Pin Power Reconstruction Methods of the Few-Group BWR Core Simulator NEREUS

An improved pin power reconstruction method has been incorporated in the few-group nodal BWR core simulator NEREUS, which is based on the analytic polynomial nodal method. With the analytic polynomial nodal method, accurate node surface fluxes are available, which are used later to reconstruct pin powers. The intranodal homogeneous thermal flux is corrected using a semi-empirical proportional relation between surface transition components of the homogeneous and heterogeneous fluxes. This correction method is effective for BWR calculations, especially for controlled assemblies or mixed loading of off-set assemblies. A unified model accounting for effects of spectral histories, caused by spectral interactions between fuel assemblies and the control blade insertion, was also developed for intranodal burnup correction. The change in pin powers due to the control blade history can be predicted well, without laborious assembly depletion calculations with control blade insertion. R-factors used in critical power ratio calculations are also reconstructed from the pin powers. The NEREUS pin power reconstruction method was verified against heterogeneous multi-assembly depletion calculations.     

An effective homogenization method for heterogeneous assemblies

An effective homogenization method has been developed for heterogeneous assemblies such as fuel assemblies with and without control blades in BWR and control-rod channels in FBR. Effective homogenized cross sections are calculated so as to preserve the integrated reaction rates in a heterogeneous assembly in each group by iteratively changing the cross section used in homogeneous super-cell calculations in a model composed of the heterogeneous assembly and a fuel region. The method has been applied to the rod-worth calculation for pin rods in the fast critical assembly ZPPR-10 and to the power-density calculation of a test BWR core.     

Application of Quick Subchannel Analysis Method for Three-Dimensional Pin-by-Pin BWR Core Calculations

Three-dimensional pin-by-pin core analysis is considered to be a candidate for the next-generation BWR core calculation method. In our previous study, the applicability of the transport and burnup calculations for a three-dimensional pin-by-pin BWR core analysis was investigated. However, the thermal-hydraulics calculation has not yet been studied in this framework. In the conventional core analysis code, the bundlewise thermal-hydraulics calculation is adopted. In the actual core analysis, the power distribution inside a fuel assembly is tilted at the region adjacent to a control blade or the core peripheral region. In these regions, the consideration of the subchannel-wise void distribution has an impact on the fission rate distribution. Therefore, an evaluation of the detailed void distribution inside an assembly, i.e., the incorporation of the subchannel wise void distribution, is desirable for the pin-by-pin BWR core analysis. Although several subchannel analysis codes have been developed, these subchannel analysis codes generally require a large computational effort to estimate the subchannel-wise void distribution in a whole BWR core. Therefore, to analyze a whole BWR core within a reasonable computation time, it was necessary to apply a fast subchannel analysis code. In this paper, a quick subchannel analysis code dedicated to pin-by-pin BWR core analysis is newly developed, and the void distribution of the present subchannel analysis code is compared with the prevailing subchannel analysis code NASCA using three-dimensional single-assembly geometries. Since the present subchannel analysis code is used for a coupled neutronics/thermal-hydraulics analysis, the results of the coupling calculation are also compared with those of NASCA. The calculation result indicates that the void distribution difference between NASCA and the present subchannel analysis code is slightly less than 10%. This result indicates that the prediction accuracy of the present subchannel analysis code will be reasonably appropriate for a pin-by-pin BWR core analysis. Furthermore, the results show that the calculation time of the present subchannel analysis code is only 10 min for a hypothetical three-dimensional ABWR quarter-core geometry using a single CPU. This calculation time is sufficient for a pin-by-pin BWR core analysis.     

Core Design and Operating Strategies for Better Daily Load Following Performance in BWR Cores

New core design and operating strategies have been proposed for daily load following of an improved BWR core with large power swing.

The core concepts were based on the WNS core which uses an axially two-zoned enrichment fuel. One principal design strategy utilized was to reduce power in the lower portion of the core by adjusting a division point of the axially two-zoned enrichment fuel. One operating strategy introduced is for controlling Xe distributions. This method, coupled with a direct power distribution control by control rods, could decrease the xenon induced power change in the lower part of core.

The BWR core designed and operated under the new strategies was shown to meet the daily load demand with large power swing: 1-h reduction in power from 100 to 50%; 8-h hold at 50% power; 1-h increase in power from 50 to 100%; and 14-h hold at 100% power.     

