Mixing of high-Schmidt number scalar
in regular/fractal grid turbulence:
Experiments by PIV and PLIF
Y. Sakai*, K. Nagata*, H. Suzuki*, and R. Ukai*
* Department of Mechanical Science and Engineering, Nagoya University
<Contents>
1. Introduction --- Background, Motivation and Purpose
2. Experimental apparatus and conditions
PIV (Particle Image Velocimetry)
PLIF (Planer Laser-Induced Fluorescence
3. Results and Discussions
4. Conclusions
1. Introduction (1)
The turbulent mixing phenomena can be observed
in many industrial and natural flows
e.g. chemical reactor, combustion chamber, pollutant diffusion, etc.
(Hill, 1976)
(Tominaga, et.al., 1976)
(Fantasy of Flow, 1993)
1. Introduction (2)
The understanding the physics of turbulence and mixing phenomena
is very important to the engineering application, e.g., the design of
high efficient inner mixer.
Recently, a research group of Imperial college has discovered a “new”
turbulence, so called a “fractal/multiscale-generated turbulence”.
D.Hurst & J.C. Vassilicos, Phys. Fluids, vol.19, 035103 (2007)
R.E. Seoud, J.C. Vassilicos, Phys. Fluids, vol.19, 1015108 (2007)
N. Mazellier & J.C. Vassilicos, Phys. Fluids, vol.22, 075101 (2010)
J.C. Vassilicos, Phys. Letters A, vol.375 (2010), pp.1010-1013.
P.C. Valente & J.C. Vassilicos, J.Fluid Mech., submitted
which can be described by the self-preserving single-length
scale theory (W.K. George & H.Wang, Phys. Fluids, vol.21, 025108 (2008)).
1. Introduction (3)
The low-blockage space-filling fractal turbulence has the following properties
(1) very much higher turbulence intensities u’/U and
Reynolds number Reλ than regular grid turbulence
L0
(2)Exponential decay law of turbulence intensity
t0
: wake-interaction length scale
L0: biggest bar length of the grid
t0: the biggest bar thickness of the grid
x*
N. Mazellier & J.C. Vassilicos, Phys. Fluids,
vol.22, 075101 (2010), Fig.5
L0
t0
1. Introduction (4)
(3) Integral length scale Lu and the Taylor length scale λ are independent
of the downstream position x and also Reλ
R.E. Seoud & J.C. Vassilicos, Phys. Fluids, vol.19, 105108 (2007), Fig.2 and Fig.9
Lu ～L0,
λ～L0Re0-1/2 ,
where Re0=U∞t０/ν
Lu/λ～ Re01/2
Lu and λ are determined
only by the initial conditions
1. Introduction (5)
(4) Kinematic dissipation rate εis proportional to u’2 rather than u’3 !
 ~ 3u2U  x* ~ C u3 Lu ,
1
C ~ Re ~
t0 L0
u U 
This characteristic means
the lower dissipation
with the same turbulence intensity
R.E. Seoud & J.C. Vassilicos, Phys. Fluids, vol.19,
105108 (2007), Fig.10.
as compared with the normal
regular grid turbulence.
These properties (1)～(4) lead to the possibility of
“high efficient industrial mixer”
“to generate an intense turbulence with the reduced dissipation and even
design the level of turbulence fluctuation” (Mazellier & Vassilicos, 2010)”
1. Introduction (6) :
purpose of this study
In order to develop
the innovative industrial mixer (Fractal super mixer),
we investigate the diffusion and mixing process of high-Schmidt
number scalar in regular/fractal grid turbulence of the liquid phase
by the PIV and PLIF technique.
Note : all the data processing systems of PIV and
PLIF have been developed in our laboratory by my
collaborators and students.
