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Journal of Applied Mechanics and Technical Physics

2018 year, number 3

Analytical Solutions and Parametric Studies of the Schamel Equation for Two Different Ion-Acoustic Waves in Plasmas

D. Daghan1, O. Donmez2
1Nigde Omer Halisdemir University, Nigde, Turkey, TR-51350
2American University of the Middle East, Egaila, Kuwait
Keywords: Schamel equation, direct integration, solitons, ion-acoustic plasma

Abstract >>
A numerical investigation of the properties of two different ion-acoustic solitons has been performed by using analytical solutions of the Schamel equation. A new type of the analytical solution of the Schamel equation that describes soliton propagation with a negative phase velocity has been found for the first time. This new type of the solution has been applied to investigate the physical properties of two different plasmas and to understand the effect of nonextensivity and the effect of trapped electrons on ion-acoustic waves in a superthermal plasma. It is shown that the soliton amplitude and width depend on the nonextensivity parameter, superthermality of the electron distribution, and characteristic trapping parameter.

Cascade Magnetocumulative Generator on the Basis of Inductively Coupled Circuits with a Variable Coupling Coefficient

S. D. Gilev, V. S. Prokop'ev
Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia, 630090
Keywords: magnetocumulative generator, cascade systems, generation of electromagnetic energy, magnetic cumulation, inductively coupled circuits, generator-load correlation

Abstract >>
A circuit of a multicascade magnetocumulative generator based on a dynamic variation of the coupling coefficient of inductively coupled circuit is proposed. Each cascade contains two circuits including two pairs of inductively coupled coils. One pair of coils is subjected to simultaneous straining, and one of the coils in the other pair is arranged with the back-to-back connection. It is shown that the energy in the load can be gradually increased (from one cascade to another) by using additional cascades. By an example of a two-cascade system, the proposed circuit is compared to the known circuits of cascade system design based on the magnetic cumulation principle (generator with a step-up transformer and dynamic transformer). Within the framework of the model that ignores the ohmic resistance of conductors, it is demonstrated that the proposed circuit allows one to obtain a greater energy in the high-inductance load than the circuits with the step-up or dynamic transformer owing to a change in the sign of the magnetic flux in the secondary circuit. It is found that the increase in energy in the new circuit is independent of the coupling coefficient (at high values of this coefficient) and become greater as the number of cascades is increased.

Emergence of Fluid Rotation in the Marangoni Boundary Layer in the Region of Local Cooling of the Free Boundary

V. A. Batishchev
Southern Federal University, Rostov-on-Don, Russia, 344090
Keywords: free boundary, boundary layer, cooling, bifurcation, thermocapillary effect, rotatio

Abstract >>
Rotation bifurcation in a steady axisymmetric thermocapillary flow of an incompressible fluid filling a semi-infinite space bounded by the free surface with a nonuniform distribution of temperature is studied. The fluid flow is calculated on the basis of Navier-Stokes equations under the assumption of small diffusion coefficients. It is shown that the bifurcation triggers a rotational regime in a thin Marangoni boundary layer in the case of local cooling of the free boundary near the axis of symmetry and in the presence of an external flow; there is no rotation outside this layer. In the case of local heating of the free boundary, rotation is not observed

One-Directional Thermogravitational Movement of Viscous Fluid in a Flat Channel with a Given Flow Rate

E. N. Cheremnykh1,2
1Institute of Computational Modeling Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, Russia, 660036
2Siberian Federal University, Krasnoyarsk, Russia, 660036
Keywords: Oberbeck-Boussinesq equations, convection, numerical experiments

Abstract >>
This paper touches upon an initial-boundary-value problem that describes the unidirectional thermogravitational motion of fluid in a plane channel in the case of solid immobile upper and lower walls with temperature distribution thereon and in the case of a heat-insulated upper wall. The motion is caused by a joint effect of the longitudinal temperature gradient and given nonstationary flow rate. The initial-boundary-value problem is inverse relative to the pressure gradient along the channel. An exact stationary solution is obtained. A solution of the nonstationary problems in Laplace images is determined, and the results of numerical calculations are presented.

