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.     

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.     

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.     

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.     

Experimental investigation of cathode spots on metallic electrodes protruding in plasma flow

The behavior of cathode spots on metallic electrodes is investigated. The dependence of the basic characteristics of the spots (current per spot, life time, rate of displacement, average area and so forth) on the nature of the flow of the plasma past the surface of the electrode, the surface temperature of the electrode, the total current in the electrode, and the magnetic field is obtained. The investigations were done in connection with the study of the operation of electrodes of open cycle magnetohydrodynamic generators. The experiments were conducted with copper electrodes introduced in the plasma formed by the combustion products of natural gas with potassium added to it.     

Influence of the hall effect on the characteristics of a MHD generator with two pairs of electrodes

The characteristics of segmented-electrode MHD generators with Hall currents are at present the object of considerable interest. Various types of electrode connections ate being examined: ordinary segmented-electrode generators, Hall generators, mixed-type generators, and Montardy generators. Research is being pushed in several directions. In some cases infinitely fine segmentation is assumed [1--4]. In these studies it is considered that the current density j in the duct is everywhere uniform; the net characteristics or the most favorable electrode connection angle are determined. In another group of studies periodic problems are solved, it being assumed that the processes taking place in a single elementary celi are repeated in the other ceils; fringe effects are not taken into account. In this case it is usually assumed that the lengths of the electrodes and insulators are finite, but small as compared with the duct height [5–7 ]. Finally, in a last group of studies nonperiodic problems are considered. In [3] Vatazhin solves the problem of the current distribution in a duct with a single pair of electrodes between infinitely long insulators. In [8] a general expression is found for the current density function in the case of an arbitrary number of electrode pairs and for any scheme of electrode connection at finite electrode and insulator dimensions. However, numerical calculations are made only for the periodic problem, whose solution is also obtained in [8]; the effect of segment pitch on the characteristics of a Montardy generator is studied.The present author has investigated the influence of the Hall effect on the characteristics of a MHD generator having two pairs of electrodes with symmetrical and crossed electrode connections. Although it is obvious that in practice only multisegment ducts will be employed, the examination of a generator with two pairs of electrodes makes possible the qualitative anatysis of the various effects observed in segmented-electrode ducts in which the electrodes are connected in different ways. Numerical calculations, based on formulas obtained by solving the corresponding problems, have been made on a M-20 computer. Integrated characteristics of the various generator systems have been obtained as a function of electrode and insulator length, external loads, and Hall parameter w.In conclusion, the author thanks A. B. Vatazhin and A. N. Kraiko for their helpful advice.     

Mutual relationship of adsorption processes on the surface of a cathode and the processes taking place in the parts of a heavy-current plasma discharge close to the electrodes

The effect of alkali metal vapor on the work function of the cathode material in various MHD installations has as yet been little studied [1]. Nor has the mutual influence of adsorption processes on the cathode surface and processes taking place in the parts of a plasma discharge close to the electrodes, although this information is extremely vital in order to make a correct determination of the emission characteristics of cathodes in plasma. The manner in which the electrode becomes coated with the plasma material determines the work function of the electrode and thus the discharge current density and cathode potential drop _s. On the other hand, the degree of coverage of the cathode with the adsorbed particles depends substantially on the value of _s. In this paper we shall propose a method of calculating the emission characteristics of cathodes during a heavy-current plasma discharge allowing for the mutual influence of the processes in question. The problem is solved in a one-dimensional setting for an automatic thermionic-emission discharge (discharge of the spotless type).Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 29–32, September–October, 1972.     

Motion of a conductive piston in a channel with variable inductance

The motion of a conductive piston in the channel of a magnetohydrodynamic (MHD) generator of the conduction type with compound electrodes is considered. Formulas are obtained for calculation of the energy characteristics of the pulse MHD generator for various operational regimes. It is shown that in an MHD generator at magnetic Reynolds number values Re_m = ₀u₀ 1 (where ₀ is the permeability of a vacuum, is the electrical conductivity of the piston, u₀ is the initial velocity, and is the characteristic dimension), the energy transferred to an ohmic load may significantly exceed the values obtained in [1, 2]. Conditions for high-efficiency transformation of piston kinetic energy to electrical energy are considered for limiting values of the ratio of the latter to initial magnetic field energy in the generator channel.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 41–46, November–December, 1973.The authors thank V. I. Yakovlev for his helpful evaluation.     

