1. Experimental Study of Mixing at the External Boundary of a Submerged Turbulent Jet A. Eidelman, T. Elperin, N.Kleeorin, G.Hazak, I.Rogachevskii, S.Rudykh, O.Sadot, I. Sapir-Katiraie

2. Outline  Motivation and objectives  Experimental setup  Instrumentation and data processing  Velocity parameters of the jet flow  Measurements of the phase function of mixing  Determination of the phase function PDF parameters  Results and conclusions

3. Motivation and objectives  An important property of mixing is a sharp increase of mixing rates observed by Konrad (1976). It is attributed to the onset of small-scale turbulence within large-scale coherent motions. Studies of this effect (i.e., Hussain & Zaman, 1980; Huang & Ho, 1990; Moser & Rogers, 1991; Dimotakis, 2000; Meyer, Dutton & Lucht, 2006) have demonstrated complex nonlinear dynamics of this phenomenon.  However, it is not clear how such mixing states are attained. The uncertainty is strengthened by the differences in experimental results obtained in gaseous and liquid flows (Miller and Dimotakis, 1991). The difference in behavior is attributed to a Schmidt number effect that is high in liquid and low in gaseous flows.  We investigate the mixing in the submerged air jet using the incense smoke characterized by a significantly larger Schmidt numbers than employed in the previous studies of gas flow mixing. In the present study we focus on the internal structure of the fluid mixing before the molecular effect predominates. It is a first stage of the study.  In our study we use the approach used by Hazak et al. (2006). It was based on the phase function measurements, suggested by Drew (1983) for mixing studies, and determination of its characteristics.

4. equality define a characteristic scale, where is a number of a statistical moment, and a property of a ratio equality where, and are parameters characterizing the length scale and a deviation from the exponential PDF, accordingly. Ratios of the PDF moments Background The study of Hazak et al. (2006) have revealed that PDF of the sizes of the regions occupied by the heavy fluid can be described by the Gamma function distribution in a flow with Rayleigh-Taylor instability in the linear electric motor experiments and in DNS was used for the determination of the PDF parameters in their study.

5. Experimental setup 1 – Nd-YAG laser, 2 –trajectory of the laser beam, 3 –light sheet optics, 4 – CCD camera, 5 – system computer. Test section.

6. Scheme of a jet flow and measurements 1 – channel with transparent walls, 2 – tube with a jet nozzle, 3 – submerged jet, 4 – light sheet optics, 5 – laser light sheet, 6 – image area, 7 – CCD camera.

7. Jet velocity field Re100808430 U o, m/s15.112.6 Re t 18401370 u, m/s2.762.06 Re λ 166144 λ, mm0.91.0 ε, m 2 /s 3 2100870 η, μm3644 u k, m/s0.420.34 Parameters

8. Measurements in a jet flow Jet coordinates and a range of measurements Binary jet image averaged over an ensemble

9. PDF of light intensities Blue line – in the jet.Red line in the surrounding fluid.

10. Determination of a jet boundary  Normalization of images in order to eliminate fluctuations of an initial concentration of particles.  Defining of a threshold for image binarization with histograms of light distributions inside a jet and in an external fluid.  Images conversion into a binary form.  Ensemble averaging over 50 binary images.  Determination of a jet boundary and of an angle of the jet expansion with a threshold 0.5 that means an equal probability of a jet fluid and of an external fluid over the boundary.

11. Phase function

12. Determination of a phase function parameters  Turn of binary images on different angles.  Measurement of phase functions of an ensemble of images for each turn angle.  Determination of a homogeneity range of the phase functions for all set of the angles.  Plotting of the histograms of the phase functions obtained over each line.  Fit of the histograms of the phase functions with the  Fit of the histograms of the phase functions with the Gamma function distribution

13. Mean phase function across a jet Circles: Re=10000 Triangles: Re=8400 Measured in a range centered at

14. Normalized histograms do not show universal property of power dependence z/D = 0.36 z/D = 0 z/D = - 0.36z/D = - 0.91

15. Normalized histograms do not show an exponential behavior z/D = 0.36 z/D = 0 z/D = - 0.36z/D = - 0.91

16. Fit of the phase function PDF Blue circles: PDF of jet fluid,Red circles: PDF approximation Magenta circles: exponent part of PDFGreen circles: power part of PDF

17. Ratios of PDF moments are equal, if

18. Power r vs. distance from the jet boundary Circles: Re=10000 Triangles: Re=8430

19. Scale λ vs. distance from the jet boundary Circles: Re=10000 Triangles: Re=8430

20. Conclusions  PDF of the phase function of jet mixing can be described with the Gamma distribution that is similar to the PDF of a phase function during mixing induced by Rayleigh-Taylor instability.  The parameters of Gamma distribution can be determined using a fit of the measured histogram of the phase function. A method of an equality of the PDF moments can be applied, if fragments sizes is larger than 10λ 1.  The measured power r is close to 1, and the characteristic scale λ increases from 0.05 to 1 D from a periphery to an internal part of a jet.  There is no evident dependence of both parameters on Re number at Re ~ 10 4, although the range of Re was not large.  There is a difference in the parameters of Gamma distribution for mixing induced by Rayleigh-Taylor instability and for mixing at the external boundary of a turbulent jet caused, probably, by the different physical mechanisms of mixing in these two cases.

21. References Dimotakis, P. E. The mixing transition in turbulent flows. J. Fluid Mech. 409, 69, 2000. Drew, D.A. Mathematical modeling of two-phase flow. Ann. Rev. Fluid Mech. 15, 261, 1996. Eidelman, A., Elperin, T., Kapusta, A., Kleeorin, N., Krein, A., Rogachevskii, I. Oscillated grid turbulence facility for turbulent transfer studies. Nonlinear Processes in Geophysics, 9, (3-4), 201-205, 2002. Hazak, G., Elbaz, Y., Gardner, J. N., Velikovich, A. L., Schmitt, A. J., and Zalesak, S. T. Size distribution and energy spectrum in the mixed state induced by Rayleigh-Taylor instability. Phys. Rev. E 73, 047303, 2006. Huang, L. S. & Ho, C. M. Small-scale transition in a plane mixing layer. J. Fluid Mech. 210, 475–500, 1990. Hussain, A. K. M. F., and Zaman, K. B. M. Q. Vortex pairing in a circular jet under controlled excitation. Part 2. Coherent structure dynamics. J. Fluid Mech. 101, 493– 544, 1980. Konrad, J. H. An experimental investigation of mixing in two-dimensional turbulent shear flows with applications to diffusion-limited chemical reactions. PhD Thesis, California Institute of Technology, Pasadena, California, 1976. Meyer, T. R., Dutton, J. C., and Lucht, R. P. Coherent structures and turbulent molecular mixing in gaseous planar shear layers. J. Fluid Mech. 558, 179-205, 2006. Miller P. L., Dimotakis P. E. Reynolds number dependence of scalar fluctuations in a high Schmidt number turbulent jet. Phys. Fluids, A 3 (5), 1156-63, 1991. Moser, R. D. and Rogers, M. M. Mixing transition and the cascade to small scales in a plane mixing layer. Phys. Fluids A 3, 1128–1134, 1991. Yule, A. J. Large-scale structure in the mixing layer of a round jet. J. Fluid Mech. 89, 413, 1978.