*Corresponding author: Manato Yamaguchi, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasugakouen 6-1, Kasuga, Fukuoka, Japan e-mail: 2es09190m@s.kyushu-u.ac.jp

A WIND TUNNEL STUDY ON DRAG COEFFICIENT FOR COMPLEX ARRAYS OF VARIOUS TYPES OF ROUGHNESS ELEMENTS

Manato Yamaguchi*, Jun Tanimoto*, Aya Hagishima*, Yoshiki Kikuchi*, Sheikh Ahmad Zaki**, Akashi Mochida*** * Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Japan.

** Department of Mechanical Engineering, College of Science and Technology, University of Technology Malaysia. *** Department of Architecture & Building Science, Graduate School of Engineering, Tohoku University, Japan.

Abstract Drag coefficients (Cd) and vertical wind profile for regular arrays with several types of obstacles are measured in a systematic series of wind tunnel experiments to obtain the effect of complex geometry of obstacles on Cd and air flow dynamics. Three types of roughness are used for this study. The first two of them (RB-1.5 and RB-3.13; urban-like roughness) are regularly arrayed rectangular blocks, and regularly array of small human-shape figures is the last one (HM). Based on the comparison between RB-3.13 and HM, it might be likely that the geometric complexity such as secondary morphemic feature, bossy surface etc can be negligible if concerned on Cd.Moreover the normalized peak of turbulent intensity max*TI for various measurement conditions indicates that friction velocity u* should be an effective scaling parameter for turbulent flow statistic in roughness sublayer.

Key words: Drag coefficient, The normalized peak of turbulent intensity, Complex geometry

1. INTRODUCTION

In recent years, it is the one of important issues how urban geometry affects on the airflow, dispersion and heat transfer in urban areas. Thus various researches using both wind tunnel experiment and computational fluid dynamics have been performed. Most of these works focus on the effect of layout, spacing, and height variability of obstacles using regular arrays of rectangular blocks, however real urban surface consists of not only rectangular buildings but also other various obstacles with complex shape, such as vehicles, vegetation, pedestrians, and signs. Therefore we investigated the effect of complex geometry of each obstacle of regular arrays on several aerodynamic parameters, such as drag coefficient (Cd), roughness length (zo) and displacement height (d).

2. EXPERIMENTAL SET-UP

2.1. Instrumentation

The experiment was conducted in the closed circuit wind tunnel with a test section of 1m high, 1.5m wide and 8m long. A side view of the experimental setup is shown in Fig.1. The horizontal drag force acting on the array fixed on the floating element (720mm720mm) was directly measured with a strain gauge (Interface, MB5), and the reference wind velocity was measured using a Pitot-static tube, which was positioned at the height of 500mm above the leeward edge of the floating element. Moreover the vertical profile of the mean wind velocity above the array was measured with a hot-wire split film anemometer. The measurement of wind profile was performed at 4 points in a horizontal plane of the central unit area of the floating element, as shown in Fig.2, and we estimated the spatially averaged mean profile at 20 different altitudes. The experiments of drag force and mean wind profile were performed under the condition of the reference wind velocity 8ms-1.

The seventh International Conference on Urban Climate, 29 June - 3 July 2009, Yokohama, Japan

Fig.1 Schematic side view of experimental setup Fig.2 Measurement points of vertical wind profile

2.2. Definition of Geometric Parameter

We use five geometric parameters to identify the arrays. Three of those are the parameters to explain the roughness packing density, namely plan area index p, frontal area index f, and volume index v. The latter two are the parameters to explain the morphological characteristic of each obstacle, namely aspect ratio based on projected area p, and aspect ratio based on the volume of obstacle v. They are defined by the following expressions;

VHA

AA,

HAV,

AA,

AA

==

=== fp

fp

dd

ff

d

pp v,v

where, Ap is horizontal projected area of obstacle, Af is vertical projected area of obstacle from the mean wind direction, V is volume of the obstacle, H is obstacle height, and Ad is unit plan area for one obstacle (see Fig.2). p is always larger than v for obstacle with complex configuration such as the human models.

