Transition Scenario of Periodic and Quasiperiodic Flow Bifurcations in Symmetric Communicating Channels

Abstract

The flow transition scenario in symmetric communicating channels has been investigated using direct numerical simulations of the mass and momentum conservation equations in the Reynolds numbers range of Re = [170–227]. The governing equations are solved for laminar and time-dependent transitional flow regimes by the spectral element method, using a periodic computational domain, for a periodic length of nL and an aspect ratio of r = aˆ / (2Lˆ) = 0.0405, where aˆ = 2a is the height of block within the channel, n an integer and Lˆ = L + 1 is the periodic length. Periodic computational domains with n = 1 and 2 are used in this investigation to determine the periodic length effect on the flow pattern characteristics. Numerical investigations with different domain meshes are carried out for determining the appropriate discretization for capturing transitional time-dependent flows. The numerical results show a transition scenario with two-flow Hopf bifurcations which develop as the pressure gradient is increased from a laminar to a time-dependent flow regime. The first Hopf bifurcation occurs to a critical Reynolds number of Rec1 and leads to a time-dependent periodic flow characterized by a fundamental frequency ω1. Further increases in the pressure gradient lead to successive quasi periodic flows after a second Hopf bifurcation B2 occurring to a critical Reynolds number Rec2 < Rec1, with two fundamental frequencies ω1 and ω2, and linear combinations of both frequencies—where the fundamental frequency ω1 increases continuously—and ω2 > ω1. This transition scenario is somewhat different from the Ruelle-Takens-Newhouse transition scenario obtained for symmetric wavy channels; in symmetric wavy channels, periodic and quasi periodic flow regimes develop as the Reynolds number increases. The friction factor for the symmetric communicating channel in the transitional regime is higher than the friction factor for the Poiseuille plane channel. The qualitative and quantitative behavior is compared to other channel geometries that also develop other transition scenarios.