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Tip effects on three-dimensional flow structures over low-aspect-ratio plates: mechanisms of spanwise fluid transport

Published online by Cambridge University Press:  20 March 2024

Yichen Zhu Open the ORCID record for Yichen Zhu [Opens in a new window] ,
Jinjun Wang Open the ORCID record for Jinjun Wang [Opens in a new window]  and
Jiaxin Liu Open the ORCID record for Jiaxin Liu [Opens in a new window]
Yichen Zhu
Affiliation:
Fluid Mechanics Key Laboratory of Education Ministry, Beijing University of Aeronautics and Astronautics, Beijing 100191, PR China
Jinjun Wang*
Affiliation:
Fluid Mechanics Key Laboratory of Education Ministry, Beijing University of Aeronautics and Astronautics, Beijing 100191, PR China
Jiaxin Liu
Affiliation:
Fluid Mechanics Key Laboratory of Education Ministry, Beijing University of Aeronautics and Astronautics, Beijing 100191, PR China
*
†Email address for correspondence: jjwang@buaa.edu.cn
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Abstract

Three-dimensional flows over low-aspect-ratio rectangular flat plates (${A{\kern-4pt}R} = 1.00$–$1.50$) are investigated using tomographic and planar particle image velocimetry techniques. The chord-based Reynolds number is $5400$, and the angle of attack is fixed at $6^\circ$. This study reveals for the first time the interplay between spanwise fluid transport and downwash, both originating from the tip effects. Spanwise fluid transport promotes the formation and subsequent coherent development of leading-edge vortices, whereas downwash stabilizes the flow. Specifically, two mechanisms related to spanwise fluid transport are revealed. First, the spanwise fluid transport enhances the intensity of the reversed flow, promoting the shear layer roll-up and vortex shedding. Second, the near-wall spanwise flow interacts with the shed C-shape vortices, thereby strengthening the vortex heads. In particular, through these interactions, spanwise fluid transport can sustain the coherence of the C-shape vortices until the vortex heads split in a regular fashion. Consequently, the C-shape vortices are transformed into novel Þ-shape vortices for the plates of ${A{\kern-4pt}R} \leq 1.25$, which supplements the previously discovered transformation from C-shape to M-shape vortices for larger ${A{\kern-4pt}R}$ plates. Downstream of this novel vortex-splitting transformation, two fundamental processes contribute to the formation of hairpin vortices. The above comprehensive understanding of complete vortex evolution routine provides valuable insights into the tip effects on the formation of three-dimensional flows over low-${A{\kern-4pt}R}$ plates.

JFM classification

Vortex Flows: Vortex dynamics Wakes/Jets: Separated flows

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JFM Papers
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Journal of Fluid Mechanics , Volume 983 , 25 March 2024 , A35
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© The Author(s), 2024. Published by Cambridge University Press

