Volume 97, №5
IDENTIFICATION OF THE CHARACTERISTICS OF THERMAL ENGINEERING MATERIALS UNDER CONDITIONS OF NONSTATIONARY HEATING WITH CHANGES IN PRESSURE BY SOLVING INVERSE HEAT EXCHANGE PROBLEMS. 1. DEVELOPMENT OF COMPUTING ALGORITHMS
Modern space technology is characterized by structures that operate under conditions of intense, often extreme,
thermal infl uences. The general trend in the development of technology is associated with an increase in the number
of critical heat-loaded technical objects with rougher conditions for their thermal loading with simultaneously
increasing reliability and service life, reducing material consumption. For spacecraft, ensuring thermal conditions
is one of the most important sections of design, determining the main design decisions. Characteristic features of
modern heat-loaded structures of space technology are nonstationarity, nonlinearity, multidimensionality, and the
conjugate nature of heat and mass transfer processes. These features limit the possibility of using many traditional
computational-theoretical and experimental research methods. Highly porous thermal insulation materials with low
thermal conductivity are widely used in the thermal protection designs of modern space technology objects. These
materials typically have an open-pore structure. This leads to the fact that the thermophysical properties of these
materials depend signifi cantly on the gas pressure of the medium in which heat-protective structures based on them
operate. It can also be noted that as the ambient pressure increases, a more intense increase in the thermal conductivity
coeffi cient is observed. The purpose of this work is to develop a complex of experimental and mathematical tools
for a system of identifi cation of the properties of highly porous materials operating under conditions of not only
changing thermal loads, but also of variable pressure
Author:
S. A. Budnik, A. V. Nenarokomov, D. M. Titov, V. L. Reviznikov
Keywords:
highly porous materials, inverse heat transfer problems, iterative regularization method, processing of experimental measurements
Page:
1095
IDENTIFYING THE THERMAL-CONDUCTIVITY TENSOR OF A NITROGEN THERMAL PROTECTION BY THE ITERATIVE REGULARIZATION METHOD
Consideration is given to the method of parametric identifi cation of a symmetric thermal-conductivity tensor for a
cryogenic nitrogen thermal protection thermostatting an aluminum skeleton of a cylindrical nitrogen-fi lled vessel.
This problem is solved as the problem of seeking the global minimum of the root-mean-square residual functional
between the theoretical fi eld of temperatures and the registered maximum thermal-protection temperature. To this end,
it is necessary to solve the "primal" problem of heat transfer between the thermal protective coating with a selected
initial approximation of components of the thermal-conductivity vector and their basis functions taking account
of their dependence on temperature. The method of conjugate directions has been selected as the most accurate
optimization method of fi rst order of convergence. To implement this method, it is necessary to fi nd components of
the gradient of the residual functional under study. The descent step in this method is sought from the minimum of
the target functional at each computational iteration, which corresponds to the iterative regularization method. A
criterion for the cessation of the iterative process is the superposition of errors that introduce ill-posedness into the
formulation of the problem under study
Author:
N. O. Borshchev
Keywords:
iterative regularization method, method of conjugate directions, thermal-balance method, cryogenic temperature
Page:
1108
INVERSE PROBLEM OF THERMAL DIAGNOSTICS OF MULTIPLY CONNECTED STRUCTURES WITH HETEROGENEOUS MATERIALS
A study has been made of the inverse problem on determining the thermophysical characteristics of multiply
connected structures with heterogeneous materials, that are taken as the sign of their diagnostics. The procedure
of diagnostics is based on solution of the inverse problem on determining the thermophysical characteristics of
objects in a variational formulation. The quality functional for this formulation is new, not used before in the theory
of inverse problems and diagnostics. The theorem of singe-valued solvability of the inverse problem in question has
been proved, the iterative algorithm of its solution has been presented, and the extreme properties of the quality
functional have been established. The proposed procedure is based on observations beyond an object and allows
diagnostics in a nondestructive noncontact regime. Initial data with an error and the infl uence of the standard on
solution are discussed.
Author:
A. M. Pashaev, A. D. Iskenderov, M. A. Musaeva
Keywords:
variational method, inverse problem, solvability, thermal diagnostics, thermophysical characteristics.
Page:
1121
EXPERIMENTAL INVESTIGATION OF HEAT EXCHANGE IN COOLING THE SURFACE BY A SYSTEM OF SUBMERGED DIELECTRIC-LIQUID JETS
Heat exchange on a heat-stressed surface and the critical heat fl ow from it in the process of cooling this surface by a system of distributed impact submerged microjets of a dielectric liquid, depending on the velocity of these jets, were investigated experimentally for the case where the initial subcooling of the liquid in the jets to the saturation temperature comprises 40 ± 2o
C. The experiments were conducted for 36 jets of the HFE-7100 dielectric liquid with
an initial diameter of 174 μm, outfl owing from the nozzles positioned at a distance of 1 mm from a cooling surface. It
was established that the heat transfer coeffi cients of this surface and the critical heat fl ow from it are determined by
the velocity of the jets, acting on the surface, and the initial subcooling of the cooling liquid, and that they are much
larger than those in the case of pool boiling of the cooling liquid on the surface and in the case of its cooling by a
single jet of a liquid with a small subcooling to the saturation temperature.
