A low-order model for slamming in a flexible-channel flow

Abstract

In simulations, large-amplitude self-excited oscillations of high-Reynolds-number flow in a finite-length flexible channel often exhibit vigorous repetitive ’slamming’ motion, during which the channel briefly becomes almost completely occluded over a very short lengthscale near its downstream end before rapidly reopening. Here we analyse this near-singular behaviour using an established one-dimensional PDE model of the two-dimensional physical system. Working in a distinguished asympotic limit, we systematically derive a low-order differential/algebraic model for the flow when it is close to the slamming state. The shape of the channel near the constriction is determined by a balance between membrane tension and fluid inertia; this region is also the predominant site of viscous dissipation, which balances energy changes distributed along the channel. The reduced model accurately captures a set of steady solution branches and their stability and shows how slamming is strongly coupled to the properties of the rigid channel downstream of the membrane. A singularity is identified in the low-order model which may explain the violent readjustment of the flow at the end of a slamming event.