#### Volume 93, №1

**INFLUENCE OF SEPARATING-CASCADE STREAMS ON THE DURATION OF A TRANSIENT PROCESS**

A study has been made of the transient process with the example of obtaining germanium enriched with a ^{72}Ge isotope to 50% in a cascade of gas centrifuges. The infl uence of the values of outgoing cascade streams on the dynamics of the concentration of isotopes and the duration of the transient process has been shown. Conditions for the change in the values of outgoing cascade streams have been established, with which the minimum duration of the transient process is attained and the effi ciency of operation of the cascade rises.

**Author:**
A. A. Ushakov, A. A. Orlov, and V. P. Sovach

**Keywords:**
cascade, isotope, separation, germanium, nonstationary process, mathematical model, isotope mixture

**Page:**
1

**ON THE DYNAMICS OF MOTION AND REFLECTION OF TEMPERATURE SOLITONS IN WAVE HEAT TRANSFER IN LIMITED REGIONS**

Based on the new analytical solution of the problem of wave heat transfer, the dynamics of motion, interaction,
and refl ection of isolated temperature waves (solitons) in limited regions under the action of isolated temperature
pulses of rectangular shape and the mechanism of refl ection of temperature solitons from the opposite boundary
are investigated. In accord with this mechanism, fi rst the entire energy of a soliton is absorbed and then a reversetravelling temperature wave originates with the same space carrier as in the direct wave. During interaction of
subsequent solitons with the refl ected ones, their energies are fi rst added up and then are separated into opposite
directions (as a result of dissipation), preserving the kinematic characteristics. Since the time of action of isolated
waves is proportional to several relaxation times and the depth of heating is equal to the limited number of
nanometers, such investigations are of great interest also for the case in relativistic mechanics where high-power
radiations interact with the surfaces of solid bodies

**Author:**
V. F. Formalev, É. M. Kartashov, and S. A. Kolesnik

**Keywords:**
isolated thermal wave, wave heat transfer, wave heat conduction equation, limited body, thermal diffusivity, relaxation time, analytical solution

**Page:**
10

**ON THE PROBLEM OF REJECTION OF LOW-POTENTIAL HEAT FROM HIGH-POWER SPACE SYSTEMS**

Consideration has been given to the problems of organization of the operating process in spacecraft heat-exchange
devices for rejecting low-potential heat to outer space. It has been shown that as far as the heat-rejection effi ciency
and weight-size characteristics are concerned, droplet radiant coolers outperform all the existing designs of heat
exchangers. The use of droplet radiant coolers at heat-rejection powers exceeding 100 kW, i.e., at megawatt powers,
is particularly efficient. A description of individual elements has been given, and results of investigations of the
processes of generation of flows of monodisperse droplets and their collection under ground conditions and under
microgravity and high-vacuum conditions have been presented. The latter were investigated from the results obtained
in experiments on spacecraf

**Author:**
G. V. Konyukhov, A. V. Bukharov, and V. G. Konyukhov

**Keywords:**
droplet radiator cooler, monodisperse droplet fl ows, droplet-fl ow generator, passive droplet collector, active droplet collector, microgravity, spacecraft

**Page:**
16

**IRREVERSIBILITY OF HEAT-TRANSFER PROCESSES IN DOUBLE-FLOW CELLS OF VARYING FLOW HYDRODYNAMICS**

Consideration has been given to the infl uence of the hydrodynamics and phase state of the fl ows in a double-fl ow
heat-exchange cell on the entropy production in it. For the case of the Newtonian kinetics of heat transfer in such
a cell, the authors have obtained formulas for calculating the entropy production in it as a function of the heattransfer coeffi cient, the heat load, the temperatures, and the water equivalents of the flows in the cell.

