On rimming flows with shocks

Benilov, E. S.; Lapin, Vladimir; O’Brien, S.

doi:10.1007/s10665-011-9512-2

Cited by 13 publications

(17 citation statements)

References 16 publications

(37 reference statements)

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“…A similar conclusion has been drawn for flows on the inside of a horizontal rotating cylinder (Benilov, Lapin & O'Brien 2012). Note, however, that the small-Re assumption used to obtain these results restricts their applicability to 6 E. S. Benilov The present paper examines liquid films and flows with a small slope of the free surface, but an unrestricted Reynolds number.…”

Section: Introductionsupporting

confidence: 72%

Hydraulic jumps in a shallow flow down a slightly inclined substrate

Benilov

2015

J. Fluid Mech.

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This work examines free-surface flows down an inclined substrate. The slope of the free surface and that of the substrate are both assumed small, whereas the Reynolds number Re remains unrestricted. A set of asymptotic equations is derived, which includes the lubrication and shallow-water approximations as limiting cases (as Re → 0 and Re → ∞, respectively). The set is used to examine hydraulic jumps (bores) in a two-dimensional flow down an inclined substrate. An existence criterion for steadily propagating bores is obtained for the (η, s) parameter space, where η is the bore's downstream-to-upstream depth ratio, and s is a non-dimensional parameter characterising the substrate's slope. The criterion reflects two different mechanisms restricting bores. If s is sufficiently large, a 'corner' develops at the foot of the bore's front -which, physically, causes overturning. If, in turn, η is sufficiently small (i.e. the bore's relative amplitude is sufficiently large), the non-existence of bores is caused by a stagnation point emerging in the flow.

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Section: Introductionsupporting

confidence: 72%

Hydraulic jumps in a shallow flow down a slightly inclined substrate

Benilov

2015

J. Fluid Mech.

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“…As an alternative to traditional VOF methods, a number authors such as [8], [9], [10], [10] and [11] have used depth-averaged numerical approximations to study the behaviour of thin-film rimming flows. These methods may be refered to as the Eulerian Thin-Film Models (ETFM) and by removing the requirement for the film thickness to be explicitly resolved using a computational grid, a significant reduction in the computational cost is obtained.…”

Section: Introductionmentioning

confidence: 99%

“…In the ETFM approach, the three-dimensional (3D) Navier-Stokes equations are depth-averaged across the film thickness to obtain a set of 2D thin-film equations. The results from the numerical work of [8], [9] and [11] show that for 2D rimming flows, depending on the amount of liquid in the film, and the balance between viscous, gravitational and inter-facial shear stresses, three different types of steady flow regimes are attainablesmooth, shock and pool -as illustrated in Figure 2. Smooth solutions are obtained when, the surface shear is sufficient to overcome gravitational forces and circulate the film around the chamber forming a uniform film profile as shown in Figure 2a.…”

Section: Introductionmentioning

confidence: 99%

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The Depth-Averaged Numerical Simulation of Laminar Thin-Film Flows With Capillary Waves

Kakimpa

Morvan

Hibberd

2016

Journal of Engineering for Gas Turbines and Power

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Thin-film flows encountered in engineering systems such as aeroengine bearing chambers often exhibit capillary waves and occur within a moderate to high Weber number range. Although the depth-averaged simulation of these thin-film flows is computationally efficient relative to traditional VOF methods, numerical challenges remain particularly for solutions involving capillary waves and in the higher Weber number, low surface tension range. A depth-averaged approximation of the Navier-Stokes equations has been used to explore the effect of surface tension, grid resolution and inertia on thin-film rimming solution accuracy and numerical stability. In shock and pooling solutions where capillary ripples are present, solution stability and accuracy are shown to be highly sensitive to surface tension. The common practice in analytical studies of enforcing unphysical low Weber number stability constraints is shown to stabilise the solution by artificially damping capillary oscillations. This approach however although providing stable solutions is shown to adversely affect solution accuracy. An alternative grid resolution based stability criteria is demonstrated and used to obtain numerically stable shock and pooling solutions without recourse to unphysical surface tension values. This allows for the accurate simulation of thin-film flows with capillary waves within the constrained parameter space corresponding to physical material and flow properties. Results obtained using the proposed formulation and solution strategy show good agreement with available experimental data from

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“…As a result there is a considerable and steadily growing literature on both coating and rimming flows. Following the work by Pukhnachev (1977) and Moffatt (1977), important contributions have been made by many authors, including Johnson (1988), Preziosi & Joseph (1988), Melo & Douady (1993), Thoroddsen & Mahadevan (1997), Hosoi & Mahadevan (1999), Duffy & Wilson (1999), Peterson et al (2001), Wilson et al (2002b), Ashmore et al (2003), Hinch & Kelmanson (2003), Acrivos & Jin (2004), Evans et al (2004), Benilov & O'Brien (2005), Evans et al (2005), Villegas-Díaz et al (2005), Benilov (2006), Noakes et al (2006), Chen et al (2007), Benilov et al (2008), Hunt (2008), Benilov et al (2009), Kelmanson (2009), Shrager et al (2009), Tougher et al (2009), Chicharro et al (2011), Pougatch & Frigaard (2011), Thiele (2011), Benilov et al (2012), Leslie et al (2012), and Williams et al (2012). The recent review article by Seiden & Thomas (2011) focuses on pattern formation and segregation in rimming flows of dilute suspensions and granular materials, but also provides probably the most complete overview of the literature on coating and rimming flows of pure fluids currently available.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional coating and rimming flow: a ring of fluid on a rotating horizontal cylinder

2013

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This version is available at https://strathprints.strath.ac.uk/42349/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output.Under consideration for publication in J. Fluid Mech. The steady three-dimensional flow of a thin, slowly varying ring of Newtonian fluid on either the outside or the inside of a uniformly rotating large horizontal cylinder is investigated. Specifically, we study "full-ring" solutions, corresponding to a ring of continuous, finite and non-zero thickness that extends all the way around the cylinder. In particular, it is found that there is a critical solution corresponding to either a critical load above which no full-ring solution exists (if the rotation speed is prescribed) or a critical rotation speed below which no full-ring solution exists (if the load is prescribed). We describe the behaviour of the critical solution and, in particular, show that the critical flux, the critical load, the critical semi-width and the critical ring profile are all increasing functions of the rotation speed. In the limit of small rotation speed, the critical flux is small and the critical ring is narrow and thin, leading to a small critical load. In the limit of large rotation speed, the critical flux is large and the critical ring is wide on the upper half of the cylinder and thick on the lower half of the cylinder, leading to a large critical load. We also describe the behaviour of the non-critical full-ring solution, and, in particular, show that the semi-width and the ring profile are increasing functions of the load but, in general, non-monotonic functions of the rotation speed. In the limit of large rotation speed, the ring approaches a limiting non-uniform shape, whereas in the limit of small load, the ring is narrow and thin with a uniform parabolic profile. Finally, we show that, while for most values of the rotation speed and the load the azimuthal velocity is in the same direction as the rotation of the cylinder, there ...

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On rimming flows with shocks

Cited by 13 publications

References 16 publications

Hydraulic jumps in a shallow flow down a slightly inclined substrate

Hydraulic jumps in a shallow flow down a slightly inclined substrate

The Depth-Averaged Numerical Simulation of Laminar Thin-Film Flows With Capillary Waves

Three-dimensional coating and rimming flow: a ring of fluid on a rotating horizontal cylinder

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