Author:
A. S. Shamirzaev, A. S. Mordovskii, V. V. Kuznetsov
Keywords:
impact microjets, subcooled boiling, dielectric liquid, heat transfer, critical heat fl ow
Page:
1129
PERFORMANCE ANALYSIS OF A HVAC SYSTEM WITH A HEAT RECOVERY WHEEL FOR A HOSPITAL BUILDING
An eff ective heating, ventilation, and air conditioning system has been designed for a three storey north-oriented
hospital building. The heat load of this building was calculated using the Hourly Analysis Program software with
regard for the recovery of the energy from the exhaust air stream with the use of a heat recovery wheel reducing
the temperature of the supply air stream and lowering the load on the air handling unit in the building. The results
obtained show that a heat recovery wheel attached to a heating, ventilation, and air conditioning system makes it
possible to improve the indoor air quality with conservation of 30% of the the electrical energy.
Author:
N. Alam, M. Mohiuddin, D. Sharma, S. P. Patil, M. Warimani, Z. Hasan, S. A. Zaki, N. Othmanh
Keywords:
heating, ventilation, and air conditioning system, heat recovery wheel, air handling unit, heat load
Page:
1135
THE EFFECT OF REVERSE AND OPPOSITE INJECTION ON THE FILM COOLING PERFORMANCE OF A SYMMETRICAL TURBINE BLADE
A numerical investigation on the fi lm cooling performance of a symmetrical turbine blade is carried out for reverse
injection (RH), forward injection (FH), and opposite injection (OH) which combines forward and reverse injection
holes. Another objective of this work is to study the eff ect of the distances between the injection holes, and three
diff erent distances are considered. Five confi gurations are computed for fi ve blowing ratios. A coolant fl ow is injected
through holes inclined at 110 and 70o
for reverse and forward jets, respectively. The laterally averaged fi lm cooling
eff ectiveness is obtained using commercial software ANSYS-CFX. In addition, several velocity vectors and contours
are presented for analyzing the thermal behavior. The numerical model is based on the Navier–Stokes equations and
the Reynolds stress turbulence model (SSG-RSM). The obtained results enable one to choose confi gurations with
high fi lm cooling eff ectiveness for diff erent blowing ratios.
Author:
K. Boualem, F. Ben Ali Kouchih, O. Ladjedel, T. Yahiaoui,A. Azzi
Keywords:
reverse injection, forward injection, opposite injection, symmetrical turbine blade
Page:
1143
MODELING CORROSION PRODUCT DEPOSITION PROCESSES IN PIPELINES OF HEAT SUPPLY SYSTEMS
A physical description is given of the formation of corrosion product deposits on the surfaces of pipelines of heat
supply systems, and an investigation has been made into the eff ects of various factors on this process. An analysis
has been made of the existing models of formation of corrosion deposites. A mathematical model has been developed
for the formation of corrosion product deposites in the liquid′s motion through pipelines of heat supply systems in the
region of linear velocity of the growth of deposits at a constant temperature of the heat transfer agent. The model is
based on equations of conservation of the mass of dissolved depolarizer and solid particles suspended in the solution. The parametric calculations performed on the basis of the developed mathematical model have shown a possibility for the existence of a maximum in the thickness of the corrosion product deposit layer through the pipe length.
Author:
A. B. Garyaev, M. Yu. Yurkina, T. A. Matukhnov, O. D. Matukhnova
Keywords:
deposits, corrosion product, mathematical model, heat supply system, pipelines, particles
Page:
1151
ANALYTICAL MODEL OF MICROEXPLOSION OF A HYDROCARBON–WATER COMPOSITE DROPLET
An analytical solution of the problem of heating a composite spherical droplet consisting of a liquid hydrocarbon
and a microdroplet of water in a hot gas fl ow is presented. A microdroplet of water is located in the center of a
droplet of hydrocarbon. At the hydrocarbon–water interface, the conjugation conditions are specifi ed; at the outer
boundary of the hydrocarbon droplet — a condition of convective heat exchange. The unsteady temperature of a
drop is represented by an analytical formula, which is an expansion of the solution in terms of eigenfunctions of the
Sturm–Liouville problem. The eigenvalues are found numerically from the characteristic equation. A condition for
the orthogonality of eigenfunctios in a composite droplet with discontinuous thermophysical properties is derived.
The results of calculations using the obtained analytical formula are in satisfactory agreement with the experimental
data. Erroneous methods are discussed in previously presented publications by other authors.
