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Journal of Applied Mechanics and Technical Physics

2015 year, number 4

Roll Waves in Channels with an Active Gas Phase

A. Boudlal1, V. Yu. Liapidevskii2,3
1Laboratory of Mechanics of the Lille University of Science and Technology, UMR CNRS 8107 in Lille, France
2Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
3Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: катящиеся волны, гиперболические уравнения, разрывные решения, устойчивость волновых пакетов, roll waves, hyperbolic equations, discontinuous solutions, stability of wave packets

Abstract >>
A mathematical model of the flow of a thin layer of heavy liquid under an elastic shell filled with gas is constructed. By means of mass exchange with the environment, the gas phase is active and supports a self-organized wave motion in the liquid layer. The conditions under which small perturbations are transformed into quasiperiodic wave packets of finite amplitude, which move in the same direction, are found. It is shown that the structure of the waves is similar to that of roll waves in open channels.

Modeling of a Supersonic Flow around a Cylinder with a Gas-Permeable Porous Insert

S. G. Mironov1,2, A. A. Maslov1,2, T. V. Poplavskaya1,2, S. V. Kirilovskiy1,2
1Novosibirsk State University, Novosibirsk, 630090 Russia
2Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: сверхзвуковое обтекание, газопроницаемые пористые материалы, численное моделирование, эксперимент, supersonic flow, gas-permeable porous materials, numerical simulation, experiment

Abstract >>
Results of an experimental and numerical study of a supersonic (M = 4.85) flow around a streamwise-aligned cylinder with a gas-permeable porous insert on the frontal face in the range of Reynolds numbers ReD = (0.1−2.0) · 105 are presented. The numerical study is performed by using the Ansys Fluent software system and a porous medium model based on a quadratic law of filtration. The parameters of the quadratic dependence are calculated on the basis of experimental data for an air flow in a porous material. Flow fields are obtained, and the wave drag of the model is calculated as a function of the porous insert length and the Reynolds number. Results of numerical simulations are compared with wind tunnel measurements.

Effect of the Volume Concentration of a Set of Water Droplets Moving Through High-Temperature Gases on the Temperature in the Wake

G. V. Kuznetsov, P. A. Strizhak
Tomsk Polytechnic University, Tomsk, 634004 Russia
Keywords: тепломассоперенос, испарение, капли воды, водяной пар, высокотемпературные газы, heat and mass transfer, evaporation, water droplets, water vapor, high-temperature gases

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The processes of heat and mass transfer and phase transformations during motion of a set of water droplets through high-temperature gases have been studied numerically. The regimes and conditions of formation of zones of significant joint influence of the droplets on the integral characteristics of heat and mass transfer are determined. The values of the dimensionless parameters describing the dependence of the temperature of the gases in the wake of a small set droplets on their volume concentration and arrangement are calculated. The variations in these dimensionless parameters during motion of droplets through high-temperature gases are described.

Experimental Study of the Turbulent Field Behind a Perforated Vortex Generator

C. Habchi1, T. Lemenand2, D. Della Valle3,4, A. Al Shaer5, H. Peerhossaini6
1Notre Dame University, Louaize, Lebanon
2LUNAM University, IMIS ISTIA, Angers, France
3LUNAM University, LTN CNRS, UMR 6607, Nantes, France
4ONIRIS, Food Processing Dept., GEPEA, Nantes, France
5Lebanese International University LIU, Mechanical Engineering Dept, Beirut, Lebanon
6Universite Paris Diderot, Paris, France
Keywords: вихревой след, турбулентность, кинетическая энергия, энергетический спектр турбулентности, лазерные велосиметры, эффект Доплера, vorticity, turbulent kinetic energy, turbulence power spectra, laser Doppler velocimetry

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The influence of the wake vortex arising behind a perforated tab on the mixing process in heat exchangers and chemical reactors is analyzed. The preliminary step of this study, i.e., investigation of the turbulent field generated by a single perforated tab, is presented here. For this aim, laser Doppler velocimetry measurements are conducted downstream from a perforated trapezoidal vortex generator placed in a wind tunnel. It is shown that two shear layers are generated by the tab. The first shear layer is located at the upper edge of the tab, and the other is ejected from the perforation edges. These shear layers are characterized by high turbulent kinetic energy levels, which are profitable for meso-mixing enhancement. Finally, a spectral study shows that the turbulent macro-scale is nearly the same for typical locations in the shear layers shed from the tab and perforation edges.

