Hydrodynamic behavior of two-dimensional tandem-arranged flapping flexible foils in uniform flow is investigated numerically by an immersed boundary-lattice Boltzmann method. The leading edge of the leading foil is forced to undergo both heave and pitch motions, while the leading edge of the trailing foil is forced to undergo heave motion only. Of particular interests are the effects of stream-wise gap distance Gx (Gx/c = 0.25–1.75, where c denotes the length of the foil) and the phase difference Φ between the heave motions of the foils (Φ/π = −1.00 to 1.00) on the hydrodynamic characteristics of the foils, such as the propulsive force, the propulsive efficiency, the passive deformation, and the flow field around the foils. For the leading foil, because of the existence of the trailing foil and the resulting gap flow between the foils, the propulsive performance is noticeably influenced by Φ at small Gx/c values and such an influence is weakened with increasing Gx/c. For the trailing foil, the propulsive performance is primarily affected by Φ, and the physics behind such a strong effect is that Φ dictates the manner by which the vortices shed from the leading foil interact with the trailing foil. In contrast, the interaction of the vortices shed from the leading foil with the trailing foil is not significantly affected by Gx/c because the trailing foil experiences similar vortices shed from the leading foil, regardless of Gx/c. With different Gx/c and Φ/π values, three distinct deformation states of the foils, namely, the symmetric periodic state, the asymmetric periodic state, and the irregular state, are identified and are mapped out in the (Φ/π, Gx/c) space. Good correlation between the deformation state of the foils and the propulsive performance of the trailing foil has been observed.Hydrodynamic behavior of two-dimensional tandem-arranged flapping flexible foils in uniform flow is investigated numerically by an immersed boundary-lattice Boltzmann method. The leading edge of the leading foil is forced to undergo both heave and pitch motions, while the leading edge of the trailing foil is forced to undergo heave motion only. Of particular interests are the effects of stream-wise gap distance Gx (Gx/c = 0.25–1.75, where c denotes the length of the foil) and the phase difference Φ between the heave motions of the foils (Φ/π = −1.00 to 1.00) on the hydrodynamic characteristics of the foils, such as the propulsive force, the propulsive efficiency, the passive deformation, and the flow field around the foils. For the leading foil, because of the existence of the trailing foil and the resulting gap flow between the foils, the propulsive performance is noticeably influenced by Φ at small Gx/c values and such an influence is weakened with increasing Gx/c. For the trailing foil, the propulsive ...

中文翻译：

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二维串联排列的柔性翼片在均匀流动中的水动力行为

采用浸入式边界格子Boltzmann方法数值研究了二维串联排列拍动柔性箔在均匀流动中的流体动力学行为。前翼的前缘被迫承受升沉和俯仰运动，而后翼的前缘仅被迫承受升沉运动。特别令人感兴趣的是流向间隙距离 Gx（Gx/c = 0.25–1.75，其中 c 表示箔的长度）和箔的起伏运动之间的相位差 Φ（Φ/π = -1.00）的影响到 1.00) 对箔的流体动力学特性，例如推进力、推进效率、被动变形和箔周围的流场。对于前翼，由于尾翼的存在以及由此产生的翼之间的间隙流动，在 Gx/c 值较小时，推进性能受 Φ 显着影响，这种影响随着 Gx/c 的增加而减弱。对于尾翼，推进性能主要受 Φ 的影响，这种强烈影响背后的物理原理是 Φ 决定了从前翼脱落的涡流与尾翼相互作用的方式。相比之下，从前翼脱落的涡流与尾翼的相互作用不受 Gx/c 的显着影响，因为尾翼经历了从前翼脱落的类似涡流，而与 Gx/c 无关。使用不同的 Gx/c 和 Φ/π 值，箔的三种不同的变形状态，即对称周期状态、不对称周期状态和不规则状态，被识别并映射在 (Φ/π, Gx /c) 空间。观察到叶片变形状态与尾翼推进性能之间具有良好的相关性。采用浸入式边界格子Boltzmann方法对二维串联排列的柔性叶片在均匀流动中的流体动力学行为进行了数值研究。前翼的前缘被迫承受升沉和俯仰运动，而后翼的前缘仅被迫承受升沉运动。特别令人感兴趣的是流向间隙距离 Gx（Gx/c = 0.25–1.75，其中 c 表示箔的长度）和箔的起伏运动之间的相位差 Φ（Φ/π = -1.00）的影响到 1.00) 对箔的流体动力学特性，例如推进力、推进效率、被动变形，以及箔片周围的流场。对于前翼，由于尾翼的存在以及由此产生的翼间间隙流动，推进性能在小 Gx/c 值时受 Φ 显着影响，并且这种影响随着 Gx/c 的增加而减弱。对于尾翼，推进...