Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-13T13:16:28.145Z Has data issue: false hasContentIssue false
  • English
  • Français

Differential diffusion of high-Schmidt-number passive scalars in a turbulent jet

Published online by Cambridge University Press:  10 October 2008

T. M. LAVERTU ,
L. MYDLARSKI  and
S. J. GASKIN
T. M. LAVERTU
Affiliation:
GE Global Research Center, 1 Research Circle, Niskayuna, NY 12309, USA
L. MYDLARSKI
Affiliation:
Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, QC, H3A-2K6, Canada
S. J. GASKIN
Affiliation:
Department of Civil Engineering and Applied Mechanics, McGill University, 817 Sherbrooke Street West, Montreal, QC, H3A-2K6, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

The separate evolution, or differential diffusion, of high-Schmidt-number passive scalars in a turbulent jet is studied experimentally. The two scalars under consideration are disodium fluorescein (Sc ≡ ν/D = 2000) and sulforhodamine 101 (Sc = 5000). The objectives of the research are twofold: to determine (i) the Reynolds-number-dependence, and (ii) the radial distribution of differential diffusion effects in the self-similar region of the jet. Punctual laser-induced fluorescence (LIF) measurements were obtained 50 jet diameters downstream of the nozzle exit for five Reynolds numbers (Re ≡ uod/ν = 900, 2100, 4300, 6700 and 10600, where u0 is the jet exit velocity, d is the jet diameter, and ν is the kinematic viscosity) and for radial positions extending from the centreline to the edges of the jet cross-section (0 ≤ r/d ≤ 7.5). Statistics of the normalized concentration difference, Z, were used to quantify the differential diffusion. The latter were found to decay slowly with increasing Reynolds number, with the root mean square of Z scaling as Zrms ≡ 〈Z2〉1/2 ∝ Re−0.1, (or alternatively 〈Z2〉 ∝ Re−0.2). Regardless of Reynolds number, differential diffusion effects were found to increase away from the centreline. The increase in differential diffusion effects with radial position, along with their increase with decreasing Reynolds number, support the hypothesis of increased differential diffusion at interfaces between the jet and ambient fluids. Power spectral densities of Z were also studied. These spectra decreased with increasing wavenumber – an observation attributed to the decay of the scalar fluctuations in a turbulent jet. Furthermore, these spectra showed that significant differential diffusion effects persist at scales larger than the Kolmogorov scale, even for moderately high Reynolds numbers.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 612 , 10 October 2008 , pp. 439 - 475
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Antonia, R. A. & Zhao, Q. 2001 Effect of initial conditions on a circular jet. Exps. Fluids 31, 319–323.CrossRefGoogle Scholar
Batchelor, G. K. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5, 113–133.CrossRefGoogle Scholar
Benson, D. M., Bryan, J., Plant, A. L., Gotto, A. M. & Smith, L. C. 1985 Digital imaging fluorescence microscopy: spatial heterogeneity of photobleaching rage constants in individual cells. J. Cell Biol. 100, 1309–1323.CrossRefGoogle Scholar
Bergmann, V., Meier, W., Wolff, D. & Stricker, W. 1998 Application of spontaneous Raman and Rayleigh scattering and two-dimensional LIF for the characterization of a turbulent CH4/H2/N2 jet diffusion flame. Appl. Phys. B 66, 489–502.CrossRefGoogle Scholar
Bilger, R. W. 1977 Reaction rates in diffusion flames. Combust. Flame 30, 277–284.CrossRefGoogle Scholar
