#### Volume 93, №2

**CALCULATION OF THE THERMODYNAMIC EQUILIBRIUM OF A MULTICOMPONENT TWO-PHASE SYSTEM BASED ON MINIMIZATION OF THE GIBBS POTENTIAL**

The authors have proposed a method to model the thermodynamic equilibrium of the two-phase multicomponent
system "solution–vapor" by solving a system of ordinary differential equations following from the principles of
nonequilibrium thermodynamics and statistical physics. Calculation of the thermodynamics of liquid and vapor
phases was based on the equation of state. During the solution of the system of ordinary differential equations, the
authors determined the molar volumes of the solution and the vapor, the molar composition of the phases, and the
pressures of the onset of boiling of the solution and condensation of the vapor. The proposed method is fundamentally
different from the popular empirical Rachford–Rice method. Results of calculating with this method have been
presented.

**Author:**
I. V. Derevich and A. A. Panova

**Keywords:**
Gibbs potential, thermodynamic equilibrium, nonequilibrium thermodynamics, thermodynamic equation of state, fugacity, phase-equilibrium line

**Page:**
247

**ESTIMATION OF THE MAXIMUM OUTPUT OF THE PROCESS OF RECTIFICATION OF A CONTINUOUS MIXTURE WITH REGARD FOR THE IRREVERSIBILITY OF THE HEAT AND MASS TRANSFER IN IT**

The problem on estimation of the maximum production rate of a cascade of rectifi cation columns, in which a
continuous mixture is separated into fractions at their boiling points, and of the corresponding amount of heat
expended in the rectifi cation process is considered. A method is proposed for determining the order of separating a
continuous mixture in such a cascade, minimizing the total heat losses in it, in the case where the temperatures in
the dephlegmator and boiler of its columns are close to the boiling temperatures of the interfacial mixture fractions.

**Author:**
A. I. Balunov and A. M. Tsirlin

**Keywords:**
continuous mixture, rectifi cation, thermodynamic optimization, entropy production, realizable regimes

**Page:**
261

**INITIAL STAGE OF IMPREGNATION AND EXTRACTION IN MODELING A POROUS MEDIUM BY A TWO-CONTINUA MODEL**

The initial stage of impregnation (extraction) is investigated on the basis of the model of mass transfer in a
porous material consisting of two continua (bidisperse model) with its specifi cs of diffusion processes in each of
them. Particular emphasis was placed on considering asymptotic (analytical) representations of the solutions of
corresponding problems under typical additional conditions, in particular, for a body of fi nite dimensions.

**Author:**
A. I. Moshinskii

**Keywords:**
two-continua model, impregnation, extraction, porous body

**Page:**
271

**ANALYTICAL REGULARITIES OF FILLS OF CO-SIZED AND DIFFERENT-SIZED PARTICLES**

Refi ned analytical dependences have been presented for assessing basic parameters of co-sized and different-sized
randomly arranged particles and/or granules of fi lls, which make it possible to rigorously assess the properties of
the fi lls by the average particle (granule) size, the relation of the average sizes of large and small particles, and
the porosity. The presented procedure takes account of the actual properties of powder fi lls and their clustering.
It permits determining the porosity, the coeffi cient of internal friction, and the average coordination number of
particles or granules in the fi lls. The results obtained from the proposed dependences are in good agreement with
experimental data

**Author:**
Yu. N. Kryuchkov

**Keywords:**
fi lls, model, coeffi cient of internal friction, clustering, structure, coordination number, critical coordination number, packing density, porosity, particle size

**Page:**
280

**SIMULATION OF THE FORMATION OF A MIXTURE OF LOOSE MATERIALS**

Simulation of the formation of a mixture of powders is carried out. The problem has been solved by the method of
discrete elements in the approximation of bidisperse package of spherical particles. Dependence of the mixture
porosity on the sizes of the particles of mixed powders and on adhesive interaction of particles is shown.

