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2021 year, number 1
V. P. Zamuraev, A. P. Kalinina
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: ethylene combustion, axial injector, supersonic flow, throttling jet, transonic flow
Abstract >>
A supersonic flow in a channel with a variable cross section is numerically simulated in the case of ethylene injection along the channel under the action of a jet generating a throttling effect. The averaged NavierStokes equations closed by the ke turbulence model are solved. Ethylene combustion is modeled with the use of one reaction. The results are compared with experimental data on the pressure distribution over the channel wall. It is found that gasdynamic pulses produce an irreversible effect on the flow structure. The formation of a transonic flow region and its structure are described.

Yu. N. Grigoryev^{1}, I. V. Ershov^{1,2}
^{1}Institute of Computational Technologies, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia ^{2}Novosibirsk State Agrarian University, Novosibirsk, 630039, Russia
Keywords: emethod, vibrational excitation, linear stability, laminarturbulent transition, factor integral curves
Abstract >>
The influence of thermal nonequilibrium on the laminarturbulent transition is studied with the use of the e^{N} method for two widespread flow regimes in a supersonic boundary layer at the Mach number M = 4.5. The set of the actual frequencies of spatial disturbances is determined on the basis of the neutral curves for temporal disturbances. Families of the curves of Nfactors are calculated for selected frequencies. Then, based on the envelopes of these curves, the transition Reynolds number Re_{δT} for a given transition factor NT is determined. The calculations show that the transition region in the case with NT = 8 and vibrational excitation level below the dissociation limit is located 1214% downstream as compared to the transition region in a perfect gas.

A. L. Kazakov^{1}, L. F. Spevak^{2}
^{1}Institute for System Dynamics and Control Theory, Siberian Branch of Russian Academy of Sciences, Irkutsk, 664033, Russia ^{2}Institute of Engineering Science, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620049, Russia
Keywords: nonlinear convectiondiffusion equation, diffusion wave, characteristic series, exact solution, boundary element method
Abstract >>
Solutions to a nonlinear parabolic convectiondiffusion equation are constructed in the form of a diffusion wave that propagates over a zero background with a finite velocity. The theorem of existence and uniqueness of the solution is proven. The solution is constructed in the form of a characteristic series whose coefficients are determined using a recurrent procedure. Exact solutions of the considered type and their characteristics, including the domain of existence, are found, and the behavior of these solutions on its boundaries is studied. The boundary element method and the dual reciprocity method are used to develop, implement, and test an algorithm for constructing approximate solutions.

S. P. Bautin, E. I. Pon'kin
Snezhinsk Institute of Physics and Technology, Snezhinsk, 456776, Russia
Keywords: equations of gas dynamics, selfsimilar variables, characteristic Cauchy problem, gas flow into vacuum, unlimited gas compression
Abstract >>
In the space of selfsimilar variables, twodimensional flows of a polytropic gas are constructed in the form of solutions of the corresponding characteristic Cauchy problems of the standard type, which can be represented in the form of endless series. The convergence of the series is proved, and a procedure for constructing the coefficients of the series is described. It is found that in one particular case, the series breaks off and coincides with the wellknown analytical solution that was used by V. A. Suchkov to describe gas flow from an oblique wall into vacuum and by A. F. Sidorov to describe unlimited compression of prismatic gas volumes. It is shown that unlimited compression of the gas flow is by impermeable pistons moving according to different laws possible, and the gasdynamic flow parameters are studied. Highly nonuniform pressure distribution during compression of prismatic targets was obtained.

A. E. Bol'shakova, V. V. Zmushko, N. V. Nevmerzhitskii, A. N. Razin, E. D. Sen'kovskii, E. A. Sotskov
Russian Federal Nuclear Center, Sarov, 607188 Russia
Keywords: threelayer gas system, interfaces, shock waves, instability, turbulent mixing, mathematical modeling
Abstract >>
This paper presents the results of experimental and computational studies of instability development and mixing at the interfaces between gases of different densities. It is shown that instability and mixing at two interfaces of a threelayer gas systems arise after the interfaces are pass by a shock wave with a Mach number M = 1.3 which is formed on the left end and moves along the tube. Two experiments were carried out, in the first of which the central layer was filled with a heavy gas (SF6 gas), and in the second experiment, it was filled with a light gas (helium). On the left and right of the central layer is air at atmospheric pressure. The results obtained are compared.

