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Evolution of wake structures behind oscillating hydrofoils with combined heaving and pitching motion

Published online by Cambridge University Press:  28 September 2021

Suyash Verma Open the ORCID record for Suyash Verma [Opens in a new window]  and
Arman Hemmati Open the ORCID record for Arman Hemmati [Opens in a new window]
Suyash Verma
Affiliation:
Department of Mechanical Engineering, University of Alberta, Edmonton, AB T6G 2R3, Canada
Arman Hemmati*
Affiliation:
Department of Mechanical Engineering, University of Alberta, Edmonton, AB T6G 2R3, Canada
*
†Email address for correspondence: arman.hemmati@ualberta.ca
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Abstract

The wake of an oscillating teardrop hydrofoil with combined heaving and pitching motion was studied numerically at Reynolds number of 8000 and Strouhal numbers of $St=0.21{-}0.94$. The lower Strouhal number exhibited high efficiency propulsion with small thrust generation. However, larger thrust generation at high $St$ required more power, which lowered the propulsive efficiency. Quantitative assessment of vortex evolution, along with qualitative investigation of the formation and interaction of primary structures, revealed the association with elliptic instability characteristics for both co-rotating and counter-rotating vortex structures in both wakes. With respect to advection of the leading-edge vortex, the pressure distribution further depicted evidence of spanwise instability with distinct temporal evolution along the suction and pressure surfaces of the oscillating foil. Three-dimensional assessment of wake structures located downstream of the trailing edge depicted the existence of dislocations associated with primary vortex ‘rollers’. At low $St$, these were limited to fine spanwise corrugations (valleys and bulges) on weaker leading edge rollers, which enlarged as the rollers advected downstream. In contrast, at high $St$, the wake exhibited conjoint hairpin-horseshoe vortex structures that led to stronger deformations on the coupled vortex rollers. The statistical characteristics of secondary structures resembled the long wavelength mode and mode A identified previously for purely pitching and heaving foils, respectively. They also mimicked mode B for stationary cylinders. Novel wake models are introduced based on a complete vivid three-dimensional depiction of coherent wake structures.

JFM classification

Biological Fluid Dynamics: Swimming/flying Vortex Flows: Vortex shedding Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 927 , 25 November 2021 , A23
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Anderson, J.M., Streitlien, K., Barrett, D.S. & Triantafyllou, M.S. 1998 Oscillating foils of high propulsive efficiency. J. Fluid Mech. 360, 41–72.CrossRefGoogle Scholar
Barkley, D. & Henderson, R.D. 1996 Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322, 215–241.CrossRefGoogle Scholar
Birch, J.M. & Dickinson, M.H. 2003 The influence of wing-wake interactions on the production of aerodynamic forces in flapping flight. J. Exp. Biol. 206 (13), 2257–2272.CrossRefGoogle ScholarPubMed
Bose, C., Gupta, S. & Sarkar, S. 2021 Dynamic interlinking between near-and far-field wakes behind a pitching-heaving airfoil. J. Fluid Mech. 911, A31.CrossRefGoogle Scholar
Boustead, N., Ryan, K. & Sheard, G.J. 2010 Short-wave instability growth in closely spaced vortex pairs. Prog. Comput. Fluid Dyn. 10 (5/6), 276–283.CrossRefGoogle Scholar
