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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: [email protected], [email protected]
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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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References

Akoz, E. & Moored, K.W. 2018 Unsteady propulsion by an intermittent swimming gait. J. Fluid Mech. 834, 149–172.CrossRefGoogle Scholar
Alam, M.M. & Muhammad, Z. 2020 Dynamics of flow around a pitching hydrofoil. J. Fluids Struct. 99, 103151.CrossRefGoogle Scholar
Andersen, A., Bohr, T., Schnipper, T. & Walther, J.H. 2016 Wake structure and thrust generation of a flapping foil in two-dimensional flow. J. Fluid Mech. 812, R4.CrossRefGoogle Scholar
Benkherouf, T., Mekadem, M., Oualli, H., Hanchi, S., Keirsbulck, L. & Labraga, L. 2011 Efficiency of an auto-propelled flapping airfoil. J. Fluids Struct. 27, 552–566.CrossRefGoogle Scholar
Berman, G.J. & Wang, Z.J. 2007 Energy-minimizing kinematics in hovering insect flight. J. Fluid Mech. 582, 153–168.CrossRefGoogle Scholar
Bohl, D.G. & Koochesfahani, M.M. 2009 MTV measurements of the vortical field in the wake of an airfoil oscillating at high reduced frequency. J. Fluid Mech. 620, 63–88.CrossRefGoogle Scholar
Chao, L.-M., Pan, G., Zhang, D. & Yan, G.-X. 2019 Numerical investigations on the force generation and wake structures of a nonsinusoidal pitching foil. J. Fluids Struct. 85, 27–39.CrossRefGoogle Scholar
Childress, S. 1981 Mechanics of Swimming and Flying. Cambridge University Press.CrossRefGoogle Scholar
David, M.J., Govardhan, R.N. & Arakeri, J.H. 2017 Thrust generation from pitching foils with flexible trailing edge flaps. J. Fluid Mech. 828, 70–103.CrossRefGoogle Scholar
Deng, J., Sun, L. & Shao, X. 2015 Dynamical features of the wake behind a pitching foil. Phys. Rev. E 92, 063013.CrossRefGoogle ScholarPubMed
Egan, B.C., Brownell, C.J. & Murray, M.M. 2016 Experimental assessment of performance characteristics for pitching flexible propulsors. J. Fluids Struct. 67, 22–33.CrossRefGoogle Scholar
Eloy, C. 2012 Optimal Strouhal number for swimming animals. J. Fluids Struct. 30, 205–218.CrossRefGoogle Scholar
Fernex, D., Semaan, R., Albers, M., Meysonnat, P.S., Schröder, W. & Noack, B.R. 2020 Actuation response model from sparse data for wall turbulence drag reduction. Phys. Rev. Fluids 5, 073901.CrossRefGoogle Scholar
Floryan, D., Van Buren, T., Rowley, C.W. & Smits, A.J. 2017 Scaling the propulsive performance of heaving and pitching foils. J. Fluid Mech. 822, 386–397.CrossRefGoogle Scholar
Godoy-Diana, R., Aider, J.-L. & Wesfreid, J.E. 2008 Transitions in the wake of a flapping foil. Phys. Rev. E 77, 016308.CrossRefGoogle ScholarPubMed
Godoy-Diana, R., Marais, C., Aider, J.-L. & Wesfreid, J.E. 2009 A model for the symmetry breaking of the reverse Bénard–von Kármán vortex street produced by a flapping foil. J. Fluid Mech. 622, 23–32.CrossRefGoogle Scholar
Hanchi, S., Benkherouf, T., Mekadem, M., Oualli, H., Keirsbulck, L. & Labraga, L. 2013 Wake structure and aerodynamic characteristics of an auto-propelled pitching airfoil. J. Fluids Struct. 39, 275–291.CrossRefGoogle Scholar
Huera-Huarte, F.J. & Gharib, M. 2017 On the effects of tip deflection in flapping propulsion. J. Fluids Struct. 71, 217–233.CrossRefGoogle Scholar
Jayne, B.C., Lozada, A.F. & Lauder, G.V. 1996 Function of the dorsal fin in bluegill sunfish: motor patterns during four distinct locomotor behaviors. J. Morphol. 228, 307–326.3.0.CO;2-Z>CrossRefGoogle ScholarPubMed
von Kármán, T. & Burgers, J.M. 1934 General aerodynamic theory: perfect fluids. In Aerodynamic Theory (ed. W.F. Durand), vol II, Div. E, pp. 280–310. Springer-Verlag.Google Scholar
Katzschmann, R.K., DelPreto, J., MacCurdy, R. & Rus, D. 2018 Exploration of underwater life with an acoustically controlled soft robotic fish. Sci. Robot. 3, eaar3449.CrossRefGoogle ScholarPubMed
