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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: larryli@ust.hk, vik.gupta@cantab.net
†Email addresses for correspondence: larryli@ust.hk, vik.gupta@cantab.net
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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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