#### Volume 96, №3

**THERMODYNAMIC ANALYSIS OF IRREVERSIBLE PROCESSES OF THE REVERSE OSMOSIS AND DIFFUSION MACHINES**

A thermodynamic analysis of irreversible systems of reverse osmosis has been carried out. The relationship between
the effi ciency indicators of the process and the kinetics of mass transfer is analyzed, and an estimate of the limiting
capabilities of such a system is found. The conditions of the minimum irreversibility of the process at a given
performance are obtained. The thermodynamic possibilities of diff usion machines, in particular, machines that
generate energy by mixing fresh and salt water, are considered

**Author:**
A. M. Tsirlin

**Keywords:**
direct and reverse osmosis, entropy production, region of realizable regimes, diff usion machines, minimum dissipation conditions

**Page:**
555

**SIMULTANEOUS CONCENTRATION OF INTERMEDIATE MOLYBDENUM ISOTOPES IN A CASCADE WITH A GIVEN NUMBER OF GAS CENTRIFUGES IN STAGES**

A method has been developed for simultaneous concentration of molybdenum isotopes with intermediate atomic
mass in two additional products of a multi-fl ow cascade with a given number of centrifuges in stages. The method
takes into account the dependence of the separation factors of the cascade stages on the feed fl ow of gas centrifuges
and the fl ow division coeffi cient, which makes it possible to calculate the most effi cient operating modes. On its basis,
a computational experiment on the separation of molybdenum hexafl uoride was carried out. The infl uence of factors
related to the cascade feed fl ow and to the number of stages and gas centrifuges is investigated. It is shown that the
feed fl ows and the separation factors of the stages of gas centrifuge cascades diff er signifi cantly from rectangular
and rectangular-partitioned cascades

**Author:**
V. A. Palkin

**Keywords:**
separation of isotopes, isotopes of molybdenum, separation cascade, gas centrifuge, separation factor

**Page:**
568

**GENERALIZED MODEL OF THERMAL SHOCK IN DYNAMIC THERMOELASTICITY**

A generalized mathematical model of a thermal shock is developed in terms of dynamic thermoelasticity and its
application to specifi c cases of intense heating of the solid body boundary, namely, of the temperature, thermal,
heating by a medium. The model includes simultaneously three coordinate systems: Cartesian coordinates — a
massive body bounded by a fl at surface; spherical coordinates — a massive body with an internal spherical cavity;
cylindrical coordinates — a massive body with an internal cylindrical cavity. The presence of curvature of the
boundary surface dictates the initial formulation of the dynamic problem in displacements using the proposed
"compatibility" equation in displacements for dynamic models. A numerical experiment was carried out and the
wave nature of the propagation of a thermoelastic wave was described. Practically important engineering design
relations are proposed for the upper estimate of thermal stresses through stress jumps at the front of a thermoelastic
wave, obtained from operational solutions of dynamic problems. These relations allow one to quickly assess the
degree of danger of short-term dynamic stresses

**Author:**
É. M. Kartashov, S. S. Krylov

**Keywords:**
thermal shock, mathematical model, dynamic thermoelasticity, thermal stresses

**Page:**
573

**THREE-DIMENSIONAL SIMULATION OF HEAT AND MASS TRANSFER BY THE HYBRID LATTICE BOLTZMANN METHOD**

A hybrid model has been developed to analyze the process of joint mass and heat transfer in a three-dimensional
formulation. The fl ow velocity was calculated using the mesoscopic lattice Boltzmann equations, and the temperature
and concentration fi elds were obtained by fi nite-diff erence solution of the macroscopic energy and diff usion equations.
Numerical studies were performed by varying the Rayleigh and Lewis numbers and of the ratio of lift forces (BR)
due to temperature and concentration gradients. It is established that at BR ≤ 0 and BR ≥ 2 stratifi ed concentration
and thermal fi elds are formed in the cubic cavity. Three fl ow regimes are distinguished depending on BR: quasitwo-dimensional, three-dimensional nonstationary and two-dimensional. Correlation formulas are proposed for
calculating the average Nusselt and Sherwood numbers.

