#### Volume 93, №6

**CAVITATION EFFECTS ON THE WORK OF DISPERSE SHEET COLLECTORS OF FRAMELESS HEAT REMOVAL SYSTEMS IN OUTER SPACE**

The effects of cavitation processes on the work of the droplet collectors of frameless heat removal systems in outer space have been considered. The low cavitation steadiness of the centrifugal-type collectors has been substantiated. A procedure has been created for the calculation of fl ow characteristics of a belt-rotor droplet collector. A comparison has been made of the results of numerical calculation with the experimentally obtained characteristics of the functioning of such devices.

**Author:**
A. A. Koroteev, A. A. Safronov, N. A. Safronova, N. I. Filatov, and A. L. Grigor′ev

**Keywords:**
droplet collector, disperse sheet, droplet cooler–radiator

**Page:**
1311

**TRANSFER PROCESSES AS A PHYSICAL FOUNDATION OF SPRAY PYROLYSIS OF MICRON-SIZED DROPLETS OF SOLUTIONS**

The effi ciency of the process of spray pyrolysis allowing one to obtain nanoparticles from micron-sized droplets of
solutions is determined by the processes of mass transfer in a droplet and of heat and mass exchange in a vapor–gas
mixture. It is shown that the slowest and most important process of transfer is evaporation of the droplet. Nucleation
of nanoparticles in a supersaturated solution and their growth proceed much more rapidly. The lifetime of the droplet
in an aerosol reactor determines the morphology of an ensemble of nanoparticles by coalescence or Brownian
diffusion of nanoparticles.

**Author:**
S. P. Fisenko and Yu. A. Khodyko

**Keywords:**
evaporative cooling, supersaturated solution, nucleation, coalescence, Brownian diffusion

**Page:**
1317

**DISTRIBUTION OF THE DISPERSED PHASE IN A PLANE HORIZONTAL CHANNEL IN LAMINAR MOTION OF A LOW-CONCENTRATION SUSPENSION**

The author has formulated the problem of gravity stratifi cation and formation of a sediment of a hydrodynamically
low-concentration monodisperse suspension of solid particles not involved in Brownian diffusion and moving
in a horizontal plane channel during the laminar fl ow of a Newtonian dispersed phase. A solution to the initial
boundary-value problem for fi rst-order partial differential equations has been obtained in analytical form by
applying the one-sided integral Laplace transformation with respect to the axial coordinate. Using the principle of
superposition of concentration fi elds of the fractions, the solution has been generalized to the case of a polydisperse
suspension with an arbitrary particle-size-distribution density function. An estimate for the accuracy of physical
linearization on replacement of the laminar fl ow of the carrier medium by an ideal-displacement regime has been
given. A comparative analysis of computational experiments with classical experimental data for a wide range of the
sedimentation Reynolds number has shown the correctness of the proposed approach.

**Author:**
A. V. Ryazhskikh

**Keywords:**
concentration fi eld, suspension, laminar fl ow, plane channel

**Page:**
1324

**RAISING THE EFFICIENCY OF COAGULATION OF DISPERSED PARTICLES BY THE ACTION OF ULTRASONIC VIBRATIONS ON GAS-DISPERSED FLOWS IN INERTIAL DUST COLLECTORS**

The authors have presented results of experiential investigations of the process of ultrasonic coagulation of
dispersed particle in a swirling fl ow. The investigations were conducted using the proposed and developed test bed
implementing a two-stage removal of fi ne particles. At the fi rst stage (agglomeration), the formation of a swirling
fl ow and the ultrasonic pre-coagulation of fi ne particles are ensured. At the second stage, high-effi ciency trapping of
particles preformed at the fi rst stage is attained using a cyclone. As a result of the experimental investigations, the
authors have established the prospects of using a two-stage removal of fi ne particles and have revealed the optimum
conditions of ultrasonic action on a swirling gas-dispersed fl ow that ensure an enlargement of 4.5 times of particles
in the range of RM2.5 particle sizes which is the most hazardous for humans.

