Numerical Study Of The Fluid Dynamic Mechanism In Fish School And Bird Flock

The fish school or the bird flock in which individuals maintain regular formation is a common phenomenon in nature.Investigating the fluid-structure interaction in fish school and bird flock may be helpful for the design of the bio-inspired aircraft and watercraft,and may have implications for optimization of the coordinated behavior of the bio-inspired robots.In this paper,we have studied the aerodynamic and the hydrodynamic mechanism of the fish school and the bird flock through simulating the two-dimensional incompressible viscous flow by the immersed boundary method.We propose a lateral-free flexible filament which whole can flap freely in the lateral direction,and investigate the flapping characteristics and the flow structures of the filament in the wake behind a pitching foil.Four distinct flapping modes of the filament observed: flapping at the lateral side of the vortex street,flapping between vortex cores,flapping between the vortex trip and slight flapping.In the reversed Von Karman vortex streets,the filament flaps at the lateral side of the vortex streets.The drag of the filament in this mode is smaller than that of the filament flaps between vortex cores,and the St is equal to 0.3~0.4 in this mode,which is contained within St=0.2~0.4 in which fish achieves the high propulsive efficiency.In most of the Von Karman vortex streets,the filament flaps between the vortex cores,it is similar to the slaloming behavior of the fish in the wake behind the obstacle.In the vortex trip,the filament lengthens the length of the vortex trip and flaps between the vortex trips.In the compact vortex streets(little distance between adjacent cores),the filament flaps slightly,there has no vortex shed from the filament,and the pitching foil has an obvious drag reduction in this mode(the most drag reduction is up to fourteen percent compared to the isolated pitching foil).The separations between individuals also affect the fluid-structure interactions in the fish school and the bird flock.We simplify the fish school as multiple wiggling hydrofoils arranged in diagonal and triangular formations in this paper,and investigate the effects of the longitudinal spacing(D_x)and the lateral spacing(Dy)on the propulsive performance.It is found that,the optimal formation in which the school has the best propulsive efficiency is related to the wiggling motion.For two in-phase fish,the diagonal formation with D_x=0.5 and Dy=0.3 has the best propulsive efficiency;for three in-phase fish,the optimal arrangement is the reversed triangular formation with D_x=0.75;as for the anti-phase fish,the side-by-side formation is optimal.Moreover,the proplusi--ve performance of the downstream fish is better than that of the upstream fish if the longitudinal spacing is smaller than the characteristic body length,but worse if the longitudinal spacing is larger than the characteristic body length.The dual symmetry-flapping rigid airfoils in parallel configuration have superior propulsive performance.The factors of influence propulsive performance and flow field structures,such as plunging amplitude(A),plunging reduced frequency(f),distance between the dual airfoils(L)and angle of attack of airfoils(α),are studied by simulating the unsteady flow around the dual symmetry-flapping airfoils in parallel configuration.One of the dual symmetry-flapping airfoils could achieves a higher thrust force、lager vortexes and stronger jet flows than the single flapping airfoil while the flapping parameters remained the same.Moreover,the wake will be disordered if the St≥1.0(St=fA/UL),since the phenomenon of suck-back of vortices which have shed from the foil in the preceding period.In this paper,we simplify the fish school and bird flock as multiple flapping foils in regular configurations,in which the fluid-structure interactions are simulated used the immersed boundary method.We have found the relations between the motions of the flexible filament and the surrounding flow,and obtained the effects of the arranged and flapping parameters on the propulsive performance.The results are supposed to be useful for a complete understanding of the hydrodynamic mechanism of the fish school and bird flock in nature.