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Journal of Applied Mechanics and Technical Physics

2022 year, number 4

Localized Forcing of the Two-Dimensional Boundary Layer Individual Microdischarge in a Plasma Actuator

M. V. Ustinov1, I. M. Popov2, I. V. Selivonin3, I. A. Moralev3
1Central Aerohydrodynamic Institute, Zhukovsky, 140181 Russia
2Moscow Power Engineering Institute, Moscow, 111250 Russia
3Joint Institute for High Temperatures, Russian Academy of Sciences, 125412 Moscow, Russia
Keywords: plasma actuator, boundary layer, laminar-turbulent transition

Abstract >>
An experimental-theoretical study has been performed to investigate the disturbances generated in the boundary layer on a plate by individual microdischarges in a dielectric barrier discharge plasma actuator. It has been shown that disturbances in the near field behind the actuator can be interpreted as nonstationary banded structures which away from the actuator are transformed into a fan of growing Tollmien-Schlichting waves. It has been found that the length of the transition zone in which disturbances of the first type predominate is anomalously great and reaches a value of the order of 100 boundary layer displacement thicknesses. This should be taken into account when analyzing parasitic stochastic disturbances produced by plasma actuators used to control laminar-turbulent transition.

Coupled Pendulums as a Mechanical Model of a Tesla Transformer

E. I. Pa'lchikov1,2, E. E. Tarasova3, I. E. Tarasova4
1Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Novosibirsk National Research State University, Novosibirsk, 630090 Russia
3Specialized Educational and Scientific Center, Novosibirsk, 630090 Russia
4Moscow Institute of Physics and Technology, Dolgoprudny, 141701 Russia
Keywords: Tesla transformer, coupled oscillators, mechanical systems, resonance, energy transfer

Abstract >>
A resonant pulse transformer with impact excitation is compared with a system of coupled pendulums of different masses tuned to resonance. Conditions for complete energy transfer during one-half beat cycle are obtained for a Tesla transformer and coupled pendulums. The requirements for the system parameters and initial conditions necessary for complete energy transfer in the case of two spring-coupled pendulums with different masses and the same length were theoretically determined and experimentally tested for the first time. The dependence of the shortest time of energy transfer from one oscillator to another on the system parameter is obtained.

Modeling of Crystallization in a Metal Surface Layer Modified by Nanoparticles under Pulsed Induction Heating

V. G. Shchukin, V. N. Popov, O. A. Shmagunov
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: numerical simulation, metal modification, pulsed induction heating, heat transfer, nano-sized particles with a high melting point, heterogeneous nucleation, crystallization, iron-based alloy

Abstract >>
Crystallization processes in the case of modification of the surface layer of an iron-based alloy (Fe-C) subjected to a pulse action of a high-frequency electromagnetic field for substrate heating and melting are numerically simulated. The processes of heating, melting, and subsequent solidification of the metal are studied with the use of a mathematical model that describes thermodynamic phenomena. It is postulated that nano-sized particles with a high melting point uniformly distributed over the melt volume favor rapid crystallization during melt supercooling owing to heterogeneous nucleation. It is found that the nucleation and crystallization conditions in different areas of the melt volume are essentially different, and the maximum number of crystallization centers arise in regions where heat removal proceeds with the greatest rate. The particle size distribution in the crystalline structure in the solidified metal volume is estimated.

One-Dimensional Boundary Layer in the Problem of Negel-Free Zone Melting in a Magnetic Field

Yu. V. Pivovarov1, N. Yu. Pivovarov2
1Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2All-Russian Research Institute of the Fire Defense of the EMERCOM of Russia, Balashikha, 143903 Russia
Keywords: incompressible fluid, free boundary, ponderomotive force, skin layer, convective terms

Abstract >>
The behavior of the velocity component of silicon melt particles tangent to the free boundary during crucibleless zone melting in a magnetic field is studied. It is shown that the neglect of convective terms in the skin layer adjacent to the free boundary leads to erroneous results: the tangential velocity cannot reach a constant value when moving along the normal to the free boundary, which in turn leads, as shown earlier, at full solution of the problem, to an order of magnitude decrease in the characteristic velocity of melt particles outside the skin layer.

Simulation of Flow Separation in Turbojet Engine Inlets

M. F. Engulatova, D. V. Liverko, A. V. Lysenkov, S. V. Matyash, A. A. Saveliev
Zhukovsky Central Aerohydrodynamic Institute, Zhukovsky, 140180 Russia
Keywords: air intake, aerodynamic characteristics, side wind, computational fluid dynamics, optimization, Reynolds-averaged Navier-Stokes equations

Abstract >>
To take into account certification modes in optimization problems of the nacelle of a bypass turbojet engine, we developed a method for numerical determination of the characteristics of the air intake in the engine operating regime with a crosswind. The flow and aerodynamic characteristics of the air intake in these regimes were studied. Experiments were carried out in a wind tunnel to validate the calculation method based on the solution of the Reynolds-averaged Navier-Stokes equations. The laminar-turbulent transition was simulated using the the Menter turbulence  -model taking into account the compressibility of the gas.

