

30.9 3.88 − 0.84 − 0.0893 2.06

SQ1.5-st 7.7 4.94 − 1.92 − 0.0851 1.95

17.4 4.48 − 1.89 − 0.0888 2.02

30.9 3.99 − 2.21 − 0.0938 2.05

5.03 9.91 2.18 9.13 0.0864 1.98

17.4 4.89 11.29 1.47 10.00 0.0897 2.05

30.9 4.19 11.06 0.87 10.25 0.0916 2.07

ST1.5-st 7.7 5.22 13.63 0.77 9.28 0.0882 1.92

17.4 4.54 18.10 0.82 10.00 0.0909 2.08

30.9 4.08 20.38 1.87 11.75 0.0955 2.07

ST1R* 7.7 5.50 − 1.93 − − 1.99

17.4 5.54 − 2.64 − − 2.01

30.9 4.98 − 1.28 − − 1.98

ST1R 7.7 5.88 − 1.67 7.84 0.0865 1.99

17.4 5.60 − 2.71 8.69 0.0886 2.01

30.9 4.80 − 2.25 7.78 0.0776 2.01

a Obtained from Hagishima et al. (2009) and Zaki et al. (2011)

Nevertheless, considering the fact that the ratio of the frontal projected area of a block arrayto the cross-sectional area of the wind tunnel ranges approximately between 0.8 and 2.3%,we speculate that the relation between the estimated scalar transfer coefficient and roughnessgeometry is not altered by any flow acceleration.

The dew point of the air was measured on the exterior of the wind tunnel with a cooledmirror dew-point hygrometer (Shinyei, DewStar S-1) to an accuracy of ±0.2◦C. In addition,

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we measured the temperature of the salt water surface using two thermistor thermometers(TechnolSeven, DS101) to an accuracy of 0.1◦C, and adopted the averaged value for analysis.The sensors for the surface temperature measurement were fixed such that they could float onthe water surface. We had previously observed the surface temperature distribution of the saltwater using an infrared camera (NEC-Sanei, TVS-600) for a flow speed of approximately2 m s−1, and we confirmed that the temperature distribution was not very significant on thefloor. The air temperature at a height of 20L was measured using a thermistor thermometer,and the output signals from all the instruments except for those from the salinometer wererecorded every 30 s using a data logger.

The measurement procedure was as follows; first, we prepared a salt water solution witha NaCl concentration of approximately 3%; this solution consisted of purified water andNaCl with purity >99.5%. We filled bottles with this solution for salinity measurements, andsubsequently, the tank was filled with the residual water. Next, we circulated air by means ofthe wind-tunnel fans to produce a wind speed of about 2 m s−1 for approximately 2 h. Subse-quently, we collected four samples of salt water and measured the salinity of these samples.For all salinity measurements, we used volumetric bottles (0.5L) previously rinsed three timeswith the sample water. We measured the salinity of each sample five times continuously, thencalculated the mean salinity of all measured values.

The coefficients of variation (defined by the standard deviation divided by the mean val-ues) of the wind speed and specific humidity at the reference location were approximatelyless than 2% over the 2-h duration of the experiments. Therefore, the mean value for this 2-hduration is assumed to be the representative value during the experiments for the followinganalysis. We estimated the surface scalar flux E based on Eq. 4, and we calculated the scalartransfer coefficient CE using Eq. 5. We estimated qsurf as the saturated specific humidity atthe measured temperature of the water surface, and qref was estimated from the measured dewpoint outside the wind tunnel (the schematic is shown in Figs. 4 and 5) assuming humidityhomogeneity of air in both the room and the wind tunnel above the scalar boundary layer.We repeated the same process three times for each array and used the averaged values of CE

in the following analysis.

