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Wake-induced transition in the low-Reynolds-number flow over a multi-element airfoil

Published online by Cambridge University Press:  11 March 2021

Jiang-Sheng Wang
Affiliation:
Fluid Mechanics Key Laboratory of Education Ministry, Beijing University of Aeronautics and Astronautics, Beijing100191, China
Jin-Jun Wang*
Affiliation:
Fluid Mechanics Key Laboratory of Education Ministry, Beijing University of Aeronautics and Astronautics, Beijing100191, China
*
Email address for correspondence: jjwang@buaa.edu.cn

Abstract

Time-resolved particle image velocimetry and hydrogen bubble visualization are used to investigate the wake-induced transition of a 30P30N multi-element airfoil at a fixed angle of attack of 4° within the stowed chord Reynolds-number range of 1.38 × 104 to 3.05 × 104. A special transition routine, strongly affected by the slat wake, is observed in the confluent boundary layer over the 30P30N airfoil. In particular, the effects of slat-wake-triggered double-secondary vortices on the whole transition process are explored in detail. At the initial transition stage, the strong slat-wake disturbances penetrate the boundary layer of the main element and are then amplified by double-exponential growth to generate double-secondary vortices. Compared to the scenarios of simplified geometries (He et al., J. Fluid Mech., vol. 718, 2013, pp. 116–130; He & Wang, Phys. Fluids, vol. 27, 2015, 024106), the double-exponential growth provides stronger fluctuations for the transition. At the intermediate transition stage, the wake disturbances trigger the three-dimensional destabilization of these secondary vortices by direct injection or indirect induction, leading to Λ vortices. The spanwise wavelength of the consequent Λ vortices is therefore locked on by the wake disturbances. At the late transition stage, the Λ vortices evolve into hairpin vortex packets and finally contribute to an attached turbulent boundary layer above the main element. Throughout the transition process, no obvious separation occurs in the mean flow above the main element, revealing potential aerodynamic benefits.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Adrian, R.J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19 (4), 041301.CrossRefGoogle Scholar
Basley, J., Pastur, L., Lusseyran, F., Faure, T.M. & Delprat, N. 2011 Experimental investigation of global structures in an incompressible cavity flow using time-resolved PIV. Exp. Fluids 50 (4), 905918.CrossRefGoogle Scholar
Berkooz, G., Holmes, P. & Lumley, J.L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25 (1), 539575.CrossRefGoogle Scholar
Boutilier, M.S.H. & Yarusevych, S. 2012 a Effects of end plates and blockage on low-Reynolds-number flows over airfoils. AIAA J. 50 (7), 15471559.CrossRefGoogle Scholar
Boutilier, M.S.H. & Yarusevych, S. 2012 b Separated shear layer transition over an airfoil at a low Reynolds number. Phys. Fluids 24 (8), 084105.CrossRefGoogle Scholar
Burgmann, S., Dannemann, J. & Schröder, W. 2008 Time-resolved and volumetric PIV measurements of a transitional separation bubble on an SD7003 airfoil. Exp. Fluids 44 (4), 609622.CrossRefGoogle Scholar
Burgmann, S. & Schröder, W. 2008 Investigation of the vortex induced unsteadiness of a separation bubble via time-resolved and scanning PIV measurements. Exp. Fluids 45 (4), 675691.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 (4), 11691182.CrossRefGoogle Scholar
Chatterjee, A. 2000 An introduction to the proper orthogonal decomposition. Curr. Sci. 78 (7), 808817.Google Scholar
Christensen, K. & Adrian, R.J. 2001 Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid Mech. 431, 433443.CrossRefGoogle Scholar