**Author:**
V. N. Khmelev, V. A. Nesterov, and A. V. Shalunov

**Keywords:**
ultrasound, gas purifi cation, coagulation, acoustic fi eld, fractional effi ciency

**Page:**
1335

**DIGITAL SIMULATION OF A HIGH-ENERGY SYSTEM USING A BORON–ALUMINUM ADMIXTURE AS A FUEL**

Numerical modeling of the fl ow of combustion products of a fuel containing a boron–aluminum admixture in the
nozzle of a solid-propellant rocket engine has been carried out. The advantage of boron–aluminum over aluminum
in using in composite solid propellants has been shown.

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

**Keywords:**
two-phase fl ow, polydisperse ensemble of particles, two-phase loss, specifi c momentum

**Page:**
1347

**FILTRATION PRESSURE FIELD AT HIGH-AMPLITUDE PERTURBATIONS**

A study has been made of the pressure fi eld in fi ltration of a weakly compressible fl uid in a homogeneous isotropic
compressible medium at high-amplitude perturbations. The equation used in formulating the problem is nonlinear:
the densities of a porous medium and of a saturating fl uid are assumed to be dependent on the function sought.
Use is made of the fact that the dependences of the densities of the fl uid and the skeleton material on pressure are
approximated with a high degree of accuracy by the linear function. Consideration is given to one-dimensional plane
horizontal fi ltration. The porosity and permeability of a porous medium, and also the viscosity of a fi ltering medium,
are considered to be constant.
A solution to the problem has been found with asymptotic expansions where a cofactor of the compressibility
factor of the liquid acts as a small parameter. Analytical expressions have been found for the zero and fi rst expansion
factors. It has been shown that the zero expansion factor may be used to investigate the evolution of the pressure
fi eld of an incompressible liquid, whereas the expression for the fi rst factor contains information on the contribution
of nonlinearity due to the fl uid′s compressibility. Values of the zero and fi rst residual terms have been determined. It
has been proved that the zero and fi rst residual terms contain terms of only higher orders as far as the asymptoticexpansion parameter is concerned, i.e., the corresponding requirement of asymptoticity of expressions of the zero
and fi rst factors is met.
On the basis of a computational experiment, the regularities of the dependence of the contribution of the
nonlinearity under study on time and on the spatial coordinate have been established.

**Author:**
A. I. Filippov, A. A. Koval′skii, and O. V. Akhmetova

**Keywords:**
nonlinear equation, fi ltration, pressure, asymptotic expansion.

**Page:**
1353

**FILTRATION TO A VERTICAL WELL FROM A BROKEN-DOWN FORMATION IN THE CASE OF SHORT FRACTURES**

Consideration has been given to the problem of achieving a steady-state regime in the process of the well operation at a constant pressure drop between bottom-hole and formation values, and also, at a constant fl ow rate. It has been assumed that in a fracture resulting from the conduct of hydraulic formation fracturing and existing inside the well supply contour, there is uniform pressure, i.e., the characteristic times of the well operation exceed signifi cantly the periods during which the disturbances from the well affect the entire fracture. Appropriate estimates are presented for these characteristic periods depending on the fi ltration and geometric parameters of the fracture and formation, and also, on the properties of the fl uid. Accurate and approximate analytical solutions have been constructed describing the fi ltration fl ows in the "well–fracture–formation" system that make it possible to determine the pressure evolution, the well fl ow rate, and the dynamics of the well operation in achieving a steady-state regime. Formulas have been obtained determining the well fl ow rate (analogs of the Dupuit formula). Critical conditions have been proposed for the fracture extent and the supply contour radius, when hydraulic fracturing results in a substantial increase in the well fl ow rate at a steady-state regime

**Author:**
V. Sh. Shagapov, I. R. Khamidullin and Z. M. Nagaeva

**Keywords:**
hydraulic fracturing, well, fracture, fi ltration, pressure distribution, fl ow rate, integrodifferential equation