Thermal Resistance between Hexagonally Arrayed Channels

A new power-flattening method has been proposed for boiling water reactors (BWRs) which have an axially skewed power distribution caused by the void fraction distribution. In present BWRs, the skewed power distribution is avoided by using shallow control rods and/or axially distributed gadolinia fuel bundles. These means are effective for the axial power shape control, but perturb the self-power-flattening effect due to fuel burnup. The power-flattening method proposed here extensively utilizes this effect in the equilibrium cycle core. Based on this method, a new BWR core design and operating strategy, the WNS core concept, has been realized for reactor operation with no shallow control rod insertion and no fuel bundle shuffling. Studies of the WNS core has shown that the proposed power-flattening method has the potential to improve capacity factors, increase operating thermal margins and simplify reactor operations in comparison with current BWR cores.     

Investigation of axial power gradients near a control rod tip

Control rod withdrawal in BWRs induces large power steps in the adjacent fuel assemblies. This paper investigates how well a 2D/3D method, e.g., CASMO5/SIMULATE5 computes axial pin power gradients adjacent to an asymmetrical control-rod tip in a BWR. The ability to predict pin power gradients accurately is important for safety considerations whereas large powers steps induced by control rod withdrawal can cause Pellet Cladding Interaction. The computation of axial pin power gradients axially around a control rod tip is a challenging task for any nodal code. On top of that, asymmetrical control rod handles are present in some BWR designs. The lattice code CASMO requires diagonal symmetry of all control rod parts. This introduces an error in computed pin power gradients that has been evaluated by Monte Carlo calculations.     

Applicability of the Diffusion and Simplified P3 Theories for Pin-by-Pin Geometry of BWR

The pin-by-pin fine-mesh core calculation method is considered as a candidate next-generation core calculation method for BWR. In this study, the diffusion and simplified P3 (SP3) theories are applied to the BWR pin-by-pin fine-mesh calculation. The performances of the diffusion and SP3 theories for cell-homogeneous pin-by-pin fine-mesh calculation for BWR are evaluated through comparison with a cell-heterogeneous detailed transport calculation by the method of characteristics (MOC). Two-dimensional, 2 × 2 multi-assemblies geometry is used to compare the prediction accuracies of the diffusion and SP3 theories. The 2 × 2 multi-assemblies geometry consists of 9 × 9 UO₂ fuel assemblies that have two different enrichment splittings. To minimize the cell-homogenization error, the SPH method is applied for the pin-by-pin fine-mesh calculation. The SPH method is a technique that reproduces a result of heterogeneous calculation using that of homogeneous calculation. The calculation results indicated that the diffusion theory shows a discrepancy larger than that of the SP3 theory on the pin-wise fission rate distribution. In contrast to the diffusion theory, the SP3 theory shows a much better accuracy on the pin-wise fission rate distribution. The computation time using the SP3 theory is about 1.5 times longer than that using the diffusion theory. The BWR core analysis consists of various calculations, e.g., the cross section interpolation, neutron flux calculation, thermal hydraulic calculation, and burn-up calculation. The function of the calculation time for the neutron flux calculation is usually less than half in the typical BWR core analysis. Therefore, the difference in the calculation time between the diffusion and SP3 theories would have no significant impact on the calculation time of the BWR core analysis. For these reasons, the SP3 theory is more suitable than the diffusion theory and is expected to have sufficient accuracy for the 2 × 2 multi-assemblies geometry used in this study, which simulates a typical situation of the actual BWR core.     

Investigation of intranodal depletion effects

The modeling of depletion induced intranodal effects on important neutron physical parameters in nodal diffusion theory is addressed. Consideration is given to two situations where these aspects are of particular interest, namely, in mixed oxide cores where strong interaction between uranium and plutonium mixed oxide assemblies occur, and in boiling water reactor cores where significant control rod history effects are encountered. A model based on a low order polynomial representation of intranodal cross-section spatial behaviour is considered. Two approaches for determining the constraints for the polynomial fitting procedure are applied. The first one is a conventional method employing intranodal exposure values, whereas the second model combines intranodal exposure and isotopic inventory information. Numerical studies are performed in order to evaluate the relative merits of the different models. It is demonstrated that pin power predictions are significantly influenced by intranodal effects. It is also found that the combined use of intranodal isotopic inventory and exposure distributions for estimating intranodal cross-section behaviour significantly improves the accuracy in pin powers over the more traditional approach of utilizing exposure distributions only.     

