Nodal kinetics model upgrade in the Penn State coupled TRAC/NEM codes

The Pennsylvania State University currently maintains and does development and verification work for its own versions of the coupled three-dimensional kinetics/thermal-hydraulics codes TRAC-PF1/NEM and TRAC-BF1/NEM. The subject of this paper is nodal model enhancements in the above mentioned codes. Because of the numerous validation studies that have been performed on almost every aspect of these codes, this upgrade is done without a major code rewrite. The upgrade consists of four steps. The first two steps are designed to improve the accuracy of the kinetics model, based on the nodal expansion method. The polynomial expansion solution of 1D transverse integrated diffusion equation is replaced with a solution, which uses a semi-analytic expansion. Further the standard parabolic polynomial representation of the transverse leakage in the above 1D equations is replaced with an improved approximation. The last two steps of the upgrade address the code efficiency by improving the solution of the time-dependent NEM equations and implementing a multi-grid solver. These four improvements are implemented into the standalone NEM kinetics code. Verification of this code was accomplished based on the original verification studies. The results show that the new methods improve the accuracy and efficiency of the code. The verification of the upgraded NEM model in the TRAC-PF1/NEM and TRAC-BF1/NEM coupled codes is underway.     

Developing and modeling of the “Laguna Verde” BWR CRDA benchmark

Reactivity initiated accidents (RIA) and design basis transients are one of the most important aspects related to nuclear power reactor safety. These events are re-evaluated whenever core alterations (modifications) are made as part of the nuclear safety analysis performed to a new design. These modifications usually include, but are not limited to, power upgrades, longer cycles, new fuel assembly and control rod designs, etc. The results obtained are compared with pre-established bounding analysis values to see if the new core design fulfills the requirements of safety constraints imposed on the design. The control rod drop accident (CRDA) is the design basis transient for the reactivity events of BWR technology. The CRDA is a very localized event depending on the control rod insertion position and the fuel assemblies surrounding the control rod falling from the core. A numerical benchmark was developed based on the CRDA RIA design basis accident to further asses the performance of coupled 3D neutron kinetics/thermal-hydraulics codes. The CRDA in a BWR is a mostly neutronic driven event. This benchmark is based on a real operating nuclear power plant — unit 1 of the Laguna Verde (LV1) nuclear power plant (NPP). The definition of the benchmark is presented briefly together with the benchmark specifications. Some of the cross-sections were modified in order to make the maximum control rod worth greater than one dollar. The transient is initiated at steady-state by dropping the control rod with maximum worth at full speed. The “Laguna Verde” (LV1) BWR CRDA transient benchmark is calculated using two coupled codes: TRAC-BF1/NEM and TRAC-BF1/ENTRÉE. Neutron kinetics and thermal hydraulics models were developed for both codes. Comparison of the obtained results is presented along with some discussion of the sensitivity of results to some modeling assumptions.     

Consistent generation of point feedback reactivity parameters for stability and thermalhydraulic codes

This paper shows a consistent methodology to obtain the point kinetics feedback reactivity parameters to be used by stability codes, like LAPUR-5, or transient codes, like TRAC-BF1. This methodology has been implemented in the code PAPU that generates the point kinetic parameters and feedback reactivity coefficients for the LAPUR and TRAC-BF1 codes. The results of the nodal reactivities obtained with the PAPU methodology have been compared with the results of other codes for different types of perturbations. Also, the reactivity tables generated by PAPU have been used in the LAPUR-5 code obtaining good results when the DR computed by LAPUR with these reactivity tables have been compared with the experimental DR obtained from signal analysis of Cofrentes NPP.     

