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Journal of Applied Mechanics and Technical Physics

2017 year, number 1

1.
Asymptotic Theory of Neutral Stability of the Couette Flow of a Vibrationally Excited Gas

Yu. N. Grigor'ev1,2, I. V. Ershov1,3
1Institute of Computational Technologies, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Novosibirsk State University, Novosibirsk, 630090, Russia
3Novosibirsk State University of Architecture and Civil Engineering, Novosibirsk, 630008, Russia
Keywords: линейная теория устойчивости, колебательно-возбужденный газ, кривая нейтральной устойчивости, критическое число Рейнольдса, linear stability theory, vibrationally excited gas, neutral stability curve, critical Reynolds number

Abstract >>
An asymptotic theory of the neutral stability curve for a supersonic plane Couette flow of a vibrationally excited gas is developed. The initial mathematical model consists of equations of two-temperature viscous gas dynamics, which is used to derive a spectral problem for a linear system of eighth-order ordinary differential equations within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the "inviscid" and "viscous" parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. In particular, the critical Reynolds number increases with excitation enhancement, and the neutral stability curve is shifted toward the domain of higher wave numbers. This is also confirmed by means of solving an asymptotic equation for the critical Reynolds number at the Mach number M ≤4.



2.
One-Dimensional Model of Two-Phase Fluid Displacement in a Slot with Permeable Walls

S. V. Golovin1,2, M. Yu. Kazakova1,2
1Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: ячейка Хеле-Шоу с проницаемыми стенками, неустойчивость Саффмана-Тейлора, двухфазная жидкость, перенос примеси, Hele-Shaw cell with permeable walls, Saffman-Taylor instability, two-phase fluid, admixture transportation

Abstract >>
A one-dimensional model is proposed for transportation of a two-phase fluid (sand-containing fluid and pure fluid) in the Hele-Shaw cell with permeable walls through which the pure fluid can escape as the sand concentration increases. The model describes the process of pure fluid displacement with the emergence of the Saffman — Taylor instability and extends the Koval' model to the case of sand concentration variation owing to pure fluid outflow through the cell walls. The Riemann problem is analyzed. New flow configurations, which are not predicted by the Koval' model, are discovered.



3.
Influence of the Size and Wall Curvature of Nanopores on the Gas Distribution Pattern in Them

S. G. Psakh'e1,2, K. P. Zol'nikov1, A. V. Korchuganov1, D. S. Kryzhevich1, Yu. V. Grinyaev1
1Institute of Strength Physics and Materials Science, Siberian Branch, Russian Academy of Sciences, Tomsk, 634055, Russia
2Tomsk Polytechnic University, Tomsk, 634050, Russia
Keywords: нанопористые материалы, адсорбция, молекулярная динамика, водород, распределение плотности, nanoporous materials, adsorption, molecular dynamics, hydrogen, density distribution

Abstract >>
The behavior of hydrogen molecules in carbon nanopores of different shapes (slit, cylindrical, and spherical) is investigated using the molecular dynamics method. It is shown that an adsorbed molecular layer with increased density is formed near the nanopore walls, and dynamic equilibrium is established between this layer and the gas in the central region of the nanopore. The distribution of the density of gas molecules over the cross section is found to depend on the size and curvature walls of the nanopores: with a reduction in the size of the nanopores, the density of the adsorbate increases more rapidly in spherical nanopores, whose walls are characterized by greater mean curvature.



4.
Onset of Convection in a Multicomponent Fluid Layer in the Presence of a Uniform Magnetic Field

J. Prakash, R. Kumar, K. Lata
Himachal Pradesh University, Summer Hill, Shimla-171005, India
Keywords: конвекция в многокомпонентной жидкости, принцип изменения типа устойчивости, колебательные движения, комплексная скорость роста возмущений, multicomponent convection, the principle of the exchange of stabilities, oscillatory motions, complex growth rate

Abstract >>
The principle of the exchange of stabilities for magnetohydrodynamic multicomponent convection is established. If this sufficient condition holds and there are perturbations, oscillatory motions of neutral or growing amplitude can exist in the fluid. The upper bounds for the complex growth rate of such motions when at least one of the boundaries is rigid are obtained.



