压水堆驱动线落棒历程计算

控制棒落棒性能验证是核电厂安全分析的重要部分,研制驱动线落棒历程计算程序有利于验证和改进控制棒驱动线设计。基于驱动线结构特点,分析运动组件的受力情况并进行分解,选择理论或数值方法逐一求取各分力的瞬态值,从而建立驱动线落棒历程的循环步进计算程序。利用秦山核电二期工程驱动线落棒性能试验数据对理论模型和程序计算结果进行对比验证。结果证明：所建立的驱动线落棒历程计算程序适用于压水堆驱动线系统,能正确地对运动组件落棒受力与运动历程进行模拟。     

Diana — A fast and high capacity computer code for interchannel coolant mixing in rod arrays

A mathematical model and digital computer program are presented for the subchannel thermal and hydraulic analysis of sodium-cooled fast reactor fuel assemblies. The newly developed FORTRAN-IV computer code ‘DIANA’ is much more useful than many other subchannel mixing analysis codes, especially for large size fuel assemblies which contain more than about 80 subchannels, and for assemblies undergoing swelling and thermal bowing which cause deformed coolant flow ducts, because of high computing speed, reduction of necessary core memory and accurate solution by momentum conservation. Numerical solutions are presented for a deformed rod bundle which contains 179 subchannels.     

Control rod drop analysis by finite element method using fluid–structure interaction for a pressurized water reactor power plant

The control rod drop analysis is very important for safety analysis. For seismic and loss of coolant accident event, the control rod assemblies shall be capable of traveling from a fully withdrawn position to 90% insertion without any blockage and within specified time and displacement limits. The analysis has been executed by analytical method using in-house code. In this method, several field data are needed. These data are obtained from nuclear, thermal–hydraulic and mechanical design groups, peculiar codes, those work groups need to cooperate together.Following the enhancement of a computer and development of the multi-physics analysis code, a new method for the control rod drop analysis is proposed by finite element method. This analysis model incorporates the structure and fluid parts, termed as a fluid and structure interaction (FSI). Because a control rod is submerged inside a guide tube of a fuel assembly, the FSI boundary condition is applied. In this model, it is assumed that the fluid is incompressible laminar flow. The structures are modeled with the solid elements because there is no deformation due to the fluid flow. The analysis two-dimensional plane model is created in the analysis with considering an axi-symmetric geometry. Therefore, the proposed analysis model will be very simple and the design data from other fields will be unnecessary.The analysis results are compared with those of the in-house code, which have been used for a commercial design. After validation, it is found that the present analysis gives a useful tool in the design of the control rod and fuel assembly.     

控制棒落棒时间分析软件CRAC的研发与验证

紧急停堆的落棒时间对反应堆安全至关重要。为适应华龙一号堆型的新型燃料组件设计,中国核动力研究设计院研制出一款落棒时间分析软件CRAC。采用一维流体力学公式结合经验机械阻力模型的方法,构建出CRAC软件理论框架,通过软件开发标准流程完成设计编码,并利用落棒试验数据开展了CRAC软件的验证。结果表明软件计算精度与保守性能满足华龙一号堆型安全停堆时间准则分析的需求。     

Methodology for a numerical simulation of an insertion or a drop of the rod cluster control assembly in a PWR

In a pressurised water reactor, the rod cluster control assembly is a system which controls the neutronic activity of the core. It consists of long rods, connected by a spider fixture and a cylindrical system for the control drive mechanism. At its withdrawn position, the activity of the core is maximum, and at its completely inserted position, the activity of the core vanishes. In case of emergency, an effective way to shutdown the reactor is to let it drop under its own weight. An other way to verify the efficiency of the rod cluster control assembly is the insertion test. It consists in inserting the rod into its guides and in checking if the reaction friction force is not high enough to block the movement of the rod cluster control assembly.We present in this paper a methodology for a numerical simulation of an insertion or a drop of the rod cluster control assembly into its guides (discontinuous and continuous guides, guide thimble). A numerical model is elaborated in which many loads are taken into account: fluid load, gravity and friction force between the rod and the guide. The numerical results are compared to experimental measurements obtained from a full-scale structure. A good agreement between the calculated and the measured data is observed.The numerical model takes into account the possible deflection of the guide. It shows clearly that the friction force cannot be neglected when the guide is bowed. So one can locate a faulty guiding system by examining the reaction force during the insertion test. Then, the numerical model can help the decider to make his choice among different rod cluster/fuel assembly components.     

