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2019 year, number 3
V. D. Selemir, P. B. Repin, V. A. Demidov, A. S. Boriskin, A. I. Bykov, G. V. Boriskov, O. M. Tatsenko, A. S. Korshunov
Russian Federal Nuclear Center  AllRussia Research Institute of Experimental Physics, Sarov, Russia
Keywords: взрывомагнитный генератор, сверхсильное магнитное поле, изоэнтропическое сжатие, магнитокумулятивный генератор, мягкое рентгеновское излучение, magnetocumulative generator, ultrahigh magnetic field, isentropic compression, soft Xray radiation
Abstract >>
This paper describes different types of modern magnetocumulative generators, their operating principles, design, and main characteristics. Application areas of the generators for fundamental and applied studies in highenergy density physics are considered. Some investigation results are presented. Prospects for the further development of the MCG facilities designed in VNIIEF are discussed.

V. M. Fomin, V. I. Zvegintsev, E. Ya. Braguntsov
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
Keywords: прямоточный ускоритель, метаемое тело, разгонный ствол, газовая горючая смесь, ramjetintube projectile accelerator, accelerated body, acceleration barrel, gaseous combustible mixture
Abstract >>
The energy capabilities of acceleration devices are theoretically analyzed, including various ramjetintube options for gasdynamic acceleration of massive (1 to 40 kg) bodies under ground conditions up to velocities of 23 km/s. Simple quasionedimensional models for a perfect gas are used in the computations. It is demonstrated that the use of a ramjetintube with a closed exit allows the velocities of acceleration of massive bodies to be increased to 3 km/s, which is twice greater than the values that can be obtained with available gunpowderbased methods.

N. V. Bykov
Bauman Moscow State Technical University, Moscow, Russia
Keywords: газодинамический разгон, баллистическая задача Лагранжа, методы ускорения тел, однородная деформация, внутренняя баллистика, одноступенчатые баллистические установки, энергетическая эффективность, gasdynamic acceleration, ballistic Lagrange problem, methods for accelerating solids, homogeneous deformation, interior ballistics, singlestage ballistic installations, energy transfer efficiency
Abstract >>
The limiting possibilities and energy efficiency of singlestage acceleration of solid by compressed gas in a pipe (ballistic Lagrange problem) is under study. An exact partial solution of the ballistic Lagrange problem in a homogeneous deformation approximation is obtained. The calculation results are compared by different methods with the experimental data and the calculation results from other papers. It is shown that using an efficiency coefficient as a criterion for choosing an optimal solution prevents from using the effective configurations of ballistic devices.

V. I. Vishnyakov, S. M. Vishnyakova, P. V. Druzhinin, L. D. Pokrovskii
Bauman Moscow State Technical University, Moscow, Russia
Keywords: магнитореология, плоский канал, электропроводящая бингамовская жидкость, магнитное поле, magnetorheology, plane channel, electrically conducting Bingham fluid, magnetic field
Abstract >>
The influence of a sudden change in the external magnetic field on the flow of an electrically conducting Bingham fluid in a twodimensional channel is considered. It is demonstrated that a method of independent descriptions of the flow in plastic and viscous regions can be used for studying magnetohydrodynamic flows of the Bingham fluid. An exact equation is derived for the position of the plastic flow region boundary as a function of time and magnetic field induction. It is shown that the corresponding Cauchy problem has a unique asymptotically stable solution. Results of numerical integration for some values of parameters are presented; these result confirm the qualitative conclusions.

D. V. Khotyanovsky^{1,2}, S. V. Kirilovskiy^{1,2}, T. V. Poplavskaya^{1,2}, A. N. Kudryavtsev^{1,2}
^{1}Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia ^{2}Novosibirsk State University, Novosibirsk, Russia
Keywords: прямое численное моделирование, ламинарнотурбулентный переход, сверхзвуковой пограничный слой, распределенная и одиночная шероховатость, затупленное коническое тело, direct numerical simulation, laminarturbulent transition, supersonic boundary layer, distributed roughness, individual roughness elements, blunted conical body
Abstract >>
Results of direct numerical simulations of the roughnessinduced development of instability and transition to turbulence in a supersonic boundary layer on a blunted cone for the freestream Mach number M¥ = 5.95 are presented. The flow parameters and model geometry are consistent with the conditions of the experiments performed in the study. The following roughness types are considered: random distributed roughness, individual roughness elements of different shapes, and a group of regularly arranged roughness elements. The processes of the instability development and transition for different roughness types are compared, and possible mechanisms of the roughness influence on the stability of boundary layers on blunted bodies are discussed.

