5 results
On separated shear layers and the fractal geometry of turbulent scalar interfaces at large Reynolds numbers
- FAZLUL R. ZUBAIR, HARIS J. CATRAKIS
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- Journal:
- Journal of Fluid Mechanics / Volume 624 / 10 April 2009
- Published online by Cambridge University Press:
- 10 April 2009, pp. 389-411
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This work explores fractal geometrical properties of scalar turbulent interfaces derived from experimental two-dimensional spatial images of the scalar field in separated shear layers at large Reynolds numbers. The resolution of the data captures the upper three decades of scales enabling examination of multiscale geometrical properties ranging from the largest energy-containing scales to inertial scales. The data show a −5/3 spectral exponent over a wide range of scales corresponding to the inertial range in fully developed turbulent flows. For the fractal aspects, we utilize two methods as it is known that different methods may lead to different fractal aspects. We use the recently developed method for fractal analysis known as the Multiscale-Minima Meshless (M3) method because it does not require the use of grids. We also use the conventional box-counting approach as it has been frequently employed in various past studies. The outer scalar interfaces are identified on the basis of the probability density function (p.d.f.) of the scalar field. For the outer interfaces, the M3 method shows strong scale dependence of the generalized fractal dimension with approximately linear variation of the dimension as a function of logarithmic scale, for interface-fitting reference areas, but there is evidence of a plateau near a dimension D ~ 1.3 for larger reference areas. The conventional box-counting approach shows evidence of a plateau with a constant dimension also of D ~ 1.3, for the same reference areas. In both methods, the observed plateau dimension value agrees with other studies in different flow geometries. Scalar threshold effects are also examined and show that the internal scalar interfaces exhibit qualitatively similar behaviour to the outer interfaces. The overall range of box-counting fractal dimension values exhibited by outer and internal interfaces is D ~ 1.2–1.4. The present findings show that the fractal aspects of scalar interfaces in separated shear layers at large Reynolds number with −5/3 spectral behaviour can depend on the method used for evaluating the dimension and on the reference area. These findings as well as the utilities and distinctions of these two different definitions of the dimension are discussed in the context of multiscale modelling of mixing and the interfacial geometry.
Mixing in turbulent jets: scalar measures and isosurface geometry
- Haris J. Catrakis, Paul E. Dimotakis
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- Journal of Fluid Mechanics / Volume 317 / 25 June 1996
- Published online by Cambridge University Press:
- 26 April 2006, pp. 369-406
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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 × 103 ≤ Re ≤ 18 × 103, 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.
On intermittency and the physical thickness of turbulent fluid interfaces
- ROBERTO C. AGUIRRE, HARIS J. CATRAKIS
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- Journal:
- Journal of Fluid Mechanics / Volume 540 / 10 October 2005
- Published online by Cambridge University Press:
- 27 September 2005, pp. 39-48
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The variability of the physical thickness of fully developed turbulent interfaces is examined using scalar measurements in the outer far-field regions of round jets at a Reynolds number of $\Re\,{\sim}\,20\,000$ and Schmidt number of $\Sc\,{\sim}\,2000$. The interfacial thickness is considered in terms of the inverse magnitude of the scalar gradient across the interface and its relation to the scalar dissipation rate. The thickness variations and their conditional statistics are examined on outer interfaces at a resolution of ${\sim}\,1000^3$ with data that capture the full transverse extent of the flow. At the resolution of the present measurements, the interfaces are observed to exhibit highly intermittent thickness variations that consist of striation patterns, or undulations, along the interfacial surfaces. The conditional probability density of the interfacial thickness is found to be nearly lognormal, in agreement with previous studies. A new scale-local density measure of the interfacial thickness is formulated to examine the effects of coarse graining and the dependence of the thickness on resolution scale. The scale-local thickness density, conditionally averaged on the outer interfaces, is found to exhibit self-similarity in a range of resolved scales. This observation of self-similar behaviour, in conjunction with intermittency, provides a physical ingredient useful for studies of phenomena sensitive to turbulent interfaces.
