12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022]]STATISTICAL CHARACTERISTICS OF THREE-COMPONENT TURBULENCEINTENSITIES FOR HIGH REYNOLDS NUMBER PIPE FLOW USING LDVMarie Ono
National Metrology Institute of Japan
Advanced Industrial Science and Technology
1-1-1 Umezono, Tsukuba, Ibaraki, Japan
ono.marie@aist.go.jp

Noriyuki Furuichi
National Metrology Institute of Japan
Advanced Industrial Science and Technology
1-1-1 Umezono, Tsukuba, Ibaraki, Japanfuruichi.noriyuki@aist.go.jp

Yoshiyuki Tsuji
Graduate school of engineering
Nagoya University
Furocho, Nagoya, Aichi
c42406a@cc.nagoya-u.ac.jp

ABSTRACTIn this study, we report three components (streamwise,
wall-normal and spanwise) turbulence intensity profiles fromReτ = 990 to Reτ = 20750 using laser Doppler velocimetry(LDV) at high Reynolds number actual flow facility (Hi-Reff).
These profiles were measured by changing the angle of themeasurement line and the angle of the beam with respect topipe. The LDV specific issues such as the spatial resolution
and the fringe distortion are considered to measure reliable
experimental data. These issues that influences turbulence
statistics are evaluated by a wire rotary device and reflected tothe measurement by new correction method. The corrected
results of 3 components turbulence intensity profiles agree
well with the previous DNS data until Reτ = 8000 and with theprevious experimental data at high Reynolds number. The
streamwise and spanwise turbulence intensities growincluding the peak values depending on Reynolds number up
to Reτ=20750. Moreover, streamwise inner peaks are good
agreement with previous experimental results of TBL. On thewall-normal turbulence intensities measurement, the peakvalues asymptote to (v +)2 = 1.3 with Reynolds number
increases. The logarithmic region or constant region are
clearly observed in 3 components for Reτ > 11200, The
positions are same between streamwise and spanwise
component (y/R = 0.05~0.25), but different with the wallnormal component (y/R = 0.015~0.07).

et al., 2017). The logarithmic region in the outer region, which
is based on attached eddy model (Perry & Chong, 1982), isclearly observed for the streamwise components at highReynolds number, however, it has not been well discussed forthe wall-normal and spanwise component including theposition where it is emerged. High Reynolds number data isnecessary to establish these scaling laws. However, the lack ofreliable experimental data because large-scale facilities are
required and we cannot avoid the issues from velocity
measurement devices for high Reynolds number experiments.
The main objective of this study is to establish the scaling
law for the turbulence intensity profile of three components.
To this end, the issues for the measurement devise, which islaser Doppler velocimetry (LDV), are well consideredespecially for the spatial resolution and the fringe distortion,
applied new approach to correct the results measured at highReynolds number (Ono et al. 2022). Based on those precise
measurement, we discuss on the Reynolds number
dependency of the streamwise inner peak and the logarithmic
behaviour of three-component turbulence intensity profiles in
the pipe flow.

LDV SPECIFIC ISSUES
While LDV has relatively higher spatial resolution thanother methods for velocity measurement and can measure atnear the wall, however, it has several issues to achieve the

INTRODUCTION
To establish scaling laws of a mean velocity andturbulence intensity in a wall-bounded flow at high Reynolds
number has studied by many researchers. Major concerns in astatistic of the turbulence intensity profile are an inner peak,an outer peak of streamwise component and an outerlogarithmic region of 3 component behaviours at highReynolds number. It is well known that the value of the innerpeak increases with Reynolds number, but it has not beenclarified whether it is finite/infinite. The scaling law for the
inner peak is also still under discussion (Marusic et al. 2017,
Chen and Sreenivasan, 2018). For the outer peak observed inhigh Reynolds number pipe flow, it is still not unclear whether
it has somewhat physical meaning of the turbulence or itcomes from measurement issue (Hultmark et al., 2012, Willert(a)Detected as fastervelocity than expected(b)

Detected as slower
velocity than expected

Figure 1. (a) The fringe distortion in LDV measurement and(b) The effects of finite the control volume (spatial resolution).

