Hall effects on steady hydromagnetic flow in a rotating channel in the presence of an inclined magnetic field

Effects of Hall current on a steady hydromagnetic (MHD) fully developed flow in a rotating environment within a parallel plate channel in the presence of an inclined magnetic field is studied. From an extension of literature [13] subject to a forced oscillation it is observed that the present paper is methodically more correct to work first in the steady state where forced oscillation becomes insignificant and then new results are expected for an unsteady MHD flow under the influence of a pulse-oscillator. Exact solutions of the governing equations are obtained in a closed form. The graphical representation for the velocity and the induced magnetic field are depicted graphically and the heat transfer at both the plates are presented in tables.     

Calculations of the parameters of the air plasma produced by an electron beam in the channel of an MHD generator with a nonequilibrium conductivity

Approximate analytic expressions for calculating the electron density in both steady and unsteady plasmas produced by pulsed electron beams are derived and proved to agree well with numerical calculations. It is shown that the algorithm for calculating the parameters of a nonequilibrium plasma in the channel of an MHD plasma generator depends on the type of generator. The effect of the magnetic field strength on the electron density and electric conductivity of the air plasma produced by an electron beam in the channel of a Faraday MHD generator is investigated. The influence of the parameters of the flow and ionizer on the efficiency of an MHD generator with a nonequilibrium conductivity is analyzed.     

带通道插件管道流磁流体动力学效应的数值模拟

采用二维完全发展流模型对聚变反应堆包层带通道插件和压力平衡槽隙的矩形磁流体管流的MHD效应进行数值模拟,分析速度分布,MHD压降随哈德曼数以及通道插件的电导率的变化规律.与无插件磁流体管流相比,带绝缘通道插件管流MHD压降显著降低,MHD压降随哈德曼数的增加而减小,通道插件材料的电导率增加MHD压降系数减小.压力平衡槽隙处的回流与通道插件的电导率有关.在宏观上计算结果与实验结果和简化理论结果一致.     

Calculation of the electric potential and Lorentz force acting on a locally ionized region in a magnetohydrodynamic flow placed in a nonuniform magnetic field

An analytical solution to electrodynamic equations for the electric potential in a locally ionized magnetohydrodynamic (MHD) flow in the nonuniform magnetic field produced by a straight-line conductor is found. Analytical formulas are obtained to evaluate the volume density of the Lorentz force and the integral Lorentz force acting on the locally ionized region of the MHD flow. It is shown that the MHD action on the locally ionized flow in the nonuniform magnetic field can be used to control the elevating force as well as the ratio of the elevating force to the drag force.     

A note on unsteady hydromagnetic flow in a rotating channel permeated by an inclined magnetic field in the presence of an oscillator

Ghosh [Czech. J. Phys.46 (1996) 85] has extended the problem of an unsteady hydromagnetic flow (MHD) in a rotating environment permeated by an inclination of a uniform magnetic field with the positive direction of the axis of rotation; a fluid-pulse oscillator is applied along the axis of rotation in order to explain the validity of a physical situation of a steady flow under the conditions and configurations as stated by Ghosh in the paper cited above. It is investigated that the unsteady MHD flow has an intrinsic stability subject to Ghosh inertial frequency in relation withG _MK ² =(16K ⁴ −M ⁴ sin⁴ θ)^1/2, where MHD flow stability parameter of the Earth’s liquid core is taken into account, which seems to have disappeared in the literature since 1942. It is important to say that the thermonuclear reaction indicates a maximum dissipation of energy into smallest eddies when the kinetic energy is transformed into heat.     

Viscous Slip MHD Flow over a Moving Sheet with an Arbitrary Surface Velocity

The magnetohydrodynamic(MHD) flow induced by a stretching or shrinking sheet under slip conditions is studied.Analytical solutions based on the boundary layer assumption are obtained in a closed form and can be applied to a flow configuration with any arbitrary velocity distributions. Seven typical sheet velocity profiles are employed as illustrating examples. The solutions to the slip MHD flow are derived from the general solution and discussed in detail. Different from self-similar boundary layer flows, the flows studied in this work have solutions in explicit analytical forms. However, the current flows require special mass transfer at the wall, which is determined by the moving velocity of the sheet. The effects of the slip parameter, the mass transfer at the wall, and the magnetic field on the flow are also demonstrated.     

