#### Volume 90, №4

**DEVELOPMENT OF THE SCIENCE OF THERMODYNAMICS**

History of discovery of three basic laws of thermodynamics and their formulations are presented.

**Author:**
S. Kakaç

**Keywords:**
caloric, heat, work, heat engine, absolute temperature, energy, laws of thermodynamics, availabilityexergy, entropy

**Page:**
763

**DESCRIPTION OF THE STEADY-STATE OPERATION OF A BIOCHEMICAL REACTOR USING A DIFFUSION MODEL**

Consideration has been given to nonlinear boundary-value problems of steady-state operation of a biochemical reactor. Nontrivial solutions of these problems have been found using equations of a diffusion model with homogeneous boundary conditions. A study has been made of the operating regimes of the reactor under different conditions of biomass transfer in it.

**Author:**
A. I. Moshinskii

**Keywords:**
biochemical reactor, diffusion model,stability, logistic and hyperbolic laws, Péclet number

**Page:**
770

**THEORETICAL AND EXPERIMENTAL STUDY OF CHEMICAL TRANSFORMATIONS OF A METHANE–HYDROGEN–COAL PARTICLES MIXTURE IN A RAPID-COMPRESSION MACHINE**

Results of an experimental and numerical study of the ignition of a stoichiometric methane–air mixture in the presence of coal particles of diameters 20–52 μm in the range of temperatures 850–1150 K and pressures 1.5–2.0 MPa are presented. It has been found that the particles begin to burn at a temperature of the oxidizing medium above 850 K. At a temperature above 1000 K, burning particles reduce the time and limiting temperature of ignition of the methane–air mixture. A comparison has been made of the calculated data on ignition-delay times of coal in an aircoal mixture and on ignition-delay times of methane and coal in a methane–air–coal mixture with the experimental data. A satisfactory agreement is shown between the data on ignition-delay times of coal and ignition-delay times of methane in all the mixtures in question.

**Author:**
A. V. Fedorov, D. A. Tropin, O. G. Penyazkov V. V. Leshchevich and S. Yu. Shimchenko

**Keywords:**
ignition, methane–air mixture, coal dust, coal microparticles, detailed chemical kinetics, mathematical modeling, rapid-compression machine

**Page:**
781

**DETERMINATION OF THE VOLUME OF WATER FOR SUPPRESSING THE THERMAL DECOMPOSITION OF FOREST COMBUSTIBLES**

From the results of experimental studies of the processes of suppressing the thermal decomposition of the typical forest combustibles (birch leaves, fi r needles, asp twigs, and a mixture of these three materials) by water aerosol, the minimum volumes of the fi re-extinguishing liquid have been determined (by varying the volume of samples of the forest combustibles from 0.00002 m^{3 }to 0.0003 m^{3 }and the area of their open surface from 0.0001 m^{2 }to 0.018 m^{2}). The dependences of the minimum volume of water on the area of the open surface of the forest combustible have been established. Approximation expressions for these dependences have been obtained. Forecast has been made of the minimum volume of water for suppressing the process of thermal decomposition of forest combustibles in areas from 1 cm^{2 }to 1 km^{2 }, as well as of the characteristic quenching times by varying the water concentration per unit time. It has been shown that the amount of water needed for effective suppression of the process of thermal decomposition of forest combustibles is several times less than is customarily assumed.

**Author:**
R. S. Volkov, A. O. Zhdanova, G. V. Kuznetsov, and P. A. Strizhak

**Keywords:**
forest combustible, thermal decomposition, quenching, water, minimum volume, water concentration

**Page:**
789

**MODELING OF THE EXTRACTION OF A TARGET COMPONENT FROM BODIES OF SPHERICAL SHAPE IN A SEMICONTINUOUS PROCESS**

A problem of extraction of a target component from bodies of spherical shape in an apparatus of semicontinuous action (periodic for the solid phase and continuous for the liquid phase), in which the liquid phase is completely mixed, has been formulated and solved analytically. The kinetics of the process has been analyzed with a numerical method at different values of the specifi c fl ow rate of the liquid phase. Recommendations have been given on the use of the solution obtained for calculating the kinetics of extraction of low-molecular-weight compounds from the granules of fi berizing polymeric materials.

