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

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.