On the formation modes in vortex interaction for multiple co-axial co-rotating vortex rings

Abstract

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.

Effect of pressure evolution on the formation enhancement in dual interacting vortex rings

“…By satisfying the constraints (interval time, particle size, and particle concentration) of the DPIV measurement and after alignment, the velocity measurement and vorticity calculation uncertainties are 1% and 3%, respectively. [19] Stepping motor Arduino Board Mega 2560 is used to control the stepper motor, which is a development microcontroller board for writing velocity program. Two vortex rings with the same formation time are successively produced with interval time ranging from 0 to 3 s. The velocity type is sinusoidal with a maximum of 0.05 m/s, as shown in Fig.…”

“…In multiple vortex rings, Krueger [11] generated a string of identical vortex rings intermittently and found that the largest relative force would occur at small formation time and large interval. Qin [19] proposed two interaction modes: formation enhancement mode with open flux window and formation restraint mode with closed flux window. The flux windows allow fluid to transport and entrain, generating additional circulation in vortex formation by increasing overpressure.…”

An objective-adaptive refinement criterion based on modified ridge extraction method for finite-time Lyapunov exponent (FTLE) calculation

“…The data we used in this article is an experimental data conducted by vortex ring generator. The experimental apparatus has been published by Suyang Qin in [30,31]. Fig.…”

Lagrangian analysis of the formation and mass transport of compressible vortex rings generated by a shock tube*

“…The framework of LCS has been used to study the ICVRs for some time. [16][17][18] In this paper, both FTLE field and elliptic LCS are used to show the mass transport and dynamic genesis of CVRs.…”