V. I. Rizov
University of Architecture, Civil Engineering and Geodesy, Sofia, 1046, Bulgaria
Keywords: inhomogeneous material, multilayered beam, smoothly changing height, material nonlinearity, delamination
Abstract >>
The influence of the smoothly changing beam height on delamination in multilayered inhomogeneous beam configurations consisting of longitudinal vertical layers is investigated. A solution to the strain energy release rate is obtained for a delamination crack located arbitrarily between the layers, assuming a linear change in the height over the beam length. The solution obtained is verified by considering the energy balance. The strain energy release rate is also analyzed for the cases of parabolic and tangent changes in the height over the beam length.

V. N. Mamonov, A. F. Serov
Kutateladze Institute of Thermophysics, Siberian Branch Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: gasliquid flow, volumetric concentration of gas phase, ultrasonic flow meter, flow transparency coefficient for ultrasonic pulses
Abstract >>
A method is proposed for determining the volume concentration of the gas phase in gasliquid flow using an ultrasonic flow meter. The method is based on the experimental determination of the transparency coefficient of the gasliquid flow to the ultrasonic pulses used in the flow meter to measure the flow rate. The transparency coefficient is determined as the ratio of the number of reliable ultrasonic pulses to the number of emitted pulses, and it is shown that due to the scattering of probing pulses, the presence of the phase in the form of gas bubbles leads to a decrease in the transparency coefficient. The ultrasonic flow meter was calibrated in airwater flow at volumetric air concentrations in the flow of 019%. The results show that the proposed method can be used to measure the volumetric concentration of the gas phase in gasliquid flow up to values of the order of 30%.

D. Soltani, M. Shafaee
University of Tehran, Tehran, Iran
Keywords: liquid jet, coaxial gas flow, forced perturbation, primary breakup, VOF
Abstract >>
In this study, a numerical simulation is used to show the physics of a coupled forced perturbation and liquid jet in the presence of a lowvelocity coaxial gas flow. The volume of fluid (VOF) approach is employed to capture the liquidgas interface. A sinusoidal velocity with a finite frequency and amplitude is applied at the liquid jet inlet to define a forced perturbation. An annular gas flow with a velocity lower than that of the liquid jet is imposed to examine its influence on the liquid jet breakup mechanism. The annular gas flow is modulated by the sinusoidal velocity inlet, and the effect of this flow on the liquid jet breakup mechanism is analyzed. Different ratios of the gas velocity to liquid velocity are studied. The results indicate that the lowvelocity gas flow can considerably affect the behavior of the liquid jet, and this effect becomes more significant as the amplitude of the forced perturbation increases.

M. Mohammadian
Islamic Azad University, Gorgan, Iran
Keywords: algebraic method, nonlinear damped oscillator, nonlinear damping ratio, RungeKutta method
Abstract >>
In the current paper, a modified algebraic method (MAGM) is proposed as an effective semianalytical technique for solving nonlinear damped oscillatory systems. A polynomial is supposed as the trial solution, and its unknown coefficients are easily determined through the algebraic method (AGM). In order to improve the solution, the Laplace transformation is applied to the series solution, and then the Padé approximants of the resultant equation are constructed. Finally, the inverse Laplace transformation is adopted to obtain a periodic solution for the nonlinear problem under consideration. The proposed method is then applied for obtaining approximate analytical solutions of a damped rotatory oscillator as well as nonlinear vibrations of a flexible beam excited by an axial force. The results are compared with those obtained by the fourthorder RungeKutta method, and good agreement is observed.

V. V. Novotryasov
Il'ichev Pacific Oceanological Institute, Far Eastern Branch, Russian Academy of Sciences, Vladivostok, 690041, Russia
Keywords: stratified shallow water, extended Kortewegde Vries equation, cubic and quadratic nonlinearity, highfrequency dispersion, solitary internal waves, internal wave bore, field studies
Abstract >>
A method for determining the background parameters of weakly dispersing media is formulated within the framework of the theory of lowintensity wave bores in such media. An analytical model of an undular (cnoidal) bore on a pycnocline of a stratified shallow sea is used to obtain expressions for calculating the coefficients of the extended Kortewegde Vries equation: the velocities of linear internal waves, highfrequency dispersion, quadratic and cubic nonlinearities, i.e., the parameters characterizing the hydrophysical background over which the bore propagates. These parameters are calculated from data of direct measurements of bore characteristics: their waveforms, nonlinear velocity, mass and amplitude of leading solitons, as well as the frequencies of the waves that close the region in which the bore propagates. The efficiency of the proposed method is confirmed by the results of numerical simulation.

