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.      

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.     

Multirail electromagnetic launcher powered from a pulsed magnetohydrodynamic generator

The operation of an electromagnetic multirail launcher of solids powered from a pulsed magnetohydrodynamic (MHD) generator is studied. The plasma flow in the channel of the pulsed MHD generator and the possibility of launching solids in a rapid-fire mode of launcher operation are considered. It is shown that this mode of launcher operation can be implemented by matching the plasma flow dynamics in the channel of the pulsed MHD generator and the launching conditions. It is also shown that powerful pulsed MHD generators can be used as a source of electrical energy for rapid-fire electromagnetic rail launchers operating in a burst mode.     

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.     

Magnetohydrodynamic interaction in hypersonic air flow past a blunt body

Hypersonic MHD air flow past a blunt body in the presence of an external magnetic field is considered. The MHD effect on the flow consists in a significant increase in the shock wave stand-off from the body surface and a significant reduction in the heat flux to the wall (up to 50%). It is shown that even in the presence of a strong Hall effect the intensity of the magnetohydrodynamic interaction in the plasma behind the shock wave remains at a high level commensurable with the ideal case of the absence of a Hall effect.     

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.     

Analysis of two-phase flow magnetohydrodynamic generator performance in terms of flow and electrical conductivity distribution parameters

A general method is presented for analyzing two-phase flow in magnetohydrodynamic generators. The method utilizes the time and flow-area-averaged kinematic, dynamic and electromagnetic quantities, and develops prediction capabilities of the generator performance parameters in terms of two fundamental physical parameters. These parameters are the flow and the electrical conductivity-flow distribution coefficients. The flow coefficient takes into consideration flow and relative velocity distribution, and the electrical conductivity-flow coefficient expresses the distribution of electrical conductivity with flow at any cross-sectional area of the generator duct.

The flow and electrical conductivity-fiow distribution coefficients depend primarily on the two-phase flow regime and on the ratio of volumetric flow rates of the two phases in the duct. This conclusion has been established by examining the experimental data. Examination of the experimental data has also revealed the values of these coefficients for bubbly and churn-turbulent flow regimes for the wide range of ratios of volumetric flow rates. The analysis develops expressions for two-phase MHD generator load factor, electromagnetic pressure distribution across and along the generator channel, the distribution of the electromagnetic fields and interaction parameter.     

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.     

Averaging of magnetohydrodynamic streams and applicability of the hydraulic approximation to the calculation of MHD flows in channels

At the present time the hydraulic approximation equations are used widely for calculating MHD flows in channels. Several years ago these solutions were considered as a method of expanding our ideas of the qualitative effect of various factors on the MHD flow in the channel of a MHD device. Today, however, the hydraulic analysis methods are beginning to be used for calculations on specific systems. In this case the selection of a particular design solution frequently is based on an analysis of the over-all characteristics (efficiency, power delivered to the external load, etc.) obtained from the hydraulic calculation, where a few percent rather than tens of percent are taken into account.On the other hand, it is known [1] that in gas dynamics the results of the hydraulic calculation for the same specific nonuniform stream may differ by an order of magnitude of tens of percent depending on the averaging method used, since the magnitude of this difference depends on the degree of nonuniformity of the actual stream.We may expect that the nonuniformity of the MHD streams will be far greater than for the gas dynamic flows as a result of the nonuniformities of the force and the thermal effect of the currents flowing in the stream. These nonuniformities may be associated, for example, with the nonuniform distribution of the currents in the channel cross section because of the nonuniform electrical conductivity, which may be significant in spite of the weak nonuniformity of the temperature distribution, or with the presence in the cross section of forces associated with the induced longitudinal component of the magnetic field, the presence of anisotropy of the electrical conductivity, etc.Moreover, in contrast with gas dynamics, in the design of various MHD devices several characteristics (power delivered to the external load, various efficiencies, etc.) which may be calculated in terms of the average value of the gas dynamic parameters are of great importance. Thus, it seems probable that the question of the applicability of the hydraulic approximation to the calculation of MHD flows in channels, the rational selection of the means for averaging the actual flows, the comparison of the results of the hydraulic calculations with the experimental data, and so on, may be far more significant than was the case for the study of gas dynamic flows.     

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.     

Boundary layer development in an MHD duct

This study presents a method of calculation for two-dimensional, steady-state, laminar flow in the entrance region of an MHD duct. The electrically conducting fluid in the free stream is compressible whereas the medium in the boundary layer itself is taken to be incompressible. Thus, the density is variable in the axial direction of the duct only, and the momentum and energy equations for the boundary layer are uncoupled. These equations are solved using an extended Von Kármán-Pohlhausen method as described by U. P. Hwang for a compressible MHD flow with zero electric field. In this study, however, the electric field is essentially not zero and the MHD duct can work as a generator. The equations of the insulator boundary layer are solved in the assumption that the displacement thickness of the electrode boundary layer equals that of the insulator boundary layer, so the total influence of the varying effective crossection on the free stream is taken into account. In this way a quick method of calculating the MHD flow in the entrance region of a duct is obtained.     

Influence of a Longitudinal Magnetic Field on the Hall Effect in the Plasma Accelerator Channel

An analytic model of steady-state two-dimensional flows in coaxial plasma-accelerator channels in the presence of a longitudinal magnetic field is proposed. The solution of the problem is found in the smooth channel approximation for the MHD equations of an ideal two-component plasma. An example of the developing axisymmetric flows is given and the features of the plasma-dynamic processes are investigated. It is found that the Hall effect and the anode flow zone can be reduced using a longitudinal field and plasma rotation.     

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.     

