An ignition-temperature model with two free interfaces in premixed flames†

In this paper we consider an ignition-temperature zero-order reaction model of thermo-diffusive combustion. This model describes the dynamics of thick flames, which have recently received considerable attention in the physical and engineering literature. The model admits a unique (up to translations) planar travelling wave solution. This travelling wave solution is quite different from those usually studied in combustion theory. The main qualitative feature of this travelling wave is that it has two interfaces: the ignition interface where the ignition temperature is attained and the trailing interface where the concentration of deficient reactants reaches zero. We give a new mathematical framework for studying the cellular instability of such travelling front solutions. Our approach allows the analysis of a free boundary problem to be converted into the analysis of a boundary value problem having a fully nonlinear system of parabolic equations. The latter is very suitable for both mathematical and numerical analysis. We prove the existence of a critical Lewis number such that the travelling wave solution is stable for values of Lewis number below the critical one and is unstable for Lewis numbers that exceed this critical value. Finally, we discuss the results of numerical simulations of a fully nonlinear system that describes the perturbation dynamics of planar fronts. These simulations reveal, in particular, some very interesting ‘two-cell’ steady patterns of curved combustion fronts.     

Nonlinear dynamics and chaos analysis of one-dimensional pulsating detonations

To understand the nonlinear dynamical behaviour of a one-dimensional pulsating detonation, results obtained from numerical simulations of the Euler equations with simple one-step Arrhenius kinetics are analysed using basic nonlinear dynamics and chaos theory. To illustrate the transition pattern from a simple harmonic limit-cycle to a more complex irregular oscillation, a bifurcation diagram is constructed from the computational results. Evidence suggests that the route to higher instability modes may follow closely the Feigenbaum scenario of a period-doubling cascade observed in many generic nonlinear systems. Analysis of the one-dimensional pulsating detonation shows that the Feigenbaum number, defined as the ratio of intervals between successive bifurcations, appears to be in reasonable agreement with the universal value of d = 4.669. Using the concept of the largest Lyapunov exponent, the existence of chaos in a one-dimensional unsteady detonation is demonstrated.     

常温下JB-9014钝感炸药的DSD参数研究

 爆轰冲击波动力学（DSD）是目前研究爆轰波非理想传播的有效途径。利用爆轰冲击波动力学的广义几何光学模型,研究了大长径比药柱中爆轰波非理想传播现象,根据常温下Ф10~30 mm药柱的直径效应实验数据,通过非线性优化方法——遗传算法,确定了一套JB-9014钝感炸药的DSD参数。这套DSD参数对JB-9014药柱中定态波形和爆速的计算与实验结果符合。     

Controlled detonation initiation in hypersonic flow

Experimental evidence of controlled detonation initiation and propagation in a hypersonic flow of premixed hydrogen-air is presented. This controlled detonation initiation is created in a hypersonic facility capable of producing a Mach 5 flow of hydrogen-air. Flow diagnostics such as high-speed schlieren and OH* chemiluminescence results show that a flame deflagration-to-detonation transition occurs as a combined result of turbulent flame acceleration and shock-focusing. The experimental results define three new distinct regimes in a Mach 5 premixed flow: deflagration-to-detonation transition (DDT), unsteady compressible turbulent flames, and shock-induced combustion. A two-dimensional implicit-LES (ILES) simulation, which solves the compressible, reactive Navier-Stokes equations on an adapting grid is conducted to provide additional insight into the local physical mechanism of detonation transition and propagation.     

碳氢混合燃料（C5~C6）气云爆轰胞格结构实验研究

 改进烟迹技术之后，在初始为常温常压的条件下，进行了碳氢混合燃料（C₅~C₆）的气云爆轰胞格结构实验研究，得到了清晰的胞格烟迹记录，同时讨论了燃料气云的当量比和起爆能对胞格结构的影响。实验表明：C₅~C₆混合燃料的爆轰波胞格宽度和胞格长度均随当量比的增加而线性增大；随着起爆能的不断增大，混合燃料的胞格宽度和胞格长度均是先增大后减小，且当起爆能足够高时，在胞格结构内可观察到精细结构的存在。     

低温下JB-9014钝感炸药DSD参数研究

 爆轰冲击波动力学（Detonation Shock Dynamics,DSD）是目前研究爆轰波非理想传播的有效途径。利用DSD的广义几何光学模型,研究了大长径比药柱中爆轰波非理想传播现象,根据-30 ℃下直径为10～30 mm药柱的直径效应实验数据,利用遗传算法确定了低温下JB-9014钝感炸药的DSD参数。由DSD参数计算得到了JB-9014药柱中的定态波形和爆速,计算结果与实验结果符合。     

