Flow-induced self-sustained oscillations in a straight channel with rigid walls and elastic supports

Abstract

This work considers the two-dimensional flow field of an incompressible viscous fluid in a parallel-sided channel. In our study, one of the walls is fixed whereas the other one is elastically mounted, and sustained oscillations are induced by the fluid motion. The flow that forces the wall movement is produced as a consequence that one of the ends of the channel is pressurized, whereas the opposite end is at atmospheric pressure. The study aims at reducing the complexity of models for several physiological systems in which fluid-structure interaction produces large deformation of the wall. We report the experimental results of the observed self-sustained oscillations. These oscillations occur at frequencies close to the natural frequency of the system. The vertical motion is accompanied by a slight trend to rotate the moving mass at intervals when the gap height is quite narrow. We propose a simplified analytical model to explore the conditions under which this motion is possible. The analytical approach considers asymptotic solutions of the Navier-Stokes equation with a perturbation technique. The comparison between the experimental pressure measured at the midlength of the channel and the analytical result issued with a model neglecting viscous effects shows a very good agreement. Also, the rotating trend of the moving wall can be explained in terms of the quadratic dependence of the pressure with the streamwise coordinate that is predicted by this simplified model.