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.     

An equation of state for the detonation product of copper oxide/aluminum nanothermite composites

An equation of state (EOS) for the detonation product of the copper oxide/aluminum (CuO/Al) nanothermite composites is developed based on the Chapman–Jouguet (CJ) theory and the nanothermite detonation experiment. The EOS is implemented into a coupled computational fluid dynamics and computational solid dynamics code through the material point method for the model-based simulations of the detonation response of the CuO/Al nanothermite material placed in a small well. The simulations demonstrate the validity of the formulated EOS to catch the essential feature of the detonation response of the CuO/Al nanothermite. The EOS parameters are determined by comparing simulated and experimentally measured pressure–time histories.     

Experimental investigations of detonation initiation by hot jets in supersonic premixed flows

<正>A new method to initiate and sustain the detonation in supersonic flow is investigated.The reaction activity of coming flow may influence the result of detonation initiation.When a hot jet initiates a detonation wave successfully, there may exist two types of detonations.If the detonation velocity is greater than the velocity of coming flow,there will be a normal detonation here.Because of the influence of boundary layer separation,the upstream detonation velocity is much greater than the Chapman-Jouguet(CJ) detonation velocity.On the other hand,if the detonation velocity is less than the velocity of coming flow,an oblique detonation wave(ODW) will form.The ODW needs a continuous hot jet to sustain itself.If the jet pressure is lower than a certain value,the ODW will decouple.In contrast,the normal detonation wave can sustain itself without the hot jet.     

Experimental observations of detonation in ammonium-nitrate-fuel-oil (ANFO) surrounded by a high-sound-speed, shockless, aluminum confiner

Detonations in explosive mixtures of ammonium-nitrate-fuel-oil (ANFO) confined by aluminum allow for transport of detonation energy ahead of the detonation front due to the aluminum sound-speed exceeding the detonation velocity. The net effect of this energy transport on the detonation is unclear. It could enhance the detonation by precompressing the explosive near the wall. Alternatively, it could decrease the explosive performance by crushing porosity required for initiation by shock compression or destroying confinement ahead of the detonation. At present, these phenomena are not well understood. But with slowly detonating, non-ideal high explosive (NIHE) systems becoming increasing prevalent, proper understanding and prediction of the performance of these metal-confined NIHE systems is desirable. Experiments are discussed that measured the effect of ANFO detonation energy transported upstream of the front by a 76-mm-inner-diameter aluminum confining tube. Detonation velocity, detonation front-shape, and aluminum response are recorded as a function of confiner wall thickness and length. Detonation shape profiles display little curvature near the confining surface, which is attributed to energy transported upstream modifying the flow. Average detonation velocities were seen to increase with increasing confiner thickness, while wavefront curvature decreased due to the stiffer, subsonic confinement. Significant radial sidewall tube motion was observed immediately ahead of the detonation. Axial motion was also detected, which interfered with the front-shape measurements in some cases. It was concluded that the confiner was able to transport energy ahead of the detonation and that this transport has a definite effect on the detonation by modifying its characteristic shape.     

The dynamics of a non-premixed rotating detonation engine from time-resolved temperature measurements

The structure and dynamics of a hydrogen-air rotating detonation engine (RDE) are described based on 100-kHz laser absorption spectroscopy measurements of water temperature at four simultaneous locations within the detonation channel. The analysis focuses on the evolution of the flowfield over a 200 ms period for three separate air mass flow rate cases. Two-dimensional unwrapped visualizations of the temperatures show a flowfield structure containing regions with the detonation front, combustion products, oblique shock, and refilling reactants, qualitatively agreeing with previous simulations and experiments. A major conclusion is that water from the combustion products is measured throughout all space and time in the RDE, including near the injector, implying the presence of performance loss processes such as burning upstream of the detonation wave or the back recirculation of combustion products with fresh fuel–air. By analyzing the elevated temperatures of the reactants during the refill process, one estimation for the mass fraction of combustion products in the reactants is as high as 20–30% on average. This product mass fraction is found to be inversely proportional to the bulk air mass flow rate and decreases as time progresses. This indicates these non-ideal processes are more significant closer to RDE ignition for poorer performing operating conditions. For the largest air mass flow case, water temperatures near the nominally cold plenum conditions likely corroborate the presence of a recirculation region on the RDE inner body. Analysis of inter- and intra-cycle temperature dynamics further support non-ideal processes occurring behind the detonation wave and during the refill process. As a whole, the data indicates that the RDE performance is better as time progresses away from ignition or for higher air mass flow rates. These data are also important for comparison with numerical models.     

