The detonation burning of a fuel mixture resulting from a double explosion

A study is made of the propagation of a multifront detonation burning in a fuel mixture consisting of a gaseous fuel and an oxidant with additions of combustible solid or liquid particles arising as a result of a double point explosion. In such combustible media it is possible for there to be propagation of several detonation or burning fronts following one after the other. The easily igniting gaseous fuel burns in the first detonation wave, which propagates in the gaseous mixture with particles which are heated by the products of the explosion, ignite and burn in the second detonation wave or in the flame front. Self-similar regimes of propagation of such waves in an idealized formulation were studied in [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 126–131, March–April, 1985.     

Intensification of a detonation wave in the zone of secondary reactions in a two-phase medium

A method is proposed for the numerical calculation of one-dimensional nonsteady-state flows of a mixture of a gas with particles, based on the separation of a system of differential equations for a two-phase medium into two subsystems. The problem is solved concerning the propagation of a plane detonation wave in a mixture of a detonating gas with particles, behind the front of which secondary chemical reactions are taking place between the vapors of the particle material and the detonation products. The velocity profiles of the gas and of the thermodynamic functions behind the detonation wave front are determined, and also the dependence of the detonation velocity on the distance to the point of initiation. The conditions for intensification of the detonation wave are obtained in the zone of secondary reactions.Leningrad. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 92–96, September–October, 1972.     

Cellular detonations in bidispersed gas-particle mixtures

Formation of cellular detonation in bi-fractional stoichiometric mixtures of aluminum particles and oxygen is investigated numerically. The detonation cell size depends on the particle diameters and relative concentration of the fractions. Certain degeneration of cellular detonation is obtained when compared to the monodisperse mixtures. It is characterized by maximal pressure decrease, transverse wave relaxation and detonation front rectification. Complete degeneration of cellular detonations and stable propagation of a plane detonation front is found in some bi-fractional mixtures. The numerical results are confirmed by acoustic analysis of the detonation structures. This paper is based on work that was presented at the 21st International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

石化装置工业尺度管道爆轰传播实验研究

针对石化装置罐区大口径、长距离管道内火焰传播缺乏系统研究的问题,设计搭建了DN50～DN500工业尺度管道火焰传播实验装置,并开展了丙烷/空气、乙烯/空气等可燃气体在不同管径下的实验研究。实验结果表明:可燃气体积分数对火焰传播及爆轰有一定影响,当接近化学计量浓度时,爆轰加速距离更短,更易形成稳态爆轰,而当可燃气混合气为贫燃或富燃状况时,爆轰加速距离则会增长;火焰爆轰传播速度、爆轰压力与管道管径基本无关,受可燃气种类影响更大;对应体积分数为6.6%的乙烯/空气和体积分数为4.2%的丙烷/空气混合气体,爆轰压力分别是初始压力的15.17和14.47倍,DN150以下管径内的爆轰压力远高于ISO16852标准给出的参考值。罐区连通管道阻火器选型安装时,应结合安装位置选用合适的阻火器。     

Shock and detonation wave diffraction at a sudden expansion in gas–particle mixtures

Numerical modeling of the propagation of shock and detonation waves is carried out in a duct with an abrupt expansion for a heterogeneous mixture of fine particles of aluminum and oxygen. A considerable difference from corresponding flows in pure gas is found. The influence of the size and mass loading of particles on the flow and shock wave structure behind the backward-facing step is determined. As in gaseous detonations, three types of scenarios of detonation development are obtained. Specific features of the flow structure are revealed such as deformation of the combustion front due to interaction between the relaxation zone and the vortex structure. The influence of particle size and channel width on detonation propagation is analyzed. This paper is based on work that was presented at the 21th International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

Investigation of the detonation regimes in gaseous mixtures with suspended starch particles

