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2015 year, number 5

1.
MATHEMATICAL MODEL OF MOTION OF A MIXTURE OF GASES AND HOLLOW MICROSPHERES WITH SELECTIVE PERMEABILITY

A. S. Vereshchagin1,2,3, V. M. Fomin1,2,3
1Khristianovich Institute of Theoretical and AppliedMechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Novosibirsk State University, Novosibirsk, 630090 Russia
3Novosibirsk State Technical University, Novosibirsk, 630073 Russia
Keywords: проницаемость, гелий, микросфера, математическая модель, механика многофазныхсред, permeability, helium, microsphere, mathematical model, mechanics of multiphase media

Abstract >>
A mathematical model of motion of solid particles withselective permeability and a mixture of moving gases is developedwith the use of averaging principles of mechanics of multiphase media.The derived system of quasi-linear partial differential equations isstudied for a particular one-dimensional isothermal case.



2.
COMPUTATION OF WAVE INTERFERENCE AND RELAXATION OF PARTICLES AFTER PASSING OF A SHOCK WAVE

I. A. Bedarev, A. V. Fedorov
Khristianovich Institute of Theoretical and AppliedMechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: ударные волны, скоростная и тепловая релаксация частиц, численноемоделирование, shock waves, thermal and velocity relaxation of particles, numericalsimulations

Abstract >>
Interaction of a shock wave with a system of motionlessor relaxing particles is numerically simulated. Regimes of the gas flowaround these particles are described, and the influence of the initialparameters of the examined phenomenon on the flow pattern is analyzed.The drag coefficient of particles is calculated as a function of theMach number behind the shock wave at a fixed Reynolds number. Thedynamics of heat exchange for particles of different sizes(10$\mu$m--1mm) is determined, and the laws of thermal relaxationafter passing of a shock wave over the system of particles are found.The times of thermal and velocity relaxation of particles are estimatedas functions of the Reynolds number, and the predicted relaxation timeis compared with the corresponding empirical dependences.



3.
ENGINEERING MODELING OF THE LAMINAR–TURBULENT TRANSITION: ACHIEVEMENTS AND PROBLEMS (REVIEW)

A. V. Boiko, S. V. Kirilovskiy, A. A. Maslov, T. V. Poplavskaya
Khristianovich Institute of Theoretical and AppliedMechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: пограничный слой, ламинарно-турбулентный переход, газодинамическиепакеты, моделирование, boundary layer, laminar--turbulent transition, gas-dynamicsoftware packages, simulation

Abstract >>
Currently available methods of computing thelaminar--turbulent transition (LTT), including methods used ingas-dynamic software packages, are analyzed from the viewpoint of LTTsimulation accuracy.



4.
VORTICAL STRUCTURES BEHIND A TRANSVERSE JET IN A SUPERSONICFLOW AT HIGH JET TO CROSSFLOW PRESSURE RATIOS

A. O. Beketaeva1, P. Bruel2, A. Zh. Naimanova1
1Institute of Mathematics at the Ministry of Education andSciences of the Kazakhstan Republic, Alma-Ata, 050010 Kazakhstan
2National Center of ScientificResearch (CNRS), Pau, France
Keywords: численное моделирование, сверхзвуковое течение, совершенный газ, пограничный слой, уравнения Навье--- Стокса, параметрнерасчетности, ударнаяволна, numericalsimulation, supersonic flow, perfect gas, boundary layer, Navier--Stokes equations, jet pressure ratio, shock wave

Abstract >>
A three-dimensional supersonic turbulent flow withsymmetric normal injection of circular jets from the channel walls isnumerically simulated. The initial Favre-averaged Navier-Stokesequations closed by the $k$--$\omega$ turbulence model are solved by analgorithm based on an ENO scheme. The mechanism of the formation ofvortical structures due to the interaction of the jet with the freestream is studied for jet to crossflow total pressure ratios rangingfrom 3 to 50. It is known from experiments reported in the literaturethat, for $n\ge 10$, mixing of the jet with the high-velocity flowleads to the formation of a pair of vortices and of an additionalseparation zone near the wall behind the jet. It is demonstrated thatthe present numerical results are consistent with such findings andthat the pressure distribution on the wall ahead of the jet in theplane of symmetry is also in reasonable agreement with availableexperimental data.