**Author:**
An. A. Akhremenkov, S. Yu. Boikov, and A. M. Tsirlin

**Keywords:**
irreversibility, heat transfer, fl ow hydrodynamics, mixing, displacement

**Page:**
28

**THERMOHYDRODYNAMICS OF A SPRAY DRYING INSTALLATION WITH CONVECTIVE-RADIATIVE ENERGY SUPPLY**

Results are presented of experimental investigations of the working parameters of a spray drying installation with a
combined supply of heat by convection and infrared radiation, the density of the heat fl ux in the infrared radiation
device, and the intensity of mixing the gas phase. The analysis of the obtained data shows that the supply of heat to
the chamber by infrared radiation and the latter′s impact on the liquid′s spray pattern makes it possible to increase
signifi cantly the moisture intensity of the chamber, to decrease the heat rate for evaporation of moisture, and to raise
the installation′s effi ciency

**Author:**
P. V. Akulich and D. S. Slizhuk

**Keywords:**
spray drying, thermohydrodynamics, convective-radiative drying

**Page:**
38

**RADIATIVE-CONVECTIVE HEAT EXCHANGE OF A BUILDING WITH THE ENVIRONMENT ON EXPOSURE TO SOLAR RADIATION**

The results of computational investigations of the aerodynamics of a building located in the urban area with a high
density of buildings and of its heat exchange with the environment are presented. A three-dimensional numerical
model of nonstationary processes of transfer of momentum and heat on interaction of the building with the wind
under the conditions of diurnal variations of the solar radiation intensity and air temperature has been constructed.
The model allows one to estimate the basic parameters of the heat exchange of the building with the environment
under different seasonal conditions

**Author:**
B. I. Basok, V. G. Novikov, B. V. Davydenko, T. G. Belyaeva, M. P. Novitskaya, and R. Ya. Sorokovoi

**Keywords:**
building, numerical simulation, solar radiation, radiative-convective heat exchange

**Page:**
45

**INFRARED BIOENGINEERING FEEDBACK CABIN FOR RECOVERING FUNCTIONAL RESERVES OF A HUMAN ORGANISM**

An energy-effective mobile infrared cabin has been developed for activating the functional reserves of a human
organism in medicinal, health-improving, and sports practice has been developed. The cabin maintains deep
penetration of optical radiation into the tissues of a human being by using near infrared band radiators. The
distinctive feature of the facility being proposed is the realization of bioengineering feedback by recording basic
physiological indices of the user and automatic control of the infrared procedure parameters based on the results
of monitoring. Minimization of thermal load generated by infrared radiators on the user′s organism allows one to
expand the sphere of application of the infrared cabin by eliminating the limitations on using it by patients with
arterial hypertension and cardiovascular insuffi ciency

**Author:**
A. N. Osipov, M. Kh.-M. Tkhostov, M. M. Mezhennaya N. I. Stetyukevich, V. F. Shevtsov, V. A. Kul′chitskii, V. Yu. Drapeza, M. V. Davydov, and D. A. Kotov

**Keywords:**
infrared radiation, infrared cabin, infrared band, bioengineering feedback, automatic control, monitoring, physiological indices of a human being

**Page:**
54

**CONJUGATE HEAT TRANSFER: ANALYSIS VIA INTEGRAL TRANSFORMS AND EIGENVALUE PROBLEMS**

An integral transform approach to the solution of the problem on conjugate heat transfer, combining the singledomain formulation with the convective eigenfunction expansion basis within the total integral transformation
framework, which leads to a nonclassical eigenvalue problem, is presented. The problem on the conjugate heat
transfer in the transient two-dimensional incompressible laminar fl ow of a Newtonian fl uid in a parallel-plate
channel is considered to illustrate the hybrid numerical-analytical approach. To demonstrate the improvement
of the convergence rate achieved with the methodology proposed, a critical comparison against the traditional
total integral transformation solution of the diffusive eigenvalue problem is provided, and results are presented
and discussed for three representative situations realized with different Peclet numbers: Pe = 1, 10 and 100.
A remarkable improvement of the convergence rate, obtained especially with the large Péclet numbers, offers
evidence of the validity of the expansion constructed upon the nonclassical eigenvalue problem proposed.