**Page:**
1363

**DEVELOPED REGIME OF MOTION IN HYDRAULIC FRACTURE IN A DOUBLE-POROSITY MEDIUM**

A study is made of a two-dimensional coupled problem on slow motions of a liquid in a hydraulic fracture and
on deformations and fi ltration induced by these motions in a porous medium with double porosity that has two
components: the porosity proper and the fracturing. The motions are produced by pumping the liquid into the well.
Flow inside the fracture is described by hydrodynamics equations in a hydrostatic approximation. A certain ordered
series of interdependent geomechanical processes occurring during the hydraulic fracturing is established. In the
main space around the fracture, the liquid moves in the porous component of the two-phase medium. In the boundary
layer, there are mixed processes: in addition to the motion of the liquid by the fractures, we have its crossfl ow
between the fractures and the pores. These effects are investigated as a fi rst approximation for a certain small
parameter which is represented by the relative time. In contrast to the well-known classical problem with double
porosity, in this case the indicated problem is rigorously solved with account of elastic deformations of the skeleton.
In actual fact, the present paper is a continuation of the previous work of the author in an analogous formulation in
a zero approximation, in which the boundary layer is trivial and is reduced to the boundary layer in a medium with
ordinary porosity. Examples of solving concrete problems are given

**Author:**
A. V. Karakin

**Keywords:**
fracturing, porosity, poroelasticity, double porosity, hydraulic fracture

**Page:**
1373

**DETERMINING HYDRAULIC RESISTANCE WITH THE BINOMIAL LAW OF FILTRATION OF HYDROCARBONS IN A POROUS MEDIUM WITH ALLOWANCE FOR THE INFLUENCE OF THE INITIAL GRADIENT**

Hydraulic resistance and the Reynolds number are important parameters of fl ow, because of which determining them
is necessary when hydrodynamic fl ow is calculated and modeled. In the present work, the authors give formulas for
determining the Reynolds number and hydraulic resistance with the binomial law of fi ltration of hydrocarbons in a
porous medium with allowance for the infl uence of the initial gradient, and also obtain a formula for the velocity as
a function of these parameters

**Author:**
T. Sh. Salavatov and I. R. Gasanov

**Keywords:**
hydraulic resistance, Reynolds number, binomial fi ltration law, initial gradient

**Page:**
1387

**MATHEMATICAL MODELING OF THE PROCESS OF CONVECTIVE DRYING OF MATERIALS TAKING INTO ACCOUNT THEIR SHRINKAGE**

he authors have discussed the physical regularities of internal mass transfer in drying colloidal capillary-porous
materials, which is characterized by the fact that in addition to the phenomenon of mass conductivity (diffusion of
moisture) in a fi xed coordinate system, the transfer of moisture by the matrix of the material due to its shrinkage
is observed. As applied to this case, for a body in the shape of an unbounded plate dried symmetrically from both
surfaces, a mathematical model has been written that describes mass conductivity and convective transfer of
moisture in the body. The convective transfer of moisture depends on the normal coordinate to the plate's surface:
it is maximum at the surface of the plate and is equal to zero in its central plane. The authors have formulated the
problem describing the process of symmetric drying of an unbounded plate on the basis of the convective-diffusion
equation with a uniform initial distribution of the concentration and a boundary condition of mass transfer of the
third kind. It has been noted that the formulated problem can be solved by numerical methods. For analysis of the
degree of infl uence of the convective component on internal mass transfer, an analytical solution to the problem at
constant parameters of the process has been obtained. According to the obtained solution, calculations of the change
in the volume mean relative concentration as a function of the Fom number have been performed for the internal
problem (Fom = 100) and the mixed diffusion problem (Fom = 10). It has been shown that the maximum effect of the
infl uence of the convective component is observed for the intradiffusion problem.

**Author:**
S. P. Rudobashta, É. M. Kartashov, and G. A. Zueva

**Keywords:**
convective drying, mass conductivity, shrinkage, kinetic calculation, plate

**Page:**
1394

**EXPERIMENTAL INVESTIGATION OF THE REGIMES OF THERMAL ACTION ON A LAYER OF SOIL EXPOSED TO INERT HEATING**

A typical porous material enriched with organic matter, soil, is considered. Investigation of the thermal regimes of
such materials exposed to a high-temperature action is important for solving ecological and environmental protection
problems, and also those of agriculture. Many authors have established that thermal action on the near-surface soil
can have a negative effect on both the soil itself, and further development of grass and forest stands. There is a need
for the development of a system of geomonitoring accounting for thermophysical processes in the soil at the level
of mathematical models. Verifi cation of such models requires the conduct of experiments. In this investigation, we
propose an experimental setup for physical simulation of heat transfer processes in a layer of typical soil exposed to
high temperature whose source is an inert heater. A set of thermocouples is set up in the soil layer at different depths.
Typical curves are presented demonstrating time dependences at different depths of the layer, as are the results of the
analysis of temperature dependences

