Stability of gas mixture flow with a stabilized detonation wave in a plane channel with a constriction

The stability of a flow with a stabilized detonation wave is studied within the framework of a detailed kinetic mechanism of the chemical interaction. The flow is due to the initiation of detonation combustion of a stoichiometric hydrogen-air mixture that enters into a plane channel with a constriction at a supersonic velocity greater than that of the self-sustained detonation propagation. The flow under consideration is numerically investigated using the software package developed by the authors. It is established that the flow formed in the channel, whose geometric parameters ensure the detonation stabilization in the case of the inflow Mach number M₀ = 5.2, is stable against strong disturbances of a certain type. The effect of an increase in the inflow Mach number and the dustiness of the combustible gas mixture entering into the channel on the stabilization of detonation combustion in the flow is investigated.     

Investigation of certain techniques for stabilizing detonationwaves in a supersonic flow

The salient features of detonation wave propagation in a supersonic flow of a stoichiometric hydrogen-air mixture in plane channels of both constant and variable cross-section are numerically investigated for the purpose of determining the conditions ensuring stabilized detonation. The propagation of a detonation wave formed in a variable-cross-section channel is studied. For different inflow Mach numbers the geometric parameters of a channel providing the detonation combustion stabilization are determined. An investigation of detonation wave stabilization in a supersonic flow of a combustible gas mixture in a plane channel with parallel walls using additional weak discharges is continued. The effects of the flow Mach number, the additional discharge energy, and the discharge location on detonation wave stabilization are studied.     

Supersonic H2-air combustions behind oblique shock waves

In order to study the mechanisms of initiation and stabilization of H₂-Air combustions (stoechiometric mixture initially atT ₀=293 K andp ₀=0.5 bar) in supersonic flow conditions behind an oblique shock wave (OSW), an original technique is used where OSW is generated in this mixture by the lateral expansion of the burnt gas behind a normal CJ gaseous detonation propagating into a bounding reactive mixture. Four Mach numberM of propagation of OSW are considered in the study, namelyM=7.7-6.1-4.4 and 3. Depending on the Mach numberM and inclinaison angle of OSW different regimes of combustion may occur in the driven mixture. For high values ofM (6.1 and 7.7) delayed steady overdriven oblique detonation waves (SODW) were obtained with a near CJ detonation wave as the critical regime. It was found that SODW obtained correspond quite well to prediction of the polar method. When thermal conditions behind the OSW are lower, either for high Mach number 6.1 and 7.7 for smaller angle than the previous case, or for lower Mach number, 4.4 and 3, the flame initiated at the apex is stabilized as a turbulent oblique flame behind the OSW. With much lower conditions, no combustion appears in the H₂-Air mixture.     

圆球诱发斜爆轰波的数值研究

斜爆轰发动机是飞行器在高马赫数飞行条件下的一种新型发动机,具有结构简单、成本低和比冲高等优点.但是斜爆轰发动机的来流马赫数范围广,来流条件复杂,为实现斜爆轰波的迅速、可靠引发,采用钝头体来诱发.利用Euler方程和氢氧基元反应模型,对超声速氢气/空气混合气体中圆球诱导的斜爆轰流场进行了数值研究.不同于楔面诱发的斜爆轰波,球体首先会在驻点附近诱发正激波/爆轰波,然后在稀疏波作用下发展为斜激波/爆轰波.模拟结果显示,经过钝头体压缩的预混气体达到自燃温度后,会出现两种流场:当马赫数较低时,由于稀疏波的影响,燃烧熄灭,钝头体下游不会出现燃烧情况;而当马赫数较高时,燃烧阵面能传到下游.分析表明,当钝头体的尺度较小时,驻点附近的能量不足以诱发爆轰波,只会形成明显的燃烧带与激波非耦合结构;当钝头体的尺度较大时,流场中不会出现燃烧带与激波的非耦合现象,且这一特征与马赫数无关.通过调整球体直径,获得了激波和燃烧带部分耦合的燃烧流场结构,这一流场结构在楔面诱发的斜爆轰波中并不存在,说明稀疏波与爆轰波面的相互作用是决定圆球诱发斜爆轰波的关键.     

Functional mathematical model of a hydrogen-driven combustion chamber for a scramjet

A functional mathematical model of a hydrogen-driven combustion chamber for a scramjet is described. The model is constructed with the use of one-dimensional steady gas-dynamic equations and parametrization of the channel configuration and the governing parameters (fuel injection into the flow, fuel burnout along the channel, dissipation of kinetic energy, removal of some part of energy generated by gases for modeling cooling of channel walls by the fuel) with allowance for real thermophysical properties of the gases. Through parametric calculations, it is found that fuel injection in three cross sections of the channel consisting of segments with weak and strong expansion ensures a supersonic velocity of combustion products in the range of free-stream Mach numbers M_∞ = 6–12. It is demonstrated that the angle between the velocity vectors of the gaseous hydrogen flow and the main gas flow can be fairly large in the case of distributed injection of the fuel. This allows effective control of the mixing process. It is proposed to use the exergy of combustion products as a criterion of the efficiency of heat supply in the combustion chamber. Based on the calculated values of exergy, the critical free-stream Mach number that still allows scramjet operation is estimated.     

