The effect of retarding torque during a flow transient for Tehran Research Reactor

The primary cooling system of the Tehran Research Reactor (TRR) has been analysed for a possible flow transient phenomenon caused by power cut-off. All the components of the TRR primary cooling loop that offer resistance to the coolant flow are physically modelled. Differential equations of motion for the coolant in the primary piping of the TRR and for the rotating parts of the centrifugal pump are then derived. The equation of flow motion is solved simultaneously with momentum conservation equation of the rotating parts of the pump which predicts the TRR pump speed during the flow transient. Electrical and mechanical losses are measured for the TRR three-phase induction motor in order to calculate the motor retarding torque during the event. The results of the present study are compared with the other similar primary loop results. The present model shows good agreement with the existing experimental and theoretical studies.     

Analysis of pump start-up transients

A computer programme has been developed to study pump start-up transients. Predictions of this programme have been verified experimentally. Parametric studies indicate that an increase in fluid inertia increases the acceleration head, while an increase in the moment of inertia of rotating parts decreases the acceleration head. Also for systems where the ratio of moment of inertia of rotating parts to fluid inertia is low, pump speed goes marginally beyond the steady speed during the start-up transient.     

Flow transients performance in an MTR-type research reactor

During a flow coastdown event leading to slowing down coolant flow, the rate of heat removal from the fuel element must be sufficiently high to prevent meltdown. It is essential to estimate the flow rate change and the decay heat removal capability. In many studies complete pump operating characteristics are used in analytical solutions of the problem. Under the coastdown phenomenon, retarding torque replaces motor torque. In order to determine this torque, all the induction motor losses during the event are identified and where possible these loss parameters are measured. Stator and rotor core losses, stator and rotor stray load losses and magnetizing saturation and rotor conductor skin effects are taken into account. The basics equations for coolant flow and for the rotating parts of the centrifugal pump are subsequently derived for an MTR-type research reactor such Tehran Research Reactor (TRR). Then the equation of flow motion is solved with another one which predicts the pump speed during the coastdown transient. The results of the present work are validated by comparison with experimental and analytical studies of the similar work. The model shows good agreement with the present literature.     

Simulation of transient flow caused by pump failure: Point-Implicit Method of Characteristics

A Point-Implicit Method of Characteristics (PIMOC) and an improved pump formulation are presented in this paper for the efficient simulation of transient flows caused by pump failure. The proposed methods can essentially be considered as modifications to the newly introduced Implicit Method of Characteristics (IMOC) by the authors. The IMOC, however, requires more computational effort than the conventional explicit version due to the fact that IMOC requires the solution of a nonlinear system of equations at each time step. To alleviate this problem, a Point-Implicit version of the IMOC is proposed here which requires less computational effort while enjoying all the advantages of the original IMOC. The proposed method is based on the observation that the assembled equations at each interior point of the pipe segments are uncoupled from those of the other points, including nodal points, which are used to define the system layout. These equations can, therefore, be separately solved for the unknown head and flow at these points before the remaining equations are assembled to form the final system of equations. The solution of the resulting system of equations with a size equal to twice as the number of nodes yields the value of head and flow at the remaining nodal points. To further improve the convergence of the method for the simulation of pump failure, an improved formulation of the pump is also proposed. In the proposed formulation, one of the pump characteristic parameters is also used to formulate the behavior of the pump elements. The proposed Point-Implicit Method and improved pump formulation are used to solve a set of numerical examples and the results are compared with those of original IMOC. For this, the element-wise formulations of two new devices namely junction and check-valve are also introduced. The experiments show improved efficiency of the proposed methods compared to the original IMOC.     

Transient behaviour of a parallel pump in nuclear research reactors

A theoretical analysis of the fast transients of a parallel pump, based on inertia of the rotating parts and inertia of the fluid, is proposed. It leads to total torque, total head, and total system resistance during transient periods. The equations indicate that an increase in coolant inertia increases the acceleration head. While an increase in the moment of inertia of rotating parts decreases the acceleration head. The model is used to analyze the behaviour of the Tehran Research Reactor (TRR) primary coolant loop parallel pump during a fast startup. The results of present model are compared with similar studies and good agreement is observed.     