2.4 Measurement Accuracy

The salinity change over a duration of two hours was approximately 0.02% for all arrays,indicating that the experimental error due to the salinometer in the measurement of the evapo-ration flux is less than 1%. In addition, the amount of evaporation as estimated by the salinitychange coincided with a decrease of approximately 0.4 mm in water level; this value wasmuch smaller than the minimum size of the blocks (25 mm). Moreover, since we confirmedby visual inspection that there were no waves on the water surface for a wind speed of 2 m s−1,we assumed that the amount of water loss during the experiment was minimal. Hence, weconsidered the change in geometry due to both evaporation and water losses to be negligible.

The accuracy of the salinity method was preliminarily investigated by comparing theestimated mass transfer coefficients with those for a smooth surface measured by the waterevaporation method (Narita 2007). In this method, the evaporation is directly calculated bythe measured mass of a wet paper filter before and after exposure to the air flow.

The experimental details of our study are described as follows: the tank embedded in thewind-tunnel floor was covered by a flat plastic plate to which a filter paper of 1 mm thicknesswas glued. Water was sprayed carefully only on the paper filter until the entire paper surfacewas completely moist. The paper dimensions were designed to be identical to those of thetank used in the salinity method. The surface temperature of the paper surface was measured

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using thermistor thermometers (TechnolSeven, DS101) by inserting them into the middleof the paper. The measurements for the reference wind speed, air temperature and specifichumidity were obtained by using the same procedure as that for the salinity method. The massof the paper with the plastic plate was measured using a mass balance (A&D, EP-60KA) withan accuracy of 0.001 kg; the measurement corresponded to approximately 1% of evaporation.

Moreover, we measured the mass transfer coefficients k and scalar transfer coefficients CE

of a smooth surface with no obstacles both along the relevant fetch and the measuring watertank based on the procedure given in Sect. 2.3. The averaged value and standard deviationfor three trials as obtained using the salinity and water evaporation methods are given inTable 2; the variations for three trials were very small for both methods. The difference inthe averaged values of CE between the water evaporation and salinity methods is 2%.

As a reference, we also compared the mass transfer coefficients obtained by the salinitymethod with those obtained using the well-known empirical relationship between the Nusseltnumber Nu and the Reynolds number Re. For heat transfer phenomena, the dimensionlessrelationship between Nu and Re under turbulent boundary-layer conditions can be expressedas follows (Incropera and DeWitte 2002):

Nu = 0.037Re4/5 Pr1/3, (7)

where the Nusselt number Nu = hl/λ, the Reynolds number Re = ul/ν and the Prandtlnumber Pr = ν/a(∼ 0.71). In these relations, h denotes the convective heat transfer coef-ficient, l denotes the representative length, λ denotes the heat conductivity, ν denotes thereference flow speed, ν denotes the kinematic viscosity, a(= λ/ρCp) denotes heat diffu-sivity, ρ denotes air density and Cp denotes the heat capacity of air. Under the assumptionof similarity between mass and heat transfer, the dimensionless relationship between theSherwood number Sh and Re can be written as

Sh = 0.037Re4/5Sc1/3, (8)

where the Sherwood number Sh = kl/ρD and the Schmidt number Sc = ν/D(= 0.69).In these relations, k denotes the mass transfer coefficient and D denotes vapour diffusivity.Based on Eqs. 7 and 8, the mass transfer coefficients can be estimated by:

k = h

CpLe−2/3, (9)

where Le(= a/D = Sc/Pr ≈ 0.97) denotes the Lewis number. When we apply this rela-tion to estimate the mass transfer coefficient at an air temperature of 20◦C and flow speed of1.9 m s−1, k and CE have approximate values of 10.89×10−3 kg m−2 s−1 and 4.76 × 10−3,respectively, as given in Table 2.