V. V. Prokof'ev, S. A. Ocheretyanyi, E. A. Yakovlev
Research Institute of Mechanics, Moscow, 119192, Russia
Keywords: jet, cavity, negative cavitation number, cavitation selfoscillations, surging, pulsed jets
Abstract >>
The possibility of using jet fluid flows in the presence of an artificial cavity with a negative cavitation number to generate periodic pulsed jets is studied. Flow in a line consisting of a cavitator, an artificial gas cavity, and a converging nozzle through which liquid and gas flow into the atmosphere is investigated. Regimes in which the liquid flow is close to intermittent are experimentally found. For such flow regimes, a onedimensional model for estimating the flow rate of liquid portions from the nozzle is proposed.

A. N. Sibin, A. A. Papin
Altai State University, Barnaul, 656049 Russia
Keywords: multiphase filtration, porous medium, melting snow, phase transition, saturation, numerical solution
Abstract >>
Equations of nonisothermal twophase filtration are used to solve the problem of motion of water and air in melting snow. The investigated mathematical model is verified using experimental data.

M. Bragov^{1}, A. V. Kuznetsov^{2}, G. G. Savenkov^{2,3}, T. I. Sycheva^{3}, E. V. Shchukina^{3}
^{1}Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, 603950, Russia ^{2}Mashinostroitel'nyi Zavod "Armalit", SaintPetersburg, 198097, Russia ^{3}Kontsern "MPOGidropribor", SaintPetersburg, 194044, Russia
Keywords: lowcarbon steel, longterm storage, dynamic tests, split Hopkinson pressure bar, fractal dimension
Abstract >>
Dynamic properties of lowcarbon steel are investigated using the Kolsky method (the split Hopkinson pressure bar method). Changes in the properties of the steel after 50 years of storage are determined, and the destroyed samples are subjected to metallographic studies. The fractal dimension of the fracture contours is determined. It is shown that, the longterm storage of steel introduces no significant changes in its properties.

V. L. Kotov, A. M. Bragov, V. V. Balandin, A. Yu. Konstantinov, Vl. Vl. Balandin
Research Institute of Mechanics, Nizhny Novgorod, 603600, Russia
Keywords: frozen soil, strength, compressibility, Mohr  Coulomb  Tresca, penetration, conical striker
Abstract >>
Data of an experiment to determine the ultimate strength of frozen soil under uniaxial compression in the range of deformation rate values 4002700 s1 are presented. Final expressions are obtained for the coefficients of the quadratic approximation that depend on the impact velocity of the stress normal to the surface of the striker and the experimentally determined physical and mechanical parameters of the soil  shock adiabat and the dynamic strength in compression. The obtained formulas are verified on the basis of comparison with the known data of experiments on the introduction of a steel conical striker into frozen sandy soil. It is shown that the difference between the results of bilateral evaluations and experiments does not exceed 15.

H. Zharfi
Esfarayen University of Technology, Esfarayen, I.R. Iran
Keywords: primary and secondary creep, time, temperature gradient, rotating disk, FGM, GDQ method
Abstract >>
Primary (unsteady) and secondary (steady) regimes of creep deformation of a rotating disk made of an AlSiC functionally graded material (FGM) is investigated using the generalized differential quadrature (GDQ) method. The disk is subjected to three different types of the temperature gradient in the radial direction, and a temperature dependence of the material properties is assumed. The primary and secondary creep is described by Norton's law in which the creep parameters depend on the volume fraction distribution of SiC reinforcement particles, temperature, and particle size. It is shown that the creep rates are strongly dependent on the temperature gradient type, prevailing temperature, and content of reinforcing particles at any point of the disk.

M. Pang, Y. Fang, Y. Q. Zhang
College of Civil Engineering and Architecture, Hangzhou, 310058, China
Keywords: viscoelastic orthotropic graphene sheet, free and forced vibrations, highorder surface stress effect, viscoelastic Pasternak medium, structural damping
Abstract >>
Transverse vibrations of a doublelayered viscoelastic orthotropic graphene sheet system are investigated. The two sheets in the system are coupled by the viscoPasternak medium. General governing equations for free and forced vibrations of the doublelayered graphene sheet system with a highorder surface stress effect are formulated. Theoretical solutions for the damped vibrational frequency, damping ratio, and relative deflection of the two sheets with simply supported boundary conditions are obtained. The effects of the highorder surface stress on the damped frequency and damping ratio of the system for inphase and outofphase free vibrations are discussed. The impacts of the highorder surface stress, structural damping, medium damping, Winkler modulus, and shear modulus of the medium on the relative deflection of the two sheets for forced vibrations are investigated. It is demonstrated that the highorder surface stress effects on the vibrational properties of the system are more significant than those of the conventional surface stress.

