Slender bodies of revolution with minimum wave drag in nonequilibrium supersonic flow

We examine the problem of finding the generatrix shape of a body of revolution which travels at supersonic speed and has minimum wave drag. We assume that any number of nonequilibrium processes can take place in the flow. The pressure distribution over the body surface is taken in the linear approximation [1, 2]. A survey of studies using linear theory to find bodies of revolution of optimal form in supersonic perfect gas flow can be found in [3]. The solution of the problem of finding the form of two-dimensional slender bodies of minimum wave drag in nonequilibrium supersonic flow was obtained in [4]. In the following we examine the optimization of only those bodies of revolution for which the leading point lies on the axis of symmetry.The author wishes to thank A. N. Kraiko for his helpful comments.     

Wave drag of slender star-shaped bodies at moderate supersonic flight velocities

At large supersonic flight velocities, star-shaped bodies have a significant advantage over axisymmetric bodies as regards the wave drag [1–3]. The majority of the more recent investigations on star-shaped bodies has been experimental (Conor, Zubin, and Ostapenko have given a review [4]; among the theoretical studies, those of Lapygin and Ostapenko [5–7] should be mentioned), but no new information about the wave drag of star-shaped bodies was obtained in these studies. In the present paper, the wave drag of star-shaped bodies at moderate supersonic flight velocities is considered.     

Investigation of supersonic radiative flow past bodies at low altitudes

The radiative heat transfer problem for bodies traveling through the earth's atmosphere, as formulated in [1, 3], is considered in the case of low altitudes, i.e., for high gas densities and optical thicknesses in the shock layer. These factors require the use of improved methods of calculation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 182–184, May–June, 1991.     

Nonsteady supersonic flow over spiked bodies

In longitudinal supersonic flow over spiked cylinders nonsteady regimes can occur in which a separation zone is periodically generated at the spike, grows vigorously in size, and then vanishes. Several authors [1–6] have investigated the physical pattern of flow with separation zone fluctuations (using shadowgraphs) and have determined the boundaries of existence of the nonsteady regime as a function of the ratio between the spike length and diameter of the cylinder. The authors, however, did not systematically study the dependence of the pulsation frequency on the freestream Mach and Reynolds numbers or on the relative diameter and tip angle of the spike. We have undertaken such an investigation. We are concerned primarily with the influence of the dimensionless parameters on the Strouhal number Sh of the separation zone pulsations at a spike attached to the front of a flat-ended cylinder. Earlier investigations [4–6] have been carried out using motion pictures with film speeds up to 32·10³ frames/sec. In the present study we used high-speed motion pictures with a speed of 6.25· 10⁵ frames/sec. This speed allowed us to determine the precise sequence of phases of the pulsations and their relative durations, as well as the speed at which the boundaries of the separation zone move.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 118–124, September–October, 1976.     

Base pressure of bodies of revolution when gas is blown through their surface into a supersonic flow

One of the most important problems of high-velocity aerodynamics is the investigation of the base pressure and the wake flow behind bodies of revolution under the conditions of surface mass transfer. The present paper reports careful experimental investigations of the flow past bodies of revolution in the presence on their surface of a transverse mass flux, especially at a low blowing intensity. These investigations have yielded new data on the dependence of the base pressure on the main determining parameters, extending and making more accurate the modern picture of the mechanism by which surface mass transfer influences the base pressure and its connection with the state of the boundary layer.     

Conditions of supersonic flow around multiwedge bodies

An experimental study was made of some schemes for flow around multiwedge bodies at supersonic flow velocities. On the basis of data on the distribution of the pressure, on visualization of the flow, and on optical measurements, an analysis was made of the structure of the flow. Zones of breakaway of the flow were observed at the lateral surfaces of the lobes. In the nose part of a multiwedge body there is a three-dimensional configuration of attached plane shock waves, going over into a combined detached nonaxisymmetric wave directed toward the base of the body.     

Vibrations of slender bodies at high angle of attack in supersonic flow

The method of curved bodies [1] is extended to the case of arbitrary angle of attack within the framework of the law of plane sections [2].     

Experimental investigation of boundary-layer transition at supersonic velocities

It is usually assumed that for geometrically similar bodies the state of the boundary layer and the location of the laminar-turbulent transition region are determined by the principal similarity parameters-the Mach M and Reynolds Re numbers. However, it has recently been found that at supersonic velocities the parameter (/U), calculated from the free-stream velocity and viscosity and having the dimension of length, has a considerable influence on the transition.Novosibirsk. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 30–34, March–April, 1972.     

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.     

Hypersonic flow past ducted blunt bodies of revolution

Chernyi [1, 2] has examined the problem of hypersonic flow past a ducted cone with sharp leading edge. In the following we present an analysis of the characteristic features of this problem in the case of a blunt leading edge. We use hypersonic theory for flow past slender bodies with nose blunting of relatively small dimensions [1, 3, 4], based on replacing the nose by a concentrated force and use of the nonsteady analogy. It has been shown in [4, 5] that within the framework of this theory the effect of the violation of the law of plane sections and also the effect of the chemical and physical transformations of the gas in the high-entropy layer is qualitatively equivalent to a change in the drag coefficient of the nose. This approach makes it possible to establish useful similarity laws. The development of these ideas in the direction of the study of the flow structure behind the bow shock wave and analysis of the parameters defining this structure is given in [6–8] in which, in particular, the role of the entropy distribution with respect to the streamlines in the transitional section between the nose and the side surface was clarified and the important practical empirical result was established that this distribution is universal for noses of any form for given flow conditions. In the following these results are extended to blunt bodies of revolution with a duct in the nose. We examine the flow region which is external to the duct under the assumption that the external flow regime corresponds to maximum flow rate through the duct. A characteristic feature of the problem is associated with the additional characteristic linear dimension r₀, which determines the gas mass lost through the duct.     

Properties of two- and three-dimensional separation flows at supersonic velocities

The results are given of experimental investigations into three-dimensional separation of a turbulent boundary layer in the neighborhood of oblique shock waves, wedge-shaped obstacles, and sweptback steps at Mach numbers M = 2, 2.25, 2.5, 3, 4 and Reynolds numbers Re = u/v = (30–36)· 10⁶ m^–1. The characteristic regimes of the separated flows are considered. There is a discussion of the results of comparison and generalization of the pressure distribution in the two- and three-dimensional separation regions, and empirical dependences are also given for determining some geometrical parameters of these regions. An analogy is found in the characteristic pressures, and pressure distribution for a number of two- and three-dimensional separation flows, which suggests that one could use some of the known methods of analysis of two-dimensional separation of a turbulent boundary layer to calculate estimates for the three-dimensional case. This is confirmed by a comparison of calculated and experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–50, May–June, 1979.I am grateful to A. M. Kharitonov and V. S. Dem'yanenko for helpful comments made during the work and for discussion of this paper, and also to V. M. Filatov for assistance in some of the experiments.