Numerical investigation of the first bifurcation for the flow in a rotor-stator cavity of radial aspect ratio 10

Olivier Daube (1) , Patrick Le Quéré (1)

1 LIMSI - Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur

The nature of transition to unsteadiness of rotor–stator disk flows of large radial aspect ratio is investigated by means of several numerical tools which consist in computing the base flow even when unstable, performing linearized or non-linear time integrations starting from initial conditions of different amplitudes and computing the spectrum of the Jacobian using the ARPACK library. From these numerical experiments we conclude that,in a cavity of radial aspect ratio 10,the transition to unsteadiness occurs through a subcritical Hopf bifurcation. In addition these calculations show the existence of a large amplitude chaotic branch for values of the Reynolds number far below the linear stability threshold,and onto which the solutions are attracted for large subcritical values due to the strong non-normality of the Jacobian of the evolution operator.

Mots clés: Rotor–stator disk flow; Hopf bifurcation; Subcriticality; Non-normality

Domaines: Physique [physics]; Mécanique des fluides [physics.class-ph]

Olivier Daube, Patrick Le Quéré. Numerical investigation of the first bifurcation for the flow in a rotor-stator cavity of radial aspect ratio 10. Computers and Fluids, 2002, 31, pp.481-494. ⟨hal-01847878⟩