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Journal of Applied Mechanics and Technical Physics

2022 year, number 1

Creation of Special Shock Tunnels and Investigation of Cumulation of Liquid Cylindrical Shells in a Rotating System

V. K. Kedrinskii
Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: cumulation, implosion of a cylindrical shell, rotating system

Abstract >>
Two schemes of shock tunnels and results of experimental investigations of cumulation of liquid cylindrical shells in a rotating system are presented. The first scheme is used to study one-dimensional compression (classical cumulation) of a rotating cylindrical shell under explosive loading by an annular piston. Experimental results are estimated with the use of the model of dynamics of one-dimensional cylindrical cumulation in a quiescent unbounded liquid. In the second scheme, a bore jump is found on the inner surface of the rotating gas cavity; this structure is formed by the piston in the case of shock loading of the gas cavity and its downstream propagation along the axis of symmetry.

Free Interaction of the Flow in a Laminar Boundary Layer with an Upstream Moving Expansion Wave

I. I. Lipatov1,2, V. N. Petrukhanov2, G. M. Timofeev2
1Central Aerohydrodynamic Institute (TsAGI), Zhukovskii, 140180 Russia
2Moscow Institute of Physics and Technology, Dolgoprudnyi, 141700 Russia
Keywords: expansion wave, boundary layer, viscous-inviscid interaction, three-layer structure

Abstract >>
The processes of interaction of an expansion wave with the flow in a laminar boundary layer are studied with the use of the theory of free interaction. Numerical solutions of a nonlinear problem are found for various values of the dimensionless velocity of wave motion. Distributions of pressure-induced friction stress on the surface are obtained.

Effects of the Laser-Water-Jet Processing of Silicon Carbide

Y. Chen1, X. Li1, X. Chen2, H. Li1, X. Xu2
1School of Mechanical Engineering, Hefei University of Technology, Hefei, 230009 China
2School of Mechanical and Electrical Engineering, Anhui Jianzhu University, Hefei, 230601 China
Keywords: Laser-water-jet processing, silicon carbide, water-jet angle, water-jet velocity

Abstract >>
The effects of the water-jet velocity and its angle on the laser-water-jet processing results are studied. It is found that the depth of laser-water-jet processing gradually increases with an increase in the water-jet angle; however, this increasing trend becomes less pronounced as the water-jet angle increases from 60 to 75°C. As the water-jet velocity increases, the depth of laser-water-jet processing gradually increases.

Generation of Two-Dimensional Unsteady Motion in a Viscous Incompressible Fluid of Finite Depth

P. Kundu1, B. N. Mandal2
1Department of Mathematics, Jadavpur University, Kolkata, 700032, India
2Indian Statistical Institute, Kolkata, 700108, India
Keywords: unsteady motion, viscous fluid, Laplace and Fourier transforms, method of steepest descent, free surface depression

Abstract >>
The problem of generation of two-dimensional unsteady motion in a viscous incompressible fluid of finite depth is investigated here. The motion is generated due to initial disturbances in the form of prescribed surface pressure or displacement at the free surface. The Fourier transform with respect to space and the Laplace transform with respect to time are used to obtain the form of the free surface in terms of multiple integrals. Finally, an asymptotic form of the free surface is obtained using the method of steepest descent.

Search for Stationary Poiseuille Flows for an Incompressible Polymer Fluid in Channels with Perforated Walls

A. M. Blokhin1,2, R. E. Semenko1,2
1Novosibirsk State University, Novosibirsk, 630090, Russia
2Sobolev Institute of Mathematics (SIM), Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: viscoelastic fluid, Poiseuille flow, stationary solutions

Abstract >>
The problem of the flow of a viscoelastic fluid in a flat channel with permeable walls and a constant flow through the walls is considered. The problem is formulated using the equations of the modified Vinogradov - Pokrovskii mesoscopic model. For the case of the presence of a flow through the walls, a method for setting the boundary conditions is proposed, which ensures that the resulting solution is consistent with the solutions obtained with no account for the flow. A computational algorithm for finding solutions is considered both in the presence of flow through the walls and in its absence.

Motion of Aqueous Solution of a Polymer with a Free Boundary

O. A. Frolovskaya1,2
1Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Novosibirsk State University, Novosibirsk, 630090, Russia
Keywords: aqueous solutions of polymers, layered flows, flows with free boundaries

Abstract >>
This paper describes a problem of unsteady flow of an aqueous polymer solution in a strip with a free boundary, the condition on which includes the time derivative of the desired function. A solution to this problem is constructed for a layered flow in a strip of constant width. The dependence of variation of the strip width with time on a parameter proportional to relaxation viscosity is studied.

