Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-23T17:52:56.600Z Has data issue: false hasContentIssue false
  • English
  • Français

Machine learning the kinematics of spherical particles in fluid flows

Published online by Cambridge University Press:  25 October 2018

Zhong Yi Wan  and
Themistoklis P. Sapsis Open the ORCID record for Themistoklis P. Sapsis [Opens in a new window]
Zhong Yi Wan
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Themistoklis P. Sapsis*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: sapsis@mit.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Numerous efforts have been devoted to the derivation of equations describing the kinematics of finite-size spherical particles in arbitrary fluid flows. These approaches rely on asymptotic arguments to obtain a description of the particle motion in terms of a slow manifold. Here we present a novel approach that results in kinematic models with unprecedented accuracy compared with traditional methods. We apply a recently developed machine learning framework that relies on (i) an imperfect model, obtained through analytical arguments, and (ii) a long short-term memory recurrent neural network. The latter learns the mismatch between the analytical model and the exact velocity of the finite-size particle as a function of the fluid velocity that the particle has encountered along its trajectory. We show that training the model for one flow is sufficient to generate accurate predictions for any other arbitrary flow field. In particular, using as an exact model for trajectories of spherical particles, the Maxey–Riley equation, we first train the proposed machine learning framework using trajectories from a cellular flow. We are then able to accurately reproduce the trajectories of particles having the same inertial parameters for completely different fluid flows: the von Kármán vortex street as well as a two-dimensional turbulent fluid flow. For the second example we also demonstrate that the machine learned kinematic model successfully captures the spectrum of the particle velocity, as well as the extreme event statistics. The proposed scheme paves the way for machine learning kinematic models for bubbles and aerosols using high-fidelity DNS simulations and experiments.

JFM classification

Drops and Bubbles: Bubble dynamics Mathematical Foundations: Computational methods Drops and Bubbles: Drops and Bubbles
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 857 , 25 December 2018 , R2
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Babiano, A., Cartwright, J. H. E., Piro, O. & Provenzale, A. 2000 Dynamics of a small neutrally buoyant sphere in a fluid and targeting in Hamiltonian systems. Phys. Rev. Lett. 84 (25), 5764–5767.Google Scholar
Benczik, I. J., Toroczkai, Z. & Tél, T. 2002 Selective sensitivity of open chaotic flows on inertial tracer advection: catching particles with a stick. Phys. Rev. Lett. 89 (16), 164501.Google Scholar
Cartwright, J. H. E., Feudel, U., Károlyi, G., de Moura, A., Piro, O. & Tél, T. 2010 Dynamics of finite-size particles in chaotic fluid flows. In Nonlinear Dynamics and Chaos: Advances and Perspectives, pp. 51–87. Springer.Google Scholar
Crowe, C., Troutt, T. & Chung, J. 1996 Numerical models for two-phase turbulent flows. Annu. Rev. Fluid Mech. 28, 11.Google Scholar
Daitche, A. & Tél, T. 2014 Memory effects in chaotic advection of inertial particles. New J. Phys. 16, 073008.Google Scholar
Haller, G. & Sapsis, T. P. 2008 Where do inertial particles go in fluid flows? Physica D 237 (5), 573–583.Google Scholar
Hochreiter, S. & Schmidhueber, J. 1997 Long short-term memory. Neural Comput. 9 (8), 1–32.Google Scholar
Jung, C., Tél, T. & Ziemniak, E. 1993 Application of scattering chaos to particle transport in a hydrodynamical flow. Chaos 3, 555–568.Google Scholar
Marcu, B., Meiburg, E. & Newton, P. 1995 Dynamics of heavy particles in a Burgers vortex. Phys. Fluids 7, 400.Google Scholar
Martin, J. & Meiburg, E. 1994 The accumulation and dispersion of heavy particles in forced two-dimensional mixing layers: I. The fundamental and subharmonic cases. Phys. Fluids 6, 1116.Google Scholar
Maxey, M. R. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26 (4), 883–889.Google Scholar
Sapsis, T. P. & Haller, G. 2008 Instabilities in the dynamics of neutrally buoyant particles. Phys. Fluids 20, 17102.Google Scholar
Sapsis, T. P. & Haller, G. 2009 Inertial particle dynamics in a hurricane. J. Atmos. Sci. 66, 2481–2492.Google Scholar
Sapsis, T. P. & Haller, G. 2010 Clustering criterion for inertial particles in two-dimensional time-periodic and three-dimensional steady flows. Chaos 20 (1), 017515.Google Scholar
Sapsis, T. P., Haller, G. & Peng, J. 2011 Predator Prey interactions in jellyfish feeding. Bull. Math. Biol. 73, 1841–1856.Google Scholar
Sapsis, T. P., Ouellette, N. T., Gollub, J. P. & Haller, G. 2011 Neutrally buoyant particle dynamics in fluid flows: comparison of experiments with Lagrangian stochastic models. Phys. Fluids 23, 093304.Google Scholar
Sudharsan, M., Brunton, S. L. & Riley, J. J. 2016 Lagrangian coherent structures and inertial particle dynamics. Phys. Rev. E 93, 033108.Google Scholar
Tang, L., Wen, F., Yang, Y., Crowe, C., Chung, J. & Troutt, T. 1992 Self-organizing particle dispersion mechanism in a plane wake. Phys. Fluids A 4, 2244.Google Scholar
Tio, K K., Linan, A., Lasheras, J. & Ganan-Calvo, A. 1993 On the dynamics of buoyant and heavy particles in a periodic Stuart vortex flow. J. Fluid Mech. 253, 671.Google Scholar
Vasiliev, A. A. & Neishtadt, A. I. 1994 Regular and chaotic transport of impurities in steady flows. Chaos 4, 673.Google Scholar
Vlachas, P. R., Byeon, W., Wan, Z. Y., Sapsis, T. P. & Koumoutsakos, P. 2018 Data-driven forecasting of high dimensional chaotic systems with LSTM networks. Proc. R. Soc. A 474, 20170844.Google Scholar
Wan, Z. Y., Vlachas, P. R., Koumoutsakos, P. & Sapsis, T. P. 2018 Data-assisted reduced-order modeling of extreme events in complex dynamical systems. PLoS One 13 (5), e0197704.Google Scholar