Flow of a dual-temperature plasma in the channel of a disk-magnetohydrodynamic generator,taking account of nonequilibrium ionization and recombination reactions

The establishment of a supersonic one-dimensional flow of a dual-temperature, partially ionized plasma is investigated in the channel of a disk-MHD generator, taking account of nonequilibrium ionization and recombination reactions. A detailed formulation of the problem is given in [1]; flows are considered in the absence of ionization and recombination reactions and in the case of equilibrium reactions.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 6, pp. 135–142, November–December, 1972.     

Instability and flow of a weakly conducting fluid in the presence of oxidation-reduction reactions at electrodes and recombination

Experiments show that a weakly conducting fluid in a plane-parallel system of electrodes is set into motion if the field intensity is sufficiently great [1–5]. The loss of stability is due to the formation of charges near the electrodes and the influence of the Coulomb forces on these charges. The formation of the space charges is usually attributed to oxidation-reduction electrode reactions and bulk recombination of the ions formed at the electrodes [1–4]. In the present paper, the stability of a weakly conducting fluid in a plane-parallel system of electrodes with symmetric distribution of the space charge is studied. The methods of the theory of solution bifurcation are used to construct the stationary flow which arises after the loss of stability and to investigate the stability of this flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 20–26, July–August, 1981.     

The effect of gas motion on the reaction kinetics of vibrationally excited molecules

The effect is considered of gas motion on the kinetics of reactions whose energy threshold is overcome as the result of vibrational excitation of the reactant molecules. The conditions are determined for which such an effect may be realized. An expression is obtained for the rate of thermal dissociation of diatomic molecules considered as harmonic oscillators representing a small impurity in a monoatomic inert gas; the expression depends explicitly and nonlinearly on the divergence of the flow velocity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 100–105, November–December, 1984.     

Calculation of hydrogen-air combustion behind detached shock wave for supersonic flow past a sphere

Many of the published theoretical studies of quasi-one-dimensional flows with combustion have been devoted to combustion in a nozzle, wake, or streamtube behind a normal shock wave [1–6].Recently, considerable interest has developed in the study of two-dimensional problems, specifically, the effective combustion of fuel in a supersonic air stream.In connection with experimental studies of the motion of bodies in combustible gas mixtures using ballistic facilities [7–9], the requirement has arisen for computer calculations of two-dimensional supersonic gas flow past bodies in the presence of combustion.In preceding studies [10–12] the present author has solved the steady-state problem under very simple assumptions concerning the structure of the combustion zone in a detonation wave.In the present paper we obtain a numerical solution of the problem of supersonic hydrogen-air flow past a sphere with account for the nonequilibrium nature of eight chemical reactions. The computations encompass only the subsonic and transonic flow regions.The author thanks G. G. Chernyi for valuable comments during discussion of the article.     

Experimental investigation of the emission in the unsteady flow region behind strong shock fronts in mixtures of co and CO2 with nitrogen and argon

Mixtures of CO (or CO₂) gases and N₂ behind strong shock fronts at temperatures 4000–10 000 ° K have been investigated with a view to elucidating the mechanism of the physicochemical processes in the unsteady region of the gas flow behind a shock front leading to the behavior of strongly radiating CN and C₂ molecules and C atoms and also determining the quantitative characteristics of the chemical reactions. A shock tube was used in the investigations, which made it possible to obtain the intensity distribution of the radiation of several components — CN, C₂, and C — behind shock fronts.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 120–129, March–April, 1981.We thank S. A. Losev and O. P. Shatalov for assisting in the work and for valuable discussions.     

Motion of a gas shock layer with a free boundary under nonadiabatic conditions

This paper is a study of the effect of heat input (removal) on the characteristics of a shock layer produced by a gas at high supersonic velocity encountering a mobile boundary, which for generality is assumed to be free. We will use the Chernyi method, which was employed previously to solve the problem of a shock layer in an adiabatic flow [1, 2]. The results obtained can be useful for analysis of the effect of radiation (absorption) and processes involving the relaxation of internal degrees of freedom of molecules, condensation, chemical reactions, etc., whose effect on the gasdynamics of the flow in a shock layer may be similar to heat input or removal [3–5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 152–154, May–June, 1976.The author thanks A. K. Rebrov for discussion of the results.     

