Mixing in turbulent jets: scalar measures and isosurface geometry

Abstract

Experiments have been conducted to investigate mixing and the geometry of scalar isosurfaces in turbulent jets. Specifically, we have obtained high-resolution, highsignal-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 x lo3 < Re < 18 x lo3, 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 scaledependent generalization of power-law-fractal geometry. A connection between scaledependent-fractal geometry and the distribution of scales is established and used to compute the distribution of spatial scales in the flow.

Scale Distributions and Fractal Dimensions in Turbulence

“…The geometry of such phenomena can be quantified in terms of (constant) fractal dimensions, where power-law behavior is observed [1][2][3][4] or, in other cases, in terms of extensions of the fractal framework [5][6][7][8][9][10][11]. In turbulent mixing and combustion, in particular, such measures are useful for estimating the volume-fill fraction of isosurfaces of species composition.…”

“…This framework can be used to compute the LEB-scale pdf for level sets derived from multidimensional measurements in turbulence, for example. Experiments were conducted to measure the jet-fluid concentration in the far field of liquid-phase turbulent jets for Reynolds numbers, 4.5 3 10 3 # Re # 18 3 10 3 , at a Schmidt number, Sc Ӎ 1.9 3 10 3 [11]. Figure 4 depicts a level set of 2D spatial measurements of concentration at Re Ӎ 9 3 10 3 , recorded perpendicular to the jet axis (z͞d j 275, where d j is the jet-nozzle diameter) using laser-induced fluorescence and digital-imaging techniques.…”

“…The smallest (diffusion) scale of the concentration field is estimated to be log 10 ͑l D ͞d b ͒ Ӎ 23.0, on the jet axis. For each level set, the d b -sized bounding box was identified and partitioned into contiguous l boxes to compute the (coverage) fraction of the number of boxes that cover the level set, as a function of scale [11]. The dimension increases smoothly with the scale l and spans the full range of possible values for such data (error bars indicated if larger than symbol size).…”

Entropic-Skins Geometry to Describe Wall Turbulence Intermittency

“…The last decade showed that the multi-scale structure of turbulent interfaces is indeed much more complicated than simple scale invariance. Let us quote the work by Dimotakis and his collaborators who showed that fractal dimension has a scale-dependent character [17] as well as several studies in the field of turbulent combustion showing that pure fractal behaviour can only be a limit [18,19]. After these precisions, we should indicate that the scale-dependency of fractal dimensions or scaling exponents are not the central point of this study.…”

Effect of Gravity on Sheared Turbulence Laden With Bubbles or Droplets

“…Clusters are thereafter defined from iso-concentration contours, as regions where the concentration is higher than a prescribed level. In parallel with the analysis of scalar mixing of Catrakis & Dimotakis (1996), these will be referred to as level sets. The objects identified from this analysis are then characterized by their perimeter, P, their area, A, and the concentration level, Cduste.…”