BWR Assembly Research Articles

Application of the depth-averaged liquid film model to the annular flow regime in BWR fuel assemblies

The flow regime found in the downstream half of the BWR assembly can be described as an annular film flow with a central core of vapour with suspended droplets. This study presents the application of the fluid film model available in STAR-CCM+ to analyze the interplay between the vapour flow and the liquid film dynamics. The film model, based on depth-averaged equations, can be used to simulate film depth and velocity over complex geometries. Built on sound mathematical basis and applied to a wide variety of areas, the fluid film model, however, has not been widely used to study annular flow in nuclear fuel assemblies. Applying this model to a simplified geometry of a single rod with different gaps, the basic relationship between the vapour velocity, liquid film thickness and velocity distribution along the circumference of the rod is clarified. The minimum vapour velocity required to transport a liquid film along the surface of a fuel rod of a specific length against gravity was found using first-principles force balances. The model was then applied to a real, but simplified assembly geometry where the resulting flow pattern was primarily affected by the presence of part length rods. The minimum velocity required to transport a liquid film along the fuel rods in the assembly against gravity was found to be close to the range of velocities obtained using sub-channel codes. Strong circumferential variation in the wall shear across a short arc-length was observed for some fuel rods. The variation in wall shear also results in a corresponding variation in film velocity and film thickness and presumably has a strong impact on the local heat and mass-transfer characteristics. Cross flow from high resistance regions in the assembly towards lower resistance regions has a strong impact in terms of variations in the film thickness on the rods that are the furthest away from the low resistance paths.The modelling palette for the depth-averaged film model contains several features that can extend the validity of the modelling used in this study, such as the presence of droplets in the vapour core, deposition of droplets on to the film, heat transfer and boiling, and the influence of spacers in disrupting the liquid film. These features were not considered in this study and remain avenues for future work. The use of time-averaged turbulence modelling results in damping of unsteadiness of the vapour flow and perturbations in the film thickness. For better estimates of unsteady effects use of turbulence models such as the Large Eddy Simulation method is recommended. Current state-of-the-art in predicting dispersed annular flow using liquid film models is limited to single rods. The generalized depth-averaged film model can be applied to complex geometries including the effect of spacers.

The material-region-based 2D/1D transport method

The 2D/1D transport method is the dominant method for high-fidelity direct whole-core transport calculations, which attracts a lot of attention in recent decades. In the 2D/1D method, some sources of deviation are introduced, including spatial and angular approximation of leakage term and cross-section homogenization for 1D axial calculation. These approximations are analyzed and a material-region-based 2D/1D transport method with anisotropic leakage term, which avoids cross-section homogenization, as well as reduces spatially flat leakage approximation, are developed to improve accuracy at the expense of acceptable memory and efficiency loss. Finally, a BWR assembly case, the C5G7 benchmark and a rod-cluster assembly case are tested to verify the accuracy and performance of the material-region-based 2D/1D method.

Analysis of Void Reactivity Coefficient for 3D BWR Assembly Model

The effect of BWR fuel assembly 3D model on void reactivity coefficient (VRC) estimation is investigated. VRC values were calculated for different BWR assembly models applying deterministic T-NEWT and Monte Carlo KENO-VI functional modules of SCALE 6.1 code package. The difference between deterministic T-NEWT and Monte Carlo KENO-VI simulations is negligible (0.18 pcm/%). The influence of the assumed more detailed coolant density profile was estimated as well. VRC increases with the application of a larger number of coolant density values across fuel assembly height. It was shown that the coolant density profile described by 6 values per height could be considered sufficient from prospect of VRC estimation, as a more detailed density profile has impact below 1% on total assembly void effects. VRC values were decomposed to values for individual nodes and isotopes, since decomposition provides useful insights to describe the overall behaviour of VRC in detail.