**Author:**
A. É. Nee

**Keywords:**
method of lattice Boltzmann equations, fi nite diff erence method, natural convection, mass transfer

**Page:**
585

**EVALUATION OF HEAT TRANSFER IN A FLEXIBLE FIBROUS HEAT-INSULATING COMPOSITION**

A model of the structure of a fl exible heat-insulating composition is proposed, which is a highly porous fi brous material, felt, covered on all sides with a cloth. The entire composition is stitched-out with thread. The felt, cloth, and sewing thread are made of silicon oxide fi bers of various diameters. An algorithm is proposed for calculating the eff ective thermal conductivity of its components: radiative and conductive in the solid phase and molecular through the gas in pores. To estimate the radiative component of thermal conductivity in the fi brous core, the Mie theory and the approximation of an optically dense medium were used. The calculation results agree with the experimental data obtained by the stationary method on fl at samples in the temperature range from 20 to 800^{o}C in vacuum and in an
inert gas medium

**Author:**
A. V. Zuev, Yu. P. Zarichnyak, N. N. Vorob′ev, S. L. Barbot′koa

**Keywords:**
fi bers, fl exible, thermal insulation, structure model, thermal conductivity, calculation

**Page:**
594

**SIMULATION OF THE PROCESS OF HEAT AND MASS TRANSFER IN COMPOSITE MATERIALS DURING FIRE**

Based on theoretical and experimental data, a refi ned mathematical model of thermochemical destruction of a
multilayer composite material has been constructed. It has been established that the lining with a swelling material
provides reliable protection of the body from the action of fi re. Accounting for the fl ow of heat across the body made
it possible to more accurately predict the state of the protected structure. The results of numerical calculations are
compared with well-known data

**Author:**
D. P. Kasymov, V. V. Perminov, A. A. Shevlyakova, A. S. Yakimov

**Keywords:**
swelling fi re-protective coating, porous steel, thermal conductivity

**Page:**
604

**HEAT TRANSFER OF AN ELECTRICALLY CONDUCTING LIQUID DURING THE REMOVAL OF HEAT FROM THE EXTERIOR SURFACE OF A SPHERICAL LAYER, AT SMALL VALUES OF THE MAGNETIC REYNOLDS NUMBER**

Results of the numerical modeling of the nonstationary heat transfer and magnetic hydrodynamics of an electrically
conducting liquid in a spherical layer have been presented. A study has been made of the infl uence of small values of
the magnetic Reynolds number and the dissipation of Joule heat on the evolution of the structure of liquid fl ow, the
temperature fi eld, magnetic induction, and the distribution of Nusselt numbers

**Author:**
S. V. Solov′ev

**Keywords:**
mathematical modeling, nonstationary heat transfer, magnetic hydrodynamics, magnetic Reynolds number, Joule-heat dissipation, spherical layer

**Page:**
612

**THERMAL RESISTANCE OF A TUBULAR RADIATOR OF THE HYBRID SYSTEM FOR COOLING CIRCULATING WATER**

Modern types of cooling towers for cooling liquids include hybrid type units making it possible to eff ectively remove
heat from process equipment while meeting environmental safety requirements. A cooling tower with a hybrid system
of cooling the circulating water of industrial enterprises has been developed. Its design features are the use of a
sprinkler block with inclined-corrugated contact elements and a tubular radiator to exclude direct contact of the
main fl ow of circulating water with air. The purpose of this work is to determine the main resistance to heat transfer
during the fl ow of wetting water past the outer surface of the radiator pipes in a hybrid cooling tower. Mathematical
description of cooling the circulating water in a hybrid cooling tower has been developed. The results of theoretical
studies have shown that the value of the thermal power removed from the surface of pipes in a hybrid system for
cooling circulating water is signifi cantly aff ected by the temperature characteristics of the heat carrier, wetting
(cooling) liquid, as well as their fl ow regimes. Comparison of experimental and theoretical data on the change in the
heat power removed from the surface of the radiator tubes confi rmed the adequacy of the developed mathematical
description of the cooling process in the developed hybrid cooling tower

**Author:**
I. N. Madyshev, V. V. Khar′kov, V. É. Zinurov

**Keywords:**
hybrid cooling tower, heat transfer, thermal resistance

**Page:**
627

**INTERFEROMETRIC DATA ANALYSIS OF CONVECTIVE HEAT TRANSFER UNDER A DOWNWARD-FACING HORIZONTAL CIRCULAR PLATE**

Interferometric data are analyzed to investigate heat transfer under a heated horizontal circular plate suspended in
air at ambient temperature. To achieve an accurate reconstruction of the axisymmetric temperature fi eld, the twodimensional continuous wavelet transform and the Chebyshev wavelet method are used in the fringe shift process
and in the Abel inversion, respectively. The results obtained are evidence for good agreement with the Nusselt
number correlation given in the previous work. For the investigated Rayleigh numbers, the medium is axisymmetric
and stratifi ed in the vicinity of the plate. The accuracy of interferometric techniques is very sensitive to the methods
used in the post-processing of the interferometric data.

