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Journal of Applied Mechanics and Technical Physics

2019 year, number 5

Numerical Simulation of the Operation of a Wide-Aperture Electron Gun with a Grid Plasma Emitter and Beam Output into the Atmosphere

V. T. Astrelin1,2, M. S. Vorobyov3, A. N. Kozyrev4, V. M. Sveshnikov2,4
1Budker Institute of Nuclear Physics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Novosibirsk National Research State University, Novosibirsk, 630090, Russia
3Institute of High Current Electronics, Siberian Branch, Russian Academy of Sciences, Tomsk, 634055, Russia
4Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: ускоритель электронов, плазменный катод, сеточная (слоевая) стабилизация, численное моделирование, декомпозиция областей, квазиструктурированные сетки, electron gun, plasma cathode, grid/layer stabilization, numerical simulation, domain decomposition, quasi-structured grids

Abstract >>
Numerical simulation of physical processes in the electron-optical system of the DUET accelerator was carried out using the ERA-DD code. Calculations were carried out on adaptive quasi-structured grids developed by the authors. A mathematical model for the emission plasma surface deformable when solving the problem is proposed. In this model, the problem is considered in a two-dimensional axisymmetric approximation and the front of the electron entrance to the computational domain is represented as a set of circular arcs connected by necks. In order to increase the accuracy of the calculations, it is proposed to split the multi-scale extended domain into two subdomains and alternately solve self-consistent problems in the subdomains using the alternating Schwartz method. The beams are simulated by the method of current tubes, and the electric field potential is calculated by the finite volume method. The obtained characteristics of the beam are compared with experimental data. It is shown that for the operating parameters of the beam source, its losses on the accelerator elements are minimal and are primarily due to the imperfect alignment of the holes in the mask and the reference grid, as well as to deviations of electron beams generated by structures localized on the periphery of the emission electrode.

Analytical Solution of Equations of the Physical Theory of Meteors for a Non-Fragmenting Body with Ablation in a Nonisothermal Atmosphere

M. D. Bragin1,2, G. A. Tirskiy2,3
1Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047, Russia
2Moscow Institute of Physics and Technology, Dolgoprudny, 141701, Russia
3Institute of Mechanics, Moscow, 119192, Russia
Keywords: физическая теория метеоров, метеороид, торможение, унос массы, неизотермическая атмосфера, physical theory of meteors, meteoroid, deceleration, ablation, nonisothermal atmosphere

Abstract >>
Analytical solutions of equations of the physical theory of meteors for a non-fragmenting meteoroid in an isothermal atmosphere are derived. The ablation parameter is defined as a power-law function of velocity of trajectory motion. An expression relating the meteoroid mass and its velocity and an expression relating the meteoroid velocity, its initial parameters, and atmospheric pressure are obtained. In addition, simple approximate formulas for the meteoroid mass and velocity at the initial trajectory segment and relations for determining the extreme values of the basic dynamic characteristics of the meteoroid (deceleration, dynamic pressure, ablation rate, mid-section area, and kinetic energy per unit path) are also derived.

Dynamics of Separation Points during Impact of a Floating Circular Cylinder

M. V. Norkin
Southern Federal University, Rostov-on-Don, 344090, Russia
Keywords: идеальная несжимаемая жидкость, круговой цилиндр, отрывной удар, линеаризованная модель, динамика точек отрыва, число Фруда, число кавитации, ideal incompressible fluid, circular cylinder, separation impact, linearized model, dynamics of separation points, Froude number, cavitation number

Abstract >>
The 2D problem of vertical separation impact of a circular cylinder under the free surface of a heavy fluid is considered. The problem is studied in a linearized formulation corresponding to small velocities of the body and fluid and taking into account the dynamics of separation points of the cavitation zone. A coupled nonlinear problem is formulated, which includes a mixed boundary-value problem of potential theory with one-sided constraints on the surface of the body and an equation defining the law of motion of the cylinder. Examples demonstrating the dynamics of separation points during forced or free cylinder motions are considered. Numerical results obtained using the proposed mathematical model are compared with the results of asymptotic analysis of the initial nonlinear problem for small times.

