×

zbMATH — the first resource for mathematics

Global instability in the onset of transonic-wing buffet. (English) Zbl 1430.76343
J. Fluid Mech. 881, 3-22 (2019); corrigendum ibid. 901, Article ID E1, 6 p. (2020).
Summary: Global stability analysis is used to analyse the onset of transonic buffet on infinite swept and unswept wings. This high-Reynolds-number flow is governed by the unsteady Reynolds averaged Navier-Stokes equations. The analysis generalizes earlier studies focused on two-dimensional airfoils. For the unswept wing, results show spanwise-periodic stationary modes in addition to the earlier-observed oscillatory mode. The oscillatory mode is nominally two-dimensional with a spanwise wavelength greater than ten wing chords. The stationary modes of instability exist over two bands of spanwise wavelengths centred around an intermediate wavelength of one wing chord, and around a short wavelength of one tenth of a wing chord. The intermediate-wavelength modes have a flow structure characteristic of airfoil buffeting modes, concentrated at the shock and in the shear layer downstream of the shock. The short-wavelength modes are only concentrated in the shear layer downstream of the shock. These stationary modes can lead to spanwise-periodic flow structures for the unswept wing. For the swept wing, these stationary modes become unsteady travelling modes and contribute to the more complex buffeting-flow structures observed on swept wings as compared with unswept wings. The spanwise-wavelength bands of the travelling modes translate to different frequencies, resulting in a broad-banded unsteady response for the swept wing. For a \(30^°\) swept wing, the frequencies associated with the intermediate-wavelength modes are approximately 10 times higher than the swept-wing generalization of the long-wavelength oscillatory mode, and approximately 6 times higher than the long-wavelength mode for the unswept wing. These instability characteristics are in good agreement with experimental observations.

