Inter-subassembly heat transfer of sodium cooled fast reactors: Validation of the NETFLOW code

This paper describes the prediction of temperature at the exit of subassemblies of a sodium cooled fast reactor using the NETFLOW code. Until present time, this plant dynamics calculation code is expected as a tool of nuclear education, and has been validated using data obtained at facilities or reactors cooled with water or sodium. A natural circulation test was conducted in the experimental fast reactor ‘Joyo’ with a 100 MW irradiation core. Also a turbine trip test was conducted in the prototype fast breeder reactor ‘Monju’. These tests were chosen to validate a model to calculate inter-subassembly heat transfer consisting of heat conduction and heat transfer by inter-wrapper flow. Based on the calculation for the natural circulation test in primary and secondary loops of ‘Joyo’, the model to calculate the heat transfer in radial direction of the inter-subassemblies simulated reasonable sodium temperature behaviors at the exit of subassemblies. Good agreement was also obtained in prediction of temperatures at the exit of the ‘Monju’ subassemblies. Through these validations, it was shown that the one-dimensional plant dynamics code NETFLOW could trace temperatures at the exit of the subassemblies of fast reactors with the inter-subassembly heat transfer model.     

Transient experiments on fast reactor core thermal-hydraulics and its numerical analysis: Inter-subassembly heat transfer and inter-wrapper flow under natural circulation conditions

Sodium experiments were conducted on core thermal-hydraulics simulating a scram transient of a large scale fast breeder reactor using the test facility PLANDTL-DHX with seven fuel subassemblies. The influence of inter-subassembly heat transfer on temperature distribution in the subassembly was revealed via measurements. The flow in the gap between neighboring subassemblies called inter-wrapper flow (IWF) was also studied in relation to its capability of cooling the subassemblies. A computational model is presented for predicting the transient without IWF. The multi-dimensional numerical analysis model employs an empirical correlation to simulate mixing effects between adjacent subchannels. It was shown that the present computational method could evaluate the transient behavior of thermal-hydraulics in the subassemblies accurately from forced to natural circulation accompanied by inter-subassembly heat transfer and flow redistribution in the subassembly. The cooling effects of IWF on the fuel subassemblies were found in spite of natural circulation flow reduction in the primary loop attributable to temperature decreases in the upper non-heated section in the core. The inter-wrapper flow can effectively cool the core under extreme conditions of low flow rates through the core.     

Analytical studies on local flow blockages in LMFBR subassemblies, using the UZU code

Extensive experimental and analytical studies on local flow blockages in LMFBR subassemblies have been performed in several countries. However, analytical tools have not yet been established. In the present study, therefore, a three-dimensional analytical code, UZU, has been developed for analysing important factors which affect the flow and temperature fields in locally blocked subassemblies.In the UZU code a subchannel approach was employed and the finite difference equations, consisting of momentum, mass and energy balances, were solved by the SOR method. The special features of this code are: (1) fluid properties are functions of local fluid temperature, consequently buoyancy is included in the momentum equations, (2) fluid flow properties, such as turbulent friction factors and eddy diffusivities, are expressed as functions of local fluid velocities, geometries and physical properties, (3) peripheral subchannels are treated separately from inner ones, (4) thickness and porosity of a blockage plate can be considered and (5) a blockage at the upstream end of a grid spacer can be dealt with.The validity of the code was proven by comparison with the measured velocity, pressure and temperature distributions in simulation experiments conducted in parallel with the code development.     

Incipient Boiling of Sodium in Seven-Pin Bundle under Forced Convection Conditions

Experimental studies were carried out on incipient boiling of sodium flowing in an electrically heated seven-pin bundle under forced convection.

In the first series of experiments temperature distributions in the bundle were measured under non-boiling conditions. The measured temperature distributions agreed fairly well with the calculation by the NORMAL code.

