Investigation of unsteady supersonic flow past conical bodies

A study is made of the three-dimensional supersonic flow of ideal gas past conical bodies executing harmonic oscillations in the plane of the angle of attack about some angle β₀ in accordance with the law α = α₀ cos ωt, so that the total angle of attack is β = β₀ + α₀ cos ωt.     

Investigation of supersonic three-dimensional flow past pointed axisymmetric bodies

The flow pattern near bodies of revolution with very long cylindrical and pointed nose sections is studied in the framework of an ideal gas model by means of a numerical method based on MacCormack's difference scheme. The existence of internal shock waves, oriented in both the longitudinal and the transverse directions, in the shock layer is established. The variation of the aerodynamic coefficients of the configuration with its length, angle of attack, and free stream Mach number is investigated. The calculated and experimental data are compared, and the connection between the flow parameters on the body surface and the position of the separation line of the boundary layer on its lateral face is established. A method of calculating the influence of the boundary layer on the values of the aerodynamic coefficients of bodies of revolution of large aspect ratio at small angles of attack is proposed. Axisymmetric flow near blunt bodies has been studied in detail in [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 127–133, September–October, 1986.The author expresses his gratitude to A. N. Pokrovskii for his help in calculating the boundary layer parameters on the surfaces of the considered configurations.     

Investigation of transonic and supersonic flow past a pair of bodies

Transonic and supersonic flows past a pair of bodies have been experimentally investigated. The leading bodies were spheres, cylinders, and cones, while the trailing bodies were flat-ended circular cylinders. The leading and trailing bodies were joined by cylindrical rods of various lengths, aligned with the axis of symmetry. For these models, the pattern of flow between the bodies and the Mach number dependence of the drag coefficientC _x were determined in the acceleration and deceleration flow regimes in a wind tunnel. The experimental results are used to analyze the properties of the flow between the bodies and the variation of the aerodynamic coefficients of the models. The reasons for the hysteresis in the behavior of the coefficients in the acceleration and deceleration stages are discussed. The influence of the shape and dimensions of the leading body on the modelC _x is evaluated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 158–164, March–April, 1998.     

Method of calculating supersonic three-dimensional flow past smooth bodies

A method is suggested in [1] for calculating supersonic flow past smooth bodies that uses an analytic approximation of the gasdynamic functions on layers and the method of characteristics for calculating the flow parameters at the nodes of a fixed grid. In the present paper this method is discussed for three-dimensional flows of a perfect gas in general form for cylindrical and spherical coordinate systems; relations are presented for calculating the flow parameters at the layer nodes, results are given for the calculation of the flow for specific bodies, and results are shown for a numerical analysis of the suggested method. Three-dimensional steady flows with plane symmetry are considered. In the relations presented in the article all geometric quantities are referred to the characteristic dimension L, the velocity components u, v, w and the sonic velocitya are referred to the characteristic velocity W, the density is referred to the density of the free stream, and the pressure p is referred to w².     

Study of supersonic flow past axisymmetric bodies of different form

A method is proposed in [1] for calculating supersonic flow past smooth bodies. The present article presents a computational scheme and calculational formulas for determining the gasdynamic functions at the nodes of the lines=const. A comparison is made of certain of the results obtained with the results of other studies [2, 3]. Results are also presented of the calculation of the flow of a perfect gas past ellipsoids of revolution (=2.3) and inverted cones with spherical and ellipsoidal blunting.The author wishes to thank G. F. Telenin for his guidance in the present study.     

Linear theory of supersonic flow past ruled bodies of three-dimensional configuration

The problem of flow past bodies with a ruled surface connecting an n-ray star in the initial section with a circular midsection is solved in a linear formulation with the use of the equation for resistance obtained earlier by the author [1]. Bodies of the investigated class have a substantial advantage in comparison with an equivalent cone and, for not very slender bodies, also in comparison with Kármán's ogival-shaped body. The resistance of the investigated bodies depends little on n.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 94–101, July–August, 1978.     

Numerical investigation of supersonic flow past blunt bodies with protruding spikes

A procedure for the calculation of a supersonic flow of ideal gas near axisymmetric blunt bodies with protruding spikes is developed. The flow past a frustum of a cone with a protruding spherically blunt cylindrical spike as a dependence on the ratio K of the spike length1 to the diameter D of the flat end of the body and the Mach number M of the oncoming flow is studied. Several steady flow regimes are obtained, including the formation of circulation zones and internal shock waves in the shock layer. It is shown that mounting a spike in front of the frustum of a cone can lead to a 40–50% reduction in its drag. A full investigation of the variation of the drag coefficient as a dependence on K is carried out for M = 3.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 119–127, May–June, 1986.The authors express their gratitude to V. A. Levin for the formulation of the problem and his constant attention to the work.     

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).     

The pattern and restructuring of supersonic flow past a pair of bodies

The pattern of symmetric and asymmetric supersonic flow past a pair of isolated/connected bodies is analyzed. Semiempirical dependences of the critical parameterl ^*, determining direct and reverse flow restructuring, on the geometry and permeability of the bodies and the Mach and Reynolds numbers are derived using experimental data. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 158–165, January–February, 1994.     

