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.     

Time‐domain BEM solution of convection–diffusion‐type MHD equations

The two‐dimensional convection–diffusion‐type equations are solved by using the boundary element method (BEM) based on the time‐dependent fundamental solution. The emphasis is given on the solution of magnetohydrodynamic (MHD) duct flow problems with arbitrary wall conductivity. The boundary and time integrals in the BEM formulation are computed numerically assuming constant variations of the unknowns on both the boundary elements and the time intervals. Then, the solution is advanced to the steady‐state iteratively. Thus, it is possible to use quite large time increments and stability problems are not encountered. The time‐domain BEM solution procedure is tested on some convection–diffusion problems and the MHD duct flow problem with insulated walls to establish the validity of the approach. The numerical results for these sample problems compare very well to analytical results. Then, the BEM formulation of the MHD duct flow problem with arbitrary wall conductivity is obtained for the first time in such a way that the equations are solved together with the coupled boundary conditions. The use of time‐dependent fundamental solution enables us to obtain numerical solutions for this problem for the Hartmann number values up to 300 and for several values of conductivity parameter. Copyright © 2007 John Wiley & Sons, Ltd.     

Review on the application and prospect of magnetohydrodynamics in aeronautical engineering

介绍了磁流体动力学在航空工程中的主要应用方式,主要包括：磁流体冲压组合发动机、磁流体涡轮组合发动机、燃烧室后磁流体发电、表面磁流体发电、磁流体加速风洞、磁流体推力矢量、进气道大尺寸磁流体流动控制、边界层分离流动控制、边界层转捩控制、飞行器头部热流控制等;探讨了磁流体技术在应用中存在的关键科学与技术问题,对导电流体的产生、磁流体实验设备与实验技术、多场耦合机理及数值模拟方法等进行了分析;最后对磁流体技术在航空工程上的应用与发展进行了总结与展望.     

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.      

磁流体动力学在航空工程中的应用与展望

介绍了磁流体动力学在航空工程中的主要应用方式,主要包括:磁流体冲压组合发动机、磁流体涡轮组合发动机、燃烧室后磁流体发电、表面磁流体发电、磁流体加速风洞、磁流体推力矢量、进气道大尺寸磁流体流动控制、边界层分离流动控制、边界层转捩控制、飞行器头部热流控制等;探讨了磁流体技术在应用中存在的关键科学与技术问题,对导电流体的产生、磁流体实验设备与实验技术、多场耦合机理及数值模拟方法等进行了分析;最后对磁流体技术在航空工程上的应用与发展进行了总结与展望.     

Numerical simulation of magnetohydrodynamic flow in a toroidal duct of square cross-section

We present numerical simulation results of the quasi-static magnetohydrodynamic (MHD) flow in a toroidal duct of square cross-section with insulating Hartmann walls and conducting side walls. Both laminar and turbulent flows are considered. In the case of steady flows, we present a comprehensive analysis of the secondary flow. It consists of two counter-rotating vortex cells, with additional side wall vortices emerging at sufficiently high Hartmann number. Our results agree well with existing asymptotic analysis. In the turbulent regime, we make a comparison between hydrodynamic and MHD flows. We find that the curvature induces an asymmetry between the inner and outer side of the duct, with higher turbulence intensities occurring at the outer side wall. The magnetic field is seen to stabilize the flow so that only the outer side layer remains unstable. These features are illustrated both by a study of statistically averaged quantities and by a visualization of (instantaneous) coherent vortices.     

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.     

