a CEA, Cadarache
Within the framework of long term prospective studies, an inherently-safe Sodium Fast Reactor (SFR) core, named CADOR (Core with Adding DOppleR effect), is studied at CEA (French commissariat ` a l’´ energie atomique et aux ´ energies alternatives). This core concept mainly relies on its enhanced Doppler effect. The behavior of this innovative core design, when facing severe accident transients resulting from unprotected sequences, is currently assessed in order to demonstrate the benefits of such a core configuration in terms of margins with respect to multiple safety criteria. This paper focuses on the Total Instanta- neous Blockage (TIB) sequence that has been simulated out with the analytical tool BETINa. This is a fast-running tool based on the coupling between low- dimensional models and advanced statistical techniques. Firstly, a reference transient study enables to highlight the slow kinetic of this transient in compar- ison with more conventional homogeneous cores such as SuperPhenix. This is explained by the low power of the CADOR sub-assemblies in this core concept and to their high thermal inertia compared to previous SFR cores. Then, a parametric analysis allows to further understand the core behavior, focusing on the influence of the thermal or hydrodynamic propagation of molten material to the neighbouring sub-assemblies and on the axial location of the hexcan failure. These parameters are indeed identified as explaining a large part of the total
A New Breakdown Methodology to Estimate Neutronic Model Biases Applied to APOLLO3 ® SFRCore Calculations
V. Jouault, J.-M. Palau, G. Rimpault, J.-F. Vidal
CEA, DEN, DER/SPRC/LEPh, Cadarache, F-13108 Saint-Paul-lez-Durance, Contact :firstname.lastname@example.org Abstract – This paper presents a new breakdown methodology to estimate independently model biases for each approximations of a given calculation scheme. This new methodology is set to be applied on the new French deterministic neutron transport code APOLLO3 ® , and be a part of its advanced V&V process. The first step of the method is the identification of approximations of the different solvers. Then, we measure the impact of each relevant approximation on core characteristics. To do so, we use ad-hoc TRIPOLI-4 ® multi- group calculations, either using APOLLO3 ® cross section, or making it generate its own multi-group cross sections. The methodology is applied on the ASTRID CFV core, and gives satisfactory results. It allows us to evaluate the impact of changes in the calculation scheme, leading to an improved calculation scheme and excellent results for reactivity and reactivity effects, especially in voided configurations.
The miniature fission chamber measurements require a fast converter column calibration which is not independent of the fission sections to be measured. However, they have a relative interest when looking at the spectrum distribution within the core. Given the axial heterogeneity of the core, they will be valuable for understanding the physics of shape of the flux either in nominal conditions or in voided conditions. The measurement of the kinetic characteristics of the GENESIS core is accurate only with the neutron noise method. This method requires that the neutron return by the reflective media is minimized and therefore requires a homogeneous core configuration with fertile covers (to be designed with TRIPOLI4). Greater accuracy of possible measurements associated with a renovation of MASURCA minimizing background noise.
In the context of the safety increase of the integrated Sodium-cooled Fast Reactor, we present an original safety complementary disposal to prevent or mitigate the consequences of a hypothetical severe accident consecutive to a loss of reactor cooling sequence. This disposal is set by ad-hoc empty transfer tubes, in place of some fuel sub-assemblies present in the reactor core, using an innovative passive hydraulic lock. It is based on the concept of hydraulic diode controlled by the flowrate of primary pumps. In case of the loss of the primary flow, it provides a direct flow path between the hot pool, equipped with decay heat removal exchangers, and the cold pool, leading to an easier passage of colder sodium towards the cold pool to promote core cooling by natural convection. In addition, it provides an easy way to discharge corium towards the core catcher in the hypothetical case of severe accident. In this paper, we focus on the assessment of the hydraulic lock function and of the small magnitudes of the perturbations induced by our disposal on the thermal-hydraulic behaviour of the reactor during normal operations. Through an analytical analysis and a multi-scale numerical approach, ranging from the local scale (CFD) to the system one, we claim that the lock function is kept during the normal situations at various power regimes. The leak flow represents no more than 1% of the primary pump flow. In addition, no important reactor thermal-hydraulic perturbation is brought by adding transfer tubes in the core. This is true for normal steady states, whatever the power is, but also for a full-power loss of forced flow accidental transient leading to the natural convection cooling.
