Chaos, synchronization, and desynchronization in a liquid-fueled diffusion-flame combustor with an intrinsic hydrodynamic mode

Mitigation of limit cycle oscillations in a turbulent thermoacoustic system via delayed acoustic self-feedback

We report the occurrence of amplitude death (AD) of limit cycle oscillations in a bluff body stabilized turbulent combustor through delayed acoustic self-feedback. Such feedback control is achieved by coupling the acoustic field of the combustor to itself through a single coupling tube attached near the anti-node position of the acoustic standing wave. We observe that the amplitude and dominant frequency of the limit cycle oscillations gradually decrease as the length of the coupling tube is increased. Complete suppression (AD) of these oscillations is observed when the length of the coupling tube is nearly 3 / 8 times the wavelength of the fundamental acoustic mode of the combustor. Meanwhile, as we approach this state of amplitude death, the dynamical behavior of acoustic pressure changes from the state of limit cycle oscillations to low-amplitude chaotic oscillations via intermittency. We also study the change in the nature of the coupling between the unsteady flame dynamics and the acoustic field as the length of the coupling tube is increased. We find that the temporal synchrony between these oscillations changes from the state of synchronized periodicity to desynchronized aperiodicity through intermittent synchronization. Furthermore, we reveal that the application of delayed acoustic self-feedback with optimum feedback parameters completely disrupts the positive feedback loop between hydrodynamic, acoustic, and heat release rate fluctuations present in the combustor during thermoacoustic instability, thus mitigating instability. We anticipate this method to be a viable and cost-effective option to mitigate thermoacoustic oscillations in turbulent combustion systems used in practical propulsion and power systems.

Gravitational effect on the nonlinear dynamics of a buoyant turbulent flame

This study numerically examines the gravitational effect on the nonlinear dynamics of a buoyant turbulent flame utilizing analytical methods based on complex networks and dynamical systems. A dense (sparse) network structure is formed in the near (far) field in low gravity, as shown by the degree and cluster coefficient in the spatial network. The global dynamics of the vertical flow velocity fluctuations in the intermittent luminous zone is synchronous with that of the temperature fluctuations in low gravity. The synchronized state disappears as the gravity level is increased, leading to a desynchronized state. These behaviors are clearly identified by the symbolic recurrence plots.

Rijke tube: A nonlinear oscillator

Dynamical systems theory has emerged as an interdisciplinary area of research to characterize the complex dynamical transitions in real-world systems. Various nonlinear dynamical phenomena and bifurcations have been discovered over the decades using different reduced-order models of oscillators. Different measures and methodologies have been developed theoretically to detect, control, or suppress the nonlinear oscillations. However, obtaining such phenomena experimentally is often challenging, time-consuming, and risky mainly due to the limited control of certain parameters during experiments. With this review, we aim to introduce a paradigmatic and easily configurable Rijke tube oscillator to the dynamical systems community. The Rijke tube is commonly used by the combustion community as a prototype to investigate the detrimental phenomena of thermoacoustic instability. Recent investigations in such Rijke tubes have utilized various methodologies from dynamical systems theory to better understand the occurrence of thermoacoustic oscillations and their prediction and mitigation, both experimentally and theoretically. The existence of various dynamical behaviors has been reported in single and coupled Rijke tube oscillators. These behaviors include bifurcations, routes to chaos, noise-induced transitions, synchronization, and suppression of oscillations. Various early warning measures have been established to predict thermoacoustic instabilities. Therefore, this review article consolidates the usefulness of a Rijke tube oscillator in terms of experimentally discovering and modeling different nonlinear phenomena observed in physics, thus transcending the boundaries between the physics and the engineering communities.

