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Experimental investigation of fractal features of passive scalar mixing in turbulent pipe flow

Published online by Cambridge University Press:  19 August 2025

Huixin Li Open the ORCID record for Huixin Li [Opens in a new window] ,
Duo Xu Open the ORCID record for Duo Xu [Opens in a new window]  and
Guowei He Open the ORCID record for Guowei He [Opens in a new window]
Huixin Li
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, No. 15 Beisihuanxi Road, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, No. 1 Yanqihu East Rd, Beijing 101408, PR China
Duo Xu*
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, No. 15 Beisihuanxi Road, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, No. 1 Yanqihu East Rd, Beijing 101408, PR China
Guowei He
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, No. 15 Beisihuanxi Road, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, No. 1 Yanqihu East Rd, Beijing 101408, PR China
*
Corresponding author: Duo Xu, duo.xu@imech.ac.cn
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Abstract

In this study, we present a fractal dimension analysis of high Schmidt number passive scalar mixing in experiments of turbulent pipe flow. By using the high-resolution planar laser-induced fluorescence technique, the scalar concentration fields are measured at Reynolds numbers $10\,000$, $15\,000$ and $20\,000$. In the inertial–convective range, the iso-scalar surface exhibits self-similar fractal characteristics, giving fractal dimension $1.67 \pm 0.05$ from the two-dimensional measurements over a range of length scales. This fractal dimension is approximately independent of the criteria of extracting the iso-scalar surfaces, the corresponding thresholds and the Reynolds numbers examined in this study. The crossover length scale, beyond which the $1.67 \pm 0.05$ fractal dimension is exhibited, is about ten times the Kolmogorov length scale, in agreement with previous studies. As the length scales decrease to be smaller than this crossover length scale, the fractal dimension, calculated from the one-dimensional signals, increases and approaches a saturation at approximately 2 (with the additive law) in the viscous–convective range, manifesting the space-filling characteristics, as theoretically predicted by Grossmann & Lohse (1994, Europhys. Lett., vol. 27, 347). This observation presents first-time experimental evidence for the fractal characteristics predicted by Grossmann and Lohse for the high Schmidt number passive scalar mixing.

JFM classification

Mixing: Turbulent mixing Turbulent Flows: Pipe flow

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JFM Papers
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Journal of Fluid Mechanics , Volume 1017 , 25 August 2025 , A27
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© The Author(s), 2025. Published by Cambridge University Press

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Supplementary material: File

Li et al. supplementary movie

(a) Time sequence of the scalar concentration field. (b) The iso-scalar surfaces extracted using several thresholds, each of which is indicated by a color.
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