3.3 Burn-up parametrization of the cross section libraries
In the previous section, it has been shown the importance of the cross section time depen- dency for core calculations. In a cell case, where no leakage model is applied, the MICRO SIGMA ZERO model leads to a reactivity difference of the order of 100 pcm (0.8% of the overall reactivity loss). The flux shifts towards lower energy and the cross sections are not condensed using the proper time-dependent weight flux. Until now, the MICRO SIGMA EVOLVING model has used a cross section library with a number of burn-up tabulation points equal to 34. The lattice depletion is performed following the time steps enlisted in the table of appendix C. 33 time intervals ∆t are used in lattice depletion. These intervals are accurate to represent, during the evolution, actinide and fission product concentrations. The correct representation of Np239 equilibrium concentration, for instance, explains the high number of time steps at the beginning of the calculations. Actinides and fission products are correctly estimated and this fact allows to properly represent the reactivity variations. Nevertheless, the aim of lattice calculations is the creation of cross section libraries and not the correct representation of isotope concentrations. As a consequence, the number of time intervals can be diminished in lattice depletion calculations. In fact, it is not important, at lattice step, to correctly represent the reactivity variations and time intervals can be reduced in order to create cross section libraries with a coarser burn-up mesh parametrization. The goal is to provide a cross section library which is more accurate than the MICRO SIGMA ZERO one, but which does not require a number of lattice steps equal to 34 to be created. Concerning TDT-MOC 1968 energy group lattice calculations, evolution time intervals ∆t have been consecutively divided by 2, from 33 to 16,8,4,2 and, finally, to a single interval covering the evolution from 0 to 1440 days. Corresponding cross section libraries have been created. Constant integration scheme has been used in order to avoid negative values for the reaction rates. Convergence test has not been performed in order to avoid the division of the time interval by 2.
the injected flowrate at equilibrium, meaning that there is no flowrate between the tube and the hot pool (negligible value in practise).
The singular head loss values in the 3D element and in the injectors are chosen in order to respect these CFD-prescribed global values. These head losses have been regularly applied all along the tube height. Moreover, the M-TT design envisaged for our typical SFR usually included the presence of an upper neutron shielding in the upper part of the tube. This has been taken into account by the use of a higher head loss value. Following this upscaling-like process, we approximatively recover the CFD value for the injected flowrate at equilibrium (𝑄 𝑖𝑛𝑗 ~ 5 kg/s and 𝑄 𝑟𝑒𝑠 ~ 0 kg/s) under the reduced pressure difference of 0.16 bar, cf. Fig. 12.
Key Words: Material Buckling Experiments, MASURCA, ERANOS.
Unfortunately, the neutron balance of Sodium Fast Reactor (SFR) cores is badly known due to the lack of accuracy in evaluated nuclear data. This is the case for the material balance of the ASTRID (Advanced Sodium Technological Reactor for Industrial Demonstration) SFRcore under detailed development at CEA. The material buckling offers a way to improve that situation when experi- mentally accessed from the curvatures of the different fission rate traverses in cores built in the MASURCA critical facility. This provides access to the neutron balance of the fissile zone, whereas the critical mass, much easier to obtain experimentally, depends also on the neutron reflection to the peripheral areas of the core. This analysis takes advantage of the use of recent deterministic codes with a detailed assessment of the experimental uncertainty.
IV. RESULTS ON A SIMPLIFIED SFRCORE 1. Geometries
In order to compare and validate the different homogenization methods with minimum biases against Monte Carlo TRIPOLI-4® (Ref. 14) reference calculations, a very simple SFRcore has been modeled. It is composed of a finite hexagonal lattice of CFV-like pins axially limited to the fissile height. This “regular” core has been made critical by adjusting the number of hexagonal rings in a configuration without reflector (3D Monte Carlo continuous energy TRIPOLI-4® simulations has been used for this, the corresponding geometry is given on Figures 1 and 2). The core is small, contained in a cylinder of 90 cm diameter and 80 cm in height. In a second configuration, a 14-cm thick steel reflector has been radially added to model a more realistic (and more challenging) situation (cf. Figure 3).
