Home – Home – Jornals – Journal of Applied Mechanics and Technical Physics 2002 number 1

This paper gives an introduction to
formalization of Galilean-invariant and
thermodynamically consistent equations
of mathematical physics in which
unknowns are transformed in rotations by
irreducible representations of integer
weights. This formalization is based on
the theory of representations of the
group SO(3).

This paper presents a study of the
effect of a magnetic field and variable
viscosity on steady two-dimensional
laminar Darcy forced convection flow
over a flat plate with variable wall
temperature in a porous medium in the
presence of blowing (suction). The fluid
viscosity is assumed to vary as an
inverse linear function of temperature.
The derived fundamental equations on the
assumption of small magnetic Reynolds
number are solved numerically by using
the finite difference method. The
effects of variable viscosity, magnetic
and suction (or injection) parameters on
the velocity and temperature profiles as
well as on the skin-friction and heat-
transfer coefficients were studied. It
is shown that the magnetic field
increases the wall skin-friction while
the heat-transfer rate decreases.

The high velocity oblique collision of
samples of beryllium (beryllium and
stainless steel)was studied
experimentally. The disturbance
amplitudes of beryllium, magnesium,
aluminum, copper, and steel were
compared. It is established that for the
same Mach numbers, the disturbance
amplitude for beryllium is maximal. The
low plasticity and high brittleness of
beryllium determine the nature of
formation of a welded joint. Fusion and
mixing of the metals occur in a very
narrow zone, which practically cannot be
seen in microsections. Under oblique
collision of beryllium and steel, a
solid solution layer of elevated
hardness is attached to the interface.

A wide class of solutions of Euler
equations with quadratic pressure are
described. In Lagrangian coordinates,
these solutions linearize exactly
momentum equations and are characterized
by special initial data: the Jacobian
matrix of the initial velocity field has
constant algebraic invariants. The
equations are integrated using the
method of separation of the time and
Lagrangian coordinates. Time evolution
is defined by elliptic functions. The
solutions have a pole<!dash!>type
singularity at a finite time. A
representation for the velocity vortex
is given.

The paper studies the dynamics of a thin
curved vortex in a potential flow of an
ideal incompressible fluid. The flow is
specified by a number of geometrical
restrictions and does not satisfy the
Biot-Savart law. The form of the derived
equation of the vortex dynamics
coincides with the form of the well-
known equation of local induction for
self-induced vortex motion. The
parameters of the new equation are
simultaneously flow parameters, and in
this sense, they do not show uncertainty
typical of classical equations. The
coefficient of the new equation can take
any specified values not necessarily
much greater than unity, as required
according to the concept of local
induction)and generally is a function of
a natural filament parameter.

A paradox of the blunt edge of an
airfoil in an unsteady ideal flow is
established, which states that the
solution of the nonlinear problem of
unsteady flow around a blunt-edged
airfoil subject to strict boundary
conditions at this edge is physically
meaningless. The paradox is a
consequence of the adopted model of the
unsteady fluid flow near the blunt edge,
which assumes inflection of streamlines.
It is established that the solution of
the problem by local replacement of the
blunt edge by a sharp edge using the
hypothesis on the smoothness of
streamlines near the trailing edge is
physically meaningful.

Simulation was performed of the behavior of a vapor bubble in a liquid under laser irradiation in laboratory experiments. A mathematical model was developed to analyze the effect of heat conduction, diffusion, and mass transfer on the bubble dynamics under compression and expansion. It is found that at the stage of collapse, intense condensation occurs on the bubble wall, which results in a significant (more than 15- fold)decrease in bubble mass and an increase in pressure (to 10⁵ atm)and temperature (to 10⁴ K) Results of numerical calculations of the radius of the first rebound and the amplitude of the divergent shock wave in water are compared with experimental data. It is shown that small (about 1%)additives of an incondensable gas lead to a considerable decrease in mass transfer on the bubble wall.

The complex approach developed
previously for the numerical solution of
problems of optimization and designing
of airfoils is applied to solve the
problem of increasing the lift-to-drag
ratio of subsonic airfoils used.