**Author:**
S. P. Rudobashta, M. K. Kosheleva, and É. M. Kartashov

**Keywords:**
extraction, semicontinuous process, kinetics, polymer, mass conduction, mass transfer, residence time.

**Page:**
797

**SWIRLING FLOWS IN CYCLONE CHAMBERS WITH NOZZLES OF SMALL FLOW SECTION**

Experimental studies have been made of the hydrodynamics of cyclone chambers of varying geometry with tangential nozzles of small flow section. The character of the velocity and pressure distribution in the volume of such a chamber has been revealed. Dependences have been obtained for calculation of the tangential velocity at the periphery of a cyclone chamber and its resistance coeffi cient in a wide range of the flow sections (0.00138 ≤ α ≤ 0.024). For the fi rst time a relationship has been established between the phenomenon of the ejection of air into a cyclone chamber and the twist factor in its central region.

**Author:**
E. A. Pitsukha and Yu. S. Teplitskii

**Keywords:**
hydrodynamics, cyclone chamber, swirling fl ow, ejection, twist factor

**Page:**
806

**MATHEMATICAL MODELS OF MASS TRANSFER PROCESSES IN SOILS WITH ACCOUNT FOR THEIR INTERACTION WITH RAINFALL**

Equations of physicochemical mechanics for swelling soils interacting with rainfall in the course of the process of surface discharge are obtained. The behavior of unsaturated swelling soils in anomalous conditions of surface discharge has been analyzed. A comparison with the data of normal conditions of the surface discharge regime has been carried out.

**Author:**
N. E. Galiullina and M. G. Khramchenkov

**Keywords:**
mass transfer, swelling soils, surface discharge, subsurface drainage

**Page:**
511

**SORPTIVE ACTIVITY AND HYDROPHOBIC BEHAVIOR OF AEROGELS BASED ON REDUCED GRAPHENE OXIDE AND CARBON NANOTUBES**

A study has been made of the possibility of obtaining three-dimensional porous aerogel structures based on reduced graphene oxide and carbon nanotubes. Carbon nanotubes in the structure of the fi nished aerogel based on reduced graphene oxide were grown by thermal decomposition of ferrocene into cyclopentadienyl and iron ions which served as the source of carbon and a catalyst respectively. The obtained composite aerogels exhibit high sorptive activity for organic liquids of different densities.

**Author:**
F. Sultanov, B. Bakbolat, Ch. Daulbaev,a,b UDC 539.23 A. Urazgalieva,a,b Z. Azizov,a Z. Mansurov, M. Tulepov, and S. S. Pei

**Keywords:**
aerogel, graphene, carbon nanotubes, sorption, reduction

**Page:**
826

**PROVIDING THE EFFICIENCY AND DISPERSION CHARACTERISTICS OF AEROSOLS IN ULTRASONIC ATOMIZATION**

This article is devoted to the investigation of the process of atomization of liquids under the action of ultrasonic vibrations. It has been shown that the ultrasonic atomization parameters are determined by the regimes of action (vibration frequency and amplitude of the atomization surface), the liquid properties (viscosity, surface tension), and the thickness of the liquid layer covering the atomization surface. To reveal the dependences of the effi ciency of the process at various dispersion characteristics of produced liquid droplets, we propose a model based on the cavitation-wave theory of droplet formation. The obtained results can be used in designing and using ultrasonic atomizers producing an aerosol with characteristics complying with the requirements on effi ciency and dispersivity for the process being realized.

**Author:**
V. N. Khmelev, A. V. Shalunov, R. N. Golykh, UDC 534.29.66.084:534-18 V. A. Nesterov, R. S. Dorovskikh, and A. V. Shalunova

**Keywords:**
ultrasound, atomization, viscosity, aerosol, layer thickness, capillary wave

**Page:**
831

**REGULAR THERMAL CONDITIONS IN THE PROCESS OF HEAT TREATMENT OF THIN POLYMER MATERIALS**

This paper presents the results of investigations of the process of heat treatment of thin flat polymer materials under regular thermal conditions. Equations are presented for calculating the duration of the process of heat treatment of the polymers, mean integral temperatures, and heat fluxes. Comparison has been made between the experimental and calculated values of the main parameters of the process. The structural-mechanical properties of the polymers upon their exposure to heat fl uxes have been considered.