The paper describes how to use the global reactivity feedback coefficients to assess simply the core behavior during the main unprotected transients. The analytical equations to evaluate the safety trends are provided. The paper shows that the ULOF and ULOHS inherent behavior can be roughly predicted thanks to a very limited list of estimators build essentially on the k, g, h coefficients. For example, we show that the power of the core when the sodium starts to boil during an ULOF does not depend on the primary pumps halving time. The ULOSSP scenario is more complex but can also be evaluated by this analytical approach, which is used to compare four different types of SFRcore. The limitations of this approach are also discussed. Of course this approach is not dedicated to the safety demonstration but is consistent to assess the pre-conceptual safety issues. Furthermore, the k, g, h approach can be completed with some simplified thermal-hydraulic modelling (for decay heat removal or natural convection) and be use for other issues : reactivity transient, load following studies or passive shutdown systems specifications.
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Abstract – In the framework of the development of the Sodium Fast Reactor technology (SFR) the analysis of all possible scenarios leading to perturbation of nominal operating condition is exploited. Among these scenarios attention is being paid on reactivity modification due to core assemblies bowing and deformation, and to lattice readjustments consequent to earthquakes. A computational scheme based on the spatial projection method fulfilling a good compromise between the accuracy of stochastic codes and the quick runtime of deterministic codes has been developed and used to determine the reactivity changes issued from core lattice deformations and irregularities. The calculation of reactivity changes induced by core deformation is achieved by modifying the isotopic concentrations of assemblies concerned by displacements, by projecting the deformed lattice geometry on that corresponding to regular reference case. This methodology was validated by comparison with stochastic codes, and good agreements between the results achieved and those obtained by the Monte Carlo code TRIPOLI4 are observed. The deterministic code available at CEA for fast reactors, i.e. ERANOS/PARIS, has been used to solve neutron transport equation in a full 3D core representation and to calculate the reactivity changes due to core flowering and compaction. In this work, such a method has been used to determine the maximal positive/negative reactivity insertion corresponding to a postulated mechanical energy supplied to an SFRcore, as much as the lattice deformation causing it. The results presented in this paper, represent a first step in the assessment of a favourable calculation scheme that can be easily scaled-up to large-sized core and used for the future application in core design and safety analysis.
The main goal of our research project is to study the sodium boiling stability in a/several SFRs assembly(-ies). Considering the very dynamic context, developing then implementing a semi-analytical approach (in opposition to the numerical only-approach typically used by system codes) inspired by the methodology developed for BWRs (study of stability and bifurcations associated with fixed and singular points of the system) has many advantages. Furthermore, we would like to capitalize on the knowledge acquired during these analyses on BWRs while also taking advantage of implementing a complementary procedure, called Asymptotic Numerical Method (ANM), studied extensively at the Aix-Marseille University . This would allow us to further develop the analytical side of the approach, hence giving our study a very general view of the stability map of sodium boiling in a SFRcore. Our goals within this PhD thesis are therefore to show the usability of this ANM on a BWR case, to validate it. Then we are planning to adapt this method to the SFR case and analyze the stability and bifurcations of sodium boiling with this semi-analytical approach.
Fig. 1. Typical transition scenario for the 60 GWe French fllet (dark=current PWR, green=EPR, blue=SFR).
In order to achieve sustainability, SFRcore has to exhibit self-breeding performances to master the plutonium inventory when equilibrium is reached. As scenarios do investigate long term deployment configurations, some of them require tools for nuclear phase-out studies. For these particular scenarios, the need does focus on nuclear systems that enable to reduce the fleet plutonium inventory in an efficient way. To do so, one can choose either to develop dedicated tools such as Accelerator Driven System or to rely on inherent flexibility of SFR.
When the resonant condition is achieved, it can lead to novel optical features with stronger enhancement. For example, the control by optical Stark effect (OSE) (see fig. 25) of coherent quantum schemes of spins in semiconductors could promote new physical principles to be used in devices, with the poten- tial for realizing quantum devices based on spin qubits. The optical Stark shift is proportional to the square of the electric field magnitude of subreso- nant light and to the dipole moment characterizing light-matter interaction, divided by the energy detuning (defined as the difference between resonant bandgap and sub-resonant excitation). The control of both OSE and the spin manipulation has been achieved by tuning plasmon resonance intensity and frequency in Au-CdSe core/shell nanostructures . The demonstration of a sizable OSE has been achieved at substantial energy detuning in a cavity- free colloidal metal-semiconductor core/shell hetero-nanostructure . In that case, the metal surface plasmon is tuned to resonate spectrally with a semiconductor exciton transition. In addition, this resonantly enhanced OSE exhibits polarization dependence, thus providing a viable mechanism for coherent ultrafast spin manipulation within colloidal nanostructures.
