Numerical investigation of the first bifurcation for the flow in a rotor-stator cavity of radial aspect ratio 10
Résumé
The nature of transition to unsteadiness of rotorstator 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.