RAPID Operator-Free Fast Reactor Concept without Any Control Rods Reactor Concept and Plant Dynamics Analyses

The 1,000kWe metal fueled sodium-cooled fast reactor concept “RAPID” to achieve highly automated reactor operation has been demonstrated. RAPID (Refueling by All Pins Integrated Design) is designed for a terrestrial power system which enables quick and simplified refueling. It is one of the successors of the RAPID-L, the operator-free fast reactor concept designed for lunar base power system. The essential feature of the RAPID concept is that the reactor core consists of an integrated fuel assembly instead of conventional fuel subassemblies. In this small-size reactor core, 14,000 fuel pins are integrated and encased in a fuel cartridge. Refueling is conducted by replacing a fuel cartridge. The reactor can be operated without refueling for up to 10 years.

Unique challenges in reactivity control systems design have been addressed in the RAPID concept. The reactor has no control rod but involves the following innovative reactivity control systems: lithium expansion modules (LEM) for inherent reactivity feedback, lithium injection modules (LIM) for inherent ultimate shutdown, and lithium release modules (LRM) for automated reactor startup. All these systems adopt ⁶Li as a liquid poison instead of B₄C rods. In combination with LEMs, LIMs and LRMs, RAPID can be operated without an operator. In this paper, the RAPID reactor concept and its transient characteristics are presented.     

On the multiplication factor and reactivity definitions for subcritical reactor systems

An analysis is made on the merit of different functions adopted for weighting neutron processes in subcritical nuclear reactor systems, as it appears in expressions of relevant integral quantities, such as reactivity worths, prompt neutron lifetimes, etc. All weight functions may be shown to depend on some sort of explicit or implicit, real or fictitious, system control. Associated with the importance function relevant to the reactor power control, the multiplication factor k_sub and generalized reactivity values ρ_gen are defined. The difference (1-k_sub)/k_sub is shown to be the more appropriate index for generally representing the ADS subcriticality. However, in certain circumstances, when an accidental event is studied in which the criticality condition may be surpassed during the transient, it appears more appropriate to take into account the standard multiplication factor (k_eff) and the reactivity values to which the transient is associated and for the definition of which the standard adjoint flux is adopted.     

小型长寿命核能系统燃料物理性能的研究

本文在简要说明世界上小型长寿命核能系统研究现状的基础上,提出了使用钍-铀燃料和铅-铋冷却剂构造小型长寿命堆芯的设想,并为此进行了一系列燃料物理性能的研究.对于长寿命核能系统的堆芯物理设计,使反应性随燃耗变动最小非常重要,同时应该尽可能地提高堆芯的燃耗以满足长寿命运行的需求.本文使用MCNP和MCBurn程序详细计算分析了使用不同的初始驱动燃料、不同栅格、燃料成分和类型、富集度条件下,燃料栅元的燃耗反应性变化等性能,并对其进行了能谱、转换比、富集度变化等方面的分析,经过对比初步确定了使用钍-铀燃料构造长寿命堆芯的物理条件,并以此为起点构造出一个堆芯,计算给出了反应性空泡系数等安全参数.     

On using alternative perturbation theory methodologies in the evaluation of reactivity effects in ADS cores

Core-average Doppler and coolant void reactivity coefficients, as well as the kinetic parameters (β_eff and Λ), have been determined for sub-critical accelerator-driven systems employing lead–bismuth eutectic (LBE) and helium gas coolants. To determine these parameters use is made of the standard procedure for analyzing critical reactors, which is based on “perturbation-theory” (PT), while in addition two dedicated methodologies for sub-critical systems, i.e. “inhomogeneous perturbation-theory” (IPT) and “heuristically based generalized perturbation-theory” (HGPT), have been employed to compute these parameters in a more rigorous manner.The two methods (PT and IPT/HGPT) are found to give similar results for each application and despite a smaller target k_eff-value, the sensitivity of the method is small in the case of the gas-cooled system, thus confirming the adequacy of the standard procedure. As regards the coolant void reactivity coefficient in the gas-cooled ADS, this finding can mostly be attributed to the fact that the core is always transparent with respect to the source neutrons, irrespective of the specific helium content.The sensitivity of the Doppler coefficient is also rather low in the case of the LBE cooled system. However, the dedicated methods are needed for the correct prediction of the coolant void reactivity coefficient, especially if minor actinides are introduced into the core. More important, in this case, is the fact that the PT-approach does not produce conservative results. Finally the sensitivity of the reactivity and kinetic parameters to the different methods is of the same order as that due to uncertainties in nuclear data and therefore these will need to be included in any overall evaluation of the impact of uncertainties on steady-state and transient ADS performance.     

