Florian Fichot

Average momentum equation for interdendritic flow in a solidifying columnar mushy zone

Abstract This paper deals with the derivation of the macroscopic momentum transport equation in a non-homogeneous solidifying columnar dendritic mushy zone using the method of volume averaging. One of the originalities of this study lies in the derivation of an associated closure problem for the determination of the spatial evolution of the effective transport properties in such a complex situation. In this analysis—where the phase change has been included at the different stages of the derivation—all the terms arising from the averaging procedure (geometrical moments, phase interactions, interfacial momentum transport due to phase change, porosity gradients, etc.) are systematically estimated and compared on the basis of the characteristic length-scale constraints associated with the porous structures presenting evolving heterogeneities. For dendritic structures with “moderate” (but not small) evolving heterogeneities, we show that phase change and non local effects could hardly affect the determination of the permeability and inertia tensors. Finally, a closed form of the macroscopic momentum equation is proposed and a discussion is presented about the need to consider inertia terms and the second Brinkman correction (explicitly involving gradients of the liquid volume fraction) in such non-homogeneous systems.

Macroscopic modeling of columnar dendritic solidification

This paper deals with the derivation of a macroscopic model for columnar dendritic solidification of binary mixtures using the volume averaging method with closure. The main originalities of the model are first related to the explicit description of evolving heterogeneities of the dendritic structures and their consequences on the derivation of averaged conservation equations, where additional terms involving porosity gradients are present, and on the determination of effective transport properties. These average properties are defined by the associated closure problems taking into account the geometry of the dendrites and the local intensity of the flow. The macroscopic solute transport is obtained by considering macroscale non-equilibrium giving rise to macroscopic dispersion and interfacial exchange phenomena. Mass exchange coefficients are accurately explicited as a function of the local geometry.

Improvement of Core Modeling in ICARE/CATHARE: Application to the Calculation of a Six-Inch-Break LOCA Leading to a Severely Degraded Situation

Abstract In order to analyze the course of a hypothetical severe accident, the French “Institut de Radioprotection et de Sûreté Nucléaire” in the last decade has developed computer codes that have been extensively used for supporting the Level 2 Probabilistic Safety Assessment (PSA2) and, in general, for the safety analysis of French pressurized water reactors (PWRs). In particular, the computer code ICARE/CATHARE V1 is a tool that has been widely validated and intensively used within the framework of the PSA2 of the 900-MW(electric) French PWR. This code has been tested on many accident scenarios, and the results obtained have been considered to be satisfactory and reliable up to the end of the early degradation phase. But, severe accidents in PWRs are characterized by a continuous evolution of the core geometry due to chemical reactions, melting, and mechanical failure of the rods and other structures. These local variations of the porosity and other parameters lead to multidimensional flows and heat transfers. So, the lack of a multidimensional two-phase thermal-hydraulic model appeared to be prejudicial to achieve best-estimate reactor studies with ICARE/CATHARE V1 in the case of large core blockages and/or in the case of large cavity appearance. In accordance, a full multidimensional modeling (covering both the fluid flow and the corium behavior) was developed and introduced in a new ICARE/CATHARE version referenced as V2, which includes two options for the thermal-hydraulic modeling: either one-dimensional (1D) or two-dimensional (2D). The first part of this paper demonstrates that without activating the new V2 models, ICARE/CATHARE V2(1D) is able to reproduce the results obtained with ICARE/CATHARE V1 on the basis of a 6-in.-break loss-of-coolant accident. Then, in order to illustrate some of the new V2 modeling improvements, the last part is focused on the results obtained with ICARE/CATHARE V2(2D), and a preliminary comparison is made with ICARE/CATHARE V2(1D). This 1D-2D comparison points out in particular the important role that could be played in the course of a severe accident by the multidimensional flow pattern.

