Modeling the dynamics of colliding particles in a turbulent shear flow

A kinetic model for the probability density function (PDF) of the particle velocity in a turbulent flow with account for particle collisions is presented. The model is tested by comparison with the results of a numerical experiment for a nonstationary homogeneous shear layer. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 105–112, July–August, 1998. The study received financial support from the International Science Foundation INTAS (project No. 94-4348) and the Russian Foundation for Basic Research (project No. 97-01-00398).     

Two-dimensional instability of a tangential discontinuity in dispersive media

The instability of a tangential discontinuity in a compressible dispersive medium with respect to small two-dimensional perturbations is demonstrated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 16–23, January–February, 1997. The work was carried out with support from the Russian Foundation for Fundamental Research (project No. 96-01-01340).     

Exact solution of the system of equations of the second-order kinetic moments for a two-scale homoenergetic affine monatomic gas flow

The exact solution of the system of equations for the second-order kinetic moments (stresses) is investigated for a flow with two microscales when an unsteady shear flow is superimposed on a one-dimensional unsteady gas flow.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 156–166, May–June, 1995.The work was carried out with financial support from the Russian Foundation for Fundamental Research (project No. 93-013-16407).     

Aerosol aspiration into a tube from a calm medium

The problem of aerosol aspiration into a thin-walled tube from a calm medium is solved. The dependence of the aspiration coefficient on the Stokes number and the steady-state settling velocity is investigated. The results obtained are compared with the calculations [1, 2] and the experimental formula [3]. Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 104–109, March–April, 2000. The work received financial support from the Russian Foundation for Basic Research (project No. 96-01-00111).     

Flow of fluids with substantially different mobilities through a porous medium in the presence of phase transitions: Boundary layer phenomena, spatial phase structures, and instability of the flow

A model of flow through a porous medium with phase transitions which permits an efficient qualitative investigation is proposed for two fluids with sharply different (high-contrast) mobilities. It is shown that the model problem of flow toward a unit sink is singularly perturbed and can be solved using analytic asymptotic matching methods. The nature of the singularity is associated with violation of the condition of the flow contrast in certain zones. The solution can be unstable depending on the direction of interphase mass transfer and the zone in which the process takes place. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 124–135, March–April, 2000. The work was carried out with support from the European Foundation INTAS (grant No. 94-4367) and the Russian Foundation for Basic Research (project No. 95-01-01179a).     

Effect of hall dispersion on the propagation of linear waves in isotropic-pressure magnetohydrodynamics

The effect of finite Hall dispersion on the propagation of linear waves is studied within the framework of isotropic magnetohydrodynamics. It is shown that the presence of finite dispersion does not lead to instability of the uniform plasma state. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 205–206, May–June, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 94-01-01383).     

Nonlinear regimes of convection of an elasticoviscous fluid in a closed cavity heated from below

The two-dimensional thermal convection of a elasticoviscous fluid in a horizontal cylinder with a square cross-section heated from below is investigated. For describing the rheological properties of the fluid the Oldroyd model with the upper convective derivative is used. The investigation is carried out numerically using the finite-difference method. The instability limits of mechanical equilibrium with respect to monotonic and oscillatory perturbations are determined. Supercritical convection regimes are investigated numerically. Perm. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 5–11, July–August, 2000. This work was carried out with financial support from the Program of State Financial Support for Leading Science Schools (grant No. 96-15-96084).     

Stability of a spanwise nonuniform boundary layer flow

The linear stability of a boundary layer flow with a spanwise-periodic nonuniformity in the velocity profile is investigated. This flow can be considered as a model of a streaky structure occurring in the boundary layer at a high freestream turbulence level. It is shown that for a small nonuniformity amplitude symmetric modes similar to Tollmien-Schlichting waves are the most unstable. At higher nonuniformity amplitudes, antisymmetric modes, qualitatively different from Tollmien-Schlichting waves and having a larger phase velocity, are the most amplified. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 54–63, November–December, 1998. The study was carried out with the support of the International Scientific and Technical Center (project No. 199-95) and the Russian Foundation for Basic Research (project No. 95-01-01201a).     

Particle interaction in a flow with a parabolic velocity profile

The hydrodynamic interaction of two rigid spherical particles in a viscous incompressible fluid with the velocity at infinity represented by a second-degree polynomial in the coordinates is considered. An analytical solution of the problem is suggested. The forces and torques exerted on the particles and also the linear and angular particle velocities are calculated. The results are compared with previous theoretical and experimental data. Saransk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 84–91, January–February, 2000. The work received financial support from the Russian Foundation for Basic Research (project No. 98-01-03295).     

Resonant interactions of two waves in a model of a two-layer fluid

The behavior of long-wave perturbations on the interface between two layers of different fluids with interfacial interaction taken into account, which can be described by the quasiperiodic solutions of a pseudodifferential equation, is considered. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 92–98, January–February, 2000. The work was supported financially by the Russian Foundation for Basic Research (project No. 96-01-01766) and by the Siberian Branch of the Russian Academy of Sciences (project No. IG-43-97).     

