Numerical analysis of liquid metal MHD flows through circular pipes based on a fully developed modeling

Magnetohydrodynamics (MHD) laminar flows through circular pipes are studied in this paper by numerical simulation under the conditions of Hartmann numbers from 18 to 10000. The code is developed based on a fully developed modeling and validated by Samad's analytical solution and Chang's asymptotic results. After the code validation, numerical simulation is extended to high Hartmann number for MHD circular pipe flows with conducting walls, and numerical results such as velocity distribution and MHD pressure gradient are obtained. Typical M-type velocity is observed but there is not such a big velocity jet as that of MHD rectangular duct flows even under the conditions of high Hartmann numbers and big wall conductance ratio. The over speed region in Robert layers becomes smaller when Hartmann numbers increase. When Hartmann number is fixed and wall conductance ratios change, the dimensionless velocity is through one point which is in agreement with Samad's results, the locus of maximum value of velocity jet is same and effects of wall conductance ratio only on the maximum value of velocity jet. In case of Robert walls are treated as insulating and Hartmann walls as conducting for circular pipe MHD flows, there is big velocity jet like as MHD rectangular duct flows of Hunt's case 2.     

Development of a potential based code for MHD analysis of LLCB TBM

A two dimensional solver is developed for MHD flows with low magnetic Reynolds’ number based on the electrostatic potential formulation for the Lorentz forces and current densities which will be used to calculate the MHD pressure drop inside the channels of liquid breeder based Test Blanket Modules (TBMs). The flow geometry is assumed to be rectangular and perpendicular to the flow direction, with flow and electrostatic potential variations along the flow direction neglected. A structured, non-uniform, collocated grid is used in the calculation, where the velocity (u), pressure (p) and electrostatic potential (?) are calculated at the cell centers, whereas the current densities are calculated at the cell faces. Special relaxation techniques are employed in calculating the electrostatic potential for ensuring the divergence-free condition for current density. The code is benchmarked over a square channel for various Hartmann numbers up to 25,000 with and without insulation coatings by (i) comparing the pressure drop with the approximate analytical results found in literature and (ii) comparing the pressure drop with the ones obtained in our previous calculations based on the induction formulation for the electromagnetic part. Finally the code is used to determine the MHD pressure drop in case of LLCB TBM. The code gives similar results as obtained by us in our previous calculations based on the induction formulation. However, the convergence is much faster in case of potential based code.     

Research on operational characteristics of passive residual heat removal system under rolling motion

The operational characteristics of passive residual heat removal system under rolling motion were investigated experimentally. The passive residual heat removal system under rolling motion was simulated with the advanced RELAP5 code. The results are consistent with experiments. The relative discrepancy between calculating and experimental results is less than 10%. The modified condensation heat transfer model can also be used to calculate the condensation heat transfer coefficient with droplet carryover precisely. The fluctuation of condensate temperature and steam pressure is not noticeable. As the power becomes larger for the same rolling motion, the oscillation amplitude of condensate flow rate becomes larger. The effect of rolling motion upon heat transfer coefficient and flow resistance was investigated with experimental results. Rolling motion can increase the flow resistance in a great extent. The more serious the rolling is, the more the flow resistance is. Additional pressure drop does not effect on average flow velocity. The decreasing of average flow velocity is due to the decreasing average gravity pressure drop and the increasing of flow resistance. The contribution of gravity pressure drop on the decrement of average flow velocity is less than 20%. The other is due to the increasing flow resistance. In the present paper, the experimental results are listed first, and then the simulation results comparing with the experimental results are listed in the second part. At last, the effect of rolling motion is investigated theoretically.     

海洋条件下任意管道内附加压降的势函数分析和矢量代数积分方法

在海洋条件下,由于管道平移和摇摆运动会引入附加的体积力作用而产生附加压降。为了获得具有普遍适用性和便于应用的附加压降理论计算结果,从非惯性坐标系下流体动力学动量方程出发,将管道运动划分为平移和摇摆运动方式,应用流体力学势函数分析方法分别获得平移运动和摇摆运动离心力产生的附加压降计算关系式。根据附加压降物理定义,将管道摇摆运动划分为正交摇摆、平行摇摆2种基本方式,采用矢量代数积分方法获得摇摆运动切向力产生的附加压降计算关系式,并讨论了这些关系式的适用性。理论分析结果表明,海洋条件下任意管道内各项附加压降都可得到精确求解。     

控制棒组件在流体环境中下落时所受阻力的计算

基于流体力学和边界理论,探讨了控制棒组件在下落过程中所受的流体阻力。对控制棒组件的3种部件－－控制棒束、驱动杆、星形爪在下落时所受的流体阻力分别按SU／PG迎风修正的有限元数值方法及基于边界层理论的近似解析法进行求解,完成了控制棒组件下落过程的时程分析,并得出该组件的下落参数（位置和速度）与瞬时流体阻力的关系。     