Numerical modeling of carbon monoxide neutralization by metered water injection into a high-temperature mixture of combustion products

A closed mathematical model of the flow of a two-phase mixture consisting of evaporating water droplets and a chemically reacting multicomponent gas is described. The effect of the real droplet heating and evaporationkinetics on the gas-phase chemical reactions in a mixture of combustion products is studied within the framework of this model.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 96–106, November–December, 1993.     

Electrization of dielectric liquids flowing in tubes

The methods of the mechanics of continuous media [1] are used to consider the problem of electrization of dielectric liquids flowing in tubes [2–6]. According to modern ideas [2–6], there is always dissolved in such liquids a slight admixture of an electrolyte, whose molecules in such a dilute solution dissociate to a certain extent into positively and negatively charged ions. On the walls, oxidizing and reducing reactions take place, as a result of which the negative and positive ions, respectively, give up to the wall surplus electrons or take missing electrons from it. Thus, a positive (respectively, negative) total electric charge is induced in the liquid by the flow. We consider in this paper the electrization of a dielectric liquid in laminar flow in a circular cylindrical tube. We find the distribution of the electric charge in the liquid, the maximal electric current, and the dependence of the length over which the distribution of the electric charge in the tube is established on the tube radius, the Debye radius of the liquid, and the Péclet diffusion number.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 41–47, November–December, 1979.We thank V. V. Gogosov for helpful comments made in a discussion of thwe work.     

Analysis of the hydrodynamic interaction between cascades of thin profiles taking account of vortex wake evolution

The papers [1–5] are devoted to an investigation of aspects of the hydrodynamic interaction of cascades of profiles in a nonlinear formulation: it is shown experimentally in [1] and theoretically in [2] that the free vortex sheet ruptures upon meeting a profile; taking account of the evolution of vortex wakes, the flows around two cascades of solid profiles of infinitesimal [3] and finite [4] density are computed; results of an experimental investigation of the dynamic reactions of the flow on two mutually moving cascades of thin profiles are presented in [5]. The interference between two cascades of thin profiles in an inviscid, incompressible fluid flow is examined in this paper, where a modified method from [6] is used.Translated from Zhurnal Prikladnoi MekhaniM i Tekhnicheskoi Fiziki, No. 4, pp. 61–65, July–August, 1976.The author is grateful to D. H. Gorelov for discussing the research.     

An exact solution of the navier-stokes equations for a chemically reacting mixture of gases

An exact solution of the Navier-Stokes equations is presented for the flow of a viscous heat-conducting chemically reacting mixture of gases in a two-dimensional expanding channel. The conditions for the existence of an exact solution of the source type are: the chemical reactions must be equimolecular in an equilibrium mixture of gases, and they must be second order forward and backward in a nonequilibrium mixture. Numerical results are obtained for the flow of a four-component equilibrium mixture of gases in a two-dimensional nozzle for various Mach numbers (M) and Reynolds numbers (Re).Translated from Zhurnal Prikladnoi Mekhanika i Tekhnicheskoi Fiziki, No. 4, pp. 49–56, July–August, 1973.     

Nonequilibrium hypersonic flow of carbon dioxide gas over blunt bodies

The Navier-Stokes equations are used to investigate hypersonic flow of carbon dioxide gas over blunt bodies with allowance for nonequilibrium development of chemical reactions and vibrational relaxation of the CO₂ molecules. The problem is solved by the method of stabilization by means of an implicit difference scheme that includes the use of Newton's iterative process. The results are given of calculations of the flow field, the convective heat flux, and the frictional stresses on the surface of blunt cones with spherical noses. The influence of admixtures on the flow field and the heat fluxes is investigated. The results of the calculations are compared with the locally self-similar solution for the neighborhood of the front stagnation point.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 199–202, September–October, 1979.     