An experimental investigation of the effect of oxygen on the erosion of a multichannel tungsten cathode

The problem of the preservation of electrodes and the reduction of their depletion to a minimum has decisive significance among the practical questions of maintaining the efficiency of steady sources and plasma accelerators during an extended period of operation. For this purpose electrodes are made, as a rule, out of the refractory metals in familiar designs. In particular, tungsten, which has the highest phase-transition; temperatures among all the metals, thus permitting an appreciable reduction in the evaporation rate of the material under the thermally stressed operating conditions of these devices, is attractive. However, there exist other factors besides evaporation which affect the integrity of hot tungsten electrodes and their ablation (chemical processes, erosion in microarcs, ion bombardment, and so on). One of these factors requiring special investigation is the chemical interaction of tungsten with the oxygen contained in the working medium as an industrial impurity. Such an impurity can, for example, be present in industrially pure alkali and alkali-earth metals used as the working media. In addition, these metals can be contaminated by the oxygen of the air in the process of different industrial operations, in particular, in connection with the servicing of the supply system. The entrance into the working material of oxygen liberated from the structural elements of the supply route and the operating cavities of the plasma source is not excluded. In practice it is impossible to eliminate oxygen, even when using contemporary methods of deep cleaning of lithium, due to its great affinity for oxygen. The actual role of the oxygen impurity and the necessity for taking it into account in connection with the creation and operation of plasma devices can only be revealed as a result of direct experimental investigation on samples having an electrode. geometry similar to the class of sources or accelerators in question. Results are presented in this article of an experimental investigation of the erosion of a multichannel tungsten electrode [1–4] and a coaxial source of lithium plasma [5]. The use of lithium as the main plasma-forming material ensured the maintainance of a discharge distributed over the electrodes and having a small value of the potential drop next to the cathode, which lies below the threshold of cathode erosion upon bombardment of the surface of polycrystalline tungsten by lithium ions [6]. Thus, the phenomena of cathode destruction associated with microarcs and ion bombardment could be exluded from consideration in practice. Thus evaporation and chemical ablation due to interaction with the oxygen of the working medium remain the principal, competing processes contributing to the erosion of the cathode mass. Therefore, in order to obtain reliable quantitative relationships which characterize differential erosion due to oxidation and evaporation, the oxygen content in the working medium was varied in the experiments described within limits extending beyond the framework of the usual industrial impurity, which does not exceed tenths of a percent. One should note that in the process of investigating the role of an industrial oxygen impurity in causing the erosion of a tungsten cathode in a lithium plasma its direct effect was revealed on the anomalous current of a hollow cathode, which is characterized by the recorded average densities of the discharge current exceeding significantly the values of the emission current given at the same surface temperature by the Richardson-Schottky equation [7–9].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 67–73, May–June, 1979.The authors express their gratitude to S. S. Kellin, N. P. Mezhevov, and V. N. Belinskii for their participation in the preparation and performance of the experiment.     

Hall效应对三维磁流体发生器的影响

应用三维非理想低磁雷诺数磁流体五方程模型发展了对带有强制项的Navier-Stokes方程组采用熵条件格式, 对椭圆型电势方程采用SOR进行迭代的数值方法,研究了Hall效应对磁流体旁路超燃冲压发动机中磁流体发生器流动及性能的影响.磁流体发生器采用电子束获得有效可靠的电导率. 计算结果表明,Hall效应可引起流场和电场的扭曲, 从而诱导出不稳定二次流的发展与演变,并破坏Joule热的分布. 对这些磁流体现象作出了较详细的分析.最后计算了磁流体发生器的性能参数, 说明Hall效应将导致磁流体发生器的性能下降.      

The uniqueness of the solution of boundary-value problems of a thermal model of discharge

The paper is devoted to a nonlinear analysis of superheating [1, 2] instability of an electric discharge stabilized by electrodes [3] in the framework of a thermal model [4] where the stability of the discharge relative to the long-wave and short-wave perturbations is proved in a linear approximation. Similar boundary-value problems arise in the theories of chemically and biologically reacting mixtures [5–7], thermal breakdown of dielectrics [8], thermal explosion [9], in the investigation of nonlinear waves in semiconductors and superconductors [10, 11], and in the investigation of Couette flow with variable viscosity [12]. The uniqueness of the one-dimensional steady solutions of the thermal model of discharge and the stability relative to the small spatial perturbations, respectively, for the exponential and step dependence of the electrical conductivity on the temperature are proved in [3, 13]. The uniqueness of the solutions in the one-dimensional case for the same electrode temperature and arbitrary dependences of the electrical and thermal conductivity on the temperature is established in paper [14]. In the present paper, the existence and uniqueness of steady solutions of the thermal model of discharge in a three-dimensional formulation for arbitrary fairly smooth electrical and thermal conductivity functions of the temperature in the case of isothermal isopotential electrodes are proved analytically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 140–145, January–February, 1986.The author expresses his gratitude to A. G. Kulikovskii and A. A. Barmin for the formulation of the problem and their discussions.     

Boundary layer development in supersonic MHD generators

A numerical model of the turbulent boundary layers in the gas dynamic channel of a supersonic MHD generator is constructed. This model describes the development and structure of the layers in the nozzle, on the electrode and insulating walls of the duct, in the two-dimensional approximation. The characteristics of the boundary layers in various generator operating regimes are investigated numerically. The integral boundary layer thicknesses characterizing the nonuniformity of the gas dynamic and electrodynamic quantities are calculated. The limits of applicability of the integral calculation method are determined for typical MHD generator operating conditions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 35–41, May–June, 1990.The authors wish to thank A. B. Vatazhin, V. A. Bityurin, and V. A. Zhelnin for discussing the formulation of the problem, A. A. Yakushev for participating in the discussion of the results, and Yu. V. Rakseeva and L. V. Yashina for preparing the article.     

Electrical breakdown in air in a transverse magnetic field

The electrical breakdown of gases in a transverse magnetic field is discussed in references [1–16]. Attention has mainly been concentrated on the case of coaxial electrode geometry [1–10]. The existing experimental data on breakdown between plane-parallel electrodes [11–14] relate to a narrow range of variation of the parameters characterizing breakdown (P, d, H, U). The author has made an experimental study of the process of electrical breakdown in air in a transverse magnetic field between plane-parallel electrodes of finite size in the pressure interval from 650 to 5·10^–3 mm Hg at gap lengths of from 1 to 140 mm and magnetic inductions from 0 to 10 600 G.     

Mathematical Model for the Solid Electrolyte Fuel Cell Cathode

An analytically solvable mathematical model for the cathode of a solid polymer electrolyte fuel cell is proposed. The problem of diffusion in a multicomponent air-vapor mixture in a porous cathode and water transport due to hydrodynamic and electroosmotic forces is solved. The volt-ampere characteristic of the fuel cell is determined taking into account the polarization characteristics and finite conductivity of the electrolyte. An expression is obtained for the thickness of the electrochemical-reaction zone, which gives an estimate of the catalyst efficiency. It is shown that the finiteness of the rate of oxygen diffusion into the reaction zone limits the current density and the fuel cell efficiency. A comparison of the results with available theoretical and experimental data shows that the solutions obtained for the model coincide with the solutions for the more complex Bernardi and Verbrugge model.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 27–37, September–October, 2005.     

Internal waves in a two-layer electrically conducting fluid in the presence of a magnetic field

The propagation of linear and nonlinear internal waves along the interface between two weakly conducting media differing in density and electrical conductivity is investigated and the influence of MHD interaction effects on their characteristics is analyzed. It is shown that in this system the waves propagate with dispersion and dissipation, and for harmonic waves of infinitesimal amplitude there exists a range of wave numbers on which propagating modes do not exist. For waves of finite amplitude a nonlinear Schrödinger equation with a dissipative perturbation is obtained and its asymptotic solution is found. It is established that the presence of electrical conductivity and an applied magnetic field leads to a decrease in the amplitude and the frequency of the envelope of the wave train.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 104–108, September–October, 1990.     

