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Instabilities in Source-Sink Flows for Rotating Machines: Numerical Results

DOI: 10.1615/ICHMT.1994.IntSympHetatTransTurb.380
pages 553-563

P. Maubert
I.M.F.M.-U.M.34 C.N.R.S., 1 rue Honnorat, F-13003 Marseille, France

A. Chaouche
I.M.F.M.-U.M.34 C.N.R.S., 1 rue Honnorat, F-13003 Marseille, France

Anthony Randriamampianina
Département de Modélisation Numérique, Institut de Recherche sur les Phénomènes Hors Equilibre, Unité Mixte de Recherche CNRS 6594, 1, rue Honnorat, 13003 Marseille, France

Emilia Crespo del Arco
Departamento de Fisica Fundamental, U.N.E.D., Apdo. Correos 60.141, 28080 Madrid, Spain

Patrick Bontoux
Département de Modélisation Numérique, Institut de Recherche sur les Phénomènes Hors Equilibre, Unité Mixte de Recherche CNRS 6594, 1, rue Honnorat, 13003 Marseille, France

要約

This study concerns the stability of the steady laminar boundary-layer flow of a homogeneous fluid which occurs in a rotating annulus, whose inner and outer vertical walls are, respectively, a sink and a source of fluid. A pseudo-spectral numerical method is used to study the axisymmetrical time dependent flow regimes that appear for high values of the Taylor number, when the source-sink flow rate is increased. In these conditions, the flow evolves from a steady S to a chaotic NP flow regime, through the sequence of bifurcations S P1 QP P5 NP, where P1 is an oscillatory regime, QP is a quasiperiodic regime with two incommensurate frequencies and P5 is periodic with two basic frequencies which are in a ratio one to five. The first bifurcation S P1 is associated to a break of symmetry with respect to the midheight of the annulus. The entry flow travels radially down the cavity in the same way as in the steady flow, but it wavers and then is sucked to the Ekman layers. A second transition P1 QP is characterized by the apparition of a second frequency. Although it is not visible in the flow patterns, the power spectrum investigation shows that this instability is localized near the Ekman layers. Frequency locking results in a transition QP P5, and finally jn a chaotic motion. Investigations with different initial conditions have not shown any evidence of hysteresis in the described transitions. Comparison with experimental studies on the stability of the Ekman layers developed in a similar configuration gives a good agreement for the estimated critical values of the local parameters characteristic of the flow, the Rossby number and the Reynolds number computed with local measured values.

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