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.     

Detonation of explosive Proppant: RDX-containing water-saturated sand

The results of experimental investigations and thermodynamic calculations of the detonation of explosive proppant, an RDX-containing water-saturating sand, are reported. The material studied is of interest for use as an explosive additive to propping material injected into hydraulic fractures of oil-bearing beds. The tests were conducted in duralumin casings with cylindrical or planar inner channels. The dependences of the detonation velocity on the RDX content in the mixture in the range of 14 to 74 wt %, RDX and sand particle size, and initial temperature are examined. The critical detonation diameter of the charge decreases with increasing content RDX in the mixture, being only several millimeters at RDX contents of 30 wt % and above. Polydisperse RDX provides a high detonability of such mixtures; use of narrow particle size RDX fractions, especially coarse (0.4–0.7 mm), significantly increases the critical detonation diameter. As the initial temperature of the mixture is increased from 20 to 90°C, the critical detonation width decreases severalfold. The detonation of mixtures in a convergent planar channel occurs at a constant rate, which differs little from the detonation velocity measured in a cylindrical channel. Reaching the place where the opening of the channel is less than the critical width, detonation fails abruptly. Thermodynamic calculations of the detonation characteristics of the explosive proppant are performed using the BKWS equation of state under the assumption that the sand component behaves as an inert additive, being in mechanical equilibrium with the detonation products of the RDX-water mixture. A satisfactory agreement with the experimental data on the detonation velocity and its dependence on the RDX content is demonstrated. This makes it possible to conclude that RDX mixed with water-saturated sand detonates within a narrow reaction zone without significant convective heat transfer to the inert additive.     

Changes in the product composition during the detonation of an unconfined volume of a combustible mixture

For a model problem the solution to which describes the main features of changes in the parameters of the medium in the detonation of an unconfined gas mixture charge of in the air, direct numerical simulation, without of simplifying assumptions on changes in the composition of the mixture, was performed to study changes in the composition of the detonation products, determine the limits of applicability of the chemical equilibrium mixture model, and verify a previously obtained sufficient condition of applicability of the chemical equilibrium mixture model. The results of determining the limits of applicability of the chemical equilibrium mixture model previously obtained using an approximate method were confirmed.     

An experimental investigation of the propagation mechanism of critical deflagration waves that lead to the onset of detonation

The reflection of a CJ detonation from a perforated plate is used to generate high speed deflagrations downstream in order to investigate the critical conditions that lead to the onset of detonation. Different perforated plates were used to control the turbulence in the downstream deflagration waves. Streak Schlieren photography, ionization probes and pressure transducers are used to monitor the flow field and the transition to detonation. Stoichiometric mixtures of acetylene–oxygen and propane–oxygen were tested at low initial pressures. In some cases, acetylene–oxygen was diluted with 80% argon in order to render the mixture more “stable” (i.e., more regular detonation cell structure). The results show that prior to successful detonation initiation, a deflagration is formed that propagates at about half the CJ detonation velocity of the mixture. This “critical” deflagration (which propagates at a relatively constant velocity for a certain duration prior to the onset of detonation) is comprised of a leading shock wave followed by an extended turbulent reaction zone. The critical deflagration speed is not dependent on the turbulence characteristics of the perforated plate but rather on the energetics of the mixture like a CJ detonation (i.e., the deflagration front is driven by the expansion of the combustion products). Hence, the critical deflagration is identified as a CJ deflagration. The high intensity turbulence that is required to sustain its propagation is maintained via chemical instabilities in the reaction zone due to the coupling of pressure fluctuations with the energy release. Therefore, in “unstable” mixtures, critical deflagrations can be supported for long durations, whereas in “stable” mixtures, deflagrations decay as the initial plate generated turbulence decays. The eventual onset of detonation is postulated to be a result of the amplification of pressure waves (i.e., turbulence) that leads to the formation of local explosion centers via the SWACER mechanism during the pre-detonation period.     

Detonation models of fast combustion waves in nanoscale Al-MoO3 bulk powder media

The combustion of nanometric aluminum (Al) powder with an oxidiser such as molybdenum trioxide (MoO₃) is studied analytically. This study focuses on detonation wave models and a Chapman-Jouget detonation model provides reasonable agreement with experimentally-observed wave speeds provided that multiphase equilibrium sound speeds are applied at the downstream edge of the detonation wave. The results indicate that equilibrium sound speeds of multiphase mixtures can play a critical role in determining speeds of fast combustion waves in nanoscale Al-MoO₃ powder mixtures.     