Page 8
Page. 9
２．Experimental apparatus and conditions
100 mm
High-Sc-number scalar
100 mm
Grid
1500 mm
Contraction
z
Regular grid
Optical filter
x
Camera
Lens
Flow
y
Splitter plate
Rohdamine B
High speed camera
(Ametek Phanton V210)
Measuring area [mm2]
Sampling frequency [Hz]
Sampling resolution [mm2]
Thickness of sheet [mm]
PC
Laser
PIV
Camera
Fractal grid
PLIF
Single-lens reflex
camera (Nikon D700)
7.5(x) x 40(y)
2,000
25(x) x 100(y)
0.4(x) x 0.4(y)
1.0
0.03(x) x 0.03(y)
0.5
---
Schmidt Number
Sc  2,100
Re M eff  2,500
Page. 10
Configurations of Regular/Fractal Grids
Parameters for regular/fractal grids are as follows,
N : number of fractal iterations
Df : fractal dimension
s : blockage ratio
tr : thickness ratio of the largest
to the smallest bar
Meff : effective mesh size
M eff
Parameter
N
4T 2

1s
PM
T 2 : Area of the tunnel’s cross
section [m2]
PM: Fractal perimeter’s length [m]
ReMeff=U0Meff/ν＝2,500
4
Regular
Fractal
grid
grid
フラクタル次元
1
4
Df
2.0
2.0
s
0.36
0.36
tr
1
9.76
Df = 1.5
1 Df = 2.0
Meff
5.68[mm]
2 10[mm]
3
tmin
tmax
tr  tmax tmin
Page. 11
Image processing for PIV
Taking images
Digitizing
Polyester particles: Mean diameter 50mm
Specific gravity 1.03
over 7 particles in the interrogation region
Removing back ground level
Fourier interpolation to obtain 16 times number of pixcels
Checking accuracy of dataprocessing by comparison of the
present data with the LDV result
Recursive cross-correlation procedure × 2 stages
1st stage
10-1
x 3 times
10-2
Euu
Offset cross-correlation analysis
Removing error vectors
10-3
2nd stage (in the smaller interrogation region)
10-4
Offset cross-correlation analysis
Removing error vectors
x 3 times
Present
LDV
10-5 0
10
101
102
k [1/m]
Gradient method
(sub pixel analysis)
Obtain velocity vectors
ReM = 2500
x/Meff = 20
103
Page. 12
Image processing for PLIF
t1
Camera
Single-lens reflex camera (Nikon D700)
Bit depth ：14bits
Sensor ：full size CMOS sensor
PLIF processing
Change of luminance at
different times
Good S/N ratio
Large dynamic range
High sensitivity
1. Digitizing
2. Correction by the back ground image
3. Applying the improved algorithm*
Measured image
back ground image
Time variations of quantum yield
and laser intensity
Spatial decay of laser intensity
Non-dimensional images
0
1
Reference:
t2
＊ Suzuki,H., Nagata,K., Sakai,Y., Ukai,R., Experiments in Fluids, submitted
Page. 13
3. Results and
Discussions
3.1 Results by PIV
Page. 14
1.4
1.4
1.2
1.2
1
1
0.8
Regular grid
0.6
0.4
M=Meff
-1
0
y/M
x/M=10
x/M=15
x/M=20
x/M=30
x/M=40
1
U/U0
U/U0
Vertical profiles of mean streamwise velocity U
x/M= 40
x/M= 60
x/M= 80
x/M=100
x/M=120
0.8
Fractal grid
M=Meff
0.6
0.4
-2
-1
0
y/M
1
For fractal grid turbulence,
x/Meff >40
The profile becomes uniform
2
Instantaneous fluctuating velocity vector fields
Page. 15
Fluctuating velocities in the fractal grid turbulence are much larger than in
the regular grid turbulence
y/Meff
2
0
tU0/Meff
-2
y/Meff
2
Regular grid turbulence x/Meff = 40
0.15
0.0
0
tU0/Meff
-2
Fractal grid turbulence x/Meff = 40
Downstream variations of turbulent fluctuation relative intensity urms2/U02
10-1
Fluctuation intensity of
fractal grid turbulence is
10-2
urms2 /Uo2
much larger
than that of regular grid
turbulence
10-3
10-4 1
10
Run RGT (PIV: present)
Run FGT (PIV: present)
regular grid turbulence (DNS: Suzuki, et al., 2009)
fractal grid turbulence (DNS: Suzuki, et al., 2009)
x/Meff
102
Decay law for turbulence relative intensity
Fractal grid
Regular grid
2
urms
U 02  a  x M eff 
n  1.19
10-2
n
urms2/ Uo2 = A exp{- B(x/x*)}
A = 0.037
B = 2.16
a  0.077
urms2/ Uo2
urms2/U02
10-1
10-3
10-2
Power decay law
10
-4
101
exponential
decay law
Run FGT (PIV: present)
x/Meff
10-3
0.2
0.4
0.6
0.8
1
*
x/x
: wake-interaction length scale
(N. Mazellier & J.C. Vassilicos, 2010)
1.2
Page. 20
Downstream variations of the length scales, Lu, λx and their ratio Lu/λx
100
101
Regular
Fractal
x/M
λx/M
eff
M
LuL/M
u /eff
Regular
Fractal
100
10-1
10-1
101
x/M
x/M
eff
102
101
101
102
x/M
x/M
eff
For regular grid, Lu,λx and Lu/λx
gradually increase in the downstream
direction.
Lu / x
Regular
Fractal
For fractal grid, Lu, λx and Lu/λx are
almost constant.