Author:
I. V. Derevich, D. I. Matyukhina
Keywords:
composite hydrocarbon fuel, eigenfunctions and eigenvalues, Sturm–Liouville problems, conjugation conditions, spherical Bessel functions
Page:
1159
EXACT SOLUTIONS TO SOME THERMOKARST MODELING PROBLEMS
Exact solutions have been constructed for some problems on thawing frozen soil in the process of water seeping
into it as a result of the melting of underground ice and the associated violation of the mechanical integrity of the
soil (thermokarst). Factors of thermokarst in frozen soil, determined by the specifi cs of heat and mass transfer in
it, have been identifi ed. The infl uence of the porosity of rocks, which changes during their melting, on the course
of the thermokarst formation as a whole has been studied. An analytical solution to the problem of thermokarst is
constructed. An expression was obtained for the rate of thermokarst formation in frozen soil.
Author:
M. G. Khramchenkov
Keywords:
thermokarst, heat of ice melting, phase transition temperature, Lamé–Clapeyron problem, mathematical model, front speed
Page:
1171
ONE-DIMENSIONAL MODEL FOR CALCULATING A NANOAEROSOL FLOW IN A CONTINUOUS REACTOR IN THE PRESENCE OF DIFFUSION AND COAGULATION OF PARTICLES
The infl uence of the deposition of nanoparticles of an aerosol, moving in a continuous reactor at a constant velocity,
on the channel walls of the reactor and of the coagulation of these particles as a result of their Brownian diff usion
on the nanoaerosol parameters was investigated. A simple one-dimensional model, adequately defi ning the diff usion, coagulation, and deposition of nanoaerosol particles in a wide range of change in its Knudsen number, has
been constructed. It is shown analytically that, as the distance from the inlet of the reactor increases, the volume
fraction of particles in the nanoaerosol decreases by the exponential law, and the radius of the clusters formed in the
nanoaerosol as a result of the coagulation of its particles increases and tends to a limiting (maximum) value. A nonlinear integro-diff erential equation for the radius of such clusters has been obtained, and, from it, compact formulas
for approximate calculation of its limiting radius have been derived. The characteristic distributions of the radii of
clusters and of their concentrations along the reactor channel, calculated by the numerical method, are presented.
It was established that, if this channel has a fairly large length, the clusters moving in it increase to their limiting
size. The infl uence of the determining parameters of the fl ow of a nanoaerosol at the inlet to the continuous reactor
on the distribution of its dispersion characteristics along the reactor channel, on the limiting size of the clysters in it,
and on the characteristic length of the channel, at which the processes of deposition and coagulation of nanoaerosol
particles are completed, is discussed. A comparison of the results of calculations of the parameters of a nanoaerosol
moving in a continuous reactor by the one- and two-dimensional models has shown that the simple one-dimensional
model defi nes the behavior of these parameters quite adequately.
Author:
T. R. Amanbaev
Keywords:
nanoaerosol, continuous reactor, diff usion, deposition, coagulation, clusters, Knudsen number
Page:
1176
MASS CONDUCTIVITY IN DRYING CAPILLARY-POROUS COLLOIDAL MATERIAL SUSCEPTIBLE TO SHRINKAGE
The mass transfer (diff usion) properties of a colloidal capillary-porous material (pears cut into plates 5 mm thick for convective drying) as a function of the moisture content of the material at diff erent temperatures of the drying agent (air) were studied experimentally. Since the pear sample shrinks signifi cantly during drying, the change in sample thickness during the process was taken into account when calculating the mass conductivity coeffi cient. At the same time, the linear shrinkage of the specifi ed material was studied. The dependences of the mass conductivity coeffi cient on the moisture content of the material k = f(u) were obtained from drying curves based on the zonal method at a constant temperature of the drying agent tdr. They represent dependences concave to the abscissa axis that increase with moisture content, which is typical of dried materials. The minimum values of the mass conductivity coeffi cient on the graphs k = f(u) vary from 0.3∙10–10 m2
/s at 30o C to 2.2∙10–10 m2
/s at 60o
C. With a change
in the moisture content of the material, the mass conductivity coeffi cient changes multiply. The shrinkage data for
engineering calculations was described by equation. The possibility of describing the temperature dependence of
the mass conductivity coeffi cient (moisture diff usion) by Arrhenius equation is shown. The values of the Arrhenius
equation parameters are obtained.
Author:
S. P. Rudobashta, V. M. Dmitriev
Keywords:
convective drying, mass conductivity, shrinkage, capillary-porous colloidal material
Page:
1186
QUASI-DIFFUSION SEPARATION ACTIVATION OF SHEAR DEFORMATIONS IN A FAST GRAVITATIONAL GRANULAR MATERIAL FLOW
The paper presents the results of a study of the eff ects of separation of spherical particles with diff erent densities
in a fast gravitational fl ow on a rough slope with varying fl ow parameters in order to increase the effi ciency of
the process. The determining role of the eff ect of quasi-diff usion separation in the process has been established,
the intensive manifestation of which is facilitated by the formation of s-shaped profi les of the fraction of voids and
velocity in the fl ow. The results of an experimental and analytical study of the effi ciency of particle separation by
density in a fast gravitational fl ow when shear deformations are activated by longitudinal pulses are presented. It
has been established that when particles are exposed to the pulse eff ect from the open surface of the fl ow, its central
part develops a zone with a typical s-shaped infl ection in the velocity profi le and void fraction, which functions like
a quasi-diff usion separator that increases the effi ciency of the process.