**Author:**
E. N. D′yachenko and N. N. D′yachenko

**Keywords:**
method of discrete elements, porosity, adhesive interaction

**Page:**
287

**NUMERICAL INVESTIGATION OF THE INFLUENCE OF PROPERTIES OF THE GAS COMPONENT OF A SUSPENSION OF SOLID PARTICLES ON THE SPREADING OF A COMPRESSED GAS-SUSPENSION VOLUME IN A BINARY MEDIUM**

The process of propagation of the normal shock from a gas suspension to a pure gas is modeled numerically. Different
gases are considered as the carrier medium of the high-pressure chamber of a shock tube. The infl uence of properties
of the gas component of the gas suspension on the process of outfl ow of a dust-laden medium into a low-pressure
chamber and on the spatial distribution of the temperature of solid particles is investigated

**Author:**
D. A. Tukmakov

**Keywords:**
gas suspension, shock waves, numerical modeling, interphase heat transfer

**Page:**
291

**INFLUENCE OF THE CONCENTRATION OF WATER DROPLETS IN AN AEROSOL CLOUD ON THE CHARACTERISTICS OF THEIR COLLISIONAL INTERACTION**

The authors have presented results of experimental investigations into the process of collisions of water droplets in a gas medium with variation of the basic parameters in wide ranges corresponding to advanced gas-vapor-droplet technologies: sizes (radii) 0.1–1 mm, velocities of travel 0–10 m/s, angles of interaction (attack) 0–90^{o}
, relative volume concentration 0.1–10^{–3}–8.5·10^{–3} m^{3}
of water/m^{3}
of the gas, velocity of motion of the fl ow 0–10 m/s, and temperature 20–1000^{o}
C; directions of fl ows: opposing, codirectional, and lateral. In processing the experimental
results, the emphasis was on the infl uence of the relative volume concentrations of the droplets on the characteristics
of their interaction. The relative probabilities of four typical regimes of interaction of the droplets have been
calculated: recoil, coagulation, spread, and breakup (reduction in size). Parametric ranges have been shown for
droplets for which the concentration growth of the latter in an aerosol leads to an increase in the probability of
coagulation, recoil, and size reduction. Also, the authors have presented ranges of variation of the concentration
of droplets in a gas medium, in which the probabilities of all the investigated interaction schemes are high. The
experimental results have been processed with the existing approaches to generalization by calculating the angular
factor of interaction and the Weber number.

**Author:**
O. V. Vysokomornaya, G. V. Kuznetsov, P. A. Strizhak, and N. E. Shlegel′

**Keywords:**
water droplets, interaction, collisions, relative volume concentration of droplets, statistical analysis, relative probability

**Page:**
298

**ASSESSING THE PARAMETERS OF THE WELLBORE ZONE FROM THE RESULTS OF VERTICAL INTERFERENCE TESTING OF A GAS STRATUM**

A mathematical model of the process of vertical interference testing of the gas stratum penetrated by an imperfect
well has been constructed. The infl uence of the parameters of the wellbore zone on pressure curves in the active
and reactive intervals of the well has been investigated. From the results of vertical interference testing, we can
determine the parameters governing the skin factor: the permeability of the stratum and the permeability and radius
of the wellbore zone

**Author:**
M. N. Shamsiev, M. Kh. Khairullin, and P. E. Morozov

**Keywords:**
vertical interference testing, skin factor, permeability, radius of the wellbore zone, inverse problem

**Page:**
310

**HIGH-TEMPERATURE INDIRECT COMPACTION OF POWDER MATERIALS WITH ACTIVE ACTION OF AN EXTERNAL FRICTION FORCE**

On the basis of theoretical analysis of the rheodynamics of a powder material in the process of its indirect compaction
with active action of an external friction force, the infl uence of this friction force on the density distribution of the
material in the bulk of its sample was investigated. The advantages of the indicated compaction method over the
one-side high-temperature compaction of powder materials, used most frequently in power metallurgy and in selfpropagating high-temperature synthesis technologies, were substantiated

**Author:**
A. M. Stolin, L. S. Stel'makh, and S. V. Karpov

**Keywords:**
indirect compaction, active external friction force, rheodynamics, self-propagating high-temperature synthesis, density distribution, compressive stress

**Page:**
317

**ADSORPTION DEHYDRATION OF TRANSFORMER OIL OF SELECTIVE TREATMENT**

The adsorption dehydration of a transformer oil of selective treatment with the use of KSK silica gel, permutite NaA,
and of natural zeolites (fl asks of Kilachevsk deposit and clinoptilolite zeolite) has been studied.

