Computational Stability Analysis of a Channel Flow with a Large Deformation Compliant Insert

Abstract

We consider a fluid-conveying channel with a compliant insert, or wall, undergoing flow-induced deformations. The objective is to understand the mechanism that can cause selfexcited oscillations of a fundamental system that underpins a host of both engineered (e.g. flexible-pipes, membrane filters) and biomechanical (e.g. blood flow, airway flow) applications. The computational model is developed using the open-source fluid-structure interaction software oomph-lib that accounts for unsteady laminar flow interacting with large-amplitude deformations of a thin flexible wall. The fluid loading on the compliant wall comprises both pressure and viscous stresses while the wall mechanics includes flexural and tensile forces. The discretised equations for the coupled fluid and structural dynamics are combined to yield a single monolithic matrix differential equation for fluid and wall variables, which is solved through a timestepping procedure. We present a brief summary of validations performed that demonstrate the appropriateness of oomph-lib as a modelling tool for the system. Cases are then presented to contrast the system in stable and unstable conditions and we offer an explanation of the physical causes of non-linear saturated oscillation by examining the nature of wall deformations and their effect on the pressure gradient along the wall. We surmise that instability occurs principally through fluctuating energy transfers between wall and fluid that are driven by separation-point changes over each cycle of oscillation.