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Journal of Applied Mechanics and Technical Physics

2019 year, number 4

Homogenization of Harmonic Maxwell Equations with Allowance for Interphase Surface Currents: Layered Structure

Y. Amirat1, V. V. Shelukhin2,3
1University of Auvergne, Clermont-Ferrand, France
2Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
3Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: уравнения Максвелла, межфазные токи, гомогенизация, двух-масштабная сходимость, Maxwell equation, interphase currents, homogenization, two-scale convergence

Abstract >>
The Maxwell equations for a composite two-component layered material with a periodic structure in the field of a time-harmonic source acting along the layer are considered. Two-scale homogenization of the equations is performed with allowance for complex conductivity of interphase layers and their thickness. The boundary-value problem for systems of differential equations with boundary conditions is reduced to a problem in a weakly variational formulation. Unique solvability of the problem is established. The case of low frequencies of interphase surface currents of different intensities with allowance for the frequency-dependent wave length and skin layer length is analyzed. Macro-equations are derived, and effective material constants are determined, such as the magnetic and dielectric permeabilities and electrical conductivity. Conditions at which the effective parameters depend on interphase currents are described. It is found that the effective dielectric permeability can be negative at specially chosen parameters of interphase layers, if the effective dielectric permeability is determined on the basis of the effective wave number.

Rotational Motion of Finned Shaped-Charge Liners

S. S. Rassokha, S. V. Ladov, A. V. Babkin
Bauman Moscow State Technical University, Moscow, 105005, Russia
Keywords: оребренная кумулятивная облицовка, кумулятивная струя, вращение, finned shaped-charge liner, shaped-charge jet, rotation

Abstract >>
The rotational motion of finned shaped-charge liners is studied. It is shown that the main factors affecting the rotation of a shaped-charge jet are the position of the jet-forming layer and the distribution of the circumferential velocity in the liner cross-section. The proposed method can be used to estimate the average angular velocity of the jet with consideration of the size of the finned shaped-charge liner and the properties of its material. It is shown that the results are consistent with available experimental data.

Modeling of High-Porosity Copper-Based Mixtures under Shock Loading

K. K. Maevskii, S. A. Kinelovskii
Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: уравнение состояния, ударная адиабата, термодинамическое равенство, пористая гетерогенная среда, медь, equation of state, Hugoniot adiabat, thermodynamic equality, porous heterogeneous medium, copper

Abstract >>
A thermodynamically equilibrium model is applied for simulating thermodynamic parameters of shock loading of both pure materials and mixtures of homogeneous and porous materials. The model includes a modified equation of state, which has only one fitting parameter determined on the basis of experimental data. The thermodynamic parameters of shock loading of copper and copper-based mixtures with porosities of 1-10 at pressures above 5 GPa are calculated. The results of these calculations are compared to available experimental data (Hugoniot adiabats, double compression by shock waves, and temperature estimates). The possibility of modeling the compression of the mixture as a whole and each component separately is demonstrated.

Analysis of Stability of the Boundary Layer on a Flat Plate under a Finite-Thickness Two-Layer Compliant Coating

A. E. Darzhain1,2, A. V. Boiko3,4, V. M. Kulik5, A. P. Chupakhin1,2
1Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Novosibirsk State University, Novosibirsk, 630090, Russia
3Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
4Tyumen State University, Tyumen, 62500, Russia
5Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: податливые покрытия, пограничный слой, гидродинамическая неустойчивость, compliant coatings, boundary layer, hydrodynamic instability

Abstract >>
Results of studying stability of the Blasius boundary layer on a two-layer compliant coating in the linear formulation are reported. The computations are based on experimental parameters of viscoelasticity of a real coating, which reveal the dependences of its elasticity modulus and loss coefficient on frequency. Parametric investigations of the influence of the coating layer thicknesses and free-stream velocity on flow stability, in particular, on the critical Reynolds number, are performed. Regions of a nonmonotonic behavior of the critical Reynolds number are found, which allow one to determine the optimal thicknesses of the upper and lower layers for intense interaction with the flow. An explanation of this effect is proposed.

Control of the Formation of a Transonic Region in a Supersonic Flow by using a Throttling Jet and Near-Wall Heat Release

V. P. Zamuraev1,2, A. P. Kalinina1,2
1Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Novosibirsk State University, Novosibirsk, 630090, Russia
Keywords: горение водорода и этилена, сверхзвуковой поток, поперечные струи, околозвуковой режим, hydrogen combustion, supersonic flow, transverse jets, transonic flow regime

Abstract >>
Starting of an air-breathing engine with fuel injection distributed along the combustion chamber is numerically simulated. Issues of principal importance are the presence of a compressed are jet generating a throttling effect and preliminary deceleration of the flow to transonic velocities. Averaged Navier-Stokes equations closed by the SST, SST κ-ω, or κ-ε turbulence models are solved. Hydrogen and ethylene combustion is simulated by one reaction. The computations are performed for various values of the turbulent kinetic energy in the flow. A pulsed transonic regime of hydrogen and ethylene combustion is discovered.