In the second series of experiments incipient-boiling (IB) phenomena were investigated, with particular reference to the IB superheat and the voiding patterns. The IB wall superheat decreased with increase in flow velocity. The observed coolant voiding was limited in the central subchannel because of the steep radial temperature gradient in the bundle. In order to describe this voiding process a two-dimensional voiding model was required.     

快堆燃料组件热工流体力学计算研究

对于钠冷快堆,在燃料和包壳最高温度等设计限值下,为获得较高的堆芯出口温度,需深入分析燃料组件内的热工流体力学问题,准确预测组件内的冷却剂温度分布。本文在CRT模型和F.C.Engel等人工作的基础上,提出了ICRT压降关系式,用以计算冷却剂在湍流区、过渡流区和层流区的棒束压降;引入CRT模型和WEST对流传热模型,改进了SUPERENERGY子通道分析程序,并将改进程序与原程序计算结果进行了对比,结果表明：最热子通道出口温度略有降低,液膜温压略有增加;并用计算流体力学软件CFX对中国实验快堆单盒燃料组件活性段进行了三维数值模拟,将计算结果用CRT模型、ICRT压降关系式及改进后的SUPERENERGY子通道分析程序进行了验证,相互符合较好。     

Heat transfer from a totally blocked fuel subassembly of a liquid metal fast breeder reactor: II. Numerical simulation

Fast breeder nuclear reactors used for power generation, have fuel subassemblies in the form of rod bundles enclosed inside tall hexagonal cavities. Each subassembly can be considered as a porous medium with internal heat generation. A three-dimensional analysis is carried out here to estimate the heat transfer due to natural convection, in such an anisotropic, partially heat generating porous medium, which corresponds to the typical case of blocked flow in a fuel subassembly inside the reactor core. Using the finite volume technique, the temperatures at various locations inside hexagonal cavity are obtained. The simulations by the three-dimensional code developed are compared with the results of experiments [Suresh, Ch.S.Y., Sateesh, G., Das, Sarit K., Venkateshan, S.P., Rajan, M., 2004. Heat transfer from a totally blocked fuel subassembly of a liquid metalfast breeder reactor. Part 1: Experimental investigation. Nucl. Eng. Design, present issue] conducted using liquid sodium as the heat transfer fluid. Further, the code is used to predict the maximum temperature in typical liquid metal fast breeder reactors to find the power level where the liquid sodium starts boiling. It helps to decide the power level for initiation of monitoring the temperature for the purpose of reactor control.     

Pressure drop and heat transfer in gas-cooled rod bundles

Extensive experimental and analytical investigations of fluid flow and heat transfer in gas-cooled rod bundles have been carried out. Different bundle geometries with partially or fully roughened rod surfaces were tested in a carbon dioxide loop. An advanced and comprehensive measuring control and instrumentation are important design features of this experiment. Comprehensive thermal hydraulic subchannel analysis computer codes have been developed in order to assist fuel element design calculation for gas-cooled reactors. The experiments, codes and their verification procedure are described and the results of comparisons between measured and calculated pressure and temperature distributions are given.     

A numerical study of flow in the Thermal-Hydraulic Out-of-Reactor Safety facility expansion tank

A new, fast-running, two-dimensional computer code was developed to model the flow and temperature patterns in the expansion tank of the Thermal-Hydraulic Out-of-Reactor Safety (THORS) facility. The THORS facility, located at the Oak Ridge National Laboratory (ORNL), is an engineering-scale sodium loop used for thermal-hydraulic testing of simulated Liquid Metal Fast Breeder Reactor (LMFBR) subassemblies. In the computer model, the fluid is considered Boussinesq and a simple turbulence model is provided so that a wide range of inlet conditions can be studied. A vorticity-stream function formulation is used on a uniform finite difference grid. The model also includes the thermal response of the tank wall. The results of simulated experiments for natural circulation and forced flow conditions are compared. Inflow boundary conditions were adjusted to simulate boiling in the THORS test section upstream of the expansion tank during some runs made with the code. Streamline and isotherm plots of the results are presented. All cases studied reached thermally stratified conditions in the tank, and regions of buoyancy and convection-dominated flow are observed.     

