Numerical study of three-dimensional detonation structure transformations in a narrow square tube: from rectangular and diagonal modes into spinning modes

Three-dimensional (3-D) detonation structure transformations from rectangular and diagonal modes into spinning modes in a narrow square tube are investigated by high-resolution simulation. Numerical simulations are performed with a Riemann solver of the HLLC-type, new cell-based structured adaptive mesh refinement data structure, high-order, parallel adaptive mesh refinement reactive flow code. A simplified one-step kinetic reaction model is used to reveal the 3-D detonation structure. The four different types of initial disturbances applied in the ZND profiles lead to the structures of rectangular in phase, rectangular out of phase, rectangular partial out of phase and diagonal, respectively, during the initial stages of detonation propagation. Eventually, all these detonation structures evolve into the self-sustained spinning detonations. The asymmetric disturbance leads to a stable spinning detonation much faster than the rest. The important features in the formation of spinning detonation are revealed using a 3-D visualization, and a remarkable qualitative agreement with experimental and numerical results is obtained with respect to the transverse wave dynamics and detonation front structures. The transverse wave collisions produce the unburnt gas pockets and the energy to sustain the detonation front propagation and distortion. The periodic pressure oscillation of front plays a complex role as it shifts the reaction zone structure with an accompanying change in the driving energy of transition and the detonation parameters which result in the more distorted front and the unstable detonation. Eventually, the unstable distorted detonation evolves into a spinning detonation.     

环形方管道中爆轰胞格的三维研究

通过实验和三维数值模拟研究了爆轰波在环形管道内的传播。实验采用烟迹板记录了爆轰波的胞格结构。数值模拟基于带化学反应的三维Euler方程,采用五阶精度的WENO格式捕捉激波,采用具有TVD性质的三阶Runge-Kutta法处理时间项,并结合并行技术,对爆轰波的传播进行了数值研究。结果表明,环形管道外壁为收敛壁面,由于其对流场的压缩效应,外壁面及附近的胞格较小,且较均匀。而内壁为发散壁面,其对流场起稀疏效应,内壁面及附近的胞格较大,且呈周期性变化。同时, 不同壁面的胞格结构均出现了拍波(slapping wave),其形状呈弯曲的折线。     

Comparison of critical conditions for DDT in regular and irregular cellular detonation systems

Abstract. The results of an experimental study of DDT in mixtures with regular and irregular detonation cellular structures are presented. Experiments were carried out in a tube 174 mm i. d. with obstacles (blockage ratios were 0.1, 0.3, and 0.6). Mixtures used were hydrogen–air and stoichiometric hydrogen–oxygen diluted with , Ar, and He. The critical conditions for DDT are shown to depend on the regularity of the cellular structure of test mixtures. The critical values of the cell sizes in Ar- and He-diluted mixtures are shown to be significantly smaller than those in -diluted mixtures. This means that systems with a highly regular detonation cellular structure have far less capacity for undergoing DDT compared to irregular ones with the same values of detonation cell sizes. Received 18 November 1999 / Accepted 15 May 2000     

爆轰波在阻尼管道中声吸收的实验研究

实验旨在研究气相爆轰波在阻尼管道 (管壁上衬有吸收材料 )中传播时的衰减现象。先是在光滑管壁的管道中产生稳定的具有胞格结构的爆轰波 ,然后使其通过专门设计的管壁上衬有吸收材料 (金属丝网或不锈钢纤维 )的阻尼段。利用高速摄影、压力传感器和烟迹技术等手段 ,记录和测试了阻尼段对几种混合气体爆轰波的传播速度、爆压及胞格结构产生的影响。实验分别在方管和圆管中进行。发现在某些条件下爆轰波可以被衰减成强爆燃。     

Dynamics study of detonation-wave cellular structure 1. Statistical properties of detonation wave front

We have investigated the evolution of cellular detonation-wave structure as a gaseous detonation travels along a round tube and measured cell lengths as a function of the initial pressure of the gas. We have tested acetylene-containing combustible gas mixtures with different degrees of regularity. Along with the smoked-foil technique, an emission method has been used to the measure current and average values of the detonation cell length. The method is based on the detection of an emission spectrum behind the detonation front in the spectral range corresponding to local gas temperatures that are much higher than those for the Chapman-Jouguet equilibrium condition. This technique provides quasi-continuous cell-length measurements along the normal to the detonation front over the length of several factors of ten times the tube. Our study has experimentally identified the steady states of detonation structure in round tubes, referred to here as the single detonation modes. When the state of a single mode is fully established, then both the flow structure and the energy release at detonation front develop strictly periodically along the tube at a constant frequency inversely proportional to the cell length of the mixture. The mixture regularity has had no influence on the occurrence of the detonation mode, which is defined by the value of initial pressure or the total energy release of the mixture. Outside of the pressure range where a detonation mode was most likely to occur, the detonation front is unstable and may exhibit an irregular cellular pattern. Monitoring the evolution of cells over a long distance revealed that the local gas emissivity, which is time dependent and corresponds to axial pulsations of the detonation structure, has the appearance of a superposition of separate harmonics describing the states of emissivity oscillations and cell structure of single detonation modes. Received 18 October 1999 / Accepted 10 June 2001     

