Numerical study on three-dimensional C-J detonation waves: detailed propagating mechanism and existence of OH radical

An unsteady three-dimensional simulation is performed for a hydrogen/air C–J detonation in a rectangular tube, where a detailed chemical reaction model is used to reveal the C–J detonation structure. In this simulation, detailed propagating detonation structures for a diagonal mode are described in three-dimensions. The detonation front structures, the line of triple points, and the strong explosions at the corners of the rectangular tube are revealed by using a three-dimensional numerical visualization. From the spatial isosurface profiles of H₂ mass fraction, it is confirmed that the triple point lines have a role of “shutter” to generate unburned gas pockets and become of a ring shape behind the detonation front due to its explosion. The explosion process and its influence on an induction delay are observed by visualizing the spatial isosurface profiles of OH mass fraction. Moreover, a high “peninsula-shaped” OH mass fraction area, which has been experimentally reported, is reproduced on the side wall of the rectangular tube.     

一种准二维柱面爆炸波加载装置的设计与验证

基于竖直爆轰管和径向Hele-Shaw Cell,设计并搭建了一套准二维柱面爆炸波加载装置,可以实现对Hele-Shaw Cell内部材料界面的径向冲击加载.竖直爆轰管内部的预混气体在底部点燃后,形成向上传播的冲击波,冲击波冲破爆轰管开口与Hele-Shaw Cell底板开孔之间的隔膜后,被Hele-Shaw Cell...     

Stability characteristic of hypersonic flow over a blunt wedge under freestream pulse wave

To investigate the stability characteristic of hypersonic flow under the action of a freestream pulse wave, a high-order finite difference method was employed to do direction numerical simulation (DNS) of hypersonic unsteady flow over an 8° half-wedge-angle blunt wedge with freestream slow acoustic wave. The evolution of disturbance wave modes in the boundary layer under a pulse wave and a continuous wave are compared, and the wall temperature effect on the hypersonic boundary layer stability for a pulse wave disturbance is discussed. Results show that, both for a pulse wave and a continuous wave in freestream, the disturbance waves inside the nose boundary layer are mainly a fundamental mode; the Fourier amplitude of pressure disturbance mode in the boundary layer for a pulse wave is far less than that for a continuous wave, and the band frequency of the former is wider than that of the latter. All disturbance modes decay rapidly along the streamwise in the nose boundary layer. In the non-nose boundary layer, the dominant mode is transferred from fundamental mode into second harmonic. The transformation of dominant mode for a pulse wave appears much earlier than that for a continuous wave. Different frequency disturbance modes present different changes along streamline in the boundary layer, and the frequency band narrows around the second harmonic mode along the streamwise. Keen competition and the transformation of energy exist among different modes in the boundary layer. Wall temperature modifies the stability characteristic of the hypersonic boundary layer, which presents little effect on the development of fundamental modes and cooling wall could accelerates the growth of the high frequency mode as well as the dominant mode transformation.     

Experimental study of the influence of annular nozzle on acoustic characteristics of detonation sound wave generated by pulse detonation engine

Acoustic characteristics of the detonation sound wave generated by a pulse detonation engine with an annular nozzle, including peak sound pressure, directivity, and A duration, are experimentally investigated while utilizing gasoline as fuel and oxygen-enriched air as oxidizer. Three annular nozzle geometries are evaluated by varying the ratio of inner cone diameter to detonation tube exit diameter from 0.36 to 0.68. The experimental results show that the annular nozzles have a significant effect on the acoustic characteristics of the detonation sound wave. The annular nozzles can amplify the peak sound pressure of the detonation sound wave at 90° while reducing it at 0° and 30°. The directivity angle of the detonation sound wave is changed by annular nozzles from 30° to 90°. The A duration of the detonation sound wave at 90° is also increased by the annular nozzles. These changes indicate that the annular nozzles have an important influence on the acoustic energy distribution of the detonation sound wave, which amplify the acoustic energy in a direction perpendicular to the tube axis and weaken it along the direction of the tube axis.     

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.     

