Intercomparisons of Experimental Convective Heat Transfer ...

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Jan 10, 2005 - Authors; Authors and affiliations. Aya HagishimaEmail author; Jun Tanimoto; Ken-ich Narita. Aya Hagishima. 1. Email author; Jun Tanimoto. 1.
Boundary-Layer Meteorology (2005) 117: 551–576 DOI 10.1007/s10546-005-2078-7

 Springer 2005

INTERCOMPARISONS OF EXPERIMENTAL CONVECTIVE HEAT TRANSFER COEFFICIENTS AND MASS TRANSFER COEFFICIENTS OF URBAN SURFACES AYA HAGISHIMA1,*, JUN TANIMOTO1 and KEN-ICH NARITA2 1

Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1, Kasuga-koen, Kasuga-shi, 816-8580, Fukuoka, Japan; 2 Department of Engineering, Nippon Institute of Technology, Japan

(Received in final form 10 January 2005)

Abstract. The convective heat transfer coefficient (CHTC) of an urban canopy is a crucial parameter for estimating the turbulent heat flux in an urban area. We compared recent experimental research on the CHTC and the mass transfer coefficient (MTC) of urban surfaces in the field and in wind tunnels. Our findings are summarised as follows. (1) In full-scale measurements on horizontal building roofs, the CHTC is sensitive to the height of the reference wind speed for heights below 1. 5 m but is relatively independent of roof size. (2) In full-scale measurements of vertical building walls, the dependence of the CHTC on wind speed is significantly influenced by the choice of the measurement position and wall size. The CHTC of the edge of the building wall is much higher than that near the centre. (3) In spite of differences of the measurement methods, wind-tunnel experiments of the MTC give similar relations between the ratio of street width to canopy height in the urban canopy. Moreover, this relationship is consistent with known properties of the flow regime of an urban canopy. (4) Full-scale measurements on roofs result in a non-dimensional CHTC several tens of times greater than that in scale-model experiments with the same Reynolds number. Although there is some agreement in the measured values, our overall understanding of the CHTC remains too low for accurate modelling of urban climate. Keywords: Convective heat transfer coefficient, Intercomparison, Mass transfer coefficient, Urban canopy model, Wind-tunnel experiment.

Symbols: a: Cm: c p: D: FX:

thermal diffusivity [m2 s)1]; transfer coefficient Cm ¼ hD =U; specific heat of air at constant pressure [J kg)1]; diffusivity [m2 s)1]; scalar flux of substance X [kg m)2 s)1];

* E-mail: [email protected]

552 H: h: hD: Lfl: Nu: Pr: q: Q E: QG: QH: Q*: Re: Sc: Sh: St: Sfl: Tair: Ts: Te: DT: U: Ud: W: x: a: e: q: qair,X: qs,X: k: m: kp :

AYA HAGISHIMA ET AL.

canopy height [m]; convective heat transfer coefficient (CHTC) [W m)2 K)1]; mass transfer coefficient (MTC) [m s)1]; incident longwave radiation [W m)2]; Nusselt number Nu=hx/k; Prandtl number Pr=m/a; sum of the convective and radiative heat gain of building surfaces [W m)2]; turbulent latent heat flux [W m)2]; conductive heat flux of the ground surface [W m)2]; turbulent sensible heat flux [W m)2]; net radiation [W m)2]; Reynolds number Re=Ux/m; Schmidt number Sc=m/D; Sherwood number Sh=hDx/D; Stanton number St ¼ h=qcp U; incident solar radiation [W m)2]; air temperature [K]; surface temperature [K]; sol-air temperature [K] (It is a technical term used in building science.); Ts  Tair ; wind speed [m s)1]; wind speed at d metres above the target surface [m s)1]; width of street of urban canopy [m]; representative length [m]; solar absorptivity; emissivity; density of air [kg m)3]; concentration of substance X in the air [kg m)3]; concentration of substance X adjacent to the surface [kg m)3]; heat conductivity [W m)1 K)1]; coefficient of kinematic viscosity [m2 s)1]; plan area density of obstacles

