Technical Papers
Aug 14, 2024

Transonic Buffet in Flow Past a Low-Reynolds-Number Airfoil

Publication: Journal of Aerospace Engineering
Volume 37, Issue 6

Abstract

For propeller-driven Mars airplanes operating at low Reynolds numbers, the speed of the rotor tips may reach transonic. To date, only a few studies have investigated the transonic buffet in flow past low-Reynolds-number airfoils. In this study, direct numerical simulations of high-speed flow (M=0.2, 0.6, and 0.8) past a NACA 0012 airfoil are performed with a low Reynolds number of Rec=23,000, where transonic buffet is observed at M=0.8. We first investigated the effects of Mach number on the aerodynamic performance and flow fields. Dynamic mode decomposition (DMD) and linear stability analysis (LSA) are used to analyze the flow instability mechanisms of the transonic buffet. Results showed that the multiple high-frequency oscillations are related to the vortex shedding at the trailing edge of the airfoil, and the low-frequency oscillation is caused by Type C shock motions. Both of them are confirmed to be self-sustained in feedback cycles.

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Data Availability Statement

Some or all data, models, or code generated or used during the study are proprietary or confidential in nature and may only be provided with restrictions.

Acknowledgments

The funding support of the National Natural Science Foundation of China (Grant No. 12372221) is acknowledged.