Device for Creating a Pressure Differential using Differential Pumping

E. V. Domarov, Yu. I. Golubenko, N. K. Kuksanov, R. A. Salimov, S. N. Fadeev, I. K. Chakin
Budker Institute of Nuclear Physics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: differential pumping, extraction device, electron accelerator

Abstract >>
The paper describes the design of an electron extraction device using differential pumping. An assessment of the vacuum conditions for the transition from the viscous to the molecular regime is considered, which makes it possible to confirm the correctness of the choice of the parameters of the differential pumping system, which makes it possible to confirm the correctness of the choice of the parameters of the differential pumping system. The problem of heat removal from differential pumping diaphragms in a compact all-metal body of the extraction device.

Effect of the Intensity of Mechanical Processing of Bronze Particles on the Characteristics of Coatings Formed by the Method of Cold Gas-Dynamic Spraying

A. E. Chesnokov, S. V. Klinkov, V. F. Kosarev, A. V. Smirnov, V. S. Shikalov
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: cold gas-dynamic spraying, bronze, coatings, high-energy planetary mill, microhardness, porosity, X-ray diffraction analysis

Abstract >>
The influence of mechanical processing of CuAl10Fe3Mn2 bronze particles with different energy input intensities on the process of deposition of coatings by the method of cold gas-dynamic spraying and the properties of these coatings is studied. It is shown that the deposition efficiency varies depending on the microhardness and porosity of deposited particles. The increase in the porosity (from 2 to 8%) of the resultant coatings for different regimes and intensities of mechanical processing of deposited particles is explained. It is found that the size of the coherent scattering region, material microhardness, and roughness of coatings obtained from the mechanically treated powder have similar values regardless of the intensity of energy input by milling bodies to the processed material.

Experimental Study of Effectiveness of Reinforced Vibration Absorbing Coatings

V. Yu. Kirpichnikov1, A. P. Koshcheev1, A. I. Syatkovskii2
1Krylov State Research Center, Saint-Petersburg, 196158, Russia
2OAO Plastpolimer, Saint-Petersburg, 195197, Russia
Keywords: vibration absorption, vibration excitability, reinforcing coatings, resonant frequencies, viscoelastic layer

Abstract >>
The vibration levels of a metal plate are measured in the absence and presence of either one reinforced coating on its surface or one reinforce coating (or two of them) with the same or different thickness placed on it. The effectiveness of various schemes for lining the plate with coatings is determined and compared.

Rapid Flutter Analysis for Low-Aspect-Ratio Wings with a Control Surface

M. Basiri1, H. Farrokhfal1, M. Mosayebi1, R. Koohi2
1Malek-Ashtar University of Technology, Shahinshahr, 115/83145, Iran
2Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, 8418148499, Iran
Keywords: flutter, rapid analysis, low aspect ratio, control surface, doublet point method, equivalent plate method

Abstract >>
An effective method and fast modeling in vibration and flutter analyses of low-aspect-ratio composite wings and wings with a control surface in a subsonic flow are proposed. An equivalent plate method is used for structural modeling. The doublet point and the U - g methods are applied to calculate unsteady aerodynamic loads and flutter analysis, respectively. The obtained results are in good agreement with the literature data.

Evolution of the Bed Forms Produced by Purified Turbulent Flow over a Non-Cohesive Bottom

K. S. Koroleva, I. I. Potapov
Computing Center FEB RAS, Khabarovsk, 680000, Russia
Keywords: channel processes, bed deformations, bed-load sediments, bed erosion, bed waves, wave packet

Abstract >>
This paper considers the problem of purified turbulent flow over an erodible bed. A mathematical model of the problem is proposed which includes the Reynolds equations and transport equations for turbulent kinetic energy and turbulence dissipation. The bed surface evolution is described using the bed deformation equation and the original analytical model of bed-load sediment transport. An algorithm based on the control volume method is proposed for solving the problem. Numerical solution of the problem shows that when the bed is eroded by a purified flow, a wave packet of low-steepness bed waves is formed. It is also shown that the velocity of bed waves obtained by the numerical solution is in good agreement with the velocity of bed waves calculated by asymptotic analytical formula.