Whereas the estimated values of CE by the salinity method and water evaporation methodshow good agreement, the value of CE as obtained using Eq. 9 is approximately 10% largerthan that obtained with the salinity method. This discrepancy is possibly attributed to thedifference in the boundary-layer conditions of the momentum and scalar between our experi-ment and those of Eq. 7 (Incropera and DeWitte 2002). For example, the approach flow of ourwind tunnel to the measured area is not completely uniform. Thus, we regard the estimatesobtained by using Eq. 7 as a reference for rough comparison only. On the basis of the aboveinvestigations, we conclude that the accuracy of the salinity method is acceptable under theexperimental conditions of our study.

All the experiments were performed under identical conditions of flow speed (approxi-mately 2 m s−1, as given in Table 3). The Reynolds number, based on the dimension of the

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blocks and the flow speed at 20L , was approximately 3300, and the roughness Reynolds num-ber, Re*, based on the friction velocity u∗ and roughness length z0, was approximately 60.According to Snyder and Castro (2002), a boundary layer over a fully rough surface (wherethe effect of viscosity is negligible) is observed if Re∗ > O(1); hence, the Re∗ value for ourexperiment satisfied the criteria for a fully rough surface (similar to a real urban surface).Moreover, Hagishima et al. (2009) have confirmed that the Reynolds number dependency ofmomentum exchange is weak under the condition of Uref = 2 m s−1 by measuring the dragcoefficient of SQ1 with λp = 17.4%. However, according to Uehara et al. (2003), the valueof Uref = 2 m s−1 is the lower limit for the Reynolds number dependency of flow velocityaround a block array. According to their chart for the estimation of the effect of the Reynoldsnumber, the mean wind speed at a distance of 10 mm from a floor surface possibly decreasesby approximately 2–3% as compared with the mean wind speed under the condition when theReynolds number dependency is not being considered. Since we could not obtain the windprofiles inside the canopy under various conditions of freestream velocity due to limitations inthe experimental apparatus, a more detailed discussion on the Reynolds number dependencyof wind flow velocity is beyond the scope of this study. Instead, the data corresponding to thereference wind speed at 20L are given in Table 3 to clearly state the experimental conditionsof the current study.

In addition, it is noteworthy that the effect of molecular diffusion cannot be neglected forscalar transport phenomena (unlike momentum transfer) even though a fully rough conditionis achieved. As mentioned in Pascheke et al. (2008), the dimensionless transfer coefficients,referred to as CE in this study, vary with the conditions of flow speed. For example, Barlowand Belcher (2002) reported that the dimensionless transfer coefficients for the street surfaceof a 2-D canyon under the condition of a small aspect ratio, H/W , (referred to as the Stantonnumber in our study) range from 1.7 × 10−3 to 2.0× 10−3 under the condition when Uref isapproximately >4 m s−1. In contrast, the CE value for a smooth surface in the present studyis 4.32 × 10−3; this is significantly greater than that obtained by Barlow and Belcher (2002).In general, a larger flow speed is more preferable in order to reduce the Reynolds numberdependency; however, Uref = 2m s−1 is the critical wind speed for our measurements withthe salinity method under the condition that there is no wave on the water surface. Underthese circumstances, although the reference wind speed differs slightly for the various arrays,and it is smaller than those of previous studies, we focus on the comparison of CE for arrayswith various geometries.

3 Results and Discussion

3.1 Transfer Coefficient CE for a Uniform Array Comprised of Cubes

The relations between the estimated values of CE and λp are shown in Fig. 6, and the resultfor a smooth surface with no obstacle is shown as the reference. In addition, the Cd valuesmeasured by Hagishima et al. (2009) for arrays with configurations identical to those in ourstudy are plotted. The term Cd is expressed as follows:

Cd(z) = τ0

0.5ρairUref (z)2 (10)

where τ0 denotes the total surface shear stress for an urban area and Uref (z) denotes the meanflow speed at a reference height z. The reference mean flow speed for both CE and Cd wasmeasured at a height of 20L .

