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![Measurements of the mean square tumbling rate, $\langle {{\dot{p}}_{i}}{{\dot{p}}_{i}}\rangle $ 〈 p ˙ i p ˙ i 〉 > , as a function of the fit length for both jacks (blue) and crosses (red). To determine the true value, we extrapolate to zero fit-length by fitting the data to a stretched exponential [32].](publication/264312750/figure/fig4/AS:1132493617008652@1647018927938/Measurements-of-the-mean-square-tumbling-rate-langle.jpg)
Measurements of the mean square tumbling rate, $\langle {{\dot{p}}_{i}}{{\dot{p}}_{i}}\rangle $ 〈 p ˙ i p ˙ i 〉 > , as a function of the fit length for both jacks (blue) and crosses (red). To determine the true value, we extrapolate to zero fit-length by fitting the data to a stretched exponential [32].
Source publication
![Experimental setup (figure reproduced from [33]). In the octagonal flow...](publication/264312750/figure/fig1/AS:1132493617020940@1647018927635/Experimental-setup-figure-reproduced-from-33-In-the-octagonal-flow-between_Q320.jpg)
We introduce a new method to measure Lagrangian vorticity and the rotational
dynamics of anisotropic particles in a turbulent fluid flow. We use 3D printing
technology to fabricate crosses (two perpendicular rods) and jacks (three
mutually perpendicular rods). Time-resolved measurements of their orientation
and solid-body rotation rate are obtained...
Citations
... Notable exceptions are Ref. [44] (tumbling and spinning rates of cylinders) and Ref. [48] (solid body rotation rates of jacks and crosses). Examples also include numerical studies with prolate and oblate ellipsoids modeled as point-particles and carried out by Ref. [19] (all rotation rates) and Ref. [20] (tumbling and spinning rates). ...
The motion, settling, and dispersion of microplastics in the ocean are determined by their rotational dynamics. We present experiments on elongated, large aspect ratio, and mildly curved plastic fibers slightly longer than the Kolmogorov length scale. Exploiting their uniquely identifiable three dimensional orientation, we perform original optical Lagrangian investigations and provide a set of homogeneous data on their rotation rates around their longitudinal axis -- spinning rate -- and transversal axes -- tumbling rates -- which we explain in the context of the general features of turbulence.
... Advancements in measurement systems could enable simultaneous assessments of particle orientation and settling trajectory and higher resolution for capturing smaller snow particles. Systems such as a high-magnification, high-resolution 3D PTV [66,67], or a digital inline holography setup with an expanded field of view [42,68] and higher sampling rate, hold promise for the desired measurements. Finally, the variability of field conditions presents an additional layer of complexity. ...
Research on settling dynamics of snow particles, considering their complex morphologies and real atmospheric conditions, remains scarce despite extensive simulations and laboratory studies. Our study bridges the gap through a comprehensive field investigation into the three-dimensional (3D) snow settling dynamics under weak atmospheric turbulence, enabled by a 3D particle tracking velocimetry (PTV) system to record > a million trajectories, coupled with a snow particle analyzer for simultaneous aerodynamic property characterization of four distinct snow types (aggregates, graupels, dendrites, needles). Our findings indicate that while the terminal velocity predicted by the aerodynamic model aligns well with PTV-measured settling velocity for graupels, significant discrepancies arise for non-spherical particles, particularly dendrites, which exhibit higher drag coefficients than predicted. Qualitative observations of 3D settling trajectories highlight pronounced meandering in aggregates and dendrites, in contrast to the subtler meandering observed in needles and graupels, attributable to their smaller frontal areas. This meandering in aggregates and dendrites occurs at lower frequencies compared to that of graupels. Further quantification of trajectory acceleration and curvature suggests that the meandering frequencies in aggregates and dendrites are smaller than that of morphology-induced vortex shedding of disks, likely due to their rotational inertia, and those of graupels align with the small-scale atmospheric turbulence. Moreover, our analysis of vertical acceleration along trajectories elucidates that the orientation changes in dendrites and aggregates enhance their settling velocity. Such insights into settling dynamics refine models of snow settling velocity under weak atmospheric turbulence, with broader implications for more accurately predicting ground snow accumulation.