核电厂反应堆主泵推力轴承启动阻力矩测试方法

为了获得核电厂反应堆主泵推力轴承在寿期内的极限启动阻力矩,确保执行事故余热排出功能的辅助电机可以在极端工况启动主泵,提出了推力轴承启动阻力矩（指启动瞬间的阻力矩）的测试方法并设计了试验装置,采用正交试验法对影响推力轴承启动阻力矩的3个影响因素（粗糙度、比压、润滑油温）进行研究,采用单因素法测试不同停机时间（指静止加载时间）对推力轴承启动阻力矩的影响,研究表明3个影响因素在规定的控制范围内变化时,启动阻力矩变化较小,而停机时间对推力轴承启动阻力矩影响较大。基于试验确定的极限启动阻力矩开展辅助电机设计,通过了推力轴承样机与主泵样机的反复启停试验验证。本文研究可为辅助电机启动阻力矩的设计提供准确可靠的输入。      

启停对推力轴承可靠性与阻力矩的影响测试

为了测试反复启停对钠冷快堆（SFR）一回路主泵推力轴承可靠性和阻力矩的影响，采用适用于小样本的分散系数法设计了可靠性统计方案，制造了3套巴氏合金推力瓦和1台上部组合轴承样机，设计并搭建了试验台，测试了启动阻力矩随停机加载时间的变化情况，模拟推力轴承的真实情况并开展了反复启停试验。试验研究表明，启动阻力矩均会随着停机加载时间的延长而不断增大；反复启停对推力瓦的磨损寿命影响较小，置信度0.9时，推力轴承启停125次不发生失效的可靠度超过0.99996；反复启停会影响推力轴承的阻力矩，随着启动次数的增多，推力轴承的阻力矩呈缓慢上升趋势，证明开展主泵电机启动能力设计时，必须要考虑启停次数的影响。本文研究可为主泵电机启动能力设计提供参考。      

Erratum

Nuclear power plants are presently designed to withstand instantaneous pipe severance in combination with the maximum seismic loads. The hypothetical combination of these two unlikely events leads to system designs which are very expensive and require dynamic event devices such as pipe whip restraints which have the potential for deleterious interaction with the piping system during normal operations. These present pipe rupture criteria are based on the a priori hypothesis that the instantaneous guillotine pipe break is possible, rather than from a consideration of the manner in which cracks might open or extend in a real piping system. The objective of this study is to help establish the basis for understanding how cracks which might exist in the primary piping of a pressurized water reactor (PWR) would open and extend so that improved criteria can be developed based on this information.One of the regions where loss of pressure boundary integrity must be postulated is the terminal end of the cold leg at the reactor vessel inlet nozzle. This region (including the effects of the reactor vessel and the primary pump) is modelled for analysis with the MARC general purpose finite element program. A circumferential crack, one-half circumference long, is considered to suddenly occur around the outside of the elbow when the pipe is at normal operating pressure. The most severe part of the safe shutdown earthquake (SSE) loading transient is applied simultaneously with the initiation of the crack.The plastic dynamic analysis of the crack opening effects in the discharge leg pipe is performed using the MARC program until the maximum opening occurs. The J-integral plastic crack extension criterion is computed for all times during the transient. The results indicate that none of the cracks will extend significantly and that the opening areas are small fractions of the flow area of the pipe.     

