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Journal of Applied Mechanics and Technical Physics

2017 year, number 4

Generation of Electromagnetic Energy in a Magnetic Cumulation Generator with the use of Inductively Coupled Circuits with a Variable Coupling Coefficient

S. D. Gilev, V. S. Prokop'ev
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk,630090, Russia
Keywords: магнитная кумуляция, магнитокумулятивный генератор, электромагнитная энергия, магнитный поток, индуктивно связанные контуры, коэффициент связи, согласование генератора с нагрузкой, magnetic cumulation, magnetic cumulation generator, electromagnetic energy, magnetic flux, inductively coupled circuits, coupling coefficient, generator-load coupling

Abstract >>
A method of generation of electromagnetic energy and magnetic flux in a magnetic cumulation generator is proposed. The method is based on dynamic variation of the circuit coupling coefficient. This circuit is compared with other available circuits of magnetic energy generation with the help of magnetic cumulation (classical magnetic cumulation generator, generator with transformer coupling, and generator with a dynamic transformer). It is demonstrated that the proposed method allows obtaining high values of magnetic energy. The proposed circuit is found to be more effective than the known transformer circuit. Experiments on electromagnetic energy generation are performed, which demonstrate the efficiency of the proposed method.

Measurement of Temperature in Gaseous and Liquid Reacting Media upon Their Shock Compression

V. V. Pai1, M. A. Gulevich1, I. V. Yakovlev1, V. I. Lysak2, S. V. Kuz'min2, S. V. Khaustov2
1Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Volgograd State Technical University, Volgograd, 400131, Russia
Keywords: ударная волна, детонация, термопарный метод, измерение температуры, shock wave, detonation, thermocouple method, temperature measurement

Abstract >>
This paper describes the results of measurement of the temperatures of gaseous and liquid reacting media, carried out by the thermocouple method with the use of a battery (copper-constantan-copper) of planar thermocouples, placed in the medium under study. It is shown that convective heat transfer lasting for 0.5-1.5 μs equalizes the temperatures of “hot” thermocouple junctions and environment. The relationship between the voltage on the thermobattery and time, which occurred in this type of heating, was determined by a pulse oscilloscope. The measured maximum voltage was used to determine the temperature of the medium. A series of experiments was carried out on measuring the temperature of water and emulsion explosive matrix, which were compressed by a shock wave, as well as the detonation products of ammonite with sodium hydrogencarbonate at various mass ratios. The estimates of heat fluxes from the detonation products to the metallic surfaces of the thermobattery contacting with them are obtained.

Symmetry Groups of Integrodifferential Equations for Linear Thermoviscoelastic Materials with Memory

L.-Q. Zhou1,2, S. V. Meleshko2
1Guizhou University of Finance and Economics, Guiyang, Guizhou, 550025, China
2Suranaree University of Technology, Nakhon Ratchasima, 30000, Thailand
Keywords: линейная термовязкоупругость, группы симметрии, частично инвариантные решения, интегродифференциальные уравнения, linear thermoviscoelasticity, symmetry groups, partially invariant solutions, integrodifferential equations

Abstract >>
The group analysis method is applied to a system of integrodifferential equations corresponding to a linear thermoviscoelastic model. A recently developed approach for calculating the symmetry groups of such equations is used. The general solution of the governing equations for the system is obtained. Using subalgebras of the admissible Lie algebra, two classes of partially invariant solutions of the considered system of integrodifferential equations are studied.

Estimates of the Evolucion of Small Perturbations by Radial Spreading (Drain) of a Viscous Ring

D. V. Georgievskii, G. S. Tlyustangelov
Lomonosov Moscow State University, Moscow, 119991, Russia
Keywords: растекание, сток, вязкая жидкость, возмущение, метод интегральных соотношений, неравенства Фридрихса, оценки устойчивости, невязкий предел, spreading, drain, viscous fluid, perturbation, method of integral relations, Friedrichs inequalities, stability estimates, inviscid limit

Abstract >>
The evolution of small perturbations of the kinematic and dynamic characteristics of the radial flow of a flat ring filled with a homogeneous Newtonian fluid or an ideal incompressible fluid is studied. When the flow rate is specified as a function of time, the basic motion is completely defined by the incompressibility condition regardless of the properties of the medium. For the streamfunction, we obtained a biparabolic equation with four homogeneous boundary conditions, which simulate adherence to the expanding (narrowing) walls of the ring. Upper-bound estimates of the perturbation are obtained using the method of integral relations for quadratic functionals. The case of exponential decay of initial perturbations is considered on a finite or infinite time interval. Justified The admissibility of the inviscid limit in the given problem is substantiated, and and both upper- and lower-bound estimates for this limit are obtained.

