Two-dimensional gas flows under heterogeneous combustion of solid porous media

Two-dimensional unsteady gas flows in porous media with heterogeneous-combustion centers are investigated under forced filtration and free convection. With the use of numerical methods, it is shown that complex gas flows including vortex ones can arise under the combustion of solid porous media. In the case of forced filtration, the gas tends to flow around the heated portion of an object preferring to flow along cold regions. Under natural convection, the vortex gas flows, which can exist for a reasonably long time and strongly affect the oxidizer inflow into the reaction zone, arise at the initial moment of the process in the combustion zone and in its vicinities.     

Numerical model of two-dimensional heterogeneous combustion in porous media under natural convection or forced filtration

A novel mathematical model and original numerical method for investigating the two-dimensional waves of heterogeneous combustion in porous media are proposed and described in detail. The mathematical model is constructed within the framework of the model of interacting interpenetrating continua and includes equations of state, continuity, momentum conservation and energy for solid and gas phases. Combustion, considered in the paper, is due to the exothermic reaction between fuel in the porous solid medium and oxidiser contained in the gas flowing through the porous object. The original numerical method is based on a combination of explicit and implicit finite-difference schemes. A distinctive feature of the proposed model is that the gas velocity at the open boundaries (inlet and outlet) of the porous object is unknown and has to be found from the solution of the problem, i.e. the flow rate of the gas regulates itself. This approach allows processes to be modelled not only under forced filtration, but also under free convection, when there is no forced gas input in porous objects, which is typical for many natural or anthropogenic disasters (burning of peatlands, coal dumps, landfills, grain elevators). Some two-dimensional time-dependent problems of heterogeneous combustion in porous objects have been solved using the proposed numerical method. It is shown that two-dimensional waves of heterogeneous combustion in porous media can propagate in two modes with different characteristics, as in the case of one-dimensional combustion, but the combustion front can move in a complex manner, and gas dynamics within the porous objects can be complicated. When natural convection takes place, self-sustaining combustion waves can go through the all parts of the object regardless of where an ignition zone was located, so the all combustible material in each part of the object is burned out, in contrast to forced filtration.     

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).     

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.     

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.     

Combustion and explosion of hydrogen-air mixtures under conditions imitating elements of gas-laden rooms

The time evolution of the processes of combustion and explosion with regard to safety problems in handling reactive gas mixtures was studied. The explosion safety for reaction volumes and gas-laden rooms can be assessed only if data on the possible consequences of the emergencies under conditions close to real ones or modeling them are available. The propagation of nonplanar explosion waves with a short positive phase in volumes with variable cross section is an essentially unsteady process. Until recently, the regularities of the evolution of the characteristics of such waves during their propagation in a reactive mixture with heat release virtually have not been studied. At the same time, these processes determine the character of combustion, and, therefore, the possibility of their formalization provides the opportunity to treat the entire variety of combustion regimes. Only a knowledge of general laws of the interaction of unsteady gasdynamic processes and gaskinetic processes in a reactive medium makes it possible to control combustion regimes purposefully and effectively. The present work is devoted to studying the propagation of combustion in cavities with a geometry imitating elements of reaction volumes and rooms filled with a hydrogen-air mixture. Results for a pyramid-shaped cavity capable of cumulating flows and waves are considered and compared to those obtained using a conical cavity [1–5].     

超燃冲压发动机推进性能理论分析

超燃冲压发动机的正推力问题和超声速燃烧的稳定性问题是制约超燃冲压发动机发展的两个关键气动物理问题.虽然经过50多年的研究,但是目前国内外对这两个关键问题的机理还没有研究清楚.文章首次将CJ爆轰理论应用于超燃冲压发动机推进性能分析,给出了这两个关键气动问题的理论分析结果.分析结果表明,燃烧室入口空气静温对发动机的推进性能产生重要影响.当爆轰波的爆速大于隔离段内空气来流的速度时,会向隔离段上游传播,导致发动机不起动.飞行Mach数Ma=6~8是超燃发动机的临界不稳定范围,飞行Mach数Ma>9,超声速燃烧将变得稳定.      

