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.     

Unsteady quasi-one-dimensional flows of relaxing nitrogen tetroxide

The decay of an arbitrary discontinuity and the reflection of a fan of rarefaction waves from a fixed wall in dissociating nitrogen tetroxide are considered. The system of the equations of gas dynamics and the equation of the conservation of the mass of component i have been integrated numerically by MacCormack's method. It is shown that the kinetics has a significant influence on the characteristics of a shock wave and a contact discontinuity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 159–164, July–August, 1981.     

Diffusion separation of chemical elements on a catalytic surface

An asymptotic expansion of the solution, for large Schmidt numbers, of the system of equations of a chemically nonequilibrium multicomponent boundary layer on the catalytic surface of a blunt body [1] is used to obtain expressions for the diffusion fluxes of the reaction products and chemical elements and the heat flux as functions of the gradients of the reaction product concentrations, chemical element concentrations and enthalpy across the boundary layer. It is shown that when the body is exposed to a supersonic air flow, the diffusion separation of the chemical element oxygen depends importantly on the atom concentration at the outer edge of the boundary layer and the nature of the homogeneous and heterogeneous catalytic reactions. If the surface promotes the rapid recombination of oxygen atoms and is chemically neutral with respect to nitrogen atoms, then an excess of the chemical element oxygen is formed on the body. Otherwise we get an enhanced concentration of the element nitrogen. As distinct from the case of an ideally catalytic wall [2–4], on a surface possessing the property of catalytic selectivity the diffusion separation of chemical elements takes place even when only atoms are present at the outer edge of the boundary layer. On a chemically neutral surface diffusion separation may be caused by homogeneous recombination reactions between oxygen and nitrogen atoms if their rate constants are essentially different.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 115–121, July–August, 1988.     

Flow of a supersonic low-density jet of nitrogen and nitrogen-hydrogen mixture over a blunt body

This paper gives the results of electron-beam measurements of the rotational temperature of nitrogen and its concentration in front of a spherically blunt cylinder situated on the axis of a supersonic rarefied jet of nitrogen and nitrogen-hydrogen mixture.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 50–55, November–December, 1972.     

On the recombination mechanism of atomic nitrogen near a catalytic surface in a stream of dissociated air

It is shown that the heterogeneous recombination of nitrogen atoms on a catalytically active surface in a stream of dissociated air is accompanied by intense gas-phase recombination of the nitrogen in exchange reactions whose rate is determined by the rate of heterogeneous recombination of atomic oxygen.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 156–158, May–June, 1980.     

Possibility of forming an inverted distribution over the rotational levels of nitrogen in an expanding gas stream

A number of theoretical papers have been devoted to an investigation of the relaxation kinetics of the population of a system of rotational levels of molecules in a stream of gas freely expanding from a sonic nozzle [1–3]. The complexity of the task of constructing models of relaxation and of collisions consistent in accuracy, however, as well as the difficulties in solving the resulting system of kinetic and gas-dynamic equations, lead to the necessity of using substantial approximations. Some disagreement between the experimental data and calculated results [1, 2] requires an evaluation of the accuracy of the various approximations used and further refinement of the theoretical models. In contrast to [1], in order to bring out the possible mutual influence of nonequilibrium energy exchange between the degrees of freedom of nitrogen molecules and the variation of the gas-dynamic parameters, the calculation presented below is based on a numerical solution of a self-consistent system of kinetic and gas-dynamic equations for the populations of rotational states and the temperature, density, and velocity of gas in the stream. Collisional probabilities of rotational transitions, calculated with allowance for the long-range part of the potential of the interaction between molecules [4], are used for this.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 9–16, May–June, 1986.     

Effect of surface catalytic activity on nonequilibrium heat transfer in a subsonic jet of dissociated nitrogen

The present paper investigates experimentally and numerically the effect of the heterogeneous recombination of atoms on the heat transfer of models in a subsonic jet of dissociated nitrogen for the conditions of an experiment in the VGU-2 plasma generator and determines the effective probabilities of the heterogeneous recombination of nitrogen atoms for a number of materials at high temperatures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 166–172, May–June, 1985.     

Identification of the Ten Inertia Parameters of a Rigid Body

Standard experiments for identifying inertia parameters of a rigid body only provide a subset of the inertia parameters of the body [1–10]. In addition, they do not use in the estimation process the complete information included in the equations of motion of the rigid test body. The objective of the work described in this paper is the simultaneous, automatic experimental identification of the ten inertia parameters of a rigid body using the complete information hidden in the nonlinear model equations of the test body. This task has been solved in several steps:– mathematical modelling of the special motions of a rigid body in space. These model equations have been mapped into a form suitable for identification purposes (identification hypothesis)– design of a special measurement robot for performing the identification experiments– laboratory experiments providing test data used for the identification experiments– identification of the inertia parameters and accuracy tests.The accuracy of the identified parameters is satisfactory.     