... Noteworthily, contrasting with the aforementioned advancements specifically targeted at vorticity measurement, a different line of inquiry has employed multi-view cameras to facilitate 3D rotation assessments. These methods, exemplified by work from Zimmermann et al. (2011), Klein et al. (2012, and Marcus et al. (2014), concentrate on capturing both the trajectories and rotational motion of either anisotropic particles or spherical particles with embedded markers. Although these multi-view techniques are potent in capturing 3D particle dynamics, their application to vorticity measurement presents specific challenges. ...
Investigating vorticity dynamics provides an effective way for understanding the fundamental mechanisms of fluid flows across diverse scales. However, experimental vorticity measurements often suffer from limited spatial and temporal resolution, hindering our capability to probe into small-scale dynamics in various flows, particularly turbulence. In Li et al. (Exp Fluids 63:161, 2022), we introduced a novel holographic vorticimetry technique for direct vorticity measurements by tracking the three-dimensional rotations of tracers with internal markers. This study further extends it to investigate the intricate vorticity dynamics during the evolution of elliptical vortex rings with different aspect ratios. Based on the shadowgraph imaging quantifying the axis-switching cycles and vortex ring deformation, holographic vorticimetry is applied to measure the vorticity distribution within the millimeter-size core of elliptical vortex rings during their evolution. Specifically, our method resolves an even vorticity spread near the core center that rapidly decays within a few hundred microns. Additionally, our results reveal the intricate vorticity fluctuations associated with the folding-unfolding behaviors during the vortex ring evolution. These subtle vorticity changes informed by simulations have not been captured by previous experiments due to limited resolution. Furthermore, we find that higher aspect ratios yield larger initial vorticity and vorticity fluctuations but also prompt earlier inception of instabilities, causing vortex core distortion. These opposing effects result in a non-monotonic vorticity evolution trend. Overall, our measurements demonstrate the efficacy of holographic vorticimetry by measuring the intricate vorticity variations in unsteady vortex flows, paving the way for capturing the vorticity dynamics of small-scale turbulence structures.
Graphical abstract
... For small fibers in the slender body limit, S F is proportional to Sv 2 and has a weak logarithmic dependence on the particle aspect ratio. The most accessible case of small and neutrally buoyant, non-spherical particles in turbulence has been studied extensively in simulations [57,69,54] and experiments [52,43,37,23] and a review is given by Voth and Soldati [65]. The particle dynamics depend only on particle shape and possibly Reynolds number, and preferential alignment with the local velocity gradients results in reduced tumbling rates compared to randomly oriented particles. ...
We present experimental and computational results for the orientation distributions of slender fibers and ramified particles settling in an isotropic turbulent flow. The rotational dynamics of the particles is modeled using a slender-body theory that includes the inertial torque due to sedimentation that tends to rotate the particles toward a broadside orientation. The particles are assumed to rotate due to viscous forces associated with the turbulent velocity gradients occurring on the particle length scale. In the simulations, the turbulence is obtained from a stochastic model of the velocity gradient in a Lagrangian reference frame. In the experiments, the turbulence is generated by active jets in a vertical water tunnel. It is well known that axisymmetric particles rotate according to Jeffery's solution for the rotation of a spheroidal particle if one adopts an appropriate effective aspect ratio. We show that the same result applies to a ramified particle consisting of three coplanar fibers connected with equal angles at a central point which rotates like a thin oblate spheroid. The orientation statistics can be quantified with a single non-dimensional parameter, the settling factor $S_F$, defined as the ratio of rotations due to sedimentation and turbulent shear. For low values of $S_F$, we observe nearly isotropically oriented particles, whereas particles become strongly aligned near the horizontal plane for high values of $S_F$. The variance of the angle away from horizontal scales as $S_F^{-2}$ for $S_F \gg 1$, but the orientation distribution is non-Gaussian due to turbulent intermittency in this limit.