Experiments on flows, boiling and heat transfer in porous media: Emphasis on bottom injection

This paper deals with basic experiments conducted to analyse the effect of the particles’ shape and size distribution on intrinsic properties of porous beds as well as two-phase flow and heat transfer in these porous media.Structural, transport properties, flow laws and heat transfer with phase-change phenomena in several kinds of porous media are presented and discussed. The porosity of stacks constituted by spheres of various sizes is analysed. A variation law of the porosity as a function of the standard deviation of the particle size distribution is proposed. The porosity, tortuosity, permeability and inertial coefficient of the flow law in randomly stacked fibres are established experimentally and theoretically. The porosity of such media is found to vary from 0.35 to 0.92 according to the fibre aspect ratio. Tortuosity and Kozeny–Carman parameters are determined by both electric and hydrodynamic methods. These parameters are found to vary with the porosity of the fibrous bed. New relations of permeability and inertial coefficient are derived from experimental results. Finally, a pressure drop relation is proposed for fibrous beds.Convective boiling phenomena, with emphasis to application on bottom injection, are experimentally determined for fibrous porous media. Temperature field determination evidences the formation of three distinct zones in the porous medium: a liquid zone, a two-phase zone and a superheated zone. For higher heat flux density, a fourth zone is found in which vapour and liquid are in thermal non-equilibrium. A one-dimensional analytical model of pressure drop in two-phase configuration has been performed. Comparisons with experimental data are found in good agreement with the results of this model for moderate heat fluxes. For higher heat flux values, discrepancies are found. These cases correspond to the appearance and the evolution of the thermal non-equilibrium two-phase zone. Heat transfer characteristics at the heated walls are analysed. Formation of vapour in the neighbourhood of the heated walls has a strong influence on the heat transfer coefficient. This behaviour may be related to the critical heat flux phenomenon encountered in usual ducts.     

摇摆对非能动余热排出系统自然循环能力影响的试验研究

在摇摆台架上对摇摆条件下的非能动余热排出系统的自然循环能力及其相关特性进行了试验研究。分析了附加压降和重位压降对流动特性的影响,以及摇摆条件下的重位压降和流动阻力对流速的影响。结果表明:摇摆条件下,非能动余热排出系统自然循环能力下降。摇摆振幅越大,平均凝水流量越小,波动幅度越大;凝水流量最小值随摇摆振幅的增大而下降很多,但凝水流量最大值变化较小。系统参数变化与摇摆周期关系不大。附加压降不会对平均流速产生影响,重位压降对平均流速的影响与周期无关。重位压降对流速的影响比流动阻力的影响小得多。随着摇摆振幅的增加,流动阻力对平均流速的影响略有降低。     

矩形通道高宽比对两相流动阻力和流型关系的影响

在可视化观察的基础上,实验研究了矩形通道高宽比对两相流动阻力和流型关系的影响。实验选择了3种通道尺寸的实验段,截面宽度相同,全部为43 mm,高度分别为1.41、3和10 mm,根据受限因子C_o,前两个实验段属于窄通道,第3个属于常规通道。实验结果表明：高宽比不同时,随着气相流速的增加,通道内两相流动压降呈不同的变化趋势。对于10 mm通道,低气相流量时重位压降占主要成分,而对于1.41 mm和3 mm通道,摩擦压降占主要成分;随着气相流量的增大,总压降中摩擦压降的比例也增大;对于10 mm矩形通道,可利用压降变化规律确定搅混流的发生范围。     

Hydraulic resistance of fluids flowing in channels at supercritical pressures (survey)

This literature survey is devoted to hydraulic resistance of water and carbon dioxide flows at supercritical pressures. The objectives are to assess previous studies that were done in the area of hydraulic resistance of fluids at supercritical pressures flowing in channels of various geometries and to understand the specifics of pressure drop at these conditions. The literature search showed that the majority of experimental data were obtained in vertical tubes, some data were obtained in horizontal tubes and just a few of them in other flow geometries including bundles. In general, hydraulic resistance data are limited compared to the heat transfer data at supercritical pressures. Differences in pressure drop between supercritical and subcritical forced convection seem to be related to significant variations in thermophysical properties near the critical and pseudocritical points. Due to these variations, satisfactory analytical and numerical methods have not yet been developed especially in turbulent flows and at high heat fluxes. In general, the pressure drop in supercritical fluid flow consists of four components: pressure drop due to frictional resistance, due to local flow obstruction, due to acceleration of flow and due to gravity. The total pressure drop at supercritical pressures can be estimated using general correlations for pressure drop at subcritical pressures with correction factors for the effect of significant thermophysical properties variations and high heat fluxes. Only one paper was devoted to pressure drop in tight short bundles cooled with water at supercritical pressures. Therefore, more experimental work is needed to estimate the total pressure drop in various bundle designs with the objective of providing reliable information for designing supercritical water nuclear reactors.     

