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Linear-eddy modelling of turbulent transport. Part 3. Mixing and differential molecular diffusion in round jets

Published online by Cambridge University Press:  26 April 2006

Alan R. Kerstein
Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551-0969, USA


The linear-eddy model of turbulent mixing represents a spatially developing flow by simulating the time development along a comoving transverse line. Along this line, scalar quantities evolve by molecular diffusion and by randomly occurring spatial rearrangements, representing turbulent convection. The modelling approach, previously applied to homogeneous turbulence and to planar shear layers, is generalized to axisymmetric flows. This formulation captures many features of jet mixing, including differential molecular diffusion effects. A novel experiment involving two unmixed species in the nozzle fluid is proposed and analysed.

Research Article
© 1990 Cambridge University Press

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Antonia, R. A., Prabhu, A. & Stephenson, S. E. 1975 Conditionally sampled measurements in a heated turbulent jet. J. Fluid Mech. 72, 455480.Google 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, 113133.Google Scholar
Bilger, R. W. 1976 The structure of diffusion flames. Combust. Sci. Technol. 13, 155170.Google Scholar
Bilger, R. W. 1989 Turbulent diffusion flames. Ann. Rev. Fluid Mech. 21, 101135.Google Scholar
Bilger, R. W. & Dibble, R. W. 1982 Differential molecular diffusion effects in turbulent mixing. Combust. Sci. Technol. 28, 161172.Google Scholar
Broadwell, J. E. 1988 Molecular mixing and chemical reactions in turbulent shear flows. In Disorder and Mixing: Diffusion, Convection, and Reaction (ed. E. Guyon, Y. Pomeau, E. Charlaix & J.-P. Nadal), Part 5. Martinus Nijhoff.
Broadwell, J. E. 1989 A model for reactions in turbulent jets: Effects of Reynolds, Schmidt, and Damköhler numbers. In Turbulent Reactive Flows (ed. R. Borghi & S. N. B. Murthy), p. 257. Springer.
Broadwell, J. E. & Breidenthal, R. E. 1982 A simple model of mixing and chemical reaction in a turbulent shear layer. J. Fluid Mech. 125, 397410.Google Scholar
Broadwell, J. E. & Dimotakis, P. E. 1986 Implications of recent experimental results for modeling reactions in turbulent flows. AIAA J. 24, 885889.Google Scholar
Broadwell, J. E. & Mungal, M. G. 1988 Molecular mixing and chemical reactions in turbulent shear layers. In 22nd Symp. (Intl) on Combustion, pp. 579587. The Combustion Institute.
Brown, G. L. & Roshko, A. 1974 On density effects and large structures in turbulent mixing layers. J. Fluid Mech. 64, 775816.Google Scholar
Cruyningen, I. van, Lozano, A. & Hanson, R. K. 1989 Interpretation of planar laser-induced fluorescence flowfield images. Proc. ASME Winter Conf. (in press).Google Scholar
Curl, R. L. 1963 Dispersed phase mixing: I. Theory and effects in simple reactors. AIChE J. 9, 175181.Google Scholar
Dahm, W. J. A. 1985 Experiments on entrainment, mixing and chemical reactions in turbulent jets at large Schmidt numbers. Ph.D. thesis, Caltech.
Dahm, W. J. A. & Dimotakis, P. E. 1987 Measurements of entrainment and mixing in turbulent jets. AIAA J. 25, 12161223.Google Scholar
Dimotakis, P. E., Miake-Lye, R. C. & Papantoniou, D. A. 1983 Structure and dynamics of round turbulent jets. Phys. Fluids 26, 31853192.Google Scholar
Dowling, D. R. 1988 Mixing in gas phase turbulent jets. Ph.D. thesis, Caltech.
Dowling, D. R. & Dimotakis, P. E. 1990 Similarity of the concentration field of gas-phase turbulent jets. J. Fluid Mech. (in press).Google Scholar
Drake, M. C., Bilger, R. W. & Stårner, S. H. 1982 Raman measurements and conserved scalar modeling in turbulent diffusion flames. In 19th Symp. (Intl) on Combustion, pp. 459467. The Combustion Institute.
Durbin, P. A. 1980 A stochastic model of two-particle dispersion and concentration fluctuations in homogeneous turbulence. J. Fluid Mech. 100, 279302.Google Scholar
Effelsberg, E. & Peters, N. 1983 A composite model for the conserved scalar pdf. Combust. Flame 50, 351360.Google Scholar
Givi, P., Ramos, J. I. & Sirignano, W. A. 1985 Probability density function calculations in turbulent chemically reacting round jets, mixing layers and one-dimensional reactors. J. Non-Equilib. Thermodyn. 10, 75104.Google Scholar
Gouldin, F. C., Schefer, R. W., Johnston, S. C. & Kollmann, W. 1986 Nonreacting turbulent mixing flows. Prog. Energy Combust. Sci. 12, 257303.Google Scholar
Kerstein, A. R. 1986 Computational study of propagating fronts in a lattice-gas model. J. Statist. Phys. 45, 921931.Google Scholar
Kerstein, A. R. 1988 A linear-eddy model of turbulent scalar transport and mixing. Combust. Sci. Technol. 60, 391421.Google Scholar
Kerstein, A. R. 1989 Linear-eddy modeling of turbulent transport. II: Application to shear layer mixing. Combust. Flame 75, 397413.Google 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.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics, pp. 130134. Pergamon.
Namazian, M., Schefer, R. W. & Kelly, J. 1988 Scalar dissipation measurements in the developing region of a jet. Combust. Flame 74, 161170.Google Scholar
Papantoniou, D. A. 1985 Observations in turbulent buoyant jets by use of laser-induced fluorescence. Ph.D. thesis, Caltech.
Papantoniou, D. A. & List, E. J. 1989 Large-scale structure in the far field of buoyant jets. J. Fluid Mech. 209, 151190.Google Scholar
Pope, S. B. 1985 Pdf methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11, 119192.Google Scholar
Sawford, B. L. 1985 Lagrangian statistical simulation of concentration mean and fluctuation fields. J. Clim. Appl. Met. 24, 11521166.Google Scholar
Uberoi, M. S. & Singh, P. I. 1975 Turbulent mixing in a two-dimensional jet. Phys. Fluids 18, 764769.Google Scholar
Warhaft, Z. 1984 The interference of thermal fields from line sources in grid turbulence. J. Fluid Mech. 144, 363387.Google Scholar
Wygnanski, I. & Fiedler, H. 1969 Some measurements in the self-preserving jet. J. Fluid Mech. 38, 577612.Google Scholar