Unsupervised neural network model optimized with evolutionary computations for solving variants of nonlinear MHD Jeffery-Hamel problem

A heuristic technique is developed for a nonlinear magnetohydrodynamics(MHD) Jeffery-Hamel problem with the help of the feed-forward artificial neural network(ANN) optimized with the genetic algorithm(GA) and the sequential quadratic programming(SQP) method. The two-dimensional(2D) MHD Jeffery-Hamel problem is transformed into a higher order boundary value problem(BVP) of ordinary differential equations(ODEs). The mathematical model of the transformed BVP is formulated with the ANN in an unsupervised manner. The training of the weights of the ANN is carried out with the evolutionary calculation based on the GA hybridized with the SQP method for the rapid local convergence. The proposed scheme is evaluated on the variants of the Jeffery-Hamel flow by varying the Reynold number, the Hartmann number, and the angles of the walls. A large number of simulations are performed with an extensive analysis to validate the accuracy, convergence, and effectiveness of the scheme. The comparison of the standard numerical solution and the analytic solution establishes the correctness of the proposed designed methodologies.     

倾斜非均匀磁场下导电方管磁流体管流的数值模拟研究

热核聚变反应堆液态金属包层应用中的一个重要问题是液态金属在导电管中流动和强磁场相互作用产生的额外的磁流体动力学压降.这种磁流体动力学压降远远大于普通水力学压降.美国阿贡国家实验室ALEX研究小组,对非均匀磁场下导电管中液态金属磁流体动力学效应进行了实验研究,其实验结果成为液态金属包层数值验证的标准模型之一.液态金属包层在应用中会受到不同方向的磁场作用,本文以ALEX的非均匀磁场下导电方管中液态金属管流实验中的一组参数为基础,保持哈特曼数、雷诺数和壁面电导率不变,采用三维直接数值模拟的方法,研究了外加磁场与侧壁之间的倾角对导电方管内液态金属流动的速度、电流和压降分布的影响.研究结果表明:沿流向相同横截面上的速度、电流以及压力分布均随磁场的倾斜而同向旋转.倾斜磁场均匀段,横截面上的高速区位于平行磁场方向的哈特曼层和平行层交叉位置,压力梯度随磁场倾角的增大先增大后减小.倾斜磁场递减段,在三维磁流体动力学效应作用下,横截面上的高速射流位置向垂直磁场方向偏移.磁场递减段的三维磁流体动力学压降随磁场倾角的增大而增大.随磁场倾斜,截面上的射流峰值逐渐减小,二次流增强,引发层流向湍流的转捩.      

Steady MHD Couette flow with temperature-dependent physical properties

The influence of variation in physical variables on the steady magnetohydrodynamic (MHD) Couette flow with heat transfer is studied. An external uniform magnetic field is applied perpendicular to the parallel plates and the fluid is acted upon by a constant pressure gradient. The viscosity and the thermal as well as electric conductivities are assumed to be temperature dependent. The two plates are kept at two constant but different temperatures, and the viscous and Joule dissipations are considered in the energy equation. A numerical solution for the governing nonlinear coupled equations of motion and the energy equation is obtained. The effect of the temperature-dependent viscosity, thermal conductivity, and electrical conductivity on both the velocity and temperature distributions is examined. H.A. Attia - On leave from: Dept. of Eng. Mathematics and physics, El-Fayoum University, El-Fayoum, Egypt     

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.     

Performance investigation of plasma magnetohydrodynamic power generator

magnetohydrodynamic (MHD) power generator system involves several subjects such as magnetohydrodynamics, plasma physics, material science, and structure mechanics. Therefore, the performance of the MHD power generator is affected by many factors, among which the load coefficient k is of great importance. This paper reveals the effect of some system parameters on the performance by three-dimensional (3D) numerical simulation for a Faraday type MHD power generator using He/Xe as working plasma. The results show that average electrical conductivity increases first and then decreases with the addition of magnetic field intensity. Electrical conductivity reaches the maximum value of 11.05 S/m, while the applied magnetic field strength is B = 1.75 T. When B > 3T, the ionization rate along the midline well keeps stable, which indicates that the ionization rate and three-body recombination rate (three kinds of particles combining to two kinds of particles) are approximately equal, and the relatively stable plasma structure of the mainstream is preserved. Efficiency of power generation of the Faraday type channel increases with an increment of the load factor. However, enthalpy extraction first increases to a certain value, and then decreases with the load factor. The enthalpy extraction rate reaches the maximum when the load coefficient k equals 0.625, which is the best performance of the power generator channel with the maximum electricity production.     

