Michael Johnson

Christophe Journeau

Ken-Ichi Matsuba

Yuki Emura

Kenji Kamiyama

Characterization of high-temperature nuclear fuel-coolant interactions through X-ray visualization and image processing

Keywords: fuel-coolant interaction, sodium-cooled fast reactor, X-ray image processing, particle tracking, fuel debris Graphical

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

French and Japanese organizations are collaborating on sodium-cooled fast-neutron reactors (SFRs), which offer the prospect of low-carbon energy production, combined with sustainable use of uranium resources. A particular focus of this research concerns severe accidents in SFRs. In the hypothetical case of a core-disruptive accident (CDA), caused by, for instance, an unprotected loss of flow, the nuclear fuel would rapidly melt. To mitigate the prompt criticality risk, corium discharge tubes are designed to relocate molten nuclear fuel outside the core area before a high reactivity is reached [START_REF] Bertrand | Status of severe accident studies at the end of the conceptual design of ASTRID: Feedback on mitigation features[END_REF]. The discharge of a coherent jet of molten core material, through these corium discharge tubes [START_REF] Bertrand | Status of severe accident studies at the end of the conceptual design of ASTRID: Feedback on mitigation features[END_REF], or control rod guide tubes [START_REF] Tobita | Development of the evaluation methodology for the material relocation behavior in the core disruptive accident of sodium-cooled fast reactors[END_REF], to the core catcher plenum of the SFR [START_REF] Journeau | Corium-Sodium and Corium-Water Fuel-Coolant-Interaction Experimental Programs for the PLINIUS2 Prototypic Corium Platform[END_REF] presents a number of significant heat and mass transfer challenges for nuclear engineers.

SFRs potentially offer significant advantages over water-cooled reactors during a loss of electrical power, as the large safety margin to the coolant boiling temperature and enhanced coolant specific heat capacity improve the capacity for decay heat removal by natural convection. Nonetheless, ensuring containment integrity and maintaining in vessel retention of the molten fuel during a post-accident scenario remains essential. Experimental investigation of fuel-coolant interactions (FCI) is critical to understanding the dynamics of melt fragmentation, debris bed formation, the potential for energetic vapor explosions [START_REF] Journeau | Corium-Sodium and Corium-Water Fuel-Coolant-Interaction Experimental Programs for the PLINIUS2 Prototypic Corium Platform[END_REF], and for validating FCI modeling codes such as SCONE [START_REF] Zabiégo | The SCONE software for corium-sodium interaction[END_REF].

The optical opacity of sodium presents additional challenges, beyond those in water-cooled reactors, for the experimental visualization of FCIs. In the absence of such visual data, significant conclusions have been drawn from in situ temperature and pressure measurements and post-interaction debris characterization. The greatly enhanced thermal effusivity ( c p ρλ) of sodium, relative to water, dictates that the initial interface temperature between molten fuel and coolant is closer to that of the coolant. This reduces the potential for stable film boiling at the melt coolant interface [START_REF] Schins | Boiling and fragmentation behaviour during fuel-sodium interactions[END_REF], although film boiling can still be achieved when the sodium is close to saturation [START_REF] Magallon | Pouring of 100-kg-Scale Molten UO2 into Sodium[END_REF] or substantial melt superheats are observed [START_REF] Hu | Fragmentation characteristics of molten materials jet dropped into liquid sodium pool[END_REF]. This implies a departure from the classical explosion model [START_REF] Corradini | Vapor explosions in light water reactors: A review of theory and modeling[END_REF][START_REF] Berthoud | Vapor Explosions[END_REF], characterized by rapid heat transfer in the aftermath of the sudden destabilization of the vapor film [START_REF] Sher | Film boiling collapse in solid spheres immersed in a sub-cooled liquid[END_REF]. The collapse of unstable vapor pockets extending from the melt surface during nucleate or transition boiling regime would explain the sequence of, typically weak [START_REF] Mizuta | Fragmentation of uranium dioxide after molten uranium dioxide-sodium interaction[END_REF], pressure pulses observed during interactions between alumina and uranium oxide with sodium [START_REF] Mizuta | Fragmentation of uranium dioxide after molten uranium dioxide-sodium interaction[END_REF][START_REF] Schins | Boiling and fragmentation behaviour during fuel-sodium interactions[END_REF] in contrast to the solitary but pronounced pressure spikes on vapor film destabilization in water-cooled environments [START_REF] Zabiégo | The KROTOS KFC and SERENA/KS1 tests: experimental results and MC3D calculations[END_REF]. The pressure buildup in the gas-filled ullage during 100 kg scale UO 2 -Na interactions at the FARO-TERMOS facility [START_REF] Magallon | Pouring of 100-kg-Scale Molten UO2 into Sodium[END_REF] was similarly modest in magnitude and no shock wave was observed. Furthermore, the elevated pressures were only observed once the, initially cool (627 K), coolant approached saturation temperature within the mixing zone.

Sodium interactions have also been observed to differ from fuel-water interactions in terms of fragmentation dynamics, implied from their characteristic debris morphologies. Intermediate-scale (< 4 kg melt) interactions between prototypic oxide fuel melts and sodium at the BETULLA facility [START_REF] Schins | Boiling and fragmentation behaviour during fuel-sodium interactions[END_REF] revealed both smooth, high-sphericity debris and fractured particles exhibiting irregular morphologies with significantly enhanced specific surface areas. Similarly irregular debris morphologies were observed for alumina [START_REF] Toyooka | Experimental discussion on fragmentation mechanism of molten oxide discharged into a sodium pool[END_REF] and metallic copper and aluminum melts [START_REF] Hu | Fragmentation characteristics of molten materials jet dropped into liquid sodium pool[END_REF]. The smooth debris population is thought to result from hydrodynamic fragmentation, which is greatly enhanced in the presence of a vapor flux counter-current to the jet [START_REF] Schins | Boiling and fragmentation behaviour during fuel-sodium interactions[END_REF]. The rough-surfaced, irregular debris morphologies are better explained by thermal fragmentation events [START_REF] Schins | Boiling and fragmentation behaviour during fuel-sodium interactions[END_REF][START_REF] Tyrpekl | Material effect in the nuclear fuel-coolant interaction: Analyses of prototypic melt fragmentation and solidification in the KROTOS facility[END_REF]. The diminished temperature at the melt-coolant interface is thought to promote rapid solidification of the outer melt surface [START_REF] Iwasawa | Melt jet-breakup and fragmentation phenomena in nuclear reactors: A review of experimental works and solidification effects[END_REF][START_REF] Uršič | Eulerian modelling of melt solidification impact during fuel-coolant interaction[END_REF][START_REF] Iwasawa | Scaling analysis of melt jets and solidification modes[END_REF]. Extreme temperature gradients across a thin outer crust layer, shrinkage cracking of the crust, [START_REF] Schins | Break up time of fragmenting-solidifying UO2 spheres when quenched in sodium[END_REF], pressurization of the internal liquid-phase melt [START_REF] Mizuta | Progress report on the molten UO2 drop experiment[END_REF][START_REF] Peng | Preliminary study on the fuel-coolant interaction triggered by thermal effect[END_REF] and the rapid vaporization of entrained coolant [START_REF] Gross | Characterization of Fragmented Fuel From a Thermal Fuel-Sodium Interaction[END_REF][START_REF] Fauske | On the Mechanism of Uranium Dioxide-Sodium Explosive Interactions[END_REF] may all impose mechanical stresses on the melt crust and instigate thermal fragmentation.

