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2016 year, number 3

Unsteady Self-Similar Viscous Flow Near a Critical Point

O. A. Frolovskaya
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: нестационарность, автомодельность, критическая точка, unsteadiness, self-similarity, critical point

Abstract >>
The problem of unsteady viscous incompressible fluid flow near a critical point is considered. Self-similar solutions describing plane and axisymmetric flows are constructed.

Numerical Study of the Exact Solution of the Navier-Stokes Equation Describing Free-Boundary Fluid Flow

E. N. Zhuravleva
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: течение вязкой несжимаемой жидкости, уравнения Навье -- Стокса, течения со свободными границами, инвариантные и частично инвариантные решения, численные решения, incompressible viscous fluid, Navier-Stokes equations, free-boundary flows, invariant and partially invariant solutions, numerical solutions

Abstract >>
This paper presents a numerical study of the partially invariant solutions of the Navier-Stokes equations for the plane case which describes unsteady flow in a layer bounded by a straight solid wall and a free boundary parallel to it. It is found that for different values of the initial flow velocity, there may be the establishment a steady state with a decrease or an increase in the initial layer thickness can be established or the layer thickness can be increased infinitely due to liquid inflow from infinity.

Transformation of the Bridge During Separation of a Droplet

Yu. D. Chashechkin, E. V. Prokhorov
Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526, Russia
Keywords: капля, сопло, отрыв, поверхностное натяжение, вязкость, структурные элементы, сателлит, перемычка, характерные масштабы, динамика, drop, nozzle, separation, surface tension, viscosity, structural elements, satellite, bridge, characteristic scales, dynamics

Abstract >>
The geometry of flows resulting from separation of hanging drops of liquids with significantly different physical properties (alcohol, water, glycerin, oil) was studied by high-speed video recording. The dynamics of the processes is studied for characteristic shapes of bridges: with slightly nonuniform thickness and with thinning of the upper and lower ends. It is shown that the change of the shape of the separated bridge has a number of stages determined by the properties of the liquid. As a result, the bridge is transformed into a small droplet - a satellite droplet.

Pattern Formation in a Nonequilibrium Phase Transition for a Generalized Burgers-Fisher Equation

Q. Huang1, J. Tang2, L. Zhang2, K. Ouyang3
1Yancheng Institute of Technology, Yancheng, 22405, China
2Hunan University, Changsha, 410082,China
3State Grid Hunan Electric Power Corporation Research Institute, Changsha, 410007, China
Keywords: обобщенное уравнение Бюргерса -- Фишера, неравновесный фазовый переход, бифуркационное решение, формирование шаблона, generalized Burgers-Fisher equation, nonequilibrium phase transition, bifurcation solution, pattern formation

Abstract >>
A nonequilibrium phase transition of a generalized Burger-Fisher equation describing biological pattern formation with a periodic boundary condition is examined. In the presence of a weak external force, some approximate bifurcation solutions near a critical point and new spatially periodic patterns are obtained by using the perturbation method in an infinite-dimensional space. The result shows that the external force delays the bifurcation.

Specific Features of Unsteady Exhaustion of a Gas-Particle Mixture into Vacuum

D. V. Sadin, V. M. Varvarskii
Alexander Mozhaysky Military Space Academy, St. Petersburg, 197198, Russia
Keywords: истечение в вакуум, газодисперсная среда, жесткость уравнений, TVD-схема, exhaustion into vacuum, gas--particle mixture, stiffness of equations, TVD scheme

Abstract >>
Two-dimensional unsteady exhaustion of a one-velocity gas-particle mixture into vacuum is analyzed in extreme equilibrium cases of heat transfer. Domains of existence of a one-dimensional Riemann wave and side expansion wave and the boundary of the expansion region are obtained. In the case of temperature equilibrium, the reverse flow is found to occupy a large region extending beyond the boundaries defined by the angles of expansion of an ideal gas and a gas-particle mixture with thermally insulated phases. Exhaustion of a nonequilibrium two-phase medium in terms of velocities and temperatures into vacuum is numerically simulated. It is demonstrated that a barrel structure with wavy expansion of the gas and combined discontinuities in the expanding gas-particle mixture is formed.

