Chaos in thermal pulse combustion

An experimental thermal pulse combustor and a differential equation model of this device are shown to exhibit chaotic behavior under certain conditions. Chaos arises in the model by means of a progression of period-doubling bifurcations that occur when operating parameters such as combustor wall temperature or air/fuel flow are adjusted to push the system toward flameout. Bifurcation sequences have not yet been reproduced experimentally, but similarities are demonstrated between the dynamic features of pressure fluctuations in the model and experiment. Correlation dimension, Kolmogorov entropy, and projections of reconstructed attractors using chaotic time series analysis are demonstrated to be useful in classifying dynamical behavior of the experimental combustor and for comparison of test data to the model results. Ways to improve the model are suggested. (c) 1995 American Institute of Physics.     

An investigation of nonlinear dynamics of a thermal pulse combustor

Nonlinear dynamics of a thermal pulse combustor was investigated using a coupled fourth order lumped combustor model. The effects of optically thin radiation from the combustor gases to the wall are also investigated. The system response changes from steady combustion to extinction through oscillatory combustion as the wall temperature is lowered. The qualitative results suggest a transition to chaos through a period-doubling route prior to extinction. The presence of chaos is also confirmed by quantitative measures like correlation dimension and Lyapunov exponent. The system dynamics is qualitatively similar in presence and absence of radiation. However, inclusion of radiative heat loss leads to extinction at higher temperatures and also increases the predicted range of wall temperatures for which limit cycle behaviour is obtained. A measure for monitoring the proximity of the system to extinction has been developed using the time series data.     

Bifurcation analysis of steady states and limit cycles in a thermal pulse combustor model

Oscillatory behaviour of state variables is desirable in pulse combustors, as properly designed pulsations lead to improved performances, such as higher thermal efficiency and lower emissions compared to steady combustors. In the present work, we perform a systematic investigation of the stability of steady states and limit cycles of a pulse combustor model through numerical continuation. Different bifurcation parameters such as tailpipe friction factor, wall temperature, convective heat transfer coefficient, inlet temperature and inlet fuel mass fraction are varied to identify the complete ranges of those parameters at which limit cycles can be expected. This analysis identifies alternative stable periodic regimes in parameter space (e.g. friction factor). In addition, a few performance indicators such as amplitude of oscillations, cycle-averaged heat transfer and cycle-averaged specific thrust are compared between different ranges of friction factor yielding limit cycle oscillations. The comparison clearly shows that, depending upon the application, friction factor can be chosen from different regimes. The time-integration of the model is also performed to support the bifurcation results obtained from numerical continuation, wherever appropriate. The complete stability margin of limit cycle oscillations for those bifurcation parameters can be useful for improved design of the combustor and for determining the optimal operating conditions of pulse combustors.     

等离子体源离子注入过程中半圆形碗状样品的两维温度分布

等离子体源离子注入过程(PSII)中样品温度是一个非常重要的参量。由于注入到样品上的能量很大，导致样品温度很高，所以在实验中获知样品的温度分布有着很重要的意义。本文利用热传导方程建立了半圆形碗状样品内部温度升高模型，研究样品内温度演化过程。以注入离子束流作为能量输入项，热辐射为能量损失项，并考虑了热辐射过程中样品的形状因子的影响。考察了离子注入过程中样品上所施加负偏压的脉冲宽度和频率对样品温度分布的影响。研究结果显示，脉冲频率达到一定值后，样品温度不再随频率增加而升高。     

Transient temperature profile in the gain medium of CW- and end-pumped passively Q-switched microchip laser

The transient temperature profile in CW- and end-pumped passively Q-switched (PQS) microchip laser is investigated qualitatively by treating the population inversion (thereby the thermal load) as the sawtooth function of the time. The numerical results reveal not only the dynamics of thermal buildup, but also the dependence of the quasi-steady-state temperature rise and the repetitively oscillatory amplitude on the incident pump power and the pulse repetition rate of PQS laser. The abruptly ascending branch of the repetitive temperature oscillation is synchronized with the pulsing stage of PQS laser. As the result, the abrupt temperature transition during the pulsing stage would introduce the fluctuation into the PQS pulse parameters (pulse energy, pulse width, and peak power) via temperature-dependent stimulated emission and thermal lensing effect.     