Increasing Viscous Oil Recovery in the Microbubble Filtration Mode using Supercritical Fluid Systems

A. V. Radaev1, A. N. Sabirzyanov2
1Institute of Applied Research, Academy of Sciences of the Republic of Tatarstan, Kazan, 420111, Russia
2Kazan National Research Technological University, Kazan, 420015, Russia
Keywords: supercritical fluid, oil recovery efficiency, two-phase filtration, microbubble recovery mode, rims of supercritical CO and water

Abstract >>
An experimental stand has been developed to study oil recovery using supercritical fluid systems of bulk and composite homogeneous porous materials in the mode of miscible and microbubble filtration of a mixture of oil and supercritical carbon dioxide. A device for visualizing the emergence of supercritical CO2 microbubbles from the experimental cell with a porous medium has been designed. The oil recovery by supercritical CO2 and rims of supercritical CO2 and water from a homogeneous bulk porous medium has been experimentally studied. It has been shown that the miscible mode of viscous oil recovery by supercritical CO2 is most efficient and the efficiency of viscous oil recovery in the microbubble mode can be increased using rims of supercritical CO2 and water. The mechanism of oil recovery enhancement in the region of microbubble recovery of viscous oil by supercritical CO2 is described.

Two-Layer Stationary Creeping Thermocapillary Flow in a Three-Dimensional Channel

V. K. Andreev, E. N. Lemeshkova
Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, 660036, Russia
Keywords: interface, thermocapillarity, inverse problem

Abstract >>
We study the problem of three-dimensional stationary creeping flow of two immiscible liquids in a channel with solid parallel walls, one of which a given temperature distribution is maintained and the other is hear-insulated. Thermocapillary forces act on the flat interface. Temperature in the liquids depends quadratically on the horizontal coordinates, and the velocity field has a special form. The resulting conjugate problem for the Oberbeck- Boussinesq model is inverse and reduces to the system of ten integro-differential equations. The total energy condition is taken into account on the interface. The problem has up to two solutions and if the heat fluxes are equal, then it has one solution. Characteristic flow structures are constructed for each of the solutions. The influence of dimensionless physical and geometric parameters on the flows is investigated

Thermodynamic Calculation of the Natural Gas Pressure Reduction in a Turboexpander

O. M. Sokovnin, N. V. Zagoskina, S. N. Zagoskin
OLNI Company, Kirov, 610050, Russia
Keywords: natural gas, multistage turboexpander, pressure reduction, mathematical model

Abstract >>
A mathematical model of stepwise natural gas pressure reduction in a multistage turboexpander has been developed using a thermodynamic approach taking into account the real gas properties. It has been shown that the maximum use of natural gas overpressure energy is provided when the outlet-to-inlet pressure ratio is above the critical value at each stage. The change in the temperature of the natural gas and its technical work at each stage of the turboexpander have been numerically determined. It has been found that the rate of temperature drop and the increment in the technical work of natural gas increase from stages to stage of the turboexpander. Comparison of the calculated and experimental values of the performance parameters of the gas turboexpanders showsthat they are in good agreement.

Dual Variational Model of the Temperature State of the Disk of a Unipolar Generator

V. S. Zarubin, V. N. Zimin, G. N. Kuvyrkin, I. Yu. Savel'eva
Bauman Moscow State Technical University (BMSTU), Moscow, 105005, Russia
Keywords: unipolar direct-current generator, temperature state of the disk, variational form of the mathematical model

Abstract >>
A dual variational form of a mathematical model of the steady process of heat conduction in a rotating disk of a unipolar direct-current generator is constructed. The model contains two alternative functionals that have coinciding stationary points at which these functionals reach the same extreme values (minimum and maximum if the desired temperature distribution in the disk is unique). This property of the functionals makes it possible to estimate the error of the approximate solution of the considered nonlinear heat conduction problem and control its convergence. The features of the radial temperature distribution in the disk are revealed, and the influence of thermal conductivity and electrical resistivity of the disk material (both dependent on temperature) on this distribution is established. The limiting value of the temperature coefficient of electrical resistivity is determined, at which a steady temperature distribution in a disk of a hyperbolic profile is impossible.