Injection of a Hydrate-Forming Gas into a Snow Block Saturated with the Same Gas

V. Sh. Shagapov1,2, A. S. Chiglintseva2, A. A. Rusinov3, M. K. Khasanov4, I. G. Khusainov4
1Institute of Mechanics and Machinery, Kazan, Russia, 420111
2Mavlyutov Institute of Mechanics, Ufa, Russia, 450054
3Bashkir State University, Birsk, Russia
4Bashkir State University, Sterlitamak, Russia
Keywords: gas injection, filtration, snow block, self-similar solution, hydrate formation, volume region, Leibenson linearization

Abstract >>
The problem of injection of a hydrate-forming gas (methane) into a snow block, whose pores in the initial state are saturated by the same gas. Self-similar solutions describing the temperature and pressure fields and the snow, hydrate, and gas distributions in the block are constructed. It is shown that three characteristic zones can be distinguished, depending on the initial thermobaric state of the snow-methane system and the rate of gas injection into the filtration region: a near zone, in which snow completely is converted into hydrate and, consequently, the hydrate layer is saturated with gas; an intermediate zone, in which gas, snow, and hydrate are in phase equilibrium; a far zone filled with gas and snow. It is shown that the length of the heated zone decreases with increasing initial snow content in the block and with decreasing injected gas pressure. It is also shown that the length of the region of hydrate formation increases with increasing permeability. It is also noted that the heating of the intermediate zone occurs more rapidly.

Model for Multiphase Fluid Flows with Interphase Interaction Taken into Account

V. A. Balashov, E. B. Savenkov
Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia, 125047
Keywords: квазигидродинамическая система уравнений, многофазная гидродинамика, диффузная граница, quasi-hydrodynamic system of equations, multiphase hydrodynamics, diffuse boundary

Abstract >>
A quasi-hydrodynamic system of equations describing flows of a heat-conducting viscous compressible multiphase multicomponent fluid is constructed taking into account surface effects. The system was obtained by generalizing the methods of obtaining a single-phase quasi-hydrodynamic system and a multicomponent flow model taking into account the surface effects based on the concept of microforces and microstresses. The equations are derived using the Coleman-Noll procedure. The results of the calculations show that the constructed model is applicable for modeling multiphase multicomponent flows with allowance for surface effects on the interfaces.

Hydroelastic Effects of the Camber Ratio on a Ducted Marine Propeller in a Wake Flow

N. M. Nouri, S. Mohammadi, M. K. Neyestanaki, E. Beygi
Iran University of Science and Technology, Narmak, Tehran, Iran
Keywords: осесимметричное погруженное тело, винт в кольцевой насадке, кривизна скелетной линии профиля, спутный след, гидроупругость, разложение по собственным модам, axisymmetric underwater vehicle, ducted propeller, camber ratio, wake flow, hydroelastic, modal analysis

Abstract >>
The effects of the camber ratio on the hydrodynamic and structural behaviors of a NACA-based ducted marine propeller in the wake flow behind an underwater axisymmetric body are numerically studied by computational fluid dynamics methods, in particular, the finite element method. The results are presented in terms of the efficiency, deflection, pressure coefficient, and natural frequencies. It is shown that the wake flow strongly affects the performance of the selected propulsion system. It is shown that the distributions of the camber ratio over the blades of the propeller nonlinearly changes its resistance against cavitation occurrence and deflection, and also changes its hydrodynamic performance and vibrational behavior.

Numerical Analysis of Secondary Flows around an Oscillating Cylinder

A. N. Nuriev1, A. G. Egorov2, O. N. Zaitseva2
1Nizhny Novgorod State University, Nizhny Novgorod, Russia, 603950
2Kazan Federal University, Kazan, Russia, 420008
Keywords: вторичные стационарные течения, акустические течения, режимы течения, уравнение Навье-Стокса, численное моделирование, secondary stationary flows, acoustic flows, flow regimes, Navier-Stokes equation, numerical simulation

Abstract >>
This paper considers methods for controlling secondary flows arising near an oscillating circular cylinder by changing two process control parameters: the dimensionless amplitude and the vibrational Reynolds number. A direct numerical modeling study is performed. It is shown that by varying the indicated parameters in a relatively small range, it is possible not only to intensify mass transfer processes, but also change the direction of the main secondary flows.