基于刚柔耦合的改进型控制棒组件变形通道落棒行为分析

燃料组件在堆芯内经历长期辐照后易产生弯曲形变，影响控制棒的安全落棒，因此亟需研究变形通道下控制棒落棒行为影响机制。通过数值模拟手段对导向管发生弯曲变形后的落棒行为规律进行分析研究，利用刚柔耦合方法分别计算直型、C型、S型导向管内的落棒行为，分析整个落棒行程、速度、加速度、沿程碰撞力随时间的变化情况，对比直型和2种不同变形通道对落棒行为的影响。研究结果表明，刚柔耦合方法可以较好地模拟变形通道下的落棒行为，C型落棒未发生卡滞，S型落棒卡滞于第2道弯折处。本研究将有助于为弯曲变形导致落棒卡涩问题的极限弯曲阈值提供判断依据，为工程设计提供参考。      

控制棒水压驱动系统落棒减速部件三维流场分析

控制棒水压驱动系统是清华大学为低温核供热堆研制的新型内置式控制棒驱动技术,控制棒水力减速部件是水压驱动系统的关键部件之一,在保证落棒时间的前提下,通过其对落棒过程进行减速,降低控制棒快速落棒过程的冲击力,避免控制棒十字翼的变形和损坏。本文分析了控制棒水压驱动系统落棒减速机理,利用CFD软件FLUENT对驱动系统水力减速箱流道进行了三维流场数值分析,并分析了对应不同落棒位置水力减速箱流道在不同边界条件下的流场分布特性。在流场分析结果的基础上计算得到了水力减速箱侧壁孔流道和底部缓冲腔流道流量系数随落棒位移的变化,将该结果与驱动系统落棒减速理论模型联立,获得了控制棒落棒位移曲线,理论计算结果同冷态落棒性能实验结果符合得很好,从而验证了流场分析结果的正确性,在此基础上分析了落棒过程减速箱内外差压和落棒速度与水力减速箱流量系数的关系,为控制棒水压驱动系统落棒减速部件的设计和优化提供了指导。     

Derivation of coupling coefficient from rod drop measurements in two-point reactors

A method is proposed to determine the reactivity coupling coefficient of a zero-power coupled-core system, based on the control rod drop measurements. We derive a two-point version of the formula for a rod drop experiment. The formula is very simple and the experimental procedures are convenient as well as conventional rod drop measurements.

For experimental determination of the coupling coefficient, experiments were carried out in the UTR-KINKI reactor, a light-water-moderated and graphite-reflected reactor. The validity of the proposed method is demonstrated by close agreement in the coefficients between the present result and the previous ones from reactor-noise measurements.     

水压驱动控制棒快速落棒冲击研究

控制棒水压驱动系统是由清华大学核能与新能源技术研究院发明的一项新型驱动技术。在快速落棒过程中,控制棒通过水力缓冲器进行缓冲。进行了控制棒水力缓冲性能实验,得到快速落棒过程中控制棒的关键缓冲性能参数;在实验结果基础上,运用达朗贝尔原理,将控制棒在冲击过程中所受的最大惯性力作为等效静载荷作用到控制棒上,利用有限元软件ABAQUS计算控制棒在最恶劣情况下的变形和应力分布,将计算结果与实验结果比较,验证了用简化模型代替非线性瞬态动力学分析的可行性。同时得到了控制棒在快速落棒冲击过程中不发生破坏的判据,为控制棒和水力缓冲器的设计和优化奠定了基础。     

