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- Title
A LOW-ORDER MODEL FOR SLAMMING IN A FLEXIBLE-CHANNEL FLOW.
- Authors
FENG XU; JENSEN, OLIVER E.
- 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 length scale 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.
- Subjects
FLUID mechanics; ASYMPTOTIC expansions; REYNOLDS number; ENERGY dissipation; INERTIA (Mechanics)
- Publication
Quarterly Journal of Mechanics & Applied Mathematics, 2015, Vol 68, Issue 3, p299
- ISSN
0033-5614
- Publication type
Article
- DOI
10.1093/qjmam/hbv009