Electric field in the transverse cross section of the channel of an MHD generator

During the motion of a partially ionized gas in magnetohydrodynamic channels the distribution of the electrical conductivity is usually inhomogeneous due to the cooling of the plasma near the electrode walls. In Hall-type MHD generators with electrodes short-circuited in the transverse cross section of the channel the development of inhomogeneities results in a decrease of the efficiency of the MHD converter [1]. A two-dimensional electric field develops in the transverse section. Numerical computations of this effect for channels of rectangular cross section have been done in [2, 3], At the same time it is advisable to construct analytic solutions of model problems on the potential distribution in Hall channels, which would permit a qualitative analysis of the effect of the inhomogeneous conductivity on local and integral characteristics of the generators. In the present work an exact solution of the transverse two-dimensional problem is given for the case of a channel with elliptical cross section stretched along the magnetic field. The parametric model of the distribution of the electrical conductivity of boundary layer type has been used for obtaining the solution. The dependences of the electric field and the current and also of the integral electrical characteristics of the generator on the inhomogeneity parameters are analyzed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 3–10, January–February, 1973.     

Dynamics of a nonuniformly conducting gas flow in a magnetic field

The dynamics of a nonuniformly conducting gas flow in the channel of a MHD generator are investigated on the basis of numerical modeling. The initial shape of the plasmoids periodically entering the MHD channel qualitatively correspond to that noted in [6, 7]. The alkali metal seed is uniformly distributed over the entire flow. The mechanism of dynamic interaction of the plasmoids and the low-conductivity gas flowing over them, the variation of the shape of the plasmoids and the evolution of the gas dynamic structure of the flow are studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 135–145, September–October, 1989.     

The boundary layers of a fully ionized two-temperature plasma with given component temperatures at an electrode

The flow of a plasma with different component temperatures in the boundary layers at the electrodes of an MHD channel is investigated without any assumptions as to self-similarity. For the calculation of the electron temperature, the full energy equation for an electron gas [1] is solved with allowance for the estimates given in [2]. In contrast to [3, 4], the calculation includes the change in temperature of electrons and ions along the channel caused by the collective transport of energy, the work done by the partial pressure forces, and the Joule heating and the energy exchange between the components. The problem of the boundary layers in the flow of a two-temperature, partially ionized plasma past an electrode is solved in simplified form by the local similarity method in [5–7]. In these papers, either the Kerrebrock equation is used [5, 6] or the collective terms are omitted from the electron energy equation [7].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 3–10, September–October, 1972.The author thanks V. V. Gogosov and A. E. Yakubenko for interest in this work.     

Subsonic Radiation Gas Dynamics in a Laser Plasma Generator Channel

The radiation gasdynamic processes in the channel of an air laser plasma generator operating at atmospheric pressure are analyzed. In the multigroup approximation a numerical radiation gasdynamic model is formulated on the basis of the equations of motion of a viscous heat-conducting gas and the selective thermal radiation transport equation. Laminar and turbulent subsonic generator operation regimes are considered.For the purpose of approximately describing the turbulent gas and plasma mixing the Navier-Stokes equations averaged after Reynolds and the k-ε turbulence model are used. The problem is solved in the time-dependent two-dimensional axisymmetric formulation.Strong radiation-gasdynamic interaction regimes are investigated. In these regimes the energy losses due to radiation from the high-temperature region of the laser plasma and the absorption of its thermal self-radiation by the surrounding plasma and gas layers (radiation reabsorption) appreciably affect the gasdynamic flow structure. Two methods of integrating the selective thermal radiation transport equation in the generator channel are discussed. In one of these the thermal radiation transport is calculated inside the heated volume and in the other the radiation heat fluxes are calculated on the surfaces bounding the volume. The results of calculating the spectral and integral radiation heat fluxes on the inner surface of the generator are given.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, 2005, pp. 126–143.Original Russian Text Copyright © 2005 by Surzhikov.     