**Author:**
N. V. Baranovskii, V. I. Maksimov, A. S. Razva, and A. V. Bazarov

**Keywords:**
soil, forest fi re, inert heating, impact, experiment, temperature curve

**Page:**
1402

**INVESTIGATION AND ESTIMATION OF INTERFACE ENERGY CHARACTERISTICS**

A new equation has been obtained for calculating the equilibrium contact wetting angle on the basis of the capillary constant evaluated from the shape of a real droplet of liquid on a solid surface. The value of the surface tension of liquid is determined experimentally using the geometric parameters of the liquid droplet on a solid surface. The proposed equations make it possible to determine the equilibrium contact wetting angle of the solid body surface with thermodynamic parameters σ_{liq–g,} σ_{s.b–liq} and σ_{s.b–g }on the interface between three phases:
solid body–liquid–gas.

**Author:**
V. M. Gasanov

**Keywords:**
A new equation has been obtained for calculating the equilibrium contact wetting angle on the basis of the capillary constant evaluated from the shape of a real droplet of liquid on a solid surface. The value of the surface tension of liquid is determined experimentally using the geometric parameters of the liquid droplet on a solid surface. The proposed equations make it possible to determine the equilibrium contact wetting angle of the solid body surface with thermodynamic parameters σliq–g, σs.b–liq and σs.b–g on the interface between three phases: solid body–liquid–gas.

**Page:**
1408

**NUMERICAL SIMULATION OF THE COOLING OF MELT DROPLETS AS APPLIED TO THE TECHNOLOGY OF PRODUCTION OF METAL POWDERS**

Problems on the development of mathematical models for control of the technological processes of producing powders
of metals from their melts and for optimization of these processes were considered. A numerical simulation of the
solidifi cation of melt droplets in a turbulent cold-gas jet has been performed with the use of a complex mathematical
model, and results of this simulation were used for estimating the infl uence of different factors on the fl ying of a melt
droplet in a gas fl ow until it is solidifi ed.

**Author:**
K. N. Volkov and V. N. Emel'yanov

**Keywords:**
plasma technology, droplet, melt, powder, numerical simulation

**Page:**
1412

**INVESTIGATION OF THE STATE AND METHOD OF CONTROLLING THE PARAMETERS OF A TWO-PHASE VAPOR SYSTEM IN ITS FLOW IN A CHANNEL**

A wide area for application of vapor in heat power industry has been shown. Due to this, the problem of maintaining
and controlling the dryness of steam during its transportation through steam pipelines remains of current importance.
Quite detailed theoretical investigations into the steam parameters during its fl ow in the pipe have been carried out.
A comparative analysis of steam velocity and temperature epures as a function of certain parameters and assumed
approximations has been conducted. All calculations have been brought to quantitative results. As a result of the
implemented analysis, it has been shown that the uncertainty of exact values of some quantities does not play a
crucial role in common patterns of the formation of a dropping liquid.
As a result of numerical investigations into the kinetics of steam condensation, the specifi c volume and density
of the droplet condensate across the pipe have been identifi ed. The obtained results and the proposed methodological
approach to identifying steam parameters have been used in the development and further improvement of a device to
measure dryness of steam whose original design was proposed earlier by one of the authors. The functional diagram
and the prototype model of the batchbox of the measuring device are given in this investigation.

**Author:**
B. Yu. Kaplan and E. L. Stupitskii

**Keywords:**
pipeline, dryness of steam, condensate, kinetics, steam dryness control, steam temperature, steam velocity

**Page:**
1424

**ON THE MECHANISM OF DETONATION COMBUSTION OF NANOSTRUCTURED SILICON WITH A SOLID-PHASE OXIDANT**

The physical mechanism of detonation combustion of nanostructured silicon with a solid-phase oxidant at a velocity
of the combustion front of 1000–3000 m/s has been proposed. Thermodynamic characteristics of combustion of model
solid-phase mixtures "silicon–ammonium perchlorate" with different equivalent ratios of their components have
been calculated at different pressures. It has been established that a characteristic feature of detonation combustion
of nanostructured silicon with a solid-phase oxidant is the stationary velocity of motion of the detonation front with a
signifi cant defect (10–15%) with respect to the Chapman–Jouguet detonation velocity. The detonation (supersonic)
and subsonic regimes of combustion of nanostructured silicon with a solid-phase oxidant have been determined.