Brede, M., Eckelmann, H. & Rockwell, D. 1996 On secondary vortices in the cylinder wake. Phys. Fluids 8, 2117.CrossRefGoogle Scholar
Calderon, D.E., Cleaver, D.J., Gursul, I. & Wang, Z. 2014 On the absence of asymmetric wakes for periodically plunging finite wings. Phys. Fluids 26, 071907.CrossRefGoogle Scholar
Cerretelli, C. & Williamson, C.H.K. 2003 The physical mechanism for vortex merging. J. Fluid Mech. 475, 41–77.CrossRefGoogle Scholar
Chandar, D.D.J. 2019 On overset interpolation strategies and conservation on unstructured grids in OpenFOAM. Comput. Phys. Commun. 239, 72–83.CrossRefGoogle Scholar
Chiereghin, N., Bull, S., Cleaver, D.J. & Gursul, I. 2020 Three-dimensionality of leading-edge vortices on high aspect ratio plunging wings. Phys. Rev. Fluids 5, 064701.CrossRefGoogle Scholar
Cleaver, D.J., Wang, Z. & Gursul, I. 2012 Bifurcating flows of plunging aerofoils at high Strouhal numbers. J. Fluid Mech. 708, 349–376.CrossRefGoogle Scholar
Cleaver, D.J., Wang, Z., Gursul, I. & Visbal, M.R. 2011 Lift enhancement by means of small-amplitude airfoil oscillations at low Reynolds numbers. AIAA J. 49 (9), 2018–2033.CrossRefGoogle Scholar
Deng, J. & Caulfield, C.P. 2015 Three-dimensional transition after wake deflection behind a flapping foil. Phys. Rev. E 91, 043017.CrossRefGoogle ScholarPubMed
Deng, J., Sun, L. & Shao, X. 2015 Dynamical features of the wake behind a pitching foil. Phys. Rev. E 92, 063013.CrossRefGoogle ScholarPubMed
Dewey, P.A., Carriou, A. & Smits, A.J. 2012 On the relationship between efficiency and wake structure of a batoid-inspired oscillating fin. J. Fluid Mech. 691, 245–266.CrossRefGoogle Scholar
Dickinson, M.H., Farley, C.T., Full, R.J., Koehl, M.A.R., Kram, R. & Lehman, S. 2000 How animals move: an integrative view. Science 288 (5463), 100–106.Google Scholar
Dong, H., Mittal, R. & Najjar, F.M. 2006 Wake topology and hydrodynamic performance of low-aspect-ratio flapping foils. J. Fluid Mech. 566, 309–343.CrossRefGoogle Scholar
von Ellenrieder, K.D., Parker, K. & Soria, J. 2003 Flow structures behind a heaving and pitching finite-span wing. J. Fluid Mech. 490, 129–138.CrossRefGoogle Scholar
Fazle Hussain, A.K. 1986 Coherent structures and turbulence. J. Fluid Mech. 173, 303–356.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
Gemmell, B.J., Colin, S.P., Costello, J.H. & Dabiri, J.O. 2015 Suction-based propulsion as a basis for efficient animal swimming. Nat. Commun. 6, 8790.CrossRefGoogle ScholarPubMed
Gibeau, B., Koch, C.R. & Ghaemi, S. 2018 Secondary instabilities in the wake of an elongated two-dimensional body with a blunt trailing edge. J. Fluid Mech. 846, 578–604.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
Guglielmini, L. & Blondeaux, P. 2004 Propulsive efficiency of oscillating foils. Eur. J. Mech. B/Fluids 23 (2), 255–278.CrossRefGoogle Scholar
Gungor, A. & Hemmati, A. 2020 Wake symmetry impacts the performance of tandem hydrofoils during in-phase and out-of-phase oscillations differently. Phys. Rev. E 102, 043104.CrossRefGoogle ScholarPubMed
He, X. & Gursul, I. 2016 Point vortex model of deflected wakes of oscillating airfoils. AIAA J. 54 (11), 3647–3651.Google Scholar
Hemmati, A. & Smits, A.J. 2019 The effect of pitching frequency on the hydrodynamics of oscillating foils. J. Appl. Mech. 86 (10), 101010.CrossRefGoogle Scholar
Hemmati, A., Van Buren, T. & Smits, A.J. 2019 Effects of trailing edge shape on vortex formation by pitching panels of small aspect ratio. Phys. Rev. Fluids 4, 033101.CrossRefGoogle Scholar
