Measurement and scaling analysis of critical energy for direct initiation of gaseous detonations

In this paper, the critical energies required for direct initiation of spherical detonations in four gaseous fuels (C₂H₂, C₂H₄, C₃H₈ and H₂)–oxygen mixtures at different initial pressures, equivalence ratios and with different amounts of argon dilution are reported. Using these data, a scaling analysis is performed based on two main parameters of the problem: the explosion length R _o that characterizes the blast wave and a characteristic chemical length that characterizes the detonation. For all the undiluted mixtures considered in this study, it is found that the relationship is closely given by R_o ? 26 l{R_{\rm o} \approx 26 \lambda} , where λ is the characteristic detonation cell size of the explosive mixture. While for C₂H₂–2.5O₂ mixtures highly diluted with argon, in which cellular instabilities are shown to play a minor role on the detonation propagation, the proportionality factor increases to 37.3, 47 and 54.8 for 50, 65 and 70% argon dilution, respectively. Using the ZND induction length Δ _I as the characteristic chemical length scale for argon diluted or ‘stable’ mixtures, the explosion length is also found to scale adequately with R_o ? 2320 D_I{R_{\rm o} \approx 2320 \Delta_I} .     

高电压点火有效能量的测量及相关问题

建立了测量高电压点火产生的爆炸波参数装置,利用PCB压力传感器测定了在空气中高压电火花产生的爆炸波压力及其到达时间。改变点火能量和测试距离,得到了爆炸波的变化趋势和传播规律,并探讨了爆炸波各参数的标度尺寸。结果表明,电火花产生的爆炸波符合Hopkinson-Sachs爆炸相似律。把1/4周期放电能量与数值模拟结果进行比较,得知初始1/4周期放电能量(点火能量)与爆炸波能量基本吻合;因此,1/4周期放电能量可被视为作用于直接起爆引起爆轰的有效能量。进一步探讨了高电压点火各能量的分布;结果表明,储存于电容的总能量1/2CU2中约91%消耗于能量损失和欧姆损耗,初始1/4周期放电能量仅约占2%,其余的点火能量只起到加热混合物的作用。     

气相爆轰波起爆与传播机理研究进展

对近年来气相爆轰起爆及传播在数值模拟和实验方面的研究工作进行了综述,结合作者近几年在这一领域开展的工作,评述了目前的研究热点和难点,简要指出了未来的研究方向。着重介绍了黏性扩散、详细化学反应机理、爆轰胞格不稳定性在爆轰起爆和传播理论和计算研究中的作用,以及爆轰波传播过程中实验技术和理论预测模型的进展。     

C2H2-O2-Ar和C2H2-N2O-Ar直接起爆形成爆轰的临界能量

采用高压电点火进行直接起爆形成爆轰,起爆能量通过放电过程中电流的输出信号确定。首先通过实验测定并对比C2H2-O2-Ar和C2H2-N2O-Ar等2种混合物在各种初始状态下直接起爆形成爆轰的临界起爆能量。实验结果表明,在相同状态下C2H2-N2O-Ar混合物的临界起爆能量显著高于C2H2-O2-Ar混合物的。进一步基于各物质爆炸特征长度和爆轰临界管径的参量关系对临界起爆能量差异性进行分析,得到了C2H2-N2O-Ar混合气体的爆轰临界管径预测曲线,并在此基础上得出C2H2-N2O-Ar混合物爆炸特征长度与临界管径的关系为r0=2.5dc,而C2H2-O2-Ar两者关系为r0=2dc。结果清晰地表明,使用N2O 作为氧化剂,爆炸特征长度与爆轰临界管径之间的比例因数增大,表明该物质直接起爆形成爆轰所需的起爆源单位能量增大,因而直接形成爆轰的临界能量相应提高。     

Minimum tube diameters for steady propagation of gaseous detonations

Recent experimental results on detonation limits are reported in this paper. A parametric study was carried out to determine the minimum tube diameters for steady detonation propagation in five different hydrocarbon fuel–oxygen combustible mixtures and in five polycarbonate test tube diameters ranging from 50.8 mm down to a small scale of 1.5 mm. The wave propagation in the tube was monitored by optical fibers. By decreasing the initial pressure, hence the sensitivity of the mixture, the onset of limits is indicated by an abrupt drop in the steady detonation velocity after a short distance of travel. From the measured wave velocities inside the test tube, the critical pressure corresponding to the limit and the minimum tube diameters for the propagation of the detonation can be obtained. The present experimental results are in good agreement with previous studies and show that the measured minimum tube diameters can be reasonably estimated on the basis of the \(\lambda \) /3 rule over a wide range of conditions, where \(\lambda \) is the detonation cell size. These new data shall be useful for safety assessment in process industries and in developing and validating models for detonation limits.     

