Sergey Stepanyan

Nicolas Minesi

Erwan Pannier

Gabi D Stancu

Christophe O Laux

Hydrodynamic effects induced by nanosecond repetitive pulsed discharges

The intense energy released in a burst of nanosecond sparks is shown to induce hydrodynamic effects over large spatial scales of the order of a centimeter. This gas motion transports the active species produced by the discharge into the surrounding space. The present work is dedicated to the detailed measurements of the energy deposited in plasma and its redistribution in space through hydrodynamic degrees of freedom.

I. Introduction

anosecond Repetitively Pulsed (NRP) discharges have been developed for various applications such as Plasma-Assisted Ignition (PAI) [1][2][3][4][5], lean flame stabilization [6][7][8], aerodynamic flow control [9][10][11][12], biodecontamination and nanomaterial synthesis [13][14][15]. The peculiarity making nanosecond plasmas attractive for these applications is the fast gas heating phenomenon and its consequences [16]. Fast heating occurs in air-containing mixtures due to dissociative quenching reactions between molecular oxygen and electronically excited nitrogen molecules produced by electron impact during the discharge [17,18]. The ultrafast gas heating in atmospheric pressure air plasmas occurs within a few tens of nanoseconds in the discharge afterglow. Nearly full dissociation of molecular oxygen [18][19][20][21][22][23][24] is another feature of nanosecond plasmas which provides large amounts of reactive chemical species.

A known consequence of the fast gas heating by nanosecond plasmas is the formation of shock waves and hydrodynamic effects [25,26]. It has been shown in [25] that the thin channel of gas excited by a single spark propagates over a few millimeters within tens of microseconds. It has been also demonstrated for combustible mixtures of propane [27][28][29][30][31][32] that the burst of nanosecond sparks can cause wrinkling of the flame front and lead to its acceleration due to the hydrodynamic motion induced by nanosecond plasma. The effect of nanosecond sparks on the formation of ignition kernel was particularly considered in [33,34].

The modeling performed by Castela et al [35] showed that the hot gas core produced by the spark develops into an expanding torus of reactive hot gas, and that the fresh gas recirculates inside the interelectrode region. This was confirmed by LIF and by PIV (particle image velocimetry) in [START_REF] Seydou | 18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics[END_REF].

Hydrodynamic expansion following the nanosecond spark should be studied because the energy deposited in t h e plasma redistributes in space during a period typically shorter than the ignition delay time. This means that preformation of the ignition kernel occurs due to hydrodynamic motion induced by the intense heat release in the nanosecond plasma. Parametric studies are required to understand these phenomena, i.e expansion dynamics should be studied for different gas mixtures, speeds of external flow, distances between the electrodes and different frequencies of applied pulses in the case of repetitive discharges.

The present work is focused of the investigation of hydrodynamic effects induced by nanosecond repetitive sparks. The main part of experimental information was obtained by electrical measurements and optical diagnostics including Planar Laser-Induced Fluorescence (PLIF), Schlieren, emission spectroscopy and fast imaging.

II. Experimental setup

The majority of experiments presented here were performed for nanosecond sparks initiated by overvoltage pulses between pin-to-pin electrodes. The pressure was always 1 atm. The pins used in the present work had tips of conic shape with a radius of curvature of about 50 μm and were made of stainless steel. It should be noted that for different pin-electrodes (i.e. for various pin-tip radii of curvature) no difference was observed, neither in the energy deposition nor in the hydrodynamic effects induced by the plasma [START_REF] Stepanyan | [END_REF]. So the results presented here for pin-to-pin geometry can be considered to be quite general. Some additional experiments were performed in pin-to-plane geometry. The distance between the electrodes was in the range 0.5-7 mm. The spark discharges were created with an FID FPG 30-100MC4K generator producing pulses of 10-ns duration, amplitudes up to 30 American Institute of Aeronautics and Astronautics 2 Repetition Frequency (PRF) up to 100 kHz. The electrical characteristics of the discharge were monitored by high voltage probes (Lecroy PPE), current probes (Pearson model 6585) connected to the electrodes system, and a 1-GHz digitizing oscilloscope (LeCroy Wavepro 7100). The procedure for energy measurements in this configuration can be found elsewhere [13].

Comparison of the nanosecond discharge was performed with an AUDI coil system widely used as a car igniter. For this system, discharge breakdown occurs during the first tens of nanoseconds. After this stage the spark discharge transforms into an arc that lasts up to a few milliseconds. The typical value of total energy deposition in this case is a few tens of mJ.

Figure 1 presents a schematic of the experimental setup used to monitor the long discharge afterglow. Schlieren diagnostics were combined with PLIF, emission spectroscopy, and emission imaging. This set of optical diagnostics allows characterizing the distribution of the gas number density and the production of active species.

The hydrodynamic effects induced by ns sparks were monitored with Schlieren diagnostics. A Cavilux light source was used to provide short light pulses (~10 ns) at high frequencies (up to 900 kHz). The light produced by the source was collimated with a 1-m focal-length plano-convex lens directed to the discharge location. Then the light partially deflected due to gradients of gas number density was directed to a spherical mirror of 2-m focal length. A knife-edge was placed at the focal spot of the mirror to cut 80% of the light produced by the source. A second spherical mirror of 2-m focal length was placed between the knife-edge and the CCD camera in order to provide a 1.8 magnification. An intensified fast camera (Photron SA-X2) was used to record either Schlieren images or spontaneous emission of the active species produced in the plasma.

The spatial distribution of active species produced in the discharge, such as OH and NO, was characterized by monitoring the PLIF intensity from the area corresponding to the discharge afterglow at temporal scales of 200 μs. A frequency-doubled dye laser (Continuum ND6000) with Rhodamine 590 dye, pumped by a Nd:YAG laser (Continuum) at 532 nm, was used to excite the Q1(6) transition of OH[(X, v''=1)→ (A, v''=1)] at 282.935 nm. LIF emission was collected through band pass filters (CORION 10BPF10-310 centered at 310 nm with 11 nm FWHM for OH*) placed in front of the CCD camera. The laser sheath for PLIF was formed by a combination of cylindrical (f=15 cm) and spherical (f=10 cm) lenses. The height of the sheath was 10 mm and its thickness was 0.2 mm. The laser frequency was 10 Hz, with a pulse width of 6-ns FWHM.

The discharge, laser and cameras were synchronized with a gate-and-delay generator (BNC Model 575).

III. Experimental results

Hydrodynamic effects induced by sparks are governed by the dynamics of energy release in the plasma. Therefore, the monitoring of hydrodynamic effects by optical diagnostics must be coupled with the measurements of the energy deposited in plasma. Figures 2a-f present the results of energy measurements obtained for a burst of eight pulses for various conditions in ambient air. For all the presented results the discharges were initiated by pulses of 10 ns duration and of voltage amplitude 30 kV in open circuit. Burst frequencies we re within the 5-100 kHz range. The speed of the external air flow was varied between 0 and 40 m/s. One can see that for higher burst frequencies (>5 kHz) the energy deposited in the second pulse of the burst is always lower than in the first one. This is attributed to the change of gas density and gas content before the second pulse by the discharge initiated in the first pulse. At lower burst frequencies (~5 kHz) the energy deposited in the second and other pulses is practically the same as in the first pulse. Therefore, at the considered conditions the effect of discharge coupling occurs at frequencies higher than 5 kHz. In case of coupling the energy deposited in each new spark stabilizes after a few first pulses in the burst.

The same dependence of the energy deposition on the burst frequency is observed for pure argon and oxygen (see figure 2g. As the result the discharges initiated in these gases induce hydrodynamic affects at similar temporal and spatial scales, as demonstrated in [START_REF] Stepanyan | [END_REF].

A summary of the results on energy measurements is presented in figure 2h. The average energy deposited per pulse in the burst changes quite smoothly for inter-electrode gap distances of 2-7 mm, for the flow speed range 0-40 m/s, and for all gases considered (air, oxygen, nitrogen, argon). Values measured for all the considered conditions are within the range 1.5-3.5 mJ per pulse in the burst. It should be noted that for all the considered conditio ns a transition streamer arc described in [38] occurs within a nanosecond or so. Figure 3 demonstrates images of total emission before and after streamer-arc transition for a single nanosecond spark initiated in ambient air by a 10 ns pulse of 30 kV. Discharge emission before the transition is mostly due to molecular nitrogen and after the transition is due to ions of atomic nitrogen. Radial profiles of the discharge before and after the transition to the arc are presented in figure 4. One of the main peculiarities of the transition to the arc is the temperature rise up to 40000 K at nanosecond scale (see [38] for more details). This provides high level temperature gradients and as a consequence shock waves and hydrodynamic motion of the gas in the area around the electrodes.

The results of the energy measurements presented in figure 2 for the case with external flow of air may look confusing because the energy decreases after the first pulse and then increases after a few pulses. It has been alread y mentioned that the energy deposition depends on the gas density and gas content. In the case of the external gas flo w it also depends on the flow speed. The gas treated by a discharge is advected by the flow. Depending on the discharge frequency and the flow speed, the next discharge will be either initiated as a relatively straight channel between the pins or as a curved channel passing through the active medium created in the previous pulse and advected by the flow before the new one. Figure 5 presents the images of total emission for two cases: the discharge in ambient quiescent air and in an external air flow of 40 m/s. In both cases the discharge was initiated by a burst of 30 kV pulses (10 ns duration each) at 100 kHz. The external air flow was directed perpendicularly to the pin electrode axis. One can see that the nanosecond spark placed in the external gas flow passes in each new pulse through the previously created active medium. This continues until the spark cha nnel length becomes too long and the spark extinguishes and restarts as a straight channel again. At the considered conditions, the extremity of the curved spark channel can be at 1.5 cm from the electrode axis before the discharge restarts again between the electrodes. The visible volume of the discharge is also significantly larger than in the first pulse due to both length and thickness of the spark channel. All considered factors affect the energy deposition dynamics and cause the results presented in figure 2.

The high reproducibility of single-pulse nanosecond discharges allows to acquire phase-locked images for PLIF and Schlieren diagnostics. It has also been verified that the hydrodynamic effects induced by nanosecond sparks at given conditions are also reproducible up to times of the order of milliseconds. This allowed scanning with PLIF the shape of the active medium arising in the discharge afterglow of a single nanosecond spark.