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     

Pulsating one-dimensional detonations in hydrogen–air mixtures

The propagation of one-dimensional detonations in hydrogen–air mixtures is investigated numerically by solving the one-dimensional Euler equations with detailed finite-rate chemistry. The numerical method is based on a second-order spatially accurate total-variation-diminishing scheme and a point implicit time marching algorithm. The hydrogen–air combustion is modelled with a 9-species, 19-step reaction mechanism. A multi-level, dynamically adaptive grid is utilized, in order to resolve the structure of the detonation. Parametric studies for an equivalence ratio range of 0.4–2.0, initial pressure range of 0.2–0.8 bar and different degrees of detonation overdrive demonstrate that the detonation is unstable for low degrees of overdrive, but the dynamics of wave propagation varies with fuel–air equivalence ratio and pressure. For equivalence ratios less than approximately 1.2 and for all pressures, the detonation exhibits a short-period oscillatory mode, characterized by high-frequency, low-amplitude waves. Richer mixtures exhibit a period-doubled bifurcation that depends on the initial pressure. Parametric studies over a degree of overdrive range of 1.0–1.2 for stoichiometric mixtures at 0.42 bar initial pressure indicate that stable detonation wave propagation is obtained at the high end of this range. For degrees of overdrive close to one, the detonation wave exhibits a low-frequency mode characterized by large fluctuations in the detonation wave speed. The McVey–Toong short-period wave-interaction theory is in qualitative agreement with the numerical simulations; however, the frequencies obtained from their theory are much higher, especially for near-stoichiometric mixtures at high pressure. Modification of this theory to account for the finite heat-release time significantly improves agreement with the numerically computed frequency over the entire equivalence ratio and pressure ranges.     

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.     

Direct blast initiation of spherical gaseous detonations in highly argon diluted mixtures

In this study, direct initiation of spherical detonations in highly argon diluted mixtures is investigated. Direct initiation is achieved via a high voltage capacitor spark discharge and the critical energy is estimated from the analysis of the current output. Stoichiometric acetylene–oxygen mixtures highly diluted with 70% argon is used in the experiment. Previous investigations have suggested that detonations in mixtures that are highly diluted with argon have been shown to be “stable” in that the reaction zone is at least piecewise laminar described by the ZND model and cellular instabilities play a minor role on the detonation propagation. For the acetylene–oxygen mixture that is highly diluted with argon, the experimental results show that the critical energy where the detonation is “stable” is in good agreement with the Zel’dovich criterion of the cubic dependence on the ZND reaction length, which can be readily determined using the chemical kinetic data of the reaction. The experimental results are also compared with those estimated using Lee’s surface energy model where empirical data on detonation cell sizes are required. Good agreement is found between the experimental measurement and theoretical model prediction, where the breakdown of the 13λ relationship for critical tube diameter – and hence a different propagation and initiation mechanism – is elucidated in highly argon diluted mixtures and this appears to indicate that cellular instabilities do not have a prominent effect on the initiation process of a stable detonation.     

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.     

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。     

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.     

An experimental investigation of the onset of detonation

An experimental configuration is devised in the present investigation whereby the condition at the final phase of the deflagration to detonation transition (DDT) process can be generated reproducibly by reflecting a CJ detonation from a perforated plate. The detonation products are transmitted downstream through the plate, generating a turbulent reaction front that mixes with the unburned mixture and that drives a precursor shock ahead of it at a strength of about M = 3. The gasdynamic condition that is generated downstream of the perforated plate closely corresponds to that just prior to the onset of detonation in the DDT process. The turbulence parameters can be controlled by varying the geometry of the perforated plate; thus, the condition leading to the onset of detonation can be experimentally investigated. A one-dimensional theoretical analysis of the steady wave processes was first performed, and the experimental results show good agreement, indicating that the present experimental condition can be theoretically described. Two different detonation tube geometries (one with a square cross-section of 300 mm by 300 mm and the other with a circular cross-section of 150 mm) are used to demonstrate the independence of the tube diameter at the critical condition for DDT. Perforated plates with different hole diameters (d = 8, 15, and 25 mm) were tested, and the hole spacing to hole diameter ratio was maintained at 0.5. Different hydrogen–air mixtures were tested at normal temperature and pressure. For the plate with 8 mm holes, the onset of detonation is never observed. For the plate with 15 mm holes, successful initiation of a detonation is achieved for 0.8 < < 1.75 in both detonation tubes. For the plate with 25 mm holes, detonation initiation is observed for 0.7 < < 2.1 in the square detonation tube and for 0.8 < < 1.6 in the smaller circular detonation tube.     

Chemical control of combustion and detonation in carbon oxide and hydrogen mixtures with air

The paper presents data on the control of combustion and detonation in CO and H₂ mixtures with air by small additives. The dependence of the kinetics of combustion and detonation characteristics on the initial mixture composition observed experimentally is in agreement with the predictions of theory taking into account the special features of reaction chains of the combustion of carbon monoxide in the presence of hydrogen-containing impurities. Works ignoring the chain character of the combustion of H₂ and CO are critically reviewed.     