**Author:**
A. Ait Haj Said, M. Elfagrich, Y. Dahanic

**Keywords:**
natural convection, circular plate, downward-facing plate, holographic interferometry, wavelet transformation, Abel inversion, Nusselt number

**Page:**
636

**CHARACTERISTICS OF VISCOPLASTIC FLUID FLOW AT VARIOUS HEAT TRANSFER REGIMES ON THE WALLS OF A SUDDEN CONTRACTION CHANNEL**

Consideration is given to the problem of laminar axisymmetric fl ow of viscoplastic fl uid in a channel with a sudden
cross-sectional contraction under the conditions of a variable ambient temperature. A mathematical process model
is presented that includes a vortex transfer equation, the Poisson equation for the stream function, and the energy
equation with account for viscous dissipation. To describe the rheological properties of a fl uid, use is made of
a modifi ed Schwedoff –Bingham model within whose framework account is taken of the dependence of apparent
viscosity on temperature. In the course of solving the problem, the false transient method and the numerical fi nite
diff erence methodology were employed. Two heat transfer regimes on the channel walls are investigated: in the fi rst
case, a constant temperature value is assigned over the entire length of the wall, and, in the second case, a constant
temperature is assigned on the walls in the vicinity of the inlet and outlet, and in the vicinity of the contraction plane,
zero heat fl ux is assessed. The infl uence of thermal conditions on the structure of the fl ow and local pressure losses
are assessed. The results of calculations in the form of distributions of fl ow characteristics as a function of the basic
parameters of the problem are provided.

**Author:**
K. E. Ryl′tseva, G. R. Shrager

**Keywords:**
numerical simulation, channel contraction plane, viscoplastic medium, fl ow, viscous dissipation, boundary conditions, local resistance, unyielded region

**Page:**
649

**KINETICALLY AND AGGREGATIVELY UNSTABLE OIL DISPERSE SYSTEMS**

An analysis is made of kinetically and aggregatively unstable non-Newtonian oil disperse systems and of the reasons
for the occurrence of this instability that are associated with the coalescence of droplets and their settlement. In
this connection, the authors have proposed models of thinning and rupture of the interphase non-Newtonian fi lm
between two joined droplets, and also the model of change in the thickness of the interphase fi lm. The Ostwald–de
Waele model satisfactorily describing pseudoplastic properties of oil was taken as the basis for the investigation.
A model of settlement of particles in a non-Newtonian oil was proposed. The proposed models were compared with
the existing experimental data, which has shown their effi ciency. Consideration has been given to the conditions of
self-organization of aggregatively and kinetically unstable disperse systems. It has been noted that such systems, in
the case of infi nite time, have no hereditary memory

**Author:**
G. I. Kelbaliyev, D. B. Tagiyev, M. R. Manafov, F. R. Shykhyeva

**Keywords:**
aggregative and kinetic instability, disperse systems, coalescence of droplets, non-Newtonian oil, sedimentation of particles, self-organization, hereditary memory

**Page:**
660

**UNIFIED APPROACH TO MODELING EQUILIBRIUM FLOWS OF DETONATING GASES**

An approximate model of chemical equilibrium is formulated for modeling detonation processes in reacting gas
mixtures. In comparison with exact (more detailed) models, this model uses additional physical assumptions allowing
one not only to expand the scope of its application, but also to signifi cantly simplify the form of the system of
equations being solved. It is shown that for adequate (consistent with experiment) calculations of the gas dynamics of
detonation fl ows, it is quite suffi cient to describe the components of detonation products by a standard and limited set
of substances. A procedure has been proposed to unambiguously determine the molar fractions of these substances
in a state of chemical equilibrium, employing only the relative concentrations of atoms such as oxygen, carbon,
hydrogen, nitrogen, and any other monatomic inert substances, such as argon