Hydrodynamic motion induced by a single nanosecond spark has already been described before [25,27,33]. Figure 6 demonstrates typical Schlieren (top row) and OH PLIF (bottom row) images obtained in the afterglow of a single spark initiated in air by a single pulse of 10-ns duration and 30-kV amplitude. The gap between the pin-to-pin electrodes in this case was 1 mm. Each Schlieren image consists of two parts that correspond to different amounts of light cut by the knife-edge. Approximately 30 percent of light produced by a Schlieren light sourc e was cut for the left-side pictures and 80 percent for the right-side pictures. Therefore, for the considered conditions the left-side pictures present well the gradients corresponding to the hot gas core expanding after the spark, and the right-side pictures are representative of the density gradients corresponding to the shock wave induced by the plasma. One can see from figure 6 how the intense energy release in a thin plasma channel induces a shock wave and the following expansion of the active medium. At approximately three microseconds the shock wave degrades to a sound wave and detaches from the active medium. At this moment the expansion speed of the active medium becomes about 50 m/s per second and decreases to 20 m/s in the next 100 s. Figure 7 demonstrates the Schlieren results obtained for the same conditions as for figure 6, but for a longer temporal scale. The result is practically identical for various conditions [25,27,33], and is valid for a single submicrosecond spark initiated between pin-to-pin electrodes at normal conditions: about 100 s after the discharge, the scale of the expanded active medium is about 5 mm. Then the expansion becomes diffusive (<1 m/s) and the active medium practically does not change in shape before its complete decay.

The Schlieren images presented in figure 7 show that in the case of a burst of two pulses the result will be different for the period between pulses of 20 s (50 kHz) and 100 s (10 kHz). Schlieren images presented in figure 7 show that the gas density near the electrode tips at 20 s after the spark is lower than at 100 s. The gas content at these moments is obviously also different. The last two statement correlate well with energy measurements presented above (see figure 2a). For multiple discharges (NRP discharge), the shape of the expanded hot gas corresponds to a superposition of single discharges. It strongly increases with the number of pulses in the burst. Figures 8 present Schlieren images obtained for a burst of 30 sparks in ambient air initiated at 30 kHz. The duration of each pulse was 10 ns and the voltage amplitude was 30 kV. The interelectrode distance was 2 mm for the image on the left and 7 mm for the image on the right. The total energy deposited in the burst was 60 mJ for the 2-mm gap and 90 mJ for the 7-mm gap. The estimated volume was 0.3 cm 3 for the 2-mm gap and 0.9 cm 3 for the 7-mm gap. Therefore, the average density was 0.2 mJ/mm 3 for the 2-mm gap and 0.1 mJ/mm 3 for the 7-mm gap. It should be noted that both cases correspond to volumes that are significantly larger that the ignition kernel produced by a conventional spark ignition system (for more details see [START_REF] Stepanyan | [END_REF]), whereas the volumetric energy density is still sufficient for ignition of combustible mixtures. Thus NRP can be considered as an efficient tool to redistribute spatially the energy deposited in the plasma during a period shorter than a typical ignition delay time.

IV. Conclusions

We have shown how the energy deposited in a repetitive nanosecond spark depends on different factors such as gas content, pulse frequency, interelectrode distance and speed of external flow. For all the cons idered conditions the values of the energy deposited per pulse were within the range 1.5-3.5 mJ. It has also been demonstrated that varying parameters of nanosecond repetitive spark one can tailor the spatial redistribution of the energy deposited in the plasma and the volume occupied by the active medium. Thus repetitive nanosecond sparks are a useful tool for the ignition of lean mixtures and the stabilization of lean flames.

Figure 1 .

 1 Figure 1. Experimental setup. Combination of synchronized PLIF and Schlieren diagnostics. The focal length of the lenses for Schlieren is 1 m. Both spherical mirrors have focal distances of 2 m.

Figure 2 .

 2 Figure 2. Energy deposited in a burst of sparks initiated in ambient air by 8 pulses (10 ns, 30 kV) at different frequencies. The distance between the electrodes was 2 mm.

Figure 3 .

 3 Figure 3. Total emission produced by a single nanosecond spark initiated in ambient air by a 10 ns pulse of 30 kV. The distance between the electrodes was 1 mm. Transition streamer-arc occurs at 8-10 ns. Camera gate was 2 ns.

Figure 4 .

 4 Figure 4. Profiles obtained by total emission produced by a single nanosecond spark before (red color filled circles) and after (blue filled barssquares) transition to the arc. Discharge conditions are the same that as for figure 3 (ambient air, 10 ns pulse, 30 kV).

Figure 5 .

 5 Figure 5. Comparison of total emission produced by a burst of nanosecond sparks. The Ppulse number is marked on at the top. The discharge was initiated in ambient air buy a burst of 20 pulses of 10 -ns duration each and of 30-kV amplitude. Burst frequency was 100 kHz. The distance between the electrodes was 2 mm.

Figure 6 .

 6 Figure 6. Schlieren and OH LIF images obtained in the afterglow of a single nanosecond spark. The discharge was initiated in ambient air by a single pulse of 10-ns duration and 30-kV amplitude.

Figure 7 .

 7 Figure 7. Schlieren images obtained in the long afterglow of a single nanosecond spark. The discharge was initiated in ambient air by a single pulse of 10-ns duration and 30-kV amplitude.

Figure 8 .

 8 Figure 8. Schlieren images for a burst of 30 sparks at 30 kHz for a 22-mm inter-electrode gap between the electrodes (to the left) and a 7-mm gap (to the right). Each pulse was of 10-ns duration and 30-kV amplitude. The discharge was initiated in ambient air. Both images were obtained at 1000 s.

Downloaded by UNIVERSITY OF ADELAIDE -INTERNET on January 14, 2018 | http://arc.aiaa.org | DOI: 10.2514/6.2018-0930

Acknowledgments

This work was supported by the FAMAC project (Grant no. ANR-12-VPTT-0002) and the PLASMAFLAME project (Grant no.ANR-11-BS09-0025). The authors thank Dr. Denis Packan (ONERA) for lending the light source for Schlieren measurements.


N Terranova
email: nicholas.terranova@unibo.it

M Sumini

P Archier
email: pascal.archier@cea.fr

O Serot

D Bernard

C De Saint

A MODEL FOR FISSION YIELD UNCERTAINTY PROPAGATION BASED ON THE URANIE PLATFORM

Keywords: Fission yields, covariances, URANIE, uncertainty propagation, latin hypercube sampling

In the present work, we analyze how fission yields uncertainties can be propagated in a burn-up calculation. The first part of the work is dedicated to the fission yield covariances generation in CONRAD (COde for Nuclear Reaction Analysis and Data Assimilation) to be used in the neutronic code APOLLO2. Fission yield covariance files are in fact unavailable in present nuclear databases such as JEFF-3.2 and ENDF/B-VII. To propagate such uncertainties, we adopted a statistical method which has a solid theoretical base and a relatively simple implementation. Fission yields have been therefore treated as random variables to be sampled from a normal input parameter multivariate distribution, taking into account correlations. Successively, a statistical representative number of calculations are carried out with the different sampled input data. An output multivariate probability distribution for core characteristics is then inferred. Random variable sampling and statistical post-processing has been performed using URANIE, a sensitivity and uncertainty analysis platform based on ROOT. This methodology is applied on a simplified geometry, leaving further developments for more complicated layout to future works.

INTRODUCTION

Future innovative nuclear systems will require strict safety-by-design standards. Accurate uncertainty quantifications of engineering parameters are therefore needed and several efforts have being spent for cross section uncertainty estimation and improvement to upgrade the basic nuclear data knowledge to be applied in nuclear design calculation tools [START_REF] Palmiotti | Combined Use of Integral Experiments and Covariance Data[END_REF].

Fission products yields (FY) are fundamental nuclear data for burn-up and activation calculations, including those on decay heat, shielding, dosimetry, fuel handling, waste disposal and safety [START_REF] Mills | Fission Product Yields Evaluation[END_REF]. Nowadays full uncertainty information are not always available in the actual nuclear database and the nuclear community expressed the need for full fission yield covariance matrices to be able to produce inventory calculation results that take into account complete uncertainty data [START_REF] Fiorito | Fission yield covariance generation and uncertainty propagation through fission pulse decay heat calculation[END_REF][START_REF] Pigni | Investigation of Inconsistent ENDF/B-VII.1 Independent and Cumulative Fission Product Yields with Proposed Revisions[END_REF].

In this work, some FY best estimates and associated uncertainty evaluation methodologies are shown. The main goal is to generate reliable and physically consistent FY covariances and to propagate FY uncertainties in a coupled transport-depletion quasi-static calculation on a simplified geometry. In the present study, we will start talking about mass, isotopic, isomeric and cumulative FY, showing the models we adopted to generate covariances through a Bayesian methodology. Afterwards we describe the development of a straightforward methodology in order to achieve statistical uncertainty quantifications of neutronic parameters, relying on Monte Carlo random or quasi-random sampling of the FY which have been supposed random variables governed by Gaussian multivariate distributions.

The sampling procedures of the FY data, required to generate the input files to be used in the depletion calculation, have been performed through URANIE [START_REF] Gaudier | URANIE: The CEA/DEN Uncertainty and Sensitivity Platform[END_REF]. The "Sensitivity and Uncertainty" platform URANIE developed at CEA provides algorithms and methods to accomplish sensitivity and uncertainty analysis, statistical processing, large-scale data analysis and code validation. URANIE is based on the data analysis framework ROOT, an object-oriented and petaflopic computing system developed at CERN.

In the final part of this work, some preliminary results will be shown, followed by a brief discussion on future developments and improvement of this methodology for more advanced applications.

FY MODELS AND COVARIANCE GENERATION

In this section, a brief description of the fission yield models we used in a Bayesian procedure to estimate covariances will be presented. Covariances can be in fact generated simultaneously together with best estimates using the Generalized Least Square Method (GLSM, see ref. [START_REF] Saint | Uncertainty Evaluation of Nuclear Reaction Model Parameters Using Integral and Microscopic Measurements with the CONRAD Code[END_REF] for further information). To generate covariances, we used the GLSM and the data analysis modules available in CONRAD (COde for Nuclear Reaction Analysis and Data assimilation) developed at CEA-Cadarache [START_REF] Archier | CONRAD Evaluation Code: Development Status and Perspectives[END_REF].

Fission Yield Basic Definitions

Generally it is good practice calling primary fission fragments the isotopes born just after the scission process, before the emission of prompt neutrons [START_REF] Wagemans | The Nuclear Fission Process[END_REF]. Secondary fission fragments are afterwards obtained once prompt neutrons are emitted. We talk about fission products when the radioactive decay comes into play.

Independent FY (IFY) are those referring to secondary fission fragments distribution. IFY are crucial for decay and elementary fission heat calculations since they allow to determine the initial concentration of the fission fragments inventory that will release energy through the radioactive decay. FY are usually differentiated in: 1. Mass FY, which give the distribution of the isobaric fission fragments; 2. Isotopic FY, which take into account the charge distribution for a fixed mass A; 3. Isomeric FY, which consider the isomeric repartition of the fission fragments if metastable states are available.

In the following sections, we will refer to mass IFY by using the symbol Y (A). Since no ternary fission are considered in the present treatment, we obtain

A Y (A) = 2 (1)
Isotopic IFY, denoted as Y (A, Z), are given once the charge distribution is considered through the fraction f (A, Z) such that

Y (A, Z) = Y (A)f (A, Z) (2)
Z Y (A, Z) = Y (A) (3)
Isomeric IFY, denoted as Y (A, Z, M ), where M is the isomeric state that identifies a metastable state (T 1/2 > 1.0 ms), are similarly given by

Y (A, Z, M ) = Y (A, Z)R(A, Z, M ) (4)
M Y (A, Z, M ) = Y (A, Z) (5)
where R(A, Z, M ) is the isomeric ratio that describes the repartition into the available metastable states of the fission fragments.

