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.     

Some self-similar solutions of two-temperature hydrodynamic equations with allowance for nonlinear heat conduction and exothermic reactions

Processes occurring in plasma produced as a result of the interaction of powerful radiation fluxes with matter can be divided into three stages: absorption of radiation on the matter boundary, subsequent heating and compression of the central part of the target for the purpose of creating the conditions necessary for the initiation of an exothermic reaction and, finally, propagation of an exothermic reaction wave through the ambient matter. The present paper is devoted to an investigation of the last stage, a reaction wave igniting initially cold matter. The main method for the theoretical investigation of the processes described is a numerical solution of the equations of motion of a two-temperature gas with allowance for the physical processes occurring in a completely ionized medium: electron heat conduction, radiative losses, energy transfer between electrons and ions, and others. In view of the complicated nonlinear nature of the system of partial differential equations describing the process, searches for possible self-similar solutions are of interest. These solutions can be used as tests in calculating a complete system of equations; by means of them it is also possible to investigate asymptotic laws of exothermic reaction wave propagation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 145–151, March–April, 1986.     

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.     

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.     

Strongly exothermic explosions in a cylindrical pipe: a case study of series summation technique

In this paper, the steady state solutions for the strongly exothermic decomposition of a combustible material uniformly distributed in a heated cylindrical pipe under Bimolecular, Arrhenius and Sensitised reaction rates, neglecting the consumption of the material are examined. Analytical solutions are constructed for the governing nonlinear boundary-value problem using perturbation technique together with a special type of Hermite–Padé approximants and important properties of the temperature field including bifurcations and thermal criticality are discussed.     

Spatial motion of a chemically active medium near a caustic

A study is made of the three-dimensional problem of determining the parameters of motion of a gaseous chemically active medium near a caustic, the envelope curve of the rays of the wave fronts in the geometrical acoustics approximation. Two limiting processes whereby perturbations propagate [1] can be distinguished, depending on the ratio of the reaction time of the chemical reaction to a macroscopic time: a quasifrozen process and a quasiequilibrium process. The problem is considered in a linear formulation in [2-6] in the absence of viscosity, thermal conductivity, and chemical reactions. Nonlinear equations are derived in [7–10] for an arbitrary nondissipative medium near a caustic. In the present paper Ryzhov's method [1] is used to derive the nonlinear equations of motion of the medium for both types of process. The pressure distributions near and on the caustic itself are found for an incident step wave. The effect of the chemical reaction on how the flow parameters are distributed in the vicinity of the caustic is ascertained. Equations are derived for an inhomogeneous initially moving fluid near a caustic. A nonlinear equation containing a highest derivative of third order is obtained in the vicinity of the caustic for the case of special media in which the limiting velocities of sound in the mixture at rest are close in value. It is shown that the solution of the corresponding linear equation is expressed in the form of a quadrature from the solution for a chemically inert medium and contains oscillations near the wave fronts.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 81–91, March–April, 1977.     

Structure of a shock wave in which multiple ionization of the atoms is taking place

Ionization relaxation in a shock wave of very large amplitude is considered, the atoms behind the front of the shock wave being multiply ionized. In calculating the structure of the shock wave and the kinetics of ionization, allowance is made for the electron component of the thermal conductivity which plays an important role in this. A simplified method of calculating the kinetics of multiple ionization is proposed, and an application of this method is presented. The results of the structure calculation show that, as a result of heating by thermal conduction, the gas is considerably ionized even in front of the jump in compression, while the electron component of the thermal conductivity passes through a maximum.Translated from Zhurnal Prikladnoi Mekhnika i Tekhnicheskoi Fiziki, No. 5, pp. 11–21, September–October, 1970.     

Stability of shock waves with finite relaxation region

A theoretical investigation is made into the amplification of sound in a moving nonequilibrium medium and it is shown that an instability can arise in a sufficiently strong shock wave accompanied by an exothermic process with finite relaxation region, the instability being due to the spontaneous growth of fluctuations resulting from amplification of acoustic waves in the region of exothermic relaxation and their trapping in a narrow layer near the shock wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 176–179, September–October, 1982.I thank S. V. Iordanskii for posing the problem and great interest in the work.     

Development of two- and three-dimensional perturbations in the case of an ionization instability in a channel with nonconducting walls

An lonization instability of a plasma bounded by nonconducting walls is investigated taking into account electron thermal conduction. The wave vector is considered directed at some angle to the magnetic field direction. Perturbations with a wave vector orthogonal to the magnetic field induction vector turn out to be most unstable. A relatively simple formula to compute the neutral curve separating the stability and instability domains is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 119–123, May–June, 1976.     

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.     

Thermal mechanism of wave damping in a gas-liquid mixture

The effect of interphase heat transfer on the process of propagation of a wave in a monodisperse gas-liquid mixture is investigated. A three-wave equation of the Boussinesq type is derived and formulas for the dependence of the thermal components of the dissipative coefficients on the thermophysical parameters of the mixture are obtained. The limits of applicability of the short-wave method are determined. The theoretical and experimental values of the phase wave velocity are compared and found to be in good agreement.Yerevan. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 75–83, November–December, 1994.     

Spatial localization of thermal perturbations in heating a medium with bulk heat absorption

Solutions are constructed of a type of thermal wave describing stationary and nonstationary heating processes of a medium with constant thermal conducting and with bulk heat absorption.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 96–101, September–October, 1973.     

