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).     

Stability of a compressible swirling flow in a circular pipe

The stability of an axisymmetric flow of viscous gas in a circular pipe, which models the Burgers vortex in the pipe axis neighborhood, is studied within the linear theory framework. Neutral curves for the most unstable disturbances are calculated. The influence of the characteristic Mach number on the flow stability is investigated. It is shown that for a given model velocity distribution the Mach number affects only the temperature and pressure profiles of the main undisturbed flow. In this case, for the disturbance types considered, as the Mach number increases, the critical Reynolds number corresponding to loss of stability decreases. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 35–41, January–February, 1999. The work received financial support from the Russian Foundation for Basic Research (project No. 96-01-00586).     

Motion of a deformable droplet of magnetic fluid in a rotating magnetic field

The problem of the magnetic field-driven rotation of a magnetic fluid droplet in a viscous nonmagnetic fluid is solved analytically and experimentally. The shape of the droplet and the magnetic fields and velocities of both fluids are calculated in the weak-field approximation. The droplet is flattened for any relations between the parameters of the system. The instability of the axisymmetric shape of the droplet is established experimentally. A result of the instability is a sudden change in the droplet shape from a flattened ellipsoid of revolution to a triaxial ellipsoid elongated in the equatorial plane. The critical magnetic Bond number is determined. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 22–30, January–February, 2000. The work was carried out with the support of the Russian Foundation for Basic Research (project No. 98-01-00182).     

Effect of heat transfer on the plane-channel poiseuille flow of a thermo-viscous fluid

A steady-state plane channel flow of viscous incompressible fluid with no-slip and heat transfer boundary conditions is considered. The flow is induced by a fixed pressure difference and the fluid viscosity depends on the temperature in accordance with a power law. It is shown numerically that the dependence of the Peclet number on the nondimensional pressure difference is not single-valued. An investigation of the solution’s dependence on the Biot number shows that for Biot numbers greater than unity the velocity profile has a point of inflection. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 75–80, March–April, 2000. The work received financial support from the Russian Foundation for Basic Research (project N97-01-00063).     

Supersonic boundary layer on a plate. Comparison of calculation and experiment

For verifying the method of calculating the boundary layer in liquid rocket engine (LRE) nozzles developed by the authors on the basis of a differential three-parameter turbulence model, the boundary layer on a plate in a zero-gradient flow is calculated. Over a wide range of variation of the free-stream Mach number, the temperature factor, and the Reynolds number, based on the momentum thickness of the boundary layer, the calculation agrees satisfactorily with the known experimental data, with respect to both integral and local flow and heat transfer characteristics. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 64–78, November–December, 1998. The work received financial support from the Russian Foundation for Basic Research (project No.96-012-00260).     

Hypersonic flow past a supersonic two-phase source

The interaction of a uniform hypersonic gas flow with a supersonic two-phase gas-particle source is considered. In the symmetry-axis neighborhood between the bow and termination shock waves, an approximate analytical solution for the carrier-phase parameters is found. On the basis of parametric numerical calculations, the behavior of the particle trajectories and the concentration distribution in the shock layers are studied for both continuum and free-molecule flow regimes around the particles. The appearance of regions with multiple intersections of the particle trajectories and the formation of "layer structures" in the particle concentration distributions (particle accumulation regions near the envelopes of the particle trajectories) are indicated. The dependence of the number of the high concentration layers on the governing parameters is studied. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 134–147, May–June, 1998. The work received financial support from the Russian Foundation for Basic Research (project No. 96-01-00313) and the National Foundation for Natural Sciences of China (joint RFBR-NFNS grant No.96-01-00017c).     

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).     

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).     

Charging and coagulation of water aerosols with a small admixture of highly radioactive droplets

The mechanism of electrocoagulation of water aerosols with a small admixture of highly radioactive droplets is examined. A corresponding mathematical model describing the processes of ionization, electrization and coagulation of radioactive water aerosols is developed. The time dependence of the ion concentration and the charge and concentration of the nonradioactive droplets and of the charge and radius of the radioactive droplets is numerically investigated for a number of typical aerosols. It is shown that the electrocoagulation process may lead to an increase in the radius of the droplets from 5–10 to 30–40μm in ≃10⁴ sec ≃3 h and, consequently, may play a significant part in the development of aerosols with a droplet radius of up to 20μm, when gravitational coagulation is unimportant. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 90–96, March–April, 1994.     

