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Journal of Applied Mechanics and Technical Physics

2020 year, number 4

Damped Natural Vibrations of Fluid in a Well Interfaced with a Reservoir

V. Sh. Shagapov1, R. A. Bashmakov2, G. R. Rafikova1, Z. Z. Mamaeva1
1Mavlutov Institute of Mechanics, Russian Academy of Sciences, Ufa, 450054 Russia
2Bashkir State University, Ufa, 450000 Russia
Keywords: собственные колебания, собственные частоты, гидроудар, скважина, фильтрация жидкости, затухающие колебания, natural vibrations, natural frequencies, water hammer, well, fluid filtration, damped vibrations

Abstract >>
We study the natural vibrations of the liquid column in a vertical oil well that occur during a sharp shutdown or opening of the well (water hammer). In this case, the period of vibrations and the intensity of their damping are determined not only by the length and diameter of the liquid column in the well and the rheological properties of the liquid, but also by the reservoir characteristics of the bottomhole formation zone (in particular, permeability coefficients, quality of well perforation and properties of the fractures formed). Solutions to the problem of natural damping vibrations of the liquid column in the well are found using a mathematical model describing the movement of the liquid column in the well and the filtration in the bottomhole zone. Characteristic equations for determining complex frequencies (frequency of vibration and damping coefficient) are obtained. The dependences of vibration frequency, damping coefficient and damping decrement on reservoir permeability values are studied; the amplitude of vibrations at different points of the well is found.

Influence of the Dissipative Properties of aqueous Foam on the dynamics of Shock Waves

R. Kh. Bolotnova, E. F. Gainullina
Mavlutov Institute of Mechanics, Russian Academy of Sciences, Ufa, 450054, Russia
Keywords: ударная волна, водная пена, пакет OpenFOAM, численное моделирование, shock wave, aqueous foam, OpenFOAM package, numerical modeling

Abstract >>
The shock wave (SW) propagation in an aqueous foam layer is investigated for the conditions of new published experimental data with visualization of the dynamics of the foam's volume liquid fraction under SW impact. A mathematical model has been developed that describes the behavior of the foam as a non-Newtonian fluid taking into account the effective Herschel-Bulkley viscosity, interfacial heat transfer processes according to the Ranz-Marshall model and realistic equations of state that describe the thermodynamic properties of aqueous foam components. The model is numerically implemented in the solver created by the authors in the OpenFOAM package. The influence of the behavior of the aqueous foam on the SW evolution is analyzed.

Wave Dynamics of Shell-Covered Inclusions in a Viscoelastic Medium

D. A. Gubaidullin, Yu. V. Fedorov
Institute of Mechanics and Mechanical Engineering, Kazan, 420111, Russia
Keywords: акустические волны, пузырьки газа, прослойка жидкости, вязкоупругая оболочка, модифицированное уравнение Рэлея - Ламба, межфазный теплообмен, дисперсионное уравнение, acoustic waves, gas bubbles, liquid interlayer, viscoelastic shell, modified Rayleigh-Lamb equation, interfacial heat transfer, dispersion equation

Abstract >>
A modified Rayleigh-Lamb equation is obtained, which takes into account the radial vibrations of a liquid drop that is covered by a viscoelastic shell, whose center contains a gas bubble, and which is placed in a viscoelastic medium. For the case of small vibrations of the inclusion, the heat transfer problem for gas, liquid phase, viscoelastic shell, and carrier liquid is solved. A dispersion equation is derived for a bubble medium. The influence of the inclusion shell and the viscoelasticity of the carrier phase on the dynamics of acoustic waves is investigated. Calculation results are compared with experimental data.

Waves in a Porous Medium with a Gas Hydrate Containing Layer

A. A. Gubaidullin1,2, O. Yu. Boldyreva1
1Tyumen the Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Tyumen, 625026, Russia
2Tyumen State University, Tyumen, 625003, Russia
Keywords: пористая среда, газовый гидрат, волны, отражение, porous medium, gas hydrate, waves, reflection

Abstract >>
This study describes the propagation of harmonic and pulsed waves in a layered porous medium, with one of its layers containing gas hydrate. It is shown that the resulting wave pattern makes it possible to predict the presence of a hydrate in a layer and its thickness provided that thermobaric conditions for the existence of the gas hydrate are fulfilled.