1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022(c)(c)
with respectof velocity
Deviation[%]toof velocity
Deviation
the center of the control volume [%]

(a)

z

6
: Focal length = 160 mm: Focal length = 200 mm

4
2
0
-2
-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Position from center of control volume [mm]Figure 2. (a) Wire rotary device, (b) Distribution of burst signal amplitude and determination of the control volume
size, (c) Influence of fringe distortion on different focal length.

precise measurement. In this paper, two important issues,
which are the fringe distortion (Fig. 1(a)) and the spatial
resolution (Fig. 1(b)) for measurement, are focused since thoseare critical factors for high Reynolds number measurement.
The fringe distortion may strongly influence to the turbulence
intensity at the outer region. On the other hand, the spatial
resolution derived the size of the control volume may strongly
influence to it at the inner region where has large velocity
gradient, especially the value of the inner peak. Those
influences of LDV have been pointed out in the previous,
however, there is no established correction methods especiallyfor high Reynolds number.
In this experiment, a wire rotary device (Fig.2(a)) wasused to obtain detail information of the size of the fringe
spacing and the control volume. The absolute velocity of LDV
was calibrated based on the rotating speed of the tungsten wireattached to the rotor. By the traversing the rotor, the velocity
at each position in the control volume can be obtained. In
Fig.2(c), the deviation from the velocity at the centre in thecontrol volume is investigated. This result is clear evidence
that the fringe distance is distorted, namely fringe distortion.
The turbulence intensity is overestimated by this fringe
distortion because particles which have same velocity aredetected as different velocity depending on the passing
position in the control volume. Thus, we apply new correction
method based on the probability density function. The
measured probability density function PM(u; V) of the velocity
fluctuation is estimated by the integration of PA(u, z) over thecontrol volume,1

𝑙/2

𝑃M (𝑢; 𝑉) = ∫−𝑙/2 𝑃A (𝑢; 𝑧)𝑠(𝑧, 𝑉)𝑑𝑧,
𝑉(1)

where l is the major diameter of the control volume, s(z, V) is
the infinitesimal volume at the z position. PA(u; z) is expressedusing base PDF PB,
𝑃A (𝑢; 𝑧) =𝑃B {[𝑢 − 𝑈(𝑧)]/𝜎(𝑧)}
,
𝜎(𝑧)

(2)

where U(z) is mean velocity and (z) is standard deviation atz. With assuming the base PDF PB is invariant in the control
volume, PA(u; z) at the centre of the control volume can be
estimated inversely to satisfy Eq.(1).
Contrary to hot wire measurements, the turbulence
intensity at near wall is overestimated in LDV measurement
due to the velocity gradient in the control volume. Durst et al.
(1995) reported the following,
′2
′2
𝑢𝑚𝑒𝑎𝑠
= 𝑢𝑐𝑣
+

′2
𝐿2 𝑑𝑈𝑐𝑣 2 𝐿2 𝑑 2 𝑢𝑐𝑣
(
) + (
),
2
16 𝑑𝑦
32 𝑑𝑦

(3)

(u’+)2as the relation between the measured and the actual turbulence
intensity at the center of the control volume. Where, umeas'2
indicates the measured turbulence intensity in the control
volume, Ucv and ucv'2 are the mean velocity and turbulence
intensity at the centre of the control volume, respectively. L isthe actual length considered as the spatial resolution and it isimportant parameter for the precise measurement. The size ofthe control volume can be calculated from the optical andgeometric parameters of LDV, however it does not give any
guarantee for it in the actual measurement. In this presentation,
the size of the control volume was obtained by the wire rotarydevice and the turbulence intensity measurement using threedifferent spatial resolutions. As shown in Fig.2(b). thedistribution of the burst signal amplitude is measured by thewire rotary device, and the major length l is determined bycertain threshold of it. The threshold level is determined toFig. 3 The turbulence intensity profiles Reτ=8610
measured by three different control length
L+(𝐿+ = 𝐿𝑢𝜏 /𝜈). Closed symbols are uncorrected
results. Open symbols are corrected by Eq. (3).