After the prompt neutron evaporation, the fission fragments are still too rich in neutrons and β - decays are necessary. Usually, a secondary fission fragments is located at 3 charge units far from the β --decay stable line. For nuclei very far from stability, the half-lives are reduced such that for a 6-units far isotope we find T 1/2 = 1 s. To take into account radioactive decay cumulative FY are used. Cumulative FY are in fact the summation of all the contributions to a given isotope overall the entire decay time, since the fission process happened. In formulas [START_REF] Mills | Fission Product Yields Evaluation[END_REF] we can write:

C i = Y i + N j=0 C j b(j → i) (6)
where i indicates a generic triplet (A, Z, M ) i and b(j → i) is the branching ratio which gives the probability that an isomer (A, Z, M ) j decays into (A, Z, M ) i . With N , we have indicated all our fission fragments inventory. In matrix form, the last equation can be written as

C = Q Y (7)
where

Q = (I -B) -1 (8)
indicating with B the branching ratio matrix, with I the identity matrix and finally with C and Y respectively the cumulative and the independent FY vectors.

Isotopic Fission Yield Model

Unfortunately, a precise self-consistent physical model with good predictive capabilities for the fission process cannot be provided yet. The knowledge about fission still has large margins of improvement and many problems are challenging physicists. To generate covariances, we based the GLS analysis on semi-empirical models based on phenomenological postulations. In this section, we will give only a general overview on the models used in this work, without pretending to be exhaustive and leaving the interested reader to specialized references for further research on the topic.

Isomeric IFY can be expressed as:

Y post (A, Z, M ) = ∞ ν i =0 Y pre (A + ν i ) • p A+ν i (ν i ) • f (A + ν i , Z) • R(A, Z, M ) (9)
where we took into account the probability for a primary fission fragment of mass (A + ν i ) to evaporate ν i prompt neutrons. In the Eq. 9, we specified post and pre-neutron distributions to distinguish the yields before and after the prompt neutron emission.

For the mass pre-neutron yields, we used a five-Gaussian distribution representing the Brosa fission modes [START_REF] Brosa | Nuclear Scission[END_REF]. To represent yields after prompt neutron emission, so the independent fission yields, it is necessary to multiply this distribution by the prompt neutron emission probability p A (ν i ). We supposed it based on Gaussian distributions [START_REF] Terranova | Covariance Matrix Evaluations for Independent Mass Fission Yields[END_REF]. The average number of prompt neutron emitted by a primary fragment follows the saw-tooth curve [START_REF] Wagemans | The Nuclear Fission Process[END_REF], responsible for the asymmetry of the post-neutron mass yield distribution.

The charge distribution f (A, Z) has been represented using the Wahl model [START_REF] Wahl | Nuclear charge distribution and delayed neutron yields for thermal neutron induced fission of 235 U, 233 U, 239 Pu and for spontaneous fission of 252 Cf[END_REF]. Wahl developed a semi-empirical model based on the Unchanged Charge Density hypothesis, modified by a correction term to take into account polarization phenomena.

The isomeric ratio R(A, Z, M ) has been calculated using the Madland and England model. Madland and England developed a simplified model to calculate branching isomeric ratio for FY prediction [START_REF] Madland | The Influence of Isomeric States on Independent Fission Product Yields[END_REF], proposing a one-parameter model able to directly provide the ratio R(A, Z, M ).

The Madland-England model is based on the following assumptions [START_REF] Madland | The Influence of Isomeric States on Independent Fission Product Yields[END_REF]:

1. Fission fragments are formed with a density distribution, P (J), of total angular momentum, J, given by

P (J) = P 0 (2J + 1)e -(J+ 1 2 ) 2 J 2 rms , (10)
which is predicted by the statistical model [START_REF] Bethe | Nuclear Physics B. Nuclear Dynamics, Theoretical[END_REF].

2. J rms is constant for all the fragment masses but varies with the incident neutron energy.

3. The branching mechanism is quite straightforward: fragments with J closer to the angular momentum J m or J g decays to the metastable or to the ground state respectively. Fragments with J exactly in the middle between J m and J g follows an equal repartition between both.

APOLLO2 Fission Yields Library Generation

The neutronic code APOLLO2 has the capability to perform burn up calculations in a quasistatic formulation for the Boltzmann and the Bateman equations. The input file is characterized by a list of about 120 fission products for the fast and thermal fission of several actinides. In this work we considered only the thermal fission of 235 U, generating its correlation matrix for APOLLO2 using CONRAD (see Fig. 1). The APOLIB (APOLLO2 library) used in this work is based on the European nuclear data library JEFF-3.1.1. As previously mentioned, no fission yields covariance files are available in JEFF. Our main goal was to reproduce as much as possible the JEFF library for fission yields, including associated covariances. Therefore JEFF files were used as pseudo-experimental data in the adjustment procedure and covariances were produced through the GLSM applied to the models briefly described in the paragraphs before (see ref. [START_REF] Terranova | Covariance Matrix Evaluations for Independent Mass Fission Yields[END_REF]).

The reported fission yields in APOLLO2 are partial cumulative fission yields. Long-lived isotopes are in fact allowed to decay in the evolutionary part of the calculation, when the elapsed time becomes significant compared to the half lives of the considered isotopes. In the next section, the method used in URANIE to sample the fission yields preserving the correlations calculated by CONRAD is explained.

MONTE CARLO SAMPLING OF FISSION YIELDS AS RANDOM VARIABLES

In the last years, many statistical methods have been employed to estimate the uncertainty propagation of cross section uncertainties [START_REF] Kinoshita | Uncertainty Quantification of Neutronics Characteristics using Latin Hypercube Sampling Method[END_REF][START_REF] Yamamoto | Uncertainty Quantification of BWR Core Characteristics Using Latin Hypercube Sampling Method[END_REF][START_REF] Hernandez-Solis | Uncertainty and Sensitivity Analysis Applied to the DRAG-ONv4.05 Code Lattice Calculations and Based on JENDL-4.0 Data[END_REF][START_REF] Diez | Nuclear Data Uncertainty Propagation in Depletion Calculations Using Cross Section Uncertainties in One-group or Multi-group[END_REF][START_REF] Rochman | Nuclear Data Uncertainty Propagation: Perturbation vs. Monte Carlo[END_REF].

In this section, a similar Monte Carlo sampling generally used for cross sections and now applied to fission yields (considered as random variable) is described. Sampled fission yields are successively used in APOLLO2 input files describing a burn-up problem for a highly enriched LWR UOX cell.

The procedure for uncertainty estimation of core characteristic such as k inf using the Monte-Carlo based sampling method is presented in Fig. 2.

Figure 2. Flow chart for the procedure we adopted to estimate the uncertainty associated to core characteristics in a burn-up calculation.

This procedure can be summarized as follows:

1. Evaluation of fission yield covariance matrix for the fast and thermal fission of several actinides.

2. Monte Carlo based sampling of fission yields using URANIE and generation of corresponding input files for APOLLO2 with randomly perturbed FY.

3. Performing of core analysis using each perturbed FY library and then post-processing of the obtained core characteristics.

Let us now describe in the following paragraphs the Monte Carlo sampling procedure performed by the code URANIE and applied in the present work.

FY Monte Carlo Sampling

FY have been considered as random variables following a multivariate normal distribution. Thanks to the URANIE libraries, FY are sampled based on the covariance data previously calculated by CONRAD, and then subsequent burn-up calculations are carried out using the sampled fission yields.

A random variable vector y, which is described by a multivariate normal distribution, can be expressed as:

y = µ + L s ( 11
)
where µ is the mean vector for y which represents the FY vector and s is the multivariate standard normal random vector [START_REF] Kinoshita | Uncertainty Quantification of Neutronics Characteristics using Latin Hypercube Sampling Method[END_REF]. The matrix L is expressed by

L = T √ D (12)
where T and D derive from the Cholesky decomposition of the covariance matrix C = TDT t , since the matrix C is in principle a Hermitian matrix. T is the lower triangular and D is diagonal matrix. The matrix L should give:

C = LL t (13)

Latin Hypercube Sampling

In this paragraph a brief introduction on the latin hypercube sampling (LHS) method is provided. In the LHS, each input parameter domain is subdivided into N intervals, where N is the number of samples [START_REF] Kinoshita | Uncertainty Quantification of Neutronics Characteristics using Latin Hypercube Sampling Method[END_REF]. Such intervals have an identifying number i = 1 • • • N . The N interval numbers for each parameter domain are independently shuffled in order to form P random interval number sequences, where P is the number of parameters.

For example, supposing to have two fission yields y 1,2 that must be sampled N = 10 times, shuffling the interval numbers we generate P = 2 arrays of 10 integers. Each pair formed by elements with the same array index j provides the indices for the sub-domain in the (N × P )dimensional space where perform the j-th uniform random sampling for the parameters. Once all the samples are performed, a N × P matrix R LHS = ( r 1 r 2 • • • r N ) of random numbers is generated. To generate the multivariate standard normal random vector s, the inverse transform is used [START_REF] Kinoshita | Uncertainty Quantification of Neutronics Characteristics using Latin Hypercube Sampling Method[END_REF]. Once the cumulative function is given,

F (s) = s -∞ f (t)dt ( 14
)
where f (t) is the normal distribution, the multivariate standard normal vector can be obtained by solving s = F -1 ( r) for each of the N column of R LHS .

Practical Considerations on the FY sampling

As previously mentioned, we chose to model FY random variables as normal distributions. The first problem we had to face using a symmetric distribution was the negative tails that can be significant for very low FY. In the present work, we did not sample yields smaller than ≤ 10 -9 . Since we were interested mainly on core characteristics, the effects of such FY have been considered negligible. Furthermore URANIE gives the possibility to set bounds in random variable sampling, then negative values were discarded. Positive defined probability distributions can eventually give better results and future developments of this work will analyze the application of such distributions (e.g. the log-normal distribution).

Another interesting point in this statistical uncertainty analysis is the determination of the minimum number of calculations needed to infer a reliable coverage of the output parameter population, with the related confidence. The theory of designing the sample size for non-parametric multivariate tolerance regions [START_REF] Ackermann | Designing the Sample Size for Non-Parametric, Multivariate Tolerance Regions[END_REF] has been proposed and used in several works on uncertainty propagation in nuclear reactor field [START_REF] Hernandez-Solis | Uncertainty and Sensitivity Analysis Applied to the DRAG-ONv4.05 Code Lattice Calculations and Based on JENDL-4.0 Data[END_REF][START_REF] Glaeser | Uncertainty and Sensitivity Analysis of a Post-Experiment Calculation in Thermal Hydraulics[END_REF], and its complete description goes beyond the scope of this section. However, the essential aspects will be here presented for the sake of completeness.