Deng, S.-C., Pan, C., Wang, J.-J. & He, G.-S. 2018 On the spatial organization of hairpin packets in a turbulent boundary layer at low-to-moderate Reynolds number. J. Fluid Mech. 844, 635668.CrossRefGoogle Scholar
Di Luca, M., Mintchev, S., Su, Y., Shaw, E. & Breuer, K. 2020 A bioinspired separated flow wing provides turbulence resilience and aerodynamic efficiency for miniature drones. Sci. Robot. 5 (38), 19.CrossRefGoogle ScholarPubMed
Durbin, P. & Wu, X. 2007 Transition beneath vortical disturbances. Annu. Rev. Fluid Mech. 39 (1), 107128.CrossRefGoogle Scholar
Floreano, D. & Wood, R.J. 2015 Science, technology and the future of small autonomous drones. Nature 521 (7553), 460466.CrossRefGoogle ScholarPubMed
Green, M., Rowley, C. & Haller, G. 2007 Detection of lagrangian coherent structures in three-dimensional turbulence. J. Fluid Mech. 572, 111120.CrossRefGoogle Scholar
Hain, R., Kähler, C. & Radespiel, R. 2009 Dynamics of laminar separation bubbles at low-Reynolds-number aerofoils. J. Fluid Mech. 630, 129153.CrossRefGoogle Scholar
Haller, G. 2001 Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Physica D 149 (4), 248277.CrossRefGoogle Scholar
Haller, G. & Yuan, G. 2000 Lagrangian coherent structures and mixing in two-dimensional turbulence. Physica D 147 (3), 352370.CrossRefGoogle Scholar
He, G.-S., Pan, C., Feng, L.-H., Gao, Q. & Wang, J.-J. 2016 Evolution of Lagrangian coherent structures in a cylinder-wake disturbed flat plate boundary layer. J. Fluid Mech. 792, 274306.CrossRefGoogle Scholar
He, G.-S. & Wang, J.-J. 2015 Flat plate boundary layer transition induced by a controlled near-wall circular cylinder wake. Phys. Fluids 27 (2), 024106.CrossRefGoogle Scholar
He, G.-S., Wang, J.-J. & Pan, C. 2013 Initial growth of a disturbance in a boundary layer influenced by a circular cylinder wake. J. Fluid Mech. 718, 116130.CrossRefGoogle Scholar
He, G.-S., Wang, J.-J., Pan, C., Feng, L.-H., Gao, Q. & Rinoshika, A. 2017 Vortex dynamics for flow over a circular cylinder in proximity to a wall. J. Fluid Mech. 812, 698720.CrossRefGoogle Scholar
Hosseini, S.M., Vinuesa, R., Schlatter, P., Hanifi, A. & Henningson, D.S. 2016 Direct numerical simulation of the flow around a wing section at moderate Reynolds number. Intl J. Heat Fluid Flow 61, 117128.CrossRefGoogle Scholar
Hosseinverdi, S. & Fasel, H.F. 2019 Numerical investigation of laminar–turbulent transition in laminar separation bubbles: the effect of free-stream turbulence. J. Fluid Mech. 858, 714759.CrossRefGoogle Scholar
Istvan, M.S. & Yarusevych, S. 2018 Effects of free-stream turbulence intensity on transition in a laminar separation bubble formed over an airfoil. Exp. Fluids 59 (3), 52.CrossRefGoogle Scholar
Jenkins, L.N., Khorrami, M.R. & Choudhari, M. 2004 Characterization of unsteady flow structures near leading-edge slat: part I. PIV Measurements. AIAA Paper 2004-2801.Google Scholar
Jensen, A., Pedersen, G.K. & Wood, D. 2003 An experimental study of wave run-up at a steep beach. J. Fluid Mech. 486, 161188.CrossRefGoogle Scholar
Jones, L., Sandberg, R. & Sandham, N. 2008 Direct numerical simulations of forced and unforced separation bubbles on an airfoil at incidence. J. Fluid Mech. 602, 175207.CrossRefGoogle Scholar
Jones, L., Sandberg, R. & Sandham, N. 2010 stability and receptivity characteristics of a laminar separation bubble on an aerofoil. J. Fluid Mech. 648, 257296.CrossRefGoogle Scholar
Kurelek, J.W., Kotsonis, M. & Yarusevych, S. 2018 Transition in a separation bubble under tonal and broadband acoustic excitation. J. Fluid Mech. 853, 136.CrossRefGoogle Scholar
Kurelek, J.W., Lambert, A.R. & Yarusevych, S. 2016 Coherent structures in the transition process of a laminar separation bubble. AIAA J. 54 (8), 22952309.CrossRefGoogle Scholar
