Numerical simulation of a one-dimensional flexible filament mimicking anguilliform mode of swimming using discrete vortex method

Abstract

The article discusses the numerical simulation of swimming dynamics of a onedimensional flexible filament in inviscid conditions using the discrete vortex method (DVM). The DVM is used to reduce the computational cost of mesh generation in these types of unsteady problems. To mimic the anguilliform mode of swimming, we have applied the relevant kinematics in the flexible filament motion. Various parameters like wavelength, tail oscillation amplitude, amplitude growth factor, and frequency were varied to quantify the coefficient of thrust and swimming efficiency. For the ranges of parameters covered in our simulations, we identified the boundary between the drag regime and the thrust regime. Further, the role of tail oscillation amplitude with Strouhal number on the transition from the drag to thrust regime is examined. We showed that the wake vortices assume a Bénard–von Kármán (BvK) configuration in the drag producing regime and rearranges to reverse Bénard–von Kármán (rBvK) configuration in the thrust producing regime. The resultant wake vortex distribution, contour map, and associated velocity field are presented to clarify the differences between BvK in the drag regime, axisymmetric vortex distribution in the vicinity of the transition regime of drag and thrust regimes, and rBvK in the thrust regime. Thus, we have identified the optimum parameter regimes to obtain high thrust or achieve swimming efficiency of two-dimensional (2D) flexible filaments. Finally, we believe our numerical simulations can be extended to elucidate the wake vortice’s dynamics of flexible filaments in 2D flows or pitching motion of rigid airfoils in quasi-2D flows.