Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
28
1&2
2001
Numerical Simulation of Nonlinearly Viscous Fluid Flows in a Two-Dimensional Cavity
1-8
Y. V.
Shlapak
Physical and Technical Research Centre of National Academy of Sciences of Ukraine, Kyiv, Ukraine
A. M.
Gomilko
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The article addresses a problem of determination of a steady flow of nonlinearly viscous incompressible fluid in a two-dimensional cavity with a velocity prescribed over its boundary. The method of augmented Lagrangian and approximation by the finite elements are used to obtain the numerical solution. Numerical simulation of viscous and nonlinearly viscous fluid flows in a square cavity with driving top wall is performed. Results of calculations on the fine mesh allow to describe the eddy structures. Comparison with results in newtonic fluids is given.
Analysis of Two-Dimensional Vortex Structure Interaction
9-18
A. A.
Gourjii
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The analysis of numerical and experimental data of mixing processes of passive impurity under nonsymmetrical interaction (exchange interaction) of two-dimensional vortex structures in fluid stratified on density is carried out. The comparative analysis of experimental data and numerical results shows that the viscous effects during an interaction of vortex structures don't render an appreciable influence on mixing processes during whole interaction. An estimation of a period of time, during which the model of an ideal fluid can be used for studying processes of mixing in real fluids, is given.
Sound Effect on Dynamics and Stability of Fluid Sloshing in Zero-Gravity
19-41
A. N.
Timokha
National Academy of Sciences of Ukraine, Institute of Mathematics, Tereschenkivska 3, 01601 Kiev, Ukraine
I. A.
Lukovsky
National Academy of Sciences of Ukraine, Institute of Mathematics, Tereschenkivska 3, 01601 Kiev, Ukraine
Theoretical study of acoustic interaction affecting the dynamics and stability of limited fluid volume in zero-gravity is carried out. Two main acoustic effects on a fluid surface are analyzed. The first is the change of dynamic characteristics of fluid sloshing in zero-gravity due to acoustic loading; the second is the movement of a "fluid cork" along the tube (acoustic pumping). Mathematical analysis is based on the averaging of original free interface problem. This allows to reduce a free interface problem to a free boundary problem on surface waves with additional nonlinear terms in the dynamic condition on an unknown surface. Nonlinear phenomena are described per structuring a series of analytical and numerical-analytical solutions. These examples concern the cylindrical vessel with gravity vector along the directrix and, hence, comparison of the results with solutions of capillary problem becomes available. The experimental conclusion that acoustic loads can give rise to equilibrium shapes contrasting to capillary surfaces is confirmed. Also the phenomena of acoustic stabilization and destabilization of "fluid-gas" interface are demonstrated including the case when such a destabilization causes the acoustic pumping.
On the Degeneration of Velocity Perturbations in a Stratified Fluid
42-53
V. I.
Nikishov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, 8/4, Zhelyabov St.,
Kyiv, 03057, Ukraine
R. V.
Khristyuk
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
Relationships describing the behaviour of the amplitudes of the velocity perturbations in a stratified fluid are determined by using the multi-scale method. Different steps of the final stage are considered. The decay rates of the various motion types (internal waves, layer and vortical structures) are compared to one another. Critical values of the horizontal scales of perturbations are found. This allows to determine the long-lived perturbations.
Wave Disturbances of Stratified Fluid due to Vertical Jet
54-65
Igor T.
Selezov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Zhelyabov St., 8/4, Kyiv, 03680, MSP, Ukraine
S. G.
Shpakova
Institute of Hydromechanics of National Academy of sciences of Ukraine, Kyiv, Ukraine
P.
Huq
The Graduate College of Marine Stidies Robinson Hall University of Delaware, Newark, USA
The statement and solution of a new problem are presented for fluid wave motions at the injection of vertical axisymmetric jet into a stable stratified fluid, which density linearly increases with the depth. Flow in the jet is assumed to be potential, the motion of stratified fluid is described by Boussinesq's approximation. The dispersion equation is derived and analysed. The conditions of wave existence are found and the analysis of phase and group velocities and wave modes is presented. It is shown that in outer medium the wave disturbances propagate along the jet as it was observed in experiments.
Instability of Two-Dimensional Ventilated Supercavity in a Free Jet
66-78
V. N.
Semenenko
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The mathematical model of the plane unsteady supercavity based on the 2-nd linearized M. Tulin's scheme with infinite wake and finite pressure at infinity is constructed. Stability of the ventilated supercavity in both the infinite stream and the free jet is investigated. Obtained results are in good agreement with both the experimental data on the plane ventilated cavity pulsation and our previous solution based on the 1-st kinematically closed M. Tulin's scheme with singular pressure at infinity.