Structure of the Turbulent Flow in an Axisymmetric Submerged Gas-Saturated Jet

M. A. Pakhomov, V. I. Terekhov
Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: затопленная пузырьковая струя, структура турбулентного течения, модель переноса рейнольдсовых напряжений, submerged bubbly jet, turbulent flow structure, transport model for Reynolds stresses

Abstract >>
The structure of a vertically ascending submerged circular bubbly jet is numerically simulated by using the Eulerian approach. The influence of the concentration and diameter of air bubbles on the averaged parameters and fluctuating characteristics of the submerged turbulent two-phase jet is analyzed. An increase in the concentration and size of gas bubbles leads to jet expansion (by 35% as compared to the one-phase jet), which testifies to intensification of turbulent mixing with the ambient space. Addition of air bubbles enhances the flow turbulence (by 20% as compared to the one-phase jet).

Stokes Flow Through a Membrane Built up by Nonhomogeneous Porous Cylindrical Particles

P. K. Yadav1, P. Singh2, A. Tiwari3, S. Deo4
1Motilal Nehru National Institute of Technology Allahabad, Prayagraj, 211004, India
2National Institute of Technology Patna, Patna, 800005, India
3BITS Pilani, Pilani Campus, Rajasthan, 333031, India
4University of Allahabad, Prayagraj, 211002, India
Keywords: ячеечная модель, функция тока, закон Дарси, гидродинамическая проницаемость, cell model, stream function, Darcy equation, hydrodynamic permeability

Abstract >>
This work deals with the creeping flow of an incompressible viscous fluid through a membrane. It is assumed that the membrane is composed of nonhomogeneous porous cylindrical particles with radially varying permeability enclosing a cavity. The flow within the nonhomogeneous porous medium is governed by the Darcy equation. The flow inside the cavity and outside the nonhomogeneous porous region is governed by the Stokes equations. An analytical solution of the problem is obtained by using the cell model technique. Exact expressions for the drag force acting on the membrane and hydrodynamic permeability of the membrane are derived. The influence of radially varying permeability on flow parameters is considered. The effects of various parameters of the problem on hydrodynamic permeability of the membrane are discussed for four models. Some previous results for hydrodynamic permeability are verified as special limiting cases.

Entropy Analysis of a Convective Film Flow of a Power-Law Fluid with Nanoparticles Along an Inclined Plate

B. Vasu1, R. S. R. Gorla2, P. V. S. N. Murthy3, Beg O. Anwar4
1Motilal Nehru National Institute of Technology Allahabad, Prayagraj, 211004 India
2Cleveland State University, Ohio, 44115, USA
3Indian Institute of Technology Kharagpur, Kharagpur, India
4Salford University, Salford, M54WT, UK
Keywords: анализ энтропии, течение пленки, наножидкость, свободная конвекция, степенной реологический закон, термофорез, entropy analysis, film flow, nanofluid, free convection, power-law model, thermophoresis

Abstract >>
Entropy generation in a two-dimensional steady laminar thin film convection flow of a non-Newtonian nanofluid (Ostwald-de-Waele-type power-law fluid with embedded nanoparticles) along an inclined plate is examined theoretically. A revised Buongiorno model is adopted for nanoscale effects, which includes the effects of the Brownian motion and thermophoresis. The nanofluid particle fraction on the boundary is passively rather than actively controlled. A convective boundary condition is employed. The local nonsimilarity method is used to solve the dimensionless nonlinear system of governing equations. Validation with earlier published results is included. A decrease in entropy generation is induced due to fluid friction associated with an increasing value of the rheological power-law index. The Brownian motion of nanoparticles enhances thermal convection via the enhanced transport of heat in microconvection surrounding individual nanoparticles. A higher convective parameter implies more intense convective heating of the plate, which increases the temperature gradient. An increase in the thermophoresis parameter decreases the nanoparticle volume fraction near the wall and increases it further from the wall. Entropy generation is also reduced with enhancement of the thermophoresis effect throughout the boundary layer.

