Thrust on a Piston Driven Half-Open Tube

Abstract

The motion of the gas in and near a tube open at one end and closed at the other by a piston driven in nearly sinusoidal motion is investigated. Experiments disclose that when the frequency of the piston motion is near the fundamental acoustic resonance frequency of the gas column an intermittent air jet associated with a system of vortex rings is expelled from the tube's open end. This results in an appreciable average thrust on the tube which, however, is much less than might be expected from purely acoustic considerations. A theoretical analysis has been made which takes account of the intermittent vortex and jet formation, as well as of the acoustic radiation field. The analysis leads to formulas for the average thrust and power dissipation and to a relation between the driving frequency and the amplitude of the gas motion at the open end. An empirical parameter κ which represents the fraction of energy dissipated in vortex motion appears in these formulas. It is found possible to evaluate this parameter in terms of the observed thrust at resonance. From this datum the curve of thrust versus driving frequency is calculated and is found to agree well with experiment.