Transition of plane overdriven detonation wave to the Chapman-Jouguet regime

The asymptotic laws of behavior for plane, cylindrical, and spherical infinitely thin detonation waves were found in [1, 2] for increasing distance from an igniting source in those cases in which the waves changed into Chapman-Jouguet waves as they decayed. It was shown that the plane overdriven detonation wave approaches the Chapman-Jouguet regime asymptotically, while the transition of the cylindrical or spherical strong detonation wave into the Chapman-Jouguet wave may occur at a finite distance from the initiation source.Similar conclusions are valid for the propagation of stationary steadystate detonation waves which arise with flow of combustible gas mixtures past bodies.However, numerous experiments [3, 4] on firing bodies in a detonating gas show that the overdriven detonation wave which forms ahead of the body decays and decomposes into an ordinary compression shock and a slow combustion front. To establish why the wave does not make the transition to the Chapman-Jouguet regime, in the following we consider the propagation of a plane detonation wave and account for finite chemical reaction rates. We use the very simple two-front model (ordinary shock wave and following flame front). Conditions are found for which transition to the Chapman-Jouguet regime does not occur. We first consider the propagation of an unsteady plane wave and then the steady plane wave. It is found that for all the mixtures used in these experiments transition to the Chapman-Jouguet regime is not possible within the framework of the assumed model.     

Spherically imploding detonation waves initiated by two-step divergent detonation

The detonation chamber developed by K. Terao and H. G. Wagner in Göttingen has been improved, in order to concentrate the combustion energy more effectively to a focus, so that imploding detonation waves are initiated by two-step divergent detonation waves in a hemispherical space having an effective diameter of 500 mm. The imploding detonation waves are investigated by measuring their propagation velocity using ion probes and pressure variations at different positions in the space by a piezoelectric pressure transducer, while the temperature in the implosion center is measured by a laser light scattering method. The results suggest that the peak pressure at the detonation front increases with the propagation to the center more rapidly than that in the Göttingen apparatus, while the propagation velocity is almost the same. A temperature from 10⁷ K to 10⁸ K is also observed in the focus of the imploding detonation waves.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.     

Ionization in gaseous detonation waves

Using numerical simulations the spatial and temporal evolution of the electrical conductivity in ionized gas mixtures produced by detonation is investigated in mixtures with and without potassium seeding. Without flow seeding, the magnitude of the electrical conductivity is observed to be too small for significant magnetohydrodynamic forces to affect the conducting flow. This is consistent with past observations. With potassium seeding the electrical conductivity can be increased by 4–5 orders of magnitude, however, a critical percentage of seed particles is observed for which detonation is no longer sustainable. Therefore, there are limits to the electrical conductivity that can be achieved in burned gas mixtures. To further understand the dynamics of the physics involved a parametric study is conducted by varying the ambient pressure, the nitrogen dilution and the potassium seeding percentage. In order to reach these conclusions, a detailed kinetic mechanism of 26 species and 65 reactions has been compiled from the available literature and validated for applications of detonation and ionization chemistry. From the computed mass fractions the mixture-averaged electrical conductivity is then computed.     

Propagation of detonation waves in plane channels with obstacles

The detonation wave propagation in plane channels filled with a stoichiometric hydrogen-air mixture at rest under standard conditions is numerically modeled with account for the actual kinetics of the chemical interaction. The calculations show that the stable cellular structure of the detonation wave formed in a plane channel with parallel walls is not always uniquely determined by its width. The effect of transverse walls and sharp expansion of the channel on the propagation of the cellular detonation wave is studied. The conditions of conservation and restoration of detonation are determined.     

Calculating the structure of detonation waves

Some results of calculations are shown which have been obtained for detonation waves with the fission of the explosive material occurring at a finite rate.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 73–80, May–June, 1971.     

On regular reflection of detonation waves

The boundaries of regular reflection of detonation waves by a rigid wall are calculated. It is assumed that detonation is initiated at the point of reflection when a shock wave is incident on the wall at a finite angle in a gas fuel mixture, the detonation propagating instantaneously along the reflected front.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 178–180, March–April, 1983.     