Tolerance limits give a statistical interval where, with a given confidence, a proportion of a sampled population belongs to. Wilks, in his work [START_REF] Wilks | Determination of Sample Sizes for Setting Tolerance Limits[END_REF], calculates the sample size in order to guarantee the coverage of a population (more generally: of a domain), with the required confidence. As also reported in [START_REF] Hernandez-Solis | Uncertainty and Sensitivity Analysis Applied to the DRAG-ONv4.05 Code Lattice Calculations and Based on JENDL-4.0 Data[END_REF], supposing just one output parameter, for the one-sided tolerance limit case the minimum sample size n is given by:

1 -α n = β (15)
to infer the α × 100(%) of the output population with a β × 100(%) of confidence. The coverage of the output population from the (1 -α) × 100(%) to α × 100(%) with a β × 100(%) of confidence is obtained with a sample size given by:

1 -α n -n(1 -α)α (n-1) = β (16)
H. Ackermann and K. Abt [START_REF] Ackermann | Designing the Sample Size for Non-Parametric, Multivariate Tolerance Regions[END_REF], in their work "Designing the sample size for non-parametric, multivariate tolerance regions", provided approximate formulas and tables for the determination of the sample size constructing inner and outer limits for a multivariate tolerance region such as:

n = m χ 2 α,2m 2m -1 √ β + 1 1 -β (17)
where m is a parameter indicating the number of blocks (i.e. the portion of the hyperspace defined by the variables to be sampled) left out the tolerance limits. χ 2 α,2m is the α percentile of the χ 2 distribution with 2m degrees of freedom.

As previously discussed, to set up our methodology of FY uncertainty propagation in burn-up calculations, we tested a simplified geometry performing a statistical processing on core characteristics (see Sec. 4). We chose the several k inf at different burn-up steps as output parameters, subsequently used to calculate the reactivity loss. Eq. 17 allows to construct tolerance regions provided with inner or outer limits, depending on α.

We decided to adopt a sample size of 1000, a value that reasonably showed convergence for the output multivariate distribution. Furthermore, as previously mentioned, we relied on sample size optimization techniques such as the LHS, whose better efficiency against traditional random sampling has been already shown [START_REF] Kinoshita | Uncertainty Quantification of Neutronics Characteristics using Latin Hypercube Sampling Method[END_REF]. It has been demonstrated that for highly correlated output parameters the minimum sample size is lower than for independent non-correlated ones, and we will look for a correlation analysis for the output parameter results as part of the further developments of the method. In the next section a simple burn-up calculation for a PWR-UOx-cell has been set up in order to perform 1000 calculations with different sampled FY data sets.

PRELIMINARY RESULTS ON A HIGHLY ENRICHED PWR CELL

In this section, we present some preliminary results on a simplified geometry implemented in APOLLO2 we decided to use as a test case to develop the present method of FY uncertainties propagation in burn-up calculations. In future developments using this methodology, we will study the possibility to include more complex geometry such as the Jules Horowitz Reactor (JHR), the high flux experimental reactor under construction at CEA-Cadarache. Without entering to much into the details of the neutronic problem, considering that it has just the scope to be a test case for the feasibility of the present methodology, the geometry is mainly constituted by a zircalloy-cladded UOX cell moderated by light water. In Table I the main measures are reported.

The UOX fuel has been set with an enrichment of 19.75 %, because we wanted to start already with some of the JHR reference conditions. The calculations have been performed using the collision probabilities solver available in APOLLO2 with 26 burn-up steps, from 37.5 MW.d.t -1 to 10000 MW.d.t -1 , and a specific power of 100 W.g -1 .

For each sampled data sets of FY coming from 235 U(n th , f ) reaction, a quasi-static problem has been solved with APOLLO2 using a URANIE complementary C++ interface able to generate samples, create APOLLO2 input files and collect k inf at each burn-up step during the depletion calculations.

Results

In Fig. 3 the normalized counts for ∆ρ = ρ EOC -ρ BOL , the reactivity loss at the burn-up step of 10000 MW.d.t -1 , and the relative reactivity loss compared to the nominal case are reported together with a Gaussian distribution. The post-processing has been performed using the estimators for mean and standard deviation to check if the averages were equal to the nominal case and to calculate the associated uncertainties on core characteristics. The ∆ρ are nicely reproduced by a multivariate Gaussian distribution, which shows how the uncertainties on 235 U FY can have considerable effects on the reactor neutronics. The relative reactivity loss distribution shows as the method converges (mean value equal to zero) and gives an estimation of the impact which the fission yield uncertainties, generated in this work, have on cycle length (∼ 1.6%).

This study has shown the feasibility and the relevance of FY uncertainty propagation in burn-up calculations. The simplified geometry has allowed us to perform calculations on single processors and, for future developments of this methodologies in more complex geometries, multi-processing is surely needed.

CONCLUSIONS

In the present work, we have shown a model to propagate FY uncertainties in burn-up calculations. FY covariances, still missing in the actual nuclear databases, have been generated using CONRAD for the thermal fission of 235 U and used in a Monte Carlo Latin Hypercube Sampling to generate several APOLLO2 input files with different FY data sets sampled using URANIE. Performing the statistical post-processing on core characteristic for a simplified geometry, the methodology has given promising results and has shown the importance of FY uncertainty propagation to estimate the uncertainty associated to neutronic parameters.

In future developments of this methodology, more complex geometries will be treated, such as the experimental high flux reactor Jules Horowitz. Besides, more fissioning systems, at thermal and fast incident neutron energies, will be considered in FY covariances generation.

Figure 1 .

 1 Figure 1. Fission yield correlation matrix for the thermal fission of 235 U for the fission products used in APOLLO2 calculations.

Figure 3 .

 3 Figure 3. PDF for the ∆ρ at the burn-up step of 10000 MW.d.t -1 (EOC) and representation of the relative ∆ρ compared to the nominal case.

Table I .

 I Geometry of the PWR-cell used in the APOLLO2 burn-up calculation.

	Cell Characteristics (cm)
	R f uel	0.4098
	R i,cladding	0.4180
	R e,cladding	0.4750
	Square Pitch	1.2620
	4.1 Geometry Description and Calculation Set-Up

ACKNOWLEDGMENTS

The present work has been performed thanks to a research collaboration between the University of Bologna and the CEA (Cadarache), and it is part of the PhD project of the corresponding author. A considerable support has been given in URANIE utilization by the research group of DEN/DER/SPRC/LECy.


A Zoia

J C Trama

S Lahaye

Y Nagaya

Keywords: Criticality, Verification & Validation, MVP, TRIPOLI-4®, MCNP

This paper presents a joint work conducted at CEA Saclay and JAEA Tokai aimed at comparing the Monte Carlo codes TRIPOLI-4® and MVP on a selection of ICSBEP benchmarks. Our goal is to establish a common set of Monte Carlo input decks, as a basis for rigorous inter-code comparison in criticality-safety. As a reference, we will use the MCNP Criticality Validation Suite: other Monte Carlo developers might easily join this effort in the future. For the purpose of inter-code comparison, the TRIPOLI-4® and MVP input decks have been exactly translated from those of MCNP, without any further assumptions. Both TRIPOLI-4® and MVP have been run with the same ENDF/B-VII.0 evaluated nuclear data and, as far as possible, the same simulation options as in the original LANL work (same initial source, same number of active and discarded cycles and neutrons per cycle).

INTER-CODE COMPARISON OF TRIPOLI® AND MVP ON THE MCNP CRITICALITY VALIDATION SUITE E. Brun *

INTRODUCTION

In this work, we will present the joint work conducted at CEA Saclay and JAEA Tokai with the aim of comparing the Monte Carlo codes TRIPOLI-4® [START_REF]TRIPOLI-4®, CEA, EDF and AREVA Reference Monte Carlo Code[END_REF] and MVP [START_REF] Nagaya | MVP/GMVP II: General Purpose Monte Carlo Codes for Neutron and Photon Transport Calculations Based on Continuous Energy and Multigroup Methods[END_REF] on a selection of ICSBEP benchmarks [START_REF]International Handbook of Evaluated Criticality Safety Benchmark Experiments[END_REF]. Our goal is to establish a common set of Monte Carlo input decks, as a basis for rigorous inter-code comparison in criticality-safety. As a reference, we will use the MCNP [START_REF]X-5 Monte Carlo Team[END_REF] Criticality Validation Suite [START_REF] Brown | Verification of MCNP5-1.60[END_REF][START_REF] Brown | Verification of MCNP5-1.60 and MCNP6.1 for Criticality Safety Applications[END_REF]: other Monte Carlo developers might easily join our effort in the future. For the purpose of intercode comparison, the TRIPOLI-4® and MVP input decks have been accurately translated from those of MCNP, without any further assumptions. Both TRIPOLI-4® and MVP have been run with the same ENDF/B-VII.0 evaluated nuclear data and, as far as possible, the same simulation options as in the original LANL work (same initial source, same number of active and discarded cycles and neutrons per cycle). This paper is organized as follows. In section 1, we briefly recall the main features of the TRIPOLI-4® and MVP Monte Carlo codes. Then, in section 2 we present the simulation results obtained on the MCNP Criticality Validation Suite benchmark. Conclusions will be finally drawn in section 3.

TRIPOLI-4® AND MVP MONTE CARLO CODES

In this section, we provide an overview of TRIPOLI-4® and MVP Monte Carlo codes, illustrating their specific features.

TRIPOLI-4®

TRIPOLI® is the generic name of a Monte Carlo radiation transport codes family dedicated to shielding, reactor physics with depletion, criticality safety and nuclear instrumentation. Monte Carlo codes have been continuously developed at CEA since the mid-60s, at Fontenay-aux-Roses first, then at Saclay. The code TRIPOLI-4®, the fourth generation of the family, is the cornerstone of the CEA Radiation Transport Software Suite, which also includes the lattice and core family of deterministic codes dedicated to reactor physics analysis APOLLO2 and APOLLO3® [START_REF] Sanchez | APOLLO2 Year 2010[END_REF], the depletion code MENDEL [START_REF] Lahaye | First verification and validation steps of MENDEL release 1.0 cycle code system[END_REF], the photon pointkernel code with buildup factors NARMER, the nuclear reaction analysis tool CONRAD [START_REF] De Saint-Jean | Status of CONRAD, a nuclear reaction analysis tool[END_REF][START_REF] Archier | Recent Developments in the CONRAD Code regarding Experimental Corrections[END_REF] and the nuclear data processing system GALILEE [START_REF] Coste-Delclaux | GALILEE: a nuclear data processing system for transport, depletion and shielding codes[END_REF]. TRIPOLI-4® is the reference industrial code for CEA (laboratories and reactors), EDF (operating 58 PWRs), and branches of AREVA. It is also the reference code of the CRISTAL Criticality Safety package [START_REF] Gomit | CRISTAL criticality package 12 years later and new features[END_REF] developed with IRSN and AREVA.