Perturbation theory formulas for the effect of the dimensions on the critical mass in a fast reactor

This paper deals with a method for calculating the critical mass of a reactor provided with a sufficiently thick reflector as a function of the composition of the core and its dimensions.The working formula is obtained by an application of the theory of similarity to the usual first-approximation scheme of perturbation theory. For the calculation of the coefficients of the formula it is necessary to have the spatial and energy spectra of the neutron fluxes and values calculated numerically for some fixed volume of the reactor with a sufficiently thick reflector. By means of the coefficients so obtained for the formula it is possible to predict the critical mass over a wide range of variation of the dimensions of the core (over a change by about a factor two).If the size of the core goes beyond the limits of the interval thus accessible, one has to calculate the coefficients for a new range of the dimensions, and this requires a new numerical computation of the spectra.In this paper we give a formula containing coefficients calculated for a certain typical spectrum of a fast reactor for a number of isotopes contained in the core. The formula is checked by a nine-group calculation for volumes of the core ranging from 200 to 1000 cubic decimeters. The constants for the nine-group calculation were obtained from Soviet and foreign material published up to 1955.In conclusion the writer thanks Active Member of the Academy of Sciences of the Ukrainian SSR A.I. Leipunskii, G.I. Marchuk, and L.N. Usachev for a discussion of the work.     

Non-linear response of point-reactors to stochastic inputs

Statistical properties of the non-linear response of a point reactor to a white Gaussian reactivity insertion and an external source are investigated through the general Fokker-Planck theory for linear systems with random coefficients. The autocorrelation function and power spectral density of the reactor power are obtained, and the effect of non-linearities on the corner frequencies is discussed. The response to a Gaussian (not necessarily white) reactivity insertion and an arbitrary neutron source is also considered in the absence of delayed neutrons.     

Assessments of the kinetic and dynamic transient behavior of sub-critical systems (ADS) in comparison to critical reactor systems

The neutron kinetic and the reactor dynamic behavior of Accelerator Driven Systems (ADS) is significantly different from those of conventional power reactor systems currently in use for the production of power. It is the objective of this study to examine and to demonstrate the intrinsic differences of the kinetic and dynamic behavior of accelerator driven systems to typical plant transient initiators in comparison to the known, kinetic and dynamic behavior of critical thermal and fast reactor systems. It will be shown that in sub-critical assemblies, changes in reactivity or in the external neutron source strength lead to an asymptotic power level essentially described by the instantaneous power change (i.e. prompt jump). Shutdown of ADS operating at high levels of sub-criticality, (i.e. k_eff 0.99), without the support of reactivity control systems (such as control or safety rods), may be problematic in case the ability of cooling of the core should be impaired (i.e. loss of coolant flow). In addition, the dynamic behavior of sub-critical systems to typical plant transients such as protected or unprotected loss of flow (LOF) or heat sink (LOH) transients are not necessarily substantially different from the plant dynamic behavior of critical systems if the reactivity feedback coefficients of the ADS design are unfavorable. As expected, the state of sub-criticality and the temperature feedback coefficients, such as Doppler and coolant temperature coefficient, play dominant roles in determining the course and direction of plant transients. Should the combination of these safety coefficients be very unfavorable, not much additional margin in safety may be gained by making a critical system only sub-critical (i.e. k_eff0.95). A careful optimization procedure between the selected operating level of sub-criticality, the safety reactivity coefficients and the possible need for additional reactivity control systems seems, therefore, advisable during the early design phase of any ADS systems in order to assure a benign transient response of the particular ADS design under investigation to typical plant transient initiators.     

