Open Access

ARTICLE

Data-Driven Upscaling of Orientation Kinematics in Suspensions of Rigid Fibres

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1 ICTEAM, Université catholique de Louvain, Av. Georges Lemaitre 4, Louvain-la-Neuve B-1348, Belgium.
2 Arts et Métiers ParisTech, Boulevard du Ronceray 2, BP 93525, 49035 Angers cedex 01, France.
3 ICI & ESI GROUP Chair, Ecole Centrale de Nantes, Rue de la Noe 1, F-44300 Nantes, France.
4 Aragon Institute of Engineering Research, Universidad de Zaragoza, Edificio Betancourt. Mariade Luna, s.n., 50018 Zaragoza, Spain.
5 PIMM & ESI GROUP Chair, ENSAM ParisTech, Boulevard de l’Hôpital 151, F-75013 Paris, France.
6 Deptartment of Mechanical Engineering, University of Delaware, Newark, DE 19716, United States.

* Corresponding Author: Adrien Scheuer. Email: .

(This article belongs to the Special Issue: Data-driven Computational Modeling and Simulations)

Computer Modeling in Engineering & Sciences 2018, 117(3), 367-386. https://doi.org/10.31614/cmes.2018.04278

Abstract

Describing the orientation state of the particles is often critical in fibre suspen-sion applications. Macroscopic descriptors, the so-called second-order orientation tensor (or moment) leading the way, are often preferred due to their low computational cost. Clo-sure problems however arise when evolution equations for the moments are derived from the orientation distribution functions and the impact of the chosen closure is often unpre-dictable. In this work, our aim is to provide macroscopic simulations of orientation that are cheap, accurate and closure-free. To this end, we propose an innovative data-based approach to the upscaling of orientation kinematics in the context of fibre suspensions. Since the physics at the microscopic scale can be modelled reasonably enough, the idea is to conduct accurate offline direct numerical simulations at that scale and to extract the corresponding macroscopic descriptors in order to build a database of scenarios. During the online stage, the macroscopic descriptors can then be updated quickly by combining adequately the items from the database instead of relying on an imprecise macroscopic model. This methodology is presented in the well-known case of dilute fibre suspensions (where it can be compared against closure-based macroscopic models) and in the case of suspensions of confined or electrically-charged fibres, for which state-of-the-art closures proved to be inadequate or simply do not exist.

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