Role of buoyancy-driven vortices in inducing different modes of coupled behaviour in candle-flame oscillators
TL;DR: In this paper, the authors investigated the physical mechanism behind the occurrence of different dynamical modes of coupled behavior of two oscillatory flames produced by separate bundles of candles, referred to as candle-flame oscillators, as the distance between them is varied.
Abstract: We investigate the coupled behaviour of two oscillatory flames produced by separate bundles of candles, referred to as candle-flame oscillators, as the distance between them is varied. Each bundle consists of four candles whose individual flames are fused so that the resultant flame produces self-sustained limit cycle oscillations. The recent study by Manoj et al. [Scientific Reports 8, 11626 (2018)] has reported the occurrence of four different modes of coupled behaviour, which include in-phase synchronization, amplitude death, anti-phase synchronization, and desynchronization by observing the flame dynamics of such coupled candle-flame oscillators. Here, we investigate the physical mechanism behind the occurrence of these different dynamical modes. Towards this purpose, we perform simultaneous measurements of the flow field around the candle flames using high-speed shadowgraph and of the reaction zone of each flame using high-speed CH* chemiluminescence imaging. We notice that these modes are distinguished by the distinct features of the flame dynamics and the corresponding buoyancy-induced flows surrounding the flames. We observe that the difference in the interaction of vortices, formed due to the instability of buoyancy-induced flows around each flame at various distances, plays a significant role in inducing different modes of coupled dynamics between the oscillators. Furthermore, we find that the change in the length scales of vortices shed around the flames is a contributing factor in increasing the frequency of the oscillators during the transition from in-phase to anti-phase mode of synchronization.
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TL;DR: In this paper, it was shown that the flickering mode transition from in-phase to anti-phase is caused by a transition of the inner side vortex pattern from symmetric to staggered, similar to the instability in the wake of a bluff body that initiates the Karman vortex street.
Abstract: A study finds that for two adjacent buoyant flames the flickering mode transition from in-phase to anti-phase is caused by a transition of the inner-side vortex pattern from symmetric to staggered. This mechanism is similar to the instability in the wake of a bluff body that initiates the Karman vortex street.
8 citations
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TL;DR: An experimental study reveals the synchronization route to weak chimera via quenching, clustering, and chimera states in a single system of four coupled candle-flame oscillators, and reports the discovery of multiphaseweak chimera along with experimental evidence of the theoretically predicted states of in-phase chimera and antiphase chimera.
Abstract: Synchronization and chimera are examples of collective behavior observed in an ensemble of coupled nonlinear oscillators. Recent studies have focused on their discovery in systems with least possible number of oscillators. Here we present an experimental study revealing the synchronization route to weak chimera via quenching, clustering, and chimera states in a single system of four coupled candle-flame oscillators. We further report the discovery of multiphase weak chimera along with experimental evidence of the theoretically predicted states of in-phase chimera and antiphase chimera.
6 citations
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TL;DR: In this article , a Wasserstein-space-based methodology for dynamical mode recognition of triple flickering buoyant diffusion flames in an isosceles triangle arrangement was proposed.
Abstract: Triple flickering buoyant diffusion flames in an isosceles triangle arrangement, as a nonlinear dynamical system of coupled oscillators, were experimentally studied. The focus of the study is two-fold: we established a well-controlled gas-fuel diffusion flame experiment, which well remedies the deficiencies of prevalent candle-flame experiments, and we developed a Wasserstein-space-based methodology for dynamical mode recognition, which is validated in the present triple-flame systems but can be readily generalized to the dynamical systems consisting of an arbitrary finite number of flames. By use of the present experiment and methodology, seven distinct stable dynamical modes were recognized, such as the in-phase mode, the flickering death mode, the partially flickering death mode, the partially in-phase mode, the rotation mode, the partially decoupled mode, and the decoupled mode. These modes unify the literature results for the triple flickering flame system in the straight-line and equal-lateral triangle arrangements. Compared with the mode recognitions in physical space and phase space, the Wasserstein-space-based methodology avoids personal subjectivity and is more applicable in high-dimensional systems, as it is based on the concept of distance between distribution functions of phase points. Consequently, the identification or discrimination of two dynamical modes can be quantified as the small or large Wasserstein distance, respectively.
5 citations
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TL;DR: In this article, the local extinction and nonlinear behavior of a premixed methane/air flame under acoustic excitation were investigated experimentally using high speed photography and high speed schlieren imaging.
Abstract: The local extinction and the nonlinear behavior of a premixed methane/air flame under acoustic excitation are investigated experimentally. High-speed photography and high-speed schlieren imaging ar...
4 citations
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TL;DR: In this article , the triple flickering buoyant diffusion flames of methane gas in equilateral triangle arrangement, as a nonlinear dynamical system of coupled oscillators, were computationally investigated.
Abstract: Triple flickering buoyant diffusion flames of methane gas in equilateral triangle arrangement, as a nonlinear dynamical system of coupled oscillators, were computationally investigated. The four distinct dynamical modes (in-phase, death, rotation, and partially in-phase), that were originally observed in candle-flame experiments, were computationally reproduced for the first time. The four modes were interpreted from the perspective of vortex interaction and particularly of vorticity reconnection and vortex-induced flow. Specifically, the in-phase mode is caused by the periodic shedding of the trefoil vortex formed by the reconnection of three toroidal vortices; the death mode is due to the suppression of vortex shedding at small Reynolds numbers; the rotation mode appears as three toroidal vortices alternatively shed off with a constant phase difference; the partially in-phase model is caused by the vorticity reconnection of two toroidal vortices leaving another one shedding off in anti-phase. This work well establishes a bridge between the vortex dynamics and the nonlinear dynamics of the triple-flame system, which is believed to play a key role in understanding larger dynamical systems of multiple flickering flames.
