Volume 95, №3

THERMODYNAMIC ANALYSIS OF MULTISTAGE MECHANICAL SEPARATION PROCESSES
From the viewpoint of thermodynamics at a fi nite time, the limiting possibilities of mechanical separation systems
are considered. Lower limits of energy expenditure are obtained for separation systems with a given performance.
It is shown that these expenditures do not tend to zero, when one of the components of the mixture being separated
tends to a unit concentration. The estimates obtained are used to analyze multistage separation systems with recycles
and, in particular, isotope separation systems. For each systems, relationships between the fl ows, contact surfaces,
and the stage number are found, which follow from the conditions of minimum dissipation under the assumption of
the constancy of the enrichment factor. A condition of the optimality of the order of separation of multicomponent
mixtures in mechanical systems has been obtained.  
Author:  A. M. Tsirlin , A. I. Sukin , B. Andresen
Keywords:  multicomponent mixtures, multistage mechanical separation systems, realizability region, contact surface, entropy production, isotope separation
Page:  557

ACTUAL EFFICIENCY OF PISTON MACHINES
A thermodynamic analysis has been performed for the operation of piston machines using ideal and real gases as a working body in direct and inverse Carnot cycles. An interrelationship has been established between the fugacity coeffi cient of the working body (real gas) and the effi ciency of a piston thermal machine. Calculating formulas have been obtained for identifying the dependence of the effi ciency of such machines on the characteristics of their working body. Verifi cation has been conducted for the proposed method of thermodynamic potentials and the relations obtained on its basis connecting the actual effi ciency of a thermal machine with the fugacity coeffi cient of its working body  
Author:  V. G. Kiselev , A. A. Kalyutik , I. D. Naletov
Keywords:  piston machine, thermal engine, thermodynamic potentials, Carnot cycle, ideal gas, effi ciency
Page:  570

SPECIFIC FEATURES OF THE SYNTHESIS OF CERAMIC-METAL MATERIALS IN AN UNSTEADY COMBUSTION REGIME
A mathematical model has been constructed and investigated by numerical methods for unsteady gasless combustion of a binary mixture under the conditions of thermocapillary fl ow of the melt of one of the components. Various unsteady regimes have been identifi ed for the propagation of a synthesis wave depending on mass concentrations of components and the initial porosity of the mixture. An investigation has been made into the process of forming the macrostructure of synthesis products in a self-sustained oscillating regime of combustion. A possibility in principle has been shown for combustion of mixtures with excess of a low-melting component at a higher rate than in combustion of a mixture of a stoichiometric composition.  
Author:  O. V. Lapshin , V. A. Prokofiev
Keywords:  reagent melting, thermocapillary convection, conductive and convective combustion regimes, numerical modeling
Page:  581

ON THE CONFINED COMBUSTION OF A HYDRATE
A mathematical model of confi ned combustion of a gas hydrate has been presented that assumes full evaporation
of water on the "hydrate–gas" boundary. In accordance with this assumption, the processes of diff usion of the gas
through a liquid layer and the formation of a foam structure are excluded from the theoretical model, which leads to
its signifi cant simplifi cation. The infl uence of the transfer coeffi cient on the temperature and concentration fi elds of
the components of the gas mixture, and also their action on the intensity of decomposition of the gas hydrate have been
analyzed based on numerical calculations. It has been established that both the intensity of combustion of methane
and the intensity of decomposition of the gas hydrate grow with increase in the values of transfer coeffi cients. Here,
the speed of decomposition of the gas hydrate decreases with time. It has been shown that in the case of confi ned
combustion a burnout regime is likely to occur, with the hydrate decomposition occurring due to the heat stored in
the gas mixture  
Author:  I. K. Gimaltdinov , I. M. Bayanov , M. V. Stolpovskii , A. S. Chiglintseva
Keywords:  gas hydrate, combustion, phase transition, transfer coeffi cients.
Page:  591

