Hostname: page-component-7c8c6479df-7qhmt Total loading time: 0 Render date: 2024-03-27T13:13:51.226Z Has data issue: false hasContentIssue false

Experimental study of the fine-scale structure of conserved scalar mixing in turbulent shear flows. Part 1. Sc [Gt ] 1

Published online by Cambridge University Press:  25 July 2018

Kenneth A. Buch
Affiliation:
Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI 48109-2118, USA Present address: Sandia National Laboratories, Diagnostic and Reacting Flow Department, PO Box 969, MS 9051, Livermore, CA 94551-0969, USA.
Werner J. A. Dahm
Affiliation:
Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI 48109-2118, USA

Abstract

We present results from an experimental investigation into the fine-scale structure associated with the mixing of a dynamically passive conserved scalar quantity on the inner scales of turbulent shear flows. The present study was based on highly resolved two- and three-dimensional spatio-temporal imaging measurements. For the conditions studied, the Schmidt number (Scv/D) was approximately 2000 and the local outerscale Reynolds number (Reσ≡ uσ/v) ranged from 2000 to 10000. The resolution and signal quality allow direct differentiation of the measured scalar field ζ(x, t) to give the instantaneous scalar energy dissipation rate field (Re Sc)−1 ∇ζċ∇ζ(x, t). The results show that the fine-scale structure of the scalar dissipation field, when viewed on the inner-flow scales for Sc ≡ 1, consists entirely of thin strained laminar sheet-like diffusion layers. The internal structure of these scalar dissipation sheets agrees with the one-dimensional self-similar solution for the local strain–diffusion competition in the presence of a spatially uniform but time-varying strain rate field. This similarity solution also shows that line-like structures in the scalar dissipation field decay exponentially in time, while in the vorticity field both line-like and sheet-like structures can be sustained. This sheet-like structure produces a high level of intermittency in the scalar dissipation field – at these conditions approximately 4% of the flow volume accounts for nearly 25% of the total mixing achieved. The scalar gradient vector field ∇ζ(x, t) for large Sc is found to be nearly isotropic, with a weak tendency for the dissipation sheets to align with the principal axes of the mean flow strain rate tensor. Joint probability densities of the conserved scalar and scalar dissipation rate have a shape consistent with this canonical layer-like fine-scale structure. Statistics of the conserved scalar and scalar dissipation rate fields are found to demonstrate similarity on inner-scale variables even at the relatively low Reynolds numbers investigated.

