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Laminar spread of a circular liquid jet impinging axially on a rotating disc

Published online by Cambridge University Press:  07 February 2019

B. Scheichl Open the ORCID record for B. Scheichl [Opens in a new window]  and
A. Kluwick
B. Scheichl*
Affiliation:
Institute of Fluid Mechanics and Heat Transfer, Faculty of Mechanical Engineering, Technische Universität Wien, Tower BA/E322, Getreidemarkt 9, 1060 Vienna, Austria AC2T research GmbH (Austrian Excellence Center for Tribology), Viktor-Kaplan-Straße 2/C, 2700 Wiener Neustadt, Austria
A. Kluwick
Affiliation:
Institute of Fluid Mechanics and Heat Transfer, Faculty of Mechanical Engineering, Technische Universität Wien, Tower BA/E322, Getreidemarkt 9, 1060 Vienna, Austria
*
†Email address for correspondence: bernhard.scheichl@tuwien.ac.at
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Abstract

The steady laminar annular spread of a thin liquid film generated by a circular jet which impinges perpendicularly in direction of gravity on the centre of a rotating disc is examined both analytically and numerically. Matched asymptotic expansions of the flow quantities provide the proper means for studying the individual flow regimes arising due to the largeness of the Reynolds number formed with the radius of the jet, its slenderness and the relative magnitude of the centrifugal body force. This is measured by a suitably defined Rossby number, $Ro$. The careful analysis of jet impingement predicts a marked influence of gravity and surface tension on the film flow, considered in the spirit of a shallow-water approach, only through the vorticity imposed by the jet flow. Accordingly, associated downstream conditions are disregarded as the local Froude and Weber numbers are taken to be sufficiently large. Hence, the parabolic problem shaped from the governing equations in a rigorous manner describes the strongly supercritical spread of a developed viscous film past an infinite disc, essentially controlled by $Ro$. Its numerical solutions are discussed for a wide range of values of $Ro$. The different flow regimes reflecting varying effects of viscous shear and centrifugal force are elucidated systematically to clarify the surprising richness of flow phenomena. Special attention is paid to the cases $Ro\gg 1$ and $Ro\ll 1$. The latter, referring to relatively high disc spin, implies a delicate breakdown of the asymptotic flow structure, thus requiring a specific analytical and numerical treatment. Finally, the impact of gravity and capillarity and thus of the disc edge on the film flow is envisaged in brief.

JFM classification

Geophysical and Geological Flows: Rotating flows Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 864 , 10 April 2019 , pp. 449 - 489
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Copyright
© 2019 Cambridge University Press 

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