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Journal of Applied Mechanics and Technical Physics

2012 year, number 3

On the Mechanism of Reverse Motion of a Cathode Spot

V. A. Pavlov
Keywords: vacuum arc, cathode spot, reverse motion
Pages: 3-10

Abstract >>
The mechanism of reverse motion of a vacuum arc cathode spot in an external magnetic field is explained based on a description the spot and its surroundings as a localized set of slow magnetosonic waves. Reverse motion of this plasma perturbation results from the anomalous dispersion property of slow magnetosonic waves. The transverse displacement component of the cathode spot is oriented in the direction of transverse motion of the total energy flux. The proposed mechanism can be one of the competing mechanisms of reverse motion and can be used to construct new models for the reverse motion of cathode spots.

Numerical Simulation of Interaction of Deformable Gas-Permeable Packets of Grids with Shock Waves

E. G. Glazova, A. V. Kochetkov
Keywords: metallic grids, interpenetrating continua, elastoplastic deformation, explosion, Godunov scheme
Pages: 11-19

Abstract >>
A mathematical model that describes a one-dimensional approximation of interrelated processes of unsteady deformation of plane, cylindrical, and spherical packets of metallic woven grids and wave processes in the gas contained in pores is presented. Nonlinear equations of dynamics of two interpenetrating continua are solved numerically with the use of a modified Godunov scheme. Solutions of problems of the shock wave impact on plane and cylindrical packets of grids are obtained. Numerical results are found to agree with available experimental data. The character of explosive waves passing through a cylindrical packet of grids is studied.

Nucleation and Growth of a Gas Bubble in Magma

M. N. Davydov
Keywords: explosive volcanic eruption, decompression, bubble dynamics, viscosity
Pages: 20-29

Abstract >>
The dynamics of a "collective" gas bubble in the magma melt during its decompression was numerically studied on the basis of a complete mathematical models of an explosive volcanic eruption. It is shown that the bubble size distribution obtained for the nucleation process has one peak, which allows considering a "collective" bubble. The main stages of bubble growth due to gas diffusion and changes in the viscosity of the medium are determined. It is shown that the high viscosity of the melt makes possible the transition from the Rayleigh equation to a simpler relation for the radial velocity of the bubble.

Effect of Distributed Gas Injection on Aerodynamic Characteristics of a Body of Revolution in a Supersonic Flow

V. M. Fomin, V. I. Zapryagaev, A. V. Lokotko, V. F. Volkov
Keywords: supersonic flow, body of revolution, nose cone, gas-permeable porous material, drag coefficient
Pages: 30-37

Abstract >>
Results of experimental and numerical investigations of the effect of gas injection through a permeable porous surface on the drag coefficient of a cone-cylinder body of revolution in a supersonic flow with the Mach number range Mh = 3-6 are presented. It is demonstrated that gas injection through a porous nose cone with gas flow rates being 6-8% of the free-stream flow rate in the mid-section leads to a decrease in the drag coefficient approximately by 5-7%. The contributions of the decrease in the drag force acting on the model forebody and of the increase in the base pressure to the total drag reduction are approximately identical. Gas injection through a porous base surface with the flow rate approximately equal to 1% leads to a threefold increase in the base pressure and to a decrease in the drag coefficient. Gas injection through a porous base surface with the flow rate approximately equal to 5% gives rise to a supersonic flow zone in the base region.

Control of Disturbances of a Hypersonic Viscous Shock Layer on a Flat Plate

S. V. Kirilovskiy, T. V. Poplavskaya, I. S. Tsyryulnikov
Keywords: hypersonic flow, receptivity of the shock layer, direct numerical simulation, Navier-Stokes equations, control of disturbances
Pages: 38-47

Abstract >>
Receptivity of a viscous shock layer on a flat plate aligned at an angle of attack to external multiwave acoustic perturbations is studied. It is shown that external acoustic waves and periodic controlled perturbations introduced from the surface of the plate mounted at an angle of attack smaller than 20o generate entropy-vortex disturbances with a similar spatial distribution in the viscous shock layer. This result allows numerical implementation of the interference method of controlling disturbances generated in the viscous shock layer on the plate by external acoustic waves at one frequency and at a spectrum of frequencies by introducing blowing-suction perturbations on the plate surface with appropriate amplitudes and phases.