O. M. Sokovnin, N. V. Zagoskina, S. N. Zagoskin
LLC “OLNI”, Kirov, Russia
Keywords: природный газ, регулятор давления, математическая модель, предотвращение гидратообразования, natural gas, pressure regulator, mathematic model, prevention of hydrate formation
Abstract >>
A mathematical model for reducing the pressure of natural gas in a direct acting pressure regulator is developed. It is shown that, if an outputinput pressure ratio typical for practice is lower than a critical value, the pressure reduction process comes down to two stages: partial expansion of gas with throttling in the orifice plate of the pressure regulator and subsequent expansion in its casing. The values of the gas temperature in the characteristic sections of the pressure regulator are determined. It is established that the temperature drops at the first stage of pressure reduction and rises as the flow in the pressure regulator casing expands and decelerates. A method for minimizing the possibility of formation of gas hydrates in the pressure regulator is proposed.

V. V. Novotryasov, M. S. Permyakov
Il'ichev Pacific Oceanological Institute, Far Eastern Branch, Russian Academy of Sciences, Vladivostok, Russia
Keywords: мелкое море, натурные измерения, внутренний волновой бор, столообразный солитон, shallow sea, field measurements, internal wave bore, tablelike soliton
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This paper presents the results of an analysis of field measurements of a wave bore in the pycnocline of a shallow sea using vertical located thermistors. Hydrodynamic interpretation of the spacetime structure of the bore is performed using a mathematical model of a weakly dispersed shallow sea which takes into account the influence of cubic nonlinearity and lowfrequency dispersion. The limiting amplitude and minimum duration of the soliton solutions of the model are determined. An algorithm for evaluating these parameters based on measurements of the pulsations of isotherms induced by the bore is proposed. The limiting amplitude and minimum duration of solitary waves in the pycnocline in the coastal the Sea of Japan are evaluated.

L. A. Tkacheva
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
Keywords: поверхностные волны, изгибногравитационные волны, плавающая упругая пластина, дисперсионные соотношения, критическая скорость, волновые силы, деформации, преобразование Фурье, метод Винера  Хопфа}, surface waves, flexuralgravity waves, floating elastic plate, dispersion relations, critical speed, wave forces, deformations, Fourier transform, WienerHopf technique
Abstract >>
The problem of waves generated in a fluid and an ice sheet by a pressure region moving on the free surface of the fluid along the edge of the semiinfinite ice sheet was solved using the WienerHopf method. The load applied in some region simulates an air cushion vehicle, and the ice sheet is modeled by a thin elastic plate of constant thickness on the surface of an ideal incompressible fluid of finite depth. In a moving coordinate system, the plate deflection and the fluid elevation are assumed to be steady. The wave forces, the elevation the free surface of the fluid, the deflection and deformation of the plate at various speeds of the load were investigated. It has been found that at nearcritical load speeds, the ice sheet has a significant effect on the wave forces (wave resistance and side force) acting on the body moving on the free surface, and this effect is most pronounced at small distances from the edge. It has been shown that for some values of the speed, ice thickness, and load pressure, breaking of the ice sheet near the edge is possible.

V. W. Shagapov^{1}, M. N. Galimzyanov^{1,2}, I. I. Vdovenko^{1,2}
^{1}Mavlyutov Institute of Mechanics, Ufa, Russia ^{2}Bashkir State University, Ufa, Russia
Keywords: перегретая жидкость, пузырьки, фазовый переход, гармонические волны, фазовая скорость, коэффициент затухания, superheated liquid, bubbles, phase transition, harmonic waves, phase velocity, attenuation coefficient
Abstract >>
The propagation of weak disturbances in a superheated waterair bubble medium is considered in the case where the bubbles contain, in addition to water vapor, an inert gas (e.g., air) which is not involved in phase transitions. Maps of stability zones of the investigated systems depending on the degree of superheating of the liquid are constructed. The influence of the initial degree of superheating on the evolution of harmonic waves is analyzed. For unstable systems, the dependence of the increment on bubble radius with increasing degree of water superheating is studied

