Early detection of thermoacoustic instability in a staged single-sector combustor for aircraft engines using symbolic dynamics-based approach.

We experimentally conduct an early detection of thermoacoustic instability in a staged single-sector combustor using a novel methodology that combines symbolic dynamics and machine learning. We propose two invariants in this study: the determinisms of the joint symbolic recurrence plots DJ and the ordinal transition pattern-based recurrence plots DT. These invariants enable us to capture the phase synchronization between acoustic pressure and heat release rate fluctuations associated with a precursor of thermoacoustic instability. The latent space consisting of DJ and DT, which is obtained by a support vector machine in combination with the k-means clustering method, can appropriately determine a transitional regime between stable combustion and thermoacoustic instability.

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.

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 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.

Spatiotemporal dynamics of turbulent coaxial jet analyzed by symbolic information-theory quantifiers and complex-network approach.

We numerically study the spatiotemporal dynamics of a turbulent coaxial jet in a model rocket engine combustor from the viewpoints of symbolic information-theory quantifiers and complex networks. The dynamic behavior of flow velocity undergoes a significant transition from a stochastic to chaotic state as the turbulent jet moves downstream. The small-world nature exists in the near field forming a stochastic state, whereas it disappears by the formation of a chaotic state in the far field. The dynamic behavior of hydrogen and oxygen concentrations in the far field also represents deterministic chaos. The simultaneous dynamic behavior with chaotic mixing forms the phase-synchronization state.

Early detection of thermoacoustic combustion oscillations using a methodology combining statistical complexity and machine learning.

We conduct an experimental study on early detection of thermoacoustic combustion oscillations using a method combining statistical complexity and machine learning, including the characterization of intermittent combustion oscillations. Abrupt switching from aperiodic small-amplitude oscillations to periodic large-amplitude oscillations and vice versa appears in pressure fluctuations. The dynamic behavior of aperiodic small-amplitude pressure fluctuations represents chaos. The complexity-entropy causality plane effectively captures the subtle changes in the combustion state during a transition to well-developed combustion oscillations. The feature space of the complexity-entropy causality plane, which is obtained by a support vector machine, has potential use for detecting a precursor of combustion oscillations.

Dynamic behavior of combustion instability in a cylindrical combustor with an off-center installed coaxial injector.

We have intensively studied the dynamic behavior of combustion instability in a cylindrical combustor with an off-center installed coaxial injector. The most interesting discovery in this study is the appearance of a deterministic chaos in a transition from a dynamically stable state to well-developed high-frequency thermoacoustic combustion oscillations with increasing the volume flow rate of nitrogen with which oxygen is diluted. The presence of deterministic chaos is reasonably identified by considering an extended version of the Sugihara-May algorithm [G. Sugihara and R. May, Nature 344, 734 (1990)] as a local predictor and the multiscale complexity-entropy causality plane based on statistical complexity.

Synchronization of two coupled turbulent fires.

We numerically study the scale-free nature of a buoyancy-induced turbulent fire and synchronization of two coupled turbulent fires. A scale-free structure is detected in weighted networks between vortices, while its lifetime obeys a clear power law, indicating intermittent appearances, disappearances, and reappearances of the scale-free property. A significant decrease in the distance between the two fire sources gives rise to a synchronized state in the near field dominated by the unstable motion of transverse vortex rings. The synchronized state vanishes in the far field forming well-developed turbulent plumes, regardless of the distance between the two fire sources.

Chaos of radiative heat-loss-induced flame front instability.

We are intensively studying the chaos via the period-doubling bifurcation cascade in radiative heat-loss-induced flame front instability by analytical methods based on dynamical systems theory and complex networks. Significant changes in flame front dynamics in the chaotic region, which cannot be seen in the bifurcation diagrams, were successfully extracted from recurrence quantification analysis and nonlinear forecasting and from the network entropy. The temporal dynamics of the fuel concentration in the well-developed chaotic region is much more complicated than that of the flame front temperature. It exhibits self-affinity as a result of the scale-free structure in the constructed visibility graph.

Probing and exploiting the chaotic dynamics of a hydrodynamic photochemical oscillator to implement all the basic binary logic functions.

The convective motions within a solution of a photochromic spiro-oxazine being irradiated by UV only on the bottom part of its volume, give rise to aperiodic spectrophotometric dynamics. In this paper, we study three nonlinear properties of the aperiodic time series: permutation entropy, short-term predictability and long-term unpredictability, and degree distribution of the visibility graph networks. After ascertaining the extracted chaotic features, we show how the aperiodic time series can be exploited to implement all the fundamental two-inputs binary logic functions (AND, OR, NAND, NOR, XOR, and XNOR) and some basic arithmetic operations (half-adder, full-adder, half-subtractor). This is possible due to the wide range of states a nonlinear system accesses in the course of its evolution. Therefore, the solution of the convective photochemical oscillator results in hardware for chaos-computing alternative to conventional complementary metal-oxide semiconductor-based integrated circuits.

