Comprehensive uncertainty and sensitivity analysis for coupled code calculations of VVER plant transients

The development of coupled codes, combining thermal-hydraulic system codes and 3D neutron kinetics codes, is an important step to perform best-estimate calculations for plant transients of nuclear power plants. For applications in safety analysis, these coupled codes should be validated by benchmark calculations and, preferably, by comparison with plant transient data from operating plants. In addition, the results should be supplemented by applying uncertainty and sensitivity analysis methods, which allow to identify relevant parameters of models and solution procedures affecting the results and to quantify their relative importance. Both objectives were part of the VALCO project. The aspect of validation is presented in [S. Mittag, et al., 2004. Neutron-Kinetic Code Validation against Measurements in the Moscow V-1000 Zero-Power Facility, in press; T. Vanttola et al., 2004. Validation of coupled codes using VVER plant measurements, in press], the aspect of a comprehensive uncertainty and sensitivity analysis for coupled code calculations is the topic of this contribution. The results and experiences obtained by the analysis for two plant transients in a VVER-440 and a VVER-1000, respectively, are presented and discussed.     

Validation of coupled neutron kinetic/thermal-hydraulic codes. Part 2: Analysis of a VVER-440 transient (Loviisa-1)

Several three-dimensional hexagonal reactor dynamic codes have been developed for VVER type reactors and coupled with different thermal-hydraulic system codes. Under the auspices of the European Union's Phare programme these codes have been validated against real plant transients by the participants from 7 countries. Two of the collected five transients were chosen for validation of the codes. Part 1 of this article consists of validation against VVER-1000 reactor data. This second part is focussed to validation against measured data of ‘One turbo-generator load drop experiment' at the Loviisa-1 VVER-440 reactor. The experiment was performed just after plant modernisation and more measured data was available to validation than in normal operation of real plants. Good accuracy of the results was generally achieved comparable to the measurement accuracy. The confidence in the results of the different code systems has increased, and consequences of certain model changes could be evaluated.     

Numerical boron mixing studies for Loviisa nuclear power plant

A program is in the process of studying numerically boron mixing in the downcomer of Loviisa NPP (VVER-440). Mixing during the transport of a diluted slug from the loop to the core might serve as an inherent protection mechanism against severe reactivity accidents in inhomogenous boron dilution scenarios for PWRs. The commercial general purpose Computational Fluid Dynamics (CFD) code PHOENICS is used for solving the governing fluid flow equations in the downcomer geometry of VVER-440. So far numerical analyses have been performed for steady state operation conditions and two different pump driven transients. The steady state analyses focused on model development and validation against existing experimental data. The two pump driven transient scenarios reported are based on slug transport during the start of the sixth and first loop, respectively. The results from the two transients show that mixing is case and plant specific; the high and open downcomer geometry of VVER-440 seems to be advantageous from mixing point of view. In addition the analyzing work for the ‘first pump start' scenario brought up some considerations about flow distribution in the existing experimental facilities.     

First experience with a six-loop nodalization of a VVER-440 using a new coupled neutronic-thermohydraulics system KIKO3D-RETINA V1.1D

In this paper, we introduce a new, coupled neutronic-thermohydraulics system. The three-dimensional neutron kinetic code KIKO3D and the two-phase flow code RETINA V1.1D have been coupled for modeling complex transients of nuclear power plants. Using a six-loop nodalization of a VVER-440, several test calculations have been carried out. Results obtained for a trip of one main circulation pump are compared with real measurements and reference calculations provided by other neutronic-thermohydraulics systems. The ability of our coupled system is demonstrated.     

