#### Volume 96, №1

**MATHEMATICAL MODELING OF FILTRATIONAL SOIL FAILURE IN THE COURSE OF KARST-SUFFOSION PROCESSES**

A mathematical model has been developed for filtrational soil failure (suffosion) in the course of karst-suff osion
processes. A study has been made of the relationship of filtration processes in soluble fractured rocks and the soils
overlying them. An investigation has been conducted into the effects of filtration inhomogeneity of rocks on the
specific features of the course of the suffosion processes.

**Author:**
V. M. Konyukhov, M. G. Khramchenkov, A. N. Chekalina

**Keywords:**
fi ltration, suff osion, porosity, karst-suff osion process

**Page:**
1

**ON THE RELATION BETWEEN THE RELATIVE DISPOSITION OF INJECTOR DEVICES AND THE DISPERSIVITY OF THE GENERATED AEROSOL**

The results of experimental studies of the dispersivity of an aerosol obtained using two injector devices arranged
differently mutually are presented. The dependences of the numerical and volume concentrations of droplets in the
aerosol formed in the course of variation of the relative angle of attack of jets on the size of droplets are presented.
The limiting initial distances between droplets in the aerosol, at which the sizes of the droplets practically do not
change during their free fall, are determined. Based on the research results, recommendations were formulated to
ensure predictable distributions of the droplets of liquid in a gaseous medium at different distances from the fire zone.

**Author:**
G. V. Kuznetsov, A. O. Zhdanova, I. S. Voitkov, P. P. Tkachenko

**Keywords:**
aerosol, dispersivity, droplets, injector device, jets

**Page:**
8

**MATHEMATICAL SIMULATION OF THE FORMATION OF THE SECONDARY FRAGMENTS OF LIQUID DROPLETS AS A RESULT OF THEIR COLLISION**

A mathematical simulation of the formation of the secondary liquid droplets as a result of the collision of their
primary droplets has been performed by the VOF method. The influence of diff erent factors on the conditions of
fragmentation of liquid droplets and on their integral characteristics was investigated. The ratios between the
surface areas of liquid droplets after and before their collision were calculated. It was established that the ratio
between the surface areas of the liquid droplets of equal sizes is smaller than that of the liquid droplets having
different sizes and that the centered collision of liquid droplets is most efficient. The critical Weber number of
liquid droplets, an increase in which does not cause signifi cant changes in the characteristics of their secondary
droplets, was determined.

**Author:**
D. V. Antonov, R. M. Fedorenko, P. A. Strizhak

**Keywords:**
liquid droplets, collisions, secondary fragments, size distribution, free surface, mathematical simulation

**Page:**
17

**HYDRODYNAMIC MODEL AND KINETICS OF DISPERSION OF A SOLID DISPERSE PHASE IN THE PROCESS OF MIXING IN A VISCOUS LIQUID MEDIUM**

A hydrodynamic model of the dispersion of the solid particles of pigments in a liquid in an apparatus with a highspeed stirrer (a dissolver) designed for the production of

finely dispersed and readily dispersible pigments, which can be used as a preliminary stage of the dispersion of pigments in a liquid in which their concentration is high, is
proposed. The kinetics of dispersion of solid particles in the process of their mixing in a liquid was investigated. It
is shown that the time and rate of dispersion of solid particles in a liquid are dependent on the hydrodynamic and
technological parameters of the process. Methods of increasing the output of dissolvers are proposed

