Computational modelling of a fluid-conveying flexible channel using oomph-lib

Abstract

The objective of this paper is to assess the suitability of a new, open-source, Finite Element Modelling (FEM) program called Object-Oriented Multi-Physics Finite-Element Library (oomph-lib)to study the Fluid-Structure Interaction (FSI) mechanics of a fluid-conveying two-dimensional channel that has a flexible section. Previous studies have shown that this system contains rich dynamics that can include unstable oscillations of the flexible-wall section due to the fluid loading that itself is determined by the wall motion. The fundamental system is relevant to a host of applications in both engineered (e.g. flexible-pipes, membrane filters, and general aero-/hydro-elasticity) and biomechanical (e.g. blood flow, airway flow) systems. The computational model developed using oomph-lib accounts for unsteady laminar flow interacting with large-amplitude (nonlinear) deformations of a thin flexible wall. The fluid loading on the wall comprises both pressure and viscous stresses while the wall mechanics includes inertial, flexural and tension forces. Nonlinear effects in the wall mechanics principally arises through the tension induced by its deformation and the correct modelling of its geometry throughout its motion.The discretised equations for the coupled fluid and structural dynamics are combined to yield a single (monolithic) matrix differential equation for all of the fluid and wall variables that is solved through a time-stepping algorithm so as to generate numerical simulations of the system behaviour. In this paper we present results of a systematic validation of the computational model developed. Meanflow mechanics are validated by comparison against theory for Poiseuille flow through the channel with the flexible-wall held in its undisplaced position. Appropriate comparisons of statically-loaded deformations and in-vacuo vibrations of the flexible wall are made against linear theory and the limits of linear behaviour identified. The steady-state FSI is validated by comparing large-amplitude wall deformations, pressure and skin-friction loadings with published computational results that were obtained using a different computational scheme that is not in the public domain. Finally, some preliminary results of large amplitude dynamic FSI for the system are presented and discussed. Taken together, these results demonstrate the suitability of oomph-lib as a modelling and predictive tool for the study of fluid-conveying flexible pipes.