2

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022
effects are small on spanwise and wall-normal components
because velocities are low and the velocity gradient is small.

EXPERIMENT
Experiments for the fully-developed pipe flow at highReynolds number was conducted in Hi-Reff. Water at ambient
temperature was used as the working fluid. The range of
Reynolds number was Re=990-20750. Notable features ofthis facility are steady flow by supplying from a head hank 30
m high and high accuracy flow rate measurement by static
gravimetric methods (Furuichi et al., 2015). Measurement
components are streamwise, wall-normal and spanwise. Eachmeasurement was conducted by different insertion of laser
beam as shown in Fig.4. The measurement line for streamwise
component was slightly inclined (15.1-15.7deg) to measure atnear the wall. The axisymmetric flow field was guaranteed(a) the reproducibilityRe= 6 050(a) and
6 050= 990 : Re
: Re =: Re990
from the pre-experiments
of=:Reynolds= 8 700
8 700= 1 990 : Re =: Re: Re =: Re
1 990
10 10
Re200
= 11 200= 2 990 : Re =:11
: Re =: Re
2 990
Re200
=3%
14 200 for
number was very high in Hi-Reff, which is less: Rethan
=:14
Re750
= 20 750: Re =:20
each velocity component
measurement.
: Re = 990(b)
10 (a)

Figure 4. LDV Measurements of 3components. Spanwise
component was measured on the red dashed line, streamwise
component was black, wall-normal component was blue.

4(u'+)2(u'+)2 (u' )

+ 2

(v' )

3

103 10(f)+y

00 00 01
1
101000 100 10
101 101
10
10
0
4 2
+
y
(f)(b)
(f)

2
10
1033
1044
102 :+Re = 410
10000 (Yamamoto,
Channel)y: Re = 6 000 (Pirozzoli, Pipe): Re = 8 000 (Yamamoto, Channel): Re = 4 000 (Yamamoto, Channel): Re = 6 000 (Pirozzoli, Pipe): Re(Yamamoto,= 1 000 (Chin,
Pipe): Re = 8 000
Channel): Re = 2 000 (Chin, Pipe): Re = 3 000 (Pirozzoli, Pipe): Re = 3 000 (Ahn, Pipe)

+ 2

2
2111

2

3

2
10
102 10102+ +yy3
10
103 101034

4
10
104 41010: Re = 1 000 (Chin, Pipe): Re = 2 000 (Chin, Pipe): Re = 3 000 (Pirozzoli, Pipe): Re = 3 000 (Ahn, Pipe)

3
2

1

+ 2

(w'+)2(w' )(w'+)2+ 2+ 2(v' ) + 2(w'+)2(w' ) (w' )







2

2

10

1

2

10

10

3

10

4

+

1

y

101

102

103

104

101

102 +
y

103

104

0

1

1

3
0 010-310y: Re = 6 050: Re = 8 700: Re = 11 200: Re = 14 200: Re = 20 750: Re = 8 000 (Yamamoto, Channel): Re = 8 000 (Yamamoto, Channel)= 8 000 (Yamamoto, Channel)
show
figures show logarithmicor constant law3 related to attached: Readdy
hypothesis
3
213 outer scaling. The black dotted lines in under
and
these
constants
weredeterminedbyfittingfromprecent
results.
2
1

2
10
100
1
0 0
10
00
4 100
(f)

+

y

4

4 000 (Yamamoto,
Channel): Re =: Re
4 000
Channel) = (Yamamoto,
6 000 (Pirozzoli,: Re =: Re
6 000Pipe) Pipe) = (Pirozzoli,
8 000 (Yamamoto,
Channel): Re =: Re
8 000
Channel) = (Yamamoto,