Characterization of FCIs for water-cooled reactor reactor configurations has included droplet scale (< 0.7 g) investigations of the fragmentation mechanism with molten tin [START_REF] Park | Fine fragmentation of molten droplet in highly subcooled water due to vapor explosion observed by X-ray radiography[END_REF][START_REF] Hansson | Simultaneous high speed digital cinematographic and X-ray radiographic imaging of a intense multi-fluid interaction with rapid phase changes[END_REF], intermediate-scale (150-650 g) experiments with low-temperature Wood's metal [START_REF] Acharya | Investigation of molten fuel coolant interaction phenomena using real time X-ray imaging of simulated woods metal-water system[END_REF][START_REF] Bang | Experiment and modeling of jet breakup in fuel-coolant interactions[END_REF], tungsten-bismouth oxides [START_REF] Manickam | On the fragmentation characteristics of melt jets quenched in water[END_REF], aluminum, lead and bismuth [START_REF] Lu | Visual investigation on the breakup of high superheated molten metal during FCI process[END_REF], and kilogram-scale (2-6 kg) tests using prototypic corium [START_REF] Zabiégo | The KROTOS KFC and SERENA/KS1 tests: experimental results and MC3D calculations[END_REF][START_REF] Brayer | Analysis of the KROTOS KFC test by coupling X-Ray image analysis and MC3D calculations[END_REF][START_REF] Brayer | Application of X-Ray radioscopy for investigations of the 3-phase-mixture resulting from the fragmentation of a high temperature molten material jet in water[END_REF][START_REF] Singh | X-Ray diagnostics on corium-sodium interactions during a severe accident scenario[END_REF]. These tests have enabled the visualisation of hydrodynamic jet fragmentation during premixing [START_REF] Brayer | Application of X-Ray radioscopy for investigations of the 3-phase-mixture resulting from the fragmentation of a high temperature molten material jet in water[END_REF][START_REF] Manickam | On the fragmentation characteristics of melt jets quenched in water[END_REF] and the propagation of melt fragment clouds after an explosion was triggered [START_REF] Park | Fine fragmentation of molten droplet in highly subcooled water due to vapor explosion observed by X-ray radiography[END_REF][START_REF] Hansson | Simultaneous high speed digital cinematographic and X-ray radiographic imaging of a intense multi-fluid interaction with rapid phase changes[END_REF]. The potential for X-ray visualization to elucidate an alternative fragmentation regime predicted for SFRs has not yet been fully realised. An X-ray device was employed at the THINA facility for 5 kg-scale interactions between iron/alumina melts and sodium [START_REF] Kaiser | Experiments on the behaviour of a hot melt injected into sodium[END_REF], for an alternative experimental configuration where the melt is injected into the coolant from below. However, the X-ray imaging appears to use a limited number of photodiodes purely to obtain an estimate of the sodium void fraction as a function of [START_REF] Matsuba | Distance for fragmentation of a simulated molten-core material discharged into a sodium pool[END_REF] time, rather than to provide a detailed view of the multi-phase interaction. A higher specification X-ray imaging system was used to observe the interaction between 0.9 kg aluminum and sodium at the MELT facility [START_REF] Matsuba | Distance for fragmentation of a simulated molten-core material discharged into a sodium pool[END_REF]. The enhanced X-ray imaging revealed local coolant boiling and vapor expansion which lead to rapid jet fragmentation shortly after quenching, before the propagation of a hydrodynamic jet instability [START_REF] Matsuba | Distance for fragmentation of a simulated molten-core material discharged into a sodium pool[END_REF]. The rapid fragmentation resulted in a large increase in melt-coolant heat transfer area, accelerating melt cooling and inhibiting subsequent hydrodynamic fragmentation. The X-ray imaging presented with artefacts and limitations in pixel resolution which suggest that extensive post-processing would be required for a detailed and quantitative characterization of the interaction [START_REF] Matsuba | Distance for fragmentation of a simulated molten-core material discharged into a sodium pool[END_REF].

A new experimental investigation of a kilogram-scale interaction between molten stainless steel and sodium is presented, using X-ray visualization to supplement ex situ debris analysis. To maximize these radiographic data, a new software program, SPECTRA (Software for Phase Extraction and Corium Tracking Analysis), is under development at the CEA for the processing of X-ray images acquired during FCI experiments in sodium and water-cooled environments alike. In particular, this study presents novel algorithms for the tracking of discrete melt fragments through the imaging window, alongside approaches for the segmentation and 3D reconstruction of individual melt fragments from the 2D X-ray images.

Materials and methods

As part of a series of FCI experiments being performed by JAEA at the MELT test facility in Oarai, Japan, an FCI experiment, FCINA-30-1, was conducted between kilogram-scale (< 5 kg) stainless steel 316 at 1973 K and 573 K sodium. The main objective of this FCI experiment is to confirm the fragmentation behavior revealed by previous experiments conducted at the MELT facility [START_REF] Matsuba | Distance for fragmentation of a simulated molten-core material discharged into a sodium pool[END_REF] using more representative prototypic reactor materials. Stainless steel 316 was chosen as a suitable analogue for the stainless steel cladding used for SFR fuel elements; the thermophysical properties of stainless steel 316 are characterized in Chawla et al. [START_REF] Chawla | Thermophysical properties of mixed oxide fuel and stainless steel type 316 for use in transition phase analysis[END_REF]. The MELT facility consists of a furnace and melt delivery system, a test section with associated in situ instrumentation, a debris catcher and an X-ray imaging device; a schematic is presented in Figure 1. The stainless steel was heated in the furnace crucible to 1973 K and then discharged, via an intermediate tip tray, necessary to isolate the furnace from the test section, through a centimetre-scale (< 50 mm) nozzle to the sodium pool beneath an argon-filled ullage. The majority of results will be thus presented in dimensionless form after normalization by the nozzle diameter, D 0 , initial jet velocity, v 0 , and the mass of debris recovered at the end of the experiment, m d :

L = L D 0 , Ṽ = V D 0 3 , ṽ = v v 0 , m = m m d , t = tv 0 D 0 (1)
In situ temperature data were monitored at eight thermocouples, mounted along the height of the test section on a steel support. The 110 mm internal diameter test section contains an interior debris catcher and an Al 2 O 3 thermal insulation cylinder, which reduce the effective working diameter of the interaction region to 78 mm. Radiographic images of the test section were captured for a 1.5 s duration at a frame rate of 1000 fps using the 1.8 kW rated X-ray imaging device. The X-ray source was optimized to the radiodensity of the test section and its contents during preparatory tests performed using phantom models [START_REF] Singh | X-Ray diagnostics on corium-sodium interactions during a severe accident scenario[END_REF][START_REF] Berge | Fast High-Energy X-Ray Imaging for Severe Accidents Experiments on the Future PLINIUS-2 Platform[END_REF], constructed from polyoxymethalene (POM) thermoplastic as an analogue for the sodium coolant (see Figure A.1a); optimum image contrast was obtained by operating the X-ray tube at 115 kV and 9 mA, corresponding to 1.04 kW power. These X-ray images acquired during FCINa-30-1, along with post-experiment debris analysis, will be the focus of this work. The in situ temperature data is outside the scope of this study.

X-ray image processing

SPECTRA has been developed using the App Designer platform in Matlab 2018b (Mathworks, USA). Its functionality encompasses a number of processing steps for the suppression of X-ray imaging artefacts, the segmentation or isolation of a studied phase, the tracking of discrete objects through time and space, the reconstruction of objects in 3D and the characterization of objects' size and shape factors. X-ray imaging, particularly when operated in conjunction with image intensification, can be subject to significant Gaussian noise and other imaging artefacts including, but not limited to, vignetting (the decay in intensity towards the image border) [START_REF] Berge | Fast High-Energy X-Ray Imaging for Severe Accidents Experiments on the Future PLINIUS-2 Platform[END_REF] and pincushion distortion [START_REF] Cowen | The design and imaging characteristics of dynamic, solid-state, flat-panel X-ray image detectors for digital fluoroscopy and fluorography[END_REF]. The characterization and suppression of these artefacts is fundamental to the accurate segmentation of the melt and vapor phases from the raw images. Observations from the FCINA-30-1 experiment, from several previous FCI experiments employing X-ray visualization [START_REF] Matsuba | Distance for fragmentation of a simulated molten-core material discharged into a sodium pool[END_REF][START_REF] Brayer | Analysis of the KROTOS KFC test by coupling X-Ray image analysis and MC3D calculations[END_REF][START_REF] Loewen | Fuel-Coolant Interactions: Visualization and Mixing Measurements[END_REF], and from X-ray images acquired using phantoms for calibration [START_REF] Singh | X-Ray diagnostics on corium-sodium interactions during a severe accident scenario[END_REF], a general procedure is outlined in Figure 2 detailing the various processing stages recommended to suppress imaging artefacts and isolate the melt and vapor phases from raw X-ray images prior to quantitative analysis. The various image pre-processing techniques employed within this workflow are detailed in Sections 2.1.1 to 2.1.6.

Noise reduction

Local averaging techniques such as mean, median and Gaussian filters should be avoided in preference of more selective denoising filters which better distinguish noise from fine textures. This is crucial for extracting features with low signal-to-noise ratios and those close to the pixel resolution in scale. A non-local approach which preferentially averages pixels exhibiting neighborhoods of high similarity, such as the NL-means filter [START_REF] Buades | A Review of Image Denoising Algorithms, with a New One[END_REF], is recommended.

Correction for vignetting by flat field normalization

The detected images, I d , prior to the melt arrival can be averaged to provide a suitable background, or flat field, image, I BKG , of a test section containing only the liquid coolant phase at rest. The detected images and the averaged background image are offset by an averaged dark field image, I dc , acquired In addition, flat field normalization greatly simplifies the relationship between the image intensity and the depths, or chord lengths, of the desired melt and vapor phases normal to the image, l m and l v respectively. The X-ray imaging system consists, in simplest terms, of an X-ray source, which is attenuated by the test section and its contents, before detection at a scintillator screen, which projects a photon flux in the visible spectrum at its rear surface onto a high speed CCD camera with a linear response to incident light [START_REF] Brayer | Application of X-Ray radioscopy for investigations of the 3-phase-mixture resulting from the fragmentation of a high temperature molten material jet in water[END_REF]. A photon balance between the X-ray source and the camera can be described by eq. ( 2) [START_REF] Macovski | Medical imaging systems[END_REF]:

I d (x, y) = I dc (x, y) + α max 0 η( )I S (x, y; ) exp - l 0 µ(x, y, z; )dz d (2)
where I S is the unattenuated photon source intensity, α and η( ) are the gain factor and the energy, , dependant detection efficiency of the scintillator respectively, and µ(x, y, z; ) describes the attenuation properties of materials in the photon path as a function of space and photon energy. Assuming a hardened X-ray source with a narrow energy spectrum, approaching a monochromatic source, eq. ( 2) simplifies to the Beer-Lambert relationship for 'N ' attenuating materials:

I d (x, y) = I dc (x, y) + α η ĪS (x, y) exp - N n=1 µ n l n (x, y) (3)
Taking the natural logarithm of the flat field normalized image, I ln , eliminates the dark current contribution, the scintillator efficiency and gain terms, the photon source strength and N -2 attenuation terms corresponding to the coolant and vessel infrastructure components, rendering a simplified expression containing only melt and vapor chord lengths [START_REF] Park | Fine fragmentation of molten droplet in highly subcooled water due to vapor explosion observed by X-ray radiography[END_REF][START_REF] Brayer | Application of X-Ray radioscopy for investigations of the 3-phase-mixture resulting from the fragmentation of a high temperature molten material jet in water[END_REF]:

I ln = ln ∆G ∆G BKG = l v (µ c -µ v ) + l m (µ c -µ m ) ≈ l v µ c + l m (µ c -µ m ) (4)
where µ m , µ c and µ v are the linear attenuation coefficients of the melt, coolant and vapor phases respectively (the latter being negligible in comparison with the two previous coefficients).