Filtration Model of Longitudinal Flow in a Finned Cylindrical Channel

E. V. Mosina, I. V. Chernyshev
Keywords: finned channel, filtration approximation, Brinkman equation, effective permeability, drag coefficient
Pages: 48-55

Abstract >>
The problem of laminar flow of a viscous incompressible fluid in a finned circular tube is considered. A solution is obtained in the form of series in eigenfunctions of the Laplace operator; the coefficients in the series are found numerically. For the same problem, a simpler filtration approximation is proposed in which the system of fins is modeled by a radially inhomogeneous porous layer, and fluid flow in it is described by the Brinkman equation. A formula for the effective permeability of the porous medium is obtained by varying the number and height of fins. The formula provides an accurate evaluation of the mean flow velocity and viscous drag coefficient
in finned channels.

Three-Dimensional Divergent Waves on a Model Viscoelastic Coating in a Potential Incompressible Fluid Flow

V. P. Reutov, G. V. Rybushkina
Keywords: viscoelastic coatings, hydrodynamic instability, wave divergence, three-dimensional structures
Pages: 56-67

Abstract >>
Generation of three-dimensional nonlinear waves on a model viscoelastic coating in a potential flow of an incompressible fluid is studied. Periodic nonlinear waves enhanced by the development of quasi-static instability (wave divergence) are considered. The coating is modeled by a flexible flat plate supported by a distributed nonlinearly-elastic spring foundation. Plate flexure is described on the basis of the Karman equations of the theory of thin plates. Perturbations of surface pressure in the potential flow are found in the small slope approximation to an accuracy to terms of the second order of smallness. Numerical simulation reveals a jump-like transition from two-dimensional nonlinear waves to three-dimensional wave structures, which are also observed in experiments.

Oil Recovery in the Presence of Microbubbles in the Filtration Flow

D. N. Mikhailov
Keywords: porous medium, oil reservoir, microbubbles, partial degassing, water-alternating-gas injection, indicator curve
Pages: 68-83

Abstract >>
This paper presents mathematical models for oil-gas flow taking into account the various processes due to the formation of gas micronuclei (microbubbles) in oil: slip of oil relative to the walls of the pore channels (gas lubrication), changes in oil viscosity, and motion of microbubles with respect to oil. We consider examples of oil flow in the near-wellbore zone for the case where a reduction in pressure to the saturation pressure leads to the formation of gas microbubbles and micronuclei and examples of the action of a water-gas mixture in the case where oil foams in the contact area with the injected gas, i.e., a finely dispersed mixture of oil and microbubbles is formed. The behavior of indicator curves for an oil well with the formation of microbubbles is simulated, and the effect of microbubbles on the oil recovery factor in a water-alternating-gas injection process is studied.

Numerical Solution of the Coefficient Inverse Problems on Nonstationary Filtration to a Well Intersected by a Hydraulic Fracture

E. R. Badertdinov, I. T. Salim'yanov, M. H. Khairullin, M. N. Shamsiev
Keywords: hydraulic fracture, pressure recovery curve, coefficient inverse problem, reservoir properties
Pages: 84-89

Abstract >>
A computational algorithm is proposed to determine the reservoir and hydraulic fracture properties from the results of nonstationary hydrodynamic studies of vertical wells. The problem of oil flow to a well intersected by a fracture is solved numerically. Averaged permeabilities are used for cells through which the fracture propagates.

Penetration of Fresh Water into Clay Saturated by an Electrolyte (Experiment)

V. I. Pen'kovskii, N. K. Korsakova
Keywords: electrolyte, clay particles, hydration, self-polarization potential, experiment
Pages: 90-98

Abstract >>
Penetration of distilled water into a clay soil sample saturated by a sodium chloride solution is experimentally studied. Changes in filtration characteristics of soil due to penetration of fresh water and swelling of clay particles, as well as due to the action of an electrical field on the replacement process are quantified. It is demonstrated that electrokinetic processes play a key role at the final stage of replacement of the solution by fresh water. Reasons for the emergence of clay self-polarization potentials owing to violation of electrical equilibrium conditions are studied.

