RADULESCU M I , SHARPE G J , LEE J H S , et al. The ignition mechanism in irregular structure gaseous detonations [J ] . Proceedings of the Combustion Institute , 2005 , 30 ( 2 ): 1859 - 1867 . DOI: 10.1016/j.proci.2004.08.047 http://doi.org/10.1016/j.proci.2004.08.047 https://linkinghub.elsevier.com/retrieve/pii/S0082078404001006 https://linkinghub.elsevier.com/retrieve/pii/S0082078404001006

TENG H H , ZHANG Y H , YANG P F , et al. Oblique detonation wave triggered by a double wedge in hypersonic flow [J ] . Chinese Journal of Aeronautics , 2022 , 35 ( 4 ): 176 - 184 .

张博 , 白春华 . 气相爆轰动力学特性研究进展 [J ] . 中国科学:物理学力学天文学 , 2014 , 44 ( 7 ): 665 - 681 .

ZHANG B , BAI C H . Research progress on the dynamic characteristics of gaseous detonation [J ] . Scientia Sinica Physica, Mechanica & Astronomica , 2014 , 44 ( 7 ): 665 - 681 . (in Chinese)

CLAVIN P , DENET B . Diamond patterns in the cellular front of an over driven detonation [J ] . Physical Review Letters , 2002 , 88 ( 4 ): 044502 . DOI: 10.1103/PhysRevLett.88.044502 http://doi.org/10.1103/PhysRevLett.88.044502 https://link.aps.org/doi/10.1103/PhysRevLett.88.044502 https://link.aps.org/doi/10.1103/PhysRevLett.88.044502

CALVIN P , HE L T , WILLIAMS F A . Multidimensional stability analysis of overdriven gaseous detonations [J ] . Physics of Fluids , 1997 , 9 ( 12 ): 3764 - 3785 . DOI: 10.1063/1.869520 http://doi.org/10.1063/1.869520 https://pubs.aip.org/pof/article/9/12/3764/260410/Multidimensional-stability-analysis-of-overdriven https://pubs.aip.org/pof/article/9/12/3764/260410/Multidimensional-stability-analysis-of-overdriven Multidimensional instabilities of planar detonations that lead to cellular structures are addressed by use of a distinguished limit in which the propagation Mach number is large and the difference between the specific heats at constant pressure and at constant volume is small. In this limit, the Neumann-state Mach number is small, and the fractional variations of the pressure change after the Neumann state also are small for the overdriven conditions that are considered, under which the heat release is comparable in magnitude with the thermal enthalpy at the Neumann state. The resulting post-shock flow is quasi-isobaric in the first approximation. For all linear modes the analysis provides a dispersion relation expressing the frequency and the linear growth rate in terms of the transverse wavelength. The analysis serves to demonstrate how the interactions among the entropy waves, the varying rate of heat release and the transverse flow induced by the large density change across the wrinkled shock result in the multidimensional instability. The instabilities have a large transverse length but oscillate and evolve on a short time, comparable with the transit time of a fluid particle through the detonation. The coupling with the acoustic waves is a stabilizing factor, dominant at short wavelengths for assuring a suitably large ratio of transverse wavelength to detonation thickness for instability. Even when the detonation is stable to planar disturbances, so that there is a range of stability at long wavelengths, it is shown that there always exists an intermediate range of wavelengths for which the detonation is unstable. This is true even when heat-release rates are entirely independent of temperature, corresponding to detonations that are very stable to planar disturbances. A sufficiently large temperature sensitivity modifies the multidimensional instability. The general chemical kinetics adopted, having different temperature sensitivities for induction and for heat release, the former possibly large, is of the same character as that previously developed by the first authors for describing the planar stability and nonlinear oscillations of galloping detonations but differs from one-step activation-energy asymptotics, which produces nonphysical, spurious instability under all conditions. From the present extension to multiple dimensions with moderate overdrive, inferences are drawn concerning differences that arise for strong overdrive and when Chapman–Jouguet conditions are approached.

