九州大学大学院総合理工学府報告第 37 巻 第 2 号 19-26 頁 平成 28 年 2 月

Engineering Sciences Reports, Kyushu University
Vol. 37, No. 2, pp. 19-26, FEB., 2016

An experimental study on aerodynamic interaction
between a boundary layer generated by a smooth andrough wall and a wake behind a spire
Nurizzatul Atikha RAHMAT*1,2†, Aya HAGISHIMA*3, Naoki IKEGAYA*3,
Jun TANIMOTO*3†E-mail of corresponding author: ezatikha@gmail.com(Received January 22, 2016, accepted January 25, 2016)
A wind tunnel experiment to assess the flow characteristics of the wake behind a spire mounted
normal to the wind tunnel floor was conducted to clarify the interaction between the wake flow andthe wall shear boundary layer. To reproduce the contrasting boundary layer depth, two types ofwalls—a smooth wall and a regular cube array—were adopted; for each wall, the spanwise
distribution of the streamwise velocity was measured at two downwind positions and seven heights
within and above the wall boundary layer with and without a spire. The spanwise distribution of thewake generated by the spire far above the wall boundary layer with low turbulence agreed with thewell-known function for two-dimensional (2D) wake flow, derived theoretically from thegradient-diffusion model, despite the weak asymmetry of the inflow. In contrast, the spanwise
distribution of the wake within or near the outer edge of the wall boundary layer showed different
trends from that of the 2D wake flow. In the former, the expansion of the wake width is compressedin the lateral direction by the turbulence of the wall boundary layer and the velocity deficit of thewake is sustained far from the spire.
Key words:

1.

Wind tunnel, spire, wake flow, wall shear boundary layer

Introduction

The flow field around a building has been
an important research target in the windengineering field over the last half-century forrobust structural design and the safety ofpedestrians (e.g. Hunt1)). In particular, flow
around a slender tall building or long
structures such as cables can be categorized as
widely observed typical flow around a
two-dimensional bluff body in a free turbulent
flow, which has been one of the primaryresearch areas of fluid dynamics for a century(e.g. Townsend2), Taneda3), and Hunt4)).
In contrast, for the past few decades,
intensive studies on the aerodynamic nature of
the urban boundary layer have been also
conducted for better prediction of the urban
climate. From a climatological viewpoint, theurban atmosphere has been considered as aboundary layer over a fully rough wall 5) which
consists of several layers, including aroughness sublayer and an inertial sublayer(e.g. Rotach et al.6)). Within the inertial
sublayer, vertical profiles of environmental
variables such as velocity have been known to*1 Universiti Malaysia Pahang (UMP)*2 Department of Energy and Environmental
Engineering, Graduate student*3 Department of Energy and Environmental
Engineeringsatisfy the similarity theory characterized byseveral aerodynamic parameters including theroughness length and displacement height,
which depend on urban geometry 7). A series ofour recent experimental work (e.g. Hagishima
et al.8)) has been motivated by the interest in
the relation between urban geometry andthese aerodynamic parameters. In the courseof these experiments, the authors encounteredan interesting phenomenon related to the
aerodynamic
interaction
betweenthepreviously mentioned two types of flow,
namely, wakes behind a row of spires installedat the upwind of a wind tunnel and a roughwall boundary layer developing over a blockarray. The original reason for installing spires
was to produce large-scale turbulence similar
to natural atmospheric boundary layer having
sufficient depth even with the limitation ofshort streamwise length of wind tunnels9).
Meanwhile, several previous studies haveinvestigated the characteristics of flows thatsimultaneously involve both boundary layers
and wakes behind spires. Counihan10)
measured the distribution of the velocity
defect behind a 2D surface obstacle whose
height is assumed to be smaller than theboundary layer height (BLH, or alternatively,
δ). On the contrary, Castro11) studied the20

Aerodynamic interaction between boundary layer and wake behind a spirerecovery of the boundary layer in the wake of a
two-dimensional surface-mounted obstacle.
However, these studies were mainly focusedon the vertical structure of the turbulent
boundary layer, yet the flow structure in alateral distribution is rarely reported.
With this background, this paper presents
the results of a wind tunnel experiment on
modifications in the wake flow behind a spire
because of interaction with the wall boundary
layer.