Peristaltic Flow of a Reactive Viscous Fluid Through a Porous Saturated Channel and Convective Cooling Conditions

S. Asghar1,2, Q. Hussain1, T. Hayat2,3, A. Alsaedi2
1COMSATS Institute of Information Technology, Islamabad 44000, Pakistan
2King Abdulaziz University, P.O.Box 80203, Jeddah 21589, Saudi Arabia
3Quaid-I-Azam University, 45320, Islamabad 44000, Pakistan
Keywords: перистальтика, реагирующая жидкость, пористая среда, конвекция, вязкая диссипация, закачивание, peristalsis, reactive fluid, porous medium, convective conditions, viscous dissipation, pumping

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This article addresses the heat transfer in a peristaltic flow of a reactive combustible viscous fluid through a porous saturated medium. The flow here is induced because of travelling waves along the channel walls. It is assumed that exothermic chemical reactions take place within the channel under the Arrhenius kinetics and the convective heat exchange with the ambient medium at the surfaces of the channel walls follows Newton's law of cooling. The analysis is carried out in the presence of viscous dissipation and without consumption of the material. The governing equations are formulated by employing the long-wavelength approximation. Closed-form solutions for the stream function, axial velocity, and axial pressure gradient are obtained. It is found that the temperature decreases at high Biot numbers, and the Nusselt number increases with increasing reaction parameter. The Biot number and reaction parameter produce the opposite effects on the Nusselt number.

Non-Darcy Natural Convection from a Vertical Plate with a Uniform Wall Temperature and Concentration in a Doubly Stratified Porous Medium

D. Srinivasacharya, O. Surender
National Institute of Technology, Warangal, Telangana-506004, India
Keywords: естественная конвекция, стратифицированная среда, закон Дарси - Форхгеймера, natural convection, stratified medium, Darcy-Forchheimer law

Abstract >>
In this paper, non-similarity solutions for natural convection heat and mass transfer along a vertical plate with a uniform wall temperature and concentration in a doubly stratified porous medium saturated by a fluid are obtained. The Darcy--Forchheimer-based model is employed to describe the flow in the porous medium. The nonlinear governing equations and their associated boundary conditions are initially cast into dimensionless forms by using pseudo-similarity variables. The resulting system of nonlinear partial differential equations is then solved numerically by using the Keller-box method. The effects of the buoyancy parameter, Forchheimer number, and thermal and solutal stratification parameters on the dimensionless velocity, temperature, concentration, and heat and mass transfer coefficients are studied.

Unsteady Three-Dimensional Stagnation-Point Flow and Heat Transfer of a Nanofluid with Thermophoresis and Brownian Motion Effects

S. Dinarvand1, R. Hosseini2, H. Tamim2, E. Damangir2, I. Pop3
1Islamic Azad University, Tehran, Iran
2Amirkabir University of Technology, 15875-4413 Tehran, Iran
3University of Cluj, R-3400 Cluj, Romania
Keywords: наножидкость, трехмерное течение в точке остановки потока, нестационарность, броуновское движение, термофорез, численное решение, nanofluid, three-dimensional stagnation-point flow, unsteadiness, Brownian motion, thermophoresis, numerical solution

Abstract >>
An unsteady three-dimensional stagnation-point flow of a nanofluid past a circular cylinder with sinusoidal radius variation is investigated numerically. By introducing new similarity transformations for the velocity, temperature, and nanoparticle volume fraction, the basic equations governing the flow and heat and mass transfer are reduced to highly nonlinear ordinary differential equations. The resulting nonlinear system is solved numerically by the fourth-order Runge−Kutta method with the shooting technique. The thermophoresis and Brownian motion effects occur in the transport equations. The velocity, temperature, and nanoparticle concentration profiles are analyzed with respect to the involved parameters of interest, namely, unsteadiness parameter, Brownian motion parameter, thermophoresis parameter, Prandtl number, and Lewis number. Numerical values of the friction coefficient, diffusion mass flux, and heat flux are computed. It is found that the friction coefficient and heat transfer rate increase with increasing unsteadiness parameter (the highest heat transfer rate at the surface occurs if the thermophoresis and Brownian motion effects are absent) and decrease with increasing both thermophoresis and Brownian motion parameters. The present results are found to be in good agreement with previously published results.