**Author:**
L. R. Gainullina and V. P. Tutubalina

**Keywords:**
transformer oil, adsorption dehydration, adsorbent, silica gel, zeolite

**Page:**
324

**HEAT EXCHANGE AND NONISOTHERMAL CRYSTALLIZATION IN FORMATION OF A PLANE VISCOELASTIC FILM**

The processes of heat exchange and of nonisothermal crystallization in the formation of a plane viscoelastic polymer
fi lm are investigated. The polymer melt is forced through a plane-slitted extrusion head, subjected to uniaxial
stretching and simultaneously to cooling in air, and subsequently gaining access onto a batch-off cooling roll. It is
assumed that the fi lm is wide enough, and the distance between the extruder head and the batch-off roll is minimum
to such a degree that it is possible to neglect the change in the sheet width in the process of longitudinal stretching.
A steady nonisothermal process is considered. It is also considered that the gravity and inertial forces and surface
stretching can be neglected. From the rheological point of view, the polymer melt represents a viscoelastic fl uid.
The upper-convected Maxwell model is used with viscosity depending on temperature and crystallinity degree. The
mathematical model is complemented by the equation of kinetics of nonisothermal crystallization. The problem has
been solved numerically by the method of fi nite differences

**Author:**
A. V. Baranov

**Keywords:**
viscoelastic fl uid, heat exchange, formation of plane fi lms, crystallization

**Page:**
329

**TEMPERATURE FIELD IN A WELL IN THE INTERVAL OF CONSTANT GRADIENTS WITH ACCOUNT FOR THE DEPENDENCE OF THERMAL CONDUCTIVITY ON TEMPERATURE**

The problem of nonstationary heat transfer of an ascending liquid fl ow is considered with account for the nonlinearity caused by the dependence of the thermal conductivity of oil on temperature. The method of solution represents a combination of the small parameter method with “on the average accurate” asymptotic method. By expanding in the small parameter and asymptotic parameters, the problem is reduced to a chain of linear problems. To determine the fi rst coeffi cient of expansion in the small parameter, a special splitting procedure has been developed. With the aid of the developed apparatus of the small and formal parameters, analytical dependences of temperature in a well and surrounding rocks on time and spatial coordinates have been found that take into account the anisotropy of the thermophysical properties of media. It is shown that the zero approximation of the temperature function in the small parameter, as which the temperature coeffi cient γ is taken to be, coincides with the solutions of the corresponding linear problem with a constant value of the radial component of thermal conductivity λ_{r}, with the fi rst approximation
taking into account the contribution of nonlinearity to the solution obtained.

**Author:**
A. I. Filippov, O. V. Akhmetova, M. A. Zelenova, and R. V. Siraev

**Keywords:**
thermal conductivity, heat transfer, convection, asymptotic method, analytical solution

**Page:**
336

**IMPROVEMENT OF THE POST-CRITICAL HEAT FLUX (CHF) HEAT TRANSFER MODEL USED IN THE KORSAR THERMOHYDRAULIC COMPUTER COMPLEX**

A comparison has been presented of the results of calculating the temperature of the wall and steam with the
empirical data of experiments modeling repeated impoundment of the core of water-cooled reactors. The need has
been shown to improve the model implemented in the KORSAR computer complex for the case of low mass velocities
and pressures. An engineering procedure has been proposed to account for droplets in removing heat in the region
above the wetting front.

**Author:**
N. D. Agafonova and I. L. Paramonova

**Keywords:**
repeated impoundment, wetting front, dispersed fl ow, size of droplets, distribution function, wall temperature