Author:
V. N. Dolgunin, O. O. Ivanov, K. A. Kudi
Keywords:
granular material, fast gravitational fl ow, activation of shear deformations, segregation, quasi-diff usion separation
Page:
1193
KINETIC CALCULATION OF A CONTINUOUS-ACTION TRAY-TYPE FLUIDIZED-BED DRYER
To carry out a continuous process of drying a dispersed material, tray-type dryers have come into use, which are
characterized by an improved hydrodynamic structure of the solid phase fl ow. The article presents a mathematical
description of the kinetics of drying a material based on a theoretical method that uses data on the thermophysical
characteristics of the material and takes into account longitudinal mixing of the solid phase based on a diff usion
model. An analytical solution to the corresponding problem was obtained, which expresses the change in the moisture
content of particles along the length of the tray. A technique for engineering calculation of the dryer based on this
model has been developed. An example of calculating a dryer of the type under consideration for drying corn
grain is given using literature data on the mass conductivity coeffi cient (moisture diff usion coeffi cient in grain),
phase concentration equilibrium, and longitudinal diff usion coeffi cient. The infl uence of sectioning partitions on
the kinetics of drying a dispersed material in a tray-type apparatus was analyzed. It is shown that they signifi cantly
improve the hydrodynamic structure of the fl ow, which reduces the length of the tray.
Author:
S. P. Rudobashta, G. A. Zueva, G. V. Khandogin
Keywords:
dryer, tray, dispersed material, fl uidized bed, kinetic calculation, continuous-action device
Page:
1203
INFLUENCE OF THE SURFACE TENSION OF A LIQUID ON THE CHARACTERISTICS OF THE CONE OF ITS SPRAYING BY AN EJECTION ATOMIZER
Novel experimental data have been presented on the infl uence of the surface tension of a liquid on the dispersity of
droplets in the spray cone of an ejection atomizer with forward and swirling gas feeds. The droplet-size distributions
were measured with the optical method of small angles of the indicatrix of scattering. A decrease of nearly 10–17%
in the median diameter of droplets of distilled water in the spray cone has been demonstrated with reduction in the
coeffi cient of surface tension of water as a result of adding surfactants to it.
Author:
V. A. Arkhipov, I. S. Bondarchuk, N. N. Zolotoryov, K. G. Perfi l′eva
Keywords:
ejection atomizer, spray cone, droplets, dispersity, surfactant, coeffi cient of surface tension, method of small angles of the scattering indicatrix, experimental study
Page:
1216
MATHEMATICAL SIMULATION OF THE FLOW OF A NON-NEWTONIAN TWO-PHASE MEDIUM IN A CHANNEL OF COMPLEX GEOMETRY
A mathematical model of the fl ow of a two-phase medium, whose state is defi ned by the nonlinear rheological
equation, in a curvilinear channel of parabolic shape has been constructed. Numerical calculations of the fl ow of
such a medium in this channel were performed with regard for the existence of its initial region and a centrifugal
force in the channel. A computational experiment has been conducted, and, on its basis, diff erent regimes of fl ow of a
liquid in the indicated channel were investigated depending on the rheological properties of the liquid, governed by
the Ostwald–de Waele law of state, and on the hydrodynamic situation in this channel. The numerical calculations
have shown that, in the process of development of a liquid fl ow in the channel, in its initial region, the plane velocity
profi le of the fl ow is transformed into the parabolic one. In this case, the fl ow near the wall of the channel is
decelerated, and the fl ow in the central region of the channel is, vice versa, accelerated. Because of this, in the
initial region of the fl ow, its lines and the velocity fi elds on them have bends. The nonlinearity coeffi cient of a liquid
substantially infl uences the shape of the velocity profi le of its fl ow. In the case of rotation of the channel around its
symmetry axis, the velocity profi le of the liquid fl ow in it becomes asymmetrical.
Author:
R. I. Ibyatov, F. G. Akhmadiev
Keywords:
mathematical simulation, curvilinear channel, non-Newtonian two-phase medium, computational experiment
Page:
1224
SYNTHESIS OF CHROMIUM DIBORIDE IN AN ARC-DISCHARGE ATMOSPHERIC PLASMA
The authors have described a method for synthesis of the crystalline phases of chromium boride CrB and CrB2 at
atmospheric pressure without introducing additional modifi ers improving the reactivity of the original charge. The
formation of chromium borides was implemented under the action of an arc discharge with the original vacuumfree dc electric-arc reactor. The infl uence of the parameters of the reactor on the phase composition of the obtained
samples has been investigated. It has been established that the impact of an arch discharge of strength 200 A and
duration 60 s on a mixture of Cr and B powders in a 1.0:2.55 atomic ratio ensures the formation of chromium
diboride CrB2. The properties of the obtained powders have been studied by the methods of x-ray diff raction,
scanning electron microscopy, and transmission electron microscopy.