Correction for geometric distortion

Intensification of X-ray images with a relatively large field of view (FOV) frequently results in magnification towards the image border, or pincushion distortion [START_REF] Cowen | The design and imaging characteristics of dynamic, solid-state, flat-panel X-ray image detectors for digital fluoroscopy and fluorography[END_REF]. The radial undistortion function presented by Vass and Perlaki [START_REF] Vass | Applying and removing lens distortion in post production[END_REF] is employed to ensure homogeneous pixel resolution across the images. Following correction for geometric distortion, the pixel resolution is estimated to be 116 µm.

Correction for void attenuation

Since µ m > µ c >> µ v , attenuation relative to the coolant in the background image is augmented by the melt (I ln < 0) and diminished by vapor clouds (I ln > 0). The competing attenuation effects of melt and vapor occupying the same photon path raises the potential for vapor to obscure the visibility of melt fragments and vice versa. When l v µ c ≈ l m (µ m -µ c ) the pixel intensity exhibits negligible contrast with the coolant phase, greatly complicating phase segmentation. To maximize the proportion of melt detected by image analysis, the processed image should be adjusted for the void attenuation effects prior to melt segmentation.

First, a binary mask of the vapor-filled regions is extracted by thresholding the I ln image. Second, the holes in this binary mask, where melt fragments are visible within the vapor cloud, are filled by a morphological closing operation, involving dilation, filling of enclosed regions and subsequent erosion of the mask. The vapor cloud silhouette is then reconstructed in 3D by processing the mask with the superposition of spheres model (SSM) detailed in Section 2.1.6.2. The algorithm generates a stack of images mapping the estimated chord lengths through the vapor clouds in the depth field, normal to the image, l v . The product of these chord lengths with the attenuation coefficient for liquid sodium can be used to offset the experimental images, generating a void corrected image, I vc :

I vc = l v µ c -I ln = l m (µ m -µ c ) (5)
2.1.5. Phase segmentation Since the pixel intensity has been rendered homogeneous by flat field normalization, global thresholding is sufficient to segment each phase. Melt, I m and vapor, I v images are obtained by masking the regions of the void corrected and log-normalized images which exceed the magnitude of any residual image noise, σ:

I m = I vc > σ I v = I ln > σ (6)
2.1.6. 3D reconstruction Three approaches are presented for estimating the chord lengths through objects normal to the image, or object depths, for the reconstruction of objects in 3D. These include the (1) linear attenuation (LAM), (2) superposition of spheres (SSM) and ( 3) hybrid (HM) methods respectively.

Linear attenuation method (LAM)

Following flat field normalization, void correction and thresholding, the photon balance in eq. ( 2) is reduced to a simple linear relationship between the intensity of the processed image pixel and the chord length through the melt phase, requiring only the linear attenuation coefficients of the coolant and melt to fully reconstruct the melt fragments [START_REF] Hansson | Simultaneous high speed digital cinematographic and X-ray radiographic imaging of a intense multi-fluid interaction with rapid phase changes[END_REF][START_REF] Brayer | Application of X-Ray radioscopy for investigations of the 3-phase-mixture resulting from the fragmentation of a high temperature molten material jet in water[END_REF]:

l m = 1 µ m -µ c l v µ c -ln ∆G ∆G BKG > σ (7)
The validity of eq. ( 7) relies on the fundamental assumptions that the X-ray source is temporally stable and exhibits an approximately monochromatic energy spectrum. The mass attenuation coefficients of sodium and stainless steel 316 have been characterized in the literature [START_REF] Hubbell | X-Ray Mass Attenuation Coefficients[END_REF][START_REF] Singh | Study of mass attenuation coefficients, effective atomic numbers and electron densities of carbon steel and stainless steels[END_REF]. Using the densities of sodium and stainless steel at their initial temperatures of 573 and 1973 K, the linear attenuation coefficients in the 69-81 keV range are 0.166 ± 0.014 and 4.728 ± 1.105 cm -1 respectively. The variance in the linear attenuation coefficients reflects the uncertainty in the photon energy spectrum, manifesting in significant uncertainty of up to 34 % in the predicted melt depths, and thus an alternative approach may be required.

Superposition of spheres method (SSM)

For cases where the X-ray source is not monochromatic or temporally stable, or the attenuation coefficients are not well characterized, it may be necessary to reconstruct the 3D volume from the geometry of the 2D silhouette alone. Extrapolating a third dimension from a solitary silhouette requires some gross assumptions regarding the object geometry, however certain geometric assumptions can be justified for near cylindrical coherent jets, high sphericity jet fragments or vapor clouds. First, a Euclidean distance transform (EDT) is obtained by assigning pixels within the object silhouette with their distances to the nearest phase boundary. The intensity maxima along the spine of this EDT reveal a skeleton. Pixelation artefacts at the border of the digital silhouette generally lead to an underestimation of the true Euclidean distances and so a corrected EDT is acquired from the geometric mean of the EDTs of the silhouette and a second silhouette dilated by a 3 × 3 diamond-shaped structuring element. The volume is then reconstructed from the largest spheres, centered at each pixel along the skeleton, which fit within the silhouette.

Hybrid method (HM)

If the X-ray source is stable and monochromatic, but the melt attenuation properties are poorly defined, as is likely to be the case for novel nuclear fuel element compositions, a hybrid of the LAM and SSM approaches may represent the best solution. The HM normalizes the void corrected image intensities for each object up to a maximum of unity and multiplies this normalized surface map by the maximum of the EDT. Thus, the 3D shape and surface undulations mirror those obtained by the LAM and the maximum depths normal to the silhouette are equivalent to those obtained using the SSM. A performance assessment of the various 3D-reconstruction models, using the phantom models, is included in Appendix A.

Particle tracking

Fragmentation and deformation of melt fragments dictates that objects may undergo rapid changes in size, shape, porosity and orientation during the FCI, which poses potential difficulties for particle tracking. Furthermore, distinct melt fragments can by-pass each other in the axis normal to the image and appear temporarily coalesced within the 2D FOV. A bespoke particle tracking algorithm has been developed, inspired by the tracking principles used by Crocker and Grier [START_REF] Crocker | Methods of Digital Video Microscopy for Colloidal Studies[END_REF], but introducing a flexible candidate particle assessment stage to ensure that the objects which most closely resemble each other in terms of their size and shape properties are tracked between adjacent frames. The proposed tracking algorithm entails five stages: (1) identification, (2) assessment, and (3) labeling of candidate particles, before (4) filtering, and (5) sorting the labeled particles.

The tracking algorithm requires an n × (i + 2) input array for 'n' objects and 'i' size and shape characteristics used to differentiate between the objects. The additional two mandatory fields detail the coordinates of the object centers of mass, or centroids, and the frame in which they appear within the video. Initially, a maximum displacement value, which should exceed the ratio of the maximum instantaneous fragment velocity and the video frame rate, is used to define the width of a region of interest (ROI) around each centroid. A search is then conducted to find candidate particle centroids within these ROIs in the subsequent frame. If the frame rate is high and the maximum displacement has been well defined, most objects will have no more than one solitary candidate particle in the subsequent frame, however fragmentation events may generate a number of candidate particles in close proximity to the fragmenting particle.

Having identified a list of candidate particles for each object, the candidates are assessed by means of a weighted similarity index, W SI. For the 'i' particle size and shape characteristics, a coefficient of similarity is obtained from the normalized difference in that property between the candidate and active particles,

xcp-xap xap i
. The W SI represents a weighted average of these coefficients of similarity, as shown by eq. ( 8), where the smallest W SI indicates the candidate which most closely resembles the active particle.

W SI = I i=1 ω i xcp-xap xap i I i=1 ω i (8)
The candidate selection stage uses the W SI values to label the most similar silhouettes in adjacent frames with corresponding particle numbers. The input array is then sorted by ascending particle number, and then by ascending frame number. Each instance of a given particle number represents an instantaneous sighting of a given particle. Particles with fewer than a threshold minimum sightings value are eliminated and the tracked particle numbers are adjusted.

Following tracking, the particle velocity vectors are determined. Typically, the particle displacements are acquired from the Euclidean distances between the centroids of consecutive sightings. Sightings at the border of the FOV are exceptional since the centroid does not accurately reflect the true center of mass. Consequently, the displacement of sightings on the top border of the image (entering the FOV) is calculated from the lower coordinates of bounding boxes around consecutive sightings. Similarly, the uppermost coordinates of the bounding boxes are used to track objects departing from the bottom of the FOV.

