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Triglobal resolvent analysis of swept-wing wakes

Published online by Cambridge University Press:  09 January 2023

J.H. Marques Ribeiro Open the ORCID record for J.H. Marques Ribeiro [Opens in a new window] ,
Chi-An Yeh Open the ORCID record for Chi-An Yeh [Opens in a new window]  and
Kunihiko Taira Open the ORCID record for Kunihiko Taira [Opens in a new window]
J.H. Marques Ribeiro*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA
Chi-An Yeh
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, USA
Kunihiko Taira
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA
*
†Email address for correspondence: jeanmarques@g.ucla.edu
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Abstract

Through triglobal resolvent analysis, we reveal the effects of wing tip and sweep angle on laminar separated wakes over swept wings. For the present study, we consider wings with semi-aspect ratios from $1$ to $4$, sweep angles from $0^\circ$ to $45^\circ$ and angles of attack of $20^\circ$ and $30^\circ$ at a chord-based Reynolds number of $400$ and a Mach number of $0.1$. Using direct numerical simulations, we observe that unswept wings develop vortex shedding near the wing root with a quasi-steady tip vortex. For swept wings, vortex shedding is seen near the wing tip for low sweep angles, while the wakes are steady for wings with high sweep angles. To gain further insights into the mechanisms of flow unsteadiness, triglobal resolvent analysis is used to identify the optimal spatial input–output mode pairs and the associated gains over a range of frequencies. The three-dimensional forcing and response modes reveal that harmonic fluctuations are directed towards the root for unswept wings and towards the wing tip for swept wings. The overlapping region of the forcing–response mode pairs uncovers triglobal resolvent wavemakers associated with self-sustained unsteady wakes of swept wings. Furthermore, we show that for low-aspect-ratio wings optimal perturbations develop globally over the entire wingspan. The present study uncovers physical insights on the effects of tip and sweep on the growth of optimal harmonic perturbations and the wake dynamics of separated flows over swept wings.

JFM classification

Vortex Flows: Vortex dynamics Wakes/Jets: Separated flows Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 954 , 10 January 2023 , A42
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

