#### Volume 93, №3

**INDICES OF EFFICIENCY OF MULTICOMPONENT SEPARATION IN CASCADES WITH ASSIGNED EXTERNAL CONCENTRATIONS OF THE TARGET COMPONENT**

Consideration has been given to the features of introducing indices of effi ciency of cascades based on separation
potentials of a multicomponent isotope mixture. Basic forms of potentials of two types have been presented, the
fi rst of which is dependent on just the concentration, and the second, through the inclusion of mass numbers of
separation factors, ensures the independence of the separative power of separating elements of concentrations.
On the basis of a computational experiment, the authors have selected potentials most adequately determining
separation-effi ciency indices for cascades that were optimized for the minimum criterion of the overall stream at
assigned external concentrations of the target component.

**Author:**
V. A. Palkin and E. V. Maslyukov

**Keywords:**
separation potentials, separative power, multicomponent isotope separation

**Page:**
489

**MATHEMATICAL MODELING OF ACTIVE THERMIONIC HEAT PROTECTION IN A HIGH ENTHALPY FLOW PAST A SHELL**

A mathematical model of the process of unsteady heat transfer of a thermionic heat-protection system in convective
heating has been formulated and investigated. The effects of evaporation (emission) of electrons from the surface of
the emitter on the drop in the temperature of a composite thermionic heat-protection shell have been demonstrated.
The effects of some types of heat-transfer agents in a composite shell on the heat-transfer regimes in a body have
been investigated. Qualitative agreement of the computation results with the existing data has been achieved.

**Author:**
V. P. Zimin, K. N. Efi mov, V. A. Ovchinnikov, and A. S. Yakimov

**Keywords:**
thermionic converter, emitter, collector, heat transfer, heat protection

**Page:**
497

**DIFFUSION MASS AND HEAT TRANSFER IN A PLANE AXISYMMETRIC LAYER OF A MAGNETIC FLUID**

Processes of magnetophoresis and Brownian diffusion in a suspension of magnetic nanoparticles (magnetic fl uid) in
an inhomogeneous magnetic fi eld have been considered on condition that these processes are limited by concentration
phase transitions between thermodynamic states of an ensemble of particles. Regularities of these processes have
been established with the example of a plane axisymmetric fl uid layer. It has been shown that due to the dependence
of the effective thermal conductivity of the suspension on the concentration of particles, these processes may exert a
substantial infl uence on the heat transfer through it.

**Author:**
V. G. Bashtovoi, A. G. Reks, P. P. Kuzhir, A. Yu. Zubarev, and V. S. Moroz

**Keywords:**
magnetic fl uid, concentration, magnetic fi eld, magnetophoresis, diffusion, phase transition, heat conduction

**Page:**
509

**EXPERIMENTAL VERIFICATION OF THE EFFICIENCY OF THERMAL DIAGNOSTICS OF FRICTION IN A SYSTEM OF SLIDING BEARINGS AT LOW SHAFT SPEEDS**

To assess the effi ciency of the method of thermal diagnostics of friction in a system of sliding bearings at shaft speeds
of no more than 2π rad/s, friction torque values obtained by solving an inverse heat-transfer problem and measuring
with a commercial friction machine sensor have been compared. It has been established that the agreement between
the total friction torque values obtained using fundamentally different methods is within 10–15%. The ability of the
thermal diagnostics method to identify differing friction torques in each bearing is substantiated by the recovery of
their identical values under conditions of difference of the temperature fi elds in the bearings

**Author:**
N. P. Starostin and R. S. Tikhonov

**Keywords:**
polymer bearings, thermal diagnostics of friction, friction torque, friction heat generation, slidingbearing system, heat conduction

**Page:**
519

**METHOD OF CALCULATION AND COMPARATIVE CHARACTERISTICS OF HEAT EXCHANGERS WITH HEAT TRANSFER ENHANCEMENT BY VARIOUS RANDOM ELEMENTS**