Features and performance of a coupled three-dimensional thermal-hydraulic/kinetics TRAC-PF1/NEM pressurized water reactor (PWR) analysis code

This paper summarizes the current status of the Pennsylvania State University (PSU) version of the coupled three-dimensional (3-D) thermal-hydraulic/kinetics TRAC-PF1/NEM code for pressurized water reactor (PWR) transient and accident analysis and describes applications to reactivity insertion accident (RIA) simulations as well as recent developments. The TRAC-PF1/NEM methodology utilizes closely coupled 3-D thermal-hydraulics and 3-D core neutronics transient models to simulate the vessel and a 1-D simulation of the primary system. An efficient and flexible cross-section generation procedure was developed and implemented into TRAC-PF1/NEM. These features make the coupled code capable of modeling PWR reactivity transients, including boron dilution transients, in a reasonable amount of computer time. Three-dimensional studies on hot zero power (HZP) rod ejection and main steam line break (MSLB) transients in a PWR, as well as a large break loss-of-coolant-accident (LBLOCA) and boron dilution transients, were accomplished using TRAC-PF1/NEM. The results obtained demonstrate that this code is appropriate for analysis of the space-dependent neutronics and thermal-hydraulic coupled phenomena related to most current safety issues.     

Development of a multi-dimensional thermal-hydraulic system code, MARS 1.3.1

A multi-dimensional thermal-hydraulic system code MARS has been developed by consolidating and restructuring the RELAP5/MOD3.2.1.2 and COBRA-TF codes. The two codes were adopted to take advantage of the very general, versatile features of RELAP5 and the realistic three-dimensional hydrodynamic module of COBRA-TF. In the course of code development, major features of each code were consolidated into a single code first. The resulting source programs were rewritten in standard fortran 90, and then were restructured using modular data structures based on “derived type variables” and a new “dynamic memory allocation” scheme. In addition, the Windows graphics features were implemented for user friendliness. This paper presents the developmental activities up to mars version 1.3.1 including the code consolidation, the code restructuring and modernization, and the results of the developmental assessment.     

Simulation of a main steam line break accident using a coupled “system thermal-hydraulics,three-dimensional reactor kinetics,and hot channel analysis” code

For a realistic analysis of thermal-hydraulics (T-H) transients in light water reactors, KAERI has developed the best-estimate T-H system code, MARS. The code has been improved from the consolidated version of the RELAP5/MOD3 and COBRA-TF codes. Then, the MARS code was coupled with a three-dimensional (3-D) reactor kinetics code, MASTER. This coupled calculation feature, in conjunction with the existing hot channel analysis capabilities of the MARS and MASTER codes, allows for more realistic simulations of nuclear system transients.     

COSINE子通道均相流分析程序的研发

COSINE一体化软件包的子通道安全分析程序cosSubc基于子通道控制体三维网格模型,采用轴向及横向的热工水力控制方程,包括两流体和均相流两种求解算法。本文介绍了子通道均相流程序的物理模型和数值算法,并用cosSubc均相流程序和参考程序COBRA-TF分别对典型1 000MW核电厂稳态算例进行计算分析,结果表明:cosSubc均相流程序与COBRA-TF吻合较好,具备堆芯子通道的热工水力计算能力。     

Development of Parallel Coupling System between Three-Dimensional Nodal Kinetic Code ENTREE and Two-Fluid Plant Simulator TRAC/BF1

The high-speed three-dimensional neutron kinetic code ENTRÉE was developed based on the polynomial and semi-analytical nonlinear iterative nodal methods (PNLM and SANLM) with also introducing the discontinuity factor. In order to enhance the efficiency of transient calculation, the nonlinear correction-coupling coefficients are intermittently updated based on the changing rate of core state variables. By giving the analytical form for two-node problem matrix elements, the additional computing time in SANLM was minimized. A fast algorithm was developed for the multi table macro-cross section rebuilding process. The reactivity component model was implemented based on the variation of the neutron production and destruction terms. The code was coupled with the two-fluid thermal hydraulic plant simulator TRAC/BF1 through PVM or MPI protocols. Two codes are executed in parallel with exchanging the feedback parameters explicitly. Based on the LMW PWR transient benchmark, it was shown that both PNLM and SANLM spend less than 20% excess computing time in comparison with the coarse mesh finite difference method (CFDM). The implementation of the discontinuity factor was verified based on the DVP problem. Adequacy and parallel efficiency of the coupling system TRAC/BF1-ENTREE was demonstrated based on the BWR cold water injection transient proposed by NEA/CRP.     