压水堆堆芯pin-by-pin计算环境效应处理模型研究

栅格非均匀计算过程中采用的全反射边界条件近似带来的中子射流效应和中子能谱干涉效应等环境效应对栅元均匀化常数具有较大影响。为在全堆芯pin by pin计算中处理环境效应带来的影响,本文从两个方面进行了计算分析。首先,基于棋盘式多组件问题对栅元均匀化群常数相对误差及各能群栅元不连续因子相对重要性进行了分析,可发现在等效均匀化常数中,热群不连续因子对全堆芯pin by pin计算精度的影响最重要;其次,基于最小二乘法建立了热群栅元不连续因子和堆芯中子学特征量之间的多项式函数关系,利用参数化技术提出了热群常数堆芯在线计算方法,其中堆芯中子学特征量包括扩散系数、移出截面、中子源项、归一化中子通量密度等。采用C5G7基准题和KAIST基准题进行了数值验证,计算结果表明,热群常数堆芯在线计算方法能有效降低全堆芯pin by pin计算特征值和棒功率相对误差,对处于不同燃料组件交界面附近的栅元,计算精度提升尤为显著。     

Development of Spectral History and Pin Power Correction Methods for Pin-by-Pin Core Analysis Method Using Three-Dimensional Direct Response Matrix

Spectral history and pin power correction methods have been developed for the pin-by-pin core analysis method using the three-dimensional direct response matrix (3D-DRM). The direct response matrix is formalized using four subresponse matrices in order to respond to a core eigenvalue k and thus it can be recomposed at each outer iteration in the core analysis. For core analysis, it is necessary to take into account the historical effect, which is related to spectral heterogeneity. The spectral history method is used to evaluate the nodal burn-up spectrum obtained by using the outgoing neutron current instead of the nodal flux because the 3D-DRM method does not use the nodal flux. The pin power correction method corrects the fuel rod neutron production rates obtained in the pin-by-pin calculation. These two methods were tested in a heterogeneous system. The test results show that the neutron multiplication factor error and nodal neutron production rate errors can be reduced by half during burn-up. The root-mean-square differences between the relative fuel rod neutron production rate distributions and the maximum error of relative fuel rod production rate can also be reduced by half. This means that the developed methods can reflect the effects of intra- and interassembly heterogeneities during burn-up and can be used for core analysis.     

Analysis of the MOX critical experiments BASALA by pin-by-pin core analysis method using three-dimensional direct response matrix

An analysis of the MOX critical experiments BASALA was performed to verify the pin-by-pin core analysis method using a three-dimensional direct response matrix. The BASALA experiments simulate full MOX BWR cores, and they were carried out in the EOLE critical facility of the French Atomic Energy Commission (CEA) by the Nuclear Power Engineering Corporation (NUPEC) in collaboration with CEA. The BASALA experimental cores are very heterogeneous because their size is much smaller than that of commercial power plants. The main features of the pin-by-pin core analysis method using the three-dimensional direct response matrix are that the response matrix can reflect the intra-assembly heterogeneous effect, the diffusion approximation is not involved, and the fuel rod fission rate can be directly evaluated. The maximum difference of the critical k-effective values among all nine cores analyzed was about 0.4% Δk. The root mean square differences between the calculated and measured radial fuel rod fission rate distributions in the test assembly of all cores were within 1.8% and nearly comparable to measurement error. The calculated results of the reactivity worth agreed with the measured results within 9%. These good agreements mean that the pin-by-pin core analysis method using the three-dimensional direct response matrix accurately reflects the effects of the intra- and inter-assembly heterogeneities in heterogeneous systems like the BASALA experimental cores.     