拐角空间中悬浮铝粉尘爆轰后效的三维数值模拟

建立三维的铝粉-空气两相爆轰计算模型,采用时-空守恒元解元（CE/SE）方法求解,并开发了悬浮铝粉尘爆轰的三维数值模拟程序.基于消息传递接口（MPI）技术实现了程序的并行化设计.通过对激波管问题以及爆轰管中铝粉-空气两相爆轰实验的模拟验证程序的可靠性.对拐角空间中左侧浓度为368 g·m^-3的铝粉-空气混合物两相爆轰及其在拐角空间右侧和下方空气域内形成的冲击波和温压效应开展数值模拟,获得复杂空间内爆轰波或冲击波的传播、反射以及绕射过程.结果表明：两相爆轰在离铝粉尘区域2 m远的空气域内产生的后效冲击波能达到2.66 MPa的固壁反射压力,火球燃烧范围会超出初始铝粉尘区域约0.8 m,并且造成初始铝粉尘区域附近1.5 m范围内空气的温度高达1 600 K.模拟程序可用于铝粉尘爆轰的后效研究,对工业安全及其防护具有指导意义.     

Numerical study on spinning detonations

Spinning detonations in both a circular tube and a square tube are presented in order to reveal characteristics of spinning modes by using three-dimensional simulations with a detailed chemical reaction model. The present results show a feature of a single spinning detonation which was discovered in 1926. The shock patterns in both cases are similar except the pressure trail, however, the shock wave angles and the shock wave lengths are shown to be dependent on the cross section configuration of the tube. The pitch angle, the track angle, the Mach stem angle, and the incident shock angle on the tube wall in the numerical results agree well with those in the experimental ones, and they are independent of the compositions of mixture, tube diameters, and initial pressures.     

Numerical investigation on propagation mechanism of spinning detonation in a circular tube

Spinning detonations propagating in a circular tube were numerically investigated with a one-step irreversible reaction model governed by Arrhenius kinetics. The time evolution of the simulation results was utilized to reveal the propagation mechanism of single-headed spinning detonation. The track angle of soot record on the tube wall was numerically reproduced with various levels of activation energy, and the simulated unique angle was the same as that of the previous reports. The maximum pressure histories of the shock front on the tube wall showed stable and unstable pitch modes for the lower and higher activation energies, respectively. The shock front shapes and the pressure profiles on the tube wall clarified the mechanisms of two modes. The maximum pressure history in the stable pitch remained nearly constant, and the single Mach leg existing on the shock front rotated at a constant speed. The high and low frequency pressure oscillations appeared in the unstable pitch due to the generation and decay of complex Mach interaction on the shock front shape. The high-frequency oscillation was self-induced because the intensity of the transverse wave was changed during propagation in one cycle. The high-frequency behavior was not always the same for each cycle, and therefore the low frequency oscillation was also induced in the pressure history.     

谱有限元数值分析各向异性复合板中导波色散特性

提出谱有限元方法研究层状各向异性复合板中导波的色散特性和波结构。基于三维弹性动力学方程,用有限元方法离散波导截面,波传播方向的位移用简谐波表示,得到了导波色散的特征方程。分析了单层和双层复合板中导波沿不同方向传播的色散特性和波结构,讨论了双层复合板中层厚比对相速度的影响。数值研究结果表明:导波的对称模态沿纤维方向传播时在较宽的频率范围内保持弱色散状态。双层复合板中导波基本模态的相速度在低频时受层厚比的影响较明显,随着频率的增加趋向于相速度较低的材料。数值模拟结果为导波用于复合材料定量无损检测和性能评价提供理论依据。      

Fine-tuning of nonBragg bandgaps in axisymmetric ducts via arbitrary periodic walls

We investigate the nonBragg bandgap (NBBG) resulting from interference between two transverse guided wave modes in an axisymmetric duct with periodic walls. We find that the NBBG bandwidth is proportional to both the height and shape factor of the wall undulations. The shape factor is defined as the norm of the major Fourier component of the periodic wall profile. Varying the height directly tunes the bandwidth, while manipulating the wall profile results in a slight change in the shape factor, which leads to fine-tuning of the bandgap. We also find that for a fixed height, the NBBG width is related to the area under the curve for the product of the wall profile and a half-period sine or cosine function. We propose an area estimation method according to which a larger area results in a wider NBBG. A numerical example reveals that NBBG fine-tuning can be achieved by carefully varying the shape factor. The results will benefit the design of band structures, especially subtle modifications by selecting suitable wall undulations.     