Variability in spent fuel inventory data

A new methodology has been developed to assess how representative a collection of nuclide mass estimates is of real-world spent fuel. The analysis is approached as an “applicability range” evaluation, which quantifies the fraction of the historical population that is represented by one mass estimate. The new methodology is applied to a database containing spent fuel inventory estimates for operating U.S. reactors and uses historical assembly designs as a reference. The evaluation consists of two major steps: the implementation of a sampling and randomization scheme and the calculation of the applicability range scores. The mass estimates are assigned scores for each of the assembly designs they should represent, and the scores are averaged together to find overall applicability range scores for the database estimates. The results showed that the estimates for newer, PWR assembly classes had much higher scores than estimates for older or BWR assembly classes. The applicability range methodology can be extended beyond the database analyzed in the present work to any study that needs to use one value to represent a population with broad variations and limited knowledge of the underlying distributions.

Optimization treatment of point-wise nuclear data in Monte Carlo criticality and burnup calculations

The Monte Carlo codes used for neutron transport calculations are always time consuming, a large proportion of which is possessed by the treatment of continuous-energy cross sections. In this paper, two companion methods are developed for the optimization treatment of point-wise nuclear data, the first of which is called Computational-Expense Oriented (CEO) method based on the unionized energy grid approach and reconstructs only the computationally expensive cross sections in neutron transport simulation, and the other of which is called energy bin (EB) method, a companion of CEO method when the reaction rate tallies for MC-coupling burnup calculation are performed. These two methods are implemented in the code RMC, a Monte Carlo (MC) code used for reactor analysis, and tested on fast reactor core and BWR assembly problems. The numerical results show that CEO method, in comparison with reconstructing all cross sections under the unionized grid, requires the sharply decreased computer memory while achieving almost the same computational efficiency, and EB method can optimize the processing of nuclide-specific energy grid search and thus effectively reduce the total search number while requiring very small computer memory.

Interpretation of the VENUS VIP-BWR program with APOLLO2.8 reference and optimized MOC schemes for 8 × 8 UO 2 and MOX BWR assemblies

The interpretation of the VIP-BWR program conducted in the CEN·SCK Mol VENUS critical facility (Belgium), has been performed with the new APOLLO2.8 product and its CEA2005V4.1 library based on the JEFF3.1.1 file. Both reference SHEM-MOC (281groups without equivalence) and Optimized BWR 26G (26 groups with equivalence) schemes are used for UO 2 and MOX BWR assembly calculations. The VIP-BWR program was aimed to provide an experimental database for BWR neutronics tools in mixed Gd poisoned configurations with 8 × 8 UO 2 and MOX assemblies. The experimental conditions are relatively representative of actual industrial BWR core characteristics, at least in terms of void fraction. Measured pin-by-pin power distributions enable to exact valuable information at various interfaces. For fresh (UO 2/UO 2–Gd) and recycled UO 2 (UO 2 only) cores loadings, the information is given through the “UO 2” core. In the case of partial MOX loadings (UO 2/MOX interface), the power distributions are available through the “T-MOX” core. All critical sizes are predicted within 1 with SHEM-MOC reference calculation scheme. For UO 2 core, the (C–E) on k eff are (95 ± 266) pcm and (203 ± 266) pcm for SHEM-MOC and Optimized scheme respectively. For MOX core, the results are (87 ± 214) pcm and (283 ± 214) pcm. The uncertainties take into account both measurement uncertainties and technological uncertainties such as enrichment, clad thicknesses, grid pitch or fuel densities. Average (C–E)/E on radial fission rate distributions are in excellent agreement in the UO 2 and UO 2–Gd assemblies. In mixed loading cores, the calculation shows an over prediction in the MOX fuel pin. This points out a systematic swing between UO 2 and MOX. For average fission rates in UO 2, the C/E results are within ± 0.2% with SHEM-MOC and Optimized BWR 26G. For average power in MOX, the C/E results are within ±0.5% with SHEM-MOC and ±0.9% with Optimized BWR 26G. The P MOX/P UO2 fission rate ratios are (+3.7 ± 1.8%) and (+2.5 ± 1.8%) for SHEM-MOC and Optimized BWR 26G respectively. The peak power in UO 2 and MOX cores are reproduced within ±0.8% for both schemes. These results confirm the capability of this product to correctly treat pin-by-pin power distributions in BWR UO 2 and island MOX bundles.

