Competing geometric and inertial effects on local flow structure in thick gravity-driven fluid films

Scholle, Markus; Haas, André; Aksel, Nuri; Wilson, Mark C. T.; Thompson, H. M.; Gaskell, Philip

doi:10.1063/1.3041150

Cited by 58 publications

(46 citation statements)

References 39 publications

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“…Note that this graph is equivalent to that in Fig. 4 in Scholle et al [24], which considers the corresponding free-surface film flow. Agreement between the finite element and the semi-analytical results is generally good, particularly for small clearances.…”

Section: Kinematically Induced Eddies In Stokes Flowmentioning

confidence: 99%

“…This is similar behaviour to the film case, as one might expect at first glance, given that for large mean gaps/film thicknesses the flow local to the surface of the undulating plate should become insensitive to the exact form of the distant upper boundary. However, there is a difference between the two: in the film case, it is possible to induce a substantial eddy in a previously fully attached flow by increasing the film thickness [24]; this is not possible in the rigid-plate case. This difference between the two flows is due to the different driving forces in the two cases.…”

Section: Kinematically Induced Eddies In Stokes Flowmentioning

confidence: 99%

“…The field equations (5, 6) are solved using the same Bubnov-Galerkin weighted residual finite element (FE) method used by Scholle et al [24] to investigate the corresponding problem of gravity-driven film flow over a corrugated substrate. However, the formulation is somewhat simpler in the present case, as the rigid upper plate requires less sophisticated treatment than a free-surface [25].…”

Section: Finite Element Formulationmentioning

confidence: 99%

“…The first, and principal, method involves a full finite element solution of the Navier-Stokes and continuity equations; the second is comprised of a semi-analytical variational formulation for Stokes flow, solved using Ritz's direct method. This is followed, Section 3, by the results from a comprehensive and systematic investigation of the combined effects of changes to the flow geometry and inertia present on local flow structure; comparisons with corresponding gravity-driven free-surface film flow over an inclined wavy substrate [24], are drawn. Of particular interest is the kinematic and inertial manipulation of eddies.…”

Section: Introductionmentioning

confidence: 99%

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Eddy genesis and manipulation in plane laminar shear flow

et al. 2009

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Eddy formation and presence in a plane laminar shear flow configuration consisting of two infinitely long plates orientated parallel to each other is investigated theoretically. The upper plate, which is planar, drives the flow; the lower one has a sinusoidal profile and is fixed. The governing equations are solved via a full finite element formulation for the general case and semi-analytically at the Stokes flow limit. The effects of varying geometry (involving changes in the mean plate separation or the amplitude and wavelength of the lower plate) and inertia are explored separately. For Stokes flow and varying geometry, excellent agreement between the two methods of solution is found. Of particular interest with regard to the flow structure is the importance of the clearance that exists between the upper plate and the tops of the corrugations forming the lower one. When the clearance is large, an eddy is only present at sufficiently large amplitudes or small wavelengths. 1However, as the plate clearance is reduced, a critical value is found which triggers the formation of an eddy in an otherwise fully attached flow for any finite amplitude and arbitrarily large wavelength. This is a precursor to the primary eddy to be expected in the lid-driven cavity flow which is formed in the limit of zero clearance between the plates.The influence of the flow driving mechanism is assessed by comparison with corresponding solutions for the case of gravity-driven fluid films flowing over an undulating substrate.When inertia is present, the flow generally becomes asymmetrical. However, it is found that for large mean plate separations the flow local to the lower plate becomes effectively decoupled from the inertia dominated overlying flow if the wavelength of the lower plate is sufficiently small. In such cases the local flow retains its symmetry. A local Reynolds number based on the wavelength is shown to be useful in characterising these large-gap flows. As the mean plate separation is reduced, the form of the asymmetry caused by inertia changes, and becomes strongly dependent on the plate separation. For lower plate wavelengths which do not exhibit a kinematically induced secondary eddy, an inertially induced secondary eddy can be created if the mean plate separation is sufficiently small and the global Reynolds number sufficiently large.

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Section: Kinematically Induced Eddies In Stokes Flowmentioning

confidence: 99%

Section: Kinematically Induced Eddies In Stokes Flowmentioning

confidence: 99%

Section: Finite Element Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Eddy genesis and manipulation in plane laminar shear flow

et al. 2009

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“…among others, Szumbarski and Floryan (2006), Luo et al (2008), Scholle et al (2008), Malevich et al (2008), Khanafer et al (2009), andElshafei et al (2010). One common theme among these studies is to look into the geometrical effects due to wall corrugations on the flow resistance or pressure drop in the channel.…”

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confidence: 99%

Darcy–Brinkman Flow Through a Corrugated Channel

Wang

2010

Transp Porous Med

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A perturbation analysis is carried out to the second order to give effective equations for Darcy-Brinkman flow through a porous channel with slightly corrugated walls. The flow is either parallel or normal to the corrugations, and the corrugations of the two walls are either in phase or half-period out of phase. The present study is based on the assumptions that the corrugations are periodic sinusoidal waves of small amplitude, and the channel is filled with a sparse porous medium so that the flow can be described by the Darcy-Brinkman model, which approaches the Darcian or Stokes flow limits for small or large permeability of the medium. The Reynolds number is also assumed to be so low that the nonlinear inertia can be ignored. The effects of the corrugations on the flow are examined, quantitatively and qualitatively, as functions of the flow direction, the phase difference, and the wavelength of the corrugations, as well as the permeability of the channel. It is found that the corrugations will have greater effects when it is nearer the Stokes' flow limit than the Darcian flow limit, and when the wavelength is shorter. For the same wavelength and phase difference, cross flow is more affected than longitudinal flow by the corrugations. Opposite effects can result from 180 • out-of-phase corrugations, depending on the flow direction, the wavelength, as well as the permeability.

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A consistent energy integral model for a film over a substrate featuring topographies

Pal

Sanyasiraju

Usha

2021

Numerical Methods in Fluids

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A depth‐averaged model, based on energy integral method (EIM) has been employed to capture the steady‐state free surface profiles in a gravity‐driven thin film flow of a viscous, incompressible fluid over inclined substrates with topographical features. The model incorporates inertial effects, energy balance and is consistent up to O(ε), where ε≪1, is the film thickness parameter. The governing equations are solved using a meshless numerical scheme based on radial basis functions. The predictions of the effects of inertia, inclination of the substrate, and aspect ratio of the topographical features are compared with the available finite‐element solutions and experimental observations. The steady‐state profiles generated using the EIM equations are in close agreement with the experimental observations. Being a consistent model, EIM model predictions are expected to be more reliable and accurate than the results based on the depth averaged form of the momentum equations, which are known to be not consistent. This feature is the motivating factor for the present work which is also a first attempt in implementing the meshless numerical scheme to free surface problems. The analysis paves a way for similar investigations on three‐dimensional flows related to film flow over chemically patterned substrates.

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Competing geometric and inertial effects on local flow structure in thick gravity-driven fluid films

Cited by 58 publications

References 39 publications

Eddy genesis and manipulation in plane laminar shear flow

Eddy genesis and manipulation in plane laminar shear flow

Darcy–Brinkman Flow Through a Corrugated Channel

A consistent energy integral model for a film over a substrate featuring topographies

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