Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-28T12:27:25.703Z Has data issue: false hasContentIssue false
  • English
  • Français

Phase trapping and slipping in a forced hydrodynamically self-excited jet

Published online by Cambridge University Press:  29 October 2013

Larry K. B. Li  and
Matthew P. Juniper
Larry K. B. Li*
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
Matthew P. Juniper
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In a recent study on a coupled laser system, Thévenin et al. (Phys. Rev. Lett., vol. 107, 2011, 104101) reported the first experimental evidence of phase trapping, a partially synchronous state characterized by frequency locking without phase locking. To determine whether this state can arise in a hydrodynamic system, we reanalyse the data from our recent experiment on a periodically forced self-excited low-density jet (J. Fluid Mech., vol. 726, 2013, pp. 624–655). We find that this jet exhibits the full range of phase dynamics predicted by model oscillators with weak nonlinearity. These dynamics include (i) phase trapping between phase drifting and phase locking when the jet is forced far from its natural frequency and (ii) phase slipping during phase drifting when it is forced close to its natural frequency. This raises the possibility that similar phase dynamics can be found in other similarly self-excited flows. It also strengthens the validity of using low-dimensional nonlinear dynamical systems based on a universal amplitude equation to model such flows, many of which are of industrial importance.

JFM classification

Instability: Absolute/convective instability Flow Control: Flow Control Nonlinear Dynamical Systems: Nonlinear Dynamical Systems
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 735 , 25 November 2013 , R5
Copyright
©2013 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

Aronson, D. G., Ermentrout, G. B. & Kopell, N. 1990 Amplitude response of coupled oscillators. Physica D 41 (3), 403–449.Google Scholar
Balanov, A., Janson, N., Postnov, D. & Sosnovtseva, O. 2009 1:1 forced synchronization of periodic oscillations. In Synchronization: From Simple to Complex, chap. 3. Springer.Google Scholar
Chakravarthy, S. R., Shreenivasan, O. J., Boehm, B., Dreizler, A. & Janicka, J. 2007 Experimental characterization of onset of acoustic instability in a nonpremixed half-dump combustor. J. Acoust. Soc. Am. 122 (1), 120–127.CrossRefGoogle Scholar
Davitian, J., Getsinger, D., Hendrickson, C. & Karagozian, A. R. 2010 Transition to global instability in transverse-jet shear layers. J. Fluid Mech. 661, 294–315.Google Scholar
Emerson, B., O’Connor, J., Juniper, M. & Lieuwen, T. 2012 Density ratio effects on reacting bluff-body flow field characteristics. J. Fluid Mech. 706, 219–250.Google Scholar
Getsinger, D. R., Hendrickson, C. & Karagozian, A. R. 2012 Shear layer instabilities in low-density transverse jets. Exp. Fluids 53 (3), 783–801.Google Scholar
Gyergyek, T. 1999 Experimental study of the nonlinear dynamics of a harmonically forced double layer. Plasma Phys. Control. Fusion 41 (2), 175–190.Google Scholar
Hallberg, M. P. & Strykowski, P. J. 2008 Open-loop control of fully nonlinear self-excited oscillations. Phys. Fluids 20 (4), 041703.Google Scholar
Holmes, P. J. & Rand, D. A. 1978 Bifurcations of the forced van der Pol oscillator. Q. Appl. Maths 35, 495–509.Google Scholar
Huygens, C. 1673 The pendulum clock. In Horologium Oscillatorium. Iowa State University Press, (translated in 1986).Google Scholar
Karniadakis, G. E. & Triantafyllou, G. S. 1989 Frequency selection and asymptotic states in laminar wakes. J. Fluid Mech. 199, 441–469.Google Scholar
Khalak, A. & Williamson, C. H. K. 1999 Motions, forces and mode transitions in vortex-induced vibrations at low mass-damping. J. Fluid Struct. 13, 813–851.Google Scholar
Li, L. K. B. & Juniper, M. P. 2013a Lock-in and quasiperiodicity in a forced hydrodynamically self-excited jet. J. Fluid Mech. 726, 624–655.Google Scholar
Li, L. K. B. & Juniper, M. P. 2013b Lock-in and quasiperiodicity in hydrodynamically self-excited flames: experiments and modelling. Proc. Combust. Inst. 34 (1), 947–954.Google Scholar
Mehdi-Nejad, V., Farhadi, F. & Ashgriz, N. 2005 Naturally induced oscillations in twin-fluid atomizers. In 18th Annual Conference on Liquid Atomization and Spray Systems. ILASS Americas.Google Scholar
Meliga, P. & Chomaz, J. M. 2011 An asymptotic expansion for the vortex-induced vibrations of a circular cylinder. J. Fluid Mech. 671, 137–167.CrossRefGoogle Scholar
Monkewitz, P. A. 1996 Modelling of self-excited wake oscillations by amplitude equations. Exp. Therm. Fluid Sci. 12 (2), 175–183.Google Scholar
Olinger, D. J. 1992 Lock-in states in the dripping mode of the capillary jet. Exp. Fluids 15 (2), 155–158.Google Scholar
Penelet, G. & Biwa, T. 2013 Synchronization of a thermoacoustic oscillator by an external sound source. Am. J. Phys. 81 (4), 290–297.Google Scholar
Pikovsky, A. S., Rosenblum, M. G. & Kurths, J. 2003 Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge University Press.Google Scholar
van der Pol, B. 1927 Forced oscillations in a circuit with nonlinear resistance. Phil. Mag. 3 (13), 65–80.Google Scholar
Provansal, M., Mathis, C. & Boyer, L. 1987 Bénard–von Kármán instability: transient and forced regimes. J. Fluid Mech. 182, 1–22.Google Scholar
Shampine, L. F. & Reichelt, M. W. 1997 The MATLAB ODE suite. SIAM J. Sci. Comput. 18 (1), 1–22.Google Scholar
Sreenivasan, K. R., Raghu, S. & Kyle, D. 1989 Absolute instability in variable density round jets. Exp. Fluids 7 (5), 309–317.Google Scholar
Thévenin, J., Romanelli, M., Vallet, M., Brunel, M. & Erneux, T. 2011 Resonance assisted synchronization of coupled oscillators: frequency locking without phase locking. Phys. Rev. Lett. 107 (10), 104101.Google Scholar