**Author:**
E. S. Prokhorov

**Keywords:**
gaseous detonation, gas dynamical parameters, combustion products, chemical equilibrium, carbon condensation

**Page:**
669

**ON THE VELOCITY OF PROPAGATION OF A FLAME IN A COAL–METHANE–AIR SUSPENSION**

A numerical investigation of the velocity of propagation of a fl ame in the coal dust suspended in a poor methane–air
mixture has been performed with the use of the two-velocity model of a two-phase reactive disperse gas medium. It
is shown that the presence of a small amount of methane in the air in which a coal dust is suspended increases the
velocity of propagation of a fl ame in the air suspension. An increase in the size of the coal-dust particles suspended
in a poor methane–air mixture ambiguously infl uences the velocity of propagation of a fl ame in it: the velocity of a
fl ame in a methane–air mixture containing a small amount of coal particles decreases and the velocity of a fl ame in
such a mixture with a large amount of coal particles increases with increase in their size concentration. The ranges
of application of the model of combustion of a coal–methane–air mixture, developed, were determined

**Author:**
gas suspension, coal dust, methane–air mixture, combustion, numerical simulation

**Keywords:**
K. M. Moiseeva, A. Yu. Krainov, D. A. Krainov

**Page:**
678

**SIMULATION OF THE NONSTATIONARY BURNING OF A SOLID PROPELLANT IN A COMBUSTION CHAMBER AND CALCULATION OF THE ACOUSTIC ADMITTANCE OF THE COMBUSTION SURFACE OF THIS PROPELLANT**

With the use of the model of the nonstationary burning of a solid propellant in a combustion chamber and the model
of the gas dynamics of the fl ow of the combustion products of this propellant, the nonstationary burning of a solidpropellant charge and the fl ow of its combustion products in a T chamber were numerically simulated. Simulation of
the formation and damping of the acoustic vibrations in a T chamber has been performed. Results of calculation of the
acoustic admittance of the combustion surface of a powder N are presented. The calculated theoretical dependences
of the acoustic admittance of the combustion surface of this solid propellant on the frequency of oscillations of the
pressure and on the average pressure in a T chamber are in qualitative agreements with the available corresponding
experimental dependences

**Author:**
A. Yu. Krainov, V. A. Poryazov, K. M. Moiseeva

**Keywords:**
T chamber, solid propellant, variable pressure, nonstationary burning, acoustic admittance, combustion surface

**Page:**
688

**USE OF A RESONANT VIBRATOR POSITIONED PERPENDICULARLY TO THE OPTICAL AXIS OF A COMBUSTION CHAMBER FOR AMPLIFICATION OF THE ELECTROMAGNETIC FIELD IN IT**

An electrodynamic model of a combustion chamber, in which a combustible mixture is ignited by a suberitical
streamer discharge initiated by a vibrator with the use of a microwave radiation, is presented. For localization
of this discharge in the combustion chamber, its initiator (vibrator) is positioned perpendicularly to the optical
axis of the chamber. The possibilities of amplifi cation of the electromagnetic fi eld at the poles of the vibrator in
the case where a microwave radiation is introduced into the chamber with the use of a plane horn and in the case
where a planar waveguide is used for this purpose were considered. Numerical calculations of the electric fi eld in
which a subcritical streamer discharge is formed in a combustion chamber have been performed with regard for the
geometric parameters of the initiator of this discharge. The ways of amplifi cation of the resultant electromagnetic
fi eld in the region of disposition of a vibrator in a combustion chamber were determined for the purpose of obtaining
a subcritical streamer discharge with a volumetric structure in the chamber

**Author:**
P. V. Bulat, K. N. Volkov, I. I. Esakov, P. B. Lavrov, A. A. Ravaev

**Keywords:**
microwave radiation, streamer discharge, electrodynamic model, plasma combustion

**Page:**
700

**ELECTRODYNAMIC MODEL OF A COMBUSTION CHAMBER WITH AN INITIATOR OF A SUBCRITICAL STREAMER DISCHARGE POSITIONED PARALLEL TO THE OPTICAL AXIS OF THE CHAMBER**