**Author:**
P. N. Krivosheyev, V. N. Mironov, O. G. Penyazkov, and S. I. Futko

**Keywords:**
detonation combustion, nanostructured silicon, solid-phase oxidant, gas suspension of particles, ammonium perchlorate, Chapman–Jouguet detonation, mathematical modeling

**Page:**
1439

**PHYSICAL MECHANISMS AND CONDITIONS OF EXCITATION OF VIBRATORY COMBUSTION OF SOLID FUELS**

The authors have obtained experimental characteristics of the self-oscillating process of vibratory combustion of
a solid fuel. As a result of the analysis of the obtained diagrams of amplitude and frequency characteristics of the
self-oscillating process of vibratory combustion of a solid fuel depending on the position of the combustion zone in a
Riecke tube, the fuel structure, and methods of charging, the authors have made the following assumption. Two types
of processes coexist during the vibratory combustion of a solid fuel: for the fundamental harmonics of the oscillating
process of low frequency, the energy approach known in the literature, and for harmonics of higher frequency,
the vortex mechanism. Methods of experimental verifi cation of this assumption have been developed and used.
Experimental results confi rm the proposed model of vibratory combustion of a solid fuel. A theoretical computational
procedure for the development of vibratory combustion has been worked out. A theoretical study of the motion of a
combustion wave at stochastic parameters of the process of heat release has been made.

**Author:**
O. G. Stonik, V. D. Geshele, and S. A. Kovalev

**Keywords:**
vibratory combustion, self-oscillation, acoustic radiation, ignition, combustion intensity, amplitude, frequency, solid fuel

**Page:**
1449

**INFLUENCE OF THE METHOD OF WATER SUPPLY TO THE ZONE OF A FOREST FIRE ON THE EFFICIENCY OF ITS EXTINGUISHING**

Results of experimental investigations on the effi ciency of suppression of the fl ame combustion and thermal
decomposition of forest combustible materials in a forest fi re by the local throw-down of water masses to a zone of
this fi re, the spraying of a fi ne-dispersed water over the combustion zone, and the formation of a water screen along
its perimeter are presented. Features of each of these methods are analyzed. Advantages of the combined method of
extinguishing a forest fi re, involving the space spraying of small water droplets intended to be distributed through
the fi re hotbed over a given period of time, are demonstrated.

**Author:**
G. V. Kuznetsov, A. O. Zhdanova, P. A. Strizhak, and Yu. K. Atroshenko

**Keywords:**
forest combustible material, forest fi re, fi refi ghting, water aerosol, water mass

**Page:**
1460

**TECHNICAL CARBON FROM THE PRODUCTS OF THERMOLYSIS OF DISCARDED TIRES**

Based on studies of the process of steam thermolysis of discarded tires, the possibility of obtaining a high-grade
technical carbon and of other ingredients from thermolysis products for the production of rubber has been
substantiated. The effi ciency of using composite mixtures of liquid and solid products of the thermolysis of tires as a
raw material for obtaining technical carbon is shown.

**Author:**
G. I. Zhuravskii

**Keywords:**
steam thermolysis, discarded tires, composite mixture, technical carbon, technological scheme

**Page:**
1470

**THEORETICAL REPRESENTATIONS OF THE THERMOKINETICS OF THERMAL DESTRUCTION OF POLYMERS**

A generalized theory of the thermokinetics of the process of thermal destruction of polymer materials has been
developed in the context of the kinetic thermofl uctuating concept based on unifi cation of a number of independent
approaches, namely, structurally kinetic (for describing elementary acts of the destruction process), mechanical (for
describing the local stress at the crack tip), thermodynamic (for calculating the value of safe stress). The developed
model concepts are based on experimental data relating to accumulation of disturbances in loaded samples; on force
disturbances and ruptures of bonds in the vicinity of the crack tip; on submicroscopic cracks and their characteristics;
fractographic investigations of the rupture face; and on the kinetic of growth of a main crack. A generalized formula
of the rate of crack growth is given, the tensor of stresses at the crack tip in the conditions of mechanical and thermal
loadings is calculated, the main parameters and limiting characteristics on mechanical and thermal loading of
a polymer sample are calculated, a theoretical relation of the time dependence of strength in the case of a purely
thermal loading in the full interval of thermal loadings from a safe to a critical one and at the stage of athermal
growth of the crack has been suggested. Numerical experiments are presented.

