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2015 year, number 3

Physical and Mathematical Modeling of High-Frequency Electromagnetic Exposure of Hydrocarbon Media

L. A. Kovaleva, A. A. Musin, R. R. Zinnatullin
Bashkir State University, Ufa, 450076 Russia
Keywords: высокочастотное электромагнитное поле, углеводородная жидкость, тепловая конвекция, теплообмен, математическая модель, high-frequency electromagnetic field, hydrocarbon liquid, thermal convection, heat transfer, mathematical model

Abstract >>
This paper presents the results of experimental studies and numerical simulation of heat and mass transfer in a high-viscosity hydrocarbon liquid with temperature dependent viscosity and thermal conductivity, under the influence of a high-frequency electromagnetic field with natural thermal convection taken into acount.

Temperature Waves Arising due to Absorption of Electromagnetic Radiation in Laminated Media

I. L. Khabibullin1, S. I. Konovalova2, L. A. Sadykova1
1Bashkir State University, Ufa, 450074 Russia
2Ufa State Aviation Technical University, Ufa, 450000 Russia
Keywords: электромагнитное излучение, трехслойная среда, интерференция, температурные волны, electromagnetic radiation, three-layer medium, interference, temperature waves

Abstract >>
Propagation of electromagnetic radiation in a moving three-layer medium is studied. It is shown that travelling temperature waves are formed due to interference of the incident wave with the wave reflected from the interface between the layers with radiation energy dissipation. The frequency, length, and velocity of these waves are found to depend on the electromagnetic radiation frequency, electrophysical and thermophysical parameters of the medium, and velocity of medium motion.

Plasma Effect of the Houston Horse

V. A. Pavlov, Ya. V. Tryaskin
St. Petersburg State University, St. Petersburg, 198904 Russia
Keywords: предвестник ударной волны, сгустки плазмы, эффект лошади Хьюстона, shock wave precursor, plasmoids, Houston horse effect

Abstract >>
The effect of a strong shock wave on a weakly ionized collisional plasma was studied. The structure of the ion-acoustic perturbation caused by the shock wave was numerically investigated. The effect of the nonlinearity, dispersion, and dissipation on the formation of an oscillating wave profile was shown. It is found that in some modes, an increase in the shock wave velocity leads to a sharp increase in the concentration of charged particles and a reduction in the number of perturbation maxima. This change of the flow structure can be preceded by the formation of localized regions with an increased degree of plasma ionization. It is shown that the presence of plasmoids can lead to a strong influence of charges on the neutral component.

Magnetic Field Effect on Waves in a Centrifuged Layer of a Rotating Conducting Viscous Fluid

N. V. Klueva1, V. M. Sandalov2, M. E. Tkach1, I. N. Soldatov1
1Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Nizhny Novgorod, 603024 Russia
2Lobachevskii Nizhny Novgorod State University, Nizhny Novgorod, 603950 Russia
Keywords: проводящая вязкая жидкость, инерционные волны, вращающееся магнитное поле, conducting viscous fluid, inertial waves, rotating magnetic field

Abstract >>
This paper considers wave processes in a centrifuged layer of an incompressible viscous conducting fluid in an axial magnetic field in the cavity of a rapidly rotating infinite cylinder with insulating walls. Inertial modes-solutions of the linearized boundary-value problem of magnetohydrodynamics - are represented as a superposition of helical fields. Expressions for the vorticity parameters of the helical flows forming the inertial mode at a small Stewart number are given. Dispersion curves of inertial waves are constructed, and the influence of the magnetic field on the flow field is analyzed. The critical frequencies at which the lowest (surface) mode arises are determined. The spatial and temporal stability of the modes are investigated.

Effect of an Oblique Shock Wave on the Interface between Metals

O. B. Drennov
All-Russia Institute of Experimental Physics, Sarov, 607190 Russia
Keywords: косая ударная волна, сдвиговая неустойчивость, амплитуда и длина волн возмущений, градиент скорости, oblique shock wave, shear instability, amplitude and wavelength of perturbations, velocity gradient

Abstract >>
Results of experiments on loading a pack of closely packed metal plates by an oblique shock wave are reported. Buckling of the interface between the plate is observed. It is shown that periodic wavy perturbations are formed due to the development of the Kelvin-Helmholtz instability within the time of interface turning induced by the shock wave action. The final amplitude and wavelength of perturbations are found to be determined by the thickness of the weakened layer in a plastic flow.

