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Steady flow in an annulus with a varying number of deflectors at rotational vibration

A numerical study is carried on of the dynamics of an isothermal liquid in an annulus whose boundaries make rotational vibrations. On the outer boundary, one or several deflectors are placed regularly. The problem is considered in a two-dimensional formulation. The case of high frequency oscillations is considered. As a result of oscillations, a single deflector generates a steady flow in the form of a symmetric vortex pair in the Stokes boundary layer and a coherent vortex pair in the non-viscous domain. The size of the secondary vortices grows with pulsation Reynolds number, Rep. Upon reaching a threshold value of Rep, one of the secondary vortices extends transforming into a large-scale vortex, which encircles the inner boundary of the annulus. Thus, the symmetry of steady flow is broken. Comparison of the cases with different number of activators shows that their number affects steady flow intensity, but does not influence the threshold of symmetry break.