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On the aeroelastic bifurcation of a flexible panel subjected to cavity pressure and inviscid oblique shock

Published online by Cambridge University Press:  10 May 2024

Yifan Zhang Open the ORCID record for Yifan Zhang [Opens in a new window] ,
Kun Ye Open the ORCID record for Kun Ye [Opens in a new window]  and
Zhengyin Ye
Yifan Zhang
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, PR China National Key Laboratory of Aircraft Configuration Design, Xi'an 710072, PR China
Kun Ye*
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, PR China National Key Laboratory of Aircraft Configuration Design, Xi'an 710072, PR China
Zhengyin Ye
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, PR China National Key Laboratory of Aircraft Configuration Design, Xi'an 710072, PR China
*
†Email address for correspondence: yekun@nwpu.edu.cn
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Abstract

The aeroelasticity of a panel in the presence of a shock is a fundamental issue of great significance in the development of hypersonic vehicles. In practical engineering, cavity pressure emerges as a crucial factor that influences the nonlinear dynamical characteristics of the panel. This study focuses on the aeroelastic bifurcation of a flexible panel subjected to both cavity pressure and oblique shock. To this end, a computational method is devised, coupling a high-fidelity reduced-order model for unsteady aerodynamic loads with nonlinear structural equations. The solution is meticulously tracked by continuous calculations. The obtained results indicate that cavity pressure plays a pivotal role in determining the bifurcation and stability characteristics of the system. First, the system exhibits hysteresis behaviour in response to the ascending and descending dynamic pressures. The evolution of hysteresis behaviour originates from the phenomenon of cusp catastrophe. Second, variations in cavity pressure induce three types of bifurcation phenomena, exhibiting characteristics akin to supercritical Hopf bifurcation, subcritical Hopf bifurcation and saddle-node bifurcation of cycles. The system's response at the critical points of these bifurcations manifests as long-period asymptotic flutter or explosive flutter. Lastly, the evolution of the dynamical system among these three types of bifurcations is an important factor contributing to the discrepancies observed in certain research results. This study enhances the understanding of the nonlinear dynamical behaviour of panel aeroelasticity in complex practical environments and provides new explanations for the discrepancies observed in certain research results.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 986 , 10 May 2024 , A28
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

An, X., Deng, B., Feng, J. & Qu, Y. 2021 Analysis of nonlinear aeroelastic response of curved panels under shock impingements. J. Fluids Struct. 107, 103404.10.1016/j.jfluidstructs.2021.103404CrossRefGoogle Scholar
Arnold, V.I. 2003 Catastrophe Theory, 3rd edn. Springer Science & Business Media.Google Scholar
Balajewicz, M. & Dowell, E.H. 2012 Reduced-order modeling of flutter and limit-cycle oscillations using the sparse Volterra series. J. Aircraft 49 (6), 1803–1812.CrossRefGoogle Scholar
Bhattrai, S., McQuellin, L.P., Currao, G.M.D., Neely, A.J. & Buttsworth, D.R. 2022 Experimental study of aeroelastic response and performance of a hypersonic intake ramp. J. Propul. Power 38 (1), 157–170.10.2514/1.B38348CrossRefGoogle Scholar
