Francesco Saverio D'Auria

Code validation and uncertainties in system thermalhydraulics

Abstract We describe in this paper the state of the art in the area of thermalhydraulic system codes assessment and uncertainty evaluation. System codes have been used in the past three decades in the areas of design, operation, licensing and safety of Nuclear Power Plants (NPP). Such applications require preliminary comprehensive code-user-nodalization qualification activities that we discuss in the paper. Although huge amounts of financial and human resources have been invested for the development and improvement of codes, including the user interface, the calculation results are still affected by erros. In the sophisticated nuclear technology, design and safety of NPP, these errors must be quantified. Therefore we propose uncertainty methodologies to achieve this goal. The reported analysis is based on the activities performed at University of Pisa and the experience we have acquired from the participation in a number of international projects.

Thermal-Hydraulic System Codes in Nulcear Reactor Safety and Qualification Procedures

In the last four decades, large efforts have been undertaken to provide reliable thermal-hydraulic system codes for the analyses of transients and accidents in nuclear power plants. Whereas the first system codes, developed at the beginning of the 1970s, utilized the homogenous equilibrium model with three balance equations to describe the two-phase flow, nowadays the more advanced system codes are based on the so-called “two-fluid model” with separation of the water and vapor phases, resulting in systems with at least six balance equations. The wide experimental campaign, constituted by the integral and separate effect tests, conducted under the umbrella of the OECD/CSNI was at the basis of the development and validation of the thermal-hydraulic system codes by which they have reached the present high degree of maturity. However, notwithstanding the huge amounts of financial and human resources invested, the results predicted by the code are still affected by errors whose origins can be attributed to several reasons as model deficiencies, approximations in the numerical solution, nodalization effects, and imperfect knowledge of boundary and initial conditions. In this context, the existence of qualified procedures for a consistent application of qualified thermal-hydraulic system code is necessary and implies the drawing up of specific criteria through which the code-user, the nodalization, and finally the transient results are qualified.

Review of quantitative accuracy assessments with fast Fourier transform based method (FFTBM)

Abstract In the past 10 years various methodologies were proposed to evaluate the uncertainty of BE code predictions. One common step to all methodologies is the use of experimental and plant data for the nodalization development and qualification. When thermal–hydraulic computer codes are used for simulation the questions raised are: ‘How long improvements should be added to the model, how much simplification can be introduced and how to conduct an objective comparison?’ The proposed fast Fourier transform based method (FFTBM) assists in answering these questions. The method is easy to understand, convenient to use, user independent and it clearly indicates when simulation needs to be improved. The FFTBM shows the measurement–prediction discrepancies—accuracy quantification—in the frequency domain. The acceptability factor for code calculation was determined based on several hundreds of code calculations. The FFTBM method has been applied to various international standard problems, standard problem exercises and other experiment simulations that are presented in the paper. The result shows that the quantitative comparison between thermal–hydraulic code results and experimental measurements with qualitative evaluation may assist the decision whether or not the simulation needs to be improved.

Development of a code with the capability of internal assessment of uncertainty

The internal assessment of uncertainty is a desirable capability for thermal-hydraulic system codes. This consists of the possibility of obtaining proper uncertainty bands each time a nuclear plant transient scenario is calculated. A methodology suitable for introducing such a capability into a system code is discussed. At the basis of the derivation of the code with (the capability of) internal assessment of uncertainty (CIAU), there is the uncertainty methodology based on the accuracy extrapolation (UMAE), previously proposed by the University of Pisa, although other uncertainty methodologies can be used for the same purpose. The idea of the CIAU is the identification and the characterization of standard plant statuses and the association of uncertainty to each status. One hypercube and one time interval identify the plant status. Quantity and time uncertainties are combined for each plant status. The recently released U.S. Nuclear Regulatory Commission RELAP5/MOD3.2 system code constitutes the CIAU. This is used for showing the applicability of the proposed method. The derivation of the methodology is discussed, and reference results of pressurized water reactor plant transients are shown bounded by the CIAU-calculated uncertainty bands.

Analysis of single-phase natural circulation experiments by system codes

In this paper, the results of simulations of natural circulation loop performance, obtained by Cathare and Relap codes, are reported. Both series of results are analyzed and compared with experimental data gathered in the MTT-1 loop, a rectangular natural circulation loop realized by DITEC at the University of Genova. Both Cathare and Relap codes, in absolute terms, show poor agreement with experimental data. At low power, the Cathare code shows a good capability to predict the steady state quantities, after the initial transient. On the other hand, no unstable behavior is predicted at each analyzed power level. The Relap code is able to show oscillating quantities, but not at the same power levels as in the experiments.

Scaling of natural circulation in PWR systems

Abstract This paper deals with the problem of scaling complex thermalhydraulic scenarios measured in experimental facilities which simulate Pressurized Water Reactor systems. Phenomena occurring during different phases of natural circulation between the core and the steam generators are considered. The experimental data obtained in some integral test facilities were analyzed with a large system code and for this purpose a simple model was built. The code predicted scenario and the extrapolated one for the actual plant are compared.