**Author:**
D. C. Knupp, R. M. Cotta, and C. P. Naveira-Cotta

**Keywords:**
conjugate heat transfer, internal convection, single-domain formulation, convective eigenfunction expansion basis, integral transforms, nonself-adjoint eigenvalue problem

**Page:**
60

**DISTINCTIVE FEATURES OF THE USE OF NANOFLUIDS TO ENHANCE BOILING HEAT TRANSFER**

The authors have analyzed the results of investigations of nucleate and fi lm regimes of boiling of nanofl uids. In the
nucleate regime of boiling of nanofl uids, the increase in the critical heat fl ux compared to a pure fl uid is observed;
here, there can be both an increase and a decrease in the heat-transfer coeffi cient. The increase in the critical heat
fl ux during the boiling of a nanofl uid is linked to the formation of a deposited nanoparticle layer on a heated surface,
which contributes to the change in the microcharacteristics of the process of boiling and to the decrease in the
wetting angle of the surface. Results of theoretical investigation of the fi lm boiling of a nanofl uid on a vertical heated
surface have been presented. It has been shown that the greatest infl uence on the processes of heat and mass transfer
in a vapor fi lm is exerted by the superheating of the wall, the relation of the temperature and Brownian diffusions,
and the concentration of nanoparticles in the fl uid

**Author:**
A. A. Avramenko, M. M. Kovetskaya, A. I. Tyrinov, and Yu. Yu. Kovetskaya

**Keywords:**
boiling of nanofl uids, heat transfer, critical heat fl ux

**Page:**
74

**ELASTOMERIC COMPOUNDS WITH FINE-GRAINED CARBONIC ADDITIVES**

The infl uence of three different nanomaterials (nonfunctionalized and functionalized with amino and oxygencontaining groups) forming a part of elastomeric compounds based on a natural SMR-10 rubber and a butadienenitrile BNKS-18 rubber on the interfacial interactions of these rubbers with an active and a semiactive carbons
blacks added to them was investigated. For the purpose of estimating the action of the indicated nanomaterials
incorporated into the composition of a rubber on its properties and the interaction of the rubber with a carbon black
introduced into the compound, investigations have been performed on determination of the bound rubber in such
a compound, the qualitative characteristics of the distribution of an extender in it (the modulus of elasticity and the
shear modulus of the compound in the cases of its small and large deformations, respectively, and the difference
between these moduli representing the complex dynamic modulus of the compound), and its Mooney viscosity.

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

**Keywords:**
natural rubber, butadiene-nitrile rubber, bound rubber, modulus of elasticity, shear modulus, complex dynamic modulus, Mooney viscosity, carbon nanomaterials

**Page:**
83

**SYNTHESIS OF MULTIWALL CARBON NANOTUBES BY THE CVD METHOD AND THEIR FUNCTIONALIZATION**

Results of the functionalization of multiwall carbon nanotubes by an aqueous solution of nitric acid and a mixture of
nitric and sulfuric acids with subsequent treatment of them by ultrasound are presented. The presence of functional
groups on the surface of multiwall carbon nanotubes was determined with the use of IR spectroscopy

**Author:**
T. S. Temirgaliyeva, M. Nazhipkyzy, A. Nurgain, A. Turganbay, B. Dinistanova, and Z. A. Mansurova,

**Keywords:**
multiwall carbon nanotubes, synthesis, chemical vapor deposition, functionalization

**Page:**
91

**SIMULATION OF THE SELF-ORGANIZING SYNTHESIS OF HYBRID NANOSTRUCTURES IN THE CHEMICAL VAPOR DEPOSITION OF HYDROCARBONS ON A TRANSITION-METAL CATALYST**

A physicochemical model of isothermal synthesis of a graphene–carbon nanotube structure in the process of chemical
vapor deposition of hydrocarbons on a transition-metal catalyst and a kinetic model of two-stage formation of
a multilayer graphene on such a catalyst with a high carbon solubility in the process of synthesis of the indicated
hybrid nanostructure have been developed. The existence of these stages was established. The number of graphene
layers and the length of the nanotubes in a graphene–carbon nanotube structure synthesized on a cobalt fi lm in
the process of chemical vapor deposition of hydrocarbons on it were calculated depending on the thickness of this
fi lm, the temperature of the process, and the hydrocarbon concentration in a gas mixture supplied into a reactor. It
is shown that the maximum length of such nanotubes is limited by the thickness of the catalyst fi lm on which they
are grown. The models proposed and the results of calculations performed with them can be used for optimization
of the conditions of synthesis of hybrid nanostructures in the process of chemical vapor deposition of hydrocarbons
on transition metals for the purpose of production of innovation materials and devices as well as for increasing the
effi ciency of functioning of elements used in microelectronics and nanoelectronics