22 2

5
111 1

+

y

104 10+y
1
10
1 10100
1
101
102
103
104
04 0
1
2
3
4
+
: Re = 410
000 (Yamamoto,
Channel)
10
10
10
10
(c)
y
00 0
0 0
0 0
: Re = 6 0003 (Pirozzoli, Pipe)
2
1
1
2
3
4
10 0
1011
10
1033
1044
000 (Yamamoto,102 :+Re = 810
102 + 1010Channel)
10104043 10 -3 10
0 00 0 10 -3 1 10
0 10 -3-3 10 -2 -210 + -110 -1
-2 y
-1
-22 y
0
3 -1
4
y
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
100 100
4: Re = 4 000 (Yamamoto, Channel)
2 (c)
+
+
: Re = 6 000 (Pirozzoli, Pipe)
y
y/R
(f)
y/R
y/R
y/R
(e)
y
: Re = 8 000 (Yamamoto, Channel)
4
4
324
:
: Re = 4 000 (Yamamoto, Channel)
ReRe = 4 000 (Yamamoto, Channel)=
4000(Yamamoto,
Channel)(c)5. Comparison: Returbulence(c) inner scaling and
3 (c)with previous ::DNS
Figureintensity profiles
data.
Upper
figures show
figures: Re = 6under
Re = 6 000= 6 000 (Pirozzoli, Pipe)000 (Pirozzoli,(Pirozzoli,
Pipe)
Pipe)



+
y+ y

+ 2

+ 2

+ 2 + 2

++ 22

+ 2

2

102 10: Re = 990: Re = 1 990: Re = 2 990(u'+)2 + 2(w' )(v' ) (w'(w' )) 

323 3 (a)
10(e)
(d)

(w' )

(w'+)2(v'+)2

+ 2

15
5

1

100 10 101 10
0
44 4 +y(e) (c)
0 (c)

104

(u' )

1

2

103

1 000 Pipe)(Chin, Pipe) = (Chin,: Re =: Re
1 000
2 000 Pipe)(Chin, Pipe): Re =: Re
2 000
 = (Chin,
3 000 (Pirozzoli,: Re =: Re
3 000Pipe) Pipe) = (Pirozzoli,:=
Re+ =2: 990
3 000
(Ahn,
Pipe)
:
Re
050
Re
=
3
000
(Ahn,
 = 6 Pipe): Re: (u' ) =1.6-1.44ln(y/R): Re = 8 700: Re = 1 990+ 2 990: Re = 11 200: Re = )2peak: (u'=5.04-0.72ln(y/R): Re = 14 200: Re = 20 750

00 0
410 0
101 1
10
(c) + 10y04

3 000 Pipe)(Pirozzoli, Pipe)0: Re =: Re
2 000
 = (Chin,4232 (c)3 000 (Ahn,Pipe) 4
: Re =: Re
3 000
Pipe)
 = (Pirozzoli,: Re+ =2 3 000 (Ahn, Pipe)(e)(b)(e) (f): (u': )Re=1.6-1.44ln(y/R)
 = 1 000 (Chin, Pipe)+: Re
2  = 2 000 (Chin, Pipe)3: (u' :)Repeak
3 000 (Pirozzoli, Pipe) = =5.04-0.72ln(y/R): Re = 3 000 (Ahn, Pipe)
3 32

21
5

102

2
(d)(a)
10 (e)
(c)
10

1022
1033
104
10 + : Re10104
 = 1 000 (Chin, Pipe)y : Re =: Re1 000
2 000 Pipe)(Chin, Pipe) = (Chin,

(v' )

+ 2

101

++2 2
2 +)2
(w'
)+) +2)(w'
(v'
(w'
(v'
)

1011
10

+ 2 + 2+ 2(u'(w'+) )(v'
2 (v'
) )

0 0
0
210 0
2 10(b)
0 (b)
42
(f)
(d)
(b)
10
31
1

0

1
















+ 2
+ 2
(v'
(u' )) +(v'2 +))2(v'

5
15

(v'+)2

+ 2

(u' )

