#### Volume 89, № 5

**MINIMUM DISSIPATION PROCESSES IN IRREVERSIBLE THERMODYNAMICS**

The present paper considers the conditions for minimum entropy production in thermodynamic processes at a given mean intensity of fl uxes and at fi xed coeffi cients of kinetics equations, as well as the conditions for the optimum duration of the process.

**Author:**
A. M. Tsirlin

**Keywords:**
entropy, dissipation, reversible processes

**Page:**
1067

**DISTRIBUTION OF THE TRANSIT FLOW IN THE ROTOR OF A GAS CENTRIFUGE**

The present work is devoted to computation of the distribution of the transit fl ow in the rotor of a separation gas centrifuge. The existing transit-fl ow models have been considered, the equation to fi nd the transit fl ow has been obtained, and the basic properties of the transit fl ow have been analyzed. The general equation for the transit-flow distribution has been obtained, and the transit-fl ow distribution for a simplifi ed scheme of feed supply, extraction, and waste has been calculated

**Author:**
O. E. Aleksandrov

**Keywords:**
separation gas centrifuge, internal fl ow, transit flow

**Page:**
1079

**ENTRAINMENT OF SOLID PARTICLES FROM A FLUIDIZED-BED CYCLONE CHAMBER**

An experimental study has been made of the entrainment of crushed-corn particles of diameter d = 0.88 mm from a fl uidized bed with the vortex organization of an over-bed space. The dependence of the entrainment rate on the characteristics of the fl uidized bed and the cyclone chamber has been established.

**Author:**
E. A. Pitsukha, Yu. S. Teplitskii and V. A. Borodulya

**Keywords:**
fl uidized bed, cyclone chamber, entrainment of particles, relaxation time, Stokesian particle, Froude number

**Page:**
1087

**COMPUTER SIMULATION OF THE HYDRODYNAMIC PROCESSES OF CYCLONE DUST COLLECTORS**

In the present paper, the gas-dynamic fl ow structures in dust collectors with an internal louvered element and an external dust hopper and the traditional design of the NIIOGAZ type have been considered. The character of motion of particles of various median diameters in a cyclone dust collector has also been investigated. A survey has been made of the literature of foreign and home authors dealing with questions of fi ltration of solid particles in the gas fl ow in apparatuses of the centrifugal type [1, 2]. The arrangement and principle of operation of the cyclone dust collector is presented. The computational modeling of the fl ow was carried out by solving Reynolds-averaged Navier–Stokes (RANS) equations by the CFD method with the use of a k–ε turbulence model for four modes of operation of the apparatus

**Author:**
S. V. Plashikhin

**Keywords:**
cyclone dust collector, louvered element, aerodynamic drag, fractional effi ciency

**Page:**
1093

**IDENTIFICATION OF PARAMETERS OF A FRACTURED-POROUS RESERVOIR BY THE DATA OF UNSTEADY FLUID INFLOW TO VERTICAL WELLS**

The author proposes a numerical algorithm to indentify fi ltration and capacitory parameters of a fractured-porous reservoir by the results of hydrodynamic investigations of the well on the basis of the Levenberg–Marquardt method, which belongs to the methods of minimization of second order. The algorithm makes it possible to determine the total set of such parameters of a fractured-porous reservoir as the permeability coeffi cients of fractures and blocks, the parameters of fl uid crossfl ow between blocks and fractures, the characteristic delay times, the linear dimension of matrix blocks of rock, the piezoconductivity coeffi cients of blocks and fractures of the reservoir, the reservoir pressure, and the effi ciency of the well.

**Author:**
R. V. Sadovnikov

**Keywords:**
identifi cation, fractured-porous reservoir, inverse problem, regularization, minimization methods, scaling

**Page:**
1103

**MATHEMATICAL SIMULATION OF UNSTEADY-STATE GAS–LIQUID MIXTURE FLOW IN A BED–WELL SYSTEM**

Based on theoretical investigations, the infl uence of various forms of pressure variation at the wellhead with a nonstationary fl ow of a two-phase fl uid in a bed–well system on the character of change in the bottom-hole pressure has been investigated, which makes it possible to determine this pressure from the wellhead operation parameters. The trapezoidal form of the change in pressure is considered as an example. The coupled equations of fi ltration and the equations describing nonstationary motion of a gas–liquid mixture in a pipeline have been solved jointly. Analytical formulas have been obtained allowing one to determine the bottom-hole pressure from the technological parameters at the wellhead with account for the dynamic connection of the bed–well system at different forms of change in the wellhead pressure. The infl uence of the wellhead pressure pulsation frequencies on the bottom-hole pressure dynamics has been established.

