Mixing of high-Schmidt number scalarin 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)

(Fantasy of Flow, 1993)(Tominaga, et.al., 1976)

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 (2)

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

(2)Exponential decay law of turbulence intensity

N. Mazellier & J.C. Vassilicos, Phys. Fluids, vol.22, 075101 (2010), Fig.5

: wake-interaction length scale

L0: biggest bar length of the grid

t0: the biggest bar thickness of the grid

L0

t0

L0

t0

x*

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 , Lu/λ ～ Re0

1/2

where Re0=U∞t ０ /ν

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 　 !

R.E. Seoud & J.C. Vassilicos, Phys. Fluids, vol.19, 105108 (2007), Fig.10.

32*

1 0 0

~ 3 ~ ,

~ Re ~

uu U x C u Lt LCu U

This characteristic means the lower dissipation with the same turbulence intensityas 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 Page 8

Note : all the data processing systems of PIV and PLIF have been developed in our laboratory by my collaborators and students.

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.

２． Experimental apparatus and conditions

Page. 9

100 mm

1500 mm

100 mmHigh-Sc-number scalar

Contraction

Splitter plate

Flow

Grid

xz

y

Laser

Camera

PC

Lens

Optical filter

Regular grid

Fractal grid

PIV PLIF

Camera

Measuring area [mm2]

High speed camera(Ametek Phanton V210)

7.5(x) x 40(y)

Single-lens reflex camera (Nikon D700)

25(x) x 100(y)

Sampling frequency [Hz] 2,000 ---Sampling resolution [mm2]Thickness of sheet [mm]

0.4(x) x 0.4(y)1.0

0.03(x) x 0.03(y)0.5

Rohdamine B

Sc 2,100

Schmidt Number

effRe 2,500M

Configurations of Regular/Fractal Grids Page. 10

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 barMeff : effective mesh size

T 2 : Area of the tunnel’s cross section [m2]PM: Fractal perimeter’s length [m]

12

34

フラクタル次元

Df 　 = 1.5 Df 　 = 2.0

minmax tttr tmaxtmin

Parameter Regular grid

Fractal grid

N 1 4

Df 2.0 2.0

s 0.36 0.36

tr 1 9.76

Meff 10[mm] 5.68[mm]

24 1effM

TMP

s

ReMeff=U0Meff/ν ＝

2,500 　

Image processing for PIV Page. 11

Taking images

Digitizing

Removing back ground level

Fourier interpolation to obtain 16 times number of pixcels

1st stage

Offset cross-correlation analysisRemoving error vectors

2nd stage (in the smaller interrogation region)

Recursive cross-correlation procedure × 2 stages

Obtain velocity vectorsGradient method(sub pixel analysis)

Polyester particles: Mean diameter 50mm Specific gravity 1.03 over 7 particles in the interrogation region

ReM = 2500x/Meff = 20

Checking accuracy of data-processing by comparison of thepresent data with the LDV result

100 101 102 10310-5

10-4

10-3

10-2

10-1

Present LDV

k [1/m]E u

u

x 3 times

Offset cross-correlation analysisRemoving error vectors x 3 times

Image processing for PLIF Page. 12

PLIF processing

1. Digitizing2. Correction by the back ground image3. Applying the improved algorithm*

Measured image back ground image Non-dimensional images

Camera

Bit depth ： 14bitsSensor ： full size CMOS sensor

Single-lens reflex camera (Nikon D700)

Time variations of quantum yield and laser intensitySpatial decay of laser intensity

Reference: ＊ Suzuki,H., Nagata,K., Sakai,Y., Ukai,R., Experiments in Fluids, submitted

Good S/N ratioLarge dynamic rangeHigh sensitivity

1

0

t1 t2

Change of luminance atdifferent times

Page. 13

3. Results and Discussions

3.1 Results by PIV

Page. 14

-2 -1 0 1 20.4

0.6

0.8

1

1.2

1.4

y/M

U/U

0

x/M= 40 x/M= 60 x/M= 80 x/M=100 x/M=120

-1 0 10.4

0.6

0.8

1

1.2

1.4

x/M=10 x/M=15 x/M=20 x/M=30 x/M=40

y/M

U/U

0

Regular grid Fractal grid

Vertical profiles of mean streamwise velocity U

M=Meff M=Meff

For fractal grid turbulence, x/Meff >40

The profile becomes uniform

Instantaneous fluctuating velocity vector fields Page. 15

y/Meff

-2

0

2

y/Meff

-2

0

2

Regular grid turbulence 　 x/Meff = 40

Fractal grid turbulence 　 x/Meff = 40

tU0/Meff

tU0/Meff

Fluctuating velocities in the fractal grid turbulence are much larger than in the regular grid turbulence

0.00.15

101 10210-4

10-3

10-2

10-1

x/Meff

u rm

s2 /Uo2

Run RGT (PIV: present) Run FGT (PIV: present) regular grid turbulence (DNS: Suzuki, et al., 2009) fractal grid turbulence (DNS: Suzuki, et al., 2009)