5.
NUMERICAL SIMULATION OF THE INTERACTION OF A TRANSVERSE JET WITH SUPERSONIC FLOW USING DIFFERENT TURBULENCE MODELS

K. N. Volkov, V. N. Emelyanov, M. S. Yakovchuk
Ustinova Voenmech Baltic State Technical University, St.Petersburg190005, Russia
dsci@mail.ru
Keywords: сверхзвуковой поток, струя, вдув, турбулентность, ударнаяволна, численноемоделирование, supersonic flow, jet, injection, turbulence, shock wave, numerical modeling

Abstract >>
This paper presents a numerical simulation of the flowresulting from transverse jet injection into a supersonic flow througha slot nozzle, at different pressures in the injected jet and mainflow. Calculations on grids with different resolutions use theSpalart--Allmaras turbulence model, the $k$--$\varepsilon$ model,the $k$--$\omega$ model and the SST model. Based on a comparison ofthe calculated and experimental data on pressure distribution on thewall, the length of the recirculation area and depth of penetration ofthe jet in the supersonic flow, conclusions are made about the accuracyof the calculation results of the different turbulence models and theapplicability of these models for solving similar problems.



6.
FUNCTIONAL MATHEMATICAL MODEL OF A HYDROGEN-DRIVEN COMBUSTION CHAMBER FOR A SCRAMJET

A. F. Latypov
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
latypov@itam.nsc.ru
Keywords: гиперзвуковой прямоточный воздушно-реактивный двигатель, водород, камера горения, эксергия, scramjet, hydrogen, combustion chamber, exergy

Abstract >>
A functional mathematical model of a hydrogen-driven combustion chamber for a scramjet is described. The model is constructed with the use of one-dimensional steady gas-dynamic equations and parametrization of the channel configuration and the governing parameters (fuel injection into the flow, fuel burnout along the channel, dissipation of kinetic energy, removal of some part of energy generated by gases for modeling cooling of channel walls by the fuel) with allowance for real thermophysical properties of the gases. Through parametric calculations, it is found that fuel injection in three cross sections of the channel consisting of segments with weak and strong expansion ensures a supersonic velocity of combustion products in the range of free-stream Mach numbers $\mboxM_\infty = 6\mbox--12$. It is demonstrated that the angle between the velocity vectors of the gaseous hydrogen flow and the main gas flow can be fairly large in the case of distributed injection of the fuel. This allows effective control of the mixing process. It is proposed to use the exergy of combustion products as a criterion of the efficiency of heat supply in the combustion chamber. Based on the calculated values of exergy, the critical free-stream Mach number that still allows scramjet operation is estimated.



7.
MULTIRAIL ELECTROMAGNETIC LAUNCHER POWERED FROM A PULSED MAGNETOHYDRODYNAMIC GENERATOR

A. G. Afonin1, V. G. Butov1, V. P. Panchenko2, S. V. Sinyaev1, V. A. Solonenko1, G. A. Shvetsov3, A. A. Yakushev2
1Institute of Applied Mathematics and Mechanics, Tomsk, 634050 Russia
aag@niipmm.tsu.ru
2Troitsk Institute for Innovation and Fusion Research, Troitsk, 142190 Russia
panchvictor@gmail.com
3Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
shvetsov@hydro.nsc.ru
Keywords: магнитогидродинамический генератор, многорельсовый ускоритель, циклическая нагрузка, математическая модель, совместный расчет, сверхзвуковое безударное течение, вольт-ампернаяхарактеристика, гистерезис, magnetohydrodynamic generator, multirail launcher, cyclic load, mathematical model, simultaneous calculation, supersonic shock-free flow, current--voltage characteristic, hysteresis