**Author:**
D. V. Elizarov, V. V. Elizarov

**Keywords:**
mixing, dissipation, dispersion, kinetics, solid particles, shear stress, viscous suspension

**Page:**
29

**ABSOLUTE PERMEABILITY TENSORS OF DIGITAL MODELS OF POROUS MEDIA UNDER VARIOUS BOUNDARY CONDITIONS AND DRIVING FORCES**

For the first time, a systematic investigation has been made into the infl uence of external boundary conditions and
driving forces of liquid flows in anisotropic porous media on their absolute permeability tensor. The investigations
have been perfumed on the basis of numerical simulation of a one-phase flow of an incompressible fluid in a porous
space using lattice Boltzmann equations. Consideration has been given to cases when anisotropic porous media
have permeability tensors with zero and nonzero nondiagonal components. It has been shown that in the case when
a porous medium has a permeability with zero nondiagonal components, and external boundary conditions do not
exert a substantial influence on the coefficient of medium permeability measured in the presence of a pressure
difference or a bulk force in it. In testing anisotropic porous media having a permeability tensor with nonzero
nondiagonal components, the external boundary conditions influenced significantly the filtration characteristics of
a medium. It has been established that periodic boundary conditions significantly reduce the sensitivity of filtration
characteristics of an anisotropic medium to the type of a driving force compared to nonpermeable external boundary
conditions. Anisotropic medium permeability tensors measured at the applied pressure difference are nonsymmetrical
in both types of external boundary conditions. It has been found that the permeability tensors of such a medium are
symmetrical only under periodic external conditions and in the presence of a driving bulk force.

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

**Keywords:**
permeability tensor, anisotropy, mathematical modeling, boundary conditions

**Page:**
39

**ANALYTICAL INVESTIGATIONS OF THE SPECIFIC FEATURES OF FILTRATION PROCESSES IN FORMATIONS AT A LOW SATURATION OF THE DISPLACED PHASE**

An analysis of the properties of solutions of the Buckley–Leverett equations describing the process of flooding
productive strata has been performed. It has been shown that, apart from the widely known result consisting in the
formation of a saturation jump on the front edge of the region of formation fluid displacement, a significant role, in
terms of practical use, belongs to the dynamics of formation fluid displacement in the vicinity of the back edge of the
displacement region, playing a major part at the late stage of deposits′ development when the saturation of the phase
displaced from the formation tends to zero. It has been established that in the case of oil being a wetting phase, i.e.
in developing hydrophobic oil reservoirs and also at the late stage of reservoirs′ development with a mixed type of
wettability, within the framework of the Buckley–Leverett theory, the back edge of the displacement region remains
immobile, in practice, and the maximum level of completeness in oil displacement from the formation does not occur.
It has been shown that accounting for the action of capillary forces in modeling filtration processes ensures the
mobility of the back edge of the displacement region and, accordingly, complete oil displacement from the formation.

**Author:**
A. M. Svalov

**Keywords:**
Buckley–Leverett equations, displacement region, capillary forces, convective components

**Page:**
50

**STRUCTURIZATION AND EFFECTIVE VISCOSITY OF A NON-NEWTONIAN OIL**

An analysis of the behavior of non-Newtonian oils in the process of formation and destruction of their structure with
the participation of resinous-asphaltenic materials has been performed. The conditions of formation of coagulation
structures and the possibilities of their destruction were determined. A general rheological equation defining the
possible behavior of non-Newtonian oils in different cases has been derived, and its effectiveness was substantiated
with the use of available experimental data. The dependences of the effective viscosity of non-Newtonian oils on the
rate of their shear and the content of resinous-asphaltenic materials in them were constructed. It was established
that the asphaltenes, resins, and paraffins, contained in an oil, substantially infl uence its rheological properties and,
consequently, the movement of the oil and its transportation

**Author:**
G. I. Kelbaliev, D. B. Tagiev, S. R. Rasulov, M. R. Manafov

**Keywords:**
asphaltenes, resins, structurization, eff ective viscosity, non-Newtonian liquids, rheology, shift

**Page:**
55

**BOILING-UP OF A JET OF SUPERHEATED WATER IN OUTFLOWING THROUGH CHANNELS OF DIFFERENT DIAMETERS**

An experimental study has been made of the dynamics of boiling-up of a jet of superheated water in outfl owing
through short cylindrical channels of diameters 0.33 and 0.63 mm. The change in the shape of the flashing jet at different degrees of superheating has been tracked. It has been established that upon the transition from the stationary
process of outfl ow to a nonstationary one, the opening of the jet is not full. Stepwise changes in the angle of opening
of the jet in explosive-boiling up transition at the temperature Ts = 470 K were found. From the experimental data,
the author determined the change in the opening angle of the jet of superheated water as a function of the degree of
its superheating