Transient flow analysis in reactor coolant pump systems during flow coastdown period

The rapid flow transient calculation in reactor coolant pump system is important in the safety analysis of a nuclear reactor. An accurate transient analysis of flow coastdown is also important and necessary for the design and manufacture of a reactor coolant pump. Only under the reliable work of a reactor coolant pump the safety of a nuclear power plant can be guaranteed. A mathematical model is developed for solving flow rate transient and pump speed transient during flow coastdown period. The detailed information of the centrifugal pump characteristics is not required. The flow rate and pump speed are solved analytically. The analytic solution of non-dimensional flow rate indicates that non-dimensional flow rate is determined by energy ratio β. The kinetic energy of the loop coolant fluid and the kinetic energy stored in the rotating parts are two important parameters in form of β. When the steady-state flow rate and pump speed are constant, the inertia of primary loop fluid and the pump moment of inertia are also two important parameters in flow transient analysis. For the condition all pump shafts are seized, the flow decay depends on the inertia of primary loop fluid. For the case that pump inertia is very large, the flow decay is determined by the pump inertia. The calculated non-dimensional flow rate and non-dimensional pump speed using the model are compared with published experimental data of two nuclear power plants and a reactor model test on flow coastdown transients. The comparison results show a good agreement. As the flow rate approaches to zero, the increase difference between experimental and calculated value is due to the effect of the mechanical friction loss.     

核电厂主泵倒流工况转子动态特性分析与研究

为防止核电厂主泵在反应堆冷却剂倒流产生的冲击载荷作用下发生反转,在电机上设置了由恢复弹簧和液压缓冲器组成的棘爪式防倒转装置。根据防倒转装置的结构特点及其工作原理,建立了防倒转装置的理论模型和主泵转子的运动学方程,分析了主泵倒流工况转子运动的动态特性,得到了转子的速度-位移运动轨迹。结果表明,由于反应堆冷却剂倒流产生的冲击载荷小于防倒转装置的设计载荷,主泵转子在倒流工况下经历包含6个运动状态的往复运动后,转速逐渐降低直至停止,实现了防止主泵反转的功能。      

Study and application of boiling water reactor jet pump characteristic

RELAP5/MOD2 is an advanced thermal-hydraulic computer code used to analyze plant response to postulated transient and loss-of-coolant accidents in light water nuclear reactors. Since this computer code was originally developed for pressurized water reactor transient analysis, some of its capabilities are questioned when the methods are applied to a boiling water reactor. One of the areas which requires careful assessment is the jet pump model.In this paper, the jet pump models of RELAP5/MOD2, RETRAN-02/MOD3, and RELAP4/MOD3 are compared. From an investigation of the momentum equations, it is found that the jet pump models of these codes are not exactly the same. However, the effects of the jet pump models on the M-N characteristic curve are negligible.In this study, it is found that the relationship between the flow ratio, M, and the head ratio, N, is uniquely determined for a given jet pump geometry provided that the wall friction and gravitational head are neglected. In other words, under the given assumptions, the M-N characteristic curve will not change with power level, recirculation pump speed or loop flow rate. When the effects of wall friction and gravitational head are included, the shape of the M-N curve will change. For certain conditions, the slope of the M-N curve can even change from negative to positive. The changes in the M-N curve caused by the separate effects of the wall friction and gravitational head will be presented. Sensitivity studies on the drive flow nozzle form loss coefficients, K_d, the suction flow junction form loss coefficients, K_S, the diffuser form loss coefficient, K_e, and the ratio of different flow areas in the jet pump are performed. Finally, useful guidelines will be presented for plants without a plant specific M-N curve.     

核主泵变流量过渡过程瞬态水力特性研究

为研究核主泵从设计工况向非设计工况过渡过程的瞬态水力特性及内部流动机理,应用计算流体力学软件CFX对核主泵叶轮流道内的变流量瞬态流动特性进行数值模拟计算。研究结果表明：变流量过渡时,核主泵的压力脉动沿圆周方向分布并不均匀,其变化趋势是逐渐上升到最大值后又降低,基本呈正弦变化规律,瞬态压力波动变化次数等于叶片与导叶片数之间的动静干涉次数,监测点越靠近叶片与导叶交界面,压力波动越大;由于冲角的存在造成叶轮流道内的速度呈先下降后上升的变化趋势;导叶不仅具有将动能转换为压能的功能,同时也具有有效减缓压力脉动幅度的功能;向小流量过渡时,由于流量减少,在靠近叶轮出口处出现二次回流,造成叶轮流道内速度变化幅度随流量的减少而增大。     