Kyriakides, N.K., Kastrinakis, E.G., Nychas, S.G. & Goulas, A. 1999 Aspects of flow structure during a cylinder wake-induced laminar/turbulent transition. AIAA J. 37 (10), 11971205.CrossRefGoogle Scholar
Lissaman, P. 1983 Low-Reynolds-number airfoils. Annu. Rev. Fluid Mech. 15 (1), 223239.CrossRefGoogle Scholar
Ma, L.-Q., Feng, L.-H., Pan, C., Gao, Q. & Wang, J.-J. 2015 Fourier mode decomposition of PIV data. Sci. China Technol. Sci. 58 (11), 19351948.CrossRefGoogle Scholar
Mandal, A., Venkatakrishnan, L. & Dey, J. 2010 A study on boundary-layer transition induced by free-stream turbulence. J. Fluid Mech. 660, 114146.CrossRefGoogle Scholar
Mandal, A.C. & Dey, J. 2011 An experimental study of boundary layer transition induced by a cylinder wake. J. Fluid Mech. 684, 6084.CrossRefGoogle Scholar
Marxen, O. & Henningson, D.S. 2011 The effect of small-amplitude convective disturbances on the size and bursting of a laminar separation bubble. J. Fluid Mech. 671, 133.CrossRefGoogle Scholar
Marxen, O., Lang, M., Rist, U., Levin, O. & Henningson, D.S. 2009 Mechanisms for spatial steady three-dimensional disturbance growth in a non-parallel and separating boundary layer. J. Fluid Mech. 634, 165189.CrossRefGoogle Scholar
Matsubara, M. & Alfredsson, P.H. 2001 Disturbance growth in boundary layers subjected to free-stream turbulence. J. Fluid Mech. 430, 149168.CrossRefGoogle Scholar
Mueller, T.J. & Delaurier, J.D. 2003 Aerodynamics of small vehicles. Annu. Rev. Fluid Mech. 35 (1), 89111.CrossRefGoogle Scholar
Nagarajan, S., Lele, S. & Ferziger, J. 2007 Leading-edge effects in bypass transition. J. Fluid Mech. 572, 471504.CrossRefGoogle Scholar
Olson, D., Katz, A., Naguib, A., Koochesfahani, M., Rizzetta, D. & Visbal, M. 2013 On the challenges in experimental characterization of flow separation over airfoils at low Reynolds number. Exp. Fluids 54 (2), 111.CrossRefGoogle Scholar
Ovchinnikov, V., Piomelli, U. & Choudhari, M.M. 2006 Numerical simulations of boundary-layer transition induced by a cylinder wake. J. Fluid Mech. 547, 413441.CrossRefGoogle Scholar
Pan, C., Wang, J.-J., Zhang, P.-F. & Feng, L.-H. 2008 Coherent structures in bypass transition induced by a cylinder wake. J. Fluid Mech. 603, 367389.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 (10), 116.Google Scholar
Pascioni, K.A. & Cattafesta, L.N. 2018 Unsteady characteristics of a slat-cove flow field. Phys. Rev. Fluids 3 (3), 034607.CrossRefGoogle Scholar
Prandtl, L. 1904 über Flüssigkeitsbewegung bei sehr kleiner Reibung. Verhandlungen des III. Internationalen Mathematiker Kongresses, Heidelberg, 8–13 August 1904, pp. 485–491. B. G. Teubner.Google Scholar
Qu, Y., Wang, J.-J., Feng, L.-H. & He, X. 2019 Effect of excitation frequency on flow characteristics around a square cylinder with a synthetic jet positioned at front surface. J. Fluid Mech. 880, 764798.CrossRefGoogle Scholar
Robinet, J.-C. 2013 Instabilities in laminar separation bubbles. J. Fluid Mech. 732, 14.CrossRefGoogle Scholar
Schrader, L.-U., Brandt, L., Mavriplis, C. & Henningson, D.S. 2010 Receptivity to free-stream vorticity of flow past a flat plate with elliptic leading edge. J. Fluid Mech. 653, 245271.CrossRefGoogle Scholar
Serna, J. & Lázaro, B. 2014 The final stages of transition and the reattachment region in transitional separation bubbles. Exp. Fluids 55 (4), 1695.CrossRefGoogle Scholar
Serna, J. & Lázaro, B. 2015 On the bursting condition for transitional separation bubbles. Aerosp. Sci. Technol. 44, 4350.CrossRefGoogle Scholar
Shadden, S., Katija, K., Rosenfeld, M., Marsden, J. & Dabiri, J. 2007 Transport and stirring induced by vortex formation. J. Fluid Mech. 593, 315331.CrossRefGoogle Scholar
Shadden, S.C., Astorino, M. & Gerbeau, J.-F. 2010 Computational analysis of an aortic valve jet with Lagrangian coherent structures. Chaos 20 (1), 017512.CrossRefGoogle ScholarPubMed
