Determination of the limits of applicability of the chemical equilibrium model to the detonation products of gas mixtures

The applicability of the model of a chemically equilibrium mixture to describing the evolution of the composition of the detonation products during their expansion in three typical problems involving oxygen- and air-based combustible mixtures is examined. For the detonation products of oxygen-based mixtures, the model of a chemical equilibrium mixture provides a good agreement with the kinetic calculations for all practically important initial conditions for these problems. For air-based mixtures, initial conditions at which such an agreement is observed are determined.     

A sufficient condition of applicability of the model of a chemical equilibrium mixture to describing the state of detonation products

A sufficient condition of applicability of the model of a chemical equilibrium mixture to gasdynamic calculations based on a comparison of the rate of change of the equilibrium concentrations of the products in gas-dynamic process with the rate of chemical reactions leading to the establishment of chemical equilibrium is obtained. An example of using this condition in examining the applicability of the model of a chemical equilibrium mixture to the products of detonation of spherical charges of oxyacetylene and hydrogen-air mixtures the in the air is presented.     

固体炸药爆轰的一种考虑热学非平衡的反应流动模型

基于固体炸药爆轰过程中化学反应混合区内的固相反应物与气相生成物处于力学平衡状态及热学非平衡状态的事实,提出一种考虑热学非平衡效应的反应流动模型来描述固体炸药的爆轰流动现象.该爆轰流动模型的主要特点是,在反应混合物Euler方程和固相反应物质量守恒方程的基础上,通过附加一套关于固相反应物的组分物理量的流动控制方程来表达固相反应物与气相生成物之间的热学非平衡效应.根据反应混合区内固相反应物与气相生成物这两种化学组分保持各自内能守恒的混合规则,并借助它们具有压力相等的性质以及满足体积分数总和为1的条件,推导获得的附加方程有：固相反应物的内能演化方程、体积分数演化方程及反应混合物的压力演化方程.这样,建立的爆轰模型包括：反应混合物的质量守恒方程、动量守恒方程、总能量守恒方程、压力演化方程,以及固相反应物的质量守恒方程、内能演化方程、体积分数演化方程.对所获得的爆轰模型方程组采用一个时空二阶精度的有限体积法进行数值求解,典型爆轰问题算例结果表明本文提出的固体炸药爆轰模型是合理的.     

Effect of the composition of the combustible mixture on the development of flame front instability

Numerical simulations are used to study the effect of the chemical composition of the combustible mixture on the development of the hydrodynamic instability of the flame front, its acceleration, and the possibility of transition to the detonation regime. The combustion of hydrogen-containing mixtures in confined spaces (channels) was considered. Calculations were performed within the framework of a two-dimensional hydrodynamic model for the combustion of premixed mixtures with account of viscosity, heat conduction, multicomponent diffusion, and chemical kinetics. It was demonstrated that the presence of an inert component and the deviation of the mixture composition from stoichiometry caused not only a quantitative but also a qualitative change in the character of burning of gaseous combustible mixtures.     

PETN炸药爆轰产物状态方程的理论研究

 采用van der Waals等效单组分流体模型和Ross硬球微扰理论软球修正模型,计算爆轰气相产物的状态方程;用石墨相、金刚石相、类石墨液相和类金刚石液相4种相态描述凝聚成分,由Gibbs自由能最小原理确定不同状态下的凝聚产物相态。对爆轰产物混合系统采用自由能最小原理,通过化学平衡方程组求解炸药爆轰产物系统的平衡组分。使用该理论计算PETN炸药Chapman-Jouguet（CJ）点的爆轰参数,其值与实验值符合得很好;同时计算了以CJ点为起始点的等熵卸载线,并与传统的Jones-Wilkins-Lee（JWL）状态方程的计算结果进行比较,发现计算的γ值是单调递减的,而JWL状态方程计算的γ值却出现了“双峰”现象。分析认为,传统的JWL状态方程给出的“双峰”变化,是由其函数形式自身决定的,并不对应实际物理过程。     

Detonation in an aluminum-Teflon mixture

Detonation in an aluminum-fluoroplastic-4 (Teflon) mixture is studied experimentally. To increase reactivity, the initial mixture is pretreated in a mechanochemical activator. As a result, a mechanically activated composite is obtained in the form of thin aluminum layers in a Teflon matrix. The action of a shock wave on a composite sample initiates the steady detonation regime, in which the initial and final substances are in the condensed state. Depending on the percentage composition and density of the mixture, the detonation velocity varies from 700 to 1300 m/s for the speed of sound below 100 m/s in the initial composition. The steady detonation velocity changes insignificantly when sample pores are filled with helium instead of air. The results prove that it is possible in principle to reach the steady detonation regime in reactive condensed mixtures forming final reaction products in the solid state.     

