Analytical Study of Operating Reactor Noise on a Single Channel and a Single Phase Flow Model, (I)

Basic formulas to describe the propagation of a periodically modulated driving source are derived on the distributed model of at-power reactors.

Disturbances in the neutron field are regarded as being promptly spread over the whole core in the frequency domain of usual interest for noise and frequency response analyses. On the basis of this approximation, a coupled set of kinetic equations for neutrons, fuel and coolant temperature is derived and solved for the case where a driving source of unit strength is imparted. The relations between the solutions obtained and the formulas for analyzing experiments are established. Comparisons are made qualitatively between the results and those of the lumped model. The existence of a sink and a resonance frequency is examined. The power spectral density of neutron fluctuations in a water reactor under forced circulated cooling shows a sharply varying configuration when the inlet coolant temperature fluctuations are the major noise sources. When the reactor is under natural convective cooling or under liquid metal cooling, no such characteristic features appear.     

Design and safety optimization of ship-based small nuclear power reactors

Design and safety optimization of ship-based nuclear power reactors have been performed. The neutronic and thermo-hydraulic programs of the three-dimensional X–Y–Z geometry have been developed for the analysis of ship-based nuclear power plant. Quasi-static approach is adopted to treat seawater effect and quasi-static approach is also employed to treat neutronic aspect during safety analysis.

The reactors are loop type lead–bismuth-cooled fast reactors with nitride fuel and with relatively large coolant pipe above reactor core, the heat from primary coolant system is directly transferred to water–steam loop through steam generators. The power level is 100–200 MW th and excess reactivity is about 1$. Three types of core were investigated in the optimization process: balance, tall, and pancake with five values of Z–Y size ratio.

As the optimization results, the core outlet temperature distribution is changing with the elevation angle of the reactor system. The pancake core type has larger temperature distribution change as the elevation angle changes due to the sea wave. The natural circulation capability is good for safety. However, large driving head of natural circulation may cause large temperature fluctuation as the elevation angle changes.     

Reactivity Balance for Reactor Diagnosis, (I) Accuracy of Reactivity Balance Technique in Hitachi Training Reactor

The reactivity balance method commonly used for measuring inserted anomalous reactivities was applied to the HTR (Hitachi Training Reactor).

The reactivities taken into consideration included the kinetic reactivity, as well as those associated with the control rod, power feedback, coolant inlet temperature and Xe buildup.

The reactivity balance data were obtained to cover start-up operation, as well as at various power levels including full rated power. These results obtained show that the errors associated with power feedback and with Xe buildup reactivity are both below approximately 1¢ these errors being due to the one point approximation and to inaccuracies in the constants used in the equations.

The fluctuations of residual reactivity are attributed to power fluctuations, to uncertainties in the measurement of the coolant inlet temperature and in the determination of control rod position. The scattering about the zero reactivity line caused by these fluctuations was evaluated to be within 0.8 ¢.

Anomalous reactivity was inserted artificially by means of shim rod movement, and was detected. The discrepancy between the residual reactivity calculated by this method and the actual worth of the inserted anomalous reactivity, which was a measure of the sensitivity of this technique, was within 1 ¢.     

一种低温堆核电站的动态数学模型

针对研发的采用一体化布置、全功率自然循环的低温核反应堆电站,建立了一个可用于大功率运行范围控制系统仿真的动态数学模型.模型采用了六组缓发中子动态方程(考虑了慢化剂温度和燃料温度反应性负反馈)、集中参数的堆芯传热模型以及自然循环流动模型,重点考虑了主回路自然循环对堆芯内冷却剂和燃料棒之间的传热系数、主换热器换热系数、主回路时间常数的影响.仿真结果表明,模型能够正确反映低温堆核电站的主要动态特性,可用于电站控制系统仿真.     

摇摆条件下小型反应堆堆芯入口流量分配特性数值分析

为研究摇摆条件下小型反应堆强迫循环时堆芯入口处冷却剂的流量分配特性,采用数值计算的方法,使用计算流体力学（CFD）软件STAR-CCM+建立小型反应堆模型,完成模型验证,开展摇摆条件下反应堆堆芯入口流量分配特性研究。结果表明,堆芯入口位置距摇摆轴的距离越大,摇摆幅度越大,堆芯入口冷却剂流量波动越大;长周期摇摆对流量影响较小,但随着摇摆周期减小,冷却剂流量会发生跃变。堆芯入口冷却剂分布不均匀程度随摇摆幅度的增加而增加,但对摇摆周期变化并不敏感。     

Analysis of Stochastic Fluctuations in a Natural Convection Non-Boiling Light-Water Reactor

Numerical calculations have been made of both noise spectra and relative standard deviations for stochastic fluctuations in various state quantities of a system, such as for example, neutron number, coolant temperature and coolant flow-speed.

