Numerical investigation of the forward and backward travelling waves through an undulating propulsor: performance and wake pattern

Recently, the mechanisms of natural undulatory locomotion of aquatic animal swimming have become one of the most significant issues for the researchers, swimmers and engineers. This study aims to elucidate and compare the propulsive vortical signature and performance of backward (negative undulation) and forward (positive undulation) travelling waves through a typical fishlike propulsor by a systematic numerical study. The numerical approach uses a pressure-based finite volume method solver to solve Navier-Stokes equations in an arbitrary Lagrangian-Eulerian framework domain containing a two-dimensional NACA 0012 foil moving with prescribed kinematics. Some of the important findings are: (1) time-dependent forces and pitching moments show that both mechanisms suffer from the energy losses; however, the negative undulations show less energy losses, (2) Strouhal number of undulations shows a transition point from drag-dominated regime to thrust-dominated regime for both mechanisms and a transition point from thrust-dominated regime to drag-dominated regime for positive undulation, (3) the consumed power plot shows that at lower and medium St, both mechanisms consume closely same powers, while, at higher St, the negative undulation consumes more power, (4) the efficiency plots show that the efficiency of the positive undulation is close to zero, while, the negative undulation reaches considerably higher performances, (5) low St vortical patterns of the mechanisms show some similarity, while, the patterns at medium and high St reveal appreciable discrepancies, and (6) the most significant difference between the vortical patterns of the mechanisms is appearing more regular and stronger vortices in the wake of the negative undulation.