**Page:**
346

**NUMERICAL SIMULATION OF THE TEMPERATURE FIELDS IN A SINGLE-PHASE FLOW IN AN ASYMMETRICALLY HEATED MINICHANNEL**

The heat transfer in the single-phase fl ow of a liquid in an asymmetrically heated horizontal minichannel was
investigated. Thermograms of the surface of a heater in the minichannel and the surface of its adiabatic part have been
obtained with the use of an infrared camera, and they were used to construct temperature profi les for these surfaces.
Stationary temperature distributions in the insulating foil, the heater surface, and the liquid fl ow in the minichannel
have been obtained, respectively, with the use of the Laplace equation, the Poisson equation, and the energy equation
involving the frictional heat losses. The solution of the system of these differential equations with special boundary
conditions has culminated in the solution of three sequential inverse problems on the heat conduction in the indicated
adjacent regions having different physical parameters. These problems were solved using the Trefftz method, and the
temperature of the liquid fl ow in the minichannel was calculated by the Picard–Trefftz method. The temperature
distributions obtained for the liquid fl ow and the heater surface were used to determine the heat transfer through the
liquid–heater interface. The Trefftz and Picard–Trefftz methods yielded similar local heat transfer coeffi cients and
temperature distributions

**Author:**
M. Grabowski, M. E. Poniewski, S. Hożejowska, and A. Pawińska

**Keywords:**
heat transfer, minichannel, single phase, inverse heat-transfer problem, Picard and Trefftz method

**Page:**
355

**TEMPERATURE OF MATERIAL IN THE PROCESS OF CONVECTIVE DRYING OF THIN MATERIALS IN THE FALLING RATE PERIOD OF DRYING**

A method of calculating the temperature of thin plane materials in the falling rate period of drying is considered
on the basis of analytical solution of the differential equation of nonstationary heat conduction with boundary
conditions of the third kind containing the equation of the rate of drying in the second period.

**Author:**
A. I. Ol′shanskii and A. M. Gusarov

**Keywords:**
moisture content, coeffi cient of drying, heat transfer coeffi cient, Biot number

**Page:**
364

**SCIENTIFIC AND TECHNICAL SUBSTANTIATION OF THE PROCESS OF COOLING OF A LIQUID BY FROZEN SPHERES**

The heat transfer in the single-phase fl ow of a liquid in an asymmetrically heated horizontal minichannel was
investigated. Thermograms of the surface of a heater in the minichannel and the surface of its adiabatic part have been
obtained with the use of an infrared camera, and they were used to construct temperature profi les for these surfaces.
Stationary temperature distributions in the insulating foil, the heater surface, and the liquid fl ow in the minichannel
have been obtained, respectively, with the use of the Laplace equation, the Poisson equation, and the energy equation
involving the frictional heat losses. The solution of the system of these differential equations with special boundary
conditions has culminated in the solution of three sequential inverse problems on the heat conduction in the indicated
adjacent regions having different physical parameters. These problems were solved using the Trefftz method, and the
temperature of the liquid fl ow in the minichannel was calculated by the Picard–Trefftz method. The temperature
distributions obtained for the liquid fl ow and the heater surface were used to determine the heat transfer through the
liquid–heater interface. The Trefftz and Picard–Trefftz methods yielded similar local heat transfer coeffi cients and
temperature distributions.

**Author:**
M. Grabowski, M. E. Poniewski, S. Hożejowska, and A. Pawińska

**Keywords:**
heat transfer, minichannel, single phase, inverse heat-transfer problem, Picard and Trefftz methods

**Page:**
355

**USE OF COMBINED COGENERATION–THERMAL PUMPING PLANTS FOR MUNICIPAL HEAT POWER ENGINEERING AND HEAT TECHNOLOGIES**

A procedure is suggested for determining the relative integral fuel economy of heat power engineering plants based
on the equations of balances of their thermal and electric powers. A comparative analysis of the fuel economy of
combined cogeneration–thermal pumping technology of heat generation with traditional technologies is carried out.
The results of the comparative analysis of the fuel economy of a combined cogeneration–thermal pumping plant,
boiler plant, and of autonomous thermal pumping plant, consuming line-operated electric energy from a thermal
power station are presented. Since the energy base of the cogeneration–thermal pumping plant is the cogeneration
plant, a comparison of such a plant with plants for separate production of electric and thermal energies at the
thermal power station and in the boiler room is made

**Author:**
Yu. F. Snezhkin and B. D. Bileka

**Keywords:**
cogeneration, thermal pumping, and boiler plants; thermal power stations, effi ciency, heat transformation ratio, fuel economy, heat power engineering, thermal technologies

**Page:**
376

**EXPERIMENTAL INVESTIGATION OF THE PROCESS OF COOLING WASTE TIRE PYROLYSIS PRODUCTS**

Waste tire disposal, being currently a topical problem, can be implemented by low-temperature pyrolysis in continuous units used to obtain commercial products: liquid fraction and solid coke residue. In creating such units, cooling the discharged coke residue may become a factor limiting the entire technological process. The process of cooling a bed of solid pyrolysis products in the open air has been investigated in this work. The development of heat generation has been established experimentally in bulk coke residue at a surface layer temperature of 608^{o}
C or
higher. A procedure has been developed which makes it possible to detect this effect for the process of pyrolysis of
other carbon-containing materials.