The code offers both fixed-source and criticality simulation modes. TRIPOLI-4® can simulate neutral particles: neutrons in the energy range from 20 MeV to 10 -5 eV, and photons in the energy range from 20 MeV to 1 keV. Moreover, electrons and positrons can also be simulated down to 1 keV [START_REF] Pénéliau | Electron photon shower simulation in TRIPOLI-4 Monte Carlo code[END_REF], mainly in the context of radiation detection problems and nuclear instrumentation. Neutron-photon coupling is handled by default. Photonuclear reactions may be simulated as well, if requested. The coupling between photons, electrons and positrons is taken into account by tracking the entire electro-magnetic shower. The particle transport in TRIPOLI-4® is performed in continuous-energy, and the necessary nuclear data (i.e., point-wise cross-sections, scattering kernels, secondary energy-angle distributions, secondary particle yields, fission spectra, and so on) are read by TRIPOLI-4® from any evaluation written in ENDF-6 [START_REF] Mclane | ENDF-102 Data Formats and Procedures for the Evaluation Nuclear Data File ENDF-6[END_REF] format, including (but not limited to) JEFF-3.1.1, ENDF/B-VII.1, JENDL-4.0 and FENDL-2.1 libraries. TRIPOLI-4® can directly access files in ENDF and PENDF format. The probability tables for TRIPOLI-4® for the unresolved resonance range, when present and requested, are generated by using the CALENDF code [START_REF] Sublet | CALENDF-2010: User Manual[END_REF].

MVP

MVP is a general-purpose continuous-energy Monte Carlo code for neutron and photon transport calculations, which has been developed since the late 1980s at Japan Atomic Energy Agency (JAEA). The MVP code is designed for nuclear reactor applications such as reactor core design/analysis, criticality safety and reactor shielding. The main application field is reactor physics: analysis of critical experiments, calculation of reference solutions for reactor core design, etc. The code has been domestically used in Japan since the first release in 1994 [START_REF] Mori | MVP/GMVP: General Purpose Monte Carlo Codes for Neutron and Photon Transport Calculations Based on Continuous Energy and Multigroup Methods[END_REF]. The second version was released in 2005 with extended capabilities based on the advanced Monte Carlo methodology for reactor physics applications [START_REF] Nagaya | MVP/GMVP II: General Purpose Monte Carlo Codes for Neutron and Photon Transport Calculations Based on Continuous Energy and Multigroup Methods[END_REF].

MVP implements fundamental Monte Carlo capabilities for neutron/photon transport based on the evaluated nuclear data. MVP can solve eigenvalue and fixed-source problems for neutron, photon and neutron-photon coupled transport. MVP can also solve time-dependent problems. MVP uses the specific cross section libraries, which are generated from the evaluated nuclear data in the ENDF-6 format with the LICEM code [START_REF] Mori | Production of MVP Neutron Cross Section Libraries Based on the Latest Evaluated Nuclear Data Files[END_REF]. The neutron cross sections in the unresolved resonance region are described by the probability table method. The neutron cross sections at arbitrary temperatures are available for MVP by just specifying the temperatures in the input data. The resolved resonance cross sections are obtained with the SIGMA1 method. The thermal scattering data and the probability tables are obtained with the interpolation of pre-defined temperature points. These data are automatically prepared in prior to random walk.

TRIPOLI-4® AND MVP RESULTS ON THE MCNP CRITICALITY VALIDATION SUITE

In this section, we provide an overview of the simulation results obtained with TRIPOLI-4® and MVP on the MCNP Criticality Validation Suite.

Description of the MCNP Criticality Validation Suite

The MCNP Criticality Validation Suite collects 31 benchmarks taken from the International Handbook of Evaluated Criticality Benchmark Experiments [START_REF]International Handbook of Evaluated Criticality Safety Benchmark Experiments[END_REF]. This suite encompasses several kinds of nuclear fuels: Highly-Enriched Uranium (HEU), Intermediate-Enriched Uranium (IEU), Low-Enriched Uranium (LEU), Plutonium and U-233, each associated with a distinct neutron spectrum. Also, several kinds of geometries, moderators and reflectors are considered. All configurations are evaluated at room temperature and pressure. As such, this Criticality Validation Suite provides an excellent benchmark for the validation of the criticality calculations in Monte Carlo particle transport codes. In Table I

Monte Carlo Simulation Results

In the following, we summarize our numerical simulation results for the effective multiplication factors of the 31 MCNP Criticality Suite configurations. The results have been organized as a function of the nuclear fuel type.

The experimental reactivities for each of the 31 configurations have been collected in reference [START_REF] Brown | Verification of MCNP5-1.60[END_REF] and are reported in the second column of Table II The input deck for ZEBR8H from the MCNP5-1.60 CD-ROM contained a slight inconsistency in material definitions with respect to the original ICSBEP specifications [START_REF]International Handbook of Evaluated Criticality Safety Benchmark Experiments[END_REF]; moreover, the total number of cycles in the CD-ROM was 150, instead of 250 as customary for the other configurations. The former k eff value has been obtained by running MCNP with the material specifications and the number of cycles as in the CD-ROM, whereas the latter value has been obtained running MCNP with the ICSBEP specifications and 250 cycles. TRIPOLI-4® and MVP calculations have been performed using the ICSBEP specifications and 250 cycles.

Discussion

The calculations performed with TRIPOLI-4® show a good agreement with respect to experiments; the multiplication factors of all configurations lie within 3 (combined) standard deviations, except for the ZEBR8H case. The MVP calculations also agree with the experimental values within 3 standard deviations except for ZEUS2, ZEBR8H and THOR. We suspect that for ZEBR8H probability tables might play an important role, which deserves to be further investigated. It should be remarked that the experimental uncertainties are quite large. For ZEUS2, the MVP result differs from that of TRIPOLI-4® by only 15 pcm; however, the difference from the experimental value is larger than 3 standard deviations.

Observe nonetheless that statistical uncertainty might be underestimated due to inter-cycle correlations being neglected. For THOR, the MVP result significantly underestimates the experimental value; however, numerical analyses have shown that this underestimation is strongly affected by the number of simulated cycles: by taking a 1000 active cycles, the resulting multiplication coefficient would be keff = 0.99798 (1 standard deviation = 0.00029).

For the inter-code comparisons, we provide a summary of the absolute differences ∆k in keff for T4-MCNP, MVP-MCNP and MVP-T4 in Tables VII-XI. Differences are expressed in pcm. Combined uncertainties in pcm are also given in parentheses and the number of asterisks expresses the discrepancies in terms of combined standard deviations as in reference [START_REF] Brown | Verification of MCNP5-1.60 and MCNP6.1 for Criticality Safety Applications[END_REF]: * for ∆k exceeding 1 combined standard deviation, ** for 2 combined standard deviations and *** for 3 combined standard deviations. The agreement between the codes is globally satisfactory. However, it should be noted that the largest discrepancies in the inter-code comparisons are found in the IEU configurations; a relatively large number of asterisks is observed in the tables. This could be due to the impact of the probability tables in the intermediate-energy neutron spectrum, for which each code has a specific treatment (NJOY for MCNP, CALENDF for TRIPOLI-4® and U3R-J for MVP).

CONCLUSIONS

In this work, we have presented some preliminary results aimed at extending the verification and validation database of the TRIPOLI-4® and MVP Monte Carlo codes for criticality calculations. As a reference, we have selected here the MCNP Criticality Validation Suite, which provides an ensemble of 31 reactor configurations covering a wide range of neutron spectra. Numerical simulations have shown a satisfactory agreement with respect to MCNP, although further investigations will be needed in order to fully assess the impact of probability tables in the IEU range.

For this work, we have strictly respected, as far as possible, the specifications provided in the MCNP reports concerning the Criticality Validation Suite [START_REF] Brown | Verification of MCNP5-1.60[END_REF][START_REF] Brown | Verification of MCNP5-1.60 and MCNP6.1 for Criticality Safety Applications[END_REF]. In particular, this means that the total number of cycles has been set to 250, which produces Monte Carlo uncertainties compatible with experimental error bars. Future work will focus on reducing the Monte Carlo uncertainties (with special emphasis on the Figure of Merit) and on re-evaluating the corresponding inter-code discrepancy analysis.

Table I . Description of the 31 configurations of the MCNP Criticality Validation Suite (from reference [5]) LEU configurations

 I , are summarized the identifiers of the 31 configurations (classified by fuel type), together with a short description for each case.

	BAWXI2	LEU-COMP-THERM-008, case 2	lattice of PWR fuel pins in borated water
	LST2C2	LEU-SOL-THERM-002, case 2	Bare sphere of (4.9 wt.%) uranium oxyfluoride solution
		Pu configurations
	JEZPU	PU-MET-FAST-001	Bare sphere of Pu
	JEZ240	PU-MET-FAST-002	Bare sphere of Pu (20.1 at.% 240 Pu)
	PUBTNS	PU-MET-FAST-003, case 3	3x3x3 array of small cylinders of Pu
	FLATPU	PU-MET-FAST-006	Pu sphere reflected by normal U
	THOR	PU-MET-FAST-008	Pu sphere reflected by Th
	PUSH2O	PU-MET-FAST-011	Pu sphere reflected by water
	HISHPG	PU-COMP-INTER-001	Infinite, homogeneous mix of Pu, hydrogen and graphite
	PNL2	PU-SOL-THERM-021, case 3	Sphere of Pu nitrate solution
	PNL33	MIX-COMP-THERM-002, case 4	Lattice of mixed-oxide fuel pins in borated water
	Benchmark name	ICSBEP identifier	Description
		U233 configurations
	JEZ233	U233-MET-FAST-001	Bare sphere of 233 U
	FLAT23	U233-MET-FAST-006	Sphere of 233 U reflected by normal U
	UMF5C2	U233-MET-FAST-005, case 2	Sphere of 233 U reflected by beryllium
	FLSTF1	U233-SOL-INTER-001, case 1	Sphere of uranyl fluoride solution enriched in 233 U
	SB25	U233-COMP-THERM-001, case 3	Lattice of 233 U fuel pins in water
	ORNL11	U233-SOL-THERM-008	Large sphere of uranyl nitrate solution enriched in 233 U
		HEU configurations
	GODIVA	HEU-MET-FAST-001	Bare HEU sphere
	TT2C11	HEU-MET-FAST-026, case 11	3x3x3 array of HEU cylinders reflected by paraffin
	FLAT25	HEU-MET-FAST-028	HEU sphere reflected by normal U
	GODIVR	HEU-MET-FAST-004	HEU sphere reflected by water
	UH3C6	HEU-COMP-INTER-003, case 6	Reflected uranium hybride cylindrical assemblies
	ZEUS2	HEU-MET-INTER-006, case 2	HEU platters, graphite moderator, Cu reflector
	SB5RN3	U233-COMP-THERM-001, case 6	Triangular lattice of HEU fuel pins
	ORNL10	HEU-SOL-THERM-032	Large sphere of HEU nitrate solution
		IEU configurations
	IMF03	IEU-MET-FAST-003	Bare sphere of IEU (36 wt.%)
	BIGTEN	IEU-MET-FAST-007	Cylinder of IEU (10wt.%) reflected by normal U
	IMF04	IEU-MET-FAST-004