Simulation of reactivity transients in current MTRs

This work aims at simulation of reactivity induced transients in High Enriched Uranium (HEU) and Low Enriched Uranium (LEU) cores of a typical Material Test research Reactor (MTR) using PARET code. The transient problem was forced through specification of externally inserted reactivity as a function of time. Reactivity insertions are idealized by ramps and steps. Superdelayed-critical transients, superprompt-critical transients and quasistatic transients are selected for the analysis. Ramp and step reactivity functions were employed to simulate these perturbations. The effect of initial power on transient behavior has also been investigated. The low enriched uranium core is analyzed for transients without scram. The magnitudes of maximum reactivity insertions are chosen to be in the range of $0.05 to 2.0 for different reactivity insertion times. Transient simulation with scram reveals that response of both HEU and LEU-cores is similar for selected ‘ramps’ and ‘steps’. The difference is observed in the peak values of power and coolant, clad and fuel temperatures. Trip level is achieved earlier in case of LEU-core. The peak clad temperatures in both LEU and HEU-cores remain below the melting point of aluminum-clad for the selected reactivity insertions. Simulation show that the LEU-core is more sensitive to perturbations at low power as compared to the transients at full power. For reactivity transients at low power level, power rises sharply to a higher peak value. In transients at full power, the peak power barely exceeds the trip level. The power oscillations after the first peak are observed for transients without scram.     

Neutron Density Fluctuations in Point Reactor Systems with Dichotomic Reactivity Noise

The exactly solvable stochastic point reactor model systems are analyzed through the stochastic Liouville equation. Three kinds of model systems are treated: (1) linear system without delayed neutrons, (2) linear system with one-group of delayed neutrons, and (3) nonlinear system with direct power feedback. The exact expressions for the fluctuations of neutron density, such as the moments, autocorrelation function and power spectral density, are derived in the case where the colored reactivity noise is described by the dichotomic, or two state, Markov process with arbitrary correlation time and intensity, and the effects of the finite correlation time and intensity of the noise on the neutron density fluctuations are investigated. The influence of presence of delayed neutrons and the effect of nonlinearity of system on the neutron density fluctuations are also elucidated.

When the reactivity correlation time is very short, the correlation time has almost no effect on the power spectral density, and the relative fluctuation of neutron density in the stationary state is not affected very much by the presence of delayed neutrons and also by the nonlinearity of system. On the other hand, if the reactivity correlation time is very long, the effect of the reactivity noise on the power spectral density appears at very low frequency, and the presence of delayed neutrons has an effect of reducing the neutron density fluctuations.     

Neutronic and thermo-hydraulic analyses of a small,long-life HTGR for passive decay-heat removal

Since the accident at Fukushima Daiichi Nuclear Power Plant in 2011, design concepts for nuclear reactors have been reconsidered with much greater emphasis placed upon passive systems for decay-heat removal. By considering this issue, the design parameter conditions for high temperature gas-cooled reactors (HTGRs) with passive safety features of decay-heat removal were obtained by residual-heat transfer calculation using equations for fundamental heat transfer mechanisms in our previous works. In the present study, the appropriate size of reactor core for a 100 MW_t reactor operating at 1123 K of the initial core temperature was found using the conditions. Consequently, neutronics and thermo-hydraulic analyses for the proposed reactor core were performed and the proper optimizations to control the excess reactivity and flatten the change in power peaking factor during operation were done successfully. By the systematic method to decide the core design which satisfies the condition for passive decay-heat removal, a long-life small HTGR concept whose excess reactivity was small during the operation was shown. The small excess reactivity is a significant advantage from the view point of safety in reactivity accident.     