Simulation of the Action of a Medium on a Conical Body and the Family of Phase Portraits in the Space of Quasivelocities

A. V. Andreev1, M. V. Shamolin2
1Peoples' Friendship University of Russia, Moscow, 117198 Russia
2Institute of Mechanics of the Lomonosov Moscow State University Moscow State University, Moscow 119192, Russia
Keywords: твердое тело, сопротивляющаяся среда, квазистационарность, фазовый портрет, rigid body, resisting medium, quasistationarity, phase portrait

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A mathematical model of the effect of a medium on a homogeneous rigid body whose outer surface includes a circumferential cone is considered. The complete system of equations of motion under quasistationarity conditions is given. In the dynamic part forming an independent third-order system, an independent second-order subsystem is distinguished. A new two-parameter family of phase portraits on the phase cylinder of quasivelocities is obtained.

Model for Calculating Shock-Compression Parameters of a Platelet Gradient Mixture

A. A. Golyshev, V. V. Kim, A. N. Emel'yanov, A. M. Molodets
Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, 142432 Russia
Keywords: смеси, градиентные материалы, ударные волны, высокие давления, mixture, gradient materials, shock waves, high pressure

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The shock-wave loading of a gradient mixture is numerically investigated in the pressure range of 20−150 GPa. The shock compression of a platelet gradient mixture of tungsten and porous copper is considered using a model which is a modification of the model of platelet porous materials supplemented with an algorithm for calculating changes in the thermodynamic and kinematic parameters of each particle and the sample as a whole. It is shown that the calculated parameters of the state of this shock-compressed mixture in the pressure−particle velocity coordinates are consistent with experimental data for a real tungsten−copper mixture.

Development and Deceleration of Viscoplastic Flow in a Layer Heated by Friction on a Rough Plane

A. A. Burenin1, L. V. Kovtanyuk2, G. L. Panchenko3
1Institute of Engineering and Metallurgy, Far East Branch, Russian Academy of Sciences, Komsomol'sk-on-Amur, 681005 Russia
2Institute of Automation and Control Processes, Far East Branch, Russian Academy of Sciences, Vladivostok, 690041 Russia
3Vladivostok State University of Economics and Service, Vladivostok, 690014 Russia
Keywords: упругость, пластичность, вязкость, теплопроводность, большие деформации, elasticity, plasticity, toughness, heat conduction, large deformations

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This paper presents a solution of a sequence of coupled problems of thermoelastoplasticity which study the occurrence and development of flow in a material layer under pure shear conditions, and its subsequent deceleration by slowly removing the load. The homogeneity of the stress state of the layer is excluded due to the coupling of thermal and deformation processes in the presence of a temperature dependence of the yield point. An additional source of heat is taken to be its production by friction of the material layer on a rough plane. The conditions for the occurrence of viscoplastic flow in the deformable material layer and the laws of motion of the boundaries between the elastic and plastic regions in this layer are determined, and the flow velocities and large irreversible and reversible deformations are calculated. It is shown that reversible deformations cause stresses in the flow region and the moving elastically deformed core.

Numerical Model of the Electro-Gas-Dynamics of a Gas−Particle System Based on the Equations of Motion of a Two-Velocity Two-Temperature Gas−Particle Mixture

A. L. Tukmakov
Institute of Mechanics and Engineering, Kazan' Scientific Center, Russian Academy of Sciences, Kazan', 420111 Russia
Keywords: двухскоростная двухтемпературная монодисперсная газовзвесь, электрическое поле, сила Кулона, уравнения Навье−Стокса, явная схема Мак−Кормака, two-velocity two-temperature monodisperse gas−particle mixture, electrical field, Coulomb force, Navier−Stokes equations, explicit McCormack scheme

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A mathematical model of the electro−gas−dynamics of a gas−particle system is described. A numerical method for solving the system of equations is proposed, and an analysis is made of the motion of charged solid aerosol particles in gas−particle flow in the electric field produced by the corona electrode of the atomizer, the grounded surface on which deposition is performed, and the charge of the aerosol particles in the interelectrode space. The solution is based on the two−velocity two−temperature model of a monodisperse medium without phase transitions and coagulation assuming that only the carrier medium, described by the Navier−Stokes equations for a compressible gas, has viscosity. The dispersed phase is defined by the equation of conservation of mass, the equations of conservation of momentum components taking into account the Coulomb force and aerodynamic friction, and the equation of conservation of internal energy. The system is written in generalized coordinates in dimensionless form and solved using the explicit McCormack method with splitting over the spatial coordinates and a conservative correction scheme. The velocity and density fields of the gas−particle mixture were investigated in the interelectrode space and near the surface on which solid aerosol particles in the gas−particle flow are deposited.

