Wave dynamic processes in cellular detonation reflection from wedges

When the cell width of the incident detonation wave (IDW) is comparable to or larger than the Mach stem height, self-similarity will fail during IDW reflection from a wedge surface. In this paper, the detonation reflection from wedges is investigated for the wave dynamic processes occurring in the wave front, including transverse shock motion and detonation cell variations behind the Mach stem. A detailed reaction model is implemented to simulate two-dimensional cellular detonations in stoichiometric mixtures of H ₂/O ₂ diluted by Argon. The numerical results show that the transverse waves, which cross the triple point trajectory of Mach reflection, travel along the Mach stem and reflect back from the wedge surface, control the size of the cells in the region swept by the Mach stem. It is the energy carried by these transverse waves that sustains the triple-wave-collision with a higher frequency within the over-driven Mach stem. In some cases, local wave dynamic processes and wave structures play a dominant role in determining the pattern of cellular record, leading to the fact that the cellular patterns after the Mach stem exhibit some peculiar modes. The English text was polished by Yumming Chen.     

爆轰波在突扩通道中传播的数值模拟研究

建立了描述甲烷 空气混合物爆轰波传播的单步化学反应爆轰模型 ,通过数值模拟研究了在二维突扩通道中爆轰波的强度变化和各种波行为。结果表明 :爆轰波在进入突扩通道初始阶段的衍射使爆轰波局部向爆燃转变 ;爆炸波在壁面发生马赫反射形成的高温高压区域将直接诱导自持爆轰波的重新形成。     

Numerical simulation of Mach reflection of cellular detonations

The Mach reflection of cellular detonation waves on a wedge is investigated numerically in an attempt to elucidate the effect of cellular instabilities on Mach reflection, the dependence of self-similarity on the thickness of a detonation wave, and the initial development of the Mach stem near the wedge apex. A two-step chain-branching reaction model is used to give a thermally neutral induction zone followed by a chemical reaction zone for the detonation wave. A sufficiently large distance of travel of the Mach stem is computed to observe the asymptotic behavior in the far field. Depending on the scale at which the Mach reflection process occurs, it is found that the Mach reflection of a cellular detonation behaves essentially in the same way as a planar ZND detonation wave. The cellular instabilities, however, cause the triple-point trajectory to fluctuate. The fluctuations are due to interactions of the triple point of the Mach stem with the transverse waves of cellular instabilities. In the vicinity of the wedge apex, the Mach reflection is found to be self-similar and corresponds to that of a shock wave of the same strength, since the Mach stem is highly overdriven initially. In the far field, the triple-point trajectory approaches a straight line, indicating that the Mach reflection becomes self-similar asymptotically. The distance of the approach to self-similarity is found to decrease rapidly with decreasing thickness of the detonation front.     

带隔板装药爆轰波马赫反射理论研究和数值模拟

基于三波理论和Whitham方法对带隔板装药爆轰波相互作用后发生的正规反射和非正规反射进行了理论分析,给出了爆轰波发生马赫反射时临界入射角和马赫杆增长角等参数的变化规律,提出了马赫杆高度的计算模型。基于凝聚炸药爆轰Jones-Wilkins-Lee(JWL)模型和冲击起爆的Lee-Tarver模型,利用有限元计算软件对带隔板装药爆轰波的传播过程进行了数值模拟。结果表明,发生马赫反射后,随着爆轰波的传播,马赫杆的高度不断增加。数值模拟结果与理论计算结果吻合较好,说明本文中采用的理论模型和数值模拟方法能够较准确地描述带隔板装药爆轰波马赫反射的传播过程。     