Sphere of IEU (36 wt.%) reflected by graphite ZEBR8H IEU-MET-FAST-008, case 7 Plate of IEU (37.5 w/o) reflected by U and steel ICT2C3 IEU-COMP-THERM-002, case 3 Lattice of IEU (17 wt.%) fuel rods in water STACY36 LEU-SOL-THERM-007, case 36 Cylinder of IEU (9.97 w/o) uranyl nitrate solution

Table II . Results for the 233 U configurations. name

 II the purpose of the TRIPOLI-4®-MVP inter-code comparison on the MCNP Criticality Suite benchmark, the TRIPOLI-4® and MVP input decks for the 31 configurations have been accurately translated from those of MCNP, without any further assumptions. Both TRIPOLI-4® and MVP have been run with the same ENDF/B-VII.0 evaluated nuclear data and, as far as possible, the same simulation options as in the original LANL work (same initial source, same number of active and discarded cycles and neutrons per cycle). TRIPOLI-4® and MVP results are reported respectively in the fifth and sixth columns of Table II-VI. TRIPOLI-4® calculations are performed by using the collision estimator, whereas MVP adopts the combined estimator. The effects of inter-cycle correlations on the statistical uncertainties are neglected. The input deck for SB5RN3 from the MCNP5-1.60 CD-ROM specifies 150 cycles. The former k eff value has been obtained by running MCNP with the number of cycles as in the CD-ROM, whereas the latter value has been obtained running MCNP with 250 cycles. TRIPOLI-4® and MVP calculations have been performed using 250 cycles.

		Experiment	MCNP	MCNP	TRIPOLI	MVP
		k eff (std)	k eff (std)	k eff (std)	k eff (std)	k eff (std)
	GODIVA	1.0000 (0.0010) 0.9995 (0.0005)	0.99946 (0.00059)	0.99813 (0.00093) 1.00021 (0.00066)
	TT2C11	1.0000 (0.0038) 1.0008 (0.0007)	1.00100 (0.00077)	1.00263 (0.00103) 0.99968 (0.00083)
	FLAT25	1.0000 (0.0030) 1.0034 (0.0007)	1.00343 (0.00066)	1.00335 (0.00091) 1.00272 (0.00066)
	GODIVR	0.9985 (0.0011) 0.9990 (0.0007)	0.99899 (0.00069)	0.99942 (0.00104) 0.99983 (0.00077)
	UH3C6	1.0000 (0.0047) 0.9950 (0.0008)	0.99500 (0.00081)	0.99580 (0.00106) 0.99554 (0.00068)
	ZEUS2	0.9997 (0.0008) 0.9972 (0.0007)	0.99719 (0.00074)	0.99607 (0.00110) 0.99623 (0.00072)
	SB5RN3	1.0015 (0.0028) 0.9985 (0.0013)	0.99847 (0.00131) 0.99774 (0.00092) † 0.99738 (0.00098) 0.99702 (0.00092)
	ORNL10	1.0015 (0.0026) 0.9993 (0.0004)	0.99926 (0.00037)	0.99927 (0.00098) 0.99895 (0.00031)
	Benchmark	Experiment	MCNP	MCNP	TRIPOLI	MVP
	name	k eff (std)	k eff (std)	k eff (std)	k eff (std)	k eff (std)
	IMF03	1.0000 (0.0017) 1.0029 (0.0005)	1.00291 (0.00059)	1.00137 (0.00103)	1.00356 (0.00058)
	BIGTEN	0.9948 (0.0013) 0.9945 (0.0005)	0.99450 (0.00047)	0.99451 (0.00087)	0.99591 (0.00051)
	IMF04	1.0000 (0.0030) 1.0067 (0.0005)	1.00671 (0.00065)	1.00679 (0.00099)	1.00806 (0.00061)
	ZEBR8H	1.0300 (0.0025) 1.0196 (0.0005)	1.01792 (0.00054) 1.01907 (0.00039) †	1.01983 (0.00080)	1.02069 (0.00035)
	ICT2C3	1.0017 (0.0044) 1.0037 (0.0007)	1.00370 (0.00070)	1.00481 (0.00101)	1.00363 (0.00078)
	STACY36	0.9988 (0.0013) 0.9994 (0.0005)	0.99942 (0.00058)	1.00021 (0.00103)	0.99841 (0.00060)
	†
	Benchmark	Experiment	MCNP	MCNP	TRIPOLI	MVP
	name	k eff (std)	k eff (std)	k eff (std)	k eff (std)	k eff (std)
	JEZ233	1.0000 (0.0010) 0.9989 (0.0005) 0.99889 (0.00055) 0.99911 (0.00104)	1.00060 (0.00054)
	FLAT23	1.0000 (0.0014) 0.9990 (0.0007) 0.99904 (0.00072) 0.99806 (0.00095)	0.99940 (0.00069)
	UMF5C2	1.0000 (0.0030) 0.9931 (0.0005) 0.99307 (0.00064) 0.99117 (0.00108)	0.99292 (0.00062)
	FLSTF1	1.0000 (0.0083) 0.9830 (0.0011) 0.98301 (0.00107) 0.98351 (0.00112)	0.98470 (0.00105)
	SB25	1.0000 (0.0024) 1.0053 (0.0010) 1.00528 (0.00101) 1.00167 (0.00106)	1.00511 (0.00111)
	ORNL11	1.0006 (0.0029) 1.0018 (0.0004) 1.00180 (0.00037)	1.00147 (0.00111)	1.00165 (0.00036)

-Table

VI

. The effective multiplication factor computed with MCNP5-1.60 by using the ENDF/BVII.0 nuclear data library are summarized in reference

[START_REF] Brown | Verification of MCNP5-1.60 and MCNP6.1 for Criticality Safety Applications[END_REF]

and have been reported in the third column of Table

II

-Table

VI

. The 31 MCNP input decks, including material description, geometry, and simulation parameters, are available from the CD-ROM of the MCNP5-1.60 release. All MCNP calculations from reference

[START_REF] Brown | Verification of MCNP5-1.60 and MCNP6.1 for Criticality Safety Applications[END_REF]

have been performed by using 250 cycles of 5000 neutrons each, with 50 inactive cycles. All the configurations have been independently re-run by the TRIPOLI-4® and MVP teams by using MCNP5-1.60. Both teams have obtained rigorously the same results, which are reported in the fourth column of Table

II

-Table VI. For †

Table III . Results for the HEU configurations. Table IV. Results for the IEU configurations. Table V. Results for the LEU configurations.

 III

	Benchmark	Experiment	MCNP	MCNP	TRIPOLI	MVP
	name	k eff	k eff (std)	k eff (std)	k eff (std)	k eff (std)
	JEZPU	1.0000 (0.0020) 1.0002 (0.0005) 1.00024 (0.00059) 0.99899 (0.00106)	1.00135 (0.00050)
	JEZ240	1.0000 (0.0020) 1.0002 (0.0005) 1.00019 (0.00055) 0.99896 (0.00094)	1.00064 (0.00063)
	PUBTNS	1.0000 (0.0030) 0.9996 (0.0005) 0.99956 (0.00064) 0.99872 (0.00110)	0.99867 (0.00068)
	FLATPU	1.0000 (0.0030) 1.0005 (0.0007) 1.00050 (0.00070) 1.00055 (0.00102)	0.99948 (0.00067)
	THOR	1.0000 (0.0006) 0.9980 (0.0007) 0.99803 (0.00069) 0.99753 (0.00097)	0.99671 (0.00069)
	PUSH2O	1.0000 (0.0010) 1.0012 (0.0007) 1.00121 (0.00072) 0.99942 (0.00108)	1.00062 (0.00078)
	HISHPG	1.0000 (0.0110) 1.0118 (0.0005) 1.01179 (0.00055) 1.01280 (0.00092)	1.01163 (0.00031)
	PNL2	1.0000 (0.0065) 1.0046 (0.0009) 1.00460 (0.00095) 1.00571 (0.00097)	1.00472 (0.00097)
	PNL33	1.0024 (0.0021) 1.0065 (0.0007) 1.00646 (0.00074) 1.00737 (0.00093)	1.00544 (0.00066)
		1.0007 (0.0012) 1.0013 (0.0007) 1.00133 (0.00069) 1.00312 (0.00096)	1.00074 (0.00054)
	LST2C2	1.0024 (0.0037) 0.9940 (0.0005) 0.99401 (0.00062) 0.99477 (0.00096)	0.99648 (0.00054)

Table VI . Results of the Pu configurations.

 VI

	Benchmark	∆k(T4-MCNP)	∆k(MVP-MCNP)	∆k(MVP-T4)
		(std)	(std)	(std)
	JEZ233	22 (118)	171 (77) **	149 (117) *
	FLAT23	-98 (119)	36 (100)	134 (117) *
	UMF5C2	-190 (126) *	-15 (89)	175 (125) *
	FLSTF1	50 (155)	169 (150) *	119 (154)
	SB25	-361 (146) **	-17 (150)	344 (153) **
	ORNL11	-33 (117)	-15 (51)	18 (117)
	Benchmark	∆k T4-MCNP	∆k MVP-MCNP	∆k MVP-T4
	name	(std)	(std)	(std)
	GODIVA	-133 (110) *	75 (88)	208 (114) *
	TT2C11	163 (129) *	-132 (113) *	-295 (133) **
	FLAT25	-8 (112)	-71 (93)	-63 (112)
	GODIVR	43 (125)	84 (104)	41 (130)
	UH3C6	80 (133)	54 (106)	-26 (126)
	ZEUS2	-112 (133)	-96 (103)	16 (131)
	SB5RN3	-36 (134)	-72 (130)	-36 (134)
	ORNL10	1 (105)	-31 (49)	-32 (103)
	Benchmark	∆k T4-MCNP	∆k MVP-MCNP	∆k MVP-T4
	name	(std)	(std)	(std)
	IMF03	-154 (119) *	65 (83)	219 (118) *
	BIGTEN	1 (99)	141 (69) **	140 (101) *
	IMF04	8 (118)	135 (89) *	127 (117) *
	ZEBR8H	328 (133) **	162 (52) ***	86 (87)
	ICT2C3	111 (123)	-7 (105)	-118 (128)
	STACY36	79 (118)	-101 (83) *	-180 (119) *
	Benchmark	∆k T4-MCNP	∆k MVP-MCNP	∆k MVP-T4
	name	(std)	(std)	(std)
	BAWXI2	179 (118) *	-59 (87)	-238 (110) **
	LST2C2	76 (114)	247 (82) ***	171 (110) *

Table VII . Discrepancy analysis for the 233 U configurations. Table VIIII. Discrepancy analysis for the HEU configurations. Table IX. Discrepancy analysis for the IEU configurations. Table X. Discrepancy analysis for the LEU configurations.