**Author:**
K. A. Busov

**Keywords:**
full opening, superheated liquid, explosive boiling-up, cylindrical channel, homogenous nucleation

**Page:**
64

**CONSTRUCTION OF A MATHEMATICAL MODEL OF THE FLOW CHARACTERISTICS OF A MULTIPHASE PIPELINE WITH REGARD FOR THE PHASE TRANSITIONS IN IT**

A simulation of the flow of a gas–liquid medium in a multiphase pipeline has been performed for the purpose of
diagnostics of its flow characteristics. It was established that, in the case of flow of a gas–liquid medium with phase
transitions in such a pipeline, its flow characteristics can be unstable, and this instability manifests itself as a local
decrease in the pressure loss in the pipeline

**Author:**
F. B. Ismaiylova, G. G. Ismaiylov, É. Kh. Iskenderov, Kh. T. Dzhakhangirova

**Keywords:**
multiphase pipeline, phase transition, fl ow characteristics, instability

**Page:**
73

**CONTRIBUTION TO THE SEARCH FOR THE OPTIMUM CONDITIONS FOR REDUCING WATER LOSS IN THE COOLING TOWER**

A mathematical formulation of the problem of finding the optimal size of water droplets and their initial velocity with restrictions on the cooled water temperature and water losses in the form of steam is given. In the case of free convection, such an optimization problem also becomes a boundary-value eigenvalue problem with a continuous spectrum, where the eigenvalue is the air flow at the cooling tower inlet. To free convection there corresponds the minimum flow value. The solutions are obtained for the initial temperature of the cooled water (70^{o }C) sprayed in the
tower with 1.8 kg·m–2
·s
–1. Attention is drawn to the difficulty of assessing the loss of water in the form of microscopic
droplets.

**Author:**
K. O. Sabdenov, M. Erzada, B. A. Zhakishev

**Keywords:**
cooling tower, optimal sizes of water droplets, droplet and stream entrainment, mathematical simulation

**Page:**
79

**INVESTIGATING GAS HYDRATE IGNITION AT VARIOUS HEATING SCHEMES**

Physical and mathematical models have been developed for ignition of gas hydrates in domination of different heat
transfer schemes. A numerical investigation has been made into interrelated processes of heat transfer under the
conditions of chemical reaction and exothermal and endothermal phase transformations at the stage of initiating
gas hydrates′ combustion. The model has been put through practical evaluation in comparing theoretical results of
investigations with experimental data. We have established dependences of the main characteristic of the process, viz.,
ignition delay time as a function of ambient temperature in variation of the emissivity and heat transfer coeffi cients.
We have identifi ed the limit values of the main parameters of an energy source, at which the conditions for ignition
occur steadily. The varied parameters (the emissivity and heat transfer coefficients and the heating temperature)
cover the technological conditions for a group of applications in power engineering.

**Author:**
O. S. Gaidukova, S. Ya. Misyura, P. A. Strizhak

**Keywords:**
gas hydrates, heating schemes, ignition, ignition delay time, prediction (prognostic) model

**Page:**
91

**MODELING THE PROCESS OF COMBUSTION OF METHANE HYDRATE WITH ALLOWANCE FOR NONEQUILIBRIUM DECOMPOSITION**

The authors have proposed a mathematical model of the process of combustion of methane hydrate in an enclosed
volume with allowance for the kinetics of its decomposition (nonequilibrium decomposition). Based on numerical
solution by the method of large particles, distributions of basic parameters of the system have been constructed. A
comparison has been made of the distinctive features of hydrate combustion for the cases of equilibrium decomposition
of the gas hydrate and of nonequilibrium decomposition with allowance for the kinetics. It has been shown that within
the framework of the model with nonequilibrium decomposition, the intensity of combustion at the beginning of the
process is much higher compared to the results of calculating based on the model with equilibrium decomposition.
The authors have constructed and analyzed the dependences of the temperature of the flame, the maximum pressure
of a gas mixture, and the law of motion of the phase-transition front for the two models of hydrate decomposition.