Convection in a Two-Layer Liquid System in a Finite Cylinder

E. P. Magdenko1,2
1Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, 660036, Russia
2Siberian Federal University, Krasnoyarsk, 660041, Russia
Keywords: конвекция, поверхность раздела, тау-метод, число Марангони, convection, interface, tau method, Marangoni number

Abstract >>
This paper describes a cylindrical container of finite dimensions, filled with two resting immiscible heat-conducting liquids with a common flat interface. The side walls and base of the vessel are solid, there are no external forces, and the contact angle of the interface with the side wall of the container is π/2. The interface has a surface tension whose strength linearly depends on temperature. When one of the container bases is heated to a critical temperature, there is movement inside the vessel. When modeling takes into account the energy spent on the interface deformation. The emerging spectral problem is solved by the modified Galerkin method. For various liquids, in the case of monotonous vibrations, the dependence of the critical Marangoni number on the container size and the temperature ratio, specified on the cylinder bases, is obtained, and a perturbed motion velocity field is constructed.

Edge Waves Durfing Motion of a Vessel in an Ice Channel

L. A. Tkacheva
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: поверхностные волны, изгибно-гравитационные волны, краевые волны, плавающая вязкоупругая пластина, дисперсионные соотношения, волновые силы, преобразование Фурье, метод Винера - Хопфа, surface waves, flexural-gravity waves, edge waves, floating viscoelastic plate, dispersion relations, wave forces, Fourier transform, Wiener-Hopf technique

Abstract >>
The Wiener-Hopf technique was used to obtain an analytical solution of the problem of waves arising in a liquid and ice sheet during uniform motion of a pressure region modeling an air-cushion vessel on the free surface of the liquid in an ice sheet fracture. The ice sheet is modeled by two thin semi-infinite viscoelastic plates of constant thickness, floating on the surface of an ideal incompressible liquid of finite depth and separated by a liquid free surface zone. In the moving coordinate system, the plate deflection and the liquid elevation are assumed to be steady-state. The wave forces, the elevation of the liquid free surface, the deflection and deformation of the plates at different vessel speeds and ice sheet thicknesses are investigated. It is shown that for some values of the speed, ice sheet thickness, and current pressure, destruction of the ice sheet near the edge is possible.

To the Theory of Barotropic Geostrophic Flows

A. A. Zaitsev, A. I. Rudenko
Kaliningrad State Technical University, Kaliningrad, 236035, Russia
Keywords: стационарные баротропные геострофические течения, вихрь, циклон, антициклон, радиальная и тангенциальная составляющие скорости частиц жидкости, распределение давления, функция тока, точечные вихри, stationary barotropic geostrophic flows, vortex, cyclone, anticyclone, radial and tangential components of the fluid particle velocity, pressure distribution, current function, point vortices

Abstract >>
Barotropic geostrophic flows are investigated using rectangular and polar coordinate systems. It is shown that, for the analysis of geostrophic flows with radial symmetry, the use of a polar coordinate system is preferable. Relations between the hydrodynamic characteristics, including the expressions of the fluid particle velocity components and vorticity through pressure, are obtained. It is established that, in the case of stationary barotropic flows, isobaths coincide with current lines. Stationary radially symmetric geostrophic flows are considered.

Effect of Air Blowing and Suction Through Single Slots on the Aerodynamic Performances of an Airfoil

V. I. Kornilov, I. N. Kavun, A. N. Popkov
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: крыловой профиль, турбулентный пограничный слой, щель, вдув, отсос, подъемная сила, сопротивление, airfoil, turbulent boundary layer, slot, blowing, suction, lift force, drag

Abstract >>
Steady air blowing (suction) into a turbulent boundary layer on the NACA 0012 airfoil through singular slots located on its neighboring sides near the trailing edge is studied experimentally and numerically. The investigations are performed at the Reynolds number Rec = 0.7 x 106 in the range of the angles of attack α = -6 &divede; 6oC; the intensity of the injected and sucked jet characterized by a dimensionless momentum coefficient does not reach 10-3. It is demonstrated that the result of blowing is not only an increase in the lift force, but also significant enhancement of the drag force of the airfoil. In the case of suction, the increase in the lift force is appreciably smaller despite airfoil drag reduction.