FILM COOLING FOR A CYLINDRICAL HOLE WITH DOWNSTREAM CRESCENT-SHAPED BLOCK WITH PERPENDICULAR CROSSFLOW
Recent studies reveal that an internal coolant crossfl ow plays an important role in the fl ow fi eld and fi lm cooling
performance in the near-hole region. In the present paper a single array of cylindrical holes with crescent-shaped
blocks downstream is considered. The cooling performance under the quiescent coolant plenum conditions with a
perpendicular coolant crossfl ow are studied numerically at the blowing ratios 0.5–2.5. The height-to-diameter ratio
of the crescent-shaped block varies from 0.25 to 1.0 with an interval of 0.25. Based on the numerical results, it may
be deduced that a perpendicular crossfl ow induces an asymmetric pair of in-hole vortices and a biased coolant
coverage on the surface downstream of the hole exit. However, the bias direction depends on the value of the blowing
ratio. Compared with the quiescent plenum case, the perpendicular crossfl ow reduces the cooling performance, and
the benefi ts result from the crescent-shaped block downstream.  
Author:  C. Zhang , P. F. Zhang , P. F. Ju
Keywords:  fi lm cooling, crescent-shaped block, cooling eff ectiveness, internal crossfl ow, numerical simulation
Page:  599

STABILIZED NONSTATIONARY HEAT TRANSFER IN A CHANNEL WITH A BOUNDARY REGIME ON ITS SURFACE, THAT VARIES CYCLICALLY WITH TIME
Consideration has been given to laminar fl ow of a liquid with constant properties in a channel on whose surface
the temperature or density of the heat fl ux vary with time by a periodic law. An analytical solution to the problem of
convective heat transfer in general form has been obtained, using which it has been established that heat transfer
ceases to depend on the axial coordinate away from the inlet of the heated portion. Relations have been found
to calculate stabilized heat transfer. It has been shown that at a high frequency of the process, a nonstationary
stabilized heat-transfer coeffi cient varies noticeably over the period, however, its stabilization with time occurs as
the frequency is reduced. Data on fully stabilized heat transfer have been given for various shapes of the channel,
fl ow regimes, and boundary conditions.  
Author:  M. I. Supel′nyak
Keywords:  laminar channel fl ow, nonstationary cyclic heat transfer, stabilized heat transfer, complex non-selfadjoint Sturm–Liouville problem
Page:  608

THERMAL ANALYSIS OF A COMPOSITE CENTRIFUGAL COMPRESSOR IMPELLER
A heat calculation is presented for a centrifugal compressor impeller of a small-size composite gas turbine
engine. Consideration has been given to the existing approaches to designing centrifugal compressor impellers. A
description has been given of the methods of numerical simulation of the thermal state of a polysegment impeller of
a composite centrifugal compressor under the action of a thermal load. Temperature distribution has been obtained
for each individual element of the design and the assembly on the whole. We have determined the value of the
required consumption of cooling air to ensure a standard operation of the compressor in which the values of local
temperatures on the product do not exceed permissible temperatures of operation. Conclusions have been drawn
on the possibility of using polymer composite materials in heavily loaded components of advanced aircraft engines.  
Author:  L. V. Bykov , A. D. Ezhov ,  L. A. Martynyuk , D. B. Afanas′ev , M. A. Mezentsev
Keywords:  centrifugal compressor impeller, heat loading, polymer composite materials, numerical simulation
Page:  625

SIMULATION OF THERMAL AND ELECTRIC FIELDS IN ELECTRODES WITH ALLOWANCE FOR MELTING AND FRITTING OF FILMS
A mathematical model is formulated, and a fi nite-diff erence method and computer programs have been developed
that allow eff ective computer simulation of the process of thermal breakdown of contact fi lms. The system of equations
includes the Stefan problem, the equations of electric transfer and of a switched circuit. The axial symmetry of the
boundary-value problem conditions is assumed. A fi nite-diff erence method in a spherical coordinate system is used
for the solution. During the development of the process, the radius of the conducting bridge made of a molten
material changes by several orders of magnitude. An eff ective solution of this problem is the use of a "moving" grid
by corresponding replacing the variables. The results of the work can be applied in the practice of research and
design of electrical apparatuses and other electrotechnical devices.  
Author:  R. V. Arutyunyan
Keywords:  computer simulation, electric fi eld, calculation, temperature fi eld, metal electrode, Stefan problem, fi lms.
Page:  636

