Frictional Pressure Drop for NaK-N2 Two-Phase Flow in Rectangular Cross Section Channel of Large Aspect Ratio

In this paper, the frictional pressure drop in an isothermal liquid metal-gas two-phase flow through a rectangular channel with large width-to-height ratio is treated semiempirically for a NaK-N₂ two-phase flow system.

The frictional pressure drop in the two-phase flow is compared with the following two reference values :

1. The frictional pressure drop in the liquid flowing alone in single phase with the same velocity as that of the liquid in the two-phase mixture.

2. The frictional pressure drop in the liquid flowing alone in single phase with the same mass flow rate as that of the liquid in the two-phase mixture.

The comparison with the former reference value is necessary for the prediction of friction loss in a liquid metal MHD generator channel whose medium would be two-phase mixture.

The semiempirical analysis was performed assuming the two-phase mixture to be a continuous medium with its properties, e.g. viscosity and density, defined by void fraction and the velocity determined by the total mass flow rate.

In the region of low slip and density ratio ρ_g/ρ_l the frictional pressure drop in the two-phase flow appeared to be smaller than that due to the liquid flowing alone with the same velocity as that of the liquid in the two-phase flow.

The experiments have been undertaken with the NaK-N₂ two-phase mixture flowing through a rectangular channel (4 × 60 mm²).

Data were taken over the following parameter range:

NaK velocity: 5～30 m/sec, Void fraction: 0～70%

Density ratio: 0.006～0.013, Quality: 0.07～1.10%.     

Transport and Deposition of Halide in Alkali Metal-Stainless Steel Systems, (II)

Solubility of sodium iodide in liquid sodium was determined over a temperature range of 350–800°C by using equilibration and sampling techniques.

The dissolution of a 2–3 g fragment of sodium iodide crystal into 7.5–8g sodium was made in a base cell of reversed: “J” type-stainless steel capsule, which was heated in an electric resistance furnace. After the equilibration had been established, a portion of the solution was decanted into a side arm cell of the capsule by tilting the capsule about 110° with the furnace capable of rotating round its horizontal axis. The sodium transferred to the arm cell was analyzed as a single sample.

The solubility: S in the unit of ppm by weight is expressed as a function of temperature in the unit of Kelvin in the forms

• log₁₀S=8.46—3,440/T above 660°C

• log₁₀S=9.65~4,550/T below 660°C

which fit well with Bredig's data in the higher temperature region. The partial molar excess quantities, calculated from the thermodynamic properties of sodium iodide and its individual solubility data, are in reasonable agreement with those determined for the dilute solution of the iodide in liquid sodium by Castleman & Tang.     

Void Fraction and Pressure Drop in Liquid Metal Two-Phase Flow

This paper describes a new correlation for predicting a two-phase frictional pressure drop multiplier, and discusses the pressure level effects and the mass velocity effects. This correlation predicts satisfactorily the frictional pressure drop not only for liquid metals but also for ordinary fluid two-phase flow in a wide range of flow variables.

The authors' void fraction correlation previously proposed is also compared with published data of void fraction for liquid metal two-phase flow, and is found to represent well the mass velocity effects. Wettability and magnetohydrodynamic effects are discussed briefly in relation to the hydrodynamic characteristics of liquid metal two-phase flow.     

Analysis of Two-Phase Liquid Metal MHD Induction Converter

An analysis is made on the performance characteristics of a liquid-metal MHD induction converter with liquid-gas two-phase mixture as working fluid. The equivalent electrical conductivity and the velocity vary along the generator channel in this kind of induction converter.

Two important parameters which represent the variations of the equivalent electrical conductivity and the velocity respectively are defined. With these parameters the induction equation is analytically solved with the perturbation technique.

Quantities representing generator performance, such as power densities and generator efficiency, are obtained from the perturbed magnetic field and the parameters mentioned above.

Suitable combination of values for these parameters will tend to let the effects brought by the variations of electrical conductivity and of velocity cancel each other, and the relation between these parameters is analytically derived that assures the non- perturbation of the magnetic field and of the gross output power density. In this condition of non-perturbation, the generator efficiency approaches that for the unperturbed case when the velocity variation and the inlet slip ratio are small.     