Experimental investigation of in-vessel mixing phenomena in a VVER-1000 scaled test facility during unsteady asymmetric transients

In-vessel turbulent mixing phenomena affect the time and space distribution of coolant properties (e.g., boron concentration and temperature) at the core inlet which impacts consequently the neutron kinetics response. For reactor safety evaluation purposes and to characterize these phenomena it is necessary to set and validate appropriate numerical modelling tools to improve the current conservative predictions. With such purpose, an experimental campaign was carried out by OKB Gidropress, in the framework of the European Commission Project “TACIS R2.02/02 - Development of safety analysis capabilities for VVER-1000 transients involving spatial variations of coolant properties (temperature or boron concentration) at core inlet”. The experiments were conducted on a scaled facility representing the primary system of a VVER-1000 including a detailed model of the Reactor Pressure Vessel with its internals. The simulated transients involved perturbations of coolant properties distribution providing a wide validation matrix. The main achievements of the set of experiments featuring transient asymmetric pump behaviour are presented in this paper. The potential of the obtained experimental database for the validation of thermal fluid dynamics numerical simulation tools is also discussed and the role of computational fluid dynamics in supporting the experimental data analysis is highlighted.     

Microstructure alterations in the base material, heat affected zone and weld metal of a 440-VVER-reactor pressure vessel caused by high fluence irradiation during long term operation; material: 15 Ch2MFA ≈0.15 C–2.5 Cr–0.7 Mo–0.3 V

Within the scope of the EC research project Tacis ’91 (‘RPV-Embrittlement’), trepans were taken from the highly irradiated circumferential RPV-weld of the Novovoronesh power plant unit-2 of the type VVER-440/230. The cumulated fast fluence level in this position reaches up to 6.5×10¹⁹/cm² (E>0.5 MeV). In a joint research work, the mechanical properties, the chemical composition, and the microstructure of the base material, the heat affected zone (HAZ), and the weld metal have been investigated in order to study the influence of irradiation, and of post irradiation heat treatment (475°C, 560°C) on the properties. The examination of the microstructure performed by analytical transmission electron microscopy (200 kV) shows the existence of dislocation loops (‘black dots’), irradiation induced precipitates, and segregation of copper in the carbides. These changes in microstructure, which are due to service affection (neutron irradiation, temperature) have occurred more pronounced in the weld metal and the HAZ than in the base material.     

Neutron-kinetic code validation against measurements in the Moscow V-1000 zero-power facility

Measurements carried out in an original-size VVER-1000 mock-up (V-1000 facility, Kurchatov Institute, Moscow) were used for the validation of three-dimensional neutron-kinetic codes, designed for VVER safety calculations. The significant neutron flux tilt measured in the V-1000 core, which is caused only by radial-reflector asymmetries, was successfully modeled. A good agreement between calculated and measured steady-state powers has been achieved, for relative assembly powers and inner-assembly pin power distributions. Calculated effective multiplication factors exceed unity in all cases. The time behaviour of local powers, measured during two transients that were initiated by control rod moving in a slightly super-critical core, has been well simulated by the neutron-kinetic codes.     

Fluid mixing and flow distribution in a primary circuit of a nuclear pressurized water reactor—Validation of CFD codes

The EU project FLOMIX-R was aimed at describing the mixing phenomena relevant for both safety analysis, particularly in steam line break and boron dilution scenarios, and mixing phenomena of interest for economical operation and the structural integrity.This report will focus on the computational fluid dynamics (CFD) code validation. Best practice guidelines (BPG) were applied in all CFD work when choosing computational grid, time step, turbulence models, modelling of internal geometry, boundary conditions, numerical schemes and convergence criteria. The strategy of code validation based on the BPG and a matrix of CFD code validation calculations have been elaborated. CFD calculations have been accomplished for selected experiments with two different CFD codes (CFX, FLUENT). The matrix of benchmark cases contains slug mixing tests simulating the start-up of the first main circulation pump which have been performed with three 1:5 scaled facilities: the Rossendorf coolant mixing model ROCOM, the Vattenfall test facility and a metal mock-up of a VVER-1000 type reactor. Before studying mixing in transients, ROCOM test cases with steady-state flow conditions were considered. Considering buoyancy driven mixing, experimental results on mixing of fluids with density differences obtained at ROCOM and the FORTUM PTS test facility were compared with calculations. Methods for a quantitative comparison between the calculated and measured mixing scalar distributions have been elaborated and applied. Based on the “best practice CFD solutions”, conclusions on the applicability of CFD for turbulent mixing problems in PWR were drawn and recommendations on CFD modelling were given. The results of the CFD calculations are mostly in-between the uncertainty bands of the experiments. Although no fully grid-independent numerical solutions could be obtained, it can be concluded about the suitability of applying CFD methods in engineering applications for turbulent mixing in nuclear reactors.     