Matrix calculation of radiant heat transfer in LWR fuel bundles under accident conditions

A computer code was developed for calculating the radiant heat transfer in a LWR fuel bundle under accident conditions. The calculation method is a modular one: a fuel bundle or its part is divided into unit cells, each of which is composed of a coolant subchannel surrounded by several segments of solid or imaginary faces. The view factor matrix in each cell is expanded over the whole bundle using the concept of ‘boundary face’ between cells, and the resultant heat transfer equations are simultaneously solved for solid wall temperatures. The geometrical flexibility of this method is suitable for treating various simulation experiments for accidents. The method is also effective for repeated calculations of the radiant heat transfer reflecting state or material property changes when analyzing fuel rod behaviour under accident conditions.     

竖直圆管内超临界流体混合对流传热特性理论分析

理论推导了变密度引起的浮升力效应和流动加速效应对超临界流体混合对流传热特性的影响。结果表明,浮升力效应和流动加速效应通过改变壁面边界层外缘的切应力影响湍流对传热传质的贡献,进而改变超临界流体混合对流传热特性。浮升力效应通常在加热区域入口及上游区域表现明显,而流动加速效应在主流区流体温度达到拟临界温度时更显著。与实验研究结果对比发现,新建立的浮升力因子和流动加速因子可较好地预测竖直圆管内超临界流体混合对流条件下拟临界区域的局部传热特性。     

Reactor core thermohydraulic transients with thermohydrodynamic coupling

A study of the reactor core thermohydraulics in an LMFBR has been performed for the strongly coupled thermo-hydrodynamic transients. A numerical method to solve the coupled energy-momentum equations among multichannels in a core is presented and the computer code ORIFS-TRANSIENT has been developed.The results of sample calculations for a flow coastdown transient to natural circulation following a reactor scram in a typical loop-type LMFBR are as follows: (1) the inter-subassembly coolant flow redistribution due to buoyancy forces is significant under the low flow condition, such as natural circulation; (2) the maximum coolant temperature was decreased by about 80°C (corresponding to about 22% in terms of hot channel factor) due to the flow redistribution; (3) due to thermohydrodynamic coupling between upper plenum and other regions, the maximum coolant temperature was decreased by about 9°C; (4) due to inter-subassembly heat redistribution, the maximum coolant temperature was increased by about 7°C.     

Numerical investigation of supercritical water-cooled nuclear reactor in horizontal rod bundles

The commercial CFD code STAR-CD v4.02 is used as a numerical simulation tool for flows in the supercritical water-cooled nuclear reactor (SCWR). The basic heat transfer element in the reactor core can be considered as round rods and rod bundles. Reactors with vertical or horizontal flow in the core can be found. In vertically oriented core, symmetric characters of flow and heat transfer can be found and two-dimensional analyses are often performed. However, in horizontally oriented core the flow and heat transfer are fully three-dimensional due to the buoyancy effect. In this paper, horizontal rods and rod bundles at SCWR conditions are studied. Special STAR-CD subroutines were developed by the authors to correctly represent the dramatic change in physical properties of the supercritical water with temperature. In the rod bundle simulations, it is found that the geometry and orientation of the rod bundle have strong effects on the wall temperature distributions and heat transfers. In one orientation the square bundle has a higher wall temperature difference than other bundles. However, when the bundles are rotated by 90° the highest wall temperature difference is found in the hexagon bundle. Similar analysis could be useful in design and safety studies to obtain optimum fuel rod arrangement in a SCWR.     