2.

Experimental setup

2.1 Wind tunnel device
The experiment was conducted in a closed
return wind tunnel at the laboratory of theInterdisciplinary
Graduate
SchoolofEngineering Sciences, Kyushu University,
Japan. The wind tunnel has a working section
1 m high × 1.5 m wide with a streamwise
length of 8 m. The spatial uniformity of the
inflow condition was carefully adjusted bymeans of a honeycomb layer of 10 mm
hexagonal cells with a loss coefficient of 0.2
and 9 layers of mesh screens with an
open-area ratio larger than 0.57. The
placement of the mesh screens was determinedby a trial and error method employed in apreliminary experiment and by referring toprevious experimental work by Mehta12).
2.2 Measurement conditions
In the experiment, a quasi-quarter elliptic
spire shown in Figs. 1(a) to 1(f) with a heightof 0.8 m, which is higher than the wallboundary layer, was adopted as an obstacle forgenerating the wake flow. The depth of thespire is 0.04 m (hereafter, WS) up to a verticalheight of 0.25 m.
The spire was installed in the upwind
centre position of the wind tunnel floor, andthe distributions of the streamwise velocity
behind the spire were measured at two
leeward positions: namely, the near wakeregion A (an area just behind the spire) andthe far wake region B as shown in Fig. 2.
Two types of floors (to obtain contrastingboundary layer depth) were used in the windtunnel for generating the turbulent shear
boundary layer: the first one was a smoothsurface where flat plastic plates covered thefloor of the wind tunnel with a streamwise
length of about 3.4 m, and the other was arough wall consisting of a staggered cubicalarray with a height of 25 mm (hereafter, H)
and a packing density λp of 17.4%. The
streamwise length of the smooth wall and theblock array was about 136 H and 85 WS.
2.3 Instrumentation and measurement
positions
The vertical distribution of the streamwise
velocity was measured on a laterally centred
point at the two positions A and B for both thesmooth and rough wall conditions without aspire. The measurement heights were from 0.5
H to 20 H with an interval of 0.1 H. Based onthese measurements, the boundary layerheight for each position was determined as
described in section 3.1.
In addition, the lateral distribution of thestreamwise velocity at positions A and B were
measured with and without a spire at sevenelevations including both below and above theBLH. The measurement heights below theBLH range from 0.25 δ to 1.25 δ with aninterval of 0.25 δ; 15 H and 20 H were adoptedz(a)Position A

Plan viewy800

WS = 40
x

1500

400

(b)

(c)

(d)

400

379

377

360

330

x y x y

x y

x y

x

40

39

38

33

40

Flow
0

y

(f)

(e)

900

x
Centre point
1240

Side viewyFig. 1. (a) Schematic figure of a spire and its dimensions;
top view of the spire base (wedge-shaped) showing
vertically different widths ((b) z = 0; (c) z = 250 mm; (d) z =275 mm; (e) z = 375 mm; (f) z = 500 mm). All units in mm.

1000

Position B

2193

Position of spire installation

z

800

0
400

x

Smooth surface or 17.4% block array25

Fig. 2. Schematic figure of test section and measurement
positions. All units in mm.

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九州大学大学院総合理工学報告

as the heights above the BLH. The spatial
resolution of the measurement in the spanwise
direction was 5 mm (= 0.2 H) for the range of–14 H < y < 14 H and 10 mm (= 0.4 H ) for therange of both –18 H < y < –14 H and 14 H < y <18 H, and the total number of measurement
points in the lateral line was 162.
The streamwise velocity was measured
using a split-film anemometer (Dantec
Dynamics, 55R55), which was placed at eachmeasurement position by a 3D auto traverse
system. The measurements were performed
with a reference stream velocity of
approximately 8 ms-1. The reference stream
velocity (x, y = 0, z = 20 H) was measured ateach lateral path to check the time variation of
the sensitivity of the hot-wire anemometer.
The measurement frequency and period were1000 Hz and 30 s, and the data were recorded
using a CTA unit (Kanomax, Model 1101) anda data logger (Graphtec, GL900). The
calibration of the hot-wire anemometer was
performed at least every 24 h using a pitot
tube.

