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2017 year, number 2

Theoretical Study of Limiting Regimes of Hydrate Formation during Contact of Gas and Water

V. S. Shagapov1, Yu. A. Yumagulova1, N. G. Musakaev2,3
1Institute of Mechanics and Machinery, Kazan Scientific Center, Russian Academy of Sciences, Kazan, 42011, Russia
2Tyumen the Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Tyumen, 625026, Russia
3Tyumen Industrial University, Tyumen, 625000, Russia
Keywords: газовый гидрат, диффузия, фильтрация, теплообмен, gas hydrate, diffusion, filtration, heat

Abstract >>
A mathematical model is proposed and analytical solutions are constructed for the problem of the growth of a hydrate layer during contact of gas and water for two limiting regimes of gas hydrate formation, determined by mass transfer and heat transfer. Critical values are obtained for thermal parameters and for parameters that determine the flow properties of the hydrate layer (diffusion coefficient and permeability), on which the hydrate formation regime depend.

Experimental Study of Interaction of Shock Waves with the Contact Boundary Zone and Turbulent Mixing of Different Gases

A. N. Razin, N. V. Nevmerzhitskii, E. A. Sotskov, E. D. Senkovskii, O. L. Krivonos, E. V. Levkina, S. V. Frolov, E. V. Bodrov, K. V. Anisiforov
All-Russian Research Institute of Experimental Physics, Sarov, 607188, Russia
Keywords: ударная труба, двухслойная газовая система, контактная граница, неустойчивость Рихтмайера -- Мешкова, турбулентное перемешивание, фронт ударной волны, shock tube, two-layer gas system, interface, Richtmyer-Meshkov instability, turbulent mixing, shock-wave front

Abstract >>
The interaction of a shock wave with turbulent flow has been experimentally investigated. The case where the shock wave formed on one end of the tube, passed through the interface between two resting gases with different densities (air-CO2 or air-Ar), reflected from the end of the tube and interacted with turbulent mixing zone formed at the contact boundary. The Mach number of the shock wave incident on the interface in air was M ≈ 2.37-2.57. The flow field was recorded using schlieren method and high-speed video recording. It is found that after passing the mixing zone, the shock-wave front is deformed and becomes unstable.

Measurement of Viscous Flow Velocity and its Visualization using Two Magnetic Resonances

A. V. Boiko1,2, A. E. Akulov3, A. P. Chupakhin4, A. A. Cherevko4,5, N. C. Denisenko4,5, A. A. Savelov6, Yu. A. Stankevich6, A. K. Khe4,5, A. A. Yanchenko4,5, A. A. Tulupov6
1Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Tyumen State University, Tyumen, 625003, Russia
3Institute of Cytology and Genetics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
4Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
5Novosibirsk State University, Novosibirsk, 630090, Russia
6International Tomography Center of the Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: магниторезонансная томография, велосиметрия, течение в канале, magnetic resonance tomography, velocimetry, channel flow

Abstract >>
The accuracies of measurement of the velocity field using clinical and research magnetic resonance scanners were compared. The flow velocity was measured for a fluid simulating blood in the carotid artery model connected to a programmable pump. Using phase-contrast magnetic resonance tomography, velocity distributions in the carotid artery model and were obtained and compared with the analytical solution for viscous liquid flow in a cylindrical tube (Poiseuille flow). It is established that the accuracy of the velocity measurement does not depend on the field induction and spatial resolution of the scanners.

MHD Effects on a Thermo-Solutal Stratified Nanofluid Flow on an Exponentially Radiating Stretching Sheet

T. Hayat1,2, M. Rashid1, M. Imtiaz1, A. Alsaedi2
1Quaid-I-Azam University, Islamabad, 44000, Pakistan
2King Abdulaziz University, Jeddah, 21589, Saudi Arabia
Keywords: магнитогидродинамическая наножидкость, экспоненциально растягивающаяся пластина, пористая среда, двойная стратификация, MHD nanofluid, exponentially stretching sheet, porous medium, double stratification

Abstract >>
This study is focused on the heat and mass transfer effects in a magnetohydrodynamic (MHD) flow of a viscous nanofluid saturating a porous medium past an exponentially radiating stretching sheet. The governing differential equations are transformed to a system of nonlinear ordinary differential equations by suitable transformations. It is noted that stratification affects the local Nusselt and Sherwood numbers.