REFERENCES

Amestoy, P.R., Duff, I.S., L'Excellent, J.-Y. & Koster, J. 2001 A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J. Matrix Anal. Applics. 23 (1), 15–41.CrossRefGoogle Scholar
Anderson, J.D. 2010 Fundamentals of Aerodynamics. McGraw-Hill.Google Scholar
Barkley, D., Blackburn, H.M. & Sherwin, S.J. 2008 Direct optimal growth analysis for timesteppers. Intl J. Numer. Meth. Fluids 57 (9), 1435–1458.CrossRefGoogle Scholar
Barthel, B., Gomez, S. & McKeon, B.J. 2022 Variational formulation of resolvent analysis. Phys. Rev. Fluids 7 (1), 013905.CrossRefGoogle Scholar
Brès, G.A., Ham, F.E., Nichols, J.W. & Lele, S.K. 2017 Unstructured large-eddy simulations of supersonic jets. AIAA J. 55 (4), 1164–1184.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
Burtsev, A., He, W., Hayostek, S., Zhang, K., Theofilis, V., Taira, K. & Amitay, M. 2022 Linear modal instabilities around post-stall swept finite wings at low Reynolds numbers. J. Fluid Mech. 944, A6.CrossRefGoogle Scholar
Chu, B.-T. 1965 On the energy transfer to small disturbances in fluid flow (part I). Acta Mechanica 1 (3), 215–234.CrossRefGoogle Scholar
Crouch, J.D., Garbaruk, A. & Strelets, M. 2019 Global instability in the onset of transonic-wing buffet. J. Fluid Mech. 881, 3–22.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
Edstrand, A.M., Schmid, P.J., Taira, K. & Cattafesta III, L.N. 2018 a A parallel stability analysis of a trailing vortex wake. J. Fluid Mech. 837, 858–895.CrossRefGoogle Scholar
Edstrand, A.M., Sun, Y., Schmid, P.J., Taira, K. & Cattafesta, L.N. 2018 b Active attenuation of a trailing vortex inspired by a parabolized stability analysis. J. Fluid Mech. 855, R2.CrossRefGoogle Scholar
Fage, A. & Johansen, F.C. 1927 On the flow of air behind an inclined flat plate of infinite span. Proc. R. Soc. Lond. A 116 (773), 170–197.Google Scholar
Farghadan, A., Towne, A., Martini, E. & Cavalieri, A. 2021 A randomized time-domain algorithm for efficiently computing resolvent modes. AIAA Paper 2021-2896.CrossRefGoogle Scholar
Fosas de Pando, M. & Schmid, P.J. 2017 Optimal frequency-response sensitivity of compressible flow over roughness elements. J. Turbul. 18 (4), 338–351.CrossRefGoogle Scholar
Fosas de Pando, M., Schmid, P.J. & Sipp, D. 2017 On the receptivity of aerofoil tonal noise: an adjoint analysis. J. Fluid Mech. 812, 771–791.CrossRefGoogle Scholar
Freund, J.B. 1997 Proposed inflow/outflow boundary condition for direct computation of aerodynamic sound. AIAA J. 35 (4), 740–742.CrossRefGoogle Scholar
Giannetti, F., Camarri, S. & Luchini, P. 2010 Structural sensitivity of the secondary instability in the wake of a circular cylinder. J. Fluid Mech. 651, 319–337.CrossRefGoogle Scholar
Giannetti, F. & Luchini, P. 2007 Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581 (1), 167–197.CrossRefGoogle Scholar
Gómez, F., Blackburn, H.M., Rudman, M., Sharma, A.S. & McKeon, B.J. 2016 A reduced-order model of three-dimensional unsteady flow in a cavity based on the resolvent operator. J. Fluid Mech. 798, R2.CrossRefGoogle Scholar
Halko, N., Martinsson, P.-G. & Tropp, J.A. 2011 Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions. SIAM Rev. 53 (2), 217–288.CrossRefGoogle Scholar
Harper, C.W. & Maki, R.L. 1964 A review of the stall characteristics of swept wings. Tech. Rep. NASA/TN D-2373. NASA.Google Scholar
He, W. & Timme, S. 2021 Triglobal infinite-wing shock-buffet study. J. Fluid Mech. 925, A27.CrossRefGoogle Scholar
Hill, D. 1992 A theoretical approach for analyzing the restabilization of wakes. AIAA Paper 1992-67.CrossRefGoogle Scholar