Experimental Study on Gas Carry-Under in Liquid Down Flow from a Two-Phase Mixture

The gas carry-under characteristics in liquid down flow from a two-phase mixture flow have been studied for various flow parameters, based on experiments with a small scale air- water system simulating the concept of a natural circulation BWR with no separators. For high void fraction in the riser, as the liquid superficial velocity jf increased to 0.17 m/s, the void fraction in the lower part of the downcomer αd increased sharply due to the descent of comparatively large bubbles (diameter: about 4–6mm). In the region of jf> 0.17m/s, on increasing jf, the void fraction αd increased until it reached a maximum value at jf.3. For liquid descending velocities higher than 0.3 m/s, αd became almost constant and the level of the mixture above the riser had little effect on the void fraction ad due to the phase separation of the large bubbles formed by bubble coalescence in the upper part of the downcomer. The void fraction αd increased as the void fraction αr increased until bubble coalescence occurred in the upper part of the downcomer, and αd became constant and independent of αr after the occurrence of bubble coalescence. Under the conditions of high void fractions in the riser, 0.4<αr<0.64 (upper limit of the tests), and high liquid descending velocities in the down-comer, 0.3 m/s<jf.<0.4 m/s (upper limit of the tests), the void fraction αd was represented by a dimensionless number (G = η⁴ g/σ³ pf) and by the upper limit of void fractions in bubbly flow, αd=0.3.     

The 2nd International Topical Meeting on Neutron Radiography System Design and Characterization November 12—18, 1995, the Shonan Village Center,Hayama and the Rikkyo University,Yokosuka, Japan

Framatome-ANP has developed S-RELAP5, a RELAP5/Mod2 based thermal hydraulic code, and PANBOX, a 3D core kinetics code. By coupling both codes, a powerful neutronic and thermal hydraulic plant model was developed, which is capable of calculating extremely complex transients, particularly events bearing strongly asymmetric phenomena. The capability of the code system has been tested by recalculation of several transients that occurred in Siemens built PWRs. The most complex transient was a loss of load combined with a temporary coastdown of one main coolant pump, which is presented here. Since the measured values from the data recording system of the plant were available, the calculation could be compared to measured parameters.

The key phenomenon of the transient is a highly asymmetrical neutronic condition, which was caused by:

• —the drop of 5 control rod pairs in an asymmetric pattern upon detection of “loss of load.”

• —the coastdown of one main coolant pump, due to failure to connect to the auxiliary bus, which allowed coolant in one loop to stagnate and cool. Subsequent reactivation of that pump forced a plug of cold water into one side of the core.

The physical progress of the transient is strongly dependent on this double asymmetry; therefore, a 3-D calculation is indispensable for an accurate simulation. The calculated results are in good agreement with measurements and represent an important contribution to code validation.     

Feasibility analysis of two-phase MHD energy conversion for liquid metal cooled reactors

A two-phase MHD energy conversion unit is proposed to a liquid metal cooled fast reactor. Using supercritical CO₂ as the working fluid in the gas cycle without considering friction and heat losses, the optimized cycles efficiency is obtained, which is about 5% higher than that of the gas turbine Brayton cycle with the same regenerator/compressor configurations. Based on a simple MHD power analysis and the two-phase homogeneous flow model, the important system operational conditions were estimated. The results suggest that a liquid lead pump of at least 20% of the MHD power output is needed in order to convert the 400 MW reactor heat into electricity at the specified thermal efficiency, unless a mixture foam flow of void fraction greater than 80% is achievable at very high mixture velocity.     

Preparation of Uranium Carbonitride by Reaction of UC with Ammonia

With the view to establishing a method of directly converting uranium carbide into uranium carbonitride and hydrocarbons, an attempt has been made to induce reaction between UC and ammonia under various temperatures from 25° to 600°C and pressures from 1 to 1,500 kg/cm². The reaction aimed at was realized to the extent of practical significance under pressures exceeding 500 kg/cm² at 450°C and exceeding 250 kg/cm² at 500°C. The hydrocarbons produced thereby were found to be mainly methane, indicating that the formula of the predominant reaction was

• UC+NH₃→UN_2-x+ CH₄+H₂.

Upon heating the powdery fine black product to 1,800°C in vacuo, unexpectedly marked sintering was found to occur, resulting in dense uranium monocarbonitride without any compaction pretreatment.     

Influence of the void fraction profile on the distribution parameter C0 for a bubbly gas–liquid flow in a horizontal round pipe

This paper presents the results of a numerical experiment on the influence of the void fraction profile on the distribution parameter C₀ in a horizontal bubbly two-phase flow. It was shown that for non-symmetric void fraction profiles, which occur normally in horizontal flows, the distribution parameter may be less than 1. In this case, the ratio of the volumetric flow quality β to the average void fraction α can also be less than 1.     