References

Almutairi, J., I. Alqadi, and E. Eljack. 2015. “Large eddy simulation of a NACA-0012 airfoil near stall.” In Direct and Large-Eddy simulation IX, 389–395. Cham, Switzerland: Springer.
Almutairi, J. H., L. E. Jones, and N. D. Sandham. 2010. “Intermittent bursting of a laminar separation bubble on an airfoil.” AIAA J. 48 (2): 414–426. https://doi.org/10.2514/1.44298.
Amiet, R. K. 1976. “Noise due to turbulent flow past a trailing edge.” J. Sound Vib. 47 (3): 387–393. https://doi.org/10.1016/0022-460X(76)90948-2.
Anyoji, M., T. Nonomura, H. Aono, A. Oyama, K. Fujii, H. Nagai, and K. Asai. 2014. “Computational and experimental analysis of a high-performance airfoil under low-Reynolds-number flow condition.” J. Aircr. 51 (6): 1864–1872. https://doi.org/10.2514/1.C032553.
Anyoji, M., D. Numata, H. Nagai, and K. Asai. 2015. “Effects of Mach number and specific heat ratio on low-Reynolds-number airfoil flows.” AIAA J. 53 (6): 1640–1654. https://doi.org/10.2514/1.J053468.
Aono, H., K. Kondo, T. Nonomura, M. Anyoji, and M. Yamamoto. 2020. “Aerodynamics of owl-like wing model at low Reynolds numbers.” Trans. Jpn. Soc. Aeronaut. Space Sci. 63 (1): 8–17. https://doi.org/10.2322/tjsass.63.8.
Arbey, H., and J. Bataille. 1983. “Noise generated by airfoil profiles placed in a uniform laminar flow.” J. Fluid Mech. 134 (1): 33–47. https://doi.org/10.1017/S0022112083003201.
Arcondoulis, E. J. G., C. J. Doolan, L. A. Brooks, and A. C. Zander. 2012. “On the generation of airfoil tonal noise at zero angle of attack and low to moderate Reynolds number.” In Proc., 18th AIAA/CEAS Aeroacoustics Conf. (33rd AIAA Aeroacoustics Conf.). Reston, VA: American Institute of Aeronautics and Astronautics.
Bendiksen, O. O. 2011. “Review of unsteady transonic aerodynamics: Theory and applications.” Prog. Aerosp. Sci. 47 (2): 135–167. https://doi.org/10.1016/j.paerosci.2010.07.001.
Bouhadji, A., and M. Braza. 2003a. “Organised modes and shock-vortex interaction in unsteady viscous transonic flows around an aerofoil: Part I: Mach number effect.” Comput. Fluids 32 (9): 1233–1260. https://doi.org/10.1016/S0045-7930(02)00100-7.
Bouhadji, A., and M. Braza. 2003b. “Organised modes and shock–vortex interaction in unsteady viscous transonic flows around an aerofoil: Part II: Reynolds number effect.” Comput. Fluids 32 (9): 1261–1281. https://doi.org/10.1016/S0045-7930(02)00101-9.
Brion, V., J. Dandois, J. Abart, and P. Paillart. 2017. “Experimental analysis of the shock dynamics on a transonic laminar airfoil.” Prog. Flight Phys. 9 (9): 365–386.
Brion, V., J. Dandois, R. Mayer, P. Reijasse, T. Lutz, and L. Jacquin. 2020. “Laminar buffet and flow control.” Proc. Inst. Mech. Eng. Part G: J. Aerosp. Eng. 234 (1): 124–139. https://doi.org/10.1177/0954410018824516.
Chen, B., X. Qiang, F. Wu, M. Yang, and W. Li. 2024. “Implicit large-eddy simulation of an over-expanded screeching rectangular jet.” Chinese J. Aeronaut. https://doi.org/10.1016/j.cja.2024.03.015.
Crouch, J. D., A. Garbaruk, and D. Magidov. 2007. “Predicting the onset of flow unsteadiness based on global instability.” J. Comput. Phys. 224 (2): 924–940. https://doi.org/10.1016/j.jcp.2006.10.035.
Crouch, J. D., A. Garbaruk, D. Magidov, and L. Jacquin. 2009a. “Global structure of buffeting flow on transonic airfoils.” In Proc., IUTAM Symp. on Unsteady Separated Flows and their Control, 297–306. Berlin: Springer.
Crouch, J. D., A. Garbaruk, D. Magidov, and A. Travin. 2009b. “Origin of transonic buffet on aerofoils.” J. Fluid Mech. 628 (Jun): 357–369. https://doi.org/10.1017/S0022112009006673.
Crouch, J. D., A. Garbaruk, and M. Strelets. 2019. “Global instability in the onset of transonic-wing buffet.” J. Fluid Mech. 881 (Dec): 3–22. https://doi.org/10.1017/jfm.2019.748.
Dandois, J., I. Mary, and V. Brion. 2018. “Large-eddy simulation of laminar transonic buffet.” J. Fluid Mech. 850 (Sep): 156–178. https://doi.org/10.1017/jfm.2018.470.
Elawad, Y. A., and E. M. Eljack. 2019. “Numerical investigation of the low-frequency flow oscillation over a NACA-0012 aerofoil at the inception of stall.” Int. J. Micro Air Veh. 11 (Apr): 1–17. https://doi.org/10.1177/1756829319833687.
Fukushima, Y., and S. Kawai. 2018. “Wall-modeled large-eddy simulation of transonic airfoil buffet at high Reynolds number.” AIAA J. 56 (6): 2372–2388. https://doi.org/10.2514/1.J056537.