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References

Ananda, G.K., Sukumar, P.P. & Selig, M.S. 2015 Measured aerodynamic characteristics of wings at low Reynolds numbers. Aerosp. Sci. Technol. 42, 392–406.CrossRefGoogle Scholar
Betts, C.R. & Wooton, R.J. 1988 Wing shape and flight behaviour in butterflies (Lepidoptera: Papilionoidea and Hesperioidea): a preliminary analysis. J. Expl Biol. 138, 271–288.CrossRefGoogle Scholar
Birch, D., Lee, T., Mokhtarian, F. & Kafyeke, F. 2004 Structure and induced drag of a tip vortex. J. Aircraft 41, 1138–1145.CrossRefGoogle Scholar
Buchholz, J.H.J. & Smits, A.J. 2006 On the evolution of the wake structure produced by a low-aspect-ratio pitching panel. J. Fluid Mech. 546, 433–443.CrossRefGoogle Scholar
Champagnat, F., Plyer, A., Le Besnerais, G., Leclaire, B., Davoust, S. & Le Sant, Y. 2011 Fast and accurate PIV computation using highly parallel iterative correlation maximization. Exp. Fluids 50, 1169–1182.CrossRefGoogle Scholar
Chen, P.W., Bai, C.J. & Wang, W.C. 2016 Experimental and numerical studies of low aspect ratio wing at critical Reynolds number. Eur. J. Mech. B/Fluids 59, 161–168.CrossRefGoogle Scholar
Devenport, W.J., Rife, M.C., Liapis, S.I. & Follin, G.J. 1996 The structure and development of a wing-tip vortex. J. Fluid Mech. 312, 67–106.CrossRefGoogle Scholar
DeVoria, A.C. & Mohseni, K. 2017 On the mechanism of high-incidence lift generation for steadily translating low-aspect-ratio wings. J. Fluid Mech. 813, 110–126.CrossRefGoogle Scholar
Dong, L., Choi, K.-S. & Mao, X.R. 2020 Interplay of the leading-edge vortex and the tip vortex of a low-aspect-ratio thin wing. Exp. Fluids 61, 200.CrossRefGoogle Scholar
Dovgal, A.V., Kozlov, V.V. & Michalke, A. 1994 Laminar boundary layer separation: instability and associated phenomena. Prog. Aerosp. Sci. 30, 61–94.CrossRefGoogle Scholar
Elsinga, G.E., Scarano, F., Wieneke, B. & van Oudheusden, B.W. 2006 Tomographic particle image velocimetry. Exp. Fluids 41, 933–947.CrossRefGoogle Scholar
Francis, M.S. & Kennedy, D.A. 1979 Formation of a trailing vortex. J. Aircraft 16, 148–154.CrossRefGoogle Scholar
Freymuth, P., Finaish, F. & Bank, W. 1987 Further visualization of combined wing tip and starting vortex systems. AIAA J. 25, 1153–1159.CrossRefGoogle Scholar
Green, S.I. & Acosta, A.J. 1991 Unsteady flow in trailing vortices. J. Fluid Mech. 227, 107–134.CrossRefGoogle Scholar
Gresham, N.T., Wang, Z.J. & Gursul, I. 2010 Low Reynolds number aerodynamics of free-to-roll low aspect ratio wings. Exp. Fluids 49, 11–25.CrossRefGoogle Scholar
He, K., Minelli, G., Wang, J.B., Dong, T.Y., Gao, G.J. & Krajnović, S. 2021 Numerical investigation of the wake bi-stability behind a notchback Ahmed body. J. Fluid Mech. 926, A36.CrossRefGoogle Scholar
Hunt, J.C.R., Wray, A.A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. In Center for Turbulence Research Report CTR-S88, pp. 193–208.Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Knisely, C. & Rockwell, D. 1982 Self-sustained low-frequency components in an impinging shear layer. J. Fluid Mech. 116, 157–186.CrossRefGoogle Scholar
Lengani, D., Simoni, D., Ubaldi, M. & Zunino, P. 2014 POD analysis of the unsteady behavior of a laminar separation bubble. Expl Therm. Fluid Sci. 58, 70–79.CrossRefGoogle Scholar
Lissaman, P.B.S. 1983 Low-Reynolds-number airfoils. Annu. Rev. Fluid Mech. 15, 223–239.CrossRefGoogle Scholar