Type
Research Article
Copyright
© 1996 Cambridge University Press

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

Andrews, L. C. & Shivamoggi, B. K. 1989 The gamma distribution as a model for temperature dissipation in intermittent turbulence. Phys. Fluids A 2, 105110.CrossRefGoogle Scholar
Anselmet, F., Gagne, Y., Hopfinger, E. J. & Antonia, R. A. 1984 High-order velocity structure functions in turbulent shear flows. J. Fluid Mech. 140, 6389.CrossRefGoogle Scholar
Ashurst, W. T., Kerstein, A. R., Kerr, R. M. & Gibson, C. H. 1987 Alignment of vorticity and scalar gradient in simulated Navier–Stokes turbulence. Phys. Fluids 30, 23432353.CrossRefGoogle Scholar
Batchelor, G. K. 1959 Small-scale variation of convected quantities like temperature in a turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5, 113133.CrossRefGoogle Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google 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, 134139.CrossRefGoogle Scholar
Batchelor, G. K. & Townsend, A. A. 1949 The nature of turbulent motion at large wavenumbers. Proc. R. Soc. Lond. A 199, 238255.CrossRefGoogle Scholar
Betchov, R. 1956 An inequality concerning the production of vorticity in isotropic turbulence. J. Fluid Mech. 1, 497504.CrossRefGoogle Scholar
Betchov, R. 1974 Non-Gaussian and irreversible events in isotropic turbulence. Phys. Fluids 17, 15091512.CrossRefGoogle Scholar
Bevington, P. R. 1969 Data Reduction and Error Analysis for the Physical Sciences. McGraw-Hill.Google Scholar
Biringen, S. 1975 An experimental investigation of an axisymmetric jet issuing into a coflowing stream. VKI Tech. Note 110.
Borgas, M. S. 1992 A comparison of intermittency models in turbulence. Phys. Fluids A 4, 20552061.CrossRefGoogle Scholar
Buch, K. A. & Dahm, W. J. A. 1996 Experimental study of the fine scale structure of conserved scalar mixing in turbulent shear flows. Part 2. Sc [asymp ] 1. J. Fluid Mech. (to be submitted).
Burgers, J. M. 1948 A mathematical model illustrating the theory of turbulence. Adv. Appl. Mech. 1, 171199.CrossRefGoogle Scholar
Burgers, J. M. 1950 The formation of vortex sheets in a simplified type of turbulent motion. Proc. Acad. Sci. Amst. 53, 122133.Google Scholar
Carrier, G. F., Fendell, F. E. & Marble, F. E. 1975 The effect of strain rate on diffusion flames. SIAM J Appl. Maths 28, 463500.CrossRefGoogle Scholar
Corrsin, S. 1951 On the spectrum of isotropic temperature fluctuations in an isotropic turbulence. J. Appl. Phys. 22, 469.CrossRefGoogle Scholar
Corrsin, S. 1962 Turbulent dissipation fluctuations. Phys. Fluids 5, 13011302.CrossRefGoogle Scholar
Dahm, W. J. A. & Buch, K. A. 1989 Lognormality of the scalar dissipation pdf in turbulent flows. Phys. Fluids A 1, 12901293.CrossRefGoogle Scholar
Dahm, W. J. A. & Dibble, R. W. 1988 Coflowing turbulent jet diffusion flame blowout. Proc. 22nd Intl Symp. on Combustion, pp. 801808. The Combustion Institute, Pittsburgh.Google Scholar
Dahm, W. J. A., Southerland, K. B. & Buch, K. A. 1991 Direct, high-resolution, four-dimensional measurements of the fine scale structure of Sc [asymp ] 1 molecular mixing in turbulent flows. Phys. Fluids A 3, 11151127.CrossRefGoogle Scholar
Dowling, D. R. & Dimotakis, P. E. 1991 Similarity in the concentration field of gas-phase turbulent jets. J. Fluid Mech. 218, 109141.CrossRefGoogle Scholar
Eswaran, V. & Pope, S. B. 1988 Direct numerical simulations of the turbulent mixing of a passive scalar. Phys. Fluids 31, 506520.CrossRefGoogle Scholar
Frisch, U. & Parisi, G. 1985 In Turbulence and Predictability in Geophysical Fluid Mechanics and Climate Dynamics (ed. M. Ghil, R. Benzi & G. Parisi). North-Holland.Google Scholar
Frisch, U., Sulem, P. & Nelkin, M. 1978 A simple dynamical model of intermittent fully developed turbulence. J. Fluid Mech. 87, 719736.CrossRefGoogle Scholar
Gibson, C. H. 1968a Fine structure of scalar fields mixed by turbulence. I. Zero-gradient points and minimal-gradient surfaces. Phys. Fluids 11, 23052315.CrossRefGoogle Scholar
Gibson, C. H. 1968b Fine structure of scalar fields mixed by turbulence. II. Spectral theory. Phys. Fluids 11, 23162327.CrossRefGoogle 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, 261293.CrossRefGoogle Scholar
Gibson, C. H. & Libby, P. A. 1972 On turbulent flows with fast chemical reactions. Part II–The distribution of reactants and products near a reacting surfaces. Combust. Sci. Tech. 8, 2935.CrossRefGoogle Scholar
Gibson, C. H., Stegen, G. R. & Williams, R. B. 1970 Statistics of the fine structure of turbulent velocity and temperature fields measured at high Reynolds numbers. J. Fluid Mech. 41, 153167.CrossRefGoogle Scholar
Gurvich, A. S. & Yaglom, A. M. 1967 Breakdown of eddies and probability distributions for small-scale turbulence. Phys. Fluids Suppl. 10, S59S65.CrossRefGoogle Scholar
Hill, R. J. 1978 Models of the scalar spectrum for turbulent advection. J. Fluid Mech. 88, 541562.CrossRefGoogle Scholar
Hill, R. J. 1980 Solution of Howells’ model of the scalar spectrum and comparison with experiment. J. Fluid Mech. 96, 705722.CrossRefGoogle Scholar
