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Droplet impact onto a spring-supported plate : analysis and simulations
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Negus, Michael J., Moore, Matthew R., Oliver, James M. and Cimpeanu, Radu (2021) Droplet impact onto a spring-supported plate : analysis and simulations. Journal of Engineering Mathematics, 128 . 3 . doi:10.1007/s10665-021-10107-5 ISSN 0022-0833.
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Official URL: https://doi.org/10.1007/s10665-021-10107-5
Abstract
The high-speed impact of a droplet onto a flexible substrate is a highly nonlinear process of practical importance, which poses formidable modelling challenges in the context of fluid-structure interaction. We present two approaches aimed at investigating the canonical system of a droplet impacting onto a rigid plate supported by a spring and a dashpot: matched asymptotic expansions and direct numerical simulation (DNS). In the former, we derive a generalisation of inviscid Wagner theory to approximate the flow behaviour during the early stages of the impact. In the latter, we perform detailed DNS designed to validate the analytical framework, as well as provide insight into later times beyond the reach of the proposed analytical model. Drawing from both methods, we observe the strong influence that the mass of the plate, resistance of the dashpot and stiffness of the spring have on the motion of the solid, which undergoes forced damped oscillations. Furthermore, we examine how the plate motion affects the dynamics of the droplet, predominantly through altering its internal hydrodynamic pressure distribution. We build on the interplay between these techniques, demonstrating that a hybrid approach leads to improved model and computational development, as well as result interpretation, across multiple length- and time-scales.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Drops -- Mathematical models, Fluid mechanics, Thermodynamics, Mathematical analysis, Asymptotic expansions | ||||||
| Journal or Publication Title: | Journal of Engineering Mathematics | ||||||
| Publisher: | Springer | ||||||
| ISSN: | 0022-0833 | ||||||
| Official Date: | 22 April 2021 | ||||||
| Dates: |
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| Volume: | 128 | ||||||
| Article Number: | 3 | ||||||
| DOI: | 10.1007/s10665-021-10107-5 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Reuse Statement (publisher, data, author rights): | This is a post-peer-review, pre-copyedit version of an article published in Journal of Engineering Mathematics. The final authenticated version is available online at: https://doi.org/10.1007/s10665-021-10107-5 | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 16 February 2021 | ||||||
| Date of first compliant Open Access: | 22 April 2022 | ||||||
| Related URLs: | |||||||
| Open Access Version: |
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