**Author:**
A. I. Ol′shanskii, V. I. Ol′shanskii, and R. V. Okunev

**Keywords:**
heat treatment, polymer material, regular thermal conditions

**Page:**
851

**HEAT TRANSFER IN THE ANODE REGION IN PLASMA-ELECTROLYTIC HEATING OF A CYLINDRICAL SAMPLE**

The energy balance in a three-phase system "anode–vapor/gas envelope–electrolyte" and the results of experimental determination of the heat fl uxes acting in the vapor–gas envelope are considered. To determine the fl uxes quantitatively, the calorimetric method and the theory of inverse problems of the thermal conductivity of solid bodies are used. It is shown that heat fl uxes into the anode and electrolyte increase with the voltage delivered to the electrochemical cell, whereas the heat fl ux associated with the vapor release to the atmosphere remains practically unchanged. An increase in the concentration of the current-conducting component in the electrolyte leads to a certain growth of the heat fl ux into the anode and to a decrease of the fl ux into the electrolyte. The stages of a nonstationary period of the process of plasma-electrolytic heating have been revealed, and it has been established that the time of heating the

vapor–gas envelope is several times shorter than the time of heating a sample.

**Author:**
A. V. Zhirov, P. N. Belkin, and S. Yu. Shadrin

**Keywords:**
plasma-electrolytic heating, heat fl uxes, inverse heat conduction problem

**Page:**
862

**SIMULATION OF HEAT EXCHANGE IN THE LIQUID CORE OF THE EARTH**

Results of numerical simulation of the convective heat exchange between two concentric isothermal spheres with the use of different simulation criteria are presented. The influence of these criteria on the results of calculations of the structure of the liquid fl ow and the heat transfer in the space between the indicated spheres was investigated. Equations for simulation of the heat exchange between these spheres in the case where the gravitational acceleration in the layer formed by them is directed to its center were constructed. These equations were compared with equations for simulation of the heat transfer in an analogous spherical layer in which the gravitational acceleration is directed vertically down.

**Author:**
S. V. Solov′ev

**Keywords:**
mathematical simulation, convective heat exchange, spherical space, simulation equations for heat exchange

**Page:**
873

**ANALYSIS OF THE EFFICIENCY OF A BOREHOLE HEAT EXCHANGER WITH LONGITUDINAL RIBBING**

The technique of calculating the heat engineering characteristics of a tube-in-tube type heat exchanger has been refi ned by using experimental data on heat transfer and hydraulic resistance of a ribbed tube in an annular channel. An analysis of the effi ciency of a borehole heat exchanger on the basis of various criteria is carried out.

**Author:**
S. V. Goldaev and K. N. Radyuk

**Keywords:**
geothermal well, heat exchanger, heat fl ux, rectangular rib, effi ciency criterion

**Page:**
883

**SOLUTION OF THE CLASSICAL STEFAN PROBLEM: NEUMANN CONDITION**

A polynomial solution of the classical one-phase Stefan problem with a Neumann boundary condition is presented. As a result of the multiple integration of the heat-conduction equation, a sequence of identical equalities has been obtained. On the basis of these equalities, solutions were constructed in the form of the second-, third-, fourth-, and fi fth-degree polynomials. It is shown by test examples that the approach proposed is highly effi cient and that the approximation errors of the solutions in the form of the fourth- and fi fth-degree polynomials are negligible small, which allows them to be considered in fact as exact. The polynomial solutions obtained substantially surpass the analogous numerical solutions in the accuracy of determining the position of the moving interphase boundary in a body and are in approximate parity with them in the accuracy of determining the temperature profi le in it

**Author:**
V. A. Kot

**Keywords:**
Stefan problem, Neumann boundary condition, interphase front, free boundary, integral method of boundary characteristics, heat balance integral method.

**Page:**
889

**LAPLACE TRANSFORMATION FOR AN OPTICALLY THICK GRAY GAS IN A VERTICAL CHANNEL WITH MAGNETIC BODY FORCE: ROSSELAND APPROXIMATION**

A Couette fl ow of an optically thick gray gas flowing in a vertical channel is analyzed analytically with consideration of the buoyancy effects and thermal radiation. The Rosseland diffusion flux approximation is employed to simulate the radiative heat transfer contribution. An impulsive movement and a uniformly accelerated movement of one plate are considered with the second plate being stationary. The numerical results for some special cases are compared with the exact solutions and are found to be in good agreement. The effects of the fl ow parameters on the nondimensional velocity and skin friction are revealed.