Ignition and transient dynamics of sub-limit premixed flames in microchannels

We examine, via two-dimensional numerical simulation of a model system, some unsteady transient ignition scenarios and sustained oscillatory combustion modes that can occur in a single-pass, conductive channel, premixed microburner. These issues are relevant to the problem of ignition, evolution to stable combustion and the operational modes of microcombustors. First, we describe an unsteady ignition sequence that may occur when a single-pass microburner with initially cold walls has its exit walls heated and maintained at a fixed temperature. In particular, we demonstrate that as the heat from the exit walls propagates down the microburner walls, a reaction wave is driven rapidly down the channel towards the inlet via a sequence of oscillatory ignition and quenching transients. This scenario has been observed experimentally during the ignition of a single-pass microburner. Secondly, we show how an initial axial wall temperature gradient can lead to a variety of sustained combustion modes within the channel, including stable stationary flames, regimes of periodic motion involving quenching and re-ignition, regimes of regular oscillatory combustion, and regimes consisting of a combination of re-ignition/quenching events and regular oscillatory motions, all of which have been observed experimentally.     

激光诱导等离子体的气体动力学和燃烧波扩展速度研究

针对激光对熔石英材料产生致燃损伤过程中存在的激光支持燃烧波,考虑激光作用的温度残余、目标形貌的改变、喷溅物质分布、目标表面气流状况的分布等效应,分阶段对激光支持燃烧波的过程进行建模和仿真研究.通过建立二维轴对称气体动力学模型,模拟研究包含逆韧致辐射、热辐射、热传导和对流过程在内的激光能量传输过程.此外,依据激光支持燃烧波在可见光波段具有明显的辐射特征这一特点,利用阴影法测量了激光对熔石英致燃损伤过程中的燃烧波扩展速度,得到了燃烧波演化过程图像.研究结果表明:在平行激光束作用下,燃烧波的传播是稳态的,气体动力学行为比较稳定;在聚焦激光束作用下,燃烧波的传播是非稳态的.模拟结果中得到的激光支持燃烧波扩展速度及气体动力学结构与实验结果和理论推导结果符合得很好,验证了理论模型的正确性.     

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.     

Measurements of the critical initiation radius and unsteady propagation of n-decane/air premixed flames

Unsteady flame propagation, the critical radius for flame initiation, and multiple flame regimes of n-decane/air mixtures are studied experimentally and computationally using outwardly propagating spherical flames at various equivalence ratios and pressures. The transient flame speeds, trajectories, and critical radius are measured. The experimental results are compared with direct numerical simulations using detailed high temperature kinetic models. Both experimental and numerical results show that there exist multiple flame regimes in the unsteady spherical flame initiation process. The transition between the flame regimes depends strongly on the mixture equivalence ratio (or Lewis number). It is found that there is a critical flame radius and that it increases dramatically as the mixture equivalence ratio and pressure decrease. The large increase of critical flame radius leads to a dramatic increase of the minimum ignition energy. Furthermore, the flame thickness and the radical pool concentration change significantly during the transition from the ignition flame regime to the self-sustained propagating flame regime. For the same steady state flame speeds, the predicted unsteady flame speeds and the critical flame radius differ significantly from the experimental results. Moreover, different chemical kinetic mechanisms predict different unsteady flame speeds. The existence of multiple flame regimes and the large critical radius of lean liquid fuel mixtures make the ignition of lean mixtures at low pressure and the development of a validated kinetic model more challenging. The unsteady flame regimes, speeds, and critical flame radius should be included as targets of future kinetic model development for turbulent combustion modeling.     

Mathematical modeling of convective-conductive heat transfer in a rectangular domain in a conjugate statement

The results of mathematical modeling of convection of a viscous incompressible liquid in a rectangular domain with sources of mass input and output are presented. A conjugate statement within the framework of the Boussinesq approximation is used. The regimes of forced and mixed convection in a domain have been investigated. The domain has two vertical walls and one horizontal wall of finite thickness, two zones of liquid input and output, and a free surface. A plane nonstationary problem within the framework of the Navier-Stokes model for the liquid phase and the heat conduction equation for the solid phase are considered. The distributions of the hydrodynamic parameters and temperatures characterizing the main regularities of the processes under investigation have been obtained. Circulation flows have been identified. The vortex formation mechanism and the temperature distribution in the solution domain under the regimes of forced and mixed convection and different locations of mass input and output zones have been analyzed. It has been found that natural convection should be taken into account when modeling convective heat transfer with Gr number values from 10⁵ and higher.     