控制棒水压驱动系统落棒减速性能实验研究

控制棒水压驱动系统是清华大学为低温核供热堆发明的新型的内置式控制棒驱动技术,控制棒水力减速部件是水压驱动系统的关键部件之一,通过其对控制棒落棒过程进行减速,在保证落棒时间的前提下,降低控制棒快速落棒过程的冲击力。分析了水力减速部件组成和工作原理,确定了水力减速箱侧壁开孔方案,完成了不同开孔方案工况下控制棒水压驱动系统冷态落棒减速性能实验,在实验结果的基础上对比和分析了不同方案下的落棒减速机理和落棒过程特征参数随开孔方案的变化规律。分析结果表明:随开孔面积的增大,落棒时间逐渐减小,落棒峰值速度逐渐增大。在开孔面积大于0.004 m~2时,随开孔面积的增大,落棒峰值速度增大过程趋于平缓,落棒稳定速度和落棒延迟时间变化不大,控制棒触碰碟簧速度缓慢增大。实验研究成果为控制棒水压驱动系统落棒减速部件的理论建模和设计优化提供了基础。     

Modifications to COBRA-TF to model dispersed flow film boiling with two flow,four field Eulerian–Eulerian approach – Part 1

In the case of a postulated loss of coolant accident (LOCA) in a nuclear reactor, an accurate prediction of clad temperature is needed to determine the safety margins. During the reflood phase of the LOCA, when the local void fraction is greater than 80% with the wall temperature above minimum film boiling temperature (T_min), the heat transfer process is dispersed flow film boiling (DFFB). This study has been performed to model DFFB in the reflood phase of a LOCA in a pressurized water reactor (PWR) rod bundle. The COBRA-TF computer code is utilized, since it has a detailed reflood package which takes into account the effect of spacer grids on the local heat transfer. The COBRA-TF code has also been improved to include a four field Eulerian–Eulerian modeling for the two-phase dispersed flow film boiling heat transfer regime. The modifications include adding a small droplet field to COBRA-TF as the fourth field. In addition, the spacer grid models of COBRA-TF have been revised and modified. In the first part of the paper, the results of the code predictions are presented by comparing the experimental data from rod bundle heat transfer (RBHT) experiments with the results of code simulations performed with original and modified code. Measurements and calculations for the heater rod, vapor temperatures and quench front progression have been compared and the results are described in detail. The results of the analysis performed with the modified code indicate the improvement in code predictions for the rod surface temperature, vapor temperature and quench front behavior. The results also indicate the need for improvement in the entrainment and interfacial drag models for the drop fields. The effects of spacer grids on the heat transfer, the models improved and developed for spacer grids and the results of the code calculations with these models are described in the part 2 of the paper.     

Vibration of nuclear fuel bundles

Several mathematical models have been proposed for calculating fuel rod responses in axial flows based on a single rod consideration. The spacing between fuel rods in liquid metal fast breeder reactors (LMFBRs) is small; hence fuel rods will interact with one another due to fluid coupling. The objective of this paper is to study the coupled vibration of fuel bundles. To account for the fluid coupling, a computer code (AMASS) is developed to calculate added mass coefficients for a group of circular cylinders based on the potential flow theory. The equations of motion for rod bundles are then derived including hydrodynamic forces, drag forces, fluid pressure, gravity effect, axial tension and damping. Based on the equations, a method of analysis is presented to study the free and forced vibrations of rod bundles. Finally, the method is applied to a typical LMFBR fuel bundle consisting of seven rods.     