Application of the Euler Approach to Modeling the Flow Structure in an Ascending Monodisperse Bubble Flow in a Tube

M. A. Pakhomov, V. I. Terekhov
Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: газожидкостный поток, моделирование, структура течения, турбулентность, gas-liquid flow, simulation, flow structure, turbulence

Abstract >>
Results of simulations of the flow structure in a vertical monodisperse gas-liquid flow in a tube on the basis of the Euler approach with allowance for the effect of bubbles on the averaged characteristics and turbulence of the carrier flow are reported. The carrier phase turbulence is calculated by using the transport model for the Reynolds stress tensor components. A comparison of the simulation results with available experimental data shows that the proposed apprach provides an adequate description of turbulent bubble flows in wide ranges of the local gas content and gas inclusion sizes.

Effect of the Particle Size of Bottom Sediments on the Wavelength of Bottom Perturbation in Pressure Conduits

Yu. G. Krat, I. I. Potapov
Computing Center, Far Eastern Branch, Russian Academy of Sciences, Khabarovsk, 680000, Russia
Keywords: напорный канал, донные волны, математическая модель, pressure conduit, bottom waves, mathematical model

Abstract >>
The problem of the stability of the sandy bottom surface in a rectangular pressure conduit with respect to spatially one-dimensional perturbations. The problem of bed stability is solved using an analytical formula of sediment discharge which takes into account the effect of bottom pressure on sediment movement. An analytical relationship of the bottom wavelength to the hydrodynamic flow parameters and the diameter of bottom particles is obtained and compared with experimental data.

Three-Dimensional Flow of a Viscoelastic Fluid on an Exponentially Stretching Surface

M. Bilal Ashraf1, T. Hayat2,3, S. A. Shehzad4, H. Malaikah3
1COMSATS Institute of Information Technology, Kant 47,070 Wah, Pakistan
2Quaid-i-Azam University, 45320, Islamabad 44000, Pakistan
3Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Islamabad 44000, Pakistan
4King Abdulaziz University, Jeddah 21589, Saudi Arabia
Keywords: вязкоупругая жидкость, экспоненциально растягивающаяся поверхность, теплообмен, viscoelastic fluid, exponentially stretching surface, heat transfer

Abstract >>
An analysis of a three-dimensional viscoelastic fluid flow over an exponentially stretching surface is carried out in the presence of heat transfer. Constitutive equations of a second-grade fluid are employed. The governing boundary layer equations are reduced by appropriate transformations to ordinary differential equations. Series solutions of these equations are found, and their convergence is discussed. The influence of the prominent parameters involved in the heat transfer process is analyzed. It is found that the effects of the Prandtl number, viscoelastic parameter, velocity ratio parameter, and temperature exponent on the Nusselt number are qualitatively similar.

Computational Analysis of Convective Instabilities in a Liquid Layer Subjectedto an Inclined Gradient of Temperature

D. Nezar, S. Rahal
University Hadj Lakhdar, Batna, 05000 Algeria
Keywords: конвективная неустойчивость Бенара-Марангони, гравитационная сила, термокапиллярные силы, структуры, вычислительная гидродинамика, Benard-Marangoni convective instability, gravity force, thermocapillary force, patterns, CFD

Abstract >>
A 3D numerical study of convective instabilities in a horizontal liquid layer (silicone oil with a Prandtl number Pr = 102) with an upper free surface is presented. The liquid layer is subjected to an inclined gradient of temperature. The influence of both gravity and thermocapillary forces on the formation of convective patterns is studied for different values of the liquid layer depth. Numerical results are found to be in good agreement with experimental data of other authors.

