Heat transfer in heat exchangers of sodium cooled fast reactor systems

The present paper describes the heat transfer in heat exchangers of sodium cooled fast reactors. Practical empirical correlations regarding heat transfer coefficients for intermediate heat exchangers (IHXs) and air coolers (ACs) were derived using test data obtained at the fast reactor ‘Monju’ and ‘Joyo’ and also at the 50 MW steam generator facility (50 MW SG). The correlation proposed by Seban and Shimazaki was applicable to estimate the heat transfer coefficients in both flows of IHX, i.e., primary and secondary flows, when the Péclet number was larger than 30. When the Péclet number for shell-side was small, the Nusselt number decreased as a function of the Péclet number. It was clarified that this characteristic was not caused by the heat conduction in flow direction. The heat conduction effect can be neglected even in the natural circulation conditions of the Monju plant. As for the heat transfer coefficient of AC provided in the secondary heat transport system of the fast breeder reactor, data in the above mentioned three facilities were evaluated. As a result, empirical correlations were derived for the average heat transfer coefficients of a large capacity finned air cooler made of stainless steel. These correlations could contribute to analyze the plant dynamics with better accuracy than before.     

An experimental study of inter-subassembly heat transfer during natural circulation decay heat removal in fast breeder reactors

The evaluation of core thermohydraulics under natural circulation conditions is significant to utilize passive safety features of fast breeder reactors (FBRs). Under low flow conditions, it is predicted that buoyancy effects and heat transfer through wrapper tubes, i.e. inter-subassembly heat transfer, will significantly influence the flow and temperature distributions in subassemblies. Thus, steady-state sodium experiments were carried out using a three-subassembly model. The transverse temperature distributions in the subassemblies were measured under conditions wherein inter-subassembly heat transfer occurred. A wall subchannel factor was introduced to estimate the sodium temperature near the wrapper wall, which characterizes the inter-subassembly heat transfer. This factor enables a one-dimensional system code to predict the inter-subassembly heat transfer accurately. The characteristics of the factor were studied experimentally. It was shown that a buoyancy parameter, Gr*/Re, and a heat flux ratio of wrapper wall to pin surface were essential to predict the wall subchannel factor and also the peaking factor. Experimental analyses were also carried out using a three-dimensional analysis code that modeled the multi-bundle system. Good agreement between experiments and calculations was obtained for temperature distributions influenced by the inter-subassembly heat transfer.     

Verification of NETFLOW code using plant data of sodium cooled reactor and facility

The plant simulation code NETFLOW on PC applicable to the liquid-metal cooled reactors has been developed on the basis of the models developed for single-phase and two-phase light water flow systems. The functions of this code have been verified by individual tests for light water flow systems and a sodium flow system. In order to apply this code to a sodium cooled fast reactor, several extra functions were verified using the plant data obtained using 50 MW steam generators and the Monju fast breeder reactor. Finally, the turbine trip transient of the Monju was simulated and the result was compared with the measured plant data. Good agreements were obtained in these verifications. As a result of the present study, the code can be applied as an education tool for students.     

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.     

Process optimisation of a liquid sodium economiser circuit

Economiser circuits in liquid sodium service are very common in sodium cooled fast reactor systems. Large amount of cooling in the order of 100 °C–450 °C differential temperature is common for the auxiliary liquid sodium systems such as sodium purification and impurity monitoring. A sodium to sodium heat exchanger as economiser, sodium to air heat exchanger as heat sink and electrical heater for reheating are the process equipment generally used for the liquid sodium economiser circuits. Since the specific heat transfer area and manufacturing cost for economiser heat exchanger and sodium to air heat exchanger are largely different, optimised parameters for economiser circuits with conventional heat transport medium will not hold good for liquid sodium economiser systems. An optimisation study was performed for liquid sodium economiser circuit for arriving at an optimum design by considering the technical and economical aspects with optimum energy wastage.     

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.     

A power perturbation technique for the measurement of fuel-to-coolant heat transfer coefficients in fast reactors

This technique provides a method of obtaining average fuel to coolant heat transfer coefficients for individual fuel subassemblies in fast reactors. A series of experiments on the UK prototype fast reactor (PFR) over the period 1977–1979 have demonstrated that the technique is simple, requires no special instrumentation other than thermocouples to monitor coolant outlet temperatures, and the measurement can be made during normal reactor operation. Thus it is possible to determine how heat transfer coefficients change with operating conditions and with the degree of burn-up in the fuel.The analysis of a single experiment is presented to illustrate the technique. This was conducted at a single reduced power level of 200 thermal megawatts for two different primary coolant flow rates, both steady fractions of the maximum (0.88 and 0.47). Cyclic and single-step perturbations of about 10% amplitude were impressed on the steady power and the delayed coolant temperature response at subassembly outlets was monitored. Burn-ups in the subassemblies ranged between 1.0% and 4.7%. From the measured delays at the two flows it was possible to determine the fuel time-constant and hence the fuel-to-coolant heat transfer coefficient. It was also shown that a simple, lumped-element, heat transfer model can be used to obtain sufficiently accurate estimates from measurements at just one coolant flow.Fuel surface-to-coolant thermal conductances (i.e. gap conductances) were subsequently derived from the heat transfer coefficients. These ranged between 2.4 kW m⁻² K⁻¹ and 3.3 kW m⁻² K⁻¹ with the smaller conductances being obtained for those fuel elements with the larger degree of burn-up. These values are lower than expected but consistent with a higher than expected value for the negative power coefficient of reactivity feedback which has been observed at reduced power.     