Results and discussion

The FCI is dictated in large part by the initial temperature of the melt-coolant interface, T I , and its relation to the coolant boiling curve and the melting point of the molten fuel material (in this case, steel). Various key temperatures, significant in determining the nature of the FCI [START_REF] Hu | Fragmentation characteristics of molten materials jet dropped into liquid sodium pool[END_REF][START_REF] Nishimura | Thermal fragmentation of a molten metal jet dropped into a sodium pool at interface temperatures below its freezing point[END_REF], are summarized in Table 1. The initial interface temperature was estimated using a one-dimensional heat conduction relationship for a semi-infinite geometry, including correction for the latent heat of fusion [START_REF] Hu | Fragmentation characteristics of molten materials jet dropped into liquid sodium pool[END_REF]. An interface temperature of 1485 K exceeds the coolant saturation temperature by 329 K and lies towards the upper end of the nucleate boiling regime, approaching the departure from nucleate boiling temperature, T I,DN B , at which the critical heat flux is observed [START_REF] Farahat | Transient-boiling heat transfer from spheres to sodium[END_REF][START_REF] Schins | Boiling and fragmentation behaviour during fuel-sodium interactions[END_REF]. The interface temperature is around 615 K below the homogeneous nucleation point, T I,HN , indicating that stable film boiling at the interface is unlikely.

The interface temperature is also around 215 K below the melting point of stainless steel, indicating that a solid steel crust is likely to form immediately on quenching of the melt. A combination of low initial vapor production and rapid solid crust formation would indicate low potential for hydrodynamic fragmentation, however previous experiments [START_REF] Gabor | Breakup and quench of molten metal fuel in sodium[END_REF] have demonstrated that substantial melt fragmentation is still possible in spite of rapid crust formation.

Post-experiment melt debris analysis

Following experimentation, around 18 % of the steel mass loaded into the furnace was recovered from the debris catcher, while the remaining mass either remained within the furnace crucible or the intermediate melt delivery system. The recovered debris mass, m d , is therefore considered to be the effective mass partaking in the interaction, or interaction mass. Images of selected grades of sieved melt debris are presented in Figure 3. The largest fragments, retained by the coarsest mesh (see Figure 3d accounted for 77 % of the total debris mass, and take the form of hollow, frozen jet shells, best explained by the thermal fragmentation of the jet following the formation of a solid crust layer [START_REF] Gross | Characterization of Fragmented Fuel From a Thermal Fuel-Sodium Interaction[END_REF]. The frozen jet shell morphology in Figure 3d is consistent with debris recovered from interactions between sodium and copper [START_REF] Nishimura | Thermal fragmentation of a molten metal jet dropped into a sodium pool at interface temperatures below its freezing point[END_REF] or uraniumzirconium alloy [START_REF] Gabor | Breakup and quench of molten metal fuel in sodium[END_REF] melts. Similar morphologies have been observed for zinc and tin melts quenched in water [START_REF] Sugiyama | Thermal interaction in crusted melt jets with large-scale structures[END_REF], but at much lower melt temperatures of 523-743 K, corresponding to low initial superheats of less than 50 K.

The thermal fragmentation mechanism which best explains this debris morphology begins with entrainment of coolant within the melt jet [START_REF] Mizuta | Progress report on the molten UO2 drop experiment[END_REF][START_REF] Sugiyama | Thermal interaction in crusted melt jets with large-scale structures[END_REF]. Since the temperature of the melt-coolant interface is below the melting point of stainless steel, the jet begins to form a crust layer immediately on quenching. Heat transfer from the melt to the coolant trapped within the jet shell, supplemented by the latent heat of solidification released due to crust formation, causes the trapped coolant to vaporize. Containment of the vapor within the solid jet crust generates an internal over-pressure and the thermal fragmentation event manifests when the pressure difference across the melt crust overcomes its yield strength. Shrinkage cracks formed in the crust layer during solidification [START_REF] Schins | Boiling and fragmentation behaviour during fuel-sodium interactions[END_REF][START_REF] Mizuta | Fragmentation of uranium dioxide after molten uranium dioxide-sodium interaction[END_REF] may also provide conduits for the release of pressure from within the jet. Localized expulsion of melt through the crust was previously visible from holes in the debris recovered from the uranium oxide-sodium interaction in Gross and Vollarth [START_REF] Gross | Characterization of Fragmented Fuel From a Thermal Fuel-Sodium Interaction[END_REF].

The smaller debris population is dominated by irregular, high surface-area fragments expelled from the jet during thermal fragmentation. A small number of high sphericity melt fragments, typically around 1/6 th the nozzle diameter in size, initially appear consistent with fragments formed by hydro- dynamic fragmentation; however, these likely correspond to spherical melt droplets arriving prior to the initial jet quenching due to splashing from the intermediate tip tray, as observed from the X-ray images. These near spherical fragments contribute a negligible proportion of the total debris mass. Quantitative analysis of the debris size distribution from sieve analysis will be presented in parallel with the X-ray image analysis.

3.2. Direct observations from X-ray imaging X-ray images acquired at six instances during the FCINA-30-1 experiment are presented, prior to image processing, in Figure 4. The gravity fed melt jet arrives at the coolant with a velocity of around 2.5 m s -1 . Due to the low velocity, high melt viscosity and small nozzle diameter, the melt jet deviates laterally from the nozzle and its diameter varies with time, as demonstrated by the necking at the top of Figure 4a. Minimal sodium vapor production is observed at the melt-coolant interface. This was anticipated as the nucleate boiling regime is typically characterized by discrete bubbles extending from the melt surface into the bulk fluid. On bubble detachment, the bubble is quenched by the 583 K subcooled sodium, resulting in its rapid collapse.

The jet exhibits minimal hydrodynamic fragmentation or deformation in the early stages of quenching. However, the melt delivery to the sodium pool is discontinuous and the jet divides into two distinct parts where the neck narrows to zero, as demonstrated by Figure 4b. The trailing portion of the divided jet undergoes a mild thermal fragmentation event which manifests in modest sodium vapor production. It is possible that the stress of impact between the leading jet front and the sodium pool surface causes sodium entrainment within the jet, initiating the thermal instability. This would explain why the fragmentation event occurs in close proximity to the coolant-ullage interface, however further research is required into the probable mechanisms for sodium entrainment.

Subsequently, a more energetic thermal fragmentation event, accompanied by rapid vapor expansion, is observed in images Figure 4d-e. The locus of the fragmentation event is again close to the sodium-ullage interface and originates at a location of reduced contrast with the bulk sodium, implying sodium entrainment within the jet. The interaction generates a large quantity of sodium vapor and subsequently the void fraction within the thermal insulation column appears, qualitatively, close to unity. The evacuation of liquid sodium from the FOV after the thermal fragmentation event (see Figure 4e-f) causes the melt fragments to accelerate downwards through the column. A mechanically robust solid outer crust is further evidenced by the rebounding of fragments on collision with the thermocouple support infrastructure. Thus, the X-ray images qualitatively reinforce the observations from debris analysis, with an added temporal dimension to exhibit the transient behavior. Furthermore, the FCINa-30-1 test qualitatively confirms the fragmentation behavior [START_REF] Matsuba | Distance for fragmentation of a simulated molten-core material discharged into a sodium pool[END_REF] revealed by previous experiments conducted at the MELT facility using simulant materials. However, quantitative image analysis is required to realize the full value of the X-ray data.

Image pre-processing and phase segmentation

Figure 5 presents a montage of images demonstrating various image processing steps outlined in Figure 2 prior to quantitative characterization. The major artefacts identified from the raw X-ray image in Figure 5a are vignetting and Gaussian noise; however the image also demonstrates many melt fragments enveloped by sodium vapor, illustrating the need to correct for void attenuation prior to melt segmentation.

Flat field normalization of the raw image in Figure 5a generates Figure 5b, rendering the pixel intensity more homogeneous across the image; however, the product is noisy and the region at top of the test section is partially obscured. This dark region at the top of the image corresponds to the ullage region above the sodium pool at rest. It was necessary to maintain a small ullage within the FOV to confirm the initial sodium level and visualize the initial jet quenching. Consequently, the top 11 % of the field of view had to be masked from the images prior to quantitative analysis.

Since the contents of the test section undergo the greatest evolution with time during the experiment, a mask of pixels with enhanced temporal variance can be used to isolate the test section contents. Denoising the image, isolating the test section, and globally thresholding the positive pixels 5h; the 3D characteristics are expressed as ranges due to differences between the SSM and HM calculations.

of Figure 5b isolates the vapor phase, but with large holes at the melt locations, as demonstrated by Figure 5c. Morphological closing of these holes renders the binary vapor mask in Figure 5d. The SSM is then used to reconstruct the vapor clouds in 3D, resulting in Figure 5e. Intermediate stages of the SSM are demonstrated in Figure 5d; the largest spheres which fit within the confines of the mask are superimposed at every pixel along the blue skeleton, as exemplified by the red outline centered at the pixel indicated. The product of the 3D reconstructed vapor phase and the linear attenuation coefficient for sodium is used to correct for void attenuation effects, generating the void corrected image in Figure 5f. The sodium linear attenuation coefficient is relatively constant within the range of anticipated photon energies and so void correction was not especially sensitive to the uncertainty in photon energy. While the 3D reconstruction is imperfect at the vertical extremes of the vapor region, the quantity of visible vapor in the void corrected image is greatly diminished. This is reflected by the intensity histograms presented in Figure 5i; the smaller mode of positive intensities, corresponding to the vapor regions, is largely eliminated. Both the quantity of visible melt and the contrast between the melt phase and ambient coolant are enhanced, facilitating more precise segmentation. The spikes of noise within the intensity histograms correspond to artefacts outside of the interaction region.