Author:
P. V. Povalyaev, A. Ya. Pak, K. V. Nikolaeva, S. M. Danilova-Tret'yak
Keywords:
vacuum-free electric-arc synthesis, refractory materials, arc discharge, chromium diboride, phase composition
Page:
1234
LIQUID FLOW IN PRISMATIC CHANNELS RESTING ON A PARABOLIC CONTOUR
A set of exact solutions is suggested for the Poisson equation in a plane region of a certain form for describing a fl ow
of Newtonian incompressible liquid in a channel at low Reynolds numbers. The motion of an ideal liquid in a region
bounded by a rotating contour, torsion of a rod, defl ection of a membrane at zero displacement on the boundary of
its region, and heating of a rod under certain conditions are equivalent to a mathematically formulated problem of
such a fl ow. A possibility is demonstrated to construct approximate solutions to the said problem for certain sections
of a channel, having a parabolic segment of the contour, using exact solutions to this problem. Examples are given
for the construction of fl ow regions in a prismatic channel resting on a parabolic contour
Author:
A. I. Moshinskii
Keywords:
velocity profi le, channel, parabola, cavity
Page:
1246
CORRELATION OF LOCAL FLOW ACCELERATION IN A NARROW CHANNEL AND ANOMALOUS INTENSIFICATION OF SEPARATED LAMINAR FLOW IN TWO-ROW GROOVES ON ITS WALL
The phenomenon of local acceleration of laminar fl ow at the experimental stand of the Kazan Scientifi c Center of
the Russian Academy of Sciences was substantiated by comparing the numerical predictions obtained on a digital
analog with the profi les of the longitudinal velocity component measured at Re = 1000 at three points of the 22nd
inclined groove in a narrow channel with 26 two-row grooves arranged in the form of \ / on the wall. A connection
has been established between the local acceleration of the fl ow in the channel core and anomalous intensifi cation of
separated laminar fl ow in two-row grooves on increase in the Reynolds number from 1000 to 2500. It has been found
that at Re = 2500 for grooves remote from the entrance in the longitudinal section of the channel passing through the
centers of the connecting sections of input spherical segments and trench parts, the negative relative friction reaches
minimum values of the order of –9 and is combined with the achievement of maximum velocity values in the shear
layers above the grooves (at a height of y = 0.005) of the order of 1.4.
Author:
S. A. Isaev, D. V. Nikushchenko, N. I. Mikheev, N. S. Dushin, A. A. Klyus, E. A. Osiyuk
Keywords:
separated fl ow, narrow channel, inclined groove, intensifi cation, numerical simulation, experiment
Page:
1257
EXPERIMENTAL STUDY OF FLOW NEAR A HYDROPHOBIC CYLINDER AT HIGH REYNOLDS NUMBERS
An experimental study of vortex structures in the near wake behind a circular microstructured Tefl on cylinder immersed in an oncoming water fl ow was carried out for Reynolds numbers 1.75·105
–2.85·105
using two-dimensional imaging (2D-PIV) of particles in a closed hydrodynamic stand. The results obtained are presented in the form of time-averaged velocity fi elds of fl ow and Reynolds stresses in it. Flow data showed changes in the geometric characteristics and Reynolds stresses of the wake fl ow depending on the Reynolds number in such a way that the studied parameters pass through a minimum in the region of Reynolds number 2.2·105
with subsequent increase.
This minimum of wake characteristics is likely to be associated with a crisis in the resistance of the cylinder, but
earlier in comparison with a cylinder with a nonhydrophobic surface. A signifi cant increase in the velocity of water
fl ow near the side surface of the hydrophobic cylinder was revealed, which at high Reynolds numbers leads to a
drop in the static pressure in the fl ow below atmospheric pressure, an increase in the local gas content in it, and to a
possible increase in fl ow slip on the cylinder surface.
Author:
K. G. Dobrosel′skii
Keywords:
hydrophobic cylinder, PIV, vortex wake, Reynolds stresses
Page:
1262
EFFECTS OF THE COMPOSITION OF JET FLOW COMPONENTS ON THE DYNAMICS OF PROPAGATION AND HYDRATE FORMATION FOR DEEPWATER SPILLS
Consideration is given to a mathematical model for the formation of hydrates in a jet fl ow of hydrocarbons for two
initial stages (submerged jet and plume). The purpose of the mathematical modeling is to investigate the eff ects of
various compositions of jet fl ow components on the dynamics of hydrate formation. The object of investigation is a
jet fl ow of hydrocarbons occurring in technogenic spills. The current importance of this investigation is associated
with the need to predict the dynamics of oil and gas propagation for cases of technogenic accidents in deepwater
development of deposits. A mathematical model has been created for a jet fl ow for two initial stages with account
for the infl uence of the composition of the fl ow components. Computational experiments have been carried out for
various initial values of pressure and oil volume content in the jet with a view to assessing the dynamics of gas
hydrate formation in oil emulsion. The results of the mathematical modeling included the following dependences
obtained for various versions of the composition of jet fl ow components: dependence of the temperature and mass
of the newly formed hydrate on the vertical coordinate and the dynamics of variation in the radius of the hydration
shell in bubbles. As a result of comparison of the results of a laboratory experiment with the results of mathematical
modeling a high-quality agreement has been obtained.