+ 2
(v' ) (u'+ 2)

= 6 050: Re :=Re =990 990 : Re :=Re6 050= 8 700= 1 990 : Re :=Re8 700: Re :=Re1 990
11 200= 14 200: Re :=Re2 990= 2 990 : Re :=Re
=
6 050
14
200

: Re = 990 : Re: :=ReRe = 20750:
Re=
 7508 700: Re = 1 990 : Re = 20
: Re = 11 200: Re = 2 990: Re = 14 200: Re = 20 750

58 5

0

0
0100
2
0 (b)

2

0 (a)
(a)
10
2
(a)
10 (e): Re = 1 990: Re = 2 990: Re = 4 200

RESULTS
6
Experimental results for the turbulence intensity profiles
4 =20750 are shown in Fig.5. All
from Re=990 to Re
0 0 0
2
4
3 103 proposed
experimental data is100 corrected
10 101 101 based
102 10 on 10the104 102 22correction procedure above mentioned. In the same figure, the= (Chin,
1 000 (Chin,: Re =: Re
1 000Pipe) Pipe)(b) (b)Re=Re
2 000=8000
Re =: to2 000
(Chin,Pipe) Pipe) are
DNS results for the pipe
0 and channel flow :: up
 (Chin,= (Pirozzoli,
3 000(Pirozzoli,
Re =: Re
3 000
Pipe) Pipe): Re = 6 050: Re = 990
:
Re
=
3
000
(Ahn,
Pipe)
:
Re
=
3
000
(Ahn,
Pipe)
Re =to6 050compare with the present results. For
990:drawnRe = 8: 700
also
the (d)=: Re = :1Re
990
(c)
:
Re
=
8
700
:
Re
=
11
200

:
Re
=
1
990
: Re = 2 990

+
2
:
Re
=
14
200
: Re component,= 14 200: Re= 2 990
streamwise
inner
peaks
increase
with
Reynolds+2: (u') =1.6-1.44ln(y/R)(d): Re = 20: 750: (u' ) =1.6-1.44ln(y/R)
Re = 20 750+ 2: Re  = 990(b): Re = 6 050+2: (u' number) peak =5.04-0.72ln(y/R)
increases.
results
10
1 1present experimental: (u' ) peak =5.04-0.72ln(y/R): Re = 1 990 The: Reare= 8 very700: Re = 2 990
1
 = 11 200
nice agreement
DNS result at Re=1000 and:: Re
2000.
For
: Re = 4 with200
Re
 = 14 200
20 750 higher Reynolds number, except the overlap region: Re(y =+=100500), the present results show nice agreement with DNS result.
5 noted that each DNS result shown in
However, it should be
0 0) (v' ))(u' (v'+ 2+ +2 2) (u'(u' (u'))(u'+)2

(u' )

+ 2

take same value of the inner peak value among three different
spatial resolutions. The minor axis d is determined by theformula 𝑑 = 𝑙 sin 𝜙 / cos 𝜙 ( is the half-intersection angle ofthe beams.). When the minor axis d and the major axis l are
determined, the control length L is determined by them,another optical and geometrically conditions. Fig. 3 shows
streamwise turbulence intensity profiles measured by threedifferent spatial resolution. Turbulence intensitiesare(a)
10 (a)effect isoverestimated by the control
length L and this
10
+
2
(d)
(d)
: (u' ) =1.6-1.44ln(y/R)
significantly
at near the wall.
+ 2 However, corrected
10
10 by Eq. (3): (u' ) peak =5.04-0.72ln(y/R) 10 (a)profiles are consistency.
The correction of the fringe distortion8 and5 the spatial
5
resolution were applied to 3 components. The effectsof two6
issues5 are significant on streamwise component,
5 but these





















101

10-2 2
10 +
y/R
y

10-1
103

104

100

0 0
10

101

102 +
y

103

104

10-3

10-2

(v'++
(v'

(u'+
(u'