Sensitivity analysis of an impedance void meter to the void distribution in annular flow: a theoretical study

Impedance void meters are frequently used to measure the area-averaged void fraction in pipes. This is primarily for two reasons: firstly, this method is non-intrusive since the measurement can be made by electrodes flush mounted in the walls, and secondly, the signal processing equipment is simple.Impedance probes may be calibrated by using a pressure drop measurement or a quick closing valve system. In general, little attention is paid to void distribution effects. It can be proved that in annular flow, the departure from radial symmetry has a strong influence on the measured mean film thickness. This can be easily demonstrated by solving the Laplace equation for the electrical potential by simple analytical methods. When some spatial symmetry conditions are encountered, it is possible to calculate directly the conductance of the two-phase medium without a complete calculation of the potential. A solution of this problem by using the separation of variables technique is also presented. The main difficulty with this technique is the mixed nature of the boundary conditions: the boundary condition is both of Neumann and of Dirichlet type on the same coordinate curve. This formulation leads to a non-separable problem, which is solved by truncating an infinite algebraic set of linear equations.The results, although strictly valid in annular flow, may give the correct trends when applied to bubbly flow. Finally, the theory provides an error estimate and a design criterion to improve the probe reliability.     

Numerical analysis of flowing characteristics of turbulent flow in rectangular channels in ocean environment

Because of the periodic effects of ocean waves, there are great discrepancies between the operational characteristics of nuclear power systems in ocean environment and that of land-based nuclear power systems. In some special operational status, like natural circulation, the additional forces due to ocean environment may impose so great disturbance on the coolant flow that theatres the safety operation of the systems. In the present paper, the turbulent flow in rectangular channels in ocean environments is investigated theoretically with CFD code FLUENT. The effects of several parameters on turbulent flow are analyzed. The effects of rolling motion includes two parts, the first part is the additional force parallel to flowing direction, which can affect on the pressure drop of the flow and change the flowing velocity, and the other part is the additional force perpendicular to flowing direction. In ocean environments, the flowing characteristics of turbulent flow are dominated by the additional force parallel to flowing direction. The effect of additional force perpendicular to flowing direction is very limited. In rolling and heaving motions, if the flowing velocity is the same, the flowing characteristics of turbulent flow are nearly the same, too. The bigger the Reynolds number is, the more serious the oscillation of turbulent kinetic energy and frictional resistance coefficient is, and the more the oscillation of turbulent flow is. The relationship between average frictional resistance coefficient and velocity oscillating amplitude is quadratic. And the oscillating amplitude of frictional resistance coefficient is in direct ratio with velocity oscillating amplitude.     

升潜条件下矩形窄缝通道绝热层流流动解析解

本文采用数学分析方法对矩形窄缝通道内绝热层流流动进行了研究。通过合理简化得到了分析对象的控制方程,基于固定流量和固定通道压降两种不同的边界条件,求解得出方程的解析解,从而可定量分析升潜条件对速度分布、压降、摩阻系数等的影响规律。     

快堆蒸汽发生器小泄漏下三维流场数值模拟

为了计算快堆蒸汽发生器小泄漏后钠水反应产物的传输扩散,对快堆壳管式蒸汽发生器内稳态钠流场进行了三维数值模拟,建立了蒸汽发生器内钠流场三维数值模型。管束对钠流的影响用分布阻力、体积多孔率、面渗透率来模拟,并根据横掠管束与纵掠管束的压力阻力关系式来关联管束的分布阻力。采用κ－ε湍流模型,壳和支撑板壁面采和壁面函数法来处理。模型计算压降与实验数据比较,二者吻合较好。     

Analytical evaluation of two-phase natural circulation flow characteristics under external reactor vessel cooling

This work proposes an analytical method of evaluating the effects of design and operating parameters on the low-pressure two-phase natural circulation flow through the annular shaped gap at the reactor vessel exterior surface heated by corium (molten core) relocated to the reactor vessel lower plenum after loss of coolant accidents. A natural circulation flow velocity equation derived from steady-state mass, momentum, and energy conservation equations for homogeneous two-phase flow is numerically solved for the core melting conditions of the APR1400 reactor. The solution is compared with existing experiments which measured natural circulation flow through the annular gap slice model. Two kinds of parameters are considered for this analytical method. One is the thermal–hydraulic conditions such as thermal power of corium, pressure and inlet subcooling. The others are those for the thermal insulation system design for the purpose of providing natural circulation flow path outside the reactor vessel: inlet flow area, annular gap clearance and system resistance. A computer program NCIRC is developed for the numerical solution of the implicit flow velocity equation.     

