Application of recurrence quantification analysis for early detection of lean blowout in a swirl-stabilized dump combustor

A novel recurrence-based approach for investigating multiphase flow dynamics in bubble column reactors

In chemical industries, multiphase flows in a bubble column reactor are frequently observed. The nonlinearity associated with bubble hydrodynamics, such as bubble-bubble and bubble-liquid interactions, gives rise to complex spatiotemporal patterns with increased gas or liquid velocities, which are extremely difficult to model and predict. In the current study, we propose a new, computationally efficient recurrence-based approach involving the angular separation between suitably defined state vectors and implement it on the experimental multiphase flow variables. The experimental dataset that consists of image frames obtained using a high-speed imaging system is generated by varying air and water flow rates in a bubble column reactor setup. The recurrence plots using the new approach are compared with those derived from conventional recurrence, considering standard benchmark problems. Further, using the recurrence plots and recurrence quantification from the new recurrence methodology, we discover a transition from a high recurrence state to a complex regime with very low recurrence for an increase in airflow rate. Determinism exhibits a rise for the decrease in airflow rate. A sharp decline in determinism and laminarity, signifying the quick shift to complex dynamics, is more prominent for spatial recurrence than temporal recurrence, indicating that the rise in airflow rate significantly impacts the spatial location of bubbles. We identify three regimes that appeared as distinct clusters in the determinism-laminarity plane. The bubbly regime, characterized by high values of determinism and laminarity, is separated by an intermediate regime from the slug flow regime, which has low determinism and laminarity.

Lean blowout detection using topological data analysis

Modern lean premixed combustors are operated in ultra-lean mode to conform to strict emission norms. However, this causes the combustors to become prone to lean blowout (LBO). Online monitoring of combustion dynamics may help to avoid LBO and help the combustor run more safely and reliably. Previous studies have suggested various techniques to early predict LBO in single-burner combustors. In contrast, early detection of LBO in multi-burner combustors has been little explored to date. Recent studies have discovered significantly different combustion dynamics between multi-burner combustors and single-burner combustors. In the present paper, we show that some well-established early LBO detection techniques suitable for single-burner combustor are less effective in early detecting LBO in multi-burner combustors. To resolve this, we propose a novel tool, topological data analysis (TDA), for real-time LBO prediction in a wide range of combustor configurations. We find that the TDA metrics are computationally cheap and follow monotonic trends during the transition to LBO. This indicates that the TDA metrics can be used to fine-tune the LBO safety margin, which is a desirable feature from practical implementation point of view. Furthermore, we show that the sublevel set TDA metrics show approximately monotonic changes during the transition to LBO even with low sampling-rate signals. Sublevel set TDA is computationally inexpensive and does not require phase-space embedding. Therefore, TDA can potentially be used for real-time monitoring of combustor dynamics with simple, low-cost, and low sampling-rate sensors.

Imprints of log-periodicity in thermoacoustic systems close to lean blowout

In the context of statistical physics, critical phenomena are accompanied by power laws having a singularity at the critical point where a sudden change in the state of the system occurs. In this work we show that lean blowout (LBO) in a turbulent thermoacoustic system is accompanied by a power law leading to finite-time singularity. As a crucial discovery of the system dynamics approaching LBO, we unravel the existence of the discrete scale invariance (DSI). In this context, we identify the presence of log-periodic oscillations in the temporal evolution of the amplitude of the dominant mode of low-frequency oscillations (A_{f}) existing in pressure fluctuations preceding LBO. The presence of DSI indicates the recursive development of blowout. Additionally, we find that A_{f} shows a faster-than-exponential growth and becomes singular when blowout occurs. We then present a model that depicts the evolution of A_{f} based on log-periodic corrections to the power law associated with its growth. Using the model, we find that blowouts can be predicted even several seconds earlier. The predicted time of LBO is in good agreement with the actual time of occurrence of LBO obtained from the experiment.

Early detection of lean blowout using recurrence network for varying degrees of premixedness

Lean premixed combustors are highly susceptible to lean blowout flame instability, which can cause a fatal accident in aircrafts or expensive shutdown in stationary combustors. However, the lean blowout limit of a combustor may vary significantly depending on a number of variables that cannot be controlled in practical situations. Although a large literature exists on the lean blowout phenomena, a robust strategy for early lean blowout detection is still not available. To address this gap, we study a relatively unexplored route to lean blowout using a nonlinear dynamical tool, the recurrence network. Three recurrence network parameters: global efficiency, average degree centrality, and global clustering coefficient are chosen as metrics for an early prediction of the lean blowout. We observe that the characteristics of the time series near the lean blowout limit are highly dependent on the degree of premixedness in the combustor. Still, for different degrees of premixedness, each of the three recurrence network metrics increases during transition to lean blowout, indicating a shift toward periodicity. Thus, qualitatively, the recurrence network metrics show similar trends for different degrees of premixing showing their robustness. However, the sensitivities and absolute trends of the recurrence network metrics are found to be significantly different for highly premixed and partially premixed configurations. Thus, the results indicate that prior knowledge about (i) the degree of premixedness and (ii) the route to lean blowout may be required for accurate early prediction of the lean blowout. We show that the visible structural changes in the recurrence network can be linked to the changes in the recurrence network metrics, helping to better understand the dynamical transition to lean blowout. We observe the power law degree distribution of the recurrence network to break down close to the lean blowout limit due to the intermittent dynamics in the near-LBO regime.

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.