**Author:**
K. Kalita and S. Ahmed

**Keywords:**
optically thick gray gas, vertical channel, Rosseland approximation, Laplace transform, thermo-fl uid dynamics, impulsive plate movement

**Page:**
918

**GAS DYNAMICS OF A RECESSED NOZZLE IN ITS DISPLACEMENT IN THE RADIAL DIRECTION**

Numerical simulation of gasdynamic processes accompanying the operation of the recessed nozzle of a solidpropellant rocket motor in its linear displacement is carried out. Reynolds-averaged Navier–Stokes equations closed using the equations of a k–ε turbulence model are used for calculations. The calculations are done for different rates of fl ow of the gas in the main channel and in the over-nozzle gap, and also for different displacements of the nozzle from an axisymmetric position. The asymmetry of geometry gives rise to a complicated spatial flow pattern characterized by the presence of singular points of spreading and by substantially inhomogeneous velocity and pressure distributions. The vortex fl ow pattern resulting from the linear displacement of the nozzle from an axisymmetric position is compared with the data of experimental visualization. The change in the vortex pattern of the fl ow and in the position of the singular points as a function of the fl ow coeffi cient and the displacement of the nozzle from the symmetry axis is discussed.

**Author:**
K. N. Volkov, S. V. Denisikhin, and V. N. Emel′yanov

**Keywords:**
vortex structure, nozzle, injection, numerical simulation, singular point

**Page:**
932

**COMPUTATIONAL AND EXPERIMENTAL INVESTIGATIONS OF THE COOLANT FLOW IN THE CASSETTE FISSILE CORE OF A KLT-40S REACTOR**

Results of experimental investigations of the local hydrodynamic and mass-exchange characteristics of a coolant fl owing through the cells in the characteristic zones of a fuel assembly of a KLT-40S reactor plant downstream of a plate-type spacer grid by the method of diffusion of a gas tracer in the coolant fl ow with measurement of its velocity by a fi ve-channel pneumometric probe are presented. An analysis of the concentration distribution of the tracer in the coolant fl ow downstream of a plate-type spacer grid in the fuel assembly of the KLT-40S reactor plant and its velocity field made it possible to obtain a detailed pattern of this flow and to determine its main mechanisms and features. Results of measurement of the hydraulic-resistance coeffi cient of a plate-type spacer grid depending on the Reynolds number are presented. On the basis of the experimental data obtained, recommendations for improvement of the method of calculating the fl ow rate of a coolant in the cells of the fi ssile core of a KLT-40S reactor were developed. The results of investigations of the local hydrodynamic and mass-exchange characteristics of the coolant fl ow in the fuel assembly of the KLT-40S reactor plant were accepted for estimating the thermal and technical reliability of the fi ssile cores of KLT-40S reactors and were included in the database for verifi cation of computational hydrodynamics programs (CFD codes).

**Author:**
S. M. Dmitriev, A. V. Varentsov, A. A. Dobrov, UDC 621.039 D. V. Doronkov, A. N. Pronin, V. D. Sorokin, and A. E. Khrobosto

**Keywords:**
fl oating power plant, fi ssile core, fuel assembly, spacer grid, coolant

**Page:**
941

**DETECTION OF THE AIRCRAFT VORTEX WAKE WITH THE AID OF A COHERENT DOPPLER LIDAR**

The results of the fi rst measurements in Russia of the vortex wakes left by different types of airplanes with the aid of 1.5-μm range home-made commercially manufactured coherent Doppler lidars are presented. The characteristic features of the measurement of vortex wakes by such lidars are considered. The dynamics of the vortex wake left by a Boeing 737-800 is shown.