RADIAL DISTRIBUTION OF THE TEMPERATURE IN A WELL
A theoretical investigation of the radial temperature distributions in the upward and downward fl ows of fl uid in the
borehole of a production well has been performed. The radial diff erences between the temperatures at the axis and
wall of such a well in the cases of water and oil fl ows in it were determined.  
Author:  A. Sh. Ramazanov , R. A. Valiullin , M. A. Gallyamov
Keywords:  temperature logging, geothermal gradient, convective heat transfer, radial temperature distribution
Page:  642

MAGNETOTHERMOELASTIC INTERACTION IN A ROD OF FINITE LENGTH SUBJECTED TO MOVING HEAT SOURCES VIA ERINGEN'S NONLOCAL MODEL
The generalized nonlocal thermoelastic model in the context of Eringen's nonlocal elasticity is applied to investigate
the magnetothermoelastic interactions in a rod of fi nite length placed in a magnetic fi eld with a moving source. With
the use of the Laplace transform and numerical Laplace inversion techniques, the governing equations are solved,
and the solutions in the time domain are obtained numerically. The distributions of the nonlocal thermal stress,
temperature, and the displacement in the rod are obtained and presented graphically. The eff ects of the rotational
speed and the speed of the moving heat source, nonlocal parameter, and the applied magnetic fi eld intensity on the
considered variables are discussed in detail.  
Author:  A. M. Zenkour , A. E. Abouelregal
Keywords:  nonlocal thermoelasticity, fi nite rod, moving heat source, rotation, magnetic fi eld
Page:  651

OPTIMUM THICKNESS OF CIRCULAR ANISOTROPIC HEAT SPREADERS
Heat spreaders of diff erent designs made of diff erent materials were investigated. Numerous relations for estimating
the optimum thickness and the corresponding thermal resistance of these spreaders with an acceptable accuracy
have been obtained. The superiority of certain heat spreaders was demonstrated.  
Author:  F. Falakzadeh , R. Mehryar
Keywords:  anisotropic materials, heat conduction, critical thickness, electronic devices, cooling, heat spreaders.
Page:  662

HEAT AND MASS TRANSFER OF A GAS–AIR MIXTURE IN THE STACK OF AN EVAPORATIVE COOLING TOWER
It has been proposed that the discharge of stack gases of the waste heat recovery boiler of a gas-turbine installation into the atmosphere be carried out through the stack of a cooling tower with natural air ventilation. A technique and a PC computational program have been developed for the processes of heat and mass transfer during the motion of a gas–air mixture in the stack of a cooling tower. A calculation has been performed for the processes of heat and mass transfer occurring in a chimney-type cooling tower installed at a 200 MW CCGT (combined cycle gas turbine) unit of the Syzran′ CHP (combined heat and power plant) for two variants of its operation: without discharge or with discharge of stack gases from two heat recovery boilers into the atmosphere. The calculations have been performed for the summer period of the year. The analysis of the calculation results has shown that the proposed technical solution allows an additional reduction in the temperature of the circulating water at the outlet from the cooling tower by 1.31^oC (from 28.08 to 26.77^oC) and a rise in the effi ciency of the combined cycle gas turbine unit up to 50.82%, i.e., by 0.08%.  
Author:  S. K. Ziganshina , A. A. Kudinov
Keywords:  combined-cycle plant, heat recovery boiler, stack gases, cooling tower stack, atmospheric air, circulating water, heat and mass transfer, steam turbine condenser, effi ciency.
Page:  673