Hemmati, A., Wood, D.H. & Martinuzzi, R.J. 2016 Characteristics of distinct flow regimes in the wake of an infinite span normal thin flat plate. Intl J. Heat Fluid Flow. 62B, 423–436.CrossRefGoogle Scholar
Hemmati, A., Wood, D.H. & Martinuzzi, R.J. 2018 On simulating the flow past a normal thin flat plate. J. Wind Engng Ind. Aerodyn. 174, 170–187.CrossRefGoogle Scholar
Hultmark, M., Leftwich, M. & Smits, A.J. 2007 Flowfield measurements in the wake of a robotic lamprey. Exp. Fluids 43 (5), 683–690.Google Scholar
Jones, K.D., Dohring, C.M. & Platzer, M.F. 1996 Wake structures behind plunging airfoils: a comparison of numerical and experimental results. In 34th Aerospace Sciences Meeting and Exhibit, AIAA paper 1996-78.Google Scholar
Jones, K.D., Dohring, C.M. & Platzer, M.F. 1998 Experimental and computational investigation of the Knoller-Betz effect. AIAA J. 36 (7), 1240–1246.CrossRefGoogle Scholar
Kim, Y. & Xie, Z.T. 2016 Modelling the effect of freestream turbulence on dynamic stall of wind turbine blades. Comput. Fluids 129, 53–66.CrossRefGoogle Scholar
King, J.T., Kumar, R. & Green, M.A. 2018 Experimental observations of the three-dimensional wake structures and dynamics generated by a rigid, bioinspired pitching panel. Phys. Rev. Fluids 3, 034701.CrossRefGoogle Scholar
Koochesfahani, M.M. 1989 Vortical patterns in the wake of an oscillating airfoil. AIAA J. 27 (9), 1200–1205.CrossRefGoogle Scholar
Lai, J.C.S. & Platzer, M.F. 1999 Jet characteristics of a plunging airfoil. AIAA J. 37 (12), 1529–1537.CrossRefGoogle Scholar
Le Dizès, S. & Laporte, F. 2002 Theoretical predictions for the elliptical instability in a two-vortex flow. J. Fluid Mech. 471, 169–201.CrossRefGoogle Scholar
Lentink, D., Muijres, F.T., Donker-Duyvis, F.J. & Van Leeuwen, J.L. 2008 Vortex-wake interactions of a flapping foil that models animal swimming and flight. J. Exp. Biol. 211 (2), 267–273.Google Scholar
Leweke, T., Le Dizès, S. & Williamson, C.H.K. 2016 Dynamics and instabilities of vortex pairs. Annu. Rev. Fluid Mech. 48 (1), 507–541.Google Scholar
Leweke, T. & Williamson, C.H.K. 1998 Cooperative elliptic instability of a vortex pair. J. Fluid Mech. 360, 85–119.CrossRefGoogle Scholar
McWilliams, J.C. & Zabusky, N.J. 1988 Symmetric vortex merger in two dimensions: causes and conditions. J. Fluid Mech. 195, 303–340.Google Scholar
Merrill, B.E. & Peet, Y.T. 2017 Effect of impinging wake turbulence on the dynamic stall of a pitching airfoil. AIAA J. 55 (12), 4094–4112.CrossRefGoogle Scholar
Meunier, P. & Leweke, T. 2005 Elliptic instability of a co-rotating vortex pair. J. Fluid Mech. 533, 125–159.CrossRefGoogle Scholar
Mittal, R. & Balachandar, S. 1995 Generation of streamwise vortical structures in bluff body wakes. Phys. Rev. Lett. 75, 1300.CrossRefGoogle ScholarPubMed
Moin, P. & Mahesh, K. 1998 Direct numerical simulation: A tool in turbulence research. Annu. Rev. Fluid Mech. 30 (1), 539–578.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. 62A, 44–55.CrossRefGoogle Scholar
Müller, U.K., Van Den Boogaart, J.G.M. & Van Leeuwen, J.L. 2008 Flow patterns of larval fish: Undulatory swimming in the intermediate flow regime. J. Exp. Biol. 211 (2), 196–205.Google Scholar
Najjar, F.M. & Balachandar, S. 1998 Low-frequency unsteadiness in the wake of a normal flat plate. J. Fluid Mech. 370, 101–147.CrossRefGoogle Scholar
Nazarinia, M., Lo Jacono, D., Thompson, C.M. & Sheridan, J. 2009 The three-dimensional wake of a cylinder undergoing a combination of translational and rotational oscillation in a quiescent fluid. Phys. Fluids 21, 064101.Google Scholar