Abstract >>
The operation of an electromagnetic multirail launcher of solids powered from a pulsed magnetohydrodynamic (MHD) generator is studied. The plasma flow in the channel of the pulsed MHD generator and the possibility of launching solids in a rapid-fire mode of launcher operation are considered. It is shown that this mode of launcher operation can be implemented by matching the plasma flow dynamics in the channel of the pulsed \hboxMHD generator and the launching conditions. It is also shown that powerful pulsed MHD generators can be used as a source of electrical energy for rapid-fire electromagnetic rail launchers operating in a burst mode.



8.
WAVE FLOWS INITIATED BY VERTICAL LIFTING OF A RECTANGULAR BEAM FROM SHALLOW WATER

V. V. Kuznetsova1,2, V. V. Ostapenko1,2
1Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
qznetsova-v@yandex.ru
2Novosibirsk State University, Novosibirsk, 630090 Russia
ostapenko_vv@ngs.ru
Keywords: вертикальный подъем бруса из мелкой воды, длинноволновое приближение, численное моделирование внешнего течения, vertical lifting of beam from shallow water, long-wavelength approximation, numerical simulation of external flow

Abstract >>
Theproblemofflowsinitiatedbyvertical lifting of a rectangular beam partially submerged in shallow water filling a rectangular prismatic channel with a horizontal bottom is studied in the long-wavelength approximation. The width of the beam is equal to the channel width, and its upper and lower planes are parallel to the channel bottom. In the first stage of the flow, the lower surface of the low beam is completely submerged in the liquid, which is lifted after it by hydrostatic pressure. Conditions for the well-posedness of this problem are obtained, and solutions describing the liquid flow in the region adjacent to the bottom surface of the beam and in outer regions with a free upper boundary are constructed for different laws of lifting of the beam.



9.
GAS-DYNAMIC DESIGN OF ANAXISYMMETRIC TUNNEL AIR IN LET WITH ISENTROPIC COMPRESSION

V. M. Galkin1, D. A. Vnuchkov2, V. I. Zvegintsev2
1Tomsk Polytechnical University, Tomsk, 634050 Russia
vlg@tpu.ru
2Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
vnuchkov@itam.nsc.ru
Keywords: сверхзвуковое течение, туннельный осесимметричный воздухозаборник, уравнения Эйлера, метод характеристик, изоэнтропическоерасширение, вязкоетечение, supersonic flow, axisymmetric tunnel air inlet, Euler equations, method of characteristics, isentropic expansion, viscous flow

Abstract >>
A method of designing a supersonic axisymmetric tunnel air inlet based on the problem of an inverted flow in an annular nozzle with isentropic expansion is considered. The nozzle contour is constructed by the method of characteristics. Parameters of one inlet for viscous and inviscid gas flows are calculated.



10.
REFLECTION AND REFRACTION OF ACOUSTIC WAVES AT THE INTERFACE BETWEEN A GAS AND A DISPERSE SYSTEMS

V. Sh. Shagapov1,2, V. V. Sarapulova2
1Institute of Mechanics and Engineering, Kazan' Scientific Center, Kazan', 420111 Russia
Shagapov@rambler.ru
2Birsk Branch of Bashkir State University, Birsk, 452450 Russia
Vero_nika_09@mail.ru
Keywords: акустика парогазокапельной смеси, коэффициенты отражения и преломления, полное прохождение, полное внутреннее отражение, волновод, acoustic vapor-gas-droplet mixture, reflection and refraction indices, total transmission, total internal reflection, waveguide

Abstract >>
The reflection and refraction of acoustic waves at different angles of incidence on the interface between a vapor--gas--droplet system and air are studied. From an analysis of analytical solutions, it has been found that in the case of incidence on the interface from the side of the vapor--gas--droplet medium, there is a critical angle of incidence at which the wave is completely reflected from the boundary, i.e., total internal reflection takes place. It is shown that for a certain angle of incidence on the interface both from the air side and from the mixture side and for a certain volume fraction of water in the disperse system, complete transmission of the acoustic wave through the medium is observed.



