Nonsteady burning of a solid propellant in a gaseous oxidizer flow

The burning of a solid propellant is investigated for nonsteady heat propagation in the induction zone. The equation of heat conduction in the propellant is solved in finite form for the case of a sharp change in burning rate; the time dependence of the temperature gradient at the propellant surface is obtained and used to investigate the mechanism of collapse of the diffusion flame above the surface. The combustion stability of a propellant burning in a channel with a large free volume is analyzed. The perturbations of the gas-dynamic quantities are related with the perturbations of the burning rate and hence with the properties of the induction zone in the solid phase. An analysis of the dispersion relation for the limiting case of propagation of acoustic waves in a stationary gas shows that the longitudinal acoustic perturbations that develop in the channel may grow with time, interacting with the heated subsurface layer of propellant.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fizikt, No. 4, pp. 44–52, July–August, 1971.In conclusion the author thanks B. V. Librovich for formulating and discussing the problem and A. G. Istratov and V. G. Markov for their valuable comments.     

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.     

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.     

Propagation of an ion jet near a dielectric surface

Difficulties in determining experimentally the local electrical parameters of unipolar-charged jets are arousing interest in the theoretical investigation of electrogasdynamic (EGD) flows. Free EGD jets were examined, for example, in [1–3]. In order to control the charge on the dielectric parts of aircraft surfaces, which results from their static electrification and may have certain negative consequences [4], and, moreover, to influence the flow in the boundary layer use is being made of unipolar-charged jets propagating near the dielectric [5, 6]. In [6] the case of an ion jet near a dielectric surface possessing surface conductivity was investigated. In these circumstances it is possible to neglect charge diffusion, which considerably simplifies the problem. Space charge diffusion was taken into account in [7], but subject to certain very important simplifications. The author has calculated the electrical parameters of a unipolar-charged jet propagating in a viscous incompressible gas near an ideal dielectric plate, with allowance for surface and polarization charges and, moreover, the diffusion processes near the surface. An asymptotic solution is obtained for the equations of the ionic diffusion layer as the ratio of the thickness of the diffusion layer to the thickness of the hydrodynamic boundary layer tends to zero.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 174–180, September–October, 1984.The author is grateful to V. V. Mikhailov and A. V. Kazakov for valuable advice and comments.     

Solute dispersion in a pulsating flow

The one-dimensional model proposed by Taylor [1] of the dispersion of soluble matter describes approximately the distribution of the solute concentration averaged over the tube section in Poiseuille flow. Aris [2] obtained more accurately the effective diffusion coefficient in Taylor's model and solved the problem for the general case of steady flow in a channel of arbitrary section. Many papers have been published in the meanwhile devoted to particular applications of this theory (for example, [3–5]). Various dispersion models have been constructed [6–8] that make the Taylor—Aris model more accurate at small times and agree with it at large times. The acceleration of the mixing of the solute considered in these models in the presence of the simultaneous influence of molecular diffusion and convective transport also operates in unsteady flows. In particular, the presence of velocity pulsations influences the growth of the dispersion even if the mean flow velocity is equal to zero at every point of the flow. In the present paper, the Taylor—Aris theory is extended to the case of laminar flows with periodically varying flow velocity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 24–30, September–October, 1982.     

Similarity autooscillations in a plane jet

Experimental investigations into the stability of a plane jet [1, 2] show that after the stationary flow has lost its stability a stable autooscillatory regime arises. In the present paper, an autooscillatory flow in a jet is studied theoretically on the basis of a plane-parallel flow in a fairly wide channel in the presence of a field of external forces. The external forces are such that at zero amplitude of the autooscillations they produce a Bickley—Schlichting velocity profile. The excitation of the secondary regimes is studied by the methods of bifurcation theory [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 26–32, May–June, 1979.We thank M. A. Gol'dshtik and V. N. Shtern for discussing the formulation of the problem and the results.     

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.     

Heat transfer associated with viscous two-dimensional channel flow in a transverse acoustic field

An analytic solution is proposed for the problem of the effect of a transverse resonant acoustic field on the heat transfer process in laminar two-dimensional channel flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 41–49, May–June, 1985.The author wishes to thank V. E. Nakoryakov for formulating the problem and discussing the results.     