池式钠冷快堆系统分析程序开发

针对池式钠冷快堆的特点,在对快堆系统的水力模型、热工模型和中子动力学模型进行详细分类和建模的基础上,利用FORTRAN95语言开发了可用于池式钠冷快堆事故分析的系统分析程序（FASYS程序）。以中国实验快堆为计算对象对FASYS程序模型进行了初步验证,所获得的结果和试验值与其他系统程序计算值符合良好,证明了所开发的系统分析程序的正确性。     

Turbulent velocity and temperature distribution in the central subchannel of rod bundles

In this paper a method is given for solving the momentum and heat transfer equations for the central subchannel of a reactor subassembly in general curvilinear orthogonal coordinates. For turbulent flow, the eddy diffusivities are determined by Prandtl's ‘mixing length’ hypothesis. A new method is proposed to determine eddy diffusivities parallel to the wall. The eddy diffusivities of heat are calculated from those of momentum using the relations obtained by various authors, and the results are compared in the case of sodium. To show the capability of the computer codes developed, the three-dimensional temperature field is calculated in the central subchannel of a fuel element cooled by sodium and helium. The agreement between calculated and experimental results is satisfactory.     

钠冷快堆自然循环组件子通道程序初步研发

本文为计算和分析钠冷快堆自然循环组件的热工水力特性,开发了钠冷快堆堆芯自然循环冷却组件子通道分析程序。基于61棒单组件模型,通过将本程序的结果与COBRA程序进行比较,验证了钠冷快堆堆芯自然循环冷却组件子通道分析程序对自然循环冷却组件的适用性。基于多盒组件模型,初步验证了本程序具备自然循环冷却组件的流量分配和盒间换热计算的功能。本程序能为池式快堆自然循环冷却组件提供有效的设计和分析工具。     

铅铋冷却快堆含绕丝燃料组件子通道程序开发与验证

由于铅铋冷却剂流动传热现象的复杂性,准确计算铅铋冷却含绕丝燃料组件的冷却剂和包壳温度是液态金属冷却快堆燃料组件热工分析的重点。本文基于集总参数法对守恒方程进行求解,开发了适用于铅铋冷却快堆的子通道分析程序,对液态铅铋在棒束燃料组件中的摩擦阻力模型、湍流交混模型和对流换热模型进行了适用性分析,并对7棒束大涡模拟和19棒束含绕丝传热实验进行了对比验证。结果表明：包壳和冷却剂温度的最大相对误差低于5%。程序能较好完成铅铋冷却含绕丝燃料组件的热工水力计算,可为铅铋冷却快堆设计提供支持。     

Thermal-hydraulic analyses of transients in an actinide-burner reactor cooled by forced convection of lead–bismuth

The Idaho National Engineering and Environmental Laboratory (INEEL) and the Massachusetts Institute of Technology (MIT) are investigating the suitability of lead or lead–bismuth cooled fast reactors for producing low-cost electricity as well as for actinide burning. The current analysis evaluated a pool type design that relies on forced circulation of the primary coolant, a conventional steam power conversion system, and a passive decay heat removal system. The ATHENA computer code was used to simulate various transients without reactor scram, including a primary coolant pump trip, a station blackout, and a step reactivity insertion. The reactor design successfully met identified temperature limits for each of the transients analyzed.     

SADHANA facility for simulation of natural convection in the SGDHR system of PFBR

The Prototype Fast Breeder Reactor (PFBR) is a 500 MWe sodium cooled pool type fast reactor being constructed at Kalpakkam, India. PFBR has all the reactor components immersed in the pool of sodium and the fission heat generated in the core, is removed by the sodium circulating in the pool. During normal operation this fission heat is transferred by primary sodium to secondary sodium, which in turn transfers the heat to water in the steam generator for producing steam. The removal of the decay heat generated in the reactor core after the reactor shutdown is also very important to maintain the structural integrity of reactor core components. PFBR employs two independent systems namely, Operational Grade Decay Heat Removal system (OGDHRS) and Safety Grade Decay Heat Removal System (SGDHRS) for decay heat removal. SGDHR system is a passive system working on natural convection to ensure the core coolability even under station blackout condition. It is very important to study the thermal hydraulic behavior of Safety Grade Decay Heat Removal system of PFBR to ensure its reliable operation. A scaled down model of the circuit, named SADHANA has been modeled, designed, constructed and commissioned for demonstration and evaluation of these systems. The facility has completed around 2000 h of high temperature operation. The performance of the experimental system is satisfactory and it meets all the design requirements. At 550 °C sodium pool temperature in test vessel the secondary sodium loop generated a sodium flow of 6.7 m³/h. These experiments have revealed the adequacy and capability of SGDHR system to remove the decay heat from the fast breeder reactor core after its shutdown.     