LODATO G , VERVISCH L , CLAVIN P . Direct numerical simulation of shock wavy-wall interaction: analysis of cellular shock structures and flow patterns [J ] . Journal of Fluid Mechanics , 2016 , 789 : 221 - 258 . DOI: 10.1017/jfm.2015.731 http://doi.org/10.1017/jfm.2015.731 https://www.cambridge.org/core/product/identifier/S0022112015007314/type/journal_article https://www.cambridge.org/core/product/identifier/S0022112015007314/type/journal_article The reflection on a wavy wall of a planar shock propagating at Mach number 1.5 in air is simulated in a two-dimensional geometry by solving the fully compressible Navier–Stokes equations. A high-order spectral difference numerical discretization is used over an unstructured mesh composed of quadrilateral elements. The shock discontinuity is handled numerically through a specific treatment, which is limited in space to a small portion of the computational cell through which the shock is travelling. In the conditions under investigation, the reflection on the wavy wall leads to a weak and smooth deformation of the shock front without singularities just after reflection. Long-living triple points (Mach stems) are spontaneously formed on the reflected shock at a finite distance from the wavy wall. They then propagate on the front in both directions and collide regularly, forming a periodic cellular pattern quite similar to that of a cellular detonation. Transverse waves, issued from the triple points, are generated in the shocked gas. As a result of their mutual interaction, a complex and strongly unsteady flow is produced in the shocked gas. The topology of the instantaneous streamline patterns is characterized by short-lived critical points that appear intermittently. Due to the compressible character of the unsteady two-dimensional flow, the topology of critical points which can be observed is more diverse than would be expected for incompressible two-dimensional flows. Some of them take the form of short-lived sources or sinks. The mechanism of formation and the dynamics of the triple points, as well as the instantaneous streamline patterns, are analysed in the present paper. The results are useful for deciphering the cellular structure of unstable detonations.

GAMEZO V N , DESBORDES D , ORAN E S . Formation and evolution of two-dimensional cellular detonations [J ] . Combustion and Flame , 1999 , 116 : 154 - 165 . DOI: 10.1016/S0010-2180(98)00031-5 http://doi.org/10.1016/S0010-2180(98)00031-5 https://linkinghub.elsevier.com/retrieve/pii/S0010218098000315 https://linkinghub.elsevier.com/retrieve/pii/S0010218098000315

ROY G D , FROLOV S M , BORISOV A A , et al. Pulse detonation propulsion: challenges, current status, and future perspective [J ] . Progress in Energy and Combustion Science , 2004 , 30 ( 6 ): 545 - 672 . DOI: 10.1016/j.pecs.2004.05.001 http://doi.org/10.1016/j.pecs.2004.05.001 https://linkinghub.elsevier.com/retrieve/pii/S0360128504000383 https://linkinghub.elsevier.com/retrieve/pii/S0360128504000383

安复兴 , 李磊 , 苏伟 , 等 . 高超声速飞行器气动设计中的若干关键问题 [J ] . 中国科学: 物理学力学天文学 , 2021 , 51 ( 10 ): 104702 .

AN F X , LI L , SU W , et al. Key issues in hypersonic vehicle aerodynamic design [J ] . Scientia Sinica Physica, Mechanica & Astronomica , 2021 , 51 ( 10 ): 104702 . (in Chinese)

RANKIN B A , FOTIA M L , NAPLES A G , et al. Overview of performance, application, and analysis of rotating detonation engine technologies [J ] . Journal of Propulsion and Power , 2017 , 30 ( 1 ): 131 - 143 .

魏万里 , 翁春生 , 武郁文 , 等 . 氧化剂喷注面积对连续旋转爆轰波传播特性影响的实验研究 [J ] . 兵工学报 , 2018 , 39 ( 12 ): 2345 - 2353 . DOI: 10.3969/j.issn.1000-1093.2018.12.008 http://doi.org/10.3969/j.issn.1000-1093.2018.12.008 为了研究氧化剂喷注面积对连续旋转爆轰波传播特性的影响，以H₂为燃料、空气为氧化剂，在喷孔-环缝式连续旋转爆轰发动机上开展了一系列试验研究。基于燃烧室内高频压力信号和氧化剂集气腔内的压力信号，分析了氧化剂喷注面积对连续旋转爆轰波传播过程、速度亏损和稳定性以及爆轰波波头高度的影响。试验结果表明：当推进剂质量流量不变时，增大氧化剂喷注面积，爆轰波传播速度亏损增大，爆轰波稳定性变差，同时爆轰波波头高度减小；在氧化剂喷注面积为217.1 mm²、当量比为0.9时，爆轰波平均速度达到1 800 m/s，为理论Chapman-Jouguet速度的93%，同时爆轰波表现最为稳定；当氧化剂喷注面积不变时，随着当量比的增大，爆轰波传播的稳定性先升高、后降低。