... Based on the rotational Doppler effect of the Laguerre-Gaussian beam with orbital angular momentum, Ryabtsev et al. (2016) developed a laser Doppler probe that only measures 1D vorticity at a fixed location in the flow. Using views from multiple cameras and image analysis, a number of studies demonstrated the capability to measure the rotation of spherical and small jack-like particles (Zimmermann et al. 2011a, b;Klein et al. 2012;Marcus et al. 2014). Zimmermann et al. (2011a and b) proposed an approach by tracking the unique textures on the outer surface of a sphere using two cameras from perpendicular views to investigate the rotational intermittency of large (18 mm in diameter) particles in turbulence. ...
... However, these particles have a size at centimeter-scale, limiting their ability to capture small-scale vortices in turbulence at high Reynolds numbers. Marcus et al. (2014) employed 3D-printed crosses and jacks at a smaller size (around 3 mm) to measure the Lagrangian vorticity and rotation of these particles from four cameras. However, limited by the resolution of 3D printing, the resolution of their vorticimetry is still considerably larger than the Kolmogorov scale of their experiments. ...
Current experiment techniques for vorticity measurement suffer from limited spatial and temporal resolution to resolve the small-scale eddy dynamics in turbulence. In this study, we develop a new method for direct vorticity measurement in fluid flows based on digital inline holography (DIH). The DIH system utilizes a collimated laser beam to illuminate the tracers with internal markers and a digital sensor to record the generated holograms. The tracers made of the polydimethylsiloxane prepolymer mixed with internal markers are fabricated using a standard microfluidic droplet generator. A rotation measurement algorithm is developed based on the 3D location reconstruction and tracking of the internal markers and is assessed through synthetic holograms to identify the optimal parameter settings and measurement range (e.g., rotation rate from 0.3 to 0.7 rad/frame under numerical aperture of imaging of 0.25). Our proposed method based on DIH is evaluated by a calibration experiment of single tracer rotation, which yields the same optimal measurement range. Using von Kármán swirling flow setup, we further demonstrate the capability of the approach to simultaneously measure the Lagrangian rotation and translation of multiple tracers. Our method can measure vorticity in a small region on the order of 100 µm or less and can be potentially used to quantify the Kolmogorov-scale vorticity field in turbulent flows.
Graphical abstract
... Based on the rotational Doppler effect of the Laguerre-Gaussian beam with orbital angular momentum, Ryabtsev et al. (2016) developed a laser Doppler probe that only measures 1D vorticity at a fixed location in the flow. Using views from multiple cameras and image analysis, a number of studies demonstrated the capability to measure the rotation of spherical and small jack-like particles (Zimmermann et al. 2011a(Zimmermann et al. & 2011bKlein et al. 2012;Marcus et al. 2014). Zimmermann et al. (2011aZimmermann et al. ( & 2011b proposed an approach by tracking the unique textures on the outer surface of a sphere using two cameras from perpendicular views to investigate the rotational intermittency of large (18 mm in diameter) particles in turbulence. ...
... However, these particles have a size at centimeter-scale, limiting their ability to capture small-scale vortices in turbulence at high Reynolds numbers. Marcus et al. (2014) employed 3D-printed crosses and jacks at a smaller size (around 3 mm) to measure the Lagrangian vorticity and rotation of these particles from four cameras. However, limited by the resolution of 3D printing, the resolution of their vorticimetry is still considerably larger than the Kolmogorov scale of their experiments. ...
