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Applied Mathematics Colloquium

Friday, November 9, 11:30 am
Cullimore Lecture Hall II
New Jersey Institute of Technology

Hovering of Passive Bodies in an Oscillating Airflow

Stephen Childress

Department of Mathematics

New York University

New York, NY

Abstract

We consider the possibility of levitating a body in an oscillating uniform airflow. At low Reynolds number, the Oseen approximation may be used to study the inertial contribution to the force experienced by a small sphere, and we show that the drag correction is reduced by the oscillatory component. At high Reynolds numbers, a flexible passive body in an oscillatory flow will deform and mimic the vortex shedding of an actively moving body. We describe an experiment which simulates the hovering of a flapping body based on this idea. A simple inviscid fluid model gives results in qualitative agreement with the experimental determination of oscillation amplitude for hovering as a function of frequency and body size. The experiment also has implications for the possible stability of a flapping hoverer.