

Home – Home – Jornals – Journal of Applied Mechanics and Technical Physics 2018 number 1
2018 year, number 1
I. K. Gimaltdinov^{1}, M. V. Stolpovskii^{1}, M. K. Khasanov^{2}
^{1}Ufa State Oil Technical University, Ufa, 450062 Russia ^{2}Bashkir State University, Sterlitamak, 453103 Russia
Keywords: пористая среда, газовый гидрат, фильтрация, porous medium, gas hydrate, filtration
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This paper presents a mathematical model for the methane hydratecarbon dioxide replacement by injection of carbon dioxide into a porous medium rich in methane and its gas hydrates. Numerical solutions describing the pressure and temperature variations in a reservoir of finite length are obtained. It is shown that the replacement process is accompanied by reducing the pressure and increasing the temperature of the porous medium. It is established that during the time of complete replacement of methane from a reservoir decreases with increasing permeability of the porous medium and the pressure of the injected gas.

D. Yu. Gerasimov, A. A. Sivkov
Tomsk Polytechnic University, Tomsk, 634050, Russia
Keywords: гибридный коаксиальный магнитоплазменный ускоритель, метание твердых тел, канал формирования плазменной структуры, газогенерирующее вещество, hybrid coaxial magnetoplasma accelerator, acceleration of solids, plasma structure formation channel, gasgenerating material
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It is shown that in a hybrid coaxial magnetoplasma accelerator with a channel length of 350 mm and a diameter of 23 mm, the acceleration velocity and the energy conversion efficiency increase as the length of the channel plasma structure formation filled with a gas generating material decreases from 17 to 9 mm. It is found that as the gas generating material, it is advisable to use paraffin which has a less significant deionizing effect on a highcurrent arc discharge and thus causes a less significant decrease in discharge current intensity and an increase in conductive and inductive electrodynamic forces.

A. M. Lipanov, S. A. Karskanov, A. I. Karpov
Institute of Mechanics, Ural Branch, Russian Academy of Sciences, Izhevsk, 426067 Russia
Keywords: supersonic flow, NavierStokes equations, highorder approximation, direct numerical simulation, base drag
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A supersonic flow in the near wake behind a cylinder is considered. Pressure distributions in the base region behind a circular cylinder for various Mach numbers M_{∞} are obtained and analyzed by means of direct numerical simulation based on highorder approximation algorithms. For M_{∞} = 2.46, the results obtained in the present study are compared with available experimental and numerical data. Generation of turbulent kinetic energy is calculated for various Mach numbers.

V. G. Kozlov, S. V. Subbotin
Perm State Humanitarian Pedagogical University, Perm, 614000 Russia
Keywords: вращение, внутреннее ядро, колебания, осредненное течение, дифференциальное вращение, инерционные волны, rotation, inner core, oscillations, steady flow, differential rotation, inertial waves
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Steady flow generated by oscillations of an inner solid core in a fluidfilled rotating spherical cavity is experimentally studied. The core with density less than the fluid density is located near the center of the cavity and is acted upon by a centrifugal force. The gravity field directed perpendicular to the rotation axis leads to a stationary displacement of the core from the rotation axis. As a result, in the frame of reference attached to the cavity, the core performs circular oscillations with frequency equal to the rotation frequency, and its center moves along a circular trajectory in the equatorial plane around the center of the cavity. For the differential rotation of the core to be absent, one of the poles of the core is connected to the nearest pole of the cavity with a torsionally elastic, flexible fishing line. It is found that the oscillations of the core generate axisymmetric azimuthal fluid flow in the cavity which has the form of nested liquid columns rotating with different angular velocities. Comparison with the case of a free oscillating core which performs averaged differential rotation suggests the existence of two mechanisms of flow generation (due to the differential rotation of the core in the Ekman layer and and due to the oscillations of the core in the oscillating boundary layers).

A. M. Blokhin^{1,2}, R. E. Semenko^{1,2}
^{1}Novosibirsk State University, Novosibirsk, 630090 Russia ^{2}Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: полимерная жидкость, плоский клин, стационарное обтекание клина, сильный разрыв, polymer fluid, flat wedge, steady flow past a wedge, strong discontinuity
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A problem of an incompressible polymer fluid flow past an infinite flat wedge is considered. The flow moves parallel to the plane of symmetry of the wedge and normal to the wedge rib. It is demonstrated that two surfaces of strong discontinuities are needed for the noslip condition to be satisfied on the wedge surface. Steady solutions of the problem are studied, and the flow is shown to be asymmetric with respect to the plane of symmetry of the wedge.

