Perturbation theory for nuclear fuel depletion calculations with predictor–corrector method

The perturbation theory for nuclear fuel depletion calculations with the predictor–corrector method is derived. This theory is implemented to a reactor physics code system CBZ, and the theory itself and its implementation are numerically verified. Sensitivities of nuclide number densities after fuel depletion with respect to nuclear data calculated with this theory are compared with reference sensitivities calculated by numerical differentiation, and good agreements are obtained. Importance of accurate angle integration on product of neutron flux and generalized adjoint neutron flux is also pointed out. Sensitivities in a 3×3 multi-cell system including a gadolinium-bearing fuel pin are calculated, and it is demonstrated that the derived theory yields accurate sensitivities even if coarse depletion time step division is adopted. The present work drastically increases the applicability of the depletion perturbation theory to actual problems.     

液体燃料熔盐堆三维稳态分析程序开发

液体燃料熔盐堆的物理热工特性与固体燃料反应堆有很大的不同,在分析计算中必须考虑燃料流动特性的影响,一般分析固体反应堆的程序均不能直接用于分析液体燃料熔盐堆。根据熔盐堆的流动特性,建立了液体燃料熔盐堆的三维中子动力学模型和流动传热模型,开发了针对液体燃料熔盐堆的三维稳态核热耦合程序,并以此分析了稳态情况下MOSART堆的物理热工特性。结果表明,堆芯流速对快中子和热中子影响较小,对堆芯温度和缓发中子分布影响较大。     

An Analysis of Continuous Bi-Directional Reactor Refueling

An analysis of continuous bi-directional reactor refueling is developed by one group diffusion approximation. The fundamental integro—differential equation is first converted to second order nonlinear differential equation, which is further reconverted to first order nonlinear differential equation, to finally take the form (du/dx) ²=f(u). By applying the elliptic function theory, the analytical solution for neutron flux and eigen value is obtained, and their physical characteristics are examined. Numerical results for neutron flux distribution are presented for the case where the rate of fuel feed movement is not the same for the two directions.     

Computational method for and analysis of the application of granular absorbers in VVÉR reactors

Questions concerning the compensation of excess reactivity in pressurized-water reactors by using consumable granular absorbers are examined. A method of computing the spatial-energy distribution of the neutrons in cells with a granular absorber is presented. The neutron-physical and thermophysical characteristics of fuel assemblies with fuel elements based on homogenized and heterogeneous arrangements of gadolinium in them are compared. It is shown that granular absorbers have certain advantages, specifically, they decrease the gadolinium content in the fuel elements and at the same time increase the total number of gadolinium-containing fuel elements in the fuel assemblies. This decreases the maximum power released in the gadolinium-containing fuel elements and the temperature of the fuel during the entire run. __________ Translated from Atomnaya énergiya, Vol. 100, No. 1, pp. 8–13, January, 2006.     

Azimuthal flux distribution measurements around fuel rods in reduced-moderation LWR lattices

An advanced analysis method named “micro reactor physics approach” was proposed, and the approach is needed for future reactor design considering the neutron behavior in fuel pellets. In order to validate the approach, neutron flux distribution measurements in a fuel pellet should be required. We have measured azimuthal flux distribution of fuel rods in Toshiba Nuclear Critical Assembly (NCA). A foil activation method with metallic foils was used for the measurement. Measured values were analyzed by a continuous energy Monte Carlo code MVP with the JENDL-3.3 library. The measurements are useful for the validation of an advanced fuel design method considering the neutron behavior in fuel pellets.     

Application of CANDLE burnup to block-type high temperature gas cooled reactor

The CANDLE burnup strategy, where the distributions of fuel nuclide densities, neutron flux, and power density move with the same constant speed and without any change in their shapes, is applied to the block-type high temperature gas cooled reactor. If it is successful, a burnup control rod can be eliminated, and several merits are expected. This burnup may be realized by enriched uranium and burnable poison with large neutron absorption cross-section. With the fuel enrichment of 15%, gadolinium concentration of 3.0%, and fuel cell pitch of 6.6 cm, the CANDLE burnup is realized with the burning region moving speed of 29 cm/year and the axial half-width of power density distribution of 1.5 m. When the concentration of natural gadolinium is higher, the burning region moving speed becomes slower and the burnup becomes higher, though the effective neutron multiplication factor becomes smaller. When U-235 enrichment is higher, the effective neutron multiplication factor becomes larger, the speed becomes slower, and the burnup becomes higher. When the pitch is wider, the effective neutron multiplication factor becomes larger, the speed becomes faster, and the burnup becomes higher.     

