Output-only parameter identification of a colored-noise-driven Van-der-Pol oscillator: Thermoacoustic instabilities as an example

Bonciolini, Giacomo; Boujo, Édouard; Noiray, Nicolas

doi:10.1103/physreve.95.062217

Cited by 45 publications

(40 citation statements)

References 78 publications

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“…To complete the model, it is necessary to specify the heat release terms ξ i and g i . Regarding the first, it is possible to model this stochastic forcing as a white noise source [28].…”

Section: Low-order Modelmentioning

confidence: 99%

Synchronization of Thermoacoustic Modes in Sequential Combustors

Bonciolini

Noiray

2018

Journal of Engineering for Gas Turbines and Power

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Sequential combustion constitutes a major technological step-change for gas turbines applications. This design provides higher operational flexibility, lower emissions, and higher efficiency compared to today's conventional architectures. Like any constant pressure combustion system, sequential combustors can undergo thermoacoustic instabilities. These instabilities potentially lead to high-amplitude acoustic limit cycles, which shorten the engine components' lifetime, and therefore, reduce their reliability and availability. In the case of a sequential system, the two flames are mutually coupled via acoustic and entropy waves. This additional interstages interaction markedly complicates the already challenging problem of thermoacoustic instabilities. As a result, new and unexplored system dynamics are possible. In this work, experimental data from our generic sequential combustor are presented. The system exhibits many different distinctive dynamics, as a function of the operation parameters and of the combustor arrangement. This paper investigates a particular bifurcation, where two thermoacoustic modes synchronize their self-sustained oscillations over a range of operating conditions. A low-order model of this thermoacoustic bifurcation is proposed. This consists of two coupled stochastically driven nonlinear oscillators and is able to reproduce the peculiar dynamics associated with this synchronization phenomenon. The model aids in understanding what the physical mechanisms that play a key role in the unsteady combustor physics are. In particular, it highlights the role of entropy waves, which are a significant driver of thermoacoustic instabilities in this sequential setup. This research helps to lay the foundations for understanding the thermoacoustic instabilities in sequential combustion systems.

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“…To complete the model, it is necessary to specify the heat release terms ξ i and g i . Regarding the first, it is possible to model this stochastic forcing as a white noise source [28].…”

Section: Low-order Modelmentioning

confidence: 99%

Synchronization of Thermoacoustic Modes in Sequential Combustors

Bonciolini

Noiray

2018

Journal of Engineering for Gas Turbines and Power

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“…where p designates the acoustic pressure in the combustor, ω 0 the natural angular frequency (in the present case the one of the dominant eigenmode ψ 0 ), ν the linear growth rate, whose sign defines the linear stability of the system, κ a positive constant setting out the saturation of the thermoacoustic oscillations to a limit cycle, ξ(t) a gaussian white noise of intensity Γ that represents the stochastic forcing exerted by turbulence [46]. Given the fact that thermoacoustic instabilities in combustion chambers are usually characterized by |ν| ω 0 , there are two relevant time scales to the present problem, the fast time scale of the acoustic oscillation T 0 = 2π/ω 0 and the slow one T ν = 2π/ν associated with the amplitude dynamics, and one can therefore assume p(t) = A(t) cos (ω 0 t + ϕ(t)).…”

Section: Model and Identification Of Parametersmentioning

confidence: 99%

“…P∞(A; t = 0) = N A exp [4ω 2 0 /Γ(ν 0 A 2 /2 − κA 4 /32)], where ν 0 = ν(t = 0) and N is a normalization constant. See[46] for more details.…”

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confidence: 99%

Bifurcation Dodge: Avoidance of a Thermoacoustic Instability under Transient Operation

Bonciolini

Noiray

2019

GPPS Zurich19

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Varying one of the governing parameters of a dynamical system may lead to a critical transition, where the new stable state is undesirable. In some cases, there is only a limited range of the bifurcation parameter that corresponds to that unwanted attractor, while the system runs problem-less otherwise. In this study, we present experimental results regarding a thermoacoustic system subject to two consecutive and mirrored supercritical Hopf bifurcations: the system exhibits high amplitude thermoacoustic limit cycles for intermediate values of the bifurcation parameter. Changing quickly enough the bifurcation parameter, it was possible to dodge the unwanted limit cycles. A low-order model of the complex thermoacoustic system was developed, in order to describe this interesting transient dynamics. It was afterward used to assess the risk of exceeding an oscillation amplitude threshold as a function of the rate of change of the bifurcation parameter.