Consideration has been given to the method of enhancement of a heat-transfer process due to the use of small random
metallic elements (packings) in channels of heat-exchange apparatuses. The packings ensure a laminar-to-turbulent
transition and a considerable increase in heat-transfer coeffi cients (of 30 to 60 times). Structures of two modern packing
elements and their technical data have been given, as well as expressions to calculate hydraulic-resistance and heattransfer coeffi cients. On the basis of a modifi ed method of the thermal number of transfer units, expressions have been
obtained for calculation of the tube length and the heat-transfer surface when random packings are used as intensifi ers
of the process in the apparatuses. Basic parameters of the obtained expressions are the heat-transmission coeffi cient
and modifi ed Peclét (Bodenstein) numbers with the coeffi cients of reverse mixing of heat-transfer agents. Empirical
coeffi cients at Peclét numbers have been identifi ed using a diffusion model of the structure of a heat-transfer agent
fl ow. The obtained expressions permit taking account of the infl uence of the reverse mixing of heat-transfer agents on
the structural characteristics of a heat exchanger. Examples of calculations of heat exchangers without intensifi ers
and with random packings have been given. It has been shown that during the heat exchange with different media, the
overall dimensions of the heat exchangers are reduced 20 to 25 times. The use of random packings in heat exchangers
with media of high viscosity is pressing, since the packings initiate a turbulent regime of fl ow of heat-transfer agents.

**Author:**
T. M. Farakhov and A. G. Laptev

**Keywords:**
heat exchange, enhancement, random elements, calculation method, hydraulic resistance

**Page:**
527

**THERMAL FORCE LOADING OF A PHYSICALLY NONLINEAR THREE-LAYER CIRCULAR PLATE**

The article considers the effect of a heat fl ux of constant intensity on a circular, three-layer, nonsymmetrically thick
plate subjected to the action of an axisymmetric local loading. The temperature fi eld in the plate was calculated by
the formula obtained in solving the problem of thermal conductivity by averaging thermophysical parameters over
the thickness of the packet. The materials of the layers deform physically nonlinearly. For describing the kinematics
of the packet, the hypotheses of a broken normal are adopted. In thin carrying layers, the Kirchhoff hypotheses are
valid. In the normally uncompressed relatively thick fi ller, the hypothesis on rectilinearity and incompressibility of the
deformed normal holds. The work of the fi ller in the tangential direction is taken into account. The formulation of the
corresponding boundary-value problem is given. Equilibrium equations are obtained by the variational Lagrange
method. Boundary conditions on the plate contour are formulated. The solution of the boundary-value problem is
reduced to fi nding three unknown functions: of defl ection, shear, and of radial displacement. For these functions,
an inhomogeneous system of ordinary nonlinear differential equations is written out. A method of rigid Il′yushin
solutions is applied for its solution. Iteration analytical solutions are obtained in Bessel functions at circular and
annular loadings. Their parametric analyses are made at different local loadings and for the hinged support of the
plate contour. The infl uence of temperature and nonlinearity of the materials of the layers on the displacements in
the plate is investigated numerically

**Author:**
É. I. Starovoitov, Yu. M. Pleskachevskii, and D. V. Leonenko

**Keywords:**
heat fl ux, physical nonlinearity, three-layer circular plate, local loadings

**Page:**
533

**SEMIEMPIRICAL MODEL OF CONVECTIVE HEAT TRANSFER OF TURBULENT GASES**

On the basis of the Prandtl semiempirical wall-turbulence hypothesis, the author has substantiated theoretically
the possibility of setting boundary conditions to the equations of a mathematical model of turbulent motion and
convective heat transfer of a gaseous medium on a coarse grid. It has been shown that the results of numerical
simulation are in agreement with experimental data on the heat transfer of air and high-temperature gases in tubes.

**Author:**
V. A. Kuznetsov

**Keywords:**
mathematical model, heat transfer of gases, boundary layer, turbulence, semiempirical hypothesis, adequacy

**Page:**
543

**AERODYNAMIC CHARACTERISTICS OF A ROTATING CYLINDER IN THE FORM OF A TRUNCATED CONE**

Results of experimental investigations into the aerodynamic characteristics of a rotating cylinder in the form of a
truncated cone with a smooth surface and a rough surface have been given. It has been established that the variability
of the cross section of the rotating cylinder in an air fl ow in the range of variation in the parameter of conicity 0.25–0.35
ensures a decrease in the drag coeffi cient with the values of the lift coeffi cient being preserved. The results have shown
that the presence of the rough surface of the rotating cylinder leads to an increase of 25–30% in the lift. Conditions
under which the Magnus effect contributes to the maximum increase in the lift and accordingly the increase in the
effi ciency of rotation of the cylinder in the form of a truncated cone have been determined experimentally

**Author:**
N. K. Tanasheva, L. V. Chirkova, A. N. Dyusembaeva, and K. K. Sadenova

**Keywords:**
rotating cylinder, smooth and rough surfaces, drag, lift, Magnus effect

**Page:**
551

**SIMULATION OF THE AVERAGED FLOW OF A METAL MELT IN AN ALTERNATING MAGNETIC FIELD WITH VARIABLE AMPLITUDE AND FREQUENCY**

