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Eulerian-Lagrangian method for simulation of cloud cavitation

Maeda, Kazuki and Colonius, Tim (2018) Eulerian-Lagrangian method for simulation of cloud cavitation. Journal of Computational Physics, 371 . pp. 994-1017. ISSN 0021-9991. PMCID PMC6364854. doi:10.1016/

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We present a coupled Eulerian–Lagrangian method to simulate cloud cavitation in a compressible liquid. The method is designed to capture the strong, volumetric oscillations of each bubble and the bubble-scattered acoustics. The dynamics of the bubbly mixture is formulated using volume-averaged equations of motion. The continuous phase is discretized on an Eulerian grid and integrated using a high-order, finite-volume weighted essentially non-oscillatory (WENO) scheme, while the gas phase is modeled as spherical, Lagrangian point-bubbles at the sub-grid scale, each of whose radial evolution is tracked by solving the Keller–Miksis equation. The volume of bubbles is mapped onto the Eulerian grid as the void fraction by using a regularization (smearing) kernel. In the most general case, where the bubble distribution is arbitrary, three-dimensional Cartesian grids are used for spatial discretization. In order to reduce the computational cost for problems possessing translational or rotational homogeneities, we spatially average the governing equations along the direction of symmetry and discretize the continuous phase on two-dimensional or axi-symmetric grids, respectively. We specify a regularization kernel that maps the three-dimensional distribution of bubbles onto the field of an averaged two-dimensional or axi-symmetric void fraction. A closure is developed to model the pressure fluctuations at the sub-grid scale as synthetic noise. For the examples considered here, modeling the sub-grid pressure fluctuations as white noise agrees a priori with computed distributions from three-dimensional simulations, and suffices, a posteriori, to accurately reproduce the statistics of the bubble dynamics. The numerical method and its verification are described by considering test cases of the dynamics of a single bubble and cloud cavitation induced by ultrasound fields.

Item Type:Article
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URLURL TypeDescription CentralArticle Paper
Maeda, Kazuki0000-0002-5729-6194
Colonius, Tim0000-0003-0326-3909
Additional Information:© 2018 Elsevier. Received 3 December 2017, Revised 10 April 2018, Accepted 16 May 2018, Available online 18 May 2018. The authors thank Vedran Coralic and Jomela Meng for valuable discussions on the finite volume WENO scheme, Daniel Fuster for helpful discussions on the bubble-dynamic closure, and Wayne Kreider, Adam Maxwell and Michael Bailey for their support in the companion experiments. K.M would like to acknowledge the Funai Foundation for Information Technology, for the Overseas Scholarship. This work was supported by the National Institutes of Health under grant P01-DK043881 and ONR grant N00014-17-1-267. The three-dimensional computations presented here utilized the Extreme Science and Engineering Discovery Environment, which is supported by the National Science Foundation grant number CTS120005.
Funding AgencyGrant Number
Funai Foundation for Information TechnologyUNSPECIFIED
Office of Naval Research (ONR)N00014-17-1-267
Subject Keywords:Bubble dynamics; Cavitation; Eulerian-Lagrangian method; Compressible multiphase flows; Multiscale modeling; Reduced-order modeling
PubMed Central ID:PMC6364854
Record Number:CaltechAUTHORS:20180518-133233019
Persistent URL:
Official Citation:Kazuki Maeda, Tim Colonius, Eulerian–Lagrangian method for simulation of cloud cavitation, Journal of Computational Physics, Volume 371, 2018, Pages 994-1017, ISSN 0021-9991,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86456
Deposited By: George Porter
Deposited On:18 May 2018 21:15
Last Modified:17 Feb 2022 22:29

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