The effect of magnetic field on two-phase liquid metal flow

In this paper, the basic equations of two-phase liquid metal flow in a magnetic field are derived, and specifically, two-phase liquid metal MHD flow in a rectangular channel is studied, and the expressions of velocity distribution of liquid and gas phases and the ratioK ₀ of the pressure drop in two-phase MHD flow to that in single-phase are derived. Results of calculation show that the ratioK ₀ is smaller than unity and decreases with increasing void fraction and Hartmann number because the effective electrical conductivity in the two-phase case decreases. The Project is supported by the National Natural Science Foundation of China.     

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.     

Visualisation of air–water bubbly column flow using array Ultrasonic Velocity Profiler

In the present work, an experimental study of bubbly two-phase flow in a rectangular bubble column was performed using two ultrasonic array sensors, which can measure the instantaneous velocity of gas bubbles on multiple measurement lines. After the sound pressure distribution of sensors had been evaluated with a needle hydrophone technique, the array sensors were applied to two-phase bubble column. To assess the accuracy of the measurement system with array sensors for one and two-dimensional velocity, a simultaneous measurement was performed with an optical measurement technique called particle image velocimetry(PIV). Experimental results showed that accuracy of the measurement system with array sensors is under 10% for one-dimensional velocity profile measurement compared with PIV technique. The accuracy of the system was estimated to be under 20% along the mean flow direction in the case of two-dimensional vector mapping.     

Non equilibrium gas-liquid flows in variable cross section ducts

The behaviour of two-phase high velocity flows in variable cross section ducts was investigated using a one-dimensional numerical model developed for the study of the annular flow configuration. Heat, mass, and momentum transfer between the phases during the flow were considered. The validation of the calculation procedure was made with some experimental data for the air-water couple, while the main application concerned the evaluation of momentum transfer from an expanding gas to an entrained liquid stream in droplet form. A liquid metal-gas flow was considered to simulate the process taking place in a plant where electrical power is generated by a liquid metal flowing in a magnetic field (MHD). The effectiveness of energy and momentum transfer between the liquid and the gas phase during the expansion was evaluated and the influence of nozzles with different convergence angles was investigated.     

Velocity of sound in two-phase mixtures

Velocity of sound is computed for water, ammonia, Freon-12 and isobutane in two-phase mixtures in thermodynamic equilibrium. A computational method is developed which yields the sound velocity in terms of the thermodynamic coordinates of the substance (T, x) without the use of diagrams. Corresponding velocities of sound for the four substances considered exhibit a certain similarity which is examined statistically. The relationship between the sound velocity and the critical mass flux is also investigated.     

Exact solutions of MHD second Stokes flow of generalized Burgers fluid

This work concerns with the exact solutions of magnetohydrodynamic (MHD) flow of generalized Burgers fluid describing the second Stokes problem. The modified Darcy law is taken into account. The related velocity distribution and shear stress are expressed as a combination of steady-state and transient solutions computed by means of integral transformations. The effects of various parameters on the flow field are investigated. The MHD flow results in reduction of velocity distribution and associated thickness of the boundary layer.     

Spontaneous rotation in the exact solution of magnetohydrodynamic equations for flow between two stationary impermeable disks

Magnetohydrodynamic (MHD) flow of a viscous electrically conducting incompressible fluid between two stationary impermeable disks is considered. A homogeneous electric current density vector normal to the surface is specified on the upper disk, and the lower disk is nonconducting. The exact von Karman solution of the complete system of MHD equations is studied in which the axial velocity and the magnetic field depend only on the axial coordinate. The problem contains two dimensionless parameters: the electric current density on the upper plate Y and the Batchelor number (magnetic Prandtl number). It is assumed that there is no external source that produces an axial magnetic field. The problem is solved for a Batchelor number of 0–2. Fluid flow is caused by the electric current. It is shown that for small values of Y, the fluid velocity vector has only axial and radial components. The velocity of motion increases with increasing Y, and at a critical value of Y, there is a bifurcation of the new steady flow regime with fluid rotation, while the flow without rotation becomes unstable. A feature of the obtained new exact solution is the absence of an axial magnetic field necessary for the occurrence of an azimuthal component of the ponderomotive force, as is the case in the MHD dynamo. A new mechanism for the bifurcation of rotation in MHD flow is found.     

