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System identification of a low-density jet via its noise-induced dynamics

Published online by Cambridge University Press:  08 January 2019

Minwoo Lee Open the ORCID record for Minwoo Lee [Opens in a new window] ,
Yuanhang Zhu Open the ORCID record for Yuanhang Zhu [Opens in a new window] ,
Larry K. B. Li Open the ORCID record for Larry K. B. Li [Opens in a new window]  and
Vikrant Gupta Open the ORCID record for Vikrant Gupta [Opens in a new window]
Minwoo Lee
Affiliation:
Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong
Yuanhang Zhu
Affiliation:
Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong School of Engineering, Brown University, Providence, RI 02912, USA
Larry K. B. Li*
Affiliation:
Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong
Vikrant Gupta*
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, 518055, China
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

Low-density jets are central to many natural and industrial processes. Under certain conditions, they can develop global oscillations at a limit cycle, behaving as a prototypical example of a self-excited hydrodynamic oscillator. In this study, we perform system identification of a low-density jet using measurements of its noise-induced dynamics in the unconditionally stable regime, prior to both the Hopf and saddle-node points. We show that this approach can enable prediction of (i) the order of nonlinearity, (ii) the locations and types of the bifurcation points (and hence the stability boundaries) and (iii) the resulting limit-cycle oscillations. The only assumption made about the system is that it obeys a Stuart–Landau equation in the vicinity of the Hopf point, thus making the method applicable to a variety of hydrodynamic systems. This study constitutes the first experimental demonstration of system identification using the noise-induced dynamics in only the unconditionally stable regime, i.e. away from the regimes where limit-cycle oscillations may occur. This opens up new possibilities for the prediction and analysis of the stability and nonlinear behaviour of hydrodynamic systems.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Nonlinear Dynamical Systems: Low-dimensional models
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 862 , 10 March 2019 , pp. 200 - 215
Copyright
© 2019 Cambridge University Press 

