Hostname: page-component-cb9f654ff-mnl9s Total loading time: 0 Render date: 2025-08-13T06:16:00.192Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of harmonic forcing on self-sustained oscillations in cavity flows at low Mach numbers: experiments and modelling

Published online by Cambridge University Press:  11 August 2025

Ashutosh Narayan Singh  and
Vineeth Nair Open the ORCID record for Vineeth Nair [Opens in a new window]
Ashutosh Narayan Singh
Affiliation:
Department of Aerospace Engineering, Indian Institute of technology Bombay, Mumbai, Maharashtra 400076, India
Vineeth Nair*
Affiliation:
Department of Aerospace Engineering, Indian Institute of technology Bombay, Mumbai, Maharashtra 400076, India
*
Corresponding author: Vineeth Nair, vineeth@aero.iitb.ac.in
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the effects of external harmonic forcing on flow through a duct with square cross-section containing two circular orifice plates – a double-orifice cavity – at an operating condition where self-sustained limit cycle oscillations are observed. When the oscillatory flow is periodically forced at a frequency $f_f$ near its natural frequency $f_n$ ($0.9\leqslant f_f /f_n \leqslant 1.1$), it undergoes lock-in and amplitude suppression through synchronous quenching. We observe phase-drifting (or phase-slipping) prior to lock-in that happens via a saddle-node bifurcation. However, when the flow system is forced far from its natural frequency ($0.8\leqslant f_f /f_n\leqslant 0.9$ and $1.1\leqslant f_f /f_n\leqslant 1.4$) lock-in happens via asynchronous quenching through a Neimark–Sacker bifurcation (torus death). In asynchronous quenching, phase-drifting and phase-trapping are observed before lock-in. An asymmetry is present in the synchronization map on forcing either side of the natural frequency, which becomes more pronounced in the asynchronous quenching regime. There is also an observed saturation of the synchronization map for $f_f/f_n\gt 1$ over the range of frequencies explored. Subharmonic synchronization or $1:2$ lock-in with period-two oscillations is also observed when the system is forced near $f_n/2$ ($ 0.49 \leqslant f_f /f_n \leqslant 0.51$). The route to lock-in consists of a three frequency regime where subharmonics of the forcing frequency ($f_f/2$ and $f_f/3$) play an important role in the dynamics. The transition from $1:1$ to $1:2$ lock-in occurs via a de-lock-in regime ($ 0.55 \leqslant f_f /f_n \leqslant 0.65$), where a lock-in boundary is present; i.e. the system delocks after lock-in if the amplitude is raised beyond a critical value. The de-lock-in regime is also characterized by a nonlinear phase drift after de-lock-in and a significant jump in the forcing amplitude for lock-in for $f_f/f_n=0.6$. Amplification is observed for $f_f/f_n\gt 1$ and also in the $1:2$ lock-in and de-lock-in regimes where the total signal power exceeds the unforced system’s power for small increases in forcing amplitude after lock-in. Based on these results, we identify the asynchronous quenching regime for $f_f/f_n\lt 1$ as the optimal frequency range where active control is most effective. Finally, we introduce a reduced-order phenomenological model based on vortex–acoustic interaction dynamics from first principles. The model correctly identifies the four regimes, their dynamics leading to lock-in, and asymmetry and saturation in the synchronization map.

JFM classification

Acoustics: Aeroacoustics Nonlinear Dynamical Systems: Low-dimensional models Vortex Flows: Vortex shedding

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1017 , 25 August 2025 , A4
Check for updates
Copyright
© The Author(s), 2025. Published by 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.)