Shadden, S.C., Dabiri, J.O. & Marsden, J.E. 2006 Lagrangian analysis of fluid transport in empirical vortex ring flows. Phys. Fluids 18 (4), 047105.CrossRefGoogle Scholar
Shadden, S.C., Lekien, F. & Marsden, J.E. 2005 Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D 212 (3–4), 271304.CrossRefGoogle Scholar
Shrestha, R., Benedict, M., Hrishikeshavan, V. & Chopra, I. 2016 Hover performance of a small-scale helicopter rotor for flying on mars. J. Aircraft 53 (4), 11601167.CrossRefGoogle Scholar
Simoni, D., Ubaldi, M., Zunino, P., Lengani, D. & Bertini, F. 2012 An experimental investigation of the separated-flow transition under high-lift turbine blade pressure gradients. Flow Turbul. Combust. 88 (1), 4562.CrossRefGoogle Scholar
Smith, A.M.O. 1975 High-lift aerodynamics. J. Aircraft 12 (6), 501530.CrossRefGoogle Scholar
Squire, L. 1989 Interactions between wakes and boundary-layers. Prog. Aerosp. Sci. 26 (3), 261288.CrossRefGoogle Scholar
Tanarro, Á, Vinuesa, R. & Schlatter, P. 2020 Effect of adverse pressure gradients on turbulent wing boundary layers. J. Fluid Mech. 883, A8.CrossRefGoogle Scholar
Thomas, F.O., Nelson, R. & Liu, X. 2000 Experimental investigation of the confluent boundary layer of a high-lift system. AIAA J. 38 (6), 978988.CrossRefGoogle Scholar
Van Dam, C. 2002 The aerodynamic design of multi-element high-lift systems for transport airplanes. Prog. Aerosp. Sci. 38 (2), 101144.CrossRefGoogle Scholar
Vinuesa, R., Hosseini, S.M., Hanifi, A., Henningson, D.S. & Schlatter, P. 2017 Pressure-gradient turbulent boundary layers developing around a wing section. Flow Turbul. Combust. 99 (3–4), 613641.CrossRefGoogle ScholarPubMed
Vinuesa, R., Negi, P.S., Atzori, M., Hanifi, A., Henningson, D.S. & Schlatter, P. 2018 Turbulent boundary layers around wing sections up to Rec = 1 000 000. Intl J. Heat Fluid Flow 72, 8699.CrossRefGoogle Scholar
Wang, J.-S., Feng, L.-H., Wang, J.-J. & Li, T. 2018 a Görtler vortices in low-Reynolds-number flow over multi-element airfoil. J. Fluid Mech. 835, 898935.CrossRefGoogle Scholar
Wang, J.-S., Gao, Q., Wei, R.-J. & Wang, J.-J. 2017 Experimental study on the effect of an artificial cardiac valve on the left ventricular flow. Exp. Fluids 58 (9), 126.CrossRefGoogle Scholar
Wang, J.-S. & Wang, J.-J. 2021 Vortex dynamics for flow around the slat cove at low Reynolds number. J. Fluid Mech. (submitted).Google Scholar
Wang, J.-S., Wang, J.-J. & Kim, K.-C. 2018 b Wake–shear layer interaction for low-Reynolds-number flow over multi-element airfoil. Exp. Fluids 60 (1), 16.CrossRefGoogle Scholar
Wang, S., Zhou, Y., Alam, M.M. & Yang, H. 2014 Turbulent intensity and Reynolds number effects on an airfoil at low Reynolds numbers. Phys. Fluids 26 (11), 115107.CrossRefGoogle Scholar
Wang, W.-K., Pan, C. & Wang, J.-J. 2019 Wall-normal variation of spanwise streak spacing in turbulent boundary layer with low-to-moderate Reynolds number. Entropy 21 (1), 24.CrossRefGoogle Scholar
Weyl, A. 1945 High-lift devices and tailless aeroplanes. Aircraft Engng Aerosp. Technol. 17, 292297.CrossRefGoogle Scholar
Williamson, C.H. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28 (1), 477539.CrossRefGoogle Scholar
Xu, L., Baglietto, E. & Brizzolara, S. 2018 Extending the applicability of RANS turbulence closures to the simulation of transitional flow around hydrofoils at low Reynolds number. Ocean Engng 164, 112.CrossRefGoogle Scholar
Yarusevych, S. & Kotsonis, M. 2017 Steady and transient response of a laminar separation bubble to controlled disturbances. J. Fluid Mech. 813, 955990.CrossRefGoogle Scholar
Zhou, J., Adrian, R.J., Balachandar, S. & Kendall, T. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353396.CrossRefGoogle Scholar