WEI W L , WENG C S , WU Y W , et al. Experimental research on influence of oxidant injection area on the propagation characteristics of continuous rotating detonation wave [J ] . Acta Armamentarii , 2018 , 39 ( 12 ): 2345 - 2353 . (in Chinese)

李宝星 , 王中 , 许桂阳 , 等 . 煤油燃料旋转爆轰波起爆与传播特性实验研究 [J ] . 兵工学报 , 2020 , 41 ( 7 ): 1339 - 1346 . DOI: 10.3969/j.issn.1000-1093.2020.07.011 http://doi.org/10.3969/j.issn.1000-1093.2020.07.011 为研究煤油燃料旋转爆轰波的起爆与传播特性，开展气体-液体两相旋转爆轰发动机实验研究。旋转爆轰发动机环形燃烧室内径120 mm、外径153 mm、长240 mm，煤油为燃料、富氧空气为氧化剂，通过氢气/氧气微小型脉冲爆轰发动机进行点火；基于燃烧室内的高频压力，分析气体-液体两相旋转爆轰波的起爆过程、传播特性以及发动机的工作特性。实验结果表明：混合物的反应活性至关重要，当氧化剂中氧含量偏低时，混合物反应活性低，旋转爆轰波将无法起爆，直至氧含量增加到39.2%，才能形成自持传播的爆轰波；爆轰波成功起爆后均以双波对撞模态传播，波速为815~ 920 m/s；在 贫油条件下，爆轰波传播速度随着当量比提高呈增加趋势；当空气质量流量大于822 g/s时， 发动机基本以缓燃形式工作。

LI B X , WANG Z , XU G Y , et al. Experimental research on initiation and propagation characteristics of kerosene fuel rotating detonation wave [J ] . Acta Armamentarii , 2020 , 41 ( 7 ): 1339 - 1346 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2020.07.011 http://doi.org/10.3969/j.issn.1000-1093.2020.07.011 A rotating detonation engine（RDE） was test to study the initiation and propagation characteristics of kerosene fuel rotating detonation wave. The inner diameter, outer diameter and length of RDE annular combustor are 120 mm, 153 mm and 240 mm, respectively. It is ignited by a hydrogen/oxygen micro-pulse detonation engine with kerosene and oxygen-rich air used as fuel and oxidant, respectively. The initiation process and propagation of gas-liquid two-phase rotating detonation wave, and the operation characteristics of engine are analyzed from high-frequency pressure signals in combustor. The test results indicate that the reactivity of mixtures plays an important role on the initiation of detonation wave. When the content of oxygen in the oxidant is low, the reactivity of the mixture is low, and the rotating detonation wave fails to be initiated. It is until the oxygen content increases to 39.2% that the rotating detonation wave can be formed. The rotating detonation wave always propagates in two-wave collision mode with the wave velocity range of 815-920 m/s after successful initiation. The velocity of detonation wave tends to rise with the increase in equivalence ratio under lean fuel condition. The engine mainly works in a deflagration mode when the mass flow rate of air is more than 822 g/s. Key

王放 , 翁春生 , 武郁文 , 等 . 气体与液体两相连续旋转爆轰波二维数值模拟研究 [J ] . 兵工学报 , 2020 , 41 ( 4 ): 681 - 691 . DOI: 10.3969/j.issn.1000-1093.2020.04.007 http://doi.org/10.3969/j.issn.1000-1093.2020.04.007 为研究汽油与富氧空气两相连续旋转爆轰发动机的工作特性，使用非结构化三角形网格守恒元与求解元(CE/SE)方法对气体与液体（简称气液）两相连续旋转爆轰波进行了二维数值模拟。通过数值模拟获得连续旋转爆轰波传播的不同模态，研究了进气总压和当量比对两相连续旋转爆轰波的影响，分析了不同模态下连续旋转爆轰发动机的工作特性，并对数值模拟结果进行了试验验证。结果表明：液滴的蒸发和剥离过程，延缓了液滴燃料的燃烧，导致了两相爆轰压力和温度的不完全耦合，降低了两相爆轰波的传播速度；当量比对连续旋转爆轰波的传播模态影响较大，当量比越低、越容易形成单波模态，当量比越高、越容易产生多个波头；单波模态的爆轰波压力和传播速度波动最小，双波模态居中，三波模态波动最大；发动机推力波动规律与压力波动规律相反，单波模态推力波动最大，双波次之，三波模态推力波动最小；计算所得旋转爆轰波波速与试验结果吻合较好，旋转爆轰波流场与实验研究定性一致。数值研究方法发展了非结构化CE/SE算法，研究结果对气液两相连续旋转爆轰发动机的试验研究和工程应用具有一定的指导意义。