Self-similar solutions are considered
for the unsteady dynamic-diffusion
boundary layer that forms near a
vertical wall at high Schmidt numbers
and for the dynamic boundary layer
adjacent to the dynamic-diffusion layer
at the inner edge. It is shown that a
countercurrent flow zone forms in the
flow region of the dynamic boundary
layer.

Criteria for evaluating the energy
efficiency of heat addition upstream of
the body in a supersonic gas flow are
obtained. Based on the functional
objectives of flying vehicles and the
thermodynamic model of the process,
estimates are obtained for missile- and
aircraft-type vehicles. The minimum Mach
numbers at which heat addition upstream
of the body is reasonable are evaluated.
The increase in the flight range in the
cruising regime for an aircraft-type
vehicle and on the active trajectory for
a missile-type vehicle is evaluated.
Estimates for fuel economy in launching
an aerospace plane into an Earth orbit
are given. It is shown that a
significant part of the fuel should be
spent on producing energy for gas
heating in order to obtain a noticeable
effect. The minimum necessary
"efficiency" of conversion of the fuel
energy into the gas-heating energy is
evaluated.

The problem is solved using parabolized
equations of stability for three-
dimensional perturbations of a
compressible boundary layer on a flat
plate. Nonlinearity is taken into
account by quadratic terms that are most
significant in estimates of the viscous
critical layer of the stability theory.
These terms are determined by the total
field of two acoustic perturbations, and
the equations become linear and
inhomogeneous. The calculations are
performed for one acoustic wave being
stationary in the reference system
fitted to the plate for Mach numbers
M=2;5. Solutions are presented, which
are identified very accurately with
Tollmien-Schlichting waves at a rather
large distance from the plate edge.

Based on the laws of conservation of
mass, momentum, and energy, equations of
dynamics of multiphase systems, which
are gas mixtures with hollow
microspheres with selectively permeable
shells, are obtained under the
assumption of quasi<!dash!>steadiness of
the process offilling the microspheres
by the gas. Acoustic characteristics of
the system composed of a uniform gas and
hollow permeable microspheres are
studied using a simplified (one-velocity
and one-temperature)model. The frequency
dependences of velocity and damping
coefficient of sound are determined with
regard for gas density
(pressure)relaxation inside the
microspheres. P. 69-75

Results of experimental studies are presented on relaminarization of a supersonic turbulent boundary layer behind an expansion fan for a free- stream Mach number M_∞=4 within a range of Reynolds numbers Re₁ = 8

Disturbances produced by external flow
vorticity in a supersonic boundary layer
are studied. It is shown that both
vortical and nonvortical waves play an
important role. The calculations are
performed for subsonic and supersonic
flows for a Mach number M=2. P. 83-89

Calculation results and an approximate
description of the mean velocity of
vibrational motion in a medium with drag
proportional to velocity are presented
as a function of various parameters
characterizing the system. P. 90-92

Thermal and hydrodynamic processes that
occur during impingement of a liquid
metal drop onto a multilayered substrate
are numerically studied. The
mathematical model is based on the
Navier-Stokes equations for an
incompressible liquid and on substrate
and drop heat-transfer equations that
take into account the surface-tension
forces and metal solidification. The
effect of the impact velocity, initial
drop diameter, metal overheating, and
temperature and thermophysical
characteristics of the substrate on the
morphology of the solid drop, its
height, contact-spot diameter, and total
solidification time was examined
numerically. The simulation results are
found to be in satisfactory agreement
with experimental data. P. 93-102

A model of spontaneous crystallization
of a thin melted metal layer brought
into contact with a massive substrate is
proposed. With invoking the Kolmogorov
composite crystallization theory, the
model allows one to predict the size
distribution of crystallites across the
layer, which provides a possibility of
controlling the microstructure of the
solidifying layer through a proper
choice of substrates. P. 103-108

The paper describes an experimental
study of thermal fluctuations during
transition from bubble to film boiling
of water on a wire heater and
fluctuations of the shape of a
superheated liquid jet discharged from a
high-pressure vessel. It is found that
for a heat-transfer crisis on the wire
heater and for intense volume boiling of
the superheated liquid jet, the
fluctuation power spectrum has a low-
frequency component (flicker noise)that
diverges under the law 1/f. This effect
is due to nonequilibrium phase
transitions in the system<!colon!> the
heat<!dash!>transfer crisis during
transition from bubble to film boiling
and a flow crisis during boiling of the
superheated liquid jet. P. 109-113

