Filtration combustion of a porous structure in a multicomponent gas environment

A mathematical model for describing the quasi-isobaric filtration combustion of porous materials with the formation of condensed reaction products in a multicomponent gas is developed. Two-stage combustion waves (control modes) at the counter filtration of gas mixture are examined. The effect of inert gas component on the structure of a two-stage filtration combustion wave is studied, and the critical conditions of the changeover between filtration combustion modes caused by inert gas concentration variation are determined. It is demonstrated the characteristics of the two-stage combustion front propagating in the control mode in a multicomponent gas flow depends on the porosity of the heterogeneous system.     

Numerical simulation of modes of combustion and detonation of hydrogen-air mixtures in porous medium in the framework of the mechanics of two-phase reaction mediums

Numerical simulation is carried out for combustion and detonation waves propagating through a motionless gas mixture in a porous inert charge. Computations are performed in a one-dimensional approximation by means of an EFAE computer program that was developed in the framework of the mechanics of multiphase reaction mediums. The chemical conversion of gas is modeled by a one-stage reaction of the Arrhenius type with constants selected based on existing experimental data on the ignition lags behind the reflected shock waves. Computations are performed for hydrogen-air mixtures with 35 and 15% hydrogen and compared with literature experimental data in which the initial pressure and the diameter of charged particles are varied. All three combustion modes (slow, fast, and supersonic) observed in the experiment and combustion failure under conditions lower than threshold are followed by numerical simulation. In addition, the computations qualitatively reproduced experimental data on the change of the combustion mode in the case of transfer from stoichiometric to a lean mixture and data on the combustion wave velocity and limiting conditions of combustion mode transition and failure of flame as a function of the initial pressure and the charged particle size. It is shown that supersonic waves propagating with a velocity of lower than 1100 m/s do not have a Chapman-Jouguet surface in the end of the reaction zone and it is evident that they can be related to detonation, as in the cited literature.     

计算奇异摄动法在燃烧反应系统简化中的应用

采用计算奇异摄动法构造典型燃烧反应系统的简化化学动力模型,基于燃烧反应控制方程寻找理想基向量,借助所得理想基向量实现快慢反应模态间的解耦,并给出参与性指数、原子团指针和重要性指数等关键参数,进而构造快模态状态方程和简化化学动力模型.典型CO-CH₄-Air混合燃烧反应系统的计算结果表明,由计算奇异摄动法得到的简化燃烧反应系统是原燃烧反应系统很好的近似.     

On the Nature of Concentration Limits of Combustion Wave Propagation in Powdered and Pelletized Ti + C + <Emphasis Type="Italic">x</Emphasis>Al<Subscript>2</Subscript>O<Subscript>3</Subscript> Mixtures

The applicability of the percolation theory to describe the combustion of powdered and pelletized Ti + C mixtures in the vicinity of the concentration limits of the combustion wave propagation using different methods of dilution with an inert material—fine and coarse Al₂O₃ particles—has been studied. It has been shown that the pelletized mixtures diluted with coarse inert particles by more than 50% undergo incomplete combustion; at the combustion limit, the incompleteness achieves 50%; this finding is in qualitative agreement with the percolation theory. It has been found that the obtained concentration limit of combustion (75 wt %) and the ratio of the combustion velocities of the undiluted mixture and the mixture at the propagation limit (2.6) correspond to the predictions of the percolation theory. The possibility of flame propagation at the calculated combustion temperature of the mixture below the melting point of titanium is attributed to the presence of a percolation cluster. Necessary conditions for the applicability of the percolation theory to describe the combustion processes in condensed gasless systems have been formulated.     

堆积床内非驻定过滤燃烧的一维研究

多孔介质内气体过滤燃烧不同于自由流中燃烧,燃气与多孔介质强烈换热.热波波速和燃烧波波速是燃烧过程的特征参数.以惰性堆积床内的甲烷/空气的低速过滤燃烧为例,提出一维解析模型,用摄动理论推导出燃烧波波速,用直接求解方法和格林函数方法给出充分发展后的和瞬态的燃烧温度分布,并进行计算验证.     

Structure of a pressure driven flame in porous media

The model of a combustion wave driven by local elevation of pressure in inert porous media filled with flammable gas is investigated. The combustion wave structure is studied using the Zel'dovich approach. Analytical formulae for the combustion wave speed and for values of temperature and pressure behind the flame front are derived.     