Theoretical analysis of phase-lag in low frequency laminar pulsating flow

The phase-lag between pressure gradient and flow rate in laminar pulsating flow in circular pipes and parallel-plate channels are studied theoretically. It is found that the phase-lag between pressure gradient and flow rate in low frequency (f < 0.5 Hz) pulsating laminar flow exists both in circular pipes and parallel-plate channels. The phase-lag increases with the increase of pulsating frequency, radius of the pipe and the height of the channel, however, it decreases with increase of the fluid viscosity. In addition, the phase-lag is not related to the pulsating amplitude. The analytical results show that velocity radial distribution does not affected by the low frequency pulsation and the value of phase-lag depends on the ratio of the acceleration pressure drop to the total pressure drop.     

Heat transfer of a nuclear reactor containment spray drop

Heat transfer rates to spray droplets under the conditions of a LOCA in a LWR have been evaluated by systematic solution of the governing partial differential equations subject to appropriate initial and boundary conditions. The numerical calculations are based on new correlations. The computations have been facilitated through the use of an efficient hybrid-difference scheme.Results have been provided for the average heat transfer and for the effects of the drop-size, droplet spray angle, initial injection velocity, the containment temperature and pressure on the heat transfer to the drop. The drop fall-heights before attaining thermal equilibrium with the containment atmosphere have been predicted for various conditions. The importance of accurately calculating the drag associated with a moving drop experiencing condensation has been discussed in the context of developing the results.     

Natural circulation capability of Pb-Bi cooled fast reactor: PEACER

First-principle calculations were performed to analyze the natural circulation heat removal from the core of a liquid metal reactor (LMR). The lead-bismuth (Pb-Bi) was chosen as the primary coolant for the LMR system. From the single channel analysis the temperature and the pressure drop are calculated along the fuel assembly. The total pressure drop of the core is less than 100kPa due to the large pitch-to-diameter ratio and the small height of the fuel pin. The natural circulation potential is a key characteristics of the LMR design. The steady-state momentum and energy equations are solved along the primary coolant path. The calculations are divided into two parts: an analytical model and a one-dimensional lumped parameter flow loop model. Results of the analytical model indicate that the elevation difference of 4.5m between thermal centers of the core and the steam generators could remove as much as 10% of the nominal operating reactor power. The flow loop model yielded the total pressure drop and the natural circulation heat removal capacity.     

The structure of turbulent flow through a wall subchannel of a rod bundle

An experimental investigation was performed to establish reliable information on the transport properties of turbulent flow through subchannels of rod bundles. Detailed data were measured of the distributions of the time-mean velocity, the turbulence intensities in all directions and hence, the kinetic energy of turbulence, of the shear stresses in the directions normal and parallel to the walls and of the wall shear stresses for a wall subchannel of a rod bundle of four parallel rods. The pitch to diameter ratio of the rods equal to the wall to diameter ratio was 1.07, the Reynolds number of this investigation was Re = 8.7 × 10⁴.On the basis of the data measured the eddy viscosities in the directions normal and parallel to the walls were calculated. Thus, detailed data of the eddy viscosities in direction parallel to the walls in rod bundles were obtained for the first time. The experimental results were compared with predictions by the VELASCO code. There are considerable differences between calculated and measured data of the time-mean velocity and the wall shear stresses. Attempts to adjust the VELASCO code against the measurements were not successful. The reasons of the discrepancies are discussed.     

矩形通道内脉动层流相位差实验研究

对流量脉动条件下矩形通道内的相位差进行了实验研究，通过建立的脉动层流相位差数学模型，对脉动周期、脉动振幅、通道结构尺寸和流体性质等因素进行了分析，并将实验数据与理论模型结果进行对比。结果表明：矩形通道内，脉动层流的流量变化滞后于压降变化，存在相位差，该相位差仅与脉动周期、流道结构尺寸和流体性质有关，与压降相对振幅无关。     

Drop Formation Characteristics in High Speed Agitation of Centrifugal Extractor

For the solvent extraction of reprocessing plant, mixer-settler, pulsed column are operated and centrifugal extractor is expected to be used. Mixer-settler has the defect of long contact time. It comes out to cause the solvent damage by radiation in FBR fuel reprocessing. In order to escape from the damage, pulse column and centrifugal extractor should be used for FBR spent fuel. However, the characteristics in centrifugal extractor have not yet been fully analyzed, while those of mixer-settler are advanced much. There- fore, the agitation experiment was made to find out the difference of drop formation between mixer-settler and centrifugal extractor. From the results, the average drop diameter is proportional to Weber number to the power of ?0.58, when the contact time is long. However, the agitation velocity did not affect the average drop size, when the contact time is less than 11.3 s.