 VII Concerning the T4-MCNP inter-code comparison, the keff values of the 31 configurations all lie within 3 (combined) standard deviations. As for the MVP-MCNP comparison, 29 out of 31 configurations lie within 3 (combined) standard deviations, and large discrepancies have been observed for ZEBR8H and LST2C2. To investigate the case of ZEBR8H, we have performed the criticality calculations without probability tables (i.e., infinite dilution calculations in the unresolved resonance region). TableXIIshows the results obtained for MVP and MCNP with and without probability tables. Without probability tables, the MVP result agrees with that of MCNP within 1 standard deviation; the discrepancy can be thus reasonably attributed to the probability tables. To investigate the case of LST2C2, we have performed multiple criticality calculations for the same geometry starting with different random number seeds. TableXIIIshows the results obtained for MVP and MCNP. The averaged result of MVP agrees with that of MCNP within 2 standard deviations; we might then argue that the discrepancy observed in Table X for LST2C2 may be due to the statistical fluctuations and the underestimation of the statistical uncertainty.

	Benchmark	∆kT4-MCNP		∆kMVP-T4
	name	(std)	(std)	(std)
	JEZPU	-125 (121) *	111 (78) *	236 (117) **
	JEZ240	-123 (109) *	45 (84)	168 (113)*
	PUBTNS	-84 (127)	-89 (93)	-5 (129)
	FLATPU	5 (124)	-102 (97) *	-107 (122)
	THOR	-50 (119)	-132 (98) *	-82 (119)
	PUSH2O	-179 (130) *	-59 (106)	120 (133)
	HISHPG	101 (107)	-16 (63)	-117 (97) *
	PNL2	111 (136)	12 (136)	-99 (137)
	PNL33	91 (119)	-102 (99) *	-193 (114) *

Table XI . Discrepancy analysis for the Pu configurations. Table XII. Comparison between MCNP and MVP for ZEBR8H.

 XI

	Case	k eff (std)	MVP k eff (std)
	MCNP Initial seed = 19073486328125	0.99401 (0.00062)	0.99648 (0.00054)
	MCNP Initial seed = 1	0.99509 (0.00063)	0.99659 (0.00058)
	MCNP Initial seed = 3	0.99693 (0.00060)	0.99562 (0.00053)
	MCNP Initial seed = 5	0.99506 (0.00061)	0.99576 (0.00055)
	MCNP Initial seed = 7	0.99626 (0.00062)	0.99536 (0.00059)
	Average	0.99547 (0.00028)	0.99596 (0.00025)
		1.01907 (0.00039)	1.02069 (0.00035)
	ZEBR8H (without probability tables)	1.00887 (0.00038)	1.00917 (0.00035)

ACKNOWLEDGMENTS

This work has been conducted under the auspices of a technical collaboration (STC 4.2.1) between CEA and JAEA. TRIPOLI-4® is a registered trademark of CEA. The CEA authors gratefully acknowledge EDF long time partnership with TRIPOLI-4® as well as AREVA support.


SUMMARY: Fusion facilities like ITER will produce radioactive waste during operation and dismantling phase. A part of those waste generated by this fusion machine are tritiated waste that have to be managed. One of the main issues in tritiated waste management is the confinement of tritium which presents a good ability to diffusion. One of the solutions is to trap the tritium degassed from waste directly in waste drums. In containers tritium is under gaseous form (HT and T2), tritiated water vapor (HTO and T2O) and some traces of organic bounded tritium species (OBT). As a hydrogen isotope, HT and T2 conversion in HTO and T2O is possible thanks to a reaction with a mix of metal oxides MnO2 and Ag2O [START_REF] Chaudron | Experimental evaluation of hydrogen getters as mitigation technique in a fusion reactor -17 th[END_REF] and tritiated water can be adsorbed on molecular sieve [START_REF] Lefebvre | Procédé et dispositif de réduction du dégazage de déchets tritiés issus de l'industrie nucléaire[END_REF]. This paper aims at describing a methodology of developing a trapper, with an experimental part to obtain results on trapper efficiency and a modeling part to forecast impact of trapper on tritium release rate from waste drum.

1-INTRODUCTION

ITER (International Tokamak Experimental Reactor) is a fusion machine which should demonstrate scientific and technological feasibility of fusion energy by means of D-T fusion reaction. Therefore, most of the solid radioactive waste produced during operation and dismantling phase (around 34000 tons) will result not only from activation by 14 MeV neutrons, but also from contamination by tritium [START_REF]ITER tritiated waste management by the Host state and first lessons learned for fusion development -Fusion Engineering and Design[END_REF]. Because tritiated hydrogen has a good ability to diffusion, one of the main issues in tritiated waste management is the confinement of tritium.

One of the solutions is to trap tritium degassed from waste directly in waste drums. In containers the degassing tritium can be under gaseous form (HT and T2), tritiated water vapor (HTO and T2O) and trace of organic bounded tritium species (OBT), which is not consider in the present work. To guarantee the confinement of tritium under various operating conditions, trappers have to respect some criteria as follows:

 The chemical process has to be irreversible,  The reaction has to have a rapid kinetics and a high trapping capacity,  The chemical process has to work at ambient temperature and atmospheric pressure,  Trapper has to be stable in case of incidental event (high temperature, high pressure…),  No interaction should be observed between trappers and the other radionuclides present in the drum,  Trapper should not require maintenance, because waste drums will be stored many years.

As tritium is a radioactive isotope of hydrogen with a half-life of 12.32 years, the physical and chemical properties of tritium are very similar to those of hydrogen and should react with oxides as hydrogen does. One of the best way to remove hydrogen is to convert hydrogen into water by means of a mix of manganese oxide MnO2 and silver oxide Ag2O with proportions of 90% of MnO2 and 10% of Ag2O [START_REF] Chaudron | Experimental evaluation of hydrogen getters as mitigation technique in a fusion reactor -17 th[END_REF]; according to the undermentioned reactions:

MnO2 + H2  MnO + H2O (1) Ag2O + H2  2Ag + H2O (2)
Moreover, X. Lefebvre et al. found in previous study [START_REF] Lefebvre | Procédé et dispositif de réduction du dégazage de déchets tritiés issus de l'industrie nucléaire[END_REF] that a good efficiency of 30 cm 3 of trapped tritium /g of powder is reached by adding platinum in the mix of MnO2/Ag2O and a zeolith molecular sieve, which offers an adsorption capacity of 20g of water/100 g of sieve to adsorb formed tritiated water.

The present paper aims to describe the different steps forecasted to develop a trapper for tritiated hydrogen inside radioactive waste drum. An experimental study will enable to determine the higher trapper efficiency (with testing different formulation of powders), the conversion reaction kinetics and it will enable to study the mechanism of tritiated water adsorption. Those experimental data will be used for tritium trapping modeling. The modeling part aims to determine the influence of trapper on tritium release rate from a waste drum. To that, a step of diffusion modeling will be done to find tritium release rate without trapper. Then, using kinetics data obtained during the experimental phase, trapping modeling will be established in view to determine the effect of trapper on tritium release rate.

2-STUDY OF TRITIUM TRAPPING

Trapper is a mix of oxidizing powder and molecular sieve. Tritiated hydrogen trapping require two steps. First, tritiated hydrogen molecules H-T and T2 are converted in tritiated water HTO and T2O with oxidizing powder. Then, this water formed is adsorbed irreversibly on molecular sieve.

Conversion reaction

Study of conversion reaction will enable to obtain kinetics data to model tritiated hydrogen reaction inside drum. Twenty powders will be prepared with different formulations in order to find the powder with best efficiency for HT conversion. To that, several tests will be done on a specific facility using hydrogen as a simulant of tritiated hydrogen (see paragraph 2.3).

Oxidizing powders

Formulation of powders

As V.Chaudron shows [START_REF] Chaudron | Experimental evaluation of hydrogen getters as mitigation technique in a fusion reactor -17 th[END_REF], oxidizing powder to convert hydrogen in water is a mix of 90% of MnO2 and 10% of Ag2O. As an add of catalyzers as platinum, palladium and copper to oxidizing powder can have an influence on conversion reaction efficiency [START_REF]Promoter and carrier effects in the reduction of NiO/SiO2[END_REF], four different powders will be prepared to compare catalyzer influence: a reference and three other mixes with an add of 1% of a catalyst. Oxidizing powders are prepared using the same protocol as V.Chaudron [START_REF] Chaudron | Experimental evaluation of hydrogen getters as mitigation technique in a fusion reactor -17 th[END_REF]. Both of oxides MnO2, Ag2O and catalyzer are firstly weighted, crushed in a milling machine and screened. Then, for 20 g of powder, 8 mL of water is added to soak the mix of oxides. Last step consists of heating the powder up to 100°C during 2h to remove any trace of water.

For the soak step, some salt solutions can be used, as: NaOH, KOH, CoSO4 and NiCl2 solutions, which can also improve the efficiency of the powder [START_REF] Charcosset | -Increase of reductibility of NiO by H2, due to pretreatment with salt solutions[END_REF]. So, sixteen other powders will be prepared similarly as the previous ones, but soaked with one of those four solutions as water substituent. Table 1 is a summary of the different powders to study.

Characterization of powders

As specific area of powders can have an influence on efficiency of oxidizing reaction, BET tests will be carried out to highlight relation between specific area and efficiency. As shown in Table 2, a first powder (named powder A, similar to powder number 1) with 90% of MnO2 and 10% of Ag2O was used and BET measurement indicates a very small specific area of 4m²/g, in comparison with other powders. The three other powders coming from previous research [START_REF] Chaudron | Experimental evaluation of hydrogen getters as mitigation technique in a fusion reactor -17 th[END_REF] [3] [START_REF] Lefebvre | Procédé et dispositif de réduction du dégazage de déchets tritiés issus de l'industrie nucléaire[END_REF] show good trapping capacity (which is a way to determine if a powder is efficient or not) with higher specific area. Moreover, with the aim of determining the phenomenological aspects of the trapping phenomena, characterization of this material is foreseen and other measurements will be carried out. Powders sizes will be studied and X-Ray Diffraction (XRD) analysis will be done on powder chosen before and after oxidizing reaction in order to check if compounds were formed during the reaction.

The facility

The study of the conversion reaction is developed in a facility composed of a fixed bed reactor.

As Figure 1 indicates, a mix of hydrogen and argon (as carrier gas) is done in the mixing tank in order to have a gaseous flow with a concentration around 130 Vppm of hydrogen, which corresponds nearly to the concentration of tritiated hydrogen inside package wastes [START_REF] Lefebvre | Theoretical study of the reactivity of mixed manganese and silver oxides on hydrogen simulating tritium for the limitation of outgassing from waste drums -Fusion[END_REF].Then, mixed gases pass inside the reactor which is filled with of reactive powder and glass balls (see Figure 2). There are two analyses equipments to obtain information on conversion reaction:

• A micro-gas chromatograph analyzer R-3000 SRA Instruments®, with a molecular sieve column, which enables to measure concentration of hydrogen during tests, • A hygrometer S4000 Michell Instruments®, which enables to get water concentration so that the mass balance of the reaction can be established.