不稳定性对爆轰波楔面马赫反射的影响规律研究

采用一种两步化学反应模型对胞格爆轰波的楔面马赫反射过程进行了数值研究,从而澄清和解释胞格不稳定性对马赫反射发展模式和自相似性的影响。考虑到反应欧拉方程源项的刚性问题,本文采用附加RungeKutta方法耦合非刚性对流项和刚性反应源项,对流项的离散采用五阶精度的WENO格式。计算结果表明,对于稳定胞格爆轰波而言,其马赫反射过程本质上与ZND爆轰波的马赫反射是一致的,整体上不存在自相似性,胞格不稳定性只是造成了三波点轨迹线局部小振幅的波动。在楔面顶点附近,由于马赫杆是强过驱的,爆轰波的马赫反射过程是自相似的。在远场,爆轰波马赫反射的三波点轨迹线渐近的趋向于一条直线,说明重新获得了自相似性。对于不稳定的爆轰波,由于自身的不稳定性可以与马赫反射的强度相匹配,定义其三波点的轨迹是困难的,进行自相似性分析没有意义。     

Structure of an oblique detonation wave induced by a wedge

The structure of an oblique detonation wave (ODW) induced by a wedge is investigated via numerical simulations and Rankine–Hugoniot analysis. The two-dimensional Euler equations coupled with a two-step chemical reaction model are solved. In the numerical results, four configurations of the Chapman–Jouguet (CJ) ODW reflection (overall Mach reflection, Mach reflection, regular reflection, and non-reflection) are observed to take place sequentially as the inflow Mach number increases. According to the numerical and analytical results, the change of the CJ ODW reflection configuration results from the interaction among the ODW, the CJ ODW, and the centered expansion wave.     

气相爆轰波在障碍物上Mach反射的实验验证

本文公布了气相爆轰波沿收缩管道传播时发生Mach反射的实验证据。在爆轰波通过的管道中安装不同楔角的楔块,形成管道的收缩。爆轰波在通过楔块时会发生Mach反射。利用烟熏玻璃片记录到了爆轰波Mach反射时形成的三波点迹线及其两侧胞格尺寸和密度的变化。据我们掌握的资料,这是首次用胞格结构变化的记录证实,气相爆轰波与无化学反应的空气中的冲击波一样,在一定的入射条件下会发生Mach反射。这一实验结果可使我们更深入了解爆轰波的本质,也为数值模拟气相爆轰波在障碍物上Mach反射现象提供了可对比的依据。     

甲烷-空气爆轰波传播的数值模拟

研究了甲烷-空气混合物爆轰波在二维突扩通道中传播的各种复杂行为。结果表明：爆轰波在进入突扩通道的初始阶段有局部向爆燃转变的现象；爆炸波在壁面发生马赫反射形成的高温高压区域将直接驱动自持爆轰波的重新形成。     

The evolution of a detonation wave in a variable cross-sectional chamber

A two-dimensional numerical simulation has been performed to study the interaction of a gaseous detonation wave with obliquely inclined surfaces in a variable cross-sectional chamber. The weighted essentially non-oscillatory (WENO) numerical scheme with a relatively low resolution grid is employed. A detailed elementary chemical reaction model with 9 species and 19 elementary reactions is used for a stoichiometric oxy-hydrogen mixture diluted with argon. In this work, we study the effect of area expansion and contraction on the main/gross features of the detonation cellular structures in the presence of detonation reflection, diffraction and localized explosion. The result shows that there exists a transition region as the detonation wave propagates through the converging/diverging chamber. Within the transition region, the initial regular detonation cells become distorted and irregular before they re-obtain their regularity. While the ultimate regular cell size and the length of the transition region are strongly affected by the converging/diverging angle, the width/length ratio of the cells is fairly independent of it. A localized explosion near the wall is found as the detonation wave propagates in the diverging chamber.      

A weak shock wave reflection over wedges

When a weak shock wave reflects from wedges its reflection pattern does not appear to be a simple Mach reflection. This reflection pattern is known to be von Neumann Mach reflection in which a Mach stem can not necessarily be straight. In this paper the local change of the Mach stem curvature was experimentally and numerically investigated. A distinct triple point, at which the curvature becomes infinite as appears in a simple Mach reflection, was not observed but the Mach stem curvature became a maximum between foot of the Mach stem and a point, P₁, at which an incident shock met with a reflected shock. Maximum curvature point P₂ and P₁ do not coincide for small wedge angles and tend to merge over a certain wedge angle. Experimental results agreed with numerical results. The trajectory angle of P₂ was found to be expressed well by Whitham's shock-shock angle.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