A CFD model of two-phase flow in BWRs with results of sensitivity and uncertainty analysis

A Computational Fluid Dynamics model based on a two-fluid Eulerian description of the mass and momentum equations, two-equation mixture turbulence model and energy equation for the liquid phase is developed to predict the void distribution in a BWR assembly specified in the BFBT benchmark study. The effects of uncertainties in operating conditions, (pressure mass flow rate, inlet temperature, and power input) and model parameters, (momentum and heat exchange between the phases, heat transfer from the rods) has been analyzed. The results of both analysis indicate that the model predictions are more sensitive to experimental and modelling uncertainties in the low void fraction regions of the computational domain. The model predictions are in agreement with the experimental data with experimental and model uncertainties taken into account. Finally a sensitivity analysis of the model parameters has been performed and parameters of wall heat flux and heat transfer between the phases models have been identified as the major parameters that influence the phase distribution.

Two practical methods for unionized energy grid construction in continuous-energy Monte Carlo neutron transport calculation

A considerable speed-up in continuous-energy Monte Carlo neutron transport calculation can be achieved by using the same unionized energy grid for all point-wise reaction cross sections. This speed-up results from the fact that time-consuming grid iteration is reduced to minimum, and if the unionized grid is constructed by combining the grids of all nuclides, there is no loss of data or accuracy in the calculation. The drawback of this approach is that computer memory is wasted for storing a large number of redundant data points. Memory usage may become a problem, especially in burnup calculation, in which the irradiated materials consist of several hundred actinide and fission product nuclides. The grid size easily increases to over 1 million points, requiring tens of gigabytes of memory for storing the cross section data. This paper presents two practical methods for reducing the memory demand, while trying preserve the accuracy of the original data. The calculation routines are included in the PSG2/Serpent Monte Carlo reactor physics burnup calculation code and the methods are tested in a BWR assembly burnup calculation.

Treatment of Staggered Mesh for BWR Pin-by-Pin Core Analysis

In this paper, the neutron current interpolation (NCI) method is proposed to treat the staggered mesh on the basis of the Simplified P3 (SP3) theory code. In the NCI method, the response matrix formulation is applied to the SP3 theory code, and neutron partial currents at assembly boundary are interpolated using low-order polynomial functions, i.e., flat, linear or quadratic function. The pin-by-pin fine-mesh core analysis method is considered as a candidate next-generation core calculation method for BWR. Since the number of fuel rods in BWR assembly is increased with the higher burn-up, the different types of assembly may be adjacent in a BWR core. Therefore, when the cell-homogenized pin-by-pin analysis method is applied to the BWR core analysis, it must have a capability to treat the staggered mesh. Our previous study indicates that the SP3 theory is appropriate for pin-by-pin BWR calculations. However, the SP3 theory code that can treat the staggered mesh has not been developed so far. For these reasons, the treatment method of the staggered mesh is investigated to develop such SP3 theory code. The performances of the NCI method are evaluated through comparison with the cell-heterogeneous detailed transport calculations by the method of characteristics (MOC). Two-dimensional, 2 × 2 multi-assembly geometries are used to compare the prediction accuracy of the NCI method. The 2 × 2 multi-assembly geometries consist of 9 × 9 UO2 and 10 × 10 MOX fuel assemblies. The calculation results indicate that the prediction accuracy of the NCI method is similar to that of the detailed transport calculation method.

Treatment of Staggered Mesh for BWR Pin-by-Pin Core Analysis

In this paper, the neutron current interpolation (NCI) method is proposed to treat the staggered mesh on the basis of the Simplified P3 (SP3) theory code. In the NCI method, the response matrix formulation is applied to the SP3 theory code, and neutron partial currents at assembly boundary are interpolated using low-order polynomial functions, i.e., flat, linear or quadratic function. The pin-by-pin fine-mesh core analysis method is considered as a candidate next-generation core calculation method for BWR. Since the number of fuel rods in BWR assembly is increased with the higher burn-up, the different types of assembly may be adjacent in a BWR core. Therefore, when the cell-homogenized pin-by-pin analysis method is applied to the BWR core analysis, it must have a capability to treat the staggered mesh. Our previous study indicates that the SP3 theory is appropriate for pin-by-pin BWR calculations. However, the SP3 theory code that can treat the staggered mesh has not been developed so far. For these reas...