The existence of a secondary discontinuity at the rear of a detonation front shown in experiments by Peraldi and Veyssiere (1986) in stoichiometric hydrogen-oxygen mixtures with suspended 20-m starch particles has not been explained satisfactorily. Recently Veyssiere et al. (1997) analyzed these results using a one-dimensional (1-D) numerical model, and concluded that the heat release rate provided by the burning of starch particles in gaseous detonation products is too weak to support a double-front detonation (DFD), in contrast to the case of hybrid mixtures of hydrogen-air with suspended aluminium particles in which a double-front detonation structure was observed by Veyssiere (1986). A two-dimensional (2-D) numerical model was used in the present work to investigate abovementioned experimental results for hybrid mixtures with starch particles. The formation and propagation of the detonation has been examined in the geometry similar to the experimental tube of Peraldi and Veyssiere (1986), which has an area change after 2 m of propagation from the ignition point from a 69 mm dia. section to a 53 mm 53 mm square cross section corresponding to a 33% area contraction. It is shown that the detonation propagation regime in these experiments has a different nature from the double-front detonation observed in hybrid mixtures with aluminium particles. The detonation propagates as a pseudo-gas detonation (PGD) because starch particles release their heat downstream of the CJ plane giving rise to a non-stationary compression wave. The discontinuity wave at the rear of the detonation front is due to the interaction of the leading detonation front with the tube contraction, and is detected at the farthest pressure gauge location because the tube length is insufficient for the perturbation generated by the tube contraction to decay. Thus, numerical simulations explain experimental observations made by Peraldi and Veyssiere (1986). Received 5 July 1997 / Accepted 13 July 1998     

Supersonic flow of combustible gas mixture past sphere with account for ignition delay time

Assume an axisymmetric blunt body or a symmetric profile is located in a uniform supersonic combustible gas mixture stream with the parameters M₁, p₁, and T₁. A detached shock is formed ahead of the body and the mixture passing through the, shock is subjected to compression and heating. Various flow regimes behind the shock wave may be realized, depending on the freestream conditions. For low velocities, temperatures, or pressures in the free stream, the mixture heating may not be sufficient for its ignition, and the usual adiabatic flow about the body will take place. In the other limiting case the temperature behind the adiabatic shock and the degree of gas compression in the shock are so great that the mixture ignites instantaneously and burns directly behind the shock wave in an infinitesimally thin zone, i. e., a detonation wave is formed. The intermediate case corresponds to the regime in which the width of the reaction zone is comparable with the characteristic linear dimension of the problem, for example, the radius of curvature of the body at the stagnation point.The problem of supersonic flow of a combustible mixture past a body with the formation of a detonation front has been solved in [1, 2]. The initial mixture and the combustion products were considered perfect gases with various values of the adiabatic exponent .These studies investigated the effect of the magnitude of the reaction thermal effect and flow velocity on the flow pattern and the distribution of the gasdynamic functions behind the detonation wave.In particular, the calculations showed that the strong detonation wave which is formed ahead of the sphere gradually transforms into a Chapman-Jouguet wave at a finite distance from the axis of symmetry. For planar flow in the case of flow about a circular cylinder it is shown that the Chapman-Jouguet regime is established only asymptotically, i. e., at infinity.This result corresponds to the conclusions of [3, 4], in which a theoretical analysis is given of the asymptotic behavior of unsteady flows with planar, spherical, and cylindrical detonation waves.Available experimental data show that in many cases the detonation wave does not degenerate into a Chapman-Jouguet wave as it decays, bur rather at some distance from the body it splits into an adiabatic shock wave and a slow combustion front.The position of the bifurcation point cannot be determined within the framework of the zero thickness detonation front theory [1], and for the determination of the location of this point we must consider the structure of the combustion zone in the detonation wave. Such a study was made with very simple assumptions in [5].The present paper presents a numerical solution of the problem of combustible mixture flow about a sphere with a very simple model for the structure of the combustion zone, in which the entire flow behind the bow shock wave consists of two regions of adiabatic flow-an induction region and a region of equilibrium flow of products of combustion separated by the combustion front in which the mixture burns instantaneously. The solution is presented only for subsonic and transonic flow regions.     

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.     

以DSD理论和LS方法为基础的程序燃烧法

给出了二维弯曲爆轰波后产物流场计算方法。爆轰波阵面传播规律满足Detonation Shock Dynamics (DSD)理论并用level set (LS)方法计算,波阵面传播规律与波后流场的耦合通过程序燃烧法实现,反应进程变量可作为LS函数的函数给出。爆轰波从刚性细管道向粗管道传播产生绕射的二维计算结果表明,化学反应速率不影响波后流场分布,只影响反应区结构。此方法可用于钝感炸药的驱动计算问题。     