Bilger, R. W. 1981 Molecular transport effects in turbulent diffusion flames at moderate Reynolds number. AIAA J. 20, 962–970.CrossRefGoogle Scholar
Bilger, R. W. & Dibble, R. W. 1982 Differential molecular diffusion effects in turbulent mixing. Combust. Sci. Technol. 28, 161–172.CrossRefGoogle Scholar
Brownell, C. J. & Su, L. K. 2004 Planar measurements of differential diffusion in turbulent jets. AIAA Paper 2004–2335.CrossRefGoogle Scholar
Brownell, C. J. & Su, L. K. 2007 Scale relations and spatial spectra in a differentially diffusing jet. AIAA Paper 2007-1314.CrossRefGoogle Scholar
Brownell, C. J. & Su, L. K. 2008 Planar laser imaging of differential molecular diffusion in gas-phase turbulent Jets. Phys. Fluids 20, art. 035109, 1–20.CrossRefGoogle Scholar
Chen, C. J. & Rodi, W. 1980. Vertical Turbulent Buoyant Jets: A Review of the Experimental Data. Pergamon.Google Scholar
Chen, J. Y. & Chang, W. C. 1998 Modeling differential diffusion effects in turbulent nonreacting/reacting jets with stochastic mixing models. Combust. Sci. Tech. 133, 343–375.CrossRefGoogle Scholar
Crimaldi, J. P. 1997 The effect of photobleaching and velocity fluctuations on single-point LIF measurements. Exps. Fluids 31, 90–102.CrossRefGoogle Scholar
Dibble, R. W. & Long, M. B. 2005 Investigation of differential diffusion in turbulent jet flows using planar laser Rayleigh scattering. Combust. Flame 143, 644–649.CrossRefGoogle Scholar
Dimotakis, P. E. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 69–98.CrossRefGoogle Scholar
Dimotakis, P. E. 2005 Turbulent mixing. Annu. Rev. Fluid Mech. 37, 329–356.CrossRefGoogle Scholar
Dimotakis, P. E., Miake-Lye, R. C. & Papantoniou, D. A. 1983 Structure and dynamics of round turbulent jets. Phys. Fluids 26, 3185–3192.CrossRefGoogle Scholar
Dowling, D. R. 1988. Mixing in gas phase turbulent jets. PhD dissertation, California Institute of Technology.Google Scholar
Dowling, D. R. & Dimotakis, P. E. 1990 Similarity of the concentration field of gas-phase turbulent jets. J. Fluid Mech. 218, 109–141.CrossRefGoogle Scholar
Dowling, D. R., Lang, D. B. & Dimotakis, P. E. 1989 An improved laser–Rayleigh scattering photodetection system. Exps. Fluids 7, 435–440.CrossRefGoogle Scholar
Drake, M. C., Pitz, R. W., & Lapp, M. 1986 Laser measurements on nonpremixed H2-air flames for assessment of turbulent combustion models. AIAA J. 24, 905–917.CrossRefGoogle Scholar
Ferdmann, E., ÖtüGen, M. V. & Kim, S. 2000 Effect of the initial velocity profile on the development of round jets. J. Propul. Power 16, 676–686.CrossRefGoogle Scholar
Fischer, H. B., List, E. J, Koh, R. C. Y., Imberger, J. & Brooks, N. H. 1979 Mixing in Inland and Coastal Waters. Academic.Google Scholar
Fox, R. O. 1999 The Lagrangian spectral relaxation model for differential diffusion in homogeneous turbulence. Phys. Fluids 11, 1550–1571.CrossRefGoogle Scholar
Friehe, C. A., Van Atta, C. W. & Gibson, C. H. 1971 Jet turbulence: dissipation rate measurements and correlations. AGARD CP 93, 18-1–18-7.Google Scholar
Hamamatsu Photonics 2006 Photomultiplier Tubes. Online Catalogue.Google Scholar
Jenkins, F. A. & White, H. E. 1957 Fundamentals of Optics. McGraw–Hill.Google Scholar
Kerstein, A. R. 1990 Linear-eddy modelling of turbulent transport. Part 3. Mixing and differential molecular diffusion in round jet. J. Fluid Mech. 216, 411–435.CrossRefGoogle Scholar
Kerstein, A. R., Dibble, R. W., Long, M. B., Yip, B. & Lyons, K. 1989 Measurement and computation of differential molecular diffusion in a turbulent jet. In Proc. 7th Symp. on Turb. Shear Flows, paper 14-2.Google Scholar