Viscous Dissipation and Thermal Radiation Effects on the Magnetohydrodynamic (MHD) Flow and Heat Transfer Over a Stretching Slender Cylinder

M. Kalteh1, S. Ghorbani1, T. Khademinejad2
1University of Guilan, Rasht, 3756, Iran
2Amirkabir University of Technology, Tehran, Iran
Keywords: осесимметричный поток, растягивающийся цилиндр, вязкая диссипация, тепловое излучение, метод Рунге-Кутты, axisymmetric flow, stretching cylinder, viscous dissipation, thermal radiation, Runge-Kutta method

Abstract >>
An axisymmetric magnetohydrodynamic (MHD) boundary layer flow and heat transfer of a fluid over a slender cylinder are investigated numerically. The effects of viscous dissipation, thermal radiation, and surface transverse curvature are taken into account in the simulations. For this purpose, the governing partial differential equations are transformed to ordinary differential equations by using appropriate similarity transformations. The resultant ordinary differential equations along with appropriate boundary conditions are solved by the fourth-order Runge-Kutta method combined with the shooting technique. The effects of various parameters on the velocity and temperature profiles, local skin friction coefficient, and Nusselt number are analyzed.

Free Convection Effects on a Vertical Cone with Variable Viscosity and Thermal Conductivity

G. Palani1, E. J. L. Kumar2, K.-Y. Kim3
1Dr.Ambedkar Govt. Arts College, Chennai, 600039, Tamil Nadu, India
2SRM Arts and Science College, Tamil Nadu, India
3Inha University, Incheon, 402-751, Republic of Korea
Keywords: свободная конвекция, изменяющиеся вязкость и теплопроводность, вертикальный конус, free convection, variable viscosity and thermal conductivity, vertical cone

Abstract >>
The present paper deals with a flow of a viscous incompressible fluid along a heated vertical cone, with due allowance for variations of viscosity and thermal diffusivity with temperature. The fluid viscosity is assumed to be an exponential function of temperature, and the thermal diffusivity is assumed to be a linear function of temperature. The governing equations for laminar free convection of the fluid are transformed into dimensionless partial differential equations, which are solved by a finite difference method with the Crank-Nicolson implicit scheme. Dependences of the flow parameters on the fluid viscosity and thermal conductivity are obtained.

Thermal Softening of Metallic Shaped-Charge Jets Formed by Collapse of a Shaped-Charge Liner in the Presence of a Magnetic Field

S. V. Fedorov
Bauman Moscow State Technical University, Moscow, 105005, Russia
Keywords: взрыв, кумулятивная струя, кумулятивная облицовка, магнитное поле, индукционный нагрев, термическое разупрочнение, предельное удлинение, explosion, shaped-charge jet, shaped-charge liner, magnetic field, induction heating, thermal softening, ultimate elongation

Abstract >>
This paper presents an analysis of the possibility of increasing the ultimate elongation and penetration capability of metallic shaped-charge jets in the presence of an axial magnetic field in the shaped-charge liner by the heating and thermal softening of the jet material due to a sharp increase in the magnetic-field induction in the jet formation region upon liner collapse. This process is studied by numerical simulation in a quasi-two-dimensional formulation taking into account the inertial extension of the conductive rigid-plastic rod in the presence of a longitudinal magnetic field in it.

Experimental and Theoretic Study of the Buckling of Narrow Thin Plates on an Elastic Foundation under Compression

V. D. Kurguzov, A. G. Demeshkin
Lavrentiev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: тонкие пленки, отслоение, упругое основание, потеря устойчивости, нелинейное деформирование, thin films, detachment, elastic foundation, buckling, nonlinear strain

Abstract >>
The processes of elastic strain of thin films under mechanical load are considered. The film is simulated by a longitudinally compressed plate placed on an elastic foundation. The computer model of the buckling of the narrow thin plate with a detachment portion, placed on an elastic foundation is constructed. The supercritical behavior of the plate - substrate system is studied. The experiments on the axial compression of the metal strip adhered to the rubber plate are performed, and 2 to 7 buckling modes are obtained therein. The critical loads and buckling modes obtained in the numerical calculations are compared with the experimental data. The possibility of progressive detachment of the metal plate from the foundation in excess of the critical load is shown. It is found that the use of the proposed approach, which, in contrast to other approaches, takes into account the elastic strain of the substrate, causes the dependence of critical bending stresses on the stiffness of the foundation.

