arXiv subjects

R. I. Sujith

Publications and source records attributed to R. I. Sujith.

At least 37 records · Page 2Linked to original sources

arXiv2025

A reduced-order mean-field synchronization model for thermoacoustic systems

The synchronization phenomena in thermoacoustic systems leading to oscillatory instability can effectively be modeled using Kuramoto oscillators. Such models consider the nonlinear response of flame as an ensemble of Kuramoto phase oscillators constrained to collectively evolve at the rhythm of acoustic fluctuations. However, these high-dimensional models are analytically intractable and computationally expensive. In this study, we reduce the dimensionality of such a high-dimensional model and present a low-order, analytically tractable model for predicting transitions to thermoacoustic instability. We reduce the dimensionality of the phase oscillator model coupled to the acoustic field using the Ott-Antonsen ansatz. Using the reduced-order equations, we estimate the transitions to thermoacoustic instability and compare these transitions with the experiment. We validate the model for two combustor configurations, viz., the bluff-body stabilized dump combustor and the swirl-stabilized annular combustor. The low-order model accurately captures the continuous and abrupt secondary transitions observed experimentally in these distinct combustors.

nlin.CD↗

arXiv2025

Non-monotonic emergence of order from chaos in turbulent thermo-acoustic fluid systems

Self-sustained order can emerge in complex systems due to internal feedback between coupled subsystems. Here, we present our discovery of a non-monotonic emergence of order amidst chaos in a turbulent thermo-acoustic fluid system. Fluctuations play a vital role in determining the dynamical state and transitions in a system. In this work, we use complex networks to encode jumps in amplitude scales owing to fluctuations as links between nodes representing amplitude bins. The number of possible amplitude transitions at a fixed timescale reflects the complexity of dynamics at that timescale. The network entropy quantifies the number of and uncertainty associated with such transitions. Using network entropy, we show that the uncertainty in fluctuations first increases and then decreases as the system transitions from chaos via intermittency to order. The competition between turbulence and nonlinear interactions leads to such non-monotonic emergence of order amidst chaos in turbulent thermo-acoustic fluid systems.

physics.flu-dyn↗

arXiv2024

Cross-variable amplitude-frequency coupling during intermittency in a turbulent thermoacoustic system

We investigate flame-acoustic interactions in a turbulent combustor during the state of intermittency before the onset of thermoacoustic instability using complex networks. Experiments are performed in a turbulent bluff-body stabilized dump combustor where the inlet airflow rate is varied quasi-statically and continuously. We construct a natural visibility graph from the local heat release rate fluctuations at each location. Comparing the average degree during epochs of high and low amplitude acoustic pressure oscillations during the state of intermittency, we detect frequency modulation in local heat release rate signals. Through this approach, we discover unique spatial patterns of cross-variable coupling between the frequency of heat release rate fluctuations and the amplitude of acoustic pressure fluctuations. The frequency of heat release rate lfuctuations increases in regions of flame anchoring owing to high-frequency excitation of the flow and flame during epochs of high-amplitude acoustic pressure dynamics. On the other hand, the frequency of heat release rate fluctuations decreases in regions associated with flame front distortions by large coherent vortices. In experiments with continuously varying airflow rates, the spatial pattern of frequency modulation varies with an increase in the average amplitude of acoustic pressure fluctuations owing to an increase in the epochs of periodic acoustic pressure dynamics and the size of vortices forming in the flow. Dynamic shifts in the location of flame anchoring induce low-frequency fluctuations in heat release rate fluctuations during very high-amplitude intermittent acoustic pressure dynamics. Our approach using conditional natural visibility graphs thus reveals the spatial pattern of amplitude-frequency coupling between the co-evolving flame and the acoustic field dynamics in turbulent reacting flows.

physics.flu-dyn↗

arXiv2024

Metamorphosis of transition to periodic oscillations in a turbulent reactive flow system

The emergence of periodic oscillations is observed in various complex systems in nature and engineering. Thermoacoustic oscillations in systems comprising turbulent reactive flow exemplify such complexity in the engineering context, where the emergence of oscillatory dynamics is often undesirable. In this work, we experimentally study the transition to periodic oscillations within a turbulent flow reactive system, with varying fuel-to-air ratio, represented by equivalence ratio as a bifurcation parameter. Further, we explore the change in the nature of the transition by varying a secondary parameter. In our system, we vary the thermal power input and the location of the flame stabilizer position individually as a secondary parameter. Our findings reveal five qualitatively distinct types of transitions to periodic oscillations. Two types of these transitions exhibit a continuous nature. Another two types of transitions involve multiple shifts in the dynamical states consisting of both continuous and discontinuous bifurcations. The last type of transition is characterized by an abrupt bifurcation to high-amplitude periodic oscillations. Understanding this metamorphosis of the transition - from continuous to discontinuous nature - is critical for advancing our comprehension of the dynamic behavior in turbulent reactive flow systems. The insights gained from this study have the potential to inform the design and control of similar engineering systems where managing oscillatory behavior is crucial.