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Fig. 6 Comparison of scalartransfer coefficients CE and dragcoefficients Cd for cubical arrays.Cross CE for smooth surface,filled circle CE for SQ1, filledtriangle CE for ST1, unfilledcircle Cd for SQ1, unfilledtriangle Cd for ST1. Error barindicates the standard deviationobtained for three experimentaltrials C

E

Cd

λp [%]

× 10-3 × 10-3

4

5

6

0 10 20 30 403

7

11

15

The effect of a block array on the scalar transfer for the street surface is speculated to beaffected by the following two mechanisms: (i) the decreased mean flow near the street surfacedue to a block array, which reduces the horizontal advection of the scalar, and in contrast,(ii) 3-D vortices around the blocks that effectively create a thinner sub-layer near the streetsurface and enhance vertical turbulent mixing of the scalar in air. Hence, a block array willtend to increase CE for the street surface. The fact that all values of CE for ST1 and SQ1 arelarger than those for a smooth surface indicates that the latter effect prevails in our case.

Upon comparing the tendencies of the staggered and square arrays, the values of CE forST1 plotted against λp show a positive peak at λp = 17.4%, while in contrast, the CE valuesobtained for SQ1 decrease monotonically with an increase in λp. In addition, the CE valuesfor SQ1 and ST1 are almost identical when λp = 7.7%; moreover, the CE value for ST1 islarger than that for SQ1 for larger λp values. Such a tendency is probably related to the flowcharacteristics of each array. It is well known that canopy flow can be classified into threeregimes according to the variations in λp, namely, isolated flow for a sparse canopy; wakeinterference flow for a medium roughness density condition; and skimming flow for a densecanopy (Oke 1988).

The agreement of the CE values for the above-mentioned arrays at λp = 7.7% might bedue to an isolated flow regime (it is noteworthy that this λp condition is lower than that forthe Cd peak, which probably occurs between λp = 7.7 and 17.4% for both SQ1 and ST1according to Hagishima et al. (2009)). In other words, the layout of the blocks does not affectthe scalar transfer of a street surface because the interference of airflow around each blockis weak. In contrast, in the staggered arrays, the scalar transfer of the street surface increaseswhen λp varies from 7.7 to 17.4%. Considering the variations in Cd values, the flow regimeof this condition is either isolated flow or wake interference flow. Hence, an increase in λp

indicates an increase in the number of obstacles in the salt water surface; these obstaclesgenerate 3-D airflow near the street surface, and the resultant airflow enhances the verticalmixing of the scalar and air. Such behaviour might result in an increase in CE values for anincrease in λp values. The decrease in CE values for large λp is probably caused by boththe decreased advection effect due to low flow speed near the surface and weakened verticalmixing due to a skimming flow regime.

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Fig. 7 Scalar transfercoefficients CE for arrays withuniform height. Cross smoothsurface, filled circle SQ1, filledtriangle ST1, unfilled circleSQ1.5, unfilled triangle ST1.5.Error bar indicates the standarddeviation obtained for threeexperimental trials

CE

× 10-3

3

4

5

6

λ p [%]

0 10 20 30 40

The values of CE for ST1 are larger than those for SQ1 when λp > 17.4%. This may bedue to the fact that the 3-D airflow consisting of various sizes of vortices around the blocks(Coceal et al. 2006, 2007) enhances the introduction of dry air near the street surface. Sincethe distance between blocks in the mean wind direction in ST1 is greater than that in SQ1,the leeward area of the blocks subject to the vortices in ST1 is greater than that in SQ1.

3.2 Transfer Coefficient CE for Uniform Arrays Comprised of Tall Blocks

The values of CE for uniform arrays with a height of 1.5L (SQ1.5 and ST1.5) plotted againstλp are shown in Fig. 7, and the results for a smooth surface array, SQ1 and ST1, are shownas a reference.