A. Mehmood, M. Usman
International Islamic University, Islamabad, Pakistan
Keywords: растягивающиеся и сжимающиеся поверхности, ламинарное течение пограничных слоев, всасывание поверхностью стенки, stretching/shrinking surfaces, laminar boundarylayer flow, wall suction
Abstract >>
During the recently passed last few years, viscous flows due to continuously shrinking surfaces have become very much popular among the researchers working in this particular area. Based upon the literature published over these years, it has been established that, different from the continuous stretching surface case, the flow due to a continuous shrinking surface does not admit a meaningful solution in the absence of sufficient wall suction and does admit multiple solutions if a sufficient amount of wall suction velocity is introduced. Furthermore, it has also been believed that shrinking surface flows offer more nonlinear phenomena by exposing the “interesting” characteristics of the boundarylayer flow. Using a correct selfsimilar formulation for the twodimensional shrinking sheet flow, the objective of this study is to prove that all the socalled “interesting” features of the shrinking sheet flow discovered in the previous studies are also exhibited by the stretching sheet flow. This fact consequently negates all such fascinations attributed to the shrinking sheet flow.

Yu. V. Pivovarov
Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
Keywords: конформное отображение, несжимаемая жидкость, уравнения Навье  Стокса, условия проскальзывания, вихрь, функция тока, conformal mapping, incompressible fluid, NavierStokes equation, slip condition, vortex, current function
Abstract >>
Planeparallel steady motion of a viscous incompressible fluid that partially fills a cylindrical rotating cavity is under consideration. The region occupied by the fluid is simply connected, with two points of a sliding threephase contact, and the edge angles at which the fluid approaches the walls are specified at these points. The free boundary of the fluid is curvilinear. There is a slip condition at the interface between the fluid and solid wall, which corresponds to proportionality of tangential stresses of a velocity difference of the solid and fluid particles. The flow region is conformally mapped onto a rectangular. The vortex and current function with a given slip coefficient and different rotation velocities of the cylinder are calculated.

E. A. Bondarev, I. I. Rozhin, K. K. Argunova
Institute of Oil and Gas Problems, Siberian Branch, Russian Academy of Sciences, Yakutsk, Russia
Keywords: сопряженные задачи теплообмена, транспортировка природного газа, гидраты природного газа, conjugate heat exchange problems, pipeline transport of natural gas, natural gas hydrates
Abstract >>
A computational experiment has been performed to study the effect of the change in the main pipeline cross section due to hydrate formation on hydraulic resistance and the temperature and pressure dynamics taking into account quasistationary heat exchange with permafrost ground. The case is considered where wet gas is supplied to the pipeline and the dynamics of hydrate formation is determined along with other parameters. The calculations are carried out until the outlet pressure becomes lower than standard one. The experiment showed that a model in which the hydraulic resistance coefficient is considered constant leads to a significant underestimation of the permissible pipeline operation time. Consequently, in mathematical modeling of hydrate formation in natural gas pipelines, taking into account the relationship between heat transfer and viscous friction is critical.

M. N. Shamsiev
Institute of Mechanics and Engineering, Russian Academy of Sciences, Kazan, Russia
Keywords: вертикальное гидропрослушивание, анизотропия, пористость, обратная задача, vertical interference, anisotropy, porosity, inverse problem
Abstract >>
A mathematical model of vertical interference testing of a gas reservoir penetrated by an imperfect vertical well is considered. The effect of the vertical and horizontal permeability and the degree of reservoir penetration on the pressure variation curves in the active and responding well intervals is investigated. A method for interpreting the results of vertical interference testing of a gas reservoir based the theory of inverse problems is proposed. It is shown that the results of vertical interference testing of a gas well can be used to estimate the vertical and horizontal permeability and porosity of the reservoir in the case of its full penetration.