Coupled Model of FRacture of Elastoplastic Materials Based on a Kinetic Equation of Damage Accumulation and the Pisarenko-Lebedev Strength Criterion

V. G. Bazhenov1, S. L. Osetrov1, D. L. Osetrov1, A. A. Ryabov2
1Scientific-Research Institute of Mechanics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, 603950, Russia
2All-Russian Scientific Research Institute of Experimental Physics, Sarov, 607188, Russia
Keywords: true strain diagram, coupled fracture model, strength criterion, kinetic equation of damage accumulation

Abstract >>
A coupled fracture model is proposed and implemented to investigate the deformation and fracture of elastoplastic materials. The fracture model parameters are determined by constructing true fracture strain diagrams and determining the limiting characteristics of 12Kh18N10T and 10KhSND steel. Numerical simulation results for the fracture of cylindrical rods under tension are presented. It is revealed that the type and nature of tensile fracture of cylindrical samples determined in the calculations are in good agreement with the experimental data.

Model of Change of an Ejection Angle in the Case of Penetration of an Impactor into a Massive Target

V. A. Goloveshkin1,2, N. N. Myagkov2, T. A. Shumikhin2
1Russian Technological University, Moscow, 107996, Russia
2Khristianovich Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Moscow, 125040, Russia
Keywords: penetration, ejection, high-velocity impact, analytical model, space debris

Abstract >>
A problem of penetration of a rigid impactor into a semi-infinite target is solved analytically to determine the dependence of the angle of expansion of ejection particles (ejection angle) on the penetration depth of the impactor. The problem is considered under the assumption of a plane deformed state of the target material. The mechanical properties of the target material are described using the hypothesis that the target material is incompressible and ideally plastic. An equation of motion (penetration) of the impactor on the basis of energy balance is obtained. The angles of ejection are determined from the condition of minimum power of internal forces. It is established that, in the case of impactor penetration to an infinite depth, the limiting value of the ejection angle (elevation angle) is approximately 84 °C.

Sudden Loading of an Elastic-Plastic Rod Interacting with the Environment

A. Begmatov, N. T. Mamatova
National University of Uzbekistan, Tashkent, 100174, Uzbekistan
Keywords: elastoplastic, dry friction, elastic and plastic waves, yield line

Abstract >>
The effect of external dry friction on the stress-strain state of a semi-infinite elastoplastic rod under sudden loading is under study. It is assumed that the behavior of the rod is described by the Prandtl model, and friction with the environment moving at a constant velocity occurs according to the Coulomb law with different values of the friction coefficient in the perturbed and unperturbed regions of the rod. Analytical solutions are obtained. The conditions under which the rod is an elastic body in a region (part of it) between the fronts of plastic and elastic waves are determined.

Electrical Conductivity of Fractured Materials: Hydrodynamic Analogy

L. I. Stefanovich, E. P. Fel'dman
Institute of Physics of Mining Processes, National Academy of Sciences of Ukraine, Dnepr, 49005, Ukraine
Keywords: non-conductive extended inclusions, relative incremental electrical resistance, hydrodynamic analogy, fracturing coefficient

Abstract >>
The effect of non-conducting extended inclusions (cracks) on the electrical conductivity of a conductive medium at direct current was studied using a two-dimensional model. The additional electrical resistance due to the presence of cracks was calculated using the hydrodynamic analogy between potential flow of an ideal incompressible fluid around solids and electric current flowing around cracks. The dependences of the relative additional electrical resistance of the material on the fracturing coefficient in various limiting cases were determined. Their correctness is confirmed by the results of numerical analysis of the obtained expressions for various fracturing coefficients of the sample for thin and thick samples. The cases of parallel cracks and cracks randomly oriented in different directions were investigated.

Investigation of the Thermal Stressed State of a Reactor for Producing Hydrogen from Methane

I. V. Kudinov, A. A. Pimenov, G. V. Mikheeva
Samara State Technical University, Samara, 443001, Russia
Keywords: methane pyrolysis, two-layer cylinder, boundary-value problems, thermal conductivity, thermoelasticity, integral method of thermal balance

Abstract >>
This paper presents a study of the thermal and thermally stressed state of a reactor in the form of a quartz cylinder filled with tin for producing hydrogen by methane pyrolysis. When determining the temperature state, the problem for the two-layer structure (quartz-tin) using the Heaviside function was reduced to the problem for a single-layer structure with variable (piecewise homogeneous) properties of the material. An analytical solution including algebraic polynomial functions with coefficients exponentially stabilizing in time was obtained by determining the position of the temperature disturbance front and additional boundary conditions using the integral method of heat balance. Using the obtained solution, quasi-static temperature stresses were determined in the case where the structure is a two-layer hollow cylinder (flat deformation). The layer conjugation method was used to obtain an exact analytical solution of the thermoelasticity problem, from which it follows that at the point of contact of the layers, the hoop and axial stresses have a jump (discontinuity) with a change of sign in it. It is found that in certain start-up modes, the hoop and axial stresses can exceed the tensile strength of the quartz layer. The results were used to determine start-up modes in which the stresses do not exceed permissible values.