**Author:**
S. I. Futko, B. G. Shulitskii, V. A. Labunov, and E. M. Ermolaev

**Keywords:**
graphene, carbon nanotubes, allotropes, carbon nanomaterials, hybrid nanostructures, self-organizing synthesis, nanostructured composite materials, chemical vapor deposition, cobalt catalyst

**Page:**
95

**MODELING THE ONE-STAGE SYNTHESIS OF COMPOSITE PARTICLES OF THE NUCLEUS–SHELL TYPE IN SEPARATE OXIDATION OF TITANIUM AND SILICON TETRACHLORIDES IN A PLASMACHEMICAL REACTOR**

The authors have modeled the one-stage synthesis of titania and silica composite nanoparticles in the working zone of
a plasmachemical reactor by the chloride method based on separate oxidation of titanium and silicon tetrachlorides
with pre-mixing of the reagents by bubbling. Within the framework of the developed synthesis model, the authors
have obtained data on the size of the nuclei of the composite particles, the shell thickness, and the ratio of the number
of shell-coated and uncoated particles

**Author:**
S. M. Aulchenko, and E. V. Kartaev

**Keywords:**
titania, silica, composite particles, plasmachemical reactor, single-velocity multicomponent medium, homogeneous and heterogeneous reactions, coagulation

**Page:**
108

**CHARACTERISTICS OF THE FLYING OF FOREST COMBUSTIBLE MATERIALS UPSTREAM OF A FIRE BARRAGE UNDER THE ACTION OF AN AIR FLOW**

Results of experiments on determination of the temperature, velocity, and mechanical trajectory of fragments of forest
combustible materials subjected to pyrolysis, fl ying away under the action of high-velocity air fl ow, are presented.
The effect of fl ying of such fragments over a fi re barrage was mainly investigated. The experiments were performed
with conifer needles and leaves, representing typical combustible materials in ground forest fi res. On the basis of the
experimentally determined effect of inclination of a fl ame over a fi re barrage formed of moistened forest materials,
physical and mathematical models of fl ying of fragments of forest combustible materials subjected to pyrolysis
upstream of such a fi re barrage have been developed. With the use of these models, the characteristic length of the
zone of fl ame combustion of a forest material, the height of the fl ame in this zone, and the geometric dimensions of
the fi re barrage necessary and suffi cient for reliable localization of the fl ame combustion and thermal decomposition
of forest combustible material were determined

**Author:**
D. V. Antonov, A. O. Zhdanova, G. V. Kuznetsov, N. P. Kopylov, I. R. Khasanov, and N. E. Shlegel

**Keywords:**
forest combustible material, pyrolysis, combustion, fi re barrage, wind

**Page:**
114

**FORMATION OF A TURBULENCE SPECTRUM IN THE INERTIAL INTERVAL ON THE BASIS OF THE THEORY OF STOCHASTIC EQUATIONS AND EQUIVALENCE OF MEASURES**

An analytical representation of a turbulence spectrum in the inertial interval is given based on stochastic equations for the continual laws of continuous medium and the laws of the equivalence of measures between random and deterministic motions in the theory of stochastic hydrodynamics. The analytical solution of these equations is presented in the form of spectral function E(k) ~ k^{n}
corresponding to the classical dependence E(k) ~ k–5/3 obtained
earlier by A. N. Kolmogorov in the statistical theory on the basis of dimensional considerations. The presented
solution confi rms the possibility of determining partial solutions for the spectral function depending on the wave
number on the base of single implications of the theory of stochastic hydrodynamics within the framework of which
the solutions in the fi eld of wave numbers of turbulence generation were obtained.

