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Journal of Applied Mechanics and Technical Physics

2018 year, number 1

Recovery of Methane from Gas Hydrates in a Porous Medium by Injection of Carbon Dioxide

I. K. Gimaltdinov1, M. V. Stolpovskii1, M. K. Khasanov2
1Ufa State Oil Technical University, Ufa, 450062 Russia
2Bashkir State University, Sterlitamak, 453103 Russia
Keywords: пористая среда, газовый гидрат, фильтрация, porous medium, gas hydrate, filtration

Abstract >>
This paper presents a mathematical model for the methane hydrate-carbon 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.

Increase in the Efficiency of Methane Solids Vac Hybrid Coaxial Magnetoplasma Accelerator

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, gas-generating material

Abstract >>
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 high-current arc discharge and thus causes a less significant decrease in discharge current intensity and an increase in conductive and inductive electrodynamic forces.

Direct Numerical Simulation of a Supersonic Flow in the Base Region of a Circular Cylinder

A. M. Lipanov, S. A. Karskanov, A. I. Karpov
Institute of Mechanics, Ural Branch, Russian Academy of Sciences, Izhevsk, 426067 Russia
Keywords: supersonic flow, Navier-Stokes equations, high-order approximation, direct numerical simulation, base drag

Abstract >>
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 high-order 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.

Steady Flows Generated by a Core Oscillating in a Rotating Spherical Cavity

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

Abstract >>
Steady flow generated by oscillations of an inner solid core in a fluid-filled 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).

Incompressible Polymer Fluid Flow Past a Flat Wedge

A. M. Blokhin1,2, R. E. Semenko1,2
1Novosibirsk State University, Novosibirsk, 630090 Russia
2Sobolev 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

Abstract >>
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 no-slip 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.

Effective Molecular Dynamics Model of Ionic Solutions for Large-Scale Calculations

V. E. Zalizniak1,2, O. A. Zolotov1,2, I. I. Ryzhkov2
1Institute of Mathematics and Fundamental Informatics Siberian Federal University, Krasnoyarsk 660041, Russia
2Institute 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

Abstract >>
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 Lennard-Jones potential and angularly averaged dipole-dipole and ion-dipole interactions. Lennard-Jones 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.

Calculation of Linear Stability of a Stratified Gas-Liquid Flow in an Inclined Plane Channel

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

Abstract >>
Linear stability of liquid and gas counterflows in an inclined channel is considered. The full Navier-Stokes 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.

Coefficient-by-Coefficient Averaging in a Problem of Laminar Gas Flow in a Well

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

Abstract >>
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 cross-sectional radius are obtained.

Analytic Approximate Solution for a Flow of a Second-Grade Viscoelastic Fluid in a Converging Porous Channel

M. Babaelahi
University of Qom, Qom, Iran
Keywords: метод гомотопических возмущений, жидкость второго порядка, сужающийся канал, уравнение для скорости, homotopy perturbation method (HPM), second-grade fluid, converging channel, velocity equation

Abstract >>
The problem of a two-dimensional steady flow of a second-grade 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 boundary-value 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.

Formation of Regions with High Energy and Pressure Gradients at the Free Surface of a Liquid Dielectric in a Tangential Electric Field

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

Abstract >>
The nonlinear dynamics of the free surface of an ideal incompressible non-conducting 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 counter-propagating 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.

Effect of Condensation on the Size of Strongly Underexpanded Jets Exhausting into a Rarefied Submerged Space

A. E. Zarvin, A. S. Yaskin, V. V. Kalyada
Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: сверхзвуковая струя, кластерообразование, электронно-пучковая визуализация, supersonic jet, clusterization, electron beam visualization

Abstract >>
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

Investigation of Heat and mass Transfer and Irreversibility Phenomena within a Three-Dimensional Tilted Enclosure for Different Shapes

F. Oueslati1,2, B. Ben-Beya2
1Al-Baha University, Al-Baha, 6543, Kingdom of Saudi Arabia
2University of Tunis El-Manar, El-Manar 2 2092, Tunis, Tunisia
Keywords: естественная конвекция, перенос тепла и массы, трехмерное течение, производство энтропии, наклонная камера, natural convection, heat and mass transfer, three-dimensional flow, entropy generation, tilted enclosure

Abstract >>
Three-dimensional 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.

Equilibrium State of a Reliable Elastoplastic Medium with an Expanding Spherical Cavity

K. V. Berdnikov, V. V. Struzhanov
Institute of Engineering Science, Ural Branch, Russian Academy of Sciences, Ekaterinburg, 620049 Russia
Keywords: среда Генки, полярно-симметричное деформирование, разупрочнение, метод простых итераций, сходимость, устойчивость, Hencky medium, polar-symmetric deformation, softening, method of simple iterations, convergence, stability

Abstract >>
This paper describes the problem of a stress-strain 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.