Nonorthogonal Stagnation-Point Flow over a Lubricated Surface

K. Mahmood1, M. Sajid1, N. Ali1, F. Labropulu2
1International Islamic University, Islamabad, 44000, Pakistan
2Luther College, Regina, Canada
Keywords: критическая точка, пограничный слой, метод ячеек Келлера, граничные условия скольжения, stagnation-point flow, boundary layer, Keller box method, slip boundary condition

Abstract >>
An attempt is made to study a steady two-dimensional flow of a viscous incompressible fluid incident at some angle onto a plate lubricated with a thin layer of a power-law fluid. Similar and nonsimilar solutions of the governing partial differential equations are obtained numerically by imposing the continuity of velocity and shear stress at the interface layer between the fluid and the lubricant. The Keller box method is applied to obtain the solutions. The limiting cases for full and no-slip conditions are compared

Unsteady Double Diffusive Mixed COnvection Flow over a Vertically Stretching Sheet in the Presence of Suction/Injection

M. Daba1, P. Devaraj2
1College of Natural Sciences, Jimma-378, Ethiopia
2College of Engineering Guindy, Chennai, 600025, India
Keywords: смешанная конвекция, вдув и отсос, растягиваемая пластина, силы плавучести, mixed convection, suction/injection, stretching sheet, buoyancy force

Abstract >>
An unsteady double diffusive mixed convection boundary layer flow over a vertically stretching sheet in the presence of suction/injection is investigated in this paper. The governing partial differential equations are reduced by applying suitable transformations to a set of nonlinear ordinary differential equations, which is solved by the Keller box method. The influence of various flow parameters on the velocity, temperature, and species concentration profiles of the fluid is studied. The effect of some problem parameters on the skin friction coefficient in the presence of suction/injection is considered

Modeling of Convective Structures in a Thin Layer of Silicone Oil in Air Flow under Heating

V. P. Reutov, G. V. Rybushkina
Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, 603950, Russia
Keywords: термическая конвекция, конвективные структуры, сдвиговое течение, пограничный слой, thermal convection, convection structures, shear flow, boundary layer

Abstract >>
Numerical simulation was performed to study convective structures in a thin silicone oil layer heated from below, whose free surface is exposed to air flow, generating a drift current. Transformation of the basic equations to a form suitable for spectral methods is proposed. The steady flow velocity profile obtained under laboratory experiment conditions is calculated. It is shown that increasing the Reynolds number leads to the transition from the polygonal convective cells to longitudinal (elongated along the flow) rolls. The dependence of the transitional Reynolds number on the temperature on the lower boundary of the layer is obtained. The calculation results are compared with experimental data.

Effect of Surface Permeability on the Structure of a Separated Turbulent Flow and Heat Transfer behind a Backward-Facing Step

V. V. Terekhov, V. I. Terekhov
Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: турбулентный поток, теплообмен, отрывное течение, обратный уступ, пористая стенка, вдув, отсос, теплообмен, turbulent flow, heat transfer, separated flow, backward-facing step, porous wall, injection, suction, heat transfer

Abstract >>
The structure and heat transfer in a turbulent separated flow in a suddenly expanding channel with injection (suction) through a porous wall are numerically simulated with the use of two-dimensional averaged Navier-Stokes equations, energy equations, and v2-f turbulence model. It is shown that enhancement of the intensity of the transverse mass flux on the wall reduces the separation region length in the case of suction and increases the separation region length in the case of injection up to boundary layer displacement. The maximum heat transfer coefficient as a function of permeability is accurately described by the asymptotic theory of a turbulent boundary layer.