Comparative Analysis of Methods for Modeling the Penetration and Plane-Parallel Motion of Conical Projectiles in Soil

V. G. Bazhenov1, A. M. Bragov1, A. Yu. Konstantinova1,2, V. L. Kotov1
1Lobachevskii Research Institute of Mechanics Nizhny Novgorod State University, Nizhny Novgorod, 603950 Russia
2Bakhirev State Scientific Research Institute of Mechanical Engineering, Dzerzhinsk, 606002 Russia
Keywords: удар, проникание под углом к поверхности, конический ударник, упругопластическая среда, модель локального взаимодействия, трехмерное моделирование, угловая скорость вращения, impact, penetration at an angle to the surface, conical projectiles, elastoplastic medium, local interaction model, three-dimensional modeling, angular velocity of rotation

Abstract >>
This paper presents an analysis of the accuracy of known and new modeling methods using the hypothesis of local and plane sections for solution of problems of the impact and plane-parallel motion of conical bodies at an angle to the free surface of the half-space occupied by elastoplastic soil. The parameters of the local interaction model that is quadratic in velocity are determined by solving the one-dimensional problem of the expansion of a spherical cavity. Axisymmetric problems for each of the meridional section are solved simultaneously neglecting mass and momentum transfer in the circumferential direction and using an approach based on the hypothesis of plane sections. The dynamic and kinematic parameters of oblique penetration obtained using modified models are compared with the results of computer simulation in a three-dimensional formulation. The results obtained with regard to the contact stress distribution along the generator of the pointed cone are in satisfactory agreement.

Wave Effects in Collapsible Biovessels

B. N. Klochkov
Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, 603950, Russia
Keywords: упругий сосуд, течение несжимаемой жидкости, характерная скорость, неустойчивость, дисперсионные характеристики, математическое моделирование, collapsible vessel, incompressible fluid flow, characteristic velocity, instability, dispersion characteristics, mathematical modeling

Abstract >>
Dispersion characteristics of wave processes in collapsible elastic biovessels with the biofluid flowing through them are presented. The possibility of the existence of fixed flow structures in the vessels is shown. The possibility of applying the results to the study of biological systems is considered.

Property of Reciprocity for Stratified Laminar Flows in Channels with Arbitrarily Shaped Cross Sections

P. I. Geshev1,2
1Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: симметрия, свойство взаимности, коэффициенты расхода, ламинарное течение, уравнение Навье - Стокса, функция Грина, теорема Грина, symmetry, property of reciprocity, flow rate coefficient, laminar flow, Navier-Stokes equations, Green function, Green theorem

Abstract >>
A stratified laminar flow of several fluids in a channels with an arbitrarily shaped cross section is considered. It is assumed that the hydrostatic problem of finding free boundaries between different fluids is solved and domains of motion of individual fluids are known. Under the assumption that the medium motion arises under the action of an applied pressure gradient and volume gravity forces (or forces of inertia), the property of reciprocity between the applied forces Fj and the flows of different components Qi, which is manifested as symmetry of the matrix of the flow rate coefficients Lij(Qi = LijFj), is proved in the general form. General symmetric solutions of the problem for a plane channel and a circular tube are presented. Formulas for the coefficient of increasing of the fluid flow rate owing to the presence of a near-wall layer of the gas are derived. It is shown that the flow rate of water in a partly filled channel may exceed the flow rate in a completely filled channel by more than an order of magnitude.