Towards a predictive scenario of a burning accident in a mining passage

To reveal the inner mechanisms of a combustion accident in a coalmine, the key stages and characteristics of premixed flame front evolution such as the flame shapes, propagation speeds, acceleration rates, run-up distances and flame-generated velocity profiles are scrutinised. The theories of globally spherical, expanding flames and of finger-flame acceleration are combined into a general analytical formulation. Two-dimensional and cylindrical mining passages are studied, with noticeably stronger acceleration found in the cylindrical geometry. The entire acceleration scenario may promote the total burning rate by up to two orders of magnitude, to a near-sonic value. Starting with gaseous combustion, the analysis is subsequently extended to gaseous-dusty environments. Specifically, combustible dust (e.g. coal), inert dust (e.g. sand), and their combination are considered, and the influence of the size and concentration of the dust particles is quantified. In particular, small particles influence flame propagation more than large ones, and flame acceleration increases with the concentration of a combustible dust, until the concentration attains a certain limit.     

Experimental investigation and numerical validation of explosion suppression by inert particles in large-scale duct

A large-scale duct with an explosion suppressor was designed to investigate experimentally the explosion suppression by inert particles for a CH₄/O₂/N₂ mixture. The duct is 25 m long and has an internal diameter of 700 mm. Pressure and flame signals were recorded some distance away from ignitor in the duct. Pressure tracking lines of the shock front for the different inert particle cloud densities and the inert particle diameters were made. The measured results indicate that the shock front is decoupled from the flame front in the inert particle cloud, which leads to a suppression of explosion. Also, the experiments suggest that increasing the inert particle cloud density or decreasing the inert particle diameter can enhance the ability to suppress explosion. For the purpose of validation, a two-dimensional numerical model coupled with the element chemical reaction mechanism for the simulations of the CH₄/O₂/N₂ mixture explosion suppression by the inert particles has been developed. This model makes use of the second-order TVD scheme and the MacCormack scheme to calculate gas-phase and particle-phase equations, respectively. The Strang splitting technique is used to treat the stiffness due to the coupling of the governing equations, while the implicit Gear algorithm is used to treat the stiffness due to the chemical reactions. The effect of inert particle cloud density on explosion suppression was investigated using the model. The calculated results indicate that the accumulation of inert particles slows the propagation of the gas-phase shock front and results in explosion suppression. With increased inert particle cloud density, the explosion suppression is more prominent. The calculated results show a qualitative agreement with the measured results in the large-scale duct experiment.     

Regimes of the filtration combustion of structured heterogeneous systems

An analysis of the characteristics of the combustion front in a multilayer porous system with radiative heat transfer and filtration mass transfer of gaseous reactants into the exothermic conversion zone is presented. At moderate pressures, the mass of the gas in the porous layer is smaller than that required by stoichiometry, and, therefore, filtration transport without diffusion from the ambient medium occurs. It was taken into account that the bulk heat release in the porous media can be limited by both the kinetics of the exothermic chemical reaction and the filtration transport of a gaseous reactant from the ambient medium. The effect of filtration on the characteristics of relay-race combustion was examined. The characteristics of the front and the dynamics of the conversion of the elements of the discrete system were determined. The characteristics of the relay-race filtration combustion front under conditions of heat losses into the ambient medium were examined, and the possibility of existence of two steady regimes, with a low- and a high-temperature relay-race combustion front, was demonstrated. At heat losses above a critical level, relay-race combustion extinguishes. A numerical analysis of relay-race combustion regimes under nonadiabatic conditions showed that the low-temperature front is absolutely unstable and made it possible to study the dynamics of the onset of high-temperature relay-race filtration combustion.     

Numerical simulation of a mixed-mode reaction front in a PPC engine

The ignition process, mode of combustion and reaction front propagation in a partially premixed combustion (PPC) engine running with a primary reference fuel (87% iso-octane, 13% n-heptane by volume) is studied numerically in a large eddy simulation. Different combustion modes, ignition front propagation, premixed flame and non-premixed flame, are observed simultaneously. Displacement speed of CO iso-surface propagation describes the transition of premixed auto-ignition to non-premixed flame. High temporal resolution optical data of CH₂O and chemiluminescence are compared with simulated results. A high speed ignition front is seen to expand through fuel-rich mixture and stabilize around stoichiometry in a non-premixed flame while lean premixed combustion occurs in the spray wake at a much slower pace. A good qualitative agreement of the distribution of chemiluminescence and CH₂O formation and destruction shows that the simulation approach sufficiently captures the driving physics of mixed-mode combustion in PPC engines. The study shows that the transition from auto-ignition to flame occurs over a period of several crank angles and the reaction front propagation can be captured using the described model.     

Embedded particle size distribution and its effect on detonation in composite explosives

This paper discusses the effects of stochastically varying inert particle parameters on the long-term behaviour of detonation front propagation. The simulation model involves a series of cylindrical high explosive unit cells, each embedded with an inert spherical particle. Detonation shock dynamics theory postulates that the velocity of the shock front in the explosive fluid is related to its curvature. In our previous work, we derived a series of partial differential equations that govern the propagation of the shock front passing over the inert particles and developed a computationally efficient simulation environment to study the model over extremely long timescales. We expand upon that project by randomising several properties of the inert particles to represent experimental designs better. First, we randomise the particle diameters according to the Weibull distribution. Then we discuss stochastic particle spacing methods and their effects on the predictability of the shock wave speed. Finally, we discuss mixtures of plastic and metal particles and material inconsistency among the particles.     