基于源项法的闭式回路架构对主泵性能影响的分析研究

传统的主泵流动分析平台多为简化的开式流路,与真实闭式回路运行工况存有较大差异。为探究主泵在真实回路中的流动特性与机理,以包含密封口环间隙的主泵全通道水力模型为研究对象,采用源项法进行稳态、瞬态计算分析研究。稳态计算结果表明:闭式循环回路中形成漩涡流态,致使主泵进口处发生预旋,产生入流畸变,导致湍动能有所增加,能量分布不均匀;瞬态计算结果表明:相较于开式流路,闭式回路入流畸变带来流场压力、速度、湍动能、压力脉动等特性的变化,导致泵体扬程、效率均有所下降,所受径向力、轴向力增大。闭式循环回路架构针对主泵流动性能的分析更接近真实流动。      

射流装置启泵过程的瞬态特性

射流装置由射流泵和主泵组成,引入MRX(Marine Reactor X)压水堆一回路系统中,有助于提升反应堆的固有安全性。反应堆启泵过程中,流量急剧上升导致堆芯温度变化,影响堆芯运行安全。通过计算流体力学(Computational Fluid Dynamics,CFD)方法对引入射流装置MRX一回路10%满功率(Full Power,FP)、17.5%FP和25%FP堆芯功率下启泵进行三维瞬态模拟,分析MRX一回路中射流装置流场瞬态特性。结果表明,射流装置的加入可以改善一回路自然循环能力,提高启泵工况下冷却剂初始变化流量,减缓变化趋势,改善过渡安全性;启泵过程中一回路温度存在波动现象,且堆芯功率越大,波动幅度越大,时间越长;启泵完成后射流泵喷嘴处流速较大。验证了压水堆中引入射流装置提升反应堆固有安全性的可行性,同时为进一步优化设计方案提供方向参考。     

不同初因事件下的两相排放过程热工水力特性研究

本文针对稳压器安全阀开启后的复杂两相热工水力过程进行研究,确定不同初因事件下的稳压器安全阀两相排放特性。采用自主化系统分析程序ARSAC对稳压器安全阀的上下游进行建模分析,选取三种典型的阀门排放过程,包括稳压器安全阀误开启事故、导致一个或多个稳压器安全阀开启的主蒸汽流量完全丧失事故、以及低温超压保护条件下导致的稳压器安全阀间歇性开启的安注泵误启动事故,研究稳压器安全阀开启后水封及蒸汽（或水）排放过程中涉及的复杂两相热工水力特性,结果表明：ARSAC程序能够捕捉两相排放过程中管道内部的流型变化;水封通过下游管道会形成明显的流量峰值,且不同的上游初始条件下排放过程对于下游管道造成的流量峰值及时间特性不同。通过本文的研究可以为载荷分析、安全评价及设计优化提供指导性建议。     

核主泵卡轴事故瞬变过程的水动力特性研究

为探究核主泵卡轴事故瞬变过程的水动力特性,通过动态匹配核主泵水力特性与系统管路阻力特性,建立了反应堆一回路系统的全三维简化模型。借助计算流体动力学（CFD）方法对核主泵卡轴事故工况进行了瞬态数值模拟,得到不同卡轴工况下核主泵外特性、内部压力场、叶轮叶片载荷与受力特性的瞬时变化。研究表明：卡轴时间越短,核主泵相应特性参数的瞬时变化越剧烈,事故造成影响越严重。以叶轮转速刚降为0 r/min时为节点,在卡轴时间为0.1、0.3、0.5 s三种卡轴工况下,流量分别降低到正常运行时的82.3%、61.4%、49.6%;核主泵扬程达到反向极值,分别为正常运行时的-137.7%、-87.4%、-56.9%;叶轮叶片两侧压力差值达到最大,分别为1.34、0.73、0.47 MPa,且在叶轮叶片工作面一侧和导叶流道中间部分形成相对集中的低压区;叶轮所受轴向力达到反向极值,分别为正常运行时的-159.3%、-96.5%、-65.5%。本数值预测方法对反应堆水动力系统的动态安全性评估提供了一定的数据支撑。     

