On the theory of stationary velocity of propagation of an exothermic reaction front in a condensed medium

It has been demonstrated experimentally that in the combustion of many explosives and powders in the condensed phase (k-phase) an exothermic chemical reaction occurs. Although the heat release in the k-phase is usually small in comparison with the calorific value, it may play an important role in the multistage reaction in the combustion zone.Analysis of the heat balance of the k-phase reveals that in a number of cases heating of the substance before gasification is primarily due to self-heating. According to the thermocouple measurements made by A. A. Zenin, the heat release in the k-phase during combustion of nitroglycerine N powder is more than 80% of the total quantity of heat in the heated layer of the k-phase (pressure 50 atm). This makes it possible to speak of the propagation of the exothermic reaction front in a condensed medium as the first stage in the combustion of condensed systems. Cases are also known where the propagation of the reaction front is maintained only by self-heating (flameless combustion [1]), and there are cases when such propagation is not accompanied by gasification (combustion of thermites, sometimes the polymerization process). Theoretical investigations of stationary propagation of a reaction front in a condensed medium were made in [2–6]. We note that this problem is also of interest in relation to the study of various nonstationary phenomena associated with the combustion of powders [7–9]. One of the principal theoretical problems is the derivation of a formula for the velocity of propagation of the reaction front in the k-phase. The Zel'dovich-Frank-Kamenetskii method [10] was used in [2–5] in the solution of this problem.This paper is an investigation of the applicability of the Zel'dovich-Frank-Kamenetskii method to the case of propagation of a zero-order reaction front in the k phase. A method is proposed for deriving a formula for the propagation velocity of the front leading in the case of a zero-order reaction to a formula identical to that obtained using the Zel'dovich-Frank-Kamenetskii method, and this method is then used to derive a formula for the propagation velocity of a first-order reaction front in the k-phase. The upper and lower limits of the velocity given by this formula are investigated.     

Heating zone dynamics in in situ combustion

The integrodifferential equation of the quasisteady regime of a moving in situ combustion front is obtained and its exact solution is constructed in a particular case; the possibility of the heat generated at the combustion front being projected into the region ahead of the front is analyzed and the heating zone dynamics in the reservoir and the surrounding rock are investigated. In a number of studies of in situ combustion it is assumed that an increase in the water-air factor or, what amounts to the same thing, an increase in convection velocity in the reservoir leads to the total transfer of the heat into the region ahead of the combustion front [1–3]. In [3] the area of the heating zone ahead of the combustion front was calculated in accordance with the Marx-Longenheim model [4]. Below, on the basis of exact solutions of model problems it is shown that in the case of quasisteady Newtonian heat transfer between the surrounding medium, when the latter is assumed to be a thermal reservoir, i.e., maintain a constant temperature, this projection of heat is possible if the convection velocity exceeds the velocity of the combustion front. In the case of unsteady heat transfer in accordance with the Leverrier model there is no total projection of heat into the region in question; in the steady-state regime a limited heating zone, proportional in depth to the square of the difference of the convection and combustion front velocities, is formed ahead of the front.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 166–172, July–August, 1987.The author wishes to thank V. M. Entov for his valuable advice and useful discussions.     

Wave propagation in the combustion of a low-concentration aerial suspension

In the general case the convective combustion of aerial suspensions is described by the equations of mechanics of multiphase media [1]. If the volume particle content is neglected and it is assumed that in the initial stage of convective front propagation the particles are stationary, and that during combustion their temperature is constant, then the equations for describing the combustion process reduce to the equations of gas dynamics for a distributed supply of heat and mass [2, 3]. The equations and model constant mass burning rate kinetics are used to solve the plane one-dimensional problem of the combustion of an aerial suspension in part of a region bounded on one side by a fixed wall. A small parameter proportional to the mass concentration and the heat value of the fuel is introduced. The method of matched asymptotic expansions [4] is used to construct a uniformly applicable first approximation. The solution obtained describes the wave propagation in aerial suspension combustion processes. The resulting pattern includes an inclined compression wave propagated with the speed of sound followed by a convective hot reaction product front whose propagation velocity is much less (in conformity with the small parameter introduced) than the speed of sound.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 63–73, March–April, 1986.     

Convective combustion of aerosuspensions in fuel that contains the oxidant

The convective combustion of porous gunpowder and high explosives is an intermediate stage in the transition from layered combustion to detonation [1, 2]. The theory of convective combustion of such systems is developed in [3–6]. It has now become necessary to analyze the possibility of convective combustion of aerosuspensions. The present paper develops the theory of the combustion of such systems on the basis of an analysis of the equations of gas dynamics with distributed supply of mass and heat; the problem of nonstationary motion of a convective combustion front is formulated. In the homobaric approximation [7], when the pressure is assumed to be spatially homogeneous, an analytic solution to the problem is found; this determines the law of motion of the front and the distribution of the parameters that characterize the gas and the particles in the combustion zone. Necessary conditions for the transition from convective combustion to explosion are obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 49–56, September–October, 1980.I thank R. I. Nigmatulin for helpful comments and advice, and also V. A. Pyzh and V. K. Khudyakov for discussing the work.     