Viscous Interaction Forces of Two Pulsating Spheres in a Fluid Near their Contact Point

S. V. Sanduleanu1,2
1Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526, Russia
2Moscow Institute of Physics and Technology, Dolgoprudny, 141701, Russia
Keywords: вязкое взаимодействие пузырьков, функция тока Стокса, осевая симметрия, viscous interaction of bubbles, Stokes stream function, axial symmetry

Abstract >>
We consider the interaction between two spherical bubbles of variable radii during their movement along their centerline in a viscous fluid. A stream function that satisfies the Stokes equation is found in bispherical coordinates as an expansion in Gegenbauer polynomials. Viscous forces that act on the sphere are exactly presented as infinite series. Asymptotic expressions of these forces near the bubble contact zone are derived.

Numerical Analysis of Viscous Fingering Instability due to Miscible Displacement

A. Nemati, H. Saffari, B. Z. Vamerzani, R. Azizi, S. M. Hosseinalipoor, H. Miri
Iran University of Science and Technology, Tehran, Iran
Keywords: неустойчивость вязкостного пальцеобразования, закон Дарси для двухфазной жидкости, пористая среда, поток смешивающихся жидкостей, viscous fingering instability, two-phase Darcy's law, porous media, miscible flow displacement

Abstract >>
In this study, miscible viscous fingering instability is examined numerically by using the two-phase Darcy's law and transport equations. The effects of the viscosity ratio, anisotropic permeability, and porosity on instabilities are investigated. The finger patterns and their splitting and spreading in the domain are discussed. An image processing algorithm is applied to concentration contours to quantify instability parameters, such as the breakthrough time, efficiency, and fractal dimension. It is revealed that more complex fingers are obtained as the viscosity ratio increases, while the efficiency and the breakthrough time decrease. It is demonstrated that high permeability perpendicular to the flow direction leads to instability intensification and to an increase in the fractal dimension, whereas changing the porosity does not have any considerable impact on viscous fingering instability.

Experimental Study of Impactor Motion in Saline Ice

S. I. Gerasimov1,2,3,4, A. V. Zubankov1,2, A. P. Kalmykov1, S. A. Kapinos1, E. G. Kosyak2, P. G. Kuznetsov2
1Russian Research Institute of Experimental Physics, Sarov, 607190, Russia
2Sarov State Physics and Technical Institute, Sarov, 607186, Russia
3Nizhny Novgorod State Technical University, Nizhny Novgorod, 603950, Russia
4Institute for Problems in Mechanical Engineering, Nizhny Novgorod, 603024, Russia
Keywords: поликристаллический лед, соленый лед, цилиндрический ударник, динамическая твердость, каверна, polycrystalline ice, saline ice, cylindrical impactor, dynamic hardness, cavity

Abstract >>
Results of an experimental study of the normal collision of cylindrical impactors with sea ice are presented. The dynamics of wave process development in the thickness of a salt ice obstacle and the behavior of the forces of resistance to impactor penetration are analyzed at different impact velocities. The possibility of using induction cross sections for determining the position of impactors in the obstacle in a range of initial velocities of 800-1500 m/s. Pulsed X-ray diffraction is used to obtain motion diagrams (depth versus time) and the dimensions of cavities formed

Application of Explosion Generators for Accelerating Condensed Shells by the Cascading Method

V. K. Baranov1, A. M. Glybin1, A. G. Golubinskii1, B. E. Grinevich1, P. V. Dudai1, A. A. Zimenkov1, A. V. Ivanovskii1,2, A. I. Kraev1, V. I. Mamyshev1, N. I. Sitnikova1
1All-Russian Research Institute of Experimental Physics, Sarov, 607188, Russia
2Sarov Institute of Physics and Technology, Sarov, 607189, Russia
Keywords: дисковый взрывомагнитный генератор, цилиндрический конденсированный лайнер, взрывчатое вещество, каскадная система, ударник, disk magnetic explosive generator, cylindrical condensed liner, explosive, cascade system, impactor

Abstract >>
A method is proposed for reducing the characteristic time of action of the pulse produced by explosive magnetic generators. The practical implementation of this method has been confirmed by the results of experiments.