Kerr, R. M. 1985 Higher-order derivative correlations and the alignment of small scale structures in isotropic numerical turbulence. J. Fluid Mech. 153, 3158.CrossRefGoogle Scholar
Kolmogorov, A. N. 1941 Local structure of turbulence in an incompressible fluid at very high Reynolds numbers. C.R. Acad. Sci. URSS 30, 301305.Google Scholar
Kolmogorov, A. N. 1962 A refinement of previous hypotheses concerning the local structure of turbulence in viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13, 8285.CrossRefGoogle Scholar
Kuo, A. Y. & Corrsin, S. 1972 Experiments on the geometry of the fine-structure regions in fully turbulent fluid. J. Fluid Mech. 56, 447479.CrossRefGoogle Scholar
Liew, S. K., Bray, K. N. C. & Moss, J. B. 1981 A flamelet model of turbulent nonpremixed combustion. Combust. Sci. Tech. 27, 6973.CrossRefGoogle Scholar
Maczynski, J. F. J. 1962 A round jet in an ambient co-axial stream. J. Fluid Mech. 13, 597608.CrossRefGoogle Scholar
Mandelbrot, B. B. 1974 Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. J. Fluid Mech. 62, 331358.CrossRefGoogle Scholar
Mandelbrot, B. B. 1976 Intermittent turbulence and fractal dimension: kurtosis and the spectral exponent 5/3+β. In Turbulence and Navier–Stokes Equations (ed. R. Teman). Lecture Notes in Mathematics, vol. 565, pp. 121145. Springer.CrossRefGoogle Scholar
Meneveau, C. & Sreenivasan, K. R. 1991 The multifractal nature of turbulent energy dissipation. J. Fluid Mech. 224, 429484.CrossRefGoogle Scholar
Novikov, E. A. & Stewart, R. W. 1964 Turbulent intermittency and the spectrum of fluctuations of energy dissipation. Izv. Akad. Nauk. SSSR, Geofiz. no. 3, 408413.Google Scholar
Obukhov, A. M. 1949 Structure of the temperature field in a turbulent flow. Izv. Acad. Nauk SSSR, Geogr. i Geofiz 13, 5869.Google Scholar
Obukhov, A. M. 1962 Some specific features of atmospheric turbulence. J. Fluid Mech. 13, 7781.CrossRefGoogle Scholar
Ottino, J. M. 1982 Description of mixing with diffusion and reaction in terms of the concept of material surfaces. J. Fluid Mech. 114, 83103.CrossRefGoogle Scholar
Ottino, J. M. 1989 The Kinematics of Mixing: Stretching, Chaos, and Transport. Cambridge University Press.Google Scholar
Peters, N. 1984 Laminar diffusion flamelet models in non-premixed turbulent combustion. Prog. Energy Combust. Sci. 10, 319339.CrossRefGoogle Scholar
Peters, N. & Williams, F. A. 1983 Liftoff characteristics of turbulent jet diffusion flames. AIAA J. 21, 423429.CrossRefGoogle Scholar
Pope, S. B. & Cheng, W. K. 1988 The stochastic flamelet model of turbulent combustion. Proc. 22nd Intl Symp. Combustion. The Combustion Institute, Pittsburg.Google Scholar
Prasad, R. H. & Sreenivasan, K. R. 1990 Quantitative three-dimensional imaging and the structure of passive scalar fields in fully turbulent flows. J. Fluid Mech. 216, 134.CrossRefGoogle Scholar
Reichardt, H. 1964 Turbulente Strahlausbreitung in gleichgerichteter Grundströmung. Forsch. Ing. Wes. 30, 133139.CrossRefGoogle Scholar
Richardson, L. F. 1920 The supply of energy from and to atmospheric eddies. Proc. R. Soc. Lond. A 97, 354373.CrossRefGoogle Scholar
Rogers, M. M. & Moin, P. 1987 The structure of the velocity field in homogeneous turbulent flows. J. Fluid Mech. 176, 3366.CrossRefGoogle Scholar
She, Z.-S., Jackson, E. & Orszag, S. A. 1990 Intermittent vortex structures in homogeneous isotropic turbulence. Nature 344, 226228.CrossRefGoogle Scholar
Sherman, F. S. 1990 Viscous Flow. McGraw-Hill.Google Scholar
Siggia, E. D. 1981 Numerical study of small scale intermittency in three-dimensional turbulence. J. Fluid Mech. 107, 375406.CrossRefGoogle Scholar
Sreenivasan, K. R. 1991 Fractals and multifractals in fluid turbulence. Ann. Rev. Fluid Mech. 23, 539600.CrossRefGoogle Scholar
Taylor, G. I. 1935 Statistical theory of turbulence. Proc. R. Soc. Lond. A 151, 421478.CrossRefGoogle Scholar
Tennekes, H. 1968 Simple model for the small-scale structure of turbulence. Phys. Fluids 11, 669671.CrossRefGoogle Scholar
Townsend, A. A. 1951 On the fine-scale structure of turbulence. Proc. R. Soc. Lond. A 208, 534542.CrossRefGoogle Scholar
Van Atta, C. W. & Chen, W. Y. 1970 Structure functions of turbulence in the atmospheric boundary layer over the ocean. J. Fluid Mech. 44, 145159.CrossRefGoogle Scholar
Van Atta, C. W. & Yeh, T. T. 1975 Evidence for scale similarity of internal intermittency in turbulent flows at large Reynolds numbers. J. Fluid Mech. 71, 417440.CrossRefGoogle Scholar
Ware, B. R., Cyr, D., Gorti, S. & Lanni, F. 1983 In Measurements of Suspended Particles by Quasi-Elastic Light Scattering (ed. B. E. Dahneke), p. 255. Wiley.Google Scholar
Yamamoto, K. & Hosokawa, I. 1988 A decaying turbulence pursued by the spectral method. J. Phys. Soc. Japan 57, 15321535.CrossRefGoogle Scholar
Yeung, P. K., Girimaji, S. S. & Pope, S. B. 1989 Straining and scalar dissipation on material surfaces in turbulence: implications for flamelets. Combust. Flame 79, 340365.CrossRefGoogle Scholar