Effect of Structural Stiffness on the Stability of Pulsatile Poiseuille Flow Through a Compliant Channel

Abstract

We study the asymptotic stability of steady and pulsatile Poiseuille flow through a compliant channel to investigate the effect of wall structural stiffness on the different instability branches that may exist in the Fluid-Structure Interaction (FSI) system. We implement both vertical (V) and axial-vertical (AV) structural displacement models in which the dynamics are respectively controlled by the vertical stiffness and its ratio to the axial stiffness. It is shown that reducing the wall stiffness in the axial direction causes destabilisation of the inflectional instability (II) while reducing vertical stiffness causes Divergence (D) modes to yield the critical instability. Finally, it is shown that pulsatile Poiseuille flow at the low-frequency modulation used herein is more unstable regarding the inflectional instability but more stable regarding the Divergence instability than the steady Poiseuille flow for the range of wall stiffness and streamwise disturbance wavenumber studied in the present work.