Analysis of the shock structures in a regular detonation

Time-dependent two-dimensional numerical simulations have been used to investigate the detailed shock structures and patterns of energy release in the regions of the triple points and transverse waves in a planar detonation. As the system of shock triple points evolves between collisions, they trace a well shaped cellular pattern characteristic of detonations in argon-diluted, low-pressure mixtures of hydrogen and oxygen. In the region of the triple points, the shock structure evolves continuously from a single Mach structure to a double Mach structure and finally to a complex Mach structure characteristic of spinning detonations. Most of the energy released in the region of the triple points. The amount of energy release increases as the triple point comes closer to a collision with a wall or another triple point. Just before the collision, there is a large region of energy release that covers the length of the interacting transverse waves. The result is a rectangular high-energy region which boosts the propagation of the new detonation cell.     

Effect of initial disturbance on the detonation front structure of a narrow duct

The effect of an initial disturbance on the detonation front structure in a narrow duct is studied by three-dimensional numerical simulation. The numerical method used includes a high-resolution fifth-order weighted essentially non-oscillatory scheme for spatial discretization, coupled with a third-order total variation diminishing Runge-Kutta time-stepping method. Two types of disturbances are used for the initial perturbation. One is a random disturbance which is imposed on the whole area of the detonation front, and the other is a symmetrical disturbance imposed within a band along the diagonal direction on the front. The results show that the two types of disturbances lead to different processes. For the random disturbance, the detonation front evolves into a stable spinning detonation. For the symmetrical diagonal disturbance, the detonation front displays a diagonal pattern at an early stage, but this pattern is unstable. It breaks down after a short while and it finally evolves into a spinning detonation. The spinning detonation structure ultimately formed due to the two types of disturbances is the same. This means that spinning detonation is the most stable mode for the simulated narrow duct. Therefore, in a narrow duct, triggering a spinning detonation can be an effective way to produce a stable detonation as well as to speed up the deflagration to detonation transition process.     

旋转爆轰胞格结构的实验和数值研究

对爆轰波在环形圆管(预混气体为2H2/O2/Ar)内的传播分别进行了实验和数值研究。实验研究 采用烟迹板记录了环形圆管内爆轰波的胞格结构。数值计算利用二阶附加半隐的Runge-Kutta法和五阶 WENO格式分别离散欧拉方程的时间和空间导数项,采用基元反应简化模型描述化学反应过程,得到了旋转 爆轰的流场及数值胞格结构。实验和数值模拟结果表明:爆轰波在圆环管中传播时,由于圆环的内壁发散、外 壁收敛,圆环内侧爆轰强度小于外侧,胞格尺寸较大;内侧OH 的分布区域大于外侧,浓度较低。旋转爆轰的 这种性质,使爆轰波能以稳定的角速度绕轴旋转。     

Diffraction and re-initiation of detonations behind a backward-facing step

Diffraction phenomena of gaseous detonation waves behind a backward-facing step in a tube are observed by using high-speed schlieren photography and soot-track records as well as by pressure measurements on the sidewall. Mixtures are stoichiometric oxyhydrogen and those diluted by argon at sub-atmospheric pressures. Three types of phenomena are observed, that is, continuous propagation of detonation, re-initiation after a temporal extinction of detonation and complete extinction of detonation. The continuous propagation means that the diffracted wave does not affect the main propagation although reflected shock waves from the bottom surface of the tube may affect it. The re-initiation occurs at a wall surface of the tube behind a reflected shock wave after the main detonation wave has been extinguished. Positions and conditions of the re-initiation are discussed. The complete extinction is defined as disappearance of detonation cells behind the step within a certain length of the tube. Cases exist where an ignition occurs after several reflections off the bottom and top surface of the tube.     

弯管内爆轰波传播的流场显示和数值模拟

采用激光纹影系统拍摄了爆轰波在不同位置的流场照片. 用二阶附加半隐的龙格- 库塔法和五阶WENO格式 分别离散欧拉方程时间和空间导数项,用基元反应来描述爆轰化学反应过程,获得了压力、 温度、典型组元质量分数分布及数值胞格结构和爆轰波平均速度. 结果表明：受壁面稀疏波 和压缩波影响,爆轰波阵面发生畸变. 但由于弯管曲率半径较大,未出现爆轰波熄灭. 靠近 凹壁面的激波强度大于凸壁面侧,且凹壁面侧的反应区宽度较凸壁面侧要窄. 弯管出口处的 三波点数目较入口处减少,爆轰波衰减. 在出口直段,受扰动的爆轰波可恢复为自持爆轰波. 爆轰波流场、胞格结构、平均爆轰波速度的计算和实验结果定性一致.     