Current experiment techniques for vorticity measurement suffer from limited spatial and temporal resolution to resolve the small-scale eddy dynamics in turbulence. In this study, we develop a new method for direct vorticity measurement in fluid flows based on digital inline holography (DIH). The DIH system utilizes a collimated laser beam to illuminate the tracers with internal markers and a digital sensor to record the generated holograms. The tracers made of the polydimethylsiloxane (PDMS) prepolymer mixed with internal markers are fabricated using a standard microfluidic droplet generator. A rotation measurement algorithm is developed based on the 3D location reconstruction and tracking of the internal markers and is assessed through synthetic holograms to identify the optimal parameter settings and measurement range (e.g., rotation rate from 0.3 to 0.7 rad/frame under numerical aperture of imaging of 0.25). Our proposed method based on DIH is evaluated by a calibration experiment of single tracer rotation, which yields the same optimal measurement range. Using von K\'arm\'an swirling flow setup, we further demonstrate the capability of the approach to simultaneously measure the Lagrangian rotation and translation of multiple tracers. Our method can measure vorticity in a small region on the order of 100 ${\mu}$m or less and can be potentially used to quantify the Kolmogorov-scale vorticity field in turbulent flows.
... Such questions have recently been the subject of a renewed interest. At an experimental level, particle tracking techniques allowed to reconstruct particle orientational dynamics in several turbulent water flows [9][10][11][12][13]. As to numerical studies, they consist in simulating, in addition to the fluid flow, the orientation of particles by integrating Jeffery's equation along Lagrangian trajectories. ...
... In that case, noise correlations are independent of the mean shear σ * . Also, when using such a form, the stochastic model of previous subsection is drastically simplified: all γ n 's except γ 0 vanish in the diffusion coefficient (12). The second case that we investigate consists in accounting for the single-time anisotropies of the fluid-velocity gradients that are caused by the mean shear. ...
... where W t is the exact same realisation of the Brownian motion as that entering the time evolution ofθ t . The drift and diffusion coefficients a and b, defined in (12) are periodic functions of θ t . It thus makes no difference evaluating them along the folded processθ t = θ t mod π. ...
Non-spherical particles transported by an anisotropic turbulent flow preferentially align with the mean shear and intermittently tumble when the local strain fluctuates. Such an intricate behaviour is here studied for inertialess, rod-shaped particles embedded in a two-dimensional turbulent flow with homogeneous shear. A Lagrangian stochastic model for the rods angular dynamics is introduced and compared to the results of direct numerical simulations. The model consists in superposing a short-correlated random component to the steady large-scale mean shear, and can thereby be integrated analytically. To reproduce the single-time orientation statistics obtained numerically, it is found that one has to properly account for the combined effect of the mean shear, for anisotropic velocity gradient fluctuations, and for the presence of persistent rotating structures in the flow that bias Lagrangian statistics. The model is then used to address two-time statistics. The notion of tumbling rate is extended to diffusive dynamics by introducing the stationary probability flux of the rods unfolded angle. The model is found to reproduce the long-term effects of an average shear on the mean and the variance of the fibres angular increment. Still, it does not reproduce an intricate behaviour observed in numerics for intermediate times: the unfolded angle is there very similar to a L\'evy walk with distributions of increments displaying intermediate power-law tails.
... The orientation of spheroidal particles relative to the local fluid vorticity plays a vital role in the particle rotational behavior in HIT [12][13][14] and wall turbulence, 15,16 whose applications are seen in both engineering and natural settings. One such interesting area is the investigation of the shape-dependent dynamics of phytoplankton in the ocean to understand its feeding and reproduction cycles. ...