N. V. Malay^{1}, E. R. Shchukin^{2}
^{1}Belgorod State University, Belgorod, Russia ^{2}Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia
Keywords: термофорез нагретых умеренно крупных сферических частиц, движение нагретых сферических частиц в поле градиента температуры, thermophoresis of heated moderately large spherical particles, motion of heated spherical particles in the temperature gradient field
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This paper presents the theoretical description of steady motion of a moderately large spherical aerosol particle in the external field of a temperature gradient in the Stokes approximation with Reynolds and Peclet numbers much smaller than unity. It is assumed that the average temperature of the particle surface significantly differs from the temperature of its gaseous environment. Gas dynamics equations are solved with account for the power dependence of molecule transport coefficients (viscosity and thermal conductivity) and the density of the gaseous environment on temperature. Boundary conditions are written in the linear approximation based on the Knudsen number. It is shown that the thermophoretic force and velocity substantially depend on the Knudsen number and the average temperature of the particle surface.

E. I. Kraus^{1}, A. Yu. Melnikov^{1}, V. M. Fomin^{1,2}, I. I. Shabalin^{1}
^{1}Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia ^{2}Novosibirsk State University, Novosibirsk, Russia
Keywords: лед, ударная адиабата, моделирование, разрушение, ice, shock adiabat, modeling, fracture
Abstract >>
A singlestage gasdriven setup is developed, which allows 0.5kg projectiles to be accelerated to velocities of the order of 1200 m/s. Experiments with penetration of steel projectiles into a massive ice target are performed. The experimental data are compared with the results of computations performed by the REACTOR software system and numerical calculations of destruction of a finitethickness ice target under the impact of one projectile and several projectiles. It is demonstrated that an impact of a steel ring onto a finitethickness ice target leads to knockout of the maximum volume of ice and almost complete loss of the kinetic energy of the ring.

V. V. Balandin^{1,2}, N. S. Selyutina^{2,3}, Yu. V. Petrov^{1,2,3}
^{1}Research Institute of Mechanics, Nizhny Novgorod, Russia ^{2}Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, SaintPetersburg, Russia ^{3}St. Petersburg State University, SaintPetersburg, Russia
Keywords: мерзлый песчаный грунт, прочность, скорость деформации, массовая доля льда, frozen sandy soil, strength, strain rate, mass fraction of ice
Abstract >>
Experimental dependences of the strength of frozen sandy soil on strain rate are analyzed using a structuraltemporal approach. Results of dynamic uniaxial compression tests at a temperature of 18oC and strain rates of 400 to 2600 s1 of frozen sandy soil samples of two types with a mass fraction of ice of 10 and 18% measured at room temperature are presented. The strain rate dependence of the at different temperatures of freezing of frozen sand with a mass fraction of ice of 30% was studied using known experimental data.

A. N. Martem'yanov^{1}, Yu. V. Petrov^{1,2}
^{1}Saint Petersburg State University, Saint Petersburg, Russia ^{2}Institute of Mechanics, Nizhni Novgorod, Russia
Keywords: динамическая прочность, импульсная нагрузка, составной стержень Гопкинсона, инкубационное время, горная порода, песчаник, пористость, насыщенность, dynamic strength, pulsed loading, split Hopkinson bar, incubation time, rock, sandstone, porosity, saturation
Abstract >>
Available results of laboratory investigations of the dynamic strength of various rock types are analyzed with the use of the incubation time criterion in both compression and tension cases. Based on this approach, a theoretical curve is constructed, which describes the increase in the ultimate stress of sample fracture for some types of sandstone. Incubation times for all materials considered in the study are estimated.

V. N. Paimushin^{1,2}, R. K. Gazizullin^{1}, M. A. Shishov^{1}
^{1}Kazan National Research Technical University named after A. N. Tupolev, Kazan, Russia ^{2}Kazan (Volga region) Federal University, Kazan, Russia
Keywords: волокнистый композит, волокно, связующее, косоугольное армирование, формы потери устойчивости, параметр волнообразования, критическая нагрузка, fibrous composite, fiber, epoxy, crossply stacking sequence, buckling modes, wave formation parameter, buckling load
Abstract >>
This paper proposes a refined formulation of linearized problems of internal nonuniformly scaled flat buckling modes of a rigid monolayer consisting of fibers and fiber bundles with allowance for their interaction with the surrounding matrix. Fibers are the structural elements of fibrous composites and in a subcritical (unperturbed) state under the action of shear stresses and tensile (compression) stresses in the transverse direction. The problems are formulated using equations constructed by reducing the version of geometrically nonlinear equations of the elasticity theory to onedimensional equations of the theory of rectilinear rods. These equations are based on the use of the refined Timoshenko shear model with allowance for tensioncompression strains in the transverse direction for the rigid monolayer and the transversesoft layer model with immobile boundary planes in a perturbed state for the epoxy layers. It is shown that loading samples with a structure is accompanied by constant changes in the composite structure due to implementation and alternation of the internal buckling modes with a varying wave formation parameter. This particularly allows explaining the changing of the effective shear modulus of the fibrous composite with increasing shear strains.