1. Introduction The temperatures and winds in an urban canopy directly affect the health and comfort of the city’s inhabitants, and consequently much effort has gone towards gaining a greater understanding of urban climate. In particular, improving the calculation accuracy of the thermal balance in urban areas is an important goal of urban mesoscale modelling. As a result, several surface schemes, hereafter urban canopy models (UCMs), have been established for

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use in mesoscale modelling (e.g., Kondo and Liu, 1998; Ashie et al., 1999; Masson, 2000; Kusaka et al., 2001). This paper focuses on an important parameter in UCMs: the convective heat transfer coefficient (CHTC). UCMs have become established because, unlike the one-dimensional heat conduction treatment in the previously used slab models, they can be used to precisely estimate the effects of various urban conditions on the flow structure and turbulent flux in the urban canopy. Thus, we consider only UCMs here. Figure 1 shows the basic features of single-layer and multilayer UCMs. Both types commonly include sub-models that treat certain aspects of radiative heat transfer, convective heat transfer, and the hydrodynamic effects of the buildings. The focus of our paper is on that part of the models that treats the convective heat transfer between the atmosphere and urban surfaces. The important, yet still poorly understood, parameter for this transfer is the CHTC parameter. In addition to urban climatology studies, research on the CHTC of urban surfaces has been carried out in the fields of building science and heat transfer engineering. For example, full-scale measurements of the CHTC for building surfaces have been made in the field of building science to accurately estimate the air-conditioning load. Also, wind-tunnel experiments of the CHTC for surfaces with urban-like roughness have been carried out in the field of heat transfer engineering. Such studies do not have the aim of contributing to knowledge about urban climate. Nevertheless, despite some differences in scale and method among the various studies, all relevant studies of the CHTC can contribute to knowledge about the role of urban surfaces in UCMs. For this reason, we believe it is important to review and analyze these various experimental studies on the CHTC of building surfaces and surfaces with urban-like roughness. In addition to the CHTC, we also analyze several previous experiments on the mass transfer coefficient (MTC) of urban-like canopy surfaces because mass transfer follows analogous equations to heat transfer.

(a)

Za

Tair QH ,roof

ZR ZT + d

QH

Tair

(b)

Tair

Za

QH

TR

TR QH ,wall

QH ,canopy

Tc

TW TG

Single-layer model

ZR

TW

QH , street

TG

Multi-layer model

Figure 1. Basic processes in urban canopy models (Kusaka et al., 2001). Ta is the air temperature at reference height Za, TR is the building roof temperature, Tw is the building wall temperature, Tc is the air temperature in the canopy, and TG is the road temperature.

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2. Definition of CHTC The heat balance of a thin urban surface with zero heat capacity can be written Q ¼ QH þ QE þ QG ;

ð1Þ

where Q* is the net radiation, QH is the turbulent sensible heat flux, QE is the turbulent latent heat flux, and QG is the conductive heat flux at the ground surface. The turbulent sensible heat flux from the urban surfaces can be expressed using the convective heat transfer coefficient h as QH ¼ hðTs  Tair Þ;

ð2Þ

where Ts is the surface temperature and Tair is the air temperature. The turbulent sensible heat flux can also be expressed using the Stanton number St as QH ¼ qcp ðStÞUðTs  Tair Þ;

ð3Þ

where cp is the specific heat of air at constant pressure, q is the density of air, and U is the wind speed. In UCMs, the surface temperature Ts is usually defined as the spatially averaged surface temperature of the building walls, roofs, and streets. The definition of the air temperature Tair depends on the type of UCM; in single-layer models, the air temperature in the urban canopy is represented as that at the height of the roughness length. In multi-layer models, the vertical distribution of area-averaged air temperature is considered. In the same way, the scalar flux of a substance X can be expressed by the mass transfer coefficient hD and transfer coefficient Cm as   FX ¼ hD qs;X  qair;X ;

ð4Þ

  FX ¼ Cm U qs;X  qair;X ;

