Coupled interaction between unsteady flame dynamics and acoustic field in a turbulent combustor

Dynamic behavior and driving region of spray combustion instability in a backward-facing step combustor

We numerically study the dynamic behavior and driving region of spray combustion instability in a backward-facing step combustor using analytical methodologies based on dynamical systems theory, symbolic dynamics, complex networks, and machine learning. The global dynamic behavior of a heat release rate field represents low-dimensional chaotic oscillations with deterministically aperiodic intercycle dynamics. Spray combustion instability is driven in the formation and separation region of a large-scale organized vortex induced by the hydrodynamic shear layer instability at the edge of the backstep. This region corresponds fairly to that of the hub in an acoustic-energy-flux-based spatial network. The feature importance in a random forest is valid for clarifying the feedback coupling of spray combustion instability.

Interaction of acoustic pressure and heat release rate fluctuations in a model rocket engine combustor

We experimentally clarify the interaction of acoustic pressure and heat release rate fluctuations during a transition to high-frequency combustion instability in a model rocket engine combustor. The dynamical state of acoustic pressure fluctuations undergoes a transition from high-dimensional chaotic oscillations to strongly correlated limit cycle oscillations. The coherent structure in the heat release rate field emerges with the initiation of weakly correlated limit cycle oscillations. The effect of the heat release rate on acoustic pressure fluctuations predominates during high-dimensional chaotic oscillations. In contrast, the effect of acoustic pressure on the heat release rate fluctuations markedly increases during the correlated limit cycle oscillations. These are reasonably shown by an ordinal pattern-based analysis involving the concepts of information theory, synchronization, and complex networks.

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.

Anticipating synchrony in dynamical systems using information theory

Synchronization in coupled dynamical systems has been a well-known phenomenon in the field of nonlinear dynamics for a long time. This phenomenon has been investigated extensively both analytically and experimentally. Although synchronization is observed in different areas of our real life, in some cases, this phenomenon is harmful; consequently, an early warning of synchronization becomes an unavoidable requirement. This paper focuses on this issue and proposes a reliable measure ( R), from the perspective of the information theory, to detect complete and generalized synchronizations early in the context of interacting oscillators. The proposed measure R is an explicit function of the joint entropy and mutual information of the coupled oscillators. The applicability of R to anticipate generalized and complete synchronizations is justified using numerical analysis of mathematical models and experimental data. Mathematical models involve the interaction of two low-dimensional, autonomous, chaotic oscillators and a network of coupled Rössler and van der Pol oscillators. The experimental data are generated from laboratory-scale turbulent thermoacoustic systems.

Recurrence-Based Synchronization Analysis of Weakly Coupled Bursting Neurons Under External ELF Fields

We investigate the response characteristics of a two-dimensional neuron model exposed to an externally applied extremely low frequency (ELF) sinusoidal electric field and the synchronization of neurons weakly coupled with gap junction. We find, by numerical simulations, that neurons can exhibit different spiking patterns, which are well observed in the structure of the recurrence plot (RP). We further study the synchronization between weakly coupled neurons in chaotic regimes under the influence of a weak ELF electric field. In general, detecting the phases of chaotic spiky signals is not easy by using standard methods. Recurrence analysis provides a reliable tool for defining phases even for noncoherent regimes or spiky signals. Recurrence-based synchronization analysis reveals that, even in the range of weak coupling, phase synchronization of the coupled neurons occurs and, by adding an ELF electric field, this synchronization increases depending on the amplitude of the externally applied ELF electric field. We further suggest a novel measure for RP-based phase synchronization analysis, which better takes into account the probabilities of recurrences.