**Author:**
É. M. Abbasov and S. A. Imamaliev

**Keywords:**
pulsation, gas–liquid mixture, multiphase medium, Laplace transform, mathematical model, equation of motion of a two-phase medium, averaging

**Page:**
1111

**METHANE GAS HYDRATE DECOMPOSITION IN A POROUS MEDIUM UPON INJECTION OF A WARM CARBON DIOXIDE GAS**

The characteristic features of methane gas hydrate decomposition upon injection of a warm carbon dioxide gas into a porous medium saturated with methane and its hydrate are investigated. A mathematical model is presented for heat and mass transfer in a porous medium accompanied by substitution of methane for carbon dioxide gas in the original gas hydrate. Self-similar solutions of a one-dimensional problem that describe the distribution of basic parameters in a stratum have been constructed. It is shown that there are solutions according to which methane gas hydrate may decompose either with the formation of carbon dioxide gas hydrate alone, or with the formation of both carbon dioxide gas hydrate and a mixture of methane with water. Critical diagrams of the existence of each type of solutions have been drawn.

**Author:**
M. K. Khasanov and V. Sh. Shagapov

**Keywords:**
porous medium, gas hydrate, filtration

**Page:**
1123

**CALCULATION OF THE GRANULOMETRIC COMPOSITION OF PRILLED PRODUCTS FROM THE MOST PROBABLE SIZE OF GRANULES**

The technique of calculating industrial centrifugal, static, vibrostatic, and spray granulators has been supplemented with the missing element — the calculation of the granulometric composition of a product from the most probable size of granules. Using the Kolmogorov–Avrami equation describing the degree of random conversion of granules in the space of their dimensions, constants for calculating various types of granulators have been obtained.

**Author:**
Yu. A. Taran, V. O. Bespalova, A. L. Taran and A. V. Taran

**Keywords:**
granules, granulator, granulometric composition, integral distribution function

**Page:**
1134

**"PRESSURE BLOCKING" EFFECT IN THE GROWING VAPOR BUBBLE IN A HIGHLY SUPERHEATED LIQUID**

The problem on the growth of a vapor bubble in a liquid whose superheating enthalpy exceeds the phase transition heat has been considered. A physical model of the "pressure blocking" in the bubble is presented. The problem for the conditions of the experiment on the effervescence of a butane drop has been solved numerically. An algorithm for constructing an analytical solution of the problem on the bubble growth in a highly superheated liquid is proposed

**Author:**
Yu. B. Zudin and V. V. Zenin

**Keywords:**
vapor bubble, pressure blocking, effervescence of a butane drop, analytical solution algorithm

**Page:**
1141

**BOILING OF A LIQUID ON MICROSTRUCTURED SURFACES UNDER FREE-CONVECTION CONDITIONS**

The authors have shown the possibilities of replacing complex and expensive technologies of manufacture of nanorough, microrough, and porous materials for boiling surfaces by a simple and resource-saving technique of mechanical treatment of surfaces: by the strain-cutting method. It has been established that the maximum levels of heat-transfer intensifi cation (as high as four to six times) during the boiling of distilled water and increase (of six times) in the critical heat fl uxes are inherent in surfaces obtained by the strain-cutting method with three-dimensional microfi nning with spacings of width 120–180 μm at a height of fi ns of 340–570 μm and their longitudinal spacing of 240–400 μm.

**Author:**
A. V. Shchelchkov I. A. Popov and N. N. Zubkov

**Keywords:**
boiling, intensifi cation, critical heat fl ux, microstructured surface

**Page:**
1152

**INFLUENCE OF FORCED CONVECTION ON THE SOLIDIFICATION OF METAL IN CAST-IRON AND CERAMIC INGOT MOLDS**

A nonstationary problem of solidifi cation of an ingot in molds with walls of varying thermal conductivity has been solved by the variational method with account taken of forced convection in the liquid phase of the metal. A formula for the temperature distribution in the liquid phase and the dependence of the time of advance of the solidifi cation front on its coordinates have been obtained. Numerical calculations of the time of solidifi cation of the ingot in castiron and ceramic molds have been done at different convection rates.

