Re-examination of fractal-generated
turbulence using
a smaller wind tunnel
Kouji Nagata (Dept. of Mech. Sci. & Eng., Nagoya Univ.)
Yasuhiko Sakai (Dept. of Mech. Sci. & Eng., Nagoya Univ.)
Hiroyuki Suzuki (Dept. of Mech. Sci. & Eng., Nagoya Univ.)
Hiroki Suzuki (Dept. of Mech. Sci. & Eng., Nagoya Univ.)
Fractal/multiscale-generated turbulence
＋ type
Ｉ type
Square type
・D. Hurst & J. C. Vassilicos, Scalings and decay of fractal-generated turbulence,
Phys. Fluids Vol.19, 035103 (2007).
・R. E. Seoud & J. C. Vassilicos, Dissipation and decay of fractal-generated turbulence,
Phys. Fluids 19, 105108 (2007).
・N. Mazellier & J. C. Vassilicos, Turbulence without Richardson-Kolmogorov cascade,
Phys. Fluids 22, 075101 (2010).
Purpose of this study
To perform similar experiments (at the same
Reynolds number with a similar fractal grid)
using a smaller wind tunnel to examine the
similarity of statistics
- potentially involves different wall effects
 To measure cross-sectional profiles at X/X* =
0.45 (X* is the ‘wake-interaction length scale’),
where urms exhibits a peak value
- confirmation of homogeneity in the crosssection

Our Wind Tunnel
exhaust air stream
commutation grid
Cross section (300 mm × 300 mm)
diffuser
air blower
cloth
connection
diffuser
traverse
grid
3100
Y
～
～
～～
X
～
～
Origin: grid centre
X : streamwise
Y : vertical
Z : horizontal
ピトー管
3800
9100
Comparison of the cross-section
T
Mazellier & Vassilicos (2010)
T=0.91 m, 5.4 m long
AR=5.93
Grid (BIG17): N=5, tr=17.0
Mazellier & Vassilicos (2010)
T=0.46 m, 5.0 m long
AR=10.87
Grid (SFG13): N=4, tr=13.0
Our wind tunnel
T=0.30 m, 3.8 m long
AR=12.67
Grid: N=4, tr=13.0
Experimental Conditions
ours
M&V 2010
(SFG13)
4
4
163.8
237.7
11.7
17.2
8
8
tr : thickness ratio
13.0
13.0
s : blockage ratio
0.25
0.25
18.77
26.3
T (mm) : wind tunnel width
300
460
X* (mm) : wake interaction
length scale
2290
3280
U∞ (m/s) : main velocity
14.0 7.3
10.0 5.2
Re0 : Reynolds number
14,400 6,000
14,400 6,000
t0
N : number of scales
L0 biggest bar length of the
grid
t0 : biggest bar thickness of the
grid
Lr : length ratio
Meff (mm) : effective mesh size
L0
Experimental Conditions
ours
M&V 2010
(SFG13)
4
4
163.8
237.7
11.7
17.2
8
8
tr : thickness ratio
13.0
13.0
s : blockage ratio
0.25
0.25
18.77
26.3
T (mm) : wind tunnel width
300
460
X* (mm) : wake interaction
length scale
2290
3280
U∞ (m/s) : main velocity
14.0 7.3
10.0 5.2
Re0 : Reynolds number
14,400 6,000
14,400 6,000
T
N : number of scales
L0 biggest bar length of the
grid
t0 : biggest bar thickness of the
grid
Lr : length ratio
Meff (mm) : effective mesh size
4U
T t /
ReM0 X
 L 10 s air

2
2
eff
*
P
0
t0
νairP：perimeter
：kinetic viscosity
of grid
The wake interaction length scale
(Mazellier & Vassilicos 2010 )
L20
X* 
t0
Interaction between wakes of
the largest bars occurs at X=X*
(with some assumptions)
Mazellier & Vassilicos (2010), Phys. Fluids, FIG.4
Experiment 1: centreline statistics
Conditions
Measuring positions
Reynolds number Re0  U t0 / air
Sampling frequency
Sampling number
Sampling time
Hot-wire probe
:on the centreline (X/X*=0.01~0.94)
: 6,000
11,400
: 10 kHz
: 1,048,576
: approx. 105 s
: I type, 5 mm dia.
Y
Z
X
Origin: grid centre
X : streamwise
Y : vertical
Z : horizontal
9
Results (mean velocity)
1.2
Re0=11,400
Re0=6,000
M & V (SFG13 Re0=11,400)
M & V (SFG13 Re0=6,000)
1.4
UP
1.2
1
0
Re0=11,400
Re0=6,000
M & V (SFG13 Re0=11,400)
M & V (SFG13 Re0=6,000)
1.1
Uc/UP
Uc/U
1.6
1
0.9
0.2
0.4
0.6
X/X*
0.8
1
UC : Centreline mean velocity
UP : Mean velocity characterising the constant
mean velocity plateau
U  : Main velocity
0.8
0
0.2
0.4
0.6
X/X*
0.8
1
(uc'(X)/Uc(X))/(uc'(Xpeak )/Uc(Xpeak ))
Results (rms velocity)
Exponential decay (Eq.1)
1
0.5
 uC'