The movement of a metal melt in an inhomogeneous high-frequency magnetic fi eld is considered. A system of equations
with boundary conditions defi ning the diffusion of the magnetic fi eld and the heat conduction in such a melt in the
Boussinesq approximation with account of the Joule heat released in the melt and the volume Lorentz forces acting
in it is presented. The correctness of the mathematical model proposed is demonstrated. The amplitude distributions
of the magnetic fi elds of the eddy currents induced in a metal melt, the velocity distributions of the heat fl ows in it,
and the distribution of temperatures in the melt were calculated for the control parameters of its fl ow determined by
the frequency and amplitude of the alternating magnetic fi eld acting on it. The conditions under which the structure
of this fl ow is completely determined by the parameters of the magnetic fi eld and the problem on determination of
the heat and mass transfer in the metal melt can be reduced to the calculation of its forced convection in the Lorentz
force fi eld and the temperature distribution in the melt at a defi nite velocity of its fl ow were determined.

**Author:**
I. L. Nikulin and A. V. Perminov

**Keywords:**
induction melting, electrically conducting liquid, alternating magnetic fi eld, magnetic-fi eld diffusion, inductive current, heat convection, forced convection, Boussinesq approximation, Lorentz force, metal-melt fl ow

**Page:**
556

**INFLUENCE OF THE HOMOCHRONISM NUMBER OF THE LIQUID IN A SPHERICAL LAYER ON THE HEAT EXCHANGE IN IT AND ITS MAGNETIC HYDRODYNAMICS**

Results of numerical simulation of the nonstationary convective heat exchange in the electrically conducting liquid
fl owing in the space between two concentric isothermal spheres are presented. The infl uence of the homochronism
number of the liquid on the structure of its fl ow, the temperature and magneto-induction fi elds in it, and the distribution
of local Nusselt numbers in the spherical liquid layer was investigated.

**Author:**
S. V. Solov′ev

**Keywords:**
mathematical simulation, nonstationary convective heat exchange, homochronism number, Joule heat dissipation, magnetic hydrodynamics, spherical liquid layer

**Page:**
567

**SIMULATION OF THE INTERACTION OF ICE CRYSTALS WITH THE SURFACE OF A FLYING VEHICLE**

A physical and mathematical model of the movement of nonspherical particles in the two-phase fl ow over an
aerodynamic body, allowing one to estimate the area of wetting of the body surface by these particles depending
on their stochastic orientation in the fl ow, is proposed. On the basis of the heuristic model developed earlier, the
coeffi cients of restoring the velocity components of the ice crystals colliding with the surface of a blunt-nosed body
were calculated for values of the governing parameters of the collision process varying within a wide range. It is
shown that the initial orientation of these crystals in the aerosol fl ow over the body infl uences the trajectories of their
movement in the vicinity of the body

**Author:**
I. A. Amelyushkin and A. L. Stasenko

**Keywords:**
spheroids, blunt-nosed conic body, wetting area, restoration coeffi cient, particle scattering

**Page:**
576

**COMPREHENSIVE INVESTIGATION OF SEPARATING FLOWS IN THE AREA OF DISK AND CONE STABILIZERS OF STRIKERS LAUNCHED FROM BALLISTIC INSTALLATIONS**

The distinctive features of separating fl ows occurring during the use of various ring shields and cone stabilizers to
ensure a steady fl ight of rod strikers have been investigated. The investigations were carried out using numerical
calculations, weight tests in a supersonic wind tunnel, and artillery-type ballistic tests. Data on the geometry of
separation areas have been obtained, values of the aerodynamic coeffi cients have been identifi ed, and an assessment
of the steadiness of structures′ fl ight has been made, which has been confi rmed by ballistic tests under real conditions.
Analysis of the conducted mass experiments has shown the possibility of using the investigated aerodynamic devices
for stabilizing high-aspect-ratio strikers at short distances under the conditions of high-level disturbances.