Scram and nonlinear reactor system seismic analysis for a liquid metal fast reactor

Earthquake vibrations cause large forces and stresses that can significantly increase the scram time required for safe shutdown of a nuclear reactor. The horizontal deflections of the reactor system components cause impact between the control rods and their guide tubes and ducts. The resulting frictional forces, in addition to other operational forces, delay the travel time of the control rods. To obtain seismic responses of the various reactor system components (for which a linear response spectrum analysis is considered inadequate) and to predict the control rod drop time, a non-linear seismic time history analysis is required. Nonlinearities occur due to the clearances or gaps between various components. When the relative motion of adjacent components is large enough to close the gaps, impact takes place with large impact accelerations and forces.This paper presents the analysis and results for a liquid metal fast rector system which was analyzed for both scram times and seismic responses such as bending moments, accelerations and forces. The reactor system was represented with a one-dimensional nonlinear mathematical model with two degrees of freedom per node (translational and rotational). The model was developed to incorporate as many reactor components as possible without exceeding computer limitations. It consists of 12 reactor components with a total of 71 nodes, 69 beam and pin-jointed elements and 27 gap elements. The gap elements were defined by their clearances, impact spring constants and impact damping constants based on a 50% co-efficient of restitution.The horizontal excitation input to the model was the response of the containment building at the location of the reactor vessel supports. It consists of a 10 sec safe shutdown eathquake (SSE) acceleration-time history at 0.005 sec intervals and with a maximum acceleration of 0.408 g. The analysis was performed with two Westinghouse special purpose computer programs. The first program calculated the reactor system seismic responses and stored the impact forces on tape. The impact forces on the control rod driveline were converted into vertical frictional forces by multiplying them by a coefficient of friction, and then these were used by the second program for the scram time determination.The results give time history plots of various seismic responses, and plots of scram times as a function of control rod travel distance for the most critical scram initiation times. The total scram time considering the effects of the earthquake was still acceptable but about four times longer than that calculated without the eathquake. The bending moment and shear force responses were used as input for the structural analysis (stresses, deflections, fatigue) of the various components, in combination with the other applicable loading conditions.     

Seismic Analysis of Hydraulic Control Rod Driving System

A simplified mathematical model was developed for the Hydraulic Control Rod Driving System (HCRDS) of a 200 MW nuclear heating reactor, which incorporated the design of its chamfer-hole step cylinder, to analyze its seismic response characteristics. The control rod motion was analyzed for different sine-wave vibration loadings on platform vibrator. The vibration frequency domain and the minimum acceleration amplitude of the control rod needed to cause the control rod to step to its next setting were compared with the design acceleration amplitude spectrum. The system design was found to be safety within the calculated limits. The safety margin increased with increasing frequency.     

Pressure drop for parallel flow through a roughened rod cluster

A method is described of calculating the pressure drop for parallel flow through rod clusters with artificial surface roughnesses in order to improve the heat removal. The method allows the extensive experimental data on artificial roughness to be applied to rod clusters. The method is based on universal flow parameters for roughness and on general laws describing the pressure drop in non-circular channels with rough walls. The method is tested on the basis of measured results obtained from a rod cluster with 19 rough rods. The parameters determined are in excellent agreement with data measured in rough tubes and annular gaps. In this way it is possible, given the geometrical shape of the roughness elements, to calculate pressure drops and flow distributions in artificially roughened rod clusters contained in a smooth channel. The simplistic approach using an average friction factor and an overall hydraulic diameter results in rather unrealistic flow distributions and hence temperature distributions across the cluster.     

Multi-resolution analysis for determining control rod drop time

This study describes a multi-resolution analysis (MRA) to determine the onset and end drop times of control rods. The measurement test of the drop times of control rods is normally performed during the start-up test of each reactor cycle since it is a crucial safety function to guarantee the reactor safe shutdown. The MRA with wavelet transform is particularly useful in analyzing the onset transients of rod drop as a means of capturing the unique attributes of such signals in an efficient way. This approach also allows the automated determination of rod drop time which reduces the uncertainty induced by ad hoc heuristic approaches. The test signal is generated by adding the random noise measured from real rod drop tests subtracting the wavelet-filtered noise free signal from the noisy signal leaving the noise. The signal is similar to both high sharp spikes noise and sine wave noise from the real voltage trace generated during the rod drop test. The effectiveness of the method is demonstrated by the MRA process.     