Reignition of detonations by reflected shocks

Numerical simulations are used to study the diffraction, decay, and reignition that occurs when a detonation propagates past an increase in cross-sectional area in a rectangular tube. The computations solve the time-dependent two-dimensional equations describing a reactive flow in an argon-diluted stoichiometric hydrogen-oxygen mixture at atmospheric pressure. Previous studies have shown that soon after transmission to a larger area, the reaction front decouples from the leading shock and forms a decaying blast wave (“bubble”) in the larger tube. Then, depending on the initial conditions, the detonation either continues to decay or is reignited as the bubble reflects off confining surfaces. For a strongly overdriven initiating detonation, reignition occurs through an interaction between the bubble and the original contact surface. For a more weakly driven system, reignition can occur in two ways: either in the slip line and Mach stem of the Mach reflection formed when the bubble reflects off the bottom surface of the tube, or by multiple shock interactions that occur when the reflected bubble overtakes the initial detonation front. The computations show the evolution and development of the cellular structure of the steady detonation front. Submitted to the 14th International Colloquium on the Dynamics of Energetic and Reactive Systems, Coimbra, Portugal, August, 1993     

Two-cell detonation: losses effects on cellular structure and propagation in rich H2–NO2/N2O4–Ar mixtures

Detonation experiments in H₂–NO₂/N₂O₄–Ar mixtures (Equivalence ratio 1.2 and initial pressure lower than 0.1 MPa) confined in a tube of internal diameter 52 mm reveal two propagation regimes depending on initial pressure: (1) a quasi-CJ regime is observed along with a double cellular structure at high pressures; (2) at lower pressures, a low velocity detonation regime is observed with a single structure. Transition between this two regimes happens when the spinning detonation of the larger cell vanishes. Each detonation regime is characterized by velocity and pressure measurements and cellular structure records. Coherence between all experimental data for each experiment leads in assumption that losses are responsible for the transition between one regime to another. In a second part, we study such behaviour for a two-step mixture through numerical simulations using a global two-step chemical kinetics and a simple losses model. Numerical simulations qualitatively agree with experiments. Both detonation regimes with their own cellular structures are reproduced.     

Numerical investigation on evolution of cylindrical cellular detonation

Cylindrical cellular detonation is numerically investigated by solving two- dimensional reactive Euler equations with a finite volume method on a two-dimensional self-adaptive unstructured mesh. The one-step reversible chemical reaction model is applied to simplify the control parameters of chemical reaction. Numerical results demonstrate the evolution of cellular cell splitting of cylindrical cellular detonation explored in experimentas. Split of cellular structures shows different features in the near-field and far-field from the initiation zone. Variation of the local curvature is a key factor in the behavior of cell split of cylindrical cellular detonation in propagation. Numerical results show that split of cellular structures comes from the self-organization of transverse waves corresponding to the development of small disturbances along the detonation front related to detonation instability.     

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。     

掺氢比对甲烷-氧气爆轰特性的影响

含氢多组分燃料由于其优良的燃烧特性逐渐成为研究关注的重点。为了对掺氢燃料的爆轰特性作进一步的研究,设计了长3 000 mm、管径30 mm的圆柱形半封闭燃烧室,对不同初压下的CH₄-2O₂、6CH₄-H₂-12.5O₂、3CH₄-H₂-6.5O₂（掺氢比分别为0%、5.1%、9.5%）3种预混合气的爆轰特性进行了实验研究,并采用烟熏膜、离子探针和压力传感器分别探测胞格结构、火焰位置和内部压力。结果表明,甲烷/氧气掺氢后可以有效提高爆轰波的传播速度,且掺氢浓度越高,传播速度越快;同时,氢气的掺入可减少管道出口处的速度亏损并在初始压力较低时加速火焰和激波的耦合,降低胞格尺寸,提高爆轰敏感性。     

