Interaction among multiple vortices is of particular importance to biological locomotion. It plays an essential role in the force and energy capture. This study examines the motion and dynamics of multiple co-axial co-rotating vortex rings. The vortex rings, which have the same formation time, are successively generated in a piston-cylinder apparatus by accurately controlling the interval time. The flow fields are visualized by the finite-time Lyapunov exponent and then repelling Lagrangian coherent structures (r-LCSs) are determined. Two types of vortex interactions (“strong” and “weak”) are defined by investigating the r-LCSs: a strong interaction is indicated by connected r-LCSs showing a channel for fluid transport (termed as a “flux window”); a weak interaction is indicated by disconnected r-LCSs between the vortex rings. For strong interaction, leapfrogging and merger of vortex rings can happen in the later stage of the evolution process; however, the rings are separated for weak interaction. Two distinct formation modes, the formation enhancement mode (FEM) and formation restraint mode (FRM), refer to the effect of one or multiple vortex ring(s) on the initial circulation of the subsequently formed vortex ring. In the FEM, the circulation of a vortex ring is larger than that of an isolated (without interaction) vortex ring. On the other hand, the situation is opposite in the FRM. A dimensionless number reflecting the interaction mechanism, “structure stretching number” S*, is proposed, which evaluates the induced effect of the wake vortices on the formation of a vortex ring. A limiting S* (SL*=(2±0.4)×10−4) is the bifurcation point of the two formation modes. The augmentation of circulation reaches up to 10% for the FEM when S*<SL*, while in the FRM (S*>SL*), the circulation decreases for at most 20%. The newly defined formation modes and number could shed light on the understanding of the dynamics of multiple vortex ring flows.
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.
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