Assessment of RAMONA-3B methodology with oscillatory flow tests

The instability event at the LaSalle County Plant (GE BWR-5) imposed a new challenge on the computer codes available for reactor transient analysis. While the codes were originally designed to predict non-oscillatory transients, the new requirement on the code is to model limit cycle oscillations with large amplitudes, where feed-back effects from the core and the balance of plant, and the nonlinear effects are significant. Two of the United States Nuclear Regulatory Commission's (USNRC) computer codes, namely RAMONA-3B/MODO [1] and HIPA-BWR of Engineering Plant Analyzer [2] were expected, and are shown in part in this paper, to meet the above demands.The RAMONA-3B/MOD1 has now been upgraded from the RAMONA-3B/MODO. It has a three dimensional neutron kinetics model, coupled to multi-channel nonequilibrium drift-flux formulation, and an explicit integration scheme for the thermal hydraulics.The accuracy of the thermohydraulics in the RAMONA-3B code was assessed for the new application by modelling oscillatory transients in the FR1GG test facilty. Nodalization studies showed that twenty-four axial nodes are sufficient for a converged solution; calculations with twelve axial nodes produce, in comparison to the 24-node calculation, the deviation of 4.4% in the peak gain of the power to flow transfer function.The code predicted correctly the effects of power and inlet subcooling on the transfer function gain and the system resonance frequency. For the six available tests modeled, the code-predicted peak gain differs from the experimentally obtained gain on the average by +7%, with the standard deviation of ±30%. The uncertainty in the experimental data lies between −11% and +12%. The difference between predicted and measured frequency at the peak gain on the average is −6%, with the standard deviation of ±14%.     

Validation of coupled neutron kinetic/thermal–hydraulic codes. Part 1: Analysis of a VVER-1000 transient (Balakovo-4)

Three-dimensional hexagonal reactor dynamic codes have been developed for VVER type reactors and coupled with different thermal–hydraulic system codes. In the EU Phare project SRR1/95 these codes have been validated against real plant transients by the participants from several countries. Data measured during a test in the Balakovo-4 VVER-1000 have been analysed by coupled codes. In the test, one of two working feed water pumps of the steam generators was switched off at nominal power. The steady-state assembly powers measured before and after this transient are reproduced by the codes with a maximum deviation of about 5%. The time behaviour of the most safety-relevant parameters, such as total fission power, coolant temperatures and pressures is well modelled. Thermal–hydraulic feedback effects observed in the measurement are described by the codes in a consistent manner. The analyses have shown, that an accurate treatment of the heat transfer from the fuel rods to the coolant is important. In all, the results have increased the confidence in the coupled code analyses of VVER-1000 transients.     

CFD analysis of flow field in a triangular rod bundle

The flow field was investigated in subchannels of VVER-440 pressurized water cooled reactors’ fuel assemblies (triangular lattice, P/D = 1.35). Impacts of the mesh resolution and turbulence model were studied in order to obtain guidelines for CFD calculations of VVER-440 rod bundles. Results were compared to measurement data published by Trupp and Azad in 1975. The study pointed out that RANS method with BSL Reynolds stress model using a sufficient fine grid can provide an accurate prediction for the turbulence quantities in this lattice. Applying the experiences of the sensitivity study thermal hydraulic processes were investigated in VVER-440 rod bundle sections. Based on the examinations the spacer grids have important effects on the cross flows, axial velocity and outlet temperature distribution of subchannels therefore they have to be modeled satisfactorily in CFD calculations.     

