

2013 year, number 3
V. K. Kedrinskii
Keywords: decompression wave, diffusion, saturation zone, viscosity, nucleation, gasphase concentration, microcrystallites
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The dynamics of the structure of a cavitating magma flow behind the decompression wave front is experimentally studied by the method of hydrodynamic shock tubes. It is demonstrated that a discrete system of intensely cavitating zones with alternation of low and high densities of the gas phase can be formed at a certain regime of shockwave loading of the examined fluid sample. Based on the results of a numerical analysis of the formation of an anomalous zone in the cavitating magma flow with anomalously high flow characteristics exceeding the values of these characteristics outside this zone at least by an order of magnitude, a model of an instantaneous transformation of the cavitating magma in the anomalous zone to a gasdroplet system, its ejections, and formation of a free surface on the interface is proposed. A numerical analysis shows that the characteristic wave structure and the anomalous saturation zone are fairly rapidly reconstructed in the vicinity of this free surface of the flow part remaining in the conduit after the ejections, and the abovementioned jumps of flow characteristics are again formed in the anomalous zone.

B. M. Polyashev
Keywords: electrical discharge in water, magnetic hydrodynamics, resistance to motion in liquid
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This paper considers a range of physical phenomena that occur during electrical discharge in water in the presence of a transverse magnetic field. An approximate equation of energy balance is obtained using assumptions based on the wellknown hydrodynamic concepts of a long electrical discharge in water. An experimental estimate of the reaction force impulse in a limited medium is obtained.

P. A. Polivanov, O. I. Vishnyakov, A. A. Sidorenko, A. A. Maslov
Keywords: ionic wind, barrier and sliding discharges, particle image velocimetry (PIV)
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Two types of electric discharges to be used for the purpose of air flow control are compared. The parameters measured in experiments are the electric characteristics of the discharges and the velocity of flows generated by them. The ionic wind velocity in the sliding discharge is demonstrated to be smaller than in the dielectric barrier discharge. The volume forces acting from the discharge on air and the efficiency of the electrogasdynamic action are estimated. The presence of an additional electrode in the case of the sliding discharge is found to affect the distribution of the spatial charge and change the forces, leaving the electric characteristics unchanged.

N. I. Makarenko^{}, V. K. Kostikov^{}
Keywords: free surface, elliptic cylinder, nonlinear unsteady waves, smalltime asymptotics of motion
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A problem of generation of nonlinear unsteady waves on the surface of an ideal liquid in an infinitely deep fluid due to the motion of a submerged elliptic cylinder is considered. The initial formulation of the problem is reduced to an integrodifferential system of equations for the function defining the free surface shape and for the normal and tangential components of velocity on the free surface. The smalltime asymptotics of the solution is constructed for the case of cylinder motion with a constant acceleration from the state at rest.

R. Md. Kasmani^{}, I. Muhaimin^{}, R. Kandasamy^{}
Keywords: boundary layer flow, heat and mass transfer, nanofluid, wedge
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The behavior of an incompressible laminar boundary layer flow over a wedge in a nanofluid with suction or injection has been investigated. The model used for the nanofluid integrates the effects of the Brownian motion and thermophoresis parameters. The governing partial differential equations of this problem, subjected to their boundary conditions, are solved by the Runge–Kutta–Gill technique with the shooting method for finding the skin friction and the rate of heat and mass transfer. The result are presented in the form of velocity, temperature, and volume fraction profiles for different values of the suction/injection parameter, Brownian motion parameter, thermophoresis parameter, pressure gradient parameter, Prandtl number, and Lewis number. The conclusion is drawn that these parameters significantly affect the temperature and volume fraction profiles, but their influence on the velocity profile is comparatively smaller.

S. Mukhopadhyay, P. Ranjan De, G. C. Layek
Keywords: unsteady flow, Maxwell fluid, porous medium, stretching surface, suction/blowing, thermal radiation
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An unsteady boundary layer flow of a nonNewtonian fluid over a continuously stretching permeable surface in the presence of thermal radiation is investigated. The Maxwell fluid model is used to characterize the nonNewtonian fluid behavior. Similarity solutions for the transformed governing equations are obtained. The transformed boundary layer equations are then solved numerically by the shooting method. The flow features and heat transfer characteristics for different values of the governing parameters (unsteadiness parameter, Maxwell parameter, permeability parameter, suction/blowing parameter, thermal radiation parameter, and Prandtl number) are analyzed and discussed in detail.