Code Simulation of Quenching of a High Temperature Debris Bed: Model Improvement and Validation With Experimental Results

The loss of coolant accidents with core degradation e.g. TMI-2 and Fukushima demonstrated that the nuclear safety analysis has to cover accident sequences involving a late reflood activation in order to develop appropriate and reliable mitigation strategies for both, existing and advanced reactors. The reflood (injection of water) is possible if one or several water sources become available during the accident. In a late phase of accident, no well-defined coolant paths would exist and a large part of the core would resemble to a debris bed e.g. particles with characteristic length-scale: 1 to 5 mm, as observed in TMI-2. The French “Institut de Radioprotection et de Surete Nucleaire” (IRSN) is developing experimental programs (PEARL and PRELUDE) and simulation tools (ICARE-CATHARE and ASTEC) to study and optimize the severe accident management strategy and to assess the probabilities to stop the progress of in-vessel core degradation at a late stage of an accident. The purpose of this paper is to propose a consistent thermo-hydraulic model of reflood of severely damaged reactor core for ICARE-CATHARE code. The comparison of the calculations with PRELUDE experimental results is presented. It is shown that the quench front exhibits either a 1D behavior or a 2D one, depending on injection rate or bed characteristics. The PRELUDE data cover a rather large range of variation of parameters for which the developed model appears to be quite predictive.Copyright

INTERACTION BETWEEN MOLTEN CORIUM UO2+x-ZrO2-FeOy AND VVER VESSEL STEEL

In case of in-vessel corium retention during a severe accident in a light water reactor, weakening of the vessel wall and deterioration of the vessel steel properties can be caused both by the melting of the steel and by its physicochemical interaction with corium. The interaction behavior has been studied in medium-scale experiments with prototypic corium. The experiments yielded data for the steel corrosion rate during interaction with UO2+X-ZrO2-FeOy melt in air and steam at different steel surface temperatures and heat fluxes from the corium to the steel. It has been observed that the corrosion rates in air and steam atmosphere are almost the same. Further, if the temperature at the interface increases beyond a certain level, corrosion intensifies. This is explained by the formation of liquid phases in the interaction zone. The available experimental data have been used to develop a correlation for the corrosion rate as a function of temperature and heat flux.

Experimental Study of Boiling in Porous Media

Following a long-lasting failure in the cooling system of a pressurized water reactor (PWR), the superheated core can be efficiently cooled down by reflooding. The macroscopic model used at the French Institute of Radioprotection and Nuclear Safety (IRSN) to simulate this process is based on strong assumptions on the microscopic flow patterns. This paper describes the experimental setup designed for the study of boiling in porous media with the emphasis on various pore-scale boiling regimes. The final experimental setup is a two-dimensional porous medium made of 392 cylinders randomly placed between two ceramic plates. Each heating cylinder is a RTD probe (Resistance Temperature Detector), that can give thermal measurements in every point of the test section as well as heat generation. This paper presents preliminary results: pool boiling is characterized for a single cylinder mounted in the test section and reflooding of a line of 9 cylinders is observed.Copyright

A Revised Methodology to Assess In-Vessel Retention Strategy for High-Power Reactors

The In-Vessel Retention (IVR) strategy for Light Water Reactors (LWR) intends to stabilize and isolate corium and fission products in the reactor pressure vessel and in the primary circuit. This ty ...

Past and Future Research at IRSN on Corium Progression and Related Mitigation Strategies in a Severe Accident

