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## Y. Sakai*, K. Nagata*, H. Suzuki*, and R. Ukai*

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**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 phenomenacan 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)**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)).**t0**x* L0 t0 1. Introduction (3) Thelow-blockage space-filling fractal turbulence has the following properties • very much higher turbulence intensities u’/U and Reynolds number Reλ than regular grid turbulence L0 (2)Exponential decay law of turbulence intensity : wake-interaction length scale L0: biggest bar length of the grid t0: the biggest bar thickness of the grid N. Mazellier & J.C. Vassilicos, Phys. Fluids, vol.22, 075101 (2010), Fig.5**1. Introduction (4)**(3) Integral length scale Lu and the Taylor length scale λare 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～Re01/2 where Re0=U∞t０/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! This characteristic means the lower dissipation with the same turbulence intensity as compared with the normal regular grid turbulence. R.E. Seoud & J.C. Vassilicos, Phys. Fluids, vol.19, 105108(2007), Fig.10. 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 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 thePIV and PLIF technique. Note : all the data processing systems of PIV and PLIF have been developed in our laboratory by my collaborators and students.**２．Experimental apparatus and conditions**100 mm High-Sc-number scalar 100 mm Regular grid Grid Optical filter 1500 mm Contraction z x Camera Lens Fractal grid Rohdamine B Flow y Splitter plate Schmidt Number PC Laser**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 bar Meff : effective mesh size T 2 : Area of the tunnel’s cross section [m2] 1 2 3 PM: Fractal perimeter’s length [m] 4 tmax tmin ReMeff=U0Meff/ν＝2,500 フラクタル次元 Df= 1.5 Df= 2.0**Image processing for PIV**Taking images • Polyester particles: Mean diameter 50mm • Specific gravity 1.03 over 7 particles in the interrogation region Digitizing Removing back ground level Fourier interpolation to obtain 16 times number of pixcels Checking accuracy of data-processing by comparison of the present data with the LDV result Recursive cross-correlation procedure × 2 stages 1st stage Offset cross-correlation analysis Removing error vectors x3 times 2nd stage (in the smaller interrogation region) Offset cross-correlation analysis Removing error vectors x3 times ReM = 2500 x/Meff = 20 Gradient method (sub pixel analysis) Obtain velocity vectors**Image processing for PLIF**t1 t2 Camera Single-lens reflex camera (Nikon D700) Change of luminance at different times Bit depth ：14bits Sensor ：full size CMOS sensor Good S/N ratio Large dynamic range High sensitivity PLIFprocessing Time variations of quantum yield and laser intensity Spatial decay of laser intensity Digitizing Correction by the back ground image Applying the improved algorithm* Measured image back ground image Non-dimensional images 0 1 Reference: ＊ Suzuki,H., Nagata,K., Sakai,Y., Ukai,R., Experiments in Fluids, submitted**3. Results and**Discussions 3.1 Results by PIV**Page. 14**Vertical profiles of mean streamwise velocity U Regular grid Fractal grid M=Meff M=Meff For fractal grid turbulence, x/Meff >40 The profile becomes uniform**Instantaneous fluctuating velocity vector fields**Fluctuating velocities in the fractal grid turbulence are much larger than in the regular grid turbulence y/Meff 2 0 tU0/Meff -2 Regular grid turbulencex/Meff = 40 0.15 0.0 y/Meff 2 0 tU0/Meff -2 Fractal grid turbulencex/Meff = 40**Downstream variations of turbulent fluctuation relative**intensity urms2/U02 Fluctuation intensity of fractal grid turbulence is much larger than that of regular grid turbulence**Decay law for turbulence relative intensity**Fractal grid Regular grid Power decay law exponential decay law : wake-interaction length scale (N. Mazellier & J.C. Vassilicos, 2010)**Page. 20**Downstream variations of the length scales, Lu, λx and their ratio Lu/λx λx/Meff Lu/Meff x/Meff x/Meff For regular grid, Lu,λxand Lu/λxgradually increase in the downstream direction. For fractal grid, Lu, λxand Lu/λx are almost constant.**Downstream variations of the Taylor scale turbulence**Reynolds number Reλ High Reλcan be realized by the fractal grid. Reλ in the fractal grid turbulence is around 60-120, whereas Reλ in the regular grid turbulence is around 20-30.**Checking of accuracy of PLIF data-processing system**Present only back- ground correction Ito et al.(1) Present only back-ground correction Ito et al.(1) Regular grid Meff= 20mm y/Meff y/Meff 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. • 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 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**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 M=Meff 0.5 Half-width hm show the much larger values for fractal grid than ones for regular grid. Eddy diffusivity isabout 4 times! 0.25**Downstream variation of vertical profile of scalar variance:**kc=1/2<c2> Regular M=Meff M=Meff 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 x*: the wake-interaction length scale What happens at around x*?**x/Meff=80**Regular grid x/Meff=10 Fractal grid Fractal dimension of iso-scalar surface 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**Regular grid Fractal grid M=Meff M=Meff 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**Conclusions**In this research, 1. We could develop the reliable data-processing systemof 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. the fractal grid turbulence : Reλ= 60-120. the classical turbulence. : Reλ= 20-30． 3.Diffusion and mixingof passive scalarin 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