弱磁场对Zn分枝状电解沉积物形貌的影响

用金相显微镜和原子力显微镜分析了存在外加磁场情况下的Zn分枝状电解沉积物的微观形貌 ，并且根据实验结果提出了磁场使沉积物分枝呈现螺旋状偏转的机理.1)在沉积物晶粒的早 期生长阶段，当晶粒已经形成了择优生长方向但又非常小,仍然悬浮于电解液中时，磁流体 动力学对流作用于它上面的不平衡力使得晶粒连同它的择优生长方向向着对流下方偏转，直 到晶粒足够大，和它的前一个单晶枝晶连接在一起为止.2)当晶粒和它的前一个单晶枝晶连 接在一起以后，磁流体动力学对流的作用力已不足使它偏转.此时，如果电解液的浓度比较 高，单晶枝晶的一级分枝和二级分枝之间不存在对电解质的竞争关系，则此单晶枝晶将完全 按照初期形成的晶体择优生长方向直线生长，直到新的晶粒形核为止;如果电解液浓度较低 ，造成第一级分枝与第二级分枝的竞争关系，二级分枝总在第一级分枝的上游侧生长，使得 一级分枝向下游方向偏转.通过上述两个步骤，无论是枝晶沉积物还是分形沉积物都产生螺 旋状偏转. 关键词： 电解沉积 磁流体动力学对流 晶体择优生长方向 生长形态     

Analytical solutions for the unsteady MHD rotating flow over a rotating sphere near the equator

In this paper we investigate the three-dimensional magnetohydrodynamic (MHD) rotating flow of a viscous fluid over a rotating sphere near the equator. The Navier-Stokes equations in spherical polar coordinates are reduced to a coupled system of nonlinear partial differential equations. Self-similar solutions are obtained for the steady state system, resulting from a coupled system of nonlinear ordinary differential equations. Analytical solutions are obtained and are used to study the effects of the magnetic field and the suction/injection parameter on the flow characteristics. The analytical solutions agree well with the numerical solutions of Chamkha et al. [31]. Moreover, the obtained analytical solutions for the steady state are used to obtain the unsteady state results. Furthermore, for various values of the temporal variable, we obtain analytical solutions for the flow field and present through figures.     

Computation of the electric potential and the Lorentz force in a locally ionized magnetohydrodynamic flow in a nonuniform magnetic field for a transverse flow past a circular cylinder

An analytical solution to electrodynamic equations is obtained for the electric potential in a locally ionized magnetohydrodynamic (MHD) flow for a transverse flow past a circular cylinder in the non-uniform magnetic field of a rectilinear conductor. Analytical formulas for computing the volume density of the Lorentz force acting on the flow in a locally ionized MHD flow are obtained for the case of the conducting and nonconducting surfaces of the cylinder. The influence of the Hall parameter and width of the MHD interaction region on the value of the Lorentz force is analyzed. It is demonstrated that the Lorentz force, which accelerates and not decelerates the flow, appears under certain conditions near the surface of the cylinder in the neighborhood of the critical point.     

高超声速飞行器磁控热防护系统建模分析

针对高超声速飞行器防热, 搭建了螺线管磁控热防护系统的物理模型. 采用低磁雷诺数磁流体数学模型, 分析了外加磁场强度及磁场形态对磁控热防护效果的影响. 对比了三种磁场类型(磁偶极子、螺线管、均布磁场)下磁控热防护效果的差异, 分析了螺线管几何参数对磁控热防护效果的影响. 研究表明, 磁场降低表面热流作用存在“饱和现象”; 三种磁场形态的磁控热防护能力从小到大依次为磁偶极子、螺线管、均布磁场; 相同驻点磁感应强度条件下, 增大螺线管半径有利于提高磁控热防护效果, 缩短螺线管与驻点距离不利于驻点和肩部防热, 螺线管长度对磁控热防护效果影响相对较小.     