3.

第 37 巻第2号

21

case, and it increases in the order of thestreamwise position because of the boundary
layer development.

(a)

(b)
A
B

A
B

(c)

(d)

Results and discussion

3.1 Vertical profiles of velocity for the smoothand rough surfaces without a spire
Fig. 3 shows the vertical profiles of themean, standard deviation, and skewness of thestreamwise velocity at the lateral central point(y = 0) of positions A and B for both wallconditions without a spire. The mean windprofiles over the smooth and rough surfaces
shown in Figs. 3(a) and 3(b) exhibit a clear
change in the velocity gradient at heights ofaround 3 H and 5 H, respectively, and thevelocities above these heights are almost
constant for both conditions. This difference ofheight between the smooth surface and theblock array is due to the difference in surface
drag. In addition, the height at which thechange in the velocity gradient occurs
increases with an increase in the streamwise
distance from A to B owing to the developmentof a boundary layer.
With regard to the standard deviation, thedata for the smooth wall case show the highest
values at the lowest measurement height, andthe values gradually decrease with the height.
In contrast, the values for the rough wall case
exhibit a peak at a height of around 1 H
because of the block array. The height where
the standard deviation is about 1% in thesmooth case is lower than that in the rough

(e)

(f)

Fig. 3. Vertical velocity profiles for the mean direction overboth surface conditions at the centre point of A and B forsmooth surface: (a) normalized mean velocity, (c)turbulence intensity, and (e) skewness of U; for roughsurface with a staggered cubical array with λP = 17.4%: (b)normalized mean velocity, (d) turbulence intensity, and (f)skewness of U.
Table 1 Boundary layer height determined based on anegative peak of skewness of streamwise velocity undercases without a spire.
Streamwise position

A

B

Smooth surface

60.0mm (2.4 H)

77.5mm (3.1 H)

Rough surface

103mm (4.1 H)

138mm (5.5 H)

In contrast, as shown in Figs. 3(e) and 3(f),the skewness of the streamwise velocity near
the surface decreases with the height, shows a

22

Aerodynamic interaction between boundary layer and wake behind a spire

sharp negative peak, and returns to aroundzero for both conditions. This trend isconsistent with previous experimental data by
Raupach13). By comparing the profiles of theskewness with those of the mean wind, we cansee that the height of the negative peak in theskewness profiles is consistent with the heightat which the mean velocity becomes almost
independent of the height.
Considering the fact that the mean windprofile far above the wind tunnel floor shows aweak height dependency, it is difficult toaccurately determine the 99% boundary layerheight. Hence, we treated the height of thenegative sharp peak of the skewness profile as
the BLH δ for the following analysis. Table 1
summarizes the BLH determined at eachposition for all cases.

(a) Smooth surface

3.2 Spanwise distributions of velocity
Fig. 4 presents the velocity distributions inthe spanwise direction for the smooth andrough surfaces with and without a spire atposition B for several chosen heights. The
velocity is normalized by Eq. (1) as follows.

Un(x,y,z) = U(x,y,z)/U(x,y = −18H,z = 20H) (1)The reference position of the normalization
is at y = −18 H, z = 20 H, where the influenceof the spire should be minimal. As shown in
Fig. 4(a), the velocity profile for the smoothcase without a spire at 20 H (far above theboundary layer) is almost laterally constantwith a relative standard deviation of 0.7%.
However, the profiles measured inside theboundary layer (0.25 δ and 0.5 δ) show
negatively sloped curves with a larger relative
standard deviation of 0.8%.
The profiles of the smooth case with a spireshow a clear effect of the wake of the spire, as
expected. A negative peak in velocity due tothe spire can be seen at y = 0 for the heights
0.25 δ and 0.5 δ, and two positive peaks can beobserved at y = ±6 H for these heights. With
regard to the data far above the wall boundary
layer, the position of maximum velocity deficit
is slightly shifted in the negative y direction
from the position of the spire (y = 0), and there
is no positive peak. The trend for the roughsurface case, shown in Fig. 4(b), is almost
similar to that for the smooth case; however,the profile of the case without a spire at 0.25 δ
and 0.5 δ show a larger relative standard
deviation of 1.9% and 1.1%, respectively,
compared with that of the smooth condition.