Large-scale dynamics in turbulent mixing and the three-dimensional space–time behaviour of outer fluid interfaces
- HARIS J. CATRAKIS, ROBERTO C. AGUIRRE, JESUS RUIZ-PLANCARTE, ROBERT D. THAYNE, BRENDA A. McDONALD, JOSHUA W. HEARN
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- Journal:
- Journal of Fluid Mechanics / Volume 471 / 25 November 2002
- Published online by Cambridge University Press:
- 05 November 2002, pp. 381-408
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Experiments have been conducted to investigate turbulent mixing and the dynamics of outer fluid interfaces, i.e. the interfaces between mixed fluid and pure ambient fluid. A novel six-foot-diameter octagonal-tank flow facility was developed to enable the optical imaging of fluid interfaces above the mixing transition, corresponding to fully developed turbulence. Approximately 10003 whole-field three-dimensional space– time measurements of the concentration field were recorded using laser-induced- fluorescence digital-imaging techniques in turbulent jets at a Reynolds number of Re ∼ 20 000, Schmidt number of Sc ∼ 2000, and downstream distance of ∼ 500 nozzle diameters. Multiple large-scale regions of spatially nearly uniform-concentration fluid are evident in instantaneous visualizations, in agreement with previous findings above the mixing transition. The ensemble-averaged probability density function of concentration is found to exhibit linear dependence over a wide range of concentration thresholds. This can be accounted for in terms of the dynamics of large-scale well- mixed regions. Visualization of the three-dimensional space–time concentration field indicates that molecular mixing of entrained pure ambient fluid is dynamically initiated and accomplished in the vicinity of the unsteady large scales. Examination of the outer interfaces shows that they are dynamically confined primarily near the instantaneous large-scale boundaries of the flow. This behaviour is quantified in terms of the probability density of the location of the outer interfaces relative to the flow centreline and the probability of pure ambient fluid as a function of distance from the centreline. The current measurements show that the dynamics of outer interfaces above the mixing transition is significantly different from the behaviour below the transition, where previous studies have shown that unmixed ambient fluid can extend across a wide range of transverse locations in the flow interior. The present observations of dynamical confinement of the outer interfaces to the unsteady large scales, and considerations of entrainment, suggest that the mechanism responsible for this behaviour must be the coupling of large-scale flow dynamics with the presence of small-scale structures internal to the large-scale structures, above the mixing transition. The dynamics and structure of the outer interfaces across the entire range of space–time scales are quantified in terms of a distribution of generalized level-crossing scales. The outer-interface behaviour determines the mixing efficiency of the flow, i.e. fraction of mixed fluid. The present findings indicate that the large-scale dynamics of the outer interfaces above the mixing transition provides the dominant contribution to the mixing efficiency. This suggests a new way to quantify the mixing efficiency of turbulent flows at high Reynolds numbers.
Area–volume properties of fluid interfaces in turbulence: scale-local self-similarity and cumulative scale dependence
- HARIS J. CATRAKIS, ROBERTO C. AGUIRRE, JESUS RUIZ-PLANCARTE
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- Journal:
- Journal of Fluid Mechanics / Volume 462 / 10 July 2002
- Published online by Cambridge University Press:
- 06 August 2002, pp. 245-254
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Area–volume properties of fluid interfaces are investigated to quantify the scale-local and cumulative structure. An area–volume density g3(λ) and ratio Ω3(λ) are introduced to examine the interfacial behaviour as a function of scale λ or across a range of scales, respectively. These measures are demonstrated on mixed-fluid interfaces from whole-field ∼10003 three-dimensional space–time concentration measurements in turbulent jets above the mixing transition, at Re ∼ 20000 and Sc ∼ 2000, recorded by laser-induced-fluorescence and digital-imaging techniques, with Taylor's hypothesis applied. The cumulative structure is scale dependent in Ω3(λ), with a dimension D3(λ) that increases with increasing scale. In contrast, the scale-local structure exhibits self-similarity in g3(λ) with an exponent αg ≈1.3 for these interfaces. The scale dependence in the cumulative structure arises from the large scales, while the self-similarity corresponds to the small-scale area–volume contributions. The small scales exhibit the largest area–volume density and provide the dominant contributions to the total area–volume ratio, which corresponds to ∼10 times the area of a purely large-scale interface for the present flow conditions. The self-similarity in the scale-local structure at small scales provides the key ingredient to extrapolate the area–volume behaviour to higher Reynolds numbers.