Simulation of Nonlinear Waves on the Surface of a Thin Fluid Film Moving under the Action of Turbulent Gas Flow

O. Yu. Tsvelodub1,2, D. G. Arkhipov1,2
1Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Novosibirsk State University, Novosibirsk 630090, Russia
Keywords: пленка вязкой жидкости, газовый поток, модельная система, эволюционное уравнение, эволюция возмущений, viscous fluid film, gas flow, model system, evolution equation, evolution of perturbations

Abstract >>
This paper derives a new system of equations for the simulation of the dynamics of long-wave perturbations on the surface of a thin horizontal layer of heavy viscous fluid moving under the action of turbulent gas flow. In the case of small Reynolds numbers of the fluid, this system of equations is used to derive an evolution equation for the value of deviation of the film thickness from the unperturbed level. Some solutions of this equation are given.

Dual Solutions of Casson Fluid Flows over a Power-Law Stretching Sheet

S. Haldar, S. Mukhopadhyay, G. C. Layek
The University of Burdwan, Burdwan-713104, W. B., India
Keywords: модель Кэссона вязкой жидкости, пограничный слой, cтепенной закон растяжения пленки, двойное решение, Casson fluid model, boundary layer flows, power-law stretching sheet, dual solutions

Abstract >>
A steady boundary layer flow of a non-Newtonian Casson fluid over a power-law stretching sheet is investigated. A self-similar form of the governing equation is obtained, and numerical solutions are found for various values of the governing parameters. The solutions depend on the fluid material parameter. Dual solutions are obtained for some particular range of these parameters. The fluid velocity is found to decrease as the power-law stretching parameter  in the rheological Casson equation increases. At large values of  , the skin friction coefficient and the velocity profile across the boundary layer for the Casson fluid tend to those for the Newtonian fluid.

Hydrodynamics of Spatially Inhomogeneous Real Membranes

V. A. Kirii1,2, V. S. Shelistov1,2, E. A. Demekhin1
1Financial University Supervised by the Government of the Russian Federation, Krasnodar, 350051, Russia
2Kuban State University, Krasnodar, 350040, Russia
Keywords: электрокинетическая неустойчивость, двойной электрический слой, полупроницаемые мембраны, микровихри Духина, микровихри Рубинштейна - Зальцмана, уравнения Нернста - Планка - Пуассона - Стокса, электролит, electrokinetic instability, double electric layer, semipermeable membranes, Dukhin microvortices, Rubinstein-Salzmann microvortices, Nernst-Planck-Poisson-Stokes equations, electrolyte

Abstract >>
Electrokinetic processes in the vicinity of inhomogeneous ion-selective surfaces (electrodes, membranes, microchannels, and nanochannels) consisting of alternating conducting and non-conducting regions in the presence of normal-to-surface electric current are numerically studied. An increase in the electric current density is observed in the case of some particular alternation of conducting and nonconducting regions of the surface. The voltage-current characteristics of homogeneous and inhomogeneous electric membranes are found to be in qualitative agreement. Various physical phenomena leading to the emergence of supercritical current in homogeneous and inhomogeneous membranes are detected.

Behavior of Semi-Infinite Ice Cover under Periodic Dynamic Impact

L. A. Tkacheva
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: поверхностные волны, изгибно-гравитационные волны, упругая пластина, дисперсионные соотношения, преобразование Фурье, метод Винера - Хопфа, surface waves, flexural gravitational waves, elastic plate, dispersion relations, Fourier transform, Wiener-Hopf method

Abstract >>
Oscillations of semi-infinite ice cover in an ideal incompressible fluid of finite depth under local time-periodic axisymmetric load type are considered. Ice cover is simulated by a thin elastic plate of constant thickness. An analytical solution of the problem is obtained using the Wiener-Hopf method. The asymptotic behavior of the amplitudes of oscillations of the plate and the liquid in the far field is studied. It is shown that the propagation of waves in the far field is uneven: in some directions the waves propagate at significantly greater amplitude.