Applicability of angular flux discontinuity factor preserving region-wise leakage for integro-differential transport equation

In the current core analysis, spatial homogenization is utilized to reduce the computational time. The discontinuity factor (DF) is one of the effective correction factors to reduce spatial homogenization error. The DF in diffusion equation is widely used; on the other hand the DF in transport equation has not been put to practical use although several efforts have been carried out. In this paper, the angular flux discontinuity factor (AFDF) as the DF for the integro-differential transport equation (e.g., the discrete-ordinate method, the method of characteristics) is theoretically described and its applicability is discussed. The AFDF is used to preserve the region-wise neutron leakage at each spatial mesh and defined as a ratio of heterogeneous and homogeneous angular fluxes at the homogenized region surface. In a homogeneous calculation with the AFDF, the angular flux is discontinuous at the region surface. In this paper the applicability of the AFDF to fuel pin cell homogenization is verified for one-dimensional slab geometry. As a result of this verification, it is confirmed that the AFDF has the capability to reduce the spatial homogenization error of fuel pin cell homogenization.     

Incipient Boiling of Sodium in Presence of Magnetic Field

A three-dimensional nuclear and thermo-hydrodynamic kinetics calculation code IBIS has been developed, envisaging the treatment of asymmetrical reactivity changes in a large fast breeder reactor. An example of calculation with this code is described, which reveals a difference of void propagation behavior, following a local disturbance, between homogeneous and heterogeneous cores, ascribable to the presence, in the latter case, of inner blanket layers, which act as barrier against void propagation. Of the two parameters of power-to-flow ratio and space-time variation in thermal power, the latter is the more influential on void propagation, and this makes it essential to perform three-dimensional space-dependent kinetic analysis for adequately simulating local perturbations in a heterogeneous core.     

Parallel Processing of Boiling Water Reactor Core Analysis

A parallel processing method for the analysis of a Boiling Water Reactor (BWR) core has been developed to drastically reduce the computation time. In the proposed method, a BWR core is divided into smaller segments, each of which is assigned to one of the processing elements (PE) working in parallel. The whole computing task is divided into smaller tasks that are distributed to the PEs as equally as possible.

To solve the neutron diffusion equations in BWR neutronics calculations, the three-dimensional checker-board block iterative method was adopted. In the thermal-hydraulic calculation, the whole task can be divided into parallel tasks except for the coolant enthalpy distribution calculation along a flow channel.

Parallelization efficiency of the proposed method was examined by measuring computing time on a hypercube type parallel processor with 64PEs. The computation speed gradually degrades with the number of segmentation, because of delay due to communications between PEs and to waiting time caused by unequal amount of tasks among PEs.

A 64 PE calculation was found to be from 30 to 50 times faster than the 1PE calculation. Both the axial and the radial segmentations were found to be effective in reducing computing time. If the BWR core analysis is made with a massively parallel processor consisting of more than 4,500 PEs, computing time will be reduced nearly by an order of three.     

Two-Dimensional Baffle/Reflector Constants for Nodal Code in PWR Core Design

Currently nodal codes are widely used in three-dimensional core calculation. For nodal calculations, in addition to fuel assembly homogenization constants, baffle/reflector homogenization constants (B/R constants) have to be generated. Due to the complexity of its geometrical structure, the baffle/reflector region is usually represented by the two regions, which are called flat edges and corner edges. B/R constants are generated using an equivalent one-dimensional model for each region. However, errors of 3–4% appear for fuel assemblies along core corner when one-dimensional B/R constants are used. Therefore, in order to improve the accuracy of power distribution calculation based on the nodal method, B/R constants need to be calculated by modeling the geometrical configuration of the baffle/reflector region in greater detail. For this purpose, a method of calculating two-dimensional B/R constants that reflects the geometrical configuration has been developed, in which the geometrical configuration ouside the core is treated explicitly using a two-group fine-mesh diffusion code. The two-dimensional B/R constants thus obtained have reproduced assembly power from heterogeneous calculation within 0.5%, error regardless of fuel loading patterns.     

