Phase difference effect on collective locomotion of two tandem autopropelled flapping foils

Self-directed propulsion of an unconstrained flapping swimmer at low Reynolds number: hydrodynamic behaviour and scaling laws

“…It should be emphasized that the foil can self-propel in both the x-and y-directions. Its propulsion is controlled by Newton's second law, which can be described as (Lin et al 2019b…”

“…Its propulsion is controlled by Newton's second law, which can be described as (Lin et al. 2019 b ) where is the position vector of the pivot point of the foil, is the time and is the hydrodynamic force applied on the foil surface. Here the thrust is defined as , is the lateral force and is the mass of the foil, where and are, respectively, the density and area of the foil.…”

Flow-mediated organization of two freely flapping swimmers

“…The reason may be that the self-organization in the lateral direction was not considered in the previous studies (Park & Sung 2018;Peng et al 2018). Similar to the longitudinal self-organization of two foils (Zhu et al 2014; Ramananarivo et al 2016;Lin et al 2019b), when the self-organization in the lateral direction is considered, the equilibrium separation distance in the lateral direction can be achieved by two foils via the hydrodynamic interactions. By the way, it should be noted that two foils would perform like a single foil when D x0 and D y0 become large enough.…”

“…Furthermore, it has been revealed that the emergence of orderly formation depends strongly on the phase difference and the initial distance between two foils (Newbolt, Zhang & Ristroph 2019;Lin et al 2019b). When the phase difference and the initial distance are appropriate, a compact formation can be formed by the tandem foils, in which both speed and efficiency are increased as compared with those of a single foil (Lin et al 2019b).…”

Computational Model Construction and Analysis of the Hydrodynamics of a Rhinoptera Javanica

“…The solver has approximately second-order convergence accuracy. Validations about this solver involving flow past flapping foils [24], [25] and flows over dragonfly flight [22] can be found in previous work.…”