

2017 year, number 6
Yu. V. Shan'ko
Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, 660036, Russia
Keywords: изотермические движения газа, тепловые движения газа, течения идеальной жидкости со свободной границей, переопределенные системы, точные решения, isothermal gas flow, thermal motion of gas, freeboundary ideal flow, overdetermined systems, exact solutions
Abstract >>
The overdetermined system of partial differential equations describing the twodimensional isothermal motion of a polytropic gas is studied. The system is reduced to passive form and fully integrated. The resulting solutions are treated as ideal incompressible fluid flow bounded by a free surface or a moving solid wall.

K. Hajirayat^{1,2}, S. Gholampour^{2}, I. Sharifi^{1}, D. Bizari^{1}
^{1}Baqiyatallah University of Medical Science, Tehran, Iran ^{2}Islamic Azad University, Tehran, Iran
Keywords: церебральная аневризма, разрыв аневризмы, взаимодействие конструкции с жидкостью, число Рейнольдса, число Уомерсли, сдвиговое напряжение в стенках сосуда, гемодинамика, cerebral aneurysm, aneurysm rupture, fluidstructure interaction, Reynolds number, Womersley number, wall shear stress, blood hemodynamic
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In this study, one normal subject and two patients suffering from a cerebral aneurysm with circular and elliptical necks are analyzed by using the fluidstructure interaction (FSI) method. Although the blood hemodynamic parameters increase after the occurrence of the disease, the largest increase is in the wall shear stress (by a factor of 4.16.5) as compared to the normal subject. The increase in these parameters for patients with a circular neck is more pronounced than that with an elliptical neck. The blood flow becomes slightly more turbulent after the occurrence of the cerebral aneurysm, though it still remains in the range of the laminar flow and the pulsatility of the blood flow in patients is 2845% greater than that of the normal subject. Finally, the results show that the risk of vessel rupture in the cerebral aneurysm with a circular neck is 40.8% higher than that in the case of the cerebral aneurysm with an elliptical neck.

P. V. Chuvakhov^{1,2}, V. Ya. Borovoy^{1}, I. V. Egorov^{1,2}, V. N. Radchenko^{1}, H. Olivier^{3}, A. Rogelia^{3}
^{1}Central Aerohydrodynamic Institute, Zhukovskii, 140180, Russia ^{2}Moscow Institute of Physics and Technology, Dolgoprudnyi, 141700, Russia ^{3}RheinischWestf]дlische Technische Hochschule Aachen, Aachen, 52056, Germany
Keywords: малое притупление, высокоэнтропийный слой, пограничный слой, угол сжатия, вихри Гертлера, сверхзвуковое течение, отрыв потока, присоединение потока, small bluntness, highentropy layer, boundary layer, compression corner, Gцrtler vortices, supersonic flow, flow separation, flow reattachment
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The influence of small cylindrical bluntness of the leading edge of a flat plate on the formation of spatial structures in a nominally twodimensional supersonic flow in a compression corner at the Mach number M_{∞} ≈ 8 and a laminar state of the undisturbed boundary layer is studied by the method of temperaturesensitive paints. Streamwise vortices are found in the region of reattachment of the separated flow in a wide range of Reynolds numbers (0.15 × 10^{6 }– 2.55 × 10^{6}) for various angles of flow deflection and plate lengths. It is demonstrated that the existence of these vortices induces transverse oscillations of the heat transfer coefficient; the amplitude of these oscillations may reach 30%. The maximum Stanton numbers reaching 80% are observed in the case with significant roughness of the leading edge of the flat plate. Both the maximum Stanton numbers in the reattachment region and the amplitude of transverse oscillations of the Stanton number induced by streamwise vortices are found to decrease significantly in the case of small bluntness of the leading edge. Solutions of threedimensional NavierStokes equations are derived for some test conditions. The computed results are in good agreement with experimental data, which testifies to a significant stabilizing effect of small bluntness on the intensity of streamwise vortices.

A. Ali^{1}, S. Saba^{1}, S. Asghar^{2}, D. N. Khan^{3}
^{1}COMSATS Institute of Information Technology, Kamra Road, Attock, 43600, Pakistan ^{2}COMSATS Institute of Information Technology, Park road, Chak Shahzad, Islamabad, 44000, Pakistan ^{3}Islamia College University, Peshawar, 25000, Pakistan
Keywords: несжимаемая жидкость, перенос тепла и массы, жидкость третьего порядка, магнитное поле, химическая реакция, пористая пластина, incompressible fluid, heat and mass transfer, thirdgrade fluid, magnetic field, chemical reaction, porous plate
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The heat and mass transfer effects on the flow of a conducting thirdgrade fluid over an oscillating vertical porous plate with chemical reactions are considered. Highly nonlinear governing equations of the thirdgrade fluid are solved analytically by using a multiparameter perturbation technique and compared with the numerical results obtained by the parallel shooting method. The fluid flow velocity, temperature, and concentration are analyzed as functions of the Hartmann number, suction parameter, Prandtl and Schmidt numbers, and chemical reaction parameter.