Carbon Ovide Injection into a Reservoir, Saturated with Methane and Water

M. K. Khasanov
Bashkir State University, Sterlitamak, 453103, Russia
Keywords: пористая среда, газовые гидраты, фильтрация, porous medium, gas hydrates, filtration

Abstract >>
This paper presents a mathematical model for carbon dioxide injection into a natural gas reservoir saturated with methane and water accompanied by formation of carbon dioxide hydrate in an extended region. The dependence of the coordinates of the boundaries of the region of phase transitions on the pressure of the injected gas and the initial parameters of the formation are investigated. It is established that the velocity of the near boundary of the region of hydrate formation decreases with increasing water saturation and initial temperature of the reservoir and the velocity of the far boundary of the region of phase transitions increases with increasing pressure of the injected gas and reservoir permeability. It is shown that at large initial temperatures of the reservoir, a regime is possible in which replacement of methane by carbon dioxide without hydrate formation occurs at the far interface, and at the near interface, water is completely transformed into a hydrated state.

Investigation of Heat Transfer of a He-Xe Mixture in Heated Channels with Different Shapes of Cross Section

V. E. Nakoryakov, O. V. Vitovskii
Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: теплообмен, гелий-ксеноновая смесь, число Прандтля, участок тепловой и гидродинамической стабилизации, тепловой поток, heat transfer, helium-xenon mixture, Prandtl number, Section of thermal and hydrodynamic stabilization, heat flow

Abstract >>
This paper describes the results of an experimental study of heat transfer in the case of the flow of a helium-xenon mixture with a Prandtl number approximately equal to 0.23 and the flows of pure helium and air in heated tubes of circular or triangular cross sections with a constant density of the heat flux. The region of thermal stability is studied. The law of heat transfer on the stabilized region is compared with known relationships. The approach that helps to obtain an expression for calculating the heat transfer in heat transfers with circular and triangular cross sections, which operate in a mixture heating mode on the initial region is developed.

Effect of Thermal Radiation on Heat Transfer in an Unsteady Cu-Water Nanofluid Flow over an Exponentially Shrinking Porous Sheet

M. S. Uddin1, A. Zaib2, K. Bhattacharyya3,4
1Khulna University, Khulna-9208, Bangladesh
2Federal Urdu University of Arts, Science & Technology, Gulshan-e-Iqbal Karachi, Pakistan
3Institute of Science, Varanasi-221005, Uttar Pradesh, India
4The University of Burdwan, Burdwan-713104, West Bengal, India
Keywords: тепловое излучение, неустановившееся течение, теплоперенос, неавтомодельные решения, наножидкость, сжимающаяся пластина, экспоненциальный закон, thermal radiation, unsteady flow, heat transfer, dual non-similarity solutions, nanofluid, exponentially shrinking sheet

Abstract >>
The effect of thermal radiation on an unsteady boundary layer flow and heat transfer in a Cu-water nanofluid over an exponentially shrinking porous sheet is investigated. With the use of suitable transformations, the governing equations are transformed into ordinary differential equations. Dual non-similarity solutions are obtained for certain values of some parameters. Owing to the presence of thermal radiation, the heat transfer rate is greatly enhanced, and the thermal boundary layer thickness decreases.

Experimental Study of the Boiling of Superfluid Helium (He-II) in a Porous Body

P. V. Korolev, A. P. Kryukov, Yu. Yu. Puzina
MEI National Research University, Moscow, 111250 Russia
Keywords: эксперимент, He-II, тепломассоперенос, пленочное кипение, пористая структура, experiment, He-II, heat and mass transfer, film boiling, porous structure

Abstract >>
The problems of experimental studies of the boiling of superfluid helium (He-II) on a cylindrical heater placed in a porous body are considered. A diagram of the setup, a description of the experimental cell, control and measurement means, and video recording and data processing techniques are presented. The technique of the experiment and the results are described.