**Author:**
O. A. Kalashnikova and V. V. Dremov

**Keywords:**
functional, variation, solidifi cation front, ingot mold, thermal conductivity, heat resistance, heat-transfer coeffi cient

**Page:**
1161

**MOISTURE ADSORPTION ISOTHERMS AND THERMODYNAMIC CHARACTERISTICS OF TANNIC ACID**

Moisture adsorption isotherms of tannic acid were determined at 5, 15, and 35o

C with the use of the static gravimetric method in the range 0.113–0.980 aw (aw is the water activity). It was shown that tannic acid adsorbed more water

at 5o C. The experimental data fi tted well to the Guggenheim–Anderson–de Boer and Yanniotis–Blahovec equations, giving the corresponding parameters by nonlinear regression. The monolayer moisture content, number of monolayers, and the surface area of sorption were demonstrated to decrease with increasing temperature. Mesopores dominated below the monolayer moisture content followed by the formation of macropores. The variation of the differential enthalpy and entropy with the moisture content showed that water was strongly bound to the surface of tannic acid below the moisture content 5.0 g water/100 g dry basis. The adsorption process was found to be enthalpy-driven; however, it was not spontaneous at a low moisture content, as follows from the enthalpy–entropy compensation theory. The variation of the net integral enthalpy and entropy (at a constant spreading pressure) with the moisture content exhibited maximum and minimum values, respectively. This behavior indicated that water molecules were strongly bound to the tannic acid surface at the moisture content up to its monolayer values.

**Author:**
L. Červenka and L. Cacková

**Keywords:**
tannic acid, moisture sorption, thermodynamic properties

**Page:**
1168

**USE OF A VORTEX-TYPE CONTACT CONDENSER IN ABSORPTION OF METHANOL AND FORMALDEHYDE FROM A CONTACT GAS**

Consideration has been given to the process of absorption of methanol and formaldehyde from a contact gas in the production of technical formalin. Using computer simulation, the authors set up a model of a standard flow diagram of methanol and formaldehyde absorption of a contact gas. For the process of absorption, use was made of NRTL and Lee–Kesler mathematical models which allow for the heat and mass transfer. Empirical coeffi cients for these models have been determined. The amount of methanol and formaldehyde has been established in absorption gases utilized by burning with a standard fl ow diagram and on adding a supplementary stage of condensation. A comparison has been made of experimental and calculated data of the process. A heat- and mass transfer apparatus of the vortex type has been proposed, which will make it possible to remove an environmental burden and to improve energy-resource saving. The conditions of operation of the absorber with an increase of 22% in the output have been considered.

**Author:**
L. N. Moskalev and S. I. Ponikarov

**Keywords:**
simulation, NRTL and Lee–Kesler models, environment, energy-resource saving, methanol, formaldehyde, heat and mass transfer, contact condensation

**Page:**
1179

**NUMERICAL SIMULATION OF THE INTENSIFICATION OF THE HEAT EXCHANGE IN A PLANE-PARALLEL CHANNEL WITH A CYLINDRICAL SHALLOW DIMPLE ON THE HEATED WALL**

A comparison of the results of numerical calculations of the convective heat exchange in narrow plane-parallel channels with shallow cylindrical and spherical dimples on their wall heated by a constant heat fl ow under the conditions of low-velocity turbulent water fl ow in a channel at Re = 20,000 has been performed. Hydrodynamic features of the vortex intensifi cation of the heat exchange in the indicated channels as a result of the interaction of the swirling fl ows in them with the side walls of a dimple were determined. The thermal and thermohydraulic effi ciencies of a shallow cylindrical dimple were estimated. It is shown that this dimple offers substantial advantages over a spherical dimple of the same depth.