Böttcher, L., Nagler, J. & Herrmann, H.J. 2017 Critical behaviors in contagion dynamics. Phys. Rev. Lett. 118 (8), 088301.10.1103/PhysRevLett.118.088301CrossRefGoogle ScholarPubMed
Boyer, N.R., McNamara, J.J., Gaitonde, D.V., Barnes, C.J. & Visbal, M.R. 2018 Features of shock-induced panel flutter in three-dimensional inviscid flow. J. Fluids Struct. 83, 490–506.10.1016/j.jfluidstructs.2018.10.001CrossRefGoogle Scholar
Boyer, N.R., McNamara, J.J., Gaitonde, D.V., Barnes, C.J. & Visbal, M.R. 2021 Features of panel flutter response to shock boundary layer interactions. J. Fluids Struct. 101, 103207.10.1016/j.jfluidstructs.2020.103207CrossRefGoogle Scholar
Brouwer, K.R., Gogulapati, A. & McNamara, J.J. 2017 Interplay of surface deformation and shock-induced separation in shock/boundary-layer interactions. AIAA J. 55 (12), 4258–4273.CrossRefGoogle Scholar
Brouwer, K.R. & McNamara, J.J. 2019 Enriched piston theory for expedient aeroelastic loads prediction in the presence of shock impingements. AIAA J. 57 (3), 1288–1302.10.2514/1.J057595CrossRefGoogle Scholar
Brouwer, K.R., Perez, R.A., Beberniss, T.J., Spottswood, S.M. & Ehrhardt, D.A. 2021 Experiments on a thin panel excited by turbulent flow and shock/boundary-layer interactions. AIAA J. 59 (7), 2737–2752.10.2514/1.J060114CrossRefGoogle Scholar
Brouwer, K.R., Perez, R.A., Beberniss, T.J., Spottswood, S.M. & Ehrhardt, D.A. 2022 Evaluation of reduced-order aeroelastic simulations for shock-dominated flows. J. Fluids Struct. 108, 103429.10.1016/j.jfluidstructs.2021.103429CrossRefGoogle Scholar
Cheng, Z., Lien, F., Dowell, E.H., Yee, E., Wang, R. & Zhang, J. 2023 Critical effect of fore-aft tapering on galloping triggering for a trapezoidal body. J. Fluid Mech. 967, A18.10.1017/jfm.2023.477CrossRefGoogle Scholar
Daub, D., Willems, S. & Gülhan, A. 2016 Experiments on the interaction of a fast-moving shock with an elastic panel. AIAA J. 54 (2), 670–678.CrossRefGoogle Scholar
Dowell, E.H. 1966 Nonlinear oscillations of a fluttering plate. AIAA J. 4 (7), 1267–1275.10.2514/3.3658CrossRefGoogle Scholar
Dowell, E.H. 1970 Panel flutter: a review of the aeroelastic stability of plates and shells. AIAA J. 8 (3), 385–399.10.2514/3.5680CrossRefGoogle Scholar
Dowell, E.H. 1974 Aeroelasticity of Plates and Shells. Springer Science & Business Media.Google Scholar
Dowell, E.H. 1982 Flutter of a buckled plate as an example of chaotic motion of a deterministic autonomous system. J. Sound Vib. 85 (3), 333–344.10.1016/0022-460X(82)90259-0CrossRefGoogle Scholar
Dowell, E.H. 2015 A Modern Course in Aeroelasticity, 5th edn. Springer-Verlag.Google Scholar
Gao, C. & Zhang, W. 2020 Transonic aeroelasticity: a new perspective from the fluid mode. Prog. Aerosp. Sci. 113, 100596.CrossRefGoogle Scholar
Gao, C., Zhang, W., Li, X., Liu, Y., Quan, J., Ye, Z. & Jiang, Y. 2017 Mechanism of frequency lock-in in transonic buffeting flow. J. Fluid Mech. 818, 528–561.CrossRefGoogle Scholar
Gordnier, R.E. & Visbal, M.R. 2002 Development of a three-dimensional viscous aeroelastic solver for nonlinear panel flutter. J. Fluids Struct. 16 (4), 497–527.10.1006/jfls.2000.0434CrossRefGoogle Scholar
Gramola, M., Bruce, P.J. & Santer, M.J. 2020 Response of a 3D flexible panel to shock impingement with control of cavity pressure. AIAA Paper 2020-0314.CrossRefGoogle Scholar
He, Y., Shi, A., Dowell, E.H. & Li, X. 2022 Panel aeroelastic stability in irregular shock reflection. AIAA J. 60 (11), 6490–6499.10.2514/1.J061902CrossRefGoogle Scholar