ON THE RELATION BETWEEN COMPLEX MODES AND WAVE PROPAGATION PHENOMENA

This paper discusses the well-known, but often misunderstood, concept of complex modes of dynamic structures. It shows how complex modes can be interpreted in terms of wave propagation phenomena caused by either localized damping or propagation to the surrounding media. Numerical simulation results are presented for different kinds of structures exhibiting modal and wave propagation characteristics: straight beams, an L-shaped beam, and a three-dimensional frame structure. The input/output transfer relations of these structures are obtained using a spectral formulation known as the spectral element method (SEM). With this method, it is straightforward to use infinite elements, usually known as throw-off elements, to represent the propagation to infinity, which is a possible cause of modal complexity. With the SEM model, the exact dynamic behavior of structures can be investigated. The mode complexity of these structures is investigated. It is shown that mode complexity characterizes a behavior that is half-way between purely modal and purely propagative. A coefficient for quantifying mode complexity is introduced. The mode complexity coefficient consists of the correlation coefficient between the real and imaginary parts of the eigenvector, or of the operational deflection shape (ODS). It is shown that, far from discontinuities, this coefficient is zero in the case of pure wave propagation in which case the plot of the ODS in the complex plane is a perfect circle. In the other extreme situation, a finite structure without damping (or with proportional damping), where the mode shape (or the ODS) is a straight line on the complex plane, has a unitary complexity coefficient. For simple beam structures, it is shown that the mode complexity factor can also be calculated by curve-fitting the mode to an ellipse and computing the ratio of its radii.     

Detonation in a Three-Dimensional Elbowed Channel

The results of simulation of detonation in a curved three-dimensional channel with a circular cross section of constant width blown through by a supersonic flow of a stoichiometric propane?air mixture are presented. In the bending zone, the channel wall was toroidal. The study was carried out within the framework of the one-stage combustion kinetics by the numerical method based on Godunov’s scheme in the original software package developed for multiparameter calculations and visualization of flows. The initiation of detonation occurs as a result of the formation of the shockwave configurations associated with the flow turn in the channel. Unsteady flow patterns are obtained, and their dependence on the parameters of the problem is investigated. The flow regime without detonation, the mode with the detonation wave emerging from the channel through the input cross section, and the mode with steady detonation are obtained.     

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.     

脉冲放电产生螺旋流注的等离子体特性研究

通过脉冲放电方式产生三维螺旋形的等离子体放电通道,在高速摄像机拍摄下观察到放电通道中的发光电离体以流注形式沿螺旋轨迹快速传播.建立电磁模型解释螺旋放电的形成机制,对造成对称性破缺及影响其手性性质的极向电场进行分析.研究表明,螺旋放电产生的放电通道存在两种不同的手性特征,而脉冲重复频率等放电参数及边界条件对螺旋流注的传播特性存在影响.脉冲电源驱动的电磁场在介质管内所形成的波模是极向电场形成的一个重要来源,当极向电场与轴向电场强度相近时则形成螺旋流注放电.     

Flame acceleration and the transition to detonation of stoichiometric ethylene/oxygen in microscale tubes

Flame propagation in capillary tubes with smooth circular cross-sections and diameters of 0.5, 1.0, and 2.0 mm are investigated using high-speed photography. Flames were found to propagate and accelerate to detonation speed in stoichiometric ethylene and oxygen mixtures initially at room temperature in all three tube diameters. Ignition occurs at the midpoint along the length of the tube. We observe for the first time transition to detonation in micro-tubes. Detonation was observed with both spark and hot-wire ignition. Tubes with larger diameters take longer to transition to detonation. In fact, transition distance scales with the diameter in our 1.0 and 2.0 mm cases with spark ignition. Flame structures are observed for various stages of the process. Three types of flame propagation modes were observed in the 0.5 mm tube with spark ignition: (a) acceleration to Chapman–Jouguet (CJ) detonation speed followed by constant CJ wave propagation, (b) acceleration to CJ speed, followed by the detonation wave failure, and (c) flame acceleration to a constant speed below the CJ speed of approximately 1600 m/s. The current detonation mechanism observed in capillary tubes is applicable to predetonators for pulsed detonation, micro propulsion devices, safety issues, and addresses fundamental issues raised by recent theoretical and numerical analyses.     

Detonation development in hydrogen/air mixtures inside a closed chamber: role of a cold wall

