Research on the Mechanism of Resistance Generation in Disc Acceleration Based on Lagrangian Method

During flapping wing flight or fish swimming, a large-scale vortex structure is in general generated by each stroke motion of the wing or the trail, and contributes most of the lift and thrust. As a fundamental model to characterize the wake structures of flapping flight and fish swimming, the disc vortex ring (DVR) generated by the impulsive motion of a disc contains numerous unsteady aerodynamic mechanisms. In this paper, an experimental set-up was designed to produce DVRs with different acceleration, particle image velocimetry (PIV) technique was used to measure the growth and evolution process of wake vortices, and force sensor was used to measure the instantaneous change in drag directly. PIV results show that a DVR is formed in the wake during the disc starting, and the circulation growth of DVR satisfies the Logistic growth model. Using the Lagrangian coherent structure (LCS) to analyze the formation of DVR shows that, under the interaction of the add-mass effects of disc and DVR, the vortex flow shows a significant Lagrangian drift, which contributes a significant increase of the drag. Besides, the results of the drag measurement show that the formation process of the vortex ring consists of three phases, including a peak and a valley. Based on the vorticity-moment theorem, the evolution of drag is explained in terms of the dynamics of DVR and the added-mass effects. Moreover, the findings of this paper provide a new Lagrangian perspective for understanding the mechanism of lift and thrust during flapping wing flight and fish swimming.