气相爆轰波正反射激波加速研究

实验采用压力传感器测量了指定点压力时间曲线。数值模拟基于二维反应欧拉方程和基元反应模型,采用二阶附加半隐的龙格-库塔法和5阶WENO格式分别离散时间和空间导数项,获得了指定点数值压力时间曲线。理论分析基于爆轰理论和激波动力学,分析了气相爆轰波反射过程所涉及的复杂波系演变并获得了反射激波速度。结果表明:本文数值模拟和理论计算定性上重复并解释了实验现象。气相爆轰波在右壁面反射后,右行稀疏波加速反射激波。其加速原因是:尽管激波波前声速减小,但激波马赫数增大,波前气流速度减小。在低初压下,可能还由于爆轰波后未反应或部分反应气体的作用,导致反射激波加速幅度比高初压下大。     

可燃气体中激波聚焦的点火特性

数值模拟了二维平面激波从抛物面上反射在可燃气体中聚焦的过程,研究了形 成爆轰波的点火特性. 对理想化学当量比氢气/空气混合气体,在初始压强20kPa的条件下, 马赫数2.6-2.8的激波聚焦能产生两个点火区：第1个点火区是反射激波会聚引起的,第 2个点火区是由入射激波在抛物面上发生马赫反射引起的. 这种条件下流场中会出现爆燃转 爆轰,起爆点分别分布在管道壁面、抛物反射面和第2点火区附近. 起爆机理分别为激波管 道壁面反射、点火诱导激波的抛物面反射和点火诱导的激波与第2点火区产生的爆燃波的相 互作用. 不同的点火和起爆过程导致了不同的流场波系结构,同时影响了爆轰波传播的波动 力学过程.     

On the influence of low initial pressure and detonation stochastic nature on Mach reflection of gaseous detonation waves

The two-dimensional, time-dependent and reactive Navier–Stokes equations were solved to obtain an insight into Mach reflection of gaseous detonation in a stoichiometric hydrogen-oxygen mixture diluted by 25 % argon. This mixture generates a mode-7 detonation wave under an initial pressure of 8.00 kPa. Chemical kinetics was simulated by an eight-species, forty-eight-reaction mechanism. It was found that a Mach reflection mode always occurs for a planar detonation wave or planar air shock wave sweeping over wedges with apex angles ranging from \(5^\circ \) to \(50^\circ \) . However, for cellular detonation waves, regular reflection always occurs first, which then transforms into Mach reflection. This phenomenon is more evident for detonations ignited under low initial pressure. Low initial pressure may lead to a curved wave front, that determines the reflection mode. The stochastic nature of boundary shape and transition distance, during deflagration-to-detonation transition, leads to relative disorder of detonation cell location and cell shape. Consequently, when a detonation wave hits the wedge apex, there appears a stochastic variation of triple point origin and variation of the angle between the triple point trajectory and the wedge surface. As the wedge apex angle increases, the distance between the triple point trajectory origin and the wedge apex increases, and the angle between the triple point trajectory and the wedge surface decreases exponentially.     

爆轰波在楔面上反射数值分析

应用基元反应模型和频散可控耗散格式(DCD)对氢氧爆轰波在楔面反射进行了数值模拟,计算中氢氧混合物的化学反应采用了8种组分20个反应方程式,在处理化学反应引起的刚性问题时采用了时间算子分裂的方法,模拟了爆轰波在楔面反射由马赫反射向规则反射转变的过程,得到了反射转变临界角,同时考虑了初始压力和组分的影响,并和实验及理论分析结果进行了比较,结果是令人满意的。     

Transition between regular and Mach reflection of shock waves: new numerical and experimental results

New numerical and experimental results on the transition between regular and Mach reflections of steady shock waves are presented. The influence of flow three-dimensionality on transition between steady regular and Mach reflection has been studied in detail both numerically and experimentally. Characteristic features of 3D shock wave configuration, such as peripheral Mach reflection, non-monotonous Mach stem variation in transverse direction, the existence of combined Mach-regular-peripheral Mach shock wave configuration, have been found in the numerical simulations. The application of laser sheet imaging technique in streamwise direction allowed us to confirm all the details of shock wave configuration in the experiments. Close agreement of the numerical and experimental data on Mach stem heights is shown. Received 23 November 2000 / Accepted 25 April 2001     