(b) Rough surface
Fig. 4. Spanwise distribution of velocity at B (x = 87.7 H)

20z /H (-)

z /H (-)

15
10
5
-10

0

y /H (-)

10

-10

0

y /H (-)

10(a) Smooth surface(b) Rough surface
Fig. 5. Contours of the standard deviation σU (x, y = −18 H,
z = 20 H) of the streamwise velocity for the cases with aspire at B (x = 87.7 H).

平成 27 年度

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九州大学大学院総合理工学報告

z /H (-)

z /H (-)

15
10
5
-10

0

y /H (-)

10

-10

0

y /H (-)

10(a) Smooth surface(b) Rough surface
Fig. 6. Contours of the skewness of the streamwise velocity
by the spire at B (x = 87.7 H).

The spatial distributions of the standard
deviation and skewness of the streamwise
velocity in the lateral-vertical plane at position
B for the smooth and rough cases with a spire
are shown in Figs. 5 and 6, respectively. The
standard deviation of both cases monotonicallyincreases as the position approaches both thefloor and region behind the spire, anddark-coloured regions show weak asymmetricpatterns. On the contrary, Fig. 6 indicates thatthe wake of the spire and the wall boundary
layer are rimmed with dark colored regionswith strongly negative skewness of around−1.6 to −2.0.
3.3 Spanwise variations of the velocity deficit
The 2D wake in a free shear layer is widely
characterized by the velocity deficit, which isthe velocity difference between the backgroundand wake regions. However, considering thenon-uniformity of the inflow conditions of thepresent experiment as shown in Fig. 4, for thefollowing analysis, we adopted the differenceinthenormalized
velocity
betweenexperiments with and without a spire as thevelocity deficit, which is expressed by Eq. (2).

∆Un = UnNS(x,y,z) − UnS(x,y,z)

第 37 巻第2号

23

the negative y direction (y = −0.8 H, at aheight of 20 H), and gradually decreases along
both lateral directions. This trend is almost
similar to the well-known wake flow behind a
bluff body (e.g. Schobeiri14)). The maximum
velocity deficit at around y = 0 decreases withthe decrease of the height. In addition, ∆Un
does not completely converge to zero even at
the furthermost positions (y = 18 H), possibly
due to the non-uniformity of the inflow otherthan by the spire. In contrast, positive peaks
at around y = 0 for the other four heights lower
than the BLH are much smaller than thoseabove the BLH. Furthermore, two negative
peaks can be observed at y = ±4 H, and theseaccelerated velocities gradually recover withincreasing lateral distance from y = 0.
Although such distribution patterns might bepartially caused by the asymmetric inflow of
the wind tunnel, it is obvious that the
spanwise profiles of ∆Un below the BLH aremuch different from those far above the BLH.

(a) Position A (x = 49.6 H)(2),

where superscripts S and NS refer to values
for the cases with and without a spire,
respectively. Fig. 7 shows the spanwise
distributions of the velocity deficit ∆Un definedby Eq. (2) at positions A and B for the smoothcondition.
As can be seen from the result at position A(Fig. 7(a)), ∆Un for heights above the BLH,
such as 1.23 δ (= 3.0 H), 15 H, and 20 H, showsa positive peak. However, its position isslightly shifted from right behind the spire to(b) Position B (x = 87.7 H)
Fig. 7. Velocity deficit by the spire for smooth surfaces.