ð5Þ

where FX is the scalar flux of substance X, qair,X is the concentration of substance X in the air, and qs,X is the concentration of substance X immediately adjacent to the surface. Heat transfer engineering studies use many dimensionless formulae to describe the features of heat and mass transfer. For example, the empirical relations for the Nusselt number and Sherwood number as a function of Prandtl number, Reynolds number, and so on have been presented for various experiments (e.g., Johnson and Rubesin, 1949). However, because of the difficulties in defining a representative length and wind velocity, it is unclear how to apply these equations to the complex geometry of urban surfaces. In the field of building science, the CHTC of building surfaces is also an important parameter because it affects both the building thermal load and the

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optimum size of the air-conditioning system. In this field, empirical relationships between the CHTC and wind speed for a small flat plate in the wind tunnel are used. One of the commonly used sets of equations is by Jurges (McAdams, 1954). These sets are based on fits to the CHTC for a heated copper square plate, 0.5-m on a side, which was oriented perpendicular to a uniform air flow in a wind tunnel. In regard to such empirical treatments, Cole and Sturrock (1977) pointed out several problems with results from wind-tunnel experiments using cube arrays. First, the CHTC of the surfaces of a cube depends on wind direction and differs from the CHTC of a flat plate; second, the local CHTC depends on the velocity profile at the point investigated. Also, the area-averaged CHTC depends on the length of surface. Hence, the measured CHTC of a small flat plate cannot be applied to full-scale building surfaces. To overcome these problems, many experimental studies have been made to determine the CHTC for particular types of building surfaces. For a given study, this surface will be called the target surface. Such studies have suggested new empirical relations between the CHTC and the wind speed. However, few studies consider how the CHTC depends on the particular experimental condition, such as the thermal stability, the flow structure around the buildings, and the size of the target surface. Thus, there still remains no reliable method that can be used as a sub-model in a UCM.

3. Full-Scale Measurements on Building Surfaces 3.1. HORIZONTAL

ROOF

It is difficult to observe the detailed flow structure around an actual building because one generally cannot install sufficient instrumentation in an urban street. Nevertheless, full-scale measurements can provide us with useful information of the CHTC under natural conditions. We now discuss full-scale measurements of CHTC on horizontal roofs; the studies and their measurement conditions are listed in Table I. All CHTC values discussed here were obtained as the residual of the heat balance in which the net radiation and conductive heat fluxes were either directly measured or estimated. Hereafter, we call this method the thermal balance method. Although the CHTC was originally known to be dependent not only upon wind speed but also the temperature difference between surface and air, DT, the studies of Table I do not provide sufficient information on the relationship between CHTC and DT. The most empirical relations between CHTC and wind speed are therefore approximate curves based on results obtained under conditions of various thermal stability.

S S

D

4.6 · 10.9 45 · 25 45 · 25

22.2 · 15.3 2940 2370

4/covering mortar 3/covering mortar 3/covering mortar

2/asphalt sheet roofing 1/asphalt sheet roofing 1/asphalt sheet roofing

D D

D

Roof size (m2)

DT > 0 DT > 0

DT > 0 DT < 0 U10 < 2.5 m s)1, U1.5 15 C

DT < 0, DT > 0

Condition

b

‘D’ indicates direct measurement method. ‘S’ indicates SAT meter method. The size of the SAT meter is 12.9 m · 13.1 m. There is a parapet with the height of 0.24 m around the roof. c There is a parapet with the height of 1.2 m around the roof. d There is a parapet with the height of 0.25 m around the roof.

a

Hagishima d and Tanimoto (2003) Clear et al. (2003) Clear et al. (2003)

Urano and b Watanabe (1983) c Kobayashi (1994) Kobayashi and c Morikawa (2000)

Measurement methoda

Number of storeys Surface finish

TABLE I Building parameters for the CHTC measurements on the horizontal roof.