Message encoding-decoding at 2.5 Gbits/s through synchronization of chaotic pulsing semiconductor lasers

Chaotic optical communication with fast chaotic pulsing semiconductor lasers is experimentally demonstrated. Both a pulse stream at a 500-MHz repetition rate and a pseudorandom bit sequence at a 2.5-Gbit/s bit rate are successfully transmitted. The quality of synchronization in a chaos-modulation scheme is examined. The quality of message recovery is correlated to the quality of chaos synchronization.     

混沌噪声背景下微弱脉冲信号的检测及恢复

构建了一种在混沌噪声背景下检测并恢复微弱脉冲信号的模型.首先,基于混沌信号的短期可预测性及其对微小扰动的敏感性,对观测信号进行相空间重构、建立局域线性自回归模型进行单步预测,得到预测误差,并利用假设检验方法从预测误差中检测观测信号中是否含有微弱脉冲信号.然后,对微弱脉冲信号建立单点跳跃模型,并融合局域线性自回归模型,构成双局域线性(DLL)模型,以极小化DLL模型的均方预测误差为目标进行优化,采用向后拟合算法估计模型的参数,并最终恢复出混沌噪声背景下的微弱脉冲信号.仿真实验结果表明本文所建的模型能够有效地检测并恢复出混沌噪声背景中的微弱脉冲信号.     

Theory of stability and bifurcation in a multi-quantum well laser with opto-electronic delayed feedback

This paper presents an opto-electronic feedback multi-quantum well laser system and outlines our study of the dynamics and bifurcation in a multi-quantum well laser due to the opto-electronic delayed feedback effect. We point out theoretically the conditions of stability and Hopf bifurcation of the laser. The relaxation oscillation frequency of the system is educed to be the function of the feedback level, delayed time and in-current. The route from stability to bifurcation is numerically simulated via varying the delayed time, feedback strength and in-current. The results show that the induced dynamics can be grouped into four distinct types or modes (stable, periodic pulsed, undamped oscillating or beating, and chaos), where the frequency and intensity varying with the delayed time in the two periodic regions are analyzed detailedly to find that the pulsing frequency is reduced with the long delayed time while the pulsing intensity is added with the long delayed time. And the chaotic pulsing frequency is increased with the large in-current. In addition, the carrier transport between the barrier region and the active region can characterize the dynamics in the laser to produce stable, periodic pulsed, beating and chaotic states by altering the carriers transport or escape rate value.     

Irregular phase slipping in a model for a laser with injected signal

In a model for a single mode laser with injected signal we find irregular pulsing of the output signal. During the turbulent time intervals the relative phase between the internal and the external field slips by an integer multiple of 2pi, where the multiplicity varies irregularly from pulse to pulse. Between the pulses, in the laminar time intervals, the relative phase is locked. We compare this behavior with the results of various other laser models. By the investigation of this interesting mechanism for the creation of phase chaos in a driven oscillator, we learn which properties are responsible for the irregular interruption of the phase locking. (c) 1997 American Institute of Physics.     

微型燃烧器预混腔内催化重整、积碳及流动特性模拟

因微型燃烧器内微尺度燃烧易熄火,燃烧效率不高,存在催化重整过程中的积碳、微尺度等问题,可利用甲烷和湿空气中水蒸汽预混催化重整产氢来强化燃烧,对预混腔内催化重整,积碳及流动特性进行模拟,探讨了微型预混腔中甲烷、水蒸汽重整过程中水碳比、质量流量和催化壁面温度对催化重整、积碳、流动等的影响.     

