Characterization of degeneration process in combustion instability based on dynamical systems theory.

Effect of equivalence ratio on rotating detonation combustion with n-heptane sprays

Propulsion systems such as gas turbines are susceptible to combustion instability, when operated at lean equivalence ratio [1]. During combustion instability, there is a nonlinear interaction between combustion and acoustics leading to large amplitude acoustic oscillations. These large amplitude oscillations are detrimental to the stability of the combustor and can cause damages to the structural integrity of the combustor, flame flash back or blow off. The main source of nonlinearity is in the heat release rate caused due to the velocity perturbations at the flame holder [2]. The heat release rate fluctuations are due to the variation in the flame surface area. Hence there is a need to understand the flame dynamics that contributes to the heat release rate fluctuations. The present study aims in understanding the stability of a V - flame combustor by varying the flame location inside an acoustic resonator. By varying the flame location the instability regimes of the combustor are identified. At the flame locations where the system exhibits combustion instability, acoustic pressure oscillations are acquired simultaneously with high speed images of the flame front fluctuations so that a correlation can be made between them. Tools from dynamical systems theory are applied to the pressure signal to quantify different dynamical states of the system during combustion instability. Moreover the flame dynamics at each dynamical state are investigated. It is observed that combustion instability is characterized by interesting dynamical states such as frequency locked state, quasi-periodic oscillations, period 3 oscillations and chaotic oscillations. High speed imaging of the flame reveals different interesting patterns of flame behavior during combustion instability. Flame wrinkling, roll up of flame elements, separation as islands of the flame elements and mutual annihilation of flame elements were some of the interesting flame behavior observed. This study helps in understanding the role of nonlinear heat release rate mechanism in establishing different dynamical states during combustion instability.

Large-scale rotating detonation experiments with a 500 mm outer diameter combustor are carried out in this study. The experiment used aviation kerosene (RP-3) as fuel and hot air as oxidant. Detonation is successfully initiated between the equivalent ratio of 0.85 and 1.20. The engine works steadily for 2 s and 3 s. The detonation wave modes are two-wave collision. The average speed of detonation wave is between 920 m/s and 980 m/s. The detonation wave velocity increases with the increase in equivalence ratio, and when the equivalence ratio exceeds 1.0, the increasing trend of detonation wave slows down. Through sampling and analysis of detonation gas, it is found that the uneven distribution of fuel supply pressure in large-scale rotating detonation experiment results in inconsistent local equivalent ratio and uneven combustion. The complete combustion rate based on carbon atoms is used to evaluate the combustion completeness of detonation. With the increase in equivalent ratio, the combustion changes from deflagration to detonation, and the detonation combustion completeness gets better. The combustion completeness of detonation wave is the best near the appropriate chemical equivalent ratio. Once the equivalent ratio exceeds 1.0, then oil-rich combustion occurs and the strength of the detonation wave becomes weaker.

In this study, the thermoacoustic instabilities of partially premixed hydrogen flames in a lean direct injection (LDI) multi-cluster combustor are characterised using dynamical systems theory. The combustor is operated at a range of bulk velocities (30 - 90 m/s) and equivalence ratios(0.2-0.6), and time-resolved pressure oscillations and integrated OH* chemiluminescence measurements were taken. The thermoacoustic system reveals a variety of dynamical states in pressure such as period-1 Limit Cycle Oscillation (LCO) with a single characteristic frequency, period-2 LCO with two characteristic frequencies, intermittent, quasi-periodic and chaotic states as either bulk velocity or equivalence ratio is varied. At a bulk velocity of 30 m/s, as the equivalence ratio is gradually decreased from 0.6 to 0.2, the dynamical behaviour follows a sequence from an intermittent state to a period-1 LCO, then to a quasi-periodic state, and eventually reaches a chaotic state. As the equivalence ratio is decreased for a bulk velocity of 60 m/s, the pressure oscillations evolve from a period-2 LCO to quasi-periodic state before flame blows off. The emergence of period-2 and quasi-periodic states indicates the presence of strong non-linear interactions among the cavity acoustic modes. The emergence of period-2 and quasi-periodic states indicates strong non-linear interactions among the cavity acoustic modes. These modes and their spatial behaviour are investigated using a Helmholtz solver, showing that hydrogen flames can excite a wide range of cavity acoustic modes

Combustion instability has been widely reported in several combustion types; however, there is limited information on different fuel/air mixing distances in non-premixed combustion. Setting different distances between air tube and fuel tubes, the fuel/air mixing distances (δ) are changed by structural variations of nozzles. Keeping the heat load and equivalence ratios constant, the present work aims to examine the effects of fuel/air mixing distances on combustion instability in non-premixed combustion. Experimental observations suggest that combustion oscillations occur in non-premixed combustion with flame ignited outside the nozzle rather than other types of non-premixed combustion. Quasiperiodic oscillations, limit cycle modes, and intermittency modes are found in three fuel/air mixing distances in non-premixed combustion. The calculation methods of convection time for non-premixed combustion are established in the present work. The convection time of the limit cycle oscillations is then calculated, which is further found to trigger the second resonance modes of the combustion system. The further analysis reveals that varying fuel/air mixing distances can cause influences on local equivalence ratio distributions, and the convection time are correspondingly varied. The changes in convection time affects the coupling characteristics between heat release rate fluctuations and the acoustic modes in the combustion chamber. When the thermoacoustic coupling occurs, combustion instabilities appear. This work establishes a link between combustion instability and fuel/air mixing distances in non-premixed combustion and highlights the influences on spatial distributions of local equivalence ratios and then convection time, which can provide technical guidance for actual applications in various fuel/air mixing types.