Model of Blood Circulation in Human Lower Limbs

V. I. Penkovskii, N. K. Korsakova
Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia, 630090
Keywords: математическая модель, циркуляция крови, нижние конечности, гетерогенная среда, фильтрация, артерии, вены, капилляры, метод конечных элементов, mathematical model, blood circulation, lower limbs, heterogeneous medium, filtration, arteries, veins, capillaries, finite element method

Abstract >>
A mathematical model of blood circulation in human lower limbs is proposed. The model is based on the laws of motion (filtration) of a viscous fluid in a heterogeneous medium consisting of two or more interpenetrating continua. It is assumed that the blood system consists of a distribution network of comparatively large vessels (arterioles) connected to small capillaries and a similarly structured collection network of small capillaries united into larger veins. A system of parabolic differential equations is derived, for which a problem with no initial data is posed. A periodic (in time) solution of the system corresponding to harmonic oscillations defined by the cardiac rhythm is found. Analytical solutions for particular cases of problems following from the general model of blood circulation are obtained. Numerical calculations are performed, and a numerical solution is found for a one-dimensional problem with parameters similar to those corresponding to real conditions of blood circulation with allowance for the cross-sectional area of the muscular tissue of the lower limb.

Modeling of Gas Hydrate Formation upon Injection of Carbon Oxide Gas into a Natural Reservoir

M. K. Khasanov1, M. V. Stolpovskii2, I. K. Gimaltdinov2
1Bashkir State University, Sterlitamak, Russia, 453103
2Ufa State Oil Technical University, Ufa, Russia, 450062
Keywords: пористая среда, газовый гидрат, фильтрация, углекислый газ, porous medium, gas hydrate, filtration, carbon dioxide

Abstract >>
This paper presents the results of numerical modeling of gas hydrate formation upon injection of carbon dioxide into a finite-length reservoir saturated with methane and water. It is shown that at different stages, hydrate formation can occur on both the frontal surface and in a reservoir region of finite length. The effects of pressure on the boundaries of the reservoir and the permeability and initial water saturation of the reservoir on the hydrate formation process were studied. The dependences of the time of the complete conversion of water into gas hydrate state in the entire reservoir on the injection pressure and reservoir permeability were obtained.

Low-Frequency Deceleration of a Filtration Wave in Layered-Inhomogeneous Permeable Formations

A. I. Filippov, O. V. Akhmetova, A. A. Kovalskii
Bashkir State University, Sterlitamak, Russia, 453103
Keywords: волновое уравнение, волновое поле давления, фильтрация, анизотропная среда, коэффициент поглощения, волновое число, фазовая скорость, wave equation, pressure wave field, filtration, anisotropic medium, absorption coefficient, wavenumber, phase velocity

Abstract >>
Analytical frequency dependences of the absorption coefficient, wavenumber, and phase velocity were constructed for filtration-wave fields in a highly permeable interlayer bounded from above and from below by layers having high permeability in the vertical direction. It is shown that as the frequency decreases, the phase velocity of the wave decreases to values below this velocity in the porous medium, and low-frequency deceleration occurs.

Experimental Investigation of the Strike and the Penetration of Conical Shock in the Frozen Sandy Ground

A. M. Bragov, Vl. V. Balandin, V. L. Kotov, Vl. Vl. Balandin, E. Yu. Linnik
Scientific Research Institute of Mechanics, Nizhny Novgorod, Russia, 603950
Keywords: удар, проникание, мерзлый песчаный грунт, конус, сила сопротивления внедрению, обращенный эксперимент, численный расчет, impact, penetration, frozen sandy soil, cone, force of resistance to penetration, reversed experiment, numerical calculation

Abstract >>
A reverse experiment technique is used along with the technology of measuring rods to study the impact and penetration of a steel conical shocker in frozen sandy soil. This paper presents the dependences of maximum values of the force of resistance of cones with base diameters of 10.0, 12.0, and 19.8 mm to penetration into soil on the impact velocity in the range of values 100-400 m/s. The numerical solution of the problem in an axisymmetric formulation with the use of the “Dinamika-2” software package is used to show the effect of waves reflected from the walls of the container on the contact force. A comparative analysis of the forces of resistance to penetration of the shocker into compacted dry, water-saturated, and frozen sandy soils is carried out.

Contact of Transversely Isotropic Bodies in the Herz Theory

D. A. Pozharskii
Don State Technical University, Rostov-on-Don, Russia, 344000
Keywords: анизотропия, трансверсально-изотропное тело, контак, anisotropy, transversely isotropic body, contact

Abstract >>
Within the framework of the anisotropic theory of elasticity, a three-dimensional contact problem of interaction of two massive transversely isotropic bodies, whose dimensions substantially exceed the size of the contact region. In this case, the isotropy planes of contacting elastic bodies are mutually perpendicular. Exact and numerical solutions of the problem are determined. Calculations for various transversely isotropic materials are carried out.