INFLUENCE OF THE THICKNESS OF A SPHERICAL ELECTRICALLY CONDUCTING LIQUID LAYER ON THE HEAT TRANSFER IN IT
Results of numerical simulation of the nonstationary heat transfer in a spherical layer of an electrically conducting
liquid and its magnetic hydrodynamics are presented. The infl uence of the thickness of this layer on the structure of
the liquid fl ow, the temperature and magnetic-induction fi elds, and the distribution of Nusselt numbers in the layer
was investigated with regard for the Joule heat dissipation in it  
Author:  S. V. Solov′ev
Keywords:  mathematical simulation, nonstationary heat-transfer, magnetic hydrodymanics, Joule heat dissipation, spherical liquid layer
Page:  680

DEPOSITION OF PROTECTIVE NANOSTRUCTURED DIAMOND-LIKE CARBON COATINGS ON ALUMINUM ALLOYS
λAn investigation has been made into the eff ects of preparation of the surface of aluminum alloy substrates on the adhesion to them of diamond-like carbon coatings with a high content of sp³ -bound carbon. Carbon coatings were deposited by the laser plasma method using a pulsed YAG:Nd³⁺ laser with the wavelength λ = 1064 nm, the pulse length at half-height ~20 ns, and the maximum pulse energy ~0.4 J. Highly oriented pyrolytic graphite has been used as a source of carbon. Coatings have been deposited on AMg aluminum alloy substrate. The possibility has been shown for the deposition of high-adhesion diamond-like carbon coatings with a high content of sp³ -bound carbon on aluminum alloys by the laser plasma method. An original method has been proposed for preparing the aluminum alloy surface before applying a protective carbon coating, with the said method consisting in the treatment of the substrate surface with plasma particles of an aluminum target accelerated to the energy of 1.5 keV  
Author:  V. K. Goncharov ,  G. A. Gusakov , M. V. Puzyrev
Keywords:  laser plasma, adhesion, carbon nanofi lms, aluminum alloys
Page:  693

HYBRID LATTICE BOLTZMANN EQUATION METHOD IN PROBLEMS OF COUPLED HEAT TRANSFER
A hybrid (LB–FD) mathematical model has been constructed to investigate thermogravitational convection in closed rectangular cavities limited on one side by a heat-conducting wall of fi nite thickness. Within the framework of the formulated approach, the hydrodynamics is simulated by the lattice Boltzmann equation method using a Bhatnagar– Gross–Krook approximation and a two-dimensional nine-velocity scheme, and energy and heat conduction equations are solved by the method of fi nite diff erences. Numerical simulation has been conducted in varying the Rayleigh number, thickness, and relative heat conductivity of a wall. It has been established that the developed hybrid model provides an adequate reproduction of local and average characteristics of coupled heat transfer. The computation speed of the LB–FD model is 10 times higher compared to the approach based on solving Navier–Stokes equations in transformed "vorticity–fl ow function" variables.  
Author:  A. É. Nee
Keywords:  lattice Boltzmann equation method, method of fi nite diff erences, natural convection, coupled heat transfer
Page:  700

ON THE CHOKING OF A GAS FLOW BY A GRANULAR BED
A study has been made of the eff ect of choking of a gas fl ow by isothermal and heat-releasing granular beds under
the conditions of a viscous-inertial regime of fl ow. An asymptotic expression has been obtained for the gas velocity.  
Author:  Yu. S. Teplitskii , E. A. Pitsukha , A. R. Roslik , M. V. Vinogradova
Keywords:  granular bed, choking of a gas fl ow, heat-releasing bed, viscous-inertial regime of fl ow.
Page:  708