R. Abazari
Keywords: quintic nonlinearity of the Klein–Gordon equation, (G'/G)expansion method, hyperbolic function solutions, trigonometric function solutions
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In this paper, the (G'/G)expansion method is used to obtain exact solitarywave and periodicwave solutions for nonlinear evolution equations arising in mathematical physics with the aid of symbolic computations, namely, the Klein–Gordon equation with quintic nonlinearity. Our work is motivated by the fact that the (G'/G)expansion method provides not only more general forms of solutions, but also periodic and solitary waves. As a result, hyperbolic function solutions and trigonometric function solutions with parameters are obtained. The method is straightforward and concise, and its application is promising for other nonlinear evolution equations in mathematical physics.

O. S. Pyatigorskaya, V. L. Sennitskii
Keywords: oscillating liquid, solid particles, force interaction, centerofmass motion
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The problem of motion of two “free” solid particles in a uniformly oscillating liquid is formulated and solved. In particular, it is found that the particles are capable of performing (side by side with oscillations) an average, monotonous displacement in the liquid as a whole.

E. V. Stepanova, T. O. Chaplin, Yu. D. Chashechkin
Keywords: compound vortex, mass transfer, impurity
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Experiments were performed to study oil transport in the compound vortex produced by a uniformly rotating disk in a cylindrical container. It was found that on the liquid surface in the neighborhood of the axis of rotation, light oil formed a spot with spiral branches or broke up into separate elongated drops, and the spiral branches stretched out in the direction opposite to the direction of rotation of the liquid. In the bulk of the liquid in the vicinity of the axis of its rotation, oil formed a compact body. The geometric parameters of the structural components of the flows were determined.

V. I. Pen'kovskii^{}, N. K. Korsakova^{}, L. K. Altunina^{}, V. A. Kuvshinov^{}
Keywords: unrecovered oil, capillary plugging, terrigenous structure, chemical reagent
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Various conditions of formation of motionless closed hydrocarbon inclusions are considered: viscous instability of fluid displacement and inhomogeneous rock structure. Conditions of dynamic equilibrium of the inclusion in a water flow are given for onedimensional and twodimensional motion. Distributions of the oil content in inclusions of different shapes are numerically calculated. It is found that the amount of unrecovered oil depends on the ratio of the pressure gradients in the filtration flow of water pumped into the reservoir and the characteristic capillary pressure on the boundary of immiscible phases. It is demonstrated that the use of chemical reagents can substantially reduce the effect of capillary forces and promotes oil entrainment by the overall flow.

V. V. Kadet, A. M. Galechyan
Keywords: relative permeabilities, drainage, treatment, hysteresis, percolation theory
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A mathematical model of relative permeability hysteresis in drainage and imbibition is constructed on the basis of percolation theory. It is shown that the results are in qualitatively agreement with experimental data.

S. D. Sleptsov, N. A. Rubtsov
Keywords: phase transition, singlephase Stefan problem, radiative–conductive heat transfer, gray medium, reflection ratio, emissivity
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A numerical simulation of the classical Stefan problem is performed in a modified formulation for a semitransparent gray medium. Temperature fields and the resulting radiation flux field are obtained, and the dynamics of displacement of the interface and the evolution of the temperature rise on the black left boundary of the sample for different values of the emissivity factor of the exposed right boundary are studied.

M. M. Khader^{}, A. M. Megahed^{}
Keywords: Powell–Eyring fluid, thin film flow, unsteady stretching sheet, internal heat generation, Chebyshev finite difference method
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An analysis is carried out to study the unsteady twodimensional PowellEyring flow and heat transfer to a laminar liquid film from a horizontal stretching surface in the presence of internal heat generation. The flow of a thin fluid film and subsequent heat transfer from the stretching surface is investigated with the aid of a similarity transformation. The transformation enables to reduce the unsteady boundary layer equations to a system of nonlinear ordinary differential equations. A numerical solution of the resulting nonlinear differential equations is found by using an efficient Chebyshev finite difference method. A comparison of numerical results is made with the earlier published results for limiting cases. The effects of the governing parameters on the flow and thermal fields are thoroughly examined and discussed.

A. M. Lokoshchenko, V. V. Teraud
Keywords: membrane, creep, constrained conditions, Coulomb's law, fracture
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With the use of different approaches and boundary conditions, the deformation of a long narrow rectangular membrane disposed within a rigid wedge matrix is simulated using different approaches and boundary conditions. The basic relations characterizing the stress–strain state of the membrane at different stages of deformation are obtained. The results of numerical experiments studying the characteristics of deformation of membranes are given.

