**NONSTANDARD ANALYSIS OF A CONVERGING ****SHOCK WAVE IN A NONIDEAL GAS**

L. P. Singh, Mithilesh Singh,

and A. Husain

UDC 539.1

The problem of propagation of strong plane and converging shock waves in an unsteady inviscid nonideal gas is studied. A nonstandard analysis is used to derive the jump conditions for both shock waves. It is assumed that the jump occurs on an infinitesimal interval and jump functions in the flow parameters are smooth across this interval. The distribution of the flow parameters across the shock wave is expressed in terms of the Heaviside functions. Numerical computation to study the distribution of the flow parameters is performed.

**Keywords: **converging shock wave, nonstandard analysis, nonideal gas.

**CALCULATION OF THE EQUILIBRIUM COMPOSITION ****OF MULTICOMPONENT THERMODYNAMIC SYSTEMS ****BY THE METHOD OF ENTROPY MAXIMIZATION**

M. S. Assad,a O. G. Penyazkov,a

and S. G. Skoblyab

UDC 536.46:533.6

An algorithm for calculation of the chemical equilibrium of a multicomponent heterogeneous thermodynamic system on the basis of the maximum-entropy principle has been developed. The model obtained is universal and can be used for a large number of high-temperature processes, including the combustion of alternative fuels in different-type heat engines. On the basis of the algorithm proposed, the equilibrium composition of the combustion products of hydrogen-containing fuels was calculated for different initial conditions.

**Keywords:** thermodynamic system, equilibrium, entropy, combustion products, heat engine, hydrogen-containing

fuels.

**LIGHT SCATTERING AT THE BOUNDARY ****BETWEEN TWO MEDIA**

A. P. Ivanov and V. V. Barun UDC 535.36

Coefficients of diffuse reflection and transmission of light by smooth Fresnel boundaries of an optically thick

layer illuminated by scattered radiation are calculated. Consideration is given to the absorption effect on angular diagrams of light at the boundaries. An analysis is made of asymptotic equations of radiation transfer in a medium with reflecting boundaries, and the range of their applicability is studied. Using methods of geometric optics, coefficients of reflection of directional and diffuse radiation from a rough surface are studied.

The results can find use in various areas of science and technology, specifically, in optical diagnostics of biological tissues.

**Keywords:** diffuse and specular reflection, coefficients of reflection, transmission, and brightness, surface microsites,

diagnostics.

**EXPERIMENTAL INVESTIGATION OF SHOCK-WAVE ****PROCESSES IN THE PULSED IONIZATION ****OF THE SURFACE OF A SHOCK-TUBE CHANNEL**

I. A. Znamenskaya, I. V. Mursenkova,

and N. N. Sysoev

UDC 535.31:681.7.001

The interaction of a shock wave and the gas flow behind it with the plasma formed by a surface electric discharge in a shock tube was investigated.

**Keywords:** gas-dynamic flow, pulsed discharge, shock wave, plasma sheet.

**GENERALIZATION AND CALCULATION OF THE THERMAL ****DIFFUSION FACTOR OF BINARY HYDROGEN-CONTAINING**

**
GASEOUS MIXTURES**

A. G. Shashkov,a* A. F. Zolotukhina,a

and L. R. Fokinb

UDC 536.533.1

The results of generalization of experimental data on the thermal diffusion factor αT of hydrogen-containing gaseous mixtures within the framework of similarity theory have been given. The calculated relation which makes it possible to predict the thermal diffusion factor of hydrogen-containing mixtures of nonpolar gases with a limited body of data on the substance has been obtained. The αT values of mixtures of hydrogen with

inert gases, including radon Rn, and with N2, SiH4, and GeH4 in the temperature interval 100–1500 K have

been calculated.

Keywords: thermal diffusion factor, gaseous mixtures, hydrogen, inert gases, nitrogen, silane, german, similarity theory, generalization of data.