**Author:**
M. S. Penkin, A. S. Boreisho, M. A. Konyaev, A. E. Orlov and N. A. Baranov

**Keywords:**
coherent Doppler lidar, vortex wake, safety of airplane fl ight, air transportation

**Page:**
951

**NEW FORMULAS FOR CALCULATING THE FLUID FLOW CHARACTERISTICS IN A CIRCULAR PIPE**

We propose new formulas for calculating the friction factor in pipes with smooth walls and relations between the mean and the maximum fl uid flow velocity in a pipe. The formulas are in better agreement with experimental data than the literature relations. An expression for the friction factor suitable for all fl ow conditions is proposed. The results of this work can be used in calculating the hydraulic resistance of pipes, as well as in calculating the heat and mass transfer processes in apparatuses incorporating tubular elements.

**Author:**
Yu. G. Chesnokov

**Keywords:**
turbulent fl ows, hydraulic resistance.

**Page:**
958

**BOUNDARY CONDITIONS FOR NUMERICAL CALCULATION OF GAS EXCHANGE IN PISTON ENGINES**

An estimation of the effi ciency of the technique of setting boundary conditions with the use of gas-dynamical functions to numerically calculate the intake and exhaust processes in piston engines is made. Mathematical models have been developed for different engines, and joint calculations of nonstationary gas fl ow and of the process proceeding in the cylinder have been carried out. A comparison of the obtained results with experimental data has been made, and the adequacy of the mathematical description has been confi rmed.

**Author:**
Yu. A. Grishin, V. A. Zenkin, and R. N. Khmelev

**Keywords:**
piston engine, intake and exhaust processes, mathematical simulation, boundary conditions, Godunov′s method.

**Page:**
965

**EXPERIMENTAL AND MATHEMATICAL MODELING OF HIGH-VELOCITY COLLISION OF A CONICAL STRIKER WITH VARIOUS BARRIERS**

A procedure for predicting the consequences of collisions of a metallic conical striker with various barriers has been developed. The calculation is carried out within the framework of an elastoviscous model of a continuous medium with account for the destruction of materials in axisymmetric and full spatial formulations. The interaction of colliding bodies of different composition and geometry is investigated.

**Author:**
A. N. Ishchenko, S. A. Afanas'eva, N. N. Belov, UDC 539.3 V. V. Burkin, K. S. Rogaev, M. V. Khabibullin, A. V. Chupashev, and N. T. Yugov

**Keywords:**
experimental modeling, mathematical modeling/simulation, striker, barrier, high-velocity collision, destruction

**Page:**
971

**EQUATION OF STATE FOR CALCULATING TEMPERATURE OF MATERIAL IN EXPLOSIVE PROCESSING**

An equation of state with potential and thermal pressure components has been obtained which makes it possible to calculate the temperature of a condensed medium at high energy densities. The derivation of the equation of state is based on the concepts of a covolume and a free volume for thermal motion of particles and universality of the relationship between the pressure behind the shock-wave front and the potential pressure component. For the proposed equation of state, it is necessary to know only the shock adiabat of the medium. A comparison has been made of calculation results and experimental data for the temperature behind the shock-wave front in elementary substances and chemical compounds. The obtained equation of state can be of use in practical applications and in shock-wave experiments.

**Author:**
V. F. Anisichkin

**Keywords:**
equation of state, condensed medium, shock wave, temperature

**Page:**
978

**PHYSICAL MODEL OF THE DIFFUSION INTERACTION OF ARGON BUBBLES WITH AN ALUMINUM MELT**

A physical model of diffusion interaction of argon bubbles with an aluminum melt in the process of hydrogen outgassing from it by blowing an inert gas through the porous bottom of a refi ning vessel is presented. The dependence of the effi ciency ε of the diffusion interaction of argon bubbles with the aluminum melt on the dimensionless complex criterion B has been investigated. Three characteristic regions of the dependence ε(B) have been distinguished. Analysis of this dependence made it possible to develop energy- and resource saving regimes of the technology related to the economics of argon.

**Author:**
N. I. Zakharov and I. V. Volkova

**Keywords:**
diffusion interaction, argon bubbles, aluminum melt, outgassing, energy- and resource saving.

**Page:**
988

**IDENTIFICATION OF FLOWS BY THE LOCAL DISTURBANCE METHOD**

A new method of identifi cation of flows is described. The method is based on fi xing the wake formed behind a small disturbance on the surface being destroyed in the flow. The method is first of all applied to high-temperature, dense, and aggressive media.