5.
Some Features of the Dynamics of Ferroelectric (Ferromagnetic) Heterostructures

M. O. Levi, G. Yu. Levi, V. A. Lyzhov
Southern Scientific Center, Russian Academy of Sciences, Rostov-on-Don, 344006, Russia
Keywords: электромагнитоупругость, сегнетоэлектрики, ферромагнетики, функция Грина, слоистые структуры, фазовые скорости, electromagnetoelastic, ferroelectrics, ferromagnets, Green's function, layered structures, phase velocities

Abstract >>
This paper considers the dynamic coupled problem of harmonic oscillations of a layered inhomogeneous electromagnetoelastic medium subjected to an oscillating mechanical or electrical load under various electric and magnetic field conditions specified on the surface and internal boundaries of this medium. Green's function for the medium is constructed. Dispersion curves and phase velocities for different boundary conditions and materials are obtained.



6.
Slip Effect on the MHD Channel Flow in the Presence of the Across Mass Transfer PHenomenon

S. Ijaz1, N. Saleem2, S. Munawar1,3
1School of Science and Technology, Lahore, 54000, Pakistan
2College of Business Administration, Dammam, Saudi Arabia
3Prince Mohammad Bin Fahd University, Al Khobar, 31952, Saudi Arabia
Keywords: поперечный массообмен, аналитическое решение, течение в канале, магнитогидродинамика, условия скольжения, across mass transfer (AMT), analytical solution, channel flow, MHD, slip condition



7.
Low-Speed Peristaltic Transport in a Vertical Channel Subject to the Soret and Dufour Effects

T. Hayat1,2, F. M. Abbasi3, A. Alsaedi2
1Quaid-I-Azam University, Islamabad, 44000, Pakistan
2Nonlinear Analysis and Applied Mathematics Research Group, Jeddah, 21589, Saudi Arabia
3COMSATS Institute of Information Technology, Islamabad, 44000, Pakistan
Keywords: перистальтическое движение, джоулев нагрев, эффекты Соре и Дюфура, peristaltic transport, Joule heating, Soret and Dufour effects

Abstract >>
Simultaneous effects of heat and mass transfer in peristaltic transport of a viscous fluid are considered. Mathematical modeling is provided in the presence of the Joule heating and the Soret and Dufour effects. The analysis is performed using the long wavelength and low Reynolds number considerations. Perturbation solutions are obtained for a small Brinkman number.



8.
Magnetohydrodynamic and Heat Transfer Effects on the Stagnation-Point Flow of an Electrically Conducting Nanofluid Past a Porous Vertical Shrinking/Stretching Sheet in the Presence of Variable Stream Conditions

R. Kandasamy1, V. V. Balachandar2, S. B. Hasan2
1Research Centre for Computational Mathematics, Malaysia
2Universiti Tun Hussein Onn, Johor, Malaysia
Keywords: поток вблизи точки торможения, наножидкость, броуновское движение, термофорез, магнитное поле, stagnation-point flow, nanofluid, Brownian motion, thermophoresis, magnetic field

Abstract >>
A steady two-dimensional magnetohydrodynamic stagnation-point flow of an electrically conducting fluid and heat transfer with thermal radiation of a nanofluid past a shrinking and stretching sheet is investigated numerically. The model used for the nanofluid incorporates the effects of the Brownian motion and thermophoresis. A similarity transformation is used to convert the governing nonlinear boundary-layer equations into coupled higher-order nonlinear ordinary differential equations. The result shows that the velocity, temperature, and concentration profiles are significantly influenced by the Brownian motion, heat radiation, and thermophoresis particle deposition