Fukushima, Y., and S. Kawai. 2019. “Self-sustained shock-wave oscillation mechanisms of transonic airfoil buffet.” In Proc., AIAA Scitech Forum. Reston, VA: American Institute of Aeronautics and Astronautics.
Garnier, E., and S. Deck. 2010. “Large-eddy simulation of transonic buffet over a supercritical airfoil.” In Proc., Seventh Int. ERCOFTAC Workshop on Direct and Large-Eddy Simulation VII, held at the University of Trieste, 549–554. Cham, Switzerland: Springer.
Giannelis, N. F., G. A. Vio, and O. Levinski. 2017. “A review of recent developments in the understanding of transonic shock buffet.” Prog. Aerosp. Sci. 92 (Jul): 39–84. https://doi.org/10.1016/j.paerosci.2017.05.004.
Hartmann, A., A. Feldhusen, and W. Schröder. 2013. “On the interaction of shock waves and sound waves in transonic buffet flow.” Phys. Fluids 25 (2): 026101. https://doi.org/10.1063/1.4791603.
Hilton, W. F., and R. G. Fowler. 1947. Photographs of shock wave movement. NPL R&M No. 2692. New Delhi, India: National Physical Laboratories.
Hua, S., J. Li, and C. Liu. 2005. “Direct numerical simulation of flow separation around a NACA 0012 airfoil.” Comput. Fluids 34 (9): 1096–1114. https://doi.org/10.1016/j.compfluid.2004.09.003.
Huang, R. F., and C. L. Lin. 1995. “Vortex shedding and shear-layer instability of wing at low-Reynolds numbers.” AIAA J. 33 (8): 1398–1403. https://doi.org/10.2514/3.12561.
Iovnovich, M., and D. E. Raveh. 2012. “Reynolds-averaged Navier-Stokes study of the shock-buffet instability mechanism.” AIAA J. 50 (4): 880–890. https://doi.org/10.2514/1.J051329.
Jacquin, L., P. Molton, S. Deck, B. Maury, and D. Soulevant. 2009. “Experimental study of shock oscillation over a transonic supercritical profile.” AIAA J. 47 (9): 1985–1994. https://doi.org/10.2514/1.30190.
Jonathan, H. T., W. R. Clarence, M. L. Dirk, L. B. Steven, and J. N. Kutz. 2014. “On dynamic mode decomposition: Theory and applications.” J. Comput. Dyn. 1 (2): 391–421. https://doi.org/10.3934/jcd.2014.1.391.
Jones, L. E. 2008. “Numerical studies of the flow around an airfoil at low Reynolds number.” Doctoral dissertation, School of Engineering Sciences, Univ. of Southampton.
Kingan, M. J., and J. R. Pearse. 2009. “Laminar boundary layer instability noise produced by an aerofoil.” J. Sound Vib. 322 (4–5): 808–828. https://doi.org/10.1016/j.jsv.2008.11.043.
Kojima, R., T. Nonomura, A. Oyama, and K. Fujii. 2013. “Large-Eddy simulation of low-Reynolds-number flow over thick and thin NACA airfoils.” J. Aircr. 50 (1): 187–196. https://doi.org/10.2514/1.C031849.
Kojima, Y., C. A. Yeh, K. Taira, and M. Kameda. 2020. “Resolvent analysis on the origin of two-dimensional transonic buffet.” J. Fluid Mech. 885 (Feb): R1. https://doi.org/10.1017/jfm.2019.992.
Koning, W. J., E. A. Romander, and W. Johnson. 2020. “Optimization of low Reynolds number airfoils for Martian rotor applications using an evolutionary algorithm.” In Proc., AIAA Scitech Forum. Reston, VA: American Institute of Aeronautics and Astronautics.
Koning, W. J. F., W. Johnson, and H. F. Grip. 2019. “Improved mars helicopter aerodynamic rotor model for comprehensive analyses.” AIAA J. 57 (2): 1–10. https://doi.org/10.2514/1.J058045.
Kutz, J. N., S. L. Brunton, B. W. Brunton, and J. L. Proctor. 2016. Dynamic mode decomposition: Data-driven modeling of complex systems. Philadelphia: Society for Industrial and Applied Mathematics.
Laitone, E. V. 1997. “Wind tunnel tests of wings at Reynolds numbers below 70 000.” Exp. Fluids 23 (5): 405–409. https://doi.org/10.1007/s003480050128.
Lee, B. H. K. 1990. “Oscillatory shock motion caused by transonic shock boundary-layer interaction.” AIAA J. 28 (5): 942–944. https://doi.org/10.2514/3.25144.
Lee, B. H. K. 2001. “Self-sustained shock oscillations on airfoils at transonic speeds.” Prog. Aerosp. Sci. 37 (2): 147–196. https://doi.org/10.1016/S0376-0421(01)00003-3.
Lissaman, P. B. S. 2003. “Low-Reynolds-number airfoils.” Annu. Rev. Fluid Mech. 15 (1): 223–239. https://doi.org/10.1146/annurev.fl.15.010183.001255.
Nishida, H., and T. Nonomura. 2009. “ADI-SGS scheme on ideal magnetohydrodynamics.” J. Comput. Phys. 228 (9): 3182–3188. https://doi.org/10.1016/j.jcp.2009.01.032.
Nonomura, T., and K. Fujii. 2009. “Effects of difference scheme type in high-order weighted compact nonlinear schemes.” J. Comput. Phys. 228 (10): 3533–3539. https://doi.org/10.1016/j.jcp.2009.02.018.