Nonlinear turbulence models for predicting strong curvature effects

Prediction of the characteristics of turbulent flows with strong streamline curvature, such as flows in turbomachines, curved channel flows, flows around airfoils and buildings, is of great importance in engineering applications and poses a very practical challenge for turbulence modeling. In this paper, we analyze qualitatively the curvature effects on the structure of turbulence and conduct numerical simulations of a turbulent Uduct flow with a number of turbulence models in order to assess their overall performance. The models evaluated in this work are some typical linear eddy viscosity turbulence models, nonlinear eddy viscosity turbulence models （NLEVM） （quadratic and cubic）, a quadratic explicit algebraic stress model （EASM） and a Reynolds stress model （RSM） developed based on the second-moment closure. Our numerical results show that a cubic NLEVM that performs considerably well in other benchmark turbulent flows, such as the Craft, Launder and Suga model and the Huang and Ma model, is able to capture the major features of the highly curved turbulent U-duct flow, including the damping of turbulence near the convex wall, the enhancement of turbulence near the concave wall, and the subsequent turbulent flow separation. The predictions of the cubic models are quite close to that of the RSM, in relatively good agreement with the experimental data, which suggests that these models may be employed to simulate the turbulent curved flows in engineering applications.     

Helical shell models for MHD

A shell model for magnetohydrodynamics (MHD) is derived directly from the dynamical system driving the evolution of three helical modes interacting in a triad. The use of helical modes implies that two shell variables are required for the velocity as well as for the magnetic field. The advantage of the method is the automatic conservation of all the ideal quadratic MHD invariants. The number of coupling constants is however larger than in traditional shell models. This difficulty is worked around by introducing an averaging procedure that allows to derive the shell model coupling constants directly from the MHD equations. The resulting shell model is used to explore the influence of a helical forcing on the global properties of MHD turbulence close to the onset of the dynamo regime.     

求解一维理想磁流体方程的移动网格熵稳定格式

磁流体方程的数值求解在等离子体物理学、天体物理研究以及流动控制等领域具有重要意义,本文构造了用于求解理想磁流体动力学方程的基于移动网格的熵稳定格式,此方法将Roe型熵稳定格式与自适应移动网格算法结合,空间方向采用熵稳定格式对磁流体动力学方程进行离散,利用变分法构造网格演化方程并通过Gauss-Seidel迭代法对其迭代求解实现网格的自适应分布,在此基础上采用守恒型插值公式实现新旧节点上的量值传递,利用三阶强稳定Runge-Kutta方法将数值解推进到下一时间层。数值实验表明,该算法能有效捕捉解的结构(特别是激波和稀疏波),分辨率高,通用性好,具有强鲁棒性。     

Magnetohydrodynamic control of supersonic flow past bodies: Possibilities and undesirable effects

Basic problems of super-and hypersonic magnetohydrodynamics (MHD) associated with the determination of the integral characteristics of bodies and vehicles inside which there are systems generating a uniform magnetic field are considered. Three classes of flows, namely, flow in a hypersonic multimode fixed-geometry air-intake; internal and external flow in a model of a hypersonic vehicle containing an air-intake with an MHD generator, a combustion chamber, and a supersonic nozzle; and hypersonic flow past a blunt cone are studied using numerical simulation and theoretical analysis (on the basis of the complete averaged system of Navier-Stokes equations and the electrodynamic equations). Attention is concentrated on the presence of an additionalmagnetic force acting on the system generating themagnetic field and, consequently, on the body and initiating an additional drag (in the case of a vehicle-reducing its thrust). Attractive possibilities for MHD flow control, namely, an increase in the degree of flow compression in the air-intake, a reduction in the ignition length in the combustion chamber, and a decrease in the heat flux to the nose of the body, are noted, as well as negative effects associated with the action of the magnetic force on the bodies considered.     

Numerical Analysis of Coupled Stokes/Darcy Flows in Industrial Filtrations

Free flow channel confined by porous walls is a feature of many of the natural and industrial settings. Viscous flows adjacent to saturated porous medium occur in cross-flow and dead-end filtrations employed primarily in pharmaceutical and chemical industries for solid–liquid or gas–solid separations. Various mathematical models have been put forward to describe the conjugate flow dynamics based on theoretical grounds and experimental evidence. Despite this fact, there still exists a wide scope for extensive research in numerical solutions of these coupled models when applied to problems with industrial relevance. The present work aims towards the numerical analysis of coupled free/porous flow dynamics in the context of industrial filtration systems. The free flow dynamics has been expressed by the Stokes equations for the creeping, laminar flow regime whereas the flow behaviour in very low permeability porous media has been represented by the conventional Darcy equation. The combined free/porous fluid dynamical behaviour has been simulated using a mixed finite element formulation based on the standard Galerkin technique. A nodal replacement technique has been developed for the direct linking of Stokes and Darcy flow regimes which alleviates specification of any additional constraint at the free/porous interface. The simulated flow and pressure fields have been found for flow domains with different geometries which represent prototypes of actual industrial filtration equipment. Results have been obtained for varying values of permeability of the porous medium for generalised Newtonian fluids obeying the power law model. A series of numerical experiments has been performed in order to validate the coupled flow model. The developed model has been examined for its flexibility in dealing with complex geometrical domains and found to be generic in delivering convergent, stable and theoretically consistent results. The validity and accuracy of the simulated results has been affirmed by comparing with available experimental data.     

Validation of large eddy simulation method for study of flatness and skewness of decaying compressible magnetohydrodynamic turbulence

In the present work we study potential applicability of large eddy simulation (LES) method for prediction of flatness and skewness of compressible magnetohydrodynamic (MHD) turbulence. The knowledge of these quantities characterizes non-Gaussian properties of turbulence and can be used for verification of hypothesis on Gaussianity for the turbulent flow under consideration. Prediction accuracy of these quantities by means of LES method directly determines efficiency of reconstruction of probability density function (PDF) that depends on used subgrid-scale (SGS) parameterizations. Applicability of LES approach for studying of PDF properties of turbulent compressible magnetic fluid flow is investigated and potential feasibilities of five SGS parameterizations by means of comparison with direct numerical simulation results are explored. The skewness and the flatness of the velocity and the magnetic field components under various hydrodynamic Reynolds numbers, sonic Mach numbers, and magnetic Reynolds numbers are studied. It is shown that various SGS closures demonstrate the best results depending on change of similarity numbers of turbulent MHD flow. The case without any subgrid modeling yields sufficiently good results as well. This indicates that the energy pile-up at the small scales that is characteristic for the model without any subgrid closure, does not significantly influence on determination of PDF. It is shown that, among the subgrid models, the best results for studying of the flatness and the skewness of velocity and magnetic field components are demonstrated by the Smagorinsky model for MHD turbulence and the model based on cross-helicity for MHD case. It is visible from the numerical results that the influence of a choice subgrid parametrization for the flatness and the skewness of velocity is more essential than for the same characteristics of magnetic field.     

Two‐level finite element method with a stabilizing subgrid for the incompressible MHD equations

We consider the Galerkin finite element method (FEM) for the incompressible magnetohydrodynamic (MHD) equations in two dimension. The domain is discretized into a set of regular triangular elements and the finite‐dimensional spaces employed consist of piecewise continuous linear interpolants enriched with the residual‐free bubble functions. To find the bubble part of the solution, a two‐level FEM with a stabilizing subgrid of a single node is described and its application to the MHD equations is displayed. Numerical approximations employing the proposed algorithm are presented for three benchmark problems including the MHD cavity flow and the MHD flow over a step. The results show that the proper choice of the subgrid node is crucial to get stable and accurate numerical approximations consistent with the physical configuration of the problem at a cheap computational cost. Furthermore, the approximate solutions obtained show the well‐known characteristics of the MHD flow. Copyright © 2009 John Wiley & Sons, Ltd.