The CE values for SQ1.5 decrease monotonically with an increase in λp, thereby display-ing a tendency similar to that for SQ1. Moreover, the values of CE when λp < 17.4% arealmost identical to those for SQ1. These results indicate that the influence of block heighton the CE values is insignificant, and the flow regime appears to be either isolated or wakeinterference flow when λp < 17.4%. Oke (1988) classified the flow regime based on theH and W values for square arrays. If we apply his classification to our results for blockarrays with square layouts (SQ1.5), the condition λp = 17.4% (W/H = 1.1) corresponds tothe skimming flow regime (as per the criteria given by Oke where W/H > 0.7). However,considering the similar tendencies exhibited by the CE values for both SQ1 and SQ1.5, theflow-regime classification should vary with the aspect ratio of a block. In contrast, the valueof CE when λp = 30.9% is smaller than that for SQ1 by a factor of 16%; moreover, thisCE value is less than that for a smooth surface by 12%. When λp = 30.9%, since the flowregime may be skimming for both SQ1 (H/W = 1.3) and SQ1.5 (H/W = 1.9) arrays, theCE values decrease with an increase in λp due to both the decreased advection effect dueto low wind speed near the surface and weakened vertical mixing. This discrepancy in CE

values for SQ1.5 and SQ1 indicates that the deeper canyon comprising the 1.5L blocks maysignificantly reduce the influence of both the above-mentioned effects.

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The increasing tendency of CE, which is a characteristic for ST1, is not observed for ST1.5and the largest value of CE is obtained at λp = 7.7%. As mentioned before, the results forST1 suggest the possibility that a staggered layout can effectively enhance the vertical mixingof the air around the blocks, thereby resulting in an increase in CE values when λp < 17.4%.The largest value of CE for ST1.5 at λp = 7.7% indicates that the effect of strong verticalmixing occurs under conditions of lower λp values for ST1.5 than that of ST1. The mono-tonic decrease in CE for ST1.5 may be caused by the effects of both decreased advection andweakened vertical mixing in a manner similar to that observed in ST1. In addition, the valueof CE for λp = 30.9% is smaller than that for ST1 by a factor of 21% and almost identicalto that obtained for SQ1.5. This is because the flow speed near the surface might be stronglyreduced due to the skimming flow regime.

In these arrays, the velocity at 20L for all measurements of the scalar transfer coefficientis between 1.95 and 2.06 m s−1, and the maximum velocity difference between all the mea-surements is less than 6%. This suggests that the velocity at 20L is slightly affected by theflow contraction due to a block array. Nevertheless, considering that the blockage effect ofthe arrays with 1.5L blocks at λp = 30.9% is around 2.3%, we speculate that the significantdecrease in CE for λp = 30.9% is mainly attributed to the increased packing density.

3.3 Transfer Coefficient CE for Non-Uniform Arrays

The values of CE for non-uniform arrays are shown in Fig. 8, while the results for ST1.5 andSQ1.5, which have same average block height of 1.5L , are shown as a reference.

We considered the four types of arrays with the same standard deviation for a height of0.58Hav (consisting of a 1:3 combination of cubes and tall blocks). The values of CE forST1.5-sq and ST1.5-st, in which all blocks are arranged in a staggered layout, are larger thanthose for SQ1.5-sq and SQ1.5-st for all values of λp. In other words, the staggered layoutof all blocks in an array produces a greater effective scalar transport than that for the squarelayouts. Moreover, this observation indicates that the layout configuration of all blocks maybe one of the dominant factors in determining CE. This tendency contrasts with the resultsobtained for Cd as presented in Hagishima et al. (2009); the Cd values appear to vary withthe configurations of the layout comprising tall blocks, because the wind-speed deficit ismainly due to a large pressure drag acting on the taller blocks (3L blocks). In contrast, scalartransport occurs within a sub-layer near the scalar surface installed on a street, and there isno mechanism corresponding to pressure drag on the blocks; hence, a layout of blocks withheight L adjacent to the scalar source surface may directly affect the values of CE, whereasthe layout comprising blocks with height 3L may not. From another point of view, the loca-tion of the scalar source is noteworthy; this is another reason why a layout of blocks withheight L appears to play a dominant role in the determination of CE. In the scalar transportexperiment, a scalar source, which contributes to the total scalar transport, is only installedon the floor. On the other hand, the momentum transport is mainly dominated by the pressuredrag, and the contribution of friction at the floor to the total drag force is weak, particularlyfor a highly rough surface.