WANG F , WENG C S , WU Y W , et al. Two-dimensional numerical research on two-phase rotating detonation waves [J ] . Acta Armamentarii , 2020 , 41 ( 4 ): 681 - 691 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2020.04.007 http://doi.org/10.3969/j.issn.1000-1093.2020.04.007 In order to investigate the gasoline/oxygen-enriched air continuously rotating detonation engines(RDE), the conservation elements and solution elements method (CE/SE method) based on the unstructured triangular meshes is used for the simplified 2D simulation of two-phase continuously RDE. The different propagation modes of rotating detonation waves (RDW) were obtained. The influences of total inlet pressure and equivalent ratio were studied and the operating performance of RDE was analyzed. The results show that the evaporation and stripping of droplets delay the combustion of fuel, which leads to the incomplete coupling of detonation peak pressure and peak temperature. The equivalent ratio has a great influence on the propagation mode of rotating detonation waves. A single-wave RDW is easily generated under low equivalent ratio,and a multiple RDW is generated under higher equivalent ratio. The detonation wave pressure and velocity fluctuations of single-wave mode are the smallest, those of double-wave mode are moderate and those of three-wave mode are the largest, but the thrust fluctuation law of propagation mode is opposite to that of pressure fluctuation. The thrust fluctuation of single-wave mode is the largest, followed by double-wave mode, and the thrust fluctuation of three-wave mode is the smallest. The calculated velocity and flow field of the rotating detonation agree well with the experimental results. The numerical research is meaningful for the development of unstructured-mesh CE/SE method. The calculated results have a guidance effect on the experimental research and engineering application of two-phase RDE. Key

滕宏辉 , 杨鹏飞 , 张义宁 , 等 . 斜爆震发动机的流动与燃烧机理 [J ] . 中国科学:物理学力学天文学 , 2020 , 50 ( 9 ): 090008 .

TENG H H , YANG P F , ZHANG Y N , et al. Flow and combustion mechanism of oblique detonation engines [J ] . Scientia Sinica: Physica, Mechanica & Astronomica , 2020 , 50 ( 9 ): 090008 . (in Chinese)

SONG Q G , HAN Y , CAO W . Numerical investigation of self-sustaining modes of 2D planar detonations under concentration gradients in hydrogen-oxygen mixtures [J ] . International Journal of Hydrogen Energy , 2020 , 45 ( 53 ): 29606 - 29615 . DOI: 10.1016/j.ijhydene.2020.08.014 http://doi.org/10.1016/j.ijhydene.2020.08.014 https://linkinghub.elsevier.com/retrieve/pii/S0360319920329700 https://linkinghub.elsevier.com/retrieve/pii/S0360319920329700

陈达 , 宁建国 , 李健 . 周期性非均匀介质中气相爆轰波演变模式研究 [J ] . 力学学报 , 2021 , 53 ( 10 ): 2865 - 2879 .

CHEN D , NING J G , LI J . Study on evolution model of gaseous detonation wave in periodic inhomogeneous medium [J ] . Chinese Journal of Theoretical and Applied Mechanics , 2021 , 53 ( 10 ): 2865 - 2879 . (in Chinese)

ISHII K , KOJIMA M . Behavior of detonation propagation in mixtures with concentration gradients [J ] . Shock Waves , 2007 , 17 : 95 - 102 . DOI: 10.1007/s00193-007-0093-y http://doi.org/10.1007/s00193-007-0093-y https://link.springer.com/10.1007/s00193-007-0093-y https://link.springer.com/10.1007/s00193-007-0093-y

BOECK L R , BERGER F M , HASSLBERGER J , et al. Detonation propagation in hydrogen-air mixtures with transverse concentration gradients [J ] . Shock Waves , 2016 , 26 : 181 - 192 . DOI: 10.1007/s00193-015-0598-8 http://doi.org/10.1007/s00193-015-0598-8 http://link.springer.com/10.1007/s00193-015-0598-8 http://link.springer.com/10.1007/s00193-015-0598-8