HTGR reactor physics and fuel cycle studies

The high-temperature gas-cooled reactor (HTGR) appears as a good candidate for the next generation of nuclear power plants. In the “HTR-N” project of the European Union Fifth Framework Program, analyses have been performed on a number of conceptual HTGR designs, derived from reference pebble-bed and hexagonal block-type HTGR types. It is shown that several HTGR concepts are quite promising as systems for the incineration of plutonium and possibly minor actinides.These studies were mainly concerned with the investigation and intercomparison of the plutonium and actinide burning capabilities of a number of HTGR concepts and associated fuel cycles, with emphasis on the use of civil plutonium from spent LWR uranium fuel (first generation Pu) and from spent LWR MOX fuel (second generation Pu). Besides, the “HTR-N” project also included activities concerning the validation of computational tools and the qualification of models. Indeed, it is essential that validated analytical tools are available in the European nuclear community to perform conceptual design studies, industrial calculations (reload calculations and the associated core follow), safety analyses for licensing, etc., for new fuel cycles aiming at plutonium and minor actinide (MA) incineration/transmutation without multi-reprocessing of the discharged fuel.These validation and qualification activities have been centred round the two HTGR systems currently in operation, viz. the HTR-10 and the HTTR. The re-calculation of the HTTR first criticality with a Monte Carlo neutron transport code now yields acceptable correspondence with experimental data. Also calculations by 3D diffusion theory codes yield acceptable results. Special attention, however, has to be given to the modelling of neutron streaming effects. For the HTR-10 the analyses focused on first criticality, temperature coefficients and control rod worth. Also in these studies a good correspondence between calculation and experiment is observed for the 3D diffusion theory codes.     

Impact of cross-section generation procedures on the simulation of the VVER-1000 pump startup experiment in the OECD/DOE/CEA V1000CT benchmark by coupled 3D thermal-hydraulics/neutron kinetics models

In the framework of joint effort between the Nuclear Energy Agency (NEA) of OECD, the United States Department of Energy (US DOE), and the Commissariat a l'Enerige Atomique (CEA), France a coupled three-dimensional (3D) thermal-hydraulics/neutron kinetics benchmark was defined. The overall objective of OECD/NEA V1000CT benchmark is to assess computer codes used in analysis of VVER-1000 reactivity transients where mixing phenomena (mass flow and temperature) in the reactor pressure vessel are complex. Original data from the Kozloduy-6 Nuclear Power Plant are available for the validation of computer codes: one experiment of pump start-up (V1000CT-1) and one experiment of steam generator isolation (V1000CT-2). Additional scenarios are defined for code-to-code comparison. As a 3D core model is necessary for a best-estimate computation of all the scenarios of the V1000CT benchmark, all participants were asked to develop their own core coupled 3D thermal-hydraulics/neutron kinetics models using the data available in the benchmark specifications and a common cross-section library. The first code-to-code comparisons based on the V1000CT-1 Exercise 2 specifications exhibited unacceptable discrepancies between two sets of results. The present paper focuses on the analysis of the observed discrepancies. The VVER-1000 3D neutron kinetics models are based on cross-section data homogenized on the assembly level. The cross-section library, provided as part of the benchmark specifications, thus consists in a set of parameterized two group cross sections representing the different assemblies and the reflectors. The origin of the observed large discrepancies was found mainly to lie in the methods used to solve the diffusion equation. The VVER reflector properties were also found to enhance discrepancies by increasing flux gradients at the core/reflector interface thus highlighting more the difficulties in some codes to handle high exponential flux gradients. This paper summarizes the different steps applied to analyze the neutronic codes and their predictions as well as the impact of cross-section generation procedures.     