Propagation characteristics of shock waves driven by gaseous detonation waves

We experimentally investigated propagation characteristics of the shock wave driven by a gaseous detonation wave emerging from the open end of a cylindrical detonation tube. In the present study, we visualized the shock wave and exhaust flowfields using a shadowgraph optical system and we obtained peak overpressure in the tube axial direction and the continuous shape transformation of shock waves around the tube open end. We also obtained overpressure histories of the shock wave using piezo-pressure transducers within 201 m from the open end of the tube. We normalized and classified these results by four regions using non-dimensional pressure and distance which are independent of variety of mixture and tube diameter. In the vicinity of the open end of the tube, the shock wave is nearly planar and does not significantly attenuate, and the peak overpressure maintains approximately C–J pressure. Subsequently, the shock wave attenuates rapidly, transforming from quasi-spherical to spherical. Farther from the tube open end, the shock wave propagates with approximately sound characteristic so that the peak overpressure decreases proportional to 1/r. Eventually, the shock wave begins to attenuate more rapidly than ideal sound attenuation, which may be due to the viscous effect.     

Micro-blast waves using detonation transmission tubing

Micro-blast waves emerging from the open end of a detonation transmission tube were experimentally visualized in this study. A commercially available detonation transmission tube was used (Nonel tube, M/s Dyno Nobel, Sweden), which is a small diameter tube coated with a thin layer of explosive mixture (HMX $+$ traces of Al) on its inner side. The typical explosive loading for this tube is of the order of 18 mg/m of tube length. The blast wave was visualized using a high speed digital camera (frame rate 1 MHz) to acquire time-resolved schlieren images of the resulting flow field. The visualization studies were complemented by computational fluid dynamic simulations. An analysis of the schlieren images showed that although the blast wave appears to be spherical, it propagates faster along the tube axis than along a direction perpendicular to the tube axis. Additionally, CFD analysis revealed the presence of a barrel shock and Mach disc, showing structures that are typical of an underexpanded jet. A theory in use for centered large–scale explosions of intermediate strength $(10\, < \Delta {p}/{p}_0 \lesssim \, 0.02)$ gave good agreement with the blast trajectory along the tube axis. The energy of these micro-blast waves was found to be $1.25 \pm 0.94$ J and the average TNT equivalent was found to be $0.3$ . The repeatability in generating these micro-blast waves using the Nonel tube was very good $(\pm 2~\%)$ and this opens up the possibility of using this device for studying some of the phenomena associated with muzzle blasts in the near future.     

Decoupling and recoupling of detonation waves associated with sudden expansion

Detonation propagation behavior associated with sudden expansions has been investigated both experimentally and numerically. Different mechanisms, from sustained propagation to detonation failure and reinitiation including shock and flame front decoupling and recoupling have been observed with the schlieren technique. The shock-induced flame propagation has been modeled with two-step chemistry and structured two-dimensional CFD on arbitrary geometries. The results of the numerical simulations show good correspondence to the variety of phenomena observed in experiments. Thus the numerical simulation can be used to study detonation propagation in complex geometries. It provides a tool for the design of safety devices and aids experimental investigations. Received 4 August 1995 / Accepted 25 April 1996     

Wave angle for oblique detonation waves

The flow field associated with a steady, planar, oblique detonation wave is discussed. A revision is provided for- diagrams, where is the wave angle and is the ramp angle. A new solution is proposed for weak underdriven detonation waves that does not violate the second law. A Taylor wave, encountered in unsteady detonation waves, is required. Uniqueness and hysteresis effects are also discussed.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.     

Steady,oblique, detonation waves

Normal and oblique, steady planar detonation waves have been theoretically and computationally examined using the Zeldovich, von Neumann, Döring model. Combustion is between a methane/hydrogen mixture and dry air assuming, first, complete combustion, then an equilibrium solution. Prescribed parameters are the upstream values for the pressure, temperature, and Mach number, the fuel/air equivalence ratio, a hydrogen/methane ratio, and the detonation wave angle. For a given upstream state, the angle varies from its normal wave value in increments of 10 ^o to non-integer wave angles that correspond to the Chapman-Jouguet state for complete combustion and for an equilibrium solution. For each solution, detailed results are provided for the upstream state, the state just downstream of the shock, and the two downstream states. Over 340 solutions in a report (Emanuel and Tuckness 2002) are provided, thereby establishing, for the first time, comprehensive tables that can be used to provide quick estimates, establish trends, and check CFD results. This paper describes the basis for the model, briefly outlines the analytical and numerical method, and discusses several insights.     