11.
DEVELOPMENT OF COMPLEX ANALYSIS METHODS IN FILTRATION THEORY PROBLEMS

V.N. Emikh
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
emikh@hydro.nsc.ru
Keywords: коэффициент фильтрации, критический режим, параметры конформных отображений, локальная депрессия, передислокация подвижных особых точек, линза (кайма) пресных вод, filtration coefficient, critical regime, parameters of conformal mappings, local depression, relocation of moving singular points, fresh water lens (fringe)

Abstract >>
This paper is a review of studies carried out on the basis of two-dimensional boundary-value problems of filtration theory. The role of critical regimes determining the specifics of filtration flows with moving boundaries is noted.



12.
PHENOMENOLOGICAL APPROACH TO SIMULATING HYDRAULIC FRACTURING OF A STRATUM

V.I. Pen'kovskii, N.K. Korsakova
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
penkov@hydro.nsc.ru
Keywords: гидравлический разрыв, трещиновато-пористая среда, квазистационарноеприближение, совместностьдеформаций, hydraulic fracturing, fractured porous medium, quasi-steady approximation, strain compatibility

Abstract >>
A mathematical model for hydraulic fracturing is proposed. The model is based on the presentation of the fractured portion of the stratum adjacent to the well as a heterogeneous fractured porous medium. Assumptions usually used in the theory of elastic flow are applied. Formulas for determining the size of the hydraulic fracturing zone and the degree of fracture opening under conditions of relative equilibrium are derived.



13.
GAS FILTRATION FROM AN UNDERGROUND RESERVOIR AT A LARGE INITIAL PRESSURE GRADIENT

T. P. Miroshnichenko1, N. A. Lutsenko1,2, V. A. Levin1,2
1Far Eastern Federal University, Vladivostok, 690950 Russia
taisia.miroshnichenko@gmail.com
2Institute of Automation and Control Processes, Far Eastern Branch, Russian Academy of Sciences, Vladivostok, 690041 Russia
nickl@inbox.ru
Keywords: фильтрация газа, взрыв газа, бародиффузия, gas filtration, gas explosion, barodiffusion

Abstract >>
Gas filtration from an underground reservoir through a layer of a porous medium due to an instantaneous increase in the gas pressure in the reservoir is studied. The problem is considered in a one-dimensional formulation in the general case where the temperatures of the gas and the porous medium are different and unstable, and in the case of a high specific heat of the solid phase and a high interfacial heat-transfer rate. The dynamics of the gas flow at the inlet and outlet of the underground reservoir is analyzed, the time of unloading of the system is estimated as a function of the permeability of the porous medium. It is shown that, depending on the properties of the porous layer, two characteristic gas flow regimes are possible: a fast discharge regime and a slow regime which is determined mainly by barodiffusion.



14.
EXPERIMENTAL STUDY OF HEAT TRANSFER DUE TO INTERACTION OF TWO SEPARATED FLOWS OF DIFFERENT SCALES

V. I. Terekhov, I. Ya. Smul'skii
Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
terekhov@itp.nsc.ru
Keywords: турбулентный поток, отрывное течение, обратный уступ, теплообмен, turbulent flow, separated flow, backward-facing step, heat transfer

Abstract >>
This paper describes an experimental study of heat transfer in a channel behind a backward-facing step in the presence of a disturbance in front of it in the form of a single rib in the range of the Reynolds numbers $\Re = 5000\mbox--15\,000$. The influence of the rib position and height on heat transfer intensity behind the backward-facing step is investigated. It is shown that reattachment of the flow disturbed by the obstacle intensifies the heat transfer on the surface behind the backward-facing step.