A spatial kinetic model for simulating VVER-1000 start-up transient

An accurate prediction of reactor core behavior in transients depends on how much it could be possible to exactly determine the thermal feedbacks of the core elements such as fuel, clad and coolant. In short time transients, results of these feedbacks directly affect the reactor power and determine the reactor response. Such transients are commonly happened during the start-up process which makes it necessary to carefully evaluate the detail of process. Hence this research evaluates a short time transient occurring during the start up of VVER-1000 reactor. The reactor power was tracked using the point kinetic equations from HZP state (100 W) to 612 kW. Final power (612 kW) was achieved by withdrawing control rods and resultant excess reactivity was set into dynamic equations to calculate the reactor power. Since reactivity is the most important part in the point kinetic equations, using a Lumped Parameter (LP) approximation, energy balance equations were solved in different zones of the core. After determining temperature and total reactivity related to feedbacks in each time step, the exact value of reactivity is obtained and is inserted into point kinetic equations. In reactor core each zone has a specific temperature and its corresponding thermal feedback. To decrease the effects of point kinetic approximations, these partial feedbacks in different zones are superposed to show an accurate model of reactor core dynamics. In this manner the reactor point kinetic can be extended to the whole reactor core which means “Reactor spatial kinetic”. All required group constants in calculations are prepared using the WIMS code. In addition CITATION code was used to calculate the flux, power distribution and core reactivity inside the core. To update the last change in group constants and resultant reactivity in point kinetic equations, these neutronic codes were coupled with a developed dynamic program. This study is applied on a typical VVER-1000 reactor core to show the reactor response in short time transients caused during start-up procedure.     

Simulation of the VVER-1000 pump start-up experiment of the OECD V1000CT benchmark with CATHARE and TRAC-PF1

In the framework of joint effort between the Nuclear Energy Agency (NEA) of OECD, the United States Department of Energy (US DOE), and the Commissariat a l'Energie Atomique (CEA), France a coupled three-dimensional (3D) thermal-hydraulics/neutron kinetics benchmark for VVER-1000 was defined. The benchmark consists of calculation of a pump start-up experiment labelled V1000CT-1 (Phase 1), as well as a vessel mixing experiment and main steam line break (MSLB) transient labelled V1000CT-2 (Phase 2), respectively. The reference nuclear plant is Kozloduy-6 in Bulgaria. The overall objective is to assess computer codes used in the analysis of VVER-1000 reactivity transients. A specific objective is to assess the vessel mixing models used in system codes. Plant data are available for code validation consisting of one experiment of pump start-up (V1000CT-1) and one experiment of steam generator isolation (V1000CT-2). The validated codes can be used to calculate asymmetric MSLB transients involving similar mixing patterns. This paper summarizes a comparison of CATHARE and TRAC-PF1 system code results for V1000CT-1, Exercise 1, which is a full plant point kinetics simulation of a reactor coolant system (RCS) pump start-up experiment. The reference plant data include integral and sector average parameters. The comparison is made from the point of view of vessel mixing and full system simulation. CATHARE used a six-sector multiple 1D vessel thermal-hydraulic model with cross flows and TRAC used a six-sector, 18-channel coarse-mesh 3D vessel model. Good agreement in terms of integral parameters and inter-loop mixing is observed.     

Development of Ignalina NPP RBMK-1500 reactor RELAP5-3D model

This paper deals with the development of an integrated thermal-hydraulics–neutronics model for RBMK-1500 reactors for the analysis of specific plant transients in which the neutronic response of the core is important. A successful best estimate coupled RELAP5-3D model of Ignalina nuclear power plant (NPP) has been developed. The validation of the thermal-hydraulic model has been performed using operational transients from Ignalina NPP. The results of the calculations obtained with the RELAP5-3D model compare reasonably with the real plant data. The RELAP5-3D nodal kinetics model provides reasonable agreement with Ignalina NPP reactor power and coolant density profiles. The eigenvalue is close to unity, indicating that reasonable values are calculated for the neutron fluxes.     