Two-dimensional stability of the combustion of condensed systems

The question of the combustion stability of condensed systems relative to curvature of the front is investigated in a linear approximation. Two of the simplest combustion models are examined, a gasless system and a model of flameless combustion of a solid fuel. In the first case, the combustion products are condensed, just as are the initial materials, and in the second the solid fuel is converted into a gas in which no chemical reactions occur. Boundaries of the stability of the stationary combustion mode are found. It is shown that gasless systems are less stable with respect to two-dimensional perturbations than to one-dimensional perturbations. For the flameless combustion model the result depends on the relationship between the thermophysical constants of the initial material and the products. The question of the influence of heat emission on the one-dimensional stability of the gasless composites is considered. An increase in the heat emission diminishes the stable combustion region, where a one-dimensional instability originates earlier than collapse of combustion occurs because of strong heat emission to the wall.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 51–59, September–October, 1971.     

火烧油层驱油特征的参数敏感性分析

在火烧油层驱油机理的基础上，依据油气层渗流理论，燃烧理论，建立了火烧油层驱油数学模型。用数值解法对干式和湿式两种燃烧进行了比较，得出：湿式燃烧比干式燃烧的驱油效果好。针对湿式燃烧的特点，对火烧油层驱油过程中的参数进行了敏感性分析，取得了有关结论即1）蒸汽带驱油是火烧油层过程中的一个重要机理；2）随着湿式燃烧水气比的增加，发生氧化反应的区域长度扩大，蒸汽带的温度下降，对流前缘速度增加，加速了热对流的传导，驱油效率增大；3）在湿式燃烧过程中，随着氧气利用率的降低，发生氧化反应的区域长度扩大，蒸汽带的温度下降，燃烧1立方米油砂所需空气量增加，燃烧前缘速度减少，驱油效率几乎不变；4）在湿式燃烧过程中，随着注入空气量的增加，发生氧化反应的区域长度扩大，蒸汽带的温度升高，燃烧前缘速度增加，对流前缘速度增加，加速了热对流的传导，驱油效率增大。     

Experimental flow analysis of three-dimensional separation zones in front of weirs

Some results of experimental studies are shown concerning subsonic flow in separation zones of three-dimensional turbulent boundary layers formed in front of cylindrical weirs and rectangular parallelepipeds or dashboards. The width to height ratio of the weirs was varied from 0.25 to 24, and the boundary layer thickness to weir height ratio at separation was varied from 0.2 to 2.0. Flow patterns are shown along with the effects of the setup ge-ometry, of the weir width to height ratio, of the boundary layer parameters, and of the Euler and Reynolds numbers on the flow pattern and on the coordinates of characteristic points in the separation zone. Data are furnished for determining the dimensions of three-dimensional separation zones in front of weirs. The flow and the heat transfer in three-dimensional separation zones at subsonic velocities have not yet been explored adequately. The separation data published in [1, 2, 3] are not sufficient for determining the flow pattern, the static pressure distribution, and the characteristic dimensions of a separation zone — all of which are needed for calculating the heat transfer in the separation zone [4].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 50–54, January–February, 1972.The authors thank V. S. Avduevskii for reviewing the results.     

Asymptotic analysis of stationary distribution of the front of a two-stage consecutive exothermic reaction in a condensed medium

An approximate theory of the stationary distribution of the plane front of a two-stage exothermic consecutive chemical reaction in a condensed medium is developed in the article. The method of joined asymptotic expansions is used in constructing the solutions. The ratio of the sum of the activation energies of the reactions to the final adiabatic combustion temperature is a parameter of the expansion. The characteristic limiting states of the stationary distribution of the wave corresponding to different values of the parameters figuring in the problem are shown. Approximate analytical expressions for the wave velocity and distribution of concentrations are obtained for each of the states.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 75–87, January–February, 1973.     

Application of the method of matched asymptotic expansions to the calculation of the stationary thermal propagation of the front of an exothermic reaction in a condensed medium

In this paper we use the method of matched asymptotic expansions to establish a two-term formula for the speed of propagation of the front of an exothermic reaction in a condensed medium whose thermophysical characteristics depend on the concentration of the reacting matter and the temperature. As the parameter of the expansion we use the ratio of the activation temperature to the adiabatic combustion temperature. The results are applied to the case of the combustion of nonvolatile condensed systems. We compare the approximate formula obtained with the results of a numerical integration.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 106–112, September–October, 1972.     