**Author:**
I. M. Bayanov, I. K. Gimaltdinov, and M. V. Stolpovskii

**Keywords:**
combustion, hydrate, kinetics, nonequilibrium decomposition

**Page:**
104

**MIGRATION ACTIVITY OF HEAVY METALS DURING PYROLYSIS OF DRIED SEWAGE SLUDGE IN A FIXED-BED REACTOR**

The results of a study of the pyrolysis of dried sewage sludge taken from a fi xed-bed reactor of urban wastewater
treatment plants are presented. The obtained experimental data made it possible to estimate the migration activity
of heavy metals entering into the composition of the sewage sludge. Measurements were carried out for vanadium
(V), chromium (Cr), cobalt (Co), nickel (Ni), copper (Cu), zinc (Zn), strontium (Sr), lead (Pb), rubidium (Rb),
barium (Ba), zirconium (Zr), and arsenic (As). It is shown that the emission of heavy metals upon release of volatile
substances during pyrolysis is characteristic for almost all of the studied elements, among which As, Rb, Co, and Ba
are the elements having the highest migration activity.

**Author:**
G. Ya. Gerasimov, V. V. Khaskhachikh, G. A. Sychev, V. M. Zaichenko

**Keywords:**
sewage sludge, pyrolysis, fi xed-bed reactor, heavy metals, migration activity.

**Page:**
112

**MULTICRITERIA ANALYSIS TO SUBSTANTIATE THE PROMISING NATURE OF USING WASTE AS COMPONENTS OF FUELS**

Consideration has been given to the use of municipal and industrial waste as components of a high-moisture
suspension fuel. An analysis has been made of the efficiency of such fuel as far as its technical and economic, energy,
and environmental indices are concerned with the MCDM multifactor-analysis methods. It has been established that
suspensions without impurities and suspensions with a 10% content of cardboard are the most efficient. It has been
shown that the fi nal index of efficiency of such suspensions exceeds the effi ciency of coal by 90% in some cases.
Directions for raising the effi ciency of suspension fuels whose basic components are industrial waste and municipal
solid waste have been determined.

**Author:**
G. V. Kuznetsov, G. S. Nyashina, K. Yu. Vershinina, D. S. Romanov, P. A. Strizhak

**Keywords:**
carbon waste, municipal waste, suspensions, combustion, effi ciency, MCDM multifactor analysis

**Page:**
120

**DETERMINATION OF THE DISTANCE BETWEEN THE DROPLETS OF FIRE-EXTINGUISHING AGENTS IN AN AEROSOL CLOUD AT WHICH THEY DO NOT COLLIDE**

Results of experimental investigations of the integral characteristics of the collisions of droplets of fire-extinguishing agents, having a surface tension of 0.0011–0.0014 Pa·s and a viscosity of 0.07269–0.08241 N/m, in an aerosol cloud with a droplet concentration γ d = 0–7.142 L/m^{3}
are presented. The dependence of the number of collisions of such droplets in an aerosol cloud on their Weber number and linear interaction parameter was demonstrated. It was established that the frequency of realization of each of the regime of collisions of extinguishant droplets in an aerosol cloud (rebound, scattering, coagulation, and fragmentation) depends on the sizes of the droplets and their concentration in the cloud. The distances between the extinguishant droplets in an aerosol cloud, at which they do not collide, were determined with regard for the initial sizes of the droplets, the velocities of their movement, and the temperature to which they are heated (T = 20 and 600^{o}C). A general approximate expression has been constructed
for estimating the distance between the droplets of diff erent fi re-extinguishing agents in an aerosol cloud, at which
these droplets do not collide and, consequently, do not cause signifi cant changes in the dispersivity of the cloud.