**Author:**
V. M. Zakharov, S. A. Afanas′eva, and K. V. Kostyushin

**Keywords:**
separating (detached) fl ows, stabilizer, rod striker, aerodynamic coeffi cients, steadiness of fl ight, compression shock, shadowgraph of fl uid fl ow

**Page:**
585

**PHYSICAL AND NUMERICAL MODELING OF THERMOMECHANICAL PROCESSES IN GAS–AIR SYSTEMS OF PISTON ENGINES UNDER GASDYNAMIC-NONSTATIONARITY CONDITIONS**

It is well known that as of today, internal combustion engines are the most widespread energy sources among heat
engines. Therefore, one relevant problem in the development of world energy is to improve operating processes,
and also to modernize systems and elements of piston internal combustion engines with the aim of improving their
technical and economic indices. In the present paper, the authors have given new information on nonstationary
gasdynamics and local heat transfer of pulsating fl ows in gas–air fl ow ducts of internal combustion engines, and
also have proposed methods for improving the processes in intake and exhaust systems. Experimental investigations
were conducted on full-scale models of a single-cylinder internal combustion engine with supercharging and without
it. Physical features of pulsations of gas fl ows in the engines′ gas–air fl ow ducts have been described. Calculated
and experimental dependences of the change in the instantaneous velocity and the pressure of the gas fl ow in the
gas–air fl ow ducts with time have been presented. Particular emphasis was placed on an analysis of the intensity
of heat transfer in gas–air fl ow ducts of different confi gurations. It has been shown that lateral profi ling of intake
and exhaust pipelines exerts a positive infl uence on the technical and economic indices of piston engines without
supercharging. A method to reduce pulsations of the pressure and velocity of gas fl ows (on the average, by a factor
of 2) in the intake pipeline of a supercharged internal combustion engine has been proposed, which leads to an
improvement of the reliability of the entire engine.

**Author:**
L. V. Plotnikov, B. P. Zhilkin, and Yu. M. Brodov

**Keywords:**
piston engine, gas–air systems, turbosupercharging, pulsating fl ows, nonstationary gasdynamics, local heat transfer, improvement of gas exchange.

**Page:**
594

**HEAT TRANSFER IN THE SLIP FLOW WITH AXIAL HEAT CONDUCTION IN A MICROCHANNEL WITH WALLS HAVING A CONSTANT TEMPERATURE**

The problem on thermally developed laminar slip gas fl ow with axial heat conduction in a microchannel (a micropipe
or a parallel-plate microchannel) with walls having a constant temperature was solved analytically with the use of
the self-adjoint formalism method involving the rearrangement of the energy equation for this fl ow into a system of
two partial differential equations of the fi rst order. The temperature distribution and Nusselt numbers in such a fl ow
have been determined on the assumption that it is hydrodynamically fully developed in the region of the thermal
entrance of a microchannel. The data obtained show that the heat transfer in this fl ow is substantially dependent on
the axial heat conduction in it and its rarefaction

**Author:**
Y. Haddout, A. Oubarra, and J. Lahjomri

**Keywords:**
heat transfer, forced convection, slip fl ow, axial heat conduction, rarefaction, self-adjoint formalism

**Page:**
605

**SPECIAL FEATURES OF NONLINEAR BEHAVIOR OF A POLYMER SOLUTION ON LARGE PERIODIC DEFORMATIONS**

Study of the behavior of polymer solution fl ows in the region of nonlinear viscoelasticity allows one to more accurately
evaluate the adequacy of rheological models and to describe the rheological properties of a material in more detail.
The nonlinear viscoelastic properties manifesting themselves in the process of studying the behavior of a polymer
material on signifi cant deformations were investigated with the aid of time dependences of shear stresses calculated at
different amplitudes. The present work considers the applicability of the modifi ed Vinogradov–Pokrovskii rheological
model to describing the oscillating shearing of polymer fl uids with a large amplitude. It has been established that
on increase of the deformation amplitude, the shear stresses cease to be a true harmonic, and one observes the
appearance of a "step" on their left front, which speaks of the substantial nonlinearity in the behavior of the sample.
The obtained theoretical dependences are compared with experimental data for a 5% solution of polyethylene
oxide in dimethyl sulfoxide. The comparison was made as by plotting the time dependences of normalized stresses,
so by analyzing Lissajous fi gures. Despite the simplicity, the modifi ed Vinogradov–Pokrovskii rheological model
adequately describes the behavior of polymer materials on signifi cant periodic deformations.

**Author:**
G. V. Pyshnograi, N. A. Cherpakova, and H. N. A. Al Jodac

**Keywords:**
rheology, rheological model, nonlinear viscoelasticity, oscillations, shear, polymer solutions

**Page:**
617

**LOCALIZATION OF GROUND, CROWN, AND COMBINED FOREST FIRES WITH THE USE OF A BARRIER STRIP**

A comparative analysis of the results of experimental investigations on determination of the conditions necessary and
suffi cient for the localization of ground, crown, and combined forest fi res with the use of a barrier strip of moistened
forest materials has been performed. The rational volumes of water used for the formation of such a strip in front
of a forest fi re and its sizes were determined. Different variants of localization of fl ame combustion and thermal
decomposition of forest combustible materials depending on the action of an air fl ow (wind) on them were analyzed.