Kerstein, A. R., Cremer, M. A. & McMurtry, P. A. 1995 Scaling properties of differential molecular diffusion effects in turbulence. Phys. Fluids 7, 1999–2007.CrossRefGoogle Scholar
Kolmorgorov, A. N. 1941 Dokl. Akad. Nauk SSSR 30, 301.Google Scholar
Koochesfahani, M. 1984 Experiments on turbulent mixing and chemical reactions in a liquid mixing layer. PhD dissertation, California Institute of Technology.Google Scholar
Kronenburg, A. & Bilger, R. W. 1997 Modelling of differential diffusion effects in nonpremixed nonreacting turbulent flow. Phys. Fluids 9, 1435–1447.CrossRefGoogle Scholar
Kronenburg, A. & Bilger, R. W. 2001 a Modelling differential diffusion in nonpremixed reacting turbulent flow: application to turbulent jet flames. Combust. Sci. Technol. 166, 175–194.CrossRefGoogle Scholar
Kronenburg, A. & Bilger, R. W. 2001 b Modelling differential diffusion in nonpremixed reacting turbulent flow: model development. Combust. Sci. Technol. 166, 198–227.CrossRefGoogle Scholar
Lavertu, T. M. 2006 Differential diffusion in a turbulent jet. PhD dissertation, McGill University.Google Scholar
Long, M. B., Starner, S. H. & Bilger, R. W. 1993 Differential diffusion in jets using joint PLIF and Lorenz–Mie imaging. Combust. Sci. Tech. 92, 209–224.CrossRefGoogle Scholar
Lumley, J. L. & Panofsky, H. A. 1964 The Structure of Atmospheric Turbulence. Wiley.Google Scholar
Masri, A. R., Dibble, R. W. & Barlow, R. S. 1992 Chemical kinetic effects in nonpremixed flames of H2/CO2 fuel. Combust. Flame 91, 285–309.CrossRefGoogle Scholar
Meier, W., Prucker, S., Cao, M. H. & Stricker, W. 1996 Characterization of turbulent H2/N2/air jet diffusion flames by single-pulse spontaneous Raman scattering. Combust. Sci. Technol. 118, 293–312.CrossRefGoogle Scholar
Miller, P. L. 1991 Mixing in high Schmidt number turbulent jets. PhD dissertation, California Institute of Technology.Google Scholar
Miller, P. L. & Dimotakis, P. E. 1991 a Stochastic geometric properties of scalar interfaces in turbulent jets, 1991. Phys. Fluids A 3, 168–177.CrossRefGoogle Scholar
Miller, P. L, & Dimotakis, P. E. 1991 b Reynolds number dependence of scalar fluctuations in a high Schmidt number turbulent jet. Phys. Fluids A 3, 1156–1163.CrossRefGoogle Scholar
Miller, P. L. & Dimotakis, P. E. 1996 Measurements of scalar power spectra in high Schmidt number turbulent jets. J. Fluid Mech. 308, 129–146.CrossRefGoogle Scholar
Nilsen, V. & Kosály, G. 1997 Differentially diffusing scalars in turbulence. Phys. Fluids 9, 3386–3397.CrossRefGoogle Scholar
Panchapakesan, N. R. & Lumley, J. L. 1993 Turbulence measurements in axisymmetric jets of air and helium. Part 2. Helium jet. J. Fluid Mech. 246, 225–247.CrossRefGoogle Scholar
Papanicolaou, P. N. & List, E. J. 1987 Statistical and spectral properties of tracer concentration in round buoyant jets. J. Heat Mass Transfer 30, 2059–2071.CrossRefGoogle Scholar
Papanicolaou, P. N. & List, E. J. 1988 Investigations of round vertical turbulent buoyant jets. J. Fluid Mech. 195, 341–391.CrossRefGoogle Scholar
Pitsch, H. 2000 Unsteady flamelet modelling of differential diffusion in turbulent jet diffusion flames. Combust. Flame 123, 358–374.CrossRefGoogle Scholar
Pitsch, H. & Peters, N. 1998 A consistent flamelet formulation for non-premixed combustion considering differential diffusion effects. Combust. Flame 114, 26–40.CrossRefGoogle Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 1992 Numerical Recipes in FORTRAN 77, 2nd edn.Cambridge University Press.Google Scholar
Ready, J. F. 1978 Industrial Applications of Lasers. Academic.Google Scholar
Rossi, B. 1957 Optics. Addison–Wesley.Google Scholar