Determination of Micro-Interference Parameters by Signals of Their Electromagnetic Radiation

V. D. Borisov
Teplosnabzhenie, Belovo, 652612 Russia
Keywords: электромагнитное излучение, деформация, спектрально-временной анализ, концентрационный критерий, пространственно-временной анализ, логарифмическая масштабная инвариантность, electromagnetic radiation, deformation, spectral-temporal analysis, concentration criterion, space-time analysis, logarithmic scale invariance

Abstract >>
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 space-time 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.

Quasi-Brittle Fracture of Compact Specimens with Sharp Notches and U-Shaped Cuts

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, U-образный вырез, brittle and quasi-brittle fracture, small-scale creep, necessary and sufficient criteria of fracture, elastoplastic material, edge crack, U-shaped cut

Abstract >>
A two-parameter (coupled) discrete-integral criterion of fracture is proposed. It can be used to construct fracture diagrams for compact specimens with sharp cracks. Curves separating the stress-crack length plane into three domains are plotted. These domains correspond to the absence of fracture, damage accumulation in the pre-fracture region under repeated loading, and specimen fragmentation under monotonic loading. Constants used for the analytical description of fracture diagrams for quasi-brittle materials with cracks are selected with the use of approximation of the classical stress-strain 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 crack-type effects in the form of U-shaped cuts.

Relationship between the Crack Velocity, Fractal Dimension, and Dynamic Fracture Toughness of a Material

A. M. Bragov1, A. Yu. Konstantinov1, A. V. Kuznetsov2, A. K. Lomunov1, G. G. Savenkov2,3
1Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, 603950, Russia
2Armalit Machine-building factory, St. Petersburg, 198097, Russia
3St. Petersburg State Technological Institute, St. Petersburg, 190013, Russia
Keywords: скорость трещины, фрактальная размерность, динамическая трещиностойкость, crack velocity, fractal dimension, dynamic fracture toughness

Abstract >>
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.

Mathematical modeling of Inverse Problems of Forming Taking into Account the Incomplete Reversibility Creep Strain

K. S. Bormotin1,2, N. A. Taranukha1
1Komsomolsk-on-Amur State Technical University, Komsomolsk-on-Amur, 681013, Russia
2Institute of Engineering and Metallurgy, Far East Branch, Russian Academy of Sciences, Komsomolsk-on-Amur, 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, finite-element method, iterative method

Abstract >>
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.

Delamination in a Two-Dimensional Functionally Graded Beam

V. I. Rizov
University of Architecture, Civil Engineering and Geodesy, Sofia, 1046, Bulgaria
Keywords: балка, функционально-градиентный материал, линейная механика разрушения, аналитическое решение, functionally graded beam, linear-elastic fracture mechanics, analytical approach

Abstract >>
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 linear-elastic 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.

Force Chain Characteristics and Effects of a Dense Granular Flow System in a Third Body Interface during the Shear Dilatancy Process

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, load-distribution rate

Abstract >>
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 stick-slip phenomenon is highly connected with the evolution of force chains during the shear dilatancy process. The load-distribution rate curves and patterns of the force chains are utilized to describe the load-carrying behaviors and morphologic changes of force chains separately. Force chains, namely “diagonal gridding,” “tadpole-shaped,” and “pinnate,” are defined according to the form of the force chains in the corresponding three stages.

Long-Term Strength of a Thick-Walled Pipe Filled with an Aggressive Medium, with Account for Damageability of the Pipe Material and Residual Strength

S. A. Piriev
Baku State University, Baku, AZ-1148, Azerbaijan
Keywords: агрессивная среда, концентрация агрессивной среды, интенсивность напряжений, повреждаемость, разрушение, aggressive medium, concentration of an aggressive medium, stress intensity, damageability, fracture

Abstract >>
This paper describes the study of scattered fracture of a thick-walled 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.

Study of Interaction of Frame with Concrete by Numerical Methods

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

Abstract >>
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 central-reinforced prism and pre-stressing of concrete. It is shown that the results of the calculations are in good agreement with the experimental data.

Torsional Post-Buckling of a Simply Supported Thin-Walled Open-Section Beam Resting on a Two-Parameter Foundation

Ch. K. Rao1, L. B. Rao2
1Nalla Narsimha Reddy Engineering College, Chowdariguda, 500088, India
2School of Mechanical and Building Sciences, Chennai, 600127, India
Keywords: балка, открытый профиль сечения, закритическое поведение, скручивание, основание Винклера - Пастернака, beam, open section, post-buckling, warping, Winkler-Pasternak foundation

Abstract >>
The problem of the post-buckling response of a simply supported thin-walled beam subjected to an axial compressive load and supported by the Winkler-Pasternak foundation is studied in this paper. The strains are assumed to be small and elastic. The shear deformations and the in-plane cross-sectional deformations are assumed to be negligible. The post-buckling paths of the simply supported beam are determined for different values of the Winkler and Pasternak stiffness parameters. Bifurcation points are found.