15.
CHEMICALLY REACTIVE HYDROMAGNETIC FLOW OF A SECOND-GRADE FLUID IN A SEMI-POROUS CHANNEL

Z. Abbas1, B. Ahma2, S. Ali1
1Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan
2Department of Mathematics, Faculty of Basic Sciences, University of Wah, Wah, Pakistan
Keywords: неньютоновская жидкость, магнитогидродинамическое течение, полупористый канал, химическая реакция, non-Newtonian fluid, MHD flow, semi-porous channel, chemical reaction

Abstract >>
An analysis of a second-grade fluid in a semi-porous channel in the presence of a chemical reaction is carried out to study the effects of mass transfer and magnetohydrodynamics. The upper wall of the channel is porous, while the lower wall is impermeable. The basic governing flow equations are transformed into a set of nonlinear ordinary differential equations by means of a similarity transformation. An approximate analytical solution of nonlinear differential equations is constructed by using the homotopy analysis method. The features of the flow and concentration fields are analyzed for various problem parameters. Numerical values of the skin friction coefficient and the rate of mass transfer at the wall are found.



16.
EFFECT OF NANOPARTICLES ON THE STRUCTURE AND PROPERTIES OF AN ALUMINUM ALLOY POURED INTO A MOULD WITH THE USE OF A MAGNETOHYDRODYNAMIC DISK PUMP

S. S. Katsnelson, G. A. Pozdnyakov, A. N. Cherepanov
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
savelii@itam.nsc.ru
Keywords: расплав металла, магнитогидродинамический насос, наномодификаторы, структуралитыхсплавов, metal melt, magnetohydrodynamic pump, nanomodifiers, structure of cast alloys

Abstract >>
The influence of two nanomodifiers with different compositions during their homogenization in the AL7 aluminum melt and moulding on the properties of the modified aluminum alloy is studied. Experiments are performed with the use of a centrifugal conductive magnetohydrodynamic pump. The melt is poured into a graphite mould with three cylindrical channels 38 mm in diameter and 160 mm long, which are designed for a metal mass of 500g. Two compositions are used as modifying agents: nano-scale particles of the aluminum nitride powder 40--100nm in size and metallized carbon nanotubes smaller than 25 nm, which are clad with aluminum to improve wetting of their surface. The analysis of the structure of the experimental and reference samples shows that the use of modifiers leads to refinement of the grain structure of the cast metal. According to the Hall--Petch theory, this effect may result in improvement of mechanical characteristics of the cast metal.



17.
MICROSTRUCTURE OF THE POISEUILLE FLOW IN A MODEL NANOFLUID BY MOLECULAR DYNAMICS SIMULATION

N. Razmara
Department of Mechanical Engineering, Azarbaijan Shahid Madani University, Tabriz, Iran
N.razmara@azaruniv.edu
Keywords: кластеризация, молекулярная динамика, наножидкость, наноканал, течениеПуазейля, clustering effect, molecular dynamics, nanofluid, nanochannel, Poiseuille flow

Abstract >>
The microscopic behavior of nanofluids in the Poiseuille flow in a nanochannel is examined by means of molecular dynamics simulation through visual observations and statistic analysis. For nanofluid flows inside the nanochannel, a clustering effect is observed during the time evolution of the system. The cluster moves along the centerline of the nanochannel due to the maximum velocity in the middle part of the Poiseuille flow. The attractive force is believed to be the primary culprit behind the agglomeration of nanoparticles.