**Author:**
S. A. Isaev A. I. Leontiev P. A. Baranov,c UDC 532.517:4 I. A. Popov A. V. Shchelchkov and I. P. Gabdrakhmanov

**Keywords:**
intensifi cation of heat exchange, cylindrical and spherical dimples, narrow plane-parallel channel, multiblock computational technologies, intersecting structured meshes

**Page:**
1186

**DYNAMICS OF THE END-FACE BOUNDARY LAYER AND HYDRAULIC RESISTANCE OF A VORTEX CHAMBER WITH A SIDE SWIRLER**

The results of experimental and numerical investigations of the effect exerted by air fl ow rate and fl ow twist angle on the dynamics of an end-face boundary layer in a diaphragmed vortex chamber with a multislit lateral swirler are presented. Data on the hydraulic resistance of the chamber have been obtained. It is shown that gas injection through the slits of the lateral swirler leads to the formation of fl ow in the chamber of the same structure as that formed as a result of the injection uniformly distributed over the side wall with a smaller twist angle if the static pressure losses in the chamber in both cases are equal. Generalization of the dependence of the hydraulic resistance of the chamber on the effective fl ow twist angle is obtained for the investigated range of Reynolds numbers.
The results of experimental and numerical investigations of the effect exerted by air fl ow rate and fl ow twist angle on the dynamics of an end-face boundary layer in a diaphragmed vortex chamber with a multislit lateral swirler are presented. Data on the hydraulic resistance of the chamber have been obtained. It is shown that gas injection through the slits of the lateral swirler leads to the formation of fl ow in the chamber of the same structure as that formed as a result of the injection uniformly distributed over the side wall with a smaller twist angle if the static pressure losses in the chamber in both cases are equal. Generalization of the dependence of the hydraulic resistance of the chamber on the effective fl ow twist angle is obtained for the investigated range of Reynolds numbers.

**Author:**
R. Kh. Abdrakhmanov, V. V. Lukashov, M. S. Makarov, and V. S. Naumkin

**Keywords:**
vortex chamber, lateral swirler, end-face boundary layer, laser Doppler anemometry

**Page:**
1202

**HYDRAULIC RESISTANCE AND LIBERATION OF AIR IN AVIATION KEROSENE FLOW THROUGH DIAPHRAGMS AT LOW PRESSURE**

This paper presents the results of experimental investigations of the liberation of air in gravity fl ow of aviation fuel through a pipeline with diaphragms. Experiments were carried out in the pressure range 0.2–1.0 bar and temperature range –20 to +20o C. The TC-1 kerosene was preliminarily saturated with air at atmospheric pressure. The liberation of air after the diaphragms with three ratios of the fl ow area to the cross-sectional area of the pipeline has been investigated. The results of investigations of the two-phase fl ow in several experimental pipelines containing one or two diaphragms and other local hydraulic resistances have been generalized. The obtained approximation equations permit calculating the hydraulic resistance of the diaphragm in the two-phase fl ow and the mass gas content of air after the diaphragm in pipelines of complex geometry.

**Author:**
É. L. Kitanin, E. É. Kitanina, V. A. Zherebtsov, M. M. Peganova,b S. G. Stepanov, D. A. Bondarenko, and D. Morisson

**Keywords:**
diaphragm, hydraulic resistance, chromatograph, aviation fuel, two-phase fl ow, gas content, fuel consumption

**Page:**
1212

**DISTURBANCE OF A BOW SHOCK WAVE AND OF FLOW BEHIND IT IN THE CASE OF FLOW PAST BLUNT BODIES IN POLYATOMIC GASES**

A review has been presented of the results of experimental investigations, on a ballistic unit of the Physical-Technical Institute, into the distortion of a bow shock wave and of fl ow behind the body in CCl2F2 and CF4 polyatomic gases.

The latest experimental works at the Physical-Technical Institute and abroad have also been reviewed. The distortion of the bow shock wave under the same conditions is identically manifested in the case of fl ow past a segmental body

and past a sphere alike, although for the sphere, fl ow separation occurs farther downstream of the bow shock. In the case of fl ow past a cylinder the initial distribution of the fl ow is observed in the compression zone behind the bow

shock wave.