The calculations are based on a theoretical model proposed earlier by the author for a non-boiling liquid-cooled and -moderated reactor, and carried out for the case of natural convection cooling at various values of reactor power up to 100 kW. Some of the results are compared with experiment.

It is shown that the low-frequency fluctuations, caused by coolant flow-speed fluctuations, become significant at increased power levels, and above several kW, the fluctuations in flow are visibly reflected in those of neutron number.     

Theory of Third Order Moments-Related Reactor Noise Experiments with Delayed Neutrons

Abstract

A general theory of third order moments-related reactor noise pulse experiments is presented. Detailed computation of a two-intervals moment of counts for a zero power one velocity point reactor with delayed neutrons is performed. The neutronic process is analyzed up to third order covariances via an extension of the usual mobility and diffusion matrices' approach. For this purpose, a stochastic diffusion matrix and a third order stochastic diffusion tensor are introduced. Detection effects are taken into account through a non-homogeneous Poisson distribution. No a priori approximation for the probability generating function of counts is assumed.     

Safety Analysis of Abnormal Reactivity Events in HTTR

Abstract

To confirm the safety of the High Temperature Engineering Test Reactor (HTTR) facility which is being constructed as the first high temperature gas cooled reactor in Japan, the representative abnormal reactivity events assumed in the safety analysis of the HTTR were analyzed. The HTTR is a graphite moderated and He-gas-cooled reactor with thermal power of 30 MW, inlet coolant temperature of 395°C and outlet coolant temperature of 950°C.

This report presents the analytical results of two representative events, “Abnormal control rod withdrawal from a subcritical condition” and “Abnormal control rod withdrawal during the full power operation”, showing that the safety of the HTTR is secured in conformity with the unique features of the HTTR with respect to the maximum fuel temperature, which is a key factor for the safety criteria.

The results of the safety analysis could demonstrate the safety of the HTTR facility with respect to abnormal reactivity events postulated in the HTTR, showing that the maximum fuel temperature is lower than the limit of the maximum fuel temperature of 1,600°C.     

Heats of Vaporization of UO2 and UO from UO2

In an earlier paper, a stochastic model of a power reactor has been proposed by the present author on the premise that the coolant-flow through a core is usually accompanied by random variations in the flow-rate, which are eventually largely responsible for the internal reactivity fluctuations.

In the present work, this model is extended to three different reactor systems: (a) where there exists a relaxation process corresponding to the effect of buoyant flow; (b) where a control or fuel element vibrates randomly, due to coolant flow-rate fluctuations; (c) where there are fluctuations in the inlet temperature with a non-white spectrum.

The noise spectra are derived for various state quantities with use made of the Langevin procedure. The theory is illustrated by referring chiefly to the neutron noise spectra, and comparing with the results of observations.

It is shown that the noise sources in question contribute significantly to the spectra, as compared with a low frequency component due to an inherent noise source in the coolant flow. In particular, a strong resonance peak of the spectra arises from the coupling between the random mechanical vibrations and coolant the flow-rate fluctuations.     

破口大小和二回路运行状态对核供热堆自然循环断流瞬态的影响

为研究一体化布置的核供热堆在发生破口失水事故中破口大小和从中间回路排出热量减少对断流过程的影响，选用不同的破口尺寸和不同的二回路工作状态，在５ＭＷ核供热堆热工水力模拟回路ＨＲＴＬ－５上进行了实验研究。稳态运行工况的系统压力为１．５ＭＰａ，在发生小破口失水事故后，加热功率维持为额定功率的５％以模拟剩余发热情况。实验研究并比较了不同条件下压力、温度、循环流量、液位和失水量等重要参数的变化。这些实验数据为核供热堆的安全分析提供了实验依据。     

Measurement of Temperature Fluctuations in a Natural Convection Water Loop

Investigations of reactor noise in water-cooled research reactors show that the power spectral density rises in the low frequency domain. The cause of this phenomenon is often attributed to fluctuations in the coolant temperature, but this has never been proved experimentally. The present experiment is an attempt in this direction.