V. E. Zalizniak^{1,2}, O. A. Zolotov^{1,2}, I. I. Ryzhkov^{2}
^{1}Institute of Mathematics and Fundamental Informatics Siberian Federal University, Krasnoyarsk 660041, Russia ^{2}Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, 660036 Russia
Keywords: ионный раствор, потенциал взаимодействия, молекулярная динамика, ionic solution, interaction potential, molecular dynamics
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A model of ionic solutions is proposed which can be used to calculate aqueous salt solutions in different nanostructures. The model interaction potential includes the LennardJones potential and angularly averaged dipoledipole and iondipole interactions. LennardJones potential parameters for different ions are obtained. Characteristics of aqueous solutions at various salt concentrations are calculated using the molecular dynamics method. It is shown that the calculated parameters of the hydration shells of ions are in good agreement with the theoretical and experimental data at a salt concentration of 1 mol/kg. The computational scheme used in the calculations is described. It is shown that calculations using the proposed model require less computing resources compared with the conventional models of ionic solutions.

Yu. Ya. Trifonov
Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: вязкое течение пленок, нелинейные волны, устойчивость, viscous film flow, nonlinear waves, stability
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Linear stability of liquid and gas counterflows in an inclined channel is considered. The full NavierStokes equations for both phases are linearized, and the dynamics of periodic disturbances is determined by means of solving a spectral problem in wide ranges of Reynolds numbers for the liquid and vapor velocity. Two unstable modes are found in the examined ranges: surface mode (corresponding to Kapitsa waves at small velocities of the gas) and shear mode in the gas phase. The wave length and the phase velocity of neutral disturbances of both modes are calculated as functions of the Reynolds number for the liquid. It is shown that these dependences for the surface mode are significantly affected by the gas velocity.

A. I. Filippov, O. V. Akhmetova, A. A. Kovalskii
Sterlitamak Branch of Bashkir State University, Sterlitamak, 453100, Russia
Keywords: течение газа, газовая скважина, температурное поле, асимптотический метод, ламинарный режим течения, gas flow, gas well, temperature field, asymptotic method, laminar flow regime
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This paper describes the problem of determining the temperature of laminar gas flow, in which the equation of convective heat transfer contains two variable coefficients, is reduced to nonclassical problems for zero and first asymptotic expansion coefficient with respect to a formal parameter. The Laplace  Carson transform are used to obtain analytical expressions for the temperature field of ascending laminar gas flow in a well with account for the relationships of density and velocity with spatial coordinates in zero and first asymptotic approximations. Expressions for the temperature asymptotically averaged along the cross section of the well and temperature distributions over the crosssectional radius are obtained.

M. Babaelahi
University of Qom, Qom, Iran
Keywords: метод гомотопических возмущений, жидкость второго порядка, сужающийся канал, уравнение для скорости, homotopy perturbation method (HPM), secondgrade fluid, converging channel, velocity equation
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The problem of a twodimensional steady flow of a secondgrade fluid in a converging porous channel is considered. It is assumed that the fluid is injected into the channel through one wall and sucked from the channel through the other wall at the same velocity, which is inversely proportional to the distance along the wall from the channel origin. The equations governing the flow are reduced to ordinary differential equations. The boundaryvalue problem described by the latter equations is solved by the homotopy perturbation method. The effects of the Reynolds and crossflow Reynolds number on the flow characteristics are examined.

E. A. Kochurin
Institute of Electrophysics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620016, Russia
Keywords: свободная поверхность, нелинейные волны, электрическое поле, электрогидродинамика, опрокидывание волн, жидкие диэлектрики, free surface, nonlinear waves, electric field, electrohydrodynamics, wave breaking, liquid dielectrics
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The nonlinear dynamics of the free surface of an ideal incompressible nonconducting fluid with a high dielectric constant subjected to a strong horizontal electric field is simulated using the method of conformal transformations. It is shown that at initial stages of interaction of counterpropagating periodic waves of significant amplitude, there is a direct energy cascade leading to energy transfer to small scales. This results in the formation of regions with a steep wave front at the fluid surface, in which the dynamic pressure and the pressure exerted by the electric field undergo a discontinuity. It has been demonstrated that the formation of regions with high gradients of electric field and fluid velocity is accompanied by breaking of surface waves; the inclination angles of the boundary tend to 90oC, and the surface curvature increases without bound.