Flow of Conducting Liquid Caused by a Rotating Magnetic Field
79-89
V. P.
Shamota
Donbass State Academy of Building Industry and Architecture, Makeevka, Ukraine
The flow of a liquid metal caused by a rotating magnetic field in cylindrical vessel of a final length was investigated. The semiempirical "external friction" model was used for description of this flow. The satisfactory agreement of theoretical curve and experimental data at various regimes of this flow was received.
Non-linear Mathematical Model of the Dolphin Tail Fin Motion
90-115
A. V.
Shekhovtsov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
For development of non-linear mathematical model of dolphin tail fin motion an approach based on the double and vortical layers potentials theory, and also on the singular integral equations theory was applied. At that the three-dimensional effects and influence of thickness of the fin, and also of viscosity of the medium was neglected. Using the improved method of discrete vortices a non-linear, non-stationary, two-dimensional numerical model of dolphin tail fin motion, well describing known features of its work was developed. It was revealed, that main mode of dolphin's swimming is characterized with minimal contribution of sucktion force into the thrust.
On Physical Modeling of Noises Generated by Airflow in the Elements of Respiratory System
116-134
I. V.
Vovk
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
O. I.
Vovk
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
We analysed physical and geometric characteristics of larynx and adjacent to it cavities from aerohydromechanic point. Physical model of this part of the respiratory system was built on the basis of this analysis. We developed the experimental methods that allow one to evaluate aerodynamic resistance of the physical model as well as spectra of noise, generated by the airflow along the model. We obtained a vast number of real data. Analysis of this data allowed us to draw a number of important laws. In particular, we showed that aerodynamic resistance of diaphragm, which modells the glottis, depends significantly on shape and dimensions of the last. We found out that as degree of symmetry of the glottis shape decreases and its area increases the aerodynamic resistance of diaphragm falls. It was shown that level and nature of spectra of noise generated by the airflow passing the glottis depends on shape and dimensions of the glottis as well as on airflow speed. In particular, we found that the decrease in symmetry of the glottis shape, increase of its area and decrease of airflow speed result in decrease of integral level of noise generated by the flow.
Nonlinear-Dispersive Model of Surface Wave Transformation in Littoral Zone of Sea Covered With Ice
135-150
V. V.
Yakovlev
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
V. O.
Tkachenko
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The long-wave nonlinear-dispersion model, describing the propagation of flexural-gravitational waves in an elastic plate, floating on a surface of a liquid of variable depth, is constructed. The model takes into account effects of the nonlinear dispersion and inertion, elasticity and geometrical nonlinear deflection of plates. On the basis of the general model the hierarchical sequence of more simple models is developed. This models generalize the known in the water wave theory models of Peregreen, Boussinesq and Korteweg - de Vries for the case of the flexural-gravitational waves. In the particular case of generalized equation of Korteweg - de Vries an exact solution has been obtained. This solution describes the properties of solitons and cnoidal waves in the sea covered with the broken and unbroken ice. It is shown that the flexural-gravitational waves are overturned, in comparison with the long nonlinear water waves. With regard to the solitons it means, that the trough propagates without changes of the surface form, while for the clear water the crest does. The propagation velocity of flexural-gravitational waves decreases with the increase of wave amplitude. Moreover the characteristics of flexural gravitational waves are determined by the wave amplitude and dispersion due to flexural rigidity of the plate and do not depend on water dispersion and inertial properties of the ice cover.
Lie Groups and Scale-Invariant Forms of the Prandtl Equations
151-163
A. A.
Avramenko
Institute of Engineering Thermophysics, National Academy of Sciences of Ukraine, Kiev, Ukraine
Various forms of scale-invariant variables, functions and differential equations, including the generalized Blasius equation, are obtained on a basis of Lie groups. It is shown that form of the general ordinary differential equation is determined by choice of a parametric variable. Using symmetry properties, the generalized Blasius equation is reduced to a first order equation. Two new scale-invariant solutions of the Prandtl equations are obtained. A way of transforming the one-parameter Lie algebra of the Prandtl equations, involving four subalgebras, to an algebra with three subalgebras, one of which is two-parameter subalgebra, is shown.
Pulsating Laminar Flow in a Duct with Easily Penetrable Roughness near Walls
164-172
Ye. A.
