Vortex interaction between two tandem flexible propulsors with a paddling-based locomotion

Abstract

Schooling behaviours among self-propelled animals can benefit propulsion. Inspired by the schooling behaviours of swimming jellyfish, flexible bodies that self-propel through a paddling-based motion were modelled in a tandem configuration. This present study explored the hydrodynamic patterns generated by the interactions between two flexible bodies and the surrounding fluid in the framework of the penalty immersed boundary method. The hydrodynamic patterns produced in the wake revealed flow-mediated interactions between two tandem propulsors, including vortex-vortex and vortex-body interactions. Two tandem flexible propulsors paddling with identical amplitude and frequency produced stable configurations as a result of the flow-mediated interactions. Both the upstream and downstream propulsors benefited from the tandem configuration in terms of the locomotion velocity and the cost, compared with an isolated propulsion system. The interactions were examined as a function of the initial gap distance and the phase difference in the paddling frequency. The equilibrium gap distance between two propulsors remained constant, regardless of the initial gap distance, although it did depend on the phase difference in the paddling frequency.

Intermittent swimming of two self-propelled flexible fins with laterally constrained heaving motions in a side-by-side configuration

“…2020). The COT (or the power-to-speed ratio), which is the energy required to travel a unit distance during one cycle period, is defined as follows (Park & Sung 2016): Because the structure-to-fluid mass ratio is fixed in our simulation (i.e. ρ = 1.0), the inertial effect on the COT is not considered (Park & Sung 2016).…”

“…The COT (or the power-to-speed ratio), which is the energy required to travel a unit distance during one cycle period, is defined as follows (Park & Sung 2016): Because the structure-to-fluid mass ratio is fixed in our simulation (i.e. ρ = 1.0), the inertial effect on the COT is not considered (Park & Sung 2016). The cycle-averaged horizontal speed (or cruising speed) and the cycle-averaged input power of a fin are defined as where the average input power along a fin ( P avg ) is defined as .…”

“…The COT has been suggested to compare the propulsive performance between continuous and intermittent swimmers (Chung 2009;Akoz & Moored 2018;Dai et al 2018a;Akoz et al 2019;Liu et al 2020). The COT (or the power-to-speed ratio), which is the energy required to travel a unit distance during one cycle period, is defined as follows (Park & Sung 2016):…”

“…Because the structure-to-fluid mass ratio is fixed in our simulation (i.e. ρ = 1.0), the inertial effect on the COT is not considered (Park & Sung 2016). The cycle-averaged horizontal speed (or cruising speed) (U avg ) and the cycle-averaged input power (P avg ) of a fin are defined as…”

“…To extract the thrust component of a momentum jet in the wake further, the contours of the cycle-averaged relative horizontal velocity (u rel ) behind two fins are analysed in figure 14. The value of u rel is calculated by subtracting u neg from u to take into account the moving effects of the fins in a self-propulsion system (Peng et al 2018;Wu et al 2022), as self-propelled fins propel toward the negative x-direction with a negatively induced horizontal flow around the fins (Park & Sung 2016;Park et al 2017;Jeong et al 2021;Wu et al 2022). Here, u neg is the conditionally averaged negative horizontal flow velocity around a fin.…”