Transverse subsonic flow past a cylinder

At around the critical Reynolds number Re = (1.5–4.0)·10⁵ there is an abrupt change in the pattern of transverse subsonic flow past a circular cylinder, and the drag coefficient C_x decreases sharply [1]. A large body of both experimental and computational investigations has now been made into subsonic flow past a cylinder [1–4]. A significant contribution to a deeper understanding of the phenomenon was made by [4], which gives a physical interpretation of a number of theoretical and experimental results obtained in a wide range of Re. Nevertheless, the complicated nonstationary nature of flow past a cylinder with separation and the occurrence of three-dimensional flows when two-dimensional flow is simulated in wind tunnels do not permit one to regard the problem as fully studied. The aim of the present work was to make additional experimental investigations into transverse subsonic flow past a cylinder and, in particular, to study the possible asymmetric stable flow regimes near the critical Reynolds number.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 154–157, March–April, 1980.     

Aerodynamic characteristics of permeable disks at subsonic free-stream flow velocities

A large number of investigations have been carried out to study the aerodynamic characteristics of grids and permeable plates completely covering a pipe section [1]. The theoretical bases of the external aerodynamics of permeable bodies are established in [2], where the concept of a uniformly permeable surface is introduced and the problem of flow past a permeable plate at a small angle of attack is solved. Papers [3, 4] are devoted to the solution of problems of a jet flow of ideal incompressible fluid past a permeable wedge and a plate. The flow past a wedge with a high degree of permeability at low subsonic velocities was investigated theoretically and experimentally in [5]. Papers [6, 7] are devoted to the experimental investigation of the aerodynamic characteristics of plates and disks at low subsonic velocities. The results of the experimental investigations of permeable bodies are given in [8]. In the present paper the aerodynamic characteristics of permeable disks positioned perpendicular to the direction of the oncoming flow are investigated experimentally in a wide range of variation of the perforation parameters and the subsonic free-stream flow velocities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 123–128, July–August, 1986.     

Detached flows past a cylinder with a flat end

In the framework of the Navier-Stokes equations, a numerical solution is found to the problem of longitudinal (axisymmetric) flow of a viscous perfect heat conducting gas past a cylinder with a flat front end at subsonic and transonic velocities of the oncoming flow. The flow in the neighborhood of the corner of the cylinder is investigated and a study made of the occurrence and development of detached flow along the side of the cylinder. Tie heat fluxes to the surface of the cylinder are determined, and the influence of the temperature of the wall of the cylinder on the development of the separation is found. The investigations yield the critical Reynolds number Re₀ for the occurrence of a detached flow as a function of the Mach number of the oncoming flow for the investigated bodies.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 3–10, March–April, 1979.I am grateful to Yu. A. Dem'yanov for discussing the work and for a number of valuable comments.     

Slender axisymmetric cavities in a supersonic flow

Slender axisymmetric cavities in a subsonic flow of compressible fluid were investigated in [1–4]. In [5] a finite-difference method was used to calculate the drag coefficient of a circular cone, near which the shape of the cavity was determined for subsonic, transonic, and supersonic water flows; however, in the supersonic case the entire shape of the cavity was not determined. Here, on the basis of slender body theory an integrodifferential equation is obtained for the profile of the cavity in a supersonic flow. The dependence of the cavity elongation on the cavitation number and the Mach number is determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 179–181, January–February, 1989.     

Calculation of hydrogen-air combustion behind detached shock wave for supersonic flow past a sphere

Many of the published theoretical studies of quasi-one-dimensional flows with combustion have been devoted to combustion in a nozzle, wake, or streamtube behind a normal shock wave [1–6].Recently, considerable interest has developed in the study of two-dimensional problems, specifically, the effective combustion of fuel in a supersonic air stream.In connection with experimental studies of the motion of bodies in combustible gas mixtures using ballistic facilities [7–9], the requirement has arisen for computer calculations of two-dimensional supersonic gas flow past bodies in the presence of combustion.In preceding studies [10–12] the present author has solved the steady-state problem under very simple assumptions concerning the structure of the combustion zone in a detonation wave.In the present paper we obtain a numerical solution of the problem of supersonic hydrogen-air flow past a sphere with account for the nonequilibrium nature of eight chemical reactions. The computations encompass only the subsonic and transonic flow regions.The author thanks G. G. Chernyi for valuable comments during discussion of the article.     

Investigation of heat transfer on models in subsonic jets of an induction plasmatron

The results are given of an investigation of the flow parameters in an induction plasmatron and of heat transfer on water-cooled models in subsonic jets of dissociated air in the range of pressures p = 5·10³–1.0·10⁵ N/m². The obtained experimental data confirm the well-known theoretical conclusion that the catalytic activity of the surface influences the heat fluxes at low pressures when the boundary layer flow is nonequilibrium. The problem of the flow of a subsonic jet of a viscous heat-conducting gas past a model of cylindrical shape with flat end has been solved numerically. The experimental and calculated data are compared.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 6, pp. 129–135, November–December, 1983.We are very grateful to Yu, K. Rulev and V. M. Mysova for assistance in the experiment.     

