Fig. 8: Cycleinterfaces for the subassemblies of theASTRIDcore
One of the ASTRID’s main goals is to demonstrate a full fuelcycle closing at industrial scale; in particular withthe recycling of plutonium coming from the reprocessing of the MOX fuels from PWRs. The safety and performances goals assigned to thecore by theASTRID project are maintained with that Pu in the “CFV Basic Design 16/10” core for the first core equilibrium phase of ASTRID. At the start of the Basic Design phase, in 2016, different performance phases of thecore have been defined on the life of ASTRID. Physic impacts linked to various aspects, Pu content, decay heat, for fuel subassemblies (fresh and spent) have been evaluated to identify the plutonium needs and the impacts on the subassemblies management (interim storage, handling) on ASTRID and on the different stage of thecycle, from the front to the back end, which are identified.
axially heterogeneous fuel pins, a large cladding versus small spacer wire bundle, a sodium plenum above thefuel pins, and an upper neutron shielding with both enriched and natural boron carbide. The upper shielding also maintains a low secondary sodium activity level and is made removable on-line through the sub-assembly head for washing compatibility. Calculations have been performed to increase the stiffness of the stamped spacer pads in order to analyse its effect on thecore mechanical behaviour during hypothetical radial core compaction events. Concerning the radial shielding sub-assemblies surrounding thefuelcore, heavy iterative studies have been performed in order to fulfill ASTRID requirements of minimising the secondary sodium activity level and maximising the in-core life-time. Evaluated options were reflectors sub-assemblies made of steel or MgO rods, and radial neutron shielding sub-assemblies made of B 4 C or borated steel, with different configurations in the
Fast reactors designed and operated in France, namely PHENIX and SUPERPHENIX have been fueled with uranium-plutonium dioxide. It has a very good radiation-resistance and can thus tolerate important burn-ups, and its high melting temperature compensates for its low thermal conductivity. However, due to the presence of oxygen in thefuel, the spectrum is slightly softened and combined with a lower density, the achievable breeding gain is lower than in the metal case. The main advantage of oxide fuel is the advantage of several decades of industrial experience on the use of this fuel, as it is also used in current thermal reactors, mostly as uranium dioxide and in selected reactors as uranium plutonium dioxide, the so-called MOX fuel. Carbide and nitride fuels were also investigated as potential fuels for fast reactors. Like oxide, they are refractory materials with a high melting point but have both better thermal conductivity and density than oxide, which leads to a higher breeding ratio and a lower fissile inventory than for oxide. However, their development is still underway and additional irradiation experiments are required to qualify those fuels. India is one of the countries pushing in this direction, where uranium plutonium carbide fuels have been irradiated in the Fast Test Breeder Reactor and then reprocessed  but americium carbide remains to be produced. Similarly, nitride fuel manufacturing on a conventional production line has already been demonstrated, but americium nitride transmutation targets are still being studied. In both cases, the main hardship is the low vapor pressure of americium, which evaporates during high temperature phases of the manufacturing process .
Fig. 3. SIMMER Calculation: Corium propagation under an unprotected local cooling fault situation Contrary to homogenous core, ULOF transients withthe CFV core do not show significant power excursion during the primary phase of the accident 8 . This is due to the negative sodium void worth of the CFV core, which leads to the decrease of thecore reactivity withthe decrease of the sodium density or the voiding of the upper part of thecore up to 39s, with large development of the boiling zone in the external corefuel assemblies. Up to 50s, reactivity oscillations are observed due to hydraulic instabilities (voiding/reflooding) between fuel assemblies (Fig. 4). The power of thecore during this period is in the range of 40- 80% of the nominal power. After this time, when clads melt and relocate, the reactivity variations are still limited. Later, withfuel relocation, larger reactivity increase is observed due to fuel axial compaction, leading to a mild power excursion at 68s and to the beginning of the transition phase. One can conclude that, thecore degradation during the primary phase of the accident is driven by thermal phenomena and not by neutron physics phenomena as in homogenous cores with positive sodium void worth; the associated time scale for CFV core degradation is then rather long.