Stability of Advective Flow in an Inclined Plane Fluid Layer Bounded by Solid Planes with a Longitudinal Temperature Gradient. 1. Unstable 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 жидкости, продольный градиент температуры, конвективная неустойчивость, advective flow, inclined fluid layer, longitudinal temperature gradient, convective instability

Abstract >>
The stability of steady convective flow in an inclined plane fluid layer bounded by ideally thermally conductive solid planes is studied in the presence of a homogeneous longitudinal temperature gradient under unstable stratification conditions where the layer is inclined so that the temperature is higher in the lower part than in the upper part. It is shown that the inclination leads to the transition from critical perturbations to long-wave helical perturbations. Stability maps of flow regimes are given for the entire range of Prandtl numbers and inclination angles corresponding to unstable stratification.

Filtration of Live Oil in the Presence of Phase Transitions in a Porous Medium with Inhomogeneous Permeability

R. F. Sharafutdinov, A. S. Bochkov, A. M. Sharipov, A. A. Sadretdinov
Bashkir State University, Ufa, 450000, Russia
Keywords: температура, эффект Джоуля -- Томсона, адиабатический эффект, радиально-угловая неоднородность распределения проницаемости, разгазирование, скважина, пласт, двухфазная фильтрация, temperature, Joule-Thomson effect, adiabatic effect, radial-angular nonuniformity of permeability distribution, degassing, well, reservoir, two-phase filtering

Abstract >>
The radial angular temperature distribution in a porous medium with nonuniform permeability is investigated by numerical simulation of nonisothermal filtration of live oil taking into account the degassing heat, the Joule-Thomson effect, and the adiabatic effect. It is shown that nonuniform permeability in the wellbore zone of the porous layer leads to anomalous cooling due to intense degassing in the well-permeable zone.

Hydro-Thermodynamics of a Liquid Film with CRystals on the Body Surface in an Air Flow Containing Ice Particles

A. V. Kashevarov1, A. L. Stasenko1,2
1Zhukovskii Central Aerohydrodynamic Institute, Zhukovskii, 140180, Russia
2Moscow Institute of Physics and Technology, Zhukovskii, 140180, Russia
Keywords: водно-кристаллическая суспензия, плавление кристаллов, барьерный лед, water-crystalline suspension, melting of crystals, barrier ice

Abstract >>
This paper presents a physicomathematical model for the effect of a flow of air containing ice crystals on a water film moving along the surface of a solid body. Numerical studies were carried out for the case of a cylinder in transverse flow. The influence of the effective viscosity of the suspension of crystals in the carrier water and the finite time of their melting by the hydro-thermodynamics of the solidifying film. In this case, the model used is nonlocal.

Analytical Solution of the Problem of Heat Transfer in Rarefied Gas between Two Coaxial cylinders

O. V. Germider1, V. N. Popov1, A. A. Yushkanov2
1Northern Federal University named after M.V. Lomonosov, Arkhangelsk, 163002, Russia
2Moscow State Regional University, Moscow, 107005, Russia
Keywords: уравнение Больцмана, течение газа в канале, метод характеристик, Boltzmann equation, gas flow in a channel, method of characteristics

Abstract >>
The method of characteristics was used within the framework of the kinetic approach to construct an analytical solution of the problem of heat transfer in a channel whose walls were formed by two coaxial cylinders. The main equation was the Williams kinetic equation, and the boundary condition on the channel walls was the diffusion reflection model. The vector field of the heat in the channel was determined, and the specific heat flow through the cross section of the channel was calculated. It was shown that the results obtained for a limiting case, in which the cylinder radii were significantly greater than the mean length of free path of gas molecules, were in good agreement with the results obtained for a plane channel with infinite parallel walls.