爆轰波与激波对撞爆轰状态演化机理研究

对当量比氢氧混合气体中爆轰波与激波的正面对撞过程进行了二维数值研究. 采用了二阶精度NND差分格式与改进的两阶段化学反应模型,并以数值x-t纹影图以及烟迹图记录了对撞过程. 数值研究表明,透射爆轰波受到膨胀影响首先会衰减,甚至产生局部解耦现象;然后由于三波点的碰撞又能再次重新耦合. 在爆轰波对撞过程中,由于燃烧不均匀性而产生的弱横波对爆轰胞格的形成起着重要作用.      

可燃气体中激波与障碍物作用在下游形成爆轰波的数值研究

对平面激波和单个矩形障碍物作用的过程进行了数值模拟,研究了反射产生的上行爆轰波在下游可燃气体中形成爆轰波的过程。数值结果表明,下游爆轰波形成过程主要有2种模式:爆轰波直接绕射和绕射波在上壁面反射,这和已有的实验结果是一致的。通过研究下游爆轰波的形成过程受入射激波马赫数、混合气体的压力和管道尺度的影响,分析了上游爆轰波向下游传播的波动力学过程,讨论了2种形成过程的作用规律和控制因素,阐明了下游爆轰波的形成规律。     

激波在不同三角楔面内传播特性的数值研究

激波在收缩管内的反射与聚焦会形成高温高压区,点燃可燃混合气并诱导爆轰,因此对爆轰发动机的点火具有重要意义。本文基于二维N-S方程,结合五阶WENO格式,对马赫数为6的正激波在三角形楔面内的反射与聚焦现象进行了数值研究。结果表明,楔面顶角的变化对激波的反射类型以及聚焦均有明显的影响:随着顶角的增加,激波的反射类型从马赫反射向过渡马赫反射和双马赫反射转变,且壁面上的前向射流更加明显;三波点第一次碰撞产生的高温高压区足够满足可燃混合气体的点火条件,且其温度与压力值随顶角的增加而增大;当激波在楔面上发生临界双马赫反射时,温度与压力达到最大;当顶角增加到一定值时,激波在楔面反射转变为常规反射,不会产生激波对碰,因而没有高温高压区。     

正向爆轰驱动高焓激波风洞的数值模拟

对充满氢氧可燃气体、带扩容腔的正向爆轰驱动的激波风洞进行了数值模拟。计算采用了欧拉方程,频散可控耗散差分格式（DCD）和改进的二阶段化学反应模型。在扩容腔附近采用二维轴对称计算模型,而在驱动段和被驱动段的直管道部分则采用一维计算模型。本文分析了爆轰波在管道中的传播、反射和绕射过程。计算结果表明扩容腔的尺寸对爆轰波的传播、反射、汇聚等起着决定性的作用;带扩容腔的正向爆轰驱动的激波风洞能够得到平稳的持续时间较长的气流,提高了实验的精确度和可重复性。     

Numerical investigation of shock wave reflections near the head ends of rotating detonation engines

The influence of various chamber geometries on shock wave reflections near the head end of rotating detonation engines was investigated. A hydrogen/air one-step chemical reaction model was used. The results demonstrated that the variation in flow field along the radial direction was not obvious when the chamber width was small, but became progressively more obvious as the chamber width increased. The thrust increased linearly, and the detonation height and the fuel-based gross specific impulse were almost constant as the chamber width increased. Near the head end, shock waves reflected repeatedly between the inner and outer walls. Both regular and Mach reflections were found near the head end. The length of the Mach stem increased as the chamber length increased. When the chamber width, chamber length and injection parameters were the same, the larger inner radius resulted in more shock wave reflections between the inner and outer walls. The greater the ratio of the chamber width to the inner radius, the weaker the shock wave reflection near the head end. The detonation height on the outer wall and the thrust, both increased correspondingly, while the specific impulse was almost constant as the inner radius of the chamber increased. The numerical shock wave reflection phenomena coincided qualitatively with the experimental results.