**Author:**
I. S. Voitkov, A. O. Zhdanova, S. S. Kropotova, G. V. Kuznetsov, P. P. Tkachenko

**Keywords:**
fi re-extinguishing agents, aerosol, droplets, collisions

**Page:**
130

**CHARACTERISTICS OF A TYPICAL INDOOR SEAT OF FIRE**

The paper presents the results of experimental investigations of the main characteristics of a typical indoor seat
of fire at the stages of initiating the ignition of combustible materials and in the process of their burning. Wood
material, wood fiberboard, linoleum, and plastic panels have been used as combustible materials. We registered
the characteristics of the seat of fire, viz., the temperature in the zone of burning of combustible materials, the
times of termination of their flame combustion, and thermal decomposition, the concentrations of gaseous products
of pyrolysis and combustion of these materials. The possibility of indentifying the material dominating in the seat
of fire has been substantiated. Reliable identifi cation of such material makes it possible to optimize the process of
suppressing the seat of fire.

**Author:**
A. O. Zhdanova, N. P. Kopylov, S. S. Kropotova, G. V. Kuznetsov

**Keywords:**
seat of fi re, indoor space, combustible materials

**Page:**
143

**INVESTIGATION OF THE MELTING OF SILICATE MATERIALS AS A RESULT OF EXPOSURE TO LOW-TEMPERATURE PLASMA**

The paper presents a mathematical model and the results of calculating the process of melting of silicate materials
as a result of their exposure to low-temperature plasma. In the case of a low temperature of the gaseous region
exceeding insignifi cantly the silicate melting temperature, the phase transition is preceded by a quite long induction
period characterized by the material′s heating from the initial temperature to the melting temperature. After the
completion of this stage, a melting process begins accompanied by a shift of the interphase boundary deeper into
the material. With increase in the initial gas temperature the duration of the induction period decreases. It has been
established that the velocity of the melting front propagation is determined by the initial temperature of the gas phase
and the thermophysical characteristics of the material but is weakly dependent on the fill layer thickness.

**Author:**
O. V. Matvienko, O. G. Volokitin, V. V. Shekhovtsov

**Keywords:**
silicate materials, heat transfer, melting, Stefan problem, mathematical modeling

**Page:**
150

**SIMULATION OF COMPLEX HEAT TRANSFER DURING CYCLIC DEPOSITION OF A HIGH-TEMPERATURE AEROSOL ON A SUBSTRATE**

The paper considers heat transfer during cyclic spraying of a high-temperature aerosol depositing in the form of a
condensed phase on a flat plate of fi xed thickness. A cyclically moving boundary appears with an increasing mass of
deposited material with the same thermophysical characteristics as the plate. The cycle is equal to the time of application of the aerosol within fractions of a second (heating) and to an order of magnitude longer convective-conductive and radiant cooling. To solve the formulated mathematical model analytically, the linearization of the radiant
heat flux was carried out by expanding the temperature difference of the moving boundary in a series in powers without taking into account the radiation and taking it into account with keeping the linear terms and further analyzing
the linearization error. Moreover, transformation of the spatial coordinate is applied, allowing one to transform a
region with a moving boundary into a region with a fixed boundary. A new analytical solution of a rather complicated
problem is obtained by the method of a finite cosine Fourier transform, having previously solved the problem for
eigenvalues and eigenfunctions with boundary conditions of the third kind. The results on the thermal state of the
entire system with a complex temperature profile on the outer moving boundary are obtained and analyzed.

