The three-dimensional structure of confined swirling flows with vortex breakdown (Q2706924)

The numerical solutions of unsteady three-dimensional Navier-Stokes equations are presented in order to examine the asymmetries observed in laboratory models of flows in enclosed cylinder driven by a rotating endwall. The Navier-Stokes equations are rewritten in generalized non-orthogonal curvilinear coordinates by a partial transformation that retains Cartesian velocity components as dependent variables. The transformed equations are dicretized on a non-staggered mesh via conservative finite volume scheme, and integrated in time using a dual time-stepping artificial compressibility approach enhanced with multigrid acceleration. The accuracy of the solutions is established by comparing numerically generated streamline images of stationary vortex breakdown bubbles with visualization photographs. It is shown that all asymmetric features of the bubbles observed in laboratory can be reproduced numerically with reasonable accuracy. The origin of asymmetric folds at the downstream end of bubbles is clarified, and the filling and empting mechanisms observed in laboratory tests are explained. It is also found that the asymmetric features of stationary vortex breakdown bubbles along the axis are linked to asymmetries that originate inside the stationary cover Ekman layer and the sidewall Stewartson layer, in accordance with laboratory observations.