55

0.5
Re=10=10 000
000:: Re
Re=20=20 000
000:: Re

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022
00
1011
10

1022

+

+
y

103

0
101

104

1.5

2
1.5(b) (b)Re=10: Re:=10000 000
Re=20: Re:=20000 00033 (c): Re=20 000

1.5
1Hultmark et al., 2013, Superpipe

0.50.5Re=10: Re:=10000 000
Re=20: Re:=20000 000

0 0 1
10110

102102(w'++)22
(w' )

1

22

(v'+)2(v'+)2(u'+)2(u'+)2

Willert et al., 2017, CICLoPE

5 5: Re=20 000

11Zhao ＆ Smits, 2007, Superpipe

ReD=480 000: ReD=480: 000: Re000: ReD=1 100
D=1 100 000

103103
+ +
y y

0 0 1
10110

104104(d)Willert et al., 2017, CICLoPE+
(-u'v')-u'v'+ (a) (a)10 10102102103103
+ +
y y

0.5

Zanoun et al., 2019, CICLoPE

:
:

:: Re
Re=10=10 000

10410400
10
10-3-310-2-2

10-1

100

y/R
1.51.5(d) previous experimental data at high Reynolds number pipe flow. Present(d)with3(c) (c) 6. Comparison turbulence intensity profiles
3 Figure

results of Re = 11200 and 20750 show in these figures as same symbol with Fig. 5.
1 1
+

-u'v'
+
-u'v'

(w'+)2(w'+)2

2 2

+2 2
u'
(u’+peak) peakthe figure have difference in the overlap region even thoughprevious pipe data at high Reynolds number(Zhao ＆ Smits,
0.50.5 for thissame
Reynolds number. Further discussion
1 1
2007, Hultmark et al., 2013, Zanoun et al., 2019), however,inconsistency may be necessary. Regarding the outer peak,Re=14: Re:it=14000 000
these profiles show sufficient agreement with the present
Re=20Re=10: Re:=20000 000: Re:=10000 000
was not observed even Re=20000.
results (see Fig. 6).
0 0For-3 the wall-normal
0 0 1 region
component,
around0 theoverlap
0
3
-3
-2 -2
-1 -1
1
2 2
Reynolds
10
10
10
10
10
10
10 low Reynolds
10 number,10the difference
10 can 101010310The
104104 number dependency of the inner peak value
forbe observed+ +y/Ry/Ry y is shown in Fig.7. The error bars indicate the uncertainty
between the present and DNS results. Experimental turbulencecalculated by the variation among three different spatialintensity is smaller than DNS in this region. However, forresolutions. The dotted line is the logarithmic scaling of thehigher Reynolds number region, the turbulence intensity
inner peak (Marusic et al., 2017) and the broken line is thearound the overlap region shows nice agreement each other.
asymptotic relation given by the expected dissipation ratio at
The peak values asymptote to 1.3 with Reynolds number
the near wall (Chen et al. 2021).
increases.
For the spanwise component, the peak values increase(𝑢′+ )2𝑝𝑒𝑎𝑘 = 𝐴2 ln 𝑅𝑒𝜏 + 𝐵2
(7)
with Reynolds number. The results at low Reynolds number1𝛽2′+Re = 1000 and 2000 show nice agreement between the present(𝑢 )𝑝𝑒𝑎𝑘 = 𝛼 ( − 0.25 )
(8)
4 𝑅𝑒𝜏
and DNS. For higher Reynolds number up to Re = 8000, theouter region shows nice agreement, but the difference can be
The constants of Eq. (7) and Eq. (8) obtained from precent
observed in the inner region. There is the difference of innerresults are A2 = 0.72, B2 = 3.01, α = 46, β= 0.44. Both equations
region between DNS data. Although the effect of the spatial
well represent the experimental results, while it seems that theresolution is small in other than streamwise, the inner peak ofpresent result is consistent with the later. The importance of
spanwise component need to be discussed in the future.
the present result is the consistency with results in TBL. In the
While small difference is observed as mentioned, theprevious studies for the pipe flow, they take asymptotic values
present turbulence intensity profiles for three components
and widely scattered at high Reynolds number. However, theshow high level consistency with DNS results. It is difficult tofind such consistent result for three components in theprevious studies. From this result in the low Reynolds number,the reliability in high Reynolds number region would increase.
11  : 𝑢′+2
𝑚𝑎𝑥 = 0.72 ln 𝑅𝑒𝜏 + 3.01
1
0.44
+2
Here, we make attention to the logarithmic region around-----: 𝑢′𝑚𝑎𝑥= 46 ቀ − 0.25ቁ
4𝑅𝑒𝜏
y/R=0.1 according to the previous studies (y is the wall-normal
position and R is radius of the pipe). The turbulence intensity
10
profiles based on the attached eddy model are the following,𝑢′+2 = 𝐵1,𝑢 − 𝐴1,𝑢 ln(𝑦/𝑅)𝑣′+2 = 𝐵1,𝑣𝑤′+2 = 𝐵1,𝑤 − 𝐴1,𝑤 ln(𝑦/𝑅)