Gayev
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
Stabilized motion of a viscous fluid in a long plane duct with the easily penetrable roughness (EPR) over walls (i.e., a layer with a distributed mass force proportional to the local velocity) has been considered under the periodically changing pressure gradient. By means of an analytical solution in complex numbers, distributions of the velocity and shear stress have been plotted across the duct for different time moments with the absence or presence of the EPR. The influence of the EPR on the periodical flow appeared to be drastically dependent on the frequency of pressure changes. Results may be used in pneumatics or hydroautomatics, and in biological fluid mechanics.
Asymptotic Solution of Contact Harmonic Problem for an Impenetrable Stamp on a Poroelastic Base
173-184
A. N.
Trofimchuk
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
A. M.
Gomilko
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
An asymptotic solution is obtained and analyzed for the harmonic contact problem of the oscillations of an impenetrable rigid stamp located on a liquid-saturated poroelastic half-space. When the oscillation frequency tends to zero, efficient contact stress is demonstrated, similarly to the corresponding elasticity theory problem, to have root singularity as the edge of the stamp is approached. In this case, contact porous pressure is a smooth function, and the order of decrease of its amplitude is different, depending on whether or not the viscosity of the filling liquid it taken into account.
Dynamics of a Vortex in an Angular Region and within a Cross Groove
185-195
V. O.
Gorban
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
I. M.
Gorban
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The paper deals with a numerical simulation of behaviour of two-dimensional stationary vortices in the near-wall flow that develops either in an angular region or within a cross groove. The model of ideal incompressible fluid is used. The complex potential of flow is determined by conformal transformation of physical area into the upper half-plane of auxiliary plane. The strength and coordinates of the stationary vortices were obtained against geometrical parameters that characterize the flow area. The stationary vortex was shown to have characteristic eigenfrequency. It corresponds to the frequency of the vortex precession about the stationary point under small departure of the vortex from its equilibrium. Due to eigenfrequency, both the stationary vortex and the local separation zone generated by that respond selectively on periodic perturbations of the free-stream velocity. These external disturbances cause departure of the vortex from its equilibrium. As a result, the vortex moves periodically along a closed trajectory of finite amplitude. Dependence of the amplitude of this motion on the frequency of external perturbations is resonant one. When the frequency of external perturbation is near the vortex eigenfrequency, the amplitude of the vortex motion increases abruptly that leads to intensification of mixing as well as to chaotization of motion in the local circulation zones generated by stationary vortices.
Determination of Soundproofing of Construction Units on Basis of the General Wave Propagation Theory for a Multilayered Media
196-207
L. B.
Lerman
Special Design and Engineering Office of S. P. Timoshenko's Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
A. A.
Tkachenko
Special Design and Engineering Office of S. P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The relations for calculation of soundproofing and the other acoustic characteristics of a planar construction units are presented, obtained from solving the combined problem of acousto-elasticity for a multilayered media. These relations form the basis of the developed technique that is embodied in the computational algorithms and software. The of this technique advantages are illustrated by several numerical examples. Reliability of the obtained results is verified by comparison with the experimental data, including those obtained by authors. The example of synthesis of the multilayered wall, providing the required soundproofing level, is presented.
Hydrodynamic Theory of Brownian Motion in Compressible Fluid
208-223
P. P. Y. M.
Schram
Eindhoven University of Technology, The Netherlands
I. P.
Yakimenko
Bogolyubov Institute for Theoretical Physics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The general analytic solution of the problem of time correlations in the theory of Brownian motion is obtained taking into account the compressibility of fluid and the presence of the harmonic potential. With the help of this solution the criterions for the realization of the diffusion regime on a large time scale have been formulated and the consistent limit procedure on a small time scale has been performed to approach the equilibrium value of the mean square velocity. The full asymptotic expansions have been found for the velocity autocorrelation functions and the mean square displacements of a Brownian particle which describe the so-called persistent correlations in a compressible viscous fluid.
Algebraization of the Medium Acoustic Tomography Problems Based on the Principal Informative Components
224-243
A. Ya.
Kalyuzhny
Scientific and Production Enterprise "Delta", Kyiv, Ukraine
The possibility of improving the efficiency of the solution of acoustic tomography problems is shown in the present article. It is obtained due to the representation of the field of medium parameters to be restored in the finite-dimensional basis of special form. The proposed approach is based on extreme properties of eigenfunctions of the Fisher's information operator. The coordinate basis of medium characteristics field, formed by these functions, provides minimization of a reconstruction error. The existence of the optimal dimension of the basis, which provides maximum precision of measurements at given conditions of acoustic experiment, is established. The criterion of selection of optimal basis functions, which takes into account both the statistical and systematic components of the resulting error, is formulated. A projective approach to the development of the coordinate basis is also proposed. It combines the advantages of a purely physical origin (clearness, economy) and a statistical-informational approach (minimization of errors). The structure of the information operator for the typical models of acoustic signal fields is investigated. The effectiveness of the proposed approach is illustrated by examples from the ocean acoustic tomography.
