A Three-dimensional Numerical Study Of Tadpole Swimming In Different Environments

Compared to fish which have streamlined bodies,less attention is paid to tadpole swimming.The details of the swimming mechanism of a tadpole in three dimensions are still not clear.In particular,the study on tadpoles' schooling or a tadpole swimming behind a sphere is blank.Research on tadpole swimming in different environments is of great scientific significance and engineering value.Tadpole swimming in different environments including a tadpole swimming in free stream,tadpoles' parallel schooling and a tadpole swimming behind a sphere is investigated numerically in present study.Open source software Open FOAM is used to simulate hydrodynamic performance and vortex structures of tadpole swimming.The three-dimensional Navier-Stokes equations for the unsteady incompressible viscous flow are solved.The influence of various controllable parameters is studied.Also,the effect of tadpole's blunt snout and its specific kinematics is discussed in detail.The results show that for a tadpole swimming in free stream,the wake vortex structures vary with the fluid force on the tadpole.It suggested that the kinematics of tadpoles is closely matched to their special shape.When the tadpole model obtains the optimum propulsive efficiency,its swimming speed and undulating frequency are close to the values observed in nature,which corresponds to the optimal swimming law of natural selection.In addition,with the increase of Reynolds number,the thrust coefficient and the propulsive efficiency both increase while the power consumption coefficient decreases.When tadpoles swim side-by-side in an in-phase mode,the vortex structures in the wake may merge,split and recombine,while the strength of the total backward jets and the pressure distribution in the wake of schooling tadpoles change relatively little with the decreasing lateral distance.Compared to a solitary tadpole swimming,only a small hydrodynamic advantages are got in the parallel schooling,which may be a factor that tadpoles rarely,if ever swim,side by side for any amount of time or distance in nature.The effect of the undulating frequency and the Reynolds number on the tadpoles schooling is similar to that on a solitary tadpole.For a tadpole swimming behind a sphere,the positive and negative vortices shed from the sphere interfere and merge with those shed from the tadpole.The tadpole attains hydrodynamic advantages,such as energy-saving benefits and lower drag force.As the tadpole is closer to the sphere,it can attain better swimming performance.As the tadpole's undulating frequency approaches the vortex shedding frequency of the sphere,the tadpole can save much energy in undulating swimming.As the diameter of the sphere changes,the shedding frequency of the sphere and the width of vortex pair also change,which influence the hydrodynamic performance and the flow field of tadpole swimming.