**Author:**
V. F. Formalev, R. A. Degtyarenko, B. A. Garibyan

**Keywords:**
moving boundary, complex heat transfer, convective-conductive and radiant types of heat transfer, complex relief of a boundary in time, linearization, coordinate transformation, fi nite cosine Fourier transform

**Page:**
160

**THE METHOD OF INTEGRAL TRANSFORMATIONS FOR SOLVING BOUNDARY-VALUE PROBLEMS FOR THE HEAT CONDUCTION EQUATION IN LIMITED AREAS CONTAINING A MOVING BOUNDARY**

A method of integral transformations for solving the boundary-value problems for the equation of heat conduction in
limited regions containing a moving boundary of phase transition has been developed. New integral representations
of the solutions of boundary-value problems for the heat conduction equation under different boundary conditions
assigned on the outer fixed boundaries of a limited region are obtained. The analytical expressions obtained by the
proposed method for solving the indicated boundary-value problems are convenient for calculating and studying
the temperature fi elds, as well as the velocity of motion of the interface at large Fourier numbers

**Author:**
V. V. Shevelev

**Keywords:**
integral transformation, phase transition, heat conduction, interface, limited region

**Page:**
168

**MATHEMATICAL MODELING OF A THERMAL CONVERTER WITH A CYLINDRICAL HEAT PIPELINE AND A LUMPED HEAT SOURCE**

Consideration has been given to the issues of a functional scheme and substantiation of the efficiency of thermal
converters to monitor the moisture content of a flow of liquid materials. Furthermore, in the work, two basic types of
physical models, i.e., with lumped and distributed heat sources, have been identified on the basis of a segment of a
pipeline with radial orifices, in which there are cylindrical probes with heating and thermosensitive elements across
the liquid-material flow.

**Author:**
P. M. Matyakubova, P. R. Ismatullaev, N. I. Avezova, M. M. Mahmudjonov

**Keywords:**
physical model, fl ow, moisture content, liquid material, thermosensitive element, heating element, pipeline, heat transfer

**Page:**
178

**OPTIMIZATION OF STEAM ASSISTED GRAVITY DRAINAGE IN VERIFIED INTEGRAL SIMULATOR**

An integral model of the steam assisted gravity drainage of an oil field has been developed on the basis of the law
of conservation of the masses of the phases and the law of conservation of their energy. A verifi cation of the results
of calculations performed by this model has been performed, and it was established that they are in satisfactory
agreement with the corresponding field data. It is shown that the final oil recovery factor for the Senlac oil field
comprises 32% and that the optimization of the development system of the Fengcheng field increases its oil recovery
factor by 7%.

**Author:**
A. Ya. Gilmanov, K. M. Fedorov, A. P. Shevelev

**Keywords:**
high-viscosity oil, steam assisted gravity drainage, verifi cation, optimization, steam–oil ratio, oil recovery

**Page:**
188

**PERFORMANCES OF A CYLINDRICAL HEAT PIPE USING FERROFLUID AS THE WORKING LIQUID AT DIFFERENT INCLINATION ANGLES**

In this research, the thermal performance of a cylindrical heat pipe filled with a ferrofl uid as the working liquid was tested at different inclination angles: 0, 60, and 90^{o}
. The ferrofl uid was synthesized from magnetite particles and
water as the base fluid. The heat pipe was manufactured from a copper container, and copper fibers were used as
the wick structure inside the heat pipe. The magnetite particles had an average diameter of 13 nm, as was yielded
by the transmission electron microscopy (TEM). The zeta potential value (30.25 mV) and visual analysis showed
that the ferrofl uid was stable for nine months and could be used as the working liquid in cylindrical heat pipes.
The thermal conductivity and specifi c heat of the ferrofl uid were 0.605 W/(m·K) and 4090 J/(kg∙K), respectively. The
performances of the heat pipe at diff erent inclination angles allowed the conclusion about a relatively stable thermal
resistance and temperature distribution, particularly at a higher heat input of 15 W.

