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A Lagrangian stochastic model for rod orientation in turbulent flows

Lorenzo Campana 1 Mireille Bossy 1 Jean Minier 2
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : Suspension of anisotropic particles can be found in various applications, e.g. industrial manufacturing processes or natural phenomena (micro-organism locomotion, ice crystal formation in clouds). Microscopic ellipsoidal bodies suspended in a turbulent fluid flow rotate in response to the velocity gradient of the flow. Understanding their orientation is important since it can affect the optical or rheological properties of the suspension (e.g. polymeric fluids). In this work, the orientation dynamics of rod-like tracer particles, i.e. long ellipsoidal particles (in the limit to infinity of the aspect-ratio) is studied. The size of the rod is assumed smaller than the Kolmogorov length scale but sufficiently large that its Brownian motion need not be considered. As a result, the local flow around a particle can be considered as inertia-free and Stokes flow solutions can be used to relate particle rotational dynamics to the local velocity gradient tensor A ij = ∂u i ∂x j. The orientation of a rod is described as the normalized solution of the linear ordinary differential equation for the separation vector R 12 between two fluid tracers. Separation evolves under the action of the velocity gradient tensor. Simultaneously, a re-normalization procedure R 12 R 12 is introduced to obtain the unit-vector p aligned with the rod. In this frame, the rod orientation is described by a Lagrangian stochastic model, assuming that cumulative effects of the velocity gradient tensor on the observation time interval fluctuate with a Gaussian distribution. Indeed, cumulative velocity gradient fluctuations are here represented by a white-noise tensor such that it preserves the incompressibility condition. Large observation timescale (overall objective of the work) justifies the Gaussian distribution hypotheses, with a decorrelation timescale equal to the Kolmogorov one τ η. Finally, the Lagrangian stochastic model is tested in the case of homogeneous isotropic turbulence.
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Submitted on : Monday, November 18, 2019 - 9:15:10 PM
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Lorenzo Campana, Mireille Bossy, Jean Minier. A Lagrangian stochastic model for rod orientation in turbulent flows. ICMF 2019 - 10th International Conference Multiphase Flow, May 2019, Rio de Janeiro, Brazil. ⟨hal-02369274⟩

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