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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 studied theoretically and experimentally. This study is motivated by aeronautics and geophysics applications. Precessional motion forces hydrodynamics waves called Kelvin modes whose structure and amplitude are predicted by a linear inviscid theory. When a forced Kelvin mode is resonant, a viscous and weakly nonlinear theory has been developed to predict its saturated amplitude. We show that this amplitude scales as Re1/2 for low Reynolds numbers and as θ1/3 (where θ is the precessing angle) for high Reynolds numbers. These scalings are confirmed by PIV measurements. For Reynolds numbers sufficiently large, this forced flow becomes unstable. A linear stability analysis based on a triadic resonance between a forced Kelvin mode and two free modes has been carried out. The precessing angle for which the flow becomes unstable is predicted and compared successfully to experimental measurements. A weakly nonlinear theory was developed and allowed to show that the bifurcation of the instability of precession is subcritical. It also showed that, depending on the Reynolds number, the unstable flow can be steady or intermittent. Finally, this weakly nonlinear theory allowed to predict, with a good agreement with experiments, the mean flow 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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