**Author:**
A. V. Dmitrenko

**Keywords:**
stochastic equations, equivalence of measures, spectral density, inertial interval of spectrum

**Page:**
122

**ESTIMATION OF THE AMPLITUDE OF NONLINEAR "ANTICONVECTION"**

In systems consisting of two immiscible liquids in the gravity force fi eld, convective instability may set in not only on
heating from below, but also on horizontal-homogeneous heating from above, i.e., on stable density stratifi cation of
each of the media. In a number of previous works, a linear theory of this type of instability ("anticonvections") has
been developed. In the present work, analytical estimates of the characteristics of fi nite-amplitude anticonvection
have been made for the fi rst time for the limiting case of neutral stratifi cation of one of the media

**Author:**
L. Kh. Ingel'

**Keywords:**
convective instability, anticonvection, fi nite-amplitude perturbations, two-layer media, interaction in a water–air system

**Page:**
128

**COORDINATED BOUNDARY CONDITIONS AT THE INLET TO THE COMPUTATIONAL DOMAIN WITH SIMULATION OF LAMINAR FLOW PAST A PLATE USED AS AN EXAMPLE**

The preference given to the Blasius profi le with introduction of the vertical velocity component at the inlet to the
computational domain in comparison with the simplifi ed approach based on the Pohlhausen profi le is substantiated
using the example of laminar fl ow past a plate

**Author:**
S. A. Isaev, A. D. Chornyi, Yu. V. Zhukova, D. P. Frolov, and L. P. Yunakov

**Keywords:**
laminar fl ow, plate, inlet velocity profi les, Navier–Stokes equations

**Page:**
132

**CONTROL OF THE FORMATION OF A TRANSONIC REGION IN AN AXISYMMETRIC SUPERSONIC FLOW WITH THE USE OF A JET AND A NEAR-WALL ENERGY SUPPLY**

The control action of a throttling air jet produced by a gas generator and of the energy sources positioned at the
walls of an axisymmetric channel, which models the combustion-chamber unit of a ramjet in which a gas fl ow is
decelerated, on the shock-wave structure of a supersonic gas fl ow in the channel was investigated for the purpose
of formation of a lengthy transonic region in it. A heat energy was supplied to the gas fl ow in the indicated channel
in the pulse-periodic regime, and the pressure in the gas generator was also changed periodically. The range of
energies corresponding to a stable transonic fl ow regime in the channel was determined on the basis of solution
of the nonstationary Euler equations in dimensionless variables. For comparison, the combustion of a gaseous
fuel infl owing to the channel through a slot in the channel wall upstream of the control air jet was considered. A
nonstationary gas fl ow in the channel was calculated on the basis of the Reynolds-averaged Navier–Stokes equations
with the use of the k–ω SST model of turbulence. It is shown that a controllable energy release in the channel,
providing the obtaining of a transonic fl ow regime in it analogous to that obtained on the basis of solution of the
Euler equations, can be realized with the use of a control transverse air jet

**Author:**
V. P. Zamuraev and A. P. Kalinina

**Keywords:**
supersonic fl ow, axisymmetric channel, near-wall energy sources, control jet, Euler and Navier–Stokes equations

**Page:**
136

**COMPUTATIONAL-EXPERIMENTAL INVESTIGATIONS OF THE PROCESSES OF MOTION OF A COOLANT FLOW IN THE REGION OF THE GUIDE CHANNEL BEHIND MIXING GRIDS OF FUEL ASSEMBLIES**

In the paper, the authors have presented local hydrodynamic characteristics (averaged-velocity vector fi elds) of the
fl ow behind various types of intensifi er grids of TVS-Kvadrat fuel assemblies intended for operation in pressurizedwater-reactor (PWR) cores. The structure of the fl ow behind these structural elements of the cassette has been
revealed and the infl uence of the shape and orientation of turbulizers on the stabilization (equalization) length of
transverse velocities in the characteristic regions of an assembly has been determined. The acquired information
of the experimental investigations was used during the engineering substantiation of the TVS-Kvadrat structure for
installing these assemblies into rector plants.