Gas flow in a channel in the presence of distributed injection of the gas or of a combustible gas mixture from its walls

The distributed injection of gas or of a combustible gas mixture from the walls of a plane or an axisymmetric channel into a stream of inert gas flowing through the channel is analyzed. This problem is solved using models of an ideal incompressible liquid and an ideal gas to describe the motion in the injected gas and in the oncoming stream. Integral equations are obtained in the approximation of thin-layer equations without allowance for transverse pressure gradients, for the pressure in the channel, and in the case of injection without heat release; these are solved analytically by methods of operational calculus, while in the case of combustion of the injected mixture they are solved numerically. This allows one to find the appropriate form of the contact surface separating the injection region from the oncoming stream, the position of the flame front, and the distribution of the gasdynamic parameters. It turns out that with allowance for the compressibility of the gas of the oncoming stream or of the injected gas the flow can exist only over a finite section of the channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 137–144, November–December, 1977.The author is grateful to V. A. Levin for constant attention to the work and helpful comments.     

Effects of reagent consumption and heat loss in ignition in a vessel

Two approximate analytical methods are widely used in research on thermal ignition: the stationary theory [1] and the nonstationary one [2]. The first predicts the critical explosion conditions very closely. Direct numerical integration has been used [3] to obtain a solution for thermal ignition, which indicated that ignition near the heated walls can accompany ignition at the center. The difference between the critical conditions for ignition at the wall and self-ignition can be defined only from the interaction between the initial and boundary conditions. The extent of combustion is substantial in both cases [1], and it subsequently plays a substantial part in setting up the temperature conditions in the vessel. A study is made here of the thermal decomposition of methyl nitrate vapor, which incorporates the diffusion and finite reaction rate. Monte Carlo simulation is used with a planar electrically conducting medium [4].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 192–196, January–February, 1975.     

Particle deposition on a channel wall in a turbulent disperse flow with gradient

Kinetic ideas about the motion of a set of particles (droplets) in a turbulent gas flow with gradient are used to derive a Fokker-Planck equation for the case of sufficiently large particles (more than few microns). This equation describes the process in which they are deposited on the wall of a channel. Satisfactory agreement has been obtained between the numerical solution to this equation for the deposition rate and the experimental data published in the literature. Under the assumption that the parameters of the carrier gaseous flow vary fairly slowly, a generalized equation is derived for particle diffusion in turbulent flow. This takes into account the intensity gradient of transverse pulsations in the velocity of the carrier gaseous flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 57–63, July–August, 1985.     

Convective stability of a vertical layer of a non-newtonian liquid

We consider the convective stability of a non-Newtonian (nonlinearly viscous) liquid in a two-dimensional vertical channel. We solve a nonlinear boundary value problem concerning plane-parallel stationary convection for the case of piecewise-linear and power-law type rheological characteristics. We discuss the problem concerning the stability of equilibrium and of stationary motions.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 88–95, September–October, 1973.The authors thank D. V. Lyubimov for his help in carrying out the calculations.     

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.     

On the optimal distribution of the flow rate of gas blown through the side walls of the channel of a de plasmotron (plasma generator)

It is well known that the blowing of cold gas through the side walls of the channel of a dc plasmotron (plasma generator) with longitudinal blowing over the arc leads to an increase in the useful power of the plasmotron [1]. The increase is due to the increase in the combustion voltage of the arc and also the decrease in the heat fluxes to the wall of the channel. The present paper solves the problem of the optimal distribution of the flow rate of gas blown through the side walls into the channel of a dc plasmotron of arbitrary shape F(x). The flow in the main channel and in the ducts in the side walls is described by the quasi-one-dimensional gas-dynamic equations investigated qualitatively in [2] and verified experimentally in [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 120–124, May–June, 1981.     

Estimate of the correlation between pressure pulsations and the divergence of the velocity in subsonic flows of variable density

In flows with variable density, the turbulence energy equation contains a large number of correlations, about which little is at present known [1]. One of the least studied is the correlation between the pressure and the divergence of the velocity. Usually, this correlation is ignored [2, 3]. The aim of the present paper is to estimate the pulsations of the divergence of the velocity and the correlation with the pressure pulsations in a subsonic turbulent flow with variable density. Three cases are considered: 1) mixing of gases having different densities, 2) diffusion combustion, 3) combustion of a homogeneous mixture. It is assumed that the Mach number is small, the Reynolds number large, and the coefficients of molecular diffusion and thermal diffusivity equal; external forces are absent.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 4–11, May–June, 1979.     