Article purchase

Temporarily unavailable

References

Abel, M., Ahnert, K. & Bergweiler, S. 2009 Synchronization of sound sources. Phys. Rev. Lett. 103 (11), 114301.10.1103/PhysRevLett.103.114301CrossRefGoogle ScholarPubMed
Anderson, A.B.C. 1954 A jet-tone orifice number for orifices of small thickness-diameter ratio. J. Acoust. Soc. Am. 26 (1), 21–25.10.1121/1.1907284CrossRefGoogle Scholar
Anderson, A.B.C. 1955 Metastable jet-tone states of jets from sharp-edged, circular, pipe-like orifices. J. Acoust. Soc. Am. 27 (1), 13–21.10.1121/1.1907475CrossRefGoogle Scholar
Anishchenko, V., Nikolaev, S. & Kurths, J. 2008 Bifurcational mechanisms of synchronization of a resonant limit cycle on a two-dimensional torus. Chaos 18 (3), 037123.10.1063/1.2949929CrossRefGoogle ScholarPubMed
Anishchenko, V.S., Safonova, M.A., Feudel, U. & Kurths, J. 1994 Bifurcations and transition to chaos through three-dimensional tori. Intl J. Bifurcation Chaos 4 (03), 595–607.10.1142/S0218127494000423CrossRefGoogle Scholar
Arnold, V.I. 2009 Small denominators. (i) mapping of the circumference onto itself. In Arnold-Collected Works: Representations of Functions, Celestial Mechanics and KAM Theory, 1957-1965, vol. 1, pp. 152–223. Springer Science & Business Media.10.1007/978-3-642-01742-1_10CrossRefGoogle Scholar
Baines, N.C. 2005 Fundamentals of Turbocharging. Concepts NREC.Google Scholar
Balanov, A., Janson, N., Postnov, D. & Sosnovtseva, O. 2009 Synchronization: from Simple to Complex. Springer.Google Scholar
Balusamy, S., Li, L.K.B., Han, Z., Juniper, M.P. & Hochgreb, S. 2015 Nonlinear dynamics of a self-excited thermoacoustic system subjected to acoustic forcing. Proc. Combust. Inst. 35 (3), 3229–3236.10.1016/j.proci.2014.05.029CrossRefGoogle Scholar
Barbi, C., Favier, D.P., Maresca, C.A. & Telionis, D.P. 1986 Vortex shedding and lock-on of a circular cylinder in oscillatory flow. J. Fluid Mech. 170, 527–544.10.1017/S0022112086001003CrossRefGoogle Scholar
Bauerheim, M., Boujo, E. & Noiray, N. 2020 Numerical analysis of the linear and nonlinear vortex-sound interaction in a T-junction. In AIAA 2020-2569. AIAA AVIATION 2020 FORUM.10.2514/6.2020-2569CrossRefGoogle Scholar
Bellows, B.D., Hreiz, A. & Lieuwen, T. 2008 Nonlinear interactions between forced and self-excited acoustic oscillations in premixed combustor. J. Propul. Power 24 (3), 628–631.10.2514/1.33228CrossRefGoogle Scholar
Bhavi, R.S., Pavithran, I. & Sujith, R.I. 2024 Dynamical states associated with the shift in whistling frequency in aeroacoustic system. J. Sound Vib. 592, 118606.10.1016/j.jsv.2024.118606CrossRefGoogle Scholar
Blevins, R.D. 1985 The effect of sound on vortex shedding from cylinders. J. Fluid Mech. 161, 217–237.10.1017/S0022112085002890CrossRefGoogle Scholar
Borkowski, L., Perlikowski, P., Kapitaniak, T. & Stefanski, A. 2015 Experimental observation of three-frequency quasiperiodic solution in a ring of unidirectionally coupled oscillators. Phys. Rev. E 91 (6), 062906.10.1103/PhysRevE.91.062906CrossRefGoogle Scholar
Boujo, E., Bourquard, C., Xiong, Y. & Noiray, N. 2020 Processing time-series of randomly forced self-oscillators: the example of beer bottle whistling. J. Sound Vib. 464, 114981.10.1016/j.jsv.2019.114981CrossRefGoogle Scholar
Bourquard, C., Faure-Beaulieu, A. & Noiray, N. 2021 Whistling of deep cavities subject to turbulent grazing flow: intermittently unstable aeroacoustic feedback. J. Fluid Mech. 909, A19.10.1017/jfm.2020.984CrossRefGoogle Scholar
Britto, A.B. & Mariappan, S. 2019 Lock-in phenomenon of vortex shedding in oscillatory flows: an analytical investigation pertaining to combustors. J. Fluid Mech. 872, 115–146.10.1017/jfm.2019.353CrossRefGoogle Scholar