Nonequilibrium ionization accompanying hypersonic flow of carbon dioxide gas over blunt bodies

A study is made of the nonequilibrium ionization in the shock layer when carbon dioxide gas flows over cones with spherical noses at velocity 4–7 km/sec, the density of the oncoming flow being 10^–8-10^–5 g/cm³. The influence of admixtures of nitrogen and sodium on the electron concentration is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 183–186, January–February, 1981.     

Experimental investigation of the scattering of microwave signals by spheres moving at hypersonic velocity

The scattering of radio waves by meteorites moving in the atmosphere at hypersonic velocity is significantly changed by the formation of an ionized shock layer. The flow of the gas in the shock layer is characterized by ablation of the mass of the body and complicated chemical kinetics, which makes it difficult to calculate theoretically the signal scattered by the plasma and leads to the need for an experimental study of the phenomenon, particularly in ballistic ranges. The methods of head-on or inclined probing of ballistic models by microwave signals have been developed furthest. However, in the papers devoted to this question [1–3] very restricted information is given about the method employed and the experimental results, which hinders practical realization of the method. The present work was aimed at creating a method for measuring the backward scattering of radio waves by models moving at hypersonic velocity in a ballistic range. The results are also given of an investigation into the influence of the ionized gas on the amplitude of the reflected microwave signals.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 188–190, May–June, 1981.We thank V. V. Brodskii for helpful advice in discussing the arrangement of the experiment and G. V. Glybin for assistance in preparing the microwave equipment and the ballistic range.     

Nonequilibrium condensation of metal vapor mixed with an inert gas in nozzle expansion in cluster beam generators

A closed mathematical model of flows of a mixture consisting of a homogeneously condensible vapor and an inert gas is described. This model is a further development of the pure metal vapor condensation model [1 – 4] and, as distinct from the latter, makes it possible to take into account the effect of molecules of inert gas not only on the thermodynamics of the mixture but on the detailed kinetics of the processes of the cluster formation and breakdown. The results of numerical calculations of the formation of iron and silver clusters in experimental installations are presented.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 80–91, May–June, 1995.     

Thermal dissociation of diatomic molecules in a nonisothermal boundary layer in the presence of exchange reactions

The effect of an inhomogeneous temperature field in a boundary layer on the kinetics of dissociation of diatomic molecules simulated by truncated harmonic oscillators is considered in a multicomponent mixture in the presence of exchange reactions which take place at lower vibrational levels as compared with dissociation.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 163–172, January–February, 1995.     

Propagation of a shear crack in a randomly heterogeneous body

Propagation of a crack in a randomly heterogeneous body exposed to longitudinal shear is considered (in a Born approximation). It is proved that the stress means at the crack tip have singularities on the order of (r)^–1/2. The effective coefficient of stress intensity is introduced. It is known that the propagation of a crack in a homogeneous body is of a local nature, i.e., energy consumption in the growth of the crack is completely determined by the coefficient of stress intensity, which is a local characteristic. The equivalence of the force and energy approaches is mathematically expressed by the Irwin equation [1]. An analog of the Irwin equation is obtained for the case of a randomly heterogeneous body.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 145–148, January–February, 1976.     

Numerical investigation of nitrogen rotational relaxation

The nitrogen rotational relaxation process is numerically investigated on the basis of a Monte-Carlo solution of the spatially homogeneous problem for the kinetic equation. The interaction of the molecules is described by the three-dimensional equations of motion within the framework of classical mechanics, the use of which for a gas such as nitrogen is justified at not very low temperatures. The dependence of the relaxation process on the initial values of the translational and rotational temperatures and the asymmetry parameter in the interaction potential is considered.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 124–132, March–April, 1993.The author wishes to thank V. S. Galkin for discussing the work.     