**Author:**
A. S. Baryshnikov, I. V. Basargin, S. V. Bobashev, N. A. Monakhov, P. A. Popov, V. A. Sakharov, and M. V. Chistyakova

**Keywords:**
bow shock wave, polyatomic gases, flow destabilization

**Page:**
1222

**THE GODUNOV METHOD FOR CALCULATING MULTIDIMENSIONAL FLOWS OF A ONE-VELOCITY MULTICOMPONENT MIXTURE**

V. S. Surov Computational formulas of the Godunov method are given for the equations of a generalized-equilibrium model of a heterogeneous medium on a curvilinear grid; with the use of this method, the problems of interaction of air

shock waves with bubbles of various gases are investigated. Flow of a gas–liquid mixture in a nozzle mouthpiece is considered. The Prandtl–Meyer fl ow of a water–air mixture is calculated and compared with a self-similar

solution.

**Author:**
V. S. Surov

**Keywords:**
one-velocity multicomponent mixture, hyperbolic systems of equations, Godunov method, characteristic Riemann solver, mathematical simulation

**Page:**
1227

**EXPERIMENTAL INVESTIGATION OF THE MIXED CONVECTION OF A GAS IN A RECTANGULAR ENCLOSURE WITH A LOCAL HEAT SOURCE AND HEAT REMOVAL AT THE OUTER BOUNDARIES**

The mixed convection of a gas in a parallelepiped with heat conducting walls and a local source of energy at its lower side was investigated experimentally. Local temperatures and velocities of the gas fl ow at different intensities

of its convection in this parallelepiped, characterizing the main mechanisms of the mixed convection of a gas in such a close space, were determined. The results of experimental investigations were compared with corresponding

calculation data and were in good agreement with them, which allowed the conclusion that the experimental procedure based on the thermocouple measurements and the use of PIV methods is applicable for analysis of the

regimes of fl ow of a heat-conducting viscous gas. Experiments have shown that the approach developed for the experimental investigation of the mixed convection of a gas in a rectangular enclosure with heat-conducting walls

and a local source of energy can be used in fairly wide ranges of change in the main parameters of the gas fl ow and in the conditions of supply of energy to it

**Author:**
G. V. Kuznetsov and V. I. Maksimov

**Keywords:**
mixed convection, convective heat exchange, thermocouple, heat generation, heat removal

**Page:**
1241

**TURBULENT TAYLOR–COUETTE FLOW AT LARGE REYNOLDS NUMBERS**

The problem of the steady-state turbulent fl ow of an incompressible fl uid in the clearance between two coaxial infi nite circular cylinders of radii R1 and R2, caused by the rotation of the inner cylinder of radius R1 under the conditions where the outer cylinder of radius R2 is immovable, i.e., the problem of a Taylor–Couette fl ow, was solved numerically within the framework of the model of a near-wall anisotropic turbulence with regard for the action of the centrifugal forces on the near-wall vortex structures determining the character of the fl ow between the cylinders. The profi les of the angular velocities of the fl uid fl owing along the radius of the clearance between the cylinders in the regime of completely developed turbulence were determined by numerical integration of the equation of motion of this fl uid. The results of calculations of the fl ow between the cylinders at R1/ R2 = 0.716 and Re = 105, 106, and 2·106 were compared with known solutions of the problem being considered and corresponding experimental data.

**Author:**
V. A. Babkin

**Keywords:**
near-wall turbulence, eddy viscosity, two-layer wall, flow subregions, angular-velocity profile

**Page:**
1247

**INTERNAL HEAT SOURCE IN A THERMOELASTIC HYDROSTATICALLY INITIALLY STRESSED PLATE IMMERSED IN A LIQUID**

An infi nite homogeneous isotropic generalized thermoelastic hydrostatically initially stressed plate involving an internal heat source and bordering on inviscid liquid half-spaces is considered. The normal mode analysis is used to obtain exact expressions for the displacement component, force stress, and temperature distributions. The numerical results are presented graphically for the Lord–Shulman theory of thermoelasticity when a mechanical force is applied to both of the plate sides. A comparison of the results in the presence and absence of a hydrostatic initial stress is made.