2.3. Rough Surface

The three types of staggered arrays are used for the measurement, as summarised in Table.1. First one consists of the six types of human models with the p of 3.05 and v of 7.8, hereafter HM. The second is the arrays of rectangular blocks with p = 1.5; hereafter RB-1.5. The last is the arrays of slender rectangular blocks with p = 3.13; hereafter RB-3.13. The latter two types of block arrays are used in order to investigate the aerodynamic effect of slenderness of obstacle. The measurement on arrays HM and RB-3.13 was done under four p conditions, and that on RB-1.5 was done under five p conditions. The heights of three types of obstacle are almost same, thus we call the length 37.5mm 1H as the standard length scale of roughness. Because of insufficient the human models, we could not arrange those on the whole of the floating element and the windward area (area A1, A2, B1, B2 and C as shown in Fig.3). Therefore, we arranged the target arrays for measurement on only the areas A1 and A2, the length of fetch arranging the target arrays is approximately 20 times the height of the arrays, and areas B1, B2 and C were covered with array RB-1.5 (p =17.4%) for all through the experiments. We estimated the total surface shear stress for the target array using the area ratio of A1 to B1, by proportional average of both measured drag force for the target array and measured drag force for the array RB-1.5 (p =17.4%). The estimation accuracy was confirmed for the array HM (p=4.7%) in a preliminary experiment. The measurement error caused by this procedure was 1.88%, thus it can be assumed to be negligible for the following discussion.

Table1. Obstacles used for the measurement

Split-film anemometer

Wind

13.3

H

Entrance

13.3

H

Float(720mm720mm)

Stain gage

Pitot-tube

Roughness

Split-film anemometer

Wind

13.3

H

Entrance

13.3

H

Float(720mm720mm)

Stain gage

Pitot-tube

Roughness

Human models (HM) RB-1.5 RB-3.13Array

Verticalview

Human models (HM) RB-1.5 RB-3.13Array

Verticalview

Wind

1

2 3

4

Unit plan area

Wind

1

22 3

4

Unit plan area

The seventh International Conference on Urban Climate, 29 June - 3 July 2009, Yokohama, Japan

Table2. Details of the obstacles

Fig.3 The schematic plane view of the array

3. RESULTS AND DISCUSSION

3.1. Drag Coefficient

We use the following equation to determine the drag coefficient;

,2 220H

d SUFC =

where S is the plan area of the floating element, U20H is the reference wind velocity, is the air density and F is magnitude of the drag force acting on the arrays. Figures 4 and 5 indicate the measured Cd for various p. and f, respectively. Firstly, we make a comparison between two rectangular block arrays, namely RB-1.5 and RB-3.13. Cd values for RB-3.13 are larger than those for RB-1.5 under the condition of p below 10%, it is caused by the fact that RB-3.13 has larger frontal area acting on the drag force compared with RB-1.5 for same p condition. This effect is remarkable under the isolated flow or wake interference flow, those take place over the low packing density. This explanation is consistent with the fact that Cd values for both arrays are almost same for p over 15%. In addition, f of both arrays showing Cd peaks for RB-1.5 and RB-3.13 almost same. The peak of Cd is generally assumed to be an evidence of the transition of flow regime from wake interference to skimming, hence the result indicates that f is an appropriate parameter to explain the transition of flow regime for the rectangular block array. Next, we make a comparison between HM and RB-3.13, the obstacles of these arrays have same p condition. The peaks of Cd for HM and RB-3.13 appear at different values of p, and the maximum Cd for HM array is much larger than that for RB-3.13 array. Such a different tendency implies that the arrays of obstacles with different morphology but with same geometric parameter p based on projected area generate different aerodynamic effect. Hence parameter p is not applicable to explain the effect of complexity of the shape of obstacle. Figure 6 shows the measured Cd for various volume index v. The peak value of Cd becomes larger in the order, RB-3.13, RB-1.5 and HM, and v value where Cd value takes a peak decreases in the same order. Such a tendency is consistent with the magnitude of v (aspect ratio defined by volume) for these arrays. The values of v for RB-3.13, RB-1.5 and HM are 1.5, 3.13, and 7.8, respectively. We have not yet obtained the data for rectangular block array with the value v of 7.8. Hence we cannot clarify whether the complex figure of obstacles or slenderness expressed by high is the main cause for the large drag force of HM. Therefore we will do a similar measurement using rectangular array with the same v value of HM in the future.

