Notes on gas–dynamic design of supersonic flying vehicles

It is shown that the lift–to–drag ratio of a thin delta wing is significantly lower than the lift–to–drag ratio of an infinitely long swept plate with an identical lift force. The effect of sweep on a finite wing may be used by excluding disturbances from the leading edge of the wing via introducing a hardened stream surface (wedge) and increasing the wing length. A three–shock waverider is proposed for choosing the optimal parameters. The sharp wedge may be avoided by replacing planar shock waves by a cylindrical shock wave upstream of the blunted wedge. If the leading edge of the wedge is not parallel to the rib that is a source of the expansion wave, a plate with zero wave drag, generating a lift force, may be obtained behind this rib. The system of regularly intersecting shock waves may be applied to design a forward–swept wing.     

Unseparated uniform rotational flow past a plate in a channel

The plane problem of a uniform rotational stream of ideal incompressible fluid flowing past a plate in channel with parallel walls is solved analytically. It is found that there is a unique position of the plate in which in experiences the same lift from rotational and potential streams. In an unbounded rotational stream this statement is valid when the ordinates of the plate's mid-point and the point at infinity where the characteristic velocity of the incoming stream is specified are equal.Cheboksary. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 84–91, November–December, 1994.     

Experimental investigation of the interaction of a shock wave with a magnetic field

We present certain results of an experimental investigation of the propagation of a shock wave S through a magnetohydrodynamic channel of the Faraday type. Under conditions of short circuiting of the induced currents in the supersonic stream that follows the shock wave, we registered the occurrence of a shock front T. The x-t diagrams of the motion of the S and T shock waves in the channel and behind it are determined. For a number of fixed sections in the channel, we have measured the density and degree of ionization of the gas and determined their time dependence. The investigations were performed in argon, and the ionizing shock wave propagated with Mach numbers 12–13. The magnetic field intensity was 1.5 T.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 153–183, May–June, 1971.     

Interaction of a two-dimensional nonstationary gas stream with a free cylindrical body in a channel

The stability of a circular cylinder in an unsteady gas stream is investigated in the case when shock waves are formed and interact in the flow region. The problem is of interest for simulating processes in light-gas mortars [2, 3] in which free bodies are launched by a gas stream [4] and the launching tube will be destroyed if the launched object strikes it at a high velocity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 180–184, March–April, 1981.     

Effect of the Conductance and Thickness of a Conducting Plate on the Signal from a Material–Velocity Inductive Transducer

The perturbation problem of the magnetic field of a constant–current turn located above a conducting plate set into motion by a plane shock wave with a rectangular profile is considered. It is shown that not only the velocity of the plate but also its dynamic conductivity can be determined on the basis of the electromotive force of induction recorded by means of the turn. For the case where the conductance of the plate is known for both the conducting half–space and for a plate whose thickness is comparable with the skin–layer thickness, approximatecalculated dependences for the velocity of the plate are obtained. A comparison with experimental data and the clarification of the calculated dependences allows one to conclude that the approaches proposed can be used for determining the conductance of metals in shock–wave processes.     

Boundary layer in the vicinity of the stagnation point of a body of axial symmetry in a turbulent stream

The flow in the boundary layer in the vicinity of the stagnation point of a flat plate is examined. The outer stream consists of turbulent flow of the jet type, directed normally to the plate. Assumptions concerning the connection between the pulsations in velocity and temperature in the boundary layer and the average parameters chosen on the basis of experimental data made it possible to obtain an isomorphic solution of the boundary layer equations. Equations are obtained for the friction and heat transfer at the wall in the region of gradient flow taking into account the effect of the turbulence of the impinging stream. It is shown that the friction at the wall is insensitive to the turbulence of the impinging stream, while the heat transfer is significantly increased with an increase in the pulsations of the outer flow. These properties are confirmed by the results of experimental studies [1–4].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 83–87, September–October, 1973.     

Shock Compression of a Plate on a Wedged–Shaped Target

Problems of compression of a plate on a wedge–shaped target by a strong shock wave and plate acceleration are studied using the equations of dissipationless hydrodynamics of compressible media. The state of an aluminum plate accelerated or compressed by an aluminum impactor with a velocity of 5—15 km/sec is studied numerically. For a compression regime in which a shaped–charge jet forms, critical values of the wedge angle are obtained beginning with which the shaped–charge jet is in the liquid or solid state and does not contain the boiling liquid. For the jetless regime of shock–wave compression, an approximate solution with an attached shock wave is constructed that takes into account the phase composition of the plate material in the rarefaction wave. The constructed solution is compared with the solution of the original problem. The temperature behind the front of the attached shock wave was found to be considerably (severalfold) higher than the temperature behind the front of the compression wave. The fundamental possibility of initiating a thermonuclear reaction is shown for jetless compression of a plate of deuterium ice by a strong shock wave.     

Influence of a longitudinally compressed elastic plate on the nonstationary wave motion of a homogeneous liquid

In a linear formulation, a study is made of the influence of a longitudinally compressed elastic isotropic plate on the nonstationary wave motion of a stream of homogeneous liquid of finite depth on which the plate floats. The waves are generated by periodic (in time) normal stresses applied to a restricted region of the plate surface and beginning at a certain initial time.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 68–75, September–October, 1980.     