**Author:**
A. V. Gerasimov, S. M. Dmitriev, A. A. Dobrov, D. V. Doronkov, A. N. Pronin, A. V. Ryazanov, D. N. Solntsev, and A. E. Khrobostov

**Keywords:**
reactor, core, fuel assembly, intensifi er grid, coolant hydrodynamics

**Page:**
145

**MATHEMATICAL MODELING OF THE MOTION OF SUPERCAVITATING STRIKERS AT UNDERWATER START**

The paper is devoted to the investigation of the high-velocity motion of supercavitating kinetic strikers in water with
account of the intraballistic processes in the powder chamber and outside the channel cut of the ballistic installation,
the supercavity dynamics, and also the interaction of the strikers with underwater barriers (obstacles). The process
of supercavitating motion at underwater start is modeled on the basis of solving Reynolds-averaged Navier–Stokes
equations with turbulence equations and cavitation equations for a multiphase medium. To investigate the stressstrain state and a possible destruction of solid bodies in interacting with underwater barriers of various types,
mathematical modeling is conducted on the basis of an elastoplastic model of a medium. The range of investigated
velocities is 50–850 m/s

**Author:**
A. N. Ishchenko, R. N. Akinshin, I. L. Borisenkov, A. A. Glazunov, K. N. Zhil′tsov, V. Z. Kasimov, I. M. Tyryshkin, and A. V. Chupashev

**Keywords:**
water, supercavitating kinetic striker, underwater start, supercavity, barrier, mathematical modeling

**Page:**
155

**FREE CONVECTIVE MOTION OF AIR IN A HEATED SPACE**

The evolution properties of free convective motion of air in a heated space have been investigated by numerical
modeling. The air motion is always nonstationary and turbulent. The existing technical constraint on the grid scale
makes it possible to observe only large-scale eddies. In actual practice, eddies have different dimensions and are
always in motion near the midposition; they can disappear and appear again. The larger the eddy size, the smaller
the amplitude of fl uctuations of the air temperature and velocity in them. The most intense motion is near the window
and the heating appliance. At low outdoor temperatures, it is highly likely that a fl ow of cold air moving over the
lower part of the space will appear from the window

**Author:**
B. A. Unaspekov, K. O. Sabdenov, M. Erzada, S. Sh. Auelbekov,c A. S. Taubaldieva, and O. D. Seitkaziev

**Keywords:**
buildings, temperature regime, free convection, hydrodynamics, turbulence

**Page:**
164

**EXPERIMENTAL INVESTIGATION OF A FREE TURBULENT AIR JET OUTFLOWING FROM A NOZZLE OF SQUARE SHAPE**

Experimental investigation of average characteristics of fl ow in a turbulent free air jet issuing from a nozzle of
square shape has been carried out. The investigations were carried out in the presence and absence of external
acoustic effect

**Author:**
M. S. Isataev, G. Toleuov, and M. Sultan

**Keywords:**
nozzle with square outlet cross section, elongation parameter, turbulent free air jet, acoustic effect

**Page:**
172

**EFFECT OF VARIABLE VISCOSITY AND THERMAL CONDUCTIVITY ON UNSTEADY FREE CONVECTIVE FLOW OF A MICROPOLAR FLUID PAST A VERTICAL CONE**

A numerical investigation of the effects of variable viscosity and thermal conductivity on an unsteady free convective
MHD fl ow of a micropolar fl uid past a vertical cone with variable heat fl ux, viscous dissipation, and Joule dissipation
is carried out. The fl uid viscosity and thermal conductivity are modeled by inverse linear functions of temperature.
The governing partial differential equations are reduced to nondimensional ones, which are discretized using an
effi cient and unconditionally stable implicit fi nite difference method of the Crank–Nicolson type and solved for
prescribed boundary conditions by an iterative scheme based on the Gauss–Seidel method. Numerical results are
presented for the velocity, temperature, and microrotation rate profi les. The values of the skin friction and Nusselt
number for various combinations of parameters are given

**Author:**
G. C. Hazarika, Bandita Phukan, and Sahin Ahmed

**Keywords:**
magnetohydrodynamic fl ow, viscosity, thermal conductivity, micropolar fl uid, Crank–Nicolson implicit method, microrotation

**Page:**
178

**NONSTATIONARY POROSITY AND DENSITY FIELDS AT THE STAGE OF WITHDRAWAL OF AN ACID SOLUTION FROM A CARBONATE STRATUM**

The authors have considered the problem on concentration fi elds of hydrochloric acid with account taken of the
chemical reaction as applied to the stage of withdrawal of the active solution from a carbonate stratum. Analytical
expressions to determine the porosity of the carbonate skeleton and the density of the hydrochloric acid solution,
which are applicable for engineering calculations, have been found with account of the preceding technological
processes. The results of computational experiments on the process of acidic stimulation have been analyzed, and
it has been shown that the obtained dependences can be used for calculations of cyclic stimulation of oil and gas
reservoirs, which is implemented to enhance the oil recovery