Investigation of the hypersonic viscous shock layer around blunt bodies in a nonuniform flow

Unseparated viscous gas flow past a body is numerically investigated within the framework of the theory of a thin viscous shock layer [13–15]. The equations of the hypersonic viscous shock layer with generalized Rankine-Hugoniot conditions at the shock wave are solved by a finite-difference method [16] over a broad interval of Reynolds numbers and values of the temperature factor and nonuniformity parameters. Calculation results characterizing the effect of free-stream nonuniformity on the velocity and temperature profiles across the shock layer, the friction and heat transfer coefficients and the shock wave standoff distance are presented. The unseparated flow conditions are investigated and the critical values of the nonuniformity parameter a_k [10] at which reverse-circulatory zones develop on the front of the body are obtained as a function of the Reynolds number. The calculations are compared with the asymptotic solutions [10, 12].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 154–159, May–June, 1987.     

Stability of the combustion process in elastic combustion chambers

High-frequency instability phenomena in rigid combustion chambers have been studied theoretically in [1–3]. This phenomenon is attributed to the interaction between the combustion processes and combustion-product fluctuations in the chamber. One of the possible mechanisms of formation of high-frequency instability is examined in [3], where the combustion rate is represented in the form of a retarded pressure functional. In this case, the problem is reduced to studying the stability of a certain distributed self-oscillating time-lag system.If the oscillation frequencies of the combustion products are comparable to the natural vibrations of the shell which forms the combustion chamber, then it is natural to expect that the elasticity of the chamber walls will affect the combustion process. Coupled effects of acoustoelastic instability can arise, in whose development the vibrations of the chamber wall play a substantial role. These effects are particularly undesirable from the point of view of the vibrational stability of combustion chambers.In this paper, a theory of high-frequency instability of stationary combustion is developed with allowance for elastic deformations of the combustion chamber walls. The theory is based on the mechanism of vibrational combustion [1–3], according to which the combustion front is assumed to the concentrated, while the velocity jump at the front is expressed through a retarded pressure functional. It is assumed that the combustion product flow is one-dimensional and isentropic and that the chamber is cylindrical. The deformations of the chamber are described via the moment theory of shells. The existence is revealed of additional instability regions produced by the interaction between the elastic vibrations of the chamber walls and the acoustic oscillations of the combustion products. The influence of the relation between the elastic and acoustic frequencies and of the structural damping factor in the combustion chamber walls on the stability of the stationary combustion process is examined. The problem discussed is treated as a mathematical model for more complex asymmetric problems in which the elastic and acoustic frequencies can be of the same order.     

甲烷/煤尘复合爆炸火焰的传播特性

为揭示甲烷/煤尘复合爆炸火焰的传播机理,利用气粉两相混合爆炸实验系统,在低于甲烷爆炸下限条件下,采用高速摄影机记录火焰传播图像,通过热电偶采集火焰温度,研究了煤尘种类以及甲烷体积分数对甲烷/煤尘复合火焰传播特性的影响。结果表明:挥发分是衡量煤尘燃烧特性的主导因素;随着煤尘挥发分的升高,燃烧反应增强,火焰传播速度升高,火焰温度升高;挥发分含量差异较小时,水分含量越低,燃烧反应越剧烈;在相同条件下,焦煤的燃烧反应强度最高,其次为长焰煤,最后为褐煤;随着甲烷体积分数的增加,煤尘颗粒的燃烧可由释放挥发分的扩散燃烧转变为气相预混燃烧,燃烧反应增强,火焰传播速度和火焰温度显著升高;热辐射和热对流作用促进煤尘颗粒热解,释放挥发分进行燃烧反应,维持复合火焰的持续传播;随着混合体系中甲烷体积分数的增加,混合爆炸机制由粉尘驱动型爆炸转为气体驱动型爆炸,燃烧反应增强;甲烷/煤尘复合爆炸火焰可由未燃区、预热区、气相燃烧区、多相燃烧区和焦炭燃烧区5部分组成,湍流扰动导致燃烧介质空间分布存在差异,使得燃烧区无规则交错分布。     

Investigation of the surface jet formed as a buoyant plume spreads over a horizontal surface

A surface buoyant jet formed as a vertically ascending buoyant plume spreads radially after contact with a free water surface is considered. In the case of a plume spreading in a water medium beneath the water-air interface the presence of three characteristic zones in the spreading jet has been experimentally shown: a zone of linear expansion of the lower jet boundary, a zone of constant jet width, and a jet compression zone. For these zones the dependence of the width and the buoyancy integrated over the vertical profile on the radial distance is established. On the basis of an integral method the fluid entrainment velocity is parametrized for each of the characteristic zones in the absence of heat transfer and wave formation on the free surface, and the dependence of the jet width, the values of the radial velocity averaged over vertical cross-sections, and the buoyancy on radial distance is found.St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 62–71, November–December, 1995.     