The reflection of a plane shock wave from a body with groove

When a plane shock wave impinges on bodies with grooves and when a supersonic stream of gas flows past such bodies a complicated flow pattern develops. In a number of cases oscillations of the bow wave [1–3] and an anomalous heating of the gas in the groove [4–6] have been observed. Unsteady reflection of shock waves from bodies with grooves and the processes occurring inside the grooves have been investigated comparatively little.Translated from Izvestiya Akademii Nauk SSSR, Hekhanika Zhidkosti 1 Gaza, No. 5, pp. 180–186, September–October, 1935.The authors wish to thank V. I. Ivanov for carrying out the calculations.     

Calculation of three-dimensional boundary layer on a triangular plate of finite length in a hypersonic stream

The results are given of the calculation of a three-dimensional boundary layer on a triangular plate of finite length in a regime of strong viscous interaction with an external hypersonic stream for both symmetric flow as well as in the presence of an angle of slip. The influence of the change in the pressure on the trailing edge of the plate on the boundary layer characteristics is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 46–52, September–October, 1982.     

Interaction between an external compression shock and a blunt body in a hypersonic stream

A complex shock configuration with two triple points can occur during the interaction between an external oblique compression shock and the detached shock ahead of a blunt body (for instance, ahead of a wing or stabilizer edge). This results in the formation of a high-pressure, low-entropy supersonic gas jet [1–6]. Here two flow modes are possible [1], which differ substantially in the intensity of the thermal and dynamic effects of the stream on the blunt body: mode I corresponds to the impact of a supersonic jet [2–6], while the supersonic jet in mode II does not reach the body surface in the domain of shock interaction because of curvature under the effect of a pressure drop. Conditions for the realization of the above-mentioned flow modes are investigated experimentally and theoretically, and an approximate method is proposed to determine the magnitude of the compression shock standoff in the interaction domain. Blunt bodies with plane and cylindrical leading edges are examined. The results of a computation agree satisfactorily with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 97–103, January–February, 1976.The author is grateful to V. V. Lunev for discussing the research and for useful remarks.     

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.     

Cavitation flow around a plate in a channel by a stream of heavy liquid

The nonlinear problem of cavitation flow around a plate by a stream of heavy liquid is investigated in precise formulation; the plate is located on the horizontal floor of a channel when the gravity vector is directed perpendicular to the wall of the channel. Two flow systems are considered-Ryabushinskii's and Kuznetsov's system [1]. This problem was investigated in linear formulation in [2], Similar problems were considered earlier in [3–7] for unrestricted flow. Below, on the basis of a method proposed by Birkhoff [8, 9], all the principal hydrodynamic and geometric characteristics are calculated for the problem being considered.Translated from Ivestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–9, May–June, 1973.     

Calculation of the pressure at the critical point when a shock wave is incident on a body moving with supersonic velocity

The interaction of a shock wave with a blunted body moving with supersonic velocity is considered. It is shown that under certain conditions the reflection pressure at the critical point of the body can be determined on the basis of one-dimensional theory of shock waves. The error due to the application of this theory is investigated. Equations are obtained for the maximum error as asymptotically large values of the number M of the unperturbed stream incident on the body. Conditions under which secondary reflections of the discontinuities at the critical points are possible are analyzed.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 6, pp. 94–101, November–December, 1972.     

Gas dynamics with local energy release in subsonic and supersonic flow

The flows developing in the interaction of a supersonic gas stream with a continuously operating axisymmetric energy release source or as a result of the action of pulsed periodic energy injection on a subsonic gas stream are investigated numerically. For a continuously operating energy source two types of flow can be distinguished: with a shock wave detached from the source and with a shock attached to it. Approximate formulas for the gas density in the center of the energy release zone are obtained for the cases of constantly operating and periodic energy sources.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 142–148, March–April, 1995.     

Slow gas flow around a nonuniformly heated plate

Slow flow of a rarefied gas over a nonuniformly heated plate is investigated numerically. The interaction of the oncoming stream with the flow due to the variable temperature of the gas near the body is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 181–184, September–October, 1981.     

Calculation of the breakaway flow of a flat stream of a nonviscous liquid around bodies

The article gives relationships which, within the framework of the theory of an ideal liquid, permit calculating breakaway flow around bodies of arbitrary form. It gives examples of the calculation, by numerical methods using a digital computer, of the flow of a flat stream around a round cylinder and a flat plate. The results obtained are in agreement with the experimental data in the self-similar region.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 72–82, March–April, 1972.     

On a class of exact particular solutions of the equations of transonic gas flows

The paper presents exact particular solutions of the equations of transonic gas flows, analogous to the solutions derived in [1–3] for the case of short waves. These solutions are used to construct the flow around a body in a supersonic stream with an attached shock.     

Generalization of the blunt-body problem in nonuniform supersonic flowfields

The properties of the steady-state gas flow in the shock layer associated with a blunt body immersed in a supersonic stream with an arbitrary shear-like nonuniformity are studied.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 164–170, March–April, 1996.     

Supersonic flow past a blunt wedge

A study is made of the asymptotic solution of the problem of flow past a blunt wedge by a uniform supersonic stream of perfect gas. By separation of variables it is shown that at large distances the disturbance of the flow is damped exponentially. In the case of subsonic flow behind the shock wave the exponent of the leading correction term in the expansion of the shock front is calculated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–140, July–August, 1984.