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Efficient thrust enhancement by modified pitching motion

Published online by Cambridge University Press:  21 December 2021

Zaka Muhammad Open the ORCID record for Zaka Muhammad [Opens in a new window] ,
Md. Mahbub Alam Open the ORCID record for Md. Mahbub Alam [Opens in a new window]  and
Bernd R. Noack Open the ORCID record for Bernd R. Noack [Opens in a new window]
Zaka Muhammad
Affiliation:
Center for Turbulence Control, Harbin Institute of Technology (Shenzhen), University Town, Xili, Shenzhen 518055, PR China Centres of Excellence in Science and Applied Technologies (CESAT), Islamabad 44000, Pakistan
Md. Mahbub Alam*
Affiliation:
Center for Turbulence Control, Harbin Institute of Technology (Shenzhen), University Town, Xili, Shenzhen 518055, PR China
Bernd R. Noack
Affiliation:
School of Mechanical Engineering and Automation, Harbin Institute of Technology (Shenzhen), University Town, Xili, Shenzhen 518055, PR China
*
† Email addresses for correspondence: alam@hit.edu.cn, alamm28@yahoo.com
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Abstract

Thrust and/or efficiency of a pitching foil (mimicking a tail of swimming fish) can be enhanced by tweaking the pitching waveform. The literature, however, show that non-sinusoidal pitching waveforms can enhance either thrust or efficiency but not both simultaneously. With the knowledge and inspiration from nature, we devised and implemented a novel asymmetrical sinusoidal pitching motion that is a combination of two sinusoidal motions having periods T1 and T2 for the forward and retract strokes, respectively. The motion is represented by period ratio $\mathrm{\mathbb{T}} = {T_1}/T$, where T = (T1 + T2)/2, with $\mathrm{\mathbb{T}} > 1.00$ giving the forward strokes (from equilibrium to extreme position) slower than the retract strokes (from extreme to equilibrium position) and vice versa. The novel pitching motion enhances both thrust and efficiency for $\mathrm{\mathbb{T}} > 1.00$. The enhancement results from the resonance between the shear-layer roll up and the increased speed of the foil. Four swimming regimes, namely normal swimming, undesirable, floating and ideal are discussed, based on instantaneous thrust and power. The results from the novel pitching motion display similarities with those from fish locomotion (e.g. fast start, steady swimming and braking). The $\mathrm{\mathbb{T}} > 1.00$ motion in the faster stroke has the same characteristics and results as the fast start of prey to escape from a predator while $\mathrm{\mathbb{T}} < 1.00$ imitates braking locomotion. While $\mathrm{\mathbb{T}} < 1.00$ enhances the wake deflection at high amplitude-based Strouhal numbers (StA = fA/U∞, where f and A are the frequency and peak-to-peak amplitude of the pitching, respectively, and U∞ is the freestream velocity), $\mathrm{\mathbb{T}} > 1.00$ improves the wake symmetry, suppressing the wake deflection. The wake characteristics including wake width, jet velocity and vortex structures are presented and connected with $S{t_d}( = fd/{U_\infty })$, ${A^{\ast}}( = A/d)$ and $\mathrm{\mathbb{T}}$, where d is the maximum thickness of the foil.

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 933 , 25 February 2022 , A13
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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