Ortega, J.M., Bristol, R.L. & Savas, Ö. 2003 Experimental study of the instability of unequal-strength counter-rotating vortex pairs. J. Fluid Mech. 474 (474), 35–84.CrossRefGoogle Scholar
Parker, K., von Ellenrieder, K.D. & Soria, J. 2003 Flow visualization of the effect of pitch amplitude changes on the vortical signatures behind a three-dimensional flapping airfoil. In Optical Technology and Image Processing for Fluids and Solids Diagnostics 2002. Proc. SPIE vol. 5058.CrossRefGoogle Scholar
Petra, T. 2019 Description of the overset mesh approach in ESI version of OpenFOAM. In Proceedings of CFD with OpenSource Software (ed. H. Nilsson). Technical University of Liberec.Google Scholar
Quinn, D.B., Lauder, G.V. & Smits, A.J. 2015 Maximizing the efficiency of a flexible propulsor using experimental optimization. J. Fluid Mech. 767, 430–448.CrossRefGoogle Scholar
Robichaux, J., Balachandar, S. & Vanka, S.P. 1999 Three-dimensional Floquet instability of the wake of square cylinder. Phys. Fluids 11, 560.CrossRefGoogle Scholar
Roget, B. & Sitaraman, J. 2014 Robust and efficient overset grid assembly for partitioned unstructured meshes. J. Comput. Phys. 260, 1–24.CrossRefGoogle Scholar
Ryan, K., Thompson, M.C. & Hourigan, K. 2005 Three-dimensional transition in the wake of bluff elongated cylinders. J. Fluid Mech. 538, 1–29.CrossRefGoogle Scholar
Schnipper, T., Andersen, A. & Bohr, T. 2009 Vortex wakes of a flapping foil. J. Fluid Mech. 633, 411–423.CrossRefGoogle Scholar
Senturk, U. & Smits, A.J. 2018 Numerical simulations of the flow around a square pitching panel. J. Fluids Struct. 76, 454–468.CrossRefGoogle Scholar
Smits, A.J. 2019 Undulatory and oscillatory swimming. J. Fluid Mech. 874, P1.CrossRefGoogle Scholar
Srigrarom, S. & Vincent, C.W.S. 2008 Effect of pitching and heaving motions of SD8020 hydrofoil on thrust and efficiency for swimming propulsion. In 38th AIAA Fluid Dynamics Conference and Exhibit.CrossRefGoogle Scholar
Sun, L., Deng, J. & Shao, X. 2018 Three-dimensional instabilities for the flow around a heaving foil. Phys. Rev. E 97 (1), 013110.Google ScholarPubMed
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 (2), 205–224.CrossRefGoogle Scholar
Triantafyllou, M.S., Techet, A.H. & Hover, F.S. 2004 Review of experimental work in biomimetic foils. IEEE J. Ocean. Engng 29 (3), 585–594.Google Scholar
Van Buren, T., Floryan, D. & Smits, A.J. 2019 Scaling and performance of simultaneously heaving and pitching foils. AIAA J. 57 (9), 3666–3677.CrossRefGoogle Scholar
Verma, S. & Hemmati, A. 2020 Performance of overset mesh in modeling the wake of sharp-edge bodies. Computations 8 (3), 66.CrossRefGoogle Scholar
Visbal, M.R. 2009 High-fidelity simulation of transitional flows past a plunging airfoil. AIAA J. 47 (11), 2685–2697.CrossRefGoogle Scholar
Wang, Z.J. 2000 Two dimensional mechanism for insect hovering. Phys. Rev. Lett. 85, 2216.Google Scholar
Williamson, C.H.K. 1996 Three-dimensional wake transition. J. Fluid Mech. 328, 345–407.CrossRefGoogle Scholar
Williamson, C.H.K. & Roshko, A. 1988 Vortex formation in the wake of an oscillating cylinder. J. Fluids Struct. 2 (4), 355–381.CrossRefGoogle Scholar
Wu, T.Y. 2011 Fish swimming and bird/insect flight. Annu. Rev. Fluid Mech. 43 (1), 25–58.CrossRefGoogle Scholar
Zhang, H.Q., Fey, U., Noack, B.R., König, M. & Eckelmann, H. 1995 On the transition of the cylinder wake. Phys. Fluids 7, 779.CrossRefGoogle Scholar
Zheng, Z.C. & Wei, Z. 2012 Study of mechanisms and factors that influence the formation of vortical wake of a heaving airfoil. Phys. Fluids 24, 103601.CrossRefGoogle Scholar