Velocity and Attenuation of Linear Waves in Porous Media Saturated with Gas and its Hydrate

A. A. Gubaidullin, O. Yu. Boldyreva, D. N. Dudko
Khristianovich Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Tyumen, 625026 Russia
Keywords: porous medium, gas hydrate, hydrate saturation, elastic moduli, waves, sound velocity

Abstract >>
One of the main methods of searching for gas hydrate deposits is seismic exploration and acoustic logging. For correct processing and interpretation of measurement data, it is necessary to know the acoustic properties of hydrate-containing rocks, which can be studied on the basis of laboratory experiments and adequate mathematical models. In this paper wave propagation in a hydrate-containing porous medium is investigated. The skeleton is considered to consist of grains cemented with gas hydrate, and is modeled by a homogeneous solid phase with effective parameters. The elastic moduli of the composite skeleton of a porous medium are calculated from the elastic moduli of the grain material and hydrate using a well-known method. The velocities and attenuation coefficients of linear waves are calculated within the framework of a two-velocity model of a porous medium. The calculated data are compared with the experimental data of other authors on sound velocities in hydrate-containing porous samples. The influence of the properties of the base rock, the saturating fluid, and hydrate saturation on the propagation of linear waves is studied.

Numerical Optimization of Geometric Characteristics of Vascular Anastomosis using Swar Intelligence Methods in Neurosurgery

Yu. O. Kuyanova1, A. V. Dubovoi2, A. V. Bervitskii2, D. V. Parshin1
1Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Federal Neurosurgical Center, Novosibirsk, 630048 Russia
Keywords: particle swarm method, vascular anastomosis, optimization of hemodynamic parameters

Abstract >>
Bypass surgery is widely used in the treatment of cardiovascular diseases. The problem of optimal location of cerebral vascular anastomosis is considered. An electrical circuit model of circulation of large cerebral vessels is constructed whose optimal parameters are determined numerically using swarm intelligence methods. The objective optimization function was taken to be the pressure after shunting compared with the pressure before surgery. This method was first used to solve the problem of formation of cerebral vascular anastomoses. It is shown that the obtained the results are in good agreement with the data of real surgeries.

Dynamics of Separation Points after Instant Stopping of a Circular Cylinder in a Disturbed Liquid

M. V. Norkin
Southern Federal University, Rostov-on-Don, 344090 Russia
Keywords: ideal incompressible fluid, circular cylinder, instantaneous stop, fluid separation, dynamics of separation points, cavity collapse, cavitation number

Abstract >>
We study the dynamics of a thin attached cavity formed as a result of an instantaneous stop (impact) of a circular cylinder in a disturbed fluid. The fluid flow immediately following the impact and the initial separation zone are determined using the classical model of impact with separation. To study the cavity collapse process, a direct asymptotic method is used, in which the expansions of the main hydrodynamic characteristics are carried out in terms of a small parameter equal to the dimensionless acceleration of the cylinder before impact. In the leading asymptotic approximation, a problem with one-sided constraints is formulated, from the solution of which the motion of separation points is determined and the process of collapse of a thin cavity is described. Taking into account the special equations of the boundary layer, the analysis of the internal free boundary of the fluid is carried out.

Wetting of Liquid Droplets on Two Parallel Fibers with Different Radii

H. P. Xiao, L. Chen, L. Yang
College of Physics Science and Technology, Guilin, 541004, China
Keywords: filament, wetting, equilibrium configurations, barrel-shaped droplet, bridge, column, hysteretic behavior

Abstract >>
The spreading behavior of liquid droplets bridged by filaments is theoretically studied in this work. In our model, the wetted droplets between the fibers can be in one of three different equilibrium morphologies: barrel, bridge, or liquid column. The results show that small-volume droplets undertake a reversible column-to-bridge transformation. However, two distinct transitions are observed for large-volume droplets: column-to-bridge transition in the case of separated fibers and bridge-to-barrel-to-column transition for closely spaced fibers. Particular attention is paid to a hysteretic behavior of large-volume droplets at various inter-fiber distances. It is found that the our results are in good agreement with available experimental data

Thermal-Hydraulic Features of the Turbulent Flow Through Ribbed Channels

N. S. Dhaidan, F. N. Al-Mousawi
University of Kerbala, Kerbala, Iraq
Keywords: Ribbed channels, ribs roughness, thermal-hydraulic performance, rib distribution, rib configuration

Abstract >>
Thermofluid features of the flow through ribbed ducts for various rib arrangements and configurations are investigated numerically. Simulations are performed in a wide range of Reynolds numbers. The impacts of roughness factors (rib width, rib pitch, and rib height), rib arrangements, and rib configurations on the thermal performance of ribbed channels are examine.