Calculation of plane electric fields in channels of magnetohydrodynamic instruments

The local and integral characteristics of flat MHD channels are studied with allowance for longitudinal and transverse edge effects and heterogeneities in the distributions of conductivity and stream velocity. An analysis is made of the effect of the finite dimensions of the insulating inserts in the longitudinal edge effect and of the modular construction of the side wall in the transverse edge effect on the output parameters of MHD channels. The solution of the problem is based on reduction of the initial quasilinear elliptical equation for the electrical potential with allowance for Ohm's law to an integral equation of the Fredholm type relative to the current density.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 8–16, March–April, 1974.In conclusion the authors thank L. A. Vulis, A. V. Gubarev, and A. L. Genkin for discussion of the formulation of the problem and the results of the work.     

Magnetogasdynamic generation of electrical energy in models of aircraft with a high-speed jet engine

The possibility of generating electric power in a plane model of an integral high-speed hydrogen-burning jet engine by mounting a magnetogasdynamic (MHD) generator at the combustion chamber exit is discussed. Attention is concentrated on clarifying the effect of MHD energy extraction from the stream on the aircraft’s thrust characteristics. The internal and external flows are simulated numerically. The two-dimensional supersonic gasdynamic flow inside the engine (in the air-intake, combustion chamber, MHD generator, and nozzle) and the supersonic flow past the aircraft are described on the basis of the complete averaged system of Navier-Stokes equations (in the presence of turbulence), which includes MHD force and heat sources, a one-parameter turbulence model, the electrodynamic equations for an ideal segmented MHD generator, and the equations of the detailed chemical kinetics of hydrogen burning in air. The numerical solution is obtained by means of a computer program that uses a relaxation scheme and an implicit higher-order version of the Godunov method. It is shown that MHD electric power generation can be realized without disturbing the positive balance in the relation between the thrust and the drag of the aircraft with the engine operating with allowance for the MHD drag, but with some loss of effective thrust.     

Some electrodynamic effects in a MHD generator duct

Theoretical and experimental studies made in recent years show that the plasma flow in the duct of a real MHD generator differs significantly from the quasi-uniform model of the flow in an idealized MHD duct. This difference appears primarily in the analysis of the electrodynamics of the MHD generator. Usually the actual electrical characteristics of the generator are poorer than expected, which may be caused, in particular, by flow nonuniformities and electrical leaks in the duct. The influence of these factors shows up particularly strongly in the presence of the Hall effect.Some qualitative and quantitative estimates of these phenomena have already been made in the literature. The necessity for taking into account the influence of the cold boundary layer on the effective conductance of the plasma in the duct was shown in [1]; in [2] it was shown that this influence increases markedly in the presence of the Hall effect. The influence of shunting of the plasma by the electrically conductive walls of the duct was considered in [3–5].The present paper describes an analysis of the combined influence of the effects associated with flow nonuniformities and electrical leaks for the case of anisotropy of the plasma conductivity, and an example is presented of the calculation of flow in a MHD generator with finite variation of the parameters.     

Occurrence of periodic regimes in steady supersonic mid flows due to loss of electrical conductivity of medium

A study is made of the features of supersonic magnetohydrodynamic (MHD) flows due to the vanishing of the electrical conductivity of the gas as a result of its cooling. The study is based on the example of the exhausting from an expanding nozzle of gas into which a magnetic field (Re_m 1) perpendicular to the plane of the flow is initially frozen. It is demonstrated analytically on the basis of a qualitative model [1] and by numerical experiment that besides the steady flow there is also a periodic regime in which a layer of heated gas of electric arc type periodically separates from the conducting region in the upper part of the nozzle. A gas-dynamic flow zone with homogeneous magnetic field different from that at the exit from the nozzle forms between this layer and the conducting gas in the initial section. After the layer has left the nozzle, the process is repeated. It is established that the occurrence of such layers is due to the development of overheating instability in the regions with low electrical conductivity, in which the temperature is approximately constant due to the competition of the processes of Joule heating and cooling as a result of expansion. The periodic regimes occur for magnetic fields at the exit from the nozzle both greater and smaller than the initial field when the above-mentioned Isothermal zones exist in the steady flow. The formation of periodic regimes in steady MHD flows in a Laval nozzle when the conductivity of the gas grows from a small quantity at the entrance due to Joule heating has been observed in numerical experiments [2, 3]. It appears that the oscillations which occur here are due to the boundary condition. The occurrence of narrow highly-conductive layers of plasma due to an initial perturbation of the temperature in the nonconducting gas has previously been observed in numerical studies of one-dimensional flows in a pulsed accelerator [4–6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 138–149, July–August, 1985.     