Comparison of 3D reaction rate distributions measured in an Optima2 BWR assembly with MCNPX predictions

As part of a joint research programme between the Paul Scherrer Institute (PSI) and swiss nuclear, with the co-operation of the Leibstadt nuclear power plant in Switzerland and fuel suppliers Westinghouse Sweden, measurements and calculations have been made of the axial and radial distributions of fission and 238U capture rates in the fuel rods of a Westinghouse SVEA-96 Optima2 boiling water reactor assembly. The measurements, made in the zero-energy research reactor PROTEUS at PSI, have been compared with calculations carried out using the Monte Carlo code MCNPX. The results reported are for the regions near the ends of the part-length fuel rods, which are a feature of SVEA-96 Optima2 assemblies. The sudden increase in moderation above the ends of the part-length rods leads to power peaking in the adjacent rods. Careful attention needs to be given to this phenomenon in the deployment of such fuel, the present paper providing experimental evidence for the ability of a stochastic code to predict such effects.

Advanced neutronics tools for BWR design calculations

This paper summarizes the developments implemented in the new APOLLO2.8 neutronics tool to meet the required target accuracy in LWR applications, particularly void effects and pin-by-pin power map in BWRs. The Method of Characteristics was developed to allow efficient LWR assembly calculations in 2D-exact heterogeneous geometry; resonant reaction calculation was improved by the optimized SHEM-281 group mesh, which avoids resonance self-shielding approximation below 23 eV, and the new space-dependent method for resonant mixture that accounts for resonance overlapping. Furthermore, a new library CEA2005, processed from JEFF3.1 evaluations involving feedback from Critical Experiments and LWR P.I.E, is used. The specific “2005–2007 BWR Plan” settled to demonstrate the validation/qualification of this neutronics tool is described. Some results from the validation process are presented: the comparison of APOLLO2.8 results to reference Monte Carlo TRIPOLI4 results on specific BWR benchmarks emphasizes the ability of the deterministic tool to calculate BWR assembly multiplication factor within 200 pcm accuracy for void fraction varying from 0 to 100%. The qualification process against the BASALA mock-up experiment stresses APOLLO2.8/CEA2005 performances: pin-by-pin power is always predicted within 2% accuracy, reactivity worth of B4C or Hf cruciform control blade, as well as Gd pins, is predicted within 1.2% accuracy.

Diagnostic analysis of pin-removal reactivity worth experiments in a SVEA-96+ test lattice

The present paper concerns a novel type of integral database generated in the course of the LWR–PROTEUS Phase I experiments, viz. the relative reactivity effects of removing individual fuel pins from a highly heterogeneous BWR assembly. The measurements reported were conducted in the central assembly of a 3 × 3 test-zone configuration of SVEA-96+ assemblies in PROTEUS, under full-density water moderation conditions. Calculations of the pin-removal reactivity worths have been carried out using two different LWR assembly codes, viz. CASMO-4 and BOXER. The discrepancies observed between experiment and calculation have been analysed in detail, on the basis of an extended reactivity decomposition methodology. This has allowed quantification of the different phase-space contributions (in terms of reaction rate types, energy groups and spatial regions) of a given calculated pin-removal reactivity worth, thus providing useful insights regarding the most important sources of error in each of the assembly codes investigated.

ＢＷＲ燃料集合体内の燃焼度分布が起動領域モニタ（ＳＲＮＭ）計数率に与える影響評価

ＢＷＲ燃料集合体内の燃焼度分布が起動領域モニタ（ＳＲＮＭ）計数率に与える影響評価

Effect of anisotropic scattering in neutronics analysis of BWR assembly

The anisotropic scattering effect to keff is studied for UO 2 and MOX fueled BWR assemblies. The anisotropic scattering effect increases the assembly k ∞ by 0.44% Δ k for the UO 2 assembly with 0% void fraction, and by 0.21% Δ k for the MOX assembly with 0% void fraction. This is because the anisotropic scattering effect flattens the intra-assembly thermal flux, and the absorption rate in the surrounding water gap is decreased, but the absorption rates in the MOX fuel rods are increased compared to the UO 2 rods. Therefore, the total decrease in absorption rates in the UO 2 assembly is relatively large, and the k ∞ is increased in the UO 2 assembly. The dependence of the anisotropic scattering effect on the void fraction is investigated, and the significant difference of 0.62% Δ k/ k is found for the 0% and the 80% void fractions. The BWR assemblies with Gd rods are also considered. Furthermore, the usefulness of the transport cross section is investigated, and it is found that the transport cross section gives reasonable anisotropic scattering effect, though not satisfactory.