(4)
(5)
(6)

Based on the detail analysis using indicator functions 𝛯𝑢 =𝑦 + 𝑑〈(𝑢′+ )2 〉/𝑑𝑦 + , 𝛯𝑣 = 𝑦 + 𝑑〈(𝑣′+ )2 〉/𝑑𝑦 + , 𝛯𝑤 = 𝑦 + 𝑑〈(𝑤′+ )2 〉/𝑑𝑦 + , the clear logarithmic region for Eq.(4) and (6) can befound for Re>11200 and A1,u has Reynolds number
dependency while it expected to be universal constant. In thisexperiment, A1,u=1.44, B1,u =1.60, B1,v =1.3, A1,w=0.46, B1,w
=0.99 are obtained at Re = 20750. It should be noted that thepositions where Eq.(4)-(6) are satisfied is same between
streamwise and spanwise component (y/R = 0.05~0.25), butdifferent with the wall-normal component (y/ R= 0.015~0.07).
The constants involved in Eq.(4)-(6) are slightly different to

9: Present, Pipe
: Hultmark et al., 20132012, Pipe
: Willert et al, 2017, Pipe
: Samie et al, 2018, TBL: Marusic et, al, 2015, TBL

8

7

103

104

105

Re
Figure 7. Comparison the Reynolds number dependency of
streamwise inner peak with previous experimental data andEq. (7) and Eq. (8). The constants of Eq. (7) and Eq. (8) were
determined by fitting from precent results.

4

1

0
101

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022
present results do not take asymptotic value and wellagreement with TBL results by Samie et al. (2018). The
consistency indicates possibility that the streamwise innerpeak values independence of the geometry. This result would
come from the highly considered spatial resolution of themeasurement.
Furthermore, it is reported that the relationship between
Reynolds number dependence of inner peak and thelogarithmic region with A1 = A2/2 in previous study of TBL(Marusic et al. 2017). This relation was observed at also pipe
flow in present study as 0.72 = 1.44/2 (Fig. 5(a)) by taking
account to LDV specific issues such as the fringe distortion
which affects the outer region and the spatial resolution which
affects the inner region at high Reynolds number.