Relative Controllability in Systems with Pure Delay

A linear control system with pure delay is considered. The integral-form solution of the Cauchy problem is obtained. The relative-controllability problem and the stabilization problem for a pendulum with time delay are solved__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 118–130, February 2005.The study was partially sponsored by the State Committee of Science and Technology of Ukraine (grant No. 01. 07/00081).     

Optimization of the shape of a wing in a hypersonic nonequilibrium gas flow

A variational technique of obtaining the optimal shape of a low-aspect-ratio wing with allowance for the nonequilibrium character of the flow is developed. The technique is applied to the problem of determining optimal wing shapes under terrestrial atmosphere conditions. The real-gas effect on the optimal shapes and maximum lift-drag ratio is studied. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 160–170, March–April, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 96-01-00629).     

Waves ahead of a vertical plate in a channel

The behavior of disturbances propagating with supercritical speed ahead of a plate in a channel is analyzed on the basis of the experimental results obtained by the authors and data taken from the literature. In particular, the transition from smooth to breaking waves has been found to occur at higher propagation speeds than follows from the first approximation of shallow water theory. It has also been found that for waves widely encountered in practice the value of the propagation speed agrees well with the limiting propagation speed of solitary waves obtained on the basis of the complete equations of potential fluid flow. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 82–90, January–February, 1999. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 95-01-01164) and by the Integration Program of the Siberian Branch of the Russian Academy of Sciences under grant No. 97-43.     

An analog of the Bernoulli and Cauchy-Lagrange integrals for a time-dependent vortex flow of an ideal incompressible fluid

An expression with a constant value over all space (including multiply connected domains) relating the pressure function to the square of the velocity and the characteristics of the traveling vortices is derived for a time-dependent ideal incompressible fluid flow with nonzero vorticity. When there are bodies in the flow, they must also be represented in the form of traveling vortices. For steady-state flow the formula obtained goes over into the Bernoulli integral and for time-dependent irrotational flow into the Cauchy-Lagrange integral. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 31–41, January–February, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 98-01-00156 and project No. 96-15-9603 for the support of leading science schools).     

Hydrodynamic interaction of the blade rows in the stator-rotor-stator system of an axial turbomachine

The hydrodynamic interaction of three blade rows (stator, rotor, and stator) of an axial compressor in a subsonic flow is investigated both theoretically and experimentally. It is established that the parameters of the time-dependent rotor flow may significantly depend on the relative peripheral position of the stators. The theoretical and experimental results are compared. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 145–158, May–June, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 96-01-01847) and the USA Civil Research and Development Foundation (grant No. RE1-195).     

Effect of high-frequency vibrations on the stability of advective flow

The stability of plane convective flow in a horizontal layer with a longitudinal temperature gradient under the action of longitudinal vibrations is considered. The behavior of small normal plane and spiral perturbations is investigated. It is shown that the vibrations enhance the stability with respect to almost all types of perturbations. The sole exception is plane thermal waves whose existence domain extends toward low Prandtl numbers. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 16–22, January–February, 1998. The work was supported by the Russian Foundation for Fundamental Research (project No. 94-01-01730).     

Modification of the burnett equations and shock wave structure

Questions of the applicability of simplifying modifications of the Burnett equations are studied with reference to the problem of the shock wave structure in a monatomic gas. As distinct from the complete system of Burnett equations, the order of the systems of modified equations is the same as that of the Navier-Stokes equations, and the equations are stable with respect to shortwave perturbations. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 164–176, May–June, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-01244).     

Modeling of heat transfer in a turbulent flow around a heat-conducting plate with local regions of heating

A solution of the coupled nonstationary boundary-value problem of turbulent flow around a flat heat-conducting plate of finite thickness having local regions with volume heat sources is given. For modeling the heat transfer in the boundary layer, thek-ε turbulence model is used. It is shown that the thermal conductivity of the plate material significantly affects the surface distributions of both temperature and local friction. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 79–86, November–December, 1998. The work received financial support from the International Scientific and Engineering Center (project No.199).     

Determination of the shape of the shocks ahead of a transverse jet injected into a supersonic flow

The three-dimensional shape of the shock wave formed ahead of a sonic jet flowing out into a supersonic flow through the surface of a sharp cone is determined. The shape of the wave in the longitudinal and transverse cross-sections of the model is constructed using schlieren photographs taken for various angles of rotation and freestream Mach numbers M=1.75–3. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 41–44, March–April, 1998. This research was carried out with financial support from the Russian Foundation for Basic Research (project No. 95-01-00709a).     

Incompressibility approximation in magnetohydrodynamics

With reference to the problem of the development of tiring instability in a helical geometry it is shown that, as distinct from traditional gas dynamics, in plasma dynamics the incompressibility approximation cannot generally be used for describing slow flows. This is associated with the fact that several types of disturbances whose interaction results in possible density variations of the order of unity can propagate in plasma. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 145–149, January–February, 1999. The work was carried out with partial support from the Russian Foundation for Basic Research (project No. 96-01-01572) and the German Research Society (DFG).