physics.flu-dyn↗

arXiv2024

Identifying optimal location for control of thermoacoustic instability through statistical analysis of saddle point trajectories

We propose a framework of Lagrangian Coherent Structures (LCS) to enable passive open-loop control of tonal sound generated during thermoacoustic instability. Experiments were performed in a laboratory-scale bluff-body stabilized turbulent combustor in the state of thermoacoustic instability. We use dynamic mode decomposition (DMD) on the flow-field to identify dynamical regions where the acoustic frequency is dominant. We find that the separating shear layer from the backward-facing step of the combustor envelops a cylindrical vortex in the outer recirculation zone (ORZ), which eventually impinging on the top wall of the combustor during thermoacoustic instability. We track the saddle points in this shear layer emerging from the backward facing step over several acoustic cycles. A passive control strategy is then developed by injecting a steady stream of secondary air targeting the identified optimal location where the saddle points spend a majority of their time in a statistical sense. After implementing the control action, the resultant flow-field is also analysed using LCS to understand the key differences in flow dynamics. We find that the shear layer emerging from the dump plane is deflected in a direction almost parallel to the axis of the combustor after the control action. This deflection in turn prevents the shear layer from enveloping the vortex and impinging on the combustor walls, resulting in a drastic reduction in the amplitude of the sound produced.

physics.flu-dyn↗

arXiv2024

Strange Nonchaotic Attractor in an Unforced Turbulent Reactive Flow System

We discover strange nonchaotic attractor (SNA) through experiments in an unforced system comprising turbulent reactive flow. While models suggest SNAs are common in dynamical systems, experimental observations are primarily limited to systems with external forcing. We observe SNA prior to the emergence of periodic oscillations from chaotic fluctuations. In complex systems, self-organization can lead to order, and inherent nonlinearity can induce chaos. The occurrence of SNA, which is nonchaotic yet nonperiodic in one such complex system, is intriguing.

nlin.CD↗

arXiv2024

Early warnings are too late when parameters change rapidly

Early warning signals (EWSs) forewarn a sudden transition (or tipping) from a desirable state to an undesirable state. However, we observe that EWSs detect an impending tipping past bifurcation points when control parameters are varied fast; this questions the applicability of EWSs in real-world systems. When a control parameter is changed at a finite rate, the tipping is also delayed, providing a borrowed stability (in the parameter space) before the system tips. In this study, we use the Hurst exponent as EWS in a thermoacoustic system - a horizontal Rijke tube. We find that upon receiving an EWS alert, a quick reversal of the control parameter within the region of borrowed stability cannot always prevent tipping in real-world systems. We show this failure is due to the (i) delay in receiving the EWS alert and (ii) dispersion observed in the warning points received. For fast variation of parameters, where preventive measures fall short, we demonstrate EWS-based control actions to rescue the system after tipping. Our results in a real-world system for a fast variation of parameter highlight the limits of applicability of EWSs in preventing tipping.

nlin.CD↗

arXiv2024

Identifying feedback directions in the mechanisms driving self-sustained thermoacoustic instability in a single-element rocket combustor

The occurrence of high frequency (>1000 Hz) thermoacoustic instability (TAI) sustained by mutual feedback among the acoustic field, heat release rate oscillations, and hydrodynamic oscillations poses severe challenges to the operation and structural integrity of rocket engines. Hence, quantifying the differing levels of feedback between these variables can help uncover the underlying mechanisms behind such high frequency TAI, enabling redesign of combustors to mitigate TAI. However, so far, no concrete method exists to decipher the varying levels of mutual feedback during high-frequency TAI. In the present study, we holistically investigate the mutual influence based on the spatiotemporal directionality among acoustic pressure, heat release rate, hydrodynamic and thermal oscillations during TAI of a single-element rocket engine combustor. Using symbolic transfer entropy (STE), we identify the spatiotemporal direction of feedback interactions between those primary variables when acoustic waves significantly emerge during TAI. We unveil the influence of vorticity dynamics at the fuel collar (or the propellant splitter plate) as the primary stimulant over the heat release rate fluctuations to rapidly amplify the amplitude of the acoustic field. Further, depending on the quantification of the degree of the mutual information (i.e., the net direction of information), we identify the switches in dominating the thermoacoustic driving between the variables during TAI, each representing a distinct mechanism of a thermoacoustic state. Additionally, from this quantification, we analyze the relative dominance of the variables and rank-order the mutual feedback according to their impact on driving TAI.