Numerical Simulation of the Nanoparticle Diameter Effect on the Thermal Performance of a Nanofluid in a Cooling Chamber

A. Ghafouri1, N. Pourmahmoud2, A. F. Jozaei1
1Islamic Azad University, Ahvaz, Iran
2Urmia University, Urmia, Iran
Keywords: наножидкость, диаметр наночастиц, теплопроводность, число Нуссельта, nanofluid, nanoparticle diameter, heat transfer enhancement, Nusselt number

Abstract >>
The thermal performance of a nanofluid in a cooling chamber with variations of the nanoparticle diameter is numerically investigated. The chamber is filled with water and nanoparticles of alumina (Al2O3). Appropriate nanofluid models are used to approximate the nanofluid thermal conductivity and dynamic viscosity by incorporating the effects of the nanoparticle concentration, Brownian motion, temperature, nanoparticles diameter, and interfacial layer thickness. The horizontal boundaries of the square domain are assumed to be insulated, and the vertical boundaries are considered to be isothermal. The governing stream-vorticity equations are solved by using a second-order central finite difference scheme coupled with the mass and energy conservation equations. The results of the present work are found to be in good agreement with the previously published data for special cases. This study is conducted for the Reynolds number being fixed at Re = 100 and different values of the nanoparticle volume fraction, Richardson number, nanofluid temperature, and nanoparticle diameter. The results show that the heat transfer rate and the Nusselt number are enhanced by increasing the nanoparticle volume fraction and decreasing the Richardson number. The Nusselt number also increases as the nanoparticle diameter decreases.

Block Element Method for Solving Integrated Equations of Contact Problems in V-Shaped Regions

V. A. Babeshko1, O. V. Evdokimova1, O. M. Babeshko2, A. G. Fedorenko2
1Southern Scientific Center of the Russian Academy of Sciences, Rostov-on-Don, 344006, Russia
2Kuban State University, Krasnodar, 350040, Russia
Keywords: контактные задачи, интегральные уравнения, клиновидная область, блочный элемент, факторизация, приближенные решения, сингулярные особенности, contact problems, integral equations, V-shaped region, block element, factorization, approximate solutions, singular properties

Abstract >>
This paper describes the block element method for spatial integral equations with a difference kernel in boundary-value problems of continuum mechanics and mathematical physics. The basis of the proposed method is the Wiener-Hopf method, whose generalization for a spatial case is called integral factorization method. The block element method is applied to solve problems in regions with piecewise smooth boundaries containing corner points. The developed method was used to solve the contact problem for a V-shaped stamp occupying the first quadrant. This paper describes in detail the methods of obtaining various characteristics of the solution constructed by reversing the system of one-dimensional linear integral equations typical for dynamics and static contact problems for stamps in the form of a strip.

Solution of the Problem of Linear Viscoelasticity for Multiply Connected Anisotropic Plates

S. A. Kaloerov, A. I. Zanko
Donetsk National University, Donetsk, 83001, Ukraine
Keywords: вязкоупругость, многосвязная плита, комплексные потенциалы теории изгиба плит, метод малого параметра, обобщенный метод наименьших квадратов, viscoelasticity, multiply connected plate, complex potentials of the plate bending theory, small parameter method, generalized least squares method

Abstract >>
This paper describes the method of solving the problems of linear viscoelasticity for thin plates under the influence of bending moments and transverse forces. The small parameter method was used to reduce the original problem to a sequence of boundary-value problems solved via complex potentials of the bending theory of multiply connected anisotropic plates. The general representations of complex potentials and boundary conditions for their determination are obtained. The method for determining the stress state of the plate at any time with respect to complex approximation potentials is developed by replacing the powers of the small parameter with Rabotnov operators. The problem of a plate with elliptical holes is solved. The numerical calculation results in the case of a plate with one or two holes are given. The changes of bending moments in time until stationary condition is reached and the influence of geometric characteristics of the plate on these variable are studied.

