The effects of ionization on the compression of a gas by a converging shell

One of the effective methods of obtaining a dense high-temperature plasma is compression of the gas by converging shells, which can be accelerated to high velocities by the products of an explosion either as a result of ablation caused by laser radiation, or by an electron beam [1–3]. In order to interpret the results of such experiments, it is very important to construct satisfactory physical models which enable us to obtain plausible estimates for the parameters of the plasma which are realized as a result of the compression. In a number of cases the process of compression may be described with sufficient accuracy by a system of simple hydro-dynamic equations which have particular analytical solutions (see, for example, [4–7]); however, as a rule, for more realistic estimates it is necessary to take into account the complex of physical phenomena accompanying the process, and in such cases the most effective method is numerical simulation of the process, which enables a fuller study to be made of the effect of various factors [7–9]. Compression regimes corresponding to velocities of projection of the shells of some tens of kilometers a second (attainable in experiments with laser compression of shells of a width of some microns) have at present been considered in detail in studies devoted to a pulse thermonuclear synthesis (for example, [8–10]), from which it follows that the process corresponds with sufficient accuracy to the compression of a gas which is completely ionized at the initial moment. In experiments with more massive shells (of the order of 100 m and more), the velocities attained in practice do not exceed 5–20 km/sec [1]. At such velocities, the energy densities contained in the shock wave detaching from the shell may turn out to be insufficient for complete ionization of the gas which has been compressed, and this must have an effect on its further compression and heating. The present study considers precisely these regimes of compression of gas-filled targets. The studies were carried out by the numerical method. For comparison, the studies were made in a number of cases both with allowance for ionization of the gas which was being compressed, and also on the assumption that the gas was already completely ionized at the initial moment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 155–160, January–February, 1935.In conclusion the author expresses his appreciation to S. I. Anisimov for his constant attention to this study, and to M. F. Ivanov for his help in carrying out the calculations.     

Simple waves in a plasma with anisotropic pressure

Fast and slow simple waves are studied in the framework of the anisotropic magnetohydrodynamics of Chew, Goldberger, and Low [1]. Baranov [2] has constructed fields of integral curves for fast and slow waves and in two special cases has shown that such waves break in the compression section. The possibility of breaking of a slow wave in a rarefaction section was noted by Akhiezer et al. [3]. However, their general relations in simple waves [3] have been shown to be incorrect [2, 4]. In the present paper the nature of the variation of the longitudinal and transverse plasma pressures is determined, and the problem of the breaking of fast and slow waves is completely solved. Conditions under which a slow wave breaks in a rarefaction section are found. A fast wave always breaks in a rarefaction section.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 181–183, July–August, 1988.     

Planar gas flows with weak energy supply

Perfect gas flows in an unlimited space, which occur during rectilinear motion of a system of distributed heat sources, are investigated. The next modes in order of growth of the number M are examined: the heat conductive, convective, subsonic, transonic, supersonic, hypersonic. Examples of computations are presented. Flows with distributed heat sources attract ever-increasing attention. Such flows are important, e.g., in the problem of radiation propagation [1–5], in the analysis of a gasdynamic laser resonator and the optical characteristics of a ray [6]. Changes in the density because of absorption of the ray energy, which can result in an essential redistribution of the radiation intensity, are of great interest in these problems. Theoretical investigations of a general nature with distributed heat supply [7–10] are also important for the development of further applications. Gas flows for a given distribution of relatively weak heat sources switched on at a certain time are examined in this paper.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 95–102, September–October, 1978.     

Diagnostics of rarefied gases using hot-wire anemometer

Hot-wire anemometry has been quite widely used in recent years to study low-density flows [1–3]. High sensitivity and good spatial resolution of the method make its application effective in flows with large gradients. The technique permits the determination of two thermodynamic quantities, the coefficient of heat transfer h and recovery temperature T_r. Relations coupling h and T_r with flow parameters were obtained in [4]. These relations were generalized in [3] for the case of unequal accommodation of translational and internal energy of molecules on the wire surface and nonequilibrium energy distribution in internal degrees of freedom. In order to obtain a more detailed information on the distribution of gasdynamic parameters, the hot-wire anemometer is, as a rule, used in conjunction with other diagnostic tools like the Pitot tube or electron beam [2]. The present work deals with the application of a twin-wire (perpendicular and parallel to the flow direction) hot-wire anemometer in rarefied flows without the benefit of other techniques. Furthermore, the influence of differences in the accommodation coefficients of translational and internal energies and the degree of rarefaction on the hot-wire anemometer is also investigated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 126–130, September–October, 1986.In conclusion, the authors acknowledge A. K. Rebrov for useful discussions stimulating development of studies with hot-wire anemometry.     