An electrodynamic model of a combustion chamber, in which a combustible mixture is ignited by a subcritical
streamer discharge initiated with the use of a microwave radiation, is considered. For localization of this discharge
in the combustion chamber, its initiator (a vibrator) is positioned parallel to the optical axis of the chamber. On the
basis of numerical calculations, the dependences of the structure of the electric fi eld, in which such a discharge is
formed, on the geometric parameters of the vibrator and its conductivity have been obtained. For determining an
optimum disposition of a vibrator in a combustion chamber, the calculations for its diff erent shifts from the optical
axis of the chamber have been performed. The ways of increasing the resultant electromagnetic fi eld in the region of
disposition of a vibrator in a combustion chamber for formation of a volume discharge in it were determined

**Author:**
P. V. Bulat, K. N. Volkov, I. I. Esakov, P. B. Lavrov, A. A. Ravaev

**Keywords:**
microwave radiation, electrodynamic model, plasma burning

**Page:**
710

**MODEL FOR OPTIMIZATION OF EXTINGUISHING FIRES OF SOLID MATERIALS BY COOLING**

Fires involving solid combustible materials are, as a rule, eliminated by supplying water mist onto a burning surface.
Problems of current importance include determination of optimum intensity and duration of water supply to ensure
successful suppression of combustion in the case of fi res of various strength. This paper off ers a mathematical model
of optimizing the process of fi re suppression for solid combustible materials. Using the heat conduction equation, an
analytical solution has been obtained to determine the time for water supply to the seat of fi re for its suppression,
which depends on the thermophysical properties of combustible materials, the power of the heat impact of the
combustion source on these materials, the time of free fi re development, and the intensity of water supply. The results
of the performed calculations illustrate the effi ciency of solving problems of optimizing the extinguishment of fi re
seats involving solid combustible materials

**Author:**
N. P. Kopylov, R. A. Yailiyan, E. Yu. Sushkina, S. S. Kropotova, P. A. Strizhak

**Keywords:**
solid combustible material, combustion and extinguishment regimes, optimization model, cooling method

**Page:**
717

**SPECIAL FEATURES OF RELAXATION PROPERTIES OF ELASTOMER COMPOSITIONS WITH HIGHLY DISPERSED CARBON ADDITIVES**

The infl uence of three diff erent nanostructured carbon materials: nonfunctionalized and functionalized with
oxygen- and amino-containing groups on the relaxation properties of elastomer compositions was studied. Rubber
compounds based on natural rubber and nitrile butadiene rubber were used as elastomeric matrices. Determination
of the relaxation properties of rubber compounds and rubbers based on them was carried out on the basis of
calculations of the stress relaxation coeffi cient and the conditionally equilibrium modulus. It has been established
that functionalized carbon nanomaterials exert the most signifi cant eff ect on the acceleration of relaxation processes
in rubber compounds based on polar rubber due to a possible decrease in the intermolecular interaction of its polar
groups. In compositions based on natural rubber, the introduction of functionalized nanomaterials increases the rate
of relaxation processes only in compositions with semi-reinforcing carbon black, which is due to the lower interactions
of elastomer macromolecules with chain structures of the fi ller. It has been found that in compositions based on
nitrile butadiene rubber, the use of carbon nanomaterials, in comparison with rubber without nanoadditives, leads to
an increase in the conditionally equilibrium modulus in vulcanizates with both semi-reinforcing and high-reinforcing
carbon black at a dosage of 50.0 wt.pts. Rubbers based on nonpolar rubber containing carbon nanomaterials are
characterized by increased values of conditionally equilibrium modulus only in the case of compositions with semireinforcing carbon black at a dosage of 50.0 wt.pts.

**Author:**
Zh. S. Shashok, N. R. Prokopchuk, E. P. Uss, S. A. Zhdanok, A. V. Krauklis

**Keywords:**
rubber, vulcanized rubber, carbon nanomaterials, relaxation coeffi cient, conditionally equilibrium modulus