**Author:**
A. I. Filippov, I. F. Kabirov, and T. M. Levina

**Keywords:**
extraction, density of the active solution, porosity, reaction rate constant, reaction order

**Page:**
186

**MATHEMATICAL MODEL OF MULTIPHASE NONISOTHERMAL FILTRATION IN DEFORMABLE POROUS MEDIA WITH A SIMULTANEOUS CHEMICAL REACTION**

The authors have developed a mathematical model of multiphase nonisothermal fi ltration with chemical reactions
and phase transitions in deformable porous media. A modifi ed Biot approach was used to describe fi ltration through
a deformable porous medium. Equations for the stress–strain state have been formulated in terms of displacements,
and the elastic rheology of a porous skeleton in nonisothermal form was used in the model. The dependence of the
permeability on porosity has been written in the form of a Kozeny–Carman equation. A test problem of combustion in
a low-permeability sample of a bituminous reservoir has been solved. Results of the work can be used to numerically
substantiate experiments on the technology of interbedding combustion in low-permeability beds.

**Author:**
É. M. Khramchenkov and M. G. Khramchenkov

**Keywords:**
multiphase nonisothermal fi ltration, deformable porous media, heavy crude

**Page:**
191

**APPROXIMATE SOLUTION OF THE PROBLEM ON ELASTIC-LIQUID FILTRATION IN A FRACTURE FORMED IN AN OIL STRATUM**

With the use of theoretical models of fi ltration liquid fl ows in fractures of fi nite and infi nite lengths, formed in an oil
stratum, the problem on the production of oil from a well, operating in the regimes of constant differential pressure
or constant fl ow rate in this stratum, was solved. On the basis of approximate solution of the problem on the fl ow of
oil from a stratum into a fracture formed in it by the method of successive changing stationary states, fairly simple
analytical formulas have been obtained. A comparison of the results of numerical calculations of the practically
important parameters of an oil stratum and a hydraulic fracture in it by the approximate formulas constructed and
the corresponding exact formulas, which are much more complex than the approximate formulas, has shown that
these results are almost identical. In particular, the errors in determining the evolution of the pressure fi eld in a well
and its fl ow rate by the approximate formulas did not exceed several percent. On the basis of numerical analysis
of the approximate solutions obtained, the infl uence of the porosity and permeability of the stratum, the length of a
fracture in it, and the rheological properties of the liquid saturating the stratum on the evolution of the pressure in
the fracture, the fl ow rate of a well operating in the regime of constant differential pressure in the stratum, and the
changes in the pressures in the fracture and in the well at a constant well fl ow rate was investigated.

**Author:**
V. Sh. Shagapov and Z. M. Nagaeva

**Keywords:**
oil stratum, hydraulic fracturing, fi ltration, pressure distribution, analytical and approximate solutions

**Page:**
210

**COMMENTS ON THE SELECTION OF A DISPERSED SAMPLE TO DETERMINE THE MAGNETIC SUSCEPTIBILITY OF THE SAMPLE AND THE DISPERSED PHASE PARTICLES**

An analysis has been made of fi eld experimental dependences of the magnetic susceptibility of low-concentration
colloids with different values of concentration of the dispersed phase of particles (magnetite). An attempt has been
made to generalize them to a single dependence in coordinates in which the ordinate is the concentration-rated
susceptibility and thus to determine the magnetic susceptibility of individual particles. It has been shown that the
obtained results signifi cantly exceed maximum permissible ones. Furthermore, there is contradiction in them (in
using data for one and the same colloid, but with a different concentration of the dispersed phase). This is due to the
formation of chains and aggregates of particles. Thus, to determine the magnetic susceptibility of dispersed phase
particles, it is necessary to use "hard" dispersed samples, in particular, two-fraction powder samples (with addition
of a passive fraction), which ensures the fi xation of the dispersed phase particles. Examples have been given of
concentration dependences of the magnetic susceptibility of powder samples (with a dispersed phase of magnetite
particles), and also of ferro-impurity particles of sugar sand and farina. These dependences having characteristic
linear portions make it possible to obtain data on the magnetic susceptibility of individual ferroparticles