Sahar, E. & Treves, D. 1977 Bleaching and diffusion of laser dyes in solution under high power UV irradiation. Optics Commun. 21, 20–24.CrossRefGoogle Scholar
Saylor, J. R. 1993 Differential diffusion in turbulent and oscillatory, non-turbulent, water flows. PhD dissertation, Yale University.Google Scholar
Saylor, J. R. 1995 Photobleaching of disodium fluorescein in water. Exps. Fluids 18, 445–447.CrossRefGoogle Scholar
Saylor, J. R. & Sreenivasan, K. R. 1998 Differential diffusion in low Reynolds number water jets. Phys. Fluids 10, 1135–1146.CrossRefGoogle Scholar
Shraiman, B. I. & Siggia, E. D. 2000 Scalar turbulence. Nature 405, 639–646.CrossRefGoogle ScholarPubMed
Smith, L. L., Dibble, R. W., Talbot, L., Barlow, R. S. & Carter, C. D. 1995 a Laser Raman scattering measurements of differential molecular diffusion in nonreacting turbulent jets of H2/CO2 mixing with air. Phys. Fluids 7, 1455–1466.CrossRefGoogle Scholar
Smith, L. L., Dibble, R. W., Talbot, L., Barlow, R. S. & Carter, C. D. 1995 b Laser Raman scattering measurements of differential molecular diffusion in turbulent nonpremixed jet flames of H2/CO2 fuel. Combust. Flame 100, 153–160.CrossRefGoogle Scholar
Sreenivasan, K. R. 1991 On local isotropy of passive scalars in turbulent shear flows. Proc. R. Soc. Lond. A 434, 165–182.Google Scholar
Tavoularis, S. 2005 Measurement in Fluid Mechanics Cambridge University Press.Google Scholar
Taylor, J. R. 1997 An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, 2nd edn.University Sciencebooks.Google Scholar
Tsuji, H. & Yamaoka, I. 1971 Structure analysis of counterflow diffusion flames in the forward stagnation region of a porous cylinder. Thirteenth Symp. (Intl) on Combustion, p. 723.Google Scholar
Ulitsky, M., Vaithianathan, T. & Collins, L. R. 2002 A spectral study of differential diffusion of passive scalars in isotropic turbulence. J. Fluid Mech. 460, 1–38.CrossRefGoogle Scholar
Wang, G. R. & Fiedler, H. E. 2000 On high spatial resolution scalar measurement with LIF. Part 1: Photobleaching and thermal blooming. Exps. Fluids 29, 257–264.CrossRefGoogle Scholar
Ware, B. R., Cyr, D., Gorti, S. & Lanni, F. 1983 Electrophoretic and frictional properties of particles in complex media measured by laser light scattering and fluorescence photobleaching recovery. In Measurement of Suspended Particles by Quasi-Elastic Light Scattering, pp. 255–289.Google Scholar
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203–240.CrossRefGoogle Scholar
Wiener, N. 1949 Extrapolation, Interpolation, and Smoothing of Stationary Time Series. Technology Press.CrossRefGoogle Scholar
Yeung, P. K. 1996 Multi-scalar triadic interactions in differential diffusion with and without mean scalar gradients. J. Fluid Mech. 321, 235–278.CrossRefGoogle Scholar
Yeung, P. K. 1998 Correlations and conditional statistics in differential diffusion: Scalars with uniform mean scalar gradients. Phys. Fluids 10, 2621–2635.CrossRefGoogle Scholar
Yeung, P. K. & Pope, S. B. 1993 Differential diffusion of passive scalars in isotropic turbulence. Phys. Fluids A 5, 2467–2478.CrossRefGoogle Scholar
Yeung, P. K., Sykes, M. C. & Vedula, P. 2000 Direct numerical simulation of differential diffusion with Schmidt numbers up to 4.0. Phys. Fluids 12, 1601–1604.CrossRefGoogle Scholar
Xu, G. & Antonia, R. A. 2002 a Effect of different initial conditions on a turbulent round free jet. Exps. Fluids 33, 677683.CrossRefGoogle Scholar
Xu, G. & Antonia, R. A. 2002 b Effect of initial conditions on the temperature field of a turbulent round free jet. Intl Commun. Heat Mass Transfer 29, 1057–1068.CrossRefGoogle Scholar