1990[mm]

720[mm]

720[mm]

410[

mm

]

2320[mm]

1520

[mm

]

Wind

720[

mm

]

: area A1

: area B2: area A2

: area B1 : area C

Float

1990[mm]

720[mm]

720[mm]

410[

mm

]

2320[mm]

1520

[mm

]

Wind

720[

mm

]

: area A1

: area B2: area A2

: area B1 : area C

Float Array H[mm] p v V[mm3]HM 35.7 3.05 7.8 722

RB-1.5 37.5 1.5 1.5 2.34104

RB-3.13 37.5 3.13 3.13 5.4103

The seventh International Conference on Urban Climate, 29 June - 3 July 2009, Yokohama, Japan

00.5

11.5

22.5

0 5 10 15 20p[%]

Cd

102 [

-]HMRB-1.5RB-3.13

0

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60f[%]

Cd

102 [

-]

HMRB-1.5RB-3.13

0

0.5

1

1.5

2

2.5

0 10 20 30 40v[%]

Cd

102 [

-]

HMRB-1.5RB-3.13

Fig.4 Cd-p Fig.5 Cd-f Fig.6 Cd-v3.2. Turbulence statistics of velocity of mean direction

Figure 7 Indicate the measured vertical profiles of turbulent intensity for arrays HM (p = 4.7%). They show the keen peak at the height of obstacles; it is consistent with the previous works (e.g. Kastner-Klein and Rotach 2004, Reynolds and Castro 2008). To confirm the relation between surface shear stress and turbulent intensity, we estimated the normalized peak of turbulent intensity max*TI using spatially averaged value at 1H, which is expressed by following equations;

( ) ,3

, max,4max,3max,2max*TI*TI*TI*TI

*u

z*TI u ++==

where u is standard deviation of wind velocity of mean direction, u* is the friction velocity determined by drag force measurement. max,i*TI is the maximum ( )z*TI at each measuring point i (see Fig.2). Figure 8 indicates the estimated max*TI for the various measured p. max*TI is almost constant for p and has little dependence of the shape of obstacles. It indicates that u* is the effective scaling parameter for turbulent flow statistic in roughness sublayer, as we expected.

02468

101214

0 0.5 1 1.5 2TI*[-]

z/H

[-]

Fig.7 Vertical profiles of turbulent intensity Fig.8 Spatially average of turbulence intensity 4. CONCLUSION The drag force and mean wind profile over the three types of arrays were measured, and the effect of complex geometry of obstacles was discussed in detail. That is summarized as follows. Firstly, the arrays of obstacles with different morphology but with same geometric parameter p based on projected area generate different aerodynamic effect, hence parameter p is not appropriate to estimate the aerodynamic effect of complex shape of obstacle. Secondly, the effect of slenderness of obstacles, primarily defined by v, is possibly significant on Cd,whereas geometric complexity such as secondary morphemic feature, bossy surface etc can be negligible. Lastly the peak value of turbulent intensity scaled by friction velocity is almost constant for various packing density and different shape of obstacles.

References Kastner-Klein and Rotach (2004) Mean flow and turbulence characteristics in an urban roughness sublayer. Boundary-Layer Meteorology 111: 5584, 2004. Reynolds and Castro (2008) Measurements in an urban-type boundary layer. Experiments in Fluids 45 : 141-156, 2008.

0

0.5

1

1.5

2

2.5

0 10 20 30 40p[%]

HMRB-1.5RB-3.13

0

0.5

1

1.5

2

2.5

0 10 20 30 40p[%]

HMRB-1.5RB-3.13

The seventh International Conference on Urban Climate, 29 June - 3 July 2009, Yokohama, Japan