Mean shear versus orientation isotropy: effects on inertialess spheroids’ rotation mode in wall turbulence

Abstract

The orientation of spheroidal particles dispersed in a fluid flow is known to influence the particles’ rotation mode. Rod-like and disk-like particles orient themselves differently and accordingly also rotate differently. In order to explore the role of the deterministic factors, i.e. mean shear and vorticity anisotropy, on the orientational behaviour of inertialess tracer spheroids, we adopted a purpose-made Couette–Poiseuille flow simulated numerically by Yang et al. (Intl J. Heat Fluid Flow, vol. 63, 2017, pp. 14–27). Typical wall turbulence with streamwise-oriented streaky structures caused by the locally high mean shear rate was observed only at one of the walls. The absence of mean shear at the other wall gave rise to an atypical turbulence field. Over a relatively wide and quasi-homogeneous core region, a modest mean shear rate made the vorticity field anisotropic. In spite of the mean shear, rod-like tracers were spinning and disk-like spheroids were tumbling, just as in homogeneous isotropic turbulence. We explained this phenomenon by the isotropic particle orientation and concluded that zero mean shear is not necessary for rod spinning and disk tumbling. The orientation and rotation of the Lagrangian tracer spheroids near the high shear wall were almost indistinguishable from the well-known behaviour in turbulent channel flows. Near the opposite wall, where the mean shear was negligibly small, disk-like particles aligned preferentially in the wall-normal direction and rotated similarly as in the presence of high shear. Rod-like particles, on the contrary, aligned more randomly and accordingly rotated similarly as in the core region. These observations revealed that the degree of particle orientation anisotropy has a major impact on the particle rotation mode, whereas mean shear, irrespective of the actual shear rate, only plays a secondary role in particle rotation. Deduction of the eigenvectors of the left Cauchy–Green tensor showed that the preferential orientation of the tracer spheroids was caused by the alignment of rods and disks with the strongest Lagrangian stretching and compression directions, respectively. Lagrangian stretching/compression determines the particle orientations and the particle orientation affects the particle rotation mode.

Mapping spheroid rotation modes in turbulent channel flow: effects of shear, turbulence and particle inertia

“…disks spin but rods tumble. The existence of two such qualitatively different modes of particle rotation, namely the 'centre mode' and the 'wall mode', has been documented in our recent studies (Zhao et al 2015;Yang, Zhao & Andersson 2018). However, the fluid dynamical features of a turbulent channel flow vary considerably from the buffer region where the 'wall mode' prevails, to the channel centre, which resembles HIT, and where the 'centre mode' rotation is found.…”

“…(2015 b ), Zhao & Andersson (2016) and Yang et al. (2018). Herein, however, we focus on both inertial and tracer particles.…”

“…Particle rotation in this limiting case is obtained by equating the Jeffery torque components N i to zero. Rotation of inertialess spheroids in wall turbulence has recently been explored by Challabotla et al (2015b), and Yang et al (2018). Herein, however, we focus on both inertial and tracer particles.…”

Alignment and rotation of spheroids in unsteady vortex flow

“…These tendencies were recently associated with deformations of Lagrangian fluid elements. The preferential alignment of rods and disks with Lagrangian stretching and compression directions, respectively, was first reported in HIT [7] and subsequently in wall turbulence [8,9]. Computational [10,11] and experimental [12,13] studies have confirmed the role of the preferential alignment on the rotational particle behavior, such as spinning of rods and tumbling of disks.…”

“…The intricate behavior of non-spherical particles in three-dimensional flow fields has been studied in HIT [5,7,10] as well as in wall turbulence [6,9,14]. These studies have all been carried out in statistically steady flow fields.…”