

2013 year, number 2
V. K. Andreev, V. B. Bekezhanova
Keywords: stability, nonisothermal fluid, convective flows
Pages: 171184
Abstract >>
This paper gives a review of studies of flow stability for viscous heatconducting fluids.

S. P. Aktershev, S. V. Alekseenko
Keywords: falling liquid film, flow stability, waves, integral approach, basis functions
Pages: 185194
Abstract >>
A new model is developed for describing longwave perturbations in a falling film of a viscous liquid. The model is based on an integral approach and an expansion of the velocity profile into a series in linearly independent basis functions of a boundaryvalue problem. A linear analysis of film flow stability is performed, and dispersion dependences are obtained. Results predicted by the new model are demonstrated to be in good agreement with available experimental data on the film flow over a gently sloping surface.

N. N. Fedorova^{}, I. A. Fedorchenko^{}, A. V. Fedorov^{}
Keywords: supersonic flows, mixing, internal flows, separation, turbulence, shock waves
Pages: 195206
Abstract >>
Results of modeling the interaction of a plane supersonic jet with a supersonic turbulent highenthalpy flow in a channel are reported. The problem is solved in a twodimensional formulation at external flow Mach numbers M_{∞} = 2.6 and 2.8 and at high values of the total temperature of the flow T_{0} = 1800 ÷ 2000 K. The mathematical model includes full averaged Navier–Stokes equations supplemented with a twoequation turbulence model and an equation that describes the transportation of the injected substance. The computations are performed by using the ANSYS Fluent 12.1 software package. Verification of the computational technique is performed against available experimental results on transverse injection of nitrogen and helium jets. The computed and experimental results are demonstrated to agree well. For the examined problems, in addition to surface distributions of characteristics, fields of flow parameters are obtained, which allow one to reproduce specific features that can be hardly captured in experiments. Parametric studies show that an increase in the angle of inclination and the mass flow rate of the jet leads to an increase in the depth of jet penetration into the flow, but more intense separated flows and shock waves are observed in this case.

R. I. Mullyadzhanov^{}, N. I. Yavorskii^{}
Keywords: Navier &mdash Stokes equations, submerged swirling jet
Pages: 207211
Abstract >>
This paper considers the problem of a nonaxisymmetric swirling jet of an incompressible viscous fluid flowing in a space flooded with the same fluid. The far field of the jet is studied under the assumption that the angular momentum vector corresponding to the swirling of the jet is not collinear to the momentum vector of the jet. It is shown that the main terms of the asymptotic expansion of the full solution for the velocity field are determined by the exact integrals of conservation of momentum, mass, and angular momentum. An analytical solution of the problem describing the axisymmetric swirling jet is obtained.

N. M. Zubarev, E. A. Kochurin
Keywords: nonlinear waves, interface, dielectric fluids, electrohydrodynamics, horizontal electric field
Pages: 212217
Abstract >>
The nonlinear dynamics of the interface between dielectric fluids in a strong horizontal electric field is studied. It is shown that threedimensional waves of small but finite amplitude can propagate without shape distortions either in a direction coinciding with the direction of the external field vector or in the direction opposite to this vector, along the interface of the fluids, whose density ratio is directly proportional to the ratio of their dielectric constants. For this particular case, an analytical description of the interaction of counterpropagating weakly nonlinear waves of arbitrary shape is given.

I. B. Bogoryad, N. P. Lavrova
Keywords: viscous liquid, radially arranged elastic ribs, vortex flow
Pages: 218223
Abstract >>
The boundaryvalue problem of the vortex flow of a viscous incompressible liquid in a rotating cavity having the shape of a circular cylinder in which elastic radial ribs (plates) are embedded as intense vortex sources is formulated and solved using numerical methods. The solution results are used to calculate the drag coefficient of the ribs.

K. N. Volkov
Keywords: twophase flow, particle, turbulence, unsteadiness, numerical simulation
Pages: 224237
Abstract >>
A turbulent flow of a suspension of solid particles in a gas is considered. The suspension is located in a channel with permeable walls (the pressure at the left end face of the channel follows a sinusoidal law). The flow considered here reflects the principal features of the flow in the combustion chamber of a solidpropellant rocket motor. The unsteady flow of the gas suspension is described by using the Eulerian–Lagrangian approach. A stochastic variant of the discretetrajectory approach is used for modeling the particle motion. The influence of the condensed phase on the turbulence characteristics and acoustic oscillations of the parameters of the working medium in the channel in the case of injection is discussed. The calculated results are compared with data obtained in a physical experiment.

