The dynamics of dual vortex ring flows is studied experimentally and numerically in a model system that consists of a piston-cylinder apparatus. The flows are generated by double identical strokes which have the velocity profile characterized by the sinusoidal function of half the period. By calculating the total wake impulse in two strokes in the experiments, it is found that the average propulsive force increases by 50% in the second stroke for the sufficiently small stroke length, compared with the first stroke. In the numerical simulations, two types of transient force augmentation are revealed, there being the transient force augmentation for the small stroke lengths and the absolute transient force augmentation for the large stroke lengths. The relative transient force augmentation increases to 78% for L/D = 1, while the absolute transient force augmentation for L/D = 4 is twice as much as that for L/D = 1. Further investigation demonstrates that the force augmentation is attributed to the interaction between vortex rings, which induces transport of vortex impulse and more evident fluid entrainment. The critical situation of vortex ring separation is defined and indicated, with vortex spacing falling in a narrow gap when the stroke lengths vary. A new model is proposed concerning the limiting process of impulse, further suggesting that apart from vortex formation timescale, vortex spacing should be interpreted as an independent timescale to reflect the dynamics of vortex interaction.
Of particular significance to biological locomotion is vortex ring interaction. In the wakes of animals, this unsteady process determines the changes in the impulse of counter-rotating vortex ring pairs (VRPs), which consist of two vortex rings with opposite sense of rotation. In this paper, these VRPs are proposed to be of particular importance to unsteady force generation. We carry out numerical computations, simulating the piston-cylinder apparatus, to study the transient changes in the impulse of counter-rotating VRPs composed of a positive and a negative vortex ring. We model the negative vortex ring (NeVR) of a VRP by making reasonable assumptions about their vorticity distributions and spatial locations, which are initially prescribed. The result of modelling is superimposed on the flow, which has a pre-existing positive vortex ring (PoVR), leading to a VRP. The simulation quantitatively demonstrates that the unsteady force resulting from a VRP is significantly larger compared with an isolated PoVR (without an NeVR). The force enhancement is also correlated to vortex configurations. A normalised force coefficient characterising force augmentation over the entire stroke is given. The force augmentation coefficient grows significantly and then reaches a plateau as the momentum input increases. The results are consistent with those in fully unsteady vortex interaction, which involves the generation of an NeVR. It is suggested that counter-rotating VRPs could offer a new perspective to explain unconventional force generation for biological swimming and flying.
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.
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