Synchronization framework for modeling transition to thermoacoustic instability in laminar combustors

We, herein, present a new model based on the framework of synchronization to describe a thermoacoustic system and capture the multiple bifurcations that such a system undergoes. Instead of applying flame describing function to depict the unsteady heat release rate as the flame's response to acoustic perturbation, the new model considers the acoustic field and the unsteady heat release rate as a pair of nonlinearly coupled damped oscillators. By varying the coupling strength, multiple dynamical behaviors, including limit cycle oscillation, quasi-periodic oscillation, strange nonchaos, and chaos can be captured. Furthermore, the model was able to qualitatively replicate the different behaviors of a laminar thermoacoustic system observed in experiments by Kabiraj et al.~[Chaos 22, 023129 (2012)]. By analyzing the temporal variation of the phase difference between heat release rate oscillations and pressure oscillations under different dynamical states, we show that the characteristics of the dynamical states depend on the nature of synchronization between the two signals, which is consistent with previous experimental findings.Comment: 18 pages, 7 figure

Inhibiting the onset of thermoacoustic instability through targeted control of critical regions

This experimental study investigates the dynamical transition from stable operation to thermoacoustic instability in a turbulent bluff-body stabilised dump combustor. We conduct experiments to acquire acoustic pressure and local heat release rate fluctuations and use them to characterise this transition as we decrease the equivalence ratio towards a fuel-lean setting. More importantly, we observe a significant increase in local heat release rate fluctuations at critical locations well before thermoacoustic instability occurs. One of these critical locations is the stagnation zone in front of the bluff-body. By strategically positioning slots (perforations) on the bluff-body, we ensure the reduction of the growth of local heat release rate fluctuations at the stagnation zone near the bluff-body well before the onset of thermoacoustic instability. We show that this reduction in local heat release rate fluctuations inhibits the transition to thermoacoustic instability. We find that modified configurations of the bluff-body that do not quench the local heat release rate fluctuations at the stagnation zone result in the transition to thermoacoustic instability. We also reveal that an effective suppression strategy based on the growth of local heat release rate fluctuations requires an optimisation of the slots' area-ratio for a given bluff-body position. Further, the suppression strategy also depends on the spatial distribution of perforations on the bluff-body. Notably, an inappropriate distribution of the slots, which does not quench the local heat release rate fluctuations at the stagnation zone but creates new critical regions, may even result in a dramatic increase in the amplitudes of pressure oscillations

Modeling ambient temperature and relative humidity sensitivity of respiratory droplets and their role in Covid-19 outbreaks

One of the many unresolved questions that revolves around the Covid-19 pandemic is whether local outbreaks can depend on ambient conditions like temperature and relative humidity. In this paper, we develop a model that tries to explain and describe the temperature and relative humidity sensitivity of respiratory droplets and their possible connection in determining viral outbreaks. The model has two parts. First, we model the growth rate of the infected population based on a reaction mechanism - the final equations of which are similar to the well-known SIR model. The advantage of modeling the pandemic using the reaction mechanism is that the rate constants have sound physical interpretation. The infection rate constant is derived using collision rate theory and shown to be a function of the respiratory droplet lifetime. In the second part, we have emulated the respiratory droplets responsible for disease transmission as salt solution droplets and computed their evaporation time accounting for droplet cooling, heat and mass transfer and finally crystallization of the salt. The model output favourably compares with the experimentally obtained evaporation characteristics of levitated droplets of pure water and salt solution, respectively, ensuring fidelity of the model. Droplet evaporation/desiccation time is indeed dependent on ambient temperature and relative humidity, considered at both outdoor and indoor conditions. Since the droplet evaporation time determines the infection rate constant, ambient temperature and relative humidity are shown to impact the outbreak growth rates.Comment: Revised Equations 7 and 24. This resulted in a minor change in Figure

Detection of dynamical regime transitions with lacunarity as a multiscale recurrence quantification measure

We propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry out a recurrence plot-based analysis for different paradigmatic systems and nonlinear empirical data in order to demonstrate the ability of our method to detect dynamical transitions ranging across different temporal scales. It succeeds to distinguish states of varying dynamical complexity in the presence of noise and non-stationarity, even when the time series is of short length. In contrast to traditional recurrence quantifiers, no specification of minimal line lengths is required and geometric features beyond linear structures in the recurrence plot can be accounted for. This makes lacunarity more broadly applicable as a recurrence quantification measure. Lacunarity is usually interpreted as a measure of heterogeneity or translational invariance of an arbitrary spatial pattern. In application to recurrence plots, it quantifies the degree of heterogeneity in the temporal recurrence patterns at all relevant time scales. We demonstrate the potential of the proposed method when applied to empirical data, namely time series of acoustic pressure fluctuations from a turbulent combustor. Recurrence lacunarity captures both the rich variability in dynamical complexity of acoustic pressure fluctuations and shifting time scales encoded in the recurrence plots. Furthermore, it contributes to a better distinction between stable operation and near blowout states of combustors