100
101
102
x/Meff
Downstream variations of the Taylor scale turbulence Reynolds number Reλ
Regular
Fractal
100
Re
High Reλcan be
realized by the
fractal grid.
50
0
101
102
x/M
Reλ in the fractal grid turbulence is around 60-120,
whereas
Reλ in the regular grid turbulence is around 20-30.
3.2 Results by PLIF
Checking of accuracy of PLIF data-processing system
1
10-1
Present
本研究
only back-ground
背景画像の処理のみ
correction
Ito
et al.(1)
Present
only
back本研究
ground
背景画像の処理のみ
Ito et al.(1)
correction
Ito et al.(1)
Regular grid
Meff= 20mm
kc
〈C〉
Ito et al.(1)
0.5
10-2
10-3
0
-2
Page. 23
-1
0
y/M
y/M
1
eff
2
-2
-1
0
y/Meff
y/M
1
2
kc=(1/2)<c2>
The present results by the improved data-processing system
show a good agreement with the results by the single-point LIF results.
ref.
(1) Ito, Y., et al., The effects of high-frequency ultrasound on turbulent liquid mixing with a rapid chemical reaction,
Physics of fluids , 2002, 14, pp. 4362-4371
Instantaneous fluctuating concentration field
Grid turbulence
Red: c = 0.3, Blue: c = -0.3.
Fractal grid turbulence
Note: Meff = 10 mm for the regular grid
Meff = 5.68 mm for the fractal grid
Downstream variation of vertical profile of mean scalar
Page. 25
M=Meff
Regular
M=Meff
The gradient of mean scalar profile for
fractal grid is smaller than the one for
regular grid turbulence
Fractal
0.75
0.5
0.25
M=Meff
Half-width hm show the much larger values
for fractal grid than ones for regular grid.
Eddy diffusivity is about 4 times!
Downstream variation of vertical profile of scalar variance: kc=1/2<c2>
8
Regular
hf / M
6
M=Meff
Regular
Fractal
M=Meff
4
2
0
0
100
50
x/M
Fractal
The widths of vertical profile for FG are
much larger than the ones of RG.
Notice that in case of FG, from x/Meff=100
to 120, kc decreases rapidly.
M=Meff
Mixing has been enhanced at around
x/Meff=100
Downstream variations of kc on the centerline of mixing layer
10-1
x*: the wake-interaction
kc
length scale
Regular
Fractal
10-2 -1
10
100
x/x*
101
x*  101M eff
What happens
Meff
L0[mm]
t0[mm]
x*[mm]
Regular
10
10
2
50
Fractal
5.68
53.1
4.9
575.43
at around x*?
Fractal dimension of iso-scalar surface
Regular grid
x/Meff=10
10
104
101
0
10
100
Ct=0.1
Ct=0.2
Ct=0.3
Ct=0.4
Ct=0.5
Ct=0.6
Ct=0.7
101
N( )
N( )
Fractal grid
x/Meff=80
104
103
102
5
-1.45
ts
 [pixel]
N    k
Df
ts: thickness of the laser sheet,
Ct: threshold of the scalar value
102
101
hm
102
103
103
100 0
10
Ct=0.1
Ct=0.2
Ct=0.3
Ct=0.4
Ct=0.5
Ct=0.6
Ct=0.7
101
-1.55
ts
hm
 [pixel]
102
Df : fractal dimension
hm: half-width of the mean scalar profile
103
Downstream variation of Df
Regular grid
2
1
0
0
Df
Df
2
x/M=10
x/M=20
x/M=30
x/M=40
0.4
0.6
Ct
0.8
x/M= 20
x/M= 40
x/M= 60
x/M= 80
x/M=100
x/M=120
1
M=Meff
M=Meff
0.2
Fractal grid
1
0
0
0.2
0.4
0.6
Ct
Regular grid: Df does not change in the downstream direction
Fractal grid: Df becomes large in the downstream direction
Mixing is progressing in the downstream direction
in the Fractal grid turbulence
0.8
1
Conclusions
In this research,
1. We could develop the reliable data-processing system of PIV and PLIF
in our laboratory.
2. It is reconfirmed that the fractal grid turbulence is much stronger as
compared with the classical grid turbulence at the same mesh Reynolds
number.
ReMeff  2,500
the fractal grid turbulence : Reλ= 60-120.
the classical turbulence. : Reλ= 20-30．
3. Diffusion and mixing of passive scalar in the fractal grid turbulence is
extensively enhanced in comparison with that in the regular grid turbulence
Eddy diffusivity of FGT is about 4 times as large as the one of RGT
These results are useful to the design of Fractal Super Mixer with high
turbulence and low dissipation