Supersonic flow about a body exposed to electric and magnetic fields

The feasibility of using nonmechanical (electrogasdynamic, EGD, and magnetohydrodynamic, MHD) methods to control shock-wave configurations emerging in supersonic flows is investigated. In the EGD method, the flow is heated by a gas discharge; in the MHD one, the flow is influenced by a Lorentz force arising in a gas discharge upon applying a magnetic field. The influence of the gas discharge and MHD interaction on the position of a detached shock wave appearing in a supersonic xenon flow about a semicylindrical body is studied. A discharge is initiated in the immediate vicinity of the leading edge of the body, and the variation of the shock wave position with the intensity of the discharge (discharge current density) is traced when the influence of the EGD action increases and/or an external magnetic field is applied (the influence of the MHD action increases). Preliminary data for a supersonic air flow about a body are presented.     

Effects of hall current on MHD Couette flow in a rotating system with arbitrary magnetic field

Author has studied the MHD Couette flow in a rotating environment with non- conducting walls in the presence of an arbitrary magnetic field. The solution in dimensionless form contains four pertinent flow parameters, viz. the Hartmann number, the rotation parameter which is the reciprocal of the Ekman number, the Hall current parameter, and the angle of inclination of the magnetic field to the positive direction of the axis of rotation. An interplay of hydromagnetic force and Coriolis force with an inclusion of Hall current plays a significant role in determining the MHD flow behaviour. The velocity and induced magnetic field distributions are depicted graphically. Also, the numerical results of shear stresses and the rate of mass flows are presented graphically.     

Characterization of the three-dimensional supersonic flow for the MHD generator

A numerical procedure based on a five-wave MHD model associated with non-ideal, low magnetic Reynolds number MHD flows was developed in the present study for analyzing the flow fields in the MHD generator of a MHD bypass scramjet. The numerical procedure is composed of an entropy conditioned scheme for solving the non-homogeneous Navier-Stokes equations, in conjunction with an SOR method for solving the elliptic equation governing the electrical potential. It was found that a separation would take place near the downstream edge of the second electrode, where the local adverse pressure gradient is large, and the core of the flow field is characterized as a 2-D flow due to the Hartmann effects along the direction of the magnetic field. The electric current lines would be increasingly distorted as the magnetic interactive parameter increases, and even induce an eddy current. Induced eddy current was also found in the different cross-sections along the axial direction, all of these would definitely deteriorate the performance of the MHD generator. The cross-sectional M-shape velocity profile found along the axial direction between the insulating walls is responsible for the formation of the vortex flow at the corner of the insulator cross-section, which, in turn, induces the corner eddy current at the corner. A numerical parametric study was also performed, and the computed performance parameters for the MHD generator suggest that, in order to enhance the performance of MHD generator, the magnetic interaction parameter should be elevated.     

Eigenstates in quantum dots confined by an inhomogeneous magnetic field

We study the eigenstates in quantum dots in which electrons are confined by the application of an inhomogeneous perpendicular magnetic field, focusing on the effect that the specific details of the shape of confining field has on determining these states. In contrast to the edge state picture established in studies on circular dots, we find that dots with more irregular geometries show a more complicated behavior in the interior of the dot. In particular, we find that certain states show indications of having their amplitude enhanced along particular classical periodic orbits in the interior, a phenomenon known as ‘scarring’.     

