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2013 year, number 2

Stability of Non-Isothermal Fluids (Review)

V. K. Andreev, V. B. Bekezhanova
Keywords: stability, non-isothermal fluid, convective flows
Pages: 171-184

Abstract >>
This paper gives a review of studies of flow stability for viscous heat-conducting fluids.

Model of a Wavy Flow in a Falling Film of a Viscous Liquid

S. P. Aktershev, S. V. Alekseenko
Keywords: falling liquid film, flow stability, waves, integral approach, basis functions
Pages: 185-194

Abstract >>
A new model is developed for describing long-wave 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 boundary-value 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.

Mathematical Modeling of Jet Interaction with a High-Enthalpy Flow in an Expanding Channel

N. N. Fedorova, I. A. Fedorchenko, A. V. Fedorov
Keywords: supersonic flows, mixing, internal flows, separation, turbulence, shock waves
Pages: 195-206

Abstract >>
Results of modeling the interaction of a plane supersonic jet with a supersonic turbulent high-enthalpy flow in a channel are reported. The problem is solved in a two-dimensional formulation at external flow Mach numbers M = 2.6 and 2.8 and at high values of the total temperature of the flow T0 = 1800 ÷ 2000 K. The mathematical model includes full averaged Navier–Stokes equations supplemented with a two-equation 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.

Solution of the Problem of Flow of a Non-Axisymmetric Swirling Submerged Jets

R. I. Mullyadzhanov, N. I. Yavorskii
Keywords: Navier &mdash Stokes equations, submerged swirling jet
Pages: 207-211

Abstract >>
This paper considers the problem of a non-axisymmetric 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.

Three-Dimensional Nonlinear Waves at the Interface between Dielectric Fluid in an External Horizontal Electric Field

N. M. Zubarev, E. A. Kochurin
Keywords: nonlinear waves, interface, dielectric fluids, electrohydrodynamics, horizontal electric field
Pages: 212-217

Abstract >>
The nonlinear dynamics of the interface between dielectric fluids in a strong horizontal electric field is studied. It is shown that three-dimensional 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.

Numerical Model of Liquid Flow in a Rotating Cylinder with Radially Arranged Elastic Ribs

I. B. Bogoryad, N. P. Lavrova
Keywords: viscous liquid, radially arranged elastic ribs, vortex flow
Pages: 218-223

Abstract >>
The boundary-value 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.

Unsteady Turbulent Flow of a Gas Suspension in a Channel under Conditions of Injection and Forced Pressure Oscillations

K. N. Volkov
Keywords: two-phase flow, particle, turbulence, unsteadiness, numerical simulation
Pages: 224-237

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 solid-propellant rocket motor. The unsteady flow of the gas suspension is described by using the Eulerian–Lagrangian approach. A stochastic variant of the discrete-trajectory 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.

Example of Motion of a Cylindrical Solid in a Viscous Liquid

O. S. Pyatigorskaya, V. L. Sennitskii
Keywords: solid, viscous liquid, pulsations, oscillations, external force, predominantly unidirectional motion of a body
Pages: 237-242

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 time-average 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.

Mathematical Model of Permeability of Microspheres with Allowance for Their Size Distribution

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: 243-250

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.

Existence and Uniqueness of the Solution of the Boundary-Value Problem for a Parabolic Equation of Unsteady Filtration

A. L. Kazakov, A. A. Lempert
Keywords: nonlinear filtration, partial differential equations, boundary-value problem, existence and uniqueness theorem, series, convergence
Pages: 251-258

Abstract >>
The problem of the motion of a filtration front in a zero background in the case of a power-law 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.

Generalized Closed-Form Model for Analysis of Asymmetric Shaped Charges

A. Mahdian, G. H. Liaghat, M. Ghayour
Keywords: asymmetric shaped charge, jet formation theory, asymmetric detonation wave front, liner collapse phenomenon
Pages: 259-267

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 general-form 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 closed-form 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 off-axis 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.

Effect of Ion Slip on the Time-Varying Hartmann Flow of a Non-Newtonian Viscoelastic Fluid with Heat Transfer

H. A. Attia, M. A. M. Abdeen
Keywords: MHD flow, heat transfer, non-Newtonian, viscoelastic, electrically conducting fluids, Hall current, ion slip, porous plates
Pages: 268-276

Abstract >>
Ion slip in a time-varying Hartmann flow of a conducting incompressible non-Newtonian 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.

Propagation of Harmonic Perturbations in a Thermoelastic Medium with Heat Relaxation

M. B. Babenkov
Keywords: hyperbolic thermoelasticity theory, MaxwellCattaneo law, heat-flux relaxation, wave transport of heat, second sound
Pages: 277-286

Abstract >>
The propagation of plane harmonic waves in a thermoelastic medium with heat-flux 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.

Cosserat Spectrum of the First Boundary-Value Problem of Elasticity

S. D. Algazin
Keywords: Cosserat spectrum, eigenvalue problem, numerical algorithm without saturation
Pages: 287-294

Abstract >>
The three-dimensional problem of calculating the Cosserat spectrum of the first boundary-value 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.

Modeling ElasticInelastic Processes in Shape Memory Alloys at Finite Deformations

A. A. Rogovoi, O. S. Stolbova
Keywords: finite strain, shape memory, coupled problem
Pages: 295-307

Abstract >>
An equation of state for a shape memory alloy is derived using a formalized approach to the construction of finite-deformation constitutive equations for complex media. The obtained equations were tested for coupled elastic–inelastic boundary-value problems of deformation of a sample of a shape-memory during forward and reverse martensitic transformations.

Construction of Fracture Diagrams for Plates with a Crack-Like Cut with the Use of Necessary and Sufficient Criteria

M. M. Shakirtov, A. P. Shabanov, V. M. Kornev
Keywords: crack-like cut, fracture diagrams, plastic zones
Pages: 308-314

Abstract >>
The process of tension of a plate with a narrow crack-like cut whose vertices form finite-radius semi-circumferences 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.

Computational and Experimental Study of the Fracture of a Brittle Material with an Elliptical Notch under Compression

S. V. Suknev
Keywords: fracture, geomaterials, scale effect, stress concentration, notch, nonlocal fracture criteria
Pages: 315-321

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.

Problem of Equilibrium of the Timoshenko Plate Containing a Crack on the Boundary of an Elastic Inclusion with an Infinite Shear Rigidity

N. P. Lazarev
Keywords: plate, crack, non-penetration condition, variational problem, elastic inclusion
Pages: 322-330

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 KirchhoffLove model. Conditions of mutual non-penetration 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 mid-plane) the elastic inclusion is obtained. A differential formulation of the problem equivalent to the initial variational formulation is given.

Experimental Validation of the Spectral Criterion for the Diagnosis of Periodic Rod Structures using Ferroelectric Strain Gauges

Yu. V. Esipov
Keywords: complex structures, stress indices, strain oscillations, Fourier transform, nonlinear dynamics, ferroelectric gauges
Pages: 331-336

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 ultra-wideband (102÷108 Hz) ferroelectric microgauges based on thin Pb(Zr0.53Ti0.47)O3 films 2 mm in thickness with a 0.8 mm2 contact area.

Effect of Shielding of a Part of the Casing of a Technological Explosion Chamber on its Stress State

A. A. Pikarevskii, O. I. Stoyanovskii
Keywords: explosion chamber, strain measurement, equivalent stresses, logarithmic decrement, damping parameter
Pages: 337-342

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.