Cathode spots on electrode slag films in an open-cycle MHD generator

A study has been made of the function of the electrodes (cathodes) in an open-cycle MHD generator for several different reasons [1–3], because the electrode processes have marked effects on the erosion and electrical characteristics of the electrodes. The specific features of the conditions in an MHD generator channel include, particularly, the high-temperature plasma composed of combustion products together with the deposition of potassium salts on the electrodes. These factors have a marked effect on the behavior of the cathode spots. In the case of an MHD generator fueled by coal, the plasma contains the incombustible mineral part of the fuel (ash). Therefore, the electrode surfaces receive not only potash salts, but also slag, which consists of various refractory oxides that differ from the potassium compounds in electrical conductivity, thermal conductivity, and emissivity. These films may substantially affect the parameters of the cathode spots, and hence the erosion, and the values may differ substantially from those given in [3]. We have examined the major features of the cathode spot behavior for an open-cycle MHD generator fueled by coal.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 29–33, July–August, 1976.     

Use of a three-parameter family of locally similar velocity profiles in the calculation of turbulent separation regions in a compressible gas

A method is proposed for calculating two-dimensional leading turbulent separation regions based on the use of integral relations of boundary layer theory and integral characteristics of a three-parameter family of locally similar velocity profiles. The method makes it possible to calculate the characteristics of a turbulent boundary layer, including friction and heat transfer, without separation of discontinuities and special regions and to do this in both attached and separated flow regions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhldkosti i Gaza, No. 3, pp. 24–33, May–June, 1982.I thank V. N. Shmanenkov for interest in the work and L. V. Gogish for reading and discussing the draft.     

Interaction of two supersonic radial gas flows

The flow resulting from the collision of two spherically symmetric supersonic gas streams generated by three-dimensional sources has been studied within the framework of the inviscid perfect gas model. When the characteristics of both sources are the same, the problem reduces to that of the interaction between a spherically symmetric flow and a plane barrier [1, 2]. By means of a certain passage to the limit, the flow from one of the sources can be reduced to a uniform supersonic gas flow. In this case the problem reduces to the problem of uniform gas flow past a source considered in [1, 3, 4]. The resulting flows are investigated with reference to all the parameters characterizing the two sources. The shock wave structure, both in the neighborhood of and at points remote from the axis of symmetry, is studied, together with the distributions of the gas dynamic quantities in the shock layers; certain similarity laws are established. The astrophysical applications of the problem associated, in particular, with a certain x-ray radiation mechanism in binary stellar systems [5] are of particular interest.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 159–165, July–August, 1990.The authors are grateful to V. B. Baranov for his constant interest and to S. A. Zhekov and V. V. Usov for useful discussions.     

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.     

Aerodynamics of end-wall boundary layer in a vortex chamber

The need for the inclusion of end-wall boundary layers in the study of the aerodynamics of vortex chambers has been frequently mentioned in the literature. However, owing to limited experimental data [1–3] with reliable information on the wall layers, the existing computational methods for end-wall boundary layers are not well-founded. The question of which parameters determine the formation of end-wall flow remains debatable. In some studies [4, 5], the vortex chambers are conditionally divided into short and long chambers. However, there is no unique opinion on the role of end-wall flows in vortex chambers of different lengths. It has also not been established for what geometric and flow parameters the chamber could be considered long or short. In the present study, as in [1, 5–8], solution is obtained for the end-wall boundary-layer equations using integral methods, considering the boundary layer in the radial direction in the form of a submerged wall jet. Such an approach made it possible to use the laws for the development of wall jets [9], and obtain fairly simple relations for integral parameters, skin friction, mass flow in the boundary layer, and other characteristics. Results are compared with available experimental data and computations of others authors; turbulent flow is considered; results for laminar boundary layer are given in [10].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 117–126, September–October, 1986.     

