Stability of flow in a diverging-converging channel at moderate amplitudes of corrugation

Abstract eng:
Flow in a diverging-converging channel of moderate amplitudes has been studied. The analysis is carried out up to Reynolds numbers resulting in the formation of secondary states. The first part of the analysis is based on a two-dimensional model and demonstrates that reducing the corrugation wavelength results in the appearance of an unsteady separation whose onset correlates with the onset of the travelling wave instability. The second part of the analysis is based on a three-dimensional model and demonstrates that the flow dynamics are dominated by the centrifugal instability over a large range of geometric parameters, resulting in the formation of streamwise vortices. The critical Reynolds number for the vortex onset initially decreases as the groove amplitude increases but an excessive increase leads to reduction of the centrifugal forces. The flow dynamics under such conditions are dominated by the onset of the travelling wave instability.

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