A. E. Zarvin, A. S. Yaskin, V. V. Kalyada
Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: сверхзвуковая струя, кластерообразование, электроннопучковая визуализация, supersonic jet, clusterization, electron beam visualization
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Exhaustion of supersonic argon and nitrogen jets through sonic and supersonic nozzles into a rarefied submerged space at high stagnation pressures is studied experimentally. The shapes and sizes of the jets are visualized by means of detecting radiation excited in the considered flow by an electron beam. Dependences of the geometric parameters of the jets on exhaustion and clusterization conditions at low Reynolds numbers based on the reference size of the jet are obtained. It is found that the coefficient of proportionality between the size of the first “barrel” of the supersonic jet and the degree of jet expansion increases with an increase in the stagnation pressure. Empirical dependences of the proportionality coefficient on the size of clusters formed in supersonic flows are derived for the first time

F. Oueslati^{1,2}, B. BenBeya^{2}
^{1}AlBaha University, AlBaha, 6543, Kingdom of Saudi Arabia ^{2}University of Tunis ElManar, ElManar 2 2092, Tunis, Tunisia
Keywords: естественная конвекция, перенос тепла и массы, трехмерное течение, производство энтропии, наклонная камера, natural convection, heat and mass transfer, threedimensional flow, entropy generation, tilted enclosure
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Threedimensional thermosolutal natural convection and entropy generation within an inclined enclosure is investigated in the current study. A numerical method based on the finite volume method and a full multigrid technique is implemented to solve the governing equations. Effects of various parameters, namely, the aspect ratio, buoyancy ratio, and tilt angle on the flow patterns and entropy generation are predicted and discussed.

K. V. Berdnikov, V. V. Struzhanov
Institute of Engineering Science, Ural Branch, Russian Academy of Sciences, Ekaterinburg, 620049 Russia
Keywords: среда Генки, полярносимметричное деформирование, разупрочнение, метод простых итераций, сходимость, устойчивость, Hencky medium, polarsymmetric deformation, softening, method of simple iterations, convergence, stability
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This paper describes the problem of a stressstrain state arising from expansion of a spherical cavity under increasing internal pressure. The properties of a medium are described by a single curve with a descending section (Hencky medium with softening) under the condition of nonpositivity of volume deformation. An iteration procedure for calculation of equilibrium parameters is proposed. This procedure is based on the method of simple iterations. Numerical calculations confirming the developed technique are presented.

V. D. Borisov
Teplosnabzhenie, Belovo, 652612 Russia
Keywords: электромагнитное излучение, деформация, спектральновременной анализ, концентрационный критерий, пространственновременной анализ, логарифмическая масштабная инвариантность, electromagnetic radiation, deformation, spectraltemporal analysis, concentration criterion, spacetime analysis, logarithmic scale invariance
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This paper proposes a model for determining the characteristics of the evolution of the field of microcracks in a loaded rock sample by electromagnetic radiation signals. Calculations were made, whose results were summarized in the form of spacetime tables. Factors determining changes in the hierarchy of microcracks were established. The adequacy of the model was verified using the Zhurkov concentration criterion. Areas of scale invariance were revealed on graphs of the concentration of microcracks versus their size constructed on the logarithmic coordinates.

V. M. Kornev, A. G. Demeshkin
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: хрупкое и квазихрупкое разрушение, маломасштабная текучесть, необходимые и достаточные критерии разрушения, упругопластический материал, краевая трещина, Uобразный вырез, brittle and quasibrittle fracture, smallscale creep, necessary and sufficient criteria of fracture, elastoplastic material, edge crack, Ushaped cut
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A twoparameter (coupled) discreteintegral criterion of fracture is proposed. It can be used to construct fracture diagrams for compact specimens with sharp cracks. Curves separating the stresscrack length plane into three domains are plotted. These domains correspond to the absence of fracture, damage accumulation in the prefracture region under repeated loading, and specimen fragmentation under monotonic loading. Constants used for the analytical description of fracture diagrams for quasibrittle materials with cracks are selected with the use of approximation of the classical stressstrain diagrams for the initial material and the critical stress intensity factor. Predictions of the proposed theory are compared with experimental results on fracture of compact specimens with different radii made of polymethylmethacrylate (PMMA) and solid rubber with cracktype effects in the form of Ushaped cuts.

A. M. Bragov^{1}, A. Yu. Konstantinov^{1}, A. V. Kuznetsov^{2}, A. K. Lomunov^{1}, G. G. Savenkov^{2,3}
^{1}Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, 603950, Russia ^{2}Armalit Machinebuilding factory, St. Petersburg, 198097, Russia ^{3}St. Petersburg State Technological Institute, St. Petersburg, 190013, Russia
Keywords: скорость трещины, фрактальная размерность, динамическая трещиностойкость, crack velocity, fractal dimension, dynamic fracture toughness
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This paper presents the results of experimental studies of the crack propagation velocity and dynamic fracture toughness of St. 45 steel and D16T duralumin using a modified Kolsky method on a split Hopkinson bar. The results of microfractografic analysis of samples are given, and the fractal dimension is determined. The critical stress intensity factors are determine using the obtained fractal dimension values.