**Author:**
A. O. Zhdanova, I. S. Voitkov, G. V. Kuznetsov, I. R. Khasanov,b N. E. Shlegel′, and N. P. Kopylov

**Keywords:**
ground, crown, and combined forest fi res, forest combustible materials, hotbed of fi re, barrier strip, fi re extinguishing

**Page:**
626

**IGNITION OF FOREST COMBUSTIBLE MATERIALS BY A GROUP OF CRYSTALLIZING METAL PARTICLES**

The physical mechanism of igniting a layer of forest combustible materials by a group of crystallizing metal particles
of fairly small sizes (smaller than 3–4 mm) was determined. Results of a statistical treatment of data on the induction
period between the fi rst and second microfl ame in such a layer and on the instants of time these hotbeds of fi re begin to
grow are presented. It is shown that the indicated ignition process is probabilistic in character, and recommendations
are given for the development of its mathematical model.

**Author:**
N. V. Baranovskii

**Keywords:**
forest combustible materials, ignition, crystallizing metal particle, electric discharge

**Page:**
635

**ANALYZING THE USE OF ADVANCED PROPELLANTS IN ARTILLERY AND GUN SYSTEMS FROM EXPERIMENTAL DATA OBTAINED UNDER THE CONDITIONS OF A MODEL BALLISTIC INSTALLATION**

On the basis of an experimental and theoretical approach, the authors have considered an algorithm for modeling the
behavior of advanced propellants in barreled systems of varying caliber. The proposed algorithm makes it possible
to conduct preliminary investigations into the possibility of using advanced fast-burning propellants in the existing
barreled systems and in advanced systems of varying calibers and for various purposes. A possible increment in the
muzzle velocity of a projectile due to the advanced propellants added to the propellant powder charge is assessed
without full-scale testing

**Author:**
A. N. Ishchenko, V. V. Burkin, V. Z. Kasimov, A. S. D′yachkovskii, K. S. Rogaev, N. M. Samorokova, and A. I. Zykova

**Keywords:**
barreled systems, advanced propellants, traveling charge, composite charge, shot modeling

**Page:**
641

**MODIFICATION OF CEMENT CONCRETE BY ADMIXTURES CONTAINING NANOSIZED MATERIALS **

Experimental studies of several types of nanomaterials (nanosilica, nanocarbon) and comparison of the results
of their applications in cement concrete have been carried out. It has been established that the characteristics of
cement concrete modifi ed by these nanomaterials depend on the content of the latter in concrete. The best results
were obtained with an additive in which the said nanomaterials were used simultaneously

**Author:**
S. A. Zhdanok, V. V. Potapov, E. N. Polonina, and S. N. Leonovich

**Keywords:**
aqueous sol of nanosilica, carbon nanotubes, superplasticizer, heavy-weight concrete, strength

**Page:**
648

**ASSESSING THE SIZE DISTRIBUTION OF DROPLETS OBTAINED IN A CENTRIFUGAL MASS-EXCHANGE APPARATUS **

Consideration has been given to the basic mechanisms of fragmentation of droplets in the system "liquid–liquid" in
fi lm fl ow over the working surface of the rotor of a centrifugal mass-exchange apparatus. The authors have assessed
theoretically the sizes of dispersed-phase droplets on separation of the liquid fi lm from the rotor′s working surface
and its arrival at a toroidal clearance between the intake tube and the rotor of the apparatus. It has been established
that the greatest infl uence on the formation of the particle-size distribution of an emulsion is exerted by shear stresses
in the liquid that arise in the toroidal clearance. The infl uence of the rotor speed and the rate of fl ow of the liquid on
the size distribution of droplets of the obtained emulsion has been shown. Good agreement between theoretical and
experimental data has been confi rmed experimentally

**Author:**
A. A. Kukhlenko, M. S. Vasilishin, S. E. Orlov, A. G. Karpov,a D. B. Ivanova, O. S. Ivanov, and P. P. Ivanov

**Keywords:**
centrifugal mass-exchange apparatus, emulsifi cation, droplet diameter, dispersion, shear stresses, fi lm liquid fl ow.