3 3

0.13, 0.6

10, 1.5 10, 1.5

0.6

Height of the reference wind speed (m)

556 AYA HAGISHIMA ET AL.

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By plotting the results in Figure 2, the CHTC is most sensitive to the height of the reference wind speed; both the value of the CHTC and the slope are larger for a lower reference height. To simplify the discussion, a reference speed at height x above a target surface will be called S+x. For example, the slope of the uppermost curve from Hagishima and Tanimoto (2003) with S+0.13 m is significantly steeper than the other curves. Since the CHTCs of Kobayashi (1994) with S+1.5 m and S+10 m are almost equal, the reference height of 1.5 m is assumed to be above the local boundary layer on the roof. The measured CHTCs under unstable conditions are in good agreement at wind speeds below 1 m s)1; in particular, their intercepts range within 6.4– 8.7. In contrast, at wind speeds below 2 m s)1, the measured CHTC of Kobayashi and Morikawa (2000) under stable conditions is significantly less than the other measurements. The curves of Urano and Watanabe (1983) and Hagishima and Tanimoto (2003) for S+0.6 m agree well in spite of the differences in roof size. This agreement suggests that the CHTC is relatively independent of roof size, but is inconsistent with the former remarks based on indoor experiments (e.g., Cole and Sturrock, 1977). In addition, this tendency is also inconsistent with the modelling of the local Nusselt number of a flat roof by Clear et al. (2003). The effect of the parapets around the target roofs is a possible factor. Nevertheless, since most of the real roofs have parapets, the dependence of CHTC on roof size should not be treated as the same as the results of indoor experiments using simple cube models. Nevertheless, as most real roofs have parapets, the roof-size dependence of the CHTC is probably not exactly the same as the analogous size dependence in cubicarray models.

h [W m -2 K-1 ]

25 20 15 10 5 0

0

2

U [m s-1 ]

4

6

Figure 2. Measured convective heat transfer coefficient h for horizontal building roofs at various wind speeds U. The grey thick line marks results from Urano and Watanabe (1983). Thick solid and broken lines mark results of Kobayashi (1994) for measurements done under unstable conditions with S+1.5 m and S+10 m, respectively. Thin solid and broken lines are from Kobayashi and Morikawa (2000) for measurements done under stable conditions with S+1.5 m and S+10 m, respectively. The lines with white and black circles are from Hagishima and Tanimoto (2003) with S+0.13 m and S+0.6 m, respectively. Further details of these studies are in Table I.

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Unfortunately since the measurement data for various roof sizes and the same height of the reference wind speed are not sufficient, the dependence of CHTC on roof size is only imprecisely known. In addition, there are insufficient measurements under stable conditions (Figure 3).

3.2. VERTICAL

WALLS

Cole and Sturrock (1977) pointed out that the CHTC of surfaces of an isolated cube varies with the wind direction, mainly because the wind speed near a wall varies with the wind direction, even for a constant wind speed above the canopy. However, Ito et al. (1972) made full-scale measurements, suggesting that the wind speed 0.3 m from the target surface can be used for the CHTC under various wind speeds and directions. To clarify the use of the CHTC for vertical walls, we now compare various measurements of CHTC for vertical building walls. The studies and their measurement conditions are listed in Table II. First, we compare the results of Loveday and Taki (1996) and Sharples (1984), where the height of the reference wind speed for both studies is 1 m (Figure 4a). (In this paper, we use the term ‘height above a surface’ to mean the distance away from the surface in the direction normal to the surface.) These two studies involved the measurement of the CHTCs of the walls of high buildings, which had few roughness elements such as eaves or verandas, based on the SAT meter method (the SAT meter method is described in the Appendix A). The measurement method and stability conditions of these two studies are assumed to be almost the same, though the size of the test plates (SAT meters) is different. In these studies, the effect of the wind direction on (b)

(a) Windward (L) Windward,18E (S) Windward,6c (S)

Leeward (L) Leeward,18E (S) Leeward,6c (S)

S+ 0.3m(N)

S+ 0.13m(H)

40

h [W m -2 K-1 ]

h [W m-2 K-1 ]

30 20 10 0

30 S+0.3m (I) 20 10 0

0

1

U 1 [m s-1 ]

U1-h

2

3

0

1 2 U 0.13 , U 0.3 [m s-1 ]

3

U0.13, U0.3 -h

Figure 3. Measured convective heat transfer coefficient of vertical walls on buildings at various wind speeds. ‘18E’ indicates data observed at the edge of the wall of 18th floor and ‘6c’ indicates the data observed at the central wall of the 6th floor. (H), (I), (L), (N) and (S) indicate the data of Hagishima and Tanimoto (2003), Ito et al. (1972), Loveday and Taki (1996), Narita et al. (1997) and Sharples (1984), respectively.