Three-Dimensional Simulation of Two Viscoelastic Droplets Impacting onto a Rigid Plate using Smoothed Particle Hydrodynamics

X. Y. Xu
School of Mathematics and Computer Science, Hanzhong, 723000, China
Keywords: сглаженные гидродинамические частицы, трехмерная задача, капли, вязкоупругость, численное моделирование, smoothed particle hydrodynamics, three-dimensional problem, droplets, viscoelastic, numerical simulation

Abstract >>
In this article, a smoothed particle hydrodynamics method is developed to simulate the dynamic process of the impact of two viscoelastic droplets onto a rigid plate. The Oldroyd-B fluid is considered as the rheological model to describe the viscoelastic characteristics. An artificial stress is added into the momentum equation to remove the tensile instability. The solution of the problem of two successive impacts of droplets are demonstrated to be in good agreement with the literature data. The problem of two droplets impacting simultaneously onto a rigid plate is investigated.

Chernov–Luders and Portevin–Le Chatelier Deformations in Active Deformable Media of Different Nature

L. B. Zuev
Institute of Strength Physics and Materials Science, Siberian Branch, Russian Academy of Sciences, Tomsk, 634055, Russia
Keywords: пластичность, деформация, локализация, полосы деформации, структура металлов, дефекты, дислокации, plasticity, deformation, localization, deformation bands, metal structure, defects, dislocations

Abstract >>
The development of macroscopic inhomogeneities in in the form of Chernov-Luders bands and jump-like deformation bands (Portevin–Le Chatelier effect) in plastic metal flow is studied. For these two cases, regularities in the development of deformation inhomogeneity were established, and the kinetics of motion of the fronts of Chernoff–Luders bands and jump-like deformation bands was studied. It is shown that the Chernov–Luders fronts and the jump-like Portevin–Le Chatelier deformation can be considered, respectively, as macroscopic self-oscillatory processes of switching and excitation in deformable media of different nature.

Impact Fracture Toughness Evaluation for High-Density Polyethylene Materials

M. N. D. Cherief, M. Elmeguenni, M. Benguediab
Djillali Liabes University of Sidi Bel-Abbes, Sidi Bel-Abbes, 22000, Algeria
Keywords: ударная вязкость, трехточечный изгиб, полиэтилен высокой плотности, impact toughness, three-point bending, high-density polyethylene

Abstract >>
The impact fracture behavior of a high-density polyethylene (HDPE) material is investigated experimentally and theoretically. Single-edge notched bending (SENB) specimens are tested in experiments with three-point bending and in the Charpy impact tests. An energy model is proposed for evaluating the HDPE impact toughness, which provides a description of both brittle and ductile fracture.

Roughness of the Free Surface of Thin-Walled Tubes under Compression

S. E. Aleksandrov1, E. A. Lyamina1, K. Manabe2
1Ishlinsky Institute of Problems of Mechanics, Moscow, 119526, Russia
2University of Tokyo, Tokyo, 192-0397, Japan
Keywords: тонкостенная труба, безмоментная теория оболочек, шероховатость свободной поверхности, идеально жесткопластический материал, обработка давлением, thin-walled tube, membrane theory of shells, free surface roughness, perfectly rigid material, plastic working

Abstract >>
The problem of the stress-strain state with axisymmetric steady-state deformation of thin-walled tubes is solved using the membrane theory of shells and the model of an ideal rigid-plastic material satisfying the Mises yield condition and the associated flow law. The obtained solution is used together with the empirical relation between the strain state at an arbitrary point of the free surface and the surface roughness parameters at the same point to determine the influence of some compression parameters of the tubes on the surface roughness parameters of the workpiece. The empirical relation is derived assuming that the free surface roughness parameters depend on two independent kinematic variables.