Detonation development from a hot spot has been extensively studied, where ignition occurs earlier than that in the surrounding mixtures. It has also been reported that a cool spot can induce detonation for large hydrocarbon fuels with Negative Temperature Coefficient (NTC) behavior, since ignition could happen earlier at lower temperatures. In this work we find that even for hydrogen/air mixtures without NTC behaviors, a cold wall can still initiate and promote detonation. End-wall reflection of the pressure wave and wall heat loss introduce an exothermic center outside the boundary layer, and then autoignitive reaction fronts on both sides may evolve into detonation waves. The right branch can be further strengthened by appropriate temperature gradient near the cold wall, and exhibits different dynamics at various initial conditions. The small excitation time and the large diffusivity of hydrogen provide the possibility for detonation development within the limited space between the autoignition kernel and the cold wall. Moreover, detonation may also develop near the flame front, which may or may not co-exist with detonation waves from the cold wall. Correspondingly, wall heat flux evolution exhibits different responses to detailed dynamic structures. Finally, we propose a regime diagram describing different combustion modes including normal flame, autoignition, and detonation from the wall and/or the reaction front. The boundary of normal flame regime qualitatively agrees with the prediction by the Livengood-Wu Integral method, while the detonation development from both the end wall and the reaction front observes Zel'dovich mechanism. Compared to hydrocarbons, hydrogen is resistant to knock onset but it is more prone to superknock development. The latter mode becomes more destructive in the presence of wall heat loss. This study isolates and identifies the role of wall heat loss on a potential mechanism for superknock development in hydrogen-fueled spark-ignition engines.     

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。     

LINEAR ELASTIC RESPONSE OF TUBES TO INTERNAL DETONATION LOADING

This paper deals with the structural response of a tube to an internal gaseous detonation. An internal detonation produces a pressure load that propagates down the tube. Because the speed of the gaseous detonation can be comparable to the flexural wave group speed, excitation of flexural waves in the tube wall must be considered. Flexural waves can result in much higher strains and stresses than static loading with the same loading pressures. Experiments and numerical simulations were used to determine the structural response. In the experiments, a detonation tube was instrumented with a number of strain gages. A series of experiments was carried out under different conditions. Strains were measured that exceeded the equivalent static strain by up to a factor of 3·9. Special attention was paid to the influence of the detonation speed, reflection and interference of structural waves at flanges and also at the tube end, the linearity of the response, the transient development of the deflection profile, and the influence of detonation cell size. Analytical models and finite element models were used to interpret the observations and to make quantitative predictions of the peak strain.     

Combustion wave propagation and detonation initiation in the vicinity of closed-tube end walls

There are not many studies on DDT with no obstacles and the initiation of DDT near the end of a closed tube. Therefore in the present study we experimentally investigate the mechanism of the combustion wave transition to a detonation wave when there are no obstacles. In particular, we show that a local explosion near the tube wall is necessary for the initiation of a detonation. Parameters that we varied are the wall configuration, distance between the ignition point and the wall, and initial filling pressure. The combustion waves and the compression waves are visualized using the Schlieren optical system. From the results, we found it is necessary for the combustion wave to reach four walls so that the detonation could be initiated by the local explosion. In the conditions of the present experiment, we exhibited that the local explosion did not occur in the vicinity of a single wall and four orthogonal walls; instead, the local explosion occurred in a situation with five orthogonal walls. The time of the local explosion and the detonation initiation is 2.6 ± 1.1 and 2.0 ± 0.1 times the characteristic time for the combustion wave to propagate hemispherically from an ignitor and reach the four walls.     

High resolution numerical simulation of the structure of 2-D gaseous detonations

Two dimensional numerical simulation of the structure of gaseous detonation is investigated by utilizing the single step Arrhenius kinetic reaction mechanism in both high and low activation energy mixtures, characterized by their irregular and regular detonation structure, respectively. All the computations are performed on a small Beowulf cluster with six nodes. The dependency of the structure on the grid resolution is performed and it is found that, resolution of more than 300 cells per hrl is required to demonstrate the role of hydrodynamic instabilities, (KH and RM instabilities) in detonation propagation in irregular structures, while due to the absence of fine-scale structures, resolution of 50 cells per hrl, gives the physical structure of detonation with regular structures. Results show that the transverse waves in irregular structure are significantly stronger than the transverse wave in regular structure detonation, which can enhance the burning rate of the unburned pockets behind the shock front. Results for resolution of 600 cells per hrl illustrate that, in addition to the primary mode, the interaction of large vortices with the shock front provides secondary modes in the structure which leads to the irregularity of the structure in high activation energy mixture. In contrast with the results obtained for regular structure, which no unburned gas pockets and vortices observed behind the front, the results for irregular structure reveal that most portions of the gases, escape from shock compression and create large unburned gas pockets behind the both weak section of the Mach stem and the incident wave, which will burn eventually by the turbulent mixing due to the vortices associated with hydrodynamic instabilities. Therefore, the ignition mechanism in irregular structure is due to the both shock compression and by turbulent mixing associated with hydrodynamic instabilities, while the shock compression yields the ignition mechanism in regular structure detonation.