On the question of the stability of powder combustion in a half-closed space

The influence of gas temperature perturbations on the stability of powder combustion in a rocket chamber is investigated theoretically on the basis of the Zel'dovich-Novozhilov theory of powder combustion. The influence of the bow space adjacent to the burning channel is also examined.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 74–79, November–December, 1971.     

Effect of condensed powder phase reactions on the stability of steady-state combustion processes

A study has been made of the low-frequency stability of powder combustion in a semiclosed chamber, working within the framework of a linear theory with account taken of condensed-phase (k-phase) inertia and evolution of thermal energy. The case treated is that of the first-order reaction. It is shown that k-phase exothermic chemical decomposition increases the stability of the combustion process. The results of numerical computations are interpreted.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 102–111, September–October, 1973.     

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.     

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.     

The necessary conditions for stable combustion of a powder in a half-closed chamber

The low-frequency stability of the steady-state combustion cycle is investigated in linear approximation for a powder in a half-closed chamber, taking account of incompleteness of combustion, heat losses at the walls, and dynamic erosion. The necessary conditions for stable combustion are obtained. Qualitative conclusions are drawn of the incompleteness of the chemical reactions taking place and of the destabilizing effect of thermal losses and erosion on the combustion process. Only two out of three possible steady-state mechanisms are stable. The existence of limits of combustion with respect to pressure is shown.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 90–98, November–December, 1972.     

Nonstationary problems of the combustion of aerosuspensions in fuel that contains the oxidant

A study is made of one-dimensional nonstationary problems of the combustion and detonation of aerosuspensions of unitary fuels or propellants, which contain the oxidant as well as the combustible material (gunpowder, high explosives). A numerical analysis is made of the damping of the convective combustion which occurs at relatively low mass concentrations of the fuel; the critical concentration dividing the damped and the detonation regimes is determined. It is shown that the realization of the damped or detonation regime of convective combustion at a given concentration is completely determined by the gas dynamics of the relative motion of the gas and the particles (two-velocity effect), this being governed by the coefficient of friction.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 22–27, January–February, 1981.     

Investigation of the stability of a stationary exothermic reaction front in a condensed phase

A model system of combustion theory describing an exothermic reaction in a condensed phase is investigated. The Arrhenius dependence of reaction rate on temperature is replaced by a piecewise-constant dependence. This makes it possible to find the distribution of the quantities in the stationary wave and to investigate the stability of the solution with respect to one-dimensional perturbations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 115–113, January–February, 1985.The author is grateful to G. G. Chernyi for his constant interest in the work.     

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.     

Study of the extinction of gunpowder in the combustion model with a variable surface temperature

The results of a calculation of the rate of transient combustion of gunpowder during a fall in pressure are presented; these are obtained by the numerical integration of the equations of transient-combustion theory, allowing for the variable surface temperature of the k phase. For rapid and severe pressure drops extinction always occurs, no introduction of special extinction conditions being required. The change in the rate of burning during the extinction process is of a smooth nature.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 92–100, May–June, 1973.     

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.     

Solid propellant combustion in the presence of photoirradiation

Previous studies of the nonsteady processes associated with the irradiation of propellants with light have chiefly been devoted to the question of ignition [1–3]. It is also important to consider the effect of such an easily controlled influence as light on the propellant combustion process. We have attempted to estimate the dependence of the propellant burning rate on the intensity of the luminous radiation. Cases of steady-state combustion and combustion in the presence of a light flux varying harmonically with time are considered. It is assumed that the incident light flux is absorbed in the solid phase in accordance with the Bouguer-Lambert exponential law with constant transparency index. Steady-state combustion is considered within the framework of the Zel'dovich theory [4]. It is shown that in the steady state irradiation is equivalent to a certain increase in the initial temperature of the propellant. In the case of combustion with irradiation this makes it possible to use the data on steady-state combustion without irradiation. Nonsteady combustion in the presence of a periodically varying light flux is described with the aid of the Novozhilov model [5]. A correction to the mean burning rate (u °), proportional to the square of the light flux amplitude, is obtained. In the case of an exponential dependence of the burning rate on initial temperature the correction u ° is negative. The effect of irradiation on the stability of the steady-state propellant combustion mode is discussed.Translated from Zhumal Prikladnoi Mekhaniki i Tekhnicneskoi Fiziki, No. 5, pp. 70–77, September–October, 1971.In conclusion the authors thank O. I. Leipunskii and V. B. Librovich for their valuable advice.     

Multizone combustion of condensed systems

In the general case the combustion of condensed systems is of a stage-wise character and the combustion front is multizone [1, 2]. Following the investigation of two-zone models [3–5] it became clear that, during multizone combustion, one of the zones of heat evolution is the controlling zone. The velocity of the front is equal to the velocity of the controlling zone; however, with a change in the parameters of the system, there is the possibility of a transition of the controlling role from one zone to another, as well as of the coalescence and splitting of zones. This paper discusses a generalization of the two-zone problem which makes it possible to go over to the analysis of a complex, multizone front and shows that, for a front with two reactions (in the condensed phase and in the gas) and with dispersion, there are in all three possible arrangements of the zones of heat evolution (two three-zone variants and one two-zone variant). All possible types of dependence of the combustion rate on the depth of the dispersion are found.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 99–105, November–December, 1972.     