Influence of upstream properties on detonation wave structure. Irreversible, unimolecular reaction with small rate parameter

Summary Wood's analysis of detonation wave structure for an irreversible, unimolecular reaction with small rate parameter is used to study the influence of upstream properties on the coupling between pressure rise and reaction zones. The variation of a reduced distance due to adiabatic upstream burning, upstream heat addition, and variation of heat release per unit mass of reactant is considered. is the reduced distance between the point of minimum velocity (essentially the point of maximum pressure) and the point where the temperature is some chosen fraction of the final temperature, i.e., is a measure of the coupling between pressure rise and reaction zones.The wave structure immediately downstream of the pressure rise zone is found to be most sensitive to adiabatic upstream burning but much less sensitive to upstream heat addition and variation of heat release per unit mass of reactant. The first two processes cause to decrease because the temperature and reaction rate at the pressure maximum are increased. The last process causes to increase slightly because in this case the temperature and reaction rate at the pressure maximum is decreased. The wave structure far downstream of the pressure rise zone is not altered by adiabatic upstream burning but is influenced by upstream heat addition and variation of heat release per unit mass of reactant. The latter two processes cause to decrease. It is also shown that the wave structure immediately downstream of the pressure rise zone, for detonation waves which initially consist of widely separated pressure rise and reaction zones, is very sharply altered by the three processes of upstream variation here considered. Upstream burning and upstream heat addition cause rapid reductions in || while an increase in heat release per unit mass of reactant increases || for the same reasons as noted in the case of more closely coupled waves.Available experimental data are not directly applicable to the present results. However there is sufficient similarity between theory and experiment to support the qualitative trends predicted by this idealized analysis.     

Dynamic characteristics of spherically converging detonation waves

The spherically converging detonation wave was numerically investigated by solving the one-dimensional multi-component Euler equations in spherical coordinates with a dispersion-controlled dissipative scheme. Finite rate and detailed chemical reaction models were used and numerical solutions were obtained for both a spherical by converging detonation in a stoichiometric hydrogen-oxygen mixture and a spherically focusing shock in air. The results showed that the post-shock pressure approximately arises to the same amplitude in vicinity of the focal point for the two cases, but the post-shock temperature level mainly depends on chemical reactions and molecular dissociations of a gas mixture. While the chemical reaction heat plays an important role in the early stage of detonation wave propagation, gas dissociations dramatically affect the post-shock flow states near the focal point. The maximum pressure and temperature, non-dimensionalized by their initial value, are approximately scaled to the propagation radius over the initial detonation diameter. The post-shock pressure is proportional to the initial pressure of the detonable mixture, and the post-shock temperature is also increased with the initial pressure, but in a much lower rate than that of the post-shock pressure. Zonglin Jiang is presently a visiting professor at McGill University, Canada.     

有限谱ENO格式在爆轰波数值模拟中的应用

使用有限谱ENO(EssentiallyNon Oscillatory)格式 ,采用V .P .Korobeinikov二步化学反应模型 ,对稀释的化学当量的氢气和氧气混合物中非定常自维持爆轰波进行了二维数值模拟 ,研究了波的产生和演化机理 ,分析了爆轰波的三波结构和传播过程。计算得到的爆轰波参数和结构与以前的计算和实验结果一致。研究表明 :有限谱ENO格式可以成功地模拟非定常自维持爆轰波。     

Behavior of detonation waves at low pressures

With respect to stability of gaseous detonations, unsteady behavior of galloping detonations and re-initiation process of hydrogen-oxygen mixtures are studied using a detonation tube of 14 m in length and 45 mm i.d. The arrival of the shock wave and the reaction front is detected individually by a double probe combining of a pressure and an ion probe. The experimental results show that there are two different types of the re-initiation mechanism. One is essentially the same as that of deflagration to detonation transition in the sense that a shock wave generated by flame acceleration causes a local explosion. From calculated values of ignition delay behind the shock wave decoupled from the reaction front, the other is found to be closely related with spontaneous ignition. In this case, the fundamental propagation mode shows a spinning detonation. Received 10 March 1997 / Accepted 8 June 1997     

Experimental study on spherically imploding detonation waves

Spherically imploding detonation waves propagating in a stoichiometric propane-oxygen mixture in a convergent hemispherical space having an innerdiameter of 800 mm were experimentally investigated with an intention to clarify the reason for the anomalous increase of the pressure and temperature behind the imploding detonation waves observed in a smaller vessel having an inner-diameter of 360 mm. The relations between the radial distance of the detonation front, the peak pressure, spectroscopic temperature at the imploding detonation front and those behind the shock waves reflected from the implosion focus show almost the same tendencies as in the smaller convergent space. The pressure as well as the temperature at the imploding detonation front increases, with the propagation of the implosion, more rapidly than theoretically estimated. The reason for it is attributed to the double imploding detonation waves.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

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