Abstract Reactor core degradation and in-vessel and ex-vessel corium behavior have been major research topics for the last three decades to which Institut de Radioprotection et de Sûreté Nucléaire (IRSN) strongly contributed by the coordination of or the contribution to large research programs and through the development and validation of the severe accident (SA) ASTEC code. In recent years, the balance of research efforts has trended toward analyses of pros and cons and assessments of mitigation measures. The outcomes of risk significance analysis [including fuel-coolant interaction (FCI), hydrogen combustion, and molten core–concrete interaction (MCCI) risks] performed in France and corium behavior research are described. The focus these days is on (1) in-vessel melt retention (IVMR) strategies for future reactor concepts and the need to establish the reliability of such strategies when implemented in existing reactors and (2) in-containment corium cooling for existing reactors. This paper summarizes the main achievements and remaining issues related to understanding and modeling of (1) reflooding of a degraded core where, despite substantial knowledge gained through research programs, additional efforts are required to establish the efficiency of such a measure and the associated risks for largely degraded cores; (2) corium behavior in the reactor pressure vessel (RPV) lower head where, despite the Organisation for Economic Co-operation and Development/Nuclear Energy Agency (OECD/NEA) MASCA program results, efforts remain necessary to predict RPV thermal loadings resulting from corium layer evolution and RPV resilience with and without IVMR measures (internal and/or external cooling); (3) FCI for which, despite the OECD/NEA SERENA program results, the knowledge is not sufficient to assess with confidence the induced risk of containment failure; and (4) MCCI, where the knowledge on corium cooling in the containment by top and/or bottom water flooding is insufficient to formulate conclusions regarding the efficiency of such measures. Of particular interest for top flooding are the water ingress and corium eruption processes. Specifically for top flooding, respective impacts of water ingress and corium eruption processes remain to be quantified in reactor conditions. In support of these activities, substantial efforts are also being conducted at IRSN to constantly improve and validate nuclear material property databases that are key tools for corium behavior analysis. This paper describes ongoing and future research programs performed at IRSN or internationally with IRSN coordination or participation to tackle the remaining issues and summarizes expected progress in modeling for SA codes, in risk analysis and in SA management.

Corium and Debris Coolability Studies Performed in the Severe Accident Research Network of Excellence (SARNET2)

The motivation of the work performed within the work package “Corium and Debris Coolability” of the Severe Accident Research Network of Excellence (SARNET) is to reduce or possibly solve the remaining uncertainties on the efficiency of cooling reactor core structures and materials during severe accidents, either in the core, in the vessel lower head or in the reactor cavity, so as to limit the progression of the accident. This can be achieved either by ensuring corium retention within the reactor pressure vessel or at least by limiting the corium progression and the rate of corium release into the cavity. These issues are to be covered within the scope of accident management for existing reactors and within the scope of design and safety evaluation of future reactors. The specific objectives are to create and enhance the database on debris formation, debris coolability and corium behavior in the lower head, to develop and validate the models and computer codes for simulation of in-vessel debris bed and melt pool behavior, to perform reactor scale analysis for in-vessel corium coolability and to assess the influence of severe accident management measures on in-vessel coolability. The work being performed within this work package comprises experimental and modeling activities with strong cross coupling between the tasks. Substantial knowledge and understanding of governing phenomena concerning coolability of intact rod-like reactor core geometry was obtained in previous projects. Hence the main thrust of experimental and modeling efforts concentrates mainly on the study of formation and cooling of debris beds in order to demonstrate effective cooling modes, cooling rates and coolability limits. Modeling efforts have been aimed at assessing and validating the models in system-level and detailed codes for core degradation, oxidation and debris behavior. The paper describes the work performed up to now and summarizes the main results achieved so far.Copyright

RADIATIVE CONDUCTIVITY OF NON BEERIAN POROUS MEDIA : APPLICATION TO DEGRADED ROD BUNDLES OF A NUCLEAR CORE

A 3D numerical model of a degraded experimental small-scale facility, simulating an opaque rod bundle of a nuclear reactor core has been built from gamma-ray tomography images. It has been directly characterized by both extinction cumulated distribution functions G_ext and scattering phase functions p. G_ext strongly differs from the exponential function associated with the Beer law and p strongly depends on both the incidence and the scattering directions. By assuming a diffuse wall reflection law, we have directly determined a radiative conductivity tensor with a numerical perturbation method of the generalized radiative transfer equation, associated with the previous statistical functions and introduced by Taine et al. Only the diagonal radial and axial components of this tensor are not null. They have been fitted by a simple law, only depending on the porosity, on the specific area and on the wall absorptivity.