**Author:**
N. S. Asri, A. P. Tetuko, M. Ridwan, A. Wicaksana, L. F. Nurdiyansah, E. A. Setiadi, A. M. S. Sebayang, P. Sebayang

**Keywords:**
magnetite particles, ferrofl uid, cylindrical heat pipe, inclination angle, thermal performance

**Page:**
197

**DESIGN AND PRACTICAL APPLICATION OF THERMAL HUMIDITY CONVERTERS FOR LIQUID MATERIALS**

The paper considers quality indicators and morphological tables of the main elements of thermal converters of the
moisture content of liquid materials on the basis of which the optimal structure of these converters is selected from
the quality indicators, namely, sensitivity, accuracy, reliability, and performance

**Author:**
N. I. Avezova, P. M. Matyakubova, P. R. Ismatullaev, S. A. Kodirova

**Keywords:**
quality, sensitivity, accuracy, reliability, speed, structure, optimal structure, measuring range, heat conductor, heating element

**Page:**
206

**INVESTIGATION OF THE STRUCTURE OF A CEMENT COMPOSITE MODIFIED BY HYDROTHERMAL SiO2 NANOPARTICLES AND MCNT NANOPARTICLES BY THE X-RAY PHASE ANALYSIS METHOD**

The x-ray phase analysis method has been used to study the eff ects of small doses of hydrothermal SiO_{2} nanoparticles and nanoparticles of multiwalled carbon nanotubes (MCNTs) on the structure of a Portland cement composite separately and in a combination at the age from 4 h to 28 days. It has been established that clinker minerals and Portlandite components do not diff er signifi cantly in nanomodifi ed specimens compared to control specimens, which agrees with the thermogravimetrical data for the ages of 1 and 28 days. In the region of the angles 2θ = 5–12 degrees, structural diff erences were identifi ed for the CSH gel in the nanomodifi ed specimens: at the age of 1 day (24 h), there were CSH peaks (I) in the diff raction patterns of the modifi ed specimens with Basel distances of 12.44–12.54 Å between the layers. At the age of 28 days, relatively higher peaks of a tobermorite-like structure were identifi ed with a Basel distance reaching a maximum value of 14.54 Å in a specimen modifi ed by a combination of SiO_{2} and MCNT nanoparticles. The increase in the Basel distances corresponds to a reduction
in the values of the Ca/Si ratio and an improvement in the ordering of the CSH-gel structure and agrees with the
IR-spectroscopy data having shown the higher degree of polymerization of silicon–oxygen tetrahedrons in nanomodifi ed specimens.

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

**Keywords:**
cement composite, SiO2 nanoparticles, MCNTs, x-ray phase analysis, CSH-gel structure, Basel distances, Ca/Si ratio

**Page:**
215

**CERTAIN EXACT SOLUTIONS TO THE PROBLEM OF LIQUID FLOW IN PRISMATIC TUBES**

The problems of diff erent sections of physics and mechanics share a mathematical model that is based on the
Poisson equation with a constant right-hand side and a zero (constant) value of the sought function on the contour
of a two-dimensional region. A set of exact solutions to the formulated problem is presented in the "plane" region
of certain form to describe the following problems: flow of a liquid in the channel at small Reynolds numbers;
motion of an ideal liquid during the rotation of the contour bounding the region; torsion of a rod; deflection of the
membrane at the zero displacement on the boundary of the region; heating of the rod. The possibility to construct
approximate solutions for certain cross sections of the channel, etc. by using these exact solutions is noted. Examples
are given.

**Author:**
A. I. Moshinskii

**Keywords:**
velocity profi le, channel, dimensionality, opening of the wedge, cavern

**Page:**
224

**SIMULATION OF LARGE VORTICES IN THE FLOW OF AN INCOMPRESSIBLE VISCOUS FLUID AROUND A SPHERE AT REYNOLDS NUMBERS FALLING WITHIN A LARGE RANGE**

A simulation of the large vortices, formed in the flow of an incompressible viscous fluid around a sphere at different
Reynolds numbers, has been carried out. Dependences of the local and integral characteristics of such a flow
on its initial parameters are presented. Results of the numerical calculations performed were compared with the
corresponding experimental data and with the available correlation dependences for the drag and heat-transfer
coeffi cients of a fluid flow around a sphere.