Nonomura, T., N. Iizuka, and K. Fujii. 2010. “Freestream and vortex preservation properties of high-order WENO and WCNS on curvilinear grids.” Comput. Fluids 39 (2): 197–214. https://doi.org/10.1016/j.compfluid.2009.08.005.
Nonomura, T., W. Li, Y. Goto, and K. Fujii. 2011. “Efficiency improvements in seventh-order weighted compact nonlinear scheme.” CFD J. 18 (2): 180–186.
Oyama, A., and K. Fujii. 2013. “A study on airfoil design for future Mars airplane.” In Proc., 44th AIAA Aerospace Sciences Meeting and Exhibit. Reston, VA: American Institute of Aeronautics and Astronautics.
Pearcey, H. H. 1958. A method for the prediction of the onset of buffeting and other separation effects from wind tunnel tests on rigid models. Paris: North Atlantic Treaty Organization, Advisory Group for Aeronautical Research and Development.
Poplingher, L., and D. E. Raveh. 2023. “Comparative modal study of the two-dimensional and three-dimensional transonic shock buffet.” AIAA J. 61 (1): 125–144. https://doi.org/10.2514/1.J061797.
Sandberg, R. D., L. E. Jones, N. D. Sandham, and P. F. Joseph. 2009. “Direct numerical simulations of tonal noise generated by laminar flow past airfoils.” J. Sound Vib. 320 (4–5): 838–858. https://doi.org/10.1016/j.jsv.2008.09.003.
Sartor, F., C. Mettot, and D. Sipp. 2015. “Stability, receptivity, and sensitivity analyses of buffeting transonic flow over a profile.” AIAA J. 53 (7): 1980–1993. https://doi.org/10.2514/1.J053588.
Schlichting, H. 1968. Boundary layer theory. 6th ed. Berlin: Springer.
Schmid, P. J., and D. S. Henningson. 2001. Stability and transition in shear flows. New York: Springer.
Schmid, P. J., and J. Sesterhenn. 2010. “Dynamic mode decomposition of numerical and experimental data.” J. Fluid Mech. 656 (10): 5–28. https://doi.org/10.1017/S0022112010001217.
Taira, K., S. L. Brunton, S. T. M. Dawson, C. W. Rowley, T. Colonius, B. J. Mckeon, O. T. Schmidt, S. Gordeyev, V. Theofilis, and L. S. Ukeiley. 2017. “Modal analysis of fluid flows: An overview.” AIAA J. 55 (12): 4013–4041. https://doi.org/10.2514/1.J056060.
Tam, C. K. W. 1974. “Discrete tones of isolated airfoils.” J. Acoust. Soc. Am. 55 (6): 1173–1177. https://doi.org/10.1121/1.1914682.
Tijdeman, H. 1977. Investigations of the transonic flow around oscillating airfoils. Amsterdam, Netherlands: National Aerospace Lab.
Xiao, Q., H. M. Tsai, and L. Feng. 2006. “A numerical study of transonic buffet on a supercritical airfoil.” AIAA J. 44 (3): 620–628. https://doi.org/10.2514/1.16658.
Yonezawa, K., K. Abe, and S. Sunada. 2016. “Propeller design and loss mechanisms in low-Reynolds-number flows.” J. Propul. Power 32 (6): 1378–1385. https://doi.org/10.2514/1.B35854.
Zauner, M., N. De Tullio, and N. D. Sandham. 2018. “Direct numerical simulations of transonic flow around an airfoil at moderate Reynolds numbers.” AIAA J. 57 (2): 597–607. https://doi.org/10.2514/1.J057335.
Zauner, M., P. Moise, and N. Sandham. 2023. “On the co-existence of transonic buffet and separation-bubble modes for the OALT25 laminar-flow wing section.” Flow Turbul. Combust. 110 (4): 1023–1057. https://doi.org/10.1007/s10494-023-00415-4.
Zhang, Y., X. Wu, and W. Li. 2016. “Direct numerical simulations of tonal noise generation for a two dimensional airfoil at low and moderate Reynolds numbers.” In Proc., 46th AIAA Fluid Dynamics Conf. Reston, VA: American Institute of Aeronautics and Astronautics.

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Go to Journal of Aerospace Engineering
Journal of Aerospace Engineering
Volume 37Issue 6November 2024

History

Received: Nov 17, 2022
Accepted: May 28, 2024
Published online: Aug 14, 2024
Published in print: Nov 1, 2024
Discussion open until: Jan 14, 2025

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Ph.D. Candidate, School of Aeronautics and Astronautics, Shanghai Jiao Tong Univ., Shanghai 200240, China. Email: [email protected]
Professor, School of Aeronautics and Astronautics, Shanghai Jiao Tong Univ., Shanghai 200240, China (corresponding author). Email: [email protected]
Assistant Professor, Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125. ORCID: https://orcid.org/0000-0001-6789-6209. Email: [email protected]

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