Non-Contact Measuring Section in the Problem of Hypersonic Aerodynamics

S. I. Gerasimov1,2,3,4, V. I. Erofeev4, A. G. Sirotkina2, A. V. Zubankov2, R. V. Gerasimova1,2
1All-Russian Research Institute of Experimental Physics, Sarov, 607190, Russia
2Sarov Institute of Physics and Technology, Sarov, 607186, Russia
3Alekseev Nizhny Novgorod State Technical University, Nizhny Novgorod, 603950, Russia
4Institute for Problems of Mechanical Engineering of the Russian Academy of Sciences, Nizhny Novgorod, 603024, Russia
Keywords: измерительное сечение, гиперзвуковая частица, космический 'мусор', бесконтактный способ, высокоскоростное соударение, measuring section, hypersonic particle, space debris, noncontact mode, high-velocity collision

Abstract >>
This paper considers the possibility of using measuring sections with inductive sensors to detect hypersonic particles in time in the simulation of collisions of objects with space debris. A method for determining the average velocity of hypersonic particles simulating the space debris and a method of starting the recording equipment for optical contactless detection of these particles are proposed. Results of experimental studies of the interaction of particles with a simulator of the mesh shield of the spacecraft.

Influence of the Shape of the Jet head on Its Impact on a Wetted Wall

A. A. Aganin, M. A. Il'gamov, T. S. Guseva
Institute of Mechanics and Engineering, Kazan, 420111, Russia
Keywords: удар струи, смоченная стенка, форма струи, ударные волны, нагрузка на стенке, jet impact, wetted wall, jet shape, shock waves, wall load

Abstract >>
The influence of the shape of the jet head on its impact on a wall covered with a thin layer of liquid has been studied. The conditions characteristic of the impact of the jet arising on the surface of a cavitation bubble upon its collapse near the wall have been considered. It has been established that changing the shape of the jet head can lead to a significant change in the size of the area of maximum loading of the wetted wall and in the magnitude and pattern of loading. In particular, with an increase in the degree of sharpening of the jet head, the pressure on the wall decreases and its spatial distribution becomes more uniform. Dependences of the maximum pressure and integrated wall load on the jet shape were obtained.

Effect of the Angular and Linear Parameters of Interaction of Water Droplets of Various Shapes on the Characteristics of Their Collisions

G. V. Kuznetsov1, A. K. Rebrov2, P. A. Strizhak1, N. E. Shlegel1
1Tomsk Polytechnical University, Tomsk, 634050 Russia
2Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: капли воды, форма, взаимодействие, столкновения, угловой и линейный параметры, отскок, коагуляция, разлет, дробление, water droplets, shape, interaction, collisions, angular andlinear parameters, rebound, coagulation, spreading, fragmentation

Abstract >>
The influence of the dimensionless angular and linear parameters of interaction of water droplets shaped as a sphere, an ellipsoid, and a conventionally liquid disk on the characteristics (regimes) of their collisions in air (rebound, coagulation, spreading, or fragmentation) is studied by using a system of high-speed video recording. Conditions of stable realization of this interaction are determined. Charts of the corresponding regimes are constructed and compared with available data. The characteristic sizes, the number of liquid fragments formed in collisions, and total areas of the evaporation surface are calculated. It is demonstrated that the liquid surface area in the case of collisions of conventionally liquid disks is significantly (by several times) greater than that in the case of spherical droplets.

Numerical Investigation of Interaction of Two Deformable Bubbles in an Acoustic Field

Yu. A. Pityuk1, N. A. Gumerov1,2, O. A. Abramova1, I. A. Zarafutdinov1, I. Sh. Akhatov3
1Center for Micro- snd Nanoscale Dynamics, Ufa, 450076, Russia
2Institute for Advanced Computer Studies, College Park, 21075, USA
3Skolkovo Institute of Science and Technology, Moscow, 143026, Russia
Keywords: деформация пузырька, взаимодействие пузырьков, численное моделирование, метод граничных элементов, потенциальное течение, bubble deformation, bubble interaction, numerical simulation, boundary-element method, potential flow

Abstract >>
Three-dimensional deformation of two bubbles and bubbles in a cluster in an ideal incompressible fluid exposed to an acoustic field is investigated using the boundary element method for potential flows. The dependence of the dynamics of two interacting bubbles on the frequency and amplitude of the acoustic field and the distance between them is studied. The values of the parameters of the acoustic field and the cluster for which jets are formed and the bubbles are deformed or remain spherical are determined. The behavior of two central bubbles in a structured cluster exposed to an acoustic field with different frequency and amplitude is investigated as a function of the distance between the bubbles of the cluster. A comparative analysis of the deformation of the investigated bubbles in the presence and absence of adjacent bubbles is performed.