**Page:**
653

**NONSTATIONARY STEAM–OXYGEN GASIFICATION OF SOLID FUEL IN A FIXED BED UNDER PRESSURE**

A two-dimensional model of nonstationary steam–oxygen gasifi cation of solid fuel in a fi xed bed has been constructed,
which took into account the interphase convective heat transfer, radiative-conductive heat transfer of the solid
phase, radiative and conductive heat transfer of the bed with the reactor wall, heterogeneous and homogeneous
chemical reactions, gravity force, and the aerodynamic drag force. The infl uence of the process parameters on the
thermochemical treatment of the Shubarkol′ bituminous long-fl ame coal under a pressure of 3 MPa at ratios of the
mass fractions of the steam–oxygen mixture components H2O/O2 = 45/55, 40/60, and 72/28 was studied.

**Author:**
B. B. Rokhman

**Keywords:**
fi xed bed, coal, heat conduction, heat transfer, steam–oxygen gasifi cation, conductive and radiative heat transfer, temperature, chemical reactions

**Page:**
664

**DEPENDENCE OF THE PYROCARBON STRUCTURE ON THE PARAMETERS OF THE PROCESS OF PYROLYSIS OF HYDROCARBON GASES IN AN ELECTROTHERMAL FLUIDIZED BED**

One of the variants of the nuclear reactors with increased passive protection being designed at the present time is the
reactor with fuel microelements (coated particles) and ball fuel elements. Among the principal components of this
type of nuclear fuel is pyrocarbon. Owing to its unique properties, pyrocarbon can also be used in various scientifi c
and industrial areas. Over several years, at the Institute of Gas of the National Academy of Sciences of Ukraine,
investigations were carried out on obtaining pyrocarbon coatings by means of pyrolysis of hydrocarbon gases in
reactors with an electrothermal fl uidized bed.
Based on theoretical and experimental data, the present article considers the dependence of the structure of a
pyrocarbon coating on the pyrolysis process parameters. Comparing experimental data with theoretical results
depending on the temperature and concentration of gaseous hydrocarbon, the structure of the pyrocarbon deposited
in an electrothermal fl uidized bed can be divided into three forms: laminar, isotropic, and granular (dropping).
Among the factors that infl uence the process of carbon deposition are the content of admixtures and point overheating
(cathode spots). Admixtures (mainly iron compounds) can behave as a catalyst accelerating the process of formation
of nanotubes and nanofi bers. Controlling the temperature and composition of the original material, it is possible to
obtain certain allotropic modifi cations of carbon with assigned structure

**Author:**
K. V. Semeiko, S. S. Kustovskyi, S. V. Kupriyanchuk, and R. E. Chumak

**Keywords:**
pyrocarbon, electrothermal fl uidized bed, pyrolysis, hydrocarbon gases

**Page:**
677

**OPTIMIZATION OF THE PASSIVE REGIME OF ARTIFICIAL FREEZING OF A WATER-SATURATED ROCK MASS**

An iteration computational algorithm is presented for optimization of the passive regime of artifi cial freezing of a
water-saturated rock mass, which is the longest and most cost-intensive stage in the process of shaft excavation
and carriage installation. The optimization is implemented by solving the inverse problem of determination of the
heat fl ux on the boundary of a freezing well in a horizontal rock layer. Heat transfer in the rock layer is considered
with account taken of the phase transition of the fi rst kind on the basis of the Stefan problem in a two-dimensional
formulation. The developed algorithm is based on the principle of descriptive regularization and the optimization
method of steepest descent. In the algorithm, the target functional gradient and the parameters of optimization of
the problem′s solution are determined from the solution of a conjugate problem for temperature increment. Using
the proposed algorithm, optimum regimes of passive freezing for rock layers with different thermal and physical
characteristics under varied initial conditions have been obtained.

**Author:**
M. S. Zhelnin, O. A. Plekhov, and L. Yu. Levin

**Keywords:**
freezing of soils, ice wall, inverse Stefan problem, descriptive regularization, steepest-descent method

**Page:**
685

**DETERMINATION OF THE THERMAL EFFICIENCY AND HEIGHT OF THE BLOCKS OF COUNTERCURRENT COOLING TOWER SPRINKLERS**

The problem of calculating the thermal effi ciency of the liquid and gaseous phases in a countercurrent fi lm-type
cooling tower has been solved. From the joint solution of the heat balance equation and expressions for the
thermal effi ciencies of the cooling tower liquid and gaseous phases, the relationship between the effi ciencies of
water cooling and air heating in the blocks of sprinklers has been established. At the given temperature regime
of water cooling and thermodynamic state of moist air, the thermal effi ciency of the liquid phase was determined
and then the obtained relation was used to determine the thermal effi ciency of the gas phase to be provided by the
blocks of sprinklers. To calculate the effi ciency of the blocks of sprinklers, a cellular model of fl ow structure was
used. An expression is obtained for calculating the height of the blocks at the given effi ciency of the gas phase and
construction characteristics of packing and of water and air fl ow rates. Agreement with experimental data is shown,
and the algorithm of calculation is given.

