Abstract Numerical simulations of the flow around a NACA0012 pitching foil are presented to investigate the effect of the pivot axis location on its propulsive performance for a Reynolds number R e = 16 000 . The pivot point position a is varied between the foil’s leading edge ( a = − 1 ) and its trailing edge ( a = 1 ). A wide range of values of the reduced frequency k is covered in the present analysis for several (small) values of the pitch amplitude. Simple scaling laws for the thrust, power, and efficiency are derived in terms of the pitching axis location, the Strouhal number S t and the pitch amplitude α 0 , with very good agreement with the numerical results for a ≲ 1 ∕ 4 and S t ≳ 0 . 4 . For a ≳ 1 ∕ 4 the flow is aperiodic and generates relatively less thrust with low propulsive efficiency. Although the power input presents a minimum at a = 1 ∕ 4 , the maximum efficiency is reached for − 1 ≤ a ≤ 0 , with the optimum pivot point location mainly depending on S t and the offset drag C D 0 , a parameter introduced in the scaling of the thrust coefficient. For C D 0 ∕ S t 2 ≪ 1 , the maximum efficiency, which decays as k − 1 , is reached when the foil pitches about its middle point ( a = 0 ), being practically independent of the offset drag C D 0 . As S t decreases, the optimum location of the pivot point moves upstream towards the leading edge, and the scaling laws provide quite simple estimations of the maximum propulsive efficiency for any location a of the pivot axis. The highest efficiency is found for a foil pitching about its leading edge ( a = − 1 ), with an estimated value of about ( 1 ∕ 4 ) sin α 0 ∕ C D 0 and generated for a Strouhal number about ( 2 ∕ 3 ) C D 0 .

中文翻译：

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枢轴点位置对俯仰翼推进性能的影响

摘要 NACA0012 俯仰翼周围流动的数值模拟被提出，以研究在雷诺数 Re = 16 000 时枢轴位置对其推进性能的影响。枢轴点位置 a 在箔的前缘 (a = - 1 ) 和后缘 ( a = 1 ) 之间变化。对于音调幅度的几个（小）值，在本分析中涵盖了广泛范围的降低频率 k 的值。根据俯仰轴位置、斯特劳哈尔数 S t 和俯仰幅度 α 0 推导出推力、功率和效率的简单缩放定律，与 a ≲ 1 ∕ 4 和 S t 的数值结果非常吻合≳ 0 . 4 . 对于 ≳ 1 ∕ 4，流动是非周期性的，产生的推力相对较小，推进效率较低。尽管功率输入在 a = 1 ∕ 4 处呈现最小值，但在 − 1 ≤ a ≤ 0 时达到最大效率，最佳枢轴点位置主要取决于 S t 和偏移阻力 CD 0 ，这是在推力系数的缩放。对于 CD 0 ∕ S t 2 ≪ 1 ，当箔片在其中点 (a = 0) 附近倾斜时，达到最大效率，其衰减为 k − 1，实际上与偏移阻力 CD 0 无关。随着 S t 减小，枢轴点的最佳位置向上游移向前缘，缩放定律提供了对枢轴任何位置 a 的最大推进效率的非常简单的估计。发现箔片围绕其前缘倾斜时的效率最高 (a = − 1 )，