3D Neutronic Analysis in MHD Calculations at ARIES-ST Fusion Reactors Systems

In this study, we developed new models for liquid wall (FW) state at ARIES-ST fusion reactor systems. ARIES-ST is a 1,000 MWe fusion reactor system based on a low aspect ratio ST plasma. In this article, we analyzed the characteristic properties of magnetohydrodynamics (MHD) and heat transfer conditions by using Monte-Carlo simulation methods (ARIES Team et al. in Fusion Eng Des 49–50:689–695, 2000; Tillack et al. in Fusion Eng Des 65:215–261, 2003) . In fusion applications, liquid metals are traditionally considered to be the best working fluids. The working liquid must be a lithium-containing medium in order to provide adequate tritium that the plasma is self-sustained and that the fusion is a renewable energy source. As for Flibe free surface flows, the MHD effects caused by interaction with the mean flow is negligible, while a fairly uniform flow of thick can be maintained throughout the reactor based on 3-D MHD calculations. In this study, neutronic parameters, that is to say, energy multiplication factor radiation, heat flux and fissile fuel breeding were researched for fusion reactor with various thorium and uranium molten salts. Sufficient tritium amount is needed for the reactor to work itself. In the tritium breeding ratio (TBR) >1.05 ARIES-ST fusion model TBR is >1.1 so that tritium self-sufficiency is maintained for DT fusion systems (Starke et al. in Fusion Energ Des 84:1794–1798, 2009; Najmabadi et al. in Fusion Energ Des 80:3–23, 2006).     

Application of Neutron Radiography to Visualization and Void Fraction Measurement of Air-Water Two-Phase Flow in a Small Diameter Tube

Abstract

The purpose of this study is to investigate the feasibility of visualization and void fraction measurement of air-water two-phase flow in a small diameter tube (I.D.: 4.08mm) by using the real-time neutron radiography and image processing techniques. Video images of two-phase flow were taken by using the real-time neutron radiography system (thermal neutron radiography facility No. 2) installed at the Japan Research Reactor 3 M of the Japan Atomic Energy Research Institute. The shape of bubbles and its moving behavior were clearly observed from the video images. The image corrections for dark current, shading, field intensity fluctuation and electrical system drift were examined in order to measure the void fraction from the video images. Though, generally speaking, the effect of the scattered neutron could not be ignored for quantification of the images taken by the neutron radiography, the scattered neutron could not affect the final results of void fraction in the case of a small diameter tube. The void fraction calculated from the corrected images was correlated well with the drift flux equation, indicating that the existing drift flux equation could be applied to predict the void fraction of two-phase flow in a small diameter tube. It was demonstrated that the real-time neutron radiography technique could be useful for measuring the void fraction of two-phase flow in a small diameter tube.     

Vertically Downward Two-Phase Flow, (II)

Following Part (I) of the present paper, which presented the experimental results obtained on the void distribution and average void fraction shown by nearly fully-developed, vertically downward two-phase flow of air-water mixture, this Part (?) covers the flow regime transition criteria among the three basic flow regimes : bubbly, slug and annular flows. The annular flow further was divided into two subregions of falling film flow and annular drop flow. The general situation of the transition criteria is as follows : (1) bubbly-to-slug flow transition occurs when the local void fraction in the central region of the tube is 0.3; (2) slug-to-annular drop flow transition criterion is given as a case which equations giving average void fraction for the slug flow and the annular flow are simultaneously satisfied; (3) slug-to-falling film flow transition occurs when the pressure difference between the crest of large wave and the bottom overcomes the surface tension; (4) the occurrence of liquid droplets from wave crests gives the transition criterion between the falling film flow and the annular drop flow.

These criteria were correlated to predict each flow regime boundary respectively considering flow mechanisms or from experimental results. The correlations obtained were compared with published flow regime maps for atmospheric air-water flow and showed satisfactory agreement.     

蒸汽发生器二次侧汽液两相流数值模拟

以大亚湾核电站蒸汽发生器为原型,在相似原理的指导下,建立了蒸汽发生器“单元管”三维物理模型,采用Particle模型和热力学相变模型,并基于CFX软件实现了蒸汽发生器二回路侧两相流流动与沸腾换热特性数值模拟。计算结果表明：满负荷运行时,沿传热管高度升高,蒸汽发生器的传热系数及截面含汽率均呈上升趋势,其平均传热系数的数值模拟结果与Rohsenow经验关联式计算结果间的误差为8.4%,出口质量含汽率与大亚湾核电站实际运行参数相符。热相变模型在蒸汽发生器两相流数值模拟中的成功应用,可为蒸汽发生器热工水力的准确分析提供参考。     

Prediction of Liquid Film Dryout in Two-Phase Annular-Mist Flow in a Uniformly Heated Narrow Tube Development of Analytical Method under BWR Conditions

A method was developed based on the conservation lows to predict critical heat flux (CHF) causing liquid film dryout in two-phase annular-mist flow in a uniformly heated narrow tube under BWR conditions. The applicable range of the method is within the pressure of 3–9 MPa, mass flux of 500–2,000 kg/m²·s, heat flux of 0.33–2.0 MW/m² and boiling length-to-tube diameter ratio of 200–800.