Holmes, P.J. 1977 Bifurcations to divergence and flutter in flow-induced oscillations: a finite dimensional analysis. J. Sound Vib. 53 (4), 471–503.10.1016/0022-460X(77)90521-1CrossRefGoogle Scholar
Khalil, H.K. 2002 Nonlinear Systems, 3rd edn. Prentice Hall.Google Scholar
Li, P., Yang, Y., Xu, W. & Chen, G. 2012 On the aeroelastic stability and bifurcation structure of subsonic nonlinear thin panels subjected to external excitation. Arch. Appl. Mech. 82, 1251–1267.10.1007/s00419-012-0618-4CrossRefGoogle Scholar
Li, Y., Luo, H., Chen, X. & Xu, J. 2019 Laminar boundary layer separation over a fluttering panel induced by an oblique shock wave. J. Fluids Struct. 90, 90–109.CrossRefGoogle Scholar
Liu, L. & Dowell, E.H. 2004 The secondary bifurcation of an aeroelastic airfoil motion: effect of high harmonics. Nonlinear Dyn. 37, 31–49.CrossRefGoogle Scholar
Liu, W., Wu, Y., Li, Y. & Chen, X. 2022 Effect of cavity pressure on shock train behavior and panel aeroelasticity in an isolator. Phys. Fluids 34 (12), 126101.10.1063/5.0123724CrossRefGoogle Scholar
Ljung, L. 1999 System Identification, 2nd edn. Springer.Google Scholar
Lopez, J.M. 1994 On the bifurcation structure of axisymmetric vortex breakdown in a constricted pipe. Phys. Fluids 6 (11), 3683–3693.10.1063/1.868359CrossRefGoogle Scholar
Lucia, D.J., Beran, P.S. & Silva, W.A. 2004 Reduced-order modeling: new approaches for computational physics. Prog. Aerosp. Sci. 40 (1–2), 51–117.10.1016/j.paerosci.2003.12.001CrossRefGoogle Scholar
Matsuo, K., Miyazato, Y. & Kim, H. 1999 Shock train and pseudo-shock phenomena in internal gas flows. Prog. Aerosp. Sci. 35 (1), 33–100.10.1016/S0376-0421(98)00011-6CrossRefGoogle Scholar
McNamara, J.J. & Friedmann, P.P. 2011 Aeroelastic and aerothermoelastic analysis in hypersonic flow: past, present, and future. AIAA J. 49 (6), 1089–1122.10.2514/1.J050882CrossRefGoogle Scholar
Mei, C., Abdel-Motagaly, K. & Chen, R. 1999 Review of nonlinear panel flutter at supersonic and hypersonic speeds. Appl. Mech. Rev. 52 (10), 497–527.10.1115/1.3098919CrossRefGoogle Scholar
Menon, K. & Mittal, R. 2021 On the initiation and sustenance of flow-induced vibration of cylinders: insights from force partitioning. J. Fluid Mech. 907, A37.CrossRefGoogle Scholar
Moré, J.J. & Sorensen, D.C. 1983 Computing a trust region step. SIAM J. Sci. Stat. Comput. 4 (3), 553–572.10.1137/0904038CrossRefGoogle Scholar
Morse, T.L. & Williamson, C.H.K. 2009 Prediction of vortex-induced vibration response by employing controlled motion. J. Fluid Mech. 634, 5–39.CrossRefGoogle Scholar
Oppenheim, A.V. & Schafer, R.W. 2010 Discrete-Time Signal Processing, 3rd edn. Pearson Higher Education.Google Scholar
Pasche, S., Avellan, F. & Gallaire, F. 2021 Vortex impingement onto an axisymmetric obstacle–subcritical bifurcation to vortex breakdown. J. Fluid Mech. 910, A36.10.1017/jfm.2020.1011CrossRefGoogle Scholar
Raveh, D.E. 2001 Reduced-order models for nonlinear unsteady aerodynamics. AIAA J. 39 (8), 1417–1429.10.2514/2.1473CrossRefGoogle Scholar
Raveh, D.E. 2004 Identification of computational-fluid-dynamics based unsteady aerodynamic models for aeroelastic analysis. J. Aircraft 41 (3), 620–632.CrossRefGoogle Scholar
Shinde, V., McNamara, J.J. & Gaitonde, D. 2022 Dynamic interaction between shock wave turbulent boundary layer and flexible panel. J. Fluids Struct. 113, 103660.CrossRefGoogle Scholar
Shinde, V., McNamara, J.J., Gaitonde, D., Barnes, C. & Visbal, M.R. 2019 Transitional shock wave boundary layer interaction over a flexible panel. J. Fluids Struct. 90, 263–285.CrossRefGoogle Scholar