Self-similar movement of a viscous gas in a channel

The results presented in [1] refer primarily to dropping liquids for which the influence exerted by the thermal conditions on the flow is related to the temperature dependence of the viscosity. The self-similar flow of a viscous gas in a channel with a linearly increasing wall temperature is examined in this paper. The influence exerted by the Reynolds and Prandtl numbers on heat exchange and the hydrodynamics of the flow is analyzed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 47–54, May–June, 1976.The author wishes to thank A. F. Seleznev for carrying out the calculations and V. N. Shtern for discussing the paper.     

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.     

Applicability of a one-dimensional model to the calculation of the properties of a plasma generator

Most engineering methods for calculating the properties of plasma generators use similarity theory to derive dimensionless equations to generalize experimental results [1]. Although their accuracy is acceptable for practical calculations, the equations cannot be used for a physical analysis of the local phenomena occurring in the working channel of a plasma generator. In the present paper the experimental data are compared with the results of a calculation of the local and integrated heat and gasdynamic properties of a dc plasma generator with a longitudinally injected arc. The basis of the computational method is a quasi-one-dimensional gasdynamic model of the flow of an electrically conducting gas in the channel of the plasma generator developed and studied in [2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 122–126, July–August, 1977.In conclusion, the authors thank G. A. Lyubimov for valuable remarks.     

Parameters of streamer breakdown in xenon

It is known from experiments [1–3] that the velocity of streamers, induced in the center of the interelectrode gap and propagating to the electrodes under conditions when the streamer length is comparable with the distance between the electrodes, increases linearly as the streamer length increases. This relationship is in qualitative agreement with theory [4], Nevertheless, the velocity of streamers starting from the electrodes and propagating in a long interelectrode gap remains practically constant during the whole propagation process [5, 6], In the case of short gaps (2–5 cm), constancy of the velocity is observed during the stage of the process when the length of the streamer is much less (20%) than the length of the gap [7], Since the electric field at its end controls the streamer propagation, the constancy of the streamer velocity indicates that the controlling field is constant under these conditions. A number of theoretical models were proposed in [8–13] which describe uniformly moving anode- and cathode-directed streamers (henceforth called anode and cathode streamers). Comparison of experimental data with the corresponding theoretical model enables one to determine the streamer parameters: the electric field, the charged-particle density, the current density, the channel radius, etc. In the case of an anode streamer in Xe an attempt at such a comparison was made, in particular, in [6]. However, the lack of reliable data on the value of the drift velocity and the diffusion coefficient of electrons in Xe for E/p (10² – 10³) V/cm · mm Hg allowed only rough estimates to be made. In this paper a numerical calculation is made of the drift velocity, the diffusion coefficient of electrons in Xe, and the rate of excitation of Xe atoms in the resonance level in the range of values of E/p (10¹–10³) V cm · mm Hg, and the volt-ampere characteristic of the breakdown is measured under conditions described in [6] (p₀=300 mm Hg and E 10⁴–10⁵ V/cm). Using these results, the formulas for the velocity of anode [12] and cathode [13] streamers, and experimental data [6], the parameters of the streamers studied in [6] are determined.Translated from Zhurnal Prikladnoi Meknaniki i Tekhmcheskoi Fiziki, No. 3, pp. 6–11, May–June, 1976.The authors thank A. T. Rakhimov and A. N. Starostin for useful discussions, and A. V. Markov for help with the experiments.     

Nonequilibrium viscous flow of a multicomponent gas in the vicinity of the stagnation point of a blunt body

This paper gives the results of numerical calculations characterizing the effect of variation of the shock layer parameters on the heat transfer in the case of a multicomponent nonequilibrium-dissociating air on a wall with finite catalycity in the vicinity of the stagnation point of a spherical blunt body. Similar results for the case of a binary mixture can be found in [1–3]. It is shown that a consideration of the variation of the parameters in the nonequilibrium shock layer leads to a significant increase in heat flux to the noncatalytic wall in comparison with the theory of an asymptotically thin nonequilibrium boundary layer with equilibrium parameters on its outer boundary.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 144–147, March–April, 1971.The author thanks V. V. Lunev for useful comments in the discussion of this work.