Cellular wave mode of the infiltration combustion of porous media

The paper summarizes the results of experimental studies of the structuring of the infiltration combustion front in a burning titanium powder layer. The unsteady processes of formation and propagation of cellular and nonuniform combustion waves in heterogeneous media in straight-through and semi-closed channels in conditions of restricted gas exchange and presence of inert gaseous impurities are analyzed. The structural characteristics of cellular combustion waves in a metal powder layer under conditions of natural gas infiltration are reported.     

Propagation of magnetoacoustic surface waves along static plasma slab surrounded by moving plasma and neutral gas

The existence and propagation of fast and slow magnetoacoustic surface waves (MASW) is investigated in our work by taking a theoretical model of a static plasma slab as the middle layer with a moving plasma region at the top and neutral gas medium as the bottom layer. Applying linear MHD, the dispersion relation is obtained and the propagation of magnetoacoustic surface waves, in the compressional limit for steady flow and for different values of dimensionless wave numbers, is analyzed. Steady flow of plasma along a structured atmosphere may cause enhancement of existing surface modes, disappearance of some modes and generation of new surface wave modes. The possible regions for the propagation of fast and slow surface and body waves for different mass density ratios and magnetic field ratios and with a small flow velocity are studied. Our discussion may help in analyzing more complicated cases.     

Compressive and rarefactive electromagnetic solitary structures in an opposite polarity dust-plasma medium

Nonlinear propagation of fast and slow dust-magneto-acoustic perturbation modes in an opposite polarity dust-plasma medium, consisting of positively and negatively charged dust fluids, has been investigated by using the reductive perturbation method. It is shown that the fast (slow) dust-magneto-acoustic mode may non-linearly propagate as compressive (rarefactive) solitary waves. The parametric regimes for the existence of fast and slow dust-magneto-acoustic solitary waves are obtained, and their basic features (viz. amplitude, width, and speed) are identified. The possible applications of our results in space environments and laboratory devices are also briefly discussed.     

Influence of the slow wave on the relation between the angular resonances and the leaky guided modes properties for a poroelastic plate embedded in water

A numerical study of the guided modes in a water-saturated poroelastic plate that obeys the Biot theory is presented. In the first part, we study the leaky guided modes and the angular resonances when the slow wave does not propagate. Two types of guided modes exist. The first ones occur from coupling of the fast longitudinal wave with the shear wave; most of them propagate whatever the frequency is, provided that it is not close to their cut-off frequencies. The leaky guided modes of the second type occur from coupling of the two longitudinal waves and the shear wave. These modes do not propagate (they are highly damped) as long as the slow wave remains diffusive. We show that the characteristics of the angular resonances can be linked to the leaky guided waves of the first type in the same way as for an elastic plate. The guided modes of the second type may not be associated to angular resonances. In the second part, we consider a thinner plate in a higher frequency range so that the slow wave can propagate. Once again its influence is studied both on the leaky guided modes and on the angular resonances.     

Modelling detonation of heterogeneous explosives with embedded inert particles using detonation shock dynamics: Normal and divergent propagation in regular and simplified microstructure

This paper discusses the mathematical formulation of Detonation Shock Dynamics (DSD) regarding a detonation shock wave passing over a series of inert spherical particles embedded in a high-explosive material. DSD provides an efficient method for studying detonation front propagation in such materials without the necessity of simulating the combustion equations for the entire system. We derive a series of partial differential equations in a cylindrical coordinate system and a moving shock-attached coordinate system which describes the propagation of detonation about a single particle, where the detonation obeys a linear shock normal velocity-curvature (D_n–κ) DSD relation. We solve these equations numerically and observe the short-term and long-term behaviour of the detonation shock wave as it passes over the particles. We discuss the shape of the perturbed shock wave and demonstrate the periodic and convergent behaviour obtained when detonation passes over a regular, periodic array of inert spherical particles.     

Specifics of the combustion of aluminum-water mixtures

Experimental studies of the combustion of mixtures of micron-sized flaky aluminum powder with unthickened water in different conditions at atmospheric and high pressure in nitrogen and argon are performed. The density and composition of the mixture are varied. The regularities of the combustion have been established. A filtration wave of hot hydrogen ahead of the combustion front in samples with high porosity has been revealed. For the combustion under a nitrogen atmosphere, the pressure exponent in the burning rate law is close to 0.47 in a wide range of pressures. For the combustion under an argon atmosphere at pressures above 50 atm, the pressure exponent becomes zero or negative. Aluminum powder is demonstrated to be able to burn under conditions of a separated charge, where the fuel (aluminum) and oxidizer (water) are separated by a thin partition or brought in direct contact. The fast convective burning of aluminum-water mixtures in a semiclosed volume is discovered.     