Rod- and disk-like particles preferentially align parallel and perpendicular, respectively, to the fluid vorticity, both at the early as well as later stages of the unsteady Taylor–Green vortex (TGV) flow. The early stage of the flow is laminar and comprises anisotropic large-scale Taylor–Green structures, while the later stages resemble homogeneous isotropic turbulence with Kolmogorov-type small-scale structures. The reason for the orientational behavior of inertialess spheroids in the early stage of the TGV-flow has been sought by examining the alignments of spheroidal particles, not only with vorticity but also with Lagrangian stretching and compression directions of the fluid elements in our earlier paper [Jayaram et al., “Alignment and rotation of spheroids in unsteady vortex flow,” Phys. Fluids. 33, 033310 (2021)]. This article is a sequel to the above paper in which the spheroids' alignments are studied locally, in contrast to the volume-averaged statistics studied previously, to observe the influence of the local flow field on the spheroidal alignment. It has been observed through our studies that the alignments vary periodically in space and these variations can be associated with the large-scale periodicity of the flow field originating from the initial conditions of the TGV flow. Additionally, the intense vortex stretching in the early stages of the flow evolution is seen to be largely influencing the orientation of the spheroids.
... At the same time, a wide variety of experimental measurements have been developed for determining the motion of non-spherical particles. The full motion has been studied by Marcus et al. (2014), where they measure the orientation and rotation of spheroidal particles across a range of aspect ratio in the HIT framework. Conversely, with respect to inhomogeneous flows, Carlsson et al. (2010a) provide some measurements on fibre orientation in the bulk and near wall regions of headbox geometry relevant to the paper industries. ...
... Parsa et al. (2011) presented experimental and DNS results on the probability distribution of tumbling rate of a spheroid as a function of aspect ratio. Marcus et al. (2014) develop an experimental technique to measure the tumbling rate for a wide range of aspect ratios, including disk-like particles (Λ = −1). ...
... The usually called "tumbling rate" is the root-mean-squared speed of orientation defined as dp/dt 2 1/2 , i.e. the rate of change of the orientation vector p (see, e. g., Voth and Soldati (2017)). As discussed in Chapter 2, a wide range of studies has explored the tumbling rate statistics in DNS both numerically (e. g., Byron et al. (2015); Shin and Koch (2005)) and experimentally (e. g., Parsa et al. (2012); Marcus et al. (2014)). Moreover, we want to emphasize that experimental techniques for imaging the dynamics of individual non-spherical particles in a turbulent environment have recently become available. ...
The motion of small non- spherical particles suspended in a turbulent flow is relevant for a large variety of natural and industrial applications such as aerosol dynamics in respiration, red blood cells motion, plankton dynamics, ice in clouds, combustion, to name a few. Anisotropic particles react on turbulent flows in complex ways, which depend on a wide range of parameters (shape, inertia, fluid shear). Inertia-free particles, with size smaller than the Kolmogorov length, follow the fluid motion with an orientation generally defined by the local turbulent velocity gradient. Therefore, this thesis is focused on the dynamics of these objects in turbulence exploiting stochastic Lagrangian methods. The development of a model that can be used as predictive tool in industrial computational fluid dynamics (CFD) is highly valuable for practical applications in engineering. Models that reach an acceptable compromise between simplicity and accuracy are needed for progressing in the field of medical, environmental and industrial processes.The formulation of a stochastic orientation model is studied in two-dimensional turbulent flow with homogeneous shear, where results are compared with direct numerical simulations (DNS). Finding analytical results, scrutinising the effect of the anisotropies when they are included in the model, and extending the notion of rotational dynamics in the stochastic framework, are subjects addressed in our work. Analytical results give a reasonable qualitative response, even if the diffusion model is not designed to reproduce the non-Gaussian features of the DNS experiments.The extension to the three-dimensional case showed that the implementation of efficient numerical schemes in 3D models is far from straightforward. The introduction of a numerical scheme with the capability to preserve the dynamics at reasonable computational costs has been devised and the convergence analysed. A scheme of splitting decomposition of the stochastic differential equations (SDE) has been developed to overcome the typical instability problems of the Euler–Maruyama method, obtaining a mean-square convergence of order 1/2 and a weakly convergence of order 1, as expected. Finally, model and numerical scheme have been implemented in an industrial CFD code (Code_Saturne) and used to study the orientational and rotational behaviour of anisotropic inertia-free particles in an applicative prototype of inhomogeneous turbulence, i.e. a turbulent channel flow. This real application has faced two issues of the modelling: the numerical implementation in an industrial code, and whether and to which extent the model is able to reproduce the DNS experiments. The stochastic Lagrangian model for the orientation in the CFD code reproduces with some limits the orientation and rotation statistics of the DNS.The results of this study allows to predict the orientation and rotation of aspherical particles, giving new insight into the prediction of large scale motions both, in two-dimensional space, of interest for geophysical flows, and in three-dimensional industrial applications.