Elastic Liquid Filtration to a Wellbore Through a Perpendicular Crack Formed during Hydraulic Fracturing

V. Sh. Shagapov1, Z. M. Nagaeva1,2, E. P. Anosova2
1Mavlyutov Institute of Mechanics of the Ufa Investigation Center, Russian Academy of Sciences, Ufa, 450054 Russia
2Ufa State Petroleum Technological University, Ufa, 450062 Russia
Keywords: hydraulic fracturing, fracture, oil wellbore, integro-differential equation, analytical solution, pressure distribution, fluid flow

Abstract >>
The problem of fluid withdrawal (or injection) from a reservoir into a well in the presence of a hydraulic fracture perpendicular to the wellbore in the mode of a constant pressure difference between the wellhead and the reservoir is considered. Analytical solutions are obtained that describe the evolution of pressure in the fracture and fluid flow into the well. Approximate solutions are constructed using the method of successive change of stationary states. The comparison of exact and approximate solutions of problems for determining the pressure fields in the fracture and the volumetric flow rate of fluid from the well into the fracture is carried out and it is shown that they practically coincide (the relative difference does not exceed 1-2%). In this case, the calculation time for approximate solutions is significantly reduced. This contributes to the creation of effective calculation algorithms for transient modes of well operation in reservoirs with complicated reservoir characteristics. The influence of reservoir characteristics of a reservoir and a fracture on the evolution of pressure in the fracture and fluid flow into the well is analyzed.

Simulation of Unsteady Fluid Filtration in a Reservoir with a Hydraulic Fracture

I. L. Khabibullin, A. A. Khisamov
Bashkir State University, Ufa, 450076 Russia
Keywords: formation, hydraulic fracture, unsteady filtration, analytical solution, Laplace transform method, pressure distribution, well flow rate

Abstract >>
The results of simulation of the process of unsteady fluid filtration in a formation penetrated by a well, which is crossed by a vertical hydraulic fracture of finite length, are presented. Using the method of integral Laplace transformations, an analytical solution of the system of equations describing fluid filtration in a formation and a fracture is constructed. Based on the analysis of the obtained solutions, the main characteristic features of the studied filtration process in the system reservoir - fracture.

Emitter for Discharge of Low-Potential Heat into Space with Anti-Meteoroid Protection

V. V. Mironov, L. I. Volkova, N. N. Volkov, S. S. Khamdamov, A. V. Anikin
State Scientific Centre Keldysh Research Center, Moscow, 125438 Russia
Keywords: refrigerator emitter, heat exchange, coolant, antimeteoroid protection

Abstract >>
A variant of the refrigerator emitter made of aluminum alloy with anti-meteoroid protection of the tube with a coolant in the form of a bumper, which is a radiating surface, is presented. An approximate method for calculating the stationary thermal state and pressure losses in the device has been developed. A prototype was made and tested. It is shown that the calculated and experimental data are in good agreement. A computational analysis of an efficient (efficiency parameter is equal to 3.27 kg/m2) protected (the probability of non-damage within two years is equal to 0.97) device made of aluminum alloy with a power of 570 kW is performed when the coolant is cooled from 250 to 110oC.

Plastic Structure Formation of the 1570R Alloy (System Al-Mg-Sc) using the Physical and Mathematical Theory of Metal Plasticity

V. M. Greshnov, F. F. Safin, I. V. Puchkova
Ufa State Aviation Technical University, Ufa, 450008 Russia
Keywords: plasticity, boundary value problem, plastic structure formation, structure evolution

Abstract >>
The shortcomings of the classical mathematical theory of plasticity are investigated, on the basis of which the processes of plastic deformation of metals are developed and studied. Using the previously proposed physical and mathematical theory of plasticity of metals, the process of plastic structure formation of the 1570P alloy (Al-Mg-Sc system) was studied, and the applicability of this theory to the formulation and solution of boundary value problems of plasticity in the development of modern technical devices was shown.