Global thresholding of the test section region yields the melt image in Figure 5g. Labeling regions of interconnected pixels [START_REF] Haralick | Computer and robot vision[END_REF] enables the extraction of individual discrete fragments from the segmented melt images for characterization. 3D reconstructions of the largest fragment in this particular image, attained using the HM and SSM approaches, are presented in Figure 5h.

Quantitative analysis from X-ray processing

Quantitative characterization of the complex melt fragment in Figure 5h is summarized in Table 2, revealing a predicted mass in the m = 0.031 -0.043 range. The range of mass values presented in Table 2 corresponds to the differences between the SSM and HM volume calculations. Both 3D reconstruction methods entail a number of geometric assumptions and so a discussion of their relative uncertainties in estimating the volume of the phantom models is presented in Appendix A. An underestimation in melt volumes was anticipated using the SSM due to characteristic under-predictions in the vicinity of sharp vertices [START_REF] Brayer | Application of X-Ray radioscopy for investigations of the 3-phase-mixture resulting from the fragmentation of a high temperature molten material jet in water[END_REF]. The LAM approach for volume reconstruction resulted in a significantly lower predicted fragment mass of m = 0.017 ± 0.004. Ultimately, the LAM was discounted for 3D characterization for these experimental data as the X-ray source energy and the extent of beam hardening by the test section infrastructure were too uncertain to adequately define the stainless steel mass attenuation coefficient. Furthermore, the coefficient of proportionality between pixel intensity and melt depth, 1 µm-µc , is highly sensitive to the effective photon energy for the chosen materials. Henceforth, the HM and SSM are employed to predict the total melt mass and vapor void fractions respectively. The evolution in melt mass and void fraction within the imaging window are presented in Figure 6. The first major spike in melt volume at t ≈ 37, equivalent to around 20 % of the recovered debris mass, identifies the instant of initial quenching of the jet. The acquisition of the image in Figure 4a is annotated for reference. The subsequent spike in void fraction, to a maximum approaching 0.7, corresponds to the jet fragmentation and rapid vapor expansion observed in Figure 4d-e between the two events, ∆ t * = 16, enables the precise characterization of the critical quench time prior to the thermal fragmentation event in the absence of in situ temperature measurements. Characterization has thus far been performed for each instantaneous sighting of an object within the X-ray video; however, in order to identify unique melt fragments, without double counting multiple sightings of the same mass, tracking is necessary. The tracking analysis was performed by searching a 7 6 D 0 wide neighborhood around each centroid in the subsequent frame. Where multiple candidate particles were observed within the neighborhood, the candidate most similar in estimated volume was selected. Only fragments which presented with at least five sightings were considered for quantitative analysis. Of the 28368 objects detected during segmentation, 1312 distinct melt fragments were identified using these tracking parameters with a total of 14706 instantaneous sightings. Thus, an average of over 11 sightings are available for the characterization of each melt fragment.

Two methods of validating the tracking analysis are presented in Figure 7. First, velocity vector plots for twelve selected fragments are presented in Figure 7a, showing the continuous motion of discrete fragments downwards through the imaging window. Tracking of erroneous sightings belonging to different objects are typically visible as anomalous vectors distinct from the prevailing particle motion, although coalescence events may also present as seemingly anomalous vectors as coalescence between adjacent particles manifests as a sudden displacement of the center of mass. Second, SPECTRA enables the export of montage images of each sighting corresponding to a given particle, as shown in Figure 7b. The montage demonstrates subtle changes in size, shape and orientation over time, as well as greater changes in appearance during coalescence events. The relatively large frame rate of 1000 fps, and thus the subtle changes in melt appearance between adjacent frames, greatly simplifies the identification of each sighting belonging to a given melt fragment and ensures the efficacy of the tracking algorithm. Fragment 6, tracked in yellow on the right-hand side of Figure 7a and pictured in Figure 7b, is observed over 173 individual sightings. In the second half of its descent through the imaging window the fragment exhibits sudden changes in its trajectory and axial rotation following a collision with a thermocouple housing. The fragment response to this collision represents further evidence of a solid outer crust and solid-like mechanical behavior.

A third method of validating the tracking performance involves estimation of the total mass, m T , of melt traversing the imaging window for comparison with the total mass of recovered debris. The mass of melt passing through the imaging window, can be estimated by integrating the vertical component of the melt momentum over the duration of the video:

m T = ρ m H t f ti V v y dt (9)
where ρ m is the melt density at the initial temperature, V is the fragment volume, v y , is the vertical component of the melt velocity, and f is the video frame rate. This estimate of the total melt mass in fact represents a combined assessment of the phase segmentation, tracking and volume reconstruction algorithms employed, and so different solutions will be found for the different 3D reconstruction methods. The estimated total masses found using the SSM and HM approaches respectively, correspond to 53 and 72 % of the recovered debris mass respectively. Given the difficulties and requisite assumptions to extrapolate 3D characteristics from solitary radiographic silhouettes, combined with the likelihood that some fragments are below the detectable size limit of the X-ray imaging device, this represents a positive performance.

In addition to the characterization of distinct particles, tracking also enables the analysis of particle motion. The lateral, ṽx , and vertical, ṽy , components of the melt particle velocity vectors are presented, before and after the thermal fragmentation event, in Figure 7c. These dimensionless velocities have been normalized by the magnitude of the jet velocity on arrival at the interface of the sodium pool. Prior to thermal fragmentation the melt exhibits negligible lateral displacement and a mode of downwards vertical velocities centered around 25 % of the jet velocity prior to quenching. Due to the relatively shallow height of the imaging window, the melt fragments are still decelerating as they leave the FOV and thus still exceed their characteristic terminal velocity in liquid sodium. Immediately after thermal fragmentation, the lateral and vertical velocity histograms broaden significantly and the disparity between the two histograms is greatly diminished, indicating omnidirectional expulsion from the jet shell, including significant particle motion counter to gravity. Furthermore, many missile fragments in the aftermath of thermal fragmentation exhibit velocities exceeding the initial jet velocity in magnitude.

Identification of unique fragments through tracking, combined with the characterization of their mass and a measure of characteristic length enables the calculation of a fragment size distribution from image analysis for comparison with the sieve analysis of the recovered debris. Many characteristic length measurements can be obtained from image analysis but the minimum caliper diameter offers the closest resemblance to the measure obtained by sieve analysis. The masses were calculated by reconstructing the fragments in 3D using the SSM and HM approaches respectively, assuming a density equivalent to the melt density at the initial melt temperature and averaging the resulting masses over Figure 8: Fragment size distribution analysis including (a) a comparison between sieve analysis of the debris recovered post-experiment and equivalent size distributions obtained by image analysis, where the masses have been estimated by the SSM and HM approaches for 3D reconstruction, and (b) a composite particle size distribution using sieve analysis to characterize the fine population and image analysis for the coarse population.

all sightings not in contact with the image border. A comparison of the sieve analysis and image analysis fragment size histograms is presented in Figure 8a. The jet shell fragments identified in Section 3.1, with minimum caliper lengths comparable to the nozzle diameter, account for the vast bulk of the recovered debris mass. The largest commercial sieve mesh available for this analysis was around 1/5 th the scale of the nozzle diameter and so the histogram is strongly weighted towards this largest bin. This truncation of the histogram restricts the analysis of the coarse, centimetre-scale fragments which are highly relevant to FCIs exhibiting this thermal fragmentation behavior. Conversely, while particles as small as the pixel corresponding to L = 4.2 10 -3 are theoretically detectable, image analysis best reserved for particles greater than L = 3.3 × 10 -2 many smaller fragments exhibit negligible contrast with the coolant and are thus difficult to detect. Nonetheless, the image analysis broadly strong agreement with analysis for the coarser sieve meshes.

The over-prediction of the mass of jet shell fragments by image analysis demonstrates a problem with residual double counting after tracking. Particles which temporarily disappear behind other foreground particles and then reappear in subsequent frames, for instance, may be detected as different particles, leading to false double counting. This artefact may be addressed in a revised version of the tracking algorithm, but reflects a major complication for the tracking of 3D motion from a solitary 2D imaging perspective.

There are significant advantages to characterising the melt fragment population through image rather than sieve analysis; characterization is not restricted to the limited grades of commercially available sieve meshes, enabling analysis to a much greater precision, or limited to a solitary measure of characteristic length, which can be poorly representative for particles with complex morphologies and large aspect ratios. The risk of biasing the histogram by damaging the debris during recovery or sieving is also avoided. Conversely, X-ray image analysis performs less well for sub-millimetre populations and the potential for further melt fragmentation below the imaging FOV may present a problem, although the thermal fragmentation events appear to occur very close to the surface of the sodium pool in this instance.