Calibration of the Pseudo-Reaction-Zone model for detonation wave propagation

An approach for the calibration of an advanced programmed burn (PB) model for detonation performance calculations in high explosive systems is detailed. Programmed burn methods split the detonation performance calculation into two components: timing and energy release. For the timing, the PB model uses a Detonation Shock Dynamics (DSD) surface propagation model, where the normal surface speed is a function of local surface curvature. For the energy release calculation and subsequent hydrodynamic flow evolution, a Pseudo-Reaction-Zone (PRZ) model is used. The PRZ model is similar to a reactive burn model in that it converts reactants into products at a finite rate, but it has a reaction rate dependent on the normal surface speed derived from the DSD calculation. The PRZ reaction rate parameters must be calibrated in such a way that the rate of energy release due to reaction in multi-dimensional geometries is consistent with the timing calculation provided by the DSD model. Our strategy for achieving this is to run the PRZ model in a detonation shock-attached frame in a compliant 2D planar slab geometry in an equivalent way to a reactive burn model, from which we can generate detonation front shapes and detonation phase speed variations with slab thickness. In this case, the D _n field used by the PRZ model is then simply the normal detonation shock speed rather than the DSD surface normal speed. The PRZ rate parameters are then iterated on to match the equivalent surface front shapes and surface phase speed variations with slab thickness derived from the target DSD model. For the purposes of this paper, the target DSD model is fitted to the performance properties of an idealised condensed-phase reactive burn model, which allows us to compare the detonation structure of the calibrated PRZ model to that of the originating idealised-condensed phase model.     

An experimental investigation of the propagation mechanism of critical deflagration waves that lead to the onset of detonation

The reflection of a CJ detonation from a perforated plate is used to generate high speed deflagrations downstream in order to investigate the critical conditions that lead to the onset of detonation. Different perforated plates were used to control the turbulence in the downstream deflagration waves. Streak Schlieren photography, ionization probes and pressure transducers are used to monitor the flow field and the transition to detonation. Stoichiometric mixtures of acetylene–oxygen and propane–oxygen were tested at low initial pressures. In some cases, acetylene–oxygen was diluted with 80% argon in order to render the mixture more “stable” (i.e., more regular detonation cell structure). The results show that prior to successful detonation initiation, a deflagration is formed that propagates at about half the CJ detonation velocity of the mixture. This “critical” deflagration (which propagates at a relatively constant velocity for a certain duration prior to the onset of detonation) is comprised of a leading shock wave followed by an extended turbulent reaction zone. The critical deflagration speed is not dependent on the turbulence characteristics of the perforated plate but rather on the energetics of the mixture like a CJ detonation (i.e., the deflagration front is driven by the expansion of the combustion products). Hence, the critical deflagration is identified as a CJ deflagration. The high intensity turbulence that is required to sustain its propagation is maintained via chemical instabilities in the reaction zone due to the coupling of pressure fluctuations with the energy release. Therefore, in “unstable” mixtures, critical deflagrations can be supported for long durations, whereas in “stable” mixtures, deflagrations decay as the initial plate generated turbulence decays. The eventual onset of detonation is postulated to be a result of the amplification of pressure waves (i.e., turbulence) that leads to the formation of local explosion centers via the SWACER mechanism during the pre-detonation period.     

Transverse wave generation mechanism in rotating detonation

Detonation engines are expected to be included in a number of aerospace thrusters in the future. Several types of detonation engines are currently under examination, including the rotating detonation engine (RDE). Although the RDE has been explored experimentally, its rotating detonation propagation mechanism is not well understood. This paper clarifies the detonation mechanism and dynamics of the RDE by 2D and 3D simulation using compressible Euler equations with a full chemical reaction mechanism of H₂/O₂ and H₂/Air, especially from the triple-point and transverse detonation points of view. A total variation diminishing (TVD) scheme is used for the mixture of H₂/Air, and an advection upwind splitting method difference vector (AUSMDV) scheme is used for the mixture of H₂/O₂. The use of an AUSMDV scheme provides a much clearer detonation structure than does the TVD scheme. We focus on the complex interaction mechanism of the detonation front and burned mixture gases. We found out that at this interaction point, an unreacted gas pocket appears and ignites periodically to generate transverse waves at the detonation front and maintain detonation propagation.     