Solving the Problem of Electromagnetic Elastic Bending of a Multiply Connected Plate

S. A. Kaloerov, A. V. Seroshtanov
Donetsk National University, Donetsk, 83001
Keywords: piezoplate with holes and cracks, complex potentials, generalized least squares method

Abstract >>
The problem of bending of a plate with arbitrary holes and cracks is solved with the use of complex potentials of the theory of bending of thin electromagnetic elastic plates. Moreover, with the help of comformal mapping, expansion of holomorphic functions into the Laurent series or Faber polynomials owing to satisfaction of boundary conditions by the least squares method, the problem is reduced to an overdetermined system of linear algebraic equations, which is then solved by the method of singular expansions. Results of numerical investigations for a plate with two elliptical holes or cracks and for a plate with a hole and a crack (including an edge crack) are reported. The influence of physical and mechanical properties of the plate material and geometric characteristics of holes and cracks on the basic characteristics of the electromagnetic elastic state is studied.

Analysis of Lateral Vibration of a Rectangular Plate Supported by Four Corner Points with an Additional Concentrated Mass Based on the Rayleigh-Ritz Method

T. Wu, Zh. Chen, J. Qu
Harbin Institute of Technology, Harbin, 15000 China
Keywords: Rayleigh-Ritz method, rectangular plate, lateral vibration, concentrated mass

Abstract >>
In this study, the Rayleigh-Ritz method is used to analyse the vibration of a point-supported rectangular plate with a concentrated mass. The deformation and the first-order natural frequency under various working conditions are calculated. The results are compared with those obtained by the finite element method.

Two-Criterion Fault Diagram for a Disk-Shaped Crack with Annoral Load

V. I. Smirnov1, S. A. Atroshenko2
1Emperor Alexander I St. Petersburg State Transport University, Saint Petersburg, 198103 Russia
2Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, 199178 Russia
Keywords: disc-shaped crack, critical force, structural criterion, fracture toughness, short cracks

Abstract >>
The critical load (force) is estimated for a space with a disk-shaped crack, in the case when a concentrated force acts on its edges along the circumference. It is shown that it is impossible to determine the ultimate force with the help of classical fracture criteria, so a structural strength criterion formulated for axisymmetric problems is used. The relationship between fracture toughness and crack size is investigated and a two-criteria fracture diagram is constructed.

Cylindrical Dislocation in a Nonlinear Elastic Incompressible Material

A. V. Mark
Academy of State Fire Service of the EMERCOM of Russia, Moscow, 129366 Russia
Keywords: cylindrical dislocation, geometric theory of defects, metric, Einstein equations

Abstract >>
Using the nonlinear equations of elasticity theory and the geometric theory of defects, a cylindrical dislocation in an incompressible Mooney - Rivlin body is investigated. A cylindrical dislocation consists of two hollow concentric cylinders, one of which is inserted into the other and glued after a corresponding symmetrical deformation. The approaches of the classical theory of elasticity and the geometric theory of defects are compared, which made it possible to give a physical interpretation of the tensor momentum energy density in the Einstein equations for a cylindrical dislocation.

Bending Analysis of Double Viscoelastic Nanoplates Based on the Modified Couple Stress Theory and Relaxation Theory

S. Y. Wang, Y. Fang, Y. Y. Wang, Y. Q. Zhang
College of Civil Engineering and Architecture, Hangzhou 310058, PR China
Keywords: viscoelastic nanoplate, modified couple stress theory, stress relaxation, viscoelastic Pasternak medium

Abstract >>
Based on the modified couple stress theory and stress relaxation phenomenon, the governing equation of motion for a double viscoelastic nanoplate system is established, and the bending analysis of the system is performed. Using Navier's method, an analytical solution of the transverse relative deflection for two nanoplates is obtained. The effects of geometrical and physical factors on the bending behavior of the system are discussed. It is concluded that the transverse relative deflection of two nanoplates depends upon the relaxation time, ratio of the delayed to initial extensional elastic moduli, and damping parameters.

Reproducibility and Repeatability of the Results of Strain Measurement Control of the Rolling Surface of Moving Wagon Wheels

V. S. Vyplav'en', S. A. Becher, A. O. Kolomeets, A. A. Popkov, A. S. Kochetkov
Siberian Transport University, Novosibirsk, 630049 Russia
Keywords: strain measurement, wheel flat, deformations, rolling surface defects, control of wheels in motion, wavelet transform

Abstract >>
The paper presents the results of tests of a system for monitoring the rolling surface of freight car wheelsets in motion using dynamic strain measurement. The research was carried out at a test ring under the conditions of multiple repetition of train load to evaluate the reproducibility of the results of strain measurements. During each passage of the train through the measuring section, a high-speed system with a sampling frequency of 64 kHz measured the strain of the rail neck caused by the impact of the wheels of the rolling stock. A specially developed software was used to automatically identify defective wheels from the obtained data and determine the dynamic force of wheel impact on the rail. The repeatability of strain measurement data was evaluated by comparing them with the results of visual and measuring control of the rolling stock conducted before the beginning of the tests.