**INVESTIGATION OF SHOCK-WAVE PHENOMENA ****IN COMPOSITE MATERIALS**

S. A. Afanas’eva, N. N. Belov, Yu. A. Biryukov,

V. V. Burkin, V. M. Zakharov, A. N. Ishchenko,

A. V. Skosyrskii, A. N. Tabachenko, I. E. Khorev,

and N. T. Yugov

UDC 538.91:539.3

We propose a complex experimental-theoretical approach to the investigation and development of high-energy and composite materials for the conditions of high-velocity throwing and interaction with the application of nanotechnologies. We have obtained data on the character of the high-velocity interaction of strikers made from tungsten composites by different technologies with a steel obstacle. A nanostructured material based on copper with higher strength characteristics has been developed. The conditions for increasing the muzzle velocity of a barrel throwing installation due to the application of nanocomposite fuels have been investigated and realized. A computing-experimental method for investigating the processes of high-velocity collision of bodies has been elaborated.

**Keywords: **composite materials, high-velocity throwing, shock-wave loading, piercing power of strikers.

**CHEMICAL OXYGEN-IODINE LASER: ****AEROOPTICS AND GAS DYNAMICS**

A. S. Boreisho, V. M. Mal’kov,

and A. V. Savin

UDC 532.574.7

We have investigated the interaction of regular and irregular structures — systems of shock waves, rarefaction waves, and turbulent layers — in a chemical oxygen-iodine laser.

**Keywords:** supersonic chemical lasers, gas dynamics, aerodynamics, aerooptical problems.

**NEW MODELS OF CONTINUUM MECHANICS**

V. F. Kuropatenko UDC 532.529

Possible ways of transition from traditional models of continuum mechanics to new-generation models, using a model of a multicomponent model as an example, are considered.

Keywords: conservation laws, continuous medium, differential equations, mixture, component, concentration, interaction

of components, particles.

**KINETIC PROCESSES IN THE PLASMA FORMED ****IN COMBUSTION OF HYDROCARBON FUELS**

A. M. Starik, A. M. Savel’ev,

and N. S. Titova

UDC 629.7.036+662.7+634.222.2

An analysis of the basic kinetic processes responsible for the formation of ions, electrons, charged and neutral carbon clusters and particles of nanometer size in the combustion of hydrocarbon fuels has been made. It has been shown that the formation of a polydisperse ensemble of positively and negatively charged particles is mainly caused by the ion adhesion to primary particles and secondarily formed particles and also by particle coagulation. Account must be taken not only of the Coulomb interaction but also of the van der Waals and polarization interaction between particles. The distinstice features of the deposition of polar molecules on charged particles have been considered.

**Keywords:** chemiionization, coalescence, coagulation, chemical condensation, aggregation, thermal electron

emission.

**FORMATION OF SOOT FROM POLYCYCLIC AROMATIC ****HYDROCARBONS AS WELL AS FULLERENES AND CARBON ****NANOTUBES IN THE COMBUSTION OF HYDROCARBON**

Z. A. Mansurov UDC 539.3:621.374

The eightieth anniversary of Academician, Lenin Prize Winner Rem Ivanovich Soloukhin is an important event

for the scientific association of investigators of combustion and detonation processes. R. I. Soloukhin has developed original gasdynamic laser systems based on the selective thermal excitation and mixing in a supersonic flow: efficient high-power gas-flow lasers of convective type with electric excitation and chemical lasers initiated by an electron beam. He proposed methods of measuring the rapidly changing pressure, density, temperature, and other parameters of processes occurring in shock waves.

Deputy Editor-in-Chief of the Journal "Fizika Goreniya Vzryva," Professor at Novosibirsk University R. I. Soloukhin

trained a Pleiad of Doctors and Candidates of Sciences. His fundamental investigations form the basis for the development of new directions in the physics of combustion and explosion.

In the present article, recent works on soot formation in the combustion of hydrocarbons are reviewed. The phenomenology, kinetics, and mechanism of soot formation, the influence of different factors on the formation of polycyclic aromatic hydrocarbons, fullerenes, carbon nanotubes, and soot, low-temperature cold-flame soot formation, the combustion in an electric field, and the paramagnetism of soot particles were considered from the environmental standpoint.

