Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
J Exp Biol. 2010 Jan 1;213(1):63-71. doi: 10.1242/jeb.031708.
We show experimentally that flapping foil kinematics consisting of a power downstroke and a feathering upstroke together with a properly timed in-line motion, similar to those employed in forelimb propulsion of sea turtles, can produce high thrust and be hydrodynamically as efficient as symmetrically flapping foils. The crucial parameter for such asymmetrically flapping foils is a properly sized and timed in-line motion, whose effect is quantified by a new parameter, the advance angle, defined as the angle of the foil trajectory with respect to the horizontal, evaluated at the middle of the power downstroke. We show, in particular, that optimal efficiency in high aspect ratio rigid foils, accompanied by significant thrust production, is obtained for Strouhal numbers in the range 0.2-0.6 for Reynolds number equal to 13,000, and for values of the advance angle around 0.55pi (100 deg.). The optimized kinematics consist of the foil moving back axially during the downstroke, in the direction of the oncoming flow, and rotating with a large pitch angle. This causes the force vector to rotate and become nearly parallel to the steady flow, thus providing a large thrust and a smaller transverse force. During the upstroke, the foil is feathering while it moves axially forward, i.e. away from the vorticity shed during the power stroke; as a result, the transverse force remains relatively small and no large drag force is produced. Observations from turtles confirm qualitatively the findings from the foil experiments.
我们通过实验表明，具有功率下冲程和俯仰上冲程以及适当定时的直线运动的扑翼运动学，类似于海龟前肢推进中采用的运动学，可以产生高推力并且在水动力方面与对称扑翼一样高效。对于这种非对称扑翼来说，关键参数是适当大小和定时的直线运动，其效果由一个新参数——前导角来量化，该参数定义为翼型轨迹相对于水平方向的角度，在功率下冲程的中间进行评估。我们特别表明，在高纵横比刚性翼中，最佳效率伴随着显著的推力产生，对于斯特劳哈尔数在 0.2-0.6 范围内，雷诺数等于 13000，以及前导角值约为 0.55pi（100 度），可以获得最佳效率。优化的运动学包括在向下冲程期间轴向向后移动，与来流方向相反，并以大攻角旋转。这导致力矢量旋转并几乎与稳定流平行，从而提供了大的推力和较小的横向力。在上冲程期间，翼型在轴向向前移动的同时俯仰，即远离功率冲程期间产生的涡旋；结果，横向力仍然相对较小，不会产生大的阻力。海龟的观察结果从定性上证实了翼型实验的发现。