Design and preliminary test of an annular linear induction electromagnetic pump for a sodium-cooled fast reactor thermal hydraulic experiment

An annular linear induction electromagnetic pump (ALIP) with a flow rate of 2265 L/min and a developed pressure of 4 bar was designed and fabricated to test the performance of the components of a sodium-cooled fast reactor (SFR) in a sodium thermal hydraulic experimental loop. The design characteristic of the ALIP was calculated using the electrical equivalent circuit method typically used for analyzing linear induction machines. Preliminary tests, such as verification of the moving function using an annular Al pipe, were carried out. The linearity between the input voltage, current, and magnetic flux density was verified. The developed force demonstrated an increase proportional to the square of the input current, whereas the velocity was linearly proportional to the input current. The main design variables of the pump were calculated theoretically for the SFR thermal hydraulic experimental loop. The pump was optimized for the design variables including input frequency, and the characteristics of the optimized pump were compared with those of the pump at the commercially used frequency of 60 Hz.     

Opening and extension of circumferential cracks in a pipe subject to dynamic loads

Nuclear power plants are presently designed to withstand instantaneous pipe severance in combination with the maximum seismic loads. The hypothetical combination of these two unlikely events leads to system designs which are very expensive and require dynamic event devices such as pipe whip restraints which have the potential for deleterious interaction with the piping system during normal operations. These present pipe rupture criteria are based on the a priori hypothesis that the instantaneous guillotine pipe break is possible, rather than from a consideration of the manner in which cracks might open or extend in a real piping system. The objective of this study is to help establish the basis for understanding how cracks which might exist in the primary piping of a pressurized water reactor (PWR) would open and extend so that improved criteria can be developed based on this information.One of the regions where loss of pressure boundary integrity must be postulated is the terminal end of the cold leg at the reactor vessel inlet nozzle. This region (including the effects of the reactor vessel and the primary pump) is modelled for analysis with the MARC general purpose finite element program. A circumferential crack, one-half circumference long, is considered to suddenly occur around the outside of the elbow when the pipe is at normal operating pressure. The most severe part of the safe shutdown earthquake (SSE) loading transient is applied simultaneously with the initiation of the crack.The plastic dynamic analysis of the crack opening effects in the discharge leg pipe is performed using the MARC program until the maximum opening occurs. The J-integral plastic crack extension criterion is computed for all times during the transient. The results indicate that none of the cracks will extend significantly and that the opening areas are small fractions of the flow area of the pipe.     

有芯和无芯高温重力钾热管启动性能试验研究

为研究有芯和无芯高温钾热管在重力状态下的启动性能，开展了相关对比与敏感性试验研究。得到有芯热管试验中的最优充液量为17.5 g，此充液量能避免充液量不足导致的启动升温较慢、末端温度低，也可避免充液量过大时间歇沸腾和过渡沸腾；无芯热管在启动和升温过程处于间歇沸腾工况，剧烈程度随充液量减少而降低，试验中最优充液量为9 g。在工程范围内，倾角对热管传热性能的影响可忽略。在试验状态下有芯钾热管启动性能优于无芯钾热管。     

反应堆冷却剂泵叶轮水力性能分析与优化设计

以反应堆冷却剂泵叶轮为研究对象，采用计算流体动力学（CFD）方法对其内部流场进行数值模拟，得到该泵叶轮水力性能的分析结果。根据CFD分析结果，叶片入口轮毂侧流动冲角过大，叶轮额定流量下的扬程低于设计要求，必须汽蚀余量（NPSHr）较大，需对其进行优化设计。考虑到CFD计算的偏差和实际工程经验，确定了叶轮水力性能优化目标；以叶片进口安放角、出口安放角和叶片进口边位置为优化变量，选择多种组合方案进行计算，确定了优化设计方案。对优化设计后的叶轮进行CFD计算，结果表明:相对原设计的叶轮，优化后的叶轮叶片入口处流动冲击明显减小，NPSHr大幅减小，内部流场更为合理，水力性能明显改善，优化方案满足预期目标。