**Author:**
S. K. Savel'ev and A. V. Chesnokov

**Keywords:**
visualization of fl ows, measurement methods, high-temperature fl ows, identifi cation of fl ows, velocity measurement, rotating fl ows.

**Page:**
992

**RHEOLOGY OF STRUCTURED OILS**

Rheological models of structured oils are proposed and compared with available experimental data on oils from different deposits. It is shown that structured oils can possess properties of Bingham and power-law non-Newtonian fluids.

**Author:**
G. I. Kelbaliev,a S. R. Rasulov,b A. G. Rzaev, and G. R. Mustafaevab

**Keywords:**
Rheological models of structured oils are proposed and compared with available experimental data on oils from different deposits. It is shown that structured oils can possess properties of Bingham and power-law non-Newtonian fl uids.

**Page:**
996

**INFLUENCE OF DISSIPATION ON HEAT TRANSFER DURING FLOW OF A NON-NEWTONIAN FLUID IN A POROUS CHANNEL**

A study is made of fl ow and heat transfer during the motion of a non-Newtonian (power-law) fl uid in a plane channel fi lled with porous material. The Brinkman equation is used as the equation of state, and a one-temperature model, in representing the energy equation. Account us taken of dissipative heat releases. The problem is solved for temperature boundary conditions of the fi rst kind. The authors show the infl uence of dissipation on the development of the temperature profi le, and also on the distributions of the local Nusselt number and the mass-mean temperature along the channel.

**Author:**
A. V. Baranov and S. A. Yunitskii

**Keywords:**
non-Newtonian fl uid, heat transfer, shear fl ow, plane channel.

**Page:**
1003

**TOWARD THE THEORY OF AN ELECTRIC DOUBLE LAYER IN A PLASMA**

The conditions for the appearance of a double layer are considered. A theoretical description of the latter is given. Based on experimental data on probe diagnostics of oxygen and helium plasmas, a self-consistent theory of the volume charge layer is being constructed. Analysis of the phenomenon of screening the probe potential by charged particles is carried out. The procedure used for correcting the particle temperature determined by the logarithmic operation method is presented. The problem of application of Langmuir probes, the 3/2 law, and of the theory of electric double layer in a plasma is discussed

**Author:**
S. A. Gutsev

**Keywords:**
decaying plasma, Langmuir probes, 3/2 law, theory of an electrical double layer, ion–ion plasma, Debye radius.

**Page:**
1010

**HIGH-TEMPERATURE COMPENSATION EFFECT OF DYNAMIC VISCOSITY IN MULTICOMPONENT HYDROCARBON MEDIA**

Linear dependences connecting the preexponent to the activation energy of viscous fl ow in the Frenkel–Eyring equation have been obtained for multicomponent hydrocarbon media (high-boiling distillate fractions). For these media, the kinetic compensation effect has been established whose distinctive feature is its action in the temperature range including the temperature of thermal destruction (400–450^{o} C) of the indicated media. The obtained results have been confi rmed by statistical-processing data and make it possible to predict the dynamic viscosity of multicomponent hydrocarbon systems, such as tars and other high-boiling oil distillates.

**Author:**
M. Yu. Dolomatov, G. I. Nizamova, and N. A. Zhuravleva

**Keywords:**
high-temperature compensation effect, Newtonian multicomponent hydrocarbon fl uid, high-boiling distillate, tar.

**Page:**
1020

**MOLECULAR-DYNAMIC CALCULATION OF EFFECTS APPEARING IN REMOVING A LEAD FILM FROM GRAPHENE**

By the molecular-dynamics technique, the authors have investigated the bombardment of a thin lead fi lm on graphene by a beam of Xe clusters in the range of energies 5–30 eV at an angle of incidence of 45o . Visual observation and the density profi le of the Pb fi lm point to a complete separation of the fi lm from graphene followed by the formation of a lead cluster during the bombardment with a cluster energy of 20 eV. Such bombardment leads to maximum horizontal and minimum vertical mobilities of C atoms in graphene and also generates a minimum stress in the fi lm′s plane due to vertical forces.

**Author:**
A. E. Galashev and O. R. Rakhmanova

**Keywords:**
graphene, cluster beam, mobility coeffi cients, xenon, cleaning, lead, stress tensor

**Page:**
1026