physics.flu-dyn↗

arXiv2024

Emergence of order from chaos through a continuous phase transition in a turbulent reactive flow system

As the Reynolds number is increased, a laminar fluid flow becomes turbulent, and the range of time and length scales associated with the flow increases. Yet, in a turbulent reactive flow system, as we increase the Reynolds number, we observe the emergence of a single dominant time scale in the acoustic pressure fluctuations, as indicated by its loss of multifractality. Such emergence of order from chaos is intriguing and has hardly been studied. We perform experiments in a turbulent reactive flow system consisting of flame, acoustic, and hydrodynamic subsystems interacting nonlinearly. We study the evolution of short-time correlated dynamics between the acoustic field and the flame in the spatiotemporal domain of the system. The order parameter, defined as the fraction of the correlated dynamics, increases gradually from zero to one. We find that the susceptibility of the order parameter, correlation length, and correlation time diverge at a critical point between chaos and order. Our results show that the observed emergence of order from chaos is a continuous phase transition. Moreover, we provide experimental evidence that the critical exponents characterizing this transition fall in the universality class of directed percolation. Our study demonstrates how a real-world complex, non-equilibrium turbulent reactive flow system exhibits universal behavior near a critical point.

physics.flu-dyn↗

arXiv2024

Canard explosions in turbulent thermo-fluid systems

A sudden transition to a state of high amplitude limit cycle oscillations is catastrophic in a thermo-fluid system. Conventionally, upon varying the control parameter, a sudden transition is observed as an abrupt jump in the amplitude of the fluctuations in these systems. In contrast, we present an experimental discovery of a canard explosion in a turbulent reactive flow system where we observe a continuous bifurcation with a rapid rise in the amplitude of the fluctuations within a narrow range of control parameters. The observed transition is facilitated via a state of bursting, consisting of the epochs of large amplitude periodic oscillations amidst the epochs of low amplitude periodic oscillations. The amplitude of the bursts is higher than the amplitude of the bursts of intermittency state in a conventional gradual transition, as reported in turbulent reactive flow systems. During the bursting state, we observe that temperature fluctuations of exhaust gas vary at a slower time scale in correlation with the amplitude envelope of the bursts. We also present a phenomenological model for thermoacoustic systems to describe the observed canard explosion. Using the model, we explain that the large amplitude bursts occur due to the slow-fast dynamics at the bifurcation regime of the canard explosion.

physics.flu-dyn↗

arXiv2024

Evolution of clusters of turbulent reattachment due to shear layer instability in flow past a circular cylinder

We perform large eddy simulations of flow past a circular cylinder for the Reynolds number ($Re$) range, $2\times 10^3 \leq Re \leq 4\times10^5$, spanning subcritical, critical and supercritical regimes. We investigate the spanwise coherence of the flow in the critical and supercritical regimes using complex networks. In these regimes, the separated flow reattaches to the surface in a turbulent state due to the turbulence generated by the shear layer instability. In the early critical regime, the turbulent reattachment does not occur simultaneously at all span locations. It occurs incoherently along the span in clusters. We treat strong surface pressure fluctuations due to the shear layer instability as extreme events and construct time-varying spatial proximity networks where links are based on synchronization between events. This analysis unravels the underlying complex spatio-temporal dynamics by enabling the estimation of characteristics of clusters of turbulent reattachment via the concept of connected components. In the critical regime, the number and size of the clusters increase with increase in $Re$. At higher $Re$ in the supercritical regime, they coalesce to form bigger clusters, resulting in increase in spanwise coherence of turbulent reattachment. We find that the size and number of clusters govern the variation of the time-averaged coefficient of drag ($\overline{C}_D$) in the critical and supercritical regimes. $\overline{C}_D$ exhibits power-law distribution with the most probable cluster size ($\overline{C}_D \propto E(S_C)^{-\frac{2}{5}}$) and the largest cluster size ($\overline{C}_D \propto {\overline{S}_{CL}}^{-\frac{2}{5}}$).

