Foil locomotion through non-sinusoidal pitching motion
| Autor: | Raghuraman N. Govardhan, Ratnesh K. Shukla, Anil Das |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Physics
Chord (geometry) Mechanical Engineering Reynolds number 02 engineering and technology Mechanics 01 natural sciences 010305 fluids & plasmas Root mean square symbols.namesake 020303 mechanical engineering & transports Amplitude 0203 mechanical engineering Computer Science::Sound Drag 0103 physical sciences symbols Waveform Strouhal number FOIL method |
| Zdroj: | Journal of Fluids and Structures. 89:191-202 |
| ISSN: | 0889-9746 |
| DOI: | 10.1016/j.jfluidstructs.2019.01.020 |
| Popis: | We investigate the propulsive characteristics of a neutrally buoyant foil that self propels as it pitches about its quarter chord with a prescribed time periodic waveform. For a fixed pitching frequency and amplitude, we find the foil motion to be strongly dependent on the prescribed waveform. The maximum mean self-propelling speed corresponds to a square shaped waveform for which the foil is held at the two extremes for a significant part of the pitching cycle. In contrast, the cost of transport is minimal, and therefore the energetic efficiency of pitching induced self propulsion a maximum, for a triangle shaped profile in which case the foil’s angular speed is largely held constant over the pitching period. Pitching waveform induced variations in the mean self-propelling speed ( u ¯ p ) are surprisingly well predicted with a simple power-law relationship S t r m s ∼ R e − 0 . 37 , where Reynolds number R e is based on u ¯ p and the Strouhal number S t r m s is the ratio of the root mean square foil trailing edge speed and u ¯ p . This power-law relationship is shown to arise naturally from a balance between the cycle-averaged inertial thrust generated from prescribed pitching and the enhanced drag owing to the boundary layer thinning. The imposed pitching motion induces a Reynolds number independent out of phase heave motion features of which are remarkably well predicted with a simple inviscid model for the foil’s transverse motion. For all the prescribed pitching waveforms, a maximum in the energetic efficiency is always attained over the range 0 . 3 ≤ S t ≤ 0 . 6 . The close correspondence between this Strouhal number range for maximum energetic efficiency and the optimal Strouhal number range for swimming and flying animals is indicative of the similarity between self-propelling flapping foil configurations and undulatory biolocomotion. Our results point to the significance of rigid body pitching profile as an important input parameter that can be varied independently to achieve a desired outcome such as maximization of the mean self-propelling speed or energetic efficiency. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect