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2016 year, number 4

Opening of a System of Cracks – on the Mechanism of Cyclic Lateral Eruption of the St. Helens Volcano in 1980

V. K. Kedrinskii1, M. N. Davydov1, A. A. Pilnik2, A. A. Chernov1,2
1Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: магматический расплав, волна декомпрессии, многофазная математическая модель, кавитация, вязкость, пограничный слой, щелевое вулканическое извержение, magma melt, decompression wave, multiphase mathematical model, cavitation, viscosity, boundary layer, slotted volcanic eruption

Abstract >>
The dynamic behavior of a magma melt filling a slotted channel (crack) in a closed explosive hydrodynamic structure is considered. The explosive hydrodynamic structure includes the volcano focal point with a connected vertical channel (conduit) closed by a plug and a system of internal cracks (dikes) near the dome, as well as a crater open to the atmosphere. A two-dimensional model of a slotted eruption is constructed with the use of the Iordanskii-Kogarko-van Wijngaarden mathematical model of two-phase media and the kinetics that describes the basic physical processes in a heavy magma saturated by the gas behind the decompression wave front. A numerical scheme is developed for analyzing the influence of the boundary conditions on the conduit walls and scale factors on the melt flow structure, the role of viscosity in static modes, and dynamic formulations with allowance for diffusion processes and increasing (by several orders of magnitude) viscosity. Results of the numerical analysis of the initial stage of cavitation process evolution are discussed.

Stability of Two-Layer Fluid Flow

A. V. Rodionova1, E. V. Rezanova2,3
1Institute of Mathematics and Fundamental Informatics, Siberian Federal University, Krasnoyarsk, 660041, Russia
2Altai State University, Barnaul, 656049, Russia
3Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: двухслойные течения, уравнения Обербека -- Буссинеска, испарение, линейная устойчивость, длинноволновая асимптотика, two-layer flows, Oberbeck-Boussinesq equations, evaporation, linear stability, long-wave asymptotic behavior

Abstract >>
The problem of two-layer convective flow of viscous incompressible fluids in a horizontal channel with solid walls in the presence of evaporation is considered in the Oberbeck-Boussinesq approximation assuming that the interface is a thermocapillary surface which is not deformed and taking into account the Dufour effect in the upper layer which is a mixture of gas and liquid vapor. The effects of longitudinal temperature gradients at the boundaries of the channel and the thicknesses of the layer on the flow pattern and the evaporation rate are studied under specified gas flow conditions with no vapor flow on the upper boundary of the channel. It is shown that the long-wavelength asymptotic behavior for the decrement is determined from the flow characteristics, the long-wave perturbations occurring in the system decay monotonically, and the thermal instability mechanism is not potentially the most dangerous.

Unsteady Flow of a Dusty Bingham Fluid Through a Porous Medium in a Circular Pipe

H. A. Attia1, W. Abbas2, A. L. Aboul-Hassan3, M. A. M. Abdeen3, M. A. Ibrahim4
1El-Fayoum University, El-Fayoum-63514, Egypt
2College of Engineering and Technology, Arab Academy for Science, Technology, and Maritime Transport, Cairo. Egypt
3Cairo University, Giza 12211, Egypt
4Helwan University, Cairo, Egypt
Keywords: неустойчивое течение, круглая труба, пористая среда, неньютоновская жидкость, жидкость Бингама, unsteady flow, circular pipe, porous medium, non-Newtonian fluid, Bingham fluid

Abstract >>
A time-varying flow through a porous medium of a dusty viscous incompressible Bingham fluid in a circular pipe is studied. A constant pressure gradient is applied in the axial direction, whereas the particle phase is assumed to behave as a viscous fluid. The effect of the medium porosity, the non-Newtonian fluid characteristics, and the particle phase viscosity on the transient behavior of the velocity, volumetric flow rates, and skin friction coefficients of both the fluid and particle phases is investigated. A numerical solution is obtained for the governing nonlinear momentum equations by using the method of finite differences.

MHD Flow and Heat Transfer of a Power-Law Non-Newtonian Nanofluid (Cu-H2O) over a Vertical Stretching Sheet

M. Ferdows1, M. A. A. Hamad2
1University of Dhaka, Dhaka-1000, Bangladesh
2Science Assiut University, Assiut 71516, Egypt
Keywords: наножидкость, перенос тепла, магнитогидродинамика, растягивающаяся пластина, жидкость, удовлетворяющая степенному закону, автомодельное решение, nanofluid, heat transfer, MHD, stretching sheet, power-law fluid, similarity solution

Abstract >>
A steady-state mixed convection boundary layer flow of an electrically conducting nanofluid (Cu-H2O) obeying a power-law model in the presence of an alternating magnetic field due to a stretching vertical heated sheet is investigated numerically through the use of Wolfram Mathematica. The surface stretching velocity and the surface temperature are assumed to vary as linear functions of the distance from the origin. A similarity solution is presented, which depends on the nanoparticle volume fraction, power-law parameter, magnetic field parameter, buoyancy convection parameter, and modified Prandtl number.

On the Problem of Free Deceleration of a Solid in a Resistant Medium

M. V. Shamolin
Institute of Mechanics at the Lomonosov Moscow State University, Moscow, 119192, Russia
Keywords: твердое тело, сопротивляющаяся среда, уравнения движения, фазовый портрет, solid body, resistant medium, equations of motion, phase portrait

Abstract >>
A mathematical model of the influence of a medium on a solid body with some part of its external surface being flat is considered with due allowance for an additional dependence of the moment of the medium action force on the angular velocity of the body. A full system of equations of motion is given under quasi-steady conditions; the dynamic part of this system forms an independent third-order system, and an independent second-order subsystem is identified. A new family of phase portraits on a phase cylinder of quasi-velocities is obtained. It is demonstrated that the results obtained allow one to design hollow circular cylinders (“shell cases”), which can ensure necessary stability in conducting additional full-scale experiments.

On Estimating the Complex Growth Rates in Ferromagnetic Convection with Magnetic-Field-Dependent Viscosity in a Rotating Sparsely Distributed Porous Medium

J. Prakash, R. Bala
Department of Mathematics and Statistics, Himachal Pradesh University, Shimla, 171005, India
Keywords: ферромагнитная жидкость, вращение, пористая среда, осциллирующее движение, вязкость, зависящая от магнитного поля, конвекция магнитной жидкости, ferrofluid, rotation, porous medium, oscillatory motion, magnetic-field-dependent viscosity, ferroconvection

Abstract >>
It is proved analytically that the complex growth rate of an arbitrary oscillatory motion of growing amplitude in ferromagnetic convection with magnetic-field-dependent viscosity in a rotating sparsely distributed porous medium for the case of free boundaries is located inside a semicircle in the right half of the plane whose centre is at the origin of the coordinate system and whose radius depends on the Rayleigh number, Prandtl number, Taylor number, and magnetic number. Bounds for the case of rigid boundaries are also derived.

Convective Diffusion from Gas to a Rotating Disk

E. L. Pankratov, P. B. Boldyrevskii
Lobachevsky Nizhny Novgorod State University, Nizhny Novgorod 603950, Russia
Keywords: эпитаксия из газовой фазы, конвективная диффузия, диск-подложкодержатель, epitaxy from gas phase, convective diffusion, substrate holder disk

Abstract >>
This paper presents a new method of analytical calculation of the flow rate of the gas mixture and the concentration of the growth component during gas-phase epitaxy in a reaction chamber with a rotating substrate holder disk. The concentration of the growth component is analyzed in relation to a number of epitaxy process parameters.

Simulation of Optimum Conditions for Heat and Mass Transfer in Growing Large Crystals by Horizontal Directional Solidification

V. V. Gurov, A. G. Kirdyashkin
V.S. Sobolev Institute of Geology and Mineralogy, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: эксперимент, тепломассообмен, кристаллизация из расплава, горизонтальная направленная кристаллизация, experiment, heat and mass transfer, crystallization from the melt, horizontal directional solidification

Abstract >>
This paper describes the experimental study of the conditions of heat and mass transfer in horizontal directional solidification of refractory oxide compounds in the case of heating the rear part of the container from below. It is established that such heating causes significant changes in the nature of the mass transfer in the central area of the liquid layer. As a result, a stable structure is formed, providing the liquid flow from the rear of the container to the crystallization front, mass transfer in the near-surface and near-bottom vortices, and a more efficient mixing of the melt.

Generalized Thermoelastic Problem of an Infinite Body with a Spherical Cavity under Dual-Phase-Lags

R. Karmakar, A. Sur, M. Kanoria
University of Calcutta, Kolkata, West Bengal, India
Keywords: обобщенная двухтемпературная теория термоупругости, модель с двумя фазами запаздывания, пространство состояний, векторно-матричное дифференциальное уравнение, two-temperature generalized thermoelasticity, dual-phase-lag model, state-space approach, vector-matrix differential equation

Abstract >>
The aim of the present contribution is the determination of the thermoelastic temperatures, stress, displacement, and strain in an infinite isotropic elastic body with a spherical cavity in the context of the mechanism of the two-temperature generalized thermoelasticity theory (2TT). The two-temperature Lord-Shulman (2TLS) model and two-temperature dual-phase-lag (2TDP) model of thermoelasticity are combined into a unified formulation with unified parameters. The medium is assumed to be initially quiescent. The basic equations are written in the form of a vector matrix differential equation in the Laplace transform domain, which is then solved by the state-space approach. The expressions for the conductive temperature and elongation are obtained for at small times. The numerical inversion of the transformed solutions is carried out by using the Fourier-series expansion technique. A comparative study is performed for the thermoelastic stresses, conductive temperature, thermodynamic temperature, displacement, and elongation computed by using the Lord-Shulman and dual-phase-lag models.

Improvement of the Film Cooling Effectiveness with a Small Downstream Block Body

A. Khorsi, A. Guelailia, M. K. Hamidou
University of sciences and technology of Oran «Mohamed Boudiaf», Oran, Algeria
Keywords: пленочное охлаждение, адиабатическая эффективность, угол присоединения, плоская пластина, метод конечных объемов, film cooling, adiabatic effectiveness, compound angle, flat plate, finite volume method

Abstract >>
The aim of this study is to predict the improvement in the film cooling performance over a flat plate through a single row of cylindrical holes with different streamwise angles by using the Ansys CFX software package. In order to improve the film cooling effectiveness, a short crescent-shaped block is placed downstream of a cylindrical cooling hole. The numerical results of the cylindrical hole without the downstream short crescent-shaped block are compared with experimental data.

Flow of a Thixotropic Fluid over an Exponentially Stretching Sheet with Heat Transfer

S. A. Shehzad1, T. Hayat1, A. Alsaedi1
Quaid-i-Azam University, Islamabad, 44000, Pakistan
Keywords: установившееся течение, тиксотропная жидкость, экспоненциальное растяжение, теплообмен, steady flow, thixotropic fluid, exponential stretching, heat transfer

Abstract >>
This article addresses the boundary layer flow of a thixotropic fluid past an exponentially stretching sheet with heat transfer. The governing partial differential equations are reduced to an ordinary differential equation whose solution is found by the homotopy analysis method. The numerical values of the skin friction coefficient and Nusselt number are compared with available data.

Effect of Melting on an MHD Micropolar Fluid Flow Toward a Shrinking Sheet with Thermal Radiation

K. Das1, A. Sarkar2
1College, Cooch Behar, W.B., Pin-736101, India
2Ramnagar High School, Nadia, Pin-741502, W.B., India
Keywords: микрополярная жидкость, плавление, магнитогидродинамика, тепловое излучение, сжимаемая пластина, micropolar fluid, melting, MHD, thermal radiation, shrinking sheet

Abstract >>
The effect of melting on a steady boundary layer stagnation-point flow and heat transfer of an electrically conducting micropolar fluid toward a horizontal shrinking sheet in the presence of a uniform transverse magnetic field and thermal radiation is studied. A similarity transformation technique is adopted to obtain self-similar ordinary differential equations, which are solved numerically. The present results are found to be in good agreement with previously published data. Numerical results for the dimensionless velocity and temperature profiles, as well as for the skin friction and the rate of heat transfer are obtained.

Three-Dimensional Stress and Free Vibration Analyzes of Functionally Graded Plates with a Circular Hole by the Use of the Graded Finite Element Method

K. Asemi1, H. Ashrafi2, M. Shariyat3
1Amirkabir University of Technology, Tehran, Iran
2University of Kashan, Kashan, Iran
3Toosi University of Technology, Tehran, Iran
Keywords: трехмерная теория упругости, метод градиентных конечных элементов, пластина с круговым отверстием, функционально-градиентный материал, энергетический метод Рэлея -- Ритца, свободные колебания, three-dimensional elasticity theory, graded finite element method, functionally graded material, Rayleigh-Ritz energy formulation, free vibrations

Abstract >>
Static and free vibration analyses of plates with circular holes are performed based on the three-dimensional theory of elasticity. The plates are made of a functionally graded material (FGM), and the volume fraction of the material varies continuously over the plate thickness. The effective properties of the FGM plate are estimated by using the Mori-Tanaka homogenization method. A graded finite element method based on the Rayleigh-Ritz energy formulation is used to solve the problem. The effects of different volume fractions of the material and hole sizes on the behavior of FGM plates under uniaxial tension are investigated. Natural frequencies of a fully clamped FGM plate with a circular cutout are derived. The results obtained are compared with available experimental data.

Propagation of Converging Spherical Deformation Waves in a Heteromodular Elastic Medium

V. E. Ragozina1, O. V. Dudko1,2
1Institute of Automation and Control Processes Far Eastern Branch, Russian Academy of Sciences, Vladivostok, 690041, Russia
2Far Eastern Federal University, Vladivostok, 690950, Russia
Keywords: упругость, разномодульность, динамика деформирования, разрыв деформаций, сходящаяся сферическая волна, ударная волна, elasticity, heteromodular, deformation dynamics, discontinuity of deformations, converging spherical wave, shock wave

Abstract >>
The unsteady one-dimensional boundary-value problem of shock deformation of a medium bounded by a sphere is solved. The propagation of converging deformation wavefronts in an elastic material with different tensile and compressive strength is studied. A boundary condition is obtained that provides the formation of a converging spherical shock wave with constant velocity. The mode of impact on the boundary of the heteromodular sphere is determined in which a transition zone in the form of a spherical layer of constant density can occur between the compression and tension regions.

Free Oscillations of an Anisotropic Cylindrical Ribbed Fiberglass Shell with Flowing Fluid

F. S. Latifov1, F. A. Seifullaev2, Sh. Sh. Alyev1
1Azerbaijan Architecture and Construction University, Baku, AZ1073, Azerbaijan
2Institute of Mathematics and Mechanics of National Academy of Sciences of Azerbaijan, Baku, AZ1141, Azerbaijan
Keywords: анизотропная подкрепленная ребрами оболочка, свободные колебания, собственные частоты колебаний, anisotropic ribbed shell, free oscillations, natural oscillation frequencies

Abstract >>
This paper presents the results of determining the free oscillation frequency of a structurally anisotropic, cylindrical fiberglass shell reinforced by annular ribs and containing fluid flow. Boundary Navier conditions are imposed on the ends of the shell. Natural oscillation frequencies are calculated as functions of the frequency on the fiberglass winding angle and liquid flow rate for different valuesof of wave parameters and the parameters characterizing the geometric dimensions of the shell.

Complex Oscillations of Flexible Plates under Longitudinal Loads with Account for White Noise

E. Yu. Krylova1, I. V. Papkova2, N. P. Erofeev2, V. M. Zakharov2, V. A. Krys'ko2
1Saratov Chernyshevsky State University, Saratov, 410012, Russia
2Saratov State Technical University, Saratov, 410054, Russia
Keywords: нелинейная динамика, параметрические колебания, индуцированные шумом переходы, пластина, хаос, вейвлеты, белый шум, nonlinear dynamics, parametric oscillation, noise-induced transitions, plate, chaos, wavelets, white noise

Abstract >>
This paper describes the influence of the intensity of the external additive white noise on the nonlinear dynamics of rectangular plates as mechanical systems with an infinite number of degrees of freedom. A new scenario is discovered, which is a combination of the classic Feigenbaum and Pomeau-Manneville scenarios. The classical methods of nonlinear dynamics and wavelet transforms were used to reveal the peculiarities of a modified scenario. The noise-induced transitions are investigated, and it is shown that the noise exposure is accompanied with the transition to chaotic oscillations with a lower amplitude of the driving load. It is found that the presence of external fluctuations does not affect the scenario of transition from harmonic to chaotic oscillations.