**INTRODUCTION OF REINFORCING PARTICLES INTO LIQUID ALUMINUM**

A method for introducing reinforcing microparticles of boron nitride, BN, into an aluminum melt A0 is described.
Reinforcing particles in the composition of tablets pressed in a mixture with aluminum microparticles were
introduced into liquid aluminum. The aluminum was in a crucible and was intensively stirred by a traveling and
rotating magnetic fi eld. Subsequently, the melt crystallized directionally, after which its structure was studied using
an electron microscope FEI Quanta 650FEG with an x-ray microanalysis EDAX Octane Elite attachment and an
optical microscope Hirox KH-7700. The specifi c electrical resistance of the obtained composite and its mechanical
characteristics were also determined in the experiment. In this work, the electromagnetic and hydrodynamic
characteristics of the stirred melt were calculated numerically (ANSYS MAXWELL 3D and ANSYS CFX packages,
respectively, were used). Patterns of the velocity fi elds and of the shapes of the free surface during the introduction
of particles into the liquid metal are presented. Experiments have shown that aluminum composites fi lled with
nanoparticles diff er in physical properties from aluminum composites with microparticles. With an increase in the
concentration of BN nanoparticles (100 nm) in aluminum A0 from 0 to 1.3%, its electrical resistance increases by
4%, and the ultimate strength becomes higher by 13%. With an increase in the concentration of BN nanoparticles
(3–5 μm) in aluminum A0 from 0 to 1.3%, its electrical resistance increases by 6.8%, and the ultimate strength,
respectively, only by 4%. The experiment showed that an increase in the percentage concentration of reinforcing
nanoparticles in aluminum leads to a faster increase in the ultimate strength and to a slower increase in the electrical
resistivity than with the introduction of reinforcing microparticles.

**Author:**
S. Yu. Khripchenko, V. M. Dolgikh, R. R. Siraev

**Keywords:**
MHD mixing, aluminum composite, introduction of reinforcing particles, electrical resistance, ultimate strength, numerical experiment

**Page:**
732

**NUMERICAL SIMULATION OF A TWO-DIMENSIONAL SPATIAL UNSTEADY FLOW PAST THICK AIRFOILS AND LOW-ASPECT-RATIO WINGS WITH SLOT SUCTION IN A VORTEX CELL AS APPLIED TO HYBRID AEROSTATIC AIRCRAFT**

Using numerical simulation on the basis of Reynolds-averaged Navier–Stokes equations in their closure with the
SST turbulence model, a comparison has been conducted of the self-oscillating modes of fl ow around a thick airfoil
and a low-aspect-ratio wing with a vortex cell in the presence or absence of slot suction. The inclusion of suction
with placement of a ventilator in the off take channel and with jet ejection in the vicinity of the back edge of a twodimensional airfoil, and also suction into the engine unit on the inner contour of the vortex cell of a thick airfoil
stabilize the fl ow past bodies and improve substantially their aerodynamic characteristics. In a two-dimensional
case, the aerodynamic quality increases to 7 and in a three-dimensional variant, it increases to 2.7.

**Author:**
S. A. Isaev, A. E. Usachov, S. A. Sustin, S. A. Isaev, A. E. Usachov, S. A. Sustin,

**Keywords:**
thick airfoil, low-aspect-ratio wing, vortex cell, turbulence, calculation

**Page:**
742

**GAS-DYNAMIC PROCESSES IN A ROTATING CYLINDER IN THE PRESENCE OF AXIAL TEMPERATURE GRADIENTS**

A three-dimensional fl ow of a viscous heat-conducting gas in a rapidly rotating straight circular cylinder in the
presence of axial temperature gradients is studied. At the initial stage, gas-dynamic and thermal boundary layers on
a rotating extended disk are considered. When taking into account the temperature change in density, the Dorodnitsyn
transformation is used, which makes it possible to reduce the solution of the problem to the integration of a system
of ordinary diff erential equations. Taking into account inertial eff ects, an approximate analytical solution of the
problem is obtained in the case of small values of the Prandtl number, when the thermal boundary layer thickness
exceeds the thickness of the hydrodynamic layer. The result of the calculation for an extended disk is used to estimate
the intensity of the axial circulation fl ow in a rotating cylinder of fi nite dimensions. The infl uence of the intensity of
temperature perturbation on the radial profi le of circulation in a rotor is studied

**Author:**
V. D. Borisevicha, E. P. Potanin

**Keywords:**
rotating cylinder, viscosity, thermal conductivity, circulation fl ow, temperature gradient

**Page:**
754

**INFLUENCE OF THE SWIRLING OF AN EQUILIBRIALLY DISSOCIATING GAS FLOW IN A TUBE ON HEAT EXCHANGE AND CHEMICAL REACTION IN IT**