Inhomogeneous point kinetics equations and the source contribution

Inhomogeneous point reactor kinetics equations with one-group of delayed neutrons are solved analytically for linear reactivity insertion as well as for step reactivity insertion in the presence of external neutron source using the prompt jump approximation. The solution is obtained as an infinite series. The methodology is found to be a promising tool for analyzing nuclear reactor kinetics with positive or negative ramp reactivity insertion on a sub-critical or a zero power delayed critical reactor, where the temperature reactivity feedback is negligibly small. To check the consistency and the accuracy of the analytical solution, the results are compared with the numerical solution for different sub-critical and delayed critical states. The comparison is found to be good for all kinds of positive and negative step and ramp reactivity insertions. The analytical solution is arranged into two terms, one as a function of source contribution the other without that. Using the newly rearranged solution, the importance of the source term and the contribution to the error while neglecting source term to the reactor kinetics analysis, can be realized. Contribution to the error is small (less than 0.1%) when the equilibrium power is more than about one megawatt for a medium sized LMFBR. Similarly, the importance of source contribution to the total reactor period as a function of initial equilibrium power is also realized with the newly rearranged analytical solution. The total reactor period is over predicted (larger period in place of smaller period) which is not conservative, if the source contribution is not considered, for considerably small initial equilibrium power. The percentage of error in not considering the source term in period calculation varies as a function of net reactivity and ramp rate. The percentage of error in period determination without considering the source is comparatively high for small ramp rates.     

Numerical tools applied to power reactor noise analysis

In order to be able to calculate the space- and frequency-dependent neutron noise in real inhomogeneous systems in two-group theory, a code was developed for the calculation of the Green's function (dynamic transfer function) of such systems. This paper reports on the development as well as the test and application of the numerical tools employed. The code that was developed yields the space-dependence of the fluctuations of the neutron flux induced by fluctuating properties of the medium in the two-group diffusion approximation and in a two-dimensional representation of heterogeneous systems, for both critical systems and non-critical systems with an external source. Some applications of these tools to power reactor noise analysis are then described, including the unfolding of the parameters of the noise source from the induced neutron noise, measured at a few discrete locations throughout the core. Other concrete applications concern the study of the space-dependence of the Decay Ratio in Boiling Water Reactors, the noise-based estimation of the Moderator Temperature Coefficient of reactivity in Pressurized Water Reactors, the modeling of the beam- and shell-mode core-barrel vibrations in Pressurized Water Reactors, and the investigation of the validity of the point-kinetic approximation in subcritical systems driven by an external source. In most of these applications, calculations performed using the code are compared with at-power plant measurements. Power reactor noise analysis applications of the above type, i.e. core monitoring without disturbing plant operation, is of particular interest in the framework of the extensive program of power uprates worldwide.     

从广义自持链式反应观点看加速器驱动系统

用广义自持链式反应的观点探讨了加速器驱动系统 (ADS)的基本内涵。认为次临界反应堆、质子加速器和靶所组合的整体仍可看成一个 (临界的 )自持链式反应堆。这个反应堆不同于通常临界反应堆的特点是每次裂变后的二次中子不仅包含裂变释放的中子而且还包含部分裂变释能 (通过质子加速器及靶 )所转换的中子。正是有了这些附加中子 ,使得加速器驱动系统每次裂变的有效二次中子数增加了。一个ADS系统能够稳定运行的条件是ADS的次临界堆和加速器能够相互匹配使得ADS系统的有效二次中子数达到这样的水平 ,以致在ADS系统内能够形成自持的中子链式反应。因此尽管ADS的反应堆部分是次临界的 ,但从ADS整体来看只要质子加速器与次临界反应堆匹配得当 ,ADS系统是可以像通常临界反应堆那样 ,维持自持的链式反应的 (或临界的 )。给出了ADS系统维持自持链式反应的匹配条件 (广义临界条件 )。最后根据ADS系统的特点探讨了ADS在核废物处理 (嬗变 )、提高核燃料增殖效率及核能开发中的作用。     