Parameters determining the shape of the subsonic section of a shock wave in the case of axisymmetric flow

Supersonic flow around a blunt body by an ideal gas with a constant specific heat ratio is considered. The dependence of the geometry of the subsonic section of the shock wave on the shape of the body and the freestream Mach number is studied. Analysis of the large quantity of numerical data has permitted simple approximate relations to be formulated for the principal geometrical parameters of the wave, which can be used for solving the problem of flow around a quite broad class of bodies. The question of the characteristic dimensions in such problems is also discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 77–83, July–August, 1976.In conclusion, the author expresses his thanks to V. N. Ivanova for carrying out the calculations and to é. é. Shnol' for for several useful comments.     

Calculation of supersonic gas flow over a ducted body in regimes with a detached shock wave

Calculations were made of the supersonic flow of an inviscid gas which does not conduct heat over two-dimensional and axisymmetric ducted bodies in regimes with a detached shock wave and completely subsonic gas velocity in the cylindrical duct. The investigated bodies have a pointed leading edge. The flow rate of the gas through the duct is assumed to be given. This corresponds to the presence in the exit section of the duct of a throttle or an impermeable barrier (in which case the flow rate is zero). The numerical algorithm used in the calculations is based on stabilization in time and Godunov's difference scheme [1] with separation of the shock wave. The integrated flow characteristics are given. The values of the wave resistance coefficient obtained in the calculations are compared with the values found using Taganov's approximate approach.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 160–163, May–June, 1981.I thank A. N. Kraiko for regular consultations, Yu. B. Lifshits for a helpful comment, and V. A. Vostretsov for assisting in the work.     

The application of the projection method for constructing the shape of a body with minimum drag

The problem is considered of constructing a semi-infinite axisymmetric body with minimum drag in subsonic flow of an ideal gas. This problem is formulated as the problem of finite-dimensional minimization by prescribing the shape of the body in parametric form and applying the projection method for solving a flow problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 108–113, March–April, 1985.     

Conservation of the resultant force vector in the plane of the angle of attack for slender star-shaped bodies in supersonic flows

At high supersonic flight speeds bodies with a star-shaped transverse and power-law longitudinal contour are optimal from the standpoint of wave drag [1–3]. In most of the subsequent experimental [4–6] and theoretical [6–9] studies only conical star-shaped bodies have been considered. For these bodies in certain flow regimes ascent of the Ferri point has been noted [10]. In [11] the boundary-value problem for elongated star-shaped bodies with a power-law longitudinal contour was solved for the case of supersonic flow. The present paper deals with the flow past these bodies at an angle of attack. It is found that for arbitrary star-shaped bodies with any longitudinal (in particular, conical) profile the aerodynamic forces can be reduced to a wave drag and a lift force, the lateral force on these bodies being equal to zero for any position of the transverse contour.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 135–141, November–December, 1989.     

Aerodynamic equivalence of asymmetric bodies with allowance for nonlinear body shape influence factors and angle of attack

In order to determine the aerodynamic coefficients of asymmetric bodies the principle of aerodynamic equivalence is used. In the gas dynamic function expansions in the asymmetry parameter and the angle of attack both linear and second-order terms are taken into account. This makes it possible to establish theoretically the principle of aerodynamic equivalence with allowance for nonlinear body shape influence factors and angle of attack. A universal structure of the aerodynamic characteristics of asymmetric bodies with an arbitrary cross-sectional shape is obtained. The theoretical conclusions are confirmed by the results of a numerical solution of the three-dimensional gas dynamic problem.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 116–122, November–December, 1993.     

Separated inviscid gas flow past a disk and a body with maximum critical Mach numbers

The problem of the separated axisymmetric subsonic flow of an inviscid perfect gas with the specific heat ratio 1.4 past a disk in accordance with the Riabouchinsky scheme is solved using the method developed in [1]. Formulas relating the main parameters with the base pressure coefficient and the Mach number at the free boundary are presented. Formulas which make it possible to determine the shape of the body of revolution giving the maximum critical Mach numbers are also derived.Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 166–172, May–June, 1996.     