Propagation of Cellular Modes of Titanium-Powder Layer Combustion in Air Channels,Allowing for the Effect of Natural Convection of Gas

In this paper, we have studied the effect of impurity and inert gases on the formation and propagation of cellular-combustion regimes for their inhomogeneous distribution above the surface of the reacting metal layer. The gas-dynamic aspects of the formation and steady propagation of inhomogeneous wave structures in the combustion of a titanium powder layer in through and semi-closed inclined air canals and in channels with uneven loading are considered. The gas composition heterogeneity over the reaction zone and the gas stratification, i.e., the stratification of a gas mixture of different densiies above the reacting layer, are shown to lead to the formation of inclined non-uniform and cellular fronts under conditions of a lack of active gas in the reaction zone and the loss of stability of the planar front.     

Spinning combustion regimes in gasless systems containing one melting component

The propagation of a gasless combustion wave in a continuous cylindrical sample pressed from a mixture of solid reactants has been numerically simulated with allowance made for the melting of one of the components. The melting point of the component has been assumed to be equal to the reaction rate “cutoff” temperature. Symmetric and asymmetric combustion regimes can take place in the sample, depending on the sample radius. The reaction rate cutoff temperature is an additional perturbation factor in the propagation of the gasless combustion wave.     

Characteristic analysis of low-velocity gas filtration combustion in an inert packed bed

This paper investigates the low-velocity filtration combustion of lean methane–air mixtures occurring in inert packed beds by using a modified one-temperature model, considering the axial thermal diffusion owing to the convective gas–solid heat transfer. Based on the scaling analysis of various transport terms in different conservation equations, a high-activation energy asymptotic method is applied in the flame zone and results in a set of powerful analytical solutions for combustion macrocharacteristics under the fully developed conditions. These are then combined with the eigenvalue method of the modified one-temperature model in the whole flow region to study the flame behaviour analytically and numerically. Our results have shown that the combustion wave velocity is a key characteristic parameter in the filtration combustion process. Compared with other existing theoretical results, the present analytical solutions demonstrate the intricate relationships among the combustion wave velocity, the flame speed, the peak flame temperature and the effects of the variable thermo-physical properties, and show better prediction performance for the combustion wave velocity, the flame speed and the peak flame temperature. Excellent agreements with experimental results have been observed, especially for very lean filtration combustion with stream-wise propagating combustion fronts.     

Combustion waves in composite solid material of shell–core type

In this article, an asymptotic and numerical analysis of combustion wave propagation in shell–core composite solid energetic material is undertaken based on the diffusional–thermal model with an overall Arrhenius reaction step. Flame speed and structure are found for a broad range of parameter values. Two different regimes of flame propagation are identified. In the weak recuperation regime, the temperatures of the shell and core are monotonic functions of the coordinates, and they differ only slightly in the reaction zone of the flame. In the strong recuperation regime, the temperature of the shell is significantly higher than that of the core and has a sharp peak in the reaction zone with the maximum value exceeding the adiabatic flame temperature for pure energetic material. It is found that the highest level of flame acceleration in the composite material can be attained in the strong recuperation regime. The competition of these flame propagation regimes may lead to the coexistence of multiple combustion waves travelling with different velocities. The stability is investigated of combustion waves in the practically important strong recuperation regime.     

Development of an explosion from an initiation source in a liquid high explosive

A numerical analysis of the development of combustion and explosion from a reaction hotspot in the bulk and in a thin layer of a liquid explosive placed between two flat solid surfaces is performed. A comparison of the theoretical results with experimental data shows that a satisfactory agreement between the measured and calculated flame speeds is possible only under the assumption of a multifold increase in the burning surface area due to its instability. An estimate of the parameters of the shock wave generated by an accelerating flame shows that the mechanisms of shock-wave and cavitation initiation of detonation cannot be ignored in analyzing the regimes of unsteady combustion of liquid explosives.     