An analytic solution of dense two-phase flow in a vertical pipeline

According to a mathematical model for dense two-phase flows presented in theprevious paper,a dense two-phase flow in a vertical pipeline is analytically solved,and theanalytic expressions of velocity of each continuous phase and dispersed phase arerespectively derived The results show that when the drag force between two phases dependslinearly on their relative velocity,the relative velocity profile in the pipeline coincides withDarcy’s law except for the thin layer region near the pipeline wall,and that the theoreticalassumptions in the dense two-phase flow theory mentioned are reasonable.     

Direct simulation of MHD flows in dual-coolant liquid metal fusion blanket using a consistent and conservative scheme

Direct simulation of 3-D MHD (magnetohydrodynamics) flows in liquid metal fusion blanket with flow channel insert (FCI) has been conducted. Two kinds of pressure equilibrium slot (PES) in FCI, which are used to balance the pressure difference between the inside and outside of FCI, are considered with a slot in Hartmann wall or a slot in side wall, respectively. The velocity and pressure distribution of FCI made of SiC/SiC_f are numerically studied to illustrate the 3-D MHD flow effects, which clearly show that the flows in fusion blanket with FCI are typical three-dimensional issues and the assumption of 2-D fully developed flows is not the real physical problem of the MHD flows in dual-coolant liquid metal fusion blanket. The optimum opening location of PES has been analyzed based on the 3-D pressure and velocity distributions.     

Effects of hall current on MHD Couette flow in a channel partially filled with a porous medium in a rotating system

MHD Couette flow in a channel with non-conducting walls, partially filled with a porous medium, is investigated in the presence of an inclined magnetic field in a rotating system. It is observed that the MHD flow behaviour in the channel has been influenced significantly by the Coriolis force, the hydromagnetic force with an inclusion of Hall current and the permeability of the porous medium. Effects of the parameters of these forces on the velocity distributions, induced magnetic field distributions and the skin friction have been depicted graphically and discussed.     

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.      

The analysis of two-dimensional two-phase flow in horizontal heated tube bundles using drift flux model

This paper presents the experimental study and numerical simulation of two-dimensional two-phase flow in horizontal heated tube bundles. In the experiments, two advanced measuring systems with a single-fibre optical probe and a tri-fibre-optical-probe were developed to measure respectively the local void fraction and vapor bubble velocities among the heated tube bundles. In accordance with the internal circulation characteristics of two-phase flow in the tube bundles, a mathematical model of two-dimensional two-phase low Reynolds number turbulent flow based on the modified drift flux model and the numerical simulation method to analyze the two-phase flow structures have been developed. The modified drift flux model in which both the acceleration by gravity and the acceleration of the average volumetric flow are taken into account for the calculation of the drift velocities enables its application to the analysis of multi-dimensional two-phase flow. In the analysis the distributions of the vapor-phase velocity, liquid-phase velocity and void fraction were numerically obtained by using the modified drift flux model and conventional drift flux model respectively and compared with the experimental results. The numerical analysis results by using the modified drift flux model agree reasonably well with the experimental investigation. It is confirmed that the modified drift flux model has the capability of correctly simulating the two-dimensional two-phase flow. Received on 3 September 1998     

Propagation of pressure waves in two-phase flow

We deal with a pressure wave of finite amplitude propagating in a gas and liquid medium or in the fluid in an elastic tube. We study the effects of pipe elasticity on the propagation velocity of the pressure wave. Pressure waves of finite amplitude progressing in the two-phase flow are treated considering the void fraction change due to pressure rise. The propagation velocity of the two-phase shock wave is also investigated, and the behavior of the reflection of the pressure wave at the rigid wall is analyzed and compared to that in a pure gas or liquid. The results are compared to experimental data of a pressure wave propagating in the two-phase flow in a vertical shock tube.     

Solution of magnetohydrodynamic flow in a rectangular duct by Chebyshev collocation method

In this study, matrix representation of the Chebyshev collocation method for partial differential equation has been represented and applied to solve magnetohydrodynamic (MHD) flow equations in a rectangular duct in the presence of transverse external oblique magnetic field. Numerical solution of velocity and induced magnetic field is obtained for steady‐state, fully developed, incompressible flow for a conducting fluid inside the duct. The Chebyshev collocation method is used with a reasonable number of collocations points, which gives accurate numerical solutions of the MHD flow problem. The results for velocity and induced magnetic field are visualized in terms of graphics for values of Hartmann number H≤1000. Copyright © 2010 John Wiley & Sons, Ltd.     