physics.flu-dyn↗

arXiv2023

Model adaptive phase space reconstruction

Phase space reconstruction (PSR) methods allow for the analysis of low-dimensional data with methods from dynamical system theory, but their application to prediction models, like those from machine learning (ML), is limited. Therefore, we present here a model adaptive phase space reconstruction (MAPSR) method that unifies the process of PSR with the modeling of the dynamical system. MAPSR is a differentiable PSR method that enables the use of ML methods and is based on the idea of time delay embedding. For achieving differentiable, continuous, real-valued delays, which can be optimized using gradient descent, the discrete time signal is converted to a continuous time signal. The delay vector, which stores all potential embedding delays and the trainable parameters of the model, are simultaneously updated to achieve an optimal time delay embedding for the observed system. MAPSR does not rely on any threshold or statistical criterion for determining the dimension and the set of delay values for the embedding process. The quality of the reconstruction is evaluated by the prediction loss. We apply the proposed approach to uni- and multivariate time series stemming from regular and chaotic dynamical systems and a turbulent combustor to test the generalizability of the method and compare our results with established PSR methods. We find that for the Lorenz system, the model trained with the MAPSR method is able to predict chaotic time series for nearly 7 to 8 Lyapunov time scales, which is found to be much better compared to other PSR methods (AMI-FNN and PECUZAL methods). For the univariate time series from the turbulent combustor, the long-term prediction error of the model trained using the MAPSR method stays in between that of AMI-FNN and PECUZAL methods for the regime of chaos, and for the regime of intermittency, the MAPSR method outperforms the AMI-FNN and PECUZAL methods.

physics.data-an↗

arXiv2023

Universality of oscillatory instabilities in fluid mechanical systems

Oscillatory instability (OI) emerges amidst turbulent states in experiments in various turbulent fluid and thermo-fluid systems such as aero-acoustic, thermoacoustic and aeroelastic systems. For the time series of the relevant dynamic variable at the onset of the OI, universal scaling behavior have been discovered in experiments via the Hurst exponent and certain spectral measures. By means of a center manifold reduction, the spatiotemporal dynamics of these real systems can be mapped to a complex Ginzburg-Landau equation with a linear global coupling (GCGLE). In this work, we show that the GCGLE is able to capture the universal behavior of the route to OI, elucidating it as a transition from defect to phase turbulence mediated by the global coupling.

physics.flu-dyn↗

arXiv2023

Explosive synchronization in a turbulent reactive flow system

The occurrence of abrupt dynamical transitions in the macroscopic state of a system has received growing attention. We present experimental evidence for abrupt transition via explosive synchronization in a real-world complex system, namely a turbulent reactive flow system. In contrast to the paradigmatic continuous transition to a synchronized state from an initially desynchronized state, the system exhibits a discontinuous synchronization transition with a hysteresis. We consider the fluctuating heat release rate from the turbulent flames at each spatial location as locally coupled oscillators that are coupled to the global acoustic field in the confined system. We analyze the synchronization between these two subsystems during the transition to a state of oscillatory instability and discover that explosive synchronization occurs at the onset of oscillatory instability. Further, we explore the underlying mechanism of interaction between the subsystems and construct a mathematical model of the same.

physics.flu-dyn↗

arXiv2023

Spatiotemporal Patterns Corresponding to Phase Synchronization and Generalized Synchronization States of Thermoacoustic Instability

Thermoacoustic instability in turbulent combustion systems emerges from the complex interplay among the flame, flow, and acoustic subsystems. While the onset of thermoacoustic instability exhibits global order in system dynamics, the characteristics of local interactions between subsystems responsible for this order are not well understood. In this study, we utilize the framework of synchronization to elucidate the spatiotemporal interactions among heat release rate fluctuations in the flame, velocity fluctuations in the flow, and acoustic pressure fluctuations in a turbulent combustor. We examine two forms of thermoacoustic instability, characterized by phase synchronization and generalized synchronization of the acoustic pressure and global heat release rate oscillations. Despite the presence of global synchrony, we uncover a coexistence of frequency synchrony and desynchrony in the local interaction of these oscillations within the reaction field. In regions of frequency-locked oscillations, various phase-locking patterns occur, including phase synchrony and partial phase synchrony. We discover that the local development of small pockets of phase synchrony and strong amplitude correlation between these oscillations is sufficient to trigger global phase synchronization in the system. Furthermore, as the global dynamics approach generalized synchronization, these local regions of synchrony expand throughout the reaction field. Additionally, through coupled analysis of acoustic pressure and local flow velocity fluctuations, we infer that the spatial region of flow-acoustic synchrony plays a significant role in governing thermoacoustic instabilities. Our findings imply that, in turbulent combustors, an intrinsic local balance between order, partial order, and disorder within the coupled subsystems sustains the global order during thermoacoustic instability.