8

Loveday and Taki (1996) Narita et al. (1997)

1

2.4 · 2.4 m, smooth

W 9 m · H 28 m, with few roughness W 73 m · H 31.3 m surrounded by veranda

H 18 m with few roughness W 36 m · H 78 m

Size and shape of the target surface

Window surrounded by the veranda at 7th floor Centre

Centre of wall at 4th floor Centre and edge of wall at 6th and 18th floor 7th floor

Position in the target surface

D

H 0.8 · 0.5 m E 0.71 · 0.71 m

C 0.3 · 0.3 m C 0.25 · 0.25 m

Measurement method Size of test platea

1

1 0.3

Night time, DT > 0b Night time, DT > 0

Night time DT > 0b )8C
15C

Height of the reference wind speed (m)

a ‘C’, ‘D’, ‘E’ and ‘H’ indicate the coupled heated SAT meter method, direct measurement method, evaporation method with filter paper and heated SAT meter method. b Although the information about DT is not mentioned in the original paper, DT is assumed to be above zero because of the measurement method.

Hagishima and Tanimoto (2003)

18

Sharples (1984)

8–9

6

Ito et al. (1972)

Storeys of building

TABLE II Building parameters for the CHTC measurements on the vertical building wall. INTERCOMPARISONS OF EXPERIMENTAL RESEARCH

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h D / h D o f the most d o wnstream rod

the CHTC is small. However, the dependence of CHTC on wind speed is sensitive to the measurement position. Sharples’s (1984) results indicate that the CHTC at the edge of the building wall is much higher than that near the middle. The particular choice of target building also significantly affects the CHTC. If the SAT meter size affected the measured value, the CHTC of Sharples (1984) should be greater than that of Loveday and Taki (1996). However, Figure 4a indicates the opposite tendency: the CHTCs of Loveday and Taki (1996) are higher than those of Sharples (1984) under the same wind speed. This discrepancy is probably because the target building wall of Loveday and Taki (1996) was so narrow that the depth of the local boundary layer above the measurement point was smaller. The flow near a building wall edge is more complex than that of the inner part of the walls because of the separation vortex; this interpretation is supported by the results of Sharples (1984) in that the CHTC of the edge part of the building wall is larger than that of the centre part. Thus, wall size and shape are likely to influence the measured CHTC. In contrast, the effect of the wind direction on the CHTC is small, which is consistent with Ito et al. (1972). Next, we discuss three results where the heights of the reference wind speed are under 0.3 m; they were obtained for both windward and leeward conditions. All measurements were made near the centre of the wall (Figure 4b). The CHTC of Narita et al. (1997) is half that of Ito et al. (1972) even though the same height for the reference wind speed was used. The reason for the discrepancy may be the different size of the test plates, although the measurement conditions were also different. Hagishima and Tanimoto (2003) found that the vertical-wall CHTC and its slope with wind speed are larger than those for the horizontal roof even though both measurements used the same method and height of reference wind speed. Since the size of the target vertical wall in their study was about one-tenth of that of the horizontal roof, the different slopes are likely due to the different surface sizes.

1.6 1.5 roof H/W=0.5 (N) roof H/W=1 (N) windward wall H/W=0.5 (N) windward wall H/W=1 (N)

1.4 1.3 1.2

leeward wall H/W=0.5 (N) leeward wall H/W=1 (N) street H/W=0.75 (B) ex.A street H/W=0.75 (B) ex.B

1.1 1 0.9 0.8 0

2

4

6

8

10

12

row number from windward

Figure 4. Variation of mass transfer coefficient of 2-D canopy with fetch.