9.
Action of Periodic Surface Pressure on an Ice Cover in the Vicinity of a Vertical Wall

I. V. Sturova
Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: линейная теория мелкой воды, изгибно-гравитационные волны, вязкоупругий ледяной покров, вертикальная стенка, периодическая внешняя нагрузка, краевые волны, linear shallow water theory, bending gravity waves, viscoelastic ice cover, vertical wall, periodic external load, edge waves

Abstract >>
This paper presents the solution of the linear hydroelastic problem of stabilized forced vibrations of a semi-infinite ice cover under the effect of localized external load. The ice cover is simulated by a viscoelastic thin plate, the thickness of the liquid layer is assumed to be small, and the shallow water theory is used. The liquid is limited by a solid vertical wall, and the straight edge of the elastic plate adjacent to the wall can be both free and clamped. The solution is obtained with the help of the Fourier integral transform. The behavior of the ice cover is studied in terms of the frequency of the external load and boundary conditions on the edge of the plate. It is shown that, in the case of a free edge of the plate, there are considerable bends on the edge, which could be comparable with bends at the center of the pressure impact region. It is established that, due to the existence of wave movements of the type of edge waves, the external load energy is transferred to larger distances along the free edge, and there are significant bending moments on the edge of the clamped plate, which can lead to fracture of the ice cover at sufficiently great intensity of the external load.



10.
Cavitation Deceleration of a Circular Cylinder in a Liquid after Impact

M. V. Norkin
Institute of Mathematics, Mechanics and Computer Science, Rostov-on-Don, 344090, Russia
Keywords: идеальная несжимаемая жидкость, круговой цилиндр, удар, кавитационное торможение, свободная граница, каверна, малые времена, число Фруда, ideal incompressible fluid, circular cylinder, impact, cavitation deceleration, free boundary, cavity, small times, Froude number

Abstract >>
The formation of a cavity during vertical impact and subsequent deceleration of a circular cylinder semi-submerged in a liquid is investigated. The problem with unilateral constraints is formulated to determine the initial regions of separation and contact of liquid particles and the perturbation of the internal and external free boundaries of the liquid at small times. The problem is solved using a direct asymptotic method which is effective at small times. Examples of numerical calculations of the formation of one or two cavities near the boundary of the body are given. It is shown that the acceleration of the cylinder has a significant impact on the liquid flow pattern near the body at small times.



11.
Passage of Sound Through a Discretely Inhomogeneous Thermoelastic а PLane Layer Adjacent to Heat-Conducting Liquids

L. A. Tolokonnikov, N. V. Larin
Tula State University, Tula, 300012, Russia
Keywords: отражение и прохождение звука, неоднородный термоупругий слой, теплопроводная жидкость, reflection and transmission of sound, inhomogeneous thermoelastic layer, heat-conducting liquid

Abstract >>
An analytical solution of the problem of the passage of a plane sound wave through a discretely inhomogeneous thermoelastic layer adjacent to inviscid heat-conducting liquids. Results of calculations of the dependences of the transmission coefficient on the wave incidence angle and frequency for discretely inhomogeneous and continuously inhomogeneous thermoelastic layers are given. It is shown that a thermoelastic layer with continuously inhomogeneous thickness can be simulated using a system of homogeneous thermoelastic layers.



12.
Effect of Variable Thermal Conductivity Models on the Combined Convection Heat Transfer in a Square Enclosure Filled with a Water-Alumina Nanofluid

A. Ghafouri, M. Salari, A. F. Jozaei
Islamic Azad University, Ahvaz, Iran
Keywords: наножидкость, интенсификация теплообмена, квадратная ячейка, уравнение теплопроводности, nanofluid, heat transfer enhancement, square enclosure, thermal conductivity model

Abstract >>
In this numerical study, the effects of variable thermal conductivity models on the combined convection heat transfer in a two-dimensional lid-driven square enclosure are investigated. The fluid in the square enclosure is a water-based nanofluid containing alumina nanoparticles. The top and bottom horizontal walls are insulated, while the vertical walls are kept at different constant temperatures. Five different thermal conductivity models are used to evaluate the effects of various parameters, such as the nanofluid bulk temperature, nanoparticle size, nanoparticle volume fraction, Brownian motion, interfacial layer thickness, etc. The governing stream-vorticity equations are solved by using a second-order central finite difference scheme coupled with the conservation of mass and energy. It is found that higher heat transfer is predicted when the effects of the nanoparticle size and bulk temperature of the nanofluid are taken into account.



