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Coherence resonance (CR) is a phenomenon in which the response of a stable nonlinear system to external noise exhibits a peak in coherence at an intermediate noise amplitude. We report the first experimental evidence of CR in a hydrodynamic system, a low-density jet capable of undergoing both supercritical and subcritical Hopf bifurcations. By applying noise to the jet in its unconditionally stable regime, we find that, for both types of bifurcation, the coherence factor peaks at an intermediate noise amplitude and increases as the stability boundary is approached. We also find that the autocorrelation function decays differently between the two types of bifurcation, indicating that CR can reveal information about the nonlinearity of a system even before it bifurcates to a limit cycle. We then model the CR dynamics with a stochastically forced van der Pol oscillator calibrated in two different ways: (i) via the conventional method of measuring the amplitude evolution in transient experiments and (ii) via the system-identification method of Lee et al. (J. Fluid Mech., vol. 862, 2019, pp. 200–215) based on the Fokker–Planck equation. We find better experimental agreement with the latter method, demonstrating the deficiency of the former method in identifying the correct form of system nonlinearity. The fact that CR occurs in the unconditionally stable regime, prior to both the Hopf and saddle-node points, implies that it can be used to forecast the onset of global instability. Although demonstrated here on a low-density jet, CR is expected to arise in almost all nonlinear dynamical systems near a Hopf bifurcation, opening up new possibilities for the development of global-instability precursors in a variety of hydrodynamic systems.

In self-excited combustion systems, the application of open-loop forcing is known to be an effective strategy for controlling periodic thermoacoustic oscillations, but it is not known whether and under what conditions such a strategy would work on thermoacoustic oscillations that are not simply periodic. In this study, we experimentally examine the effect of periodic acoustic forcing on a prototypical thermoacoustic system consisting of a ducted laminar premixed flame oscillating quasiperiodically on an ergodic torus at two incommensurate natural frequencies, and. Compared with that of a classical period-1 system, complete synchronization of this system is found to occur via a more intricate route involving three sequential steps: As the forcing amplitude, , increases at a fixed forcing frequency, , the system transitions first (i)to ergodic quasiperiodicity; then (ii)to resonant quasiperiodicity as the weaker of the two natural modes, , synchronizes first, leading to partial synchronization; and finally (iii)to a limit cycle as the remaining natural mode, , also synchronizes, leading to complete synchronization. The minimum required for partial and complete synchronization decreases as approaches either or , resulting in two primary Arnold tongues. However, when forced at an amplitude above that required for complete synchronization, the system can transition out of and into or . The optimal control strategy is to apply off-resonance forcing at a frequency around the weaker natural mode and at an amplitude just sufficient to cause , because this produces the largest reduction in thermoacoustic amplitude via asynchronous quenching. Analysis of the Rayleigh index shows that this reduction is physically caused by a disruption of the positive coupling between the unsteady heat release rate of the flame and the and acoustic modes. If the forcing is applied near the stronger natural mode , however, resonant amplification can occur. We then phenomenologically model this t

Low-density jets are central to many natural and industrial processes. Under certain conditions, they can develop global oscillations at a limit cycle, behaving as a prototypical example of a self-excited hydrodynamic oscillator. In this study, we perform system identification of a low-density jet using measurements of its noise-induced dynamics in the unconditionally stable regime, prior to both the Hopf and saddle-node points. We show that this approach can enable prediction of (i) the order of nonlinearity, (ii) the locations and types of the bifurcation points (and hence the stability boundaries) and (iii) the resulting limit-cycle oscillations. The only assumption made about the system is that it obeys a Stuart-Landau equation in the vicinity of the Hopf point, thus making the method applicable to a variety of hydrodynamic systems. This study constitutes the first experimental demonstration of system identification using the noise-induced dynamics in only the unconditionally stable regime, i.e. away from the regimes where limit-cycle oscillations may occur. This opens up new possibilities for the prediction and analysis of the stability and nonlinear behaviour of hydrodynamic systems.

Low-density jets are central to many natural and engineering processes. Under certain conditions, they can develop global oscillations at a limit cycle, behaving as a prototypical example of a self-excited hydrodynamic oscillator. In this study, we perform system identification of a low-density jet using measurements of its noise-induced dynamics in the unconditionally stable regime, prior to both the Hopf and saddle-node points. We show that this approach can enable prediction of (i) the order of nonlinearity, (ii) the locations and types of the bifurcation points (and hence the stability boundaries), and (iii) the resulting limit-cycle oscillations. The only assumption made about the system is that it obeys a Stuart-Landau equation in the vicinity of the Hopf point, thus making the method applicable to a variety of hydrodynamic systems. This study constitutes the first experimental demonstration of system identification using only the noise-induced dynamics in the unconditionally stable regime, opening up new possibilities for the prediction and analysis of the stability and nonlinear behavior of hydrodynamic systems.

Recent applications of nonlinear time-series analysis have shown that thermoacoustic systems can exhibit self-excited behavior more complex than simple period-1 oscillations. Such behavior has been comprehensively explored in the Rijke tube and in gas turbines, but less so in rocket engines. In this experimental study, we examine the thermoacoustic oscillations of a full-scale solid rocket motor (SRM) by means of nonlinear time-series analysis, namely phase portraits, Poincaré maps and recurrence plots. In contrast to conventional linear tools based on the Fourier transform, these nonlinear tools can enable unambiguous identification of different dynamical states, such as period-k states, quasiperiodicity and chaos. In this study, these tools reveal limit-cycle dynamics not reported before in an SRM, such as transient mode switching between unstable attractors in phase space, with transitions between period-2 and period-3 states. In summary, this study constitutes the first experimental application of nonlinear time-series analysis to a full-scale SRM, demonstrating an alternative to conventional linear tools for the characterization of nonlinear thermoacoustic oscillations in rocket engines. © 2018 Elsevier Inc.