Ke, X., Zhang, W., Cai, X. & Chen, W. 2017 Wing geometry and kinematic parameters optimization of flapping wing hovering flight for minimum energy. Aerosp. Sci. Technol. 64, 192–203.CrossRefGoogle Scholar
Koochesfahani, M.M. 1989 Vortical patterns in the wake of an oscillating airfoil. AIAA J. 27, 1200–1205.CrossRefGoogle Scholar
Lu, K., Xie, Y.H. & Zhang, D. 2013 Numerical study of large amplitude, nonsinusoidal motion and camber effects on pitching airfoil propulsion. J. Fluids Struct. 36, 184–194.CrossRefGoogle Scholar
Mackowski, A.W. & Williamson, C.H.K. 2015 Direct measurement of thrust and efficiency of an airfoil undergoing pure pitching. J. Fluid Mech. 765, 524–543.CrossRefGoogle Scholar
Marais, C., Thiria, B., Wesfreid, J.E. & Godoy-Diana, R. 2012 Stabilizing effect of flexibility in the wake of a flapping foil. J. Fluid Mech. 710, 659–669.CrossRefGoogle Scholar
Martin, N., Roh, C., Idrees, S. & Gharib, M. 2017 To flap or not to flap: comparison between flapping and clapping propulsions. J. Fluid Mech. 822, R5.CrossRefGoogle Scholar
Moriche, M., Flores, O. & García-Villalba, M. 2016 Three-dimensional instabilities in the wake of a flapping wing at low Reynolds number. Intl J. Heat Fluid Flow 62, 44–55.CrossRefGoogle Scholar
Murayama, M. & Yamamoto, K. 2008 Comparison study of drag prediction by structured and unstructured mesh method. J. Aircraft 45, 799–822.CrossRefGoogle Scholar
Murayama, M., Yamamoto, K. & Kobayashi, K. 2006 Validation of computations around high-lift configurations by structured- and unstructured-mesh. J. Aircraft 43, 395–406.CrossRefGoogle Scholar
Raspa, V., Godoy-Diana, R. & Thiria, B. 2013 Topology-induced effect in biomimetic propulsive wakes. J. Fluid Mech. 729, 377–387.CrossRefGoogle Scholar
Schnipper, T., Andersen, A. & Bohr, T. 2009 Vortex wakes of a flapping foil. J. Fluid Mech. 633, 411–423.CrossRefGoogle Scholar
Shadwick, R.E. & Lauder, G.V. 2006 Fish Physiology: Fish Biomechanics. Elsevier Science.Google Scholar
Taylor, G.K., Nudds, R.L. & Thomas, A.L.R. 2003 Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency. Nature 425, 707.CrossRefGoogle Scholar
Tian, W., Bodling, A., Liu, H., Wu, J.C., He, G. & Hu, H. 2016 An experimental study of the effects of pitch-pivot-point location on the propulsion performance of a pitching airfoil. J. Fluids Struct. 60, 130–142.CrossRefGoogle Scholar
Triantafyllou, M.S., Hover, F.S., Techet, A.H. & Yue, D.K. 2005 Review of hydrodynamic scaling laws in aquatic locomotion and fishlike swimming. Appl. Mech. Rev. 58, 226–237.CrossRefGoogle Scholar
Triantafyllou, M.S., Triantafyllou, G.S. & Gopalkrishnan, R. 1991 Wake mechanics for thrust generation in oscillating foils. Phys. Fluids A 3, 2835–2837.CrossRefGoogle Scholar
Triantafyllou, G.S., Triantafyllou, M.S. & Grosenbaugh, M.A. 1993 Optimal thrust development in oscillating foils with application to fish propulsion. J. Fluids Struct. 7, 205–224.CrossRefGoogle Scholar
Van Buren, T., Floryan, D., Wei, N. & Smits, A.J. 2018 Flow speed has little impact on propulsive characteristics of oscillating foils. Phys. Rev. Fluids 3, 013103.CrossRefGoogle Scholar
Videler, J.J. 1981 Swimming movements, body structure and propulsion in cod Gadus morhua. In Symposia of the Zoological Society of London 48, pp. 1–27.Google Scholar
Wald, R.M. 2010 General Relativity. University of Chicago press.Google Scholar
Wang, Q., Goosen, J.F.L. & Keulen, F.V. 2017 Optimal pitching axis location of flapping wings for efficient hovering flight. Bioinspir. Biomim. 12, 056001.CrossRefGoogle ScholarPubMed
White, F.M. 2003 Fluid Mechanics, 5th edn. McGraw-Hill.Google Scholar
Xiao, Q. & Liao, W. 2009 Numerical study of asymmetric effect on a pitching foil. Intl J. Mod. Phys. C 20, 1663–1680.CrossRefGoogle Scholar
Xie, Y., Lu, K., Zhang, D. & Xie, G. 2014 Computational analysis of propulsion performance of modified pitching motion airfoils in laminar flow. Math. Prob. Engng 2014, 1–13.Google Scholar
Zhang, X., He, G., Wang, S. & Zhang, X. 2018 Locomotion of a bioinspired flyer powered by one pair of pitching foils. Physical Review Fluids 3, 013102.CrossRefGoogle Scholar