Gas-Dynamic Processes in Two-Phase Flows in MHD Generators

A plane problem of a two-phase monodisperse flow of combustion products of plasma-forming composite solid propellants in the duct of a Faraday's MHD generator with continuous electrodes, including an accelerating nozzle, MHD channel, and diffuser, is considered. An algorithm based on the pseudo-transient method is developed to solve the system of equations describing the two-phase flow. Gas-dynamic processes in the channels of the Pamir-1 setup are numerically studied. It is shown that shock-free deceleration of a supersonic flow to velocities close to the equilibrium velocity of sound in a two-phase mixture and significantly lower than the velocity of sound in the gas is possible in two-phase flows.     

Hall effect in the MHD model of plasma channel flow

The steady flow regime with quasi-radial electric current and nonequipotential boundaries is obtained in calculating axisymmetric plasma flow in a coaxial channel with an azimuthal self-magnetic field. The calculations were carried out using the MHD model with allowance for the Hall effect. The regime obtained describes the flow in the stream core of the channel of a modern quasi-steady heavy-current plasma accelerator outside thin near-electrode layers. Estimates of the Hall corrections relating to these layers are given.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 56–65, September–October, 1995.     

MHD flows of a second grade fluid between two side walls perpendicular to a plate through a porous medium

Exact analytical solutions for magnetohydrodynamic (MHD) flows of an incompressible second grade fluid in a porous medium are developed. The modified Darcy's law for second grade fluid has been used in the flow modelling. The Hall effect is taken into account. The exact solutions for the unsteady flow induced by the time-dependent motion of a plane wall between two side walls perpendicular to the plane has been constructed by means of Fourier sine transforms. The similar solutions for a Newtonian fluid, performing the same motion, appear as limiting cases of the solutions obtained here. The influence of various parameters of interest on the velocity and shear stress at the bottom wall has been shown and discussed through several graphs. A comparison between a Newtonian and a second grade fluids is also made.     

An extensive numerical benchmark of the various magnetohydrodynamic flows

There is a continuous need for an updated series of numerical benchmarks dealing with various aspects of the magnetohydrodynamics (MHD) phenomena (i.e. interactions of the flow of an electrically conducting fluid and an externally imposed magnetic field). The focus of the present study is numerical magnetohydrodynamics (MHD) where we have performed an extensive series of simulations for generic configurations, including: (i) a laminar conjugate MHD flow in a duct with varied electrical conductivity of the walls, (ii) a back-step flow, (iii) a multiphase cavity flow, (iv) a rising bubble in liquid metal and (v) a turbulent conjugate MHD flow in a duct with varied electrical conductivity of surrounding walls. All considered benchmark situations are for the one-way coupled MHD approach, where the induced magnetic field is negligible. The governing equations describing the one-way coupled MHD phenomena are numerically implemented in the open-source code OpenFOAM. The novel elements of the numerical algorithm include fully-conservative forms of the discretized Lorentz force in the momentum equation and divergence-free current density, the conjugate MHD (coupling of the wall/fluid domains), the multi-phase MHD, and, finally, the MHD turbulence. The multi-phase phenomena are simulated with the Volume of Fluid (VOF) approach, whereas the MHD turbulence is simulated with the dynamic Large-Eddy Simulation (LES) method. For all considered benchmark cases, a very good agreement is obtained with available analytical solutions and other numerical results in the literature. The presented extensive numerical benchmarks are expected to be potentially useful for developers of the numerical codes used to simulate various types of the complex MHD phenomena.     

Influence of the hall effect on hypersonic flow past a wedge

This paper deals with the problem of the steady-state hypersonic flow of an inviscid compressible gas past a wedge. Inside the wedge a magnetic field is excited in a direction perpendicular to the generator. The flow in the region of perturbation is investigated on the basis of the ordinary equations of magnetohydrodynamics and Ohm's law, written for the case where the Hall effect is taken into account. The system of equations obtained has been solved numerically on a computer by the method of finite differences. The results show that for the given problem the Hall effect intensifies the magnetohydrodynamic action of the magnetic field on the flow. M. D. Ladyzhenskii [1] has also studied hypersonic flow past bodies from inside which a magnetic field is excited. He has investigated the influence of a strong magnetic field on the flow for the case where the Hall effect is neglected. The object of the present study is to determine the importance of the Hall effect.The author wishes to thank M. D. Ladyzhenskii for formulating the problem and discussing the progress of the work.     

Motion of a two-temperature plasma in the channel of a disc-type magnetohydrodynamic generator

A study was made of the fully developed homogeneous flow of a two-temperature partially ionized plasma in the channel of a disc-type Hall generator. Experiments with a disc-type generator are described in [1, 2]. In a simplified statement, the problem is analogous to that considered in [3]. The present article takes the chemical reactions of ionization and recombination into account. The energy equation for an electron gas is brought down to a differential form which permits clarification of the question of the applicability of the Kerrebrock [4] formula for the difference in the temperatures of the electrons and the heavy particles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 18–25, November–December, 1970.In conclusion, the author thanks V. V. Gogosov for his interest in the work and for his valuable observations.     

Effects of Hall current on f lows of a Burgers’ fluid through a porous medium

This paper generalizes the analysis of four magnetohydrodynamic (MHD) flow problems of an Oldroyd-B fluid discussed by Asghar et al. [Int. J. Non-linear Mech. 40, 589–601 (2005)] into three directions: (i) to discuss the problems in a porous medium using modified Darcy’s law (ii) to see the influence of Hall current (iii) to determine the effect of rheological parameter of Burgers’ fluid. Analytical solutions of velocity distribution valid at large and small times are given in each problem. Comparison has been provided for Oldroyd-B and Burgers’ fluids through graphs. The physical interpretation is also included.