Flow Bifurcations and Transition Scenarios in Confined Flows: Channel Geometry and Operational Parameter Dependency

Abstract

We have performed numerical simulations of confined flows in both symmetric and asymmetric wavy channels to investigate the flow bifurcations and transition scenarios dependency on geometrical and operational parameters. Laminar and time-dependent transitional flow regimes are obtained by direct numerical simulations of the mass and momentum equations using a computational program based on the spectral element method. Computational meshes for periodic computational domains are used to determine the transitional flow behavior for increasing Reynolds numbers and changing geometrical parameters. For the asymmetric wavy channel, the transition scenarios are highly dependent on the aspect ratio of the channel geometrical parameters. Depending on a specific geometric aspect ratio—one of the control parameters, the following scenarios develop: a) a first transition scenario with one flow bifurcation to a relatively low Reynolds numbers, Rec; b) a second scenario, with also one flow bifurcation, to a relatively high Reynolds numbers, Rec*; and, c) a third flow transition scenario with two Hopf bifurcations B1 and B2, occurring in critical Reynolds numbers Rec1 y Rec2, respectively, similar to the Ruelle-Takens-Newhouse scenario. In this third scenario, fundamental frequencies ω1 and ω2, and super harmonic combinations of both develop as the Reynolds number increases from laminar to transitional flow regimes. For the symmetric wavy channel and a high aspect ratio of r=0.375, a transition scenario with one flow bifurcation develops to a critical Reynolds numbers Rec** leading to a periodic flow. Further increases in the Reynolds number leads to successive periodic flows where the fundamental frequency ω1, increases continuously, in a scenario of frequency-doubling.