Complex network analysis of spatiotemporal dynamics of premixed flame in a Hele-Shaw cell: A transition from chaos to stochastic state

We study the dynamical state of a noisy nonlinear evolution equation describing flame front dynamics in a Hele-Shaw cell from the viewpoint of complex networks. The high-dimensional chaos of flame front fluctuations at a negative Rayleigh number retains the deterministic nature for sufficiently small additive noise levels. As the strength of the additive noise increases, the flame front fluctuations begin to coexist with stochastic effects, leading to a fully stochastic state. The additive noise significantly promotes the irregular appearance of the merge and divide of small-scale wrinkles of the flame front at a negative Rayleigh number, resulting in the transition of high-dimensional chaos to a fully stochastic state.

Low-order modeling of the mutual synchronization between two turbulent thermoacoustic oscillators

We use a low-order oscillator model to investigate the mutual synchronization of a thermoacoustic system consisting of two turbulent lean-premixed combustors coupled via a cross-talk tube. The model consists of two Van der Pol (VDP) oscillators coupled via dissipative and time-delay terms. We show that, despite its simplicity, the model can reproduce many of the synchronization phenomena observed experimentally, such as amplitude death, desynchronization (quasiperiodicity), synchronization (phase locking), and nonlinear energy pumping from a limit-cycle mode to a damped mode. This study shows that the mutual synchronization dynamics of a turbulent thermoacoustic system can be reproduced with just a simple coupled VDP model. This suggests that such a model could be used to identify new strategies for quenching limit-cycle oscillations in turbulent thermoacoustic systems, such as gas turbines and rocket engines.

Attenuation of thermoacoustic combustion oscillations in a swirl-stabilized turbulent combustor

We experimentally study the attenuation behavior of thermoacoustic combustion oscillations using causality analysis, multiscale randomness analysis, and a complex network. We supply a steady air jet from the injector rim to suppress combustion oscillations. The directional coupling between pressure and heat release rate fluctuations is significantly weakened during the suppression of combustion oscillations. The loss of the primary hub in the turbulence network plays an important role in the degeneration of combustion oscillations.

Complex network analysis of the gravity effect on premixed flames propagating in a Hele-Shaw cell

We study the effect of gravity on spatiotemporal flame front dynamics in a Hele-Shaw cell from the viewpoint of complex networks. The randomness in flame front dynamics significantly increases with the gravitational level when the normalized Rayleigh number R_{a} is negative. This is clearly identified by two network entropies: the flame front network entropy and the transition network entropy. The irregular formation of large-scale wrinkles driven by the Rayleigh-Taylor instability plays an important role in the formation of high-dimensional deterministic chaos at R_{a}<0, resulting in the increase in the randomness of flame front dynamics.

Spatiotemporal dynamics of a buoyancy-driven turbulent fire

We numerically study the spatiotemporal dynamics and predictability of a buoyancy-driven turbulent fire. A significant transition from order to disorder structures can be observed from the mean degree in the spatial horizontal visibility graph. The gravitational term (baroclinic torque term) in the vorticity equation has a significant impact on the formation of the order (disorder) structure in the near field (far field). The entropy flow transport from temperature to flow velocity fluctuations is predominant near the interface between hot combustion products and ambient air. The transfer entropy is an important measure for determining the predictability of flow velocity fluctuations in the near field obtained by reservoir computing.

Input-output system identification of a thermoacoustic oscillator near a Hopf bifurcation using only fixed-point data

We present a framework for performing input-output system identification near a Hopf bifurcation using data from only the fixed-point branch, prior to the Hopf point itself. The framework models the system with a van der Pol-type equation perturbed by additive noise, and identifies the system parameters via the corresponding Fokker-Planck equation. We demonstrate the framework on a prototypical thermoacoustic oscillator (a flame-driven Rijke tube) undergoing a supercritical Hopf bifurcation. We find that the framework can accurately predict the properties of the Hopf bifurcation and the limit cycle beyond it. This study constitutes an experimental demonstration of system identification on a reacting flow using only prebifurcation data, opening up pathways to the development of early warning indicators for nonlinear dynamical systems near a Hopf bifurcation.