Subsequently, we discuss the effects of height variations in the blocks by comparingthe two types of non-uniform (Fig. 8) and uniform arrays. In both squared and staggeredarrays, the values of CE for non-uniform arrays are smaller than those for uniform arrayswhen λp < 17.4%. This decrease may be due to the decrease in advection effects due tolarge deficits in momentum; these deficits can be estimated from the larger values of dragcoefficients for non-uniform arrays when compared with those for uniform arrays (Hagishimaet al. 2009). In contrast, when λp = 30.9%, the CE values for non-uniform arrays become

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Fig. 8 Scalar transfercoefficients CE for arrays withnon-uniform heights. a Squarelayouts with 1L blocks. Unfilledcircle SQ1.5, unfilled squareSQ1.5-sq, filled square SQ1.5-st,plus SQ1.5-st*. b Staggeredlayout with 1L blocks. Unfilledtriangle ST1.5, filled square(dark grey) ST1.5-st, filled square(grey)—SQ1.5-st. Cross refers toCE values for a smooth surface.Error bar indicates the standarddeviation obtained for threeexperimental trials

λp [%]

(b)

(a)

CE

× 10-3

× 10-3

3

4

5

6

0 10 20 30 40

3

4

5

6

CE

λp [%]

0 10 20 30 40

larger than those for uniform arrays. In particular, the CE value for SQ1.5-st* is significantlylarger than that for SQ1.5 by a factor of 18%. The large values of CE for large λp may bedue to flow characteristics that are different from that for uniform arrays. In a non-uniformarray, a strong downward motion of the airflow along the front walls of tall blocks is observedaround non-uniform canopies (e.g. in the numerical simulations by Xie et al. (2008)), and thisleads to larger CE values for non-uniform block heights under large λp conditions. However,we do not have concrete evidence to support our speculation, and we cannot explain why theCE value for SQ1.5-st* is larger than those for other non-uniform arrays.

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CE

λp [%]

(a)× 10

-3

4

6

8

10

0 10 20 30 403

5

7

9

11

13(b)× 10

-3

CE

λp [%]

0 10 20 30 40

Fig. 9 Comparison of CE values defined by Uref within or above the boundary layer. a Arrays with uni-form height for SQ1 and ST1 configurations. Filled circle SQ1(20L), unfilled circle SQ1(2L), filled triangleST1(20L), unfilled triangle ST1(2L). b Arrays with non-uniform block heights for staggered layout configu-ration. Unfilled triangle ST1.5(20L), filled diamond ST1.5-st (20L), unfilled diamond ST1.5-sq (20L), filledtriangle ST1.5(3L), filled square ST1.5-st(3L), unfilled square ST1.5-sq(3L)

3.4 Reference Height for Flow Speed

Upon considering the definition of the parameter CE, the difficult question of how the refer-ence height should be determined arises. In the previous sections, we adopted the CE valuedefined by the flow speed at 20L , which is above the boundary-layer top. As mentionedpreviously, CE is influenced by two different mechanisms, namely, advection effects andvertical mixing effects. In order to clearly understand the latter effect, one possible way isto define CE based on a reference flow speed adjacent to an array such that the effect of thedecreased advection due to momentum deficit is excluded. Since the physical meaning of theheight probably differs if the same reference heights are used because of the difference inthe roughness and boundary-layer heights, we simply define the reference height to be twicethe mean block height.