Flow Structure Formed Due to Interaction of a Supersonic Jet with a Porous Obstacle

V. I. Zapryagaev, I. N. Kavun, A. V. Solotchin
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: сверхзвуковая недорасширенная струя, пористая преграда, проницаемость, низконапорное дозвуковое течение, supersonic underexpanded jet, porous obstacle, permeability, low-pressure subsonic flow

Abstract >>
Results of studying impingement of a supersonic underexpanded air jet onto a finite-thickness porous metal obstacle whose frontal plane is normal to the jet axis and whose side surface is impermeable for the gas flow are reported. The case of a non-porous obstacle of the same diameter is considered for determining the effect of porosity on gas-dynamic characteristics of jet-obstacle interaction.

Self-Similar Solution of the Problem of a Turbulent Flow in a Round Submerged Jet

A. V. Shmidt
Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, 660036 Russia
Keywords: круглая затопленная турбулентная струя, (k-e)-модель, теоретико-групповой анализ, асимптотическое разложение, метод стрельбы, round submerged turbulent jet, k-e model, theoretical-group analysis, asymptotic expansion, shooting method

Abstract >>
A mathematical model of the flow in a round submerged turbulent jet is considered. The model includes differential transport equations for the normal components of the Reynolds stress tensor and Rodi's algebraic approximations for shear stresses. A theoretical-group analysis of the examined model is performed, and a reduced self-similar system of ordinary differential equations is derived and solved numerically. It is shown that the calculated results agree with available experimental data.

Separation of a Turbulent Supersonic Boundary Layer with Heat Supply Ahead of a Flat Step

O. B. Larin1, V. A. Levin2
1Institute of Mechanics at the Lomonosov Moscow State University, Moscow, 119192 Russia
2Institute of Automation and Control Processes, Far-East Branch, Russian Academy of Sciences, Vladivostok, 690041 Russia
Keywords: сверхзвуковой газовый поток, электрический разряд, отрыв турбулентного пограничного слоя, supersonic gas flow, electric discharge, separation of the turbulent boundary layer

Abstract >>
The influence of an electric discharge in a supersonic gas flow modeled by a heat source with a specified intensity and configuration on the development of a turbulent boundary layer ahead of a flat step is numerically studied. If the discharge power is sufficiently large, it is demonstrated that heat transfer to the wall does not affect the position of separation, which arises due to a non-zero shear stress on the body surface and is caused by the development of a reverse flow in the core of the boundary layer.

Semi-Empirical Method for Calculating Optimal Geometric Parameters of the Darrieus Rotor

D. N. Gorelov
Omsk Department of the Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Omsk, 644043 Russia
Keywords: ротор Дарье, аэродинамический расчет, экспериментальное исследование, Darrieus rotor, aerodynamic calculation, experimental studies

Abstract >>
Available experimental data on aerodynamics of the Darrieus rotor with straight blades are analyzed. Ranges of the main parameters of the rotor at which it has high energy characteristics and is able to start its motion independently and to rotate uniformly around its vertical axis are found. Based on these results, a method for calculating the geometric parameters of the rotor satisfying prescribed conditions of its exploitation is developed.

Transient Natural Convective Flow of a Nanofluid Past a Vertical Plate in the Presence of Heat Generation

P. Loganathan, P. N. Chand, P. Ganesan
Keywords: естественная конвекция, наножидкости, бесконечная вертикальная пластина, тепловыделение, natural convection, nanofluid, infinite vertical plate, heat generation

Abstract >>
In this work, an exact analysis on the effects of heat generation and nanoparticle volume concentration on an unsteady free convective flow of a nanofluid past an impulsively started infinite vertical plate is presented. Nanofluids containing nanoparticles of aluminum oxide, copper, titanium oxide, and silver with a nanoparticle volume concentration range smaller than or equal to 0.04 are considered. The governing dimensionless partial differential equations are solved by using the Laplace transform technique. The effects of heat generation and nanoparticle volume concentration on the velocity and temperature profiles are represented graphically. The expressions for the skin friction coefficient and Nusselt number are derived. The effect of heat transfer is found to be more pronounced in a silver-water nanofluid than in the other nanofluids. Comparisons with other published results are found to be in excellent agreement.