MODELING AN ELASTIC STRESS IN A COLLOID CAPILLARY-POROUS BODY IN ITS DEHYDRATION BY DEPRESSURIZATION
Consideration has been given to combined eff ects of the pressure gradient and shrinkage on the distribution of
mechanical stresses in a wood specimen subjected to dehydration by depressurization. The time variation in the
moisture distribution across the specimen cross section has been identifi ed. The observed redistribution of moisture
from the center to the specimen surface results in the pressure gradient values being relatively low. Due to a more
uniform water content, there is also a decrease in mechanical stresses associated with shrinkage. Calculations have
shown that the eff ects of shrinkage are the most substantial in the case of water content reduction below the wood
hygroscopicity limit (fi ber saturation point), and also, in the case of dehydration of large-size specimens. The obtained dependences can be used for identifying treatment regimes for various materials without deterioration in their
consumer properties.  
Author:  N. M. Gorbachev , M. A. Brich , I. A. Koznacheev
Keywords:  dehydration, thermomechanical treatment, depressurization, colloid capillary-porous body, mechanical stress, shrinkage, modeling
Page:  716

SPECIFIC FEATURES OF THE DISPLACEMENT OF LIQUID DURING FILTRATION IN A LOW-POROSITY MEDIUM
The work is devoted to the study of the displacing ability of porous media in extraction of hydrocarbons from the
latter. Using the laws of mass and momentum conservation, the expression for the coeffi cient characterizing the
displacing ability of the medium in the resilient mode of deposit exploitation has been refi ned. It is shown that the
found expression diff ers from the classical concepts, as well as from the value of the compressibility coeffi cient of the
porous medium in the fi ltration approximation. It has been established that, in the general case, the compressibility
of a porous medium includes terms that depend not only on the macroscopic characteristics, but also on the
microstructure of the porous medium. Criteria are determined, under which the elastic properties of the medium do
not depend on its microstructure: when the densities of the liquid and of the skeletal material are equal and when the
porosity is independent of pressure, then the pore structure does not aff ect the compressibility of the porous medium.
Various physical conditions of the process are identifi ed, when it is necessary to introduce special concepts of
compressibility.
It is shown that when the porosity decreases to zero, the value of the coeffi cient characterizing the displacing
ability of the medium reaches the values that signifi cantly exceed the compressibility of the liquid. At the same
time, as the porosity tends to unity, this coeffi cient tends to the value of liquid compressibility. This behavior of the
coeffi cient indicates the existence of a physical eff ect consisting in the predominant contribution of skeletal material
deformation to the displacement process in the areas of the reservoir of oil and gas with a reduced porosity  
Author:  A. I. Filippov , P. N. Mikhailov
Keywords:  elastic medium, compressibility of a two-phase system, conservation laws, pressure, porosity, density
Page:  721

THERMAL CONDUCTIVITY OF WATER–PETROLEUM EMULSIONS AT A PRESSURE OF UP TO 20 MPa
The article presents the results of measurement of the thermal conductivity of water–petroleum emulsions of direct
and reverse types at a pressure of up to 20 MPa in the temperature range 293–353 K during the change of up to
50 vol.% in the volume content of the dispersed phase in the emulsion. The previously obtained correlation is suitable
for determining the thermal conductivity of water–petroleum emulsions of direct and reverse types in a wide range
of changes in the content of dispersed phase and of temperature and pressure parameters.  
Author:  V. G. Kucherov
Keywords:  petroleums (oils), water–oil emulsions, thermal conductivity, temperature, pressure, dispersed phase, dispersion medium
Page:  728