Mendez, M.A., Raiola, M., Masullo, A., Discetti, S., Ianiro, A., Theunissen, R. & Buchlin, J.-M. 2017 POD-based background removal for particle image velocimetry. Expl Therm. Fluid Sci. 80, 181–192.CrossRefGoogle Scholar
Menon, K., Kumar, S. & Mittal, R. 2022 Contribution of spanwise and cross-span vortices to the lift generation of low-aspect-ratio wings: insights from force partitioning. Phys. Rev. Fluids 7, 114102.CrossRefGoogle Scholar
Mizoguchi, M., Kajikawa, Y. & Itoh, H. 2016 Aerodynamic characteristics of low-aspect-ratio wings with various aspect ratios in low Reynolds number flows. Trans. Japan. Soc. Aeronaut. Space Sci. 59, 56–63.CrossRefGoogle Scholar
Mueller, T.J. 1999 Aerodynamic measurements at low Reynolds numbers for fixed wing micro-air vehicles. In RTO AVT Special Course on Development and Operation of UAVs for Military and Civil Applications, pp. 1–32.Google Scholar
Mueller, T.J. & DeLaurier, J.D. 2003 Aerodynamics of small vehicles. Annu. Rev. Fluid Mech. 35, 89–111.CrossRefGoogle Scholar
Navrose, , Brion, V. & Jacquin, L. 2019 Transient growth in the near wake region of the flow past a finite span wing. J. Fluid Mech. 866, 399–430.CrossRefGoogle Scholar
Neal, J.M. & Amitay, M. 2023 Three-dimensional separation over unswept cantilevered wings at a moderate Reynolds number. Phys. Rev. Fluids 8, 014703.CrossRefGoogle Scholar
Nobes, D.S., Wieneke, B. & Tatam, R.P. 2004 Determination of view vectors from image warping mapping functions. Opt. Engng 43, 407–414.Google Scholar
Okamoto, M. & Azuma, A. 2011 Aerodynamic characteristics at low Reynolds number for wings of various planforms. AIAA J. 49, 1135–1150.CrossRefGoogle Scholar
Okamoto, M., Sasaki, D., Kamikubo, M. & Fujii, R. 2019 Disappearance of vortex lift in low-aspect-ratio wings at very-low Reynolds numbers. Trans. Japan Soc. Aeronaut. Space Sci. 62, 310–317.CrossRefGoogle Scholar
Pan, C., Xue, D., Xu, Y., Wang, J.J. & Wei, R.J. 2015 Evaluating the accuracy performance of Lucas–Kanade algorithm in the circumstance of PIV application. Sci. China Phys. Mech. Astron. 58, 1–16.CrossRefGoogle Scholar
Pandi, J.S.S. & Mittal, S. 2023 Streamwise vortices, cellular shedding and force coefficients on finite wing at low Reynolds number. J. Fluid Mech. 958, A10.CrossRefGoogle Scholar
Pelletier, A. & Mueller, T.J. 2000 Low Reynolds number aerodynamics of low-aspect-ratio, thin/flat/cambered-plate wings. J. Aircraft 37, 825–832.CrossRefGoogle Scholar
Pines, D.J. & Bohorquez, F. 2006 Challenges facing future micro-air-vehicle development. J. Aircraft 43, 290–305.CrossRefGoogle Scholar
Raffel, M., Willert, C.E., Scarano, F., Kähler, C.J., Wereley, S.T. & Kompenhans, J. 2018 Particle Image Velocimetry: A Practical Guide. Springer.CrossRefGoogle Scholar
Ribeiro, J.H.M., Neal, J., Burtsev, A., Amitay, M., Theofilis, V. & Taira, K. 2023 a Laminar post-stall wakes of tapered swept wings. J. Fluid Mech. 976, A6.CrossRefGoogle Scholar
Ribeiro, J.H.M., Yeh, C.-A. & Taira, K. 2023 b Triglobal resolvent analysis of swept-wing wakes. J. Fluid Mech. 954, A42.CrossRefGoogle Scholar
Rist, U. & Maucher, U. 2002 Investigations of time-growing instabilities in laminar separation bubbles. Eur. J. Mech. B/Fluids 21, 495–509.CrossRefGoogle Scholar
Rodríguez, D. & Gennaro, E.M. 2019 Enhancement of disturbance wave amplification due to the intrinsic three-dimensionalisation of laminar separation bubbles. Aeronaut. J. 123, 1492–1507.CrossRefGoogle Scholar
