## 1 Introduction
In order to obtain real velocity and vorticity fields of the foil, [PERSON] [19] then employed two-dimensional Digital Particle Image Velocimetry (DPIV), using hydrogen bubbles as seeding particles, to study the flow physics of a hydrofoil in angular reciprocating motion with negligible free-stream velocity to reveal the effects of aspect ratio on its hydrodynamic performance. Their results suggested that a lower aspect-ratio could improve thrust of the foil when it starts from rest, but at the expense of efficiency. After looking at a steady infinite flow field, researchers have begun to study the mechanism of fish utilizing unsteady flow field energy from the perspective of multi-body disturbance. [PERSON] [20] numerically investigated the hydrodynamic performances of a fishlike undulating foil in the wake of a D-section cylinder by using a modified immersed boundary method. Firstly, [PERSON] observed that the foil without undulation in the vortex street could gain a thrust, as a result of the fact that thepassing vortices produce reverse flows with respect to the mainstream in vicinity of the foil surface. An undulating foil is then placed behind the D-section cylinder; [PERSON] found that the undulation of foil plays different roles in its propulsion when the distance between foil and cylinder is changed. In [PERSON]'s studies, the D-section cylinder remains still. Different with [PERSON]'s model, [PERSON] [21] studied a propulsion system which was made up by tandem hydrofoils experimentally and numerically. An experimental measurement system is then developed to extract hydrodynamic loads on the foils and capture their twisting deformation during operation. The measuring data allowed researchers to assess the efficiency of the propulsion system as a function of travel speed and stroke frequency. Based on the [PERSON] study, [PERSON] [22] discussed the distance between foils, pitch angle, and other parameters' effects on tandem foils' propulsive performance. By analyzing flow field disturbance between foils, effective ways to improve propulsor performance were proposed. Meanwhile, [PERSON] [23] analyzed the hydrodynamic performance of two flapping foils with the tandem configuration, while the velocity potential theory and the boundary element method were introduced to study the interactions of the vortices and the foils. [PERSON] then found the optimal global phase shifts for the highest thrust and highest efficiency. Summarizing the above research, studies on the hydrodynamic performance of the bionic flapping foil that propelled the UUV in deep sea, have obtained excellent results. Most studies on the foils were in unsteady flow fields and focused on the steady obstacle effect on the propulsive performance of the foil, or multi-foil effect on improving system maneuverability. In comparison, for the UUV, fewer studies have been carried out on the complex flow effect; such as waves at sea, on the performance of the nearby foils, especially on the flexible foils. Most existing research was mainly on the basis of using the passive moving rigid foils as an auxiliary propulsion for merchant ships. An early concept has been proposed by some researchers that a flapping foil can be used to extract energy from the unsteady flow field, formed by free-surface waves [24; 25]. Indeed, in both experiments and theoretical analyses, it was discovered that a foil, submerging right below the free surface, could propel itself forward by using the energy from the incoming waves [24; 26; 27]. The application of the flapping foils extracting energy from the uniform flows was first proposed by [PERSON] and [PERSON] [28]. By applying a non-linear 3D panel method, [PERSON] [29] then dealt with the hydrodynamic analysis of the flapping wings, which were located beneath the hull of a ship and operated in random waves. The ship was travelling at a constant forward speed and the free wake analysis was carried out around the flapping wings to obtain detailed characteristics of the unsteady flow.