The advantages and limitations of each approach dictate that the most precise debris size distribution is obtained by combining the two methods, using sieve analysis for the finer fragments and image analysis to characterize the coarse jet-shells to greater precision. The product of this approach is presented in Figure 8b. The result produces a bimodal distribution with the bulk of the melt mass (≈ 81 %) corresponding to the population of jet shell fragments with their minor dimensions comparable to the melt delivery nozzle. The smaller mode, centered around D 0 /20, represents the finer fragments expelled from the jet during thermal fragmentation, previously pictured in Figure 3a-b. The combined fine fragment and jet shell populations exhibited a mass-weighted median particle size equivalent to roughly half the nozzle diameter, L = 0.51.

Conclusions

High resolution, fast acquisition radiographic imaging was used to visualize an FCI between molten steel and sodium in the clearest detail achieved to date. While the images suffered from some vignetting, noise and distortion artefacts, typical of such X-ray imaging configurations, comprehensive image preprocessing, alongside novel tracking and 3D reconstruction algorithms, enabled the detection of 72 % of the debris mass recovered from the test section following experimentation. This 3D reconstructed melt fragment population was then characterized in terms of its morphology, size and velocity distributions.

The X-ray images revealed thermal fragmentation of the jet, accompanied by rapid vapour expansion, originating close to the sodium-ullage interface. The formation of a solid crust at the melt interface was evidenced through the rebounding of fragments on collision with solid infrastructure and the jagged morphologies of fractured melt fragments. The thermal fragmentation event is best described through the vaporization of entrained coolant within the jet, generating an internal overpressure sufficient to fracture the outer crust. Image analysis identified spikes in the melt mass and vapor fractions within the imaging window corresponding to the initial jet quenching and thermal fragmentation event respectively, revealing a critical quench time in the of -1 s between the two events. thermal fragmentation event was also in the evolution of the fragment velocity histogram obtained by particle tracking with significant numbers of missile fragments expelled from the jet in all directions, often with velocities exceeding the initial jet velocity in magnitude.

Fragment size distributions obtained through X-ray image analysis showed broadly strong agreement with the debris size distribution from sieve analysis, however image analysis offered a greater range of size measurements and more precise characterization of coarser particles, particularly the large frozen jet shells. Conversely, sieve analysis offered the better characterization of finer, sub-millimetre fragments expelled from the jet crust on thermal fragmentation, since the radiographic contrast between the fine melt fragments and ambient coolant was significantly diminished. A composite approach combining the two methods provided the most thorough characterization of the debris population, revealing a bimodal distribution of jet shells with dimensions comparable to the delivery nozzle, which accounted for 81 % of the recovered debris mass, and a second debris population, roughly 20-times smaller, corresponding to the fragments expelled from the jet during thermal fragmentation.

  photon energy η scintillator efficiency λ thermal conductivity µ linear attenuation coefficient ν void fraction ρ density σ magnitude of image noise c p specific heat capacity f image acquisition rate l chord length normal to photon flux m mass t time v velocity v 0 jet velocity on quenching z depth normal to photon flux Acronyms W SI weighted similarity index CEA French Alternative Energies and Atomic Energy Commission EDT Euclidean distance transform FOV field of view

Figure 1 :

 1 Figure1: Schematic of the MELT facility as configured for the FCINA-30-1 test, modified from Matsuba et al.[START_REF] Matsuba | Distance for fragmentation of a simulated molten-core material discharged into a sodium pool[END_REF]

Figure 2 :

 2 Figure 2: Image processing methods used to isolate the melt and coolant phases from raw X-ray images in preparation for characterization and tracking

TemperatureTable 1 :Figure 3 :

 13 Figure 3: Four grades of melt debris fragments recovered from the FCINA-30-1 experiment classed as (a) ultra-fine ( L ≈ 8 × 10 -3 ), (b) fine ( L ≈ 2 × 10 -2 ) and (c) coarse ( L ≈ 0.16) fragments, and (d) ultra-coarse jet shell ( L > 0.19) fragments.

Figure 4 :

 4 Figure 4: Unprocessed X-ray images acquired at six instances during the FCINA-30-1 experiment demonstrating (a) the jet shortly after initial quenching, (b) necking and division of the jet, (c) a mild thermal fragmentation event, (d) the immediate aftermath of a second, more significant thermal fragmentation event, (e) complex melt morphologies and high vapor fraction following jet fragmentation and (f) accelerating melt fragments falling through the voided test section.

Figure 5 :

 5 Figure 5: Montage demonstrating various X-ray image processing steps outlined in Figure 2 including: (a) an unprocessed X-ray image, I d , acquired after the thermal fragmentation event, previously shown Figure 4e (b) the natural logarithm of the flat field normalized image, I ln, (c) the detected vapor pixels, within the masked test section (d) a binary mask of (c) with the melt-occupied holes filled by morphological processing, (e) a 3D reconstruction of the vapor phase using the SSM, (f) the log-normalized image in (b) corrected for vapor attenuation, Ivc, (g) the detected melt phase within the test section following segmentation, and (h) an individual melt fragment with a complex geometry extracted from (g) and reconstructed in 3D using the hybrid (left) and SSM (right) approaches. A comparison between the intensity histograms before and after void correction is presented in (i); the histograms have been equalized to an 8-bit scale using a factor of 160 after flat field normalization.

Figure 6 :

 6 Figure 6: Evolution of dimensionless melt mass (in blue) and void fraction (in orange) within the imaging window as a function of time, revealing the critical quench time, ∆t * , between intial jet quenching and the energetic thermal fragmentation event. The occurrence of the images in Figure 4(a) and (d) are annotated to indicate initial jet quenching and the thermal fragmentation event respectively.

Figure 7 :

 7 Figure 7: Analysis from fragment tracking including (a) velocity vectors for twelve melt particles prior to thermal fragmentation, (b) a montage of each sighting of fragment 6, and (c) a comparison of histograms of the vertical and horizontal fragment velocities prior to and immediately after the thermal fragmentation event.

Filled

Table 2 :

 2 Characterization of the complex melt fragment shown in Figure

Table A .

 A 1: Percentage errors in the estimated volume of the steel-filled regions of the phantom, as predicted by the SSM and hybrid 3D-reconstruction models.

Acknowledgements

The authors wish to thank everybody at the MELT facility for their contributions throughout the FCINA experimental program, as well as Hidemasa Yamano, Shigenobu Kubo, Frédéric Serre and Frédéric Payot for their management of this JAEA-CEA collaboration. The authors also would like to express their gratitude to Mr. S. Sato of NESI Inc. for his technical support to the measurement work during the FCINA experiment. Thank you to the CEA for their support of this work through a post-doctoral research grant, to Claude Brayer and Magali Zabiego for lending their expertise in the field of severe accidents and to Laure Schneider, Théo Hipault and Shifali Singh for their contributions to the development of SPECTRA.

Conflict of interest

The authors declare no competing interests.

Appendix A. Image calibration and uncertainty analysis

Image calibration was performed using the phantom model in Figure A.1a, constructed with a steel rod at its center (representing a corium jet) surrounded by four concentric annuli which are selectively filled with 2 mm steel balls to represent various extents of jet pre-mixing. Extensive discussion of X-ray image calibration using phantoms is detailed in a thesis by Singh [START_REF] Singh | X-Ray diagnostics on corium-sodium interactions during a severe accident scenario[END_REF]. An example X-ray image of the phantom, with its two innermost annuli filled with steel balls, is presented in Figure A.1b. The corresponding image is presented following post-processing and segmentation in Figure A.1c. The Xray image was acquired using the same imaging parameters employed for the FCINa-30-1 experiment while the same image processing procedure, detailed in Figure 2, was used to isolate the steel phase. The image processing procedure was slightly less precise for the phantom analysis than for the FCINa-30-1 images because no precisely corresponding flat field image was available, only that of the sodium-filled test section.

The estimated cross-sectional areas, or silhouette areas, of the phantom with its innermost 1, 2 and 3 annuli filled with steel balls are used to calibrate the observed pixel resolution, after correcting the images for geometric distortion. An observed resolution of 116.4 µm enabled the estimation of the phantom silhouette areas to within an accuracy of ±5.2 %.

The phantom images also enable a performance assessment of the various 3D-reconstruction models for this relatively challenging 3D geometry. The SSM assumptions become more onerous with increased departure from a spheroidal geometry, due to artificial rounding of the topology in the vicinity of sharp corners. Correspondingly, the phantom volume was under-predicted by an order of 15-24 %, with the worst performance for the phantom with three filled annuli. This error diminishes to < 4 % for near spherical geometries. The absence of an adequate flat field image precluded analysis of the LAM approach; this will be addressed with a modified phantom design for use in the new MELT testsection. The hybrid model avoids the artificial rounding of corners as the topology is determined by the attenuation profile within the silhouette, rather than by the EDT. Consequently, the error in predicted volume diminished to an order of 4-6 %.


Anne Benoist
email: anne.benoist@mom.fr

Michele Degli Esposti
email: michele.degliesposti@gmail.com

Julien Charbonnier
email: julcharbonnier@gmail.com

al-Madam and the Archaeology of the Falaj in South East Arabia

Keywords: falaj, South East Arabia, Iron Age, irrigation technology, aridity

Cordoba is famous in the U.A.E. for his investigations in the oasis of al Madam (Emirate of Sharjah) where he could demonstrate the use of a falaj (pl. aflaj) during the Iron Age period and associate it to a cultivation area and to a settlement. This settlement could be dated between the 8 th and the 4 th century BCE, that is, between the local Iron Age II and Iron Age III periods.

