The addition of polymers to turbulent pipe flows induces significant drag reduction and fundamentally modifies turbulent flow structures. This study presents a fractal dimension analysis of polymeric turbulent pipe flows using velocity fields captured via two-dimensional particle image velocimetry in the streamwise-radial plane. Two experimental datasets were generated: one by varying the polymer concentration at a constant Reynolds number (Re) and another by varying Re at a fixed polymer concentration. Friction factors were measured concurrently to quantify the extent of drag reduction. The two-dimensional fractal dimension was evaluated for isosurfaces of turbulent kinetic energy. While Newtonian turbulence exhibits a nearly constant fractal dimension at length scales exceeding a critical threshold, the introduction of polymers causes the fractal dimension to decrease monotonically with increasing concentration. Conversely, the fractal dimension remains insensitive to changes in the Reynolds number. The ratio of the critical length scale to the Kolmogorov scale varies according to both Re and polymer concentration; however, this scale ratio becomes independent of both parameters once the maximum drag reduction asymptote is reached. Spatial analysis of the one-dimensional fractal dimension across radial positions helps to further reveal the evolution of turbulence fractality. The results demonstrate that while flow inertia promotes the formation of space-filling structures, viscoelastic effects smooth these structures and transition them towards sheet-like or linear geometries. Finally, the correlation between the fractal dimension and turbulence intermittency is discussed.
Liu et al. (2026) studied this question.