BACO (Barra Combustible), a computer code for simulating a reactor fuel rod performance

The basic philosophy and mathematical structure of the fuel performance simulation code BACO is described. This code is based on a central finite-difference quasi-bidimensional approximation. Within that approximation, the thermoelastic-plastic behaviour of a in-service fuel rod is calculated by a set of equations which are linearized and solved for each time step by a sparse matrix inversion subroutine. The numerical method is shown to be stable and to converge rapidly to physically sound results for the stresses and strains. Changes in the fuel shape due to cracking and restructuring are included in the calculation within a self-consistent mathematical frame. Code convergence and accuracy are discussed by comparing some predictions against thermoelastic and plastic analytic solutions. An example of the code predictions for the rod state during a reactor shutdown is presented and discussed.     

Developing and modeling of the “Laguna Verde” BWR CRDA benchmark

Reactivity initiated accidents (RIA) and design basis transients are one of the most important aspects related to nuclear power reactor safety. These events are re-evaluated whenever core alterations (modifications) are made as part of the nuclear safety analysis performed to a new design. These modifications usually include, but are not limited to, power upgrades, longer cycles, new fuel assembly and control rod designs, etc. The results obtained are compared with pre-established bounding analysis values to see if the new core design fulfills the requirements of safety constraints imposed on the design. The control rod drop accident (CRDA) is the design basis transient for the reactivity events of BWR technology. The CRDA is a very localized event depending on the control rod insertion position and the fuel assemblies surrounding the control rod falling from the core. A numerical benchmark was developed based on the CRDA RIA design basis accident to further asses the performance of coupled 3D neutron kinetics/thermal-hydraulics codes. The CRDA in a BWR is a mostly neutronic driven event. This benchmark is based on a real operating nuclear power plant — unit 1 of the Laguna Verde (LV1) nuclear power plant (NPP). The definition of the benchmark is presented briefly together with the benchmark specifications. Some of the cross-sections were modified in order to make the maximum control rod worth greater than one dollar. The transient is initiated at steady-state by dropping the control rod with maximum worth at full speed. The “Laguna Verde” (LV1) BWR CRDA transient benchmark is calculated using two coupled codes: TRAC-BF1/NEM and TRAC-BF1/ENTRÉE. Neutron kinetics and thermal hydraulics models were developed for both codes. Comparison of the obtained results is presented along with some discussion of the sensitivity of results to some modeling assumptions.     

Natural convection analyses and verification for LMFBR cores

Analytical model requirements for core natural convection analyses are reviewed. Then results from current modeling on intra-assembly flow and heat redistribution are compared with several sources of experimental data. Also, data are described on low flow rod bundle hydraulic characteristics. Numerous sensitivity studies are also presented which show the effect and importance of various parameters on core temperatures during natural circulation, including inter-assembly flow redistribution, pump flow coastdown, rod size and fuel type, control system scram worth and shutdown power level. A system of codes for making the natural circulation predictions is also described, i.e., a plant-wide dynamic code, a whole-core system dynamic code and a hot channel dynamic analysis code. The overall approach of verifying the core related codes is presented, along with the interaction and linkage between all the codes. Confirmation of this system of three codes will bee through prototypic data obtained from EBR-II and FFTF natural circulation experiments.     

A simplified mathematical dynamic model of the HTR-10 high temperature gas-cooled reactor with control system design purposes

A simplified mathematical dynamic model of the HTR-10 high temperature gas-cooled reactor is developed based upon the fundamental conservation of fluid mass, energy and momentum. The model is formulated for coupling reactor neutron kinetics with reactivity feedback and reactor thermal-hydraulics. The reactor is nodalized to employ the lumped parameter modeling methodology, which is mathematically described by differential algebraic equations (DAEs). The developed model is implemented on a personal computer using the MATLAB/Simulink tool. A lot of numerical simulation experiments are investigated and discussed. The transient results show that the model can properly predict the reactor dynamics and can serve as the basis for the model-based control system design.