Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-17T05:19:00.220Z Has data issue: false hasContentIssue false
  • English
  • Français

Resolvent analysis on the origin of two-dimensional transonic buffet

Published online by Cambridge University Press:  20 December 2019

Yoimi Kojima Open the ORCID record for Yoimi Kojima [Opens in a new window] ,
Chi-An Yeh Open the ORCID record for Chi-An Yeh [Opens in a new window] ,
Kunihiko Taira Open the ORCID record for Kunihiko Taira [Opens in a new window]  and
Masaharu Kameda Open the ORCID record for Masaharu Kameda [Opens in a new window]
Yoimi Kojima*
Affiliation:
Department of Mechanical Systems Engineering, Tokyo University of Agriculture and Technology, Koganei, Tokyo, 184-8588, Japan
Chi-An Yeh
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA90095, USA
Kunihiko Taira
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA90095, USA
Masaharu Kameda
Affiliation:
Department of Mechanical Systems Engineering, Tokyo University of Agriculture and Technology, Koganei, Tokyo, 184-8588, Japan
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Resolvent analysis is performed to identify the origin of two-dimensional transonic buffet over an airfoil. The base flow for the resolvent analysis is the time-averaged flow over a NACA 0012 airfoil at a chord-based Reynolds number of 2000 and a free-stream Mach number of 0.85. We reveal that the mechanism of buffet is buried underneath the global low-Reynolds-number flow physics. At this low Reynolds number, the dominant flow feature is the von Kármán shedding. However, we show that with the appropriate forcing input, buffet can appear even at a Reynolds number that is much lower than what is traditionally associated with transonic buffet. The source of buffet is identified to be at the shock foot from the windowed resolvent analysis, which is validated by companion simulations using sustained forcing inputs based on resolvent modes. We also comment on the role of perturbations in the vicinity of the trailing edge. The present study not only provides insights on the origin of buffet but also serves a building block for low-Reynolds-number compressible aerodynamics in light of the growing interests in Martian flights.

