Scale-dependent alignment, tumbling and stretching of slender rods in isotropic turbulence

Abstract

We examine the dynamics of slender, rigid rods in direct numerical simulation of isotropic turbulence. The focus is on the statistics of three quantities and how they vary as rod length increases from the dissipation range to the inertial range. These quantities are (i) the steady-state rod alignment with respect to the perceived velocity gradients in the surrounding flow, (ii) the rate of rod reorientation (tumbling) and (iii) the rate at which the rod end points move apart (stretching). Under the approximations of slender-body theory, the rod inertia is neglected and rods are modelled as passive particles in the flow that do not affect the fluid velocity field. We find that the average rod alignment changes qualitatively as rod length increases from the dissipation range to the inertial range. While rods in the dissipation range align most strongly with fluid vorticity, rods in the inertial range align most strongly with the most extensional eigenvector of the perceived strain-rate tensor. For rods in the inertial range, we find that the variance of rod stretching and the variance of rod tumbling both scale as $l^{-4/3}$, where $l$ is the rod length. However, when rod dynamics are compared to two-point fluid velocity statistics (structure functions), we see non-monotonic behaviour in the variance of rod tumbling due to the influence of small-scale fluid motions. Additionally, we find that the skewness of rod stretching does not show scale invariance in the inertial range, in contrast to the skewness of longitudinal fluid velocity increments as predicted by Kolmogorov’s $4/5$ law. Finally, we examine the power-law scaling exponents of higher-order moments of rod tumbling and rod stretching for rods with lengths in the inertial range and find that they show anomalous scaling. We compare these scaling exponents to predictions from Kolmogorov’s refined similarity hypotheses.

Spinning and tumbling of long fibers in isotropic turbulence

“…For fibers longer than the Kolmogorov length η, such preferential sampling of the velocity field has not been investigated in details. Pujara et al [21] showed numerically that when the fiber length L exits the viscous regime (L < η) and enters the inertial regime (L > η), the preferential orientation switches from the local vorticity to the most extensional eigenvector of the coarse-grained strain rate tensor. This could suggest that the spinning rate of a long fiber should decrease with length, as the preferential orientation with the vorticity is lost when the fiber length is in the inertial regime.…”

Lagrangian Time Scale of Passive Rotation for Mesoscale Particles in Turbulence

“…The Coriolis term × (I • ) is generally neglected for long fibers assuming that the spinning rate is smaller than the relaxation rate of tumbling. This disputable assumption is generally justified by the weak alignment of long fibers with coarse grained vorticity (Pujara et al, 2019). The Equation (1) then reduces to a simplified Langevin equation,…”

Long non-axisymmetric fibres in turbulent channel flow

“…In recent years, significant effort has been devoted to investigating numerically the dynamics of rigid and axisymmetric ellipsoids in homogeneous and isotropic turbulence (HIT) (Shin & Koch 2005; Ni, Ouellette & Voth 2014; Byron et al. 2015; Pujara, Voth & Variano 2019) and in turbulent channel flow (Mortensen et al. 2008; Marchioli, Fantoni & Soldati 2010; Zhao, Marchioli & Andersson 2014; Zhao et al.…”

“…Anisotropic particles have applications in industrially relevant flows, such as in pulp and papermaking (Lundell, Söderberg & Alfredsson 2011) and environmental problems, like modelling of phytoplankton (Guasto, Rusconi & Stocker 2012;Basterretxea, Font-Munoz & Tuval 2020), sedimentation (Meiburg & Kneller 2010), aerosols (Kleinstreuer & Feng 2013), ice crystals in clouds (Kristjànsson, Edwards & Mitchell 2000;Shultz 2018;Jiang et al 2019) and micro-fibre pollution in oceans (Ross et al 2021). In recent years, significant effort has been devoted to investigating numerically the dynamics of rigid and axisymmetric ellipsoids in homogeneous and isotropic turbulence (HIT) (Shin & Koch 2005;Ni, Ouellette & Voth 2014;Byron et al 2015;Pujara, Voth & Variano 2019) and in turbulent channel flow (Mortensen et al 2008;Marchioli, Fantoni & Soldati 2010;Zhao, Marchioli & Andersson 2014;Zhao et al 2015;Challabotla, Zhao & Andersson 2015a,b;Marchioli, Zhao & Andersson 2016;Dotto & Marchioli 2019;Dotto, Soldati & Marchioli 2020). Natural fibres can have complex and non-regular shapes, difficult to systematically characterise.…”