On a Method for Calculating Heat Transfer in a Moving Fluid Taking into Account Energy Dissipation

I. V. Kudinov, A. V. Eremin, R. M. Klebleev, V. K. Tkachev
Samara State Technical University, Samara, 443100, Russia
Keywords: теплообмен в движущейся жидкости, переменные граничные условия, диссипация энергии, дополнительная искомая функция, дополнительные граничные условия, интегральный метод теплового баланса, heat transfer in moving fluid, variable boundary conditions, energy dissipation, additional new function, additional boundary conditions, heat balance integral method

Abstract >>
An approximate analytical solution to the heat transfer problem for a moving fluid in a cylindrical channel is obtained using an additional new function and additional boundary conditions in the heat balance integral method and taking into account energy dissipation under a first-order boundary condition that varies along the longitudinal coordinate. The use of the additional new function that determines the temperature change along the longitudinal variable in the center of the channel makes it possible to reduce the solution of the partial differential equation to the integration of the ordinary differential equation. The additional boundary conditions are found in such a way that their satisfaction for the new solution is equivalent to the satisfaction of the differential equation at boundary points.

Modeling of Synthesis of Composite Particles Consisting of a Core and a Shell on the Basis of Simultaneous Oxidation of Titanium and Silicon Tetrachlorides in a Plasma-Chemical Reactor

S. M. Aulchenko, E. V. Kartaev
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: диоксид титана, диоксид кремния, композитная частица, плазмохимический реактор, односкоростная многокомпонентная среда, гомогенная и гетерогенная реакции, коагуляция, titanium dioxide, silicon dioxide, composite particle, plasma-chemical reactor, one-velocity multispecies medium, homogeneous and heterogeneous reactions, coagulation

Abstract >>
Single-stage synthesis of composite nanoparticles of titanium dioxide and silicon dioxide in the test section of a plasma-chemical reactor with the use of a chloride method based on simultaneous oxidation of titanium and silicon tetrachlorides with preliminary mixing of the reactants by means of bubbling is simulated. Within the framework of the model developed in the study, data on the size of the composite particle core, particle shell thickness, and number of particles with and without the shell are obtained.

Experimental Investigation of a Submerged Air-Water Bubbly Flow Jet in a Water Tank as a Model of Steel Casting

A. Khan1, E. K. Spiridonov1, D. F. Khabarova1, K. Sanaullah2, A. Badahar3, M. Zwawi3, M. Algarni3, B. Felemban4
1South Ural State University, Chelyabinsk, 454080, Russia
2Ton Duc Thang University, Ho Chi Minh City, Vietnam
3King Abdulaziz University, Rabigh, Saudi Arabia
4Taif University, Saudi Arabia
Keywords: литье, гидродинамика, пузырьки, струя, подводящая трубка, casting, hydrodynamics, bubbles, jets, downcomer

Abstract >>
Small-scale air-water experiments reported here contain all the important features of the industrial caster, the mold feed pipe, and the nozzles associated with it. The liquid is introduced into the feed pipe through an annulus with the gas entering at the center. The liquid travels down the walls of the feed pipe as a film until it encounters the pipe section containing a two-phase (air-water) bubbly mixture. Drift-flux relations are derived to compute the flow parameters (gas void fraction, horizontal velocity of the jet, etc.), which are found to be in good agreement with observations. The direction of the two-phase bubbly jet emerging from the nozzle is quantified, showing an improved downward deflection angle.