... L'orientation d'une suspension diluée de fibres dans une contraction plane (en anglais : planar contraction) a été étudiée par Parsheh et al. (2005), qui ont mis en évidence que l'orientation de fibres dans un écoulement turbulent n'est pas significativement modifiée par la valeur du nombre de Reynolds, et que l'existence de l'orientation préférentielle est déterminée par le ratio entre les gradients de vitesse et l'intensité turbulente. Récemment, Parsa et al. (2012) et Marcus et al. (2014) ont observé que le taux de rotation de particules non inertielles dépend de leur orientation par rapport à la vorticité du fluide à leur position en turbulence homogène et isotrope. Les particules passent ainsi de longues périodes où leur grand axe est aligné avec la vorticité du fluide avec des vitesses de rotation faibles (spinning), mais subissent momentanément des accélérations angulaires intenses (tumbling). ...
En utilisant la simulation numérique directe (DNS), la dynamique de particules non sphériques inertielles dans un écoulement turbulent de canal a été étudiée numériquement. Un suivi lagrangien de particules, qui sont supposées ponctuelles et modélisées par des ellipsoïdes de révolution allongés, est utilisé pour étudier l’influence du rapport d’aspect et du temps de relaxation des particules sur leur interaction avec l’écoulement. La simulation numérique directe de l’écoulement permet d’obtenir une information précise sur les caractéristiques du fluide à la position des particules, qui sont nécessaire pour calculer les actions hydrodynamiques auxquelles elles sont soumises. Deux méthodes de calculs des actions hydrodynamiques ont été définies afin d’analyser leur influence sur la dynamique des particules. La première est basée sur des modèles théoriques, qui sont valides sous l’hypothèse d’un écoulement rampant à l’échelle de la particule et sont très utilisés dans la littérature. La seconde est basée sur l’utilisation de corrélations semi-empiriques, valides pour des valeurs du nombre de Reynolds particulaire modérées. Les simulations ont été réalisées jusqu’à ce que la distribution des particules atteigne un état stationnaire, afin d’obtenir une comparaison non biaisée de l’influence de la forme et de l’inertie. Quelle que soit la modélisation, les statistiques de la vitesse de translation ne dépendent pas significativement de l’allongement des particules. Il y a par contre des différences quantitatives importantes entre les statistiques de translation obtenues avec ces deux méthodes de modélisation pour les particules d’inertie élevée. Les statistiques de rotation sont affectées de façon majeure par la modélisation des actions hydrodynamiques, quelle que soit la position dans le canal. Ces observations concernant l’influence de la modélisation restent valides pour des valeurs plus élevées du nombre de Reynolds. L’augmentation de la valeur de ce paramètre cause néanmoins une uniformisation de la distribution des particules et une augmentation de l’intensité des fluctuations de la vitesse et de la vitesse angulaire de l’écoulement vu par les particules. Ces fluctuations plus intenses modifient l’orientation préférentielle des ellipsoïdes, indépendamment de leurs caractéristiques et du modèle utilisé pour calculer les actions hydrodynamiques. La comparaison des résultats obtenus par simulation avec des données expérimentales indique que les formulations bas Reynolds permettent une représentation correcte de la dynamique de particules très allongées et non inertielles.