physics.flu-dyn↗

arXiv2023

Dynamics of Minimal Networks of Limit Cycle Oscillators

The framework of mutually coupled oscillators on a network has served as a convenient tool for investigating the impact of various parameters on the dynamics of real-world systems. Compared to large networks of oscillators, minimal networks are more susceptible to changes in coupling parameters, the number of oscillators, and network topologies. In this study, we systematically explore the influence of these parameters on the dynamics of a minimal network comprising Stuart-Landau oscillators coupled with a distance-dependent time delay. We examine three network topologies: ring, chain, and star. Specifically, for ring networks, we study the effects of increasing nonlocality from local to global coupling on the overall dynamics of the system. Our findings reveal the existence of various synchronized states, including splay and cluster states, a partially synchronized state such as chimeric quasiperiodicity, and an oscillation quenching state such as amplitude death in these networks. Moreover, through an analysis of long-lived transients, we discover novel amplitude-modulated states within ring networks. Interestingly, we observe that increasing nonlocality diminishes the influence of the number of oscillators on the overall behavior in these networks. Furthermore, we note that chain networks, unlike ring networks, do not exhibit perfect synchrony among the coupled oscillators. In contrast, star networks demonstrate greater stability and are unaffected by the number of oscillators within the network. The insights from this study deepen our understanding of the dynamics of minimal networks and have implications for various fields, ranging from biology to engineering.

nlin.AO↗

arXiv2023

Frequency shifts during whistling occurs as transition between two phase synchronised limit cycles via a state of intermittency or abruptly

Self-sustained oscillations arising from the interactions between the hydrodynamic and the acoustic field are disastrous in engineering systems such as segmented solid rocket motors and large gas pipelines. These self-sustained oscillations (limit cycle oscillations) are also referred to as aeroacoustic instabilities, which can be heard as a whistle. Understanding the change in dynamical state by altering the control parameter in an aeroacoustic system is critical in designing control strategies for aeroacoustic instabilities. In this study, as the control parameter Reynolds number ($Re$) is varied, we hear a change in the whistling frequency. We show that this change in frequency occurs via the state of intermittency, which has bursts of periodic fluctuations amidst the regime of the aperiodic fluctuations in acoustic pressure fluctuations. At a higher Reynolds number, we observe an abrupt transition from one limit cycle oscillation (LCO) to another limit cycle oscillation during the shift in whistling frequency. Further, we use synchronisation theory to investigate the coupled behaviour of the acoustic and the hydrodynamic fields. The acoustic pressure ($p'$) and hydrodynamic ($v'$) fluctuations during LCO exhibit phase synchronisation. Thus, we conclude that the shift in whistling frequency is a transition between the two phase synchronised limit cycle oscillations that occurs either through the state of intermittency or abruptly. The periodic bursts of intermittency correspond to the phase-synchronised periodic $p'$ and $v'$, and the aperiodic epochs correspond to the desynchronised aperiodic $p'$ and $v'$.

physics.flu-dyn↗

arXiv2023

Early warnings of tipping in a non-autonomous turbulent reactive flow system: efficacy, reliability, and warning times

Real-world complex systems such as the climate, ecosystems, stock markets, and combustion engines are prone to dynamical transitions from one state to another, with catastrophic consequences. State variables of such systems often exhibit aperiodic fluctuations, either chaotic or stochastic in nature. Often, the parameters describing a system vary with time, showing time dependency. Constrained by these effects, it becomes difficult to be warned of an impending critical transition, as such effects contaminate the precursory signals of the transition. Therefore, a need for efficient and reliable early-warning signals (EWS) in such complex systems is in pressing demand. Motivated by this fact, in the present work, we analyze various EWS in the context of a non-autonomous turbulent thermoacoustic system. In particular, we investigate the efficacy of different EWS in forecasting the onset of thermoacoustic instability (TAI) and their reliability with respect to the rate of change of the control parameter. We consider the Reynolds number (Re) as the control parameter, which is varied linearly with time at finite rates. The considered EWS are derived from critical slowing down, spectral properties, and fractal characteristics of the system variables. The state of TAI is associated with large amplitude acoustic pressure oscillations that could lead thermoacoustic systems to break down. Our analysis shows that irrespective of the rate of variation of the control parameter, the Hurst exponent and variance of autocorrelation coefficients warn of an impending transition well in advance and are more reliable than other EWS measures. We also investigate the variation of amplitudes of the most significant modes of acoustic pressure oscillations with the Hurst exponent. Such variations lead to scaling laws which could be significant in prediction and devising control actions to mitigate TAI.

physics.flu-dyn↗