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)     

Gas injection from the surface of a triangular plate in a hypersonic flow

The flow formed as a result of gas injection through the permeable surface of a triangular plate is investigated in the regime of strong viscous-inviscid interaction between the hypersonic flow and the laminar boundary layer. The features of the flow past strongly cooled surfaces with the formation of supercritical and subcritical flow regions in the boundary layer are studied. The injected gas distribution ensuring the existence of self-similar solutions in the supercritical flow regions is obtained. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 125–133, January–February, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 96-01-01391).     

Nonstationary secondary flows in spherical layers

An experimental study of the change in secondary flow type at the main flow stability limit is presented. For spheres rotating in the same direction, it is found that the passage from the main flow to a three-dimensional secondary flow occurs via a nonstationary transition regime. The paper continues the study [1] in which the three-dimensional stability limit of the main flow in the space of the governing parameters was found. The stability limit consists of regions with specific types of secondary flows. A scheme of the changes in secondary flow type on crossing these regions is considered. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 201–204, May–June, 1998. The work received financial support from the Russian Foundation for Basic Research (project No.96-01-01340).     

Comparative analysis of turbulence models for calculating a near-wall boundary layer

The integral relations, the algebraic model, and the family of differential turbulence models widely used in theoretical and practical boundary layers studies are considered. The differential turbulence models are analyzed for fully developed incompressible-fluid flow in three regions: the viscous sublayer, the logarithmic layer, and the flow core. Numerical results are compared with analytical and experimental dependences. The numerical results for the boundary layer in a liquid rocket engine (LRE) nozzle, where compressibility, the temperature factor, and flow acceleration are significant, are presented. Recommendations on the applicability of the turbulence models considered are given. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 44–58, January–February, 1998. The work received financial support from the Russian Foundation for Fundamental Research (project No.96-01-00260).     

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).     

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).     

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).     

Numerical analysis of supersonic viscous gas flow past axisymmetric nonpointed bodies

Supersonic viscous homogeneous gas flow past axisymmetric smooth nonpointed bodies is analyzed numerically for widely varying Mach and Reynolds numbers and flow geometry. The initial equations of a viscous shock layer are solved by the stabilization method. The effect of the determining parameters on the flow character and the heat transfer distribution along the surface is analyzed. The accuracy and domain of applicability of several approximate approaches to the solution of the problem are estimated. Tomsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 107–117, January–February, 1999. This research was carried out with financial support from the Russian Foundation for Basic Research (project No. 98-01-00298).     

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).     

Effect of thermal stratification on ekman flow stability

The stability of the Ekman thermally stratified boundary layer simulating the atmospheric boundary layer is studied theoretically. The system of thermohydrodynamic equations is solved in the Boussinesq approximation. Two mechanisms of development of the vortex structures, namely, thermal and dynamic, as well as their interaction, are investigated. It is shown that a sharp boundary on which the flow characteristics change qualitatively exists between various domains of the parameters corresponding to thermal and dynamic instabilities. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 71–76, May–June, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-01118).     

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).     

Supersonic dusty-gas flows with Knudsen effect in interphase momentum exchange

On the basis of the two-continuum model of dilute gas-solid suspensions, the dynamic behavior of inertial particles in supersonic dusty-gas flows past a blunt body is studied for moderate Reynolds numbers, when the Knudsen effect in the interphase momentum exchange is significant. The limits of the inertial particle deposition regime in the space of governing parameters are found numerically under the assumption of the slip and free-molecule flow regimes around particles. As a model problem, the flow structure is obtained for a supersonic dusty-gas point-source flow colliding with a hypersonic flow of pure gas. The calculations performed using the full Lagrangian approach for the near-symmetry-axis region and the free-molecular flow regime around the particles reveal a multi-layer structure of the dispersed-phase density with a sharp accumulation of the particles in some thin regions between the bow and termination shock waves. The project supported by the National Natural Science Foundation of China (90205024), and the Russian Foundation for Basic Research (RFBR grant No. 02-01-00770 and joint RFBR-NSFC grant No. 03-01-39004)     

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).     

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).     

Kinetic model of a collisional admixture in dusty gas and its application to calculating flow past bodies

Using the methods of statistical physics, the basic kinetic equation describing the dynamics of a polydisperse admixture of solid particles in a dilute dusty-gas flow is derived. Particle rotation, inelastic collisions, and interaction with the carrier gas are taken into account. The basic kinetic equation is used to obtain a Boltzmann-type equation for the one-particle distribution function, for which the boundary conditions for the problem of dusty-gas flow past a body are formulated. On the basis of the kinetic model developed, using direct statistical modeling, the flow patterns and the fields of the dispersed-phase macroparameters in a uniform crosswise dusty-gas flow past a cylinder are obtained for various free-stream particle sizes and concentrations. Sankt-Peterburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 81–97, May–June, 2000. The work received financial support from the Russian Foundation for Basic Research (projects 96-01-01467 and 99-01-00674).     

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).     

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).     

Numerical analysis of vortex cell efficiency in laminar and turbulent flows past a circular cylinder with embedded rotating bodies

The effect of flow intensification in small-sized vortex cells on the flow pattern in the near wake downstream of a cylinder and the cylinder drag in laminar and turbulent flows is analyzed on the basis of a numerical simulation of the two-dimensional steady-state flow past a circular cylinder with rotating cylindrical bodies built into the cylinder contour. St. Petersburg, Saratov. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 88–96, July–August, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (projects Nos. 99-01-01115 and 99-01-00772).     

Pulse testing of wells in reservoirs with a nonlinear seepage law

Non-steady-state flows through porous media generated by pulse excitation are studied for flows following obeying a law with a limiting pressure gradient. The phenomena of approach to the steady-state and steady-state hysteresis due to the limiting pressure gradient are investigated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 104–110, May–June, 1998. The study was supported by the Russian Foundation for Basic Research (project No. 96-01-0748).     

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).