Stabilising falling liquid film flows using feedback control

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, resp...

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Bibliographic Details
Published inPhysics of fluids (1994) Vol. 28; no. 1
Main Authors Thompson, Alice B., Gomes, Susana N., Pavliotis, Grigorios A., Papageorgiou, Demetrios T.
Format Journal Article
LanguageEnglish
Published Melville American Institute of Physics 01.01.2016
Subjects
Active control
ACTUATORS
APPROXIMATIONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CONTROL SYSTEMS
Falling liquid films
Feedback control
FILM FLOW
Fluid dynamics
FLUID INJECTION
Free surfaces
HEAT TRANSFER
HEIGHT
Industrial applications
INTERFACES
LAYERS
LIQUIDS
Physics
STEADY-STATE CONDITIONS
Suction
Traveling waves
TRAVELLING WAVES
WALLS
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Summary: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.
ISSN:1070-6631
1089-7666
DOI:10.1063/1.4938761