The reflectors S/A in CFV v4 core comprise a bundle of 19 pins filled with MgO pellets at 96% relative density. The cladding, made of AIM1 steel, has an outer diameter of 33.6 mm and a thickness of 1 mm. Pins are separated by a 2 mm-diameter helical wire. The surface fraction of MgO is 52% inside the bundle. As MgO does not produce gas under irradiation, pins are leaktight and filled with helium at atmospheric pressure. The other parts of the reflector S/A, such as the wrapper tube, the lifting head and the spike, are similar to those of fuel S/A. Due to the high loading radial gradient in the first row adjacent to thefuel S/A, several management scenarios – to be undertaken during fuel reloading periods – have been studied to increase the reflectors life-time by limiting the damage on the cladding and the bowing of the hexagonal duct. Some of them, consisting in turning S/A of first row by 180 degrees and/or permuting S/A between different rows, can increase the lifetime between 10 and 30 years for the first row, and up to 60 years for the other rows. Preliminary thermal- hydraulic calculation have been performed withthe STAR-CCM+ CFD code to verify the need of feeding the reflectors S/A with cold sodium. It has been found out that the first row would require a sodium flow of ~0.6 kg/s to respect thermal criteria on claddings, while the others rows could be cooled by natural convection.
Extensive 3D Monte-Carlo calculations were conducted to optimise theASTRIDcore shielding, considering the best “performance vs. cost” ratio . This consisted in identifying the best arrangement for the reflector, moderator and absorber materials in the lateral shielding sub-assemblies, as well as the material in the top part of the upper neutron shielding. Concerning the lateral shielding, successive alternations of MgO and B 4 C sub- assemblies were adopted (see section II). Concerning the upper neutron shielding, the top part was filled with natural B 4 C (19.78% of 10 B), the best absorber, which gave almost as good results as 10 B-enriched B 4 C, while being much less expensive. Additional neutron shields made of borated steel skirts were added in parallel to the IHXs to decrease the secondary sodium activation to an acceptable level of about 8 Bq/cm 3 .
Figure 4 Critical mass sensitivity profiles of the Pu239 fission cross-section of for JEZEBEL Pu239, MASURCA 1AP, MASURCA ZONA2 and ASTRID CFV
The MASURCA 1AP core, the PRE-RACINE cores 12 using fuels with different Pu vectors, the ZONA2 core of the BERENICE 13 and CIRANO 14,15 programmes and also the JEZEBEL core of the ICSBEP data base offer a complementary information on Pu239 fission cross sections as it is illustrated with sensitivity profiles in Figure 4. More core analyses are necessary to provide complementary information and eventually redundant ones in order to reduce some components of neutron balance for theASTRID CFV- BD core either at Beginning of Cycle (BoC) or at End of Cycle (EoC). Sample reactivity worths measured with oscillation techniques and analyses of irradiated sample will be used in another PhD work with similar objectives. Nevertheless, there is no specific experiments devoted to ASTRID CFV-BD in this data base and the reduction of uncertainties will be limited and will have to be complemented by new measurements.
• current black-box models are not suited to cross-sections perturbations management; • models based on transport and depletion codes are too time-consuming for stochastic un-
Consequently, a new type of equivalence model is developed, and exposed in section 4.3. It is based on ANN, constructed with data calculated with neutron transport and depletion codes. The input of the model are the fresh fuel isotopy, the irradiation parameters (burnup, core frac- tionation, etc.), cross-sections perturbations and the equivalence criterion (for instance thecore target reactivity in pcm at the end of the irradiation cycle). The output of the model is the fresh fuel content such that target reactivity is reached at the end of the irradiation cycle. Those models are built then tested on databases calculated with APOLLO2 (for thermal spectra) and ERANOS (for fast spectra) transport calculation. A short preliminary uncertainty propagation and ranking study is then performed for each equivalence models.
The sodium temperature is fixed to 400°C and the sodium flowrate with a uniform velocity to 27,3 kg/s at the inlet of thefuel bundle. At the outlet, a constant pressure is provided. With these conditions, the average sodium temperature at the outlet of the heated column is 550°C.
For the deformed geometry, two cases are simulated. First, the same flowrate as for the nominal geometry is kept. Then, a modified flowrate is assessed in order to have the same pressure drop for all the sub-assemblies as it is for the nominal geometry, independently of the restriction of the flow cross- section. This hypothesis is based on the assumption that thecore pressure drop is fixed by the primary loop so that the pressure drop is the same for all sub-assemblies . The flowrate in the deformed sub-assembly is evaluated from a pressure drop model based on CFD calculations and correlations as explained hereafter.