Numerical investigation of gasdynamic features of control jets

Numerical methods, based on first order difference schemes are used to investigate features of three-dimensional subsonic and supersonic flows of an inviscid non-heat-conducting gas in control jets. Elements of the nozzle channels considered are axisymmetric, and flow symmetry arises from the nonaxial feature of the prenozzle volume and the subsonic part of the nozzle, or because of nonaxiality of elements of the supersonic part. In the first case the nozzle includes an asymmetric subsonic region in which reverse-circulatory flow is observed, and in the second case it includes a region of sudden expansion of the supersonic flow from the asymmetric stagnation zone.Translated from Izvestiya Akademii NaukSSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 126–133, November–December, 1978.The authors thank A. N. Kraiko for useful comments and M. Ya. Ivanov for his interest in this work.     

Singularities of supersonic flows around pointed bodies with a detached shock

Results are presented of a numerical investigation of the axisymmetric flow around a family of bodies with a pointing angle for which the shock is detached. It is shown that the supersonic part of the stream remains the same for all bodies of the family for a fixed value of M despite the fact that the shaper of the subsonic zone is related quite strongly to the pointing angle _*. The dependence of the shock standoff and its radius of curvature on the spreading line on the body shape is studied. Effects inherent in flows around sharply pointing bodies are discussed. A dimensionless parameter characterizing each body of the family under consideration is introduced and used to establish general flow regularities. Data illustrating the possibility of applying such parametrization are analyzed for a wider class of pointing bodies.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 111–115, July–August, 1975.     

Influence of nozzle profile on the characteristics of a gas-dynamic laser

The results are given of numerical profiling and analysis of the influence of nozzle shape and the gas-dynamic parameters on the characteristics of gas-dynamic lasers. Investigation of the two-dimensional nonequilbrium flow in a family of similar nozzles and nozzles with different angles of inclination of the contracting part show that it is expedient to choose a shape of the subsonic part that ensures a straight sonic line. Relationships between the geometrical parameters of the subsonic and transonic part of the nozzle are recommended which ensure separationless flow and a shape of the sonic surface that is nearly flat. A parametric investigation was made of the supersonic section of two classes of planar gas-dynamic laser nozzles constructed on the basis of uniform and symmetric characteristics at the exit. The parametric investigations of the influence of the degree of expansion, the total pressure and the temperature, and also the gas composition show that the smallest losses of useful vibrational energy in the cavity are achieved for nozzles constructed on the basis of uniform characteristics.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 163–167, November–December, 1982.     

Flow in the zones of separation of a turbulent boundary layer in front of a subsonic jet injected through a circular nozzle

Flow taking place in the three-dimensional region of separation formed by the interaction of a subsonic stream with a single subsonic jet emerging from a circular hole in a plate perpendicular to the stream is considered. The aim of the investigation is to discover the physical characteristics of the flow in the three-dimensional separation zone in front of a subsonic jet obstacle and to determine the principal laws governing the geometrical and hydrodynamic characteristics of the flow as functions of the parameters of the driving stream and jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 34–41, May–June, 1973.     

Method of determining the aerodynamic coefficients of asymmetric bodies with allowance for nonlinear body shape influence factors

The numerical method proposed makes it possible to determine the aerodynamic coefficients of asymmetric bodies of fairly arbitrary shape (including those with discontinuities of the transverse contour) at small solid angles of attack. The method allows an aerodynamically sound transition from the three-dimensional system of equations of gas dynamics to a two-dimensional system, which considerably simplifies the problem and reduces by an order the machine time required. The method takes into account the nonlinear body shape influence factors, which substantially improves the accuracy of the calculations. The efficiency and accuracy of the method are demonstrated by comparing the results of the calculations with the results of a numerical solution of the three-dimensional problem.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 121–128, March–April, 1992.     

On the center of pressure of a body

It is shown that under conditions of local interaction of a flow with the surface of a body the position of the center of pressure does not depend on the angle of attack or the form of the model of the flow past the body for a large class of configurations including conical, cylindrical, spherical, and flat elements. The problem of finding the shape of conical bodies with unchanged position of the center of pressure in a supersonic flow without slip was formulated by Ostapenko [1], who also found the shape of some such bodies.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 129–133, September–October, 1982.     

Structure of the long-range fields of plane symmetrical subsonic flows

Plane subsonic potential flows near finite and semi-infinite bodies, symmetrical about thex axis directed along the velocity of the incident flow, are considered. The shape of the isolines of the velocity modulus and the angle of velocity vector inclination to the symmetry axis at large distances from the bodies is found. Kazan. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 132–144, May–June, 2000. The work was financially supported by the Russian Foundation for Basic Research (project No. 99-01-00169).     

Boundary-layer development in the initial section of a tube with injection

Results are presented of a theoretical and experimental investigation of turbulent boundarylayer development in the initial section of a tube in the presence of injection. It is hence considered that there is no main flow. Formulas are derived to compute the friction coefficient and the dynamic characteristics of the flow in the hydrodynamic stabilization section for subsonic gas-motion velocities. The proposed method of computation is compared with the results of an experimental investigation.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 56–59, July–August, 1970.