On the Theory of the Development of High-Viscosity Oil Deposits Deposits using Heating

V. Sh. Shagapov1, Yu. A. Tazetdinova2, A. A. Gizzatullina3
1Mavlyutov Institute of Mechanics, Ufa Federal Research Center, Russian Academy of Sciences, Ufa, 450000, Russia
2Institute of Mechanics and Mechanical Engineering, 420111, Kazan, Russia
3Birsk Branch of Bashkir State University, Birsk, 452453, Russia
Keywords: высоковязкая нефть, тепловое воздействие на нефтяной пласт, фильтрация нефти, технология парных горизонтальных скважин, зависимость вязкости от температуры, high-viscosity oil, oil reservoir heating, oil filtration, paired horizontal well technology, temperature dependence of viscosity

Abstract >>
A theoretical model of the development of a reservoir with high-viscosity oil using the technology of paired horizontal wells was developed. The problem was solved numerically assuming that a two-well system is replaced by one hypothetical well through which heating of the reservoir and simultaneous oil extraction are performed. Heat consumption for heating the reservoir, the change in flow rate, and the mass of extracted oil for a certain period of time were analyzed for various heating temperatures, pressure drops, and induction period of the well. The obtained solutions can be used to determine heating conditions optimal in energy consumption.

Numerical Investigation of the Temperature Field in a Multiple-Zone Well during Gas-Cut Oil Movement

R. F. Sharafutdinov, I. V. Kanafin, T. R. Khabirov
Bashkir State University, Ufa, 450076, Russia
Keywords: термометрия, двухфазная фильтрация, газированная нефть, разгазирование нефти, теплота разгазирования, эффект Джоуля - Томсона, адиабатический эффект, скважина, пласт, thermometry, two-phase filtration, gas-cut oil, oil degassing, heat of degassing, Joule-Thomson effect, adiabatic effect, well, reservoi

Abstract >>
The temperature distribution in a well and reservoir are studied by numerical simulation of the nonisothermal movement of gas-cut oil in a multiple-zone well taking into account the Joule-Thomson effect, the adiabatic effect, and the heat of degassing. It is shown that the position of the boundary of the oil degassing area in the borehole can be evaluated from the temperature distribution.

Three-Dimensional Thermoelastic Analysis of a Rotating Cylindrical Functionally Graded Shell Subjected to Mechanical and Thermal Loads Based on the FSDT Formulation

M. Omidi Bidgoli, A. Loghman, M. Arefi
University of Kashan, I.R. Iran
Keywords: термоупругость, давление, поверхностное трение, температура, функционально-градиентный материал, вращающийся цилиндр, теория оболочек, поперечные сдвиги, thermoelastic, pressure, surface friction, temperature, functionally graded rotating cylinder, first-order shear deformation theory

Abstract >>
This paper presents a three-dimensional thermoelastic analysis of a rotating cylindrical functionally graded shell subjected to inner and outer pressures, surface shear stresses due to friction, an external torque, and a uniform temperature distribution. A power-law distribution is considered for thermal and mechanical properties of the material. The first-order shear deformation theory (FSDT) is employed to express the displacement field. The system of six constitutive differential equations of the problem includes the Euler equations for the energy functional. It is found that the material grading index has a significant effect on the stress and displacement fields.

Inhomogeneous Beams with Different Behaviour in Tension and Compression:A Longitudinal Crack Study

V. I. Rizov
University of Architecture, Civil Engineering and Geodesy, Sofia, 1046, Bulgaria
Keywords: неоднородная балка, нелинейный материал, продольная трещина, аналитическое исследование, inhomogeneous beam, material nonlinearity, longitudinal crack, analytical study

Abstract >>
An approach for investigating the strain energy release rate for longitudinal cracks in nonlinear elastic inhomogeneous beams is derived. The Ramberg-Osgood stress-strain relation is applied to describe the unsymmetrical mechanical behaviour of the material with respect to tension and compression. It is assumed that the beams have continuous material inhomogeneity in the height direction. Cracks can be located arbitrarily along the beam height. The approach is applied to investigate a longitudinal crack in a cantilever beam. The J-integral is used for verification of the solution.