On the Theory of Salt Washout from Water-Oil Emulsion with Fresh Water

V. Sh. Shagapov1, E. V. Galiakbarova2, I. K. Gimaltdinov2
1Mavlyutov Institute of Mechanics, Ufa, 450054, Russia
2Ufa State Petroleum Technical University, Ufa, 450062, Russia
Keywords: технология обессоливания, струйный смеситель, движение капель, desalination technology, jet mixer, droplet movement

Abstract >>
Theoretical model describing the movement of particles of saline water in oil flowing over a larger droplet of fresh water has been developed to solve the problem of cleaning oil from salts. The results of calculations of the effect of the radius and the initial velocity of a drop of fresh water on the coagulation of fresh and saline water droplets are presented.

Extraction of Material from a Porous Body into a Moving Liquid

A. I. Moshinskii
St. Petersburg Chemical and Pharmaceutical University, St. Petersburg, 197376, Russia
Keywords: пористое тело, массообмен, поток массы, двухкомпонентность, извлечение, porous body, mass transfer, mass flow, two-component, extract

Abstract >>
The nonstationary process of extracting material from a porous body simulated by a system of semi-infinite capillaries into a moving liquid is studied; the transfer rate of the material in the flow is a linear function of the cross flow coordinate. The case where the liquid velocity at the interface becomes zero is considered. It is assumed that the diffusion in the flow is quasi-stationary. Analytical dependences at the boundary of the porous material and the flow region are found for mass transfer characteristics of practical interest (concentration, diffusion flow, total diffusion flux and the total yield of the target component through the cross section of the porous body).

Numerical Study of Stress Relaxation in Nanostructures in the Course of Uniaxial Straining

I. F. Golovnev1, E. I. Golovnevaa1, M. S. Voronin2,3, E. R. Pruuel2
1Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
3Novosibirsk State Technical University, Novosibirsk, 630087, Russia
Keywords: метод молекулярной динамики, релаксация напряжения, наноразмерный стержень, дефекты кристаллической решетки, носитель необратимой деформации, molecular dynamics method, stress relaxation, nano-sized rod, crystal lattice defects, carrier of irreversible deformation

Abstract >>
Stress relaxation in a nano-sized rod containing structural defects in the course of constant-rate uniaxial straining is studied, and the reasons for the onset of this phenomenon are determined. Under the assumption that structural defects can serve as carriers of irreversible deformation of a higher level than dislocations, the problem is solved by the molecular dynamics method. It is found that stress relaxation is accompanied by the transition of the entire system to a steady state with a deeper potential minimum as compared to the system energy before the stress relaxation process, resulting in a temperature increase and reduction of the strain tensor components.

Low-Stress State of Simply-Supported Anisotropic Composite Plates

A. G. Akopyan
North Caucasus Branch of the Moscow Automobile and Road State Technical University (MADI), Lermontov, 357340, Russia
Keywords: малонапряженное состояние, изгиб плит, анизотропный, составной, ow-stress state, plate bending, anisotropic, composite

Abstract >>
The stress state in the neighborhood of the common edge of a freely supported composite wedge-shaped plate under transverse load has been studied. The materials of the constituent plates are cylindrical orthotropic. The problem is solved using the classical theory of anisotropic plates. Equations are derived for the hypersurface which, in the space of physical and geometric parameters, is the boundary of the region of parameters for which the neighborhood of the common edge of the composite plate is in a low-stress state (the stresses at the points of the common edge of the composite plate are limited).

Effect of Friction on Eigenfrequencies of Reinforced Cylindrical Shells with an Elastic Filler under Axial Compression

F. A. Seifullaev1, Sh. A. Kerimova1, N. A. Agaeva2
1Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Baku, AZ1141, Azerbaijan
2Research Design Institute “Neftegaz”, Baku, LZ1012, Azerbaijan
Keywords: оболочка, колебание, модуль упругости, деформация, полная энергия, коэффициент трения, shell, oscillation, elastic modulus, deformation, total energy, friction coefficient

Abstract >>
A variational principle is used to study the oscillations of a reinforced thin cylindrical shell with a filler under axial compression with allowance for friction on their contact surface. The dependences of frequencies of natural oscillations on the number of waves in a circumferential direction are constructed.