**Author:**
P. Ailawalia and A. Singla

**Keywords:**
thermoelasticity, hydrostatic initial stress, temperature distribution, normal mode, internal heat source

**Page:**
1255

**SIMULATION OF THE PROCESSES OF CATHODE ARC INITIATION BY A DISCHARGE OVER THE DIELECTRIC SURFACE IN THE FOREVACUUM REGION OF PRESSURES**

A physical model of cathode arc initiation by a discharge over the dielectric surface with allowance for the presence of residual gas molecules in the discharge gap is presented. This made it possible to determine the degree of residual

gas infl uence on the initiation processes and to calculate the dependence of the auxiliary discharge ignition voltage on pressure. A comparison of the results of modeling with experimental data is given.

**Author:**
A. V. Medovnik, I. Yu. Bakeev, V. A. Burdovitsin, A. V. Kazakov, and E. M. Oks

**Keywords:**
discharge over dielectric surface, forevacuum, simulation, arc discharge, initiation

**Page:**
1265

**CHARACTERISTIC FEATURES OF THE FORMATION OF A COMBINED MAGNETRON-LASER PLASMA IN THE PROCESSES OF DEPOSITION OF FILM COATINGS**

A block diagram of a facility for combined magnetron-laser deposition of coatings and of the systems of controlling and managing this process is considered. The results of analysis of the infl uence of the gas medium and of laser

radiation parameters on the emission-optical properties of laser plasma are considered. The infl uence of the laser plasma on the electric characteristics of a magnetron discharge is analyzed. The formation of the laser plasmainitiated

pulse arc discharge has been established and the infl uence of the laser radiation parameters on the electric characteristics of this discharge has been determined. The emission optical spectra of the magnetron discharge

plasma and of erosion laser plasma are compared separately and in combination

**Author:**
A. P. Burmakov, V. N. Kuleshov, and K. Yu. Prokopchik

**Keywords:**
magnetron discharge plasma, erosion laser plasma, combined magnetron-laser plasma, arc discharge, optical spectroscopy

**Page:**
1271

**NUMERICAL MODELING OF HEAT TRANSFER THROUGH A TRIPLE-PANE WINDOW**

The regularities of heat transfer through a triple-pane glass window with air and argon fi llings have been investigated by the method of numerical modeling. Distinctive features of this process have been elucidated which affect the

increase in the thermal resistance of triple-pane windows compared to double-pane ones. The thermal resistances of the triple-pane window as functions of the gas-interlayer thickness and of temperature on the window′s exterior

surface have been found.

**Author:**
B. I. Basok, B. V. Davydenko, S. A. Isaev, S. M. Goncharuk, and L. N. Kuzhel′

**Keywords:**
triple-pane window, numerical modeling, heat transfer, free convection, radiant heat transfer, thermal resistance

**Page:**
1277

**SIMULATION OF HEAT TRANSFER OF HEATING-SYSTEM AND WATER PIPELINES UNDER NORTHERN CONDITIONS**

A mathematical model of joint laying of water pipelines and of city-block heating-system pipelines is considered. The effect of radiation on the process of combined heat transfer in the heat insulation jacket between the construction elements is investigated. The results of mathematical simulation of heat losses with account of the radiant component are given.

**Author:**
A. V. Stepanov and G. N. Egorova

**Keywords:**
mathematical model, combined heat transfer, heat losses, emission coeffi cient, nonstationary temperature fi eld, general heat flux

**Page:**
1284

**INTEGRAL METHOD OF BOUNDARY CHARACTERISTICS IN SOLVING THE STEFAN PROBLEM: DIRICHLET CONDITION**

The integral method of boundary characteristics is considered as applied to the solution of the Stefan problem with a Dirichlet condition. On the basis of the multiple integration of the heat-conduction equation, a sequence of identical equalities with boundary characteristics in the form of n-fold integrals of the surface temperature has been obtained. It is shown that, in the case where the temperature profi le is defi ned by an exponential polynomial and the Stefan condition is not fulfi lled at a moving interphase boundary, the accuracy of solving the Stefan problem with a Dirichlet condition by the integral method of boundary characteristics is higher by several orders of magnitude than the accuracy of solving this problem by other known approximate methods and that the solutions of the indicated problem with the use of the fourth–sixth degree polynomials on the basis of the integral method of boundary characteristics are exact in essence. This method surpasses the known numerical methods by many orders of magnitude in the accuracy of calculating the position of the interphase boundary and is approximately equal to them in the accuracy of calculating the temperature profi le.