Results of mathematical simulation of the infl uence of the swirling of a fl ow of an equilibrially dissociating heattransfer agent (nitrogen tetroxide) in a tube on the heat transfer and the chemical reaction in it are presented. It
is shown that an increase in the intensity of swirling of such a fl ow in a tube increases the rate of heat exchange
in it, with the result that the Nusselt number of the fl ow increases. In this case, the heat transfer in the fl ow
depends not only on the integral intensity of its swirling but also on the method of organization of the fl ow
swirling. It was established that, in the case of active action of the centrifugal forces on this fl ow, the turbulent
disturbances arising in it cause its heat-transfer coeffi cient to increase, and, in the case of conservative action of
the centrifugal forces on the fl ow, its heat transfer coeffi cient decreases. It is shown that the rate of heat exchange in
the indicated fl ow can be controlled by changing the tangential component of the velocity of the fl ow along the radius
of the tube

**Author:**
O. V. Matviyenkoa, P. S. Martynov

**Keywords:**
heat exchange, chemical reaction, boundary layer, swirling fl ow, computational hydrodynamics

**Page:**
763

**COMPARISON OF CALCULATED AND EXPERIMENTAL DATA FOR SUPERSONIC FLOW AROUND A CYLINDRICAL MODEL AND EVALUATION OF POSSIBLE METHODS FOR REDUCING MAXIMUM BODY TEMPERATURES**

In development of earlier works on estimating the maximum temperatures of a shell immersed in a fl ow, a conjugate
problem of nonstationary heat transfer in a supersonic fl ow around a spherically blunted hollow cylindrical model is
considered for the conditions of some previous experimental studies [1–4]. The calculated and experimental data are
compared, and the possible ways of reducing the maximum body temperatures are evaluated both by choosing the
geometric characteristics of the model and of the thermophysical characteristics of materials, including the possible
presence of a two-layered cylindrical holder. It is shown that the obtained dimensionless relations allow one to carry
out quick estimation of the decrease in maximum temperatures

**Author:**
V. I. Zinchenko, V. D. Gol′din

**Keywords:**
supersound, thermal protection, conjugate heat transfer, heat-shielding materials

**Page:**
776

**REDUCTION IN THE INTENSITY OF HEAT AND MASS TRANSFER IN CRYOGENIC FLUID IN A HORIZONTAL RESERVOIR**

An approach is proposed to increasing the time of storage of cryogenic fl uid in a horizontal cylindrical reservoir
due to a reduction in the intensity of heat and mass transfer from its outer surface. A mathematical model has been
developed for heat and mass transfer processes in cryogenic fl uid on the basis of equations of unsteady nonisothermal
turbulent motion of incompressible fl uid. A k–ε turbulence model is used in the calculations. A comparison of the
computational data with experimental fi ndings has shown the adequacy of the proposed model. Based on the
mathematical model, a possibility is shown for organizing a cryogenic fl uid fl ow ensuring a reduction in the intensity
of transfer of superheated liquid from the boundary layer near the reservoir surface into the zone of evaporation.
We proposed a method for mechanical limitation of thermoconvective fl uid fl ow from the reservoir walls to its fl uid
evaporation surface and a device for implementing this method. This device, unlike similar existing devices, has a
small area of contact with the side surface of the reservoir and is invariant with regard to the level of cryogenic
fl uid in it. A computational experiment showed the effi ciency of the proposed approach. Using the example of liquid
nitrogen, hydrogen, and oxygen, it has been shown that the said device allows a reduction in the intensity of heating
the surface of cryogenic fl uid evaporation in the reservoir and an increase in the time of its storage.

**Author:**
V. I. Ryazhskikh, A. A. Khvostov, D. A. Konovalov, V. A. Sumin, A. V. Ryazhskikh

**Keywords:**
cryogenic technology, gravitational heat convection, mathematical modeling

**Page:**
785

**MOTION OF A GAS–LIQUID MIXTURE IN THE BED–PIPELINE SYSTEM SUBJECT TO HEAT TRANSFER**

A model of nonstationary motion of a gas–liquid mixture in a bed–pipeline system, with a new source included in the
main line has been constructed taking into account heat transfer between a gas–liquid mixture fl ow in a rising pipe
and the medium around the fl ow, and solutions to boundary-value problems are given. In the fi rst approximation,
the infl uence of a change in the rheological properties of the gas–liquid mixture with temperature on the dynamics
of its motion is determined. Analytical formulas have been obtained making it possible to determine the dynamics
of pressure at the bottom of the well and the productivity of the bed depending on the parameters of the system.
Numerical calculations are carried out at practical values of the system parameters.