**Author:**
V. D. Vanyushkin, S. K. Popov, and I. N. Svistunov

**Keywords:**
pyrolysis, waste tires, coke residue cooling, heat generation (exotherm), porosity

**Page:**
384

**KINETICS OF NONEQUILIBRIUM MELTING OF A MACROSYSTEM UNDER THE ACTION OF A VOLUME HEAT SOURCE**

A kinetic model of nonequilibrium melting of a macrosystem under the action of a volume heat source formed in its
bulk has been constructed. In this model, the melting of such a system is defi ned with account of the thermodynamic
fl uctuations of its order parameter, playing a great role in the superheating of the system and in the attainment by it of
the absolute instability point at which the initially metastable solid phase of the system becomes absolutely unstable
relative to the infi nitely small fl uctuations of its liquid phase. Analytical solutions of the kinetic equations defi ning
the melting of a macrosystem have been obtained for different rates of its heating by an internal volume heat source.

**Author:**
E. E. Slyadnikov, Yu. A. Khon, P. P. Kaminskii, and I. Yu. Turchanovskii

**Keywords:**
macrosystem, nonequilibrium phase transition, heat source, kinetic equations

**INFLUENCE OF THE CONCENTRATION OF THE FILLER AND OF THE TYPE OF MATRIX ON THE PROPERTIES OF THERMOPLASTICS FILLED WITH SHUNGITE NANOPARTICLE**

The infl uence of a shungite fi ller on thermophysical and electrophysical properties of thermoplastics has been
investigated. It has been shown that fi lling the thermoplastics with a shungite fi ller is particularly effi cient at a
high concentration of the fi ller. It is the thermal conductivity and the thermal diffusivity, and also the electrical
conductivity that are most substantially increased by shungite with 60 wt.% of fi lling. Here, the infl uence of shungite
is more pronounced in the case of fi lling with polyamide rather than with polyethylene, which is due to the noticeable
nucleating effect of shungite. It has been shown that at an equally high degree of fi lling, a PA6-based composite
exhibits the properties of a conductor, whereas an LDPE-based one remains a dielectric. It has been established that
shungite nanoparticles actively interact with the thermoplastic matrix, structuring the polymer and leading to an
improvement of the thermophysical and electrophysical properties of a polymeric composite

**Author:**
S. M. Danilova-Tret′yak, L. E. Evseeva, A. V. Kravtsevich, V. G. Leshchenko, K. V. Nikolaeva, N. N. Rozhkova, and L. I. Shashura

**Keywords:**
nanosize shungite fi ller, thermoplastic polymers, PA6, LDPE, composite materials, thermal conductivity, thermal diffusivity, specifi c heat, electrophysical properties

**Page:**
401

**HYDROPHILIC-OLEOPHOBIC MEMBRANES BASED ON HYDROLYSIS PRODUCTS OF METHOXYTRIMETHYLSILANE WITH ADDITIONS OF SILICA PARTICLES**

The authors have shown the possibility of obtaining hydrophilic-oleophobic membranes through the application of
an oleophobizing compound to a membrane base presented by meshes from stainless steels 100, 200, and 400. The
oleophobizing compound is methoxytrimethylsilane from whose hydrolysis oleophobic methyl groups and hydrophilic
silanol ones develop which form the type of wettability of a membrane. It has been shown that adding nanostructured
silica particles creates surface roughness with an enormous number of pores and channels, which considerably
enhances the oleophobicity of synthesized membranes. The resulting membranes exhibit high oleophobicity to
organic liquids, letting water pass through their structure. This is promising for their use in the sphere of low-cost
gravity separation of water and organic liquids.

