Numerical Investigation Of Hydrodynamic Schooling Of Bio-Inspired Self-Propulsive Flexible Plates

Inherent fluid dynamical mechanisim underlying collective swimming and flying is complex.Two issues of collective locomotion have attracted people's great attention for a long time:one of the issues is about role of flow-mediated interaction on emergence of collective pattern,which is expressed as "Lighthill conjecture".The other is about hydrodynamic advantage of active individuals in aggregates.The free locomotion of flow-structure interaction system consisting of two or multiple flapping flexible plates is studied numerically by a lattice Boltzmann(LB)-finite element(FF)-immersed bound-ary(IB)method.This study may shed some light on the mechanism for collective locomotion in view of fluid mechanics.The corresponding results and conclusions are briefly given as follows:(1)Collective locomotion of two self-propelled flapping plates initially in a side-by-side arrangement is investigated numerically.Both in-phase and antiphase oscillations for the two plates are considered.It is found that the plates will spontaneous-ly form some stable configurations as a result of the flow-mediated interaction,specifically,the staggered-following(SF)mode and the alternate-leading(AL)mode for the in-phase scenario and the moving abreast(MA)mode and the AL mode for the antiphase scenario.In the SF mode,the rear plate follows the front one with a staggered configuration.In the AL mode,the plates chase each other side-by-side alternately.In terms of propulsive speed and efficiency,the perfor-mance of the plates in the SF mode with small lateral spacing H is found to be better than those in the tandem following case(H =0)and the side-by-side case(i.e.the AL mode).To achieve higher propulsive efficiency,no matter in-phase or antiphase oscillations,the two plates with moderate bending stiffness,e.g.K ? O(1),are preferred and they should be close enough in the lateral direction.For the side-by-side configuration,the performance of each plate in the antiphase and in-phase scenarios is enhanced and weakened in comparison with that of the isolated plate,respectively.To reveal the mechanism,besides the pressure and vorticity contours,the normal force acting on the plates and the thrust induced by the normal force are also analysed.It is found that they are critical to the propulsive speed and efficiency.For two self-propelled plates,in the view of hydrodynamics,to achieve higher performance the in-phase SF mode and antiphase,flappings in the side-by-side configuration are preferred.(2)Collective locomotion of "big-small" flapping flexible plates is simulated.We in-vestigated systematically effects of initial configuration,ratio of body length and flapping amplitude on motion states of the plate-fluid system and corresponding stability and propulsive performance.For the individuals with different propul-sive speed(i.e.plates with different,bodylength or flapping amplitude),they can achieve a uniform swimming speed and form various stable configurations passive-ly from flow-mediated interaction.Two schooling states are classified as compact configuration(S0)and sparse configuration(S1,S2),respectively.The separation spacings of the stable configuration are found to be integral multiple of wave-length,i.e.S=G/?=01,2,...,Further,hydrodynamic forces experienced by the plates and corresponding hydrodynamic potential are analysed to reveal stability of the stable configurations.It is found that the staggered configurations with H=0.5-1.0 are more stable than the tandem ones(H=0)?Finally,we studied the propulsive performance of the plates and the energetic benefit of the system.When the "small" plate is placed in the wake of the "big" one,its propul-sive performance is enhanced significantly.This phenomenon of "hydrodynamic drafting" is similar to some observations in animal swimming and flying.For the overall system,the staggered configurations with H?0.2-0.3 are optimum for propulsion.(3)Collective behaviour of multiple self-propelled plates in tandem configuration is studied numerically.The Lighthill conjecture that orderly configuration may e-merge passively from hydrodynamic interactions was verified in a larger scale with up to eight plates.Both fast.mode with compact configurations and slow mode with sparse configurations were observed.The whole group may consist of subgroups and individuals with regular separations.Hydrodynamic forces expe-rienced by the plates near their multiple equilibrium locations are all springlike restoring forces,which stabilize the orderly formation and maintain group cohe-sion.For the cruising speed and efficiency of the whole group,the leading sub-group or individual plays the role of 'leading goose'.These conclusions indicate the hydrodynamic force not only acts as a restoring force to maintain schooling cohesion but also provides a drafting force to rear subgroups so as to improve their schooling performance.