高保真中子输运计算的多级加速理论及应用

为解决高保真中子输运计算耗时严重的问题,本文提出了多级加速理论。其中,针对迭代求解过程,采用迭代加速的思路,即通过等价的低分辨率系统加速以减少迭代次数;针对瞬态求解,采用时间步加速方法,通过建立多级预估校正系统,实现在大时间步长下开展准确的高保真中子输运计算。最终引入不同分辨率系统的概念,将时间步加速方法与迭代加速方法整合形成一套完整的多级加速理论,并将其应用到精细化中子物理计算程序HNET中。采用典型瞬态基准题验证HNET程序加速效果。数值结果表明：多级加速理论能够在保证高保真中子输运计算精度的同时,极大地提升计算效率。     

Research reactor power controller design using an output feedback nonlinear receding horizon control method

A constrained, output feedback nonlinear receding horizon control (NRHC) method is applied to design a research reactor power controller. The method uses a nonlinear plant model subject to state, control and terminal set constraints; a nonlinear cost function; and a high gain observer. The controller regulates reactor power from 1% to 100% of full power; considers known disturbances, such as reactivity insertions and changes in core inlet flow and temperature; and includes upper limits constraints on neutron flux, neutron flux rate, core outlet temperature and core inlet–outlet temperature difference. Simulation results show an excellent performance for power regulation and known disturbances rejection: all process variables are kept within the admissible limits avoiding the actuation of the safety systems.     

微型中子源堆低浓化堆芯的探讨

通过对２３５Ｕ富集度为１９．９％的ＵＯ２和Ｕ３Ｓｉ２－Ａｌ的弥散体２种燃料进行物理计算，从中筛选出了优化的堆芯方案，并对其静态物理参数，诸如有效倍增因子、绝对中子通量密度、上铍反射层反应性价值、反应性温度系数、控制棒价值等进行了计算。     

Methods for Solving Adjoint Equations in Nonlinear Conditionally-Critical Problems

The special features of methods for calculating the neutron value functions with respect to functionals which are determined by solving a nonlinear conditionally-critical neutron transport equation are examined. The adjoint equations for these functions are written in an abstract operator form and contain additional, compared with linear problems, terms which are orthogonal to the neutron flux. These terms take account of the contribution due to the change in the properties of the medium when neutrons are introduced into the reactor into the balance of the values. The operators of the adjoint problem are analyzed and criteria ensuring that the proposed iteration methods converge are formulated. The satisfaction of the criteria is checked for the solution of problems where the nonlinearity of the emission equations is due to the dependence of the concentration of fuel nuclei on the neutron flux. It is noted that the iteration processes converge rapidly.     

Mutual Shielding Effect in 238U-239Pu Mixture

A three-dimensional time-domain core analysis code was applied to numerical simulations for an actual regional neutron flux oscillation observed in a commercial BWR core, in order to investigate potential nonlinear behavior in its coupled neutronic and thermohydraulic system. The present study shows existence of the nonlinear reactivity interaction between the fundamental and first azimuthal spatial harmonics modes of neutron flux distribution under the regional event. The spectrum analysis of the simulated data provides a unique result, that is, temporal harmonics peaks are excited at the even- and odd-order multiples of the characteristic resonance frequency in the fundamental and first spatial harmonics responses, respectively. The numerical simulation also shows that the strong nonlinearity of the coupled neutronic and thermohydraulic dynamics locally appears where the power unstably oscillates with large amplitudes, inducing the power shift and reactivity bias which are shown in the core-wide situation under the global oscillations. This contributes to suppression of the divergence of the local power oscillation, and also to development of the saturated self-limited cycles under the regional oscillations.     

Burnup study for Pakistan Research Reactor-1 utilizing high density low enriched uranium fuel

Burnup study for Pakistan Research Reactor-1 (PARR-1), which is a typical swimming pool type MTR utilizing high density low enriched uranium fuel, was performed by using Fuel Cycle Analysis Program (FCAP). Existing equilibrium core of PARR-1, which is relatively economical but provides less neutron fluxes per unit power than the first equilibrium core, was formed by adding five more fuel elements in the first equilibrium core. This study shows that if the fuel loading is increased in the first equilibrium core of PARR-1 by replacing the fuel of density 3.28 gU/cm³ by the fuel of density 4.00 gU/cm³ then the new equilibrium core can provide 10% higher neutron fluxes at the irradiation sites and will also require 1.5 kg less fuel than that required for existing equilibrium core for one-year full power operation at 10 MW. The new core provides neutron fluxes at 13% lower cost and if the size of this core is further reduced by three fuel elements then this core can provide 20% higher thermal neutron flux at the central flux trap at 9% lower cost. A possible use of U-Mo (5 w/o Mo) fuel of density 8.5 gU/cm³ in PARR-1 with an increase in existing water channel width from 2.1 to 2.45 mm (Ann. Nucl. Energy 32(1), 29–62) would provide up to 41% more thermal neutron flux at the central flux trap at 13% lower cost than the existing equilibrium core. The power peaking factors in these cores are similar to the power peaking factors of the existing equilibrium core and these cores are likely to operate within the safety constraints as defined for the existing equilibrium core of PARR-1.     