Theory of Large Deformation of Metals

V. M. Greshnov
Ufa State Aviation Technical University, Ufa, 450000, Russia
Keywords: пластичность, ползучесть, длительная прочность, деформационная поврежденность, вязкое разрушение, плотность дислокаций, большая и интенсивная деформации, plasticity, creep, long-term strength, dislocation density, large and intense deformations

Abstract >>
This paper presents the theory of irreversible deformations that allows one to analyze large deformations of metals and determine the characteristics of the stress-strain state, deformation damage, and structural characteristics at various structural levels.

Free Vibrations of Supporting Walls Comprised of Reinforced Orthotropic Cylindrical Shells in Contact with Soil

F. S. Latifov, D. S. Ganiev
Azerbaijan University of Architecture and Construction, Baku, AZ1073, Azerbaijan
Keywords: ортотропные цилиндрические оболочки, принцип вариации, свободные колебания, потенциальная энергия, кинетическая энергия, orthotropic cylindrical shells, variational principle, free vibrations, potential energy, kinetic energy

Abstract >>
This paper describes a study of the dynamic strength characteristic - the natural vibration frequency of a supporting wall comprised of two orthotropic cylindrical shells reinforced by discretely distributed annular rods. The problem is solved using the Hamilton-Ostrogradsky variational principle. A frequency equation is constructed, its roots are determined, and their dependence on the physical and geometric parameters of the problem is investigated.

Effect of Block Medium Parameters on Energy Dissipation

K. Vang1,2, N. I. Aleksandrova3, I. Pan1, V. N. Oparin3, L. Dou2, A. I. Chanyshev3
1Liaoning University of Technology, Fuxin, 123000, China
2China University of Mining and Technology, Suzhou, 221116, China
3N.A. Chinakal Institute of Mining, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 63009, Russia
Keywords: блочная среда, волна маятникового типа, вязкоупругая прослойка, диссипация энергии, нестационарный процесс, block medium, pendulum wave, viscoelastic layer, energy dissipation, nonstationary process

Abstract >>
This paper describes energy distribution in a block medium simulated by a one-dimensional chain of masses connected by springs and dampers. Equations describing the motion of masses are solved by the methods of the theory of ordinary differential equations. The effect of the block medium parameters on energy dissipation is investigated. An approximate analytical solution is obtained that describes the total energy of a block medium at large values of time.

Energy Condition of Creep

A. S. Gulgazli
Azerbaijan State Oil and Industry University, Baku, AZ1010, Azerbaijan
Keywords: напряжения, деформации, нагружение, потенциальная энергия, ползучесть, инварианты тензора, stress, strain, load, potential energy, creep, tensor invariants

Abstract >>
The concept of a loading surface corresponding to creep strains is formulated similarly to how the concept of a loading surface corresponding to plastic strains is introduced. An equation for the loading surface corresponding to creep strains is obtained. It is proven that, in the absence of viscosity of the material, the equation of the loading surface corresponding to creep strains coincides with the equation of the loading surface corresponding to plastic strains.

Simulation of Strength of Waterproof Barriers in Porous Forms

A. M. Il'yasov, T. F. Kireev, G. T. Bulgakova
Ufa State Aviation Technical University, Ufa, 450000, Russia
Keywords: водоизолирующий барьер, пористая среда, дифференциальный метод самосогласования, идеально пластическое тело, waterproof barrier, porous medium, differential self-consistency method, perfectly plastic body

Abstract >>
Within the framework of a model of a perfectly plastic body, the strength of a two-layer waterproof barrier adjacent to the trunk of a production well in a porous medium is investigated. The barrier is formed by injecting (with subsequent solidification) synthetic resin into the porous layer through the production well. In the problem parameter space, the domains are determined, in which the strength and yield conditions of the outer and inner layers of the barrier are satisfied.