Stability of Advective Flow in an Inclined Plane Liquid Layer Bounded by Solid Planes with a Longitudinal Temperature Gradient. 2. Stable Stratification

R. V. Sagitov1, A. N. Sharifulin2
1Perm State National Research University, Perm, 614990 Russia
2Perm National Research Polytechnic University, Perm, 614990 Russia
Keywords: адвективное течение, наклонный слой, продольный градиент температуры, неустойчивость, устойчивая стратификация, advective flow, inclined layer, longitudinal temperature gradient, instability, stable stratification

Abstract >>
This paper studies the stability of steady convective flow in an inclined plane liquid layer bounded by ideally thermally conductive solid planes in the presence of a homogeneous longitudinal temperature gradient under stable stratification when the layer is inclined so that the temperature in its lower part is smaller than in the upper part.

Time-Resolved Temperature Field of Monocrystalline Silicon Irradiated by a Millisecond Pulse Laser

G. Ming, T. Yong, G. Xun, Y. Boshi, J. Guangyong
Changchun University of Science and Technology, Changchun, 130022, China
Keywords: лазер с миллисекундной длительностью импульса, импульс, монокристаллический кремний, температурное поле, метод конечных элементов, millisecond laser, pulse, monocrystalline silicon, temperature field, finite element method

Abstract >>
Based on the thermal conduction equation that takes into account phase changes and the evolution of thermophysical parameters with temperature, laser-induced heating and melting of monocrystalline silicon are studied. The changes in the behavior of silicon temperature at different places within the irradiation spot and at different time instants are investigated by the finite element and finite difference methods for a wide range of energy and duration of millisecond laser pulses with the Gaussian spatial and temporal shapes. The numerical results are compared with the experimental measurements.

Numerical Investigation of the Temperature Field in a Reservoir with Hydraulic Fracturing

R. F. Sharafutdinov, A. A. Sadretdinov, A. M. Sharipov
Bashkir State University, Ufa, 450076, Russia
Keywords: термометрия в скважинах с гидроразрывом пласта, эффект Джоуля - Томсона, адиабатический эффект, двухфазная фильтрация, thermometry in wells with hydraulic fracture of reservoir, Joule-Thomson effect, adiabatic effect, two-phase filtration, well, reservoir

Abstract >>
The temperature distribution in a reservoir with hydraulic fracture is studied by numerical modeling of transient temperature fields taking into account the Joule-Thomson effect and the adiabatic effect. It is shown that the presence of hydraulic fracture in the reservoir leads to a nonmonotonic temperature variation in the reservoir temperature: as the well pressure decreases, the temperature first decreases due to the adiabatic expansion of the fluid and then increases due to the Joule-Thomson effect. As the water-oil displacement front approaches the wellbore, the temperature decreases slightly due to the heat exchange processes in the fracture-reservoir system.

Displacement Response Analysis of a Floating Ice Plate under a Triangular Pulse Load

Ming-Yong Hu, Zhi-Hong Zhang
Naval University of Engineering, Wuhan 430033, China
Keywords: импульс треугольной формы, плавающая льдина, неустановившееся движение, преобразование Ханкеля, вязкоупругая пластина, triangular pulse load, floating ice, displacement response, Hankel transformation, viscoelastic plate

Abstract >>
The dynamic equation of a viscoelastic floating ice plate under a triangular pulse load is solved analytically through the Hankel transformation and the Laplace transformation. The effects of physical and geometrical parameters of the problem on the displacement response as a function of time and spatial coordinate are discussed.

Buckling and Postbuckling of Size-Dependent Cracked Microbeams Based on a Modified Couple Stress Theory

M. Akbarzadeh Khorshidi, M. Shariati
Ferdowsi University of Mashhad, Mashhad, Iran
Keywords: потеря устойчивости, закритическое деформирование, микробалка с трещиной, моментная теория упругости, характерный линейный размер, buckling, postbuckling, cracked microbeam, couple stress theory, size effect

Abstract >>
The elastic buckling analysis and the static postbuckling response of the Euler-Bernoulli microbeams containing an open edge crack are studied based on a modified couple stress theory. The cracked section is modeled by a massless elastic rotational spring. This model contains a material length scale parameter and can capture the size effect. The von Karman nonlinearity is applied to display the postbuckling behavior. Analytical solutions of a critical buckling load and the postbuckling response are presented for simply supported cracked microbeams. This parametric study indicates the effects of the crack location, crack severity, and length scale parameter on the buckling and postbuckling behaviors of cracked microbeams.