Magnetohydrodynamic control of supersonic flow past bodies: Possibilities and undesirable effects

Basic problems of super-and hypersonic magnetohydrodynamics (MHD) associated with the determination of the integral characteristics of bodies and vehicles inside which there are systems generating a uniform magnetic field are considered. Three classes of flows, namely, flow in a hypersonic multimode fixed-geometry air-intake; internal and external flow in a model of a hypersonic vehicle containing an air-intake with an MHD generator, a combustion chamber, and a supersonic nozzle; and hypersonic flow past a blunt cone are studied using numerical simulation and theoretical analysis (on the basis of the complete averaged system of Navier-Stokes equations and the electrodynamic equations). Attention is concentrated on the presence of an additionalmagnetic force acting on the system generating themagnetic field and, consequently, on the body and initiating an additional drag (in the case of a vehicle-reducing its thrust). Attractive possibilities for MHD flow control, namely, an increase in the degree of flow compression in the air-intake, a reduction in the ignition length in the combustion chamber, and a decrease in the heat flux to the nose of the body, are noted, as well as negative effects associated with the action of the magnetic force on the bodies considered.     

Experimental investigation of supersonic flow past blunt bodies with strong distributed injection

The entry of bodies into planetary atmospheres at high supersonic velocities is accompanied by intense evaporation of the surface due to radiative heat fluxes. A series of problems involving the conduction of investigations of such kind has been proposed by Petrov. In [1], in particular, the entry of a meteorite into an atmosphere was examined. The gasdynamic aspects of this problem have been approximately simulated by many authors by intense injection of gas in theoretical, e.g., [2–5], and experimental [6, 7] studies. The theoretical studies were based on two-layer [3, 4] or three-layer [5] schemes of gas flow between the shock wave and the surface of the body. The aim of the present work was an experimental investigation of the interaction of injection with a counter supersonic flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 84–95, May–June, 1978.     

Three-dimensional supersonic turbulent flows past conical bodies

The results of the numerical simulation of supersonic three-dimensional flow past sharp-nosed cones with circular and elliptic cross-sections in the turbulent shock-layer flow regime are presented. The calculations are performed in the local conical approximation using the system of Reynolds equations and the differential one-equation turbulence model. The numerical solutions are obtained by means of an implicit constant-direction finite-difference scheme. The emphasis is placed on the investigation of the transverse flow separation and the flow features associated with the turbulent flow regime. St.Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 99–105, January–February, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 99-01-00735).     

Features of flow in the region of the stagnation point in supersonic flow past power-law bodies

Bodies of power-law shape with a generator of the form y=x, 0.5<<1, have at the apex a vertical tangent (like blunt bodies) and infinite curvature (like sharp ones). Supersonic flow past axisymmetric bodies with power-law longitudinal profile has been studied by Radvogin in [1, 2], where on the basis of the analysis of a large quantity of numerical calculations certain empirical laws of similarity were formulated. It follows from these relations that the position and form of the subsonic sector of the shock wave are not determined by the singularity in the body's profile, but by the position on the body of the sonic point and its bluntness in relation to the cone of the critical opening angle. In O. V. Titov's work the results obtained in [1, 2] are confirmed analytically, but here it is assumed that the curvature of the shock wave and the second derivative of the curvature with respect to the longitudinal curvilinear coordinate are finite at the apex. This assumption imposes a limitation on the contour of the body; if it is satisfied, the curvature of the profile past which the flow takes place is also finite. Therefore it is natural to consider the case when this assumption is not made. In this paper we study the flow past bodies of power-law shape with shock waves of infinite curvature at the apex and finite curvature but an infinite second derivative of the curvature with respect to the longitudinal coordinate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 138–142, May–June, 1985.     

Investigation of transonic bounded gas flow past three-dimensional slender bodies

The pressure coefficient distributions induced in the process of a bounded gas flow past a schematized vehicle of the Khotol type are obtained for various transonic regimes in a wind tunnel with a perforated working section as a result of simultaneously solving the boundary-value problems for the near and far flow fields. These distributions are compared with the pressure coefficient distributions in the case of unbounded flow past the body. The additional pressure coefficient induced by the tunnel walls is calculated for subsonic flow past a vehicle in a cylindrical wind tunnel of large radius. The calculation results are consistent with the asymptotic Malmuth theory for subsonic velocities.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 149–158, March–April, 1995.     

Longitudinal oscillations of bodies of revolution and flow at supersonic velocities

The method of aerodynamic derivatives [1–3] can be used for the investigation of the flow around a body executing oscillations with a small amplitude. The characteristics of the flow are expressed in the form of functions which are determined from the solution of the linearized equations of gasdynamics and describe the flow pattern with adequate accuracy. The present article is devoted to the discussion of the results of solution of the general nonstationary problem in nonlinear formulation. Supersonic flows around a hemisphere and a cylindrical front end executing arbitrary harmonic oscillations along the axis of symmetry or experiencing the corresponding oscillations of the flow (turbulent atmosphere) are discussed as examples. The effect of the nonlinearity on the flow pattern is demonstrated for different Strouhal numbers. The results are compared with those of the linear theory and with the results obtained from the solution of the corresponding stationary problems. The solution is obtained by using the characteristic method in form [4].