Thermoacoustic instability in turbulent combustors is a nonlinear phenomenon resulting from the interaction between acoustics, hydrodynamics, and the unsteady flame Over the years, there have been many attempts toward understanding, prognosis, and mitigation of thermoacoustic instabilities Traditionally, a linear framework has been used to study thermoacoustic instability In recent times, researchers have been focusing on the nonlinear dynamics related to the onset of thermoacoustic instability In this context, the thermoacoustic system in a turbulent combustor is viewed as a complex system, and the dynamics exhibited by the system is perceived as emergent behaviors of this complex system In this paper, we discuss these recent developments and their contributions toward the understanding of this complex phenomenon Furthermore, we discuss various prognosis and mitigation strategies for thermoacoustic instability based on complex system theory

Complex system approach to investigate and mitigate thermoacoustic instability in turbulent combustors

Turbulent and vortical flows are ubiquitous and their characterization is crucial for the understanding of several natural and industrial processes. Among different techniques to study spatio-temporal flow fields, complex networks represent a recent and promising tool to deal with the large amount of data on turbulent flows and shed light on their physical mechanisms. The aim of this review is to bring together the main findings achieved so far from the application of network-based techniques to study turbulent and vortical flows. A critical discussion on the potentialities and limitations of the network approach is provided, thus giving an ordered portray of the current diversified literature. The present review can boost future network-based research on turbulent and vortical flows, promoting the establishment of complex networks as a widespread tool for turbulence analysis.

A review on turbulent and vortical flow analyses via complex networks

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.

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

We experimentally study the dynamic behavior of intermittent combustion oscillations by time series analysis in terms of nonlinear forecasting, symbolic dynamics, and statistical complexity, including the detection of the change in dynamical state based on symbolic dynamics and graph networks. We observe sudden switching back and forth between irregular small-amplitude and regular large-amplitude pressure fluctuations. The nonlinear local prediction method, permutation spectrum test, and the Renyi complexity–entropy curve clearly identify the possible presence of chaotic dynamics in small-amplitude pressure fluctuations during intermittent combustion oscillations. The network entropy in ordinal partition transition networks allows us to capture a significant change in dynamical state switching between chaotic oscillations and noisy limit cycle oscillations.

Dynamic behavior of intermittent combustion oscillations in a model rocket engine combustor

We conduct an experimental study of the attenuation behavior of thermoacoustic combustion instability from the viewpoints of complex networks and synchronization. The spatiotemporally phase-synchronized state between the vertexes in weighted networks near an injector rim is notably degenerated as thermoacoustic combustion instability is suppressed by a steady air jet issued from the injector rim. The synchronization index clearly captures the attenuation of the mutual coupling between pressure and heat release rate fluctuations. The decrease in the periodicity of noisy-periodic oscillations in a flow velocity field significantly affects the mutual coupling, resulting in the suppression of thermoacoustic combustion instability.

Attenuation behavior of thermoacoustic combustion instability analyzed by a complex-network- and synchronization-based approach.

We numerically study the spatiotemporal dynamics and early detection of thermoacoustic combustion instability in a model rocket combustor using the theories of complex networks and synchronization. The turbulence network, which consists of nodes and vertexes in weighted networks between vortices, can characterize the complex spatiotemporal structure of a flow field during thermoacoustic combustion instability. The transfer entropy allows us to identify the driving region of thermoacoustic combustion instability. In addition to the order parameter, a phase parameter newly proposed in this study is useful for capturing the precursor of thermoacoustic combustion instability.

Tatsuya Hashimoto

Papers

Spatiotemporal dynamics and early detection of thermoacoustic combustion instability in a model rocket combustor