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

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, (2007) R.E. Seoud, J.C. Vassilicos, Phys. Fluids, vol.19, (2007) N. Mazellier & J.C. Vassilicos, Phys. Fluids, vol.22, (2010) J.C. Vassilicos, Phys. Letters A, vol.375 (2010), pp 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, (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 Re λ than regular grid turbulence (2)Exponential decay law of turbulence intensity N. Mazellier & J.C. Vassilicos, Phys. Fluids, vol.22, (2010), Fig.5 : wake-interaction length scale L 0 : biggest bar length of the grid t 0 : the biggest bar thickness of the grid L0L0 t0t0 L0L0 t0t0 x*x*

1. Introduction (4) (3) Integral length scale L u and the Taylor length scale λ are independent of the downstream position x and also Re λ R.E. Seoud & J.C. Vassilicos, Phys. Fluids, vol.19, (2007), Fig.2 and Fig.9 L u ～ L 0, λ ～ L 0 Re 0 -1/2, L u /λ ～ Re 0 1/2 where Re 0 =U ∞ t ０ /ν L u 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, (2007), Fig.10. This characteristic means the lower dissipation with the same turbulence intensity 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 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 mm 1500 mm 100 mm High-Sc-number scalar Contraction Splitter plate Flow Grid x z y Laser Camera PC Lens Optical filter Regular grid Fractal grid PIVPLIF Camera Measuring area [mm 2 ] 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, Sampling resolution [mm 2 ] Thickness of sheet [mm] 0.4(x) x 0.4(y) (x) x 0.03(y) 0.5 Rohdamine B Schmidt Number

Configurations of Regular/Fractal Grids Page. 10 Parameters for regular/fractal grids are as follows, N : number of fractal iterations D f : fractal dimension  : blockage ratio t r : thickness ratio of the largest to the smallest bar M eff : effective mesh size T 2 : Area of the tunnel’s cross section [m 2 ] P M : Fractal perimeter’s length [m] フラクタル次元 D f = 1.5D f = 2.0 t max t min Parameter Regular grid Fractal grid N14 DfDf 2.0  0.36 trtr M eff 10[mm]5.68[mm] Re Meff =U 0 M eff /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 analysis Removing error vectors 2nd stage (in the smaller interrogation region) Recursive cross-correlation procedure × 2 stages Obtain velocity vectors Gradient method ( sub pixel analysis ) Polyester particles: Mean diameter 50  m Specific gravity 1.03 over 7 particles in the interrogation region Re M = 2500 x/M eff = 20 Checking accuracy of data- processing by comparison of the present data with the LDV result x 3 times Offset cross-correlation analysis Removing error vectors x 3 times

Image processing for PLIF Page. 12 PLIF processing 1.Digitizing 2.Correction by the back ground image 3.Applying the improved algorithm* Measured imageback ground imageNon-dimensional images Camera Bit depth ： 14bits Sensor ： full size CMOS sensor Single-lens reflex camera (Nikon D700) Time variations of quantum yield and laser intensity Spatial decay of laser intensity Reference: ＊ Suzuki,H., Nagata,K., Sakai,Y., Ukai,R., Experiments in Fluids, submitted Good S/N ratio Large dynamic range High sensitivity 10 t1t1 t2t2 Change of luminance at different times

Page Results and Discussions 3.1 Results by PIV

Page. 14 Regular gridFractal grid Vertical profiles of mean streamwise velocity U M=M eff For fractal grid turbulence, x/M eff >40 The profile becomes uniform

Instantaneous fluctuating velocity vector fields Page. 15 y/M eff y/M eff Regular grid turbulence x/M eff = 40 Fractal grid turbulence x/M eff = 40 tU 0 /M eff Fluctuating velocities in the fractal grid turbulence are much larger than in the regular grid turbulence

Downstream variations of turbulent fluctuation relative intensity u rms 2 /U 0 2 Fluctuation intensity of fractal grid turbulence is much larger than that of regular grid turbulence

Decay law for turbulence relative intensity Regular grid Fractal grid Power decay law exponential decay law : wake-interaction length scale (N. Mazellier & J.C. Vassilicos, 2010)

Vertical Profiles of velocity rms values, (u x ) rms and (u y ) rms Page. 18 Regular grid Fractal grid M=M eff

Anisotropy of velocity fluctuation Page. 19 ※ Comte-Bellot, G. & Corrsin, S. “The use of a contraction to improve the isotropy of grid-generated turbulence”, JFM, 1966, 25, Regular grid Fractal grid σ=0.25 All other data for regular grids: σ ＝ 0.34 Present data of regular/fractal grid turbulence show the same level of anisotropy as other data.

Page. 20 Downstream variations of the length scales, L u, λ x and their ratio L u /λ x x/M eff L u /M eff λ x /M eff For regular grid, L u,λ x and L u /λ x gradually increase in the downstream direction. For fractal grid, L u, λ x and L u /λ x are almost constant.

Downstream variations of the Taylor scale turbulence Reynolds number Re λ Re λ in the fractal grid turbulence is around , whereas Re λ in the regular grid turbulence is around High Re λ can 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 ref. The present results by the improved data-processing system show a good agreement with the results by the single-point LIF results. Regular grid M eff = 20mm Present only back-ground correction Ito et al.(1) Present only back- ground correction Ito et al.(1) y/M eff k c =(1/2)

Instantaneous fluctuating concentration field Grid turbulenceFractal grid turbulence Red: c = 0.3, Blue: c = Note: M eff = 10 mm for the regular grid M eff = 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 M=M eff Half-width h m 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: k c =1/2 The widths of vertical profile for FG are much larger than the ones of RG. Notice that in case of FG, from x/M eff =100 to 120, k c decreases rapidly. Fractal Regular M=M eff Mixing has been enhanced at around x/M eff =100

M eff L 0 [mm]t 0 [mm]x*[mm] Regular Fractal Downstream variations of k c on the centerline of mixing layer x*: the wake-interaction length scale What happens at around x*?

Fractal dimension of iso-scalar surface Regular grid Fractal grid x/M eff =10 x/M eff =80 D f : fractal dimension t s : thickness of the laser sheet, h m : half-width of the mean scalar profile C t : threshold of the scalar value

Downstream variation of D f Regular gridFractal grid Regular grid: D f does not change in the downstream direction M=M eff Fractal grid: D f 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 : Re λ = the classical turbulence. : Re λ = ． 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