Residual Stress Relaxation in a Reinforced Cylinder under Creep, Loaded by an Axial Force, Torque, and Internal Pressure

V. P. Radchenko, V. V. Tsvetkov, M. N. Saushkin
Samara State Technical University, Samara, 443100, Russia
Keywords: остаточные напряжения, поверхностное пластическое упрочнение, цилиндрический образец, ползучесть, релаксация, растяжение, кручение, внутреннее давление, краевая задача, residual stresses, surface plastic reinforcement, cylindrical sample, creep, relaxation, tension, torsion, internal pressure, boundary-value problem

Abstract >>
A method is developed for solving a boundary-value problem of residual stress relaxation in a surface-reinforced hollow cylinder under combined loading by an axial force, torque, and internal pressure. Methods for determining the stress-strain state after reinforcement and its kinetics during creep are proposed. The effect of internal pressure along with a tensile load or torque on a thick-walled cylindrical sample made of ZhS6KP alloy after air-shot peening is investigated. Computational diagrams for stress tensor components under instantaneous temperature-force loading during creep and after unloading are given and analyzed. The behavior of unreinforced and reinforced samples at the stage of steady creep after complete residual stress relaxation is compared.

Automated Flow Control System in a Baseline Test Rig for Studying Pulsed Fluid Flows

A. M. Sorokin1, A. V. Boiko1, A. P. Chupakhin2, A. A. Cherevko2
1Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: пульсирующие течения, каналы, гемодинамика, автоматизированный измерительный комплекс, pulsed flows, channels, hemodynamics, automated measurement system

Abstract >>
A system for automated investigations of pulsed fluid flows in channels with the use of a special test rig is presented. In this system, a specially developed computer code defines the pulsed flow rate of the fluid and traces whether the task is performed. The test rig is tested with the use of a flowmeter.

Complex Eigenfrequencies and Damping Properties of an Elongated Plate with Integral Damping Coating

V. N. Paimushin1,2, V. A. Firsov1, V. M. Shishkin3
1Tupolev Kazan National Research Technical University, Kazan, 420111, Russia
2Kazan Federal University, Kazan, 420008, Russia
3Vyatka State University, Kirov, 610000, Russia
Keywords: пластина, демпфирующее покрытие, логарифмический декремент колебаний, конечный элемент, комплексная частота, plate, damping coating, logarithmic decrement of vibrations, finite element, complex frequency

Abstract >>
In this paper, we consider the classical methods of surface damping of bending vibrations of thin-walled structures and a promising integral method of a damping coating consisting of two layers of material with pronounced viscoelastic properties between which a thin reinforcing layer of high modulus material is located. A finite element with 14 degrees of freedom has been developed for modeling an elongated plate with the specified damping coating taking into account the effect of transverse compression of the damping layers under high-frequency oscillations of the plate. A generalized problem of complex eigenvalues in the lower part of the spectrum of complex forms and frequencies of free vibrations of a damped plate is solved using iterations with consideration of the frequency dependence of the dynamic elastic moduli of the material. The damping properties of the plate are determined from the imaginary parts of the complex eigenfrequencies and the relative energy dissipation at resonance.

Numerical Solution of the Problem of Deformation of Elastic Solids under Pulsed Loading

I. O. Bogulskii1,2, Yu. M. Volchkov3,4
1Siberian Federal University, Krasnoyarsk, 660041, Russia
2Krasnoyarsk State Agrarian University, Krasnoyarsk, 660049, Russia
3Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
4Novosibirsk State University, Novosibirsk, 630090, Russia
Keywords: численные методы, константы диссипации, импульсное нагружение, упругие деформируемые тела, numerical methods, dissipation constants, pulsed loading, elastic deformable solids

Abstract >>
Three methods of approximation of lower non-differential terms in equations of dynamic problems of mechanics of deformable solids are studied with the use of explicit algorithms of the numerical solution based on several local approximations of each of the sought functions by linear polynomials. Additional equations based on the energy conservation law are formulated in the course of algorithm construction. The properties (dissipativity, monotonicity, and stability) of the proposed schemes are studied. Results of the numerical solution of the problem of deformation of an elastic plate with constant shear strains over the plate thickness (Timoshenko model) are presented. Results of the numerical solution of the problem of deformation of an elastic disk under pulsed loading are compared with the analytical solution of this problem.