**Author:**
A. G. Laptev and E. A. Lapteva

**Keywords:**
fl ow structure, regular packings, fi lm-type cooling towers, thermal effi ciency

**Page:**
693

**LOOP HEAT PIPES WITH A STEAM JET PUMP**

Some confi gurations of cooling systems based on two-phase loops with control of the fl ow rate of the liquid and
steam in them as well as experimental data obtained with these systems are presented. A model of an ejector-assisted
loop heat pipe has been developed, and the results of calculations with it were compared with the corresponding
experimental data

**Author:**
V. Kiseev and O. Sazhin

**Keywords:**
heat transfer device, two-phase loop, steam jet condensation, steam jet pump, ejector-assisted loop heat pipe

**Page:**
700

**CALCULATION OF CHARACTERISTICS OF RETICULAR MATERIALS BASED ON A GLASSY CARBON BY ITS OPTICAL CONSTANTS DETERMINED EXPERIMENTALLY**

Results of experimental investigation of the spectrum of optical constants of a glassy carbon produced in Russia
and of mathematical simulation, with them, of the spectral, kinetic, and thermophysical characteristics of composite
reticular materials based on this carbon are presented. The investigations were performed with compacted samples of
a composite reticular glassy carbon identical in physical properties to the glassy carbon forming the basis of highly
porous cellular materials. By the hemispherical radiant refl ectivity of these samples, illuminated at a right angle, the
spectra of optical constants (the refractive index and the absorption coeffi cient) of the glassy carbon forming their
basis were determined using the Kramers–Kronig relations, and a number of spectral characteristics of the composite
reticular glassy carbon, related to these constants, were calculated by the simple approximate relations derived by us.
The thickness of the skin layer in the samples of this composite was estimated, and some features of the interaction of the
material of their fragments with an electromagnetic radiation were determined. The data on the spectral characteristics
of the composite reticular glassy carbon were integrated into the statistical model developed earlier on the basis of the
exact electromagnetic theory for simulating the optical properties of reticular materials having an ultrahigh porosity.
This model allows one to estimate the features of the microstructure of such a material and the physical processes
proceeding in it at different spatial and time scales. Results of calculations of the spectral and kinetic coeffi cients of
the radiative transfer equation, the scattering indicatrix, the heat radiative conductivity, and the total heat conduction
of the composite reticular glassy carbon are presented. The possibilities of the model proposed are demonstrated.

**Author:**
O. M. Alifanov, V. V. Cherepanov, A. G. Shchurik, and R. A. Mironov

**Keywords:**
reticular glassy carbon, optical constants, experiment, spectral and kinetic coeffi cients, thermophysical properties, simulation

**Page:**
710

**HEAT CONDUCTION OF CERAMIC MATERIALS BASED ON MgAl2O4 AND ZnAl2O4**

Optically transparent samples of ceramic materials based on the magnesium aluminate and zinc aluminate spinels
of density close to the theoretically attainable one have been obtained, and their heat conductivity was measured
in the temperature range 50–300 K. It is shown that the heat conductivities of these ceramic materials at room
temperature are close and fall within the range 17–18 W/(m·K). At a cryogenic temperature (T = 50 K), the heat
conductivity of the ceramic materials based on the zinc aluminate spinel (180 W/(m·K)) is much higher than the heat
conductivity of the ceramic materials based on the magnesium aluminate spinel (122 W/(m·K)). The absolute heat
conductivities of the ceramic materials based on the indicated spinels are dependent on the sintering additives used
in their production.