Modeling of a self-excited pulse combustor and stability analysis

The major bottleneck for popularization and utilization of the conventional mechanical valve pulse combustors is the self-priming mode of gas supply. An aerodynamic valve (as against mechanical valve) self-excited pulse combustor of the Helmholtz-type with continuous supply of gas and air was designed and a mathematical model was established in this paper. The theoretical model employed well-stirred reactor model and a single step Arrhenius chemistry, and took those factors which might affect the combustion stability into account. The factors include the variation of the mass rate of the reactants affected by the pressure in the combustion chamber, the convective and radiation heat loss in the combustion chamber, and the heat transfer and wall friction in the tailpipe. The effect of wall temperature of combustion chamber, wall heat transfer coefficient, tailpipe length and friction coefficient on combustionstability were analyzed. The range of combustion oscillations can be predicted. It is theoretically and experimentally shown that combustion oscillations can be produced with a continuous supply of fuel and air without mechanical valves. The experimental data show qualitative agreement with predictions from the theoretical model. The theoretical model could be a tool for designing and optimizing the self-excited pulse combustor.     

Chaos in a multimode solid-state laser system

When a nonlinear crystal is placed within a multimode solid-state laser cavity, deterministic fluctuations are induced in the output intensity. In this paper, the results of our studies of the intensity noise in a diode pumped, intracavity frequency doubled Nd:YAG (neodymium doped yttrium aluminum garnet) laser will be presented. First, a novel technique to eliminate these fluctuations is described. Second, the observation of antiphase states in the laser output is discussed. These states are characterized by a cyclic periodic pulsing of the individual longitudinal mode intensities. Finally, the statistical properties of chaotic intensity fluctuations are characterized. It is be demonstrated that it is possible to accurately model the laser dynamics by a system of globally coupled, nonlinear oscillators.     

Dynamics of Optical Bistability with Kerr-nonlinear Blackbody Radiation Reservoir

In this paper we investigate the nonlinear dynamics for optical bistabile(OB) model of homogeneously broadened two-level atomic medium interacting with a single mode of the ring cavity in the presence of a Kerr-nonlinear blackbody(KNB) radiation reservoir. We show the impact of the relative temperature of the reservoir on the transition between the dynamical states via bifurcation diagrams that represents the relation between maximum values of the output field and the relative temperature for fixed input field. Specifically, decreasing the relative temperature(T_b)causes the system to bifurcate from periodic to chaotic behavior and in turn reverts back to periodic behavior with further decrease of T_b. Varying atomic detuning leads to a change in the nature of the dynamic transition between the system's states from self pulsing to chaotic behavior.     

Stable periodic motions in the problem on passage through a separatrix

A Hamiltonian system with one degree of freedom depending on a slowly periodically varying in time parameter is considered. For every fixed value of the parameter there are separatrices on the phase portrait of the system. When parameter is changing in time, these separatrices are pulsing slowly periodically, and phase points of the system cross them repeatedly. In numeric experiments region swept by pulsing separatrices looks like a region of chaotic motion. However, it is shown in the present paper that if the system possesses some additional symmetry (like a pendulum in a slowly varying gravitational field), then typically in the region in question there are many periodic solutions surrounded by stability islands; total measure of these islands does not vanish and does not tend to 0 as rate of changing of the parameter tends to 0.(c) 1997 American Institute of Physics.     

Dynamic properties of combustion instability in a lean premixed gas-turbine combustor

We experimentally investigate the dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor from the viewpoint of nonlinear dynamics. A nonlinear time series analysis in combination with a surrogate data method clearly reveals that as the equivalence ratio increases, the dynamic behavior of the combustion instability undergoes a significant transition from stochastic fluctuation to periodic oscillation through low-dimensional chaotic oscillation. We also show that a nonlinear forecasting method is useful for predicting the short-term dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor, which has not been addressed in the fields of combustion science and physics.     