Author:
S. R. Kil′dibaeva, É. I. Kharisov
Keywords:
deepwater oil spill, hydrocarbon fl ow stages, shelf, hydrate formation, submerged jet, plume
Page:
1269
WAVE DYNAMICS OF A GAS BUBBLE COATED WITH A HYPERELASTIC SHELL IN A VISCOELASTIC LIQUID
A modifi ed Rayleigh–Lamb equation has been derived which takes account of the radial oscillations of a gas bubble
coated with a hyperelastic shell and found in a viscoelastic liquid. The hyperelasticity of the shell is taken account of
on the basis of the Mooney–Rivlin model, and the viscoelasticity of the liquid, according to the Zener model in whose
particular cases the Kelvin–Voigt and Maxwell models are followed. Numerical calculations have been carried out.
An analysis has been made of the infl uence of the dimension of the bubble′s shell and its rigidity, the shear modulus
of the shell and the carrier liquid, and also the diff erence in rheological models on the radial dynamics of the gas
bubble in the external acoustic fi eld. A mathematical model has been constructed which determines the propagation
of acoustic waves in the viscoelastic liquid with encapsulated gas bubbles. A study has been made of the diff erence
in rheological models of the elastic carrier liquid, and also of the infl uence of the shell thickness on the dynamics of
acoustic waves.
Author:
Yu. V. Fedorov, R. N. Gafi yatov, D. D. Gubaidullina
Keywords:
acoustic fi eld, gas bubble, hyperelastic shell, viscoelastic liquid, forced oscillations, dispersion equation
Page:
1277
OPTIMIZATION OF PARAMETERS OF A HYDRO-STEAM TURBINE
Consideration has been given to the specifi c features of the work process of a hydro-steam turbine operating on the
principle of Segner′s wheel. A method has been suggested for the organization of entry into the turbine channels that
ensures minimum hydraulic losses. It has been shown that losses due to the friction of the rotor wheel rotating in a
steam-water medium have a number of specifi c features that do not allow their reliable calculation assessment at
present. At the same time, some maximum estimates have shown that these losses can be quite signifi cant in the turbine′s total energy balance and force one to pay serious attention to the aerodynamic properties of the periphery zone
of the turbine rotor wheel. It has been established that the diversion of the nozzle axes′ direction from the direction
of the circumferential velocity of motion of the center of the nozzles' outlet cross section with a view to preventing
structure elements from getting into their jets results in a drop of the turbine capacity, which brings about the need
for seeking a compromise solution in selecting the angle of this deviation. The calculation assessment of the optimum
ratio of the circumferential velocity of motion of the nozzle outlet section to its fi ctitious velocity corresponding to
the available heat drop in a hydro-steam turbine has shown that it lies within 0.32–0.37, depending on the nozzle
velocity coeffi cient, and the fl at pattern of the said dependence provides certain freedom to the designer in selecting
the turbine design dimensions.
Author:
B. A. Shifrin, O. O. Mil′man, V. B. Perov, A. S. Goldin
Keywords:
hydro-steam turbine, boiling-up, water–steam mixture, reactive force, nozzle, underheating, dryness, low-temperature heat
Page:
1285
MODELING THE CHARACTERISTICS DURING THE FLOW OF A SUBCOOLED LIQUID OUT OF GEOMETRICALLY SIMILAR LAVAL NOZZLES
To design hydrosteam turbines of the Segner-wheel type, it is necessary to have reliable characteristics of a Laval
nozzle with a large expansion ratio when water strongly subcooled to a saturation temperature is fed to the nozzle.
The authors have given a review of a number of works on determining the fl ow-rate coeffi cient μ and
the coeffi cient of velocity ϕ when water subcooled to a saturation temperature fl ows out of Laval nozzles. The
complexity of the process of outfl ow of a steam–water mixture has been noted, which is dependent on the relation of
the temperature and pressure at entry into the nozzle, pressure behind the nozzle and the nozzle expansion ratio, and
the confi guration of the entrance region.
Experimental data have been given on blowdowns of geometrically similar nozzles with measuring the
jet thrust and determining the fl ow-rate and velocity coeffi cients. It has been shown that the linear dimensions of
the nozzle throat do not infl uence μ when a constant relation of the length of the throat to its diameter is observed.
The velocity coeffi cient during the outfl ow of a boiling liquid depends on the linear dimensions of the expanding
section of the nozzle, i.e., testing of geometrically similar nozzles do not ensure a correct determination of . It has
been shown that the nozzles' effi ciency must be compared in the design regime when the pressure on the exit section
is equal to the pressure in the chamber where the steam–water mixture fl ows. Analysis results will be useful for
calculating and designing a reaction hydrosteam turbine.