**Keywords:** soot formation, polycyclic aromatic hydrocarbons, combustion, carbon nanotubes.

**ON THE THEORY OF TURBULENT HEAT ****AND MASS TRANSFER WITH ALLOWANCE**

**
FOR INTERMITTENCE EFFECTS**

Yu. V. Nuzhnov UDC 532.5

A new viewpoint of the mechanism of turbulent heat and mass transfer has been proposed; a mathematical

apparatus of statistical theory and a method of construction of mathematical models under the conditions of intermittent dynamic and scalar fields of nonuniform turbulent flow have been developed. A model of a turbulent axisymmetric jet for evaluation testing of the method has been constructed and the conditional and total means of the basic statistical characteristics of the jet have been calculated. It has been shown that the reason for the "different mechanism" of turbulent transfer of momentum, heat, and substance is the intermittence of not coincident dynamic and scalar fields of turbulent flow. An equation for the conditional probability density function of the concentration of a passive impurity has been derived and its solution for the axisymmetric jet in a strongly intermittent region has been given. Good agreement between the performed calculations and experimental data confirms the adopted concept of the transfer mechanism.

**Keywords:** turbulence, heat and mass transfer, statistical theory, mathematical modeling, probability density

function.

**FLOW STRUCTURE OF THE ACTIVE MEDIUM ****OF A HF LASER WITH A RADIALLY**

**
EXPANDING NOZZLE UNIT**

I. A. Fedorov UDC 621.378:535

Measurements have been made of gasdynamic characteristics of the flow of the active medium as well as energy and spectral characteristics of radiation generated by a continuous chemical HF laser with a radially expanding nozzle unit. Based on the analysis of measurement results, the flow structure of the active medium has been determined, which is formed by the "nozzle–injector" reactant mixing scheme. It has been shown that only a part of the active medium is involved in the radiation generation. Measures for improving the efficiency of its use have been proposed.

**Keywords:** flow of active medium, radially expanding nozzle unit, "nozzle–injector" reactant mixing scheme.

**MODELING OF EXPLOSION THERMAL RADIATION**

K. L. Stepanov, L. K. Stanchits,

and Yu. A. Stankevich

UDC 532.5:539.5

The hydrodynamic and radiation processes accompanying explosions of chemical explosives and fuel-air mixtures have been considered. Computer modeling of the radiation from a fire ball of explosion and a flame of diffusion combustion of a hydrocarbon fuel has been performed. The dependences of the heat flux density from the region occupied by explosion and combustion products on its temperature and geometric characteristics have been determined. Thermal load distributions on targets of different orientations in the vicinity of the energy release zone have been obtained. A comparison of the thermal parameters on radiation detectors

with the criteria of thermal affection of people and ignition of combustible materials has been made.

**Keywords:** explosion, shock wave, fire ball, thermal radiation, irradiance of targets.

**MICROMIXING MODELS FOR CALCULATING ****THE AVERAGE RATE OF A CHEMICAL**

**
REACTION IN A TURBULENT FLOW**

A. D. Chorny UDC 532.517.4, 532.526.5

A model of mixing with a chemical reaction in a uniform, isotropic turbulent flow has been developed on the

basis of the statistical-moments method for calculating the hydrodynamic characteristics of a flow and the probability density function of its mixture coefficient for the purpose of determining the correlations responsible for the chemical reaction in the flow. The results of calculations of the average rate of a chemical reaction in a flow by the multizone model and models of micromixing (the mean-square approximation and Langevin models) used for construction of equations for the probability density function were compared.

**Keywords:** micromixing, mixture coefficient, degree of development of a reaction, probability density function, intensity of segregation, rate of chemical reaction.

**ELECTROVORTEX MOTION OF A MELT ****IN DC FURNACES WITH A BOTTOM ELECTRODE**

O. V. Kazak and A. N. Semko UDC 537.84:669.001:519.63

The effect of the Lorenz force on the origination of the electrovortex motion of a metal melt in dc electric steel furnaces with a bottom electrode is evaluated. The motion of a metal melt is described by equations of magnetic hydrodynamics for isothermal liquid, which are solved by the finite element method. The numerical solution is compared with theoretical results and experimental data of other authors. From analysis of the results obtained, conclusions are drawn that the Lorenz force has a marked effect on the origination of the vortex

motion of a melt.

**Keywords:** Lorenz force, electrovortex flows, numerical modeling, dc electric steel furnaces.