Determination of trapping capacity

Trapping capacity (Ca),in cm 3 /g of powder, is an important value to determine for each powder because it will enable to find the most efficient powder that will be associated to molecular sieve for the trapping, by comparing experimental results. This physical quantity represents the volume of hydrogen trapped by the mass of powder put in the reactor. The trapping capacity is determined by means of mass balance on hydrogen and water. The amount of hydrogen consumed or water produced can be directly estimated for the breakthrough curves (see Figures 3 and4), which represent the variation of H2 and H2O concentrations at the reactor outlet (Cs). Those graphs will enable to obtain molar quantities of H2 consumed and H2O produced by the reaction, in considering H2 and H2O as perfect gases, formula (1) and ( 2) can be applied.

nH2consumed = Q ∫ (Ce -Cs)dt tf t0 (1) nH2Oproduced = Q ∫ Cs dt tf t0 (2)
Where nH2consumed and nH2Oproduced are molar quantities of consumed hydrogen and produced water. Ce and Cs are, respectively, the inlet and the outlet concentrations (mol/m 3 ) and Q is the volume flow rate (m 3 /s). Trapping capacity is calculated with volume of H2 consumed, at ambient temperature and atmospheric pressure, as:

Ca = VH2consumed mpowder in cm 3 /g (3)
As soon as powder with the best efficiency will be found, study of conversion reaction kinetics will be investigated to obtain reaction rate that will be used in modeling of trapping phenomenon. Experimental conditions will be chosen closed to X.Lefebvre's tests (ambient temperature, atmospheric pressure, 4g of powder, bed thickness of 0,4 cm, 130Vppm of H2 and gas flow around 750 mL/min) [START_REF] Lefebvre | Limitation of tritium outgassing from fusion reactors waste drums : Theoretical aspects of hydrogen oxidation -Fusion engineering and design[END_REF]. Results will be compared to theoretical model Bi-Kinetics Model (BKM) as determined by X.Lefebvre [START_REF] Lefebvre | Theoretical study of the reactivity of mixed manganese and silver oxides on hydrogen simulating tritium for the limitation of outgassing from waste drums -Fusion[END_REF].

Then experiments with adsorber (with capacity of water trapping of 20g of water/100g of adsorber) will be carried out in order to check tritium trapping efficiency of oxidation-adsorption coupling.

After obtained those experimental results, modeling of trapping phenomenon of tritiated species inside waste drum will be developed; it will be assumed adsorber will be in excess in drum to consider tritiated water formed as totally adsorbed, to focus study of diffusion on tritiated hydrogen.

3-STUDY OF TRITIUM DIFFUSION INSIDE DRUM

Behaviour of tritium inside waste

Inside waste, tritium released from the waste may be under different forms : gaseous with HT, T2 and as tritiated water vapor HTO and T2O. At the beginning of radioactive waste drum life, tritium is present in waste inside drum; as Figure 5 shows, tritium is released from waste and then released from drum. In case of chemical molecules, phenomenon to pass through wall drum is called permeation. It is a phenomenon which carried out in about seven steps : molecular dissociation (H-T, T-T, HTO and T2O); adsorption; absorption; diffusion inside metal; desorption; deadsorption and molecular recombination [START_REF] Tison | Influence de l'hydrogène sur le comportement des métaux -Rapport[END_REF]. As diffusion is mainly the limiting step of permeation [START_REF] Tison | Influence de l'hydrogène sur le comportement des métaux -Rapport[END_REF], this study with COMSOL Multiphysics ® software will be focused on diffusion of tritiated species, particularly on HT diffusion because it is more mobile than HTO [START_REF] Lefebvre | Limitation of tritium outgassing from fusion reactors waste drums : Theoretical aspects of hydrogen oxidation -Fusion engineering and design[END_REF] and because it is assumed HTO presents in drum is totally adsorbed with molecular sieve.

Diffusion phenomena through wall drum

Model equations

A cylindric geometry is used in considering an invariance with rotation following ϴ thanks to homogeneity of tritium concentration inside drum. Figure 6 shows specific volume to mass balance.

𝐃𝐃 = 𝟔𝟔, 𝟐𝟐. 𝟏𝟏𝟏𝟏 -𝟕𝟕 𝐏𝐏𝐞𝐞𝐞𝐞( -𝟔𝟔𝟔𝟔𝟔𝟔𝟔𝟔,𝟔𝟔𝟕𝟕 𝐓𝐓 ) in m 2 .s -1 𝐏𝐏𝐏𝐏 = 𝟐𝟐, 𝟑𝟑𝟏𝟏. 𝟏𝟏𝟏𝟏 -𝟕𝟕 𝐏𝐏𝐞𝐞𝐞𝐞( -𝟕𝟕𝟕𝟕𝟑𝟑𝟕𝟕,𝟕𝟕𝟔𝟔 𝐓𝐓 ) in mol.m -1 .s -1 .Pa -1/2
Partial pressure is determined thanks to a specific formula :

P = 𝐀𝐀𝐀𝐀 𝐫𝐫 [𝟏𝟏-(𝟏𝟏-𝛕𝛕) 𝐭𝐭 ]𝐏𝐏 -𝛌𝛌𝐭𝐭 𝐑𝐑𝐓𝐓

𝐟𝐟𝐟𝐟𝛌𝛌𝐟𝐟𝐟𝐟

With : Am: specific activity of tritium in waste at time 0 (Bq/g), r: packing factor (t.m -3 ), 𝛕𝛕: outgassing rate of waste inside drum, f: void fraction inside drum, Na: Avogadro's number, R: constant of perfect gases V: internal volume of the drum, and other terms are defined before.

Formula of partial pressure of tritiated hydrogen in the package is obtained with perfect gases law such as : This modeling step will enable to obtain quantity of tritium release outside drum over time because of diffusion phenomenon.

4-COUPLING OF BOTH PHENOMENA AND PARAMETRIC STUDY

For coupling of both phenomena, mass balance is written with an added reaction kinetics term beforehand determined with experimental tests: Where R is the term corresponding to trapping influence on tritium release, in mol/m 3 /s. Different parameters will be used to know the real impact they have on tritium release. Wall drum thickness and internal temperature are two main parameters that can be varied to analyze their influence on tritium release. Then for modeling, variation of wall drum thickness with a value between 3 and 5 mm and variation of internal temperature with a value between 40 and 60°C will be tested.

Figure 1 :

 1 Figure 1 : Schematic representation of the facility

Figure 3 :Figure 4 :

 34 Figure 3 : Ideal breakthrough curve of hydrogen (t0 represents the beginning of the experiment)

Figure 5 :

 5 Figure 5 : Tritium release

3. 2 . 1 

 21 Hypothesis and experimental conditions Diffusion Model development of tritiated hydrogen through wall drum, is based on different assumptions: Tritium concentration inside drum is homogeneous,  Tritium concentration outside drum is null,  Internal and external temperatures are considered constant,  Drum material is stainless steel,  Drum is a cylinder,  Tritium degassing rate of wastes per year depends linearly to the inventory of tritium in the waste,  Void fraction inside drum is not null,  Drum is considered welded and water-resistant,  At time 0 wall drum does not contain tritiated molecules.

Figure 6 :

 6 Figure 6 : Calculation conditions

Figure 7 :

 7 Figure 7 : Boundary conditions

  amout of HT released in the package by the waste such as: nreleased = n0[1 -(1 -τ) 𝑡𝑡 ]𝑒𝑒 -𝜆𝜆𝑡𝑡 , where n0 = 𝐴𝐴𝐴𝐴.𝑟𝑟.𝑉𝑉 𝜆𝜆.𝑁𝑁𝑁𝑁And Vvoid is the void volume inside drum = f.V.

  𝟐𝟐 𝐂𝐂(𝐫𝐫,𝐳𝐳,𝐭𝐭) 𝛛𝛛𝐳𝐳 𝟐𝟐 ) = -λ.C(r,z,t) + R

Table 1 :

 1 Composition of the different powders to study

	Powder	Composition	% MnO2	% Ag2O	% Catalyst	Solution of
						impregnation
	1	MnO2/Ag2O	90	10	0	Water
	2	MnO2/Ag2O + Pt	89	10	1	Water
	3	MnO2/Ag2O + Pd	89	10	1	Water
	4	MnO2/Ag2O + Cu	89	10	1	Water
	5	MnO2/Ag2O	90	10	0	KOH
	6	MnO2/Ag2O + Pt	89	10	1	KOH
	7	MnO2/Ag2O + Pd	89	10	1	KOH
	8	MnO2/Ag2O + Cu	89	10	1	KOH
	9	MnO2/Ag2O	90	10	0	NaOH
	10	MnO2/Ag2O + Pt	89	10	1	NaOH
	11	MnO2/Ag2O + Pd	89	10	1	NaOH
	12	MnO2/Ag2O + Cu	89	10	1	NaOH
	13	MnO2/Ag2O	90	10	0	CoSO4
	14	MnO2/Ag2O + Pt	89	10	1	CoSO4
	15	MnO2/Ag2O + Pd	89	10	1	CoSO4
	16	MnO2/Ag2O + Cu	89	10	1	CoSO4
	17	MnO2/Ag2O	90	10	0	NiCl2
	18	MnO2/Ag2O + Pt	89	10	1	NiCl2
	19	MnO2/Ag2O + Pd	89	10	1	NiCl2
	20	MnO2/Ag2O + Cu	89	10	1	NiCl2

Table 2 :

 2 Comparison with results in literature

		Lefebvre's	Powder	Chaudron's	Galliez's
		powder [5]	A	powder[2]	powder [3]
	Composition	90%MnO2 10%Ag2O	90%MnO2 10%Ag2O	90%MnO2 10%Ag2O	87%MnO2 13%Ag2O
	Operating conditions	1,2bar -25°C 0,01% H2	1,2bar -25°C 0,01% H2	2bar -25°C 50%H2	1,6bar -25°C 4%H2
	Trapping capacity (cm 3 /g)	23	2,23	42,5	76,4
	Specific area (m²/g)	68,6	4,7	82	161

Table 3

 3

is describing the different values of operating conditions.

Table 3 :

 3 Operating conditions

	Temperature (°C)	Pressure (bar)	Powder	Ar flow rate	H2 flow rate
			mass (g)	(L/min)	(mL/min)
	16-25	1-1,3	1-4	0,2-7	0,1-4

5-CONCLUSIONS

Trapper is an association of oxidizing powders, which may contain a catalyzer (Pt, Pd or Cu) and remains of salts, to convert HT and T2 in tritiated water, and adsorber, to catch HTO and T2O. This present work, coupling experimental and modeling, will determine the real impact of the trapper proposed on tritium release rate from a radioactive waste drum in which one tritium trapper was filed.

Next papers will develop results of experimental tests, conversion reaction kinetics and modeling.