Research On The Composite Undulation Pattern And Propulsive Performance Of Swimming Fish Propelled By Body/caudal Fin

After millennia of evolution,fish have very excellent swimming abilities,such as the fast speed,the enormous maneuverability and the high efficiency.It is of great significance for both scientific exploration and technical innovation to study the biomechanics in fish swimming.For 85% of fish in nature,the midline motions are propagated backward,and their extraordinary swimming abilities are obtained by the interactions between fish body and the surrounding fluid.However,the dynamic characteristics of midline motions and their complex interactions with the fluid flow are still not clear.In this thesis,we focus on the midline motions of BCF(Body and/or Caudal Fin)fish,and analyze the swimming mechanism in terms of the complex modal characteristics and their propulsive performance.From the perspective of modal analysis,the movements of BCF fish are in essence the forced vibrations of viscoelastic body in the fluid environment.In this thesis,the bending body of BCF fish is simplified as a homogeneous viscoelastic beam with uniform cross-section.Combined with Lighthill’s elongated body theory,a dynamic fish model is built to analyze the modal characteristics of both the free vibration and the forced vibration.The method of separable variables is adopted to study the qualitative relations between the viscoelastic parameters and the midline motions.The results show that: when the dynamic model of fish body is a proportional damping system,the standing wave is generated from the real vibration modal;when the dynamic model is a non-proportional damping system,the travelling wave is produced from the complex mode of vibration modal.Overall,this study demonstrates that the midline motions are the complex modal shapes of the vibrating fish body,revealing the complex modal characteristics of fish movements.Meanwhile,it also suggests that the viscoelastic properties of fish body have a crucial influence on the swimming performance.For the complex modal mode,the midline motions of BCF fish are decomposed into the travelling and standing components by the method of complex orthogonal decomposition(COD).The matrix with its two columns being the real and imaginary part of complex modal shape is used to define the travelling index.The value of travelling index equates the reciprocal of the relative condition number.In particular,when the traveling index is 1.0,it indicates that the wave is a ‘fully’ traveling wave.When the traveling index equates zero,it means it is a pure standing wave.Based on the analysis of more than 80 existing biological data,we find that anguilliform swimmers prefer a motion with high travelling index(0.74~0.90),while thunniform fish swim at a low range of travelling index(0.36~0.64).For subcarangiform and carangiform swimmers,their motions are a mixture of the travelling and standing waves with a median range of travelling index(0.52~0.78).These biological data can be used to verify the complex modal characteristics,and also demonstrate the corresponding relationships between BCF submodes and travelling index.According to the range of travelling index,the locomotion of BCF fish can be broadly classified into three categories: the standing-wave form(tunniform mode),the mixture wave form(subcarangiform and carangiform mode)and the traveling-wave form(anguilliform mode).This new classification is named as the approach of travelling index.In the present work,the travelling index is used to classify the BCF fish.It is different from the traditional classification,in which the fraction of the body that is displaced laterally is used.With more comprehensive and useful information,the new criterion can be classified the propulsive movements of BCF fish in quantity.To study the interactions between the undulating fish body and the surrounding fluid by the CFD(Computational Fluid Dynamics)approach,a modified LS-IB(Level-Set/Immersed Boundary)method is developed to simulate the fluid-structure interaction between the incompressible flow and the solid body with arbitrarily deforming boundaries.In detail,the level-set function and the re-initialization procedure are used to build the shape of solid body.The interactive force between the solid body and the fluid flow is simulated by the sharp-interface IB method.Direct numerical simulation(DNS)and large eddy simulation(LES)are adopted to mimic the fluid flow with different Reynolds number.The MPI(Message Passing Interface)is used in the house-developed code to improve the high-performance parallel computing.Besides,the developed LS-IB method is applied in several twoand three-dimensional benchmark problems,including flow past a cylinder/sphere,a transversely oscillating cylinder in a free-stream,vortex-induced vibrations and the self-propelled anguilliform fish.In these cases,the numerical results agree well with the previous numerical and experimental data.The presented methodology serves as a good tool for solving many practical fluid-structure interaction problems,with the advantage of the small computational cost.The proposed numerical LS-IB method is adopted to study the swimming performance of BCF fish.For anguilliform and carangiform fish,the tethered and self-propelled 2D/3D fish models are built,respectively,and their propulsive abilities are investigated in terms of the tail-beat frequency,the amplitude,the travelling index and Reynolds number.The net force and the required power,as well as the forward speed and swimming efficiency,are used to evaluate the propulsive performance.The numerical results show that for anguilliform and carangiform fish,the maximum thrust and the highest swimming efficiency are appeared when the travelling index is around 0.8 and 0.6,respectively.These results agree well with the evolution of BCF fish in nature.It is also discovered that the BCF fish with remarkable swimming abilities can be obtained by optimizing the body shape and the midline motions.Overall,these simulation results provide a theoretical guidance to design or control a robotic fish with the desired midline motions.Aimed to verify the complex modal characteristics and propulsive performance of the midline motions,a soft carangiform robotic fish is fabricated by the viscoelastic material.The bending stiffness of fish body can be modulated by changing the air pressure of the internal cavity.The experiment results show that the midline motions of robotic fish also have the complex modal characteristics,and the travelling index is largely affected by the driven amplitude,rather than the driven frequency.For the soft robotic fish,the range of travelling index is 0.58~0.70,which consists with the biological range of carangiform fish(0.52~0.78).Further,both the forward speed and the thrust are measured when the robotic fish swims at different states.The experiment results show that the swimming abilities are affected by the driving frequency and the driving amplitude.Compared with the numerical CFD results or biological data,we find that the experiment results share the similar trends among the driven conditions and the propulsive performance,which can be used to verify the propulsive abilities of midline motions qualitatively.