Pu-breeding feasibility in PWR

This study addresses the issue of alternative pathways for breeding plutonium in a 900 MWe three loop thermal pressurized water reactor (PWR), either fueled with uranium fuel (3.5% U-235) or with mixed fuel (20% MOX). During the operation of a nuclear reactor the in-core neutron flux and the ex-core neutron flux are monitored with flux detectors. At the places where those detectors operate, the guide thimbles and the vessel wall, respectively, the neutron flux can be used to irradiate material samples. This paper investigates whether it would be possible to produce plutonium by breeding it at the walls of a PWR vessel and/or in the guide thimbles. The neutron flux in the reactor and the corresponding multi-group spectra are estimated with Monte Carlo simulations for different positions at the vessel wall of a PWR operating with either UO₂ or MOX. Then the irradiation of fresh uranium samples at the vessel wall and in the guide thimbles are calculated and the isotopic composition of the irradiated samples are determined. The minimum irradiation period and the necessary minimum amount of fresh uranium to breed different grades of plutonium are derived.     

Space-dependent kinetics simulation of a gas-cooled fluidized bed nuclear reactor

In this paper we present numerical simulations of a conceptual helium-cooled fluidized bed thermal nuclear reactor. The simulations are performed using the coupled neutronics/multi-phase computational fluid dynamics code finite element transient criticality which is capable of modelling all the relevant non-linear feedback mechanisms. The conceptual reactor consists of an axi-symmetric bed surrounded by graphite moderator inside which 0.1 cm diameter TRISO-coated nuclear fuel particles are fluidized. Detailed spatial/temporal neutron flux and temperature profiles have been obtained providing valuable insight into the power distribution and fluid dynamics of this complex system. The numerical simulations show that the unique mixing ability of the fluidized bed gives rise, as expected, to uniform temperature and particle distribution. This uniformity enhances the heat transfer and therefore the power produced by the reactor.     

Fuzzy Logic Control Application for BWR Recirculation Flow Control System

There has been increasing necessity for load following and/or AFC (Automatic Frequency Control) operation along with the growth in the share of nuclear power generation in the electric power network. Fuzzy logic control was investigated for application to a BWR recirculation flow control system, in order to obtain a rapid generator power response within an allowable neutron flux overshoot. The proposed controller has two control loops, generator power and neutron flux loop. The fuzzy logic is utilized for weighing these control loops and for controlling the neutron flux. By evaluating the controller performance by numerical simulations on the step response for generator power demand with the model BWR recirculation flow system, more rapid response was obtained than that for conventional proportional plus integral controllers with no neutron flux overshoot beyond alarm activation level.     

200MW核供热堆含钆可燃毒物棒

介绍了轻水堆可燃毒物的发展和钆可燃毒物的各种性能，采用压电水堆核电厂燃料元件稳态分析程序ＦＲＡＰＣＯＮ－２，分析了２００ＭＷ核供热堆采用含钆可燃毒物棒的各种设计考虑，并根据其设计参数，对不同含钆量的可燃毒物棒进行了稳态工况的性能分析。     

Spatial stabilization of Advanced Heavy Water Reactor

Spatial oscillation in neutron flux distribution resulting from reactivity feedbacks due to fission products such as xenon is a matter of concern in large nuclear reactors. Left uncontrolled, the spatial oscillations may lead to “flux tilting” which may put the fuel integrity at peril. Hence during the design stages of any large nuclear reactor, it is essential to identify the existence of spatial instabilities and to design a suitable control strategy for regulating the spatial power distribution. In this paper, the existence of spatial instabilities in Advanced Heavy Water Reactor is investigated, which establishes that this reactor exhibits three modes of spatial instabilities. The paper further explores its stabilization using a control strategy based on feedback of total as well as spatial power distribution signals. The efficacy and robustness of the controller is demonstrated through dynamic simulations.     

Higher order methods for burnup calculations with Bateman solutions

A group of methods for burnup calculations solves the changes in material compositions by evaluating an explicit solution to the Bateman equations with constant microscopic reaction rates. This requires predicting representative averages for the one-group cross-sections and flux during each step, which is usually done using zeroth and first order predictions for their time development in a predictor–corrector calculation. In this paper we present the results of using linear, rather than constant, extrapolation on the predictor and quadratic, rather than linear, interpolation on the corrector. Both of these are done by using data from the previous step, and thus do not affect the stepwise running time.     

Study of the uncertainties due to position change of the PWR aeroball measurement system

The aeroball measurement system (AMS) is an important in-core instrumentation in German pressurized water reactors. Therefore, it is essential to know the possible uncertainties of this system. One is the lack of knowledge of the positions of balls in the guide tubes. The position changes can be up to 7 mm. Since the neutron flux distribution is not constant across the guide tubes, different reaction rates can result from the displacements. Both fuel assembly and full core calculations were carried out with the Monte Carlo code MCNP5. Differences in the reaction rates of up to 2% could be determined. In most cases, differences are only up to 0.5%. The results were hardly influenced by burnup and boron concentration in the water moderator. For fuel assemblies containing gadolinium as a burnable poison, a more pronounced reduction could be observed in the direction towards the gadolinium fuel rods. Overall, it was found that the AMS measurement values are very robust with regard to possible variations of ball positions.