The temperature fluctuation in a natural convection heat transfer loop decoupled from neutronics was measured and analyzed in the frequency domain. The test section of the loop had a rectangular channel measuring 5 mm × 50 mm in cross section and 500 mm in length. This configuration simulated a coolant channel of the MTR-type fuel element used in swimming-pool reactors. The power spectral density of the temperature fluctuation at the channel exit showed a shape similar to the power spectral density of the noise-equivalent source obtained in the Kyoto University Reactor at comparable power levels.     

Subchannel analysis of fuel assemblies of a lead–alloy cooled fast reactor

Lead–alloy cooled fast reactor is one of the six Gen-IV reactors. It has many attractive features such as excellent natural circulation performance, better shielding against gamma rays or energetic neutrons and potentially reduced capital costs. A natural circulation lead–alloy cooled fast reactor with 10 MWth is under design in China (hereafter called LFR-10MW). Fuel assemblies thermal hydraulic analysis is of vital importance for a successful design. A subchannel analysis code with flow distribution model was used to carry out the thermal hydraulic analysis. This work briefly gave the thermal-hydraulic design for the LFR-10MW and analyzed the thermal-hydraulic characteristics under steady-state condition using the subchannel analysis code. Whole core analysis was performed to locate the hottest fuel assembly using the code. The hottest fuel assembly was analyzed to obtain the cladding temperature, fuel temperature and coolant velocity. The maximum cladding temperature, the maximum fuel center temperature and the maximum coolant velocity are all below the design constraints. These results imply that the thermal-hydraulic design of LFR-10MW is feasible.     

A design study on Pb-208 cooled compact CANDLE burning reactor for future nuclear energy supply

A compact pool-type Pb-208 cooled CANDLE (Constant Axial shape of Neutron flux, nuclide densities and power shape During Life of Energy producing reactor) with a thermal power rating of 125 MWth is considered for the future nuclear energy supply. Natural Pb consists of Pb-204, Pb-206, Pb-207 and Pb-208. Pb-208 has a small capture and inelastic-scattering cross-section, which makes it possible to reduce neutron capture by coolant and to make neutron spectrum harder. In case of Pb-208 coolant instead of natural Pb, the core height and radius are reduced to 1.5 m and 1 m, respectively. The effective multiplication factor of the core, k_eff, could be increased from k_eff = 0.984 of natural Pb up to k_eff = 1.006. For increasing natural circulation head, coolant velocities in each core zone are adjusted by orifice at the core inlet position. The reactor vessel height is equal to that of a typical loop-type demonstration FBR vessel to obtain natural circulation head.     

中国先进研究堆停堆冷却措施及其主要特点

停堆后冷却问题是中国先进研究堆(CARR)重要的安全问题之一.冷却措施的实施对CARR的安全和建设投资有较重要的影响.CARR采用停堆初期的强迫循环及停堆后期全堆芯自然循环相结合的策略实现正常停堆和事故停堆后的堆芯冷却.停堆冷却的过程具体分为主泵大质量惯性飞轮惰转强迫冷却、应急堆芯冷却系统强迫冷却、自然循环功能部件动作实现全堆芯自然循环3个阶段.3个阶段既相互衔接又相互独立,每个阶段各有特点.停堆冷却策略的实施证明,CARR停堆冷却过程是可靠、有效、合理的,符合先进研究堆的发展趋势.     

Irreversible Circulation of Fluctuation in Reactor Noise

Irreversible circulation of fluctuation, α , is introduced as a new variable for the analysis of reactor noise in the normal case, which further develops our previous formulation based on the system size expansion method. It is shown that α—considered in conjunction with the variance σ—provides useful information about reactor noise, apart from the data we usually obtain on power spectral density. The relations holding between α and the conventionally used variables are given for the case of steady state. The present formalism is applied to a non-linear system with three degrees of freedom (total neutron number, fuel energy and coolant energy), to examine numerically the behavior of the fluctuations. The stability is illustrated as a phase diagram in a reactorparameter space. It is shown that the so-called soft-and hard-mode instabilities can be distinguished by observing α It is also demonstrated that appropriate processing of such quantities as α and σ will provide advance information on instabilities in power reactors.     

