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2002 year, number 4

Exact solutions for evolutionary submodels of gas dynamics

S. V. Golovin
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090
Pages: 493-502

Abstract >>
A new class of exact solutions with
functional arbitrariness describing the
motion of a polytropic gas is
constructed on the basis of invariant
submodels of rank two of the
evolutionary type. In the solutions
obtained, the velocity is a linear
function of some spatial coordinates.
These solutions describe continuous gas
dispersion and the motion with density
collapse at a finite time.

Oscillations of cylinders in a linearly stratified fluid

E. V. Ermanyuk and N. V. Gavrilov
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090
Pages: 503-511

Abstract >>
The paper studies theoretically and
experimentally hydrodynamic loads that
act on horizontally placed cylinders of
rhombic and square cross sections,
oscillating harmonically in a linearly
stratified fluid. An analytical solution
is found with the use of affine
similitude. Hydrodynamic force
coefficients were evaluated
experimentally from Fourier transforms
of records of damped oscillations in a

Waves on the free surface of a two-phase medium

V. A. Barinov and N. N. Butakova
Tymen' State University, Tyumen' 625003
Pages: 512-518

Abstract >>
A boundary-value problem is posed to
determine the wave  motion caused by
propagation of a gravity wave on the
free surface of a layer of a two-phase
medium. The problem is solved
analytically in the linear
approximation. The shape of the free
surface, the phase velocity, and the
frequency and damping factor of the wave
are determined. An example of the
solution of the problem is given.

Interaction of shock waves with a combined discontinuity in two-phase media. 2. Nonequilibrium approximation

A. A. Zhilin and A. V. Fedorov
Institute of Theoretical and Applied Mechanics,
Siberian Division, Russian Academy of Sciences, Novosibirsk 630090
Pages: 519-528

Abstract >>
Interaction of a shock wave and a
motionless combined discontinuity
separating two two-component mixtures
with different initial volume
concentrations is studied on the basis
of numerical simulation of unsteady
processes. The calculations were
performed using a modified method of
"coarse particles" and a high-accuracy
TVD difference scheme adapted to
calculation of two-phase flows. Flow
parameters determined by analytical
dependences coincide with those obtained
by numerical simulation at large times
of the process. Upon interaction of the
shock wave and the combined
discontinuity, the type of the transient
or reflected shock wave may coincide
with or differ from the type of the
incident shock wave. The possibility of
existence of a pressure difference at
the combined discontinuity boundary,
which was earlier predicted
analytically, is confirmed.

Special features of the shock-wave structure in mixtures of gases with disparate molecular masses

G. A. Ruyev, A. V. Fedorov, and V. M. Fomin*
Novosibirsk State University of Architecture and Civil Engineering, Novosibirsk 630008;
*Institute of Theoretical and Applied Mechanics, Siberian Division,
Russian Academy of Sciences, Novosibirsk 630090
Pages: 529-537

Abstract >>
Asymptotic solutions are constructed for
the problem of the shock-wave structure
in mixtures of gases with disparate
molecular masses. The effect of
emergence of a plateau on the density
profile of the light component and
nonmonotonicity of the temperature
profile of the heavy component is
described. Based on a comparison with
calculations of the full model, the
range of applicability of asymptotic
solutions is determined.

Structure of a supersonic jet with varied geometry of the nozzle entrance

V. I. Zapryagaev, A. V. Solotchin, and N. P. Kiselev
Institute of Theoretical and Applied Mechanics,
Siberian Division, Russian Academy of Sciences, Novosibirsk 630090
Pages: 538-543

Abstract >>
The structure of a supersonic
underexpanded low-pressure-ratio jet
exhausted from a nozzle with variable
geometry of the entrance section is
experimentally studied. Total pressure
distributions in the initial cross
sections of the examined jets are
obtained. Based on these distributions,
the coordinates of the mixing-region
boundaries are found. The curvature of
streamlines in the mixing layer within
the first two barrels of an
underexpanded jet is determined. A
dependence generalizing the measurement
results on the curvature of streamlines
in the first barrel of a weakly
underexpanded jet is obtained in
dimensionless coordinates.