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.     

Distinctive features of galloping detonation in a supersonic combustible-mixture flow under an inert gas layer

The problem of detonation initiation in a supersonic flow of a stoichiometric propane-air mixture occupying partially or completely the cross-section of a plane channel is considered. The initiation in the flow is produced by a step or a wall completely cutting off the flow. The study is conducted within the framework of one-stage combustion kinetics. A numerical method based on the Godunov scheme is employed. The critical conditions for detonation formation are determined in terms of the oncoming flow velocity. A previously unknown mechanism of detonation propagation is found; it is related with the presence of the combustible mixture in the wall layer under an inert gas layer. It is due to the formation of a complicated wave structure of the flow characterized by the penetration of a shock wave formed in the inert gas layer into a combustible mixture layer ahead of the detonation wave with the result that the latter layer is heated and ignited. The process as a whole is periodic in nature, as distinct from the conventional cellular detonation in a homogeneous fluid. Many problems arise in connection with the use of detonation in engines and other power plants. The most important among them are detonation excitation and stabilization in combustion chambers. The detonation initiation within a layer under conditions of unbounded space and a fluid at rest was experimentally investigated in [1]. In the case of a combustion chamber bounded in the transverse direction, some new effects accompanying the detonation might be expected.     

H2 injection and combustion in a Mach 5 air inlet through a Viscous Mach Interaction

Hydrogen injection has been investigated numerically in a flow configuration caused by strong shock–boundary layer interaction named Viscous Mach Interaction (VMI). The geometry that leads to this configuration is used as a hypersonic inlet. The subsonic zone, because of boundary layer detachment, allows hydrogen to be injected along the wall of the central body where combustion processes occur along a slip line when hydrogen is mixed with the incoming air flow far from the wall of the central body.     

Detonation combustion of hydrogen in a Laval nozzle under rarefied atmosphere conditions

Detonation combustion of a hydrogen-air mixture entering an axisymmetric convergent-divergent nozzle at a supersonic velocity is considered under atmospheric conditions at altitudes up to 24 km. The investigation is carried out on the basis of the two-dimensional gasdynamic Euler equations for a multicomponent reacting gas. The limiting altitude ensuring detonation combustion in a Laval nozzle of given geometry is numerically established for freestream Mach numbers 6 and 7. The possibility of the laser initiation of detonation in a supersonic flow of a stoichiometric, preliminarily heated hydrogen-air mixture is experimentally studied. The investigation is carried out in a shock tube under conditions simulating a supersonic flow in the nozzle throat region.     

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.     

On the influence of low initial pressure and detonation stochastic nature on Mach reflection of gaseous detonation waves

The two-dimensional, time-dependent and reactive Navier–Stokes equations were solved to obtain an insight into Mach reflection of gaseous detonation in a stoichiometric hydrogen-oxygen mixture diluted by 25 % argon. This mixture generates a mode-7 detonation wave under an initial pressure of 8.00 kPa. Chemical kinetics was simulated by an eight-species, forty-eight-reaction mechanism. It was found that a Mach reflection mode always occurs for a planar detonation wave or planar air shock wave sweeping over wedges with apex angles ranging from \(5^\circ \) to \(50^\circ \) . However, for cellular detonation waves, regular reflection always occurs first, which then transforms into Mach reflection. This phenomenon is more evident for detonations ignited under low initial pressure. Low initial pressure may lead to a curved wave front, that determines the reflection mode. The stochastic nature of boundary shape and transition distance, during deflagration-to-detonation transition, leads to relative disorder of detonation cell location and cell shape. Consequently, when a detonation wave hits the wedge apex, there appears a stochastic variation of triple point origin and variation of the angle between the triple point trajectory and the wedge surface. As the wedge apex angle increases, the distance between the triple point trajectory origin and the wedge apex increases, and the angle between the triple point trajectory and the wedge surface decreases exponentially.     