 UC



0
0
2
  x 

A
exp
 B 
2
'
 uC ( x peak ) 
  x* 


 U (x ) 
 C peak 
・・・(1)
(M & V 2010)
Re0=11,400
Re0=6,000
M & V (SFG13 Re 0=11,400)
M & V (SFG13 Re 0=6,000)
0.2
0.4
0.6
X/X*
0.8
1
u C' : Centreline rms velocity
U C : Centreline mean velocity
Mazellier &Vassilicos (2010)
Re0= 6,000
: A=2.82 B=2.06
Re0=11,400
: A=2.91 B=2.14
Our experiments
Re0= 6,000
: A=2.65 B=1.88
Re0=11,400
: A=2.63 B=1.91
Results (skewness and flatness)
1
20
Re0=11,400
Re0=6,000
M & V (SFG13 Re 0=6,000)
Su
0
Fu
-1
-2
-3
0
10
Re0=11,400
Re0=6,000
M & V (SFG13 Re 0=6,000)
0.2
0.4
0.6
X/X*
0.8
1
0
0
0.2
0.4
0.6
X/X*
0.8
1
Results (length scales)
0.5
20
0.4
0.3
Lu/
Lu/L0
Re0=11,400
Re0=6,000
vassilicos(SFG13 Re 0=11,400)
vassilicos(SFG13 Re 0=6000)
Re0=11,400
Re0=6,000
vassilicos(SFG13 Re 0=11,400)
vassilicos(SFG13 Re 0=6000)
10
0.2
0.1
0
0
0.2
0.4
0.6
X/X*
0.8
1
0
0
0.2
0.4
0.6
X/X*
0.8
1
Results (Taylor Reynolds number)
Re0=11,400
Re0=6,000
vassilicos(SFG13 Re 0=11,400)
500
400
Re
300
200
100
0
0
0.2
0.4
0.6
X/X*
0.8
1
Experiment 2: vertical profiles
Conditions
Measuring positions
Reynolds number Re0  U t0 / air
Sampling frequency
Sampling number
Sampling time
Hot-wire probe
:on the vertical (X/X*=0.1, 0.2, 0.3, 0.45, 0.6,
0.75. 0.94)
: 11,400
: 10 kHz
: 262,144
: approx. 26 s
: I type, 5 mm dia.
Y
Z
X
Origin: grid centre
X : streamwise
Y : vertical
Z : horizontal
15
Results (mean velocity U)
1.4
X/X*=0.10
X/X*=0.20
X/X*=0.30
X/X*=0.45
X/X*=0.60
X/X*=0.75
X/X*=0.94
1.3
U/U
1.2
1.1
1
0.9
0.8
0
downstream
0.1
U  : Main velocity
0.2
0.3
0.4
0.5
Y/T
downstream
1
U/Uc
0.9
0.8
0.7
0.6
0
X/X*=0.10
X/X*=0.20
X/X*=0.30
X/X*=0.45
X/X*=0.60
X/X*=0.75
X/X*=0.94
0.1
UC : Centreline mean velocity
0.2
0.3
Y/T
0.4
0.5
Results (rms velocity urms)
urms/U
0.2
X/X*=0.10
X/X*=0.20
X/X*=0.30
X/X*=0.45
X/X*=0.60
X/X*=0.75
X/X*=0.94
0.1
downstream
0
0
0.1
0.3
0.4
0.5
Y/T
0.2
urms/U
0.2
X/X*=0.10
X/X*=0.20
X/X*=0.30
X/X*=0.45
X/X*=0.60
X/X*=0.75
X/X*=0.94
0.1
downstream
0
0
U  : Main velocity
0.1
0.2
0.3
Y/T
0.4
0.5
U: local mean velocity
Results (skewness)
downstream
1
1
0
Su
0
Su
-1
-1
X/X*=0.10
X/X*=0.20
X/X*=0.30
X/X*=0.45
X/X*=0.60
X/X*=0.75
X/X*=0.94
-2
-3
0
0.1
0.2
0.3
-2
enlarge
0.4
0.5
Y/T
Su
0.5
downstream
0
X/X*=0.10
X/X*=0.20
X/X*=0.30
X/X*=0.45
X/X*=0.60
X/X*=0.75
X/X*=0.94
-0.5
0
0.1
0.2
0.3
Y/T
0.4
0.5
-3
0
Re0=11,400
Re0=6,000
M & V (SFG13 Re 0=6,000)
0.2
0.4
0.6
X/X*
0.8
1
Results (flatness)
20
X/X*=0.10
X/X*=0.20
X/X*=0.30
X/X*=0.45
X/X*=0.60
X/X*=0.75
X/X*=0.94
Re0=11,400
Re0=6,000
M & V (SFG13 Re 0=6,000)
Fu
Fu
20
10
10
enlarge
0
0.1
0.2
0.3
0.4
0.5
Y/T
5
downstream
4
Fu
X/X*=0.10
X/X*=0.20
X/X*=0.30
X/X*=0.45
X/X*=0.60
X/X*=0.75
X/X*=0.94
3
2
0
0.1
0.2
0.3
Y/T
0.4
0.5
0
0
0.2
0.4
0.6
X/X*
0.8
1
