The transition from steady to unsteady flow through hexagonal close packed spheres is analyzed numerically. Different flow regimes in the transition towards unsteady flow are defined and analyzed in detail and possible flow mechanisms responsible for the instabilities in unsteady flow are proposed. A direct numerical simulation based on the incompressible Navier-Stokes equations with an immersed boundary method is used for the simulation of the pressure driven flow through the hexagonal sphere pack. The simulation is performed at a comparatively low grid resolution for which the results are not yet fully converged. The flow fields after the flow is accelerated from rest and after the transients have decayed at different Reynolds numbers based on the sphere diameter are then decomposed by the proper orthogonal decomposition. From the behavior of the stream-wise superficial velocity four different flow regimes, namely the “steady, over-damped”, the “steady, under-damped”, the “unsteady, periodically fluctuating” and the “unsteady, chaotically fluctuating” flow regime, are defined. Those regimes are then confirmed by looking at the POD dimension of each flow regime. Both steady flow regimes have a POD dimension of one and can be reconstructed from only one POD-mode constant in time. For the unsteady flow regimes more POD-modes are necessary for the reconstruction of the flow field. From looking at the eigenvalue spectrum and the time coefficients from the POD, mode pairs in the POD-modes can be detected. Those mode pairs are then reconstructed giving rise to possible instability mechanisms. After all, the flow mechanisms reconstructed for the mode pairs cannot explain the temporal behavior of the stream-wise superficial velocity.
«
Login
BibTeX