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Modelling gravity-driven film flow on inclined corrugated substrate using a high fidelity weighted residual integral boundary-layer method

Veremieiev, S.; Wacks, D.H.

Modelling gravity-driven film flow on inclined corrugated substrate using a high fidelity weighted residual integral boundary-layer method Thumbnail


Authors

D.H. Wacks



Abstract

A computational investigation is conducted concerning the stability of free-surface gravity-driven liquid film flow over periodic corrugated substrate. The underpinning mathematical formulation constitutes an extension of the weighted residual integral boundary-layer (WIBL) method proposed by Ruyer-Quil and Manneville [“Improved modeling of flows down inclined planes,” Eur. Phys. J. B 15(2), 357–369 (2000)] and D’Alessio et al. [“Instability in gravity-driven flow over uneven surfaces,” Phys. Fluids 21(6), 062105 (2009)] to include third- and fourth-order terms in the long-wavelength expansion. Steady-state solutions for the free-surface and corresponding curves of neutral disturbances are obtained using Floquet theory and validated against corresponding experimental data and full Navier-Stokes (N-S) solutions. Sinusoidal and smoothed rectangular corrugations with variable steepness are considered. It is shown that the model is capable of predicting characteristic patterns of stability, including short-wave nose and isles of stability/instability as reported experimentally for viscous film flow over inclined topography, providing an attractive trade-off between the accuracy of a full N-S computation and the efficiency of an integral method. The range of parameter values for which the WIBL model remains valid is established; in particular, it is shown that its accuracy decreases with the Reynolds number and corrugation amplitude, but increases with the steepness parameter and ratio of wavelength to capillary length.

Citation

Veremieiev, S., & Wacks, D. (2019). Modelling gravity-driven film flow on inclined corrugated substrate using a high fidelity weighted residual integral boundary-layer method. Physics of Fluids, 31(2), Article 022101. https://doi.org/10.1063/1.5063013

Journal Article Type Article
Acceptance Date Dec 20, 2018
Online Publication Date Feb 1, 2019
Publication Date Feb 1, 2019
Deposit Date Feb 5, 2019
Publicly Available Date Mar 28, 2024
Journal Physics of Fluids
Print ISSN 1070-6631
Electronic ISSN 1089-7666
Publisher American Institute of Physics
Peer Reviewed Peer Reviewed
Volume 31
Issue 2
Article Number 022101
DOI https://doi.org/10.1063/1.5063013

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This is a pre-copy-editing, author-produced PDF of an article accepted for publication in [insert journal title] following peer review. The definitive publisher-authenticated version Veremieiev, S. & Wacks, D.H. (2019). Modelling gravity-driven film flow on inclined corrugated substrate using a high fidelity weighted residual integral boundary-layer method. Physics of Fluids 31(2): 022101 is available online at: https://doi.org/10.1063/1.5063013




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