**Author:**
É. M. Kartashov

**Keywords:**
time dependence of strength, longevity curve, full interval of thermal loadings; safe, critical, and limiting characteristics, parameters of the process of thermal destruction

**Page:**
1476

**NONSTATIONARY HEAT-CONDUCTION PROBLEM FOR A HALF-SPACE WITH A MULTILAYER COATING UPON CYCLIC CHANGE IN THE AMBIENT TEMPERATURE**

Using the integral Laplace transformation and generalized boundary conditions, the authors have obtained the
analytical solution to a one-dimensional nonstationary heat-conduction problem for a half-space with a multilayer
coating on piecewise uniform change in the ambient temperature. A study has been made and regularities have been
established of thermal processes occurring in the body and the coating in thermal cycling.

**Author:**
V. A. Shevchuk and A. P. Gavris′

**Keywords:**
heat conduction, half-space, multilayer coating, generalized boundary conditions, thermal cycling

**Page:**
1489

**COMBINED METHOD OF SEPARATION OF VARIABLES. 2. SEQUENCES OF DIFFERENTIAL RELATIONS: PLATE, CYLINDER, SPHERE**

By the example of the Sturm–Liouville problem, solved for the function V(y) determined in the region Ωy ∈ [0, 1]
and corresponding to problems on the nonstationary heat conduction of a lengthy plate, a lengthy cylinder, and a
sphere with symmetric boundary conditions of the fi rst, second, and third kind, the existence of infi nite sequences of
differential relations at the boundary points y = 0 and y = 1 has been established. It is shown that these sequences of
differential relations can be used to advantage in approximately solving the Sturm–Liouville problem for the function
V(y) defi ned by a power polynomial with coeffi cients determined from the solution of the corresponding systems of
linear algebraic equations.

**Author:**
V. A. Kot

**Keywords:**
heat conduction equation, boundary-value problem, method of separation of variables, differential relations.

**Page:**
1498

**RADIATIVE HEAT TRANSFER PROCESSES IN HEATING OPEN PLATFORMS**

The results of a numerical analysis of the parameters of the system of radiative heating of an open platform, a fl at car of size 10 × 75 m, are presented. The temperature of the radiator of size 0.3 × 9 m was 600–900 K. The temperature of the atmospheric air varied in the range from –10 to +10^{o}
C at a wind velocity of up to 5 m/s. As the criterion of heating comfortably a human being, the temperature at the level of his head (175 cm) was taken. As a result of the computational experiment, the dependences of the temperature of the heated platform on the temperature and the height of the radiator mounting, as well as on the direction and velocity of wind, were obtained. It has been established that the temperature at the level of the top of the human being's head is equal from 2–3 to 16–18^{o}
C when the radiators are disposed at a height of 4–8 m from the platform surface at the surrounding air temperature of 0o C and wind velocity of 0.5–5 m/s. It is shown that on decrease of the air temperature to –10^{o}
C the installation of wind
protection is required.

**Author:**
A. A. Red'ko, I. A. Red'ko, Yu. A. Burda, A. F. Red'ko, and S. V. Pavlovskii

**Keywords:**
numerical analysis, radiative heating, open platform, comfort, short-wave emitters.

**Page:**
1520

**REDUCTION OF HYDRODYNAMIC MIXING MODELS ON THE BASIS OF THE DMD ALGORITHM**

With the use of decomposition into dynamic modes, reduced models of hydrodynamic mixing have been constructed
and rather exact space–time pictures of impurity distribution for various periodic regimes of mixing have been
obtained with substantial reduction of computational expenditures. It is shown that after processing the results of
solution of the problem on mixing in a rectangular cavern with mobile bottom and lid by the DMD method, the gain
in the information storage amounts to more than 80%. The proposed approach can also be applied for processing
experimental data.

