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).     

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).     

Transonic transition behind a shock wave traveling through a dust-gas mixture

The results of investigating shock-wave interaction with a particle cloud on the range of transonic relative velocities are presented. Transition of the two-phase flow from the supersonic to the subsonic regime during phase velocity relaxation under conditions of well-expressed gas-phase nonstationarity was observed. The effect of gas acceleration in the subsonic phase interaction region, previously predicted by the authors on the basis of the accelerating screen model, is confirmed experimentally. The presence of a substantial chaotic component of the particle longitudinal velocity, which indicates close internal phase interactions of the collision type, is demonstrated. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 165–173, July–August, 2000. The work received financial support from the Russian Foundation for Basic Research (project N98-01-00722) and INTAS (project N97-2027).     

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).     

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).     

Propagation of a thermal detonation wave in a water-corium system

The problem of the unsteady propagation of a thermal detonation wave in a high-temperature-melt-water system up to the steady-state regime is considered on the basis of the three-dimensional and three-temperature vapor explosion model. The basic laws of wave evolution are analyzed and the wave structure is studied. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 115–125, July–August, 2000. The work was supported by the Russian Foundation for Basic Research (project No. 98-02-17766) and the International Science and Technology Center (project No. 408).     

Anomalous gravitational instability of mechanical equilibrium during diffusion mixing in isothermal three-component gas mixtures

A theoretical model determining the condition of onset of free gravitational convection in an isothermal ternary gas mixture with inhomogeneous concentrations and stable vertical density stratification (the density is lower at the top than at the bottom) is developed. The model is in satisfactory agreement with the experimental data on the determination of the boundaries between diffusion zones under conditions of mechanical equilibrium and convective mixing in a gravity force field in a vertical capillary connecting two vessels with ternary gas mixtures. Almaty. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 185–192, May–June, 2000. The work was carried out with financial support from the Science Foundation of the Kazakhstan Republic and the Russian Foundation for Basic Research (project No. 98-01-00879).     

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).     

Properties of the nonequilibrium high-velocity “Tails” of the molecular distribution function in plane couette flow of a compressible gas

The results of an analytic and numerical investigation of the properties of the high-velocity “tails” of the distribution function are given for the solution of the BGK model of the kinetic Boltzmann equation for plane Couette flow of a compressible gas. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 183–190, July–August, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00573; grant in support of leading science schools No. 96-15-9603).     

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).     

Modeling of the catalytic properties of high-temperature surface insulation in a dissociated carbon dioxide — Nitrogen mixture

A model of the heterogeneous catalysis of a dissociated carbon dioxide — nitrogen mixture on high-temperature heat-shield coatings is developed; the model takes into account nonequilibrium adsorption-desorption reactions of nitrogen and oxygen atoms and carbon dioxide molecules and their recombination in the Eley-Rideal reactions. On the basis of a comparison of the calculated heat fluxes in dissociated carbon dioxide with those measured on the VGU-4 plasma generator of the Institute for Problems in Mechanics of the RAS, the parameters of the catalysis model in question are chosen for three modern oxidant-resistant coating materials. The performances of these coatings are compared for the conditions of Mars Miniprobe entry into the Martian atmosphere. Their usability for the entry path considered is shown. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 106–116, January–February, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 99-01-00259) and the “Integratisya“ Federal Program (project No. 2.1–414).     

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).     

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).     

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).     

Non-stationary effects in hypersonic nonuniform dusty-gas flow past a blunt body

In the framework of the two-fluid model, a hypersonic flow of a nonuniform dusty gas with low inertial (non-depositing) particles around a blunt body is considered. The particle mass concentration is assumed to be small, so that the effect of particles on the carrier phase is significant only inside the boundary layer where the particles accumulate. Stepshaped and harmonic nonuniformities of the particle concentration ahead of the bow shock wave are considered and the corresponding nonstationary distributions of the particle concentration in the shock layer are studied. On the basis of numerical study of nonstationary two-phase boundary layer equations derived by the matched asymptotic expansion method, the effects of free-stream particle concentration nonuniformities on the thermal flux, and the friction coefficient in the neighborhood of stagnation point are investigated, in particular, the most “dangerous” nonuniformity periods are found. The project supported by the Russian Foundation for Basic Research (project No. 96-01-00313) and the National Natural Science Foundation of China (joint RFBR-NSFC grant No. 96-01-00017c)     

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).     

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).     

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).     

Stability of a fluid interface under tangential vibrations

The stability of the interface between two immiscible fluids of different density which occupy a plane horizontal layer performing harmonic horizontal oscillations is considered. Within the framework of the ideal fluid model a transformation reducing the problem of small plane perturbations to the Mathieu equation is found. Resonance instability domains associated with the formation of capillary-gravitational waves are investigated. A model which takes into account dissipation processes due to the presence of viscous friction is constructed. The role of the viscous dissipation in suppressing resonance instability is discussed. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 25–31, May–June, 1998. The work was carried out with partial support from the Russian Foundation for Basic Research (project No. 95-01-00386).     

Observation of standing waves of large amplitude in harmonic Faraday resonance

Stationary two-dimensional gravity waves on the free surface of a homogeneous fluid in a rectangular vessel in the presence of vertical oscillations excited in harmonic Faraday resonance with identical frequencies are investigated. For the second mode, the dependence of the amplitude on the excitation frequency is found and the wave profiles are obtained. The experimental results are compared with the theoretical model. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 185–188, January–February, 2000. The work was supported by the Russian Foundation for Basic Research (project No. 99-01-01080) and CONACYT (Mexico, Catedra Patrimonial, S. Ya. Sekerzh-Zen’kovich, Ref. 489100-2, Exp. 950060).