Saturated state of the nonlinear small-scale dynamo

We consider the problem of incompressible, forced, nonhelical, homogeneous, and isotropic MHD turbulence with no mean magnetic field and large magnetic Prandtl number. This type of MHD turbulence is the end state of the turbulent dynamo, which generates folded fields with small-scale direction reversals. We propose a model in which saturation is achieved as a result of the velocity statistics becoming anisotropic with respect to the local direction of the magnetic folds. The model combines the effects of weakened stretching and quasi-two-dimensional mixing and produces magnetic-energy spectra in remarkable agreement with numerical results at least in the case of a one-scale flow. We conjecture that the statistics seen in numerical simulations could be explained as a superposition of these folded fields and Alfvén-like waves that propagate along the folds.     

Study of MHD dynamo effect at the outlet from plasma accelerator in the presence of longitudinal magnetic field

Properties of compressible flows in the quasi-stationary plasma accelerator have been studied in the presence of an additional longitudinal magnetic field and the arising rotation of plasma flow. Numerical study was carried out within the framework of two-dimensional magnetic hydrodynamics (MHD) model of the axisymmetric plasma flows taking into account the finite conductivity of medium and radiation transport. Dynamics of compressible plasma flows is accompanied by the MHD dynamo effect or generation of magnetic field on a conical shock wave forming at the outlet from the accelerator.     

Intermediate shocks in three-dimensional magnetohydrodynamic bow-shock flows with multiple interacting shock fronts

Simulation results of three-dimensional (3D) stationary magnetohydrodynamic (MHD) bow-shock flows around perfectly conducting spheres are presented. For strong upstream magnetic field a new complex bow-shock flow topology arises consisting of two consecutive interacting shock fronts. It is shown that the leading shock front contains a segment of intermediate 1-3 shock type. This is the first confirmation in 3D that intermediate shocks, which were believed to be unphysical for a long time, can be formed and can persist for small-dissipation MHD in a realistic flow configuration.     

Three-dimensional MHD flow over a shrinking sheet: Analytical solution and stability analysis

The magnetohydrodynamic(MHD) steady and unsteady axisymmetric flows of a viscous fluid over a two-dimensional shrinking sheet are addressed. The mathematical analysis is carried out in the presence of a large magnetic field. The steady state problem results in a singular perturbation problem having an infinite domain singularity. The secular term appearing in the solution is removed and a two-term uniformly valid solution is derived using the Lindstedt–Poincaré technique. This asymptotic solution is validated by comparing it with the numerical solution. The solution for the unsteady problem is also presented analytically in the asymptotic limit of large magnetic field. The results of velocity profile and skin friction are shown graphically to explore the physical features of the flow field. The stability analysis of the unsteady flow is made to validate the asymptotic solution.     

Formation of compression shocks in a nonequilibrium plasma flow in a magnetic field

Plasma flow in a linearly widening, ideally sectioned, short-circuited magnetohydrodynamic (MHD) channel is studied. MHD flows are classified into two types: continuous flows and flows with a compressional MHD shock in plasmas that are stable and unstable against the onset of ionization instability. Specific features in the evolution of a stationary compression MHD shock are investigated, and its position as a function of the Stewart number is determined. It is found that, in a plasma flow in which ionization instability develops, a compression MHD shock arises at lower values of the MHD interaction parameter than in a stable plasma flow. An unidentified type of instability of MHD discontinuities is revealed.     

带引流条导电矩形管磁流体湍流大涡数值模拟

为研究引流条对磁流体湍流的影响，采用自主开发的低磁雷诺数流固耦合磁流体相干结构模型大涡模拟求解器，对均匀磁场作用下平行层内带引流条导电矩形管和标准导电矩形管中液态金属湍流进行了数值模拟研究。结果表明，外加垂直流动方向的均匀磁场与流动的导电流体相互作用产生与流动方向相反的洛伦兹力，能够抑制磁流体的湍流脉动，这种抑制作用随着哈特曼数增大而增强。在弱导电率条件下，当Re=16350、Ha=212 时，两种管道中的流动均转换为层流流动状态。管道内壁面摩擦系数随着哈特曼数的增大而增大。引流条能在其近壁局部区域增强横向速度，有效激发湍流，但在弱壁面导电率条件下，带引流条导电矩形管壁面摩擦系数较标准矩形管大。