Transition of the flow in a symmetric channel with periodically expanded grooves

Transition of the flow in a periodically grooved channel is numerically investigated for periodicity indices m=1 up to 6 by assuming the two-dimensional and fully developed flow field, where m is defined as a number of grooves in which the flow repeats periodically. Critical Reynolds numbers for the onset of a self-sustained oscillatory flow from a steady-state flow are evaluated by numerical simulations. It is found that the bifurcations occur at the critical Reynolds numbers as a result of Hopf bifurcation, and a period in the streamwise direction of the oscillatory flow is twice as long as the groove pitch of the channel. In addition, flow visualization with the aluminum dust method is carried out to confirm the results obtained from the numerical simulations. The experimental results are in good agreement with the numerical ones.