Flow instability in a plane sudden expansion followed by a curved duct

Instabilities detection and characterization for a laminar flow of an incompressible fluid through a two-dimensional plane sudden expansion followed by a curved duct, is carried out numerically using a finite-volume method. The objective of the present study is to characterize the first critical Reynolds number Re_c1 in which a third recirculation zone appears and the second critical number Re_c2 in which the flow becomes unstable with periodic oscillations of the flow variables. The results indicate that instabilities occur for the different sudden expansion aspect ratios, AR, investigated including AR = 1/2, 1/3 and 1/4, at different critical Reynolds numbers Re_c2 and that the curved pipe with AR = 1/4 is the more sensitive geometrical model that produces instabilities at lowest critical Re_c2 number. The flow field for different sudden aspect ratios, critical Re numbers, and the mechanisms responsible for the appearance of these instabilities are presented and discussed in detail.