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“…Nonlinear wave processes are observed in a variety of engineering and physics applications such as acoustics [1,2], combustion noise [3,4], jet noise [5][6][7], thermoacoustics [8,9], surface waves [10], and plasmaphysics [11], requiring nonlinear evolution equations to describe the dynamics of perturbations. In the case of high amplitude planar acoustic wave propagation, two main nonlinear effects are present: acoustic streaming [2,12] and wave steepening [1,13].…”

Section: Introductionmentioning

confidence: 99%

Spectral energy cascade and decay in nonlinear acoustic waves

Gupta

Scalo

2018

Phys. Rev. E

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We present a numerical and theoretical investigation of nonlinear spectral energy cascade of decaying finite-amplitude planar acoustic waves in a single-component ideal gas at standard temperature and pressure (STP). We analyze various one-dimensional canonical flow configurations: a propagating traveling wave (TW), a standing wave (SW), and randomly initialized Acoustic Wave Turbulence (AWT). Due to nonlinear wave propagation, energy at the large scales cascades down to smaller scales dominated by viscous dissipation, analogous to hydrodynamic turbulence. We use shock-resolved mesh-adaptive direct numerical simulations (DNS) of the fully compressible onedimensional Navier-Stokes equations to simulate the spectral energy cascade in nonlinear acoustic waves. The simulation parameter space for the TW, SW, and AWT cases spans three orders of magnitude in initial wave pressure amplitude and dynamic viscosity, thus covering a wide range of both spectral energy cascade and the viscous dissipation rates. The shock waves formed as a result of energy cascade are weak (M < 1.4), and hence we neglect thermodynamic non-equilibrium effects such as molecular vibrational relaxation in the current study. We also derive a new set of nonlinear acoustics equations truncated to second order and the corresponding perturbation energy corollary yielding the expression for a new perturbation energy norm E (2) . Its spatial average, satisfies the definition of a Lyapunov function, correctly capturing the inviscid (or lossless) broadening of spectral energy in the initial stages of evolution -analogous to the evolution of kinetic energy during the hydrodynamic break down of three-dimensional coherent vorticity -resulting in the formation of smaller scales. Upon saturation of the spectral energy cascade i.e. fully broadened energy spectrum, the onset of viscous losses causes a monotonic decay of in time. In this regime, the DNS results yield ∼ t −2 for TW and SW, and ∼ t −2/3 for AWT initialized with white noise. Using the perturbation energy corollary, we derive analytical expressions for the energy, energy flux, and dissipation rate in the wavenumber space. These yield the definitions of characteristic length scales such as the integral length scale (characteristic initial energy containing scale) and the Kolmogorov length scale η (shock thickness scale), analogous to K41 theory of hydrodynamic turbulence (A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 30 , 9 (1941)). Finally, we show that the fully developed energy spectrum of the nonlinear acoustic waves scales as E k k 2 −2/3 1/3 ∼ C f (kη), with C ≈ 0.075 constant for TW and SW but decaying in time for AWT. arXiv:1809.02202v1 [physics.flu-dyn]

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Output-only parameter identification of a colored-noise-driven Van-der-Pol oscillator: Thermoacoustic instabilities as an example

Cited by 45 publications

References 78 publications

Synchronization of Thermoacoustic Modes in Sequential Combustors

Synchronization of Thermoacoustic Modes in Sequential Combustors

Bifurcation Dodge: Avoidance of a Thermoacoustic Instability under Transient Operation

Spectral energy cascade and decay in nonlinear acoustic waves

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