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Linear-eddy modelling of turbulent transport. Part 6. Microstructure of diffusive scalar mixing fields

Published online by Cambridge University Press:  26 April 2006

Alan R. Kerstein
Alan R. Kerstein
Affiliation:
Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551–0969, USA
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Abstract

The linear-eddy approach for modelling molecular mixing in turbulent flow involves stochastic simulation on a one-dimensional domain with sufficient resolution to include all physically relevant lengthscales. In each realization, molecular diffusion is implemented deterministically, punctuated by a sequence of instantaneous, statistically independent ‘rearrangement events’ (measure-preserving maps) representing turbulent stirring. These events emulate the effect of compressive strain on the scalar field. An inertial-range similarity law is incorporated.

The model reproduces key features of scalar power spectra, including dependences of spectra! amplitudes and transition wavenumbers on Reynolds and Schmidt numbers. Computed scaling exponents governing scalar power spectra, higher-order fluctuation statistics such as structure functions, and the spatial distribution of scalar level crossings are close to measured exponents. It is inferred that the characterization of stirring as a sequence of independent events (the model analogue of eddies) leads to a useful representation of mixing-field microstructure.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 231 , October 1991 , pp. 361 - 394
Copyright
© 1991 Cambridge University Press

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References

Andrews, L. C., Phillips, R. L., Shivamoggi, B. K., Beck, J. K. & Joshi, M. L. 1989 A statistical theory for the distribution of energy dissipation in intermittent turbulence. Phys. Fluids A 1, 999–1006.Google Scholar
Andrews, L. C. & Shivamoggi, B. K. 1990 The gamma distribution as a model for temperature dissipation in intermittent turbulence. Phys. Fluids A 2, 105–110.Google Scholar
Antonia, R. A., Hopfinger, E. J., Gagne, Y. & Anselmet, F. 1984 Temperature structure functions in turbulent shear flows. Phys. Rev. A 30, 2704–2707.Google Scholar
Antonia, R. A. & Sreenivasan, K. R. 1977 Log-normality of temperature dissipation in a turbulent boundary layer. Phys. Fluids 20, 1800–1804.Google Scholar
Ashurst, W. T., Kerstein, A. R., Kerr, R. M. & Gibson, C. H. 1987 Alignment of vorticity and scalar gradient with strain rate in simulated Navier-Stokes turbulence. Phys. Fluids 30, 2343–2353.Google Scholar
Baldyga, J. & Bourne, J. R. 1984a A fluid-mechanical approach to turbulent mixing and chemical reaction. Part I. Inadequacies of available methods. Chem. Engng Commun. 28, 231–241.Google Scholar
Baldyga, J. & Bourne, J. R. 1984b A fluid-mechanical approach to turbulent mixing and chemical reaction. Part II. Micromixing in the light of turbulence theory. Chem. Engng Commun. 28, 243–258.Google Scholar
Baldyga, J. & Bourne, J. R. 1984c A fluid-mechanical approach to turbulent mixing and chemical reaction. Part III. Computational and experimental results for the new micromixing model. Chem. Engng Commun. 28, 259–281.Google Scholar
Batchelor, G. K. 1952 The effect of homogeneous turbulence on material lines and surfaces. Proc. R. Soc. Lond. 213, 349–366.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, 113–133.CrossRefGoogle Scholar
Batchelor, G. K., Howells, I. D. & Townsend, A. A. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 2. The case of large conductivity. J. Fluid Mech. 5, 134–139.Google Scholar
Broadwell, J. E. & Bbeidenthal, R. E. 1982 A simple model of mixing and chemical reaction in a turbulent shear layer. J. Fluid Mech. 125, 397–410.Google Scholar
Broadwell, J. E. & Mungal, M. G. 1988 Molecular mixing and chemical reactions in turbulent shear layers. 22nd Symp. (Intl.) on Combustion, pp. 579–587. The Combustion Institute.