Effect of the Permeability of the Porous Shell on the Vapor Film Thickness During Boiling of Superfluid Helium in Microgravity

P. V. Korolev, A. P. Kryukov, Yu. Yu. Puzina
MPEI National Research University, Moscow, 111250 Russia
Keywords: гелий-II, тепломассоперенос, пленочное кипение, невесомость, пористая структура, helium-II, heat and mass transfer, film boiling, microgravity, porous structure

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This paper presents a theoretically study of the boiling of superfluid helium on a cylindrical heater placed in a coaxial porous shell in microgravity. Steady-state transfer processes at the interface are studied using molecular-kinetic methods. The Boltzmann transport equation is solved by the moment method based on the four-moment approximation in the form of a two-sided Maxwellian. The obtained solution is used to calculate the heat flux density in film boiling on a cylindrical heating surface in the case where the film thickness is comparable to the diameter of the heater. The motion of the normal component of the superfluid liquid in pores is described by equations that take into account heat and mass transfer in superfluid helium. The relation between the vapor film thickness and the structural characteristics and geometrical dimensions of the porous shell is obtained. Analysis of the results of the calculations is given.

On the Use of the Homotopy Analysis Method for Solving the Problem of the Flow and Heat Transfer in a Liquid Film Over an Unsteady Stretching Sheet

T. Khademinejad, M. R. Khanarmuei, P. Talebizadeh, A. Hamidi
Department of Mechanical Engineering, Amirkabir University of Technology, Tehran 15875-4413, Iran
Keywords: метод гомотопического анализа, преобразование подобия, теплообмен в пленке жидкости, homotopy analysis method, similarity transformation, heat transfer in a liquid film

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In this paper, the effects of viscous dissipation, nonuniform heat source/sink, magnetic field, and thermal radiation on the heat transfer characteristics of a thin liquid film flow over an unsteady stretching sheet are analyzed by the homotopy analysis method. The effects of various physical parameters on the heat transfer characteristics are found. The study shows that the thermal radiation parameter has a significant effect on the surface temperature. It is also found that nonuniform heat sinks are better suited for cooling purposes. Furthermore, the limiting cases are obtained and are found to be in good agreement with numerical results previously published by other authors.

Dynamics of the Antiplane Strain of a Nonlinear Elastic Body

B. D. Bondar'
Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: динамика, антиплоская деформация, задача для перемещения, нагрузка, нелинейность, тип уравнения, упругий потенциал, условие совместности, dynamics, antiplane strain, displacement problem, load, nonlinearity, type of the equation, elastic potential, compatibility condition

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The dynamic antiplane strain of an incompressible cylindrical body is studied in a nonlinear formulation in actual variables. A representation of the velocity and acceleration through the displacement is obtained. The problem of the body deformation with account for geometrical and physical nonlinearities is reduced to an initial boundary-value problem for the displacement. The displacement found is used to determine the pressure and stresses. For a body with a quadratic elastic potential, plane waves and self-similar motion are studied. The linear potential is used to investigate the deformation of a hollow elliptical cylinder for which analytical expressions for displacement and stresses are found and the external load is determined. It is shown that, due to the degeneration of the inner cavity of the body to a plane section, the load on the section remains limited.

Stability of Equilibrium of a Compressible Hyperelastic Hollow Sphere

E. B. Osipova
Il'ichev Pacific Oceanology Institute, Far East Branch, Russian Academy of Sciences, Vladivostok, 690041 Russia
Keywords: сжимаемый гиперупругий шар, устойчивость равновесия, compressible hyperelastic sphere, stability of equilibrium

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An analytical algorithm for studying the stability of the equilibrium of compressible hyperelastic sphere with Lagrange variables is proposed. The problem is solved in a spherical coordinate system in a general three-dimensional formulation using linearized stability theory and the method of separation of variables with respect to the radial displacement, the displacement due to the rotation, and the resulting strain in the principal directions. Results of numerical and graphical analysis of the stress--strain state for a three-layer-sphere are used to analyze the gravity stress--strain state of the lithosphere of the Kuril island arc system.