Phase dynamics of a detuned single-mode laser

We report measurements on the phase dynamics of a detuned single mode laser which has in the past shown correspondence to the complex Lorenz equation. The corresponding ranges of periodic pulsing, of detuned chaos and of windows within the chaotic domain are investigated.Invited paper     

Prediction of soot and thermal radiation in a model gas turbine combustor burning kerosene fuel spray at different swirl levels

Combustion of kerosene fuel spray has been numerically simulated in a laboratory scale combustor geometry to predict soot and the effects of thermal radiation at different swirl levels of primary air flow. The two-phase motion in the combustor is simulated using an Eulerian–Lagragian formulation considering the stochastic separated flow model. The Favre-averaged governing equations are solved for the gas phase with the turbulent quantities simulated by realisable k–? model. The injection of the fuel is considered through a pressure swirl atomiser and the combustion is simulated by a laminar flamelet model with detailed kinetics of kerosene combustion. Soot formation in the flame is predicted using an empirical model with the model parameters adjusted for kerosene fuel. Contributions of gas phase and soot towards thermal radiation have been considered to predict the incident heat flux on the combustor wall and fuel injector. Swirl in the primary flow significantly influences the flow and flame structures in the combustor. The stronger recirculation at high swirl draws more air into the flame region, reduces the flame length and peak flame temperature and also brings the soot laden zone closer to the inlet plane. As a result, the radiative heat flux on the peripheral wall decreases at high swirl and also shifts closer to the inlet plane. However, increased swirl increases the combustor wall temperature due to radial spreading of the flame. The high incident radiative heat flux and the high surface temperature make the fuel injector a critical item in the combustor. The injector peak temperature increases with the increase in swirl flow mainly because the flame is located closer to the inlet plane. On the other hand, a more uniform temperature distribution in the exhaust gas can be attained at the combustor exit at high swirl condition.     

Spatial correlation in the ambient core noise field of a turbofan engine

An acoustic transfer function relating combustion noise and turbine exit noise in the presence of enclosed ambient core noise is investigated using a dynamic system model and an acoustic system model for the particular turbofan engine studied and for a range of operating conditions. Measurements of cross-spectra magnitude and phase between the combustor and turbine exit and auto-spectra at the turbine exit and combustor are used to show the presence of indirect and direct combustion noise over the frequency range of 0-400 Hz. The procedure used evaluates the ratio of direct to indirect combustion noise. The procedure used also evaluates the post-combustion residence time in the combustor which is a factor in the formation of thermal NO(x) and soot in this region. These measurements are masked by the ambient core noise sound field in this frequency range which is observable since the transducers are situated within an acoustic wavelength of one another. An ambient core noise field model based on one and two dimensional spatial correlation functions is used to replicate the spatially correlated response of the pair of transducers. The spatial correlation function increases measured attenuation due to destructive interference and masks the true attenuation of the turbine.     

Statistical characteristics of pressure oscillations in a premixed combustor

This paper describes an investigation of the statistical characteristics of self-excited and noise-driven pressure oscillations in a premixed combustor. This work was motivated by observations that certain characteristics of these oscillations appear random and cannot be entirely characterized within a deterministic framework (e.g., spontaneous, noise-induced transitions of the combustor from stable to unstable operation or cycle-to-cycle variations in the oscillating pressure). In an effort to elucidate these stochastic elements, we performed an analysis of cycle-to-cycle variations in combustor pressure whose results are described in this paper. Data obtained from our combustor shows that the probability density function of the amplitude of these oscillations transitions from a Rayleigh to a Gaussian-type distribution as the combustor moves from stable to unstable operation. These data also show that the instability phase is nearly uniformly distributed; i.e., there is no phase value with maximum probability of occurrence. We also describe a theoretical analysis of the statistical features of a non-linear combustor model that is forced by random noise. Solutions of this model are presented and shown to be in agreement with measured data. The good agreement between the predictions and measured data suggest that the analysis presented in this paper provides a useful framework for interpreting many other apparently random features of combustor stability characteristics; for example, cyclic variability, “fuzziness” in stability boundaries, or noise-induced transitions.