Downstream variations of turbulent fluctuation relative intensity urms2/U0

2

Fluctuation intensity of fractal grid turbulence is much largerthan that of regular grid turbulence

Decay law for turbulence relative intensity

10110-4

10-3

10-2

10-1

x/Meff

u rm

s2 /U02

2 20

n

rms effu U a x M

1.19n 0.077a

0.2 0.4 0.6 0.8 1 1.210-3

10-2

x / x*

u rm

s2 / Uo2

Run FGT (PIV: present)

urms2/ Uo

2 = A exp{- B(x/x*)} A = 0.037 B = 2.16

Regular grid Fractal grid

Power decay law

exponential decay law

: wake-interaction length scale (N. Mazellier & J.C. Vassilicos, 2010)

Page. 20

101 102

10-1

100

x/M

x /

M

RegularFractal

101 10210-1

100

101

x/M

L u /

M

RegularFractal

101 102100

101

RegularFractal

x/Meff

L u / x

Downstream variations of the length scales, Lu, λx and their ratio Lu/λx

x/Meff x/Meff

L u/Mef

f

λ x/Mef

f

For regular grid, Lu,λx and Lu/λx

gradually increase in the downstream direction.

For fractal grid, Lu, λx and Lu/λx are almost constant.

101 1020

50

100

x/M

Re

RegularFractal

Downstream variations of the Taylor scale turbulence Reynolds number Reλ

Reλ in the fractal grid turbulence is around 60-120,

whereas Reλ in the regular grid turbulence is around 20-30.

High Reλcan be realized by the fractal grid.

3.2 Results by PLIF

Checking of accuracy of PLIF data-processing system Page. 23

(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

ref.

The present results by the improved data-processing system show a good agreement with the results by the single-point LIF results.

 

Regular gridMeff= 20mm

-2 -1 0 1 2

0

0.5

1 本研究 背景画像の処理のみ Ito et al.(1)

〈C〉

y/M-2 -1 0 1 2

10-3

10-2

10-1

y/Mk c

本研究 背景画像の処理のみ Ito et al.(1) Present

only back-ground correction Ito et al.(1)

　　　　　　　

　　 Present only back-　　 ground correction Ito et al.(1)

y/Meff y/Meff kc=(1/2)<c2>

Instantaneous fluctuating concentration field

Grid turbulence Fractal grid turbulence

Red: c = 0.3, Blue: c = -0.3. 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

Fractal

Regular

The gradient of mean scalar profile for fractal grid is smaller than the one for regular grid turbulence

0.5

 

 

 

0.25

0.75

M=Meff

M=Meff

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>

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.

  

  Fractal

Regular

0 50 1000

2

4

6

8

x/M

h f /

M

RegularFractal

M=Meff

M=Meff

M=Meff

Mixing has been enhanced at around x/Meff=100

Meff L0[mm] t0[mm] x*[mm]Regular 10 10 2 50

Fractal 5.68 53.1 4.9 575.43

10-1 100 10110-2

10-1k c

x/x*

Regular Fractal

Downstream variations of kc on the centerline of mixing layer

x*: the wake-interaction length scale

 * 101 effx M

What happensat around x*?

Fractal dimension of iso-scalar surface

100 101 102 103100

101

102

103

104

[pixel]

N(

)

Ct=0.1 Ct=0.2 Ct=0.3 Ct=0.4 Ct=0.5 Ct=0.6 Ct=0.7

-1.45

tshm

100 101 102 103100

101

102

103

104

105

Ct=0.1 Ct=0.2 Ct=0.3 Ct=0.4 Ct=0.5 Ct=0.6 Ct=0.7

ts

hm

-1.55

[pixel]

N(

)

Regular grid Fractal gridx/Meff=10 x/Meff=80

fDN k Df : fractal dimension

ts: thickness of the laser sheet, hm: half-width of the mean scalar profile

Ct: threshold of the scalar value

Downstream variation of Df

0 0.2 0.4 0.6 0.8 10

1

2

Ct

Df

x/M=10 x/M=20 x/M=30 x/M=40

0 0.2 0.4 0.6 0.8 10

1

2

x/M= 20 x/M= 40 x/M= 60 x/M= 80 x/M=100 x/M=120

Ct

Df

Regular grid Fractal grid

Regular grid: Df does not change in the downstream direction

M=MeffM=Meff

Fractal grid: Df becomes large in the downstream direction

Mixing is progressing in the downstream direction in the Fractal grid turbulence

Conclusions

1. We could develop the reliable data-processing system of PIV and PLIF in our laboratory.

In this research,

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.

3. Diffusion and mixing of passive scalar in the fractal grid turbulence is extensively enhanced in comparison with that in the regular grid turbulence

the fractal grid turbulence : Reλ= 60-120.the classical turbulence. : Reλ= 20-30 ．

Re 2,500effM

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

Thank you very much for your attention !