MSC:
76H05 Transonic flows
76E09 Stability and instability of nonparallel flows in hydrodynamic stability
76D25 Wakes and jets
Keywords:
high-speed flow
Software:
SLEPc
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bartels, R. E. & Edwards, J. W.1997 Cryogenic tunnel pressure measurements on a supercritical airfoil for several shock buffet conditions. NASA Tech. Mem. 110272.
[2] Benoit, B. & Legrain, I.1987 Buffeting prediction for transport aircraft applications based on unsteady pressure measurements. AIAA Paper 87-2356.
[3] Crouch, J. D., Garbaruk, A. & Magidov, D.2007Predicting the onset of flow unsteadiness based on global instability. J. Comput. Phys.224, 924-940. · Zbl 1123.76018
[4] Crouch, J. D., Garbaruk, A., Magidov, D. & Travin, A.2009aOrigin of transonic buffet on aerofoils. J. Fluid Mech.628, 357-369. · Zbl 1181.76092
[5] Crouch, J. D., Garbaruk, A., Magidov, D. & Jacquin, L.2009bGlobal structure of buffeting flow on transonic airfoils. In IUTAM Symposium on Unsteady Separated Flows and Their Control, pp. 297-306. Springer.
[6] Dandois, J.2016Experimental study of transonic buffet phenomenon on a 3D swept wing. Phys. Fluids28, 1985-1994.
[7] Deck, S.2005Numerical simulation of transonic buffet over a supercritical airfoil. AIAA J.43, 1556-1566.
[8] Garbaruk, A. & Crouch, J. D.2011Quasi-three dimensional analysis of global instabilities: onset of vortex shedding behind a wavy cylinder. J. Fluid Mech.677, 572-588. · Zbl 1241.76195
[9] Giannelis, N. F., Vio, G. A. & Levinski, O.2017A review of recent developments in the understanding of transonic shock buffet. Prog. Aeronaut. Sci.92, 39-84.
[10] Gioria, R. S., He, W., Perez, J. M. & Theofilis, V.2016 Modal and non-modal global instability analysis of low-Re massively separated flow around a NACA 0015 airfoil. AIAA Paper 2016-3778.
[11] Herbert, Th.1983On perturbation methods in nonlinear stability theory. J. Fluid Mech.126, 167-186. · Zbl 0517.76050
[12] Hernandez, V., Roman, J. E., Tomas, A. & Vidal, V.2007 Krylov-Schur methods in slepc. SLEPc Tech. Rep., http://slepc.upv.es/documentation/reports/str7.pdf.
[13] Iorio, M. C., Gonzalaz, L. M. & Ferrer, F.2014Direct and adjoint global stability analysis of turbulent transonic flows over a NACA0012 profile. Intl J. Numer. Meth. Fluids76, 147-168.
[14] Iovnovich, M. & Raveh, D. E.2014Numerical study of shock buffet on three-dimensional wings. AIAA J.53, 449-463.
[15] Jackson, C. P.1987A finite-element study of the onset of vortex shedding in flow past variously shaped bodies. J. Fluid Mech.182, 23-45. · Zbl 0639.76041
[16] Jacquin, L., Molton, P., Deck, S., Maury, B. & Soulevant, D.2009Experimental study of shock oscillation over a transonic supercritical profile. AIAA J.47, 1985-1994.
[17] McDevitt, J. B. & Okuno, A. F.1985 Static and dynamic pressure measurements on a NACA0012 airfoil in the Ames high Reynolds number facility. NASA Tech. Paper 2485.
[18] Molton, P., Dandois, J., Lepage, A., Brunet, V. & Bur, R.2013Control of buffet phenomenon on a transonic swept wing. AIAA J.51, 761-772.
[19] Ohmichi, Y., Ishida, T. & Hashimoto, A.2017 Numerical investigation of transonic buffet on a three-dimensional wing using incremental mode decomposition. AIAA Paper 2017-1436.
[20] Plante, F., Laurendeau, E., Dandois, J. & Sartor, F.2017 Study of three-dimensional transonic buffet on swept wings. AIAA Paper 2017-3903.
[21] Plante, F., Dandois, J. & Laurendeau, E.2019 Similitude between 3D cellular patterns in transonic buffet and subsonic stall. AIAA Paper 2019-0300.
[22] Poplingher, L. & Raveh, D. E.2018 Modal analysis of transonic shock buffet on 2D airfoil. AIAA Paper 2018-2910.
[23] Rodriguez, D. & Theofilis, V.2011On the birth of stall cells on airfoils. Theor. Comput. Fluid Dyn.25, 105-117. · Zbl 1272.76124
[24] Roe, P. L.1981Approximate Riemann solvers, parameters vectors and difference schemes. J. Comput. Phys.43, 357-372. · Zbl 0474.65066
[25] Sartor, F., Mettot, C. & Sipp, D.2015Stability, receptivity and sensitivity analysis of buffeting transonic flow over a profile. AIAA J.53, 1980-1993.
[26] Sartor, F. & Timme, S.2017Delayed detached-eddy simulation on shock buffet on half wing-body configuration. AIAA J.55, 1230-1240.
[27] Shur, M., Spalart, P. R., Squires, K. D., Strelets, M. & Travin, A.2000Three-dimensionality in Reynolds-averaged Navier-Stokes solutions around two-dimensional geometries. AIAA J.43, 1230-1242.
[28] Shur, M., Strelets, M. & Travin, A.2004High-order implicit multi-block Navier-Stokes code: ten-years experience of application to RANS/DES/LES/DNS of turbulent flows. In 7th Symposium on Overset Composite Grids and Solution Technology.
[29] Spalart, P. R.2000 Trends in turbulence treatments. AIAA Paper 2000-2306.
[30] Spalart, P. R. & Allmaras, S. R.1994A one-equation turbulence model for aerodynamic flows. La Recherche Aérospatiale1, 5-21; also AIAA Paper 92-0439.
[31] Spalart, P. R., Belyaev, K., Garbaruk, A., Shur, M., Strelets, M. & Travin, A.2017Large-eddy and direct numerical simulations of the Bachalo-Johnson flow with shock-induced separation. Flow Turbul. Combust.39, 865-885.
[32] Spalart, P. R., Strelets, M. & Travin, A.2006Direct numerical simulation of large-eddy-break-up devices in a boundary layer. Intl J. Heat Fluid Flow27, 902-910.
[33] Sugioka, Y., Koike, S., Nakakita, K., Numata, D., Nonomura, T. & Asai, K.2018Experimental analysis of transonic buffet on a 3D swept wing using fast-response pressure-sensitive paint. Exp. Fluids59, 108, 1-20.
[34] Theofilis, V.2011Global linear instability. Annu. Rev. Fluid Mech.43, 319-352. · Zbl 1299.76074
[35] Thiery, M. & Coustols, E.2006Numerical prediction of shock induced oscillations over a 2D airfoil: influence of turbulence modeling and test section walls. Intl J. Heat Fluid Flow27, 661-670.
[36] Timme, S.2018 Global instability of wing shock buffet. Arxiv e-prints, arXiv:1806.07299 (physics.flu-dyn).
[37] Timme, S.2019 Global shock buffet instability on NASA common research model. AIAA Paper 2019-0037.
[38] Zebib, A.1987Stability of viscous flow past a circular cylinder. J. Engng Maths21, 155-165. · Zbl 0632.76063
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.