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WANG Y , HUANG C Y , DEITERDING R , et al. Propagation of gaseous detonation across inert layers [J ] . Proceedings of the Combustion Institute , 2021 , 38 : 3555 - 3563 . DOI: 10.1016/j.proci.2020.07.022 http://doi.org/10.1016/j.proci.2020.07.022 https://linkinghub.elsevier.com/retrieve/pii/S1540748920302133 https://linkinghub.elsevier.com/retrieve/pii/S1540748920302133

NING J G , CHEN D , LI J . Numerical studies on propagation mechanisms of gaseous detonations in the inhomogeneous medium [J ] . Applied Sciences , 2020 , 10 ( 13 ): 4585 . DOI: 10.3390/app10134585 http://doi.org/10.3390/app10134585 https://www.mdpi.com/2076-3417/10/13/4585 https://www.mdpi.com/2076-3417/10/13/4585 Numerical simulation of propagation mechanisms of gaseous detonations in the inhomogeneous medium is studied by using the reactive Euler equations coupled with a two-step chemical reaction model. The inhomogeneity is generated by placing artificial temperature perturbations with different wavelengths and amplitudes. The motivation is to investigate the effect of artificial perturbations on the evolution or amplification of cellular instability. The results show that, without artificial perturbations, a planar ZND detonation can evolve into a fully-developed cellular detonation after a distance because of the amplification of the cellular instability. With the artificial perturbations evolved in, at the early stage, the artificial perturbations control the transverse wave spacing by suppressing the amplification of the cellular instability. However, after a steady-state, the cellular instability starts to amplify itself again and eventually transits to a fully-developed cellular detonation. It is demonstrated that the presence of the artificial perturbations delays the formation of the cellular detonation, and the increase of instability factor can slow down this delay. It is also found that, if the wavelength of the artificial perturbations is close to the transverse wave spacing of the cellular detonation in the homogeneous medium, synchronization of these two factors occurs, and hence a cellular detonation with extremely regular cell pattern is immediately formed. The temperature discontinuity causes the front to be more turbulent with the presence of weak triple-wave structure locally besides the natural transverse waves. The artificial perturbations can increase the intrinsic instability, and hence changes the propagation mechanism of the detonation front. In contrast, large artificial perturbations could prohibit the propagation but reduce cellular instability. It is concluded that the competition of artificial perturbations with intrinsic detonation instability dominates the evolution of cellular structures of the detonation front.

TANG-YUK K C , LEE J H , NG H D , et al. Transmission of cellular detonation waves across a density/temperature interface[C]// Proceedings of the 27th International Colloquium on the Dynamics of Explosions and Reactive Systems . Beijing, China: ICDERS , 2019 .

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NG H D , BOTROS B B , CHAO J , et al. Head-on collision of a detonation with a planar shock wave [J ] . Shock Waves , 2006 , 15 ( 5 ): 341 - 352 . DOI: 10.1007/s00193-006-0022-5 http://doi.org/10.1007/s00193-006-0022-5 https://link.springer.com/10.1007/s00193-006-0022-5 https://link.springer.com/10.1007/s00193-006-0022-5

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HE L , LEE J H S . The dynamical limit of one-dimensional detonations [J ] . Physics of Fluids , 1995 , 7 ( 5 ): 1151 - 1158 . DOI: 10.1063/1.868556 http://doi.org/10.1063/1.868556 https://pubs.aip.org/pof/article/7/5/1151/259593/The-dynamical-limit-of-one-dimensional-detonations https://pubs.aip.org/pof/article/7/5/1151/259593/The-dynamical-limit-of-one-dimensional-detonations The stability problem of one-dimensional piston supported gaseous detonations has been examined via both linear stability analysis and direct numerical simulation. It has been demonstrated that for other parameters being fixed, there are two critical values of the reduced activation energy, Ec1 and Ec2, according to which the propagation of planar detonation may be classified into three regimes: (i) when the reduced activation energy Ea is smaller than the first critical value, Ea<Ec1, the propagating detonation is stable: (ii) when Ec1<Ea<Ec2, the galloping oscillations appear in the propagation of detonations; (iii) when Ec2<Ea, the period of oscillations becomes infinitely large, the planar detonation cannot propagate via autoignition mechanism. Regime (iii) has never been pointed out in previous works. This regime occurs since the strong hydrodynamical instability effect makes the leading shock decay to a very low level which is too weak to cause a rapid autoignition.

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