Plane Strain Dynamics of an Incompressible Nonlinear-Elastic Body

V. D. Bondar'
Novosibirsk State University, Novosibirsk, 630090, Russia
Keywords: нелинейная модель упругости, квадратичный потенциал, волновые и автомодельные решения, nonlinear elasticity model, quadratic potential, wave and self-similar solutions

Abstract >>
Nonlinear elasticity model in current state variables is used to study the plane strain dynamics of an incompressible body, and a system of nonlinear equations of displacement and pressure is obtained. In the absence of bulk forces and in the assumption of quadratic elastic potential, the resulting equations that describe plane waves, self-similar motions, and stress fields in these motions are solved and studied. It is shown that several solutions of a certain type are possible both in wave and self-similar cases.

Dynamic Buckling of a Cylindrical Shell with a General Boundary Condition under an Axial Impact

Y. Gui, J. Xu, J. Ma
Department of Aeronautics and Astronautics, Fudan University, Shanghai, 200433, China
Keywords: упругая цилиндрическая оболочка, краевые условия общего вида, энергетическое уравнение, динамическое выпучивание, elastic cylindrical shell, general boundary condition, energy equation, dynamic buckling

Abstract >>
The dynamic buckling of an elastic cylindrical shell with a general boundary condition (composed of stiffness and damping) under an axial impact by a rigid body is considered. A dynamic equation is derived to obtain the axial stress and radial displacement of the shell. Then, by substituting the results into the energy equation, the critical condition for the dynamic buckling of the shell is obtained. The influence of the general boundary condition on the critical velocity of the impactor is analyzed. The results reveal that the boundary condition exerts no effect on the dynamic buckling of the shell before the stress wave becomes reflected from the fixed end face of the shell. After reflection, the critical velocity decreases with increasing impactor mass and stiffness, but increases with increasing damping. At times smaller than the instant when the stress wave reaches the fixed end face of the shell, the dynamic buckling occurs earlier at greater values of damping and stiffness. After stress wave reflection, the earlier dynamic buckling is observed at smaller values of damping and stiffness.

Investigation on the Damage Mechanisms and Penetration Performance of Jacketed Rods with Different Striking Velocities

K. Tang1, J. Wang1, X. Chen1, N. Zhou2
1National Key Laboratory of Transient Physics, Nanjing University of Science and Technology, Nanjing, 210094, China
2Department of Criminal Science and Technology, Nanjing Forest Police College, Nanjing, 210023, China
Keywords: стержни с облицовкой, вольфрам марки 93W, алюминиевый сплав марки 1060Al, титановый сплав марки TC4, сталь марки 4340, преграда, соударение, проникание, разрушение

Abstract >>
Ballistic experiments, numerical simulations, and theoretical model investigations of the penetration performance of homogeneous and jacketed rods into a semi-infinite target are presented. The striking velocities vary between 0.9 and 3.3 km/s. The effects of the jacket material, striking velocity, and initial kinetic energy on the penetration performance and damage mechanisms are analyzed. The results show that jacketed rods provide better penetration performance than homogeneous rods with the same initial kinetic energy. For a fixed ratio of the jacket radius to the core radius, it is preferable to use a jacket material with a lower density and strength that can provide the lowest required flexural stiffness.

Synthesis of Composites Made of Powder Mixtures (Ti, C, AND Al) in Controlled Heating

N. V. Bukrina1, A. V. Baranovskii2
1Institute of Strength Physics and Materials Science, Siberian Branch, Russian Academy of Sciences, Tomsk, 634055, Russia
2Tomsk Polytechnic University, Tomsk, 634050, Russia
Keywords: высокотемпературный синтез, тепловой взрыв, математическое моделирование, high-temperature synthesis, thermal explosion, mathematical simulation

Abstract >>
Synthesis of a composite of powder mixtures is experimentally studied in a thermal explosion. A mathematical model for initiating a reaction that allows for the main physical and chemical phenomena changing the phase composition of a compact is formulated. It is shown that simulation results qualitatively agree with experimental data.

Determining Stresses in an Adhesion Bond with a Nonglued Region in the Longitudinal Direction using a Simplified Two-Dimensional Theory

S. S. Kurennov
National Aerospace University Kharkiv Aviation Institute, Kharkiv, 61000, Ukraine
Keywords: клеевое соединение, аналитическое решение, двумерная модель, adhesion bond, analytical solution, two-dimensional model

Abstract >>
A simplified two-dimensional model of a lapped adhesion bond is proposed. The problem of a stress state of an adhesion bond, along the surfaces of which nonglued regions are located, is solved analytically in the assumption that the cross-sectional displacements of carrier layers equal zero. The resulting solution is a functional series, with eigenfunctions being nonorthogonal. It is shown that the presence of nonglued regions may significantly increase stresses near the edge of the adhesion layer.