Generation of Gas Flows in Symmetric Neutralizer

S. T. Barashkin, M. S. Gadel'shin, B. T. Porodnov
Keywords: cylindrical neutralizers, target, subsonic flow, gas-dynamic parameters, experiment, probability
Pages: 99-104

Abstract >>
This paper presents the results of experimental studies of the lengthwise distribution of the total and static pressure and the total flow of carbon dioxide in symmetrical neutralizers. These distributions are found to depend on the flow regimes and geometrical characteristics of gas injection. It is established that the density of the gas target per unit gas flow rate increases with increasing portion of the gas injected at the center of the neutralizes.

Calculation of Expansion of a Packed Bed of a Disperse Material Subjected to Pulsed Fluidization

A. V. Fedorov, I. A. Fedorchenko, M. S. Vasilishin, A. G. Karpov, O. S. Ivanov
Keywords: fluidization, numerical modeling, experiment, multiphase medium flow
Pages: 105-116

Abstract >>
Pulsed fluidization of a packed bed of a disperse material is studied experimentally and numerically. Mathematical modeling of the process is performed within the framework of the approaches of mechanics of heterogeneous media on the basis of an experimental study of the bed uplift height as a function of the pressure difference in the fluidized bed. A detailed dynamic flow pattern corresponding to one pulse of the experimental setup is obtained numerically, velocity and pressure distributions inside the bed are found, and the maximum height of the bed uplift is determined. The results obtained are demonstrated to be in reasonable agreement with experimental data on the uplift height as a function of the pressure difference.

Finite-Difference Solution of Unsteady Natural Convection Flow Past a Nonisothermal Vertical Cone under the Influence of a Magnetic Field and Thermal Radiation

E. Thandapani, A. R. Ragavan, G. Palani
Keywords: vertical cone, cone apex, magnetohydrodynamics, radiation, finite differences, skin friction
Pages: 117-132

Abstract >>
An analysis is performed to study the heat transfer characteristics of natural convection over a vertical cone under the combined effects of a magnetic field and thermal radiation. The cone surface is subjected to a variable surface temperature. The fluid considered is a gray absorbing/emitting, but non-scattering medium. The boundary layer equations governing the flow are reduced to non-dimensional equations using non-dimensional quantities valid in the free-convection regime. The resulting non-dimensional governing equations are solved by an implicit finite-difference method of the Crank-Nicolson type, which is rapidly convergent and unconditionally stable. Numerical results are obtained for velocity, temperature, local and average skin friction, and local and average Nusselt numbers for various values of parameters occurring in the problem and are presented in the graphical form. Excellent agreement of the results obtained with available data is demonstrated.

Boiling of a Liquid in a Porous Medium under a Pressure Drawdown Influence

V. S. Shagapov, A. R. Nurislamov, A. R. Khabibullina
Keywords: pressure drawdown influence, boiling of liquid, porous medium, self-similar solutions
Pages: 133-143

Abstract >>
The problem of the boiling of a liquid which initially completely saturates a porous medium under a pressure drawdown influence is considered in a planar one-dimensional formulation and a radial self-similar formulation. The influence of the initial state of the medium and pressure drawdown on the filtration boiling process is analyzed. Boiling regimes are identified, and a criterion for distinguishing between these regimes is determined.

Change in the Electrical Resistance of the Friction Zone of Metal Composites with the Addition of a Pb-Sn Melt

V. V. Fadin, M. I. Aleutdinova
Keywords: metal composite, friction in a current collection mode, friction surface, actual contact area, electrical resistance of friction zone
Pages: 144-149

Abstract >>
Volt-ampere characteristics of the sliding zone of steel-base metal composites in a current collection mode are presented. Friction is implemented at a current density of 100 A/cm2 for the cases of absence and presence of a Pb-Sn melt in the friction zone. An elementary model of rough surface contact is proposed to assess the relation between the area occupied by the melt and the current density. It is shown that the addition of molten low-melting metals is an effective way to reduce the electrical resistance of the friction zone of sliding electrical contact.