Resonantly forced inhomogeneous reaction-diffusion systems

The dynamics of spatiotemporal patterns in oscillatory reaction-diffusion systems subject to periodic forcing with a spatially random forcing amplitude field are investigated. Quenched disorder is studied using the resonantly forced complex Ginzburg-Landau equation in the 3:1 resonance regime. Front roughening and spontaneous nucleation of target patterns are observed and characterized. Time dependent spatially varying forcing fields are studied in the 3:1 forced FitzHugh-Nagumo system. The periodic variation of the spatially random forcing amplitude breaks the symmetry among the three quasi-homogeneous states of the system, making the three types of fronts separating phases inequivalent. The resulting inequality in the front velocities leads to the formation of "compound fronts" with velocities lying between those of the individual component fronts, and "pulses" which are analogous structures arising from the combination of three fronts. Spiral wave dynamics is studied in systems with compound fronts. (c) 2000 American Institute of Physics.     

Effect of Cellular Instability on the Initiation of Cylindrical Detonations

The direct initiation of detonations in one-dimensional(1 D) and two-dimensional(2 D) cylindrical geometries is investigated through numerical simulations. In comparison of 1 D and 2 D simulations, it is found that cellular instability has a negative effect on the 2 D initiation and makes it more difficult to initiate a sustaining 2 D cylindrical detonation. This effect associates closely with the activation energy. For the lower activation energy,the 2 D initiation of cylindrical detonations can be achieved through a subcritical initiation way. With increasing the activation energy; the 2 D cylindrical detonation has increased difficulty in its initiation due to the presence of unreacted pockets behind the detonation front and usually requires rather larger source energy.     

On the two-dimensional instability of square-wave detonations

In order to elucidate the basic mechanisms responsible for the cells developing on detonation fronts, the two-dimensional instability of planar Chapman-Jouguet detonations is studied by the use of a square-wave model. It has been shown that there are two main instability mechanisms: the high sensitivity of the heat release rate to temperature and the hydrodynamic effect arising from the interface (reaction front) subject to the influence of the deflection of streamlines across the perturbed shock. Since for ordinary gaseous detonations the density across the shock is very large, the instability related to this pure hydrodynamic effect is very strong. An exact dispersion relation is derived and it is shown that the instability of square-wave detonations is described by a differential-difference equation of advanced type, which has a set of an infinite number of unstable solution branches with the growth rate increasing with the number of modes. The nonlinear solution shows that the discontinuity develops from smooth initial data within a finite time. Therefore the results obtained from square-wave detonations cannot be applied directly to describe the observed instability patterns. By carrying out a Taylor development of the terms with advanced time, a dispersion relation of a polynomial form is obtained and the high-frequency instability is eliminated. On the basis of the linear results with a regular reaction model, a phenomenological nonlinear equation of the fourth order for the position of the detonation surface is obtained by carrying out a Taylor series development. One-dimensional numerical solution of the phenomenological nonlinear equation shows typical nonlinear phenomena such as periodic oscillation, period doubling and dynamic quenching.     

Transformation of Nanosecond Laser Pulses under the Conditions of Total Internal Reflection from a Layer with Thermal Nonlinearity

The nonlinear, total internal reflection of a laser pulse from an absorbing layer of finite thickness in the presence of a retrodirective mirror has been considered in the framework of the plane-wave approximation. The dynamics of reflection of a pulse from a nonlinear layer has been investigated on the basis of the solution of Maxwell equations for a refracted wave and constitutive equations for a medium with thermal nonlinearity. The numerical solution of the unsteady equations obtained allows one to determine the evolution of the reflectance of a layer. The time evolution of the energy parameters and the shape of the reflected and transmitted pulses has been numerically simulated.     

Nonlinear dynamics and chaos regularization of one-dimensional pulsating detonations with small sinusoidal density perturbations

In this work, we explore the effect of initial density variation in the combustible mixture on the nonlinear dynamics of one-dimensional gaseous detonation propagation. Studies of nonlinear dynamical behavior of one-dimensional pulsating detonation are frequently based upon the reactive Euler simulations with one-step Arrhenius chemistry. In regions of the control parameters space, i.e., activation energy E_a, the 1-D detonation dynamics are shown to exhibit chaotic behavior at values of 28.5 and 30.0. Using small sinusoidal initial density perturbations, this investigation shows the emergence of various nonlinear temporal patterns as a function of the perturbation wavelength. It demonstrates that the cooperative behavior between the intrinsic instability and imposed small perturbation can lead to regularization of chaotic oscillations in one-dimensional gaseous pulsating detonation. Hence, by means of a small perturbation, an otherwise chaotic motion is rendered more stable and predictable. This result thus has implications for how intrinsically unstable detonation dynamics can be controlled.     