The two-phase annular-mist flow was modeled with the three-fluid streams with liquid film, entrained droplets and gas flow. Governing equations of the method are mass continuity and energy conservation on the three-fluid streams. Constitutive equations on the mass transfer which consist of the entrainment fraction at equilibrium and the mass transfer coefficient were newly proposed in this study.

Confirmation of the present method were performed in comparison with the available film flow measurements and various CHF data from experiments in uniformly heated narrow tubes under high pressure steam- water conditions. In the heat flux range (q“<2MW/m²) practical for a BWR, agreement of the present method with CHF data was obtained as, (Averaged ratio)±(Standard deviation)=0.984±0.077, which was shown to be the same or better agreement than the widely-used CHF correlations.     

Basic Studies on Two-Phase Flow with the Use of Electrical Void-Meter

Further basic knowledge has been gained on the behavior of two-phase flow through the following experiments. An electrical void-meter based on transducement of void fraction into impedance is employed to measure the void distribution along a heater in an annular channel.

Experiments have further been conducted on the “velocity slip ratio (V_g/V₁)” to correlate the void-fraction (R_g,) with the volume flow rate ratio (F_g). The resulting equation takes the form R_g= 0.92-F_g and the ratio V_g/V_g= 1.08, for slug flow in a vertical pipe.

Statistical methods have been applied in analyzing the two-phase flow. It is shown that the speed of voids in a two-phase flow can be determined with a cross-correlation function calculated from two time series of void-fraction fluctuation measured at two points along the channel.     

Hydrodynamic and Hydraulic Studies on Void Fractions in Two-Phase Flow

For gas-liquid two-phase flow, two kinds of fundamental equations have been proposed by the methods of hydrodynamics and hydraulics. The hydrodynamic equation, to avoid analytical difficulties, does not deal with two-phase flow itself, but with a hypothetical liquid flow which has actual physical quantities in the region where the liquid phase really exists and has the imaginary physical quantities of liquid in the region where the gas exists, for each instant, and with a hypothetical gas flow similarly. The hydraulic equation differs from the usual form in the treatment of friction term or interaction, and has better physical insight. These equations are analyzed mathematically and some relationship between physical quantities centering void fraction are discussed. Hydrodynamic equation shows the void fraction distribution to have relation to pressure loss and velocity distributions, and, for the case of laminar two-phase flow with axial symmetry, explicit expression is presented. By hydraulic equation, the relation between void fraction and other variables are discussed. For the upward two-phase flow with constant flow area, gas-liquid interaction force is discussed theoretically and experimentally.     

Redistribution of Gaseous Phase of Liquid Metal Two-Phase Flow in a Strong Magnetic Field

In the previous paper, the authors pointed out the motion of bubble or gaseous phase in the direction to the both side walls due to the pinch effect caused by the induced magnetic field in the liquid metal two-phase flow under the strong magnetic field. In the present paper, to clarify the existence of the pinch effect experimentally, an experimental study was performed.

Firstly the distributions of the void fraction in the cross section perpendicular to the flow were measured at three locations in the flow direction for the various strength of the applied magnetic field. Secondly a magnetic field was superposed on the induced magnetic field by the outer coil to disturb the pinch effect by the cancel of the induced magnetic field with the superposed one, resulting in the evident redistribution of the void-fraction profile obtained above.

From these experiments it is concluded that the pinch effect will play an important role to redistribute the bubble or gaseous phase in the liquid metal two-phase flow under the strong magnetic field and that the effect is more promoted with increasing magnetic interaction number defined as a ratio of the electromagnetic force to the inertia of the fluid.     

摇摆对窄矩形通道内两相流摩擦压降特性影响

本文以窄矩形通道内两相流为研究对象,分析了不同摇摆工况对两相流动摩擦阻力特性的影响。通过对试验数据分析,结果表明,改变摇摆周期对窄矩形通道内两相流的瞬态摩擦压降波动幅值的影响很小,只是改变了其瞬态摩擦压降变化频率,对其平均摩擦压降无影响。同时,采用L-M法对比分析摇摆与静止条件下的φ²_l(φ²_g) -X变化曲线发现,摇摆状态下窄矩形通道内的两相摩擦压降可采用静止条件下φ²_l(φ²_g) -X变化曲线进行计算。