13.
Effects of the Chemical Reaction and Heat Generation or Absorption on a Mixed Convection Boundary Layer Flow over a Vertical Stretching Sheet with Nonuniform Slot Mass Transfer

N. Samyuktha1, R. Ravindran1, M. Ganapathirao2
1National Institute of Technology, Tiruchirappalli, 620015, Tamil Nadu
2Mathematics and Basic Science, Neemrana, 301705, Rajasthan
Keywords: неравномерный массообмен через щелевое отверстие, смешанно-конвекционный поток, растягиваемая пластина, химическая реакция, выделение тепла, nonuniform slot suction, mixed convection, stretching sheet, chemical reaction, heat generation

Abstract >>
An analysis is performed to study the effects of the chemical reaction and heat generation or absorption on a steady mixed convection boundary layer flow over a vertical stretching sheet with nonuniform slot mass transfer. The governing boundary layer equations with boundary conditions are transformed into the dimensionless form by a group of nonsimilar transformations. Nonsimilar solutions are obtained numerically by solving the coupled nonlinear partial differential equations using the quasi-linearization technique combined with an implicit finite difference scheme. The numerical computations are carried out for different values of dimensionless parameters to display the distributions of the velocity, temperature, concentration, local skin friction coefficient, local Nusselt number, and local Sherwood number. The results obtained indicate that the local Nusselt and Sherwood numbers increase with nonuniform slot suction, but nonuniform slot injection produces the opposite effect. The local Nusselt number decreases with heat generation and increases with heat absorption.



14.
Prediction of Creep Rupture in 2.25Cr–1Mo Notched Bars

J. Jelwan
The Holy Spirit University of Kaslik, Jounieh, Lebanon
Keywords: поврежденность, ползучесть, образцы с надрезами, экспериментальные данные, damage, creep, notched bars, experimental data

Abstract >>
This paper re-examines the creep life methodology based on the continuum damage mechanics (CDM) of the Kachanov and Rabotnov theory. Uniaxial creep and multiaxial creep rupture formulations are presented taking into account the primary creep effect. The scalar damage parameter is computed up to time-to-rupture as a function of time and stress. The methodology implemented is based on the uniaxial time-to-rupture obtained experimentally. The times-to-rupture for bars with different notches are calculated. It is demonstrated that the use of the damage parameter is vital to indicate the critical damage location where failure occurs. Results are compared to those obtained experimentally. It is shown that the primary creep inclusion has a significant effect on the damage distribution zone.



15.
Experimental Investigation and Dimensionless Analysis of Forming of Rectangular Plates Subjected to Hydrodynamic Loading

H. Babaei, T. Mirzababaie Mostofi, M. Alitavoli, A. Saeidinejad
University of Guilan, Rasht, 3756-41635, Iran
Keywords: деформирование, прямоугольная пластина, гидродинамика, ударник, ударная волна, deformation, rectangular plate, hydrodynamics, drop hammer, shock wave

Abstract >>
This paper describes an experimental setup consisting of a drop hammer and a shock tube filled with a liquid, where a shock wave is formed, and results of experiments performed with fully clamped rectangular plates subjected to an impact load of the water shock wave. The results are presented in terms of the central deflection of the plates as a function of the kinetic energy of the drop hammer. The singular value decomposition method is used in conjunction with dimensionless numbers to obtain analytical dependences of the central deflection of the plates on the impact load parameters.