Convolutional neural networks to predict the onset of oscillatory instabilities in turbulent systems

Many fluid dynamic systems exhibit undesirable oscillatory instabilities due to positive feedback between fluctuations in their different subsystems. Thermoacoustic instability, aeroacoustic instability, and aeroelastic instability are some examples. When the fluid flow in the system is turbulent, the approach to such oscillatory instabilities occurs through a universal route characterized by a dynamical regime known as intermittency. In this paper, we extract the peculiar pattern of phase space attractors during the regime of intermittency by constructing recurrence networks corresponding to the phase space topology. We further train a convolutional neural network to classify the periodic and aperiodic structures in the recurrence networks and define a measure that indicates the proximity of the dynamical state to the onset of oscillatory instability. We show that this measure can predict the onset of oscillatory instabilities in three different fluid dynamic systems governed by different physical phenomena.

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.

Early detection of thermoacoustic instabilities in a cryogenic rocket thrust chamber using combustion noise features and machine learning

We present a data-driven method for the early detection of thermoacoustic instabilities. Recurrence quantification analysis is used to calculate characteristic combustion features from short-length time series of dynamic pressure sensor data. Features like recurrence rate are used to train support vector machines to detect the onset of instability a few hundred milliseconds in advance. The performance of the proposed method is investigated on experimental data from a representative LOX/H ₂ research thrust chamber. In most cases, the method is able to timely predict two types of thermoacoustic instabilities on test data not used for training. The results are compared with state-of-the-art early warning indicators.

Condensation in the phase space and network topology during transition from chaos to order in turbulent thermoacoustic systems

The emergence of oscillatory dynamics (order) from chaotic fluctuations is a well-known phenomenon in turbulent thermoacoustic, aero-acoustic, and aeroelastic systems and is often detrimental to the system. We study the dynamics of two distinct turbulent thermoacoustic systems, bluff-body and swirl-stabilized combustors, where the transition occurs from the state of combustion noise (chaos) to thermoacoustic instability (order) via the route of intermittency. Using unweighted complex networks built from phase space cycles of the acoustic pressure oscillations, we characterize the topology of the phase space during various dynamical states in these combustors. We propose the use of network centrality measures derived from cycle networks as a novel means to characterize the number and stability of periodic orbits in the phase space and to study the topological transformations in the phase space during the emergence of order from chaos in the combustors. During the state of combustion noise, we show that the phase space consists of several unstable periodic orbits, which influence the phase space trajectory. As order emerges in the system dynamics, the number of periodic orbits decreases and their stability increases. At the onset of oscillatory dynamics, the phase space consists of a stable periodic orbit. We also use network centrality measures to identify the onset of thermoacoustic instability in both the combustors. Finally, we propose that the onset of oscillatory instabilities in turbulent systems is analogous to Bose-Einstein condensation transition observed for bosons, if we define phase space cycles as particles and the periodic orbits as energy levels.

Recurrence network analysis exploring the routes to thermoacoustic instability in a Rijke tube with inverse diffusion flame

Inverse diffusion flame (IDF) is a reliable low NO_x technology that is suitable for various industrial applications including gas turbines. However, a confined IDF may exhibit thermoacoustic instability, a kind of dynamic instability, which is characterized by catastrophically large amplitude pressure oscillations. Transition to such instability for an inverse diffusion flame is less explored compared to other types of flame. In the present study, thermoacoustic instability in a Rijke tube with IDF is achieved by varying air flow rate and input power independently, and the onset of thermoacoustic instability is examined using the framework of recurrence network (RN). During the transition to thermoacoustic instability, we find new routes and two new intermediate states, here referred to as "amplitude varying aperiodic oscillations" and "low amplitude limit cycle-like oscillations." Furthermore, we show that recurrence network analysis can be used to identify the dynamical states during the transition to thermoacoustic instability. We observe an absence of a single characteristic scale, resulting in a non-regular network even during thermoacoustic instability. Furthermore, the degree distributions of RN during combustion noise do not obey a single power law. Thus, scale-free nature is not exhibited during combustion noise. In short, recurrence network analysis shows significant differences in the topological information during combustion noise and thermoacoustic instability for IDF with those for premixed flames, reported earlier.