S. I. Gerasimov^{1,2,3,4}, A. V. Zubankov^{1,2}, V. I. Erofeev^{4}, V. A. Kikeev^{3,4}, N. A. Trepalov^{1}, A. P. Kalmykov^{1}, S. A. Kapinov^{1}, A. G. Sirotkina^{2}
^{1}Research Institute of Experimental Physics, Sarov, 607190, Russia ^{2}Sarov State Physics and Technical Institute, Sarov, 607190, Russia ^{3}Nizhny Novgorod State Technical University, Nizhny Novgorod, 603950, Russia ^{4}Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, 603024, Russia
Keywords: highspeed video recording, contactless chronographic section, sand, PIV method
Abstract >>
Experimental data on the motion parameters of a steel spherical impactor with a diameter of 13.5 mm that moves in a sandy medium at a velocity of 1470 m/s are presented. Induction sensors and the PIV (particle image velocimetry) method are used to record the motion of the impactor near a sandy obstacle and in a sandy medium, which allow one to visualize a surface wave via highspeed video recording of the sand surface. The values of the parameters characterizing the impactor motion in the sandy medium and the surface wave propagation are obtained.

M. G. Petrov
Siberian Aeronautical Research Institute Named after S. A. Chaplygin, Novosibirsk, 630051 Russia
Keywords: metal alloys, composites, fracture, plastic strain, longevity, creep, fatigue, rheology
Abstract >>
Experimental data on the failure and deformation of various materials are considered from the viewpoint of the kinetic concept of fracture as thermodynamic processes occurring over time. Mathematical modeling of the general and local plastic flows in materials is based on rheological models of a solid with due allowance for damage accumulation. The prediction of the longevity of materials under constant or variable temperature and force conditions is performed by time steps, including situations with changes in the material structure. A single fracture criterion is used, which implies that fracture occurs after reaching a threshold damage concentration (concentration criterion) in a certain volume of the solid body.

O. V. Gomonova, S. I. Senashov
Reshetnev Siberian State University of Science and Technology, Krasnoyarsk, 660037Ю, Russia
Keywords: elastoplastic problem, conservation laws, plane stress state, uniaxial tension
Abstract >>
This paper describes a solution to the problem of determining the elastic and plastic deformation regions arising in a plate that is under tension and weakened by two circular holes in the case of a plane stress state. A method for solving the problem is based on the use of conservation laws.

Yu. V. Popov, G. V. Belov, V. A. Markov, V. I. Pusev, V. V. Selivanov, V. V. Frolov
Bauman Moscow State Technical University, Moscow, 105005, Russia
Keywords: Riera's approach, onboard equipment, mechanical equivalent, bulk perforated samples, highspeed deformation, impact, load
Abstract >>
Load on the structure from the side of the onboard equipment at the moment of the aircraft impact on it is investigated. The estimation of the correctness and applicability of the model of the aircraft, presented in the form of a rigidplastic rod (Riera's approach), is carried out when studying the effect of onboard equipment. To simulate this impact, we used volumetric perforated aluminum alloy samples. Calculations were carried out using the proposed model in a onedimensional approximation, as well as direct threedimensional modeling of the impact by the finite element method using the LSDYNA package. Both of these approaches make it possible to study the process of loading a rigid wall. The quantitative and qualitative differences between these approaches and Riera's approach are shown.

M. Sadovskii, O. V. Sadovskaya, I. V. Smolekho
Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, 660036, Russia
Keywords: liquid crystal, Cosserat continuum, moment interactions, dynamics, electric field
Abstract >>
We study dynamic processes in liquid crystals using a simplified mathematical model in which a liquid crystal is considered as a finely dispersed continuous medium with rotating particles which has elastic resistance to volume deformation and viscoelastic resistance to relative rotation of the particles. The oscillatory regime of rotational motion described by the KleinGordon equation for tangential stress is studied. Moment interactions of particles due to the inhomogeneity of the rotation field are taken into account. The dispersion properties of a subsystem of two equations for tangential stress and angular velocity are investigated. These equations are used to numerically analyze the rotation field in the liquid crystal under the action of tangential stress caused by the thermal expansion of a metal plate at the boundary. We consider the problem of perturbation of an extended layer of a 5CB liquid crystal by means of an electric field generated by charges on capacitor plates located periodically along the layer. Singularities of the electric potential at the ends of the capacitor plates are selected explicitly. Some results of computations simulating the Fréedericksz effect in the liquid crystal layer are presented.