Detonation combustion of hydrogen in a convergent-divergent nozzle with a central coaxial cylinder

The feasibility of steady detonation combustion of a hydrogen-air mixture entering at a supersonic velocity in an axisymmetric convergent-divergent nozzle with a central coaxial cylinder is considered. The problem of the nozzle starting and the initiation of detonation combustion is numerically solved with account for the interaction of the outflowing gas with the external supersonic flow. The modeling is based on the gasdynamic Euler equations for an axisymmetric flow. The calculations are carried out using the Godunov scheme on a fine fixed grid which allows one to study in detail the interaction of an oblique shock wave formed in the diffuser with the nozzle axis. It is shown that a central coaxial cylinder ensures the starting with the formation of supersonic flow throughout the entire nozzle and stable detonation combustion of a stoichiometric hydrogen-air mixture in the divergent section of the nozzle.     

Experimental and numerical studies on transmission of gaseous detonation to a less sensitive mixture

A phenomenon of detonation transmission from one gaseous mixture (donor) to another of lower sensitivity (acceptor) was studied experimentally and numerically. The objective was to study effects of a donor mixture length and acceptor mixture sensitivity on the possibility of detonation transmission. Experiments were carried out in detonation tube 9.5–12 m long and 174 mm id. Three types of donor mixtures were used in the driver: stoichiometric acetylene/air, stoichiometric hydrogen/air, and 20% of hydrogen/air. Air mixtures with 14–29.6% of hydrogen were used as acceptors. Driver length varied from 0.17 to 5.6 m. Detonation transmission was studied for an abrupt opening of interface between two mixtures. Series of 1D and 2D calculations were made to simulate the problem numerically. Both, results of experiments and calculations revealed a set of parameters that effect transmission process. Critical conditions were determined as minimum driver length expressed in terms of characteristic chemical reaction length scales of acceptor mixture. They were shown to depend on differences in reaction rates and energy contents of donor and acceptor mixture. Received 6 January 1997 / Accepted 20 March 1997     

A numerical simulation of reflection processes of a detonation wave on a wedge

Abstract. A two dimensional numerical simulation has been performed to study reflection processes of detonation waves on a wedge. The numerical scheme adopted is the flux corrected transport scheme and a two-step chemical reaction is assumed for a stoichiometric oxyhydrogen mixture diluted with argon. Transverse wave structures of the detonation are produced by artificial disturbances situated in front of a one-dimensional Chapman-Jouguet detonation wave. Numerical grids are generated by solving a Laplace equation. Results show that in the case where Mach reflection occurs, the cells in the Mach stem are smaller than those in the incident wave and are distorted in shape. There is also an initiating stage during which the cells in the Mach stem are created. The critical angle beyond which Mach reflection cannot occur is discussed. Received 15 October 1999 / Accepted 27 March 2000     

气/固/液三相混合物燃烧转爆轰过程实验研究

利用多相燃烧爆炸实验系统,通过高压喷粉/喷雾以及高能点火等过程,对化学当量比条件下3种 典型燃料空气炸药,即硝基甲烷/铝粉/空气、硝酸异丙酯/铝粉/空气、乙醚/铝粉/空气三相混合物的燃烧转爆 轰过程进行了实验研究,同时根据实验结果对比了3种三相混合物的燃爆性能。得到了三相悬浮混合物燃烧 转爆轰过程的宏观规律以及三相混合物燃爆性能随质量浓度变化的规律。     

Detonation diffraction from an annular channel

In this study, gaseous detonation diffraction from an annular channel was investigated with a streak camera and the critical pressure for transmission of the detonation wave was obtained. The annular channel was used to approximate an infinite slot resulting in cylindrically expanding detonation waves. Two mixtures, stoichiometric acetylene–oxygen and stoichiometric acetylene–oxygen with 70% Ar dilution, were tested in a 4.3 and 14.3 mm channel width (W). The undiluted and diluted mixtures were found to have values of the critical channel width over the cell size around 3 and 12 respectively. Comparing these results to values of the critical diameter (d _c ), in which a spherical detonation occurs, a value of critical d _c /W _c near 2 is observed for the highly diluted mixture. This value corresponds to the geometrical factor of the curvature term between a spherical and cylindrical diverging wave. Hence, the result is in support of Lee’s proposed mechanism [Lee in Dynamics of Exothermicity, pp. 321, Gordon and Breach, Amsterdam, 1996] for failure due to diffraction based on curvature in stable mixtures such as those highly argon diluted with very regular detonation cellular patterns.     

Investigation of detonation initiation in aluminium suspensions

Detonation initiation is investigated in aluminium/oxygen and aluminium/air mixtures. Critical conditions for initiation of spherical detonations are examined in analogy with the criteria defined for gaseous mixtures, which correlate critical parameters of detonation initiation to the characteristic size of the cellular structure. However, experimental data on the detonation cell size in these two-phase mixtures are very scarce, on account of the difficulty to perform large-scale experiments. Therefore, 2D numerical simulations of the detonation cellular structure have been undertaken, with the same combustion model for Al/air and Al/O₂ mixtures. The cell size is found to be λ = 37.5 cm for a rich (r = 1.61) aluminium–air mixture, and λ = 7.5 cm for a stoichiometric aluminium-oxygen mixture, which is in reasonable agreement with available experimental data. Calculations performed in large-scale configurations (up to 25 m in length and 1.5 m in lateral direction) suggest that the critical initiation energy and predetonation radius for direct initiation of the unconfined detonation in the aluminium–air mixture are, respectively, 10 kg of TNT and 8 m. Moreover, numerical simulations reveal that the structure of the detonation wave behind the leading front is even more complicated than in pure gaseous mixtures, due to two-phase flow effects. 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.     