CONTROLLING THERMOMECHANICAL CHARACTERISTICS OF GAS FLOWS IN THE TURBOCHARGER OUTLET DUCT
The author has obtained data on gasdynamic and heat-transfer characteristics of nonstationary fl ow of a gas in
the outlet duct of the centrifugal compressor of a turbocharger for supercharging piston engines. It has been shown
that an equalizing grid installed in the outlet duct of the turbocharger centrifugal compressor reduces 2 to 3 times
the amplitude of pulsations of the gas-fl ow velocity in this duct, decreases its turbulence by 30%, and enhances
heat transfer in the duct by 13–25% compared to the basic duct without a grid. It has been established that cutting
grooves in the indicated channel leads to an increase of 9–12% in the gas turbulence in it; the local coeffi cient of
heat transfer in this duct increases 35% compared to the basic duct. Based on the numerical modeling of processes
occurring in the piston-engine′s turbocharger, the authors has demonstrated a positive eff ect from the equalizing grid
being installed in the outlet duct to the turbocharger centrifugal compressor and from the grooves being cut on its
walls, which consists in increasing the power of the engine by 2% and its effi ciency, by 0.25%.  
Author:  L. V. Plotnikov
Keywords:  turbocharger, centrifugal compressor, piston engine, gasdynamics, heat transfer, effi ciency indices.
Page:  734

MATHEMATICAL SIMULATION OF THE SUPERSONIC GAS FLOW OVER A WEDGE WITH AN ATTACHED SHOCK WAVE AND HIGH-TEMPERATURE EFFECTS
The development of a supersonic gas fl ow over a wedge in the process of interaction of a plane shock wave with the
wedge was mathematically simulated on the basis of solution of the Euler equations for the nonstationary fl ow of a
compressible inviscid gas in a two-dimensional space with regard for the high-temperature eff ects of ionization and
dissociation of the gas arising in the gas fl ow due to the balanced chemical reactions proceeding in it. The results of
solution of the problem on the supersonic gas fl ow over a wedge within the framework of the perfect-gas and real-gas
models were compared. The infl uence of the high-temperature eff ects in this fl ow on its characteristics and the angle
of inclination of a shock wave in it to the wedge was investigated.  
Author:  K. N. Volkov , V. N. Emel′yanov , A. G. Karpenko , S. S. Tolstoguzov
Keywords:  aerodynamics, supersonic fl ow, numerical simulation, shock wave, physicochemical processes, wedge
Page:  742

INTEGRAL CHARACTERISTICS OF MOTION OF DROPLETS OF LIQUIDS IN GAS MEDIA
The authors have given results of experimental investigations into the integral characteristics of motion of droplets of liquids in gas media as functions of the velocity of motion of a medium and its temperature and of the concentration of a vapor in it. Emphasis was placed on recording the size distributions of liquid droplets on diff erent portions of motion of the gas medium. A study has been made of the velocity of motion of the gas and its temperature and of the concentration of the vapor in it on the distribution of the droplets in a vapor–gas fl ow. The authors have been determined conditions with which each of the indicated parameters exerts a decisive infl uence on droplet distributions in the gas medium, and also conditions with which the infl uence of these parameters is small. Ratios of the rate of decrease in the size of the droplets to the velocity of their motion have been computed using the results of the conducted experiments. The distributions of liquid droplets in a moving gas medium ahead of the combustion front have been predicted under the conditions corresponding to the localization of and fi ghting a forest fi re.  
Author:  I. S. Voitkov , N. P. Kopylov , S. S. Kropotova , G. V. Kuznetsov , P. P. Tkachenko
Keywords:  droplets of a liquid, gas medium, forest fi re, size distribution of droplets, temperature, vapor–gas fl ow.
Page:  752

MAPS OF INTERACTION REGIMES OF WATER DROPLETS IN A GAS MEDIUM WITH ACCOUNT OF HIGH-SPEED SPATIAL VIDEO RECORDING
The authors give results of the performed comparative analysis of typical maps of interaction regimes of water droplets (recoil, scatter, breakup, and coagulation). Using a group of high-speed spatial video recording cameras, spatial and two-dimensional recording of collisions of droplets has been performed. The scientifi c novelty of the work is that the authors have corrected the ideas of the reasons for the diff erences of the existing maps of interaction regimes with account taken of the typical regularities of spatial recording of the droplet interaction. The most-in demand schemes of processing of experimental results have been used with account of the dimensionless angular and linear parameters of interaction, and also of the ranges of variation of the Weber number making it possible to assess the contribution of the dimensions and velocities of the droplets in determining the conditions of coagulation, recoil, scatter, and breakup in the latter. Diff erences of the interaction regimes in boundary (limiting) implementation conditions, and also in the number and dimensions of droplets formed upon the breakup have been singled out.  
Author:  O. V. Vysokomornaya , N. E. Shlegel′ , P. A. Strizhak
Keywords:  droplet of a liquid, interaction, collisions, recoil, coagulation, scatter, breakup
Page:  763