Author:
O. O. Mil′man, A. S. Goldin, B. A. Shifrin V. B. Perov, A. V. Ptakhin, V. S. Krylov, A. V. Kondrat′ev
Keywords:
Laval nozzle, effi ciency, throat, fl ow-rate coeffi cient, velocity coeffi cient, expansion ratio, reactive force, pressure, temperature, steam–water mixture
Page:
1296
DISCHARGE FROM THE CYLINDER OF A PISTON ENGINE
Consideration is given to problems of calculating the exhaust from the engine cylinder through a "valve–valve pipe"
system at all fl ow modes. It has been shown that there is a need to determine the exhaust parameters precisely in the
cross section of the valve pipe outlet and also to clarify the moment of blocking the fl ow in the valve and at the valve
pipe outlet. Based on the idea of analogy with a sudden expansion of the passage section of a conditional channel,
relations have been obtained for determining the fl ow coeffi cient of the valve system. The results of calculations
using these relations are in good agreement with the results of blowdowns of the valve system of a real engine.
To simplify fl ow calculations and visualize the fl ow modes in the system using the criteria of the similarity theory
and gas-dynamic functions, a method has been developed for constructing a universal two-parameter gas-dynamic
characteristic (map) of a valve system similar to maps of compressors and turbines. In this case, the values of fl ow
coeffi cients in all the modes represented by the maps will be almost the same for systems of various scale and having
identical parameters of geometric expansion.
Author:
Yu. A. Grishin. F. B. Barchenko
Keywords:
piston engine, "valve–valve pipe" system, fl ow shut-off , fl ow coeffi cient, gas-dynamic map, similarity criteria
Page:
1313
PASSIVE CONTROL OF THE FLOW AROUND A CYLINDER BY USING GEOMETRIC MODIFICATIONS
The present study is aimed at reducing the drag loads on cylinders by using a passive control technique which consists in shape modifi cation for streamlined and bluff bodies, particularly those used in aeronautics. Various shapes of elliptic and ovate-elliptic cross sections were tested with studying the eff ect of geometric parameters, namely, the radius ratio and axial ratio. The fl ow around the proposed geometries was studied numerically using k–ε, k–ω, and Spalart–Allmaras turbulence models at the Reynolds numbers from 104
to 2.4∙104
. The results obtained
were compared with those for a circular cylinder of constant radius, showing a signifi cant weakening of aerodynamic
forces acting on the cylinder with modifi ed shapes, especially at high Reynolds numbers, for both elliptic and ovateelliptic geometries with a better performance for the latter
Author:
F. Djemil, O. Ladjedel, F. Zemani, M. Belharizi, T. Yahiaoui, L. Adjlout
Keywords:
fl ow control, cylinder shape modifi cation, pressure coeffi cient, drag coeffi cient
Page:
1326
ON THE ORGANIZATION OF BURNING IN A HIGH-VELOCITY FLOW WITH A DOUBLE-BELT SUPPLY OF FUEL
The burning in a two-section channel with an abrupt enlargement of its cross section in the process of doublebelt supply of diff erent-type gaseous fuels into it at a Mach number of the fuel fl ow M = 2.2 and at its stagnation
temperature of 1700 K was numerically investigated. For the ignition of a hydrocarbon fuel fed into the channel
along its axis (the fi rst supply belt) and for the formation of a transonic regime of burning of the fuel, it was subjected
to a gasdynamic pulse action, and, after this action was terminated, for the maintenance of the burning regime, the
second belt of supply of a fuel (hydrogen or a hydrocarbon fuel) into the channel and the side supply of an air jet
into it were organized. The Reynolds-averaged Navier–Stokes equations were solved with the use of the k–ε model
of turbulence. The burning of a fuel in the channel was simulated by gross reactions. It was established that the use
of hydrogen as a fuel in the second supply belt makes it possible to maintain the transonic burning regime in the
channel. In this case, the side air jet breaks the shock-wave formation in the second section of the channel and, in so
doing, provides a high-velocity homogeneous fuel fl ow in it.
Author:
V. P. Zamuraev, A. P. Kalinina
Keywords:
gaseous hydrocarbon fuel, hydrogen, burning, high-velocity fl ow, throttling jet, transonic regime
Page:
1338
STUDY OF THE INFLUENCE OF EDGE EFFECTS DURING FUEL COMBUSTION IN A CLOSED VOLUME
An experimental study of the combustion of model pasty fuel in a constant volume (a manometric bomb) is presented. The defi nition of the combustion law of model pasty fuel is given, and the infl uence of edge eff ects on the fuel
combustion surface due to the use of the container with the fuel and the central insert is considered. The possibility
of increasing the combustion surface of paste-like fuel by creating longitudinal cylindrical channels in the sample
under study using perforated plastic inserts was also investigated.