In low-density axisymmetric jets, the onset of global instability is known to depend on three control parameters, namely the jet-to-ambient density ratio S, the initial momentum thickness 0 and the Reynolds number Re. For sufficiently low values of S and 0, these jets bifurcate from a steady state (a fixed point) to a self-excited oscillatory state (a limit cycle) when Re increases above a critical value corresponding to the Hopf point, ReH. In the literature, this Hopf bifurcation is often regarded as supercritical. In this experimental study, however, we find that under some conditions, there exists a hysteretic bistable region at ReSN < Re < ReH, where ReSN denotes a saddle-node point. This shows that, contrary to expectations, the Hopf bifurcation can also be subcritical, which we explore by evaluating the coefficients of a truncated Landau model. The existence of subcritical bifurcations implies the potential for triggering and the need for weakly nonlinear analyses to be performed to at least fifth order if one is to be able to predict saturation and bistability. We conclude by proposing a universal scaling for ReH in terms of S and 0. This scaling, which is insensitive to the super/subcritical nature of the bifurcations, can be used to predict the onset of self-excited oscillations, providing further evidence to support Hallberg & Strykowski's concept (J. Fluid Mech., vol. 569, 2006, pp. 493-507) of universal global modes in low-density jets. © 2017 Cambridge University Press.

Aims and Objectives: The study was designed with a broad objective of studying the imaging findings of the common interstitial lung diseases and to assess the severity of the disease and determine the reversibility capability of the pulmonary parenchymal damage in ILD’s. Patients and Methods: This was a prospective, observational study in which we evaluated 50 patients suspected of having interstitial lung diseases based on radiographic or clinical findings, by high resolution computed tomography (HRCT) over a period of one year. Results: Out of the 50 patients, majority of them had idiopathic pulmonary fibrosis (n=16) followed by interstitial pulmonary involvement in patients of rheumatoid arthritis (n=13), scleroderma (n=10) and systemic lupus erythematosis (n=9). The less common ILD’s included were Occupational lung disease (n=1) and Mycosis fungoides (n=1). Conclusion: HRCT of the lung in cases of the suspected interstitial lung diseases forms an invaluable tool for accurate and early identification and in conjunction with the clinical findings can obviate the need of lung biopsy in diagnosis of ILD’s.

Low-density jets are known to bifurcate from a steady state (a fixed point) to self-excited oscillations (a periodic limit cycle) when the Reynolds number increases above a critical value corresponding to the Hopf point, ReH. In the literature, this Hopf bifurcation is often considered to be supercritical because the self-excited oscillations appear only when Re>ReH. However, we find that under some conditions, there exists a hysteretic bistable region at ReSN

Planar dense wakes can be found in many industrial processes, such as combustion and paper-making. Confinement is known to make such wakes more locally absolutely unstable, but this destabilizing effect has not been comprehensively examined in real wakes bounded by a finite streamwise domain. For example, it is not known (i) how long the confinement walls should be and (ii) what the critical values of the operating parameters should be for global instability to occur. In this experimental study, we try to answer these questions by examining a planar dense wake consisting of a central stream of CO2 (dense gas) sandwiched by two identical outer streams of air (light gas). The wake is confined by solid walls of variable length, which act as an adjustable confinement. We find that the confinement length has a strong influence on the hydrodynamic stability of the wake: (a) self-excited global oscillations appear only when the confinement length exceeds a critical value and (b) the streamwise location of the wavemaker changes with confinement length. Knowledge of how long the confinement walls should be for global instability to occur under various conditions could be useful for optimizing industrial processes.

Forced synchronization is a process in which a self-excited system subjected to external forcing starts to oscillate at the forcing frequency ff in place of its own natural frequency fn. There are two motivations for studying this in thermoacoustics: (i) to determine how external forcing could be used to control thermoacoustic oscillations, which are harmful to many combustors; and (ii) to better understand the nonlinear interactions between self-excited hydrodynamic and thermoacoustic oscillations. In this experimental study, we examine the response of a ducted premixed flame to harmonic acoustic forcing, for two natural states of the system: (1) a state with periodic oscillations at f1 and a marginally stable mode at f2; and (2) a state with quasiperiodic oscillations at two incommensurate frequencies f1 and f2. When forcing the periodic state, we find that the forcing amplitude required for lock-in increases linearly with \ff−f1\ and that the marginally stable mode becomes excited when ff≈f2. When forcing the quasiperiodic state, we find that the system locks into the forcing when ff≈f1 or f2 or 1/2(f1+f2). These findings should lead to improved control of periodic and aperiodic thermoacoustic oscillations in combustors.

Combustion noise, which refers to irregular low-amplitude pressure oscillations, is conventionally thought to be stochastic. It has therefore been modeled using a stochastic term in the analysis of thermoacoustic systems. Recently, however, there has been a renewed interest in the validity of that stochastic assumption, with tests based on nonlinear dynamical theory giving seemingly contradictory results: some show combustion noise to be stochastic while others show it to be chaotic. In this study, we show that this contradiction arises because those tests cannot distinguish between noise amplification and chaos. We further show that although there are many similarities between noise amplification and chaos, there are also some subtle differences. It is these subtle differences, not the results of those tests, that should be the focus of analyses aimed at determining the true nature of combustion noise. Recognizing this is an important step towards improved understanding and modeling of combustion noise for the study of thermoacoustic instabilities.