**Author:**
V. A. Kot

**Keywords:**
heat-conduction equation, Stefan problem, Dirichlet condition, moving interphase boundary, approximation, identical equality

**Page:**
1289

**COMPUTATIONAL INVESTIGATION OF THE TRANSPORT OF BURNING PARTICLES**

**Author:**
O. V. Matvienko A. I. Fil′kov and A. M. Grishin

**Keywords:**
forest fire, fire site, burning particles, convective column, heat exchange, turbulence

**Page:**
1315

**SIMULATION OF THE WORKING PROCESS OF A SUPERSONIC COMBUSTOR WITH A VORTEX IGNITER-STABILIZER**

Results of numerical simulation and experimental investigation of the working process of a vortex igniter-stabilizer are presented. It is shown that a high-temperature pulsating swirling jet provides reliable ignition of a fuel and its

stable combustion at a main-fl ow velocity of up to 2.5 M.

**Author:**
Sh. A. Piralishvili D. M. Markovich A. S. Lobasov and I. M. Vereshchagin

**Keywords:**
stabilization of a flame, swirling fl ow, acoustic vibrations, supersonic flow, ignition.

**Page:**
1325

**THE GRÜNEISEN FUNCTION FOR SOME POLYMERIC MATERIALS AND THEIR MIXTURES**

The dependence of the Grüneisen function of some polymeric materials on their density and temperature has been investigated. It is shown that in polymers having a complex macromolecular structure the temperature of the polymer vitrifi cation varies depending on the rate of the effect exerted on them and, as a consequence, the relationship between the molecular and intramolecular values of the Grüneisen function undergoes a change. A comparative analysis of the results of calculations and experimental data is made. Their good agreement is obtained.

**Author:**
A. M. Kugotova, A. Kh. Tsechoeva, B. I. Kunizhev and A. Kh. Adzhiev

**Keywords:**
polymers, Grüneisen function, density, temperature, volume, pressure

**Page:**
1333

**COMPUTATION OF THE HEAT FLUX IN A CYLINDRICAL DUCT WITHIN THE FRAMEWORK OF THE KINETIC APPROACH**

Within the framework of the kinetic approach, the authors have solved the problem on rarefi ed-gas fl ow in a cylindrical duct in the presence of the longitudinal temperature gradient. The Williams kinetic equation was used

as the basic equation, and the diffuse-refl ection model, as the boundary condition on the duct wall. This enabled the authors to consider the solution of the problem in linearized form. To fi nd a linear correction to the locally

equilibrium distribution function, the problem was reduced to solution of a linear homogeneous partial differential equation of fi rst order. A solution to the latter was constructed with the method of characteristics. With account taken of the obtained solution and on the basis of the statistical meaning of the distribution function of gas molecules by coordinates and velocities, the authors constructed the profi le of the heat-fl ux vector in the duct and computed the heat fl ux through the duct cross section. A numerical analysis of fi nal expressions was made. A comparison with analogous results obtained with the discrete-ordinates method has shown that the solution procedure proposed in the work leads to correct results in a wide range of values of the duct radius

**Author:**
O. V. Germider, V. N. Popov, and A. A. Yushkanov

**Keywords:**
Boltzmann kinetic equation, model kinetic equations, method of characteristics, gas flow in a cylindrical duct.

**Page:**
1338

**COMPUTER SIMULATION OF THE ELASTIC PROPERTIES OF TITANIUM ALLOYS FOR MEDICAL APPLICATIONS**

Results of a computer simulation of the elastic properties of α+β- and β-titanium alloys, used for medical purposes, within the framework of the molecular-dynamics method are presented. It is shown that β-titanium alloys are best

suited for the use as bone implants because of their small moduli of elasticity. The advisability of the use of the molecular-dynamics method for the study of the elastic properties of titanium alloys, serving as bone implants, is

demonstrated.

**Author:**
Elsa Paz Estevez, R. M. Burganova and Yu. V. Lysogorskii

**Keywords:**
titanium alloys of medical application, modulus of elasticity, molecular dynamics, MedeA-LAMMPS

**Page:**
1344