User effects on the thermal-hydraulic transient system code calculations

Abstract Large thermalhydraulic system codes are widely used to perform safety and licensing analyses of nuclear power plants to optimize operational procedures and the plant design itself. Evaluation of the capabilities of these codes are accomplished by comparing the code predictions with the measured experimental data obtained from various types of separate effects and integral test facilities. During these comparisons of the code results, there has been a continuous debate on the way how the code user influences the predicted system behaviour. This rather subjective element might become a crucial point with respect to the quantitative evaluation of the code uncertainties which is essential if the “best estimate codes are used for licensing procedures”. The International Standard Problem Exercises (ISPs) proposed by the OECD/NEA-Committee for the Safety of Nuclear Installations (CSNI) and by IAEA (International Atomic Energy Agency) and thermalhydraulic code assessment activity undertaken by USNRC (US Nuclear Regulatory Commission) under International Code Assessment and Application Program (ICAP) demonstrate the large effort put in this framework by organizations all over the world. In recent years, some attempts have been made to establish methodologies to evaluate the accuracy and the uncertainty of the code predictions and consequently judgement on the acceptability of the codes. In none of the methodologies has the influence of the code user on the calculated results been directly addressed. In this paper, the results of the investigations on the user effects for the thermalhydraulic transient system codes will be presented and discussed on the basis of some case studies. The general findings of the investigations show that in addition to user effects, there are other reasons that affect the results of the calculations and which are hidden under user effects. Both the hidden factors and the direct user effects will be discussed in detail and general recommendations and conclusions will be presented to control and limit them.

Best-Estimate Model Calibration and Prediction through Experimental Data Assimilation—II: Application to a Blowdown Benchmark Experiment

Abstract This work presents a paradigm application of a new methodology for simultaneously calibrating (adjusting) model parameters and responses, through assimilation of experimental data, to the benchmark transient thermal-hydraulic experiment IC1, performed at London’s Imperial College. Following the description of the experimental setup, the corresponding mathematical model is developed and solved numerically. The sensitivities of typically important responses (e.g., temperatures, pressures) to model parameters are computed by applying both the forward and the adjoint sensitivity analysis procedures. These sensitivities not only identify the most important model parameters but also propagate, within the data assimilation procedure, parameter uncertainties for obtaining predictive best-estimate quantities, with reduced best-estimate uncertainties (i.e., “smaller” values for the variance-covariance matrices). This assimilation procedure also provides a quantitative indication of the degree of agreement between computations and experiments. In particular, the paradigm application presented in this work indicates the path for validating and calibrating thermal-hydraulic computational models used for reactor safety analyses. The concluding remarks highlight several important open issues, the resolution of which would significantly advance the area of predictive best-estimate modeling, while opening new avenues for applications in nuclear reactor engineering and safety.

Use of a natural circulation map for assessing PWR performance

The present paper deals with the Natural Circulation (NC) phenomenon in Pressurized Water nuclear Reactors (PWR). In the first part, data gathered from relevant experiments in PWR simulators are considered. These allowed the establishment of a flow map that has been used for evaluating the NC performance of various reactor concepts. In the second part, a theoretical study has been completed to assess the power removal capability by NC from the core of a PWR having the current geometric configuration. Taking as reference a PWR equipped with U-tube steam generators, two-phase conditions occur in the core at power levels greater than 20% nominal power. Therefore, for core power larger than this value the reactor cannot be classified any more as a PWR. The study shows that from a thermohydraulic point of view, the core can operate at power levels close to the current nominal value without experiencing thermal crisis. Limited consideration has been given to the neutronic design of the core.

Determination of Code Accuracy in Predicting Small-Break LOCA Experiment

Quantitative evaluation of thermal-hydraulic code uncertainties is a necessary step in the code assessment process, especially if best-estimate codes are utilized for licensing purposes. With the goal of quantifying code accuracy, researchers in the past developed a methodology based on the fast Fourier transform (FFT) that consisted of qualitative and quantitative code assessment. Here, the FFT-based method is applied to International Atomic Energy Agency (IAEA)-Standard Problem Exercise (SPE)-4 test results with pre- and posttest code calculations of the IAEA-SPE-4 experiment. Four system codes (ATHLET, CATHARE, MELCOR, and RELAP5) are used for calculations of the experiment, performed at the PMK-2 facility, which simulated a cold-leg break in a VVER-440 plant. The results show that the posttest calculations had better accuracy than did the pretest calculations. None of the best three pre- and posttest calculations were able to predict core dryout, which was the most important phenomenon observed during the test. The results obtained can give an objective indication of the capability of the aforementioned codes in predicting relevant variables characterizing the transient (too few experimental parameters may limit full application of the FFT-based methodology).