A method of evaluating local turbulent diffusivity of heat in a gridded fuel subassembly

In evaluating the turbulent diffusivity of heat associated with the coolant flow past a grid spacer within an FBR fuel subassembly, a heat diffusion technique is usually employed. However, measurement of subchannel bulk coolant temperature using thermocouples usually involves difficulty due to a steep and non-linear temperature gradient in the subchannels adjacent to a heater pin.A series solution of the heat conduction equation for the coolant flow in subchannels past a grid spacer and a heated section of a dummy fuel pin was derived under a slug flow approximation where the boundary conditions on dummy fuel pins were satisfied by means of the point-matching technique. The solution may be utilized in analyzing the turbulent diffusivity of heat within subchannel coolant flow as a function of distance from a grid spacer based on the measured temperature distribution on the wall of dummy fuel pins, which may be obtained without affecting the subchannel coolant temperature.In an illustrative example, the turbulent diffusivity of heat was most exaggerated at about 50 mm beyond a grid spacer and was approximately five times larger than the corresponding diffusivity without a grid spacer.     

Heat transfer from a totally blocked fuel subassembly of a liquid metal fast breeder reactor: Part I. Experimental investigation

The safety issues of liquid metal fast breeder reactors (LMFBR) are crucial due to the fact that a highly reactive and hazardous fluid like liquid sodium is used as coolant. One of the extreme cases, which can occur in a fuel subassembly of an LMFBR, is a total blockage of liquid inside the subassembly, which may lead to boiling of sodium. The present study addresses this problem by conducting experiments on a 19-rod bundle assembly enclosed inside a tall hexagonal enclosure. Liquid sodium is used as the heat transfer fluid. The natural convection mode of heat transfer is the main focus of investigation with a co-flowing air through an annular packed bed to simulate the neighbouring subassemblies. The maximum temperature achieved under different rates of power generations and air flow conditions are observed. Also the radial temperature distributions at different planes under different operating conditions of power and air flow rates have been observed. The results are of significant importance for validating analysis for the purpose of prediction of boiling incipience in an LMFBR subassembly under totally blocked condition.     

Two-phase turbulent mixing and buoyancy drift in rod bundles

This paper describes the development of generalized relationships for single- and two-phase intersubchannel turbulent mixing in vertical and horizontal flows, and lateral buoyancy drift in horizontal flows.The relationships for turbulent mixing, together with a recommended one for void drift, have been implemented in a subchannel thermalhydraulics code, and assessed using a range of data on enthalpy migration in vertical steam–water flows under BWR and PWR diabatic conditions. The intent of this assessment was to optimize these relationships to give the best agreement with the enthalpy migration data for vertical flows. The optimized turbulent mixing relationships were then used as a basis to benchmark a proposed buoyancy drift model to give the best predictions of void and enthalpy migration data in horizontal flows typical of PHWR CANDU¹ reactor operation under normal and off-normal conditions.Overall, the optimized turbulent mixing and buoyancy drift relationships have been found to predict the available data quite well, and generally better and more consistently than currently used models. This is expected to result in more accurate calculations of subchannel distributions of phasic flows, and hence, in improved predictions of critical heat flux (CHF).     

10 mm垂直单管通道内超临界水传热弱化现象的实验与数值分析

超临界压力下的流体因拟临界点附近物性的剧烈变化,形成了非常奇特的传热现象。因流体密度突变,在低流量下会引起强烈的浮升力作用,对超临界流体的流动和传热均有极大影响。本工作通过实验获得10 mm单管内传热弱化现象的实验数据,并采用改进的低雷诺数湍流模型,使用数值方法模拟该传热弱化现象。计算结果表明,不同于以往传统的模型会高估壁面温度,改进的低雷诺数湍流模型能较好预测实验结果。数值模拟结果还揭示了浮升力对湍流剪切应力和速度分布的影响,进而引起传热弱化和传热恢复。     

数值反应堆堆芯通道级三维热工水力程序CorTAF开发及初步验证

堆芯是核动力系统的核心部件,其完整性是反应堆安全运行的重要前提。传统核反应堆堆芯热工水力分析方法无法满足未来先进核动力系统的高精度模拟需求。本文依托开源CFD平台OpenFOAM,针对压水堆堆芯棒束结构特点建立了冷却剂流动换热模型、燃料棒导热模型和耦合换热模型,开发了一套基于有限体积法的压水堆全堆芯通道级热工水力特性分析程序CorTAF。选取GE3×3、Weiss和PNL2×6燃料组件流动换热实验开展模型验证,计算结果与实验数据基本符合,表明该程序适用于棒束燃料组件内冷却剂流动换热特性预测。本工作对压水堆堆芯安全分析工具开发具有参考和借鉴意义。     