**Author:**
É. M. Abbasova, N. A. Agaeva

**Keywords:**
heat exchange, gas–liquid mixture, viscosity, diff erential equation, Laplace transform

**Page:**
794

**MATHEMATICAL SIMULATION OF THE INJECTION OF GAS INTO A STRATUM SATURATED PARTIALLY WITH WATER WITH REGARD FOR THE NONEQUILIBRIUM HYDRATE FORMATION IN THE STRATUM**

A mathematical model of the injection of methane into a porous stratum saturated initially with methane and water,
constructed with regard for the nonequilibrium formation of a gas hydrate in the stratum, is presented. Distributions
of the pressure and temperature in such a stratum and of its saturation with the hydrate formed in it were determined
and analyzed. It is shown that, in the general case, the formation of a gas hydrate in a porous stratum proceeds with
the formation of three characteristic regions in it: a near region with pores containing the gas and the hydrate, a far
region saturated with gas and water, and an intermediate region dividing the near and far regions and containing
the gas, the hydrate, and the water. It was established that, with time, the length of the intermediate region decreases.
The hydrate-formation processes calculated by the equilibrium and nonequilibrium schemes were compared. It is
shown that the higher the permeability of a stratum, the larger the diff erence between the results of calculations by
these schemes

**Author:**
M. K. Khasanov, S. R. Kil'dibaeva, M. V. Stolpovskii

**Keywords:**
gas hydrate, nonequilibrium phase transition, porous medium, methane, filtration

**Page:**
809

**HYDRODYNAMIC MODELING OF CYCLIC OPERATION OF UNDERGROUND GAS STORAGES**

A method to calculate the process of cyclic operation of underground gas storages in a gas regime has been developed.
Based on this method, technological indices of the VIIa–VII horizon of the III block of the Karadag underground gas
storage have been predicted as far as the total volume of the gas in the period of injection and extraction in accordance
with seasonal demand is concerned. Here, phase states of the gas and water were corrected using the equation of state.

**Author:**
I. A. Shiraliyev

**Keywords:**
underground gas storage, extraction, injection, porosity, permeability, pressure

**Page:**
817

**MATHEMATICAL MODEL OF FILTRATION OF SOLUTIONS IN A POROUS MEDIUM WITH SEMIPERMEABLE INCLUSIONS. OSMOTIC CONVECTION**

The author gives generalized equations of fi ltration of solutions in porous media containing semipermeable
inclusions, that take account of the osmotic eff ect. Corrections describing this eff ect are usually small, but in some
cases they play a key role, since osmosis is the main or only reason for the motion of a solution. With the developed
model, the author has solved a new problem on osmotic convection

**Author:**
M. M. Ramazanov

**Keywords:**
solution, osmosis, generalized mathematical model, osmotic convection, semipermeable inclusion

**Page:**
823

**THE EFFECT OF DIFFUSION AND MICROCONCENTRATION ON PLANE WAVES IN A GENERALIZED THERMOELASTIC MATERIAL**

The governing equations for a linear, isotropic, homogeneous, thermoelastic material with diff usion and
microconcentration in a plane have been stated in accordance with the Lord and Shulman theory of generalized
thermoelasticity. The plane harmonic solutions of these equations have been obtained. It has been shown that there
exist four dispersive coupled longitudinal waves and two uncoupled transverse waves. A half-space with thermally
insulated surface has been taken for exploring the refl ection of these plane waves. For an incident plane wave, the
coeffi cients of refl ection and energy shares of the refl ected waves have been presented graphically. The numerical
results have made possible to observe the eff ects of the diff usion and microconcentration parameters on the speeds,
refl ection coeffi cients, and the energy ratios

**Author:**
H. Singlaa, B. Singh

**Keywords:**
generalized thermoelasticity, diff usion, microconcentration, plane waves, refl ection coeffi cients, energy ratios

**Page:**
834