4 citations
References
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TL;DR: Molecular and physical techniques combined with physiological and medical studies are addressing questions concerning the dynamics of physiological rhythms and are transforming the understanding of the rhythms of life.
Abstract: Complex bodily rhythms are ubiquitous in living organisms. These rhythms arise from stochastic, nonlinear biological mechanisms interacting with a fluctuating environment. Disease often leads to alterations from normal to pathological rhythm. Fundamental questions concerning the dynamics of these rhythmic processes abound. For example, what is the origin of physiological rhythms? How do the rhythms interact with each other and the external environment? Can we decode the fluctuations in physiological rhythms to better diagnose human disease? And can we develop better methods to control pathological rhythms? Mathematical and physical techniques combined with physiological and medical studies are addressing these questions and are transforming our understanding of the rhythms of life.
1,126 citations
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01 Jan 2003
TL;DR: In this article, the basic principles of direct chaotic communications are presented for modeling diversity by chaos and classification by synchronization in high-dimensional dynamical systems, including cycled attractors of coupled cell systems and dynamics with symmetry.
Abstract: Cycling attractors of coupled cell systems and dynamics with symmetry- Modelling diversity by chaos and classification by synchronization- Basic Principles of Direct Chaotic Communications- Prevalence of Milnor Attractors and Chaotic Itinerancy in 'High'-dimensional Dynamical Systems- Generalization of the Feigenbaum-Kadanoff-Shenker Renormalization and Critical Phenomena Associated with the Golden Mean Quasiperiodicity- Synchronization and clustering in ensembles of coupled chaotic oscillators- Nonlinear Phenomena in Nephron-Nephron Interaction- Synchrony in Globally Coupled Chaotic, Periodic, and Mixed Ensembles of Dynamical Units- Phase synchronization of regular and chaotic self-sustained oscillators- Control of dynamical systems via time-delayed feedback and unstable controller
1,017 citations
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TL;DR: This work examines the synchronization of complex population oscillations in networks of model communities and in natural systems, where phenomena such as unusual ‘4- and 10-year cycle’ of wildlife are often found.
Abstract: Population cycles that persist in time and are synchronized over space pervade ecological systems, but their underlying causes remain a long-standing enigma1,2,3,4,5,6,7,8,9,10,11. Here we examine the synchronization of complex population oscillations in networks of model communities and in natural systems, where phenomena such as unusual ‘4- and 10-year cycle’ of wildlife are often found. In the proposed spatial model, each local patch sustains a three-level trophic system composed of interacting predators, consumers and vegetation. Populations oscillate regularly and periodically in phase, but with irregular and chaotic peaks together in abundance—twin realistic features that are not found in standard ecological models. In a spatial lattice of patches, only small amounts of local migration are required to induce broad-scale ‘phase synchronization’12,13, with all populations in the lattice phase-locking to the same collective rhythm. Peak population abundances, however, remain chaotic and largely uncorrelated. Although synchronization is often perceived as being detrimental to spatially structured populations14, phase synchronization leads to the emergence of complex chaotic travelling-wave structures which may be crucial for species persistence.
878 citations
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TL;DR: In this paper, two distinct vortices were visualized in the flames studies: large toroidal vortice outside the luminous flame and small roll-up vorticles inside the luminescent flame.
Abstract: Planar visualization was employed to study flame structure and low frequency flame oscillation. Two distinct vortices were visualized in the flames studies: large toroidal vortices outside the luminous flame and small roll-up vortices inside the luminous flame. The flame oscillation frequency and the convective velocity of the toroidal vortices were measured for ethylene, methane, and propane diffusion flames over a wide range of test conditions. The frequency was typically in the range 10 to 20 Hz and the convective velocity was approximately, 0.8 m/s. The frequency of the toroidal vortices was found to correlate with the flame oscillation frequency. The potential effects of the toroidal vortices on the flame dynamics at low fuel flow rates are discussed, for example, low frequency flame oscillation, non-linear flame bulge motion, and quenching of the luminous flame surface.
136 citations
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TL;DR: In this paper, it was shown that the instability of the annular flow is responsible for the flickering of large diffusion flames, and the authors have confirmed this phenomenon and proposed a theoretical explanation.
Abstract: Large diffusion flames are known to flicker at a frequency (∼12Hz) that is remarkably insensitive to flow rate, burner size, or gas composition. We have confirmed this phenomenon and propose a theoretical explanation. We note that, in addition to the forced convection associated with a tube-burner diffusion flame, there is strong natural convection generated by the hot gases. This bouyancy-induced flow surrounds the forced component and depends only on the thermomechanical properties of the hot and cold gas, together with g , the gravitational acceleration. We argue that it is the instability (of modified Kelvin-Helmholtz type) of this annular flow that is responsible for the flickering. A paradigm for this flow is defined by the infinite candle , an ideal plane diffusion flame in which the flow field is induced solely by buoyancy. The infinite candle admits a similarity solution. An inviscid, parallel flow stability analysis of this flow-field yields a frequency for which the spatial growth of the disturbance is a maximum. This is within a factor of 2 of the observed frequency.
125 citations
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