Synchronization transition from chaos to limit cycle oscillations when a locally coupled chaotic oscillator grid is coupled globally to another chaotic oscillator

Some physical systems with interacting chaotic subunits, when synchronized, exhibit a dynamical transition from chaos to limit cycle oscillations via intermittency such as during the onset of oscillatory instabilities that occur due to feedback between various subsystems in turbulent flows. We depict such a transition from chaos to limit cycle oscillations via intermittency when a grid of chaotic oscillators is coupled diffusively with a dissimilar chaotic oscillator. Toward this purpose, we demonstrate the occurrence of such a transition to limit cycle oscillations in a grid of locally coupled non-identical Rössler oscillators bidirectionally coupled with a chaotic Van der Pol oscillator. Further, we report the existence of symmetry breaking phenomena such as chimera states and solitary states during this transition from desynchronized chaos to synchronized periodicity. We also identify the temporal route for such a synchronization transition from desynchronized chaos to generalized synchronization via intermittent phase synchronization followed by chaotic synchronization and phase synchronization. Further, we report the loss of multifractality and loss of scale-free behavior in the time series of the chaotic Van der Pol oscillator and the mean field time series of the Rössler system. Such behavior has been observed during the onset of oscillatory instabilities in thermoacoustic, aeroelastic, and aeroacoustic systems. This model can be used to perform inexpensive numerical control experiments to suppress synchronization and thereby to mitigate unwanted oscillations in physical systems.

Dynamical systems approach to study thermoacoustic transitions in a liquid rocket combustor

Liquid rockets are prone to large amplitude oscillations, commonly referred to as thermoacoustic instability. This phenomenon causes unavoidable developmental setbacks and poses a stern challenge to accomplish the mission objectives. Thermoacoustic instability arises due to the nonlinear interaction between the acoustic and the reactive flow subsystems in the combustion chamber. In this paper, we adopt tools from dynamical systems and complex systems theory to understand the dynamical transitions from a state of stable operation to thermoacoustic instability in a self-excited model multielement liquid rocket combustor based on an oxidizer rich staged combustion cycle. We observe that this transition to thermoacoustic instability occurs through a sequence of bursts of large amplitude periodic oscillations. Furthermore, we show that the acoustic pressure oscillations in the combustor pertain to different dynamical states. In contrast to a simple limit cycle oscillation, we show that the system dynamics switches between period-3 and period-4 oscillations during the state of thermoacoustic instability. We show several measures based on recurrence quantification analysis and multifractal theory, which can diagnose the dynamical transitions occurring in the system. We find that these measures are more robust than the existing measures in distinguishing the dynamical state of a rocket engine. Furthermore, these measures can be used to validate models and computational fluid dynamics simulations, aiming to characterize the performance and stability of rockets.

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

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.

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

We experimentally investigate the nonlinear dynamics of a thermoacoustically self-excited aero-engine combustion system featuring a turbulent swirling liquid-fueled diffusion flame in a variable-length combustor. We focus on the steady-state dynamics via simultaneous measurements of the acoustic pressure in the combustor and the heat release rate (HRR) from the flame. When the combustor length is increased following the onset of thermoacoustic instability, we find that the pressure signal transitions from a period-1 limit cycle to chaos, whereas the HRR signal remains chaotic owing to the presence of an intrinsic hydrodynamic mode in the flame. When the hydrodynamic mode is filtered out of the data, we find that the pressure and HRR signals are in generalized synchronization. However, when the hydrodynamic mode is retained in the data, we find that the pressure and HRR signals are either weakly phase synchronized or desynchronized. This study has two main contributions: (i) it shows that a liquid-fueled diffusion-flame combustor can exhibit dynamics as complex as those of its gaseous-fueled premixed-flame counterparts and (ii) it highlights the need to be exceptionally careful when selecting a diagnostic signal from which to calculate nonlinear measures of self-excited thermoacoustic oscillations, because our experiments show that the pressure and HRR signals can be desynchronized by the presence of a hydrodynamic mode in the flame at a frequency different from that of the dominant thermoacoustic mode.

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

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.