Numerical study of self-sustained oblique detonation in a non-uniform mixture

Self-sustained oblique detonation behind a spherical projectile formed in a non-uniform H₂/O₂/Ar mixture was numerically investigated. A hypersonic combustible mixture flow around a 4.76 mm diameter body was modeled to be flowing at 2500 m/s and 100 kPa. The concentration gradient was prescribed applying the Gaussian distribution to hydrogen concentration. Axisymmetric Euler equations including a detailed kinetics of 9 species and 27 elementary reactions were solved with an explicit 2nd-order time integration scheme combined with point implicit method for chemical reaction. Oblique detonation was always obtained when the mixture on the centerline was stoichiometric, as it is for a uniform mixture, and a broader range of equivalence ratio could sustain oblique detonation far from the sphere. Local detonation angle was revealed to reasonably match Chapman-Jouguet analytical solutions with a minor difference attributed to curvature, less reactive composition, and the concentration gradient. Also, a strongly fuel-rich region encountered decoupling of the shock-flame, in which an abrupt deflection of the shock front appeared. These decoupling phenomena can be attributed to a slower kinetics of a less reactive mixture. All of interesting findings in this study will also benefit understanding of various form of detonation in non-uniform mixture taking advantage of the analogy between them.     

Mathematical modeling of the chemical inhibition of the detonation of hydrogen-air mixtures

A mathematical modeling of the chemical inhibition of the detonation of hydrogen-air mixtures is performed. It is demonstrated that a one-dimensional model of detonation based on a chain-branching mechanism of hydrogen combustion makes it possible to describe the main regularities of the effect of inhibitors on detonation. The calculation results, which are in good agreement with the available experimental data, show that inhibition causes a narrowing of the concentration limits of detonation and an increase in the critical diameter of detonation.     

Propagation of detonation in fuel–air mixtures in flat channels

The wide scatter of the values of the measured detonation cell size in fuel + air mixtures restricts the applicability of this parameter in the estimation of the geometric limits of detonation propagation, including in rectangular channels whose height is much larger than their width. The critical channel height for the propagation of detonation has been experimentally determined for hydrogen + air, propane + air, and ethylene + air mixtures. In order to reveal the specific features of the propagation and decay of detonation in a narrow channel, numerical simulation has been carried out for a hydrogen + air mixture with account taken of the cellular structure of the detonation wave.     

Deposition of inertial particles from turbulent flow in channels at high Reynolds numbers

On the basis of the previously developed asymptotic theory of turbulent particle-laden flow with particle deposition in channels coupled with the transport model for the particle Reynolds stress, an asymptotic solution to the problem on the deposition of particles in the limit of high Reynolds numbers was obtained. The numerical calculations confirmed the presence, in the region of the transition from the diffusion-impaction regime of particle sedimentation to the inertia-moderated regime, bifurcation phenomenon of a solution found previously in earlier studies. Features of particle accumulation in the viscous sublayer are analyzed. On the basis of the numerical solution, correlations for particle deposition velocity were obtained. Boundary conditions of the wall-function type for particle concentration whose use allows widening the applicability limits of the equilibrium Eulerian models in terms of particle inertia are proposed.     

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。     

基于统计物理的爆轰产物物态方程研究

用van der Waals等效单组分流体模型和Ross硬球微扰理论软球修正模型，计算爆轰气相产物的状态方程；用石墨相、金刚石相、类石墨液相和类金刚石液相４种相态描述凝聚成分，由Gibbs自由能最小确定不同状态下的凝聚产物相态.对爆轰产物混合系统采用Gibbs自由能最小原理，通过化学平衡方程组求解炸药爆轰产物系统的平衡组分，计算结果与Becker-Kistiakowsky-Wilson (BKW)和Lennard-Jones-Devonshire结果相近.使用该理论对炸药的爆轰参数做了预言，与BKW，Jo 关键词： 爆轰产物 物态方程 化学平衡方程组     

爆轰产物物态方程及CHBr3相变的理论研究

 由吉布斯自由能最小计算处于化学平衡状态的气体和固体混合系统的平衡组分。以BKW和VLW作为爆轰产物的物态方程对几种炸药爆轰参数作了预言，计算结果与实验值吻合得非常好。另外，还对CHBr₃的冲击压缩分解作了化学平衡计算，给出了冲击压缩曲线，对文献[6]中提出的CHBr₃在55~60 GPa存在相变的看法提出了质疑。     

Nonlinear dynamics of self-sustained supersonic reaction waves: Fickett's detonation analogue

The present study investigates the spatiotemporal variability in the dynamics of self-sustained supersonic reaction waves propagating through an excitable medium. The model is an extension of Fickett's detonation model with a state-dependent energy addition term. Stable and pulsating supersonic waves are predicted. With increasing sensitivity of the reaction rate, the reaction wave transits from steady propagation to stable limit cycles and eventually to chaos through the classical Feigenbaum route. The physical pulsation mechanism is explained by the coherence between internal wave motion and energy release. The results obtained clarify the physical origin of detonation wave instability in chemical detonations previously observed experimentally.     