**Author:**
S. S. Balabanov, A. V. Belyaev, and P. A. Popov

**Keywords:**
spinel, magnesium aluminate, zinc aluminate, heat conductivity

**Page:**
719

**HYDRAULIC RESISTANCE OF PIPES WITH UNIFORM CONTINUOUS ROUGHNESS OF VARYING PROFILE**

Results of experimental investigation into the hydraulic resistance to the air fl ow in pipes with cut metric triangular,
rectangular, and round threads have been presented. The height of the thread profi le varied from 0.25 to 1.25 mm.
Conditions have been identifi ed for the occurrence of a regime with full manifestation of roughness when the hydraulic
resistance coeffi cient is independent of the Reynolds number. It has been established that the highest resistance
is demonstrated by pipes with a rectangular thread. Generalizing relations have been obtained for calculating
the dependence of the hydraulic resistance coeffi cient of the pipes on the relative roughness of their surface Δ
(0.008–0.055) and the Reynolds number (6000–250,000).

**Author:**
A. V. Zlobin and S. É. Tarasevich

**Keywords:**
hydraulic resistance, metric thread, roughness

**Page:**
725

**SIMULATION OF TWO-PHASE FLUID FLOW IN THE DIGITAL MODEL OF A PORE SPACE OF SANDSTONE AT DIFFERENT SURFACE TENSIONS**

A study is made of the infl uence of surface tension on two-phase drainage fl ows in a porous medium. Computational
fi ltration experiments are conducted in a three-dimensional digital microtomographic model of sandstone. To
simulate two-phase fl ows, use is made of lattice Boltzmann equations; interfacial phenomena and wetting effects
are described using the color-gradient-based method. Calculations are carried out at the same rate of injection of
a nonwetting fl uid and at a ratio of the viscosities of nonwetting and wetting phases of 1:10. Results are obtained
according to which growth in the interfacial tension contributes to the rise in the effi ciency of displacement of the
wetting fl uid, which is recorded at the moment the injected phase breaks through, and to the decrease in the effi ciency
after its breakthrough. It is established that distinctive features of fl ows with capillary fi ngering that arise at high
surface tensions are the stepwise character of travel of the leading front and the growth of displacement channels
in directions different from the hydrodynamic pressure difference. It is shown that interfacial tension is a parameter
whose variation enables us to change the type of two-phase fl ow. Increase in the interfacial tension contributes to the
transition of the fl ow with viscous fi ngering to a fl ow with capillary fi ngering. The effi ciency of displacement of the
wetting fl uid in the transition crossover zone is the lowest.

**Author:**
T. R. Zakirov and M. G. Khramchenkov

**Keywords:**
two-phase fl ows, surface tension, digital core, simulation, lattice Boltzmann equations (method), capillary fi ngers

**Page:**
733

**SEMICOMMERCIAL DESALINATION OF WATER BY THE METHOD OF CAPACITIVE DEIONIZATION**

Investigations into the parameters of a CDI desalinator operating according to a two-step demineralization
scheme have been conducted. The process of desalination has been analyzed in conjunction with electrophysical
measurements. Various capabilities of postproduction tuning of demineralizer regimes have been demonstrated:
recuperation of part of the energy of the dischargeable CDI cell to a chargeable one, reduction in the discharge
period due to the application of reverse polarity voltage pulses, and rise in the effi ciency by organizing the procedure
of taking account of the actual voltage on working electrodes inside the CDI cell. The potential for raising the output
of the desalinator has been indicated.

**Author:**
desalination, salt solution, volume deionization, porous electrode, sorption of ions, degree of desalination, energy effi ciency

**Keywords:**
S. A. Zhdanok, A. S. Zhdanok, A. G. Chervyak, E. A. Matveichik, and S. V. Shushkov

**Page:**
743

**FLUIDIZATION OF A MULTICOMPONENT BED IN A REACTOR FOR CO-TORREFACTION OF WASTE COAL AND BIOMASS**

A study has been made of the hydrodynamic characteristics of the transition of a multicomponent bed consisting of
coal sludge and straw pellets to a fl uidized state. It has been shown that increase in the fraction of large particles
(pellets) in the bed leads to a decrease in its relative height and in the amplitude of pulsations of the pressure
difference in it; this contributes to the rise in the degree of conversion of chemical reations occurring in the bed.
The possibility of assessing the minimum fl uidization velocity of a multicomponent bed from the dependence of the
standard deviation of a pulsation of the pressure difference in it on the velocity of air blown though the bed has been
proved.

**Author:**
R. L. Is′yomin, S. N. Kuz′min, A. V. Mikhalyov, O. Yu. Milovanov, D. V. Klimov, A. V. Nebyvaev, and V. V. Khaskhachikh

**Keywords:**
torrefaction, fl uidization, coal sludges, biomass, multicomponent bed.

**Page:**
750