Wear Resistance of Knives Made of DI37-VI (11Kh4V2MF3S2-VI) Steel during Cutting with Addition of an Abrasive Material

O. I. Stoyanovskii1, A. N. Maznichevskii2, A. A. Pikarevskii1, E. S. Vasyukova2
1Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia, 630090
2Limited Liability Company "Laboratory of Special Metallurgy", Chelyabinsk, Russia, 454047
Keywords: износостойкость, дисперсионно-твердеющие стали, аустенизация, карбиды, микроструктура, ускоренный абразивный износ, wear resistance, precipitation hardening steels, austenization, carbides, microstructure, accelerated abrasive wear

Abstract >>
A method of thermal treatment of DI37-VI steel exhibiting precipitation hardening is developed with due allowance for the steel microstructure and determining the chemical composition of carbides and the matrix after each operation. In the case of low-temperature tempering, the mechanical properties of steel are found to be little different from its properties obtained by means of multiple high-temperature tempering (aging); in the latter case, however, the wear resistance of steel in the case of cutting of steel bars is 1.5 times higher. It is demonstrated that the wear resistance of steel is significantly affected by the chemical composition of carbides and the matrix.

Fractal Model of the Nanofiller Structure Affecting the Degree of Reinforcement of Polyurethane-Carbon Nanotube Nanocomposites

G. V. Kozlov, I. V. Dolbin
Kabardino-Balkarian State University, Nalchik, Russia, 360004
Keywords: нанокомпозит, полиуретан, углеродные нанотрубки, фрактальная структура, степень усиления, перколяция, nanocomposite, polyurethane, carbon nanotubes, fractal structure, degree of reinforcement, percolation

Abstract >>
A percolation model of nanocomposite reinforcement is under study. It is shown that the degree of reinforcement of polyurethane - carbon nanotube nanocomposites depends on the structure of nanofillers, which are annular formations. This structure is most accurately characterized by its fractal dimension. It is established that the creation of a structure with negative percolation indices allows for a significant increase in the degree of reinforcement of considered nanocomposites at low nanofiller concentrations.

Acoustic-Emission Control of the Deformation and Fracture of High-Pressure Metal-Composite Tanks

A. M. Lepikhin1, V. V. Moskvichev1,2, A. P. Chernyaev2
1Institute of computational Technologies, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, Russia, 660049
2Nauka Special Design and Technological Bureau, Krasnoyarsk, Russia, 660036
Keywords: металлокомпозитный бак, испытания на прочность, повреждения, акустико-эмиссионный контроль, metal-composite tank, strength tests, damage, acoustic-emission control

Abstract >>
This paper presents the results of experimental studies of damage accumulation in a metal-composite high-pressure tank in pneumatic strength tests. The deformation and fracture of the composite structure, accompanied by matrix cracking and fiber rupture, are analyzed. It is shown that the cracks and fractures generate acoustic-emission signals of various types. The results of acoustic-emission control were used to develop a criterion for ranking tanks based on the strength characteristics of the pressure composite shell.

Identification of Parameters of Short-Time Creep of Plexiglas by Means of Studying Decaying Flexural Oscillations of Test Samples

V. N. Paimushin1,2, V. A. Firsov1, V. M. Shishkin3
1Kazan National Research Technical University named after A. N. Tupolev, Kazan, Russia, 420111
2Kazan Federal University, Kazan, Russia, 420008
3Vyatka State University, Kirov, Russia, 610000
Keywords: вязкоупругий материал, ядро наследственности, конечный элемент, метод прямого поиска, целевая функция, viscoelastic material, hereditary kernel, finite element, direct search method, object function

Abstract >>
A technique for identification of hereditary properties under conditions of short-time creep of Plexiglas is developed. The technique is based on experimental determination of shifting of the center of decaying flexural oscillations of vertically fixed test samples after their preliminary curing in a static bent state. Mathematically, the technique is based on using the finite element method and integral equations of the theory of hereditary viscoelasticity with the Koltunov-Rzhanitsyn hereditary kernel. An object function is constructed for identification of rheological parameters of this kernel. The minimum of this function is found by the direct search method, which does not require the function gradient to be known. The hereditary kernel of Plexiglas averaged on the basis of data for several test samples is obtained as a function of time.