K. S. Bormotin^{1,2}, N. A. Taranukha^{1}
^{1}KomsomolskonAmur State Technical University, KomsomolskonAmur, 681013, Russia ^{2}Institute of Engineering and Metallurgy, Far East Branch, Russian Academy of Sciences, KomsomolskonAmur, 681005, Russia
Keywords: обратные задачи формообразования, вариационные неравенства, единственность, теория неполной обратимости деформации ползучести, сходимость, метод конечных элементов, итерационный метод, inverse problems of forming, variational inequalities, uniqueness, theory of incomplete reversibility of creep strain, convergence, finiteelement method, iterative method
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Functionals of direct and inverse problems of forming structural elementsare constructed taking into account the theory of incomplete reversibility of deformations. Formulations of these problems are given, and the uniqueness of their solutions is proved. An iterative method for solving inverse problems of forming structural elementsis proposed. Numerical solutions of these problems are obtained using a finite element method.

V. I. Rizov
University of Architecture, Civil Engineering and Geodesy, Sofia, 1046, Bulgaria
Keywords: балка, функциональноградиентный материал, линейная механика разрушения, аналитическое решение, functionally graded beam, linearelastic fracture mechanics, analytical approach
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An analytical study of delamination in the crack lap shear beam is performed. It is assumed that the material is functionally graded along the width and height of the beam. Delamination is studied in terms of the total strain energy release rate by applying methods of linearelastic fracture mechanics. An additional analysis of the total strain energy release rate is performed by considering the strain energies in the beam cross sections ahead of and behind the crack front for verification. The effects of the crack location and material gradient on delamination are evaluated.

S. Q. Hou, W. Wang, Z. Y. Wang, Z. W. Hu, K. Liu
Hefei University of Technology, Tunxi Road 193, Hefei, 230009, Anhui, China
Keywords: течение гранулированной среды, силовые цепочки, сдвиговая дилатансия, коэффициент нагрузки, коэффициент распределения, granular flow, force chains, shear dilatancy, loaddistribution rate
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In order to investigate the characteristics of force chains in a granular flow system, a parallel plate shear cell is constructed to simulate the shear movement of an infinite parallel plate and observe variations in relevant parameters. The shear dilatancy process is divided into three stages, namely, plastic strain, macroscopic failure, and granular recombination. The stickslip phenomenon is highly connected with the evolution of force chains during the shear dilatancy process. The loaddistribution rate curves and patterns of the force chains are utilized to describe the loadcarrying behaviors and morphologic changes of force chains separately. Force chains, namely “diagonal gridding,” “tadpoleshaped,” and “pinnate,” are defined according to the form of the force chains in the corresponding three stages.

S. A. Piriev
Baku State University, Baku, AZ1148, Azerbaijan
Keywords: агрессивная среда, концентрация агрессивной среды, интенсивность напряжений, повреждаемость, разрушение, aggressive medium, concentration of an aggressive medium, stress intensity, damageability, fracture
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This paper describes the study of scattered fracture of a thickwalled pipe filled with an aggressive medium, which creates uniform pressure on the inner surface of the pipe. It is assumed that the aggressive medium affects only the value of instantaneous strength. Damageability is described by an integral operator of the hereditary type. The problem is solved with allowance for residual strength of the pipe material behind the fracture front. Numerical calculation is carried out, and relationships between the fracture front coordinate and time for various concentrations of the aggressive medium and residual strength behind the fracture front are constructed.

V. M. Tikhomirov, A. S. Samoshkin
Siberian State Transport University, Novosibirsk, 630049, Russia
Keywords: армированный бетон, упругопластический материал, контактный слой, численное моделирование, разрушение бетона, reinforced concrete, elastoplastic material, contact layer, numerical modeling, fracture of concrete
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This paper describes the study of deformation of reinforced concrete. A mathematical model for the interaction of reinforcement with concrete, based on the introduction of a contact layer, whose mechanical characteristics are determined from the experimental data, is developed. The limiting state of concrete is described using the Drucker  Prager theory and the fracture criterion with respect to maximum plastic deformations. A series of problems of the theory of reinforced concrete are solved: stretching of concrete from a centralreinforced prism and prestressing of concrete. It is shown that the results of the calculations are in good agreement with the experimental data.

Ch. K. Rao^{1}, L. B. Rao^{2}
^{1}Nalla Narsimha Reddy Engineering College, Chowdariguda, 500088, India ^{2}School of Mechanical and Building Sciences, Chennai, 600127, India
Keywords: балка, открытый профиль сечения, закритическое поведение, скручивание, основание Винклера  Пастернака, beam, open section, postbuckling, warping, WinklerPasternak foundation
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The problem of the postbuckling response of a simply supported thinwalled beam subjected to an axial compressive load and supported by the WinklerPasternak foundation is studied in this paper. The strains are assumed to be small and elastic. The shear deformations and the inplane crosssectional deformations are assumed to be negligible. The postbuckling paths of the simply supported beam are determined for different values of the Winkler and Pasternak stiffness parameters. Bifurcation points are found.