Experiment 3: cross-sectional profiles
Conditions
Measuring positions
Reynolds number Re0  U t0 / air
Sampling frequency
Sampling number
Sampling time
Hot-wire probe
:Y-Z plane (X/X*=0.45)
: 11,400
: 10 kHz
: 262,144
: approx. 26 s
: I type, 5 mm dia.
23×23=529
measuring points
Y
Y
Z
Origin: grid centre
X : streamwise
Y : vertical
Z : horizontal
X
Z
20
Traverse system
Y-Z unit
Pulse motor
Slider
Actuator
PC
Controller
http://fa.sus.co.jp/
DC24V
(uc'(X)/Uc(X))/(uc'(Xpeak )/Uc(Xpeak ))
Centreline statistics
at X/X*=0.45
1
0.5
0
0
Re0=11,400
Re0=6,000
M & V (SFG13 Re 0=11,400)
M & V (SFG13 Re 0=6,000)
0.2
0.8
1
20
1
Re0=11,400
Re0=6,000
M & V (SFG13 Re 0=6,000)
Su
Fu
0
-1
-2
-3
0
0.4
0.6
X/X*
10
Re0=11,400
Re0=6,000
M & V (SFG13 Re 0=6,000)
0.2
0.4
0.6
X/X*
0.8
1
0
0
0.2
0.4
0.6
X/X*
0.8
1
Uc /Ud
u 'c / u ' d
Mazelier & Vassilicos 2010
Results (mean velocity)
U /U
0.5
0.8600
0.8700
0.8800
0.8900
0.9000
0.9100
0.9200
0.9300
0.9400
0.9500
0.9600
0.9700
0.9800
0.9900
1.000
1.010
1.020
1.030
1.040
1.050
1.060
1.070
1.080
1.090
1.100
1.110
1.120
1.130
1.140
1.150
1.160
1.170
1.180
1.190
1.200
0.4
Y/T
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
Z/T
0.4
0.5
Uc /Ud
u 'c / u ' d
DNS at Re0=2,125
(Suzuki et al., Int. Rev. Physics 2010)
X/X*=0.21
X/X*=0.42
X/X*=0.64
Instantaneous streamwise velocity (white: high, black: law)
Results (rms velocity)
urms / U 
0.5
0.04000
0.04200
0.04400
0.04600
0.04800
0.05000
0.05200
0.05400
0.05600
0.05800
0.06000
0.06200
0.06400
0.06600
0.06800
0.07000
0.07200
0.07400
0.07600
0.07800
0.08000
0.08200
0.08400
0.08600
0.08800
0.09000
0.09200
0.09400
0.09600
0.09800
0.1000
Y/T
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
Z/T
0.4
0.5
Uc /Ud
u 'c / u ' d
Results (skewness)
Su
0.5
0.4
Y/T
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
Z/T
0.4
0.5
-0.8000
-0.7500
-0.7000
-0.6500
-0.6000
-0.5500
-0.5000
-0.4500
-0.4000
-0.3500
-0.3000
-0.2500
-0.2000
-0.1500
-0.1000
-0.05000
0
0.05000
0.1000
0.1500
0.2000
0.2500
0.3000
0.3500
0.4000
0.4500
0.5000
Results (Flatness)
Fu
0.5
2.400
2.450
2.500
2.550
2.600
2.650
2.700
2.750
2.800
2.850
2.900
2.950
3.000
3.050
3.100
3.150
3.200
3.250
3.300
3.350
3.400
3.450
3.500
3.550
3.600
0.4
Y/T
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
Z/T
0.4
0.5
Conclusions

Normalised centreline statistics agree well with those of
Mazellier & Vassilicos (2010).

Cross-sectional profiles of statistics have been obtained at
X/X*=0.45, where urms exhibits a peak value. The profiles
show axisymmetric profiles near the centre of the test
section.
Future studies:
- To obtain cross-sectional profiles at several streamwise
locations
- To measure spatial correlations using two hot-wire probes
Thank you for your attention