06/02133 Study of the spatial discretization and temperature distribution approximation effects on BWR assembly calculations: Tohjoh, M. et al. Annals of Nuclear Energy, 2006, 33, (2), 170–179.

06/02133 Study of the spatial discretization and temperature distribution approximation effects on BWR assembly calculations: Tohjoh, M. et al. Annals of Nuclear Energy, 2006, 33, (2), 170–179.

Study of spectral heterogeneities for the interpretation of calculational trends in predicting pin power distributions in a SVEA-96+ BWR assembly

Detailed energy spectra have been calculated with the codes CASMO-4 and BOXER for neutron reaction rates in individual regions of a Westinghouse SVEA-96+ BWR fuel assembly immersed in water at room temperature, as investigated in Core 1A of the LWR-PROTEUS Phase I experimental program. First, results in 39 energy groups from the two codes were compared for 123 regions to characterise the lattice heterogeneity and to identify spectral trends qualitatively. Second, the various regions were classified into 4–5 broad spectral categories for quantitative comparisons. Third, results were collapsed to 2 groups, and then finally to 1 group, in order to obtain the principal neutron balance components, as also to derive and compare integral parameters such as the multiplication factor and average number of neutrons emitted per fission. These detailed spectral heterogeneity studies have led to the interpretation of certain trends in the prediction of experimental pin power distribution maps, which were not recognised earlier, providing a clear physical explanation for the observed discrepancies.

Effects of void uncertainties on the void reactivity coefficient and pin power distributions for a 10 × 10 BWR assembly

An important source of uncertainty in boiling water reactor physics is associated with the precise characterisation of the moderation properties of the coolant and by-pass regions, with significant impact on reactor physics parameters such as the lattice neutron multiplication, the neutron migration area and the pin-by-pin power distribution. In this paper, the effects of certain relevant void-fraction uncertainties on reactor physics parameters have been studied for a BWR assembly of the type Westinghouse SVEA-96 using CASMO-4, HELIOS/PRESTO-2 and MCNP4C. The SVEA-96 geometry is characterised by the sub-division of the assembly into four different sub-bundles, by means of an inner by-pass with a cruciform shape. The study has covered: (a) the effects of different cross-section data libraries on the void coefficient of reactivity, for a wide range of void fractions; (b) the consideration of a water film inside the sub-bundle walls, and (c) the impact of partly inserted absorber blades producing very different void fractions in different sub-bundles.

Study of the spatial discretization and temperature distribution approximation effects on BWR assembly calculations

The effects of the spatial discretization and temperature distribution approximation on the BWR assembly calculation were studied using the continuous energy Monte Carlo burn-up calculation under several conditions. The radial-division, temperature-distribution, and azimuthal-division effects of a fuel pellet for BWR fuel (8 × 8, wide-water-rod) were investigated. The calculation results indicate that the effect of the temperature distribution approximation on the assembly calculation is negligible, even if a pin-averaged temperature was assigned to all fuel pins. The effect of the spatial discretization of fuel pellets in the azimuthal direction brings about a 0.15%dk/k prediction error in k-infinity. This effect is caused by the change of the burn-up characteristics in the Gd-rods. Therefore, the azimuthal-division of Gd-rods is desirable to reduce the spatial discretization effect for BWR assembly with higher Gd fuel rods.

Natural circulation and stability performance of BWRs (NACUSP)

