Numerical studies are presented on the propulsive performance and vortex dynamics of multiple hydrofoils pitching in an in-line configuration. The study is motivated by the quest to understand the hydrodynamics of multiple fin–fin interactions in fish swimming. Using the flow conditions (Strouhal and Reynolds numbers) obtained from a solitary pitching foil of zero net thrust, the effect of phase differences between neighboring foils on the hydrodynamic performance is examined both in position-fixed two- and three-foil systems at Reynolds number $Re=500$. It is found that the three-foil system achieves a thrust enhancement up to 118% and an efficiency enhancement up to 115% compared to the two-foil system. Correspondingly, the leading-edge vortex (LEV) and the trailing-edge vortex (TEV) of the hindmost foil combine to form a ‘2P’ wake structure behind the three-foil system with the optimal phase differences instead of a ‘2S’ wake, a coherent wake pattern observed behind the optimal two-foil system. The finding suggests that a position-fixed three-foil system can generate a ‘2P’ wake to achieve the maximum thrust production and propulsive efficiency simultaneously by deliberately choosing the undulatory phase for each foil. When increasing Reynolds number to 1000, though the maximum thrust and propulsive efficiency are not achieved simultaneously, the most efficient case still produces more thrust than most of the other cases. Besides, the study on the effects of three-dimensionality shows that when the foils have a larger aspect ratio, the three-foil system has a better hydrodynamic performance, and it follows a similar trend as the two-dimensional (2D) foil system. This work aids in the future design of high-performance underwater vehicles with multiple controlled propulsion elements.

数值研究介绍了多个水翼在直线配置中俯仰的推进性能和涡流动力学。该研究的动机是为了了解鱼类游泳中多个鳍 - 鳍相互作用的流体动力学。使用从零净推力的孤立俯仰翼片获得的流动条件（斯特劳哈尔数和雷诺数），在雷诺数的位置固定的两翼和三翼系统中检查相邻翼片之间的相位差对流体动力学性能的影响$\mathrm{电阻}\mathrm{电子}=500$. 结果表明，与两翼系统相比，三翼系统实现了高达 118% 的推力增强和高达 115% 的效率提升。相应地，最后翼的前缘涡（LEV）和后缘涡（TEV）结合在三翼系统后面形成具有最佳相位差的“2P”尾流结构，而不是“2S”尾流，在最佳两箔系统后面观察到的连贯尾流模式。该发现表明，位置固定的三翼系统可以产生“2P”尾流，通过故意选择每个翼的波动相位，同时实现最大推力产生和推进效率。当雷诺数增加到 1000 时，虽然不能同时达到最大推力和推进效率，最有效的情况仍然比大多数其他情况产生更多的推力。此外，对三维效应的研究表明，当箔片具有较大的纵横比时，三箔系统具有更好的流体动力学性能，其趋势与二维（2D）箔系统相似。这项工作有助于未来设计具有多个受控推进元件的高性能水下航行器。