The role played by freedom of association and collective bargaining rights is a highly challenged aspect, mainly due to the effects of “closed shop” unions, widely thought of as negative, in some Latin American countries (Elliott, 2003). Nonetheless, the unions' legitimacy usually lies in the challenge they present to the excessive and abusive powers of employers, which are often inadequately regulated by the public authorities and advantaged by other core standard violations, such as forced labour and child labour. The monopsonic behaviour of the employer leads to the labour being underpaid (Granger, 2003; Martin and Maskus, 1999; Morici and Shulz, 2001; Shelburne, 2004). The firms that have a monopsonic recruitment advantage can ration out their labour demand, and, therefore, production and exports, in order to put pressure on the price of labour. Consequently, not all available unskilled workers will be hired, reducing the country’s low-skilled labour endowment.
So far, the question has been tackled from a unilateral point of view: do countries respecting core labour standards trade more with the world? Trade relations concern instead country pairs and are influenced by bilateral trade costs such as tariffs, transport and insurance costs. Moreover, labour standards might influence these bilateral trade costs for a number of reasons. For example, preferential agreements may include provisions on labour standards. Bagwell & Staiger (1998) posit that two countries respecting labour standards should conclude more reciprocal tariff reductions, which imply lower trade costs. Our empirical study sets out to check whether labour standards affect bilateral trade relations as well as the total trade of countries.
In Sodium Fast Reactors (SFR), mass transfer occurs due to the difference of solubility in the sodium of the steel elements at the hot parts and the cold parts of the primary vessel. Corrosion (element release in the sodium) takes place at the hot parts (773K or higher), namely the upper parts of the core and of the intermediate heat exchangers (IHX), the elements are transported in the sodium and deposited in the cold parts (when their concentration exceeds their solubility limit), the lower part of the IHX, the primary pumps (PP), and the lower part of the core. As the claddings are activated under the neutron flux, one part of the release elements are radionuclides, the deposition of which leads to the contamination of the components (IHX, PP). The main radioactive contaminants are 54 Mn and 60 Co.
Atomic Energy Commission (CEA)
DEN, DANS, DM2S, SEMT, Mechanics and Systems Simulation Laboratory (LM2S) F-91191, Gif sur Yvette, France
A sodium fast reactor (SFR) fuel bundle is usually a strong hexagonal tube containing around 200 fuel pins made of steel. These pins should not touch each other to avoid overheating and damage of the bundle, which constitutes the first confinement barrier. For that purpose a steel wire is often wrapped around each pin from the bottom to the top with a helical shape. This technology maintains a distance between pins and ensures a proper mixing of the sodium, two necessary conditions so as to avoid hot points and damage. Nevertheless the intense fast neutron irradiation induces a significant isotropic swelling and creeping of the pins. If continued, this progressively generates contact closures (phase 1), then mainly a helical bow of the pin (phase 2), and in the end, a strong ovalisation of the cladding sections (phase 3). At such an interaction level, there is a possibility of cladding damage due to thermal creep accumulation.
Fuel pins are arranged in a bundle enclosed inside a hexagonal tube (Figure 1-b). Many hundreds assemblies are main constituents of the reactor core. These assemblies are maintained by their spikes (Figure 2) at the bottom of the core in a lattice. During a dynamic loading, the core lattice shakes assemblies which will bend and impact each other locally on spacer pads. The shock will generate acceleration on pins and cause dynamic stresses. Then, a high number of pin-to-pin collisions, up to 15000, will occur in the bundle between the spacer wire of a pin and the clad of a nearby one.
13 harmonics used, see Figure 3). To reduce these oscillations inherent to the method, the only way is to increase the number of available flux harmonics. But the traditional technique based on the power iteration method and a filtering technique is not efficient to compute a large number of harmonics. Moreover, to study the leakage component of the sodium void effect in the CFV con- cept, axial harmonics are required. They usua lly are higher-order than the radial ones, which com- plicates considerably their computation. In practice, getting by the filtering technique several axial harmonics is impracticable in 3D full model. Some other tools might do better, such as the one based on coupled-core theory presented here after.