Identification of the Elastic and Damping Characteristics of Carbonfiber Reinforced Plastic Based on a Study of Damped Flexural Vibrations of Test Specimens

V. N. Paimushin1,2, V. A. Firsov2, I. Gyunal2, V. M. Shishkin3
1Kazan Federal University, Kazan, 420008, Russia
2Tupolev Kazan National Research Technical University, Kazan, 420111, Russia
3Vyatka State University, Kirov, 610000, Russia
Keywords: теоретико-экспериментальный метод, тест-образец, внутреннее демпфирование, аэродинамическое демпфирование, целевая функция, theoretical-experimental method, test specimen, internal damping, aerodynamic damping, target

Abstract >>
A theoretical-experimental method for determining the elastic and damping characteristics of materials based on analysis of vibrograms of damped flexural vibrations of test specimens with different structures is proposed. It is shown that during tension-compression and shear of a carbon plastic reinforced with Porcher 3692 carbon fabric, with EDT-69NM polymer binder, the dynamic elastic modulus decreases considerably with increasing frequency of its deformation in the range of 0-120 Hz. The amplitude dependences of the logarithmic vibration decrements of the carbon fiber reinforced plastic are determined Bb minimizing the discrepancy between the experimental and calculated internal-damping parameters of the test specimens in tension-compression and shear.

Wave Processesin a Hollow Cylinderin an Inhomogeneous Prestress Field

A. O. Vatulyan, V. A. Yurov
Southern Federal University, Rostov-on-Don, 344090, Russia
Keywords: предварительные напряжения, волновые процессы, цилиндр, дисперсионное уравнение, численный эксперимент, prestresses, wave processes, cylinder, dispersion equation, numerical experiment

Abstract >>
Wave processes in an isotropic hollow cylinder located in an inhomogeneous prestress field are studied. The dispersion equation of the problem is investigated, and some features of the structure of the dispersion curves in relation to the type of pre-stressed state are identified. Formulas describing the behavior of the dispersion curves in the neighborhood of radial resonances are derived using the perturbation method.

Extremality Conditions of Elastic Constants and Main Anisotropy Axes

N. I. Ostrosablin
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: линейно-упругие материалы, анизотропия, постоянные упругости, условия экстремальности, главные оси анизотропии, триклинная сингония, кубическая сингония, linear-elastic materials, anisotropy, elastic constants, extremality conditions, main anisotropy axes, triclinic crystal system, cubic crystal system

Abstract >>
This paper describes the derivation of extremality conditions of each elasticity coefficient (Young's modulus, shear modulus, et al.,) for the general case of linear-elastic anisotropic materials. The stationarity conditions are obtained, and they determine the orthogonal coordinate systems being the main anisotropy axes, where the number of independent elasticity constants decreases from 21 to 18 and, in some cases of anisotropy, to 15 or lower. An example of a material with cubic symmetry is given.

Calculation of the Effective Stiffness of Corrugated Plates by Solving the Problem on the Plate Cross-Section

A. G. Kolpakov1, S. I. Rakin2
1Siberian State University of Telecommunications and Informatics, Novosibirsk, 630108, Russia
2Siberian State University of Communications, Novosibirsk.630049, Russia
Keywords: гофрированные пластины, эффективные жесткости, понижение размерности задачи, corrugated plates, effective stiffness, reducing the dimension of the problem

Abstract >>
It is shown that for corrugated, in particular multilayer, plates, the tree-dimensional cell-averaging problem can be reduced to the two-dimensional problem on the cross section of the plate periodicity cell. This significantly increases the accuracy of numerical calculation of the effective stiffness of corrugated plates. Numerical calculations of the stiffness of a plate with sinusoidal corrugation were performed, and the results were compared with available data.