Numerical modelling of long flexible fibers in homogeneous isotropic turbulence

Abstract

We numerically investigated the transport, deformation and buckling events of an isolated elastic fiber in Taylor-Green vortices and studied the dynamics of long filaments in homogeneous isotropic turbulence. The fiber is modelled by an assembly of spherical beads. The contact between beads enforces the inextensibility of the filament while bending is accounted for by the Gears Bead Model (GBM) proposed by Delmotte et al. (2015). In the cellular Taylor-Green flow, the buckling probability is a function of a dimensionless number, called Sperm number, which is a balance between the compression rate of the flow and the elastic response of the filament. The shapes of the filament and its ability to buckle have been successfully validated through comparisons with experiments from the work by Quennouz et al. (2015). The deformation statistics of long flexible fibers in sustained homogeneous isotropic turbulence were analyzed for various flow and fiber material conditions. Two regimes have been identified depending on the ratio of fiber length to persistence length which is a measure of turbulent forcing to flexibility. The numerical results are in good agreement with existing experimental data (C. Brouzet et al., Phys. Rev. Lett. 112, 074501 (2014)) validating the assumptions of our model for the configurations we investigated.

Spinning and tumbling of long fibers in isotropic turbulence

“…The problem also bears an important aspect of fluid mechanics that relates the rotational dynamics of anisotropic particles to the velocity gradient tensor in turbulence [4]. Although most studies to date have primarily focused on the dynamics of rigid particles smaller than the Kolmogorov length (η) [4,[11][12][13], some have extended this interest to rigid inertial fibers [5][6][7]9,10] as well as to flexible fibers [14][15][16][17][18][19]. Previous theoretical and numerical studies on inertialess fibers shorter than the Kolmogorov length η have shown that such small particles strongly align with the local vorticity [11,13].…”

Investigation of shear-induced rearrangement of carbon nanotube bundles using Taylor–Couette flow

“…The disaggregation and morphologies of rod-like particles are affected by the scale of the smallest vortexes. [63][64][65] When the particles are larger than the scale of smallest vortexes, the disaggregation and the buckling behaviors are dominant. 65 The scale of the smallest vortexes can be dened as Kolmogorov's length scale L k , which decreases as the Reynolds number increases (L k $ Re À3/4 $ (u in /n) À3/4 ).…”

“…[63][64][65] When the particles are larger than the scale of smallest vortexes, the disaggregation and the buckling behaviors are dominant. 65 The scale of the smallest vortexes can be dened as Kolmogorov's length scale L k , which decreases as the Reynolds number increases (L k $ Re À3/4 $ (u in /n) À3/4 ). 64,65 Thus, the average thickness of CNT bundles should decrease as u in increases.…”

“…65 The scale of the smallest vortexes can be dened as Kolmogorov's length scale L k , which decreases as the Reynolds number increases (L k $ Re À3/4 $ (u in /n) À3/4 ). 64,65 Thus, the average thickness of CNT bundles should decrease as u in increases. In agreement with this prediction, CNT bundles subjected to u in ¼ 450 rpm were thicker (avg.…”

Deformability of discs in turbulence

“…More recently, it has been shown that, in the flexible regime, the statistics of the fibre deformations depend on the fibre length (Gay, Favier & Verhille 2018; Sulaiman et al. 2019) and that the dynamics of the deformation is given by the coherent structures of the flow (Allende, Henry & Bec 2018; Rosti et al. 2018).…”