Response of critical tube diameter phenomenon to small perturbations for gaseous detonations

In this experimental study, the critical tube diameter phenomenon of gaseous detonations is investigated in both stable and unstable mixtures with focus on the failure mechanism. It was previously postulated that in unstable mixtures, where the cellular detonation front is highly irregular, the failure is caused by the suppression of local re-initiation centers linked to the dynamics of instabilities. In stable mixtures, typically with high argon dilution, the detonation structure is very regular and the failure mode is attributed to the excessive curvature of the global front. In order to differentiate between these two failure mechanisms, flow perturbations are introduced by placing an obstacle resulting in a minimal blockage ratio of approximately 8 %. The obstacle is placed at the tube exit, before the detonation diffraction. Results show that the perturbations caused by the obstacle only have an effect on undiluted (i.e., unstable) mixtures, causing a decrease in the minimum initial pressure required for successful detonation transmission. This thus demonstrates that local hydrodynamic instabilities play an important role for the critical tube diameter phenomenon in undiluted, unstable mixtures. In contrast, the results for the stable, argon-diluted mixture exhibit little variation in critical initial pressure between the perturbed and unperturbed cases. This can be attributed to the minimal effect of the perturbations on global curvature for the emergent detonation wave. The geometry of the perturbation is also tested, while holding the blockage area constant, by varying the number and position of the obstacle(s). The results demonstrate that the transmission of a detonation is independent of the blockage geometry and is only a function of its imposed blockage area. Consequently, the change in required minimum pressure for transmission shows an identical behavior in unstable mixtures for different perturbation geometries while the transmission characteristics of the stable mixture remain unaffected.     

Critical energy for direct initiation of detonation induced by laser ablation

This study describes experimental work examining the critical energy for direct initiation of detonation by laser ablation in a stoichiometric acetylene–oxygen mixture. The amount of input energy, the target material, and the surface roughness of the target were varied to study their effects on shock wave generation. Aluminum and stainless steel were used as target materials. The propagating shock wave induced by laser ablation was observed using high-speed shadow imaging. The critical energy for direct initiation of detonation was calculated using the strong blast wave theory. The critical input energy for aluminum was found to be lower than that for stainless steel. Because the thermodynamic critical temperature of aluminum is lower than that of stainless steel, aluminum caused a phase explosion more easily than stainless steel, thus resulting in direct initiation of detonation with a lower amount of input energy. The effects of surface roughness on critical input energy and shock wave generation were negligibly small. The critical initiation energy was estimated to be \(10.3 \pm 0.2\) mJ, which is in agreement with the experimental data obtained in previous work. The estimated critical initiation energy was independent of the target material. However, other predictions of the critical initiation energy by using the cell size overestimated this value because of the scatter in cell size data of an unstable cellular structure. Furthermore, interaction between plasma plumes formed by laser ablation and those formed by breakdown near the target surface might have contributed to requiring a lower amount of energy for initiating detonation.     

Critical tube diameter for detonation transmission and critical initiation energy of spherical detonation

Two experimental setups are used to study propagation and attenuation of blast waves. In the first one, the blast wave is generated by a spherical detonation, and in the second one, the blast wave is created by the diffraction of a planar detonation propagating in a tube. The similarity of these phenomena appears clearly by means of dimensionless space-time and pressure-space diagrams of shock wave propagation. Dimensionless variables are expressed as a function of the supplied energy. Two energy formulations are proposed: a piston model and a bulk energy model. The established diagrams cover a wide range of industrial applications. Under critical conditions, the energy released by a planar detonation is correlated to the ignition source energy supply and a relationship which links the critical radius of detonation to the critical tube diameter. Received 5 July 1997 / Accepted 13 July 1998     