Burning structures and propagation mechanisms of nanothermites

Nanothermites demonstrate attractive combustion characteristics such as tunable reactivity and high energy density. There is however a lack of fundamental understanding on their burning structures and reaction mechanisms due to the multi-scale complexity associated with the material and reaction heterogeneities. This gap in turn hinders the optimization of nanothermite design with desirable microstructures and controllable burning properties. In this work, a high-speed microscopy imaging system was used to reveal the burning structure of Al/CuO nanothermites and to investigate the propagation mechanism of its flame front at micron and sub-millimeter scales which have not been studied. An Al/CuO nanothermite film was fabricated as a model structure. First, the previously proposed reactive sintering was confirmed as a micron-scale burning characteristic. Then, at the sub-millimeter scale, it was demonstrated that the non-uniform burning propagation of nanothermite films is featured with distinguishable roles of the active burning sites and the pre-ignition sites. The active burning sites are clusters of reactive sintering particles and the pre-ignition sites appear in the preheating regions where Al and CuO particles have not yet participated in the reaction due to insufficient ignition energy. These pre-ignition sites form randomly and are subsequently ignited by heat transferred from the adjacent active burning sites, resulting in an active burning propagation tangentially along the propagation front. At the same time, as the thermite reaction of nanoparticles in the unburnt region is initiated, the propagation front advances in the normal direction. This experimental work reveals that the burning propagation mechanism of nanothermite films is governed by active burning propagation in both tangential and normal directions of the propagation front. Although the rates of these two modes are on the same order of magnitude, the tangential propagation of active burning is slightly faster, implying that pre-ignition sites are readily ignited with lower ignition energy.     

Characteristic regimes of premixed gas combustion in high-porosity micro-fibrous porous media

Dynamical behaviour of the premixed flame propagating in the inert high-porosity micro-fibrous porous media has been studied numerically. Effects of mixture filtration velocity, equivalence ratio and burner transverse size on the flame structure have been investigated and the regions of existence of different combustion regimes have been determined. It was found that the influence of the hydrodynamic instability on the flame dynamics is significant in the case of the moderate and high filtration velocities and this effect is negligible at the low velocities. At the moderate filtration velocities the effect of hydrodynamic instability manifests in the flame front deformation and in particular in the flame inclination. It was found that the flame can be stabilized within the whole interval of the filtration gas velocity, whereas in the ordinary porous media the standing wave is settled only at fixed value of gas filtration velocity. This finding is in line with recent experimental results on combustion in micro-fibrous porous media (Yang et al., Combust. Sci. Tech. 181 (2009), 1–16). Possible physical interpretation of the flame anchoring effect may be given on the base of present numerical analysis. At the high filtration velocities the hydrodynamic instability manifests itself in periodical appearance of the moving wrinkles on the flame front surface which forms non stationary high temperature trailing spots behind the leading part of the flame front. Such dynamics may be associated with splitting wave structures which were revealed in previous experiments (Yang et al., Combust. Sci. Tech. 181 (2009), 1–16).     

Numerical modeling of self-propagating polymerization fronts: The role of kinetics on front stability

Frontal propagation of a highly exothermic polymerization reaction in a liquid is studied with the goal of developing a mathematical model of the process. As a model case we consider monomers such as methacrylic acid and n-butyl acrylate with peroxide initiators, although the model is not limited to these reactants and can be applied to any system with the similar basic polymerization mechanism. A three-step reaction mechanism, including initiation, propagation and termination steps, as well as a more simple one-step mechanism, were considered. For the one-step mechanism the loss of stability of propagating front was observed as a sequence of period doubling bifurcations of the front velocity. It was shown that the one-step model cannot account for less than 100% conversion and product inhomogeneities as a result of front instability, therefore the three-step mechanism was exploited. The phenomenon of superadiabatic combustion temperature was observed beyond the Hopf bifurcation point for both kinetic schemes and supported by the experimental measurements. One- and two-dimensional numerical simulations were performed to observe various planar and nonplanar periodic modes, and the results for different kinetic schemes were compared. It was found that stability of the frontal mode for a one-step reaction mechanism does not differ for 1-D and 2-D cases. For the three-step reaction mechanism 2-D solutions turned out to be more stable with respect to the appearance of nonplanar periodic modes than corresponding 1-D solutions. Higher Zeldovich numbers (i.e., higher effective activation energies or lower initial temperatures) are necessary for the existence of planar and nonplanar periodic modes in the 2-D reactor with walls than in the 1-D case. (c) 1997 American Institute of Physics.