Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384 Marseille, France
CNRS, UMR 8107, 59650 Villeneuve d'Ascq, France Université Lille Nord de France, 59000 Lille, France.
Philos Trans A Math Phys Eng Sci. 2014 Jul 28;372(2020). doi: 10.1098/rsta.2013.0345.
To calculate the energy costs of swimming or flying, it is crucial to evaluate the drag force originating from skin friction. This topic seems not to have received a definite answer, given the difficulty in measuring accurately the friction drag along objects in movement. The incoming flow along a flat plate in a flapping normal motion has been considered, as limit case of a yawed cylinder in uniform flow, and applying the laminar boundary layer assumption it is demonstrated that the longitudinal drag scales as the square root of the normal velocity component. This lends credit to the assumption that a swimming-like motion may induce a drag increase because of the compression of the boundary layer, which is known as the 'Bone-Lighthill boundary-layer thinning hypothesis'. The boundary-layer model however cannot predict the genuine three-dimensional flow dynamics and in particular the friction at the leeward side of the plate. A multi-domain, parallel, compact finite-differences Navier-Stokes solution procedure is considered, capable of solving the full problem. The time-dependent flow dynamics is analysed and the general trends predicted by the simplified model are confirmed, with however differences in the magnitude of the friction coefficient. A tentative skin friction formula is proposed for flow states along a plate moving at steady as well as periodic normal velocities.
要计算游泳或飞行的能量成本，评估源自皮肤摩擦的阻力至关重要。由于难以准确测量运动物体的摩擦阻力，这个问题似乎还没有明确的答案。本文考虑了平板在拍动正常运动中的来流，作为均匀流中偏航圆柱的极限情况，并应用层流边界层假设，证明纵向阻力与法向速度分量的平方根成正比。这证明了游泳样运动可能由于边界层的压缩而导致阻力增加的假设，这被称为“Bone-Lighthill 边界层变薄假说”。然而，边界层模型无法预测真实的三维流动动力学，特别是平板背风侧的摩擦。本文考虑了一种多域、并行、紧凑差分纳维-斯托克斯求解程序，能够求解完整的问题。分析了时变流动力学，证实了简化模型预测的一般趋势，但摩擦系数的大小存在差异。提出了一个用于平板在稳态和周期性法向速度下运动的流动状态的暂定摩擦系数公式。