Visualization of deflagration-to-detonation transitions in a channel with repeated obstacles using a hydrogen–oxygen mixture

The deflagration-to-detonation transition in a 100 mm square cross-section channel was investigated for a highly reactive stoichiometric hydrogen oxygen mixture at 70 kPa. Obstacles of 5 mm width and 5, 10, and 15 mm heights were equally spaced 60 mm apart at the bottom of the channel. The phenomenon was investigated primarily by time-resolved schlieren visualization from two orthogonal directions using a high-speed video camera. The detonation transition occurred over a remarkably short distance within only three or four repeated obstacles. The global flame speed just before the detonation transition was well below the sound speed of the combustion products and did not reach the sound speed of the initial unreacted gas for tests with an obstacle height of 5 and 10 mm. These results indicate that a detonation transition does not always require global flame acceleration beyond the speed of sound for highly reactive combustible mixtures. A possible mechanism for this detonation initiation was the mixing of the unreacted and reacted gas in the vicinity of the flame front convoluted by the vortex present behind each obstacle, and the formation of a hot spot by the shock wave. The final onset of the detonation originated from the unreacted gas pocket, which was surrounded by the obstacle downstream face and the channel wall.     

Mechanisms of detonation transmission in layered H2-O2 mixtures

When a plane detonation propagating through an explosive comes into contact with a bounding explosive, different types of diffraction patterns, which may result in the transmission of a detonation into the bounding mixture, are observed. The nature of these diffraction patterns and the mode of detonation transmission depend on the properties of the primary and bounding explosives. An experimental and analytical study of such diffractions, which are fundamental to many explosive applications, has been conducted in a two channel shock tube, using H₂-O₂ mixtures of different equivalence ratios as the primary and bounding or secondary explosive. The combination of mixtures was varied from rich primary / lean secondary to lean primary / rich secondary since the nature of the diffraction was found to depend on whether the Chapman-Jouguet velocity of the primary mixture,D _p, was greater than or less than that of the secondary mixture,D _s. Schlieren framing photographs of the different diffraction patterns were obtained and used to measure shock and oblique detonation wave angles and velocities for the different diffraction patterns, and these were compared with the results of a steady-state shock-polar solution of the diffraction problem. Two basic types of diffraction and modes of detonation reinitiation were observed. WhenD _p>D _s, an oblique shock connecting the primary detonation to an oblique detonation in the secondary mixture was observed. WithD _p<D _s, two modes of reinitiation were observed. In some cases, ignition occurs behind the Mach reflection of the shock wave, which is transmitted into the secondary mixture when the primary detonation first comes into contact with it, from the walls of the shock tube. In other cases, a detonation is initiated in the secondary mixture when the reflected shock crosses the contact surface behind the incident detonation. These observed modes of Mach stem and contact surface ignition have also been observed in numerical simulations of layered detonation interactions, as has the combined oblique-shock oblique-detonation configuration whenD _p>D _s. WhenD _p>D _s, the primary wave acts like a wedge moving into the secondary mixture with velocityD _p after steady state has been reached, a configuration which also arises in oblique-detonation ramjets and hypervelocity drivers.     

Wave dynamic processes in cellular detonation reflection from wedges

When the cell width of the incident detonation wave (IDW) is comparable to or larger than the Mach stem height, self-similarity will fail during IDW reflection from a wedge surface. In this paper, the detonation reflection from wedges is investigated for the wave dynamic processes occurring in the wave front, including transverse shock motion and detonation cell variations behind the Mach stem. A detailed reaction model is implemented to simulate two-dimensional cellular detonations in stoichiometric mixtures of H ₂/O ₂ diluted by Argon. The numerical results show that the transverse waves, which cross the triple point trajectory of Mach reflection, travel along the Mach stem and reflect back from the wedge surface, control the size of the cells in the region swept by the Mach stem. It is the energy carried by these transverse waves that sustains the triple-wave-collision with a higher frequency within the over-driven Mach stem. In some cases, local wave dynamic processes and wave structures play a dominant role in determining the pattern of cellular record, leading to the fact that the cellular patterns after the Mach stem exhibit some peculiar modes. The English text was polished by Yumming Chen.