Shukla, P. & Alam, M. 2011 Nonlinear stability and patterns in granular plane Couette flow: Hopf and pitchfork bifurcations, and evidence for resonance. J. Fluid Mech. 672, 147–195.10.1017/S002211201000594XCrossRefGoogle Scholar
Silva, W.A. 1993 Application of nonlinear systems theory to transonic unsteady aerodynamic responses. J. Aircraft 30 (5), 660–668.CrossRefGoogle Scholar
Silva, W.A. 2005 Identification of nonlinear aeroelastic systems based on the Volterra theory: progress and opportunities. Nonlinear Dyn. 39, 25–62.CrossRefGoogle Scholar
Silva, W.A. & Bartels, R.E. 2004 Development of reduced-order models for aeroelastic analysis and flutter prediction using the CFL3Dv6.0 code. J. Fluids Struct. 19 (6), 729–745.CrossRefGoogle Scholar
Sjöberg, J., Zhang, Q., Ljung, L., Benveniste, A., Delyon, B., Glorennec, P., Hjalmarsson, H. & Juditsky, A. 1995 Nonlinear black-box modeling in system identification: a unified overview. Automatica 31 (12), 1691–1724.CrossRefGoogle Scholar
Spottswood, S.M., Beberniss, T.J., Eason, T.G., Perez, R.A., Donbar, J.M., Ehrhardt, D.A. & Riley, Z.B. 2019 Exploring the response of a thin, flexible panel to shock-turbulent boundary-layer interactions. J. Sound Vib. 443, 74–89.10.1016/j.jsv.2018.11.035CrossRefGoogle Scholar
Spottswood, S.M., Eason, T. & Beberniss, T. 2013 Full-field, dynamic pressure and displacement measurements of a panel excited by shock boundary-layer interaction. AIAA Paper 2013-2016.Google Scholar
Strogatz, S.H. 2018 Nonlinear Dynamics and Chaos, 2nd edn. CRC Press.CrossRefGoogle Scholar
Subramanian, P., Sujith, R.I. & Wahi, P. 2013 Subcritical bifurcation and bistability in thermoacoustic systems. J. Fluid Mech. 715, 210–238.CrossRefGoogle Scholar
Urzay, J. 2018 Supersonic combustion in air-breathing propulsion systems for hypersonic flight. Annu. Rev. Fluid Mech. 50, 593–627.CrossRefGoogle Scholar
Visbal, M.R. 2012 On the interaction of an oblique shock with a flexible panel. J. Fluids Struct. 30, 219–225.CrossRefGoogle Scholar
Visbal, M.R. 2014 Viscous and inviscid interactions of an oblique shock with a flexible panel. J. Fluids Struct. 48, 27–45.10.1016/j.jfluidstructs.2014.02.003CrossRefGoogle Scholar
Wei, W. & Yabuno, H. 2019 Subcritical Hopf and saddle-node bifurcations in hunting motion caused by cubic and quintic nonlinearities: experimental identification of nonlinearities in a roller rig. Nonlinear Dyn. 98, 657–670.CrossRefGoogle Scholar
Willems, S., Gülhan, A. & Esser, B. 2013 Shock induced fluid-structure interaction on a flexible wall in supersonic turbulent flow. Prog. Flight Phys. 5, 285–308.10.1051/eucass/201305285CrossRefGoogle Scholar
Ye, K., Zhang, Y., Chen, Z. & Ye, Z. 2022 Numerical investigation of aeroelastic characteristics of grid fin. AIAA J. 60 (5), 3107–3121.CrossRefGoogle Scholar
Ye, L. & Ye, Z. 2018 Effects of shock location on aeroelastic stability of flexible panel. AIAA J. 56 (9), 3732–3744.10.2514/1.J056924CrossRefGoogle Scholar
Ye, L. & Ye, Z. 2021 Theoretical analysis for the effect of static pressure differential on aeroelastic stability of flexible panel. Aerosp. Sci. Technol. 109, 106428.10.1016/j.ast.2020.106428CrossRefGoogle Scholar
Zhang, W., Jiang, Y. & Ye, Z. 2007 Two better loosely coupled solution algorithms of CFD based aeroelastic simulation. Engng Appl. Comput. Fluid Mech. 1 (4), 253–262.Google Scholar
Zhu, Y., Su, Y. & Breuer, K. 2020 Nonlinear flow-induced instability of an elastically mounted pitching wing. J. Fluid Mech. 899, A35.CrossRefGoogle Scholar
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