C2H4-O2混合气体直接起爆的临界能量

主要基于化学动力学和Ng模型,对C2H4-O2混合气体的爆轰胞格尺寸进行预测;结合Lee表面积能量模型,预测物质在不同初始压力和化学当量比的条件下,直接起爆引起球面爆轰的临界起爆能量。直接起爆实验主要采用高压电点火提供起爆能量,起爆能量通过放电过程中电流的输出信号确定。结果表明,理论预测与实验值较吻合。首先,通过化学动力学计算得出ZND模型的爆轰参数,利用Ng模型得出爆轰胞格尺寸与ZND诱导区长度之间的比例因数A 在不同初始压力与当量比的条件下分别为:A=43.815(1+p1/p0)-0.12371和A=8.531exp(/3.135)+28.644,在此基础上对爆轰胞格尺寸进行定量预测。胞格尺寸的理论预测与实验结果吻合。其次,把爆轰胞格尺寸作为中间特征参数并结合Lee的表面积能量模型,提出可以预测临界起爆能量的定量模型,并得出C2H4-O2混合气体直接起爆的临界起爆能量与初始压力和化学当量比的参量拟合关系分别为Ec=0.332(p1/p0)-2.017和Ec=exp[3.951(-1.401)2-1.9]。     

Reflection of a spherical blast wave from a planar surface

Numerous authors have carried out rather extensive studies in the last twenty to thirty years of the problem of the interaction of shock and blast waves with obstacles in their paths. Owing to the complexity of the problem, they assumed certain limiting cases for the shock wave interactions in which the parameters behind the shock wave were usually taken to be constants. The first wave diffraction studies involving variable parameters behind the front were presented in [1, 2], wherein a development of the theory of “short waves” (blast waves at a substantial distance from the center of an explosion) and their reflection from a planar surface was given. The theory of short waves assumes that the jump in pressure at the wave front and the region over which the parameters vary are small. The problem concerning reflection of a blast wave from a surface was also considered in [3, 4], wherein a solution in the region behind the reflected wave was obtained at initial times. The initial stage in the reflection of a blast wave from a planar, cylindrical, or spherical surface (the one-dimensional case) was studied in [5]. In this paper we investigate the interaction of a spherical blast wave, resulting from a point explosion, with a planar surface; we consider both regular and non-regular reflection stages. In solving this problem we use S. L. Godunov's finite-difference method. We obtain numerical solutions for various values of the shock strength at the instant of its encounter with the surface. We present the pressure fields in the flow regions, the pressure distribution over the surface at various instants of time, and the trajectories of the triple point. The parameter values at the front of the reflected wave are compared with results obtained from the theory of regular reflection of shock waves.     

Mass minimization for a spherical screen with a specified level of transmitted wave energy

A layered spherical screen with minimum weight exposed to a spherical wave is synthesized from a finite set of elastic homogeneous isotropic materials under constraints imposed on the wave energy transferred through the screen and the screen thickness. The necessary optimality conditions are obtained and an example of calculation of the optimal structure is given. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 217–222, September–October, 2000.     

LES and RANS modelling of under-expanded jets with application to gaseous fuel direct injection for advanced propulsion systems

A density-based solver with the classical fourth-order accurate Runge-Kutta temporal discretization scheme was developed and applied to study under-expanded jets issued through millimetre-size nozzles for applications in high-pressure direct-injection (DI) gaseous-fuelled propulsion systems. Both large eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) turbulence modelling techniques were used to evaluate the performance of the new code. The computational results were compared both quantitatively and qualitatively against available data from the literature. After initial evaluation of the code, the computational framework was used in conjunction with RANS modelling (k-ω SST) to investigate the effect of nozzle exit geometry on the characteristics of gaseous jets issued from millimetre-size nozzles. Cylindrical nozzles with various length to diameter ratios, namely 5, 10 and 20, in addition to a diverging conical nozzle, were studied. This study is believed to be the first to provide a direct comparison between RANS and LES within the context of nozzle exit profiling for advanced high-pressure injection systems with the formation of under-expanded jets. It was found that reducing the length of the straight section of the nozzle by 50% resulted in a slightly higher level of under-expansion (∼2.6% higher pressure at the nozzle exit) and ∼1% higher mass flow rate. It was also found that a nozzle with 50% shorter length resulted in ∼6% longer jet penetration length. At a constant nozzle pressure ratio (NPR), a lower nozzle length to diameter ratio resulted in a noticeably higher jet penetration. It was found that with a diverging conical nozzle, a fairly higher penetration length could be achieved if an under-expanded jet formed downstream of the nozzle exit compared to a jet issued from a straight nozzle with the same NPR. This was attributed to the radial restriction of the flow and consequently formation of a relatively smaller reflected shock angle. With the conical nozzle used in this study and a 30 bar injection pressure, an under-expanded hydrogen jet exhibited ∼60% higher penetration length compared to an under-expanded nitrogen jet at 100 μs after start of injection. Moreover, the former jet exhibited ∼22% higher penetration compared to a nitrogen jet issued through the conical profile with 150 bar injection pressure.     