Subsonic compressible cavitation flow past a plate at small cavitation numbers

A solution of the problem of symmetric inviscid compressible cavitation flow past a plate at small cavitation numbers is presented. Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 94–104, July–August, 1998. This research was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00111).     

Effect of volume energy supply on swirled flows in a subsonic cocurrent stream

The results of a numerical investigation of the effect of thermal energy supply on a swirling viscous heat-conducting gas flow in a subsonic cocurrent stream are presented. The initial stage of development of the swirling flow in the neighborhood of the vortex axis with constant circulation in the outer flow region is considered for two different distributions of the streamwise velocity vector component which simulate a swirling jet-type flow and a wake flow with a streamwise velocity deficit. The effect of local volume energy supply in the neighborhood of the vortex axis, the circulation of the azimuthal velocity component, and the longitudinal pressure gradient in the inviscid stream on the development of the swirling flow and the process of breakdown of cocurrent vortex flows is investigated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 47–53, November–December, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00586).     

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).     

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).     

Deposition of inertial particles from a turbulent pipe flow

An explicit formula is derived for the rate of deposition of large particles (droplets) on a tube wall in two-phase turbulent flow. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 68–75, March–April, 1998. The work was financially supported by the International scientific foundation INTAS (grant No. 94-4348) and by the Russian Foundation for Fundamental Research (project No. 97-01-00398).     

Two-parameter model of a turbulent flow with a dispersed-particle admixture

Using a two-point probability density function for the particle distribution over velocities and coordinates, a closed model of the particle effect on the turbulent flow characteristics is formulated. The processes of turbulent dissipation and turbulent energy transfer across the spectrum are studied. Different models of two-phase turbulence are compared. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 40–56, July–August, 1998. The work received financial support from INTAS (grant No. 94-4348) and the Russian Foundation for Basic Research (project No. 98-01-00-353).     

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).     

Rarefied flow in a channel and a periodic system of channels

the steady two-dimensional isothermal rarefied flow in a channel formed by two parallel flat plates of finite length is studied on the basis of the numerical solution of a linearized kinetic problem. The channel may either be isolated or constitute a cell of a periodic cascade consisting of zero-thickness plates arranged one above the other. As the channel length increases, the flow in it approaches the asymptotic one-dimensional Poiseuille flow. It is shown that the asymptotic dependence of the gas flow rate on the low Knudsen number corresponding to an infinitely long channel is already attained for a channel of length equal to several channel widths, if the flow rate is referred to the pressure gradient at the middle of the channel rather than to the mean pressure difference at the channel ends. The effect of the boundary conditions imposed on the channel entrance is investigated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 166–175, May–June, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 98-01-00443).     

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).     

Separationless flow past a body of revolution with simultaneous suction and ejection of fluid

The problem of the axisymmetric potential flow past a body of revolution with a channel along the axis in the presence of a recirculation flow zone near the body, first proposed by G. Yu. Stepanov, is solved. Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 14–21, January–February, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 96-01-00123).     

Laminar boundary layer in a flow past an aerofoil with a circular cavity

The paper describes a numerical study of a method of preventing the separation of a laminar boundary layer from the forward section of a symmetric aerofoil, the flow past which does not separate at zero angle of incidence. In order to increase the maximum angle of incidence at which the flow has still not separated, a circular cavity (vortex cell) located almost completely inside the aerofoil is introduced on the segment vulnerable to separation. The asymptotics of the corresponding flow at high Reynolds number are described using the Prandtl-Batchelor model. Krasnodar. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 52–57, March–April, 1998. The work was financially supported by the International Science Foundation (grants M4K000 and M4K300) and by the Russian Foundation for Fundamental Research (project No. 96-01-01290).