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4. Scale-Model Experiments It is well known that the flow structure in the roughness sublayer of an urban-like canopy can be divided into three groups according to the areal density of the roughness elements, hereafter roughness density. These are skimming flow, wake interference, and isolated flow (Oke, 1987). Thus, it is generally assumed that the CHTC for an urban surface depends strongly on the flow regime and the roughness density. To clarify the relation between the CHTC and the flow structure of an urban canopy, scale-model experiments should be a valuable tool because one can easily change the measurement conditions, such as the model shape, street pattern, and wind direction. In addition, if measurements are made in a wind tunnel, not only the CHTC but also the detailed flow structure around the models can be obtained simultaneously, a task that is almost impossible in full-scale measurements. For example, Meinders et al. (1998) found a relation between the flow pattern and the distribution of CHTC values on a three-dimensional (3-D) canopy, a relation that is greatly affected by the canopy shape. We compare the former scale-model experiments on the CHTC and the MTC of an urban canopy in this section. 4.1. EFFECT

OF FETCH

Barlow et al. (2004) used the naphthalene sublimation method to investigate the effect of fetch on the MTC of a 2-D canopy with H/W=0.75. The 2-D canopy of their experiment consisted of nine rods of square cross-section placed on the floor of the wind tunnel to simulate nine rows of buildings. They clarified that the MTCs downstream of the second or third row were nearly equal regardless of variations of the vertical profile of the approaching flow. In spite of the differences of the measurement method, model size, and upstream condition, the results of Narita et al. (2000) based on the evaporation method with filter paper show a similar tendency (Figure 4). The MTCs decreases significantly from the first row to the third row. Fluctuations in the MTC behind the fourth row are relatively small; the MTC ratios for the fourth row to that of the last row are generally 0.9–1.1. This tendency is consistent with the well-known fetch effect in the flow characteristic of roughness sublayers, as pointed out by Barlow et al. (2004). 4.2. EFFECT

OF CANOPY GEOMETRY

The effect of an approaching flow on the MTC of the canopy can be negligible downstream of about the fourth row, as mentioned in the previous

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section. Also, the effect of canopy geometry on the MTC becomes dominant in these regions. Here we compare two experiments that reveal the relationship between the MTC of a 2-D canopy surface and the model geometry. Figure 5 shows the relationship between the normalised MTC of a 2-D canopy and H/W, the ratio of model height to street width. Narita et al. (2000) confirmed that the relations between MTC and H/W have a similar tendency for wind speeds of 2, 4, and 6 m s)1, and adopted their average. Barlow et al. (2004) obtained the Stanton number from five cases with wind speeds ranging between 4 and 13 m s)1. For H/W1.0, where the flow regime is likely to be skimming, the values are roughly without change. According to the former wind-tunnel experiments on a sparse canopy, it is expected that the canopy with lower density has a larger area of separation and reverse flow above the roof top. Hence, the mass transfer should be greater with smaller values of H/W. For a dense canopy with skimming flow, the flow above the roof has little separation or reverse region, as shown by Brown et al. (2000). The smooth flow around the roof may cause a small effect of H/W on MTC. The value of MTC from Narita et al. (2000) is nearly the same as that from Barlow et al. (2004). The measured MTCs of a street are below 0.7, as found by Barlow et al. (2004), the only known study of the MTC for a street. Under conditions of wake interference (H/W=0.6), the MTC of the street is close to that of the leeward side of the building. On the other hand, the MTCs of a street under conditions of skimming flow (H/W=1 and 2) are larger than those of the leeward wall. We will make another comparison of the MTC of a street by roof(N) roof(B) street(B)

leeward(N) leeward(B)

windward(N) windward(B)

n o rmalized h D

1.2 1 0.8 0.6 0.4 0.2 0

1

2

3

H/W

Figure 5. Measured mass transfer coefficients for various values of height to width ratios H/W. (N) marks data of 2-D canopy 18H downstream of the edge of canopy arrangement by Narita et al. (2000). (B) is the data of 8th row by Barlow et al. (2004). The MTCs are normalised by the results in each case for the roof with H/W=1.