Stability of flows with discontinuity surfaces

A study is made in the linear formulation of flows with homogeneous distribution of the parameters in expanding regions separated by boundaries that are either discontinuity surfaces of an arbitrary nature or surfaces with effective boundary conditions. Examples of such flows are the decay of an arbitrary discontinuity [1] and flow in a tube with a region of heat release [2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 10–18, September–October, 1982.We thank A. G. Kulikovskii for helpful discussions.     

Electric arc in hydrogen flow at high pressure

The interaction of an electric arc with laminar hydrogen flow at a pressure of 100 atm is examined with account for the transverse flows. Results of calculations are presented for a current strength of 30 A and tube radius 0.3 cm. It is shown that for these parameters radiation plays the defining role in the heat transfer process.The electric arc in a gas stream without account for radiation has been studied previously in [1–4] and with account for radiation in [5]. However, in these studies only the longitudinal velocity component was taken into account in the energy equation.The authors wish to thank A. T. Onufriev for his interest in this study.     

Theory of vortical helical ideal gas flows in laval nozzles

An asymptotic solution is found for the direct problem of the motion of an arbitrarily vortical helical ideal gas flow in a nozzle. The solution is constructed in the form of double series in powers of parameters characterizing the curvature of the nozzle wall at the critical section and the intensity of stream vorticity. The solution obtained is compared with available theoretical results of other authors. In particular, it is shown that it permits extension of the known Hall result for the untwisted flow in the transonic domain [1]. The behavior of the sonic line as a function of the vorticity distribution and the radius of curvature of the nozzle wall is analyzed. Spiral flows in nozzles have been investigated by analytic methods in [2–5] in a one-dimensional formulation and under the assumption of weak vorticity. Such flows have been studied by numerical methods in a quasi-one-dimensional approximation in [6, 7]. An analogous problem has recently been solved in an exact formulation by the relaxation method [8, 9]. A number of important nonuniform effects for practice have consequently been clarified and the boundedness of the analytical approach used in [2–7] is shown.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 126–137, March–April, 1978.The authors are grateful to A. N. Kraiko for discussing the research and for valuable remarks.     

Calculation of interaction of a turbulent near-wake behind a step with a supersonic jet

Existing computational methods [1–5] do not enable one to calculate complex flows behind steps, accounting for nonuniformity of the incident supersonic flow and the effect of compression and expansion waves arriving in the near-wake region. For example, computational methods based on the methods of [1] or [2] are used mainly in uniform supersonic flow ahead of the base edge and, for the most part, cannot be used to calculate flow in annular nozzles with irregular conditions. An exception is reference [6], which investigated flow in an annular nozzle behind a cylindrical center-body. The present paper suggests a method, based on references [7, 8] for calculating the base pressure behind two-dimensional and three-dimensional steps, washed by a supersonic jet.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 43–51, November– December 1977.     

Use of direct variational methods to optimize axisymmetric Laval nozzles in the case of equilibrium and nonequilibrium two-phase flows

In the construction of the optimal profile of a Laval nozzle when there are subsonic regions in the flow, the use of effective methods such as the general method of Lagrangian multipliers [1] becomes very difficult. In the present paper, direct variational methods are therefore used. For nozzles, these methods were used for the first time to profile the supersonic parts of nozzles in the case of nonequilibrium two-phase flows by Dritov and Tishin [2]. For equilibrium flows, they have been used to optimize supersonic nozzles [3, 4] and in the construction of a profile of the subsonic part of a nozzle ensuring parallel sonic flow in the minimal section of the nozzle [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 181–183, January–February, 1982.I thank A. N. Kraiko for a number of helpful comments in a discussion of the formulation of the problem.     

Secondary flows beside a cylinder in a complex sound field

It is known that steady flows arise beside a solid surface in the presence of a sound field which can to a certain extent exert an effect on the processes of heat and mass exchange [1–3]. As a rule, all papers from this area refer to the case in which one can represent the sound field in the form of a single wave. However, situations are often encountered in practice in which the sound field is complex; i.e., it consists of several vibrations whose amplitudes and frequencies are unlike in the general case. The secondary flows which form beside a circular cylinder placed in a complex soundfield are investigated in this paper.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 56–64, November– December, 1977.The author expresses his gratitude to V. A. Murga and I. I. Tyurlik for the computer calculations.     

Numerical study of steady supersonic separated flow past spatial lifting systems

At the present, spatial lifting systems are usually calculated numerically using linear approximation. However, the practical application of such systems at moderate and large angles of incidence requires new approaches that allow for various nonlinear effects such as large disturbances, flow separation, and jumps in entropy across shock waves. The existing investigations [3, 4] generally cover only simple systems (bodies of revolution, wings, and so on). Here, a numerical method is proposed for investigating supersonic flows past complicated spatial systems. The method extends and continues the well-known methods widely used to solve analogous problems in subsonic aerodynamics [5, 6]. Some examples of the computation of the aerodynamic parameters for flows past wings and spatial lifting systems are also given.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 142–148, May–June, 1993.     

