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

Abstract

The rotational behaviour of non-spherical particles in turbulent channel flow is studied by Lagrangian tracking of spheroidal point particles in a directly simulated flow. The focus is on the complex rotation modes of the spheroidal particles, in which the back reaction on the flow field is ignored. This study is a sequel to the letter by Zhao et al. (Phys. Rev. Lett., vol. 115, 2015, 244501), in which only selected results in the near-wall buffer region and the almost-isotropic channel centre were presented. Now, particle dynamics all across the channel is explored to provide a complete picture of the orientational and rotational behaviour with consideration of the effects of particle aspect ratio ranging from 0.1 to 10 and particle Stokes number from 0 (inertialess) to 30. The rotational dynamics in the innermost part of the logarithmic wall layer is particularly complex and affected not only by modest mean shear, but also by particle inertia and turbulent vorticity. While inertial disks exhibit modest preferential orientation in either the wall-normal or cross-stream direction, inertial rods show neither preferential tumbling nor spinning. Examination of the co-variances between particle orientation, particle rotation and fluid rotation vectors explains the qualitatively different ‘wall mode’ rotation and ‘centre mode’ rotation. Inertialess spheroids transition between the two modes within a narrow zone ($15<z^{+}<35$) in the buffer region. If the spheroids have inertia, the transition zone between the two modes shifts to the inner part of the logarithmic layer, i.e. $z^{+}\geqslant 40$. We ascribe the transition of inertialess spheroids from the ‘wall mode’ to the ‘centre mode’ rotation to the changeover between the time scales associated with mean shear and small-scale turbulence. Inertial spheroids, however, transition between the two rotational modes when the Kolmogorov time scale becomes comparable to the time scale for particle rotation, i.e. the effective Stokes number is of order unity. The aforementioned findings reveal, in addition to the effects of particle shape and alignment, the importance of the characteristic local time scale of fluid flow for the rotation of both tracer and inertial spheroids in turbulent channel flows.