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Barlow et al. (2004) with the measured distribution by Narita et al. (2000) in the next section. The MTCs of the vertical windward wall from two experiments generally decreases with increasing H/W. In addition, the normalised MTC of the vertical windward wall by Narita et al. (2000) is close to 0.9 for the range of H/W=0.8–1.0. The relation between H/W and MTC of the windward wall of Narita et al., (2000) is similar to that of Barlow et al. (2004). However, most MTC values of Barlow et al. (2004) are larger than those of Narita et al. (2000) under the same H/W. The difference of these two experiments is especially large under the condition of H/W=2. The MTCs of the leeward wall for two experiments decreases with increasing H/W for H/W below 0.3 and above 0.7, related to regimes of isolated flow and skimming flow, respectively. The MTC values for a leeward wall of Barlow et al. (2004) are smaller than those from Narita et al. (2004 ) under the same H/W. This tendency is reversed from that of a windward wall. The difference between these two experiments is particularly large under the condition of H/W=2. The reason why the wall MTCs from the two experiments do not agree is possibly connected with the differences in model size, reference wind speed, surface roughness, and coefficients of molecular diffusion. The reason why the molecular diffusion coefficients are different comes from the fact that Narita et al. (2000) used water evaporation, whereas Barlow et al. (2004) used naphthalene sublimation. 4.3. DISTRIBUTION

OF TRANSFER COEFFICIENT ON EACH SURFACE

OF THE ROUGHNESS ELEMENTS

In this section, we compare the following three experiments on the distribution of CHTC and MTC of canopy surfaces. One experiment, by Aliaga et al. (1994), involved the CHTC of a 2-D canopy using the thermal balance method. In that study, ribs with a height of 25 mm were arranged on the wind-tunnel floor under the conditions of H/W=0.09 and 0.25. The Reynolds numbers based on the rib height are about 78,000 and 52,000. The second experiment, by Chyu and Goldstein (1986), involved the MTC of a 2-D cavity using the naphthalene sublimation method. The depth of the cavity was 6.35 mm and the Reynolds number based on the cavity depth is about 15,000. During the measurements, the entire surface inside the cavity and the floor around the cavity was coated with naphthalene. The third experiment, by Narita et al. (2000), involved the MTC of a 2-D canopy using the evaporation method (using filter paper). They measured the distribution of the MTC of a 2-D canopy with a model having ribs of height 60 mm. The Reynolds number based on the rib height is about 15,000. The MTC for the 2-D canopy was measured using filter paper

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60-mm wide and 10-mm long. The filter paper’s position on the model surface was changed for every measurement. Hence, the boundary condition of mass transfer of Narita et al. (2000) is not analogous to that of Chyu and Goldstein (1986). First, we discuss the data for the 2-D canopy of Narita et al. (2000); Figure 6 shows that the MTC for the roof is nearly independent of position and H/W. The MTC of the street under the condition of H/W=2 is much smaller than that of the wall and roof. Conversely, the MTC of the street is larger on average than that of the leeward wall for H/W=0.5–1. Also, the MTC on the street peaks at a distance of 0.5H from the windward vertical wall. On the leeward wall, the MTC values depend on H/W; for H/W=2, the MTC is larger for higher positions. In contrast, the MTC peaks at a height of 0.4H when H/W=1. Next, we discuss the differences between Narita et al. (2000) and Chyu and Goldstein (1986). In general, the trends are similar in both studies, but the MTC of Chyu and Goldstein (1986) is more sensitive to position than that of Narita et al. (2000). For example, for H/W=0.5 and 1, the MTC values in the street have peaks at about the same position for both studies. However, the peak values of Chyu and Goldstein (1986) are larger than those of Narita et al. (2000). The windward wall shows the same features. Such a tendency is likely to be caused by the difference in the boundary condition of mass roof

A D

windward B

leeward

E

C

street MTC / av erag ed MTC of street, H/W=1

A 3.5

leeward

B

H/W=0.5 (C) H/W=1 (C) H/W=0.67 (N)

3

street

C windward

D

3

4

roof

E

H/W=0.5 (N) H/W=1 (N) H/W=2 (N)

2.5 2 1.5 1 0.5 0 0

1

2

5

x/H

Figure 6. MTC measurements from models of Narita et al. (2000), marked (N), and Chyu and Goldstein (1986), marked (C). Reynolds numbers based on the model height are about 1.5 · 104 for both studies.