Thecore management studies are carried out on a core managed with 4 batches of 72 S/As and an irradiation cycle of 360 efpd. The S/As can be unloaded when their decay power is lower than 3 kW or 1 kW if a clad failure has been detected. The load factor of the reactor is 0.7 during the transition phase from start-up core to equilibrium core and then it is 0.9. From these data, fuel S/As must remain during 1 core irradiation cycle (360 efpd) in internal storage or for 3 to 4 cycles in debugging positions (with a clad failure) before being unloaded.
3. Layout of the CFV core (CFV V4) 3.1 Fuel S/As
The number of thefuel pins and S/A is optimized according several criteria : fuel cladding mechanical interaction by power increase, control rod withdrawal, core pressure drop. The number of thecore Pu enrichment zones and the enrichment ratio between zones is determined with respect to the flattening and the stability of thecore power distribution during the irradiation. This CFV core is composed of 288 fuel S/As : 180 in the inner core and 108 in the outer core. The main geometrical characteristics are gathered in .
Corresponding author: Thierry BECK, email@example.com
The French 600 MWe Advanced Sodium Technological Reactor for Industrial Demonstration (ASTRID) project has reached the end of its Conceptual Design phase. Thecore design studies are being conducted by the CEA with support from AREVA and EDF. Innovative design choices for thecore have been made to comply withthe GEN IV reactor objectives, marking a break withthe former Phénix and SuperPhénix Sodium Fast Reactors. The main objective to improve safety compared with current GEN II or III reactors led to a core design that demonstrates intrinsically safe behaviour. A negative sodium void worth is achieved thanks to a new fuel sub- assembly design including (U,Pu)O 2 and UO 2 axially heterogeneous fuel pins, a large cladding/small spacer wire bundle, a sodium plenum above thefuel pins, and upper neutron shielding with both enriched and natural boron carbide (B 4 C) which also maintain a low secondary sodium activity level. As these Na-bonded B 4 C pins can lead to the retention of unacceptable amounts of sodium, the whole upper neutron shielding has been made removable on-line through the sub-assembly head just before the washing operations. Finite elements calculations have been performed to increase the stiffness of the stamped spacer pads in order to analyse its effect on thecore mechanical behaviour during hypothetical radial core flowering and compaction events. More generally, all design choices for ASTRID have been made withthe permanent objective of minimising the sub-assembly height to decrease the overall costs of the boiler reactor and thefuelcycle.
Proof: By definition of the bounded core, 0 ∈ C b (N, , 0) for any flat game (N, , 0) ∈ Γ. Hence, C b
satisfies ZIG. By Lemma 4.3, the bounded core satisfies the remaining axioms as well. In order to show the uniqueness part, let σ be a solution that satisfies the seven foregoing axioms. Hwang and Sudh¨ olter (2001, Theorem 4.1) show that σ coincides withthecore on the set of classical games provided |U | > 5. Hence, by CRGP and RGP, it suffices to show that σ coincides withthe bounded core for any two-person game that is not a classical game. Indeed, assume that this property holds. Take x ∈ σ(N, , v). By RGP of σ, for any S ⊆ N , |S| = 2, x S ∈ σ(S, S , u) = C b (S, S , u), where u is the reduced game. Then
Proposition 4.7 Let Γ tb ⊆ Γ 0 ⊆ Γ such that Γ 0 does not contain non-balanced two-person games. Then
the bounded core on Γ 0 is the unique solution that satisfies ZIG, COV, WRGP, RCP cg , CRGP, and BOUND.
It should be noted that the results on thecore of NTU games (see Section 7 of the aforementioned paper) may be generalized to NTU games with precedence constraints in a canonical way. Moreover, examples are presented that show that each axiom employed in the various characterizations is logically independent of the remaining axioms. Suitable modifications of these examples may be used to show the logical independence of the axioms employed in Theorem 4.4 and Proposition 4.7. Finally it should be remarked that the assumption |U | > 5 is already crucial for the results on classical games.