Detonation interaction with a diffuse interface and subsequent chemical reaction

We have investigated the interaction of a detonation with an interface separating a combustible from an oxidizing mixture. The ethylene-oxygen combustible mixture had a fuel-rich composition to promote secondary combustion with the oxidizer in the turbulent mixing zone that resulted from the interaction. Diffuse interfaces were created by the formation of a gravity current using a sliding valve that initially separated the test gas and combustible mixture. Opening the valve allowed a gravity current to develop before the detonation was initiated. By varying the delay between opening the valve and initiating the detonation it was possible to achieve a wide range of interface conditions. The interface orientation and thickness with respect to the detonation wave have a profound effect on the outcome of the interaction. Diffuse interfaces result in curved detonation waves with a transmitted shock and following turbulent mixing zone. The impulse was measured to quantify the degree of secondary combustion, which accounted for 1–5% of the total impulse. A model was developed that estimated the volume expansion of a fluid element due to combustion in the turbulent mixing zone and predicted the resulting impulse increment.      

Fundamentals of rotating detonations

A rotating detonation propagating at nearly Chapman–Jouguet velocity is numerically stabilized on a two-dimensional simple chemistry flow model. Under purely axial injection of a combustible mixture from the head end of a toroidal section of coaxial cylinders, the rotating detonation is proven to give no average angular momentum at any cross section, giving an axial flow. The detonation wavelet connected with an oblique shock wave ensuing to the downstream has a feature of unconfined detonation, causing a deficit in its propagation velocity. Due to Kelvin–Helmholtz instability existing on the interface of an injected combustible, unburnt gas pockets are formed to enter the junction between the detonation and oblique shock waves, generating strong explosions propagating to both directions. Calculated specific impulse is as high as 4,700 s.      

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.     

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.     

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.     

球面聚心气相爆轰波传播过程的数值研究

应用频散可控耗散格式对球面聚心气相爆轰波的传播过程进行了数值模拟 研究. 通过跟踪波阵面上压力和温度变化，分析这些参数在爆轰波传播过程中的演变规律， 及其与几何尺度和初始条件之间的依赖关系. 研究结果表明，仅在远场波面压力的变化近似 只依赖于r/R，对称中心附近则需要考虑初始半径$R$的影响；波面压力与初始压力的变化呈 线性关系；汇聚过程中温度升高比压力慢得多.     

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.     

Propagation of blast waves with exponential heat release and internal heat conduction and thermal radiation

The problem of reactive blast waves in a combustible gas mixture, where the heat release at the detonation front decays exponentially with the distance from the center, is analyzed. The central theme of the paper is on the propagation of reactive blast into a uniform, quiescent, counterpressure atmosphere of a perfect gas with constant specific heats. The limiting cases of Chapman-Jouguet detonation waves are considered in the phenomenon of point explosion. In order to deal with this problem, the governing equations including thermal radiation and heat conduction were solved by the method of characteristics using a problem-specific grid and a series expansion as start solution. Numerical results for the distribution of the gas-dynamic parameters inside the flow field are shown and 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.     

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     

Aluminum Particles–air Detonation at Elevated Pressures

The effect of initial pressure on aluminum particles–air detonation was experimentally investigated in a 13 m long, 80 mm diameter tube for 100 nm and 2 μm spherical particles. While the 100 nm Al–air detonation propagates at 1 atm initial pressure in the tube, transition to the 2 μm aluminum–air detonation occurs only when the initial pressure is increased to 2.5 atm. The detonation wave manifests itself in a spinning wave structure. An increase in initial pressure increases the detonation sensitivity and reduces the detonation transition distance. Global analysis suggests that the tube diameter for single-head spinning detonation or characteristic detonation cell size would be proportional to (d ₀: aluminum particle size, p ₀: initial pressure). Its application to the experimental data results in m ~ O(1) and n ~ O(1) for 1 to 2 μm aluminum–air detonation, thus indicating a strong dependence on initial pressure and gas-phase kinetics for the aluminum reaction mechanism in detonation. Hence, combustion models based on the fuel droplet diffusion theory may not be adequate in describing micrometric aluminum–air detonation initiation, transition and propagation. For 2 μm aluminum–air mixtures at 2 atm initial pressure and below, experiments show a transition to a “dust quasi-detonation” that propagates quasi-steadily with a shock velocity deficit nearly 40% with respect to the theoretical C–J detonation value. The dust quasi- detonation wave can propagate in a tube with a diameter less than 0.4–0.5 times the diameter required for a spinning detonation wave.