Modifications to COBRA-TF to model dispersed flow film boiling with two flow,four field Eulerian–Eulerian approach – Part 2

In the first part of the paper, the modifications performed to improve the dispersed flow film boiling model in COBRA-TF have been described. The improvements were achieved by adding a small droplet field to the code’s solution scheme. The conservation equations, the source terms for the equations and the models developed were summarized. In this paper, the effects of spacer grids on the dispersed flow heat transfer and COBRA-TF modifications for the spacer grid models are presented. The results of the code predictions are presented by comparing the experimental data from Rod Bundle Heat Transfer experiments with the results of code simulations performed with original and modified code. Measurements and calculations for the spacer grid temperature have been compared. The results of the analysis performed with the modified code indicate the improvement in code predictions for the spacer grid temperature.     

Analysis of an ADS spurious opening event at a BWR/6 by means of the TRACE code

The paper presents the results of a post-event analysis of a spurious opening of 8 relief valves of the automatic depressurization system (ADS) occurred in a BWR/6. The opening of the relief valves results in a fast depressurization (pressure blow down) of the primary system which might lead to significant dynamic loads on the RPV and associated internals. In addition, the RPV level swelling caused by the fast depressurization might lead to undesired water carry-over into the steam line and through the safety relief valves (SRVs). Therefore, the transient needs to be characterized in terms of evolution of pressure, temperature and fluid distribution in the system. This event has been modeled by means of the TRACE and TRAC-BF1 codes. The results are in good agreement with the plant data.     

Critical Power Characteristics in 37-rod Tight Lattice Bundles under Transient Conditions

Critical power characteristics in the postulated abnormal transient processes that may be possibly met in the operation of Innovative Water Reactor for Flexible Fuel Cycle (FLWR) were investigated for the design of the FLWR core. Transient Boiling Transition (BT) tests were carried out using two sets of 37-rod tight lattice rod bundles (rod diameter: 13 mm; rod clearance: 1.3 mm or 1.0 mm) at Japan Atomic Energy Agency (JAEA) under the conditions covering the FLWR operating condition (P_ex = 7:2 MPa, T_in = 556 K) for mass velocity G = 400-800 kg/(m² s). For the postulated power increase and flow decrease transients, no obvious change of the critical power against the steady one was observed. The traditional quasi-steady characteristic was confirmed to be working for the postulated power increase and flow decrease transients. The experiments were analyzed with TRAC-BF1 code, where the JAEA newest critical power correlation for the tight lattice rod bundles was implemented for the BT judgment. The TRAC-BF1 code showed good prediction for the occurrence or the non occurrence of the BT and for the exact BT starting time. The traditional quasi-steady state prediction of the BT in transient process was confirmed to be applicable for the postulated abnormal transient processes in the tight lattice rod bundles.     

A moving subgrid model for simulation of reflood heat transfer

In the quench front and froth region the thermal-hydraulic parameters experience a sharp axial variation. The heat transfer regime changes from single-phase liquid, to nucleate boiling, to transition boiling and finally to film boiling in a small axial distance.One of the major limitations of all the current best-estimate codes is that a relatively coarse mesh is used to solve the complex fluid flow and heat transfer problem in proximity of the quench front during reflood. The use of a fine axial mesh for the entire core becomes prohibitive because of the large computational costs involved. Moreover, as the mesh size decreases, the standard numerical methods based on a semi-implicit scheme, tend to become unstable.A subgrid model was developed to resolve the complex thermal-hydraulic problem at the quench front and froth region. This model is a Fine Hydraulic Moving Grid (FHMG) that overlies a coarse Eulerian mesh in the proximity of the quench front and froth region. The fine mesh moves in the core and follows the quench front as it advances in the core while the rods cool and quench. The FHMG software package was developed and implemented into the COBRA-TF computer code. This paper presents the model and discusses preliminary results obtained with the COBRA-TF/FHMG computer code.     