Three-dimensional chemically nonequilibrium viscous shock layer on a catalytic surface with allowance for associated heat transfer

A three-dimensional flow of dissociating air past blunt bodies is investigated in the framework of the thin viscous shock layer theory. Multicomponent diffusion and homogeneous chemical reactions, including dissociation, recombination, and exchange reactions, are taken into account. The generalized Rankine-Kugoniot conditions are specified on the shock wave and the conditions which take into account the heterogeneous catalytic reactions, on the surface of the body. The viscous shock layer equations are solved together with the heat equations inside the coating, which is carbon with a deposited thin film of SiO₂, or quartz. The case of a thermally insulated surface is also considered. The problem for the case of the motion of a body along the re-entry trajectory into Earth's atmosphere is investigated numerically. The temperature of the surface and the heat flux toward it are given as a dependence on the height (tine) of the flight for different cases of the specification of the catalytic reactions. It is shown that the difference between the heat fluxes towards the thermally insulated surface and the fluxes toward the heat-conducting surface in the neighborhood of the stagnation point is of the order of 6–12% for all the cases considered. This makes it possible to decouple the solution of the problem of heat conduction in the body.Translated fron Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 140–146, November–December, 1985.deceased     

Asymptotic law of expansion of a cavity in the presence of hydrodynamic singularities in the flow

The asymptotic law of expansion of an axisymmetric half-body of finite resistance exposed to a flow of an ideal incompressible fluid and its relation with the force acting on the half-body were obtained in [1]. It is obvious that the deformation of the nose of the body will not change the form of the expressions found. It will be shown below how the asymptotic law and magnitude of hydrodynamic reactions change for half-bodies of finite resistance in the presence of sources (sinks) in the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 153–155, May–June, 1977.The author thanks G. Yu. Stepanov for attention to the work.     

Numerical investigation of the structure of nonequilibrium three-dimensional hypersonic flow past blunt bodies

Three-dimensional dissociating air flow past blunt bodies is investigated within the framework of the parabolized Navier-Stokes equations in the thin layer approximation. Multicomponent diffusion, barodiffusion and homogeneous chemical reactions, including dissociation-recombination and exchange reactions, are taken into account. The boundary conditions are assigned in the free stream and at the surface of the body with allowance for heterogeneous catalytic reactions and slip effects. The problem of flow at zero angle of attack past blunt bodies possessing two planes of symmetry is investigated numerically for flow patterns varying from smeared layer structure to almost ideal flow (Re=50-10⁵). The flow conditions corresponded to the motion of a body with lift along a re-entry trajectory [1]. The contribution of the chemical reactions in the shock wave as compared to the diffusion flux at the edge of the shock wave was estimated. The edge of the shock wave is assumed to correspond to the point at which the density profile has the greatest slope. The influence of slip effects and barodiffusion on the flow characteristics is demonstrated. The results of the calculations are compared with calculations based on the thin viscous shock layer model [2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 143–150, September–October, 1987.The author wishes to express his thanks to G. A. Tirskii and V. V. Lunev for useful discussions and valuable advice.     

Investigation of the flow and heat transfer of viscous reacting fluids in long tubes

Heat transfer and resistance in the case of laminar flow of inert gases and liquids in a circular tube were considered in [1–4], the justification of the use of boundary-layer type equations for investigating two-dimensional flows in tubes being provided in [4]. The flow of strongly viscous, chemically reacting fluids in an infinite tube has been investigated analytically and numerically in the case of a constant pressure gradient or constant flow rate of the fluid [5–8]. An analytic analysis of the flow of viscous reacting fluids in tubes of finite length was made in [9, 10]. However, by virtue of the averaging of the unknown functions over the volume of the tube in these investigations, the allowance for the finite length of the tube reduced to an analysis of the influence of the time the fluid remains in the tube on the thermal regime of the flow, and the details of the flow and the heat transfer in the initial section of the tube were not taken into account. In [11], the development of chemical reactions in displacement reactors were studied under the condition that a Poiseuille velocity profile is realized and the viscosity does not depend on the temperature or the concentration of the reactant; in [12], a study was made of the regimes of an adiabatic reactor of finite length, and in [13] of the flow regimes of reacting fluids in long tubes in the case of a constant flow rate. The aim of the present paper is to analyze analytically and numerically in the two-dimensional formulation the approach to the regimes of thermal and hydrodynamic stabilization in the case of the flow of viscous inert fluids and details of the flow of strongly viscous reacting fluids.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 17–25, January–February, 1930.     