JFM classification

Aerodynamics: High-speed flow Compressible Flows: Shock waves
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 885 , 25 February 2020 , R1
Copyright
© 2019 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anyoji, M., Numata, D., Nagai, H. & Asai, K. 2015 Effects of Mach number and specific heat ratio on low-Reynolds-number airfoil flows. AIAA J. 53 (6), 1640–1654.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
Crouch, J. D., Garbaruk, A., Magidov, D. & Travin, A. 2009 Origin of transonic buffet on aerofoils. J. Fluid Mech. 628, 357–369.CrossRefGoogle Scholar
Dandois, J. 2016 Experimental study of transonic buffet phenomenon on a 3D swept wing. Phys. Fluids 28 (1), 016101.CrossRefGoogle Scholar
Deck, S. 2005 Numerical simulation of transonic buffet over a supercritical airfoil. AIAA J. 43 (7), 1556–1566.CrossRefGoogle Scholar
Delery, J. M. 1985 Shock wave/turbulent boundary layer interaction and its control. Prog. Aerosp. Sci. 22 (4), 209–280.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
Fukushima, Y. & Kawai, S. 2018 Wall-modeled large-eddy simulation of transonic airfoil buffet at high Reynolds number. AIAA J. 56 (6), 2372–2388.CrossRefGoogle Scholar
Gao, C., Zhang, W., Kou, J., Liu, Y. & Ye, Z. 2017 Active control of transonic buffet flow. J. Fluid Mech. 824, 312–351.CrossRefGoogle Scholar
Giannelis, N. F., Vio, G. A. & Levinski, O. 2017 A review of recent developments in the understanding of transonic shock buffet. Prog. Aerosp. Sci. 92, 39–84.CrossRefGoogle Scholar
Grossi, F., Braza, M. & Hoarau, Y. 2014 Prediction of transonic buffet by delayed detached-eddy simulation. AIAA J. 52 (10), 2300–2312.CrossRefGoogle Scholar
Iovnovich, M. & Raveh, D. E. 2012 Reynolds-averaged Navier–Stokes study of the shock-buffet instability mechanism. AIAA J. 50 (4), 880–890.CrossRefGoogle Scholar
Iovnovich, M. & Raveh, D. E. 2015 Numerical study of shock buffet on three-dimensional wings. AIAA J. 53 (2), 449–463.CrossRefGoogle Scholar
Jacquin, L., Molton, P., Deck, S., Maury, B. & Soulevant, D. 2009 Experimental study of shock oscillation over a transonic supercritical profile. AIAA J. 47 (9), 1985–1994.CrossRefGoogle Scholar
Jeun, J., Nichols, J. W. & Jovanović, M. R. 2016 Input–output analysis of high-speed axisymmetric isothermal jet noise. Phys. Fluids 28 (4), 047101.CrossRefGoogle Scholar
Jovanović, M. R.2004 Modeling, analysis, and control of spatially distributed systems. PhD thesis, University of California, Santa Barbara, CA.Google Scholar
Jovanović, M. R. & Bamieh, B. 2005 Componentwise energy amplification in channel flows. J. Fluid Mech. 534, 145–183.CrossRefGoogle Scholar
Koning, W. J. F., Johnson, W. & Grip, H. F. 2019 Improved Mars helicopter aerodynamic rotor model for comprehensive analyses. AIAA J. 57 (9), 3969–3979.CrossRefGoogle Scholar
Lee, B. H. K. 2001 Self-sustained shock oscillations on airfoils at transonic speeds. Prog. Aerosp. Sci. 37 (2), 147–196.CrossRefGoogle Scholar
Levy, L. L. 1978 Experimental and computational steady and unsteady transonic flows about a thick airfoil. AIAA J. 16 (6), 564–572.CrossRefGoogle Scholar
McCormick, D. C. 1993 Shock/boundary-layer interaction control with vortex generators and passive cavity. AIAA J. 31 (1), 91–96.CrossRefGoogle Scholar
McDevitt, J. B. & Okuno, A. F.1985 Static and dynamic pressure measurements on a NACA 0012 airfoil in the Ames high Reynolds number facility. NASA Tech. Rep. TP-2485. National Aeronautics and Space Administration.Google Scholar
McKeon, B. J. & Sharma, A. S. 2010 A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336–382.CrossRefGoogle Scholar
Munday, P. M. & Taira, K. 2018 Effects of wall-normal and angular momentum injections in airfoil separation control. AIAA J. 56 (5), 1830–1842.CrossRefGoogle Scholar
Munday, P. M., Taira, K., Suwa, T., Numata, D. & Asai, K. 2015 Nonlinear lift on a triangular airfoil in low-Reynolds-number compressible flow. J. Aircraft 52 (3), 924–931.CrossRefGoogle Scholar
Nitzsche, J. 2009 A numerical study on aerodynamic resonance in transonic seperated flow. In International Forum on Aeroelasticity and Structural Dynamics, Seattle, WA, IFASD Paper 2009-126.Google Scholar
Ohmichi, Y., Ishida, T. & Hashimoto, A. 2018 Modal decomposition analysis of three-dimensional transonic buffet phenomenon on a swept wing. AIAA J. 56 (10), 3938–3950.CrossRefGoogle Scholar
Sartor, F., Mettot, C. & Sipp, D. 2014 Stability, receptivity, and sensitivity analyses of buffeting transonic flow over a profile. AIAA J. 53 (7), 1980–1993.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
Seegmiller, H. L., Marvin, J. G. & Levy, L. L. Jr 1978 Steady and unsteady transonic flow. AIAA J. 16 (12), 1262–1270.CrossRefGoogle Scholar
Shi, J., Hu, C. & Shu, C. W. 2002 A technique of treating negative weights in WENO schemes. J. Comput. Phys. 175 (1), 108–127.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., Hemati, M.S., Brunton, S.L., Sun, Y., Duraisamy, K., Bagheri, S., Dawson, S.T.M. & Yeh, C.-A. 2019 Modal analysis of fluid flows: applications and outlook. AIAA J. doi:10.2514/1.J058462.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
Yeh, C.-A. & Taira, K. 2019 Resolvent-analysis-based design of airfoil separation control. J. Fluid Mech. 867, 572–610.CrossRefGoogle Scholar
Zhang, W. & Samtaney, R. 2016 Biglobal linear stability analysis on low-Re flow past an airfoil at high angle of attack. Phys. Fluids 28 (4), 044105.CrossRefGoogle Scholar