Measurement of energy release rates for delaminations in composite materials

Conventional measurements of energy release rates,G _I andG _II, for delaminations in composite materials, generally utilize loads, crack lengths and simple standard specimen geometries. In this work, a more widely applicable measurement method, using phase shifting moiré and the J integral, is presented. The experimental technique described requires only fringe-pattern information and the elastic constants for the measurements—thus it can be used when the standard methods are inapplicable. Using conventional double-cantilever beam and end-notched flexure specimens, the energy release rate has been measured simultaneously by the moiré method and the standard methods, with good agreement found between the two. This development will for the first time permit the experimental validation of new finite-element routines as they are developed.Paper was presented at the 1993 SEM Spring Conference on Experimental Mechanics held in Dearborn, MI on June 7–9.     

地下工程爆破振动信号能量分布特征的小波包分析

根据爆破振动信号具有短时非平稳的特点 ,利用小波包分析技术对地下工程爆破振动信号的能量分布特征进行了研究。首先 ,简略介绍了小波变换与小波包分析的特点 ;其次 ,基于MATLAB(MaterialsLab oratory)对段药量和爆源距离等不同条件下记录的 8条爆破振动信号进行小波包分析 ,得到了爆破振动信号在不同频带上的能量分布图 ;最后 ,分析了爆破振动信号能量的分布特征。本分析手段为研究地下工程爆破地震效应特别是振动速度 频率相关安全准则提供了一种有效的分析技术。     

Determination of flow activation energy at viscosity maximum for spherical and wormlike micelles of different lengths and flexibility

Steady shear rheological measurements were carried out on aqueous solutions containing 15 mM cetyltrimethylammonium bromide (CTABr) and a constant value of [MX] and temperature for MX = 2,3-; 2,4-; 2,5-; 2,6-; 3,4-; and 3,5-Cl₂BzNa with Bz^?representing C₆H₃CO_2?. Plots of zero shear viscosity (η ₀) vs. [MX] at 35 °C and 15 mM CTABr show the presence of single maximum and double maxima for MX = 2,3- and 3,5-Cl₂BzNa, respectively. Turbidity data (absorbance at 600 nm vs. [MX]) coupled with η ₀vs. [MX] data at 35 °C reveal indirectly the presence of vesicles along with wormlike micelles (WM) at MX / CTABr > 0. 7 for MX = 3,5-Cl₂BzNa. Temperature dependence of η ₀in the vicinity of the viscosity maximum shows nonlinear and linear Arrhenius behavior, within the temperature range of 20–55 °C, for MX = 2,3-; 2,4-; 2,5-; 3,4-; and 3,5-Cl₂BzNa, respectively. The values of η ₀, $\dot {\gamma }_{\text {cr}} $ (critical shear rate), and flow activation energy correlate with CTABr micellar binding constants of counterions.     

Comparison with experiment for TVD calculations of blast waves from a shock tube

Harten's second-order-accurate total-variation-diminishing (TVD) scheme is applied to calculation of flow from the open end of a shock tube. Comparison of numerical results with available experimental data for overpressure at selected points around the shock tube exit shows good agreement. Numerically indicated positions of the moving shock front and Mach stem also compare well with flow shadowgraph data. Where the problem geometry is sufficiently simple and rectangular gridding can be used, Harten's method affords a good choice for blast wave calculations.     

筒仓泄料过程中阻塞现象的数值模拟

基于颗粒材料离散颗粒模型及颗粒流方案,通过数值试验研究了筒仓泄料过程中影响颗粒流发生阻塞的若干因素,给出了阻塞概率随筒仓底部开口半径及倾角、颗粒间摩擦系数及颗粒粒径分布的关系曲线.基于颗粒簇的概念,进一步研究了颗粒形状的影响,并对颗粒材料阻塞时的力链分布特征进行简要分析.     

Bounds for interpolating complex effective moduli of viscoelastic materials from measured data

The complex effective moduli of viscoelastic materials can be experimentally measured by a number of techniques giving relaxation data for materials at discrete frequencies. In this paper we present a method which allows one to find bounds on the moduli of the material at the unmeasured frequencies. Our bounds can be very tight, and are, therefore, good approximations to the data. Using our bounds, experimentalists can concentrate their efforts on gathering highly accurate data at only a few frequencies and numerically generate data at other frequencies that may be of interest. Received: 10 August 1999 Accepted: 21 December 2000