The microarc operating regime of MHD generator electrodes

The preliminary results of an investigation of the operation of MHD generator electrodes at relatively high current densities are reported. The experiments were conducted in the channel of a MHD generator, driven by combustion products, with both cooled metal and silicon carbide electrodes. Observation and photographs of the electrodes revealed that at sufficiently high currents microarcs appear at the electrode surface. The phenomenological aspects of arc behavior under conditions characteristic of MHD generator operation are examined. The electrode-insulator interface has an important influence on arc behavior, as does the film of potassium compounds deposited on the electrode surface. These characteristics of the microarcs may be of considerable significance in relation to electrode erosion processes.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 1, pp. 130–134, January–February, 1970.     

Calculation of turbulent friction on a plate with distributed injection of polymer solution into the boundary layer

An expression is proposed for the mixing length on a permeable surface with polymer injection. Relations between mixing length and injection, useful for calculating boundary layers into which dilute polymer solutions are injected, are proposed. The numerical solution is compared with the available experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 169–171, March–April, 1991.Tha author wishes to thank V. A. Ioselevich for his interest in the work and V. A. Aleksin for useful comments on the numerical method.     

Motion of a fluid between rotating cones

A study is made of the steady axisymmetric flow of a viscous fluid between two cones rotating in opposite ways round a common axis. It is shown that as in the case of the flow of fluid swirled by plane disks rotating at different speeds [1], there can be two regimes of motion in the system: a Batchelor regime with quasirigid rotation of the fluid outside the boundary layers [2] and a Stewartson regime in which the azimuthal flow is concentrated only in the boundary layers [3]. In the Stewartson regime, a boundary layer analogous to that in the single disk problem (see, for example, [4–6]) forms in the region of each cone far from the apex. For the flows outside the boundary layers, simple expressions are found which make it possible to obtain a conception of the circulation of the fluid as a whole. With minor alterations, the results can be applied to the case of the rotation of other curved surfaces.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 58–64, March–April, 1985.The author thanks A. M. Obukhov for suggesting the subject and for his interest in the work, and A. V. Danilov and S. V. Nesterov for useful discussions.     

Thermal boundary layer on models disintegrating in a high-enthalpy gas stream

Results are presented of experimental disintegration by a high-enthalpy gas stream of models made of asbestos material and graphite. The high-temperature aerodynamic shock-layer heating was modeled using an electrodeless plasma generator, which allowed the thermal boundary layer to be studied on the disintegrating models under convective and radiative heating conditions. The profiles of rotational and vibrational temperature in the multicomponent boundary layer, measured using the CN molecule, coincided.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 26–31, January–February, 1976.The authors thank N. A. Generalov for his interest in the work and for fruitful discussions.     

Semiempirical method of calculating overexpanded turbulent separated flow in a conical laval nozzle

A mathematical model of separated nozzle flow is developed. The model takes into account the effect of the boundary layer and the pressure variation over the entire separation zone inside the nozzle. The effect of the geometric and gas dynamic factors on the separated flow pattern is investigated numerically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 60–66, November–December, 1988.     

Transient Dynamic Response of Elastoplastic Thick Plates Resting on Winkler-Type Foundation

A direct domain/boundary element method (D/BEM) for the dynamicanalysis of elastoplastic thick plates resting on Winkler-typefoundation is presented. The formulation presented includes the effectsof shear deformation and rotatory inertia following Reissner–Mindlin'sdeformation theory assumption. The method employs the elastostaticfundamental solution of the problem resulting in both boundary anddomain integrals due to inertia, plasticity and foundation pressureterms. By discretizing the integral equations and integrating theresulting matrix equation of motion by an explicit time integrationscheme the history of the plate dynamic response can be obtained.Applications are shown for impacted elastoplastic Reissner–Mindlinplates with smooth boundaries on several different foundations.     

Solution of the problem of optimum boundary layer control on the porous surface of a turbine blade

Problems of the optimization of coolant injection into a laminar compressible gas boundary layer are considered within the framework of the integral method of boundary layer calculation [1].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 17–24, November–December, 1993.