Wave Propagation in Two-Dimensional Block Media with Viscoelastic Layers (Theory and Experiment)

V. A. Saraikin1,2, A. G. Chernikov1, E. N. Sher1
1Institute of Mining, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630091 Russia
2Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: блочная среда, контакт блоков и прослоек, нестационарные волны, низкочастотная часть спектра, вязкость, затухание, block media, contact of blocks and interlayers, unsteady waves, low-frequency part of the spectrum, viscosity, damping

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A model of a medium consisting of parallel layers of elastic rectangular blocks separated by deformable viscoelastic interlayers is considered. The model is proposed for describing the low-frequency part of the spectrum in waves propagating in media with such a structure. For a two-dimensional assembly consisting of 36 blocks, the results of numerical calculations are compared with experimental data.

Model of a Mode II Shear Crack

V. V. Glagolev, M. V. Devyatova, A. A. Markin
Tula State University, Tula, 300600 Russia
Keywords: характерный размер, граничное интегральное уравнение, линейная упругость, идеально упругопластическая модель, characteristic size, boundary integral equation, linear elasticity, ideally elastoplastic model

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Based on the model of a physical cut and a material layer on its continuation, elastic and elastoplastic problems of determining the stress−strain state inside and outside the layer in the case of loading of cut edges by an antisymmetric system of forces are posed and solved. The solution of the elastic problem is compared with the solution obtained within the framework of the Neuber−Novozhilov model. In contrast to the latter model, the proposed approach provides results consistent with experimental data on the process of formation of fracture regions. Based on the analysis of the discrete solution of the problem, regions of plastic deformation and regions of possible fracture are found.

Modified Theory of Local Strain Energy Density for Sharp V-Notches

Yu. N. Ovcharenko
Tula State University, Tula, 300600 Russia
Keywords: V-образный вырез, плотность энергии деформации, схемы нагружения первого и второго типов, квазихрупкое разрушение, начальное направление развития трещины, локальный критерий разрушения, V-notch, strain energy density, loading schemes of the first and second types, quasi-brittle fracture, initial direction of crack propagation, local fracture criterion

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A new approach is proposed to estimate the fracture of bodies with V-shaped notches under loading of two types. Two examples of quasibrittle fracture are considered: with an initial straight crack and with a sharp V-notch. Experimental data are obtained on the fracture of V-notched specimens under bending.

Boundary Element Solution of the Plane Elasticity Problem for an Anisotropic Body with Free Smooth Boundaries

A. B. Tyagnii
Novosibirsk State Technical University, Novosibirsk, 630073 Russia
Keywords: упругость, анизотропия, плоская задача, комплексное сингулярное интегральное уравнение, граничный элемент, аналитическое интегрирование, elasticity, anisotropy, plane problem, complex singular integral equation, boundary element, analytical integration

Abstract >>
A boundary singular integral equation of the plane problem was constructed using an approach based on the representation of the unknown Lekhnitskii complex potentials in the form of Cauchy type integrals with unknown densities on the boundary of the region occupied by the body. The contours of the holes and cuts and the shape of the outer boundary are exactly or approximately represented in the form of a sequence of straight and curved (in the form of elliptical arcs) boundary elements. The unknown densities on the boundary elements are approximated by a linear combination of some regular functions or complex functions that have a known singularity. In the numerical solution of the integral equation by the collocation method or by the least-squares method and in the subsequent calculations of the stress--strain state, the integrals of all types along the boundary elements are calculated analytically, which significantly increases the accuracy of the results.

Mechanical Characteristics of High-Quality Laser Cutting of Steel by Fiber and CO2 Lasers

V. M. Fomin, A. A. Golyshev, A. G. Malikov, 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, СО2-лазер, волоконный лазер, критерии качества реза, скорость резки, laser cutting, CO2 laser, fiber laser, cut quality criterion, cutting velocity

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The quality of cutting of low-carbon and stainless steel by beams of fiber and CO2 lasers with oxygen or nitrogen being used as a process gas is compared. The cut surface roughness for sheets from 3 to 10 mm thick is determined. Domains of optimal (in terms of the minimum roughness criterion) application of lasers of various types in the space of dimensionless parameters (Peclet number and dimensionless power) are found. It is demonstrated that the CO2 laser is more effective for laser-oxygen cutting, while the fiber laser is more beneficial for cutting with the use of a neutral gas.