Stability of surfaces of strong discontinuity in gases

The existence of solutions with surfaces of strong discontinuity is one of the principal features of the continua whose motions are described by systems of differential equations of hyperbolic type. Shock waves in gas dynamics, magnetohydrodynamics and in solids, detonation waves and combustion fronts, contact discontinuities, etc. are well-known examples of these surfaces. The discontinuities are usually investigated in accordance with the following scheme: 1) derivation of the boundary conditions on the discontinuity from the input system of differential equations in integral form; 2) verification of the fulfilment of the evolution conditions; 3) solution of the problem of the discontinuity structure and, when the occasion requires, obtaining supplementary boundary conditions; 4) investigation of the stability of the discontinuity. Only after obtaining positive results in all fours stages can we assert that the existence of the discontinuity is theoretically justified and that it can be used for constructing the solutions of particular boundary value problems. In the present paper attention will be concentrated on the problem of the stability of discontinuities, all the material, with the exception of the general results of Sec.1, being concerned with gas media and relating to discontinuities on whose surface the normal mass flow is nonzero. Having no way of exploring all the aspects of the problem of the stability of discontinuities in the same detail within the limited context of this paper, the authors hope to demonstrate the most general ideas and approaches which could subsequently be used to investigate the stability of discontinuities in various particular models of continua.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 3–22, March–April, 1996.     

The convective instability of Maxwell fluid-saturated porous layer using a thermal non-equilibrium model

A linear stability analysis is carried out to study viscoelastic fluid convection in a horizontal porous layer heated from below and cooled from above when the solid and fluid phases are not in a local thermal equilibrium. The modified Darcy–Brinkman–Maxwell model is used for the momentum equation and two-field model is used for the energy equation each representing the solid and fluid phases separately. The conditions for the onset of stationary and oscillatory convection are obtained analytically. Linear stability analysis suggests that, there is a competition between the processes of viscoelasticity and thermal diffusion that causes the first convective instability to be oscillatory rather than stationary. Elasticity is found to destabilize the system. Besides, the effects of Darcy number, thermal non-equilibrium and the Darcy–Prandtl number on the stability of the system are analyzed in detail.     

Stability of the replacement of a non-Newtonian fluid layer in a porous medium

When petroleum is extracted from strata by replacing it with other fluids, the question arises of the stability of the interface. Uniformity in the injection horizons is in practice achieved by such methods as using polymer additives to thicken the replacing fluid or introducing an intermediate layer with non-Newtonian properties between the replacing fluid and the fluid being replaced. In this article the stability of the interface of non-Newtonian fluids being filtered exponentially is investigated in a linear formulation. The condition governing the stability of the interface of two non-Newtonian fluids is found and the influence of the thickness of the intermediate layer on the stability is also demonstrated. The presence of the layer is found to be essential for certain parameters of fluids moving in a porous medium if the replacement is to be stable.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 183–186, March–April, 1976.The author wishes to thank V. N. Nikolaevskii for suggesting the subject for this investigation and A. T. Listrov for his constant interest in the work.     

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.     

Simulation of the thermal recovery process in a layered reservoir

The thermohydrodynamic interaction of the layers in a layered oil reservoir in the presence on in situ combustion is considered.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 122–128, May–June, 1994.     

Modeling of an intense-noise-generating flow

The possibility of creating a model flow generating noise spectra characteristic of an internal combustion engine exhaust without combustion processes is demonstrated. Some data on the spectra of acoustic disturbances produced by changes introduced into the gas flow behind the cylinder exit are presented. Possible ways of acting on the large-scale hydrodynamic structures in the flow in order to attenuate the induced acoustic oscillations are discussed.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 83–91, March–April, 1995.     

Calculation of one transient mode of combustion of a condensed system

A one-dimensional process representing the combustion of a powder sample on a metal substrate at constant pressure is considered on the basis of a two-phase model of the thermal decomposition of a condensed system. The results of numerical computer calculations are presented. Qualitative comparison is made with experiment.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 23–30, January–February, 1972.     

Effect of nonisothermality of the surface of a thin profile on the stability of a laminar boundary layer

Investigations of the stability of a subsonic laminar boundary layer have shown that, other things being equal, the stability of the laminar flow is considerably improved by cooling the entire surface of the body to a constant temperature T_w=const lower than the temperature of the free stream [1–3]. This is attributable to an increase in the critical Reynolds number of loss of stability and a decrease in the range of unstable perturbations of the Tollmien-Schlichting wave type when the surface is cooled. Recently, in the course of investigating the stability of laminar flow over a flat plate it was found [4, 5] that a similar improvement in flow stability can be achieved by raising the temperature of a small part of the surface near the leading edge of the plate. In this study we examine the possibility of delaying the transition to turbulent flow by creating a nonuniform temperature distribution along the surface of thin profiles, where the development of an adverse pressure gradient in the outer flow has a destabilizing effect on the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 36–42, September–October, 1986.In conclusion, the authors wish to thank M. N. Kogan for useful discussions of their results.