**Author:**
K. N. Volkov, V. N. Emel'yanov, I. V. Teterina

**Keywords:**
computational fl uid dynamics, simulation, large vortices, sphere, drag, heat transfer

**Page:**
236

**THE CHARACTERISTIC FEATURES OF GAS DYNAMICS AND HEAT TRANSFER OF STATIONARY AND PULSATING FLOWS IN THE INTAKE SYSTEM OF A PISTON ENGINE**

Data on gas dynamics and heat transfer of stationary and pulsating flows along the length of the intake system of a
piston engine are presented. The studies were carried out on full-scale models of a piston engine for different initial
conditions. The infl uence of gas-dynamical nonstationarity on the thermal-mechanical characteristics of flows is
shown experimentally. It has been established that the degree of turbulence of pulsating flows is an order of magnitude
higher than in a stationary flow, and the intensity of heat emission, on the contrary, is 5–13% less. It is shown that
the values of the degree of turbulence tend to decrease (up to 2 times) when air moves along the length of the intake
system, and the change in the intensity of heat emission has a parabolic form, which is typical of both stationary and
pulsating flows. The results obtained can be used for refi ning engineering methods of calculating the processes of gas
exchange and developing the means of improving the intake systems of piston and composite engines

**Author:**
L. V. Plotnikov

**Keywords:**
piston engine, intake system, gas fl ows, gas dynamics, turbulence degree, local heat emission, comparative analysis

**Page:**
246

**NUMERICAL MODEL OF ULTRASONIC AGGLOMERATION OF SUBMICRON PARTICLES IN RESONANT GAS GAPS**

Theoretical substantiation of the physical principle of increasing the efficiency of ultrasonic agglomeration of
submicron particles is proposed, which is based on the creation of resonant conditions for forming vortex flows
in gas gaps. The generated vortex flows lead to a local increase in the concentration of particles, which increases
the frequency of collisions and, consequently, the efficiency of agglomeration. A numerical model of this process is
proposed. The results of calculations carried out on the basis of the numerical model made it possible to ascertain
that the efficiency of agglomeration when creating vibrations by a flexurally oscillating radiator (a collection of
vortex flows is formed) is more than four times higher than in the case of creating vibrations using a piston radiator
(one little-eff ective vortex flow is generated).

**Author:**
V. N. Khmelyov, R. N. Golykh, V. A. Nesterov, A. V. Shalunov

**Keywords:**
ultrasound, gas cleaning, coagulation, agglomeration, acoustic fi eld, fractional effi ciency, resonant gap, vortex flow

**Page:**
255

**INDIRECT, WITH RESPECT TO THE NONLINEARITY EQUATION, MEASUREMENT OF THE RADIATING CAPACITY AND TEMPERATURE OF OPAQUE MATERIALS**

This work is aimed at improving metrological characteristics and expanding the areas of application of optical
thermometry of opaque objects, including the method of two-color compensative pyrometry with an apriori averaged
adjustment previously developed by the authors. A nonlinearity equation has been obtained that connects the
nonlinearity coefficient of spectral distribution of directional emissivity on an average wavelength of the registered
radiation with a value of spectral directional emissivity on one of boundary wavelengths via the measured brightness
temperature on three wavelengths. It has been established that the number of numerical solutions of the equation at
various qualitative and quantitative characteristics of spectral distributions is from 1 to 3. To determine a correct
solution, analytical and algorithmic methods of its identification have been proposed. On the basis of the equation,
linear, two-range, and parabolic methods of determining spectral directional emissivity have been developed. It
has been established that the methodological errors of temperature measurements by the two-range method are
5–7 times lower than the errors of the linear method. For signifi cant nonlinearities, the parabolic method errors are
1.13–1.24 times lower than the linear method errors. In this case, for the two-range method, the combined errors for
two-color compensative pyrometry are lower than the errors for spectral ratio pyrometry and for energy pyrometry
110 and 7 times respectively

**Author:**
L. F. Zhukov, D. A. Petrenko

**Keywords:**
nonlinearity equation and coeffi cient, spectral distribution of directional emissivity, object temperature, brightness temperature, parabola

**Page:**
266