Spall Fracture of an VNZh-90 Alloy under a Shock Wave Load

I. R. Trunin1,2, I. A. Tereshkina1,2, A. M. Podurets1,2, V. G. Simakov1,2, M. I. Tkachenko1,2, V. A. Bragunets1, A. N. Balandina1, E. E. Shestakov1,2
1All-Russian Scientific Research Institute of Experimental Physics, Sarov, 607190, Russia
2Sarov State Physics and Technical Institute, Sarov, 607186, Russia
Keywords: сплав вольфрама с никелем и железом, откольное разрушение, поврежденность, металлографический анализ, численное моделирование, tungsten alloy with nickel and iron, spall fracture, damage, metallographic analysis, numerical simulation

Abstract >>
Based on the results of experiments carried out using a gas gun, data are obtained on the fracture of a VNZh-90 alloy (tungsten - nickel - iron) under a shock wave load in a pressure range of 2.5-4.0 GPa. Spall strength, which, depending on the degree of fracture, varies in a range of 1.00 to 1.25 GPa, and the nature of fracture are determined. Metallographic analysis is used to determine the damage parameter values. It is revealed that, under these conditions, the fracture comprises several stages, occurs in a (Ni-Fe) bond, and the W particles do not fracture. It is shown that experimental results are in good agreement with the results of numerical calculations.

On one Type of Self-Oscillations of Composite Structures

M. K. Tleulinov
Kazan National Research Technical University named after A.N. Tupolev, Kazan, 420111, Russia
Keywords: составная конструкция, автоколебания, катастрофическая потеря устойчивости, несущая и управляющая поверхности, composite structure, self-oscillations, catastrophic buckling, bearing and control surfaces

Abstract >>
Oscillations of a structure of a catastrophic type, comprised of a bearing and controlling surfaces are under study. It is shown that this process is self-oscillatory. Calculation results are given.

Flapwise Bending Vibration Analysis of a Double Tapered Rotating Nonlocal Euler–BernoullI Beam by the Differential Transform Method

I. Kurt1, M. O. Kaya2
1Yildiz Technical University, Istanbul, Yildiz , 34349, Turkey
2Istanbul Technical University, Istanbul, Maslak, 34469, Turkey
Keywords: нелокальная теория упругости, конусообразная балка, балка Эйлера - Бернулли, метод дифференциального преобразования, свободные колебания, nonlocal elasticity theory, tapered beam, Euler-Bernoulli beam theory, differential transform method, free vibration analysis

Abstract >>
Transverse (out-of-plane) vibrations of a rotating nanobeam tapered both in width and thickness are studied on the basis on the Euler-Bernoulli beam theory. The nonuniform nanobeam is modeled with allowance for a small-scale effect contained in the nonlocal Eringen elasticity theory. The axial force due to rotating movement (centrifugal stiffening) of the beam is included into the model. The governing partial differential equation of the structure is solved by implementing the differential transform method (DTM). The variations of the taper ratio, rotational velocity, hub radius, and nonlocal small-scale parameter are taken into consideration. Comparisons of the present results with available data are performed.

New Visualization and Measurement Techniques for Ballistic Processes and Dynamic Flows

M. Yu. Sotskii, D. V. Gelin, I. S. Krutov, D. A. Lysov, V. A. Markov, I. V. Markov, M. Yu. Chetvernin
Bauman Moscow State Technical University, Moscow, 105005, Russia
Keywords: измерительный зонд, баллистический эксперимент, видеорегистрация, электропровод, технические решения, measuring probe, ballistic experiment, video recording, electric wire, technical solutions

Abstract >>
A laboratory technique for accelerating a measuring probe in a ballistic experiment was used to perform a series of experiments with high-speed video recording of the process from the start of motion of the measuring probe and electric wire in the starting device to the end of motion of the probe in the target. Advantages of the developed probing technique are discussed. The conditions and technical solutions providing continuous recording of the motion parameters of measuring probe on the flight path and in the target medium are proposed based on the result of video recording of the dynamic gas flow in the starting device and the evolution of the electric wire shape.