Experimental and Theoretical Analysis of the Deformation of Transversely Isotropic Plates in Creep

I. A. Banshchikova, V. A. Blinov
Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: пластина, ползучесть, трансверсально-изотропный материал, кручение, плоское напряженное состояние, plate, creep, transversely isotropic material, torsion, plane stress

Abstract >>
This paper presents the results of calculations and experiments on the torsion of plates made of isotropic and transversely isotropic BT-20 and 1163T alloys with reduced resistance to creep strain in the direction perpendicular to the median surface. The numerical modeling results for plates of different thickness that belong to the class of rigid and flexible plates made with the use of the pure bending theory and the finite element method are compared. It is established that during the deformation of the plate of anisotropic material into an alternating saddle-shaped surface, the curvature values are smaller than in the case of a plate of a isotropic material. The calculation carried out ccording to the pure bending theory yields an upper estimate of the curvature ifference during the strain of the plates of transversely isotropic and sotropic materials.

Numerical and Experimental Study on the Dynamic Behavior of a Sea-Star Tension Leg Platform Against Regular Waves

М. М. Abaiee, M. J. Ketabdari, А. Ahmadi, H. Alemi Ardakani
Amirkabir University of Technology, Tehran, Iran
Keywords: платформа с натяжными опорами типа "морская звезда", модельное исследование, метод граничных элементов, модифицированный метод Эйлера, дифракция, излучение, sea-star TLP, model test, BEM, MEM, diffraction, radiation

Abstract >>
This paper describes an experimental work on a 1:100 scaled model of a miniature sea-star tension leg platform (TLP) in a wave flume. Two different numerical models are developed: finite element model (FEM) based on the Morison equation and boundary element model (BEM) based on a 3D diffraction/radiation theory. The developed codes are used to calculate hydrodynamic forces and related coefficients. The nonlinear hull/tendon coupled dynamic equation of a mini sea-star TLP is solved by using a modified Euler method (MEM). The results of numerical modeling of the motion response behavior of the platform in different degrees of freedom are compared with experimental data. This comparison shows good agreement between the results. Furthermore, this modeling reveals that the first-order diffraction method and quasi-static tendon modeling are sufficient in general for the hydrodynamic analysis of the sea-star TLP.

Some Considerations on Instability of Combined Loaded Thin-Walled Tubes with a Crack

M. Shariati, A. Akbarpour
Ferdowsi University of Mashhad, Mashhad, Iran
Keywords: трещина, конечно-элементная модель, неустойчивость, тонкостенные трубы, сложное нагружение, crack, finite element model, instability, thin-walled tubes, combined loading

Abstract >>
Instability of a thin-walled stainless steel tube with a crack-shaped defect under combined loading is studied in this paper. Furthermore, the effects of the tube length, crack orientation, and crack length on the buckling behavior of tubes are investigated. The behavior of tubes subjected to combined is analyzed by using the finite element method (by Abaqus software). For cracked tubes with a fixed thickness, the buckling load decreases as the tube length and the ratio of the tube length to its diameter increase. Moreover, the buckling load of cracked tubes under combined loading also decreased with increasing crack length.

Slip Effects on a Mixed Convection Flow of a Third-Grade Fluid Near the Orthogonal Stagnation Point on a Vertical Surface

J. Tariq, M. Irfan
FBAS, International Islamic University, Islamabad, 44000, Pakistan
Keywords: жидкость третьего порядка, теплоперенос, эффекты скольжения, вязкая диссипация, точки остановки потока, численное решение, third-grade fluid, heat transfer, slip effects, viscous dissipation, stagnation point flow, numerical solution

Abstract >>
A mixed convection flow of a third-grade fluid near the orthogonal stagnation point on a vertical surface with slip and viscous dissipation effects is investigated. The governing partial differential equations for the third-grade fluid are converted into a system of nonlinear ordinary differential equations by using a similarity transformation. The effects of various parameters, including the Weissenberg number, third-grade parameter, local Reynolds number, Prandtl number, Eckert number, mixed convection parameter, velocity slip, and thermal slip on the velocity and temperature profiles, local skin friction coefficient, and local Nusselt number are discussed.