Generalized variables in boundary-layer theory

Independent variables are widely used in boundary-layer theory to construct efficient methods of solving problems. The Dorodnitsyn variables in Lees' form [1] are the most common and general. This form combines the transformations proposed by Dorodnitsyn [2], Blasius [3], and Mangler-Stepanov [4, 5]. As is well known, transformation of the boundary-layer equations to Dorodnitsyn variables in Lees' form leads to a generalized single system of equations describing plane and axisymmetric gas flows. An analogous generalization of the Mises [6] and Crocco [7] variables is carried out below.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 166–168, September–October, 1976.     

Method of mean-mass parameters for a three-dimensional boundary layer in a flow with vorticity

When a gas flows with hypersonic velocity over a slender blunt body, the bow shock induces large entropy gradients and vorticity near the wall in the disturbed flow region (in the high-entropy layer) [1]. The boundary layer on the body develops in an essentially inhomogeneous inviscid flow, so that it is necessary to take into account the difference between the values of the gas parameters on the outer edge of the boundary layer and their values on the wall in the inviscid flow. This vortex interaction is usually accompanied by a growth in the frictional stress and heat flux at the wall [2, 3]. In three-dimensional flows in which the spreading of the gas on the windward sections of the body causes the high-entropy layer to become narrower, the vortex interaction can be expected to be particularly important. The first investigations in this direction [4–6] studied the attachment lines of a three-dimensional boundary layer. The method proposed in the present paper for calculating the heat transfer generalizes the approach realized in [5] for the attachment lines and makes it possible to take into account this effect on the complete surface of a blunt body for three-dimensional laminar, transition, or turbulent flow regime in the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 80–87, January–February, 1981.     

Investigation of flow past blunt bodies with allowance for radiation by the large-particle method

Much recent work has been done on developing methods of solving gas-dynamic problems in which radiation plays a part (see, for example, [1–7]). This is because the temperature in the shock layer associated with flight in the atmosphere at hypersonic velocities can reach values exceeding 10⁴ °K. In such a case, heat transfer by radiation can make an important contribution to the total heat transfer. With increasing flight velocities, the importance of radiation in heat transfer increases and then becomes predominant. In the present paper, the large-particle method as developed by Belotserkovskii and Davydov [8] is developed to calculate flows with radiation around blunt bodies, including the case when there is distributed blowing from the surface of the bodies into the shock layer, which simulates ablation of a heat-shielding covering under the influence of strong heating by radiation. The results are given of systematic calculations of flow past blunt bodies of various shapes by a stream of radiating air, and the results are compared with the data of other methods.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 106–112, July–August, 1982.     

On radiative heat transfer in a plane layer of an absorbing medium

Recently there has arisen increased interest in the study of radiative heat transfer between geometrically simple systems, both as autonomous problems and as elements of more complex problems.Problems of this kind have been treated by many authors [1–111 who have considered gray, diffusely emitting and absorbing boundaries and gray nonscattering media. In most cases these investigations were restricted either to the derivation of approximate formulas for the net radiative flux, without an exact analysis of the temperature distribution in the layer [5–7], or to numerical computation [1–4], In the latter case, with the exception of [8], which contains a numerical analysis for the case of optical symmetry, no attempt was made to analyze the effect of the optical properties of the boundaries on the temperature field in the layer.These papers can be divided into two groups according to the method of analysis used. The first group includes papers based on the integral equations of radiative transfer, with the corresponding integral analytical methods [1, 2], Similar in nature are [3, 4] which use the slab method, applicable to electrical-analog computation, as well as a recent paper [8] based on probability methods.The second group of papers [5–7] is based on the so-called differential methods. Of particular interest is [7], which develops these methods to an advanced degree. In several papers the problem of radiative transfer is analyzed in conjunction with more complex problems (cf., e.g. [10, 11]).In the present work we shall attempt to carry out an approximate analytical study of problems connected with radiative heat transfer in a plane layer of an absorbing, emitting, nonscattering gray medium with temperature-independent optical properties. The layer is bounded by two parallel, diffusely emitting and diffusely reflecting, isothermal, gray planes.The paper presents the fundamental formulation of the problem, which consists in: (a) the determination of the net heat flux on the basis of given temperature distribution (direct formulation), and (b) the determination of the temperature distribution on the basis of given distribution of the net radiative heat source per unit volume and boundary temperatures (inverse formulation). The analysis is based on integral methods appropriate to the integral equations which represent the net total and hemispherical radiation flux densities [12].The author would like to thank S. S. Kutateladze for his interest in this work.     