Analysis of reactivity induced accidents at Pakistan Research Reactor-1

Analysis of reactivity induced accidents in Pakistan Research Reactor-1 (PARR-1) utilizing low enriched uranium (LEU) fuel, has been carried out using standard computer code PARET. The present core comprises of 29 standard and five control fuel elements. Various modes of reactivity insertions have been considered. The events studied include: start-up accident; accidental drop of a fuel element on the core; flooding of a beam tube with water; removal of an in-pile experiment during reactor operation etc. For each of these transients, time histories of reactor power, energy released and clad surface temperature etc. were calculated. The results reveal that the peak clad temperatures remain well below the clad melting temperature during these accidents. It is concluded that the reactor, which is operated safely at a steady-state power level of 10 MW, with coolant flow rate of 950 m³/h, will also be safe against any possible reactivity induced accident and will not result in a fuel failure.     

基于流量功率比恒定的小型铅基快堆运行研究

为开展小型铅基快堆运行策略研究,建立堆芯传递函数模型,利用比例-积分-微分（PID）控制器,结合控制棒驱动机构,分别设计堆芯流量功率比恒定与堆芯稳定核功率的运行方案。分别建立不同运行策略下的控制系统,开展一回路流量阶跃和堆芯反应性扰动仿真。结果表明,在引入一回路流量阶跃下降工况下,稳定核功率运行方案由于堆芯功率恒定而导致堆芯出口温度过高;在流量功率比恒定方案下,堆芯功率跟随一回路流量下降从而保证堆芯出口温度迅速稳定在安全范围内;在阶跃反应性扰动下,2种方案均可迅速调控堆芯功率的上冲幅度和超调量,堆芯出口温度基本维持恒定。      

A comprehensive approach of reactor safety research aiming at elimination of recriticality in CDA for commercialization of LMFBR

This paper discusses requirement and necessity for elimination of recriticality issue in hypothetical core disruptive accident in future fast reactors, and also necessity of a new comprehensive approach of safety research to achieve this objective. A theoretical investigation of the initiating phase consequences in an unprotected loss-of-flow accidents is shown as an example. A generalized model for core behavior is developed in order to clarify a requirement for mechanism to introduce a negative reactivity (controlled material relocation concept) aiming at elimination of recriticality.     

A study on reactivity insertion controlled LMR cores with metallic fuel

An inherently safe core concept with metallic fuel for sodium cooled fast reactor is proposed that has a negative void reactivity at the loss of coolant events without scram as well as a small excess reactivity during the operation cycle. The relationship of sodium void reactivities and burn-up reactivities to different core configurations has been studied quantitatively to clarify the core concept for large metallic fuel reactors. It has shown that the sodium void reactivity is greatly dependent on the core shapes while the excess reactivity is on the fuel compositions. It has also indicated that the core configuration that enables to enhance the neutron streaming through the region above the active core at coolant voiding is most effective to decrease sodium void reactivity.

A 3000 MWt core composed of the flat inner core and annular outer core where the fuel volume fraction is relatively high and the sodium plenum is placed just above the active core region has been selected as a candidate core.

The maximum excess reactivity of the candidate core at UTOP is about 0.4 $ and it can be reduced to approximately zero by power or inlet temperature adjustment during the operation cycle, meanwhile the sodium void reactivity is as low as -1.3 $ in negative that is enough to prevent ULOF sequences.     

Preliminary study of the tight lattice pressured heavy water reactor loaded with Pu／U and Th／U mixed fuels

To improve nuclear fuel utilization efficiency and prolong fuel cycle burn-up,a tight ptich lattice pressured heavy water reactor was investigated as an alternative of next generation of power reactors.It is shown that the high conversion ratio and negative coolant void reactivity coefficient are challenges in the reactor core physics designs.Various techniques were proposed to solve these problems.In this work.a tight pitch lattice and mixed fuel assemblies pressured heavy water reactor concept was investigated.BY utilizing numerical simulation technique,it is demonstrated that reactor core mixed with Pu/U and Th/U assemblies can achieve high conversion ratio(0.98) ,long burn-up(60GWD/t)and negative void reactivity coefficients.