Mixing in turbulent jets: scalar measures and isosurface geometry

Experiments have been conducted to investigate mixing and the geometry of scalar isosurfaces in turbulent jets. Specifically, we have obtained high-resolution, high-signal-to-noise-ratio images of the jet-fluid concentration in the far field of round, liquid-phase, turbulent jets, in the Reynolds number range 4.5 × 10^3 ≤ Re ≤ 18 × 10^3, using laser-induced-fluorescence imaging techniques. Analysis of these data indicates that this Reynolds-number range spans a mixing transition in the far field of turbulent jets. This is manifested in the probability-density function of the scalar field, as well as in measures of the scalar isosurfaces. Classical as well as fractal measures of these isosurfaces have been computed, from small to large spatial scales, and are found to be functions of both scalar threshold and Reynolds number. The coverage of level sets of jet-fluid concentration in the two-dimensional images is found to possess a scale-dependent-fractal dimension that increases continuously with increasing scale, from near unity, at the smallest scales, to 2, at the largest scales. The geometry of the scalar isosurfaces is, therefore, more complex than power-law fractal, exhibiting an increasing complexity with increasing scale. This behaviour necessitates a scale-dependent generalization of power-law-fractal geometry. A connection between scale-dependent-fractal geometry and the distribution of scales is established and used to compute the distribution of spatial scales in the flow.

[1]  H. Takayasu.  Differential Fractal Dimension of Random Walk and Its Applications to Physical Systems , 1982 .

[2]  W. Mccomb,et al.  The physics of fluid turbulence. , 1990 .

[3]  F. Hausdorff.  Dimension und äußeres Maß , 1918 .

[4]  D. Olivari,et al.  Fractal and multifractal characteristics of a scalar dispersed in a turbulent jet , 1994 .

[5]  K. Sreenivasan.  FRACTALS AND MULTIFRACTALS IN FLUID TURBULENCE , 1991 .

[6]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[7]  C. Meneveau,et al.  The fractal geometry of interfaces and the multifractal distribution of dissipation in fully turbulent flows , 1989 .

[8]  V. R. Kuznetsov,et al.  Turbulence and combustion , 1990 .

[9]  Charles Meneveau,et al.  The fractal facets of turbulence , 1986, Journal of Fluid Mechanics.

[10]  Masuo Suzuki.  Finite-Size Scaling for Transient Similarity and Fractals , 1984 .

[11]  R. W. Bilger,et al.  Turbulent flows with nonpremixed reactants , 1980 .

[12]  P. Miller.  Mixing in High Schmidt Number Turbulent Jets , 1991 .

[13]  Hideki Takayasu,et al.  Fractals in the Physical Sciences , 1990 .

[14]  Benoit B. Mandelbrot,et al.  Fractal geometry: what is it, and what does it do? , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[15]  L F Richardson,et al.  The problem of contiguity : An appendix to statistics of deadly quarrels , 1961 .

[16]  A. Vincent,et al.  The spatial structure and statistical properties of homogeneous turbulence , 1991, Journal of Fluid Mechanics.

[17]  Kenneth Falconer,et al.  Fractal Geometry: Mathematical Foundations and Applications , 1990 .

[18]  A. Kolmogorov,et al.  Entropy and "-capacity of sets in func-tional spaces , 1961 .

[19]  John Mantzaras,et al.  Geometrical properties of turbulent premixed flames : comparison between computed and measured quantities , 1992 .

[20]  M. Borgas,et al.  The multifractal lagrangian nature of turbulence , 1993, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[21]  Constantin,et al.  Fractal geometry of isoscalar surfaces in turbulence: Theory and experiments. , 1991, Physical review letters.

[22]  Remarks on the Navier-Stokes Equations , 1991 .

[23]  T. Vicsek.  Fractal Growth Phenomena , 1989 .

[24]  B. Mandelbrot.  On the geometry of homogeneous turbulence, with stress on the fractal dimension of the iso-surfaces of scalars , 1975, Journal of Fluid Mechanics.

[25]  Alexander S. Mikhailov,et al.  Foundations of Synergetics II , 1990 .

[26]  B. Mandelbrot,et al.  Fractals: Form, Chance and Dimension , 1978 .

[27]  Geometric and analytic studies in turbulence , 1994 .

[28]  J. Chilès.  Fractal and geostatistical methods for modeling of a fracture network , 1988 .

[29]  P. Dimotakis.  Some issues on turbulent mixing and turbulence , 1993 .

[30]  G. F. Lane-Serff.  Investigation of the fractal structure of jets and plumes , 1993, Journal of Fluid Mechanics.

[31]  Peter Constantin,et al.  Navier-Stokes equations and area of interfaces , 1990 .

[32]  Peter Constantin,et al.  Geometric Statistics in Turbulence , 1994, SIAM Rev..

[33]  C. Tricot.  Curves and Fractal Dimension , 1994 .

[34]  The geometry of turbulent advection: sharp estimates for the dimensions of level sets , 1994 .

[35]  B. Mandelbrot.  How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension , 1967, Science.

[36]  Axel Brandenburg,et al.  The Fractal Dimension of Iso-Vorticity Structures in 3-Dimensional Turbulence. , 1992 .

[37]  Katepalli R. Sreenivasan,et al.  Quantitative three-dimensional imaging and the structure of passive scalar fields in fully turbulent flows , 1990, Journal of Fluid Mechanics.

[38]  E. Guenther,et al.  Turbulence, Fractals, and the Solar Granulation , 1991 .

[39]  P. Dimotakis,et al.  Stochastic geometric properties of scalar interfaces in turbulent jets , 1991 .

[40]  H. Willaime,et al.  Geometry of isothermal and isoconcentration surfaces in thermal turbulence , 1993 .

[41]  W. Ashurst.  A simple illustration of turbulent flame ball growth , 1995 .

[42]  Alan R. Kerstein,et al.  Linear-eddy modeling of turbulent transport. Part V: Geometry of scalar interfaces , 1991 .

[43]  Geoffrey Ingram Taylor,et al.  Diffusion by Continuous Movements , 1922 .

[44]  Richard C. Miake-Lye,et al.  Structure and dynamics of round turbulent jets , 1983 .

[45]  D. Mark,et al.  Scale-dependent fractal dimensions of topographic surfaces: An empirical investigation, with applications in geomorphology and computer mapping , 1984 .

[46]  P. Dimotakis,et al.  Reynolds number dependence of scalar fluctuations in a high Schmidt number turbulent jet , 1991 .