The NMR microimaging studies of the interplay of mass transport and chemical reaction in porous media

PFG NMR is employed to perform a comparative study of the filtration of water and propane through model porous media. It is shown that the dispersion coefficients for water are dominated by the holdup effects even in a bed of nonporous glass beads. It is demonstrated that correlation experiments such as VEXSY are applicable to gas flow despite the large diffusivity values of gases. The PFG NMR technique is applied to study the gravity driven flow of liquid-containing fine solid particles through a porous bed. The NMR imaging technique is employed to visualize the propagation of autocatalytic waves for the Belousov-Zhabotinsky reaction which is carried out in a model porous medium. It is demonstrated that the wave propagation velocity decreases as the wave crosses the boundary between the bulk liquid and the flooded bead pack. The images detected during the catalytic hydrogenation of alpha-methylstyrene on a single catalyst pellet at elevated temperatures have revealed that the reaction and the accompanying phase transition alter the distribution of the liquid phase within the pellet.     

Combustion regimes of particle-laden gaseous flames: influences of radiation,molecular transports,kinetic-quenching,stoichiometry

We study flat flames propagating steadily in a reactive gaseous premixture which is seeded with an inert solid suspension. Our main assumptions are: (i) the two-reactant, one-step overall reaction we choose as the combustion process has a rate which vanishes at and below a prescribed temperature (Tc) and resumes the Arrhenius form at higher temperatures; (ii) both phases are considered as continua and have the same local speed and temperature; (iii) radiation among the particles follows the Eddington approximation specialized to a grey medium and the attenuation length markedly exceeds the conduction - convection length in the gas; (iv) the activation energy is large.

The first regimes we consider comprise a thin flame front (dominated by molecular transports, convection and chemistry) embedded in much thicker radiation - convection zones. Jump conditions across the former are derived analytically and then used as targets in a shooting method to analyse the thickest zones and compute the burning speed (U). Such regimes only exist for equivalence ratios () above a load-dependent critical value which corresponds to a turning point of the U() curve. This turning point is due to radiative heat losses from the thin flame front to the cooler adjacent zones, which lead to extinction.

Over restricted, well defined ranges of composition other regimes may also exist, which have monotonic temperature profiles culminating slightly above Tc. When they are too thick to be affected by molecular transports and are thus similar to coal-dust -air flames, their structure, domain of existence and speed are investigated analytically and numerically. The corresponding U() curve exhibits an upper limit equivalence ratio * characterized by an end-point, beyond which such regimes cannot exist. The influence of molecular diffusion is then accounted for and shown to modify the results only slightly.     

Numerical study of sporadic combustion waves in straight channels of different diameters

The dynamics of flames propagating in straight channels filled with a stationary low-Lewis-number premixed gas mixture is studied numerically. A method for determining the propagation velocity of a sporadic combustion wave consisted of separate flame spots is proposed. Dependencies of the sporadic combustion wave propagation velocity, the residual fuel concentration and the number of flame spots on the channel size and the value of radiation heat losses are obtained. Analysis of numerical results show that for the channels of diameter exceeding some value the number of separate cup-like fragments constituting sporadic combustion wave is proportional to the channel cross-sectional area. At smaller diameters, the number of flame spots changes insignificantly and is one or two. It is shown that one of the universal characteristics of the sporadic combustion wave depending only on mixture properties but independent on system geometry is the area necessary to accommodate one reacting spot. Flame velocity which is another fundamental combustion characteristic is found to be almost independent on channel size starting from some critical diameter. This diameter, however, depends on mixture properties or radiative heat loss intensity and corresponds to the sporadic flame containing from several to ten reacting spots. Thus, the main properties of sporadic combustion waves in wide channels can be determined by numerical modeling of the flame propagation in the relatively narrow channels in which the flame consists of 1–10 cup-like fragments.