**Author:**
F. Sultanov, Ch. Daulbaev, B. Bakbolat, O. Daulbaev and Z. Mansurov

**Keywords:**
membranes, silane, oleophobicity, hydrophilicity, silica, separation

**Page:**
409

**PROBLEM ON CONJUGATE NONSTATIONARY HEAT EXCHANGE IN SUPERSONIC FLOW OVER A BLUNT-NOSED CONE AT AN ANGLE OF ATTACK**

The fl ow of a gas over a conic body, having a nose blunted over a sphere, with a supersonic velocity at different
angles of attack was considered. The possibility of control of the temperature regime of such a body in the case
of three-dimensional gas fl ow over it was investigated. The dependence of the temperature of the surface of the
indicated body on the material of which it is made, the angle of attack of the body, and other constitutive parameters
of the problem on conjugate nonstationary heat exchange between the body and the gas fl ow over it was determined
for standard conditions of an aerodynamic experiment. Results of numerical solution of this problem for different
angles of attack of the body were processed in the criteria form. The dependences obtained allow one to estimate
the degree of decrease in the maximum temperature at the surface of a blunt-nosed conic body depending on the
thermophysical parameters of the material of which this surface is made, including in the case of nonstationary gas
fl ow over it. It is shown that a uniform heating of the peripheral part of such a body and a marked decrease in the
temperature of its windward part at large angles of attack can be provided with the use of highly heat-conducting
materials for these parts of the body

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

**Keywords:**
aerodynamic heating, conjugate heat exchange, angle of attack, heat-insulating materials, laminar boundary layer

**Page:**
416

**CALCULATION AND EXPERIMENTAL INVESTIGATIONS OF THE VENTURI TUBE AS A HYDRODYNAMIC OSCILLATOR**

A mathematical model of an unsteady turbulent cavitation liquid fl ow in a Venturi tube with pressure self-oscillations
has been constructed on the basis of the system of continuity and Navier-Stokes equations, the k–ε model of turbulence,
and a complete cavitation model. The amplitude–frequency characteristics of the pressure oscillations in a Venturi
tube, calculated and obtained experimentally, were compared.

**Author:**
A. S. Korneev, D. A. Zhebynev, and A. M. Fel′dman

**Keywords:**
Venturi tube, cavitation, pressure oscillations, amplitude–frequency characteristics, experiment, calculation

**Page:**
428

**DEVELOPMENT OF A MATHEMATICAL MODEL OF INTRABALLISTIC PROCESSES FOR A GUN-START OF A GROUP OF SUPERCAVITATING STRIKERS**

A mathematical model of a shot from a smoothbore ballistic installation for a gun start of a group of supercavitating
strikers has been developed. To verify the mathematical model, experimental investigations into high-velocity
launching of a group of bodies on a hydroballistic testing facility have been conducted. A comprehensive parametric
investigation has been conducted to determine conditions for loading the ballistic installation to achieve the required
muzzle velocity, ensuring a supercavitating regime of motion for a group of strikers in water

**Author:**
A. N. Ishchenko, V. V. Burkin, V. Z. Kasimov, S. A. Afanas′eva, A. S. D′yachkovskii, and K. S. Rogaev

**Keywords:**
mathematical model, group launching, supercavitating motion

**Page:**
436

**REGIMES OF MOTION OF WATER–AIR FLOW IN A SHORT VERTICAL TUBE WITH THE UNDERFEED OF PHASES**

Results of experimental investigation of adiabatic motion of a water–air fl ow in a short vertical tube with the
underfeed of phases and the injection feed of water have been presented. It has been shown that the size of the gap
between the bottom edge of the tube and the level of liquid in the apparatus casing has a decisive infl uence on the
regime of fl ow. Conditions for the occurrence of characteristic hydrodynamic regimes, and also the heat loss in the
active zone of a contact-apparatus model have been determined.