INTERCOMPARISONS OF EXPERIMENTAL RESEARCH

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transfer between the two experiments. Narita et al. (2000) used filter paper with a length of H/6 and a width of H. Hence, the measured MTC was not affected by advection from other source areas. On the other hand, in Chyu and Goldstein’s experiments, the entire model surface was coated with naphthalene. Therefore, some of the naphthalene sublimed from the upper surfaces would be blown into the bottom of the windward wall and also into the street near the leeward wall, thus causing the air near these regions to have a higher density of naphthalene and thus a smaller sublimation rate. The spatial average of the multipoint data of the MTC for a street from Narita et al. (2000) can also be compared with the results of Barlow et al. (2004), as presented in Figure 5. The data of Barlow et al. (2004) in Figure 5 were obtained by measuring the weight change of naphthalene, which was coated on the street surface. Thus, the resulting value is the spatially averaged MTC. Both studies were for MTCs of a 2-D canopy that had a sufficient number of rows on the windward side. Thus, the approaching flows in the wind tunnel are likely very similar for both cases. In brief, the MTC of a street by Barlow et al. (2004) for H/W=2 is overestimated and that for H/W=0.5 is underestimated, compared with the results of Narita et al. (2000). For example, the MTC of a street of Narita et al. (2000) is smaller than that of a leeward wall for H/W=2. The reverse tendency is observed for H/W=0.5. In contrast, the MTC for the street in Barlow et al. (2004) is larger than that for the leeward wall for H/W=2, and is almost the same as that of the leeward wall for H/W=0.5. For H/W=1, the results of both studies are similar. The disagreements are likely caused by the differences in the boundary condition of mass transfer. Narita et al. (2000) used the same source size for measurements under various H/W conditions, which have different street widths, and therefore Reynolds number based on the size of wet filter paper is constant under various H/W. In contrast, Barlow et al. (2004) measured the MTC of the naphthalene-coated street under various H/W conditions with the same value of H. Therefore, the Reynolds number based on the street source size of naphthalene differs from H/W. Therefore, the MTC of Barlow et al. (2004) is underestimated compared with that by Narita et al. (2000) for small H/W, where the street size is large, due to the effect of advection. Accordingly, in future measurements of MTC and CHTC of an urban-like canopy, it should be required to discuss both the effect of geometry and source size separately. For the case of a sparse canopy, measurements of MTC in one study have a different dependence on position (Figure 7). For H/W=0.09, Aliaga et al. (1994) confirmed that, based on visualization using yarn tufts, the flow regime is an isolated flow. The peak of the CHTC of Aliaga et al. (1994) is a distance of 5H from point B, which was consistent with the observed point of reattachment from the flow visualization. Also, the CHTC increases rapidly at a distance of 11H from point B; this result is connected with the separation point, which was observed at a distance of 10H from point B.

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The CHTC of Aliaga et al. (1994) for H/W=0.25, a flow regime that was observed to be wake interference, increases monotonically from point B to point C. In contrast, the MTC of Chyu and Goldstein (1986) has a sharp peak near point C. Since the MTC of Narita et al. (2000) for H/W=0.5 in Figure 6, which is also in the wake interference regime, has a similar tendency, the difference in measurement methods and Reynolds number may have caused the difference in results between Aliaga et al. (1994) and Chyu and Goldstein (1986). BETWEEN FULL-SCALE AND SCALE-MODEL EXPERIMENTS

4.4. COMPARISONS

Previous heat-transfer engineering studies have found that the Nusselt number for a flat plate under turbulent forced convection can be expressed as Nu ¼ CRem Prn ;

ð6Þ

where Nu is the Nusselt number, Pr is the Prandtl number, and Re is the Reynolds number; C, m and n are empirical parameters. Johnson and Rubesin (1949) showed that C=0.0296, m=4/5, and n=2/3 under the condition of turbulent flow with 0.5