For uniform cubical arrays, the reference height is set at 2L . The values of CE definedby Uref (2L) and Uref (20L) for SQ1 and ST1 are shown in Fig. 9a; for SQ1, the tendency ofCE(2L) to decrease with increase in λp is similar to that for CE(20L). The slight decreasein CE(2L) values with increasing λp may be caused by the change of the flow regime fromisolated to skimming flow. In addition, it is probable that this transition of the flow regimecauses a reduction in flow speed near the scalar surface and weakens the scalar exchangebetween air and the street canyon. This result implies that the effects of the deficit of thewind speed for CE(2L) are not very significant for different values of λp for the SQ1 array.In contrast, the CE(2L) curve for ST1 shows a clear peak at λp = 17.4%, and is due to thestrongly enhanced vertical mixing of air for the staggered layout at λp = 17.4%.

For non-uniform arrays, the reference height is set at 3L , and the results for CE definedby Uref (3L) for non-uniform arrays are shown in Fig. 9b. As a reference, the CE(3L) valuesfor ST1.5 are also plotted. As mentioned previously, the values of CE(20L) for non-uniformarrays are smaller than those for uniform arrays when λp values are small, and the oppositetrend can be observed for larger λp values. In contrast with the CE(20L) values, the values

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Fig. 10 Scalar transfercoefficients CE for horizontalrandom arrays. Unfilled diamondST1R, filled diamond ST1R*,filled triangle ST1, cross flatsurface. Error bar indicates thestandard deviation obtained forthree experimental trials

CE

× 10-3

3

4

5

6

λp [%]

0 10 20 30 40

of CE(3L) for non-uniform arrays are larger than those for ST1.5 for all λp values. Thisimplies that advection effects are possibly reduced for non-uniform arrays; however, verticalmixing is enhanced due to the heterogeneity of the block height, thereby leading to a strongervertical downflow into the canopy. In addition, the increasing tendency of CE(3L) againstλp is observed for both non-uniform arrays when λp varies from 17.4 to 30.9%. This impliesthat the vertical mixing of air due to a strong downward flow along the windward walls oftall blocks leads to increased CE values even under the conditions of large λp. Paschekeet al. (2008) determined the dimensionless transfer coefficients for a cubical staggered arrayCM10S (corresponding to ST1 in this study), and a non-uniform height array RM10S, andthey showed that the coefficient for RM10S is 6% larger than that for CM10S when the coef-ficient is defined by the flow speed at mean block height. These observations are consistentwith our results as shown in Fig. 9b.

3.5 Transfer Coefficient CE for Horizontal Random Arrays

The relation between CE and λp for a horizontal random array is shown in Fig. 10, wherethe results for ST1 are also plotted as a reference. We first discuss the effect of the differencesin rotation angles on CE values by comparing the data for ST1R and ST1R*. When λp valuesvary from 7.7 to 17.4%, the values of CE for ST1R and ST1R* are larger than those forST1. Considering that all three arrays are in a staggered layout, the rotation of the blockssignificantly enhances the scalar transfer when λp = 7.7 and 17.4%, thereby resulting in largeCE values. In contrast, the values of CE for ST1R and ST1R* at λp = 30.9% are close tothose for ST1. Since the flow pattern is considered to be skimming flow for this λp value, theeffect due to the rotation of the blocks may not be significant.

The values of CE for three λp values of 7.7, 17.4 and 30.9% are plotted with respect tothe standard deviation of the rotation angle, σθ , in Fig. 11, and the results for ST1 are usedas the reference at σθ = 0. The curve clearly shows that the effects of the rotation rangeson CE differ according to the values of λp. When λp = 7.7%, the CE value increases withincrease in σθ . Because the flow regime is classified as isolated flow in this case, the effects

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Fig. 11 Scalar transfercoefficients for horizontalrandom arrays with respect tostandard deviation for rotationangle, σθ . The result for ST1 isshown at 0 as a reference. Filledtriangle ST1, filled diamondST1R*, unfilled diamond ST1R,line 7.7%, dashed line 17.4%,dotted line 30.9%. Error barindicates the standard deviationobtained for three experimentaltrials