CONTROL OF THE SYNTHESIS OF COMPOSITE CORE–SHELL-TYPE PARTICLES IN A CONTINUOUS PLASMACHEMICAL REACTOR
Characteristics of composite titanium dioxide and silicon dioxide nanoparticles with a structure of the core–shell type, synthesized by the chloride method in a continuous plasmachemical reactor with supply of reagents by diff erent schemes, were investigated. For the composite nanoparticles obtained by these schemes, data on the size of the core of the particles, the thickness of their shell, and the ratio between the number of the particles covered with a shell and the number of the particles with no shell in a unit volume of the reactor have been obtained  
Author:  S. M. Aul′chenko , E. V. Kartaev
Keywords:  titanium dioxide, silicon dioxide, composite particle, plasmachemical reactor, multicomponent medium, homogeneous and heterogeneous reactions, coagulation
Page:  774

INFLUENCE OF RADIAL CHANGE IN GAS DENSITY ON NONLINEAR HYDRODYNAMIC EFFECTS IN ITS FLOW OVER A ROTATING DISK
A laminar boundary layer in a gas fl ow near a disk rotating at a constant angular velocity under the conditions of a signifi cant radial redistribution of the gas density is investigated. The analysis is performed on the basis of a selfsimilar transformation for the gas density varying according to a power law in the radial direction. Calculation of the boundary layer characteristics in the gas fl ow was made by the Slezkin–Targ method. The dependence of the resistance forces acting on the disk on the gas compressibility is investigated. It is shown that an increase in the radial gradient of the gas density leads to a noticeable increase in azimuthal friction forces in the boundary layer near the disk. The results obtained for an extended disk are used to estimate the intensity of the circulation fl ow in a rotating cylinder of fi nite dimensions at a small ratio of the height of the cylinder to its radius. As follows from the calculation results, an increase in the gas compressibility parameter leads to an increase in its circulation rate  
Author:  V. D. Borisevich , E. P. Potanin
Keywords:  laminar boundary layer, self-similar transformation, Slezkin–Targ method, intensity of circulation in the cylinder, gas compressibility
Page:  781

ACOUSTICS OF A VISCOELASTIC FLUID WITH GAS BUBBLES COATED WITH A VISCOELASTIC SHELL
An equation of radial vibrations of a gas bubble covered with a viscoelastic shell in a viscoelastic fl uid is obtained on the basis of the Kelvin–Voigt and Maxwell rheological models. For a bubble medium subjected to small perturbations, a dispersion equation is written with account for the interphase heat transfer. Based on the indicated rheological models, the infl uence of the viscoelastic shell of the bubble on the dynamics of the acoustic waves generated by the bubble has been investigated. The results of calculations for particular cases are compared with the experimental data available in the literature.  
Author:  D. A. Gubaidullin , Yu. V. Fedorov
Keywords:  acoustic wave, gas bubble, viscoelastic fl uid, dispersion equation, Kelvin–Voigt and Maxwell models
Page:  788

