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Dynamics of a fluid inside a precessing cylinder

Published online by Cambridge University Press:  05 August 2009

Romain Lagrange ,
Patrice Meunier ,
Christophe Eloy  and
François Nadal
Romain Lagrange
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre / Université de Provence, IRPHE – UMR 6594, Technopôle de Château-Gombert, 49, rue Joliot Curie, B.P. 146, 13384 Marseille Cedex 13, France
Patrice Meunier
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre / Université de Provence, IRPHE – UMR 6594, Technopôle de Château-Gombert, 49, rue Joliot Curie, B.P. 146, 13384 Marseille Cedex 13, France
Christophe Eloy
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre / Université de Provence, IRPHE – UMR 6594, Technopôle de Château-Gombert, 49, rue Joliot Curie, B.P. 146, 13384 Marseille Cedex 13, France
François Nadal
Affiliation:
Commissariat à l'Énergie Atomique (CEA/CESTA), France
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Abstract

The instability of a fluid inside a precessing cylinder is studiedtheoretically and experimentally. This study is motivated byaeronautics and geophysics applications. Precessional motion forceshydrodynamics waves called Kelvin modes whose structure andamplitude are predicted by a linear inviscid theory. When a forcedKelvin mode is resonant, a viscous and weakly nonlinear theory hasbeen developed to predict its saturated amplitude. We show that thisamplitude scales as Re1/2 for low Reynolds numbers and asθ1/3 (where θ is the precessing angle) for highReynolds numbers. These scalings are confirmed by PIV measurements.For Reynolds numbers sufficiently large, this forced flow becomesunstable. A linear stability analysis based on a triadic resonancebetween a forced Kelvin mode and two free modes has been carriedout. The precessing angle for which the flow becomes unstable ispredicted and compared successfully to experimental measurements. Aweakly nonlinear theory was developed and allowed to show that thebifurcation of the instability of precession is subcritical. It alsoshowed that, depending on the Reynolds number, the unstable flow canbe steady or intermittent. Finally, this weakly nonlinear theoryallowed to predict, with a good agreement with experiments, the meanflow in the cylinder; even if it is turbulent.

Keywords

PrecessionKelvin modesinstabilitytriadic resonancePrécessionmodes de Kelvininstabilitérésonance triadique
Type
Research Article
Information
Mechanics & Industry , Volume 10 , Issue 3-4: 19e Congrès français de mécanique (CFM 2009) , May 2009 , pp. 187 - 194
Copyright
© AFM, EDP Sciences, 2009

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