Damping of tubes due to internal two-phase flow

Two-phase internal flow is present in many piping system components. Although two-phase damping is known to be a significant constituent of the total damping, the energy dissipation mechanisms that govern two-phase damping are not well understood. In this paper, damping of three different clamped–clamped tubes subjected to two-phase air–water internal axial flow is investigated. Experimental data are reported, showing a strong dependence of two-phase damping on void fraction, flow velocity and flow regime. Data-points plotted on two-phase flow pattern maps indicate that damping is greater in a bubbly flow regime. The two-phase damping ratio reaches a maximum value at the highest void fraction before the transition to a churn flow regime. An analytical model that relates the two-phase damping ratio to the interface surface area is proposed. The model is based on rigid spherical bubbles in cubic elementary flow volumes. The analytical results are well correlated with the experiments.     

Analytical solution of magnetohydrodynamic sink flow

An analytical solution to the famous Falkner-Skan equation for the magnetohydrodynamic (MHD) flow is obtained for a special case, namely, the sink flow with a velocity power index of −1. The solution is given in a closed form. Multiple solution branches are obtained. The effects of the magnetic parameter and the wall stretching parameter are analyzed. Interesting velocity profiles are observed with reversal flow regions even for a stationary wall. These solutions provide a rare case of the Falkner-Skan MHD flow with an analytical closed form formula. They greatly enrich the analytical solution for the celebrated Falkner-Skan equation and provide better understanding of this equation.     

Influence of hall effect and ion slip on velocity and temperature fields in an MHD channel

The combined influence of viscosity, Hall effect and ion slip on hydrodynamic fields and on heat transfer is investigated. The exact solutions for velocity, induced magnetic field and temperature are derived for the laminar MHD flow in a flat channel assuming a small magnetic Reynolds number, finely segmented electrodes, fully developed flow and uniform heat flux at channel walls. The internal generation of heat is not considered. The Kantorowitsch method of variational calculus is employed to approximate the complicated velocity distribution.     

高浓度固-液两相流紊流的动理学模型

采用分子动理学方法,基于固-液两相流液相分子或颗粒相颗粒的Boltzmann方程,对Boltzmann方程分别取零矩和一次矩,则得到高浓度固-液两相流紊流的连续方程和动量方程,再和较成熟的低浓度两相流连续方程和动量方程比较,取低浓度两相流控制方程中较成熟合理的有关项和高浓度时由动理学方法推导出的颗粒间碰撞项,则得到高浓度固-液两相流紊流的最终控制方程:连续方程和动量方程.     

Magnetohydrodynamic heat transfer in two-phase flow between parallel plates

This study dealt with two-phase magnetohydrodynamic (MHD) flow and heat transfer in a parallel-plate channel. Both phases were incompressible and the flow was assumed to be steady, one-dimensional and fully developed. The present study was expected to be useful in the understanding of the effect of the presence of slag layers on the heat transfer characteristics of a coal-fired MHD generator.The problem was investigated, in which one of the two fluids was assumed to be electrically non-conducting. The transport properties of the two fluids were taken to be constant, and the plates were assumed to be maintained at constant and equal temperatures. In this case, the governing differential equations were linear, and an exact solution was obtained. Results were presented for various height and viscosity ratios for the two fluids and for two values of the electric field loading parameter. The governing equations were also solved numerically in order to verify the exact solution.     

颗粒材料中致密波结构研究

采用一维两相流模型与相应颗粒构形应力函数,研究了致密波的形成及其结构．用简化两相流模型系统地讨论致密波对有关因素的依赖关系．分析指出：小于基体材料音速的致密波仅能在非理想颗粒材料中存在,从波前到波后,所有状态物理量光滑过渡．大于基体材料音速的致密波,波头可能存在间断．应力函数与致密粘性确定后,致密波速度决定致密波结构、宽度、终态压实度．采用一维两相流模型模拟了活塞驱动颗粒床形成致密波这一动态过程．用线方法（MOL）对该方程组求数值解．计算表明,经过短暂的非稳态过程,颗粒床中形成一稳态致密波．分析了活塞速度与初始孔隙率对致密波结构的影响,并对简化两相流模型与两相流模型的计算结果进行了对比．