V. V. Bulatov, Yu. V. Vladimirov
Ishlinsky Institute of Problems of Mechanics, Russian Academy of Sciences, Moscow, 119526, Russia
Keywords: стратифицированная среда, внутренние гравитационные волны, дальние поля, равномерная асимптотика, волновой фронт, stratified medium, internal gravitational waves, far fields, uniform asymptotics, wave front
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The problem of constructing asymptotics of the far fields of internal gravitational waves generated by an oscillating localized source of perturbations moving in a stratified flow of finite depth. The velocity of the perturbation source does not exceed the maximum group velocity of an individual wave mode. The wave pattern consists of waves of two types: annular and wedgeshaped. Solutions are obtained that describe the asymptotic behavior of ring waves, which are expressed in terms of the Hankel function. The asymptotics of wedgeshaped waves are expressed in terms of the Airy function and its derivative.

V. V. Kadet, A. M. Galechyan
Gubkin Russian State University of Oil and Gas, Moscow, 119991 Russia
Keywords: относительные фазовые проницаемости, дренаж, пропитка, гистерезис, теория перколяции, реология, relative permeabilities, drainage, impregnation, hysteresis, percolation theory, rheology
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A complex mathematical model for hysteresis of relative permeabilities based on percolation theory is developed. The model take into account the change in the surface properties of the pore space and the rheology of percolating fluids during the transition from drainage to impregnation, which gives rise to hysteresis. It is shown that accounting for the change in the rheology of the percolation fluids, along with accounting for the hydrophobization of the surface of the pore space, provides a better agreement between the calculated and experimental curves of relative permeabilities.

V. Ya. Rudyak, E. G. Bord
Novosibirsk State University of Architecture and Civil Engineering, Novosibirsk, 630008, Russia
Keywords: наножидкость, гидродинамическая устойчивость, ламинарнотурбулентный переход, течения Пуазейля, nanofluid, hydrodynamic stability, laminarturbulent transition, Poiseuille flow
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Stability of plane and cylindrical Poiseuille flows of nanofluids to comparatively small perturbations is studied. Ethylene glycolbased nanofluids with silicon dioxide particles are considered. The volume fraction of nanoparticles is varied from 0 to 10%, and the particle size is varied from 10 to 210 nm. Neutral stability curves are constructed, and the most unstable modes of disturbances are found. It is demonstrated that nanofluids are less stable than base fluids; the presence of particles leads to additional destabilization of the flow. The greater the volume fraction of nanoparticles and the smaller the particle size, the greater the degree of this additional destabilization. In this case, the critical Reynolds number significantly decreases, and the spectrum of unstable disturbances becomes different; in particular, even for the volume fraction of particles equal to 5%, the wave length of the most unstable disturbances of the nanofluid with particles approximately 20 nm in size decreases almost by a factor of 4.

S. P. Kiselev^{1,2}, V. P. Kiselev^{1}, V. N. Zaikovskii^{1}
^{1}Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia ^{2}Novosibirsk State Technical University, Novosibirsk, 630092, Russia
Keywords: радиальное сопло, сверхзвуковое течение, псевдоскачок, пограничный слой, численное моделирование, эксперимент, radial nozzle, supersonic flow, pseudoshock, boundary layer, numerical simulation, experiment
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Results of experimental investigations and numerical simulations of supersonic gas flows in radial nozzles with different nozzle widths are presented. It is demonstrated that different types of the flow are formed in the nozzle with a fixed nozzle radius and different nozzle widths: supersonic flows with oblique shock waves inducing boundary layer separation are formed in wide nozzles, and flows with a normal pseudoshock separating the supersonic and subsonic flow domains are formed in narrow nozzles (micronozzles). The pseudoshock structure is studied, and the total pressure loss in the case of the gas flow in a micronozzle is determined.

M. Y. Malik, M. Khan, T. Salahuddin
QuaidiAzam University, Islamabad, 44000, Pakistan
Keywords: магнитогидродинамическое течение, жидкость Карро, растягиваемый лист, метод ячеек Келлера, MHD flow, Carreau fluid, stretching sheet, Keller box method
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The present analysis deals with a twodimensional MHD flow of the Carreau fluid over a stretching sheet with a variable thickness. The governing partial differential equations are converted into an ordinary differential equation by using the similarity approach. The solution of the differential equation is calculated by using the Keller box method. The solution is studied for different values of the Hartmann number, Weissenberg number, wall thickness parameter, and powerlaw index. The skin friction coefficient is calculated. The present results are compared with available relevant data.