Nonsteady-state nonisothermal flow of a magnetic liquid in a plane channel

Magnetic liquids are finding wider and wider use in various fields of technology [1]. Such liquids can be used as heat exchange fluids in equipment which generates a magnetic field under conditions of weightlessness [2] and in a number of other applications. The efficiency of heat exchange equipment is determined to a significant degree by the temperature of the magnetic liquid. In connection with this fact, it is of interest to examine nonisothermal flows at a temperature near the Curie point, where the dependence of volume magnetization M on temperature is expressed most clearly. In this case the character of the liquid flow will be affected not only by the dependence of saturation volume magnetization on temperature, but also by temperature inhomogeneity caused by development of external heat sources and sinks produced by the magnetocaloric effect. We note that although this is a weak effect [3], the temperature redistribution over channel section which it produces may be significant. With a high gradient in the external magnetic field H even a small change in temperature can significantly change the force acting on a magnetic liquid element. The unique features of magnetic liquid flow at a temperature close to the Curie point can be investigated by simultaneously solving the equations of motion and thermal conductivity.Translated from Zhurnal Prikladnoi Mekhaniki i Technicheskoi Fiziki, No. 1, pp. 93–96, January–February, 1984.The author expresses his gratitude to the participants in K. B. Pavlov's scientific seminar for their evaluation of the study.     

Solution of a variational problem for the flow in an MHD generator

The most complete study and construction of extremal plasma flow regimes in the channel of an MHD generator may be accomplished using the methods of variational calculus. The variational problem of conducting-gas motion in an MHD channel was first discussed in [1]. The general formulation of the problem for the MHD generator was considered in [2]. Solutions of variational problems for particular cases of extremal flows are given in [2–5].The present study obtains the solution of the variational problem of the flow of a variable conductivity plasma in an MHD generator which has maximal output power for given channel length or volume. An analysis of the solution is made, and a comparison of the extremal flows with optimized flow in a generator with constant values of the electrical efficiency and flow Mach number is carried out.     

Axisymmetric mixed flows in magnetogasdynamics

In contrast with conventional gasdynamics, in magnetogasdynamics there are several types of mixed flows. A detailed study of such plane flows was first made by Kogan [1]. After this, intensive work was done on the magnetogasdynamic mixed flows [2–13], with the plane case being considered in all the studies except [9]. In [9] the equations of the possible mixed flows for the axisymmetric case were obtained in terms of the disturbance velocity components.The axisymmetric mixed flows are studied in detail in the present paper. The exact equations of motion are obtained for the velocity potential and the streamfunction, and the corresponding approximate equations are obtained for all the transitional regimes (transonic, hypercritical, trans-Alfvenic, transonic-trans-Alfvenic). Simple particular solutions are obtained for these approximate equations.For greater generality the entire study is made simultaneously for the plane and axisymmetric cases.The author wishes to thank S. V. Fal'kovich for his interest in the study and for valuable discussions.     

Instabilities of nonuniform flows of acoustically active media

The analytic methods and results of investigating the acoustic instability of nonuniform steady channel flows are reviewed. The study is based on the system of equations describing the motion of an electrically conducting gas at low magnetic Reynolds numbers [25]. This makes it possible to consider the acoustic effects in plasma and nonconducting gas flows within the framework of a unified approach.Based on paper presented to the fluid mechanics sections of the Seventh Congress on Theoretical and Applied Mechanics, Moscow, August 1991.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 31–46, September–October, 1992.     

Boundary layer on a blunt body in a flow of dusty gas

The problem of interaction of gas-dust flows with solid surfaces arose in connection with the study of the motion of aircraft in a dusty atmosphere [1–2], the motion of a gas suspension in power generators, and in a number of other applications [3]. The presence of a disperse admixture may lead to a significant increase in the heat fluxes [4] and to erosion of the surface [5]. These phenomena are due to the joint influence of several factors — the change in the structure of the carrier-phase boundary layer due to the presence of the particles, collisions of the particles with the surface, roughness of the ablating surface, and so forth. This paper continues an investigation begun earlier [6–7] into the influence of particles on the structure of the dynamical and thermal two-phase boundary layer formed around a blunt body in a flow. The model of the dusty gas [8] has an incompressible carrier phase. The method of matched asymptotic expansions [9] is used to obtain the equations of the two-phase boundary layer. In the frame-work of the refined classification made by Stulov [6], it is shown that the form of the boundary layer equations is different in the presence and absence of inertial precipitation of the particles. The equations are solved numerically in the neighborhood of the stagnation point of the blunt body. The temperature and phase velocity distributions in the boundary layer, and also the friction coefficients and the heat transfer of the carrier phase are found for a wide range of the determining parameters. In the case of an admixture of low-inertia particles that are not precipitated on the body, it is shown that even when the mass concentration of the particles in the undisturbed flow is small their accumulation in the boundary layer can lead to a sharp increase in the thermal fluxes at the stagnation point.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 99–107, September–October, 1985.I thank V. P. Strulov for a discussion.