Model of Polymorphic Transformation of Material in a Shock Wave. 1. Carbon

S. A. Kinelovskii
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: полиморфизм, ударная волна, графит, алмаз, фазовый переход, polymorphism, shock wave, graphite, diamond, phase transition

Abstract >>
This paper considers a model that can be used to describe polymorphic phase transition in a shock wave based on experimental data on the compression of material by a shock wave. It is assumed that the phase transition in a non-porous material has a martensitic character and occurs in the stationary shock wave that arises in the immediate vicinity behind the first one. Conditions for the occurrence of this shock wave are determined. The model has been tested for non-porous pyrolytic graphite. It has been shown that the model satisfactorily describes the experimental results obtained in various studies for this type of graphite.

Performance Study of Hybrid Bolted-Bonded Vertical T- and L-Joints with Composite Adherends Subjected to Underwater Shock Pressure

E. Selahi
Islamic Azad University, Marvdasht, Iran
Keywords: болтовые соединения, подводная ударная волна, композиты, разрушение, T- и L-образные соединения, bolted-bonded joint, underwater shock pressure, composites, performance and failure analysis, T-joint, L-joint

Abstract >>
Three-dimensional explicit dynamic simulations are carried out to study the failure of hybrid bolted-bonded vertical T- and L-joints under noncontact underwater explosion shock pressure. In this modelling, adherends are fibrous laminated composites having an orthotropic behavior, while bolts and adhesive layers exhibit an isotropic behavior. It is found that hybrid vertical T- and L-joints display appreciably higher joint resistance to underwater explosion shock pressure than adhesive T- and L-joints.

Elastoplastic Tension Problem for a Plate with a Circular Hole with Account for Crack Nucleation in an Elastic Deformation Region

V. M. Mirsalimov
Azerbaijan Technical University, Baku, AZ1073, Azerbaijan
Keywords: тонкая пластина, упругопластическая задача, граница раздела упругих и пластических деформаций, зона предразрушения, зарождение трещины, thin plate, elastoplastic problem, interface between elastic and plastic deformations, pre-fracture zone, crack nucleation

Abstract >>
A plane elastoplastic problem related to stress distribution in a thin plate with a circular hole is considered with account for nucleation and development of cracks in an elastic region. It is assumed that the circular hole is located in the plastic deformation region. It is considered that loading is accompanied by crack nucleation and the fracture of the plate material in the elastic deformation region of the plate. The problem is solved using the perturbation theory and the theory of singular integral equations.

Nonlinear Vibrations of the Immersed Dagger-Shaped Atomic Force Microscope Cantilever in Different Liquids Studied by Experimental and Theoretical Methods

A.H. Gholizadeh Pasha, A. Sadeghi
Islamic Azad University, Damavand, Iran
Keywords: атомно-силовой микроскоп, консоль кинжальной формы, демпфирование, балка Тимошенко, погружение в жидкость, atomic force microscope, dagger-shaped cantilever, damping effect, Timoshenko beam theory, immersion in liquid

Abstract >>
In this paper, the nonlinear dynamic behavior of an immersed dagger-shaped atomic force microscope cantilever in different liquids has been investigated for the first time. The Timoshenko beam theory, which considers rotatory inertia and shear deformation effects, has been used for modeling the cantilever. The nonlinear tip-sample interaction force has been modeled by using the Hertzian contact theory. Water, methanol, acetone, and carbon tetrachloride are considered as the immersion environments. In most cases, the softening behavior has been observed for the cantilever. The resonant frequency is found to decrease with an increase in the liquid viscosity. The experimental results have been compared with the theoretical predictions and are found to be in good agreement.