Brown, R.S., Dunlap, R., Young, S.W. & Waugh, R.C. 1981 Vortex shedding as a source of acoustic energy in segmented solid rockets. J. Spacecr. Rockets 18 (4), 312–319.10.2514/3.57822CrossRefGoogle Scholar
Cao, L. 1997 Practical method for determining the minimum embedding dimension of a scalar time series. Physica D: Nonlinear Phenom. 110 (1–2), 43–50.10.1016/S0167-2789(97)00118-8CrossRefGoogle Scholar
Chanaud, R.C. & Powell, A. 1965 Some experiments concerning the hole and ring tone. J. Acoust. Soc. Am. 37 (5), 902–911.10.1121/1.1909476CrossRefGoogle Scholar
Culick, F.E.C. & Magiawala, K. 1979 Excitation of acoustic modes in a chamber by vortex shedding. J. Sound Vib. 64 (3), 455–457.10.1016/0022-460X(79)90591-1CrossRefGoogle Scholar
Dotson, K.W., Koshigoe, S. & Pace, K.K. 1997 Vortex shedding in a large solid rocket motor without inhibitors at the segment interfaces. J. Propul. Power 13 (2), 197–206.10.2514/2.5170CrossRefGoogle Scholar
Fraser, A.M. & Swinney, H.L. 1986 Independent coordinates for strange attractors from mutual information. Phys. Rev. A 33 (2), 1134.10.1103/PhysRevA.33.1134CrossRefGoogle ScholarPubMed
Giannakopoulos, K. & Deliyannis, T. 2001 Jump phenomenon in an OTA simulated LC circuit. Intl J. Electron. 88 (1), 1–11.10.1080/00207210150198239CrossRefGoogle Scholar
Gloerfelt, X. & Lafon, P. 2008 Direct computation of the noise induced by a turbulent flow through a diaphragm in a duct at low Mach number. Comput. Fluids 37 (4), 388–401.10.1016/j.compfluid.2007.02.004CrossRefGoogle Scholar
Gollub, J. & Benson, S.V. 1980 Many routes to turbulent convection. J. Fluid Mech. 100 (3), 449–470.10.1017/S0022112080001243CrossRefGoogle Scholar
Gottwald, G.A. & Melbourne, I. 2004 A new test for chaos in deterministic systems. Proc. R. Soc. Lond. Ser. A: Math. Phys. Engng Sci. 460 (2042), 603–611.10.1098/rspa.2003.1183CrossRefGoogle Scholar
Grassberger, P. & Procaccia, I. 1983 Characterization of strange attractors. Phys. Rev. Lett. 50 (5), 346.10.1103/PhysRevLett.50.346CrossRefGoogle Scholar
Guan, Y., Gupta, V., Kashinath, K. & Li, L.K.B. 2019 a Open-loop control of periodic thermoacoustic oscillations: experiments and low-order modelling in a synchronization framework. Proc. Combust. Inst. 37 (4), 5315–5323.10.1016/j.proci.2018.07.077CrossRefGoogle Scholar
Guan, Y., Gupta, V., Wan, M. & Li, L.K.B. 2019 b Forced synchronization of quasiperiodic oscillations in a thermoacoustic system. J. Fluid Mech. 879, 390–421.10.1017/jfm.2019.680CrossRefGoogle Scholar
Guan, Y., He, W., Murugesan, M., Li, Q., Liu, P. & Li, L.K.B. 2019 c Control of self-excited thermoacoustic oscillations using transient forcing, hysteresis and mode switching. Combust. Flame 202, 262–275.10.1016/j.combustflame.2019.01.013CrossRefGoogle Scholar
Guan, Y., Murugesan, M. & Li, L.K.B. 2018 Strange nonchaotic and chaotic attractors in a self-excited thermoacoustic oscillator subjected to external periodic forcing. Chaos Interdiscip. J. Nonlinear Sci. 28 (9).10.1063/1.5026252CrossRefGoogle Scholar
Guan, Y., Yin, B., Yang, Z.& Li, L.K.B. 2024 Forced synchronization of self-excited chaotic thermoacoustic oscillations. J. Fluid Mech. 982, A9.10.1017/jfm.2024.91CrossRefGoogle Scholar
Hearn, G. & Metcalfe, A. 1995 Spectral Analysis in Engineering: Concepts and Case Studies. Butterworth-Heinemann.Google Scholar
Heywood, J.B. 1988 Internal Combustion Engine Fundamentals. Mcgraw-hill.Google Scholar
Hirschberg, A. & Rienstra, S.W. 2004 An introduction to aeroacoustics. Eindhoven University of Technology.Google Scholar
Huerre, P. & Rossi, M. 1998 Hydrodynamic instabilities in open flows. In Hydrodynamics and Nonlinear Instabilities, (ed. C. Godrèche & P. Manneville), pp. 81–294. Cambridge University Press.10.1017/CBO9780511524608.004CrossRefGoogle Scholar
