STABILITY OF CONFINED SWIRLING FLOW WITH AND WITHOUT VORTEX BREAKDOWN

A numerical investigation of steady states, their stability, onset of oscillatory instability, and slightly supercritical unsteady regimes o f an axisymmetric swirling flow of a Newtonian incompressible fluid in a closed circular cylinder with a rotating lid is presented for aspec t ratio (height/radius) 1 less than or equal to gamma less than or equ al to 3.5. Various criteria for the appearance of vortex breakdown are discussed. It is shown that vortex breakdown takes place in this syst em not as a result of instability but as a continuous evolution of the stationary meridional flow with increasing Reynolds number. The depen dence of the critical Reynolds number Re-cr and frequency of oscillati ons omega(cr) on the aspect ratio of the cylinder gamma is obtained. I t is found that the neutral curve Re-cr(gamma) and the curve (cr)(gamm a) consist of three successive continuous segments corresponding to di fferent modes of the dominant perturbation. The calculated critical pa rameters are in good agreement with the available experimental and num erical data for gamma < 3. It is shown that the onset of the oscillato ry instability does not depend on the existence of a separation bubble in the subcritical steady state. By means of a weakly nonlinear analy sis it is shown that the axisymmetric oscillatory instability sets in as a result of a supercritical Hopf bifurcation for each segment of th e neutral curve. A weakly nonlinear asymptotic approximation of slight ly supercritical flows is carried out. The results of the weakly nonli near analysis are verified by direct numerical solution of the unstead y Navier-Stokes equation using the finite volume method. The analysis of the supercritical flow field for aspect ratio less than 1.75, for w hich no steady vortex breakdown is found, shows the existence of an os cillatory vortex breakdown which develops as a result of the oscillato ry instability.