Analysis of the thrust characteristics of jet nozzles designed by various methods

A comparative numerical analysis of the thrust characteristics of axisymmetric jet nozzles designed by various methods is carried out. “Extremal“ nozzles designed by variational methods in the absence/presence of internal shocks (I), so-called “truncated“ nozzles with a uniform characteristic (II), and nozzles designed by the method of conjugate circular arcs (III) are considered. A comparison is carried out for both perfect and real gases (in the latter case the boundary layer gas viscosity is taken into account). It is shown that extremal nozzles are the most efficient, while truncated nozzles are somewhat less so. The thrust characteristics of nozzles designed by the method of conjugate circular arcs for both inviscid and viscous flow are inferior to those of extremal nozzles by 0.7–1%. Moscow, Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 152–162, January–February, 2000. The research was carried out with financial support from the Russian Foundation for Basic Research (project No. 99-01-00891).     

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).     

“Non-free” interaction of plane shock waves and the boundary layer in the neighborhood of the leading edge of a plate with slip

The interaction between a normally impinging shock wave and the boundary layer on a plate with slip is studied in the neighborhood of the leading edge using various experimental methods, including special laser technology, to visualize the supersonic conical gas flows. It is found that in the “non-free” interaction, when the leading edge impedes the propagation of the boundary layer separation line upstream, the structure of the disturbed flow is largely identical to that in the developed “free” interaction, but with higher parameter values and gradients in the leading part of the separation zone. The fundamental property of developed separation flows, namely, coincidence of the values of the pressure “plateau” in the separation zone and the pressure behind the oblique shock above the separation zone of the turbulent boundary layer, is conserved. Moscow. e-mail: ostap@inmech.msu.su. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 57–69, May–June, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 97-01-00099).     

One-dimensional mathematical model of the combustion chamber of a hydrogen/air hypersonic ramjet

A mathematical model of the supersonic combustion chamber of a hydrogen/air hypersonic ramjet is proposed. The model is developed on the basis of a “burn-out curve”, that is, the dependence of the combustion efficiency on the longitudinal coordinate and the design features of the chamber. The burn-out curve, which describes the mixing and burning of hydrogen and air, is assumed to be known from previous numerical and experimental studies of these processes under supersonic flow conditions. Other physical and chemical processes which take place in the combustion chamber, such as excitation of internal molecular degrees of freedom, hydrogen and oxygen dissociation, OH and NO formation, etc., are assumed to be equilibrium. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 146–154, January–February, 1997. The work was carried out with the support of the Russian Foundation for Fundamental Research (project No. 93-013-17514).     

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).     

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).     

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).     

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).     

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).     

Nonlocal turbulent transport in a buoyant vortex ring during the ascent of a thermal in a stratified atmosphere

The flow initiated by a hot gas cloud (thermal) in a stratified atmosphere is calculated on the basis of theκ-ε turbulence model and the transport model for the Reynolds stresses and turbulent fluxes and the results obtained are compared The nonlocal nature of the turbulent transport in a vortex ring and its effect on certain flow characteristics are explained In particular, the calculations carried out using the Reynolds stress model show much slower cooling of the temperature-vortex torus than those based calculated on theκ-ε-model Modification of theκ-ε-model to take the effect of curvature of the streamlines approximately into account makes it only partially possible to reproduce the results obtained on the basis of the Reynolds stress model Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 12–20, January–February, 1999. The research was carried out with support from the Russian Foundation for Basic Research (project No. 95-01-00544a).     

Nonequilibrium kinetics of the gas-phase reactions of high-velocity molecules: Description by perturbation methods and simulation by statistical methods

Data on the numerical solution of a system of kinetic Boltzmann equations for a homogeneous multicomponent mixture of reacting gases with molecules of different “colors” that change in the reactions are given. The solution is obtained using a well-known version of the direct statistical simulation (Monte-Carlo) method, namely, the majorant frequency method, under conditions when the molecules belonging to the high-velocity “tails” of the corresponding distribution functions enter into the color change reaction. The properties of the numerical solution are compared with solutions obtained within the framework of the usual perturbation methods. It is shown that to obtain correct solutions over the range of threshold molecular velocities it is necessary to modify substantially the procedure of the perturbation method, while the traditional approach can be used only on the range of thermal particle velocities. Earlier, this was definitely established for distributions of the reacting molecules over their internal degrees of freedom and for the distributions of reactant-molecules participating in a high-threshold reaction. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 176–184, May–June, 2000. The work was carried out with financial support from the Russian Foundation for Fundamental Research (project No. 96-01-00573) and the Government Program for Leading Science Schools (grant No. 96-15-9603).     

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).     

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).     

Type of reflection of a near-wall shock wave in the process of diffraction from a square channel

The results of an experimental and numerical investigation of the process of diffraction of shock waves from a square channel at a ninety-degree convex corner are presented for various incident shock wave Mach numbers M₀ (1.4<M₀<7). The type of reflection of the near-wall fragment of the diffracting shock wave from the wall and the wave velocity are determined as functions of M₀, direction, and time. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 145–151, January–February, 2000. The work was carried out with partial support from the Russian Foundation for Basic Research (project No. 96-02-16170a).     

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).     

Effect of a local stationary flow disturbance on separated boundary layer stability

The separated flow past a transverse barrier on a plate surface is modeled in a wind tunnel. The linear stability of the two-dimensional laminar flow in the separation zone is investigated in the presence of a stationary disturbance imposed on the flow and concentrated in a narrow spanwise region. It is experimentally shown that the local flow nonuniformity leads to a change in the flow stability features, such as the frequencies of the growing oscillations, their growth rate, and the dispersion characteristics. As a result, the transverse velocity gradients induced in the separation zone exert a strong destabilizing influence on the flow. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 174–178, January–February, 2000. The study was carried out with the support of the INTAS Foundation under grant No, 96-2225.     

Properties of hypersonic separated flows at moderate reynolds numbers

The hypersonic rarefied flow past a flat plate with a transverse barrier and past a plate with a bend in the generator (a compression angle) is studied at Reynolds numbers Re≤10⁴. Direct statistical modeling (Monte Carlo method) is used to investigate the characteristics of the separated flow formed on the plate as a function of the Reynolds number, the surface temperature, the barrier dimensions, and the internal degrees of freedom of the molecules. The results obtained are compared with those for analogous high-Re flows. The possibility of using the similarity criteria derived for the continuum flow regime is considered. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 134–144, January–February, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 97-01-00577) and the Program of State Support for Leading Scientific Schools (grant No. 96-15-9606).     

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).     

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).     

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).