From the beginning of BWR technology it was realized that a BWR can become unstable under particular circumstances caused by a feedback between the thermal-hydraulics and the neutronics. This instability can result in oscillations of the power and the flow rate, which is an unwanted phenomenon. The NACUSP project addresses the stability issues in current and future BWRs by expanding the basic understanding through well structured testing and analyses of experimental data, by analyses of existing operational stability data from three different European reactors (Forsmark, Leibstadt, Cofrentes), by applying this knowledge via efficient models and validated computer codes to operating reactors and reactor designs, and by developing general guidelines for reactor operation and design on how to avoid BWR instabilities. In order to cover the parameter range as efficiently as possible, four existing, sophisticated thermohydraulic test facilities (CLOTAIRE [Gouirand, J.M., 1988. CLOTAIRE Program, description and manufacturing of the mock-up, CEA Cadarache, DRE/STRE/LGV 88–876.] DESIRE [van de Graaf, R., van der Hagen, T.H.J.J., Mudde, R.F., 1994. Two-phase flow scaling laws for a simulated BWR assembly. Nucl. Eng. Des. 148, 455–462.] CIRCUS [de Kruijf, W.J.M., van der Hagen, T.H.J.J., Mudde, R.F., 2000. CIRCUS; a natural circulation two-phase flow facility, Eurotherm Seminar No. 63, 6–8 September 1999 Genoa, Italy, 391–395] and PANDA [Dreier, J., Huggenberger, M., Aubert, C., Bandurski, T., Fischer, O., Healzer, J., Lomperski, S., Strassberger, H.-J., Varadi, G., Yadigaroglu, G., 1996. The PANDA facility and first test results, Kerntechnik 61, 214–222]) have been selected. To extrapolate from small-scale separate-effect testing conditions to full-scale integral reactor conditions one needs to rely on the performance of computer codes (MONA [Hoyer, N., 1994. MONA, a 7-Equation Transient two-phase flow model for LWR dynamics, Proceedings of the International Conference on New Trends in Nuclear System Thermohydraulics, pp. 271–280], ATHLET [Krepper, E., Prasser, H.-M., 1999. Natural circulation experiments at the ISB-VVER integral test facility and calculations using the thermal-hydraulic code ATHLET. Nucl. Technol. 128, 75–86], RAMONA-3(-5) [Grandi, G., Hoyer, N., Belblidia, L., 1998. Two-fluid thermal hydraulics capabilities of RAMONA-5, Proceedings of the International Conference on the Physics of Nuclear Science and Technology, October 5–8, 1998, Long Island, NY, USA, 1621–1625], LAPUR-V [Otaduy, P.J., March-Leuba, J., 1990. LAPUR User's Guide, NUREG/CR-542, ORNL/TM-11285], DWOS, FLICA [Toumi, I., Bergeron, A., Gallo, D., Royer, E., Caruge, D., 2000. FLICA-4: a three-dimensional two-phase flow computer code with advanced numerical methods for nuclear applications, Nucl. Eng. Des. 200, 139–155], SAPHYR, RELAP5/MOD3 [Idaho National Engineering Laboratory, 1995. RELAP5/MOD3 Code Manual, Vols. 1–6, INEL-95/0174, NUREG/CR-5535], TRAC-BF1 [Idaho National Engineering Laboratory, 1992. TRAC-BF1/MOD1; an advanced best-estimate computer program for BWR accident analysis, Vols. 1–3, EGG-2626, NUREG/CR-4356]. For specific items CFD codes are applied as well. Within NACUSP a linear stability analysis tool is developed. Four of the three experimental facilities within the project have yielded a large, unique database. Natural-circulation and stability characteristics at nominal pressure were collected from extensive experiments at the DESIRE facility. Low-pressure characteristics were measured at the PANDA (large scale) and the CIRCUS (small scale) facility. The phenomena encountered (flow rate and stability trends, the occurrence of flashing induced oscillations) can be explained from basic physical models and are now well understood. Several thermal-hydraulic codes have been benchmarked—some successfully, others with limited success—against these data. The CLOTAIRE (nominal pressure, large scale) facility has been modified and is now ready for experiments. Nuclear power plant data from three BWRs (Cofrentes, Forsmark and Leibstadt) have been collected. A very complete set of reactor data was obtained from measurements at the Leibstadt BWR during cycle-19. During this test, which was performed within the NACUSP project, safe reactor operation was demonstrated at extreme conditions, covering the entire power-flow map. State-of-the-art, coupled thermal-hydraulic—neutronics codes are being benchmarked on these data. The development of an easy to use, rapid and efficient analytical tool for parametric studies on BWR stability is in progress. The last year of NACUSP will be devoted to finalising the before mentioned activities and to use the tools developed and the experience obtained for developing general guidelines for designing and operating BWRs.