On the contrary, at position B (Fig. 7(b)),
positive peaks in ∆Un near y = 0 at heights
above the BLH (15 H and 20 H) are about 23%
smaller compared to those at position A, andthe changes in the slopes of the distributions
are more gradual. Such a tendency in therecovery of the velocity deficit according to thestreamwise distance is a common feature of

24

Aerodynamic interaction between boundary layer and wake behind a spire

wake flow. In contrast, the values of thepositive peaks for the other five heights from0.25 δ to 1.25 δ are almost the same as those at
position A. In other words, the velocity deficit,
due to the spire, far above the BLH with low
turbulence gradually recovers as thestreamwise distance increases, whereas thatwithin the wall shear boundary layer withhigh turbulence is sustained far away from thespire.

the smooth surface case (Figs. 7(a) and 7(b))
and downward position B of the rough surfacecase (Fig. 8(b)). Furthermore, at downwind
position B (Fig. 8(b)), the acceleration ofvelocity below the BLH at around y = ± 6 H isevident compared to position A (Fig. 8(a)).
Although determining the precise reason forthis tendency is difficult due to the
non-uniformity of the inflow condition, theinstallation of the spire might be a cause forthe flow acceleration15).
It is known that the velocity deficit due to a
2D obstacle in a free shear flow can be
expressed by a self-similar general function
based on the gradient-diffusion model16) as
follows:g(y/y0.5) = exp (-α (y/y0.5)2)(3),

where α is an empirical constant and y0.5 is thehalf wake width.
(a) Position A (x = 49.6 H)(b) Position B (x = 87.7 H)
Fig. 8. Velocity deficit by the spire for rough surfaces.

The velocity deficit of the rough surface
case, shown in Fig. 8, is almost consistent withthe above-mentioned tendency for the smoothcase. The distributions of ∆Un far above theBLH for the rough case exhibit a positive peaknear y = 0, and the deficit becomes mild at the
downward position B compared with positionA, similar to the smooth surface condition.
However, the velocity deficit profiles of therough surface case are significantly higher
than the corresponding profiles for the smoothsurface case, probably due to the underlying
blocks and its canopy flow, which hinder thedevelopment of a wake. Similar results werereported for shallow turbulent wakes
generated on smooth and rough surfaces by
Tachie and Balachandar15).
With regard to the rough case below theBLH at position A (Fig. 8(a)), ∆Un at y = ± 18 H
appears to be positive in contrast to the data of(a) Smooth surface(b) Rough surface
Fig. 9. Normalized velocity deficit by the spire at position
B (x = 87.7 H).

Fig. 9 shows a comparison of the spanwise
distributions of the velocity obtained by thisequation and that obtained by themeasurements at position B. The constant α,

平成 27 年度

九州大学大学院総合理工学報告

included in Eq. (3), was determined to be 2.76
and 2.68 for the smooth and rough cases,
respectively, based on the measured data at 20
H. As previously mentioned, the spanwise
profiles of the velocity deficit, shown in Figs. 7
and 8, are not perfectly symmetric. Thus, inthe vertical axis of Fig. 9, the velocity deficit∆Un is reduced by the minimum value of ∆Un
in the lateral measurement line (hereafter,∆Uminn), and normalized by the value ( ∆Umaxn ∆Uminn), where ∆Umaxn is the maximum valueof ∆Un in the lateral measurement line.
Henceforth, we refer to (∆Umaxn − ∆Uminn) as
the normalized maximum velocity deficit for
simplicity. The horizontal axis is the spanwise
distance normalized by the half wake widthy0.5. y0.5 is determined by the distance between
two positions where ∆Un = 0.5(∆Umaxn − ∆Uminn),
in accordance with the vertical axis. Becauseof the slightly heterogeneous inflow condition,
the origin of the spanwise direction was
shifted by yP to align the peak of (∆Un −∆Uminn)/(∆Umaxn − ∆Uminn) with the coordinate
origin.
The data for both surface conditions at theheights of 15 H and 20 H agree with theestimations from Eq. (3), except for the slight
discrepancy at ∣(y − yP)/y0.5 ∣> 1, where it does
not coincide with 0. This indicates that in thepresent experiment the flow structure far
above the wall boundary layer can be
categorized as a typical 2D wake of a bluff
body in a free stream in spite of the
non-uniform inflow condition. On the contrary,
the normalized profiles of all heights below
1.25 δ show significant departure from Eq. (3).
In particular, the data at 0.25 δ, 0.5 δ, and 0.75
δ show remarkably different trends from theaccelerated velocity at ∣(y − yP)/y0.5 ∣> 0.5.
Although it is not certain whether such flow
acceleration is caused by either theasymmetrical lateral distribution of the inflow
or the interaction between the wake and thewall boundary layer, the discrepancy of theflow field within and above the BLH is evident.
3.4 Vertical distributions of the maximum
velocity deficit and half wake widthFig. 10 indicates how vertical distributionsof the normalized maximum velocity deficit
are modified with the change of streamwise
distance. The vertical axis is the heightnormalized by the BLH at each streamwise
position.
The normalized maximum velocity deficit
increases with height from near the floor,

