Existence of a sharp transition in the peak propulsive efficiency of a low-Re pitching foil

Das, Anil and Shukla, Ratnesh K and Govardhan, Raghuraman N (2016) Existence of a sharp transition in the peak propulsive efficiency of a low-Re pitching foil. In: JOURNAL OF FLUID MECHANICS, 800 . pp. 307-326.

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Abstract

We perform a com prehensive characterization of the propulsive performance of a thrust generating pitching foil over a wide range of Reynolds (10 <= Re <= 2000) and Strouhal (St) numbers using a high-resolution viscous vortex particle method. For a given Re, We show that the mean thrust coefficient (C-T) over bar increases monotonically with St, exhibiting a sharp rise as the location of the inception of the wake asymmetry shifts towards the trailing edge. As a result, the propulsive efficiency too rises steeply before attaining a maximum and eventually declining at an asymptotic rate that is consistent with the inertial scalings of St(2) for (C-T) over bar and St(3) for the mean power coefficient, with the latter scaling holding, quite remarkably, over the entire range of Re. We find the existence of a sharp increase in the peak propulsive efficiency (at a given Re) in the Re range of 50 to approximately 1000, with eta(max) increasing rapidly from about 1.7% to the saturated asymptotic value of approximately 16 %. The Si at which eta(max) is attained decreases progressively with Re towards an asymptotic limit of 0.45 and always exceeds the one for transition from a reverse von Karman to a deflected wake. Moreover, the drag-to-thrust transition occurs at a Strouhal number St, that exceeds the one for von Karman to reverse von Kaman transition. The Stir and the corresponding power coefficient (C-p,C-tr) over bar are found to be remarkably consistent with the simple scaling relationships St(tr) similar to Re-0.37 and (C-p,C-tr) over bar similar to Re-1.12 that are derived from a balance of the thrust generated from the pitching motion and the drag force arising out of viscous resistance to the foil motion. `File fact that the peak propulsive efficiency degrades appreciably only below Re approximate to 10(3) establishes a sharp lower threshold for energetically efficient thrust generation from a pitching foil. Our findings should he generalizable to other thrust-producing flapping foil configurations and should aid in establishing the link between wake patterns and energetic cost of thrust production in similar systems.

Item Type:	Journal Article
Publication:	JOURNAL OF FLUID MECHANICS
Publisher:	CAMBRIDGE UNIV PRESS
Additional Information:	Copy right for this article belongs to the CAMBRIDGE UNIV PRESS, 32 AVENUE OF THE AMERICAS, NEW YORK, NY 10013-2473 USA
Keywords:	propulsion; vortex shedding; wakes/jets
Department/Centre:	Division of Mechanical Sciences > Mechanical Engineering
Date Deposited:	19 Aug 2016 10:21
Last Modified:	19 Aug 2016 10:21
URI:	http://eprints.iisc.ac.in/id/eprint/54451

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