Inertialаstage of Bar Buckling under Longitudinal Compression

M. A. Il'gamov1,2
1Blagonravov Institute of Mechanical Engineering, Moscow, 117901 Russia
2Mavlyutov Institute of Mechanics, Ufa, 450054 Russia
Keywords: стержень, динамическое сжатие, инерционные и упругие силы, динамическое выпучивание, bar, dynamic compression, inertial and elastic forces, dynamic buckling

Abstract >>
The problem of dynamic buckling of a bar under the influence of a compressive force is solved with inclusion of inertial and elastic forces in different stages of the process. The duration of the inertial phase is determined. It is shown that in solids and gas-liquid media, the duration of the inertial stage for real parameters of structural members can be longer than the duration of impact loading.

Modeling of an Inhomogeneous Coating of an Elastic Cylinder with Given Sound-Reflecting Properties

L. A. Tolokonnikov, N. V. Larin, S. A. Skobel’tsyn
Tula State University, Tula, 300012, Russia
Keywords: отражение звука, упругий цилиндр, неоднородный упругий слой, законы неоднородности, sound reflection, elastic cylinder, inhomogeneous elastic coating, inhomogeneity laws

Abstract >>
The inverse problem of determining the inhomogeneity laws of a coating of an elastic cylinder that provide the smallest reflection of a plane acoustic wave in a certain angular sector and in a given frequency range. A functional that expresses the reflection intensity is constructed by direct solution of the direct problem, and an algorithm for minimizing it is proposed. Analytical expressions describing the mechanical parameters of the inhomogeneous coating.

Critical Velocities in Fluid-Conveying Single-Walled Carbon Nanotubes Embedded in an Elastic Foundation

Ch. K. Rao1, L. B. Rao2
1Nalla Narasimha Reddy Group of Institutions, Madian Guda, Near Naarapalli, Uppal, Hyderabad, India
2VIT University, Chennai Campus, Vandalur-Kelambakkam Road, Chennai-600127, Tamil Nadu, India
Keywords: критическая скорость, однослойная углеродная нанотрубка, нелокальная теория упругости, двухпараметрическое основание, critical velocity, SWCNT, nonlocal elasticity theory, two-parameter foundation

Abstract >>
The problem of stability of fluid-conveying carbon nanotubes embedded in an elastic medium is investigated in this paper. A nonlocal continuum mechanics formulation, which takes the small length scale effects into consideration, is utilized to derive the governing fourth-order partial differential equations. The Fourier series method is used for the case of the pinned-pinned boundary condition of the tube. The Galerkin technique is utilized to find a solution of the governing equation for the case of the clamped-clamped boundary. Closed-form expressions for the critical flow velocity are obtained for different values of the Winkler and Pasternak foundation stiffness parameters. Moreover, new and interesting results are also reported for varying values of the nonlocal length parameter. It is observed that the nonlocal length parameter along with the Winkler and Pasternak foundation stiffness parameters exert considerable effects on the critical velocities of the fluid flow in nanotubes.

Active Control of a Clamped L-Connected Plate Power Flow by using a Piezoelectric Actuator

J.-X. Li, Zh.-B. Chen, Y.-H. Jiao
Harbin Institute of Technology, Harbin, China
Keywords: пластина L-образной формы, пьезоэлектрический актуатор, активный контроль, волновое приближение, мощность потока, L-connected plate, piezoelectric actuator, active control, wave approach, power flow

Abstract >>
The dynamic response of a clamped L-connected plate and an actively controlled vibratory power flow are studied. The vibratory power flow is suppressed by a piezoelectric patch, which is bonded on the L-connected plate. The electric patch is considered as an actuator. The feedforward least mean square algorithm is used to deduce the optimal piezoelectric patch control moment. Actuator operation with close-to-optimal moments is studied with allowance for the presence of in-plane waves.