Jou, W.H. & Menon, S. 1990 Modes of oscillation in a nonreacting ramjet combustor flow. J. Propul. Power 6 (5), 535–543.10.2514/3.23253CrossRefGoogle Scholar
Juniper, M.P., Li, L.K.B. & Nichols, J.W. 2009 Forcing of self-excited round jet diffusion flames. Proc. Combust. Inst. 32 (1), 1191–1198.10.1016/j.proci.2008.05.065CrossRefGoogle Scholar
Kamin, M., Mathew, J. & Sujith, R.I. 2019 A numerical study of an acoustic–hydrodynamic system exhibiting an intermittent prelude to instability. Intl J. Aeroacoust. 18 (4–5), 536–553.10.1177/1475472X19859858CrossRefGoogle Scholar
Karniadakis, G.E. & Triantafyllou, G.S. 1989 Frequency selection and asymptotic states in laminar wakes. J. Fluid Mech. 199, 441–469.10.1017/S0022112089000431CrossRefGoogle Scholar
Karthik, B., Chakravarthy, S.R. & Sujith, R.I. 2008 Mechanism of pipe-tone excitation by flow through an orifice in a duct. Intl J. Aeroacoust. 7 (3-4), 321–347.10.1260/1475-472X.7.3.321CrossRefGoogle Scholar
Kashinath, K., Li, L.K.B. & Juniper, M.P. 2018 Forced synchronization of periodic and aperiodic thermoacoustic oscillations: lock-in, bifurcations and open-loop control. J. Fluid Mech. 838, 690–714.10.1017/jfm.2017.879CrossRefGoogle Scholar
Koopmann, G.H. 1967 The vortex wakes of vibrating cylinders at low Reynolds numbers. J. Fluid Mech. 28 (3), 501–512.10.1017/S0022112067002253CrossRefGoogle Scholar
Kushwaha, A.K., Worth, N.A., Dawson, J.R., Gupta, V. & Li, L.K.B. 2022 Asynchronous and synchronous quenching of a globally unstable jet via axisymmetry breaking. J. Fluid Mech. 937, A40.10.1017/jfm.2022.139CrossRefGoogle Scholar
Kyle, D.M. & Sreenivasan, K.R. 1993 The instability and breakdown of a round variable-density jet. J. Fluid Mech. 249, 619–664.10.1017/S0022112093001314CrossRefGoogle Scholar
Li, L.K.B. & Juniper, M.P. 2013 a Lock-in and quasiperiodicity in a forced hydrodynamically self-excited jet. J. Fluid Mech. 726, 624–655.10.1017/jfm.2013.223CrossRefGoogle Scholar
Li, L.K.B. & Juniper, M.P. 2013 b Lock-in and quasiperiodicity in hydrodynamically self-excited flames: experiments and modelling. Proc. Combust. Inst. 34 (1), 947–954.10.1016/j.proci.2012.06.022CrossRefGoogle Scholar
Li, L.K.B. & Juniper, M.P. 2013 c Phase trapping and slipping in a forced hydrodynamically self-excited jet. J. Fluid Mech. 735, R5.10.1017/jfm.2013.533CrossRefGoogle Scholar
Matveev, K.I. 2005 Reduced-order modeling of vortex-driven excitation of acoustic modes. Acoust. Res. Lett. Online 6 (1), 14–19.10.1121/1.1815253CrossRefGoogle Scholar
Matveev, K.I. & Culick, F.E.C. 2003 A model for combustion instability involving vortex shedding. Combust. Sci. Technol. 175 (6), 1059–1083.10.1080/00102200302349CrossRefGoogle Scholar
Minorsky, N. 1967 Comments on asynchronous quenching. IEEE Trans. Autom. Control 12 (2), 225–227.10.1109/TAC.1967.1098559CrossRefGoogle Scholar
Mondal, S., Pawar, S.A. & Sujith, R.I. 2019 Forced synchronization and asynchronous quenching of periodic oscillations in a thermoacoustic system. J. Fluid Mech. 864, 73–96.10.1017/jfm.2018.1011CrossRefGoogle Scholar
Nair, V. & Sujith, R.I. 2016 Precursors to self-sustained oscillations in aeroacoustic systems. Intl J. Aeroacoust. 15 (3), 312–323.10.1177/1475472X16630877CrossRefGoogle Scholar
Nayfeh, A.H. & Balachandran, B. 2008 Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods. John Wiley & Sons.Google Scholar
Noiray, N., Durox, D., Schuller, T. & Candel, S. 2007 Passive control of combustion instabilities involving premixed flames anchored on perforated plates. Proc. Combust. Inst. 31 (1), 1283–1290.10.1016/j.proci.2006.07.096CrossRefGoogle Scholar