压水堆堆芯Pin-by-pin均匀化计算中非均匀泄漏修正模型研究

在压水堆堆芯Pin-by-pin均匀化计算中采用均匀泄漏修正模型及非均匀泄漏修正模型对组件计算的中子能谱进行修正,本文研究了Pin-by-pin均匀化计算中均匀泄漏修正模型及非均匀泄漏修正模型的实现方式,提出了非均匀泄漏修正模型和栅元均匀化方法的联合实现方式,并分析比较了不同栅元均匀化扩散系数产生方式的计算效果。数值结果表明,非均匀泄漏修正模型及由其产生的中子泄漏系数能有效提高压水堆堆芯Pin-by-pin计算的精度。     

Development of a control rod depletion methodology for the Westinghouse NEXUS system

The NEXUS project is an effort to merge and modernize the methods employed in Westinghouse PWR and BWR steady-state reactor physics codes. The NEXUS system relies on a once-through nodal cross-section generation methodology with an innovative and efficient technique for pin power recovery. The pin power methodology overcomes a well-known limitation of existing methodologies, namely the incapacity to properly account for heterogeneity changes due to the depletion environment. The so-called control rod history problem where control rods are repeatedly inserted and withdrawn during core depletion is a good example of such a case. In addition to the control rod history impact on pin power distributions, the insertion of control rods during extended periods leads to significant control rod depletion that affects the reactivity worth of the control rods which in turn can have a significant impact on pin powers. The importance of accurately predicting pin powers, combined with the need to adequately estimate the reactivity worth and nuclear end of life of control rods in BWRs and in generation III+ PWRs, has motivated the development of a novel control rod depletion model. This methodology and its numerical qualification, initially for PWR application only, is the topic of this paper. The focus is on describing the salient features of the model and on illustrating its performance by means of numerical experiments. It is shown that together with the NEXUS pin power recovery model, the control rod depletion methodology accurately predicts the reactivity feedback from repeated control rod insertions in a PWR core.     

Modal processing of the Local Power Range Monitors signals in BWR NPP

In a boiling water reactor (BWR), the power distribution can be varied both axially and radially by control rod manipulation and by void content variations in the moderator. As an example of accidental situations in nuclear power plants (NPP), we consider the power oscillations that can occur in a BWR NPP under certain circumstances. An interesting problem is to study and characterize these instabilities analyzing the neutronic power signals obtained from the Local Power Range Monitors (LPRMs) installed in the reactor core. Several techniques exist to detect and classify the possible oscillations in a BWR. The power modal decomposition method and the signal component analysis methodologies are reviewed. The performance of these techniques is compared analyzing Records 9 and 10 of cycle 14 of the OECD Ringhals 1 Stability Benchmark.     

Cold-neutron tomography of annular flow and functional spacer performance in a model of a boiling water reactor fuel rod bundle

Dryout of the coolant liquid film at the upper part of the fuel pins of a boiling water reactor (BWR) core constitutes the type of heat transfer crisis relevant for the conditions of high void fractions. It is both a safety concern and a limiting factor in the thermal power and thus for the economy of BWRs. We have investigated adiabatic, air-water annular flows in a scaled-up model of two neighboring subchannels as found in BWR fuel assemblies using cold-neutron tomography. The imaging of the double suchannel has been performed at the ICON beamline at the neutron spallation source SINQ at the Paul Scherrer Institute, Switzerland. Cold-neutron tomography is shown here to be an excellent tool for investigating air-water annular flows and the influence of functional spacers of different geometries on such flows. The high-resolution, high-contrast measurements provide the spatial distributions of the coolant liquid film thickness on the fuel pin surfaces as well as on the surfaces of the spacer vanes. The axial variations of the cross-section averaged liquid hold-up and its fraction in the gas core shows the effect of the spacers on the redistribution of the two phases.     

Moderator Temperature Coefficient in BWR Core

Temperature dependences of infinite multiplication factor k∞ and neutron leakage from the core must be examined for estimation of moderator temperature coefficient. Temperature dependence on k∞ has been investigated by many researchers, however, the dependence on neutron leakage of a BWR with cruciformed control rods has hardly been done. Because there are difficulties and necessity on calculations of three space dimensional and multi-energy groups neutron distribution in a BWR core.

In this study, moderator temperature coefficients of JPDR-II (BWR) core were obtained by calculation with DIFFUSION-ACE, which is newly developed three-dimensional multi- group computer code. The results were compared with experimental data measured from 20 to 275°C of the moderator temperature and the good agreement was obtained between calculation and measurement.

In order to evaluate neutron leakage from the core, the other two calculations were carried out, adjusting criticality by uniform absorption rate and by material buckling. The former underestimated neutron leakage and the latter overestimated it. Discussion on the results shows that in order to estimate the temperature coefficient of BWR, neutron leakage must be evaluated precisely, therefore the calculation at actual pattern of control rods is necessary.