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Stabilising falling liquid film flows using feedback control
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Thompson, Alice B., Gomes, Susana N., Pavliotis, G. A. and Papageorgios, Demetrios (2016) Stabilising falling liquid film flows using feedback control. Physics of Fluids, 28 (1). 012107 . doi:10.1063/1.4938761 ISSN 1070-6631.
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Official URL: https://doi.org/10.1063/1.4938761
Abstract
Falling liquid films become unstable due to inertial effects when the fluid layer is sufficiently thick or the slope sufficiently steep. This free surface flow of a single fluid layer has industrial applications including coating and heat transfer, which benefit from smooth and wavy interfaces, respectively. Here, we discuss how the dynamics of the system are altered by feedback controls based on observations of the interface height, and supplied to the system via the perpendicular injection and suction of fluid through the wall. In this study, we model the system using both Benney and weighted-residual models that account for the fluid injection through the wall. We find that feedback using injection and suction is a remarkably effective control mechanism: the controls can be used to drive the system towards arbitrary steady states and travelling waves, and the qualitative effects are independent of the details of the flow modelling. Furthermore, we show that the system can still be successfully controlled when the feedback is applied via a set of localised actuators and only a small number of system observations are available, and that this is possible using both static (where the controls are based on only the most recent set of observations) and dynamic (where the controls are based on an approximation of the system which evolves over time) control schemes. This study thus provides a solid theoretical foundation for future experimental realisations of the active feedback control of falling liquid films.
| Item Type: | Journal Article | |||||||||||||||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Liquid films -- Mathematical models, Hydrodynamics -- Mathematical models, Fluid mechanics | |||||||||||||||||||||
| Journal or Publication Title: | Physics of Fluids | |||||||||||||||||||||
| Publisher: | American Institute of Physics | |||||||||||||||||||||
| ISSN: | 1070-6631 | |||||||||||||||||||||
| Official Date: | 12 January 2016 | |||||||||||||||||||||
| Dates: |
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| Volume: | 28 | |||||||||||||||||||||
| Number: | 1 | |||||||||||||||||||||
| Article Number: | 012107 | |||||||||||||||||||||
| DOI: | 10.1063/1.4938761 | |||||||||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||||||||
| Publication Status: | Published | |||||||||||||||||||||
| Reuse Statement (publisher, data, author rights): | This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. | |||||||||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||||||||
| Date of first compliant deposit: | 28 October 2019 | |||||||||||||||||||||
| Date of first compliant Open Access: | 30 October 2019 | |||||||||||||||||||||
| RIOXX Funder/Project Grant: |
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