O. S. Pyatigorskaya, V. L. Sennitskii
Keywords: solid, viscous liquid, pulsations, oscillations, external force, predominantly unidirectional motion of a body
Pages: 237242
Abstract >>
The problem of motion of a pulsating solid (an infinitely long circular cylinder) in an oscillating viscous liquid in the presence (or absence) of an external stationary force is considered. The perturbation method is applied. It is found that the solution of the timeaverage motion of a body exists if and only if body pulsations, liquid vibrations, and external forces satisfy a certain relation. The presence of a plane analog of the phenomenon of predominantly unidirectional motion of a compressible solid in an oscillating liquid is established.

A. S. Vereshchagin^{}, I. V. Kazanin^{}, V. N. Zinov'ev^{}, A. Yu. Pak^{}, A. F. Fomina^{}, V. A. Lebiga^{}, V. M. Fomin^{}
Keywords: permeability, helium, microsphere, mathematical model, distribution
Pages: 243250
Abstract >>
A mathematical model of helium absorption by a sorbent consisting of hollow spherical particles with allowance for the distributions of permeability coefficients and particle sizes is constructed. A possibility of reconstructing the permeability coefficients of the microsphere materials from the known sorption curves and particle size distribution is demonstrated. The model is analyzed and tested by examples of two different sorbents.

A. L. Kazakov, A. A. Lempert
Keywords: nonlinear filtration, partial differential equations, boundaryvalue problem, existence and uniqueness theorem, series, convergence
Pages: 251258
Abstract >>
The problem of the motion of a filtration front in a zero background in the case of a powerlaw dependence of the filtration coefficient on gas density is considered, and the existence and uniqueness theorem for solutions in the class of analytic functions is proved. The solution is constructed in explicit form, recurrence formulas for computing the coefficients in the series are obtained, and the convergence of the series is proved by the majorant method. The filtration front construction procedure is proposed.

A. Mahdian^{}, G. H. Liaghat^{}, M. Ghayour^{}
Keywords: asymmetric shaped charge, jet formation theory, asymmetric detonation wave front, liner collapse phenomenon
Pages: 259267
Abstract >>
This paper presents a model that has less constraints than similar models and explains the collapse phenomenon in any desired order of geometrical asymmetries and in the presence of symmetric and asymmetric generalform wave fronts. It seems that, in this model, a complete generalized form of the classical jet formation theory has been developed. Available models that describe the symmetric jet and slug formation phenomenon are very good in such conditions. But the liner and confinement asymmetries, detonation wave front asymmetries, and other specifications, such as manufacturing tolerances, can affect the collapse and the behavior of the jet and slug. Some proposed models that describe asymmetric cases are not closedform models or are only applicable for limited conditions, such as small asymmetries and a planar wave front. With the presented model, effects of concave, plane, and convex wave fronts on the offaxis velocity of the jet, other parameters of the jet and slug, and effects of an asymmetric wave front on jet formation for a completely symmetric liner and confinement geometry can be evaluated.

H. A. Attia^{}, M. A. M. Abdeen^{}
Keywords: MHD flow, heat transfer, nonNewtonian, viscoelastic, electrically conducting fluids, Hall current, ion slip, porous plates
Pages: 268276
Abstract >>
Ion slip in a timevarying Hartmann flow of a conducting incompressible nonNewtonian viscoelastic fluid between two parallel horizontal insulating porous plates is studied with allowance for heat transfer. A uniform and constant pressure gradient is applied in the axial direction. An external uniform magnetic field and uniform suction and injection through the surface of the plates are applied in the normal direction. The two plates are maintained at different but constant temperatures; the Joule and viscous dissipations are taken into consideration. Numerical solutions for the governing momentum and energy equations are obtained with the use of finite differences, and the effect of various physical parameters on both the velocity and temperature fields is discussed.

