Vortex instability in a diverging–converging channel

Abstract

Linear stability of flow in a diverging–converging channel is considered. The flow may develop under either the fixed mass or the fixed pressure gradient constraint. Both cases are considered. It is shown that under certain conditions the divergence–convergence of the channel leads to the formation of a secondary flow in the form of streamwise vortices. It is argued that the instability is driven by centrifugal effect. The instability has two modes and conditions leading to their onset have been identified. These conditions depend on the amplitude and the length of the channel diverging–converging section and can be expressed in terms of a critical Reynolds number. The global critical conditions describing the minimum critical Reynolds number required to create the instability for the specified amplitude of the variations of the channel opening are also given. It is shown that the flow developed under the fixed mass constraint is slightly more unstable than the flow developed under the fixed pressure constraint. This difference increases with an increase of the amplitude of the channel divergence–convergence.