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References

Bonciolini, G., Ebi, D., Boujo, E. & Noiray, N. 2018 Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation. R. Soc. Open Sci. 5 (3), 172078.Google Scholar
Boujo, E. & Noiray, N. 2017 Robust identification of harmonic oscillator parameters using the adjoint Fokker–Planck equation. Proc. R. Soc. Lond. A 473 (2200), 20160894.Google Scholar
Brunton, S. L., Proctor, J. L. & Kutz, J. N. 2016 Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proc. Natl Acad. Sci. USA 113 (15), 3932–3937.Google Scholar
Dijkstra, H. A., Wubs, F. W., Cliffe, A. K., Doedel, E., Dragomirescu, I. F., Eckhardt, B., Gelfgat, A. Y., Hazel, A. L., Lucarini, V., Salinger, A. G., Phipps, E. T., Sanchez-Umbria, J., Schuttelaars, H., Tuckerman, L. S. & Thiele, U. 2014 Numerical bifurcation methods and their application to fluid dynamics: analysis beyond simulation. Commun. Comput. Phys. 15, 1–45.Google Scholar
Dusek, J., Le Gal, P. & Fraune, P. 1994 A numerical and theoretical study of the first Hopf bifurcation in a cylinder wake. J. Fluid Mech. 264, 59–80.Google Scholar
Fraser, A. M. & Swinney, H. L. 1986 Independent coordinates for strange attractors from mutual information. Phys. Rev. A 33, 1134–1140.Google Scholar
Gupta, V., Saurabh, A., Paschereit, C. O. & Kabiraj, L. 2017 Numerical results on noise-induced dynamics in the subthreshold regime for thermoacoustic systems. J. Sound Vib. 390, 55–66.Google Scholar
Hallberg, M. P. & Strykowski, P. J. 2006 On the universality of global modes in low-density axisymmetric jets. J. Fluid Mech. 569, 493–507.Google Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22 (1), 473–537.Google Scholar
Jackson, C. P. 1987 A finite-element study of the onset of vortex shedding in flow past variously shaped bodies. J. Fluid Mech. 182, 23–45.Google Scholar
Kabiraj, L., Steinert, R., Saurabh, A. & Paschereit, C. O. 2015 Coherence resonance in a thermoacoustic system. Phys. Rev. E 92, 042909.Google Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59 (2), 308–323.Google Scholar
Kyle, D. M. & Sreenivasan, K. R. 1993 The instability and breakdown of a round variable-density jet. J. Fluid Mech. 249, 619–664.Google Scholar
Landau, L. D. 1944 On the problem of turbulence. Dokl. Akad. Nauk SSSR 44 (8), 339–349.Google Scholar
Mevel, L., Benveniste, A., Basseville, M., Goursat, M., Peeters, B., Van der Auweraer, H. & Vecchio, A. 2006 Input/output versus output-only data processing for structural identification: application to in-flight data analysis. J. Sound Vib. 295 (3), 531–552.Google Scholar
Monkewitz, P. A., Bechert, D. W., Barsikow, B. & Lehmann, B. 1990 Self-excited oscillations and mixing in a heated round jet. J. Fluid Mech. 213, 611–639.Google Scholar
Nayfeh, A. H. 1981 Introduction to Perturbation Techniques. Wiley.Google Scholar
Nayfeh, A. H. & Mook, D. T. 1979 Nonlinear Oscillations. Wiley.Google 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.Google Scholar
Pikovsky, A. S. & Kurths, J. 1997 Coherence resonance in a noise-driven excitable system. Phys. Rev. Lett. 78, 775–778.Google Scholar
Price, S. J. & Valerio, N. R. 1990 A non-linear investigation of single-degree-of-freedom instability in cylinder arrays subject to cross-flow. J. Sound Vib. 137 (3), 419–432.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
Raghu, S. & Monkewitz, P. A. 1991 The bifurcation of a hot round jet to limit-cycle oscillations. Phys. Fluids A 3, 501–503.Google Scholar
Roberts, J. 1986 Stochastic averaging: an approximate method of solving random vibration problems. Intl J. Non-Linear Mech. 21, 111–134.Google Scholar
Schmidt, M. & Lipson, H. 2009 Distilling free-form natural laws from experimental data. Science 324 (5923), 81–85.Google Scholar
Shimizu, M. & Kawahara, G. 2018 Construction of low-dimensional system reproducing low-Reynolds-number turbulence by machine learning. Phys. Rev. E (submitted). arXiv:1803.08206v1.Google Scholar
Sipp, D. & Lebedev, A. 2007 Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows. J. Fluid Mech. 593, 333–358.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
Stratonovich, R. L. 1963 Topics in the Theory of Random Noise. Gordon and Breach.Google Scholar
Stratonovich, R. L. 1967 Topics in the Theory of Random Noise: General Theory of Random Processes; Nonlinear Transformations of Signals and Noise. Gordon and Breach.Google Scholar
Stuart, J. T. 1960 On the non-linear mechanics of wave disturbances in stable and unstable parallel flows. Part 1. The basic behaviour in plane Poiseuille flow. J. Fluid Mech. 9, 353–370.Google Scholar
Takens, F. 1981 Detecting strange attractors in turbulence. Lect. Notes Math. 898, 366–381.Google Scholar
Thompson, P. A. & Troian, S. M. 1997 A general boundary condition for liquid flow at solid surfaces. Nature 389 (6649), 360.Google Scholar
Thothadri, M. & Moon, F. C. 2005 Nonlinear system identification of systems with periodic limit-cycle response. Nonlinear Dyn. 39 (1–2), 63–77.Google Scholar
Ushakov, O. V., Wünsche, H. J., Henneberger, F., Khovanov, I. A., Schimansky-Geier, L. & Zaks, M. A. 2005 Coherence resonance near a Hopf bifurcation. Phys. Rev. Lett. 95, 123903.Google Scholar
Wiesenfeld, K. 1985 Noisy precursors of nonlinear instabilities. J. Stat. Phys. 38 (5), 1071–1097.Google Scholar
Xu, Y., Gu, R., Zhang, H., Xu, W. & Duan, J. 2011 Stochastic bifurcations in a bistable Duffing–Van der Pol oscillator with colored noise. Phys. Rev. E 83 (5), 056215.Google Scholar
Yamapi, R., Filatrella, G., Aziz-Alaoui, M. A. & Cerdeira, H. A 2012 Effective Fokker–Planck equation for birhythmic modified van der Pol oscillator. Chaos 22 (4), 043114.Google Scholar
Zakharova, A., Vadivasova, T., Anishchenko, V., Koseska, A. & Kurths, J. 2010 Stochastic bifurcations and coherence like resonance in a self-sustained bistable noisy oscillator. Phys. Rev. E 81 (1), 011106.Google Scholar
Zhu, W. Q. & Yu, J. S. 1987 On the response of the van der Pol oscillator to white noise excitation. J. Sound Vib. 117 (3), 421–431.Google Scholar
Zhu, Y.2017 Transition to global instability in low-density axisymmetric jets: bistability, intermittency and coherence resonance. Master’s thesis, The Hong Kong University of Science and Technology.Google Scholar
Zhu, Y., Gupta, V. & Li, L. K. B. 2017 Onset of global instability in low-density jets. J. Fluid Mech. 828, R1.Google Scholar