Viscous Flow In A Channel With A Sudden Expansion

Abstract

A theoretical investigation of two-dimensional and viscous flows in a symmetric channel with a sudden expansion with right angles is presented. The analysis explores the flow states around a critical Reynolds number Rec where asymmetric states appear in addition to the basic symmetric states when #e > #6cThe size of the asymmetric perturbation changes like \/#e #6cLinear stability studies of the various equilibrium states show that the symmetric states have a stable mode of perturbation when #e Ee^. The asymmetric states have an asymptotically stable mode of disturbance. As a result, the symmetric flow states always evolve into the asymmetric states when #e > #e . Space-and time-accurate numerical simulations using the unsteady Navier-Stokes equations are used to demonstrate the evolution of perturbations in the flow. A weakly nonlinear analysis of the flow dynamics also shows that the evolution of the perturbation's amplitude can be described by the Landau equation. The analytical solution shows good agreement with the unsteady simulations. The present work provides the possible mechanism by which two-dimensional flows in a suddenly expanding channel transition from symmetric to asymmetric states.