Effect of energy release in the shock layer on supersonic flight

The presence of an energy release zone in a supersonic stream leads to the formation of perturbations propagated from the source of energy release [1, 2]. The action of such a stream on a body past which it flows is determined by the strength of the source and the configuration and location of the energy release zone. The dependence of the aerodynamic characteristics of a blunt cone on the parameters of the source of energy release is analyzed on the basis of the results of a numerical integration of the equations of motion of the gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 178–182, July–August, 1987.The author wishes to thank V. P. Stulov for his interest in the work and useful suggestions.     

Supersonic flow past weak sources of radiation

In the cited works [1, 2], a study was made of supersonic flow round a source of x-ray radiation by stellar wind. It was found that if the energy release is sufficiently high, a bow shock wave forms in the flow, and a zone of low density and high temperature of the gas arises behind the source. If the influx of energy to the gas is small, the flow remains supersonic everywhere [2]. The question of the formation of a shock wave in the case of weak heating through of the gas by the radiation was not considered in [2]. However, on the basis of the qualitative analogy between supersonic flow past impermeable bodies and radiation sources, one would naturally expect that if the power of the energy release is low a shock wave which does not intersect the axis of symmetry could appear. The following article indicates the conditions under which this actually occurs, and a quantitative analogy is established between supersonic flow past thin bodies and sources of radiation, and the range of flow where such an analogy is absent is also determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 133–136, July–August, 1984.The author thanks V. P. Stulov and M. M. Gilinskii for discussing this work and for their extremely useful comments.     

Blast wave propagation in air from a gaseous charge

In the point explosion problem it is assumed that an instantaneous release of finite energy causing shock wave propagation in the ambient gas occurs at a space point. The results of the solution of the problem of such blasts are contained in [1–4]. This point model is applied for the determination of shock wave parameters when the initial pressure in a sphere of finite radius exceeds the ambient air pressure by 2–3 orders of magnitude. The possibility of such a flow simulation at a certain distance from the charge is shown in papers [4, 5] as applied to the blast of a charge of condensed explosive and in [6, 8] as applied to the expansion of a finite volume of strongly compressed hot gas. In certain practical problems the initial pressure in a volume of finite dimensions exceeds atmospheric pressure by a factor 10–15 only. Such cases arise, for example, in the detonation of gaseous fuel-air mixtures. The present paper considers the problem of shock wave propagation in air, caused by explosion of gaseous charge of spherical or cylindrical shape. A numerical solution is obtained in a range of values of the specific energy of the charge characteristic for fuel-air detonation mixtures by means of the method of characteristics without secondary shock wave separation. The influence of the initial conditions of the gas charge explosion (specific energy, nature of initiation, and others) is investigated and compared with the point case with respect to the pressure difference across the shock wave and the positive overpressure pulse.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 110–118, May–June, 1986.     

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.     

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.     

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.     

Reflection of an Oblique Shock Wave in a Reacting Gas with a Finite Relaxation–Zone Length

Reflection of an oblique shock wave in a reacting gas with a finite length of the chemical–reaction zone is studied. Shock polars for an arbitrary heat release behind the oblique shock wave are constructed. Transition criteria from regular to Mach reflection and back are obtained. It is shown that transition criteria are significantly changed if the reaction–zone length is taken into account.     

Evolution of shock waves in polydisperse gas suspensions with a nonuniform particle concentration distribution

The results of a numerical investigation of the laws of shock wave propagation in polydisperse (two-fraction) gas suspensions with a non-uniform initial particle concentration distribution are presented. Examples of shock wave propagation in extended layers of a gas suspension with linearly increasing, linearly decreasing and sinusoidal laws of variation of the particle concentration are considered. It is shown that when shock waves pass through layers of a gas suspension with increasing and decreasing laws of variation of the particle concentration, respectively, amplification and attenuation of the waves are observed; when shock waves travel through gas suspensions with a periodic law of variation of the particle concentration the pressure distribution behind the wave fronts is nonmonotonic. The solutions corresponding to polydisperse and monodisperse gas suspensions with an effective particle size are examined. The nonequilibrium and thermodynamic-equilibrium solutions are compared.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 183–190, September–October, 1991.     

Efficiency of the induction interaction of a blob of conducting gas with an electrical circuit in which an external electromotive force is included

The possibility of increasing the efficiency of a magnetohydrodynamic energy conversion by including an external emf source in the operating winding is investigated. Values of the average electrical efficiency which can be obtained with the used operating winding are calculated. The possibility and the limits of regulating the efficiency by varying the magnitude of the external emf, the angle of the phase shift of the external emf relative to the currents in the ionized gas, and the magnitude of the excitation magnetic field for the known nature of the flow and the parameters of the gas are determined.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 143–146, March–April, 1971.     