M. B. Babenkov
Keywords: hyperbolic thermoelasticity theory, Maxwell–Cattaneo law, heatflux relaxation, wave transport of heat, second sound
Pages: 277286
Abstract >>
The propagation of plane harmonic waves in a thermoelastic medium with heatflux relaxation is studied; in particular, the dependences of the temperature and displacement on the coordinate are analyzed in a coupled formulation. The dependences of the group and phase velocities on frequency are investigated. The influence of the frequency and parameters of the material on the amplitude of thermoelastic waves is examined. The results are compared with the available results obtained using classical thermoelasticity theory.

S. D. Algazin
Keywords: Cosserat spectrum, eigenvalue problem, numerical algorithm without saturation
Pages: 287294
Abstract >>
The threedimensional problem of calculating the Cosserat spectrum of the first boundaryvalue problem of elasticity for a body of revolution is considered. Using grids containing 900 and 3600 nodes, it is shown that the sequence of eigenvalues for a sphere found by E. Cosserat and F. Cosserat does not describe the entire range of eigenvalues.

A. A. Rogovoi, O. S. Stolbova
Keywords: finite strain, shape memory, coupled problem
Pages: 295307
Abstract >>
An equation of state for a shape memory alloy is derived using a formalized approach to the construction of finitedeformation constitutive equations for complex media. The obtained equations were tested for coupled elastic–inelastic boundaryvalue problems of deformation of a sample of a shapememory during forward and reverse martensitic transformations.

M. M. Shakirtov^{}, A. P. Shabanov^{}, V. M. Kornev^{}
Keywords: cracklike cut, fracture diagrams, plastic zones
Pages: 308314
Abstract >>
The process of tension of a plate with a narrow cracklike cut whose vertices form finiteradius semicircumferences is considered. The plate is made of a structured material whose mechanical characteristics are close to the characteristics of St.45 steel. Fracture diagrams are constructed by a numerical method, based on the necessary and sufficient criteria. A possibility of an analytical presentation of fracture diagrams is demonstrated.

S. V. Suknev
Keywords: fracture, geomaterials, scale effect, stress concentration, notch, nonlocal fracture criteria
Pages: 315321
Abstract >>
This paper presents a theoretical and experimental study of the formation of tensile cracks in a brittle geomaterial with an elliptical notch under compression with variation in the angle of inclination of the notch to the loading axis. Calculation results are compared with the experimental data obtained.

N. P. Lazarev^{}
Keywords: plate, crack, nonpenetration condition, variational problem, elastic inclusion
Pages: 322330
Abstract >>
A problem of equilibrium of a composite plate consisting of a matrix and an elastic inclusion with a through crack along the boundary of this inclusion is studied. The matrix deformation is described by the Timoshenko model, and the elastic inclusion deformation is described by the Kirchhoff–Love model. Conditions of mutual nonpenetration of the crack edges are imposed on the curve that describes the crack. Unique solvability of the variational problem is proved. A system of boundary conditions on the curve bounding (in the midplane) the elastic inclusion is obtained. A differential formulation of the problem equivalent to the initial variational formulation is given.

Yu. V. Esipov
Keywords: complex structures, stress indices, strain oscillations, Fourier transform, nonlinear dynamics, ferroelectric gauges
Pages: 331336
Abstract >>
Successive impact excitation and construction of Fourier transforms of linear and nonlinear strain responses and phase portraits of undamaged or damaged vertically suspended models of a periodic welded rod structure were used to establish the dependence of the area ratio of the phase portraits of the nonlinear and linear domains of the strain response, which characterizes the stress (damage) of the model, on the impact momentum. The dynamic strain responses were recorded using ultrawideband (10^{–}^{2}÷10^{8} Hz) ferroelectric microgauges based on thin Pb(Zr_{0.53}Ti_{0.47})O_{3} films 2 mm in thickness with a 0.8 mm^{2} contact area.

A. A. Pikarevskii, O. I. Stoyanovskii
Keywords: explosion chamber, strain measurement, equivalent stresses, logarithmic decrement, damping parameter
Pages: 337342
Abstract >>
The effect of the presence of a shield on the stress state of the casing of a real explosion chamber and the rate of decay of its vibrations was studied experimentally. Considerable decrease in the stress was observed in the shielded part of the casing and at its pole at which the shield was not installed. It was shown that the use of a local shield in the form of a shell ring significantly increased the duration of vibrations of the casing, in particular at the pole.