Dynamic transition in the structure of an energetic crystal during chemical reactions at shock front prior to detonation

Mechanical stimuli in energetic materials initiate chemical reactions at shock fronts prior to detonation. Shock sensitivity measurements provide widely varying results, and quantum-mechanical calculations are unable to handle systems large enough to describe shock structure. Recent developments in reactive force-field molecular dynamics (ReaxFF-MD) combined with advances in parallel computing have paved the way to accurately simulate reaction pathways along with the structure of shock fronts. Our multimillion-atom ReaxFF-MD simulations of l,3,5-trinitro-l,3,5-triazine (RDX) reveal that detonation is preceded by a transition from a diffuse shock front with well-ordered molecular dipoles behind it to a disordered dipole distribution behind a sharp front.     

Dynamics of Chapman-Jouguet pulsating detonations with Chain-Branching kinetics: Fickett’s analogue and Euler equations

The present study examines the spatiotemporal nonlinear dynamics of detonations over a wide range of reaction time scales away from the neutral stability region. This is addressed by one-dimensional numerical simulations with chain-branching kinetics. Fickett’s detonation analogue and Euler’s equations were used as evolution equations. A shock-fitting solver is used to reduce CPU time. Up to four thousand five hundred simulations have been carried out. Detailed bifurcation diagrams have been generated to explore the detonation dynamics. For long/intermediate reaction time scales, away from the neutral boundary, the traditional period-doubling cascade to chaos is seen. For square wave detonations, away from the neutral stability, almost periodic oscillations are recorded. This result might have implications for the existence of a characteristic length scale, the cell size, on typical cellular detonations which have a short reaction length.     

A review of direct numerical simulations of astrophysical detonations and their implications

Multi-dimensional direct numerical simulations (DNS) of astrophysical detonations in degenerate matter have revealed that the nuclear burning is typically characterized by cellular structure caused by transverse instabilities in the detonation front. Type Ia supernova modelers often use onedimensional DNS of detonations as inputs or constraints for their whole star simulations.While these one-dimensional studies are useful tools, the true nature of the detonation is multi-dimensional. The multi-dimensional structure of the burning influences the speed, stability, and the composition of the detonation and its burning products, and therefore, could have an impact on the spectra of Type Ia supernovae. Considerable effort has been expended modeling Type Ia supernovae at densities above 1×10⁷ g·cm^-3 where the complexities of turbulent burning dominate the flame propagation. However, most full star models turn the nuclear burning schemes off when the density falls below 1×10⁷ g·cm^-3 and distributed burning begins. The deflagration to detonation transition (DDT) is believed to occur at just these densities and consequently they are the densities important for studying the properties of the subsequent detonation. This work will review the status of DNS studies of detonations and their possible implications for Type Ia supernova models. It will cover the development of Detonation theory from the first simple Chapman–Jouguet (CJ) detonation models to the current models based on the time-dependent, compressible, reactive flow Euler equations of fluid dynamics.     

Detonation in gases

We review recent progress in gaseous detonation experiment, modeling, and simulation. We focus on the propagating detonation wave as a fundamental combustion process. The picture that is emerging is that although all propagating detonations are unstable, there is a wide range of behavior with one extreme being nearly laminar but unsteady periodic flow and the other chaotic instability with highly turbulent flow. We discuss the implications of this for detonation propagation and dynamic behavior such as diffraction, initiation, and quenching or failure.     

Effect of ozone addition and ozonolysis reaction on the detonation properties of C2H4/O2/Ar mixtures