On the flow around a moving plate by a traveling shock

The incidence of a weak shock on a plate moving at supersonic speed is examined theoretically. The shock overtakes the plate. Cases with constant stream parameters behind the shock front and with a nonuniform stream are considered. Formulas are obtained for the time dependence of the plate lift.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 173–176, March–April, 1972.     

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.     

Axisymmetric nonstationary flow around an obstable in a cylindrical tube

Questions associated with the interaction between a gas stream and a body in a launching tube, especially the high-speed propulsion of a body by a gas stream [1], have become of great interest in recent years. Partial destruction of the body and the formation of a gap between the body and the launching tube, through which the working gas will flow, inevitably occurs at high velocities. In this case it is possible to consider the ejection of a free body which does not come into contact with the walls of the launching tube as it is accelerated. An analogous problem occurs in the transportation of containers in a tube under the effect of a compressed gas [2], as well as in a gas-dynamic analysis of piston apparatus with different kinds of gas flow through the orifice inmoving or fixed pistons. The interaction between the gas stream and the body or the obstacle in the launching tube must be known for a theoretical investigation of all these problems. The solution is obtained by numerical integration of the nonstationary gas-dynamic equations by means of a through-computation difference scheme [3]. Values of the blockage factors are found for different freestream Mach numbers, for which the reflected shock stands off at infinity upstream. A comparison is given with the one-dimensional approximation obtained under the assumption that the body being streamlined is replaced by two jumps of a strong discontinuity on which the mass, momentum, and energy conservation conditions are satisfied. The results obtained are used in the problem of ejection of a free body from a launching tube under the effect of an unsteady gas flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 81–86, July–August, 1978.     

Nonlinear subresonance oscillations of a gas in a pipe under the influence of periodically varying pressure

A study is made of one-dimensional nonlinear oscillations of an ideal gas in a pipe one end of which is closed, the pressure being given at the other end and periodically varying with the time. For frequencies close to the subresonance ones, asymptotic equations are obtained which govern the periodic motions of the gas. Solutions containing shock waves are constructed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 151–157, March–April, 1988.The author is grateful to A. N. Kraiko and V. E. Fortov for considering the study and for their support.     

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.     

Integral inequalities in the dynamics of a gravitating gas

In the framework of Newtonian mechanics, a study is made of the spherically symmetric problem of the adiabatic motion of a gravitating perfect gas in the presence of a shock wave produced by inhomogeneous gravitational collapse or a point explosion. The method of Golubyatnikov [1, 2] is used to construct a system of integro—differential inequalities that determine, in particular, the law of motion of the shock wave if the initial state of the gas is known. The investigated examples include some self-similar and nearly self-similar solutions to the problem of the gravitational contraction of dust with the formation of a strong shock wave, possibly with the release of energy; the self-similar problem of a point explosion in a gas at rest; and also the problem of the equilibrium of a gas sphere for =4/3 and arbitrary distribution of the entropy. In these cases, the inequalities reduce to algebraic relations and can be solved numerically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 169–173, September–October, 1980.     

Calculation of the flow in ejector nozzles

A method is proposed for calculating the two-dimensional nonviscous flows in ejector nozzles of arbitrary shape, for two operating cycles: the subsonic flow cycle of a secondary stream and a cycle when the secondary stream attains critical velocity, i.e., it is cut off. In the second case, the possibility is allowed for the appearance of a direct compression shock in the supersonic part of the secondary stream.Translated from Mekhanika Zhidkosti i Gaza, No. 1, pp. 111–118, January–February, 1974.The authors thank A. N. Kraiko and M. Ya. Ivanov for useful discussions and assistance, V. V. Polyakov for interest in the project and L. P. Frolova for assistance in drawing up the task.     

Interference of oblique shock waves of one family in a hypersonic flow

A study is made of the irregular regime of interaction of two shock waves of the same direction when a hypersonic gas stream flows past bodies of complicated shape. It is shown that the rarefaction waves formed in the flow field significantly weaken the shock wave that approaches the body. This effect is confirmed by the results of an experiment and numerical calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 134–138, 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.     

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.     

Determination of the vorticity on a wing of small aspect ratio in a hypersonic stream

The theory of a thin shock layer [1–3] is used to obtain a formula for calculating the component of the vorticity in the direction of the flow on a wing of small aspect ratio in a hypersonic gas stream. It is shown that for definite shapes of the wing and flow regimes zones may occur with large local values of the vorticity, which, as is well known, have a significant influence on the structure of the flow field.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–178, September–October, 1980.