18.
MODEL OF A THERMO-ELASTIC--INELASTIC PROCESS WITH LARGE DEFORMATIONS AND STRUCTURAL CHANGES IN MATERIAL

A.A. Rogovoi
Institute of Continuous Media Mechanics, Ural Branch, Russian Academy of Sciences, Perm', 614013 Russia
rogovoy@icmm.ru
Keywords: конечные деформации, определяющее уравнение, уравнение теплопроводности, термодинамика, структурные изменения, модель адиабатическогопроцесса, finite strain, constitutive equation, heat-conduction equation, thermodynamics, structural changes, model of adiabatic process

Abstract >>
The dependence of a scalar measure of the structural changes occurring in a material under plastic deformation on a plastic strain measure and the dependence of a free energy measure on a structural change measure are constructed using experimental data that allow the expended plastic work to be divided into a latent part and a thermal part. The obtained dependences, kinematic relations, a constitutive equation, and a heat-conduction equation that satisfy the principles of thermodynamics and objectivity are used to construct a model of thermo-elastic--inelastic processes in the presence of finite deformations and structural changes in the material. The model is tested on the problem of temperature changes in the process of adiabatic elastic--plastic compression, which has experimental support.



19.
PROGRAM OF EXPERIMENTS TO DETERMINE THE TYPE OF INITIAL ELASTIC ANISOTROPY OF MATERIAL

M.Yu. Sokolova, D.V. Khristich
Tula State University, Tula, 300012 Russia
socolova-m-u@yandex.ru
Keywords: упругость, анизотропныематериалы, эксперимент, elasticity, anisotropic materials, experiment

Abstract >>
A program of experiments to identify the type of elastic anisotropy of material is proposed. The position of the principal axes of material anisotropy is determined by measuring the strains resulting from compression of a cubic sample along three of its faces. For the subsequent identification of the type of anisotropy, samples oriented along definite principal axes are used.



20.
STRESS--STRAIN STATE OF ICE COVER DURING AIRCRAFT TAKEOFF AND LANDING

A. V. Pogorelova1, V. M. Kozin2, A. A. Matyushina3
1Institute of Engineering and Metallurgy, Far Eastern Branch, Russian Academy of Sciences, Komsomol'sk-on-Amur, 681005 Russia
milova@yandex.ru
2Komsomol'sk-on-Amur State Technical University, Komsomol'sk-on-Amur, 681013 Russia
kozinvictor@rambler.ru
3Amur Humanitarian and Pedagogical State University, Komsomol'sk-on-Amur, 681000 Russia
amatiushina@gmail.com
Keywords: несжимаемая жидкость, упругая пластина, нестационарное движение, самолет, incompressible liquid, elastic plate, unsteady motion, aircraft

Abstract >>
We consider the linear unsteady motion of an IL-76TD aircraft on ice. Water is treated as an ideal incompressible liquid, and the liquid motion is considered potential. Ice cover is modeled by an initially unstressed uniform isotropic elastic plate, and the load exerted by the aircraft on the ice cover with consideration of the wing lift is modeled by regions of distributed pressure of variable intensity, arranged under the aircraft landing gear. The effect of the thickness and elastic modulus of the ice plate, takeoff and landing regimes on stress-strain state of the ice cover used as a runway.



21.
FLOWS, STRAINS, AND THE FORMATION OF JOINTS IN OBLIQUE COLLISION OF METAL PLATES

A. A. Shtertser, B. S. Zlobin
Design and Engineering Branch of the Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
asterzer@mail.ru
Keywords: косое соударение, струйное течение, локализация деформации, очищениеповерхности, схватывание, oblique collision, jet flow, strain localization, surface cleaning, seizure

Abstract >>
The processes of high-velocity oblique collision of metal plates which lead to the formation of their joints (seizure) are considered. It is found that the cleaning of the plate surface necessary for seizure results from a jet flow (particle stream), whose source is at least one of the welded materials or an interlayer of ductile material located in the initial region of collision. It is shown that additional cleaning may occur due to the emergence of rotating microregions in intense gradient flows localized in the joint area; seizure on cleaned surfaces is due to reduction of the surface energy of the system.