Effect of Boundaries of Compressible Fluid on Axisymmetric Vibrations of a Spherical Body in a Vessel
244-257
V. D.
Kubenko
S. P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
A. V.
Kuz'ma
S. P. Timoshenko's Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The axisymmetric oscillations of a semi-infinite column of ideal compressible liquid, induced by pulsations and oscillations of a spherical body in a circular cylindrical container, are considered. The potential field is constructed as a combination of series of spherical wave functions and solutions of the Helmholtz equation, taken in the integral form, in the cylindrical coordinates. The boundary-value problem, including the boundary conditions at the spherical surface of the body, rigid cylindrical wall and flat free surface, is reduced to an infinite system of the algebraic equations for coefficients of the expansion. The system is solved using the method of truncation. When constructing the pressure field, the instances of wavelengths, no less than the cavity radius, as well as two first eigenvalues of the wave number are examined in detail. Hydrodynamical forces acting on the body, pulsating near the free surface, are studied. The force values averaged for a period are analyzed. All the results are compared to the available ones for either a half-space filled with compressible fluid or infinite columns of incompressible or compressible liquids.
Displacements of the Elastic Half-Space Surface Caused by Instantaneous Axisymmetric Loading
258-273
A. G.
Kutzenko
Kyiv Taras Shevchenko National University, Ukraine
A. F.
Ulitko
Kyiv Taras Shevchenko National University, Ukraine
Valery
Oliynik
Institute of Hydromechanics of National Academy of Sciences of Ukraine
General approach to solution of axisymmetric problems on instantaneous loading of an elastic half-space is considered in the present article. Mentioned approach is based on the use of the Laplace's transform with respect to time and the Hankel's transform with respect to spatial coordinate. When originating from analysis of the functions-images it became possible to represent the displacements on the surface of half-space as multiple integrals from functions of real variables. Particular types of loads were investigated, namely, the point load (the Lamb's problem), the Hertz's distribution, and the load arising under the smooth plane stamp in the static contact problem. It has been shown that for any distributed normal load, instantly applied to a boundary of half-space, the normal displacements in an observation point become equal to their static values just after the moment when the Rayleigh's wave generated by a most distant point of the load application passes. Also, the singularities were investigated, arising in a displacement field on fronts of the Rayleigh's waves, which move a from boundary of loading zone. Obtained results give the possibility to make conclusions, useful when considering the non-stationary contact problems.
Model Researches of a Spectral-Correlation Characteristics of the Breath Noise in Human Respiratory Tract
274-291
V. V.
Krizhanovskiy
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv
The model researches of a spectral-correlation characteristics of the breath noise in human respiratory channel are held. The researches are conducted using the methods of statistical simulation. On the basis of acoustic model of a respiratory tract, offered in this paper, the estimations of a number of spectral-correlation characteristics of the breath noise are obtained, which are of importance for computer diagnostics of the lung diseases. The utility of the correlation co-processing for data, registered on a neck and thorax, is stated. It is shown, that the outcomes of such co-processing essentially depend on a correlation degree between the sources of the breath noise and on their size and position. The features, describing the correlation degree and the position of the noise sources, is determined. The obtained estimations of the spectral-correlation characteristics are compared with the experimental data. As the result, the best agreement between the model and the experimental data was demonstrated under the hypothesis about a noncorrelatedness of the breath noise sources.
Development of Convection in a Horizontally Non-Homogeneous Flow of Finite Depth
292-299
V. V.
Oleksiuk
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
O. D.
Nikishova
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The development of the thermal convection in a flow with non-homogeneous distribution of the temperature in the horizontal direction is considered. The convective flows that arise due to instability result in the great distortions of the initial distribution of the temperature. The numerical simulation of the development of the convective flows has been accomplished based on the motion equations in Boussinesq approximation by using the finite difference method. The distortions of the temperature distribution in channel current and the length of the section, where the distortions are negligible, have been determined depending on the current parameters. The results of the concrete calculations are presented.