PHYSICOMATHEMATICAL MODELING OF THE DEFORMATION OF FLEXIBLE POLYMERS IN AN ULTRASONIC WAVE
The authors have given results of the investigation into the viscoelastic properties and processes of mechanical relaxation of systems based on polyvinylchloride with a 0–3.0 vol.% content of a nanodisperse-copper powder. The systems were obtained at a frequency of 0.4 MHz at a temperature of 298–353 K. From the Alfrey–Maxwell phenomenological approach, the authors have developed a method to determine the components of viscoelastic deformation of PVC systems under shear and volume loading. The maximum infl uence of the fi ller on the viscoelastic properties of such a system was found in the range of variation in the Cu content 0.05–1.00 vol.%. A quantitative interrelation has been established between the energy-exchange processes in PVC systems and ways have been indicated of using them in dynamic mechanical and temperature fi elds.  
Author:  B. B. Kolupaev , B. S. Kolupaev , V. V. Levchuk , Yu. R. Maksimtsev ,  V. A. Sidletskii , A. P. Vlasyuk
Keywords:  composite, viscoelasticity, ultrasound, structural relaxation, dynamic viscosity.
Page:  797

MATHEMATICAL MODELS OF THE STATE OF A REAL GAS
An overview of the development of mathematical models used to describe the relationship between the parameters of the state of real gases is presented: from the fi rst van der Waals and Berthelot models to modern multicomponent equations of state with virial coeffi cients GERG-2008 and its modifi cations. The analysis of the characteristic features and limitations of the application of the considered models in determining the parameters of state of a real gas is given, the existing relationship between the individual models is shown. Examples of practical use of gas state change processes in calculations are given for each model. The existing regulations (ISO standards, GOST standards) specifying the determination of the physical properties of real gases are indicated. When considering and analyzing the equations of state of a real gas, emphasis is placed on their application to determine the parameters of the state of natural gas in the processes of transportation through trunk pipelines, pressure reduction at gas distribution stations, liquefaction, etc. The results of the work can be useful in choosing optimal mathematical models of the state of a real gas that meet the purpose of the study and provide the necessary calculation accuracy  
Author:  O. M. Sokovnin , N. V. Zagoskina ,  S. N. Zagoskin
Keywords:  mathematical models, real gases, state parameters
Page:  806

CHANGES IN THE CRYSTAL STRUCTURE OF METALS IN THE COURSE OF THEIR LASER PROCESSING
By the x-ray diff ractometry method, the authors found a change in the crystal structure of a number of metals in the zone of exposure of their surface to laser radiation with a fl ux density of 10⁴ –10⁵ W/cm² . It has been shown that on exposure of the surface of metal samples to laser radiation, their crystal structure changes, in the exposed zone, from the equilibrium structure to a distorted one (having the shape of a parallelepiped, which is diff erent from a cube). A relationship has been assumed between the disclosed eff ect and the occurrence of considerable microstresses in the zone of rapid anisotropic heating of metals  
Author:  S. V. Vasil′ev , N. G. Val′ko , A. Yu. Ivanov , A. L. Sitkevich
Keywords:  laser radiation, x-ray diff ractometry, change in the crystal structure, correlation function.
Page:  821

TOWARDS ELASTOPLASTIC DEFORMATION OF A SOLID BODY BY THE HYBRID GODUNOV METHOD AND BY THE MULTIDIMENSIONAL NODAL METHOD OF CHARACTERISTICS
The paper presents the hybrid Godunov method designed for numerical calculation of elastoplastic deformation of a solid body within the framework of the Prandtl–Reuss model with a nonbarotropic equation of state. The Mises fl ow rule (yield creation) was used as a criterion for the transition from an elastic state to a plastic state. In calculating fl ow variables on the faces of adjacent cells, use was made of a linearized Riemann solver whose algorithm employs right own vectors of the model equation system. For equations written in a divergent form, use is made of fi nite-volume formulas, and for others that are not reducible to a divergent form, fi nite diff erence relationships are employed. Also, a description is given of a multidimensional nodal method of characteristics based on a coordinate splitting of the original system of equations into a number of one-dimensional subsystems with their subsequent integration with the help of a one-dimensional nodal method of characteristics. Using the proposed methods, a number of model problems has been calculated.  
Author:  V. S. Surov
Keywords:  elastoplastic deformation of a solid body, hybrid Godunov method, multidimensional nodal method of characteristics
Page:  830

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