矩形管内临界爆轰动力学数值分析

 对矩形管内临界爆轰动力学特征进行了数值分析。采用基元反应描述爆轰化学反应过程,采用二阶附加半隐的龙格-库塔法和5阶WENO格式求解二维反应欧拉方程。对于25%氩稀释化学计量比的氢氧预混气体,当管道宽度为30 mm、初温为300 K时,产生临界爆轰的预混气体初压为3.5 kPa。在此临界条件下,获得了临界爆轰胞格结构、沿壁面的速度和峰值压力曲线及流场波系演变特征。着重对比分析了矩形管内临界爆轰与普通爆轰在爆轰波速度、平均速度、胞格宽长比、横波结构、未反应气囊及旋涡结构之间的差异,深入认识了临界爆轰的不稳定性和化学反应动力学特征。     

一维爆轰波在扰动来流中传播的数值研究

爆轰波在静止气体或定常来流中的传播得到了广泛研究, 然而在扰动来流中的传播研究较少。这方面的研究不仅是爆轰传播机制的重要组成部分, 还可为爆轰发动机的应用提供参考。文章基于两步诱导-放热总包反应模型, 开展了一维爆轰波在正弦密度扰动来流中的传播数值模拟。通过对数值结果分析, 获得了放热反应控制参数与爆轰波内在不稳定性的关系, 并在此基础上研究了扰动波长和幅值对一维爆轰波动力学过程的影响。研究发现, 在波前施加连续扰动会诱导爆轰波表现出更复杂的动力学行为, 且影响过程与爆轰波的内在不稳定性相关。对于稳定爆轰波, 扰动只在特定波长范围内引起前导激波后的压力振荡。对于不稳定爆轰波, 扰动会进一步强化其内在不稳定性。扰动幅值越大, 对爆轰波动力学过程的影响越显著。      

The effects of mixture preburning on detonation wave propagation

Pressure gain combustion in the form of continuous detonations can provide a significant increase in the efficiency of a variety of propulsion and energy conversion devices. In this regard, rotating detonation engines (RDEs) that utilize an azimuthally-moving detonation wave in annular systems are increasingly seen as a viable approach to realizing pressure gain combustion. However, practical RDEs that employ non-premixed fuel and oxidizer injection need to minimize losses through a number of mechanisms, including turbulence-induced shock-front variations, incomplete fuel-air mixing, and premature deflagration. In this study, a canonical stratified detonation configuration is used to understand the impact of preburning on detonation efficiency. It was found that heat release ahead of the detonation wave leads to weaker shock fronts, delayed combustion of partially-oxidized fuel-air mixture, and non-compact heat release. Furthermore, large variations in wave speeds were observed, which is consistent with wave behavior in full-scale RDEs. Peak pressures in the compression region or near triple points were considerably lower than the theoretically-predicted values for ideal detonations. Analysis of the detonation structure indicates that this deflagration process is parasitic in nature, reducing the detonation efficiency but also leading to heat release far behind the wave that cannot directly strengthen the shock wave. This parasitic combustion leads to commensal combustion (heat release far downstream of the wave), indicating that it is the root cause of combustion efficiency losses.     

一维过驱动爆轰波形成的数值研究

利用有限速率的基元反应模型对一维过驱动爆轰波的形成过程进行数值模拟.研究表明,在上游高温、高压、高速来流作用下首先会形成一道强激波,其波面方存在诱导区和放热区,然后诱导区和放热区界面会在来流扰动的作用下发生失稳,经过复杂的波系运动过程形成过驱动爆轰波.通过对不同初始条件下界面失稳过程的模拟和分析,研究了混合气体的组元、温度,来流的压力、温度、速度对过驱动爆轰波形成的影响.     

非均匀炸药冲击起爆和起爆后的行为

 介绍并分析了Campbell 等人及其他作者研究非均匀炸药冲击起爆和起爆后行为所获得的实验结果,但不涉及其冲击起爆条件。足够强的冲击波进入非均匀炸药后,爆轰将瞬时（指不经过感应时间）且直接（指不经过其他过程,如爆燃）被引发;非均匀炸药起爆后,其中传播的自始至终是一个不断增长的爆轰波,直至发展为正常爆轰,整个过程都是爆轰的增长（新定义）过程。不存在由反应冲击波不断增长并转变为爆轰波的所谓向爆轰的增长。所谓向爆轰的增长,实际上是爆轰的增长（按新定义）的初期;Craig原定义的爆轰的增长,实际上是爆轰的增长（按新定义）的后期;而所谓反应冲击波,实际上是增长中的初期爆轰波。爆轰的增长（按新定义）是所有猛炸药的特性,炸药反应不充分并逐渐趋于充分是爆轰的增长的化学机制。     

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。     

Theory of gaseous detonations

The objective of the present paper is to review some developments that have occurred in detonation theory over the last ten years. They concern nonlinear dynamics of detonation fronts, namely patterns of pulsating and/or cellular fronts, selection of the cell size, dynamical self-quenching, direct (blast) or spontaneous initiation, and transition from deflagration to detonation. These phenomena are all well documented by experiments since the sixties but remained unexplained until recently. In the first part of the paper, the patterns of cellular detonations are described by an asymptotic solution to nonlinear hyperbolic equations (reactive Euler equations) in the form of unsteady (sometime chaotic) and multidimensional traveling-waves. In the second part, turning points of quasi-steady solutions are shown to correspond to critical conditions of fully unsteady problems, either for (direct or spontaneous) initiation or for spontaneous failure (self-quenching). Physical insights are tentatively presented rather than technical aspects. The challenge is to identify the physical mechanisms with their relevant parameters, and more specifically to explain how the length-scales involved in detonation dynamics are larger by two order of magnitude (at least) than the length-scale involved in the steady planar traveling-wave solution (detonation thickness).     