On detonation initiation by a temperature gradient for a detailed chemical reaction models

The evolution from a temperature gradient to a detonation is investigated for combustion mixture whose chemistry is governed by a detailed chemical kinetics. We show that a detailed chemical reaction model has a profound effect on the spontaneous wave concept for detonation initiation by a gradient of reactivity. The evolution to detonation due to a temperature gradient is considered for hydrogen-oxygen and hydrogen-air mixtures at different initial pressures. It is shown that the minimal length of the temperature gradient for which a detonation can be ignited is much larger than that predicted from a one-step chemical model.     

爆轰波在弯管内传播过程数值分析

应用基元反应模型和频散可控耗散格式(DCD)对氢氧爆轰波在弯管内的传播过程进行了数值模拟.计算中氢氧混合物化学反应采用了8种组分20个反应方程式.在处理化学反应引起的刚性问题时采用了时间算子分裂的方法.计算结果表明,在弯管小曲率半径壁面附近,由于膨胀稀疏作用,爆轰波强度减弱,在局部出现前导激波与放热反应区的解藕以及二次起爆现象;在弯管大曲率半径壁面上爆轰波在马赫反射和正规反射之间相互转变,使爆轰波加强.弯管内的爆轰现象与弯管曲率半径有关.     

Initiation of detonation by conical projectiles

Initiation of detonation by a hypersonic conical projectile launched into a combustible gas mixture is investigated. From analytic considerations of the flowfield, energetic and kinetic limits are proposed to predict the conditions required to initiate an oblique detonation wave in the mixture. To experimentally investigate these limits, projectiles with cone half angles varying from 15° to 60° were launched into a stoichiometric mixture of hydrogen/oxygen with 70% argon dilution at initial pressure between 10 and 200 kPa. The projectiles were launched from a combustion-driven gas gun at velocities as great as 2.5 km/s (corresponding to 150% of the Chapman Jouguet velocity). Pictures of the flowfields generated by the projectiles were taken via schlieren photography. Five combustion regimes could be observed about the projectile ranging from a prompt and delayed oblique detonation wave formation, combustion instabilities, a wave splitting, and an inert shock wave. The two theoretical limits provide a means to interpret the observed flowfield regimes and are in satisfactory agreement with the experimental results.     

基于Mie-Grüneisen状态方程的爆轰波运动数值模拟

依据C-J（Chapman-Jouguet）理论,对爆轰问题中的气态爆轰产物和未反应炸药分别考虑不同的参考状态,并根据参考状态选用特定的Mie-Grüneisen状态方程。忽略化学反应过程,爆轰产物厚度为零的前导激波面以界面的形式存在。数值模拟中,爆轰波的演化分为波面传播以及与未反应介质相互作用两个部分。传播过程中,爆轰波的传播速度即恒定的爆速,爆轰产物在传播过程中瞬间形成,而相互作用过程则是通过Mie-Grüneisen多介质混合模型来计算爆轰波的持续冲击作用。借助于Mie-Grüneisen状态方程以及Mie-Grüneisen多介质混合模型,可以很好地模拟爆轰波的运动过程。对比理论参数及文献的计算结果发现,模拟结果具备较好的准确度。     

基于基元反应模型的H2-O2-N2爆轰数值模拟

 采用12组分、23个化学反应的基元化学反应模型,用5阶加权本质无震荡格式（WENO）、3阶TVD Runge-Kutta格式,对H₂-O₂-N₂混合气体胞格爆轰进行了数值模拟。研究了一维ZND爆轰、自维持爆轰的详细结构以及三波点附近的流动结构。计算结果表明：由横波的压力可以显著促进二维爆轰波波阵面的形成;横波的运动生成三波点,三波点造成了爆轰的自维持传播。     

Detonation propagation across a stratified layer with a diffuse interface

A study was conducted to examine detonation propagation in a stratified layer of hydrogen-oxygen-nitrogen above an inert gas in a horizontal narrow channel. The stratified layer was produced by a gravity current, generated by retracting a door initially separating a hydrogen-oxygen-nitrogen mixture in the predetonator and a heavier inert gas in the test-section. A steady detonation wave generated in the predetonator was transmitted into the stratified layer. The reactivity of the predetonator mixture was varied via the hydrogen-oxygen equivalence ratio and the amount of nitrogen dilution. Schlieren photography was used to visualize the detonation front in the test-section, and soot foils were used to obtain the cellular structure. Schlieren imaging showed a curved detonation front that decoupled at about mid channel height, into a shock wave and trailing contact surface. Both the hydrogen-oxygen-nitrogen reactivity and the type of inert gas initially in the test-section affected the distance travelled by the detonation wave in the stratified layer. The mixture composition distribution within the test-section before ignition was obtained via a three-dimensional CFD simulation. The lateral extent of the cellular structure captured on the soot foil, coincided with the calculated inert gas mole fraction contour that corresponds to a sharp increase in the ZND induction zone length, e.g., 70% argon dilution for a stoichiometric hydrogen-oxygen predetonator mixture.