House, D.C., Skene, C.S., Ribeiro, J.H.M., Yeh, C.-A. & Taira, K. 2022 Sketch-based resolvent analysis. AIAA Paper 2022-3335.CrossRefGoogle Scholar
Houtman, J., Timme, S. & Sharma, A. 2022 Resolvent analysis of large aircraft wings in edge-of-the-envelope transonic flow. AIAA Paper 2022-1329.CrossRefGoogle Scholar
Jovanović, M.R. 2004 Modeling, Analysis, and Control of Spatially Distributed Systems. University of California at Santa Barbara, Dept. of Mechanical Engineering.Google Scholar
Jovanović, M.R. & Bamieh, B. 2005 Componentwise energy amplification in channel flows. J. Fluid Mech. 534, 145–183.CrossRefGoogle Scholar
Khalighi, Y., Ham, F., Nichols, J., Lele, S.K. & Moin, P. 2011 Unstructured large eddy simulation for prediction of noise issued from turbulent jets in various configurations. AIAA Paper 2011-2886.CrossRefGoogle Scholar
Lentink, D., Müller, U.K., Stamhuis, E.J., De Kat, R., Van Gestel, W., Veldhuis, L.L.M., Henningsson, P., Hedenström, A., Videler, J.J. & Van Leeuwen, J.L. 2007 How swifts control their glide performance with morphing wings. Nature 446 (7139), 1082–1085.CrossRefGoogle ScholarPubMed
Liu, Q., Sun, Y., Yeh, C.-A., Ukeiley, L.S., Cattafesta, L.N. & Taira, K. 2021 Unsteady control of supersonic turbulent cavity flow based on resolvent analysis. J. Fluid Mech. 925, A5.CrossRefGoogle Scholar
Martini, E., Rodríguez, D., Towne, A. & Cavalieri, A.V.G. 2021 Efficient computation of global resolvent modes. J. Fluid Mech. 919, A3.CrossRefGoogle Scholar
Masini, L., Timme, S. & Peace, A.J. 2020 Analysis of a civil aircraft wing transonic shock buffet experiment. J. Fluid Mech. 884, A1.CrossRefGoogle Scholar
McKeon, B.J. & Sharma, A.S. 2010 A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336–382.CrossRefGoogle Scholar
Moarref, R., Sharma, A.S., Tropp, J.A. & McKeon, B.J. 2013 Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels. J. Fluid Mech. 734, 275–316.CrossRefGoogle Scholar
Monokrousos, A., Åkervik, E., Brandt, L. & Henningson, D.S. 2010 Global three-dimensional optimal disturbances in the Blasius boundary-layer flow using time-steppers. J. Fluid Mech. 650, 181–214.CrossRefGoogle Scholar
Paladini, E., Beneddine, S., Dandois, J., Sipp, D. & Robinet, J.-C. 2019 Transonic buffet instability: from two-dimensional airfoils to three-dimensional swept wings. Phys. Rev. Fluids 4 (10), 103906.CrossRefGoogle Scholar
Plante, F., Dandois, J., Beneddine, S., Laurendeau, É. & Sipp, D. 2021 Link between subsonic stall and transonic buffet on swept and unswept wings: from global stability analysis to nonlinear dynamics. J. Fluid Mech. 908, A16.CrossRefGoogle Scholar
Qadri, U.A. & Schmid, P.J. 2017 Frequency selection mechanisms in the flow of a laminar boundary layer over a shallow cavity. Phys. Rev. Fluids 2, 043902.CrossRefGoogle Scholar
Ribeiro, J.H.M., Yeh, C. -A. & Taira, K. 2020 Randomized resolvent analysis. Phys. Rev. Fluids 5 (3), 033902.CrossRefGoogle Scholar
Ribeiro, J.H.M., Yeh, C.-A., Zhang, K. & Taira, K. 2022 a From biglobal to triglobal resolvent analysis: laminar separated flows over swept wings. AIAA Paper 2022-2428.CrossRefGoogle Scholar
Ribeiro, J.H.M., Yeh, C.-A., Zhang, K. & Taira, K. 2022 b Wing sweep effects on laminar separated flows. J. Fluid Mech. 950, A23.CrossRefGoogle Scholar
Ricciardi, T.R., Wolf, W.R. & Taira, K. 2022 Transition, intermittency and phase interference effects in airfoil secondary tones and acoustic feedback loop. J. Fluid Mech. 937, A23.CrossRefGoogle Scholar
Schmid, P.J. & Brandt, L. 2014 Analysis of fluid systems: stability, receptivity, sensitivity. Appl. Mech. Rev. 66 (2), 024803.CrossRefGoogle Scholar