Measurement of large negative reactivity in WWER-440. Sources of uncertainty

The sources of uncertainty in measurement of large negative reactivity in WWER-440 by the inverse point kinetics method, are evaluated quantitatively on the example of measurement of the reactivity worth of the shutdown control rod system of WWER-440 at zero power. Considering the specific features of the control rod system of WWER-440, it is demonstrated that using an appropriate formulation of the inverse solution of the equations of point kinetics, the uncertainty of measured reactivity ρ/β introduced by the assumption of constancy of the parameters of kinetics can be reduced to <3–5% for the case of the discussed rod-drop test at zero power. Based on an analysis of both numerically simulated and actual rod-drop transients, it is shown that the uncertainty of measured reactivity ρ/β can be quite considerable due to the underlying delayed neutron data set—the values of ρ/β obtained using different data sets can differ by 15%. Inexact accounting of the share of ²³⁹Pu in the fission neutron source is estimated to contribute to the total uncertainty of measured ρ/β of 1%, whereas possible spatial effects are expected to result in a relative error in ρ/β of 5%.     

Crack initiation and arrest in a pressurized thermal shock test for a model pressure vessel made of VVER-440 reactor pressure vessel steel

A joint pressure vessel integrity research programme involving three partners is being carried out during 1990–1995. The partners are the Central Research Institute of Structural Materials “Prometey” from Russia, IVO International Ltd (IVO) from Finland, and the Technical Research Centre of Finland (VTT). The main objective of the research programme is to increase the reliability of the VVER-440 reactor pressure vessel safety analysis. This is achieved by providing material property data for the VVER-440 pressure vessel steel, and by producing experimental understanding of the crack behaviour in pressurized thermal shock loading for the validation of different fracture assessment methods. The programme is divided into four parts: pressure vessel tests, material characterization, computational fracture analyses, and evaluation of the analysis methods. The testing programme comprises tests on two model pressure vessels with artificial axial outer surface flaws. The first model vessel had circumferential weld seam at the mid-length of the vessel. A special embrittling heat treatment is applied to the vessels before tests to simulate the fracture toughness at the end-of-life condition of a real reactor pressure vessel. The sixth test on the first model led to crack initiation followed by arrest. After the testing phase, material characterization was performed. Comparison of calculated and experimental data generally led to a good correlation, although the work is being continued to resolve the discrepancies between the measured initiation and arrest properties of the material.     

Modeling of WWER-440 fuel pin behavior at extended burn-up

Currently, there is an ongoing effort to increase fuel discharge burn-up of all LWRs fuel including WWERs as much as possible in order to decrease power production cost. Therefore, burn-up is expected to be increased from 60 to 70 MWd/kg U. The change in the fuel radial power distribution as a function of fuel burn-up can affect the radial fuel temperature distribution as well as the fuel microstructure in the fuel pellet rim. Both of these features, commonly termed the “rim effect.” High burn-up phenomena in WWER-440 UO₂ fuel pin, which are important for fission gas release (FGR) were modeled. The radial burn-up as a function of the pellet radius and enrichment has to be known to determine the local thermal conductivity.In this paper, the radial burn-up and fissile products distributions of WWER-440 UO₂ fuel pin were evaluated using MCNP4B and ORIGEN2 codes. The impact of the thermal conductivity on predicted FGR calculations is needed. For the analysis, a typical WWER-440 fuel pin and surrounding water moderator are considered in a hexagonal pin well. The thermal release and the athermal release from the pellet rim were modeled separately. The fraction of the rim structure and the excessive porosity in the rim structure in isothermal irradiation as a function of the fuel burn-up was predicted. A computer program; RIMSC-01, is developed to perform the required FGR calculations. Finally, the relevant phenomena and the corresponding models together with their validation are presented.