Dynamics of self-excited thermoacoustic instability in a combustion system: Pseudo-periodic and high-dimensional nature.

We have examined the dynamics of self-excited thermoacoustic instability in a fundamentally and practically important gas-turbine model combustion system on the basis of complex network approaches. We have incorporated sophisticated complex networks consisting of cycle networks and phase space networks, neither of which has been considered in the areas of combustion physics and science. Pseudo-periodicity and high-dimensionality exist in the dynamics of thermoacoustic instability, including the possible presence of a clear power-law distribution and small-world-like nature.

Analysis and prediction of aperiodic hydrodynamic oscillatory time series by feed-forward neural networks, fuzzy logic, and a local nonlinear predictor.

Forecasting of aperiodic time series is a compelling challenge for science. In this work, we analyze aperiodic spectrophotometric data, proportional to the concentrations of two forms of a thermoreversible photochromic spiro-oxazine, that are generated when a cuvette containing a solution of the spiro-oxazine undergoes photoreaction and convection due to localized ultraviolet illumination. We construct the phase space for the system using Takens' theorem and we calculate the Lyapunov exponents and the correlation dimensions to ascertain the chaotic character of the time series. Finally, we predict the time series using three distinct methods: a feed-forward neural network, fuzzy logic, and a local nonlinear predictor. We compare the performances of these three methods.

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.

Dynamic state of low-Reynolds-number turbulent channel flow.

We numerically study the dynamic state of a low-Reynolds-number turbulent channel flow from the viewpoints of symbolic dynamics and nonlinear forecasting. A low-dimensionally (high-dimensionally) chaotic state of the streamwise velocity fluctuations emerges at a viscous sublayer (logarithmic layer). The possible presence of the chaotic states is clearly identified by orbital instability-based nonlinear forecasting and ordinal partition transition network entropy in combination with the surrogate data method.

Short-term prediction of dynamical behavior of flame front instability induced by radiative heat loss.

We apply nonlinear forecasting to the time series of the flame front instability induced by radiative heat loss to test for the short-term predictability and long-term unpredictability characteristic of deterministic chaos in flame front instability. Our results indicate that the flame front instability represents high-dimensional chaos generated via the period-doubling cascade process reported in our previous study [H. Gotoda, K. Michigami, K. Ikeda, and T. Miyano, Combust Theory Modell. 14, 479 (2010)], while its short-term behavior is predictable using a local nonlinear predictor based on the Sugihara-May method [H. Gotoda, H. Nikimoto, T. Miyano, and S. Tachibana, Chaos 20, 013124 (2011); G. Sugihara and R. M. May, Nature 344, 734 (1990)] as well as a generalized radial basis function network as a global nonlinear predictor. The feasibility of a new approach based on short-term prediction is also discussed in this work from the practical viewpoint of combustion systems.

Characterization of complexities in combustion instability in a lean premixed gas-turbine model combustor.

We characterize complexities in combustion instability in a lean premixed gas-turbine model combustor by nonlinear time series analysis to evaluate permutation entropy, fractal dimensions, and short-term predictability. The dynamic behavior in combustion instability near lean blowout exhibits a self-affine structure and is ascribed to fractional Brownian motion. It undergoes chaos by the onset of combustion oscillations with slow amplitude modulation. Our results indicate that nonlinear time series analysis is capable of characterizing complexities in combustion instability close to lean blowout.

Dynamic properties of combustion instability in a lean premixed gas-turbine combustor.

We experimentally investigate the dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor from the viewpoint of nonlinear dynamics. A nonlinear time series analysis in combination with a surrogate data method clearly reveals that as the equivalence ratio increases, the dynamic behavior of the combustion instability undergoes a significant transition from stochastic fluctuation to periodic oscillation through low-dimensional chaotic oscillation. We also show that a nonlinear forecasting method is useful for predicting the short-term dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor, which has not been addressed in the fields of combustion science and physics.

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.

Effect of gravity on synchronization of two coupled buoyancy-induced turbulent flames.

We study the effect of gravity on the synchronization of two coupled buoyancy-induced turbulent flames by recurrence-based analysis and machine learning. A significant change from nearly complete synchronization in the near field to partial synchronization appears in the far field under low gravity. The synchronized state is gradually lost with increasing gravity level. These results are clearly identified from cross recurrence plots and symbolic recurrence plots and by reservoir computing.