**Author:**
T. Yu. Sukharev and D. L. Reviznikov

**Keywords:**
With the use of decomposition into dynamic modes, reduced models of hydrodynamic mixing have been constructed and rather exact space–time pictures of impurity distribution for various periodic regimes of mixing have been obtained with substantial reduction of computational expenditures. It is shown that after processing the results of solution of the problem on mixing in a rectangular cavern with mobile bottom and lid by the DMD method, the gain in the information storage amounts to more than 80%. The proposed approach can also be applied for processing experimental data

**Page:**
1529

**EXACT SOLUTION FOR AN UNSTEADY ISOTHERMAL FLOW BEHIND A CYLINDRICAL SHOCK WAVE IN A ROTATING PERFECT GAS WITH AN AXIAL MAGNETIC FIELD AND VARIABLE DENSITY**

An exact solution of the problem on the propagation of a cylindrical shock wave in a rotating perfect gas with an axial
magnetic fi eld in the case of an isothermal fl ow is obtained. The initial density, magnetic fi eld strength, and the initial
angular velocity in the ambient medium are assumed to vary according to the power law. An exact similarity solution
obtained by the McVittie method for an isothermal fl ow in a rotating gas is fi rst reported. Similarity transformations
are used to transform a system of partial differential equations into a system of ordinary differential equations, and
then the product solution of McVittie is used to obtain the exact solution. The effects of the values of the gas specifi c
heat ratio, rotational parameter, and of the strength of the initial magnetic fi eld are discussed. It is shown that the
shock velocity increases and the shock strength decreases with increase in the values of these parameters. The effect
of variation in the value of the initial density index is also studied. The obtained solutions show that the radial fl uid
velocity, density, pressure, and the magnetic fi eld strength tend to zero as the axis of symmetry is approached.

**Author:**
G. Nath

**Keywords:**
shock waves, exact solution, rotating medium, perfect gas, axial magnetic fi eld

**Page:**
1538

**FLOW OF A SUPERSONIC GAS JET EMATING FROM A NOZZLE OVER A CONCAVE WALL**

The problem on the fl ow of a supersonic gas jet over a concave wall of any confi guration was solved. A method of
calculating the gas fl ow arising as a result of the interaction of a noncalculated supersonic gas jet with a plane wall
or a curvilinear one is proposed. Results of measurements of the pressure at the surface of a curvilinear obstacle, over
which a supersonic gas jet propagates, and of calculations of the gasdynamic parameters of the gas in the near-wall
region of this jet, are presented. The most characteristic regions of a noncalculated supersonic gas jet propagating
over a curvilinear refl ecting wall, which are of interest for a number of practical applications of such jets and for the
constructions of their physical and mathematical models, were determined. The determining parameters of fl ows in
a supersonic gas jet over a concave wall were defi ned ,and the conductions of their similarity were formulated with
regard for the main geometric characteristics of the jet. It is shown that the difference between supersonic gas jets
propagating over a curvilinear wall and a plane wall is the pressure difference at their inner and outer boundaries.
With the use of formulas of the oblique shock wave theory, the angles of inclination of a noncalculated supersonic
gas jet to a concave wall and its gasdynamic parameters in all the regions of the wall were determined.

**Author:**
N. I. Sidnyaev

**Keywords:**
noncalculated supersonic jet, concave wall, gasdynamic parameters

**Page:**
1548

**THERMOMECHANICAL IMPROVEMENT OF GAS–AIR SYSTEMS OF TURBOCHARGED PISTON INTERNAL-COMBUSTION ENGINES**

Original methods for improving gas–air systems of turbocharged engines have been proposed. An analysis of the
dependences of the gas-fl ow velocity and of the local heat-transfer coeffi cient in such a system on time has been
made. As the criterion of assessment of the effi ciency of these systems, use was made of the level of turbulence of
gas fl ow in them and of the averaged coeffi cient of its heat transfer. Gasdynamic and heat-transfer characteristics of
various modifi cations of the indicated systems have been considered.