船用堆燃料棒包壳疲劳寿命分析

船用堆瞬态变工况下燃料棒包壳温度和冷却剂压力波动较大,引起包壳的疲劳损伤,因此包壳疲劳寿命分析至关重要。本文利用ANSYS软件模拟船用堆瞬态变工况下燃料棒的热机械行为,结合锆包壳疲劳寿命设计曲线,考察包壳温度、冷却剂压力、燃料棒内压以及辐照对船用堆燃料棒包壳疲劳寿命的影响。计算结果表明,瞬态变工况使得包壳疲劳寿命有很大降低;包壳温度变化与冷却剂压力变化相比,前者对包壳疲劳寿命的影响小;辐照会降低包壳疲劳寿命。在不影响核动力船舶机动性的前提下,可采取一些必要的措施来降低包壳的疲劳损伤。     

Full-scale modelling of the MNSR reactor to simulate normal operation, transients and reactivity insertion accidents under natural circulation conditions using the thermal hydraulic code ATHLET

A full-scale ATHLET system model for the Syrian miniature neutron source reactor (MNSR) has been developed. The model represents all reactor components of primary and secondary loops with the corresponding neutronics and thermal hydraulic characteristics. Under the MNSR operation conditions of natural circulation, normal operation, step reactivity transients and reactivity insertion accidents have been simulated. The analyses indicate the capability of ATHLET to simulate MNSR dynamic and thermal hydraulic behaviour and particularly to calculate the core coolant velocity of prevailing natural circulation in presence of the strong negative reactivity feed back of coolant temperature. The predicted time distribution of reactor power, core inlet and outlet coolant temperature follow closely the measured data for the quasi steady and transient states. However, sensitivity analyses indicate the influence of pressure form loss coefficients at core inlet and outlet on the results. The analysis of reactivity accidents represented by the insertion of large reactivity, demonstrates the high inherent safety features of MNSR. Even in case of insertion of total available cold excess reactivity without scram, the high negative reactivity feedback of moderator temperature limits power excursion and avoids consequently the escalation of clad temperature to the level of onset of sub-cooled void formation. The calculated peak power in this case agrees well with the data reported in the safety analysis report. The ATHLET code had not previously been assessed under these conditions. The results of this comprehensive analysis ensure the ability of the code to test some conceptual design modifications of MNSR's cooling system aiming the improvement of core cooling conditions to increase the maximum continuous reactor operation time allowing more effective use of MNSR for irradiation purposes.     

一体化小型氟盐冷却高温堆瞬态特性分析

根据下一代核能系统的发展目标,提出了采用自然循环的一体化小型氟盐冷却高温堆的概念。利用修改后的RELAR5-MS系统分析程序,建立了一体化小型氟盐冷却高温堆模型,并得到其稳态特性参数。在此基础上,对其在满功率运行状态下的反应性引入事故和失热阱事故进行了分析。分析计算表明,在反应性事故工况下,由于自然循环的存在,堆芯冷却剂流量随着堆芯温度发生动态变化,最终达到新的稳态,燃料棒和冷却剂温度均处于安全限值范围内。在失热阱事故下,反应堆负反馈的特性使得堆芯功率逐渐降低并实现自动停堆,即使不考虑余热排出系统的作用,燃料组件和冷却剂温度上升缓慢,在140 h内,燃料棒和冷却剂温度均处于全限值范围内。结果表明,一回路采用自然循环冷却的一体化小型氟盐冷却高温堆具有良好的固有安全性。     

Burn up calculations for the Iranian miniature reactor: A reliable and safe research reactor

Presenting neutronic calculations pertaining to the Iranian miniature research reactor is the main goal of this article. This is a key to maintaining safe and reliable core operation. The following reactor core neutronic parameters were calculated: clean cold core excess reactivity (ρ_ex), control rod and shim worth, shut down margin (SDM), neutron flux distribution of the reactor core components, and reactivity feedback coefficients. Calculations for the fuel burnup and radionuclide inventory of the Iranian miniature neutron source reactor (MNSR), after 13 years of operational time, are carried out. Moreover, the amount of uranium burnup and produced plutonium, the concentrations and activities of the most important fission products, the actinide radionuclides accumulated, and the total radioactivity of the core are estimated. Flux distribution for both water and fuel temperature increases are calculated and changes of the central control rod position are investigated as well. Standard neutronic simulation codes WIMS-D4 and CITATION are employed for these studies. The input model was validated by the experimental data according to the final safety analysis report (FSAR) of the reactor. The total activity of the MNSR core is calculated including all radionuclides at the end of the core life and it is found to be equal to 1.3 × 10³Ci. Our investigation shows that the reactor is operating under safe and reliable conditions.