Schmidt, O.T., Towne, A., Rigas, G., Colonius, T. & Brès, G.A. 2018 Spectral analysis of jet turbulence. J. Fluid Mech. 855, 953–982.CrossRefGoogle Scholar
Skene, C.S., Ribeiro, J.H.M. & Taira, K. 2022 a CSSKENE/linear-analysis-tools: initial release. https://doi.org/10.5281/zenodo.6550726.CrossRefGoogle Scholar
Skene, C.S. & Schmid, P.J. 2019 Adjoint-based parametric sensitivity analysis for swirling M-flames. J. Fluid Mech. 859, 516–542.CrossRefGoogle Scholar
Skene, C.S., Yeh, C.-A., Schmid, P.J. & Taira, K. 2022 b Sparsifying the resolvent forcing mode via gradient-based optimisation. J. Fluid Mech. 944, A52.CrossRefGoogle Scholar
Stewart, G.W. 2002 A Krylov–Schur algorithm for large eigenproblems. SIAM J. Matrix Anal. Applics. 23 (3), 601–614.CrossRefGoogle Scholar
Strykowski, P.J. & Sreenivasan, K.R. 1990 On the formation and suppression of vortex ‘shedding’ at low Reynolds numbers. J. Fluid Mech. 218, 71–107.CrossRefGoogle Scholar
Sun, Y., Taira, K., III, L.N.C. & Ukeiley, L.S. 2017 Biglobal instabilities of compressible open-cavity flows. J. Fluid Mech. 826, 270–301.CrossRefGoogle Scholar
Taira, K., Brunton, S.L., Dawson, S.T.M., Rowley, C.W., Colonius, T., McKeon, B.J., Schmidt, O.T., Gordeyev, S., Theofilis, V. & Ukeiley, L.S. 2017 Modal analysis of fluid flows: an overview. AIAA J. 55 (12), 4013–4041.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
Taira, K., Hemati, M.S., Brunton, S.L., Sun, Y., Duraisamy, K., Bagheri, S., Dawson, S.T.M. & Yeh, C.-A. 2020 Modal analysis of fluid flows: applications and outlook. AIAA J. 58 (3), 998–1022.CrossRefGoogle Scholar
Thomareis, N. & Papadakis, G. 2018 Resolvent analysis of separated and attached flows around an airfoil at transitional Reynolds number. Phys. Rev. Fluids 3 (7), 073901.CrossRefGoogle Scholar
Timme, S. 2020 Global instability of wing shock-buffet onset. J. Fluid Mech. 885, A37.CrossRefGoogle Scholar
Torres, G.E. & Mueller, T.J. 2004 Low-aspect-ratio aerodynamics at low Reynolds numbers. AIAA J. 42 (5), 865–873.CrossRefGoogle Scholar
Trefethen, L.N., Trefethen, A.E., Reddy, S.C. & Driscoll, T.A. 1993 Hydrodynamic stability without eigenvalues. Science 261 (5121), 578–584.CrossRefGoogle ScholarPubMed
Videler, J.J., Stamhuis, E.J. & Povel, G.D.E. 2004 Leading-edge vortex lifts swifts. Science 306 (5703), 1960–1962.CrossRefGoogle ScholarPubMed
Wygnanski, I., Tewes, P., Kurz, H., Taubert, L. & Chen, C. 2011 The application of boundary layer independence principle to three-dimensional turbulent mixing layers. J. Fluid Mech. 675, 336–346.CrossRefGoogle Scholar
Yeh, C.-A., Benton, S.I., Taira, K. & Garmann, D.J. 2020 Resolvent analysis of an airfoil laminar separation bubble at $Re = 500\,000$. Phys. Rev. Fluids 5 (8), 083906.CrossRefGoogle Scholar
Yeh, C.-A. & Taira, K. 2019 Resolvent-analysis-based design of airfoil separation control. J. Fluid Mech. 867, 572–610.CrossRefGoogle Scholar
Yen, S.-C. & Hsu, C.M. 2007 Flow patterns and wake structure of a swept-back wing. AIAA J. 45 (1), 228–236.CrossRefGoogle Scholar
Yen, S.-C. & Huang, L.-C. 2009 Flow patterns and aerodynamic performance of unswept and swept-back wings. J. Fluids Engng 131 (11), 111101.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., Burstev, A., Theofilis, V. & Taira, K. 2020 a Laminar separated flows over finite-aspect-ratio swept wings. J. Fluid Mech. 905, R1.CrossRefGoogle Scholar
Zhang, K., Hayostek, S., Amitay, M., He, W., Theofilis, V. & Taira, K. 2020 b On the formation of three-dimensional separated flows over wings under tip effects. J. Fluid Mech. 895, A9.CrossRefGoogle Scholar
Zhang, K. & Taira, K. 2022 Laminar vortex dynamics around forward-swept wings. Phys. Rev. Fluids 7 (2), 024704.CrossRefGoogle Scholar