The hydrodynamics of a three-dimensional self-propelled flexible plate with a Navier slip surface was explored in an effort to assess its role in the hydrodynamics of a slip boundary that mimics the mucus layer. The Navier slip arises when the component of the tangential velocity at a wall is proportional to the strain. The immersed boundary method was employed to simulate the flow. For comparison, simulations were also performed with the no-slip condition. The clamped leading edge of the flexible plate was forced into a prescribed harmonic oscillation in the vertical direction but was free to move in the horizontal direction. For validation of the results obtained with the Navier slip, experiments were performed on a solid surface with a seaweed covering. The average cruising speed (${Ū}_C$), the input power ($\overline{P}$), and the propulsion efficiency (η) of the plate were determined as a function of the flapping frequency (f) to characterize its kinematics. The drag reduction due to the Navier slip was determined by examining the changes in the powers resulting from its effects on the Lagrangian momentum forces. The reduction in the power in the tangential direction due to the Navier slip condition is greater than that in the normal direction. The effects of the Navier slip on the force (F), power (P), and propulsion performance of the plate were evaluated. The hydrodynamic benefits of the slip condition for a self-propelled flexible body were elucidated in detail.

中文翻译：

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带有Navier滑动表面的自推式柔性板

为了评估其在模拟粘液层的滑移边界的流体动力学中的作用，研究了具有Navier滑动表面的三维自推进柔性板的流体力学。当壁上切线速度的分量与应变成比例时，就会发生纳维叶滑动。采用沉浸边界法模拟流动。为了进行比较，还使用防滑条件进行了仿真。挠性板的夹紧的前缘在垂直方向上被迫产生预定的谐波振荡，但在水平方向上可自由移动。为了验证使用Navier滑模获得的结果，在带有海藻覆盖层的固体表面上进行了实验。平均巡航速度（${Ū}_C$），输入功率（$\overline{P}$），并根据拍动频率（f）确定板的推进效率（η）以表征其运动学特性。Navier滑移引起的阻力减小是通过检查其对拉格朗日动量力的影响所引起的幂变化来确定的。由于Navier滑动条件，切线方向的屈光力减小幅度大于法线方向上的屈光率减小幅度。评估了Navier滑移对板的力（F），功率（P）和推进性能的影响。详细说明了自推式柔性体的滑移条件对流体力学的好处。