The pressure and temperature behind bodies with flat bases in a supersonic flow when inert and active gases are introduced into the base region

The effect of introducing active and inert gases into the base region behind two-dimensional and axisymmetric bodies on the pressure and temperature in that region is studied in the absence of heat transfer between the body and the base region. The flow in the mixing zone is assumed to be turbulent. To investigate the effect of introducing active gases on the parameters in the base region, a model of diffusion combustion is used. The base pressure is calculated by Korst's method [1]. For the velocity profile in the mixing zone an expression is used which results from integrating the equation of motion in von Mises variables. The temperature and concentrations of the components in the base region are determined from integral equations for the conservation of enthalpy and concentration, which make it possible to calculate the parameters in the base region for arbitrary flow rates of the active gas, including arbitrarily small rates. The results are given of calculating the base pressure when hydrogen and argon are blown into the base region. In the latter case computational and experimental results are compared.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 48–57, March–April, 1971.     

Ignition of a gas in a boundary layer at a heated plate

The problem of the ignition of a moving homogeneous gaseous combustible mixture in a boundary layer along a heated flat semiinfinite plate is one of the main problems of the ignition of a combustible mixture in a flow (for example, [1]). The formulation of the problem includes the two-dimensional equations of motion and the equations of the transfer of heat and of the reacting substance, written taking a chemical reaction into consideration, as well as boundary conditions, and should lead to determination of the steady-state fields of the concentration and the temperature and, by the same token, of the position of the combustion zone. Different approximate numerical solutions of the problem were analyzed in [1–5]. One of the most important characteristics of the process is the length of the ignition, i.e., the distance from the edge of the plate to the point at which, thanks to the intrinsic chemical heat evolution in the gas, the heat flux from the plate to the gas becomes equal to zero. In the present work, for the case of large values of the activation energy of the chemical reaction and a sufficiently great temperature difference between the wall and the flow, an approximate expression is obtained for the length of the ignition.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 142–148, September–October, 1977.The authors thank V. M. Shevtsov for his aid in making the calculations.     

Structure of detonation waves in gas suspensions of fuel containing the oxidant

The structure of detonation waves in air suspensions of unitary fuels (fuels containing an oxidant such as gunpowder and high explosives) is investigated. In such systems, complete combustion of the particles is possible at a high mass concentration of the fuel. As a result, the structure of detonation differs from that in gas-drop [1–3] and gas [4, 5] mixtures. The shock adiabats characteristic for air suspensions [6, 7] are used to investigate the field of integral curves which describe the structure of detonation waves in disperse media. Calculated distributions of the parameters which characterize the gas and particles in the detonation front are given. The influence of the rate of combustion of the particles and the intensity of interphase friction on the structure of the detonation is investigated. Results of the calculation of the structure of relaxation shock waves in gas suspensions of the solid fuel of rockets are given in [8]. Unsteady problems of convective combustion and the transition of combustion of air suspensions into detonation are analyzed in [9, 10].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 47–53, September–October, 1981.     

On the possibility of blowing a gas jet into a supersonic flow without formation of a three-dimensional boundary-layer separation zone

We consider the flow formed by the interaction of a supersonic flow and a transverse sonic or supersonic jet blown at right angles to the direction of the main flow through a nozzle whose exit section is in a flat wall. When a gas jet is blown through a circular opening [1] the pressure rises in front of the jet because of the stagnation of the oncoming flow. This leads to separation of the boundary layer formed on the wall in front of the blowing nozzle. The resulting three-dimensional separation zone leads to a sharp increase in the pressure and the heat fluxes to the wall in front of the blowing nozzle, which is undesirable in many modern applications. The aim of the present investigation was to find a shape of the exit section of the blowing nozzle for which there is no three-dimensional separation zone of the boundary layer in front of the blowing nozzle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 162–165, May–June, 1979.     

Stationary propagation of an exothermic-reaction front in a condensed medium

The problem of the propagation of an exothermic-reaction front in a condensed medium has been examined in a number of reports [1–8], in which various statements of the problem have been analyzed, the conditions of existence and uniqueness of a solution determined, and different approximate methods of determining the propagation velocity of the front suggested. In [1–6] the examination was conducted for a specific class of heat-release functions corresponding to the kinetics of exothermic transformation in homogeneous condensed systems. The propagation of the reaction front in heterogeneous sytems (condensed mixtures) was studied in [7, 8] for particular forms of the heat-release function corresponding to certain simplifying assumptions concerning the structure of the heterogeneous medium. In connection with the complexity of the structures of real condensed systems [9–11] and the diversity of the kinetic laws of interaction, in the present report the available results on a broader class of heat-release functions are generalized, and the possible approximate methods of determining the propagation velocity are analyzed.