V. B. Kurzin
Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: камера, струя, вихревая пелена, акустические колебания, обратная связь, неустойчивость, автоколебания, chamber, jet, vortex sheet, acoustic vibrations, feedback, instability, selfoscillation
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This paper describes free acoustic oscillations of gas in a chamber with a jet flowing through its nozzle in the case of nonstationary intensity component of vortex sheet flowing down from the edge of the nozzle. There is established feedback between acoustic oscillations and oscillations induced by a corresponding vortex sheet component. It is shown that, in the presence of given feedback, there could be instability of acoustic oscillations, which would result in acoustic selfvibrations in the chamber. The boundaries of the domain in which instability is formed are determined by developing a mathematical model of stable acoustic oscillations in the chamber with account for the influence of the vortex sheet.

K. N. Volkov, V. N. Emelyanov, M. S. Yakovchuk
Ustinov Voenmekh Baltic State Technical University, St. Petersburg, 190005, Russia
Keywords: управление вектором тяги, пластина, нестационарность, струя, вдув, клапан, численное моделирование, thrust vector control, plate, unsteadiness, jet, injection, valve, numerical simulation
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The transverse injection of a pulsed jet into supersonic flow for thrust vectoring in solid rocket motors is investigated. The gas flow through the injection nozzle is regulated by a piston which performs reciprocating motion. Reynoldsaveraged NavierStokes equations and the (ke)turbulence model equations are discretized using the finite volume method and moving grids. The pressure distributions on the plate surface obtained using various approaches to the description of the flow field and difference schemes are compared. The solution obtained for the case of injection of a pulsed jet is compared with the solution for the case where a valve prevents gas flow through the injection nozzle. The dependence of the control force produced by injection of gas on time is investigated.

M. N. Davydov, V. K. Kedrinskii
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: щелевое вулканическое извержение, трещина, магматический расплав, декомпрессия, кавитация, вязкость, slot volcano eruption, crack, magma melt, decompression, cavitation, viscosity
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Results of a numerical analysis of the dynamic behavior of a compressed magma melt in a slot channel with gradual opening of the diaphragm and results of simulations of its time evolution are reported. The IordanskiiKogarkovan Vijngaarden mathematical model of a twophase medium and a model that describes phase changes in the gassaturated plasma behind the front of the decompression wave being formed are used. Results of numerical simulations of the flow with allowance for specific features of the pressure dynamics in the decompression wave, mass velocity components, volume fraction of the gas phase, and its viscosity are presented.

L. A. Tkacheva
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: тонкая упругая плавающая пластина, изгибногравитационные волны, краевая мода, преобразование Фурье, метод ВинераХопфа, floating thin elastic plate, flexuralgravity waves edge fashion, Fourier transform, WienerHopf method
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The problem of the vibrations of an ice sheet with a rectilinear crack on the surface of an ideal incompressible fluid of finite depth under the action of a timeperiodic local load time is solve analytically using the WienerHopf method. The ice sheet is simulated by two thin elastic semiinfinite plates of constant thickness. The thickness of the plates may be different on the opposite sides of the crack. Various boundary conditions on the edges of the plates are consudered. For the case of contact plates of the same thickness, a solution in explicit form is obtained. The asymptotics of the deflection of the plates in the far field is studied. It is shown that predominant directions of wave propagation at an angle to the crack can be distinguished in the far field in the case of contact of two plates of different thickness. In the case of contact of identical plates, a edge waveguide mode propagating along the crack is excited. It is shown that the edge mode propagates with maximum amplitude if the vertical wall is in contact with the plate. Examples of calculations are given.

V. S. Zarubin, V. N. Zimin, G. N. Kuvyrkin
Moscow State Technical University them. N. E.Bowman, Moscow, 105005, Russia
Keywords: космический аппарат, сферическая оболочка, равновесная температура, квазистационарное распределение температуры, satellite, spherical shell, equilibrium temperature, quasistationary temperature distribution
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A thermal model of the aluminized polymer shell of a gaugeadjusting satellite for calculating the steadystate temperature distribution of this shell at its fixed orientation relative to the Sun. A modified version of the model was used to analyze the quasistationary distribution of the shell temperature in the case of its rotation with a constant angular velocity about an axis perpendicular the direction to the Sun.

V. A. Fel'dshtein
Central Research Institute of Mechanical Engineering, Korolev, 141070, Russia
Keywords: автоколебания, токонесущие проводники, численное моделирование, selfoscillations, currentcarrying conductors, numerical simulation
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This paper presents a study of the selfexcitation of thermomechanical selfoscillations of a currentcarrying conductor which depend on its electrical resistance, power of joule heat release, and the heat transfer from its surface. The conditions for the occurrence of selfoscillations are determined, and numerical simulation of the excitation of oscillations is performed.