Champagne, F. H., Friehe, C. A., Larue, J. O. & Wyngaard, J. C. 1977 Flux measurements, flux estimation techniques, and fine-scale turbulence measurements in the unstable surface layer over land. J. Atmos. Sci. 34, 515–530.Google Scholar
Clay, J. P. 1973 Turbulent mixing of temperature in water, air and mercury. PhD thesis, University of California at San Diego.
Curl, R. L. 1963 Dispersed phase mixing: I. Theory and effects in simple reactors. AIChE J. 9, 175–181.CrossRefGoogle Scholar
Dimotakis, P. E. 1989a Turbulent free shear layer mixing and combustion. Proc. Ninth ISABE (Athens), pp. 58–79.Google Scholar
Dimotakis, P. E. 1989b Turbulent shear layer mixing with fast chemical reactions. Turbulent Reactive Plows (ed. R. Borghi & S. N. B. Murthy). Lecture Notes in Engineering, vol. 40, pp. 417–489, Springer.
Dimotakis, P. E., Broadwell, J. E. & Zukoski, E. E. 1990 Combustion in turbulent jets and buoyant flames. Gas Res. Inst. Rep. GRT 90/0154.Google Scholar
Dowling, D. R. 1991 The estimated scalar dissipation rate in gas-phase turbulent jets. Phys. Fluids A, (in press).Google Scholar
Durbin, P. A. 1980 A stochastic model of two-particle dispersion and concentration fluctuations in homogeneous turbulence. J. Fluid Mech. 100, 279–302.Google Scholar
Eswaran, V. & Pope, S. B. 1988 Direct numerical simulation of the turbulent mixing of a passive scalar. Phys. Fluids 31, 506–520.Google Scholar
Fulachier, L. & Dumas, R. 1976 Spectral analogy between temperature and velocity fluctuations in a turbulent boundary layer. J. Fluid Mech. 77, 257–277.Google Scholar
Frisch, U., Sulem, P.-L. & Nelkin, M. 1978 A simple dynamical model of intermittent fully developed turbulence. J. Fluid Mech. 87, 719–736.Google Scholar
Garrett, C. 1983 On the initial streakiness of dispersing tracer in two- and three-dimensional turbulence. Dyn. Atmos. Oceans 7, 265–277.Google Scholar
Gibson, C. H. 1968a Fine structure of scalar fields mixed by turbulence. I. Zero-gradient points and minimal gradient surfaces. Phys. Fluids 11, 2305–2315.Google Scholar
Gibson, C. H. 1968b Fine structure of scalar fields mixed by turbulence. II. Spectral theory. Phys. Fluids 11, 2316–2327.Google Scholar
Gibson, C. H., Ashurst, W. T. & Kerstein, A. R. 1988 Mixing of strongly diffusive passive scalars like temperature by turbulence. J. Fluid Mech. 194, 261–293.Google Scholar
Grant, H. L., Hughes, B. A., Vogel, W. M. & Moilliet, A. 1968 The spectrum of temperature fluctuations in turbulent flow. J. Fluid Mech. 34, 423–442.Google Scholar
Gurvich, A. S. & Yaglom, A. M. 1967 Breakdown of eddies and probability distributions for small-scale turbulence. Phys. Fluids Suppl. (Proc. Kyoto Sympos. on Boundary Layers and Turbulence), 10, S59-S65.Google Scholar
Hill, R. J. 1978 Models of the scalar spectrum for turbulent advection. J. Fluid Mech. 88, 541–562.Google Scholar
Hinze, J. O. 1975 Turbulence, 2nd edn. McGraw-Hill.
Kerr, R. M. 1990 Velocity, scalar and transfer spectra in numerical turbulence. J. Fluid Mech. 211, 309–332.Google Scholar
Kerstein, A. R. 1986 Computational study of propagating fronts in a lattice-gas model. J. Stat. Phys. 45, 921–931.Google Scholar
Kerstein, A. R. 1988 A linear-eddy model of turbulent scalar transport and mixing. Combust. Sci. Technol. 60, 391–421.Google Scholar
Kerstein, A. R. 1989 Linear-eddy modeling of turbulent transport. II: Application to shear layer mixing. Combust. Flame 75, 397–413.CrossRefGoogle Scholar
Kerstein, A. R. 1990 Linear-eddy modelling of turbulent transport. Part 3. Mixing and differential molecular diffusion in round jets. J. Fluid Mech. 216, 411–435.Google Scholar
Kerstein, A. R. 1991a Linear-eddy modeling of turbulent transport. Part 4. Structure of diffusion flames. Combust. Sci. Technol. (in press).Google Scholar