Mixed Convection in a LID-Driven Cavity with an Inside Hot Obstacle Filled by an Al2O3–Water Nanofluid

Esfe M. Hemmat, M. Akbari, A. Karimipour
Islamic Azad University, Isfahan, Iran
Keywords: наножидкость, объемная доля твердой фазы, теплообмен, диаметр наночастиц, nanofluid, solid volume fraction, heat transfer, nanoparticle diameter

Abstract >>
The present paper focuses on the problem of a mixed convection fluid flow and heat transfer of an Al2O3–water nanofluid with the thermal conductivity and effective viscosity dependent on temperature and nanoparticle concentration inside a lid-driven cavity having a hot rectangular obstacle. The governing equations are discretized by using the finite volume method, and the SIMPLE algorithm is employed to couple the velocity and pressure fields. By using the developed code, the effects of the Richardson number and the diameter and volume fraction of Al2O3 nanoparticles on the flow, thermal fields, and heat transfer inside the cavity are studied. The obtained results show that the average Nusselt number for the entire range of the solid volume fraction decreases with an increase in the Richardson number and the nanoparticle diameter. The results also clearly indicate that addition of Al2O3 nanoparticles produces a remarkable enhancement on heat transfer with respect to that of the pure fluid.

Effect of Turbulence Models on the Submerged Hydraulic Jump Simulation

Y. Shekari1, M. Javan2, A. Eghbalzadeh2
1Razi University, Kermanshah, Iran
2Razi University-Water and Wastewater Research Center, Kermanshah, Iran
Keywords: трехмерное численное моделирование, затопленный гидравлический скачок, модель турбулентности, метод расширенного описания пристенного течения, three-dimensional numerical simulation, submerged hydraulic jump, turbulence model, near-wall treatment

Abstract >>
This study presents a numerical investigation and prediction of the flow field in three-dimensional submerged hydraulic jumps. The volume of fluid (VOF) method is used to simulate the free surface. The turbulent structure is simulated by using different turbulence models, such as the standard κ-ε model, RNG κ-ε model, realizable κ-ε model, and Reynolds-stress model (RSM) closure schemes. The capabilities of the turbulence models are investigated with the standard wall functions and enhanced wall treatment methods. A comparison between the numerical and experimental results shows that the numerical model is adequate for predicting the flow pattern and free surface of submerged hydraulic jumps. The RNG κ-ε turbulence model with the enhanced wall treatment method ensures the highest accuracy in the water surface simulation. Near the channel bed of a fully developed region, the RSM model with the enhanced wall treatment method shows better agreement with the experimental longitudinal velocity than the other turbulence models. The standard κ-ε model predicts the longitudinal velocity more accurately than the RNG and realizable κ-ε models.

Reactive Solute Transfer in a Stagnation-Point Flow Over a Shrinking Sheet with a Diffusive Mass Flux

K. Bhattacharyya
The University of Burdwan, Burdwan-713104, West Bengal, India
Keywords: диффузионный поток массы, течение в окрестности лобовой точки, пограничный слой, массоперенос в химически активном растворе, сжимающаяся пластина, двойные решения, diffusive mass flux, stagnation-point flow, boundary layer, reactive solute transfer, shrinking sheet, dual solutions

Abstract >>
Reactive solute transfer in a boundary-layer stagnation-point flow over a shrinking sheet with a uniform diffusive mass flux is investigated. The first-order chemical reaction is considered. By similarity transformations, the governing partial differential equations are converted into self-similar nonlinear ordinary differential equations. Then the transformed equations are solved numerically by using the shooting method. Dual solutions for the solute distribution are found. The study shows that the concentration at the point increases with increasing velocity ratio parameter for the first solution and decreases for the second solution. Due to an increase in the Schmidt number and reaction rate parameter, the concentration and concentration boundary layer thickness decrease in the presence of the mass flux.

