Abstract This paper presents a parametric study on a forced pitching hydrofoil. The non-dimensional frequency (Strouhal number, St d ) and amplitude ratio ( A ∗ ) of the hydrofoil pitching are varied as 0.21 ≤ St d ≤ 0.33 and 0.55 ≤ A ∗ ≤ 0.8, respectively. The numerical solution of the problem is obtained using unsteady Navier–Stokes equations. Coefficients of thrust, power, and efficiency of the hydrofoil are calculated and presented on the St d – A ∗ plane. The evolution of the flow structure around the pitching hydrofoil is clarified for the conditions corresponding to both drag and thrust generations. A flow model is hypothesized. A mathematical analysis of the flow model, involving Euler, Coriolis and centrifugal accelerations in a non-inertial frame, is developed to assimilate the physical insight into the thrust generation and power input. The analysis provides theoretical relationships of thrust, power, and efficiency as functions of Strouhal number and/or amplitude ratio. The data from the numerical simulation tangibly support the relationships. This subject would be handy for undergraduate and postgraduate studies.

中文翻译：

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俯仰水翼周围的流动动力学

摘要 本文介绍了一种强迫俯仰水翼的参数研究。水翼俯仰的无量纲频率（Strouhal 数，St d ）和振幅比（ A ∗ ）分别为 0.21 ≤ St d ≤ 0.33 和 0.55 ≤ A ∗ ≤ 0.8。该问题的数值解是使用非定常 Navier-Stokes 方程获得的。计算水翼的推力、功率和效率系数，并在 St d – A * 平面上显示。对于与阻力和推力产生相对应的条件，阐明了俯仰水翼周围流动结构的演变。假设流动模型。流动模型的数学分析，涉及非惯性坐标系中的欧拉、科里奥利和离心加速度，被开发以吸收对推力产生和功率输入的物理洞察力。该分析提供了作为 Strouhal 数和/或振幅比的函数的推力、功率和效率的理论关系。数值模拟的数据切实支持了这种关系。这门学科对于本科和研究生学习很方便。