Scarano, F. 2002 Iterative image deformation methods in PIV. Meas. Sci. Technol. 13, R1.CrossRefGoogle Scholar
Scherl, I., Strom, B., Shang, J.K., Williams, O., Polagye, B.L. & Brunton, S.L. 2020 Robust principal component analysis for modal decomposition of corrupt fluid flows. Phys. Rev. Fluids 5, 054401.CrossRefGoogle Scholar
Shekarriz, A., Fu, T.C., Katz, J. & Huang, T.T. 1993 Near-field behavior of a tip vortex. AIAA J. 31, 112–118.CrossRefGoogle Scholar
Simoni, D., Ubaldi, M., Zunino, P. & Bertini, F. 2012 Transition mechanisms in laminar separation bubbles with and without incoming wakes and synthetic jet effects. Exp. Fluids 53, 173–186.CrossRefGoogle Scholar
Taira, K. & Colonius, T. 2009 Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers. J. Fluid Mech. 623, 187–207.CrossRefGoogle Scholar
Toppings, C.E. & Yarusevych, S. 2021 Structure and dynamics of a laminar separation bubble near a wingtip. J. Fluid Mech. 929, A39.CrossRefGoogle Scholar
Torres, G.E. & Mueller, T.J. 2001 Aerodynamic characteristics of low aspect ratio wings at low Reynolds numbers. In Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications (ed. T.J. Mueller), pp. 115–141. AIAA.CrossRefGoogle Scholar
Visbal, M.R. 2011 Three-dimensional flow structure on a heaving low-aspect-ratio wing. AIAA Paper 2011–219.CrossRefGoogle Scholar
Visbal, M.R. 2012 Flow structure and unsteady loading over a pitching and perching low-aspect-ratio wing. AIAA Paper 2012–3279.CrossRefGoogle Scholar
Visbal, M.R. & Garmann, D.J. 2012 Flow structure above stationary and oscillating low-aspect-ratio wing. In Proceedings of the ASME 2012 Fluids Engineering Division Summer Meeting, pp. 1593–1605. ASME.CrossRefGoogle Scholar
Wang, C.Y., Gao, Q., Wang, H.P., Wei, R.J., Li, T. & Wang, J.J. 2016 Divergence-free smoothing for volumetric PIV data. Exp. Fluids 57, 15.CrossRefGoogle Scholar
Wang, J.S., Feng, L.H., Wang, J.J. & Li, T. 2018 Görtler vortices in low-Reynolds-number flow over multi-element airfoil. J. Fluid Mech. 835, 898–935.CrossRefGoogle Scholar
Welch, P. 1967 The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. 15, 70–73.CrossRefGoogle Scholar
Wieneke, B. 2008 Volume self-calibration for 3D particle image velocimetry. Exp. Fluids 45, 549–556.CrossRefGoogle Scholar
Yarusevych, S., Sullivan, P.E. & Kawall, J.G. 2009 On vortex shedding from an airfoil in low-Reynolds-number flows. J. Fluid Mech. 632, 245–271.CrossRefGoogle Scholar
Yilmaz, T.O. & Rockwell, D. 2010 Three-dimensional flow structure on a maneuvering wing. Exp. Fluids 48, 539–544.CrossRefGoogle Scholar
Yilmaz, T.O. & Rockwell, D. 2012 Flow structure on finite-span wings due to pitch-up motion. J. Fluid Mech. 691, 518–545.CrossRefGoogle Scholar
Zhang, K., Hayostek, S., Amitay, M., He, W., Theofilis, V. & Taira, K. 2020 On the formation of three-dimensional separated flows over wings under tip effects. J. Fluid Mech. 895, A9.CrossRefGoogle Scholar
Zhu, N., Zhang, Z., Gnanamanickam, E. & Gordon Leishman, J. 2023 a Space-time characterization of ship airwakes. AIAA J. 61, 681–697.CrossRefGoogle Scholar
Zhu, Y.C., Wang, J.J., Xu, Y., Qu, Y. & Long, Y.G. 2023 b Swallow-tailed separation bubble on a low-aspect-ratio trapezoidal plate: effects of near-wall spanwise flow. J. Fluid Mech. 965, A12.CrossRefGoogle Scholar
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Typical instantaneous flowfields for AR = 1.00
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