Vibration Analysis of a Viscoelastic Graphene Sheet Exposed to an In-Plane Magnetic Field using the Nonlocal Strain Gradient Theory

M. Pang, Y. Fang, Y. Q. Zhang
College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, 310058, China
Keywords: viscoelastic graphene sheet, free and forced vibrations, nonlocal strain gradient theory, in-plane magnetic field

Abstract >>
Based on the nonlocal strain gradient theory, the transverse vibration of a viscoelastic graphene sheet subjected to an in-plane magnetic field and external forces is studied. A general governing equation for the graphene sheet vibration is formulated. Theoretical solutions for undamped and damped vibrational frequencies are obtained. The influence of the in-plane magnetic field on the damping ratio and on the frequencies of the free and forced vibrations is studied within the framework of the nonlocal strain gradient theory.

Nonlinear Parametric Oscillations of a Longitudinally Reinforced Orthotropic Cylindrical Shell Filled with a Viscous Liquid

I. T. Pirmamedov1, F. S. Latifov2, A. I. Khudieva2
1Azerbaijan Technical University, Baku, AZ 1148, Azerbaijan
2Azerbaijan Architectural and Construction University, Baku, AZ 1073, Azerbaijan
Keywords: longitudinally reinforced orthotropic cylindrical shell, viscous liquid, Ostrogradsky--Hamilton principle of stationary action

Abstract >>
Nonlinear parametric oscillations of a longitudinally reinforced orthotropic cylindrical shell filled with a viscous liquid are studied. Fluid motion is described using a linearized Navier-Stokes equation. Equations of motion for a reinforced orthotropic shell filled with viscous liquid are obtained based on the Ostrogradsky-Hamilton principle of stationary action. The dependences of the ratio of the nonlinear frequency to the linear frequency on the deflection of the shell are determined for different numbers of reinforcing ribs.

Impact Analysis of Countersunk Bolt Parameters on the Load-Bearing Capacity of a Ceramic Matrix Composite and Superalloy Joint

Q. Sun1, Sh. Zhao2, Yu. Zhang2, Ch. Lv3, X. Sun4, J. Jia5, M. Li2
1Shenyang Aircraft Design and Research Institute, Aviation Industry Corporation of China, Shenyang, 110000, China
2National Key Laboratory of Science and Technology for National Defense on Advanced Composites in Special Environments, Harbin Institute of Technology, Harbin, 150080, China
3China Academy of Aerospace Aerodynamics, Beijing, 100074, China
4School of Aeronautics and Astronautics, Harbin Institute of Technology, Harbin, 150001, China
5School of Materials Science and Engineering, Harbin Institute of Technology, Harbin, 150001, China
Keywords: two-dimensional C/SiC composite, progressive damage analysis, tensile properties, bolted joint, countersunk parameters

Abstract >>
In this paper, a progressive damage analysis of two-dimensional C/SiC composites and superalloy mechanically fastened joint with a countersunk bolt is implemented to simulate the uniaxial tensile loading process by using a user-defined subroutine UMAT embedded into the general package ABAQUS. On the basis of the developed damage model, a parametric study is carried out to illustrate the effects of countersunk parameters on tensile performance for the hybrid bolted joint. It is found that there are negligible changes in the stiffness of the bolted joint, as the countersunk height varies from 1.5 to 2.5 mm for the considered bolt-head diameter cases. However, the failure load of the ceramic matrix composite and superalloy hybrid joint exhibits significant changes under different combinations of countersunk parameters. Increasing the countersunk height of the bolt intensifies the initial stress concentration and results in the redistribution of stress around the hole-edge area of the composite material plate. For the bolt-head diameter and countersunk height equal to 9.4 and 1.5 mm, respectively, the joint structure ensures the maximum load-bearing capacity for the studied joint with a countersunk bolt.