Mixing and Isosurface Geometry in Turbulent Transverse Jets

Citation

Shan, Wei-Jen Jerry (2001) Mixing and Isosurface Geometry in Turbulent Transverse Jets. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/0R6S-DY34. https://resolver.caltech.edu/CaltechETD:etd-01082002-152648

Abstract

Mixing and the geometry of jet-fluid-concentration level sets in turbulent transverse jets were experimentally studied. Jet-fluid concentration fields were measured with laser-induced fluorescence and digital imaging techniques for Reynolds numbers between 1000 and 20000. The scalar field is assessed in terms of classical measures, such as two-dimensional power spectra, as well as probability-density functions (PDFs). Enhanced scalar mixing with increasing Reynolds number is found in the evolution of PDFs of jet-fluid concentration. In the far field of the transverse jet, the scalar PDF is seen to evolve from a monotonically-decreasing function to a strongly-peaked distribution with increasing Reynolds number. Turbulent mixing is found to be flow dependent, based on differences between PDFs of scalar fields in transverse jets and axisymmetric, turbulent jets. The distribution of scalar increments is also studied for separations of varying distance and direction. A novel technique for whole-field measurement of scalar increments is introduced. Probability-density functions of scalar increments are found to trend toward exponential-tailed distributions with decreasing separation distances. The scalar field is anisotropic with decreasing scale, as seen in the two-dimensional power spectra, directional scalar microscales, and in directional PDFs of scalar increments. The geometric complexity of level-sets (iso-concentration contours) in turbulent mixing is assessed within the framework of fractal geometry. Generalized coverage statistics are introduced for anisotropic, non-self-similar geometries. This generalized coverage counting involves covering with parallelepipeds of varying size and aspect ratio. A scale-dependent measure of the anisotropy of a set is also introduced. It is shown that this scale-dependent measure transforms the generalized coverage count to isotropy through a scale-dependent normalization of the coordinates. Level sets of jet-fluid concentration in the transverse jet are found to be anisotropic at both large and small scales. The small-scale anisotropy is explained by vertically-oriented extensional strain caused by a counter-rotating vortex pair, while the large-scale anisotropy is associated with the horizontally-elongated shape of the cross-section of the transverse jet. For the special case of isotropic box-counting, the scale-dependent coverage dimension is found to vary from unity, at the smallest length scales, to 2, at the largest length scales, indicating that the isosurfaces produced by turbulent mixing are more complex than can be described by power-law fractals

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