Statistical Model of Explosive Fragmentation of a Ring

P. A. Drokin
Institute of Experimental Physics, Sarov, 607190
Keywords: тонкое кольцо, разрушение взрывом, скорость границы области пластического течения, число фрагментов, thin ring, explosion, speed of the boundary of the plastic flow region, number of fragments

Abstract >>
A model of the explosive fragmentation of a thin ring was developed which take into account the statistical dispersion of the destructive relative deformation along the length of the ring. A formula is proposed for calculating the speed of motion of the boundary of the region near the plastic rupture in which the plastic flow of the ring material is stopped. Methods of numerical and analytical calculation of the average number of fragments of the ring were developed. The calculation results were compared with known experimental data.

Determination of the Inhomogeneous Preliminary Stress-Strain State in a Piezoelectric Disk

A. O. Vatulyan1,2, V. V. Dudarev1,2, R. M. Mnukhin1
1Southern Federal University, Rostov-on-Don, Russia, 344090
2Southern Mathematical Institute, Vladikavkaz, Russia, 362027
Keywords: пьезоэлектрический диск, неоднородные предварительные напряжения, колебания, акустический метод, обратная коэффициентная задача, собственные частоты, piezoelectric disk, inhomogeneous prestresses, vibrations, acoustic method, inverse coefficient problem, natural frequencies

Abstract >>
The problem of steady radial vibrations of a thin electroelastic hollow disk in a preliminary inhomogeneous plane stress-strain state is solved. Vibrations are caused by a potential difference at the electrodes placed on the end surfaces of the disk. Equations of vibrations and boundary conditions are formulated. The preliminary stress state corresponding to the solution of the Lame problem was investigated. The direct problem of determining the displacement function is solved numerically by the shooting method. The inverse problem of determining the prestress parameter from the change in the natural frequency of the disk is formulated and solved. The accuracy of determining the prestressed state for initial put data specified with an error is analyzed.

State Equations of Nonstationary Creep under Complex Loading

I. A. Volkov1, L. A. Igumnov2, D. A. Kazakov2, D. N. Shishulin3, I. S. Tarasov1
1Volga State University of Water Transport, Nizhny Novgorod, Russia, 603950
2Scientific Research Institute of Mechanics, Nizhny Novgorod, Russia, 603022
3Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia, 603950
Keywords: нестационарная ползучесть, математическое моделирование, сложное нагружение, поверхность ползучести, материальные параметры, численный и натурный эксперименты, nonstationary creep, mathematical simulation, complex loading, creep surface, material parameters, numerical and full-scale experiments

Abstract >>
A mathematical model describing the nonstationary creep of metals under complex loading is proposed. The results of numerical simulation of creep of St.304 steel in complex regimes of block multiaxial cyclic deformation are given. The numerical calculation results obtained are compared with the data of full-scale experiments. Creep is simulated in complex deformation processes accompanied by the rotation of main regions of stress, strain, and creep strain tensors.

Effect of Thermal Treatment on Mechanical and Microstructural Properties of the Welded Joint of the Al-Mg-Li Alloy Obtained by Laser-Assisted Welding

A. M. Orishich1, A. G. Malikov1, E. V. Karpov1,2, N. A. Pavlov1, I. S. Mesenzova1
1Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia, 630090
2Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia, 630090
Keywords: лазерная сварка, алюминиево-литиевый сплав, закалка, искусственное старение, прочность, пластичность, микроструктура, фазовый состав, laser welding, Al-Li alloy, hardening, artificial aging, strength, plasticity, microstructure, phase composition

Abstract >>
Laser-assisted welding of the 1420 alloy of the Al-Mg-Li system is experimentally studied for the purpose of its optimization. Various regimes of thermal treatment of non-detachable joints obtained by means of laser welding are considered. Thermal treatment modes that allow significant enhancement of the welded joint density as compared to the as-received alloy are chosen. The ultimate normalized elongation of samples after aging is found to decrease by a factor of 3.

Estimation of Stress Concentration in a Weld Seam Formed by Explosive Welding

A. G. Kolpakov1, S. I. Rakin2
1Siberian State University of Telecommunications and Information Sciences, Novosibirsk, Russia, 630102
2Siberian State Transport University, Novosibirsk, Russia, 630049
Keywords: упругость, концентрация напряжений, сварной шов, ячеечная задача, elasticity, stress concentration, weld seam, cell problem

Abstract >>
It is shown that a weld seam formed during explosion welding at a microlevel (at a wavelength of the order of several hundred micrometers) has a wavy geometry. Stress concentration caused by local geometry of the seam is calculated for various shapes and amplitudes of the weld seam wave and combinations of joined materials.