Aerodynamics and Heat Transfer in a Separated Flow in an Axisymmetric Diffuser with Sudden Expansion

V. I. Terekhov, T. V. Bogatko
Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: отрывное течение, турбулентный теплообмен, диффузор, градиент давления, separated flow, turbulent heat transfer, diffuser, pressure gradient

Abstract >>
Results of a numerical study of the influence of a positive pressure gradient in an axisymmetric diffuser with sudden expansion of a circular tube on aerodynamics and turbulent heat transfer in regions of flow separation, reattachment, and relaxation are reported. The air flow prior to separation is assumed to be fully turbulent and to have a constant Reynolds number ReD1 = 2.75×104. The tube expansion degree is 1.78, and the apex half-angle of the diffuser is varied from 0 to 5 oC. It is found that an increase in the pressure gradient leads to a decrease in the heat transfer intensity in the separation region, and the maximum heat release point moves away from the flow separation point. The calculated results are compared with experimental data. It is shown that the behavior of the separated flow behind the step becomes significantly different as the streamwise pressure gradient changes.

Thermal Performance of a Top Heat Mode Closed-Loop Oscillating Heat Pipe with a Check Valve (THMCLOHP/CV)

N. Bhuwakietkumjohn, T. Parametthanuwat
Heat Pipe and Nanofluid Technology Research Unit Faculty of Industrial Technology and Management King Mongkut's University of Technology, North Bangkok, Thailand
Keywords: режим нагрева сверху, тепловая трубка, запорный клапан, top heat mode (THM), oscillating heat pipe (OHP), check valve (CV)

Abstract >>
The aim of this research is to investigate the heat transfer characteristics of a top heat mode closed-looped oscillating heat pipe with check valves (THMCLOHP/CV). Ethanol is used as a working fluid with filling ratios of 30, 50, and 80% of the total volume of the tube. The THMCLOHP/CV is made of a copper tube with an inside diameter of 2.03 mm. The angle of inclination is 90 oC from the horizontal axis with 40 turns, two check valves, and an evaporator length of 50, 100, and 150 mm. The operating temperatures are 44 and 55 oC. It is found that the thermal resistance decreases significantly as the working temperature is increased. Thus, the evaporator length affects the thermal resistance of the THMCLOHP/CV. The presence of the THMCLOHP/CV is clearly demonstrated to contribute to thermal performance improvement.

Influence of the Mechanical Loading of Rock Salt on the Parameters of Thermoacoustic Emission

V. L. Shkuratnik, E. A. Novikov
MISiS National Research Technological University, Moscow 119049, Russia
Keywords: термостимулированная акустическая эмиссия, каменная соль, эксперимент, структурная неоднородность, напряженно-деформированное состояние, стадии деформирования, прогнозирование разрушения, механическое одноосное нагружение, thermoacoustic emission, rock salt, experiment, structural heterogeneity, stress-strain state, deformation stage, fracture prediction, uniaxial mechanical loading

Abstract >>
This paper presents the results of experimental studies of acoustic emission occurring in rock-salt samples due to their local and volumetric heating under static mechanical loading preceding heating or occurring simultaneously with it. Thermoacoustic emission (TAE) parameters in rock salt depending on its structural heterogeneity were determined. Patterns of change in the TAE activity in test samples of the geomaterial under volumetric heating and subsequent cooling for different values of mechanical preloading were established. The established patterns can be used to predict the fracture of solid rock salt from results of measurement of s TAE in an extracted core.

Two-Dimensional Thermoelastic Analysis of a Functionally Graded Cylinder for Different Functionalities by Using the Higher-Order Shear Deformation Theory

M. Arefi
Department of Solid Mechanic, Faculty of Mechanical Engineering, University of Kashan, Kashan, 87317-51167 Iran
Keywords: деформации поперечного сдвига, термоупругость, оболочка, температура, цилиндр, энергия, shear deformation theory, thermoelastic, shell, temperature, cylinder, energy

Abstract >>
The present paper addresses application of the general shear deformation theory for the thermoelastic analysis of a functionally graded cylindrical shell subjected to inner and outer loads. The shear deformation theory and the energy method are employed for this purpose. This method presents the final relations by using a set of second-order differential equations in terms of the integral of material properties over the shell thickness. The obtained formulation can be solved for two well-known functionalities.

