Bifurcation of Low Reynolds Number Flows in Symmetric Channels

The ow elds in two-dimensional channels with discontinuous expansions are studied numerically to understand how the channel expansion ratio in uences the symmetric and non-symmetric solutions that are known to occur. For improved con dence and understanding, two distinct numerical techniques are used. The general ow eld characteristics in both symmetric and asymmetric regimes are ascertained by a time-marching nite volume procedure. The ow elds and the bifurcation structure of the steady solutions of the Navier-Stokes equations are determined independently using the nite-element technique. The two procedures are then compared both as to their predicted critical Reynolds numbers and the resulting ow eld characteristics. Following this, both numerical procedures are compared with experiments. The results show that the critical Reynolds number decreases with increasing channel expansion ratio. At a xed supercritical Reynolds number, the location at which the jet rst impinges on the channel wall grows linearly with the expansion ratio.