气相爆轰波在分叉管中传播现象的数值研究

数值研究气相爆轰波在分叉管中的传播现象.用二阶附加半隐龙格-库塔法和5阶WENO格式求解二维欧拉方程,用基元反应描述爆轰化学反应过程,得到了密度、压力、温度、典型组元质量分数场及数值胞格结构和爆轰波平均速度.结果表明:气相爆轰波在分叉管中传播,分叉口左尖点的稀疏波导致诱导激波后压力、温度急剧下降,诱导激波和化学反应区分离,爆轰波衰减为爆燃波(即爆轰熄灭).分离后的诱导激波在垂直支管右壁面反射,并导致二次起爆.畸变的诱导激波在水平和垂直支管中均发生马赫反射.分叉口上游均匀胞格区和分叉口附近大胞格区的边界不是直线,其起点通常位于分叉口左尖点上游或恰在左尖点.水平支管中马赫反射三波点迹线始于右尖点下游.分叉口左尖点附近的流场中出现了复杂的旋涡结构、未反应区及激波与旋涡作用.旋涡加速了未反应区的化学反应速率.反射激波与旋涡作用并使旋涡破碎.反射激波与未反应区作用,加速其反应消耗,并形成一个内嵌的射流.数值计算得到的波系演变和胞格结构与实验定性一致.     

Experimental and modeling analysis of detonation in circular arcs of the conventional high explosive PBX 9501

We examine the diffraction dynamics of a two-dimensional (2D) detonation in a circular arc of the conventional HMX-based, high performance, solid explosive PBX 9501, for which the detonation reaction zone length scale is estimated to be of the order of 100–150 µm. In this configuration, a steady propagating detonation will develop, sweeping around the arc with constant angular speed. We report on results from three PBX 9501 arc experiments, exploring the variation in linear speed on the inner and outer arc surfaces for the steady wave along with the structure of the curved detonation front, as a function of varying inner surface radius and arc thickness. Comparisons of the properties of the motion of the steady wave for each arc configuration are then made with a spatially-distributed PBX 9501 reactive burn model, calibrated to detonation performance properties in a 2D planar slab geometry. We show that geometry-induced curvature of the detonation near the inner arc surface has a significant effect on the detonation motion even for conventional high explosives. We also examine the detonation driving zone structure for each arc case, and thus the subsonic regions of the flow that determine the influence of the arc geometry on the detonation propagation. In addition, streamline paths and reaction progress isolines are calculated. We conclude that a common approximation for modeling conventional high explosive detonation, wherein the shock-normal detonation speed is assumed equal to the Chapman–Jouguet speed, can lead to significant errors in describing the speed at which the detonation propagates.     

Ignition of hydrogen-air mixtures under volumetric expansion

A better understanding of chemical kinetics under volumetric expansion is important for a number of situations relevant to industrial safety including detonation diffraction and direct initiation, reflected shock-ignition at obstacles, ignition behind a decaying shock, among others. The ignition of stoichiometric hydrogen-air mixtures was studied using 0D numerical simulations with time-dependent specific volume variations. The competition between chemical energy release and expansion-induced cooling was characterized for different cooling rates and mathematical forms describing the shock decay rate. The critical conditions for reaction quenching were systematically determined, and the thermo-chemistry dynamics were analyzed near the critical conditions.     

Dynamics of nonholonomic systems from variational principles embedded variation identity

Nondeterminacy of dynamics, i.e., the nonholonomic or the vakonomic, fundamental variational principles, e.g., the Lagrange-d'Alembert or Hamiltonian, and variational operators, etc., of nonholonomic mechanical systems can be attributed to the non-uniqueness of ways how to realize nonholonomic constraints. Making use of a variation identity of nonholonomic constraints embedded into the Hamilton's principle with the method of Lagrange undetermined multipliers, three kinds of dynamics for the nonholonomic systems including the vakonomic and nonholonomic ones and a new one are obtained if the variation is respectively reduced to three conditional variations: vakonomic variation, Hölder's variation and Suslov's variation, defined by the identity. Therefore, different dynamics of nonholonomic systems can be derived from an integral variational principle, utilizing one way of embedding constraints into the principle, with different variations. It is verified that the similar embedding of the identity into the Lagrange-d'Alembert principle gives rise to the nonholonomic dynamics but fails to give the vakonomic one unless the constraints are integrable.