V. P. Zhytnikov, N. M. Sherykhalina, A. A. Zaripov
Ufa State Aviation Technical University, Ufa, 450000, Russia
Keywords: задача ХелеШоу, нестационарность, квазистационарное решение, комплексные переменные, точность копирования, HeleShaw problem, nonstationarity, quasistationary solution, complex variables, copying accuracy
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The problem of simulation of electrochemical treatment by reduction to a solution of a Schwartz problem on a parametric rectangle via theta functions is solved. Various conditions are considered (nonequipotentiality of electrodes and inconsistent current output) at the boundary of the surface treated. Nonstationary, quasistationary, stationary, and limiting solutions are presented. The results of surface treatment with tool electrodes of various shapes are given. It is shown that the parameters of the processing mode significantly affect the allowance necessary to achieve highly accurate copying.

A. F. A. Algarray^{1}, H. Jun^{1}, I.E. M. Mahdi^{2}
^{1}Mechanical design Theory and Electrical Engineering, NEFUHarbinChina ^{2}Mechanical Engineering Nile Valley University, AtbaraSudan
Keywords: слоистая балка, свободные колебания, метод конечных элементов, способы закрепления торцов балки, laminated beam, free vibration, finite element method, beam end conditions
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The effects of the end conditions of crossply laminated composite beams on their dimensionless natural frequencies of free vibration is investigated. The problem is analyzed and solved by using the energy approach, which is formulated by a finite element model. Various end conditions of beams are used. Each beam has either movable ends or immovable ends. Numerical results are verified by comparisons with other relevant works. It is found that more constrained beams have higher values of natural frequencies of transverse vibration. The values of the natural frequencies of longitudinal modes are found to be the same for all beams with movable ends because they are generated by longitudinal movements only.

L. K. Sahoo^{1}, M. K. Roul^{2}, R. K. Swain^{3}
^{1}Mechanical Engineering, GIET, Bhubaneswar, Odisha, India ^{2}Mechanical Engineering, GITA, Bhubaneswar, Odisha, India ^{3}Mechanical Engineering, IGIT, Saranga, Odisha, India
Keywords: теплоперенос, естественная конвекция, радиатор в форме пластины с игольчатыми ребрами, heat transfer, natural convection, platefin heat exchanger
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Natural convection heat transfer from a vertical isothermal plate with pin fins is numerically studied by solving the NavierStokes equations along with the energy equation. The average Nusselt number for the plate with different configurations of pin fins is obtained. The average Nusselt number is found to increase with increasing aspect ratio of the fin and to decrease with increasing angle of fin inclination with respect to the plate. There is only a minor difference between the average Nusselt numbers for inline and staggered arrangement of fins for the range of parameters studied in the present work. A correlation is developed to predict the average Nusselt number of the plate as a function of fin spacing in the streamwise and spanwise directions, aspect ratio of the fin, and its angle of inclination.

S. A. Kaloerov, A. A. Koshkin
Donetsk National University, Donetsk, 83001, Ukraine
Keywords: анизотропная плита, изгиб плит, упругие включения, коэффициенты интенсивности моментов, комплексные потенциалы, обобщенный метод наименьших квадратов, anisotropic plate, bending of plates, elastic inclusions, moment intensity coefficients, complex potentials, generalized least squares method
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This paper describes a method for determining the strain state of a thin anisotropic plate with elastic arbitrarily arranged elliptical inclusions. Complex potentials are used to reduce the problem to determining functions of generalized complex variables, which, in turn, comes down to a undetermined system of linear algebraic equations, solved by singular expansions. This paper presents the results of numerical calculations that helped establish the influence of rigidity of elastic inclusions, distances between inclusions, and their geometric characteristics on the bending moments occurring in the plate. It is certain that the specific properties of distribution of moments near the apexes of linear elastic inclusions, characterized by moment intensity coefficients, occur only in the case of sufficiently rigid and elastic inclusions.

E. V. Karpov^{1,2}, A. Yu. Larichkin^{1,2}
^{1}Lavrentyer Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia ^{2}Novosibirsk State University, Novosibirsk, 630090, Russia
Keywords: циркониевый сплав, многократное нагружение, малоцикловая усталость, низкие температуры, релаксация напряжений, zirconium alloy, multiple load, lowcycle fatigue, low temperatures, stress relaxation
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This paper describes the results of an experimental study on deformation and fracture of a Zr  1% Nb zirconium alloy in the case of multiple loads at low temperatures (80^{o}C). Samples cut out of pipes and applied as fuel rod shells of heat releasing assemblies of nuclear reactors are used to conduct a series of experiments on lowcycle stretching and compression at low temperatures and study the effect of low temperature on stress relaxation in the material under a different number of preliminary loads.