Ozone is one of the strongest oxidizers and can be used to enhance detonation. Detonation enhancement by ozone addition is usually attributed to the ozone decomposition reaction which produces reactive atomic oxygen and thereby accelerates the chain branching reaction. Recently, ozonolysis reaction has been found to be another mechanism to enhance combustion for unsaturated hydrocarbons at low temperatures. In this study, the effects of ozone addition and ozonolysis reaction on steady detonation structure and transient detonation initiation and propagation processes in C₂H₄/O₂/O₃/Ar mixtures are examined through simulations considering detailed chemistry. Specifically, the homogeneous ignition process, the ZND detonation structure, the transient direct detonation initiation, and pulsating instability of one-dimensional detonation propagation are investigated. It is found that the homogenous ignition process consists of two stages and the first stage is caused by ozonolysis reactions which consume O₃ and produces CH₂O as well as H and OH radicals. The ozonolysis reaction and ozone decomposition reaction can both reduce the induction length though they have little influence on the Chapman–Jouguet (CJ) detonation speed. The supercritical, critical and subcritical regimes for direct detonation initiation are identified by continuously decreasing the initiation energy or changing the amount of ozone addition. It is found that direct detonation initiation becomes easier at larger amount of ozone addition and/or larger reaction progress variable. This is interpreted based on the change of the induction length of the ZND detonation structure. Furthermore, it is demonstrated that the ozonolysis reaction can reduce pulsating instability and make the one-dimensional detonation propagation more stable. This is mainly due to the reduction in activation energy caused by ozone addition and/or ozonolysis reaction. This work shows that both ozone decomposition reaction and ozonolysis reaction can enhance detonation for unsaturated hydrocarbon fuels.     

Dynamics and Stability of a Weak Detonation Wave

One dimensional weak detonation waves of a basic reactive shock wave model are proved to be nonlinearly stable, i.e. initially perturbed waves tend asymptotically to translated weak detonation waves. This model system was derived as the low Mach number limit of the one component reactive Navier-Stokes equations by Majda and Roytburd [SIAM J. Sci. Stat. Comput. 43, 1086–1118 (1983)], and its weak detonation waves have been numerically observed as stable. The analysis shows in particular the key role of the new nonlinear dynamics of the position of the shock wave, The shock translation solves a nonlinear integral equation, obtained by Green's function techniques, and its solution is estimated by observing that the kernel can be split into a dominating convolution operator and a remainder. The inverse operator of the convolution and detailed properties of the traveling wave reduce, by monotonicity, the remainder to a small L ₁ perturbation. Received: 17 August 1998 / Accepted: 13 November 1998     

Experimental characterization of detonation initiation modes in a confined chamber flush-mounted with small-diameter ignition tubes

This work reports the experimental characterization of detonation initiation modes in a confined chamber in respect to the different types of reacting waves generated in various small-diameter ignition tubes. Depending on the length of the tube and mixtures composition, four types of reacting waves can be generated and utilized to initiate detonation in the main chamber, namely the over-driven detonation ignition wave, CJ detonation ignition wave, high-speed deflagration ignition wave and deflagration ignition wave. Based on the mechanisms of detonation initiation in the main chamber, four initiation modes can be observed: the direct initiation, the local explosion initiation, and the fast and slow deflagration-to-detonation transition (DDT) initiation. By comparing the detonation initiation positions and flame-tip velocities, the first two modes show appreciably shorter initiation distances compared to the DDT modes. The over-driven detonation ignition wave is shown to yield a high probability of direct initiation, while contrary to expectation, the high-speed deflagration ignition wave exhibits superior initiation performance compared to the CJ detonation ignition wave. It is illustrated that the energy decay through diffraction and the effect of precursor shock wave reflection on the wall of the rectangular chamber are viable factors responsible for this observation. The deflagration ignition wave is also shown to be able to rapidly initiate the detonation near the inlet of the chamber, albeit with a lower success rate.     

Order parameter description of walk-off effect on pattern selection in degenerate optical parametric oscillators

Degenerate optical parametric oscillators can exhibit both uniformly translating fronts and nonuniformly translating envelope fronts under the walk-off effect. The nonlinear dynamics near threshold is shown to be described by a real convective Swift-Hohenberg equation, which provides the main characteristics of the walk-off effect on pattern selection. The predictions of the selected wave vector and the absolute instability threshold are in very good quantitative agreement with numerical solutions found from the equations describing the optical parametric oscillator.     

Geometric modeling and analysis of detonation cellular stability

A geometric model with a low computational complexity capable of simulating detonation behavior in physical systems is proposed. In support of the geometric model development, a series of cylindrical 1D simulations with a variable size initiation kernel are performed in hydrogen-oxygen mixtures. From these 1D simulations a detonation cell stabilization mechanism is identified. The stabilization mechanism is predicated on the size of the gap between the pressure and temperature fronts at the point where the average pressure front velocity along one cell length is equal to the CJ velocity. This gap, in a multidimensional detonation, is the ignition kernel of a subsequent blast, and dictates the formation of the subsequent cell. Serial analysis of blasts in this context leads to a unique stable blast kernel size for any mixture, which, within the uncertainty of the initial kernel state, can predict the experimental cell length for mixtures considered in this study. Using a tabulation of the 1D simulations as an input, a formulation and sample results of the geometric model are shown. The geometric model can reproduce both qualitative and quantitative features of experimental detonation cellular structure.