2. Sampling and Methods
[ 5 ] The chemical composition of mineral dust
found in ice cores is still poorly known because few techniques are available to provide information on the very low amount of dust usually present in polar ice samples (15 ng/g for Holocene and 700 ng/g for LGM [Delmonte et al., 2002]). These low amounts of material discourage the use of common geochemical techniques for major elements determination, such as X-ray fluorescence (XRF) and inductively coupled plasma – atomic emission spectrometry (ICP-AES), and additional analytical limits are set by the small volume of each ice sample (typically 10 –20 mL of melted ice) and by the risk of contamination during sample pre-treatment. Here, the geochemical characteriza- tion of dust from the EDC ice core was obtained by the PIXE technique (at the National Institute of Nuclear Physics, Legnaro, Italy), applied to 120 ice core samples, spanning the last 30 ka. The tempo- ral resolution is about one sample per 230 years for the Holocene and 300 years for the LGM; samples represent 2– 3 years of accumulation for Holocene and 4 –5 years for the LGM [Parrenin et al., 2007]. [ 6 ] Ice samples were decontaminated following the
Communication Support in Multi-core Architectures through Hardware Mechanisms and Standardized Programming InterfacesThe application constraints driving the design of embedded systems are constantly demanding higher performance and power eﬃciency. To meet these constraints, current SoC platforms rely on replicating several processing cores while adding dedicated hard- ware accelerators to handle speciﬁc tasks. However, developing embedded applications is becoming a key challenge, since applications workload will continue to grow and the software technologies are not evolving as fast as hardware architectures, leaving a gap in the full system design. Indeed, the increased programming complexity can be asso- ciated to the lack of software standards that supports heterogeneity, frequently leading to custom solutions. On the other hand, implementing a standard software solution for embedded systems might induce signiﬁcant performance and memory usage overheads. Therefore, this Thesis focus on decreasing this gap by implementing hardware mecha- nisms in co-design with a standard programming interface for embedded systems. The main objectives are to increase programmability through the implementation of a stan- dardized communication application programming interface (MCAPI), and decrease the overheads imposed by the software implementation through the use of the developed hardware mechanisms.
The transition between C and D is estimated to take about 30 years for D1 and 50 years for D2. Equilibrium is then reached around 2190-2210 depending on the option chosen for phase D. The early transition from B to D makes it possible to reach this equilibrium much faster and to overcome our dependency on natural uranium resources sooner. In this case, our independence with respect to natural uranium is gained about 60 years earlier. This early transition from phase B to D requires an increase in the treatment capacities of plants so as to recover the plutonium contained in the spent fuels, which is needed for the accelerated deployment of a 100% SFR fleet while maintaining its total power generation at a constant level.
The primary activity in this study was to conduct sensitivity analyses on the key parameters in order to identify the effects and to quantify the potential impacts of sensibilities of the outputs to the inputs. To the extent possible, each parameter was varied independently, without change in any other part of the specification. During the sensitivity analyses, some scenarios “broke” and had insufficient fuel material for the SFR fleet. This was noted in the analysis and then an effort was made to “fix” the scenario. One option was to modify additional parameters to address an imbalance in the scenario. The other option was to add an external source of fuel material and to note the amount of extra material required to complete the scenario.
Other solution concepts like the nucleolus, the kernel, etc. have been much less studied in the context of restricted cooperation. It is the main purpose of this paper to fill this gap for games with precedence constraints. Our first aim is to study the positive core (Orshan and Sudh¨ olter 2010), which is closely related to the prenucleolus. We find that the positive core can be axiomatized in a way which is very close to the classical case, up to a suitable generalization of the axioms, namely by non-emptiness (NE), rea- sonableness (REAS), covariance (COV), the reduced game property (RGP), the reconfirmation property (RCP), nondiscrimination (ND), and closedness (CLOS), the latter permitting to eliminate the relative interior of the positive core as a candidate for the solution. The positive core being unbounded unless F = 2 N , we propose likewise the bounded positive core, which has the same intuitive interpretation as for
This second step can be seen either from a purely mathematic point of view or from a mechanical one. Mathematically, it consists in choosing an interpolation function for the neutral fiber (the same for the assembly or the rods). When using polynomial func- tions, the order of the function is logically adjusted to the domi- nant shape observed in the original data, if any, resorting for instance to the basic classification provided in Section 2.1 . An alter- native strategy is to deduce the shape of the assembly from a direct mechanical computation using a beam model for the assembly and introducing the measures as imposed displacements. In this case, a Timoshenko beam model is the most relevant choice, since the assembly can undergo large levels of shearing, and some con- straints can be added to increase the fidelity to the industrial device. For instance, the curvature of the beam can be forced to zero at the grid levels to account for their effect as spacers in the assembly.