第 37 巻第2号

25

shows a steep positive peak around a height of0.75 δ, and rapidly reduces up to a height of
1.25 δ for all positions. With regard to the data
above the wall boundary layer, the normalized
maximum velocity deficit drastically increases
with the height. In addition, for both surface
conditions, the normalized maximum velocity
deficit above a height of 1.25 δ clearly shows adecrease with the streamwise distance, andthis is the well-known recovery process of thewake in a free shear flow. In contrast, the data
below the wall boundary layer indicate thatthe maximum deficit increases from position A
to downwind position B.

A
B

(a)

Smooth surface

AB(b) Rough surface
Fig. 10. Change of the maximum velocity deficit withrespect to height.

The data of the half-wake width are shownin Fig. 11 in the same manner as Fig. 10. For
both surface conditions, the data of thehalf-wake width above the BLH at position B
is larger than the corresponding data at
position A. Furthermore, the data of thehalf-wake width increase with the height fromnear the floor, show a small peak at theheights of 1.00 δ and 0.76 δ for smooth andrough surfaces, respectively, then slightly
decrease at around BLH (Fig. 11(b)), andfinally rapidly increase above BLH. It isnoteworthy that the half-wake width within

26

Aerodynamic interaction between boundary layer and wake behind a spire

the wall boundary layer is much smaller thanthat above the BLH. In other words, theexpansion of the wake in the lateral direction
behind a slender obstacle is compressed in thelateral direction by the underlying wall
surface and wall boundary turbulence, andconsequently, the velocity deficit of the wakebecomes steep compared to the ordinary 2D
wake flow in a free shear flow.

ABvelocity deficit within the wake region is moresignificant compared with the data above thewall boundary layer. Although the present
experimental data indicate an obvious
difference in the profiles of the wake flow
within and above the wall boundary layer, adetailed understanding of the features of thesedifferences has not been completely attained
because of certain limitations mainly causedby the non-uniform inflow condition of thewind tunnel. The turbulent statistics of not
only the streamwise velocity component, butalso the lateral component would be essential
for elucidating the mechanism of theinterference of the spanwise expansion of thewake due to the wall boundary turbulence, andwill be one of our future tasks.
References(a) Smooth surface

AB(b) Rough surface
Fig. 11. Change of the half wake width y0.5 with respect toheight.

4.

Conclusions

The present study was designed toinvestigate the aerodynamic interaction
between the wall shear boundary layer and thewake flow generated downwind of an isolated
slender obstacle normal to the wall. The
detailed measurements of the distributions of
the streamwise velocity above the smooth andrough wall surfaces, with and without a spire,
were conducted in a wind tunnel. The
spanwise variations of the velocity behind aspire above the wall boundary layer show good
agreement with the 2D self-similar profile fora 2D wake flow in a free shear flow, despite theweak asymmetrical inflow condition of thewind tunnel. In contrast, the spanwise profilesof the velocity within the wall boundary layer
show clear discrepancies from the 2D wakeflow: the expansion of the wake width in thelateral direction is compressed, and the1) Hunt, J. C. R. The effect of single buildings andstructures. Phil. Trans. Roy. Soc., A, 269, 457–467(1971).
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