Increasing Efficiency of Resonance Method of Fracturing an Ice Cover with the Simultaneous Movement of Two Air Cushion Vehicles

V. M. Kozin1,2, V. L. Zemlyak3, E. G. Rogozhnikova2
1Institute of Engineering Science and Metallurgy, Far Eastern Branch, Russian Academy of Sciences, Komsomolsk-on-Amur, 681005, Russia
2Amur State University of Humanities and Pedagogy, Komsomolsk-on-Amur, 681000, Russia
3Sholem Aleichem Amur State University, Birobidzhan, 679015, Russia
Keywords: резонансный метод, ледяной покров, разрушение, изгибно-гравитационные волны, интерференция, суда на воздушной подушке, resonance method, ice cover, fracture, flexural-gravitational waves, interference, air cushion vehicles

Abstract >>
This paper describes a study on the possibility of increasing the efficiency of the resonance method of fracturing an ice cover due to the flexural-gravitational wave interference occurring in simultaneous movement of several air cushion vehicles.

Elasticity Solution for a Cantilever Beam with Exponentially Varying Properties

S. Benguediab1, A. Tounsi1,2, H. H. Abdelaziz3,4,5, M. A. A. Meziane6,7
1University of Sidi Bel Abbes, Algeria
2Algerian National Thematic Agency of Research in Science and Technology, Algeria
3University Ibn Khaldoun, Algeria
4Tiaret, 14000, Algeria, Algeria
5University of Sidi Bel Abbes
6University Ibn Khaldoun
7Tiaret, 14000, Algeria
Keywords: плоская задача, функция напряжений, функционально-градиентный материал, экспоненциальный закон, аналитическое решение

Abstract >>
An analytical solution of a plane stress problem for a cantilever beam made of a functionally graded material subjected to uniform loading is constructed. The material is assumed to be isotropic with constant Poisson's ratio and exponentially varying Young's modulus through the beam thickness. Expressions for displacements, strains, and stresses are obtained.

Stochastic Wave Finite Element Method in Uncertain Elastic Media Through the Second Order Perturbation

F. Bouchoucha1, M. N. Ichchou2, M. Haddar1
1National School of Engineers of Sfax, BP. W3038 Sfax-Tunisia
2Ecole Centrale de Lyon, 36 Avenue Guy de Collongues 69130 Ecully
Keywords: стохастический метод конечных волновых элементов, дисперсия, неопределенность, возмущения второго порядка, stochastic wave finite element method, dispersion, uncertainty, second-order perturbation

Abstract >>
In this work, the stochastic wave finite element (SWFE) method for uncertain media through the second-order perturbation is formulated. A parametric approach for uncertainties is considered and combined to the finite element technique. The stochastic state space formulation is detailed in this work. The originality of this paper is the study of the second-order perturbation. The sensitivity and the precision of the SWFE approach are treated through the second-order perturbation introduced in the structural parameters. The question of the statistics of the propagation constants and the wave modes is considered. Comparisons with analytical results and Monte Carlo simulations are performed.

Energy Balance in High-Quality Cutting of Steel by Fiber and СО2 Lasers

V. M. Fomin, A. A. Golyshev, A. M. Orishich, V. B. Shulyat'ev
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: лазерная резка, СО-лазер, волоконный лазер, безразмерные параметры, энергетический баланс, laser cutting, СО laser, fiber laser, dimensionless parameters, energy balance

Abstract >>
The energy balance of laser cutting of low-carbon and stainless steel sheets with the minimum roughness of the cut surface is experimentally studied. Experimental data obtained in wide ranges of cutting parameters are generalized with the use of dimensionless parameters (Peclet number and absorbed laser energy). It is discovered for the first time that the minimum roughness is ensured at a certain value of energy per unit volume of the melt (approximately 26 J/mm3), regardless of the gas type (oxygen or nitrogen) and laser type (fiber laser with a wavelength of 1.07 mm or СО2 laser with a wavelength of 10.6 mm).