16.
Slowing Down of the Growth of a Slit of Variable Width under the Influence of a Temperature Field

B. A. Mustafayev
Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, AZ1141, Azerbaijan
Keywords: щель переменной ширины, неоднородное поле напряжений, температурное поле, контактные напряжения, сцепление, проскальзывание, slit of variable width, inhomogeneous stress field, temperature field, contact stresses, adhesion, slippage

Abstract >>
This paper touches upon changes in the temperature field near the ends of a slit of variable width under the action of an inhomogeneous stress field. The solution of the boundary-value problem on the equilibrium of the slit with partially contacting edges (there is adhesion of the edges on a certain part of the contact zone and slippage on another one) under the action of the outer inhomogeneous stress field, temperature field, and efforts on the contacting surfaces of the slit of variable width comparable with displacements in an elastic state is reduced to the problem of linear conjugation of analytic functions.



17.
Role of Unloading and Filtration of Gas in the Development of Main Cracks in a Coal Bed

E. P. Fel'dman1, N. A. Kalugina1, T. N. Meln'ik2
1Institute for Physics of Mining Processes, National Academy of Sciences Ukraine, Dnepropetrovsk, 49600, Ukraine
2Galkin Donetsk Physical-Technical Institute, Donetsk, 83114, Ukraine
Keywords: угольный пласт, газонаполненная трещина, фильтрация, диффузия, выброс, coal bed, gas-filled crack, filtration, diffusion, emission

Abstract >>
The development of main cracks in a coal bed due to rapid unloading is analyzed using the methods of theoretical physics. A fracture criterion and a criterion for the time to fracture of a site on the edge of the bed are obtained.



18.
Kinetic Physical Phenomenological Model of Creep-Rupture Strength of Metals

V. M. Greshnov, R. I. Shaikhutdinov, I. V. Puchkova
Ufa State Aviation Technical University, Ufa, 450000, Russia
Keywords: необратимая деформация, дислокационная ползучесть, вязкое разрушение, структурно-феноменологический подход, длительная прочность, irreversible deformation, dislocation creep, ductile fracture, structural-phenomenological approach, creep-rupture strength

Abstract >>
A kinetic model of creep-rupture strength is constructed using the physicomathematical theory of irreversible strains of metals. An algorithm for the mathematical modeling of the processes occurring during tension of specimens. Results of experimental verification of a uniaxial model of creep-rupture strength are given. It is shown that the proposed model differs from available models fact in that it contains physical structural parameters (scalar densities of dislocations and microcracks) and kinetic equations for them.



19.
Bending of Equally Stressed Reinforced Plates with Account for Their Weakened Resistance to the Transverse Shear

A. P. Yankovskii
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: упругие пластины, равнонапряженное армирование, изгибное деформирование, теория Рейсснера, неединственность решения, elastic plates, equally stressed reinforcement, bending deformation, the Reissner theory, nonuniqueness of solutions

Abstract >>
The hypotheses of the Reissner theory are used to formulate the problem of equally stressed reinforcement (ESR) of transversely bent elastic plates by fibers with a constant cross section. The corresponding system of governing equations and boundary conditions is performed. The model problem of ESR of rectangular elongated plates subjected to cylindrical bending with various types of loading of one of the longitudinal edges and rigid clamping of the other one. It is shown that there could exist two solutions of the problem of ESR, one of which is regular and the other one singular. The edge effects occurring in the presence of the torque applied to the edge, which significantly affects both the stress-strain state of the binder material and the reinforcement structure.



20.
Strength Evaluation of a Cement Ring Adjacent to a Production Well Bore

A. M. Il'yasov
Mavlyutov Institute of Mechanics, Russian Academy of Sciences, Ufa, 450054, Russia
Keywords: упругое идеально пластическое тело, задача Ламе, критерий текучести, цементное кольцо, elastic perfectly plastic body, Lame problem yield criterion, cement ring

Abstract >>
A model for predicting the strength of a cement ring adjacent to a production well bore without consideration of internal and temperature stresses is proposed based on solutions of the Lame problems for one- and two-layer tubes and the Huber-Mises yield criterion using the model of a perfectly plastic isotropic body.