**Author:**
A. V. Sandulyak, A. A. Sandulyak, V. A. Ershova, D. A. Sandulyak, M. N. Polismakova, and D. O. Kiselev

**Keywords:**
ferroparticles, magnetite, colloid, suspension, powder, low-concentration dispersed phase, magnetic susceptibility

**Page:**
210

**CONTROLLED METHODS TO SUPPRESS PRESSURE PULSATIONS IN MULTIPHASE PIPELINES**

The authors have proposed controlled methods to suppress (diminish) pressure pulsations in pipelines with account
taken of rheological properties and on the basis of swirling of the fl ow of piped multiphase systems. It has been
shown that by selecting the parameters of fl ows, one can decrease both the level of harmful pulsations in multiphase
pipelines and the amplitudes of suppressing action through the creation of relevant rheophysical characteristics.
Also, it has been shown that fl ow swirling may become an effi cient method to suppress pressure pulsations in
multiphase pipelines

**Author:**
G. G. Ismayilov, É. Kh. Iskenderov, F. B. Ismayilova, and G. A. Zeinalova

**Keywords:**
rheology, multiphase fl ow, pressure pulsation, suppression of pulsations, relaxation time, amplitude, fl ow swirl.

**Page:**
216

**EQUATIONS OF STATE TO DESCRIBE ISOTHERMAL COMPRESSION OF CERTAIN MOLECULAR NITRO COMPOUND CRYSTALS**

An approach to constructing semiempirical equations of state of molecular crystals of nitro compounds is suggested
allowing one to describe isothermal compression of the crystal of triaminotrinitrobenzene (1,3,5-triamino-2,4,6-
trinitrobenzene) by the familiar modulus of three-dimensional compression and sublimation heat of the crystal
obtained from experiments not related to isothermal compression. A comparative analysis of experimental data
on isothermal compression of the molecular crystal of triaminotrinitrobenzene and calculations by the proposed
equation of state have shown that the experimental and calculated values of pressure are within the limits of
experimental uncertainty

**Author:**
Yu. M. Kovalev

**Keywords:**
equation of state, molecular crystal, isothermal compression, Helmholtz energy, Debye approximation, characteristic Debye temperature, Grüneisen coeffi cient

**Page:**
223

**A NEW RAPID METHOD OF DETERMINING THE THERMAL DIFFUSIVITY OF MATERIALS AND FINISHED ARTICLES**

A new nonstationary nondestructive rapid method of determining the thermal diffusivity of materials and fi nished
articles has been suggested and tested experimentally without cutting out samples from them and preparation of
the latter. The method is based on using an infrared imager to video record the infrared radiation of the surface
originating as a result of its local stepwise heating by, say, a focused laser beam. Subsequent computer processing
of the patterns of the nonstationary thermal fi eld by the developed models and algorithms makes it possible to
determine the thermal diffusivity of a material or an article in the case of one-sided access to them

**Author:**
D. Yu. Golovin, A. G. Divin, A. A. Samodurov, A. I. Tyurin, and Yu. I. Golovin

**Keywords:**
point stepwise laser heating, infrared imager, one-sided access, thermal diffusivity

**Page:**
234

**TOWARD NUMERICAL SOLUTION OF THE PROBLEM ON STRESSED STATE OF THERMOELASTIC PHYSICALLY ORTHOTROPIC CYLINDRICAL SHELLS**

To investigate the stressed-strained state of thermoelastic anisotropic cylindrical shells the original system of
nineteen differential equations of eighth order in partial derivatives of the general theory of shells is transformed into
a system of eight differential equations of fi rst order. It is suggested to carry out numerical realization by the method
of orthogonal marching. Numerical results are presented for the case of temperature drop over the shell thickness

**Author:**
B. V. Nerubailo

**Keywords:**
thermoelastic stresses, heat-releasing fuel assembly, orthotropic, sleeve-shell, marching method, system of differential equations, Fourier series

**Page:**
241