# Study on the Propulsion Characteristics of a Flapping Flat-Plate Pumping Device
## 1 Introduction
They found that the mode starting with a maximum upward pitch and with pitch and heave in the same direction generated continuous forward thrust throughout the motion cycle, achieving a peak pumping efficiency of 34.1%. These studies collectively contribute to a deeper understanding of flapping hydrofoil propulsion by addressing a variety of influencing factors. For instance, several studies have examined the influence of motion parameters--such asflapping frequency, amplitude, and phase difference--on thrust generation and propulsion efficiency. Others have focused on structural characteristics, including hydrofoil stiffness and flexibility, and their effects on hydrodynamic performance. In addition, a number of works have addressed fluid-structure interactions and wall proximity effects, particularly under low-Reynolds-number or confined flow conditions. Collectively, these investigations offer valuable guidance for the optimization of flapping kinematics, hydrofoil geometry, and channel design in bionic propulsion systems. However, current research on flapping hydrofoils primarily focuses on kinematic parameters, hydrofoil geometry, and hydrodynamic analysis of propulsion characteristics. Most studies emphasize underwater propulsion systems or energy harvesting applications, typically using unbounded open flow fields in numerical simulations. This approach often neglects the wall effects present in confined environments and lacks investigations into performance differences under varied flapping modes. In terms of flow channel design, [PERSON] et al. [20] proposed a gradually contracting-suddenly expanding channel configuration and systematically studied the effects of three contraction geometries, dimensional ratios, and sidewall distances on emitter flow rate, energy consumption, and flow regime index through combined numerical and experimental approaches. [PERSON] et al. [21] conducted comprehensive simulations of a two-dimensional NACA0012 hydrofoil undergoing pitching motions at various wall distances, focusing on how wall proximity, pitch amplitude, and reduced frequency affect thrust coefficient and propulsion efficiency. [PERSON] et al. [22] were the first to propose integrating a flow channel structure into a flapping hydrofoil system to enhance inflow velocity and improve energy extraction performance. [PERSON] et al. [23] introduced a flapping-hydrofoil device equipped with a diffuser structure and analyzed, using orthogonal design and numerical simulation, the influence of channel design parameters on power coefficient and energy collection efficiency. [PERSON] and [PERSON] [24] proposed a novel bionic energy harvesting system consisting of tandem flapping hydrofoils placed inside a converging guide vane. They investigated the effects of channel contraction ratio, flapping frequency, and phase difference on energy harvesting performance. This study employs the CFD software Ansys Fluent-2024R2 to numerically investigate the effects of flapping motion patterns and outlet channel structures on flow characteristics and hydrodynamic performance in different pumping devices. Furthermore, it explores optimal configurations of outlet channels, aiming to provide theoretical support and practical guidance for the engineering design and application of bionic pumping systems.