The falaj system has been interpreted in the late 90 ies as a technical innovation at the origin of a redevelopment and extension of the oases in SE Arabia during the Iron Age, itself favouring a demographic and economic growth during that period. Investigations carried out on the falaj AM-2 at al-Madam by J. Cordoba and his team brilliantly illustrated its characteristics and components as well as its progressive drying up at the beginning of Iron Age III, with a deepening of the falaj's floor followed by a final abandonment of the systeman of the nearby settlement and cultivation.

Recent investigations carried out at Masafi (J. Charbonnier, A. Benoist), at Bin Ati (T. Power, P. Sheehan), and at Salut (M. Degli Esposti) have brought to light new data on the archaeology of the aflaj, which suggest a more nuanced picture of the irrigation techniques used in Iron Age oases in SE Arabia. The robust dataset built at al-Maam can thus be compared and contrasted with these new data an with the documentation from other SE Arabian sites, in orer to show that nothing as an archetypal falaj probably existed.

Introduction

The word falaj (pl. aflaj) is used in South East Arabia for designating several kinds of water tapping and water transportation systems between an underground source and a place where this water is used (settlement or cultivation area) using subterranean or at least covered galleries. One of the most important aflaj was discovered by Prof. Joachim Córdoba in the oasis of al-Madam in the Emirate of Sharjah (UAE). An Iron Age settlement site was unearthed at al-Madam 1 Thuqaibah supported by an associated falaj dubbed al-Madam 2 (AM-2). The excavated extent of the falaj included a subterranean gallery feeding an area of irrigated land characterised by agricultural plots and irrigation channels (Córdoba, 2016: 135-137). Falaj AM-2 is important because it is one of the most extensively excavated, best documented and closely dated aflaj in South East Arabia. The work of J. Córdoba and his team has therefore stimulated the construction of general theories. The present paper will attempt a critical evaluation of the archaeological evidence for the falaj in South East Arabia and consider the extent to which Falaj AM-2 supports general theories of the archetypal underground falaj often encountered in the textbooks (e.g. Cleuziou & Tosi, 2007: p. 152, Fig. 162;Magee, 2014: p. 216, Fig. 8.2).

The Archaeological Record

The discussion will focus on four aflaj for which an Iron Age II (meaning here the more conventional time span 1100-600 B.C.) dating is demonstrated or at least convincing and for which we have precise data regarding their organisation and building techniques. These include in addition to al-Madam two in al-Ain and one in Masafi, the first three located to the west of the open outwash plains of the Hajar Mountains, the last located at the confluence of steepsided mountain wadis (fig. 1). Clearly these aflaj cannot be considered representative of the entirety of South East Arabia with its many ecological zones and local traditions.

Perhaps the most important of these is Falaj AM-2. A portion of the subterranean gallery including five access shafts has been excavated by J. Córdoba and his team in the al-Madam area, over a length of 120 m (Córdoba & Del Cerro Linares, 2005). Excavations were later extended to the downstream part of the irrigation system and to the gardens, a part of which has been brought to light, including a primary channel alimenting around twenty parallel secondary channels irrigating tree plantation pits (Córdoba, 2016: 135-137).

Two aflaj were discovered and partly excavated by W. Yasin al-Tikriti in the area of al-Ain.

The first one is Hili-15, located to the south-west of a large settlement area including a collective fortified building (Hili-14) and a pottery workshop . The second one is the falaj discovered and partly excavated at Bida Bint Sa'ud (hereafter, BBS), close to a collective building including a columned hall (Bint Sa'ud House). Excavations allowed the unearthing of a cut-and-cover channel (see below) splitting into three channels after its outflow at Hili-15. This channel was followed over a total distance of 450 m with the excavation of several trenches named Hili-15 A to H. In Area H, located upstream, what appears to be the beginning of a subterranean gallery with a access shaft has also been partly explored. At BBS, a 100 m long portion of the falaj was explored digging two large and ten smaller trial trenches. It comprises a Y-shaped subterranean gallery with the two branches coming from the upstream part and joining each other in the vicinity of what appears to be a large subterranean cistern accessible by a staircase (al-Tikriti, 2002a;[START_REF] Al-Tikriti | Heading North: an ancient caravan route and the impact of the falaj system on the Iron Age culture[END_REF][START_REF] Al-Tikriti | Archaeology of the Falaj: A Field Study of the Ancient Irrigation Systems of the United Arab Emirates[END_REF].

The outflow of a falaj was recently excavated by the French Archaeological mission at Masafi-1. The related channel was unearthed over a distance of roughly 15 m to the north of a collective building which included a columned hall. The upstream part of the falaj could not be physically explored, but the geo-archaeological study of the sediment found in the channel provided data regarding the most probable place of water catchment of this irrigation system, which has been interpreted as runoff harvesting system tapping water from a valley located to the east of the settlement area (Charbonnier et al., 2017: 25).

Other aflaj have been dated to the Iron Age with varying degrees of reliability, but the available data do not allow a precise reconstruction of their shape and building techniques. This means that they cannot be directly compared and contrasted with Falaj AM-2 as documented by Córdoba. However, they are presented here to give an indication of the archaeological record and opportunities for further research. This is the case for example of one of the aflaj recorded around Salut in Oman. In the area of this ancient oasis, the remains of an aflaj system extending along the beds of the Wadis Sayfam and Bahla, over no less than 49 km in total, were surveyed and studied, showing the substantial complexity of the history of irrigation in this region. These ancient aflaj were in fact re-cut, deepened, re-used several times, which has partly or totally transformed their shape. During the latest surveys in 2016, for example, the access shafts pointing a long stretch of Falaj Salut were being recut with the use of a bulldozer and lined with cement. Given this situation, and the impossibility to access the shafts and tunnels (now more than 20 m deep), a detailed reconstruction of the Iron Age water supply system feeding the oasis is not possible. In particular, there are no grounds to establish the contemporaneity of all or part of the aflaj network of Salut. Nevertheless, geoarchaeological study has provided a much-needed radiometric date for Falaj Shaww, which was in all likelihood serving the prominent Iron Age site which overlooks the ancient oasis (Cremaschi et al. 2018: p. 136 & Table 1). The falaj tunnel had a squared section, definitely inconsistent with a natural cavity, and was surely active during the fifth-century BC, which corresponds to the Iron Age III period, i.e. the moment where evidence for aflaj abandonment are reported from the region of al-Madam.

Absolute dates are further available for a falaj near Nizwa, not far from Salut, at the outlet of which calcareous deposits were sampled and, among others, two dates at 2610 ± 130 and 2730 ± 140 were obtained [START_REF] Clark | New perspectives about Iron Age and the oasis culture in the Oman peninsula. Two conclusive seasons at al Madam (Sharjah, UAE)[END_REF]: Table 1), thus fitting into the Iron Age II period but potentially also extending into the Iron Age III (600-300 B.C.). These dates, however, can only be associated to the well-known fact that the area was certainly densely occupied during the first millennium BC, as evidenced by abundant survey data (e.g. [START_REF] Schreiber | Transformationsprozesse in Oasensiedlungen Omans[END_REF], but no direct connection with an Iron Age settlement or field system is reported, nor details on the channel structure, apart from the fact that it would tap water from the wadi gravels (Boucharlat, 2003: 168). Falaj Maysar-46 in the area of al-Moyassarthe earlier toponym was recently replaced with al-Moyassar by Sultan's decreewas published by the German team [START_REF] Weisgerber | Mehr als Kupfer in Oman -Ergebnisse der Expedition 1981[END_REF][START_REF] Yule | Valorising the Samad Late Iron Age[END_REF]. In 1981, this falaj was still visible on the surface over a distance of 3.5 km, its trajectory being marked by alignments of shafts coming from the north and the north-east of the area of Maysar. It runs near the Iron Age settlement of Maysar-42, dated to the first half of the first millennium BC (i.e. the Iron Age II period), but also next to the later settlement of Maysar-43, located 1 km downstream and dated to the Samad period (after the third century BC). Moreover, it still supplied the nearby village of Maysar in the 1970s. The schematic section of a collapsed portion of the falaj shows a high gallery, which although represented as only accessible down to a depth of around 1.5 m in the drawing of Yule (1999: p. 101, Fig. 3), was shown by Weisgerber (1981: 246) [START_REF] Mouton | Des structures légères de l'Age du Fer et un falaj ancien à Muweilah[END_REF]; Falaj D at Sohar on the Batina Coast of Oman which is supposed to be of Partho-Sasanian date (Costa & Wilkinson, 1987: 54); and Falaj Izki IZ0747 surveyed by J. Schreiber in Central Oman (2007a: 134-135). For these, in fact, an Iron Age dating is supposed only because of their proximity to Iron Age sites. In the case of Muweilah the similarities between some of its features (the location of the mother well near a depression; the reduced distance between the access shafts along the tunnel; the splitting into two gallery in its downstream section) and those of other aflaj better dated to the Iron Age are also mentioned as possible chronological indicators (Mouton, 2001: 230), although other authors consider them to be not distinctive (Boucharlat 2003: 165).