Noiray, N. & Schuermans, B. 2013 Deterministic quantities characterizing noise driven Hopf bifurcations in gas turbine combustors. Intl J. Non-Linear Mech. 50, 152–163.10.1016/j.ijnonlinmec.2012.11.008CrossRefGoogle Scholar
Odajima, K., Nishida, Y. & Hatta, Y. 1974 Synchronous quenching of drift-wave instability. Phys. Fluids 17 (8), 1631–1633.10.1063/1.1694944CrossRefGoogle Scholar
Olinger, D.J. 1993 A low-dimensional model for chaos in open fluid flows. Phys. Fluids A: Fluid Dyn. 5 (8), 1947–1951.10.1063/1.858821CrossRefGoogle Scholar
Pikovsky, A. & Maistrenko, Y.L. 2012 Synchronization: Theory and Application. vol. 109, Springer Science & Business Media.Google Scholar
Pikovsky, A., Rosenblum, M. & Kurths, J. 2001 Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge University Press.10.1017/CBO9780511755743CrossRefGoogle Scholar
Porat, B. 2008 Digital Processing of Random Signals: Theory and Methods. Courier Dover Publications.Google Scholar
Richards, G.A., Straub, D.L. & Robey, E.H. 2003 Passive control of combustion dynamics in stationary gas turbines. J. Propul. Power 19 (5), 795–810.10.2514/2.6195CrossRefGoogle Scholar
Richards, G.A., Thornton, J.D., Robey, E.A. & Arellano, L. 2004 Open loop active control of combustion dynamics on a gas turbine engine asme imece2004-59702. In ASME International Mechanical Engineering Conference.10.1115/IMECE2004-59702CrossRefGoogle Scholar
Rockwell, D. 1983 Oscillations of impinging shear layers. AIAA J. 21 (5), 645–664.10.2514/3.8130CrossRefGoogle Scholar
Rockwell, D. & Naudascher, E. 1979 Self-sustained oscillations of impinging free shear layers. Annu. Rev. Fluid Mech. 11, 67–94.10.1146/annurev.fl.11.010179.000435CrossRefGoogle Scholar
Roy, A., Mondal, S., Pawar, S.A. & Sujith, R.I. 2020 On the mechanism of open-loop control of thermoacoustic instability in a laminar premixed combustor. J. Fluid Mech. 884, A2.10.1017/jfm.2019.884CrossRefGoogle Scholar
Shampine, L.F. & Reichelt, M.W. 1997 Ode matlab solvers. J. Sci. Comput. 18, 1–22.Google Scholar
Singh, A., Mukherjee, I. & Nair, V. 2024 Instability amplitude suppression in a double orifice flow through external periodic forcing. In Turbo Expo: Power for Land, Sea, and Air, vol. 87950, pp. V03BT04A007. American Society of Mechanical Engineers.Google Scholar
Sipp, D. 2012 Open-loop control of cavity oscillations with harmonic forcings. J. Fluid Mech. 708, 439–468.10.1017/jfm.2012.329CrossRefGoogle Scholar
Sreenivasan, K.R., Raghu, S. & Kyle, D. 1989 Absolute instability in variable density round jets. Exp. Fluids 7 (5), 309–317.10.1007/BF00198449CrossRefGoogle Scholar
Stubos, A.K., Benocci, C., Palli, E., Stoubos, G.K. & Olivari, D. 1999 Aerodynamically generated acoustic resonance in a pipe with annular flow restrictors. J. Fluids Struct. 13 (6), 755–778.10.1006/jfls.1999.0226CrossRefGoogle Scholar
Takens, F. 1981 Detecting strange attractors in turbulence. In Dynamical Systems and Turbulence, vol. 1980, pp. 366–381. Springer.Google Scholar
Thompson, J.M.T. & Stewart, H.B. 2002 Nonlinear Dynamics and Chaos. John Wiley & Sons.Google Scholar
Van, A., Charles, W. & Gharib, M. 1987 Ordered and chaotic vortex streets behind circular cylinders at low Reynolds numbers. J. Fluid Mech. 174, 113–133.Google Scholar
Ziada, S. 2010 Flow-excited acoustic resonance in industry. J. Press. Vessel Technol. 132 (1), 015001.10.1115/1.4000379CrossRefGoogle Scholar
Zinn, B.T. & Lores, M.E. 1971 Application of the Galerkin method in the solution of non-linear axial combustion instability problems in liquid rockets. Combust. Sci. Technol. 4 (1), 269–278.10.1080/00102207108952493CrossRefGoogle Scholar