Kerstein, A. R. 1991b Linear-eddy modeling of turbulent transport. Part 5. Geometry of scalar interfaces. Phys. Fluids A 3, 1110–1114.Google Scholar
Kerstein, A. R. 1991c Linear-eddy modelling of turbulent transport. Part 7. Finite-rate chemistry and multi-stream mixing. Preprint.
Kraichnan, R. H. 1968 Small-scale structure of a scalar field convected by turbulence. Phys. Fluids 11, 945–953.Google Scholar
Kraichnan, R. H. 1990 Models of intermittency in hydrodynamic turbulence. Phys. Rev. Lett. 65, 575–578.Google Scholar
Lesieur, M. 1987 Turbulence in Fluids. Martinus Nijhoff.
Leslie, D. C. 1973 Developments in the Theory of Turbulence. Oxford University Press.
McMurtry, P. A. & Givi, P. 1989 Direct numerical simulations of mixing and reaction in a nonpremixed homogeneous turbulent flow. Combust. Flame 77, 171–185.Google Scholar
Meneveau, C. & Sreenivasan, K. R. 1990 Interface dimension in intermittent turbulence. Phys. Rev. A 41, 2246–2248.Google Scholar
Miller, P. L. & Dimotakis, P. E. 1991 Stochastic geometric properties of scalar interfaces in turbulent jets. Phys. Fluids A 3. 168–177.Google Scholar
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics, vol. 1. Massachusetts Institute of Technology Press.
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, vol. 2. Massachusetts Institute of Technology Press.
Ott, E. & Antonsen, T. M. 1989 Fractal measures of passively convected vector fields and scalar gradients in chaotic fluid flows. Phys. Rev. A 39, 3660–3671.Google Scholar
Pope, S. B. 1985 Pdf methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11, 119–192.Google Scholar
Prasad, R. R., Meneveau, C. & Sreenivasan, K. R. 1988 Multifractal nature of the dissipation field of passive scalars in fully turbulent flows. Phys. Rev. Lett. 61, 74–77.Google Scholar
Prasad, R. R. & Sreenivasan, K. R. 1990 The measurement and interpretation of fractal dimensions of the scalar interface in turbulent flows. Phys. Fluids A 2, 792–807.Google Scholar
Pratt, D. T. 1976 Mixing and chemical reaction in continuous combustion. Prog. Energy Combust. Sci. 1, 73–86.Google Scholar
Pumir, A., Shraiman, B. I. & Siggia, E. D. 1991 Exponential tails and random advection. Phys. Rev. Lett. 66, 2984–2987.Google Scholar
Reif, F. 1965 Fundamentals of Statistical and Thermal Physics. McGraw-Hill.
Sawford, B. L. & Hunt, J. C. R. 1986 Effects of turbulence structure, molecular diffusion and source size on scalar fluctuations in homogeneous turbulence. J. Fluid Mech. 165, 373–400.Google Scholar
She, Z.-S. & Orszag, S. A. 1991 Physical model of intermittency in turbulence: Inertial-range non-Gaussian statistics. Phys. Rev. Lett, 66, 1701–1704.Google Scholar
Shih, T.-H., Lumley, J. L. & Chen, J.-Y. 1990 Second-order modeling of a passive scalar in a turbulent shear flow. AIAA J. 28, 610–617.Google Scholar
Sreenivasan, K. R. & Prasad, R. R. 1989 New results on the fractal and multifractal structure of the large Schmidt number passive scalars in fully turbulent flows. Physica D 38, 322–329.Google Scholar
Sreenivasan, K. R., Ramshankar, R. & Meneveau, C. 1989 Mixing, entrainment and fractal dimensions of surfaces in turbulent flows. Proc. R. Soc. Lond. A 421, 79–108.Google Scholar
Taylor, G. I. 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. 20, 196–212.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. Massachusetts Institute of Technology Press.
Thomson, D. J. 1990 A stochastic model for the motion of particle pairs in isotropic high-Reynolds-number turbulence, and its application to the problem of concentration variance. J. Fluid Mech. 210, 113–153.CrossRefGoogle Scholar
Van Atta, C. W. 1971 Influence of fluctuations in local dissipation rates on turbulent scalar characteristics in the inertial subrange. Phys. Fluids 14, 1803–1804.Google Scholar
Warhaft, Z. 1984 The interference of thermal fields from line sources in grid turbulence. J. Fluid Mech. 144, 363–387.Google Scholar
Wilks, S. S. 1962 Mathematical Statistics. Wiley.