Reflection of a strong shock wave from an ellipsoid

The reflection from an ellipsoid of a strong shock wave (with uniform parameters behind the wave) moving along one axis of the ellipse is considered. Viscosity and thermal conductivity of the gas are not considered. A solution is sought in the vicinity of the critical point using the small parameter method [1]. The nonlinear differential equations for the dimensionless components of the gas velocity in this region are solved by the method of separation of variables with the additional condition of [2]. Analytical expressions are found for the flow parameters, which for the cases of an elliptical cylinder and ellipsoid of revolution coincide with the corresponding expressions obtained previously in [2].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 19–23, November–December, 1980.     

Regular reflection of a shock wave from a solid wall in a stream of fuel mixture

The two-dimensional stationary problem of regular reflection of a shock wave from a plane solid wall in a fuel gas mixture is examined in the case when the mixture is ignited at the intersection of the incident wave with the wall and a flame front is formed behind the reflected shock wave. The shock waves and the flame front are considered plane surfaces of discontinuity. The fuel mixture and the reaction products are considered perfect, inviscid, and non-heat-conducting gases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 161–163, July–August, 1978.     

Shock wave structure in a binary mixture of viscous gases

Shock wave structure was studied in [1] using Struminskii's model [2] with the assumption that viscosity and thermal conductivity exist only as interactions between components. The present study will obtain asymptotic solutions of the problem of shock wave structure in the Navier-Stokes approximation.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 48–54, September–October, 1984.     

Interaction between a plane shock wave and a spherical volume of hot gas

The two-dimensional axisymmetric problem of the passage of a plane shock wave through a thermal is investigated. Two known effects are confirmed, namely, the intense distortion of the shock front on passage through the thermal and a change in the geometry of the gaseous element characteristic of the late stage of evolution of the thermal. Certain new effects are also detected: the formation of a pendant shock at the outer edge of the hot zone, cumulation of a secondary shock on the axis of symmetry at the top of the thermal, and straightening of the distorted front as it travels away from the heated zone.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 96–100, January–February, 1988.     

Hypersonic flow past a wing at large angles of attack with detached shock wave

The thin shock layer method [1–3] has been used to solve the problem of hypersonic flow past the windward surface of a delta wing at large angles of attack, when the shock wave is detached from the leading edge (but attached to the apex of the wing) and the velocity of the gas in the shock layer is of the same order as the speed of sound. A classification of the regimes of flow past a delta wing at large angles of attack has been made. A general solution has been obtained for the problem of three-dimensional hypersonic flow past the wing allowing for nonequilibrium physicochemical processes of thermal radiation of the gas at high temperatures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 149–157, May–June, 1985.     

Distribution of radiant thermal flux over the surface of a sphere for hypersonic flow of a nonviscous radiating gas past the sphere

In the present study using the Newtonian approximation [1] we obtain an analytical solution to the problem of flow of a steady, uniform, hypersonic, nonviscous, radiating gas past a sphere. The three-dimensional radiative-loss approximation is used. A distribution is found for the gasdynamic parameters in the shock layer, the withdrawal of the shock wave and the radiant thermal flux to the surface of the sphere. The Newtonian approximation was used earlier in [2, 3] to analyze a gas flow with radiation near the critical line. In [2] the radiation field was considered in the differential approximation, with the optical absorption coefficient being assumed constant. In [3] the integrodifferential energy equation with account of radiation was solved numerically for a gray gas. In [4–7] the problem of the flow of a nonviscous, nonheat-conducting gas behind a shock wave with account of radiation was solved numerically. To calculate the radiation field in [4, 7] the three-dimensional radiative-loss approximation was used; in [5, 6] the self-absorption of the gas was taken into account. A comparison of the equations obtained in the present study for radiant flow from radiating air to a sphere with the numerical calculations [4–7] shows them to have satisfactory accuracy.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 44–49, November–December, 1972.In conclusion the author thanks G. A. Tirskii and É. A. Gershbein for discussion and valuable remarks.     

Model of the physico-chemical kinetics behind the front of a very intense shock wave in air

A model of the physico-chemical kinetics of the reactions taking place behind the front of an intense shock wave propagating in air with a speed of 9–14 km/s is proposed. The problem of describing the chemical reactions, namely, molecular dissociation and exchange reactions involving vibrationally excited molecules in the absence of vibrational equilibrium, is solved. The vital role of the vibrational excitation delay in the dissociation of oxygen and nitrogen is established. The rate of the exchange reaction between nitrogen molecules and oxygen atoms in the shock wave depends only slightly on the vibrational excitation level. It is demonstrated that the rate constants for thermally nonequilibrium dissociation reactions can be represented within the framework of the one-temperature approximation at constant vibrational temperatures of the dissociating species satisfying quasi-stationary conditions.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 169–182, March–April, 1995.     

Plane-parallel supersonic flow with a discontinuity

This article considers a plant-parallel supersonic flow, with a shock wave terminating within the flow; the shock wave is regarded as a distortion. A line of discontinuity is located ahead of the shock wave in the supersonic zone. The problem is solved by the method of indeterminate coefficients.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 95–100, July–August, 1970.The authors thank S. V. Fal'kovich for his valuable advice and for his evaluation of the results obtained.