Model of a turbulent boundary layer with explicit identification of the coherent generation structure

V. V. Bogolepov, V. A. Zharov, I. I. Lipatov, and Yu. I. Khlopkov*
Central Aerohydrodynamic Institute, Zhukovskii 140180;
*Moscow Physicotechnical Institute, Zhukovskii 140180
Pages: 544-551

Abstract >>
Using the method of moments in the space
of wavenumbers, a class of models of a
developed turbulent flow of an
incompressible fluid in a flat-plate
boundary layer is proposed. The models
are based on an analysis of the Navier

Numerical modeling of flow with chemical reactions in a strong shock wave with approximate allowance for translational nonequilibrium

V. A. Gorelov, M. M. Kuznetsov, and V. L. Yumashev
Central Aerohydrodynamic Institute, Zhukovskii 140180
Pages: 552-560

Abstract >>
The effect of translational nonequilibrium
on the course of chemical reactions in a
shock wave is studied using the "beam

Protective properties of hot-air screens

V. N. Okhitin and S. S. Men'shakov
Bauman Moscow State Technical University, Moscow 107005
Pages: 561-569

Abstract >>
An analytical and numerical study of
protective properties of hot-air screens
is performed for a plane wave with a
triangular profile. The reduction of the
shock-wave pressure behind the screen is
only observed at temperatures higher a
certain critical value; at lower
temperatures, the pressure is higher
than that in a shock wave traveling in
an isothermal gas. With allowance for
real properties of air, an analytical
relation between the critical
temperature of the hot screen and the
incident-wave intensity is obtained.

Rarefied gas flow in a channel with specular-diffuse boundary conditions for arbitrary Knudsen numbers. Onsager relations

A. V. Latyshev and A. A. Yushkanov
Moscow Pedagogical University, Moscow 107005
Pages: 570-575

Abstract >>
The problem of a rarefied gas flow in a
channel for arbitrary Knudsen numbers
has been solved analytically for the
first time in the case where the
scattering of gas molecules on the
channel walls can be described by
specular-diffuse boundary conditions.
The mean free path of gas molecules is
assumed to be constant, i.e., the
collision frequency is proportional to
molecular velocity. The gas moves under
the action of a streamwise temperature
gradient. Exact relations for heat and
mass fluxes and for mean-mass velocity
are obtained. It is shown that the
Onsager relations are valid within the
entire range of Knudsen numbers in the
problem of heat and mass transfer in a
channel. The dependence of heat and mass
fluxes on the Knudsen number (channel
thickness) is analyzed. A comparison
with available results is performed.

Drainage in ground water flow over a screen

V. N. Emikh
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090
Pages: 576-582

Abstract >>
The paper deals with construction and
investigation of a mathematical model
for ground water flow from the earth's
surface over a vertical impermeable
screen with flow interception by a drain
located on the screen surface.

Subgrid modeling of filtration in porous self-similar media

G. A. Kuz'min and O. N. Soboleva*
Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090;
*Institute of Computational Mathematics and Mathematical Geophysics,
Siberian Division, Russian Academy of Sciences, Novosibirsk 630090
Pages: 583-592

Abstract >>
Subgrid modeling of a filtration flow of
a fluid in an inhomogeneous porous
medium is considered. An expression for
the effective permeability coefficient
for the large-scale component of the
flow is derived using the scale-
invariance hypothesis. The model
obtained is verified by numerical
simulation of the complete problem.

Water injection into a geothermal reservoir

V. Sh. Shagapov, U. R. Il'yasov,* and L. A. Nasyrova**
Institute of Mechanics, Ufa Scientific Center, Russian Academy of Sciences, Ufa 450025;
*Sterlitamak State Pedagogical Institute, Sterlitamak 450103;
**Ufa Technological Institute of Service, Ufa 450000
Pages: 593-602

Abstract >>
The previously obtained criterion which
distinguishes water injection regimes
accompanied by vaporization of injected
water or vapor condensation is extended
to the radially symmetric problem. The
effects of cold liquid injection rate
and the initial temperature, pressure,
and capacity of a geothermal reservoir
on hydrodynamic and temperature profiles
are examined.