Development,assessment and application of TRAC-BF1/v2001.2 for beyond design basis BWR LOCA transients

In preparation for the possible transition to risk based licensing, it is increasingly important to demonstrate the applicability of Best Estimate codes to more extreme conditions corresponding for example to limited equipment availability. With this idea in mind, we have reviewed the application of TRAC-BF1 to Large and Small Break LOCAs. In this context this work describes the assessment and applications of the Penn State University (PSU) version 2001.2 of TRAC-BF1 with all the PSI updates, to the analysis of hypothetical Large Break (LB) LOCAs in a BWR/4 with postulated limited ECC availability. Since in contrast to a LB-LOCA in a BWR with full ECC availability, the rod surface temperatures reach relatively high values, additional assessment of the code under such conditions is required. Hence, after analyzing bottom flooding separate-effect experiments in two different heater rod bundles and a TLTA LB-LOCA test, we shall present and discuss the results of the analysis of a LB-LOCA with highly restricted Emergency Core Cooling flow in a BWR/4. In this context, we shall also assess different descretization of some terms of the 3D momentum equations, which was found to be important in the analysis of BWR Small Break LOCAs.     

Transient thermal-hydraulic analysis for reactor cores

A new computational method is presented for a transient, thermal-hydraulic, multichannel analysis. The method is developed based on the concept of artificial compressibility to preserve the elliptic character of the reactor core flow in order to satisfy the realistic pressure boundary conditions, and to account for the discontinuities of the emprical correlations simulating the flow resistances. The computer code (RETSAC) developed by implementing the method presented in this paper can be categorized as a fourth generation multichannel computer code. This new computer code has been compared with the widely used marching techniques, such as COBRA IIIC (the third generation). The numerical results clearly indicate the situations in which the marching technique may or may not be appropriate. Furthermore, the RETSAC computer code can calculate various normal or off-normal reactor core flows which the third generation codes could not handle without a substantial increase of computer time.     

Analysis of the Leibstadt power plant condensate and feedwater systems during selected operational transients

This paper presents a selection of plant analyses that were carried out by PSI in support of the Leibstadt Nuclear Power Plant (Swiss boiling water reactor). The analyses were performed as part of a collaboration between Leibstadt and PSI, to help resolve some operational problems that were experienced during the power uprate beginning in 1998. The issues under investigation were related to the behavior of the condensate and feedwater systems during transients initiated by a turbine trip, load rejection and a single feedwater pump trip, all of which increased the risk of an inadvertent reactor shutdown by reaching reactor pressure vessel water level limits. The possibility of a reactor shutdown was related to perturbations in the feedwater flow caused by transitory pump cavitation of the feedwater pumps, due to a rapid depressurization in the feedwater tank. In addition to a direct analysis of plant measurement provided by Leibstadt, steady-state and transient simulations of the events were performed at PSI using the system codes TRAC-BF1 and TRACE. Through a combination of the analysis of the plant measurements, the code simulations and an analysis of the whole plant behavior using the Leibstadt plant-simulator appropriate modifications of the plant hardware, control system and operational set points were proposed. The implementation and success of these changes were verified by a number of plant tests. Finally, the original designed plant capability not to shutdown during the aforementioned transients was demonstrated.     

Effect of compensation error in drift-flux parameters on predictions of thermal-hydraulic parameters in nuclear safety system analysis codes

