# Numerical Study on Hydrodynamic Performance of Bionic Caudal Fin
## 1 Introduction  
With the developments of marine exploitation, requirements for the underwater propulsor become higher and higher because of complex engineering applications. The traditional propellers have the disadvantages of low efficiency, poor maneuvering performance, significant noise, and other shortcomings, which greatly limit their applications in narrow, complex, and dynamic environments. To overcome these shortcomings and meet the future needs of marine exploration, it is necessary to develop improved underwater propulsion modes. After a long period of evolution, underwater creatures have the singular ability to swim, so bionic propulsion becomes a research focus of underwater propulsion [1; 2]. Human knowledge is getting enriched from the natural world of animals which have evolved through the ages to adapt nicely to the environment. Meanwhile, bionics method has been used widely in the field of engineering, and also has yielded fruitful results. In particular, various underwater propulsors imitating different bio-inspired modes have emerged in recent years. Unfortunately, the performance of recent biomimetic propulsors is far from expectation obtained by the biological mode. The reason is that the research on mechanism is not deep enough due to the complexity in modeling. Any new breakthrough in the mechanism will bring new inspiration to the developments of biomimetic propulsors. Therefore, to explore the mechanism, scholars are spending considerable efforts to reveal the essence of the problems with different research methods [3; 4; 5; 6; 7; 8; 9; 10]. Among the methods, numerical simulation method has gained growing attention because of its advantages of low input, high efficiency and simple post-processing. Especially with the developments of computer and computational fluid dynamics (CFD) in recent decades, numerical simulation method has become an important tool toinvestigate the propulsion mechanism of bio-inspired modes [11]. The application of CFD methods for solving the Navier-Stokes equations has led to significant developments in the visual simulation of fluids. However, a large number of problems in biofluid dynamics involve interactions between deformable elastic bodies and incompressible viscous fluids. These fluid-structure interaction (FSI) problems involve the complicated interplay between a viscous fluid, deformable body, and free-moving boundary, making them difficult to discern [12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23]. In the paper, tuna is chosen as the bionic prototype because of its advantages of high propulsive efficiency. In previous studies, scholars have carried out related work. Some studies employ numerical simulations to investigate the self-propulsion of fish. [PERSON] and [PERSON] carried out fluid-structure interaction simulations to investigate the hydrodynamic mechanism in carangiform swimming [24; 25]. [PERSON] _et al._ simulated the motion flapping ellipsoidal foil and analyzed the wake structures [26]. Some other studies focused on the caudal fin propulsion, but the shapes of the caudal fins were usually simplified as plates or ellipsoidal foils. [PERSON] _et al._ mainly studied the wake topology of forked and unforked fish-like plate with numerical method [15]. [PERSON] _et al._ studied experimentally the effect of adding an in-line oscillatory motion to the oscillatory heating and pitching motion of flapping foils that use a power downstroke [8]. However, the diversity of the fin morphology decides the specificity of hydrodynamic mechanism, so the analyses were not sufficient. Additionally, caudal fins in nature are usually flexible and the flexibility plays an important role in the motion. Thus, the flexibility should be considered in the modeling of the caudal fin. As is shown in [27], a water tunnel study of the effect of spanwise flexibility on the thrust, lift, and propulsive efficiency of a rectangular foil oscillating in pure heave was performed.