Resonance behavior of twin flickering (non-premixed) flames at various separation distances horizontally is examined and two oscillation modes (in-phase and anti-phase) are clearly identified depending on the distance. Our ultimate goal is to develop the acceptable mathematical model to explain such resonance behavior. There has been proposed “radiation-basis” mathematical model by physics-oriented researchers, claiming that the radiation is a primary factor to give an anti-phase mode. Our recent experimental and numerical studies, on the other hand, suggest that the radiation may not be the essential factor, rather, fluid dynamical motion shall be a key factor to cause the mode transition. Potential strategy to upgrade the mathematical model are proposed. Taking a “mathematical-scientific” approach to combustion problem is typical inter-disciplinary issue and productive interaction between physicists and combustion researchers is found to be highly recommended to develop further.
The emergence of spatiotemporal chaos produced by spatially extended nonlinear system and chaos synchronization have promoted the sharp growth of much interest in nonlinear physics and related branches of mathematical science. We have numerically studied the spatiotemporal dynamics of flow velocity field in a buoyancy-induced turbulent fire and the synchronization of two coupled turbulent fires from viewpoints of statistical complexity, complex networks, and dynamical systems theory. Two classes of dynamics: (1) low-dimensional deterministic chaos in the near field dominated by the unstable motion of toroidal vortices and (2) high-dimensional chaos in the far field forming a well-developed turbulent plume, dominate the dynamic behavior of a buoyancy-induced turbulent fire. A scale-free structure related to fractality appears in weighted networks between vortices, while its lifetime follows a clear power law, indicating intermittent appearances, disappearances, and reappearances of the scale-free nature. A significant decrease in the distance between the two fire sources gives rise to a synchronized state in the near field. The synchronized state vanishes in the far field, regardless of the distance between the two fire sources.
This paper reports suppression of self-sustained oscillations by mutual interactions between the oscillators and by delayed feedback, theoretically in the case of van der Pol oscillators and experimentally in the case of acoustic oscillators. For the acoustic oscillators, the dissipative coupling is achieved by a needle valve, whereas the delayed coupling, and also the delayed feedback, is provided by a connecting tube of a half-wavelength of the acoustic oscillations. Because only the simple components are required in the couplings, this method would be highly reliable in suppressing the oscillations.
Research on the transition to thermoacoustic instability has been gaining interest in the recent years. Traditionally, such a transition to thermoacoustic instability was considered as a Hopf bifurcation, wherein the system dynamics exhibit a direct transition from stable (combustion noise) to unstable (limit cycle oscillations) operation at a critical value of the control parameter. Recent studies have reported that the transition to thermoacoustic instability is not direct, but happens through an intermediate state called intermittency. During intermittency, bursts of large amplitude periodic oscillations emerge amongst epochs of relatively low amplitude aperiodic oscillations. The use of synchronization theory to detect the coupled behaviour of the acoustic pressure and the heat release rate oscillations has shown that these signals are desynchronized during the state of combustion noise, whereas they exhibit phase synchronization at the onset of thermoacoustic instability. During the state of intermittency, signals are phase synchronized in the periodic regimes and desynchronized in the aperiodic regimes. Synchronization theory further aids in identifying another state of the coupled oscillations called generalized synchronization that happens after the onset of phase synchronization, during which both the acoustic pressure and the heat release rate signals exhibit a strong correlation in their amplitudes as well as instantaneous phases.
After the interpretation of the kinetic mechanism of hydrogen-oxygen combustion in the early twentieth century, the elementary reaction kinetics has been considered to be one of the essential issues in the science and technology of combustion. Recent developments in the quantum chemical methodology and computational technology have provided powerful tools for the construction and improvement the reaction mechanisms of combustion. However, the underlying theories of the reaction rate constants have not been well understood nor documented, especially in the sense that they are essentially based on the molecular statistical thermodynamics. In this article, the key points in the reaction kinetics will be described with a focus on the theoretical evaluation of the rate constants. The rate law of the gas-phase elementary reaction is briefly introduced and then the statistical theory of the rate constant, transition state theory, will be described. The molecular statistical thermodynamics will be discussed as it plays a central role in the actual evaluation of the rate constants. The theory of unimolecular reactions will be also introduced.
Oblique detonation wave (ODW) in a non-uniform mixture was investigated using a two-stage light gas gun through a high-speed Schlieren photography. The concentration gradient was formed with hydrogen injection and controlled by the waiting time. Helium was used instead of hydrogen to measure the gradient by gas sampling. As the results, asymmetric curved ODW front appeared due to variable Chapman-Jouguet (C-J) speed. Asymmetric Straw-Hat type structure was also observed depending on the waiting time in which stabilized/attenuated ODW accompanied Straw Hat type structure above/below the projectile. Comparison to the cases of the uniform mixtures also revealed that the range of equivalence ratio for which ODW can be observed increases in the far field due to the absence of attenuation by the curvature effect and expansion wave, indicating that the criterion based on non-dimensional diameter is not always valid. In addition, one low-speed experimental case encountered a locally propagating detonation in a fuel-richer region, which can be attributed to a locally larger C-J speed exceeding the projectile speed.