**Author:**
P. A. Barabash, A. S. Solomakha, A. I. Gurov, and O. A. Panchenko

**Keywords:**
regimes of motion, fl ooding, water-air fl ow, bubbling, liquid fi lm.

**Page:**
443

**PRESSURE RELAXATION AFTER PRESSURIZATION IN A TUBULAR DUCT HAVING A DAMAGED SECTION**

The problem on pressure relaxation after pressurization in a tubular duct (pipeline) having a damaged section has
been considered. The pipeline is fi lled with a fl uid and is placed in the ground. An integral equation describing
pressure reduction in the pipeline has been obtained. Exact analytical and approximate solutions of the integral
equation have been found. The period of pressure half-recovery after pressurization has been considered as a
characteristic parameter determining the pressure drop rate in the pipeline. The period of pressure half-recovery
has been analyzed as a function of the geometric parameters of the pipeline, the length of the damaged section, the
properties of the fl uid, and also the fi ltration characteristics of the ground.

**Author:**
V. Sh. Shagapov, I. G. Khusainov, and Z. P. Khakimova

**Keywords:**
pressure relaxation, fl uid, tubular duct (pipeline), ground

**Page:**
452

**FILM COOLING WITH A PLATE-LENGTH-DISTRIBUTED SUPPLY OF THE COOLING AGENT INTO HEMISPHERICAL DEPRESSIONS IN ROTATION**

Results of computer modeling of fi lm cooling with a plate-length-distributed supply of the cooling agent through
angle holes in hemispherical depressions are presented. The calculations have been made in the range of variation
in the injection parameter from 0.5 to 2.0 under steady-state conditions and in rotation using the commercial ANSYS
CFX 14 software package.

**Author:**
A. A. Khalatov, N. A. Panchenko, and T. V. Donik

**Keywords:**
rotation, fi lm cooling, hemispherical depressions, computer modeling

**Page:**
459

**INFLUENCE OF THE REGION OUTSIDE A VENT ON THE EXPLOSION OF AN INDOOR GAS**

The overpressure and fl ame generated in the explosion of a gas in different regions of a room outside a vent in
it were investigated using computational fl uid dynamics. The calculation data obtained were compared with the
corresponding results of earlier large-scale experiments on this subjec t, and they show that the smaller the distance
from the vent, the larger the oscillations of the indoor overpressure and that the outside region of the vent substantially
infl uences the indoor explosion fl ow fi eld. It was established that, as the outside-region length increases, the peak
indoor overpressure approaches the experimental one, but the amplitude of the overpressure oscillations caused
by the Helmholtz and Taylor effects increases substantially in this case. The numerical simulation of the explosion
hazard of a ventilated gas in a room seems reasonable in the case where the outside region of a vent is not shorter
than the room.

**Author:**
Kai Yang, Pengfei Lv, Jiancun Gao, and Lei Pang

**Keywords:**
gas explosion, vent, numerical simulation, fl ame velocity, overpressure

**Page:**
466

**INTERACTION OF A PLANE SHOCK WAVE WITH REGIONS OF VARYING SHAPE AND DENSITY IN A FINELY DIVIDED GAS SUSPENSION**

A study has been made of the interaction between a plane shock wave in a gas or a gas suspension and regions of
square and rhombiform cross sections differing from the environment in density. A high-stability monotonic scheme
with small numerical dissipation was used for calculation. Comparisons with experiments on the refraction of the
shock wave on the interface of a binary gas have confi rmed the adequacy of the scheme. The infl uence of the densityratio factor (Atwood number), the shape of inhomogeneities, and the particle size on the shock wave structure and
the development of a Richtmyer–Meshkov instability has been shown

**Author:**
D. V. Sadin and V. A. Davidchuk

**Keywords:**
gas suspension, shock wave, material interface, refraction, Richtmyer–Meshkov instability

**Page:**
474

**MATHEMATICAL MODEL OF SYSTEM DESIGNING OF POWER-SUPPLY SYSTEMS OF AIRCRAFT AND SPACECRAFT**

The authors have presented logical and mathematical formulations of the problem of system designing of complex
systems by a combined quality criterion. Rocket engines of aircraft and spacecraft have been considered as complex
systems. The problem of system designing of a power-supply system has been formulated as a problem of ensuring its
minimum mass with assigned constraints on reliability, economic expenditures, and other parameters.

**Author:**
B. T. Erokhin, V. A. Sorokin, and A. S. Andryushin

**Keywords:**
power-supply system, quality criterion, parametric synthesis

**Page:**
484