Transition flow of a fibrous suspension in a pipe as the flow of an anisotropic fluid

The transition flow is considered of a fibrous suspension in a pipe. The flow region consists of two subregions: at the center of the flow a plug formed by interwoven fibers and fluid moves as a rigid body; between the solid wall and the plug is a boundary layer in which the suspension is a mixture of the liquid phase and fibers separated from the plug [1–3]. In the boundary region the suspension is simulated as an anisotropic Ericksen—Leslie fluid [4, 5] which satisfies certain additional conditions. Equations are obtained for the velocity profile and drag coefficient of the pipe, which are both qualitatively and quantitatively in good agreement with the experimental results [6–8]. Within the framework of the model, a mechanism is found for reducing the drag in the flow of a fibrous suspension as compared to the drag of its liquid phase.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 91–98, September–October, 1985.     

Initiation of Combustion in a Supersonic Hydrogen-Air Mixture Flow by CO<Subscript>2</Subscript>-Laser Radiation

Features of the ignition kinetics of an H₂/air mixture in the supersonic flow behind an inclined shock front are analyzed when asymmetric vibrations of a small amount (<1%) of O₃ molecules specially introduced into the initial mixture are excited by 9.7 μm wavelength radiation. It is shown that this radiation leads to intensification of the chain reactions and makes it possible to organize combustion at small distances from the front (of the order of 1 m) of even relatively weak shocks at small values of the laser radiation energies absorbed by the gas. This method of initiating combustion in a supersonic flow is 10–100 times more efficient than the thermal method.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 157–167.Original Russian Text Copyright © 2005 by Lukhovitskii, Starik, and Titova.     

Allowance for longitudinal diffusion in the neighborhood of a discontinuity of catalytic surface properties

In the investigation of flow near surfaces with discontinuous changes in the catalytic properties the question arises of the applicability of parabolic boundary and viscous shock layer equations in the neighborhood of the discontinuity. In the present paper, three types of problem are solved in which longitudinal diffusion is taken into account. In the first an insertion with different catalytic properties is placed in the neighborhood of the stagnation point, in the second the discontinuity lines of the catalytic properties are perpendicular to the oncoming flow, while in the third they are parallel. On the main surface and on the insertion surface the heterogeneous catalytic reactions are assumed firstorder reactions with various rate constants whose values vary in a wide range. The data of the solution are compared with the solution obtained using the boundary layer approximation and the regions of influence of the longitudinal diffusion are estimated. In [1–4] a problem similar to the second one was solved by the numerical method of [1] and the Wiener-Hopf method for the case of transition from a noncatalytic to a perfectly catalytic surface and the region of applicability of the boundary layer was estimated [5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 99–105, July–August, 1986.     

Anisotropic percolatory-convective diffusion in underground leaching

The two-dimensional problem of the propagation of an impurity in underground flows is investigated with allowance for chemical reactions between the solvent and the ore-bearing matrix material. The flow velocity field generated by a pair of wells (source—sink) is assumed to be steady and known. A numerical method of solving the system of equations of convective diffusion and nonequilibrium sorption is discussed. Typical isoconcentration fields are presented. The effect of the influence parameters on the principal characteristics of the leaching process is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 96–101, January–February, 1987.     

On the set of steady regimes in chemical flow reactors

An extensive literature has been devoted (see, for example, [1–3]) to the question of the existence and uniqueness of steady regimes in chemical flow reactors. In the majority of cases, exact solutions to the corresponding problems cannot be obtained because of the nonlinearity of the functions that describe the kinetics of the chemical reactions. Investigations are therefore usually made by either approximate or numerical methods. In the present paper, exact solutions are obtained to a model nonlinear boundary-value problem of the steady distribution of the concentration in a one-dimensional isothermal chemical flow reactor with longitudinal mixing, and the question of the existence and the number of steady regimes is completely investigated in a three-dimensional space of the determining parameters. The function that describes the rate of the chemical reaction is taken to be a function that simulates approximately the dependence of the rate of the autocatalytic reaction on the concentration of the initial reactant.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 177–181, May–June, 1982.