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

**Keywords:**
piston internal-combustion engines, turbocharged engines, gas–air intake and exhaust systems, gasdynamics, heat transfer, pulsating fl ows, turbulence level

**Page:**
1557

**INVERSE PROBLEM OF PIPELINE TRANSPORT OF WEAKLY-COMPRESSIBLE FLUIDS**

Nonstationary one-dimensional fl ow of a weakly-compressible fl uid in a pipeline is considered. The fl ow is described
by a nonlinear system of two partial differential equations for the fl uid fl ow rate and pressure in the pipeline. An
inverse problem on determination of the fl uid pressure and fl ow rate at the beginning of the pipeline needed for
the passage of the assigned quantity of fl uid in the pipeline at a certain pressure at the pipeline end was posed
and solved. To solve the above problem, a method of nonlocal perturbation of boundary conditions has been
developed, according to which the initial problem is split at each discrete moment into two successively solvable
problems: a boundary-value inverse problem for a differential-difference equation of second order for the fl uid
fl ow rate and a direct differential-difference problem for pressure. A computational algorithm was suggested for
solving a system of difference equations, and a formula was obtained for approximate determination of the fl uid
fl ow rate at the beginning of the pipeline. Based on this algorithm, numerical experiments for model problems were
carried out.

**Author:**
Kh. M. Gamzaev

**Keywords:**
pipeline transport, weakly-compressible fl uid, nonstationary fl ow, boundary-value inverse problem, differential-difference problem

**Page:**
1567

**APPLICATION OF AN INTEGRAL NUMERICAL TECHNIQUE FOR A TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY FIN WITH INTERNAL HEAT GENERATION**

A numerical study of convective heat transfer in a longitudinal fi n with temperature-dependent thermal conductivity
and internal heat generation is undertaken. Integral calculations are implemented on each generic element of the
discretized problem domain. The resulting systems of nonlinear equations are solved effi ciently because of the
coeffi cient matrix sparsity to yield both the dependent variable and its fl ux. In order to validate the formulation,
the effects of the thermogeometric parameter, nonlinearity due to the temperature-dependent thermal conductivity,
and of the heat transfer coeffi cient on the fi n temperature distribution are investigated. The results are found to be
in agreement with those for similar problems described in the literature and with the physics of the problem.

**Author:**
O. O. Onyejekwe, G. Tamiru, T. Amha, F. Habtamu Y. Demiss, N. Alemseged, and B. Mengistu

**Keywords:**
convective heat transfer, longitudinal fi n, temperature-dependent thermal conductivity, systems of nonlinear equations, discretized problem domain, sparsity of coeffi cient matrix, integral calculations, generic element, thermogeometric parameter

**Page:**
1574

**VARIATION IN THE STRESS STATE OF COPPER ALLOYS UNDER THE ACTION OF COLD AIR PLASMA**

An investigation has been conducted into the action of nonequilibrium low-temperature plasma of a high-frequency capacitive discharge in air at a pressure of 133.3 MPa upon the structure of brass and beryllium bronze. The absence of changes in the microstructure of alloys under the action of plasma was established using the target metallography method. It has been shown that the main effect of the plasma action is the formation of static distortions of the abovementioned materials at the level ~0.007·10^{–10} m.

**Author:**
A. G. Anisovich, I. I. Filatova, and S. V. Goncharik

**Keywords:**
nonequilibrium low-temperature plasma, microstructure, static displacement, copper alloys, stress state

**Page:**
1583

**SEMIEMPRICAL ESTIMATE OF THE TEMPERATURE OF THE MEDIUM IN THE CORONA DISCHARGE OF A PLASMA-CHEMICAL REACTOR**

Temperatures have been identifi ed in the corona hood and streamer of a plasma-chemical reactor during the formation of a polymer fi lm with carbon nanosized particles. A semiempirical procedure has been proposed to estimate these temperatures. It has been shown that in the case where the temperature in the streamer volume is ~600^{o}
C and it is ~1400^{o}
C in the corona hood, polycrystalline carbon nanoparticles are formed in the plasma-chemical reactor whose
agglomerates penetrate into the polymer fi lm.

**Author:**
E. A. Bogoslov, M. P. Danilaev, S. V. Drobyshev and V. A. Kuklin

**Keywords:**
Temperatures have been identifi ed in the corona hood and streamer of a plasma-chemical reactor during the formation of a polymer fi lm with carbon nanosized particles. A semiempirical procedure has been proposed to estimate these temperatures. It has been shown that in the case where the temperature in the streamer volume is ~600o C and it is ~1400o C in the corona hood, polycrystalline carbon nanoparticles are formed in the plasma-chemical reactor whose agglomerates penetrate into the polymer fi lm.

**Page:**
1591