Marusic, I., Chauhan, K. A., Kulandaivelu V., andHutchins N., 2015 "Evolution of zero-pressure-gradientboundary layers from different tripping conditions," J. Fluid
Mech. 783, pp. 379–411.
Marusic, I., Baars, W.J., Hutchins, N., 2017, “Scaling of
the streamwise turbulence intensity in the context of innerouter interactions in wall turbulence”, Phys. Rev. Fluids, 2-10,
pp. 1–22.
Ono, M., Furuichi, N., Kurihara N., Wada Y., Tusji, Y.,
2022, “Reynolds number dependence of inner peak turbulence
intensity in pipe flow”, Physics of Fluids, 34.
Perry, A. E., & Chong, M. S., 1982, “On the mechanismof wall turbulence”, J. Fluid Mech., 119, 173–217.
Pirozzoli, S., Romero, J., Fatica, M., Verzicco, R., Orlandi,
P., 2021, “One-point statistics for turbulent pipe flow up toReτ=6000. Journal of Fluid Mechanics”, 926, pp. 1–20.
Samie, M., Marusic, I., Hutchins, N., Fu, M. K., Fan, Y.,
Hultmark, M., Smits, A. J., 2018, “Fully resolved
measurements of turbulent boundary layer flows up toReτ=20000”, J. Fluid Mech., 851, pp. 391–415.
Willert, C. E., Soria, J., Stanislas, M., Klinner, J., Amili,O., Eisfelder, M., Cuvier, C., Bellani, G., Fiorini, T., Talamelli,A., 2017, “Near-wall statistics of a turbulent pipe flow at shear
Reynolds numbers up to 40 000”, J. Fluid Mech., 826, pp. 1–
10.
Yamamoto, Y., & Tsuji, Y., 2018, “Numerical evidenceof logarithmic regions in channel flow at Reτ=8000”, PhysicalReview Fluids, 3(1), pp. 1–10.
Zanoun, E. S., Egbers, C., Örlü, R., Fiorini, T., Bellani, G.,& Talamelli, A., 2019, “Experimental evaluation of the mean
momentum and kinetic energy balance equations in turbulent
pipe flows at high Reynolds number”. Journal of Turbulence,20(5), pp 285–299.
Zhao, R., & Smits, A. J., 2007, “Scaling of the wallnormal turbulence component in high-Reynolds-number pipeflow”, J. Fluid Mech., 576, pp 457–473.

CONCLUTION
LDV measurement parameters which influence
turbulence intensity such as the spatial resolution and thefringe distortion are evaluated by supporting of the wire rotarydevice and it is reflected to the measurement results by eachcorrection methods.
Reynolds number dependence of the streamwise innerpeak showed consistency with Eq. (7) and Eq. (8), and good
agreement with previous experimental results of TBL rather
than pipe flows. The consistency indicates possibility that thestreamwise inner peak values independence of the geometry.
On, the turbulence intensity profiles of 3 components
indicate clearly the logarithmic regions for Re > 11200, these
positions are same between streamwise and spanwise
component (y/R = 0.05~0.25), but different with the wallnormal component (y/R= 0.015~0.07). These profiles agree
well DNS data at low Reynolds number and previous
experimental data at high Reynolds number.
Moreover, the relation between the Reynolds number
dependence of streamwise inner peak and the logarithmic
region derived by the attached addy hypothesis, which is A1 =A2/2, was observed at also pipe flow in present study. We
should emphasize that these results are based on a carefully
taking account of LDV specific problems such as the fringe
distortion and the spatial resolution.

REFERENCES
Ahn, J., Lee, J. H., Lee, J., Kang, J., & Sung, H. J., 2015,“Direct numerical simulation of a 30R long turbulent pipe
flow at Reτ=3008”, Physics of Fluids, 27(6), 065110.
Chen, X., Sreenivasan, K.R., 2020, “Reynolds number
scaling of the peak turbulence intensity in wall flows”, J. Fluid
Mech., pp. 1–11.
Chin, C., Monty, J. P., & Ooi, A., 2014, “Reynolds
number effects in DNS of pipe flow and comparison withchannels and boundary layers”, International Journal of Heatand Fluid Flow, 45(1), pp. 33–40.
Durst, F., Jovanović, J., Sender, J., 1995, “LDA
measurements in the near-wall region of a turbulent pipe flow”,
J. Fluid Mech., 295, pp. 305–335.
Furuichi, N., Terao, Y., Wada, Y., & Tsuji, Y., 2015,“Friction factor and mean velocity profile for pipe flow at highReynolds numbers”, Physics of Fluids, 27(9).
Hultmark, M., Vallikivi, M., Bailey, S. C. C., Smits, A. J.,
2012, “Turbulent pipe flow at extreme reynolds numbers”,
Physical Review Letters, 108(9).

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