Effect of electrical conductivity of flow on current distribution in a magnetogasdynamic channel with allowance for the Hall effect

The effect of a magnetic field on the current distribution on a plane continuous anode situated opposite the cathode in a rectangular magnetogasdynamic channel with an external magnetic field was experimentally investigated. The distributions of the charged-particle density and the electron temperature near the outlet end of the electrodes were measured. The distribution of electrical conductivity in the flow was calculated. The electron density distribution along the channel is attributed to ambipolar diffusion of plasma to the walls. For an interpretation of the current distribution results, the method of integral relations in a linear approximation was used to solve the problem of a constant-velocity flow of a gas with variable electrical conductivity across a magnetic field in a plane magnetogasdynamic channel of constant cross section formed by electrodes of finite length and insulators. The Hall effect was taken into account. Experiments in which the effect of an external magnetic field on the current distribution on plane sectioned short electrodes in a magnetogasdynamic accelerator was investigated were described in [1]. In the present investigation, continuous long electrodes were used. These electrodes prevented the side effects due to coupling of the current to the ends of the electrode sections and helped to reveal some features of the current density distribution on the anode.     

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.     

Features of the electric current and field distributions in flows with narrow layers of highly conductive gas

A solution obtained by Fourier's method provides the basis for analyzing the influence of a narrow gas layer, of higher conductivity than the rest of the flow, on the Joule dissipation and current distribution in the terminal zone of a plane magnetohydrodynamic channel with nonconducting walls. The MHD interaction parameter, Reynolds magnetic number, and Hall parameter are assumed small. It is shown that a narrow, highly conductive layer can on occasions be replaced by a surface of discontinuity, on which well-defined relations between the electric quantities are satisfied. The presence of such a layer leads to an increase in the Joule dissipation and a reduction in the lengths of the current lines. A hopeful arrangement for a magnetohydrodynamic energy converter is one in which an inhomogeneous flow is used, consisting of a continuous series of alternating very hot and less hot zones [1,2]. For this arrangement, it is worth examining the influence of the stratified conductivity distribution of the working body on the Joule dissipation and the electric currents in the channel. Numerous papers have discussed the case of inhomogeneous conductivity in the context of MHD system electrical characteristics. A general solution was obtained in [3] for the stationary problem on the electric field in a plane MHD channel with nonconducting walls when the magnetic field and conductivity are arbitrary functions of the longitudinal coordinate. In [4], where the braking of undeformed conducting clusters was investigated, the Joule dissipation, linked with the appearance of closed eddy currents in the cluster as it enters and leaves the magnetic field, was evaluated. The relationships between the electrical quantities, on moving through a narrow layer of low-conductivity liquid, were considered in [5].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 9, No. 1, pp. 39–43, January–February, 1970.In conclusion, the author thanks A. B. Vatazhin for valuable advice and discussion.     

Propagation of surface gravity waves in a layer of electrically conducting liquid

The wave motion of a weakly conducting incompressible liquid in a transverse magnetic field is investigated within the framework of the nonlinear theory of magnetohydrodynamics. The influence of MHD interaction effects on harmonic perturbations of infinitesimal amplitude is analyzed and a long-wave equation of the Kortewegde Vries-Burgers type describing the evolution of weakly nonlinear perturbations of the free surface is derived. It is shown that the influence of the electrical conductivity leads to a change in both the dissipative and the dispersive properties of the system.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 173–175, July–August, 1989.     

On nonisothermal electroconvection

The flow from the tip of a needle electrode is caused by the Coulomb force acting on the space charge [1–3]. This charge is formed because of the dependence of the conductivity on the temperature, nonuniformity of which is due to Joule heating [1] and the electric field intensity [2] or processes near the electrode [3–5]. The present paper considers the stability of a dielectric liquid between spherical electrodes in order to elucidate the possibility of a thermoelectrohydrodynainic flow due to Joule heating. In the presence of external heating, the possibility of such a flow has been demonstrated both experimentally and theoretically [6–8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 133–137, March–April, 1980.