The Investigation on the Instantaneous Force of Unsteady Vortex Ring Flows

Abstract

The source of the instantaneous reactive force is the conservation of momentum. This paper examines the impulse, as the role of momentum of the vortex ring for unbounded flows, in an attempt to study the contribution of the impulse changes in the wake vortical structures to the reactive instantaneous force in the piston-cylinder mechanism. The generation of reactive unsteady force is explained by investigating the vortex ring wake structures. The interaction between the vortex ring and the solid orifice reach the optimal influence on the propulsion when the stroke length is equal to the formation time of the vortex ring. It is expected that the results attained from the one-dimensional unsteady motion can be applied to more common flapping motion in the animal kingdom. NomenclatureOrifice diameter, m F Force, N I Impulse, kg × m/s k Unit vector L Stroke length, m Re Reynolds number r, z Coordinates in the frame of reference S Orifice area, m 2 T Scaled time, t/t p t Physical time, s t p Stroke time, s u Velocity, m/s V Volume, m 3 ω vorticity, s −1 ρ Density, kg/m 3 φ Potential function, m 2 /s Subscript r Radial direction θ Azimuthal direction z Axial direction * Undergraduate Student, School of Aeronautics and Astronautics, 800 Dongchuan Rd., AIAA Member.