Seeds of phase transition to thermoacoustic instability

Tackling the problem of emissions is at the forefront of scientific research today. While industrial engines designed to operate in stable regimes produce emissions, attempts to operate them at 'greener' conditions often fail due to a dangerous phenomenon known as thermoacoustic instability. Hazardous high amplitude periodic oscillations during thermoacoustic instability lead to the failure of these engines in power plants, aircraft, and rockets. To prevent this catastrophe in the first place, identifying the onset of thermoacoustic instability is required. However, detecting the onset is a major obstacle preventing further progress due to spatiotemporal variability in the reacting field. Here, we show how to overcome this obstacle by discovering a critical condition in certain zones of the combustor, which indicates the onset of thermoacoustic instability. In particular, we reveal the critical value of the local heat release rate that allows us to distinguish stable operating regimes from hazardous operations. We refer to these zones as seeds of the phase transition because they show the earliest manifestation of the impending instability. The increase in correlations in the heat release rate between these zones indicates the transition from a chaotic state to a periodic state. Remarkably, we found that observations at the seeds of the phase transition enable us to predict when the onset occurs, well before the emergence of dangerous large-amplitude periodic acoustic pressure oscillations. Our results contribute to the operation of combustors in more environment-friendly conditions. The presented approach is applicable to other systems exhibiting such phase transitions. © 2022 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft

Preventing a global transition to thermoacoustic instability by targeting local dynamics

The burning of fossil fuels to generate power produces harmful emissions. Lowering such emissions in gas turbine engines is possible by operating them at fuel-lean conditions. However, such strategies often fail because, under fuel-lean conditions, the combustors are prone to catastrophic high-amplitude oscillations known as thermoacoustic instability. We reveal that, as an operating parameter is varied in time, the transition to thermoacoustic instability is initiated at specific spatial regions before it is observed in larger regions of the combustor. We use two indicators to discover such inceptive regions: the growth of variance of fluctuations in spatially resolved heat release rate and its spatiotemporal evolution. In this study, we report experimental evidence of suppression of the global transition to thermoacoustic instability through targeted modification of local dynamics at the inceptive regions. We strategically arrange slots on the flame anchor, which, in turn, reduce the local heat release rate fluctuations at the inceptive regions and thus suppress the global transition to thermoacoustic instability. Our results open new perspectives for combustors that are more environmental-friendly. © 2022, The Author(s)

Universality in the emergence of oscillatory instabilities in turbulent flows

Spontaneous emergence of periodic oscillations due to self-organization is ubiquitous in turbulent flows. The emergence of such oscillatory instabilities in turbulent fluid mechanical systems is often studied in different system-specific frameworks. We uncover the existence of a universal scaling behaviour during self-organization in turbulent flows leading to oscillatory instability. Our experiments show that the spectral amplitude of the dominant mode of oscillations scales inversely with the Hurst exponent of a fluctuating state variable following an inverse power law relation. Interestingly, we observe the same power law behaviour with a constant exponent near -2 across various turbulent systems such as aeroacoustic, thermoacoustic and aeroelastic systems.Comment: 5 pages, 4 figures and supplementary informatio

Experimental investigation of bifurcations in a thermoacoustic engine

In this study, variation in the characteristics of the pressure oscillations in a thermoacoustic engine is explored as the input heat flux is varied. A bifurcation diagram is plotted to study the variation in the qualitative behavior of the acoustic oscillations as the input heat flux changes. At a critical input heat flux (60 Watt), the engine begins to produce acoustic oscillations in its fundamental longitudinal mode. As the input heat flux is increased, incommensurate frequencies appear in the power spectrum. The simultaneous presence of incommensurate frequencies results in quasiperiodic oscillations. On further increase of heat flux, the fundamental mode disappears and second mode oscillations are observed. These bifurcations in the characteristics of the pressure oscillations are the result of nonlinear interaction between multiple modes present in the thermoacoustic engine. Hysteresis in the bifurcation diagram suggests that the bifurcation is subcritical. Further, the qualitative analysis of different dynamic regimes is performed using nonlinear time series analysis. The physical reason for the observed nonlinear behavior is discussed. Suggestions to avert the variations in qualitative behavior of the pressure oscillations in thermoacoustic engines are also provided

Universality in spectral condensation

Self-organization is the spontaneous formation of spatial, temporal, or spatiotemporal patterns in complex systems far from equilibrium. During such self-organization, energy distributed in a broadband of frequencies gets condensed into a dominant mode, analogous to a condensation phenomena. We call this phenomenon spectral condensation and study its occurrence in fluid mechanical, optical and electronic systems. We define a set of spectral measures to quantify this condensation spanning several dynamical systems. Further, we uncover an inverse power law behaviour of spectral measures with the power corresponding to the dominant peak in the power spectrum in all the aforementioned systems.Comment: 5 pages, 3 figure