Numa Manson on velocity deficits and detonation stability

This memorial paper pays tribute to Professor Numa Manson’s contributions to the understanding of detonation velocity deficits and wave stability. Manson and his colleague Guénoche postulated that a velocity deficit exists in a tube because the chemical reactions are inhibited in a thin layer adjacent to the tube walls. The hydrodynamic theory of detonation was modified to account for this, and it was shown that the deficit varies inversely with the tube diameter. Manson and his students measured detonation velocities in tubes of various diameter. An estimate of the detonation velocity for an infinite tube diameter was obtained by plotting the velocity against the reciprocal of the tube diameter, , and extrapolating the line through the data to . The relative contributions of tube geometry and surface roughness to the deficits were systematically studied. Manson was also one of the early investigators to shed light on the cellular structure of detonation by reporting “vibratory phenomena” seen as striations in streak schlieren photographs. An attempt was made to relate this phenomenon to “dispersions” in the propagation velocity and hence the wave stability. The author has extended Manson’s work by investigating detonations in tubes with yielding walls. Whereas boundary layers were responsible for the gasdynamic expansion and deficits in Manson’s rigid tubes, it was the moving boundaries that caused similar effects in the author’s investigations. The author has repeated the “nozzle” analysis of Fay and Dabora using the detonation cell length as the relevant chemical kinetic length scale, and found reasonable agreement between his experimental results and the model. When the Poitiers data are reinterpreted in light of the modified model, the trends are described quite well. More recent studies have shown that the measured deficits for mixtures characterized by irregular cellular structures do not agree with the Fay–Dabora model. Possible reasons for the discrepancy are discussed. This paper is based on the invited lecture that was presented at the 21st International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23-27, 2007.     

DDT and detonation waves in dust-air mixtures

This paper summarizes the studies of DDT and stable detonation waves in dust-air mixtures at the Stosswellenlabor of RWTH Aachen. The DDT process and propagation mechanism for stable heterogeneous dust detonations in air are essentially the same as in the oxygen environment studied previously. The dust DDT process in tubes is composed of a reaction compression stage followed by a reaction shock stage as the pre-detonation process. The transverse waves that couple the shock wave and the chemical energy release are responsible for the propagation of a stable dust-air detonation. However, the transverse wave spacing of dust-air mixtures is much larger. Therefore, DDT and propagation of a stable detonation in most industrial and agricultural, combustible dust-air mixtures require a tube that has a large diameter between 0.1 m and 1 m and a sufficient length-diameter ratio beyond 100, when an appropriately strong initiation energy is used. Two dust detonation tubes, 0.14 m and 0.3 m in diameter, were used for observation of the above-mentioned results in cornstarch, anthraquinone and aluminum dust suspended in air. Smoked-foil technique was also used to measure the cellular structure of dust detonations in the 0.3 m detonation tube. Received 11 February 2000 / Accepted 1 August 2000     

直管内胞格爆轰的基元反应数值研究

基于基元反应和二维欧拉方程，对直管内胞格爆轰进行了数值模拟。采用5阶WENO(weighted essentially nonoscillatory scheme)求解对流项，采用2阶附加半隐的龙格-库塔法处理化学反应源相引起的刚性。获得了密度、压力、温度和典型组元质量分数流场及数值胞格结构等。结果表明:网格精度的差异明显影响胞格的规则性和爆轰的平衡模数，随着网格尺度的减小，胞格由不规则变为规则。预混气组成、初压、初温及管道宽度给定，三波点数收敛为确定值。足够强度的初始扰动可再现胞格爆轰，最终形成的自持胞格爆轰模数与初始扰动的形状、大小、位置均无关。沿胞格中心线，爆轰波速度变化范围为0.88DCJ~1.5DCJ，爆轰波平均速度与CJ爆轰速度仅偏差0.88％。峰值压力与初压之比为14~50。计算爆轰波平均速度、胞格宽长比与实验值基本一致，但计算胞格宽度比实验值略小。数值模拟加深了对横波的产生和发展、未反应气囊、爆轰胞格的二次起爆等胞格爆轰特性的认识。     

Experimental study of gaseous detonation propagation over acoustically absorbing walls

The paper presents results from an experimental investigation of the propagation of gaseous detonation waves over tube sections lined with acoustically absorbent materials. The measurements were compared with results from control tests in a smooth wall section. The results show the increasing effectiveness of a perforated steel plate, wire mesh and steel wool in attenuating detonation. Received 25 October 2000 / Accepted 20 August 2001     

Experimental investigation into the detonation characteristics of hybrid RDX–ethylene–air mixtures

An experimental study is conducted to determine the detonation characteristics of 1,3,5-trinitroperhydro-1,3,5-triazine (RDX) particles dispersed in a gaseous fuel air mixture in a vertical detonation tube with an inner diameter of 200 mm and a height of 5400 mm. Experiments are performed in both ethylene–air mixtures and RDX–ethylene–air hybrid mixtures. The detonation front pressure and velocity are measured with six pressure transducers along the detonation tube. The results show that the addition of RDX assists 4.0 vol.% ethylene–air mixtures in achieving detonation. The detonation front pressure increases noticeably with dust concentration up to \(474\hbox { g/m}^{3}\) in the RDX–ethylene–air hybrid mixtures, but the velocity only increases slightly. The cellular structures of RDX–ethylene–air hybrid mixtures and ethylene–air mixtures were obtained with the use of smoked foils and exhibit irregular structures. It is found that the measured cell size has a U-shaped curve with respect to RDX concentration.