Stress Creep and Stress Relaxation in the Case of Loading and Unloading of a Cylindrical Layer with Allowance for the Development and Deceleration of a Viscoplastic Flow

A. S. Begun1, L. V. Kovtanyuk1, A. O. Lemza2
1Institute of Automation and Control Processes, Far Eastern Scientific Center, Siberian Branch, Russian Academy of Sciences, Vladivostok, 690041, Russia
2Far Eastern Federal University, Vladivostok, 690091, Russia
Keywords: упругость, пластичность, ползучесть, вязкость, большие деформации, elasticity, plasticity, creep, viscosity, large deformations

Abstract >>
The theory of large deformations is used to solve a problem of an elastic-viscoplastic material placed in a gap between two coaxial cylindrical surfaces, with one of them rotating with an alternating velocity and the other one at rest. It is shown that an increase in the stresses in a cylindrical layer due to a mechanical influence on it initially causes irreversible creep strains because of viscosity of the material and then the accumulation of plastic strains because of the arrival of stress states at the loading surface. The unloading is accompanied by a plastic strain and then a viscous one. The stress-strain parameters of the medium with a varying rotation velocity of the cylinder are calculated. Stress relaxation after its complete stop is described.

Similarity Laws in Laser Cladding of Cermet Coatings

A. A. Golyshev1,2, A. M. Orishich1,2, A. A. Filippov1
1Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Novosibirsk State University, Novosibirsk, 630090, Russia
Keywords: аддитивные технологии, лазерная наплавка, СО-лазер, карбид вольфрама, никель, микроструктура, микротвердость, безразмерные параметры, additive technologies, laser cladding, CO2 laser, tungsten carbide, nickel, microstructure, microhardness, dimensionless parameters

Abstract >>
The influence of the laser beam parameters (power, motion velocity, and focus position) on the characteristics of the track being formed (size, elemental composition, and microhardness) is studied. If the difference in the laser radiation absorption coefficients in the heat conduction and “knife-like” regimes is taken into account, then the track sizes can be determined by a unified dependence on the energy parameter. The effect of the laser beam on the chemical composition and microhardness of cermet (WC-NiCrBSi) tracks is studied. Regardless of the track formation regime, these parameters are determined by the dimensionless parameter, which describes the degree of dilution of chemical substances. It is found that a track with the maximum mass fraction of tungsten and the greatest value of microhardness is formed at small values of the dimensionless parameter, which corresponds to the heat conduction regime. The microhardness of the deposited cermet structure is observed to be 4-5 times higher than the microhardness of the substrate material.

High-Rate Extrustion of Polyethylene in the Acceleration of Projectiles in Ballistic Devices

N. V. Bykov, A. S. Karneichik, A. A. Makarov, M. S. Tovarnov
Bauman Moscow State Technical University, Moscow, 105005, Russia
Keywords: высокоскоростная экструзия, методы ускорения тел, гидродинамический эффект, внутренняя баллистика, баллистические установки, деформация, high-velocity protrusion, body acceleration methods, hydrodynamic effect, internal ballistics, ballistic devices, deformation

Abstract >>
Acceleration of projectiles in ballistic devices by means of high-rate extrusion of polyethylene through a conical nozzle is experimentally and theoretically studied. Quasi-one-dimensional gas-dynamic model of a polydisperse mixture of gas and powder particles and a viscoplastic model of a deformed piston are used. The results of numerical simulation of the process under study and the results of a series of shots from a powder ballistic device are given. The influence of the geometry of a conical transition and input velocity of the deformed body on the output velocity of a projectile is experimentally investigated.

Explosion Chambers with Metal Shields

Yu. P. Meshcheryakov1, A. A. Shtertser1,2, B. S. Zlobin1
1Design and Technology Branch of the Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: взрывная камера, металлический экран, численное моделирование, эквивалентные напряжения, explosion chamber, metal shield, numerical simulation, equivalent stresss

Abstract >>
Metal shields of various thickness made of various steels and used to protect the shells of explosion chambers from damage by debris and reduce the loads on the structural elements have been studied. Dependences of the equivalent stresses in the protective shields and shells explosion chambers and the final size of the gap between the shields and the shell on wall thickness, steel grade, and initial gap size were obtained by numerical simulation. Examples of the explosion chamber designs with protective shields are given.