Reduced-order modelling of thick inertial flows around rotating cylinders

Wray, Alexander; Cimpeanu, Radu

doi:10.1017/jfm.2020.421

Cited by 12 publications

(6 citation statements)

References 56 publications

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“…These two problems have been the subject of many notable previous studies, including the pioneering numerical investigation of coating flow by Hansen & Kelmanson (1994), the study of the critical solution in coating and rimming flow by Wilson, Hunt & Duffy (2002), the study of the effect of surface tension in rimming flow by Ashmore, Hosoi & Stone (2003), the series of studies on the subtle long-time dynamics of coating flow by Hinch & Kelmanson (2003), Hinch, Kelmanson & Metcalfe (2004), Kelmanson (2009) and Groh & Kelmanson (2014), the numerical investigations of two- and three-dimensional coating flow by Evans, Schwartz & Roy (2004, 2005), the study of a ring of fluid in coating and rimming flow by Leslie, Wilson & Duffy (2013), the bifurcation analysis of coating flow by Lin et al. (2016), the investigation of coating flow on topographically patterned and elliptical cylinders by Li, Carvalho & Kumar (2017 a , b ), the discovery of new branches of steady solutions in coating and rimming flow by Lopes, Thiele & Hazel (2018) and the formulation and analysis of a ‘thick-film’ model for coating flow by Wray & Cimpeanu (2020). In particular, Moffatt (1977) showed that (in the absence of both surface-tension and inertia effects) steady, two-dimensional, continuous and strictly positive solutions corresponding to a continuous film of fluid covering the entire cylinder, hereafter referred to as ‘full-film’ solutions, are possible only below a critical maximum load (or, equivalently, only below a critical maximum azimuthal volume flux).…”

Section: Introductionmentioning

confidence: 99%

Coating flow on a rotating cylinder in the presence of an irrotational airflow with circulation

2021

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A detailed analysis of steady coating flow of a thin film of a viscous fluid on the outside of a uniformly rotating horizontal circular cylinder in the absence of surface-tension effects but in the presence of a non-uniform pressure distribution due to an irrotational airflow with circulation shows that the presence of the airflow can result in qualitatively different behaviour of the fluid film from that in classical coating flow. Full-film solutions corresponding to a continuous film of fluid covering the entire cylinder are possible only when the flux and mass of fluid do not exceed critical values, which are determined in terms of the non-dimensional parameters $F$ and $K$ representing the speed of the far-field airflow and the circulation of the airflow, respectively. The qualitative changes in the behaviour of the film thickness as $F$ and $K$ are varied are described. In particular, the film thickness can have as many as four stationary points and, in general, has neither top-to-bottom nor right-to-left symmetry. In addition, when the circulation of the airflow is in the same direction as the rotation of the cylinder the maximum mass of fluid that can be supported on the cylinder is always less than that in classical coating flow, whereas when the circulation is in the opposite direction the maximum mass of fluid can be greater than that in classical coating flow.

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Section: Introductionmentioning

confidence: 99%

Coating flow on a rotating cylinder in the presence of an irrotational airflow with circulation

2021

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“…Viscosity controls both slow and small-scale flows, shaping our notion of 'heavy' or 'thick' substances such as honey [544], oil, gravy, or cream. Moreover, viscous flow theory underlies the behaviour of most composite flowing food products, such as emulsions, suspensions, and particle-laden fluid substances.…”

Section: Honey Dessert: Viscous Flowsmentioning

confidence: 99%

Culinary fluid mechanics and other currents in food science

Mathijssen¹,

Lisicki²,

Prakash³

et al. 2022

Preprint

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Innovations in fluid mechanics have refined food since ancient history, while creativity in cooking inspires science in return. Here, we review how recent advances in hydrodynamics are changing food science, and we highlight how the surprising phenomena that arise in the kitchen lead to discoveries and technologies across the disciplines, including rheology, soft matter, biophysics and molecular gastronomy. This review is structured like a menu, where each course highlights different aspects of culinary fluid mechanics. Our main themes include multiphase flows, complex fluids, thermal convection, hydrodynamic instabilities, viscous flows, granular matter, porous media, percolation, chaotic advection, interfacial phenomena, and turbulence. For every topic, we first provide an introduction accessible to food professionals and scientists in neighbouring fields. We then assess the state-of-the-art knowledge, the open problems, and likely directions for future research. New gastronomic ideas grow rapidly as the scientific recipes keep improving too.

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“…High performance computing tools have accelerated our understanding of thin-film flows and their control, particularly over the past two decades. From extending ROM limitations into inertial regimes [23,24], to explaining phenomena such as dripping [25,26] and extending into multi-physics contexts such as the study of electrostatic instabilities [18,27,28], the ability to inspect flow quantities in spatiotemporal detail has proven invaluable. Some progress has already been made using feedback control by applying the results of linear stability analyses to more complex problems [14,29].…”

Section: Introductionmentioning

confidence: 99%

Electrostatic control of the Navier-Stokes equations for thin films

Wray¹,

Cimpeanu²,

Gomes³

2022

Preprint

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A robust control scheme is derived and tested for the Navier-Stokes equations for two-dimensional multiphase flow of a thin film underneath an inclined solid surface. Control is exerted via the use of an electrode parallel to the substrate, which induces an electric field in the gas phase, and a resultant Maxwell stress at the liquid-gas interface. The imposed potential at the second electrode is derived using a Model Predictive Control loop, together with optimal control of a high-fidelity reduced-order model. In this implementation the interfacial shape of the fluid is successfully controlled, however the algorithm is sufficiently general to control any other quantity of interest.

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Reduced-order modelling of thick inertial flows around rotating cylinders

Cited by 12 publications

References 56 publications

Coating flow on a rotating cylinder in the presence of an irrotational airflow with circulation

Coating flow on a rotating cylinder in the presence of an irrotational airflow with circulation

Culinary fluid mechanics and other currents in food science

Electrostatic control of the Navier-Stokes equations for thin films

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