A study was performed of methods for
controlling thermal regimes in a spatial
supersonic flow around a blunt body with
the simultaneous use of gas injection
from the surface of the porous bluntness
and heat flow in the shell material. The
effect of the nonisothermicity of the
shell wall on the heat-and mass-transfer
characteristics in the boundary layer
was taken into account by solution of
the problem in a conjugate formulation.
It is shown that heat conducting
materials can be used to advantage to
reduce the maximum temperatures in the
screen zone. P. 114-119

Heat-transfer processes for a supersonic
spatial flow around a spherically
blunted cone were studied by solving
direct and inverse three-dimensional
problems taking into account heat flow
along the longitudinal and
circumferential coordinates. It is shown
that highly heat-conducting materials
can be used to advantage to decrease the
maximum temperatures on the windward
side of streamline bodies. P. 120-127

A modified Neuber

A linearized system of equations
governing elastic deformation of a thin
plate with arbitrary boundary conditions
at its faces in an arbitrary curvilinear
coordinate system is proposed. This
system of equations is the first
approximation of a one-parameter
sequence of equations of two-dimensional
problems obtained from the initial
three-dimensional problem by
approximating unknown functions by
truncated series in Legendre
polynomials. The stability problem of an
infinite plate compressed uniaxially is
solved. The results obtained are
compared with the existing solutions.
P. 133-139

The paper considers a thick-walled long
conical tube from an ideal plastic
material whose inner surface is suddenly
subjected to time-constant, uniformly
distributed pressure or is given a
velocity. An ideal-plastic zone
propagates from the inner conical
surface. It is assumed that the material
of the tube is incompressible in both
the elastic and plastic zones. The
plastic material obeys the
Houber<!ndash!>Mises plasticity
condition. P. 140-146

An asymptotic solution of the contact
problem of an elastic body indented
(without friction) by a circular punch
with a flat base is obtained under the
assumption of a small relative size of
the contact zone. The resulting formulas
involve integral characteristics of the
elastic body, which depend on its shape,
dimensions, fixing conditions, Poisson's
ratio, and location of the punch center.
These quantities have the mechanical
meaning of the coefficients of local
compliance of the elastic body.
Relations that, generally, reduce the
number of independent coefficients in
the asymptotic expansion are obtained on
the basis of the reciprocal theorem.
Some coefficients of local compliance at
the center of an elastic hemisphere are
calculated numerically. The asymptotic
model of an elastic body loaded by a
point force is discussed.
P.147-153

The dynamic strength and deformability of
basalt

The dynamic behavior of thin-wall
members manufactured from materials with
the pyroelectric effect was studied. A
variational formulation of the problem
is used, and a variational principle is
formulated that differs from the well-
known one. Correct boundary-value
problems describing the tension,
compression, and bending of a thin-wall
pyroelectric member are constructed
using the variational principle and a
number of hypotheses on the distribution
of the components of physical fields
along the width of the member. P. 162-
167

The dependence of the propagation
velocity of ultrasonic waves on the
acting stress in plastically deformable
polycrystalline metals and alloys is
examined. The relationship between the
acting stress and the velocity of
ultrasound is found to be linear; this
dependence is typical of all materials
studied. A method is proposed for
determining the time resistance to
breakdown of materials (ultimate
strength)for the case of deformation in
the region of small plastic strains
without failure of the specimens.
P. 168-170

The paper gives an exact formula for determining the intensity of an optical field at the center of a spherical particle of arbitrary radius obtained by evaluating an indeterminate form of the 0/0 type of Mie theory for the electric- field components at the center of the sphere. This formula is valid for arbitrary values of the complex refractive index of the particle material and arbitrary wavelengths of the incident radiation. An approximation for large particles and two approximations for particle sizes less than 10^-4 cm are obtained. The solution obtained for the optical- field intensity at the center of small particles coincides with the classical Lorentz formula for local fields. P. 171-173