Experimental Study of Pipelines Steel

M. Meriem-Benziane, H. Zahloul
Rheology and Mechanics Laboratory, Mechanical Engineering Department, Hassiba Benbouali University of Chlef, BP151, Chlef 02000, Algeria
Keywords: трубопровод, третья мода, разрыв, коэффициент интенсивности напряжений, работа, трещина, pipeline, mode III, tearing, stress intensity factor, essential work, crack

Abstract >>
This work is focused on an experimental study of E26-2 pipeline steel tearing by mode III. The crack propagation length is obtained as a function of the applied force magnitude for specimens of different thicknesses and widths. The critical stress intensity factor and the essential work needed for crack propagation are determined by the energy balance method. It is demonstrated that these variables depend on the pipeline thickness and specimen geometry.

Problem of a Thin Rigid Inclusion Inserted in an Interfacial Crack in the Vicinity of Its Tip

V. V. Sil'vestrov1, Yu. O. Vasil'eva2
1Gubkin Russian State University of Oil and Gas, Moscow, 119991 Russia
2Ul'yanov Chuvash State University, Cheboksary, 428015 Russia
Keywords: межфазная трещина, тонкое жесткое включение, коэффициенты интенсивности напряжений, матричная задача Римана, interface crack, thin rigid inclusion, stress intensity factors, matrix Riemann problem

Abstract >>
The problem of the stress state of a piecewise-homogeneous elastic body with a semi-infinite crack at an interface, in which near the vertex inserted a thin rigid pointed inclusion of finite length. The crack faces are loaded by predetermined stresses, and at infinity, the body is stretched by predetermined normal stresses acting along the crack. The inclusion is acted upon by external forces that have predetermined main vector and moment. The problem reduces to the matrix Riemann boundary-value problem with a piecewise constant coefficient. The solution of this problem is constructed in explicit form using the Gauss hypergeometric function. The angle of rotation of the inclusion, complex potentials, and stress intensity factors near the ends of the inclusion are obtained.

On the Theory of Plastic Structure Formation of Metals

V. M. Greshnov, I. V. Puchkova
Ufa State Aviation Technical University, Ufa 450000, Russia
Keywords: пластическое структурообразование, физико-математическая теория пластичности, интенсивная деформация, микрокристаллические металлы, plastic structure formation, physicomathematical theory of plasticity, severe deformation, microcrystalline metals

Abstract >>
Plastic structure formation in AD1 aluminum has been studied experimentally and theoretically using a physical phenomenological model of cyclic and nearly cyclic plastic deformation with large strain intensities accumulated in one and several cycles. Based on the results obtained, the proposed model of the process was verified, the concept of severe plastic deformation was refined, its role in structure formation was investigated, and the existence of a limit of grain refinement during deformation processing of metals was shown.

Accounting for the Elastic Properties of Viscoplastic Lubricant between Coaxial Rotating Cylinders

A. S. Begun1,2, A. A. Burenin3, S. G. Zhilin3, L. V. Kovtanyuk1
1Institute of Automation and Control Processes, Far East Branch, Russian Academy of Sciences, Vladivostok, 690041 Russia
2Vladivostok State University of Economics and Service, Vladivostok, 690014 Russia
3Institute of Engineering and Metallurgy, FEB RAS, Komsomolsk-on-Amur, 681005 Russia
Keywords: упругость, вязкопластичность, большие деформации, узел трения, демпфирующий слой, elasticity, viscoplasticity, large deformations, friction unit, damping layer

Abstract >>
This paper presents a solution of the boundary-value problem of the stress-strain state of a friction unit placed in the gap between rigid rotating cylinders. It is assumed that the two-layer incompressible material of these unit has elastic, viscous, and plastic properties and different values of the elastic moduli, stress limit, and viscosity. The conditions of the occurrence of viscoplastic flow, motion of the elastoplastic boundary in a deformable medium, and interaction of the latter with the contact boundary of the materials were determined. Limiting values of the characteristic rotation parameters at which the damping layer of the friction unit is not deformed plastically are given. The velocity and stress fields for acceleration and deceleration of the lubricant flow are calculated.