Dynamic Stress Concentration in a Piezoelectric Material with a Non-Circular Hole Subjected to an SH-Wave

X. L. Wang, X. J. Yang, R. Zhang
College of Civil Engineering and Transportation, Jilin, 132013, China
Keywords: пьезоэлектрический материал, некруговая полость, концентрация динамических напряжений, горизонтально поляризованная волна, комплексная переменная, конформное отображение, piezoelectric material, non-circular hole, dynamic stress concentration, SH-wave, complex variable, conformal mapping

Abstract >>
In this paper, the influence of the dynamic stress concentration in a piezoelectric material with a non-circular hole subjected to a shear wave polarized so that its particle motion and direction of propagation contained in a horizontal plane (SH-wave) is investigated. The boundary conditions of the non-circular hole can be mapped into a unit circle by applying complex variables and conformal mapping. The analytical solution of the dynamic stress concentration factor is determined by the unknown mode coefficients obtained by using the boundary conditions. Numerical examples are presented to analyze the influence of the incident wave number, piezoelectric constant of the material, and eccentricity ratio of the hole on the distribution of the dynamic stress concentration factor. The analysis reveals that the distribution of the dynamic stress concentration factor on the incident direction of the SH-wave is significantly different from that on the other side.

Fractal analysis of the structural and mechanical characteristics of the interfacial region in epoxy polymer nanocomposites

O.A. Dyshin, I. A. Gabibov, J. N. Aslanov, A.J. Suleymanova
Azerbaijan State University of Oil and Industry, Baku, Az1010, Azerbaijan
Keywords: металлополимер, межфазная область, наполнитель, нанокластер, рыхлоупакованная матрица, фрактальная размерность, микромеханическая модель, metal polymer, interfacial region, filler, nanocluster, loose-packed matrix, fractal dimension, micromechanical model

Abstract >>
On the basis of a micromechanical model of the tensile strength of a polymer composite, it is shown that, in contrast to the case of adhesion between two polymers, when a linear dependence of the thickness of the interfacial region on the degree of interfacial adhesion is observed, the strength of the material of the interfacial region in nanocomposites of the polymer - high modulus filler type decreases as its thickness increases. ... Using a fractal model of interphase interactions, estimates of the threshold values of the volume fractions of nanoclusters of the epoxy polymer matrix and metal nanoparticles of the filler are obtained, upon passing through which the process of transfer of mechanical stress from the polymer matrix to the filler is weakened. It is shown that exceeding the threshold value of the volume fraction of the filler leads to a violation of the aggregate stability of the filler and a decrease in the values of the dimensionless parameter of the micromechanical model, which characterizes the degree of interfacial adhesion. With a further increase in the volume fraction of the filler, the values of this parameter become negative, while the strength of the composite practically does not increase.

Experimental Breakup Characteristics of Round Liquid Jets of a Dilute Polymer Solution into Quiescent Air

L.F. Yu1, Z.G. Zuo2, L. Li1, S.H. Liu2, S.T. Zhao1
1Research Institute of Chemical Defence, Beijing, China
2Tsinghua University, Beijing, China
Keywords: полимер, круглая струя, моды разрушения, межфазные возмущения, нерелаксированные напряжения, polymer, round jet, breakup pattern, interfacial disturbance, unrelaxed stresses

Abstract >>
Experiments are performed on dilute polymer solutions jetting into quiescent air with a jet velocity range of 30-87 m/s. Polymer solutions are those with several hundred ppm concentrations of long-chain polyoxyethylene (millions of molecular weight) dissolved in purified water. The breakup characteristics of the jets were recorded by high-speed photography from four observation windows along the jet direction. The breakup morphologies of dilute polymer solution jets are significantly different from that of Newtonian fluids. Small-scale interfacial disturbances are suppressed, while a twisted liquid column waving with large amplitudes is observed. When the jet velocity exceeds a critical value, liquid films and filaments are peeled off successively from the liquid column. Four different breakup patterns are distinguished. The diameters of the central liquid column and the principal liquid filament are observed to decrease with increasing jet velocity.