Tumbling of Inertial Fibers in Turbulence

Anisotropic particles play a major role in many environmental and industrial turbulent flows. The modeling of their rotation dynamics is a fundamental challenge which has some important consequences in industrial processes, such as in the paper making industry. This study investigates the rotation rate of neutrally buoyant fibers longer than the Kolmogorov length ${\eta }_K$. We show that the fiber inertia is at the origin of a decrease of the rotation rate. We propose a model which describes this phenomenon. We introduce also a new Stokes number which defines the limit of validity of the classical slender body approximation.

Figure 1

The cube facility. The motor tagged with a $+$ (respectively, $-$) rotates in clockwise (respectively, counterclockwise) direction.

Figure 2

Example of trajectory reconstructed in the cube for a fiber with a diameter of $650\mu \mathrm{m}$ and a length of 10 mm. The axis units are in mm (the particle is not at scale) and this trajectory last more than 20 turnover time.

Figure 3

The main figure represents the evolution of the variance of the tumbling rate as a function of the fiber length for the different particle tested here. The dashed line represents the SB prediction [12]. In the inset, the tumbling rate is plotted as a function of the equivalent diameter $d_{\mathrm{eq}}$, the dot-dashed line represents the prediction done in [11].

Figure 4

Evolution of the transfer function as a function of the tumbling Stokes number ${\text{St}}_t$ for the all the different experimental measurements of the tumbling rate: [12] (triangle left), [11] (triangle), and this study (plain symbol). The line corresponds to the best fit of our results of Eq. (5).