Void fraction in a nuclear reactor core is one of the most important parameters in a safety analysis using nuclear reactor thermal-hydraulics system analysis codes such as TRAC-BF1, RELAP5 and TRACE. Interfacial shear term governing void fraction in the two-fluid code is often estimated by Andersen approach which uses drift-flux type correlation to compute the interfacial shear term. The accuracy of two drift-flux parameters such as distribution parameter and drift velocity is anticipated to affect the accuracy of predicted void fraction significantly. In principle, the distribution parameter and drift velocity are independent parameters which should be determined by local gas and liquid velocities and void fraction. However, due to very limited local data, the distribution parameter and drift velocity are commonly determined by area-averaged void fraction and superficial gas and liquid velocities. This “approximate method” is acceptable when the distribution parameter and drift velocity are used together. However, in the Anderson's approach, the distribution parameter and drift velocity determined by the approximate method are used separately which may cause some compensation error in code calculations. In view of the great importance in accurately computing the interfacial shear term, the effect of the compensation error on the predicted void fraction is investigated. Intensive sensitivity analysis suggests the compensation error propagating to void fraction only up to 1% for steady state computations, whereas the effect of the compensation error on the predicted void fraction for transient computations becomes larger because temporal reduction of drag force may cause the increase in void fraction. A prototypic nuclear power plant analysis for ATWS scenario suggests that the overestimation of the void fraction may affect the neutron flux calculation.     

基于两流体模型的流动沸腾瞬态数值模拟程序

基于两流体模型与固壁非稳态导热模型,结合相关关联式组合,建立了流道内流动沸腾传热的瞬态数值模拟程序。通过不同入口瞬态下流道两相流动沸腾过程的算例计算分析,确认了程序进行流动沸腾瞬态模拟的能力。通过对不同固壁加热条件下流动沸腾行为的算例计算,检验了该程序进行流壁耦合行为模拟的功能。程序可进一步向系统分析程序和子通道程序发展。     

Modifications to COBRA-TF to model dispersed flow film boiling with two flow,four field Eulerian–Eulerian approach – Part 1

In the case of a postulated loss of coolant accident (LOCA) in a nuclear reactor, an accurate prediction of clad temperature is needed to determine the safety margins. During the reflood phase of the LOCA, when the local void fraction is greater than 80% with the wall temperature above minimum film boiling temperature (T_min), the heat transfer process is dispersed flow film boiling (DFFB). This study has been performed to model DFFB in the reflood phase of a LOCA in a pressurized water reactor (PWR) rod bundle. The COBRA-TF computer code is utilized, since it has a detailed reflood package which takes into account the effect of spacer grids on the local heat transfer. The COBRA-TF code has also been improved to include a four field Eulerian–Eulerian modeling for the two-phase dispersed flow film boiling heat transfer regime. The modifications include adding a small droplet field to COBRA-TF as the fourth field. In addition, the spacer grid models of COBRA-TF have been revised and modified. In the first part of the paper, the results of the code predictions are presented by comparing the experimental data from rod bundle heat transfer (RBHT) experiments with the results of code simulations performed with original and modified code. Measurements and calculations for the heater rod, vapor temperatures and quench front progression have been compared and the results are described in detail. The results of the analysis performed with the modified code indicate the improvement in code predictions for the rod surface temperature, vapor temperature and quench front behavior. The results also indicate the need for improvement in the entrainment and interfacial drag models for the drop fields. The effects of spacer grids on the heat transfer, the models improved and developed for spacer grids and the results of the code calculations with these models are described in the part 2 of the paper.     

Development and Verification of an Efficient Spatial Neutron Kinetics Method for Reactivity-Initiated Event Analyses

A space/time nodal diffusion code based on the nodal expansion method (NEM), EPISODE, was developed in order to evaluate transient neutron behavior in light water reactor cores. The present code employs the improved quasi-static (IQS) method for spatial neutron kinetics, and neutron flux distribution is numerically obtained by solving the neutron diffusion equation with the nonlinear iteration scheme to achieve fast computation. A predictor-corrector (PC) method developed in the present study enabled to apply a coarse time mesh to the transient spatial neutron calculation than that applicable in the conventional IQS model, which improved computational efficiency further. Its computational advantage was demonstrated by applying to the numerical benchmark problems that simulate reactivity-initiated events, showing reduction of computational times up to a factor of three than the conventional IQS. The thermohydraulics model was also incorporated in EPISODE, and the capability of realistic reactivity event analyses was verified using the SPERT-III/E-Core experimental data.