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Toward particle-resolved accuracy in Euler–Lagrange simulations of multiphase flow using machine learning and pairwise interaction extended point-particle (PIEP) approximation

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Abstract

This study presents two different machine learning approaches for the modeling of hydrodynamic force on particles in a particle-laden multiphase flow. Results from particle-resolved direct numerical simulations (PR-DNS) of flow over a random array of stationary particles for eight combinations of particle Reynolds number (\({\mathrm {Re}}\)) and volume fraction (\(\phi \)) are used in the development of the models. The first approach follows a two-step process. In the first flow prediction step, the perturbation flow due to a particle is obtained as an axisymmetric superposable wake using linear regression. In the second force prediction step, the force on a particle is evaluated in terms of the perturbation flow induced by all its neighbors using the generalized Faxén form of the force expression. In the second approach, the force data on all the particles from the PR-DNS simulations are used to develop an artificial neural network (ANN) model for direct prediction of force on a particle. Due to the unavoidable limitation on the number of fully resolved particles in the PR-DNS simulations, direct force prediction with the ANN model tends to over-fit the data and performs poorly in the prediction of test data. In contrast, due to the millions of grid points used in the PR-DNS simulations, accurate flow prediction is possible, which then allows accurate prediction of particle force. This hybridization of multiphase physics and machine learning is particularly important, since it blends the strength of each, and the resulting pairwise interaction extended point-particle model cannot be developed by either physics or machine learning alone.

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Notes

  1. In fact, we should also include to this list angular velocity and angular acceleration of each neighbor. This increases the number of independent variables associated with each additional neighbor to 15.

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Acknowledgements

This material is based upon work supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA0002378, by the Office of Naval Research (ONR) as part of the Multidisciplinary University Research Initiatives (MURI) Program under Grant Number N00014-16-1-2617, and by the National Science Foundation Graduate Research Fellowship Program under Grant Nos. DGE-1315138 and DGE-1842473.

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Authors and Affiliations

  1. University of Florida, Gainesville, FL, 32611, USA

    S. Balachandar, W. C. Moore, G. Akiki & K. Liu

  2. Notre Dame University - Louaize, Zouk Mosbeh, Lebanon

    G. Akiki

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  1. S. Balachandar
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  2. W. C. Moore
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  3. G. Akiki
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  4. K. Liu
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Correspondence to S. Balachandar.

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Communicated by Maziar S. Hemati.

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Balachandar, S., Moore, W.C., Akiki, G. et al. Toward particle-resolved accuracy in Euler–Lagrange simulations of multiphase flow using machine learning and pairwise interaction extended point-particle (PIEP) approximation. Theor. Comput. Fluid Dyn. 34, 401–428 (2020). https://doi.org/10.1007/s00162-020-00538-8

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