E. P. Fel'dman, N. A. Kalugina, O. V. Chesnokova
Institute of Physics of Mining Processes of the National Academy of Sciences of Ukraine, Dnepr, Ukraine
Keywords: газ, давление, трещина, фильтрация, разрыв, пласт, стационарная разгрузка, gas, pressure, fracture, filtration, fracture, formation, stationary unloading
Abstract >>
In this paper, we consider conditions under which the gas enclosed in the main crack located at the edge of a coal or rock formation can produce fracture of the formation. Kinetic theory is developed for two competing physical processes: formation unloading due to rock pressure and gas filtration from the crack cavity into the surrounding massif. The first process promotes fracture, and the second leads to a decrease in the gas pressure causing he fracture. The evolution of the crack is determined by the ratio of the rates of these processes. It is found that a modified Griffiths criterion is a necessary but not sufficient condition for fracture. For formation fracture, it is also necessary that the unloading rate to the filtration rate exceed a certain threshold value.

Ch. Fu, X. Yang
Shanghai University, Shanghai, China
Keywords: нелокальная градиентная теория упругости, изгибная жесткость трещины, масштабный параметр, балка с трещиной, краевые условия высшего порядка, nonlocal strain gradient theory, flexibility crack model, scale parameter, cracked beam, higherorder boundary condition
Abstract >>
A sizedependent cracked Timoshenko beam model is established based on the nonlocal strain gradient theory and flexibility crack model. Expressions of the higherorder bending moment and shear force are derived. Analytical expressions of the deflection and rotation angle of the cross section of a simply supported microbeam with an arbitrary number of cracks subjected to uniform loading are obtained. The effects of the nonlocal parameter, the material length scale parameter, the presence of the crack, and the slenderness ratio on the bending behaviors of the cracked microbeam are examined. It is found that the material length scale parameter plays an important role in the cracked microbeam bending behavior, while the nonlocal parameter is not decisive. Furthermore, the cracked microbeam also exhibits a stiffening or softening effect depending on the values of the two scale parameters; if the two parameters are equal, the bending deformation of the nonlocal cracked microbeam may not be reduced to that of the classical elastic cracked Timoshenko beam. Additionally, the influence of the size effect on beam stiffening and softening becomes more significant as the slenderness ratio decreases.

V. T. Belikov, D. G. Ryvkin
Bulashevich Institute of Geophysics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia
Keywords: акустическая эмиссия, трещина, функция распределения, удельная площадь внутренней поверхности, acoustic emission, crack, distribution function, specific area of inner surface
Abstract >>
A model of disklike cracks based on amplitudefrequency spectra of acoustic emission, detected in the fracture of a concrete sample, is used to restore their size distribution function, as well as corresponding distributions of porosity and specific area of internal surface of the material. Changes in these characteristics of a solid in a time interval between the instances of detection of the spectra are studied.

E. I. Pal'chikov^{1,2}, A. V. Dolgikh^{1,2}, V. V. Klypin^{1,2}, A. M. Ryabchun^{1,2}, M. S. Samoilenko^{1}
^{1}Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia ^{2}Novosibirsk National Research State University, Novosibirsk, Russia
Keywords: спиральный генератор, импульсный рентгеновский аппарат, источник высоковольтных импульсов, helical generator, pulsed xray device, source of highvoltage pulses
Abstract >>
A prototype of a pulsed Xray apparatus with and operating voltage of 600800 kV based on a combined helical generator has been developed and tested. Compared to the classical helical generator, the total length of the helical winding is increased by adding a singlebus line, which allows matching of the wave propagation time along the helical generator line to the oscillation period in the generator with a Tesla transformer. It is shown that the proposed transformer has high efficiency. A theoretical model describing the operation of the combined generator is proposed.

