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.     

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.     

Method of curved bodies in problems of unsteady hypersonic flow past slender bodies

The method of curved bodies involves replacing the unsteady flow past a body by steady flow past a different body obtained from the original body by suitable curvature of its form. The idea of the method was proposed by Vetchinkin in 1918 and was first carried out in [1]. Here the authors started from the assumption that the pressure on the body surface is determined only by its local angle of attack.We know that this method is justified only for circular motion of a slender body with constant velocity within the framework of subsonic or supersonic linearized theory.It will be shown below that the method of curved bodies is rigorously justified for hypersonic unsteady flow past slender pointed bodies within the framework of the law of plane sections, which is often used to study unsteady flows, for example [2, 3]. Here the idea of the method involves the selection of a body of form such that for uniform translational motion its wake in a stationary, normally intersected plane coincides in time with the wake of the original body.The general theory is presented for arbitrary bodies, in particular for bodies of the type of slender oscillating wings, but attention is devoted primarily to the motion of a rigid body of rotation. In this case, in the hypersonic approximation (of the type of [4, 5]) the method also extends to slender blunted bodies.In the general case this method reduces the four-dimensional unsteady problem to a three-dimensional steady problem, which presents no particular difficulty in view of the existence of suitable methods and programs (for example [6]). Here, in contrast with the classical version of the method [1], in the general case the original body is replaced at very moment of time by a one-parameter (with parameter t₀) family of curved bodies.In the case which is most often encountered in practice of slow oscillation of the body surface, when the unsteady component of the solution is small in comparison with the steady compoent, the small-parameter method is used, which allows us to represent the solution in a simple form with an explicit linear dependence on the parameter t₀.The basic notation L body length - ₀ body characteristic relative thickness or angle of attack - ₀ characteristic Strouhal number - r₀ maximal radius of the blunt nose - ,a undisturbed medium density and speed of sound - V and M velocity and Mach number of the center of rotation or of the point x₀ - T₀ characteristic time of the unsteady motion (for example, the period of the oscillation) - T=L/V time for the body to pass a fixed plane - V²p pressure The author wishes to thank A. V. Antonets and Yu. M. Lipnitskii for carrying out the calculations and analyzing their results.     

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.     

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.     

Strong viscous interaction on slender three-dimensional bodies

Hypersonic flow of a viscous gas past axisymmetric power-law bodies in the regime of strong interaction of the laminar boundary layer with the outer inviscid flow was studied in [1, 2]. In this paper the results obtained in [1, 2] are extended to the case of flow past a slender three-dimentional body.     

Investigation of hypersonic three-dimensional flow past blunt bodies within the framework of the parabolized Navier-Stokes equations

The flow of a homogeneous gas in a three-dimensional hypersonic viscous shock layer, which includes the shock wave structure, is examined within the framework of the parabolic approximation of the Navier-Stokes equations. The Navier-Stokes equations are simplified on the basis of the asymptotic analysis carried out in [1], are written in variables of the Dorodnitsyn type [2] and are solved by the method proposed in [3, 4] extended to the case of three-dimensional flows. The flow at zero angle of attack past elliptic paraboloids, two-sheeted hyperboloids and triaxial ellipsoids is calculated. Some results of investigating the flow past such bodies are presented. Flow past a sphere in the analogous approximation was considered in [5], where a comparison was also made with the solution of the complete Navier-Stokes equations [6, 7].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 134–142, July–August, 1987.In conclusion, the authors wish to express their warm thanks to V. V. Lunev and G. A. Tirskii for useful discussion and valuable comments.     

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.     

Experimental modeling of three-dimensional modes of hypersonic flow past cylindrically-blunted bodies

Several sets of experimental studies of the structure of transverse hypersonic flow past blunt bodies (cylinder and truncated wedge) and heat transfer on them are performed in the UT-1M shock tube of the Central Aerohydrodynamics Institute. The purpose of the investigation was to obtain three-dimensional modes of hypersonic flow past the nose surfaces of blunt bodies in an artificially disturbed and nominally uniform flows. The controlled disturbances in the freestream were produced by thin threads pulled over the nozzle exit. In the experiment the flow was visualized using the Töpler method and the heat flux distribution over the cylinder was measured using luminescent temperature transformers. The experiments show that both the flow and the heat transfer in the vicinity of the cylinder nose are very sensitive to vortex disturbances in the oncoming hypersonic flow. In a nominally uniform flow (M_∞ = 8 and Re_∞ = 3160–11670) a steady three-dimensional mode of flow past the nose surface of a blunt wedge could be obtained in the form of a single vortex pair.