CE

× 10-3

σθ

3

4

5

6

0 10 20 30

of the rotation angle work to effectively enhance air mixing near a scalar surface. Whenλp = 17.4%, the increase in CE values with increasing σθ values can be observed. However,the slope for this curve is smaller than that obtained for λp = 7.7%, indicating that the rota-tion angle has a reduced influence on the air mixing under conditions of wake interferenceflow. In contrast to these two λp conditions, the slope of the CE–σθ curve at λp = 30.9% isnearly zero or slightly decreasing. This result indicates that air is not effectively introducedinto a street canyon for increased λp values because of the narrower spacing between blocksdue to the rotation angles.

4 Conclusion

We used the salinity methodology that involved wind-tunnel experiments to estimate theamount of evaporation and the scalar transfer coefficients CE from the floor surface of var-ious block arrays under different roughness packing density conditions. We adopted threetypes of roughness arrays—uniform array, non-uniform array and horizontal random array—which are similar to those used in the studies of Hagishima et al. (2009) and Zaki et al. (2011)for determining aerodynamic parameters. By combining our obtained results of CE valueswith previous data, we examined the geometric dependence of the scalar transfer efficiencyfor various configurations.

First, we measured the values of CE for uniform arrays with lattice-type square arrays andstaggered arrays with cubical blocks and tall blocks. The values of CE for a staggered cubicalarray ST1 as defined by Uref (20L) showed that the vertical mixing of air could be enhancedfor mid-range values of λp. Further, these results were confirmed by the clear peak values ofCE as defined by Uref (2L). In addition, the slender block arrays SQ1.5 and ST1.5 appear toproduce a large reduction in flow speed inside the canopy due to the skimming flow regime,thereby resulting in significantly smaller values of CE as compared with those for cubicalarrays with greater values of λp.

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Secondly, the effects of height variability were investigated using five different types ofnon-uniform arrays. For smaller values of λp, it was shown that the values of CE for uniformarrays were larger than those for non-uniform arrays; however, the opposite tendency wasobserved for increasing λp values. This is because non-uniform arrays produce large defi-cits in flow speed, thereby resulting in smaller values of CE when compared with those foruniform arrays at smaller values of λp. In contrast, tall blocks effectively introduce air insidethe canopy under dense packing conditions. This effective introduction of air was furtherconfirmed by the fact that the CE values as defined for Uref (3L) for non-uniform arrays werelarger than those for uniform arrays at all values of λp.

Thirdly, the transfer coefficients were measured for horizontal random arrays in boththe ST1R* and ST1R configurations, and it was clearly shown that horizontal randomnessstrongly affects CE. The standard deviation of the rotation angles has a positive relation withCE under sparse packing conditions, although the effects of the rotation angle reduce as λp

increases.We created a database for the scalar transfer coefficients for various types of geometrical

arrays. These results revealed the clear dependence of the transfer coefficients on geometri-cal conditions such as the plan area index, layouts and height variability. In this study, it isnoteworthy that there are edge effects both at the windward and side edges, and the scalartransfer coefficients are inevitably overestimated as compared with equilibrium coefficients.The measurement of the coefficients under approximate equilibrium conditions (similar tothose for the measurement of drag coefficient) is a subject for future studies. This type ofdatabase will assist in improving the modelling of the scalar transfer between scalar surfaces,along with improved understanding of the dependency of the coefficients on geometricalconditions. Further, it can be widely used for the validation of CFD studies addressing scalardispersion over various conditions of rough surfaces.

Acknowledgments We are deeply indebted to Mr. Satoru Suenaga, Mr. Kazuyuki Maeda and Mr. ShunsukeNaito for their valuable assistance with the wind-tunnel experiments. This research was financially supportedby a Grant-in-Aid for Scientific Research (22360238) from the Ministry of Education, Science and Culture ofJapan, and a Grant-in-Aid for Research Fellow (221511) of the Japan Society for the Promotion of Science.

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