Author:
A. N. Ishchenko, N. M. Samorokova, A. S. D′yachkovskii, K. S. Rogaev, E. Yu. Stepanov
Keywords:
manometric bomb, pasty fuel, combustion surface, edge eff ects
Page:
1346
INTEGRAL METHOD WITH THE ADOMIAN DECOMPOSITION: APPROXIMATE SOLUTION OF THE LIOUVILLE–BRATU–GELFAND PROBLEM FOR A CYLINDRICAL SPACE
A method of solving singular boundary-value problems on the basis of the combined use of the Adomian decomposition
method and a special integral relation is presented. This method was used to advantage for approximate analytical
solution of the problem on the thermal explosion in a cylindrical space, defi ned by the diff erential Liouville–Bratu–
Gelfand equation with a Dirichlet boundary condition, and the numerical results of this solution have demonstrated
the high effi ciency of the indicated method. The errors of the approximate solutions obtained with it are smaller by
as a minimum an order of magnitude than the errors of the solutions obtained on the basis of the classical Adomian
decomposition method and other its related methods.
Author:
V. A. Kot
Keywords:
singular boundary-value problem, Liouville–Bratu–Gelfand problem, problem on thermal explosion, integral method, Adomian decomposition method
Page:
1356
SPECIFIC HEAT OF ORGANIC COMPOUNDS AND POLARIZATION EFFECT
Literature data have been considered from the viewpoint of the infl uence of substituents on the mole specifi c heats Cp
at constant pressure for 14 series of organic compounds. Using the correlation-analysis method, it has been shown for the fi rst time that experimental and calculated Cp values depend not only on the inductive, resonance, and steric infl uence, but also on the polarization eff ect of variable substituents associated with a constant reactive center. In individual cases the polarization eff ect has the most signifi cant impact on Cp
Author:
N. M. Khamaletdinova, O. V. Kuznetsova, A. N. Egorochkin
Keywords:
specifi c heat, correlation analysis, classical eff ects of substituents, polarization eff ect
Page:
1383
EFFECTS OF HIGH-INTENSITY ACOUSTIC WAVES ON THE HYDROGEN VALUE OF WATER
An experimental investigation has been made into the eff ects of a high-intensity impact on the pH value and
temperature of water. Water pH and temperature dynamics has been determined at various regimes of acoustic
impact on the specimens. Acoustic impact regimes have been established at which there is a maximum rise in the pH
value and a drop in temperature. The dependence of the heat transfer rate on the intensity of acoustic vibrations has
been defi ned. A comparison has been made of the obtained experimental results on variation of water pH in cooling
with a known dependence. The results obtained in this investigation have been compared with experimental data of
other authors who have investigated the behavior of water pH in ultrasonic, laser, electromagnetic, and mechanical
impacts
Author:
A. A. Zhilin
Keywords:
acoustic impact on water, pH value, water pH variation, eff ects of impact intensity on heat transfer
Page:
1392
EMISSIVITY OF METALS OF THE SECOND GROUP OF THE PERIODIC TABLE
Results of investigating the emissivity of metals of group II of the Periodic Table in the interval of temperatures "solid
body–liquid" have been presented. Selection of the objects of investigation, i.e., metallic beryllium, magnesium,
and calcium, has been argued by the absence, in practice, of data on the emissivity of these elements in a broad
temperature range from periodic and reference literature. The measurement method was radiative, and the technique
of heating of a metal specimen, resistive. A structure of a cylindrical model of an ideal black body with an emissivity
factor no lower than 0.99 has been presented. The material of the equilibrium-radiation source was metallic tantalum.
The estimate of experimental uncertainty amounted to 5–8%. Graphic illustrations of experimental results on each
investigated element have been presented. The obtained complex experimental data on normal integral emissivity
within the limits of each phase of state of the metals grew monotonically. In the region of phase transition of the fi rst
kind, the characteristic abrupt change in the emissivity of the metals was observed. Investigation results have been
discussed and compared with the literature data of other authors. A theoretical calculation of the emissivity of these
metals from the classical electromagnetic theory has been carried out with the Foot approximation. The conclusion
has been drawn on the disagreement between the theoretical calculations on emissivity and the experimental data.
Author:
D. V. Kosenkov, V. V. Sagadeev
Keywords:
metal, beryllium, magnesium, calcium, emissivity, solid phase, liquid phase, Foot approximation
Page:
1401
MODELING UNSTEADY THERMOMECHANODIFFUSION VIBRATIONS OF A HINGEDLY SUPPORTED TIMOSHENKO BEAM
The work is devoted to investigating the infl uence of the mechanical fi eld on temperature and diff usion processes
occurring under steady bending of slender beams. The model used here takes account of the fi nite velocity of
propagation of thermal and diff usion disturbances . A mathematical formulation of the problem includes the system
of equations of unsteady fl exural vibrations of the beam with account of heat and mass transfer, that has been
obtained from the general thermomechanodiff usion model for continuous media using the generalized principle
of virtual displacements. With the example of a hingedly supported three-component beam fabricated from a zinc,
copper, and aluminum alloy and exposed to unsteady bending moments, the authors have investigated the interaction
of mechanical, temperature, and diff usion fi elds, and also have analyzed the infl uence of relaxation eff ects on the
kinetics of heat and mass transfer
Author:
A. V. Zemskov, D. V. Tarlakovskii
Keywords:
thermomechanodiff usion, Timoshenko beam, Green′s function, Fourier series, heat and mass transfer, unsteady problems
Page:
1408