Modification of Godunov's numerical scheme for solving problems of pulsed loading of soft soils

V. G. Bazhenov and V. L. Kotov
Institute of Mechanics, Nizhnii Novgorod State University,
Nizhnii Novgorod 603950
Pages: 603-611

Abstract >>
This paper considers a modification of
the "predictor" stage of Godunov's
discontinuity decay method for problems
of nonlinear deformation of soft soils.
Soil behavior is described by the
Grigoryan's taking into account
nonlinear diagrams of volumetric
deformation, shear strength, and
plasticity. Assumptions are formulated
that reduce the auxiliary problem of the
decay of a discontinuity in soils to the
well-known problem that has a unique
solution. Examples of numerical
calculations are given.

The effect of strain rate on the character of δ

Yu. V. Grinyaev, N. V. Chertova, and M. A. Chertov
Institute of the Physics of Strength and Materials Science,
Siberian Division, Russian Academy of Sciences, Tomsk 634021
Pages: 612-616

Abstract >>
An equation governing the evolution of
elastic strains (stresses) for a given
strain rate is obtained using the field
theory of defects under the assumption
of uniform defect distribution. Strain
diagrams are constructed by numerical
solution of this equation and
qualitative analysis of the phase
portrait of the corresponding dynamic
system. The effect of strain rate on the
mechanical properties of materials is

Nonlinear deformation and stability of noncircular cylindrical shells under internal pressure and axial compression

L. P. Zheleznov and V. V. Kabanov
Chaplygin Siberian Aviation Institute, Novosibirsk 630051
Pages: 617-621

Abstract >>
Stability analysis of noncircular shells
is performed with allowance for
nonlinear subcritical deformation.
Explicit expressions for the rigid
displacements of elements of noncircular
cylindrical shells are obtained and used
to construct shape functions of an
effective quadrilateral finite element
of natural curvature. A finite-element
algorithm for solving problems of
nonlinear deformation and stability of
shells is developed. Stability problem
of an elliptic cylindrical shell is
considered. The effect of the
ellipticity and subcritical nonlinear
deformation of the shell on the critical
load is studied. Results obtained are
compared with available experimental

Nonlinear laws of dry friction in contact problems of linear theory of elasticity

A. E. Alekseev
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090
Pages: 622-629

Abstract >>
A problem of elastic body deformation
with conditions of dry friction imposed
at the boundary is considered. Various
friction laws are studied, including
linear one-parameter and nonlinear two-
parameter laws. A general view of a
nonlinear function with two constants is
suggested, which determines the friction
force as a function of  normal pressure.
The problem of elastic plate compression
by rough infinite plates for a variety
of friction conditions on the contact
surfaces is solved. The plate equations
are employed, which make it possible to
specify arbitrary conditions on the
front faces without reducing the order
of differential equations. The unknown
boundary of ideal contact zones and
sliding zones is determined. Solutions
obtained by using various friction
conditions on the contact surfaces are

Fracture of spheroplast samples with different types of stress concentrators

E. V. Karpov
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090
Pages: 630-637

Abstract >>
The paper reports results of
experimental studies of stress
concentration in cylindrical samples of
spheroplasts (composites in which the
binder is dianepoxy and the filler is
glass microspheres) with some types of
concentrators and fracture of these
samples under uniaxial compression. We
performed numerical modeling of the

Stressed state near a wedge-shaped twin with a disbalance of densities of twinning dislocations

O. M. Ostrikov
Sukhoi State Technical University, Gomel' 246746, Belarussia
Pages: 638-639

Abstract >>
The influence of disbalance of densities
of twinning dislocations at the
boundaries on the stressed state inside
a wedge-shaped twin, near its top, and
in external regions adjoining the
twinning boundary is studied using a
dislocation model.