Study of radiative and convective heat transfer when a radiating mixture of carbon dioxide and nitrogen flows past the critical point of a body

The results are given of an investigation of the convective and radiative heat transfer at the leading critical point of a body in the flow of a radiating mixture of carbon dioxide and nitrogen, taking account of viscosity and thermal conductivity. The system of equations is written down under the assumption that the shock layer is thin, and its solution is obtained in the region between the body and the shock wave. It is assumed that there is local thermodynamic equilibrium throughout the compressed layer. The coefficients of absorption of the mixture are assumed to depend on the wavelength, the temperature, and the pressure. From the solution we determine the radiative and convective thermal fluxes at the wall, taking account of their interaction for temperatures behind the shock wave of 9000–12000 deg K and pressures of p=1 and 10 atm. By analyzing these results it is concluded that the effect of radiation on the convective heat transfer is insignificant, the effect being qualitatively different at large and small pressures. The fundamental contributions to the radiant thermal flux at the wall in the versions of the problem considered come from the following spectral interval: 0.128–0.33, where there is a fourth positive system of carbon monoxide bands (~43%), and 0.33–0.66, where there is an ultraviolet system of cyanogen (~40%). The contribution from the spectral interval 0.80–1.15 is ~20%. Only about 15% of the radiant energy comes from the comparatively large interval 0.45–0.80. As the pressure increases, the contribution from the ultraviolet part of the spectrum falls, and the contribution from the visible part of the spectrum increases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 39–47, March–April, 1971.     

Deviations from thermodynamic equilibrium during recombination of a dispersing plasma

The relaxation of a dense low-temperature plasma during cooling of the electrons on heavy particles and during dispersion of a plasma cluster into a vacuum is examined. The population kinetics is analyzed in the limiting cases of free escape and radiation capture. The results are presented for a numerical solution of the self-consistent (with respect to temperature and concentration of free electrons) problem of the relaxation of an atomic hydrogen plasma.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 3–10, September–October, 1973.     

Least-drag bodies moving in media subject to the locality hypothesis

A solution is constructed for the variational problem of a body of minimum drag moving at constant velocity in media in which under certain assumptions the force exerted by the medium on an area element of the body surface depends only on its orientation relative to the direction of motion (locality hypothesis). The representations of the normal (pressure) and tangential (friction) components of the force embrace a broad range of the conditions realized in the motion of a body through gases and dense media.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 95–106, January–February, 1992.     

The Effect of the Walls of an Arbitrary Tank in the Problem of Separation–Free Impact on a Floating Body

An algorithm for constructing an asymptotic power series for large depths is proposed. It allows one to use the well–known solution of the problem of impact on a rigid body floating on the surface of a fluid half–space to obtain an approximate solution of the impact problem for the same body floating on the surface of a fluid in a bounded basin. The case where the domain occupied by the fluid has two perpendicular planes of symmetry is considered. Asymptotic expressions are given for the velocity potential on the wetted part of the body surface and for the added mass. Examples of solutions are considered.     

Convective heating of a blunt-nosed body in a nonuniform hypersonic gas stream

An investigation is made into the convective heating of a blunt-nosed body in an expanding stream of heated gas. The gas parameters at the outer edge of the boundary layer are determined on the basis of a solution obtained earlier by the authors [3]. Expressions are obtained which make it possible to convert the convective heat flux to a body in a uniform gas stream to one in a nonuniform stream. Dimensionless numbers are found and their influence on the convective heat flux to the body is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 127–133, July–August, 1981.     

Body shape with minimum total radiant energy flux toward its surface

During a space vehicle's entry into a planet's atmosphere at hypersonic speed one of the important problems is the aerodynamical surface heating due to convective and radiant heat fluxes from the gas after passing through a strong shock wave. Due to the high destructive action of this heating, an important problem is the selection of the aerodynamic shape allowing the minimum heat influx to its surface. The problem of determining the shapes of an axisymmetric body from the condition of minimum total convective heat flux along the lateral face of the body was considered under various assumptions in [1–7]. There are a number of entry conditions (for example, into the earth's atmosphere with a speed of 11 km/ sec at an altitude of about 60 km [12]) during which the radiative component becomes dominant in the total heat flux toward the body. A numerical solution of the problem of hypersonic flow of a nonviscous, non-heat-conducting radiating gas around a body is obtained at this time only for a limited class of bodies and primarily for certain entry conditions (for example, [8–12]). On the basis of these calculations it is impossible to make general conclusions concerning arbitrary body shapes. Therefore, approximate methods were proposed which permit the distribution of radiant heat flux to be obtained for an arbitrary axisymmetric body in a wide range of flight conditions [13–15]. In the present work an expression is derived for the total radiant heat flux over the entire body surface and similarity criteria are found. A variational problem is formulated to determine the shape of an axisymmetric body from the condition of minimum total radiant-heat flux over the entire body surface. It is solved analytically for the class of thin bodies and in the case of a strongly radiating gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 84–89, July–August, 1976.