Numerical and Analytical Studies of the Propagation of Thermoelastic Waves in a Medium Taking into Account Heat Flow Relaxation

E. Yu. Vitokhin, M. B. Babenkov
St. Petersburg State Polytechnic University, St. Petersburg 195251, Russia
Keywords: гиперболическая задача термоупругости, закон Максвелла -- Каттанео, релаксация теплового потока, метод конечных разностей, hyperbolic thermoelastic problem, Maxwell-Cattaneo law, heat flow relaxation, finite difference method

Abstract >>
The thermoelastic problem of laser effect on metals and dielectrics is studied taking into account the finite speed of propagation of thermal waves and using a numerical finite-difference algorithm. The resulting numerical solution is compared with the analytical one. The problem is solved in coupled and uncoupled formulations. The solutions of the hyperbolic thermoelastic problem are compared with the solutions of the classical problem. Analytical expressions are obtained for the propagation speeds of the thermoelastic wave components. Times are determined at which the difference between the solutions of the hyperbolic and classical thermoelastic problems can be detected experimentally.

Flexural-Gravitational Circumferential and Radial Vibrations of a Plate Floating on Shallow Water

V. O. Shemelina
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: изгибно-гравитационные колебания, собственные колебания, гидроупругость, мелкая вода, круглая пластина, flexural-gravitational vibrations, natural vibrations, hydroelasticity, shallow water, circular plate

Abstract >>
Numerical and analytical studies of the natural and quasi-natural flexural-gravitational vibrations of an elastic plate floating on a liquid surface are performed based on shallow-water long-wave theory. Dependences of natural and quasi-natural frequencies on the geometrical parameters of the vibration region are studied for the cases of bounded and unbounded reservoirs. The effect of bottom irregularities in the form of a circular cylinder or a circular truncated cone on the natural and quasi-natural frequencies and functions is studied.

The Effect of Thermal Exposition on the Relaxation of Residual Stresses in a Reinforced Cylindrical Sample in Creep

V. P. Radchenko, M. N. Saushkin, V. V. Tsetkov
Samara State Technical University, 443100 Samara, Russia
Keywords: цилиндрический образец, поверхностное пластическое упрочнение, обработка микрошариками, остаточные напряжения, температурные выдержки, ползучесть, реологическая модель, краевая задача, релаксация напряжений, cylindrical sample, surface plastic reinforcement, treatment by microspheres, residual stresses, temperature soaks, creep, rheological model, boundary-value problem, stress relaxation

Abstract >>
This paper describes the effect of thermal exposition (high temperature soak) (T=675oC) on the relaxation of residual creep stresses in the surface reinforced solid cylindrical sample of a ZhS6UVI alloy. The analysis is performed with the use of experimental data for the residual stresses after reinforcement by microspheres and after high-temperature soaks T=675oC for 50, 150, and 300 h. The paper describes the solution technique for the boundary-value problem of creep of the reinforced cylindrical sample with the initial stress-strain state in thermal exposition. The uniaxial experimental creep curves obtained at constant stresses of 500, 530, 570, and 600 MPa to construct models describing the first and second stages of creep. The calculated and experimental data for the longitudinal (axial) component of the residual stress tensor are compared, and it is found that they are in satisfactory agreement

Technological Thermal Stresses in Shrink Fit of Cylindrical Bodies Taking into Accounting Plastic Flows

E. P. Dats1, A. V. Tkacheva2
1Vladivostok State University of Economics and Service, Vladivostok, 690990, Russia
2Institute of Engineering and Metallurgy, Far Eastern Branch, Russian Academy of Sciences, Komsomolsk-on-Amur, 681005, Russia
Keywords: упругость, пластичность, температурные напряжения, горячая посадка, остаточные напряжения, elasticity, plasticity, thermal stresses, shrink fit, residual stresses

Abstract >>
This paper presents a solution of a sequence of one-dimensional boundary-value problems of thermal stresses defining the elastic-plastic deformation processes used in the shrink fitting of cylindrical bodies. The origin and development of plastic flow in the materials of the assembly elements are studied taking into account the temperature dependence of the yield strength of these materials. During temperature equalization, the flow can slow down, followed by unloading and formation of a residual stress field providing an interference fit. The conditions of formation and motion of the boundaries of the elastic and plastic states in both plastic flow and during unloading are determined.