Transient behavior of the sodium–potassium alloy heat pipe in passive residual heat removal system of molten salt reactor

High temperature heat pipes, as highly-effective heat transfer elements, have been extensively employed in thermal management for their remarkable advantages in conductivity, isothermality and self-actuating. It is of significance to apply heat pipes to new concept passive residual heat removal system (PRHRS) of molten salt reactor (MSR). In this paper, the new concept PRHRS of MSR using sodium–potassium alloy (NaK) heat pipes is proposed in detail, and then the transient behavior of high temperature NaK heat pipe is numerically investigated using the Finite Element Method (FEM) in the case of MSR accident. The two-dimensional transient conduction model for the heat pipe wall and wick structure is coupled with the one-dimensional quasi-steady model for the vapor flow when vaporization and condensation occur at the liquid–vapor interface. The governing equations coupled with boundary conditions are solved by FORTRAN code to obtain the distributions of the temperature, velocity and pressure for the heat pipe transient operation. Numerical results indicated that high temperature NaK heat pipe had a good operating performance and removed the residual heat of fuel salt significantly for the accident of MSR.     

Characterization of heat transfer and temperature distributions in an electrically heated model of an LMFBR blanket assembly

This paper describes results of an experimental program to reduce uncertainties associated with the thermal-hydraulic design and analysis of LMFBR blanket assemblies. These assemblies differ significantly from fuel assemblies in design detail and operating conditions. In blanket assemblies, heat transfer occurs over a wide range of complex operating conditions. The range and complexity of conditions are the result of flux and power gradients which are an inherent feature of the blanket region and the power generation level in an assembly which can vary from 20 kW to 2 MW. To provide effective cooling of all assemblies and economical operation, coolant is metered to groups of assemblies in proportion to their ultimate power level. As a result, the assembly flow can be in the laminar, transition or turbulent range. Because of the wide range of heat generation rates and the range of coolant flow velocities, heat transfer from rods to coolant may take place in the forced, natural or mixed convection mode. Under low flow conditions, buoyancy affects the flow pattern in the bundle, and thus, alters the temperature distribution. The complexities are further compounded since, in addition to temperature gradients within an assembly, there are also significant temperature differences between adjacent assemblies. This results in heat transfer by conduction between adjacent assemblies, which tends to further distort flow and temperature patterns.Since these effects cannot be accurately predicted analytically, full-size radial blanket assembly heat transfer tests are being conducted using electrically heated fuel rod simulators in flowing sodium. A 61-rod electrically heated radial blanket assembly mockup of prototypic dimensions was designed, constructed and installed in a 200 gpm (45 m³/hr) sodium test loop.Heat transfer tests are being conducted over a wide range of power and sodium flow rates with this full-scale, vertical, electrical-resistance-heated rod bundle. The rod bundle is extensively instrumented by thermocouples located at six distinct elevations in the wire wrap and inside the heater cladding. Tests were conducted covering the flow range from fully turbulent to fully laminar with approximately constant power-to-flow ratio. The power input patterns included across bundle gradients of 2.8 to 1 and 2.0 to 1 maximum to minimum, uniform power input to all rods and a dished distribution with low power in the central row and high power in the two rows of rods adjacent to the duct walls.The test program provided experimentally measured axial and transverse temperature profiles for the test model over a range of anticipated plant operating conditions. The data were used to (a) determine the effect of Reynolds Number, power gradients and power-to-flow ratio on transverse and axial temperature profiles and particularly on peak and peripheral channel temperatures; (b) determine the effect of inter-assembly heat transfer on peak temperatures and temperature distributions; and (c) determine the effect of buoyancy on temperature profiles.