Quasi-Static Compression and Spreading of an Asymptotically Thin Nonlinear Viscoplastic Layer

D. V. Georgievskii, V. S. Yushutin
Keywords: viscoplastic flow, Bingham material, Prandtl problem, asymptotic expansion, compression, spreading, squeezing
Pages: 150-157

Abstract >>
The problem of quasi-static compression and spreading (squeezing) of a thin viscoplastic layer between approaching absolutely rigid parallel-arranged plates is solved using asymptotic integration methods rapidly developed in recent years in the mechanics of deformable thin bodies. A solution symmetric about the coordinate axes is sought in the same region of the layer as in the classical Prandtl problem. The layer material is characterized by a yield point and a hardening function relating the intensities of the stress and strain rate tensors . The conditions of no-flow and reaching certain values by tangential stresses are imposed on the plate surfaces. The coefficients at the terms of the asymptotic expansions corresponding to the minus first and zero powers of the small geometrical parameter are obtained. An approximate analytical solution in the case of power hardening and large Saint-Venant numbers is given. The physical meaning of the roughness coefficient characterizing the cohesion between the plates and viscoplastic material is discussed.

Nucleation of Cracks in Perforated Solids under Longitudinal Shear

S. M. Guliev
Keywords: perforated solid, prefracture zone, bonds between crack faces
Pages: 158-165

Abstract >>
The problem of fracture mechanics on nucleation of cracks emanating from circular contours of holes of perforated isotropic solids under longitudinal shear is under consideration. The solution of the equilibrium problem of a perforated solid under longitudinal shear with prefracture zones is reduced to solving an infinite algebraic system and a nonlinear singular integrodifferential equation with a kernel of the Cauchy type. Forces in crack nucleation zones are found by solving these equations. The condition of crack emergence is formulated taking into account the criterion of the limiting discontinuity of material displacements.

Chaotic Phase Synchronization of Vibrations of Multilayer Beam Structures

V. A. Krys'ko, M. I. Koch, M. V. Zhigalov, A. V. Krys'ko
Keywords: beam structures, deterministic vibrations, chaotic phase synchronization, wavelet analysis
Pages: 166-175

Abstract >>
Complex deterministic vibrations of a multilayer stack of beams linked only by boundary conditions are considered. A mathematical model of the stack is constructed taking into account the geometric and physical nonlinearities of the beams and the contact interaction of their layers. A method for the study of phase synchronization of vibrations based on wavelet analysis is developed. The influence of boundary conditions for the lower beam and different types of nonlinearity (physical, geometrical, and contact) and their combinations on the character and phase synchronization of vibrations of the multilayer stack of beams is studied.

Crack Front Penetration in Transgranular Cleavage Cracking in an Iron-Silicon Alloy

W. Lu, J. Chen, Y. Qiao
Keywords: grain boundary, fracture resistance, cleavage
Pages: 176-183

Abstract >>
Based on the analysis of the crack trapping effect of cleavage ridges and penetration of crack front segments in an iron-silicon alloy, the distance between break-through points along a high-angle grain boundary is investigated. If the break-through points are close to each other, the crack trapping effect is dominant; otherwise, the grain boundary separation in break-through windows governs the front transmission process. The relationship between the overall grain boundary fracture resistance and the break-through-point distance is quite complex. The minimum grain boundary resistance is achieved when the break-through points are about 2-3 μm apart, which is also influenced by the grain boundary shear strength, the crystallographic toughness and orientation, as well as the crack front profile.

Laboratory Observation of Slow Movements in Rocks

L. B. Zuev, S. A. Barannikova, V. M. Zhigalkin, M. V. Nadezhkin
Keywords: rocks, localized plastic flow, autowaves
Pages: 184-188

Abstract >>
It is established that the development of a localized plastic strain during compression of samples of rocks (sylvinite, marble, and sandstone) deformed by different micromechanisms has an autowave character. It is shown that the velocity of propagation of autowaves arising in the samples under compression is 10-5 to 10-4 m/s (0.3 to 3.0 km/g) and is close to the velocity of slow waves observed in the Earth's crust after earthquakes or rockbursts.