池式钠冷快堆事故余热排出系统一回路仿真研究

池式钠冷快堆事故余热排出系统采用了非能动工作原理,依靠液态钠及空气的自然对流排出堆芯余热。为研究事故工况下余热排出系统一回路的换热能力,基于FORTRAN语言,建立堆芯单通道及盒间流模型,采用全隐二阶迎风差分格式及改进的欧拉法离散求解,对事故余热排出系统一回路系统进行数值模拟,并对全厂断电事故进行仿真计算验证。结果表明:该程序能较好地反映事故余热排出系统瞬态变化过程,并可达到超实时仿真。     

ATHLET程序的钠冷快堆应用扩展及其验证

系统分析程序是对钠冷快堆的冷却剂回路系统进行全局模拟、瞬态及事故安全分析的重要工具。本工作对德国核设施与反应堆安全机构（GRS）开发的轻水堆最佳估算系统程序ATHLET进行修改,增加了钠的物性公式和传热关系式,将其适用范围扩展到钠冷快堆。为验证修改过的ATHLET程序,对法国凤凰（Phenix）反应堆系统建模,并对其自然对流实验进行模拟,将计算结果与实验数据进行比较。结果显示,ATHLET程序的钠冷快堆应用扩展具有良好的适用性。     

钠冷快堆乏燃料组件热工水力分析程序开发

为了对示范快堆乏燃料组件的热工水力特性进行分析,自主研发了钠冷快堆乏燃料组件热工水力分析程序SPATANS。该程序基于子通道分析方法,采用适用于低流量下的流动换热和交混关系式。针对乏燃料组件棒束区进行计算,得到组件不同高度处各子通道的温度、压力等热工参数,并将计算结果与三维计算流体力学FLUENT程序的结果进行对比分析。结果表明：自主研发程序的计算结果与FLUENT程序的计算结果较为吻合,偏差在工程可接受范围内,且其计算效率明显高于FLUENT程序。初步表明SPATANS程序可用于钠冷快堆乏燃料组件热工水力分析,并具有良好的应用前景。     

Improvement of the subcooled boiling model for low-pressure conditions in thermal-hydraulic codes

The functioning of the subcooled boiling model adopted in a thermal-hydraulic computer program has been investigated in detail, for low-pressure conditions, and necessary refinements have been incorporated into the code. The investigation has been carried out in two stages; in the first stage, the performance of the interfacial heat transfer/condensation is studied. Necessary refinements to the vertical flow map for the transition from bubbly to slug flow regimes and the interpolation with the ‘umbrella’ limitation that bounded the interfacial heat transfer values are carried out. Simulations of low-pressure subcooled boiling experiments were performed with the refined code version and a reasonable agreement with the experimental void fraction data was obtained. In addition, a high-pressure experiment was also simulated with the refined code version to check if these revisions do not affect the code performance at high pressures. No significant adverse effects were observed. In the second stage of the study, the performance of the wall heat flux partitioning model adapted in the code was investigated. In particular, the effectiveness of the ‘pumping factor’ formulation in the above model and its functioning at low-pressure conditions was investigated. Different ‘pumping factor’ formulations available in the literature were implemented into the code. Simulations of low-pressure subcooled boiling experiments were performed with the refined code version and the appropriate ‘pumping factors’ to be used for low-pressure conditions were determined.     

Evaluation of high plutonia (44% PuO2) MOX as a fuel for fast breeder test reactor

Uranium plutonium mixed oxide (MOX) containing up to 30% plutonia is the conventional fuel for liquid metal cooled fast breeder reactor (LMFBR). Use of high plutonia (>30%) MOX fuel in LMFBR had been of interest but not pursued. Of late, it has regained importance for faster disposition of plutonium and also for making compact fast reactors. Some of the issues of high plutonia MOX fuels which are of concern are its chemical compatibility with liquid sodium coolant, dimensional stability and low thermal conductivity. Available literature information for MOX fuel is limited to a plutonium content of 30%. Thermodynamic assessment of mixed oxide fuels indicate that with increasing plutonia oxygen potential of the fuel increases and the fuel become more prone to chemical attack by liquid sodium coolant in case of a clad breach. In the present investigation, some of these issues of MOX fuel have been studied to evaluate this fuel for its use in fast reactor. Extensive work on the out-of-pile thermo-physical properties and fuel-coolant chemical compatibility under different simulated reactor conditions has been carried out. Results of these studies were compared with the available literature information on low plutonia MOX fuel and critically analyzed to predict in reactor behaviour of this fuel containing 44% PuO₂. The results of these out-of-pile studies have been very encouraging and helped in arriving at a suitable and achievable fuel specification for utilization of this fuel in fast breeder test reactor (FBTR). As a first step of test pin irradiation programme in FBTR, eight subassemblies of the MOX fuel are undergoing irradiation in FBTR.