COMPLEX DYNAMICAL SYSTEMS

Measurement of laminar burning velocities of iso-butanol-air mixtures

Effects of fuel type and equivalence ratios on the flickering of triple flames

This work delves into the theory of dynamic systems, focusing on the analysis of entropy in both classical and topological contexts. Beginning with an exposition of fundamental concepts in dynamical systems theory, particular attention is given to topological dynamical systems (TDS). The discussion progresses to explore discrete topological entropy and its significance within dynamical systems, culminating in the introduction of topological entropy pressure as a nuanced form of this concept. The study then investigates various applications of topological entropy within dynamic systems, emphasizing its utility in understanding chaotic systems and its role in ergodic theory. A novel theory, termed Topological Ergodic Entropy Theory (TEET), is presented, offering a fresh perspective on the analysis of ergodic dynamical systems. Furthermore, the work introduces the Ergodic Theory of Turbulent Flow (ETTF), which probes the interplay between topological entropy and the ergodic properties of dynamic systems governed by the Navier-Stokes equations. Through these explorations, the findings contribute significantly to the comprehension of the intricate nature of dynamical systems and their diverse applications across mathematics and physics. By scrutinizing topological entropy and its implications in dynamical systems, this research offers novel insights into the chaotic and stochastic behaviors exhibited by these systems. Additionally, the introduction of pioneering theories like ETTF opens up new avenues for understanding and modeling turbulent phenomena, thereby enriching our understanding of complex dynamical processes.

Hyperbolicity is an important concept in dynamical system theory; however, we know little about the hyperbolicity of concrete physical systems including fluid motions governed by the Navier-Stokes equations. Here, we study numerically the hyperbolicity of the Navier-Stokes equation on a two-dimensional torus (Kolmogorov flows) using the method of covariant Lyapunov vectors developed by Ginelli et al. [Phys. Rev. Lett. 99, 130601 (2007)]. We calculate the angle between the local stable and unstable manifolds along an orbit of chaotic solution to evaluate the hyperbolicity. We find that the attractor of chaotic Kolmogorov flows is hyperbolic at small Reynolds numbers, but that smaller angles between the local stable and unstable manifolds are observed at larger Reynolds numbers, and the attractor appears to be nonhyperbolic at a certain Reynolds numbers. Also, we observed some relations between these hyperbolic properties and physical properties such as time correlation of the vorticity and the energy dissipation rate.

Some manifestations of hyperbolicity in the ocean, the important concept in dynamical systems theory, are discussed. It is shown how to identify hyperbolic points, hyperbolic trajectories and their stable and unstable manifolds solving advection equations for passive scalars in a satellite-derived AVISO velocity field and computing finite-time Lyapunov exponents by the singular-value decomposition method. To validate our simulation we use available tracks of oceanic drifters following near surface currents in some areas in the Northwestern Pacific Ocean. The tracks illustrate how drifters “feel” the presence of hyperbolic points, hyperbolic trajectories and stable and unstable manifolds and change abruptly their trajectories when approaching a hyperbolicity region.

The aim of this study was to explore retirement as an occupational transition. Twenty-nine participants aged 66 years were interviewed and the data analysed using a comparative qualitative method. The analysis showed that a new temporal structure developed where the participants were gliding into a slower rhythm. Some occupations also changed meaning when they were performed in the new circumstances of retirement. A common pattern in the transition was to go from one imbalance, where work took too much time in life, to another type of imbalance where some kind of regular commitment within retirement would have been preferable. The discussion relates the findings concerning meaning and rhythm to concepts in dynamic systems theory. The importance of regular commitments in life for experience of occupational balance and the changing perspective of the future are also discussed.

Heteroclinic networks are a mathematical concept in dynamic systems theory that is suited to describe metastable states and switching events in brain dynamics. The framework is sensitive to external input and, at the same time, reproducible and robust against perturbations. Solutions of the corresponding differential equations are spatiotemporal patterns that are supposed to encode information both in space and time coordinates. We focus on the concept of winnerless competition as realized in generalized Lotka–Volterra equations and report on results for binding and chunking dynamics, synchronization on spatial grids, and entrainment to heteroclinic motion. We summarize proposals of how to design heteroclinic networks as desired in view of reproducing experimental observations from neuronal networks and discuss the subtle role of noise. The review is on a phenomenological level with possible applications to brain dynamics, while we refer to the literature for a rigorous mathematical treatment. We conclude with promising perspectives for future research.

In this paper some connections of mathematical system theory with the problem of absolute stability of control systems are pointed out. The absolute stability problem was formulated in the early 1940s starting from some practical control problems. The considerable development of this problem in the last 25 years has been profitable for mathematical system theory. At the same time concepts of system theory provided an adequate context for a deep understanding of this problem. Such system theory concepts as blocks, interconnections, isomorphism between time domain representations, and complex domain characteristics showed themselves very useful in absolute stability and hyperstability studies. Among the main contributions of absolute stability and hyperstability studies to mathematical system theory development one can cite the concept of “block plus integral index” and the system theory interpretation of Bochner's theorem on positive functions.

Effect of equivalence ratio on combustion and emissions of a dual-fuel natural gas engine ignited with diesel