Numerical studies on autoignition and detonation development from a hot spot in hydrogen/air mixtures

Detonation development inside spark ignition engines can result in the so called super-knock with extremely high pressure oscillation above 200?atm. In this study, numerical simulations of autoignitive reaction front propagation in hydrogen/air mixtures are conducted and the detonation development regime is investigated. A hot spot with linear temperature distribution is used to induce autoignitive reaction front propagation. With the change of temperature gradient or hot spot size, three typical autoignition reaction front modes are identified: supersonic reaction front; detonation development and subsonic reaction front. The effects of initial pressure, initial temperature, fuel type and equivalence ratio on detonation development regime are examined. It is found that the detonation development regime strongly depends on mixture composition (fuel and equivalence ratio) and thermal conditions (initial pressure and temperature). Therefore, to achieve the quantitative prediction of super-knock in engines, we need use the detonation development regime for specific fuel at specific initial temperature, initial pressure, and equivalence ratio.     

Detonation properties of stoichiometric gaseous n-heptane/oxygen/argon mixtures

A study of detonation velocity and cellular structure for stoichiometric heptane/oxygen and for some stoichiometric heptane/oxygen/argon mixtures is carried out in a shock tube at low initial pressure. The critical conditions for the detonation onset and for the propagation of a self-sustained detonation wave are determined. A simplified form of the ZND model used in conjunction with a validated detailed kinetic model leads to the determination of the proportionality factor, A, between the detonation cell width, λ, and the induction distance, Δ, in the detonation wave. This A factor is of practical importance to estimate the detonation properties of n-heptane based mixtures including n-heptane/air. The prediction of detonation cell size λ for n-heptane based mixtures is discussed according to the recent semi-empirical detonation model of Gavrikov et al. The cell sizes predicted according to this detonation model are underestimated by a factor of about 8. The limitations of this model are underlined when applied to n-heptane based mixtures.     

H32.685N16.8430O3.0和H8.154N4.5770O3.0炸药爆轰参数的数值模拟

用Gibbs自由能最小原理,通过解化学平衡方程组,求解HNO型炸药H32·685N16·8430O3·0(70/30Hydrazine/HydrazineNitrate)和H8·154N4·5770O3·0(21/79Hydrazine/HydrazineNitrate)爆轰产物系统的平衡组分,计算结果与用BKW和LJD方法计算的结果相近。以Ree修正的WCA状态方程并考虑Ross软球修正的硬球微扰理论作为爆轰气相产物的物态方程,用自编的程序对H32·685N16·8430O3·0和H8·154N4·5770O3·0炸药爆轰参数作了预言,爆轰CJ点的爆速、爆压和爆温的计算结果与实验值吻合得很好。     

Geometric modeling and analysis of detonation cellular stability

A geometric model with a low computational complexity capable of simulating detonation behavior in physical systems is proposed. In support of the geometric model development, a series of cylindrical 1D simulations with a variable size initiation kernel are performed in hydrogen-oxygen mixtures. From these 1D simulations a detonation cell stabilization mechanism is identified. The stabilization mechanism is predicated on the size of the gap between the pressure and temperature fronts at the point where the average pressure front velocity along one cell length is equal to the CJ velocity. This gap, in a multidimensional detonation, is the ignition kernel of a subsequent blast, and dictates the formation of the subsequent cell. Serial analysis of blasts in this context leads to a unique stable blast kernel size for any mixture, which, within the uncertainty of the initial kernel state, can predict the experimental cell length for mixtures considered in this study. Using a tabulation of the 1D simulations as an input, a formulation and sample results of the geometric model are shown. The geometric model can reproduce both qualitative and quantitative features of experimental detonation cellular structure.     

Computational study of NOx formation in hydrogen-fuelled pulse detonation engines

The formation of NOx in hydrogen-fuelled pulse detonation engines (PDE) is investigated numerically. The computations are based on the axisymmetric Euler equations and a detailed combustion model consisting of 12 species and 27 reactions. A multi-level, dynamically adaptive grid is utilized, in order to resolve the structure of the detonation front. Computed NO concentrations are in good agreement with experimental measurements obtained at two operating frequencies and two equivalence ratios. Additional computations examine the effects of equivalence ratio and residence time on NOx formation at ambient conditions. The results indicate that NOx formation in PDEs is very high for near stoichiometric mixtures. NOx reduction requires use of lean or rich mixtures and the shortest possible detonation tube. NOx emissions for very lean or very rich mixtures are, however, fairly insensitive to residence time.     

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.