V. M. Kozin^{}, V. L. Zemlyak^{}, V. Yu. Vereshchagin^{}
Keywords: flexuralgravity waves, resonant method of ice breaking, resonant velocity
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This paper presents a mathematical model for the analysis of the stress–strain state of ice cover in the presence of a snow layer under dynamic loads. Numerical calculations were made using the model of indestructible ice, and the results were compared with experimental data.

V. V. Mikhas'kiv^{}, I. O. Butrak^{}, I. P. Laushnik^{}
Keywords: threedimensional elastic matrix, diskshaped inclusion, crack, harmonic elastic wave, dynamic stress intensity factors, method of boundary integral equations
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The propagation of harmonic elastic wave in an infinite threedimensional matrix containing an interacting lowrigidity diskshaped inclusion and a crack. The problem is reduced to a~system of boundary integral equations for functions that characterize jumps of displacements on the inclusion and crack. The unknown functions are determined by numerical solution of the system of boundary integral equations. For the symmetric problem, graphs are given of the dynamic stress intensity factors in the vicinity of the circular inclusion and the crack on the wavenumber for different distances between them and different compliance parameters of the inclusion.

F. Yongfeng, Ch. Jianjun
Keywords: stochastic loads, combined stochastic loads, structural dynamic reliability, predictive model
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In this paper addressing how to predict structural reliability and based upon thorough research, the four most common types of load stresses are integrated into three related models, using Turkstra's rule. Predictions of the combined loads are calculated, both with and without strength degeneration, using Turkstra's method and the stressstrength interference theory. An illustration is provided, demonstrating that the predictive models are practical, feasible, and consistent with standard engineering practices.

M. J. Ketabdari, A. N. Roozbahani
Keywords: plunging wave breaking, weakly compressible smoothed particle hydrodynamic, large eddy simulation, sub particle scale model
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In this paper, a numerical meshless method called the weakly compressible smoothed particle hydrodynamic (WCSPH) method, which is a twodimensional model of a weakly compressible fluid, is applied to simulate the plunging wave breaking process. This model solves the viscous fluid equations to obtain the velocity and density fields and also solves the equation of state to obtain the pressure field. The WCSPH method is demonstrated to have a higher computational efficiency than the basic SPH model. To simulate the turbulent behavior of the fluid flow in the wave breaking procedure, a sub particle scale (SPS) model is used, which is obtained from the Large eddy simulation (LES) theory. To consider the accuracy of the standard WCSPH model (WCSPH model without considering the turbulent effect), a dam break test is performed, and model results are compared with available experimental data.

M. N. Kirsanov
Keywords: instability, plane problem of the elasticity theory, inhomogeneous medium
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A possibility of degeneration of relationships between stresses and their derivatives with respect to the coordinates in the plane problem of the elasticity theory is considered. For particular dependences of the parameters of elasticity on coordinates, curves are given, for which degeneration conditions are satisfied. It is shown that even a small inhomogeneity of the medium causes stress instability.

V. V. Shevelev, R. A. Osipov
Keywords: crack, mathematical model, brittle fracture, integral equation, numerical methods
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A mathematical model of a circular diskshaped brittle crack whose faces are acted upon by cohesive forces, whose magnitude depends on the distance between the faces. An algorithm of numerical solution of the singular nonlinear improper integral equation defining the crack profile was developed which can be used for other integral equations of this type. It is shown that taking into account the coupling forces between the crack faces leads to their gradual closing with distance from the center of the crack.

A. A. Karabutov^{}, N. B. Podymova^{}, E. B. Cherepetskaya^{}
Keywords: isotropic composites, porosity, Young's modulus, laser optoacoustic method
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A laser optoacoustic method for analyzing the effect of porosity on the local isotropic Young's modulus of composite materials was proposed and experimentally implemented. Using as an example samples of a metal matrix composite based on silumin with reinforcing microparticles of silicon carbide, SiC, in various concentrations, it is shown that to provide an effective increase in Young's modulus with increasing concentration of SiC, the porosity of the final sample should not exceed 2%.

A. A. Shtertser, B. E. Grinberg
Keywords: hydroabrasive jet, submerged jet, testing, wear, wear track
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The wear of steel plates under the impact of a hydroabrasive jet was studied experimentally by varying the distance between the sample surface and the nozzle, the angle of impingement of the jet on the plate, and the abrasive concentrations in water and in the ambient medium (jet in air, submerged jet). The results are compared with available data on the structure of the jet and jet flow around an obstacle. It is shown that the addition of abrasive particles to the liquid can be used to study the liquid jet flow around an obstacle because the form of surface wear allows one to determine the region of impact of the jet core, the deceleration region, and the nearwall flow region before flow separation.