The Morphology of the Archetypal Falaj

It is widely believed that the archetypal falaj is comprised of several parts. Upstream, a well is dug to reach the source of water tapped by the falaj (fig. 2). This is the so-called mother well (umm al-falaj or umm ma'). The shape of the well itself seems to have no importance in terms of typology. There can be one or several mother wells feeding a single falaj, the higher number of the mother wells insuring a more reliable tapping of the water. When several mother wells are excavated, they can show a fan-like disposition, each well being linked to the main gallery.

Three types of aflaj are distinguished depending on the source they tap (e.g. al Ghafri 2004: 17-20;al-Sulaimani et al. 2007;Charbonnier 2017: 55), namely the dawudi falaj, tapping water from deep underground aquifers usually located in piedmont areas; the ghayl falaj, diverting wadi base flows or exploiting shallow water tables from alluvial fans; and the 'ayni falaj, directly deriving waters from springs.

The mother well feeds a subterranean gallery conveying the tapped water from its source to the irrigated area simply by gravity. The length and shape of the gallery vary from a place to the other and also changed over time [START_REF] Al-Tikriti | Archaeology of the Falaj: A Field Study of the Ancient Irrigation Systems of the United Arab Emirates[END_REF][START_REF] Boucharlat | Iron Age water drainig galleries and the Iranian 'Qanāt[END_REF]2015). Several types of galleries can be distinguished, being sometimes associated together in a single falaj. The gallery can be a tunnel dug in the ground without any masonry reinforcing it, when the natural ground is sufficiently strong or hard for no masonry to be necessary. It can also be partly built in stones or, in the early Islamic period at least, baked bricks (al-Tikriti, 2011: 118-130). The gallery can also take the shape of a channel or a trench dug in the floor, covered with some stone slabs (the so-called "cut-and-cover" technique). Between these types, there can be several variants, depending on the nature and the strength of the substratum in which the gallery is dug. A gallery can comprise a tunnelled part upstream and change into a cut-and-cover channel downstream, where it approaches the surface. The gallery is punctuated by shafts (thuqba, pl. thuqab) that are primarily used by the constructors to dig the tunnel and later serve as accesses to the falaj for its maintenance and cleaning. These access shafts usually form long, characteristic alignments in the landscape and are the best indicators of the presence of the underground tunnel.

Downstream, the outflow of the falaj can also have several shapes. The point where the water reaches the surface is locally called shari'a. It represents the first point where water can be directly drawn by inhabitants for domestic purpose or for specific collective uses. The shari'a can comprise a simple open air channel or it can be marked by a built feature including a cistern or a basin. When reaching the surface, the gallery of a falaj can also be split into several branches bringing water to different places (garden lots but also dwellings or handcraft areas).

The shari'a can also be associated to some kind of device (e.g. sluice gates) used for regulating water sharing between the people benefitting from the falaj, the latter representing all or part of the population of a village.

The underground gallery: water capture

Several catchment galleries seem to have converged to form the aflaj of Hili-15 (fig. 3) and BBS (fig. 4). Such a configuration, which increases the length of the tunnel directly in contact with the water table and thus increases the flow rate, also characterizes many still-functioning aflaj presumably dug in the Late Islamic period (Charbonnier, 2013: Figure 2;Wolski, 1965: 190). These aflaj do not appear to have had a single mother well nor did they tap into a deep aquifer, but were instead ghayl falaj, exploiting shallow water tables. This is quite a different system to the schematic diagrams that appear in textbooks (see however the scheme reported by Boucharlat [2003: fig. 2] which illustrates the case of a shallow water table).

So far, only two underground galleries have been excavated, AM-2 and BBS, and even these only partially. Our knowledge on the Iron Age digging techniques is therefore limited.

Excavated to a distance of 35 m, the AM-2 underground tunnel is the only one to have been cleared over a substantial length. Nevertheless, it is possible to make a number of observations. These well-documented Iron Age underground galleries were merely dug in the ground, without any masonry reinforcements. In al-Madam, traces observed on the side of the gallery suggest the use of a "very thin sharp pickaxe" to dig the bedrock (Del Cerro & Córdoba, 2018: 91). Iron Age underground galleries can be quite narrow as suggested by AM-2, which does not exceed 50 cm in width (Córdoba & Del Cerro 2005: 522-523), whilst the gallery of BBS is a little wider and is about 70-80 cm. Both AM-2 and BBS have more or less vertical walls and flat bottoms.

The ceiling of the gallery of AM-2 is corbelled and widens slightly in the upper part. The latter is also very deep, 4.80 m at the excavated section. This seems to suggest that the structure has been deepened in order to address the lowering of the water table (see below).

While the access shafts of AM-2 are roughly aligned, its underground gallery does not follow a straight course, but instead meanders between the access shafts. The underground gallery of falaj Hili-15 is not preserved, yet it must be noted that the open-air, primary channel into which it conveyed water downstream is also meandering. This phenomenon, which allegedly distinguished ancient (Iron Age) aflaj from later, straight tunnelled ones (Mouton, Benoist, and Córdoba, 2011: 17), is not properly explained. Al-Tikriti puts forward an interesting hypothesis: to dig the underground gallery, two groups of diggers started from two neighbouring shafts and converged toward each other. As it was undoubtedly difficult to estimate the direction underground, the groups voluntarily deviated their trajectory in the same direction so as to be sure to intersect each other (al-Tikriti 2010: 228). This, however, does not explain why the primary channel of Hili-15, which was open air, also meanders. On another hand, Del Cerro assumes that AM-2 was meandering in order to extend the length of the underground gallery and, therefore, the surface in contact with the water table, thus increasing the volume of water drained by the falaj, as explained above (Del Cerro, 2015: 251). The possible echo of the welldocumented Iron Age snake cult has also been mentioned as an additional reason for such a morphology (Mouton, Benoist, and Córdoba, 2011: 17). Downstream, when a falaj underground gallery approaches the surface, it is customary to dig it as an open trench and then cover it with stone or cement slabs in order to limit evaporation (Charbonnier, 2016). Such a construction technique, which has been termed 'cut-and-cover' by al-Tikriti, is characteristic of Hili-15 (fig. 3). Uncut stone slabs cover its gallery for about 150 m. They rest on the masonry sidewalls of the structure which are made of flat stone slabs, cut from the local calcareous substratum. Unlike Hili-15, the gallery of AM-2 leads directly to an open air trench (Del Cerro, 2015: 251; see below). The downstream end of the BBS falaj was not identified.

Access shafts and sharia: cleaning and repairing

Access shafts were excavated along the underground galleries of AM-2 and BBS, whilst a shaft was also identified along the 'cut-and-cover' section of Hili-15 (fig. 3).

The distance between the shafts varies from one falaj to another and indeed within each falaj.

For instance, it is c. 10 m downstream and c. 20 m upstream of AM-2. On the surface, AM-2 and Hili-15 shafts are circular or oval in plan while BBS shafts are oval-shaped on the outside and rectangular on the inside. Dimensions of the shafts also vary, they range between 0.4 and 0.5 m in diameter in BBS and AM-2 and are about 0.4 m wide and 0.7 m long in Hili-15. Both BBS and Hili-15 are characterized by masonry walls in the upper part. This is due to the fact they are dug in soft ground: the masonry prevents topsoil erosion and sand infiltration. The same applies to the channels and hydraulic structures located along these aflaj. On the contrary, AM-2 was dug through the hard bedrock and compact sand and is thus devoid of masonry. A kind of mortar, obtained from the calcareous bedrock, was however used to strengthen the upper part of AM-2 shafts as they were dug through looser sand (Del Cerro, 2015: 251).

During the Iron Age, access to the underground galleries for cleaning and repair was granted by the presence of small steps dug into the shaft sidewalls, and leading to the bottom of the gallery. A large double-flight staircase was instead realised along BBS for the same purpose of reaching the bottom of the gallery, c. 4 m below the ground surface (al-Tikriti, 2002b: 124).

Just as today, this access could also have been used to draw water or do the washing.

Immediately to the west of this staircase, a large 15 by 7 m open-air cistern might have been constructed in order to store falaj water when it could not be used, for example at night (al-Tikriti 2002b: 129).

Channels ('cut-and-cover'): carrying water above ground

Underground galleries lead to an open air primary channel, sometimes preceded by a 'cut-andcover gallery' (see above), whose role is to carry water to the oasis. Secondary and tertiary channels branch off from the primary channel and deliver water to each plot. Network of channels have been partially excavated at Hili and al-Madam (fig. 5). The primary channel of AM-2 is simply dug into the compact calcareous substratum, while the one of Hili-15, dug in soft ground, was furnished with masonry sidewalls. The latter is preserved on c. 500 m and measures c. 0.5 m in width (al-Tikriti, 2002b: 78). From the outlet of the underground gallery to the first plot, the primary channel of AM-2 extends over 200 m. This structure is about 1 m wide and 0.5 m deep and has a roughly rectilinear layout (Córdoba, 2013: 148). Although at present the AM-2 irrigation system has not been completely unearthed, the primary channel appears to continue along the entire system and feed secondary channels that branch-off at right angles.

At the Bin Ati site in Qattara Oasis in al-Ain, a negative linear feature c. 25 m long was exposed in the Energy Centre (ENR) area of excavations [START_REF] Power | An Iron Age Ceramic Sequence from the Bayt Bin Ati, al-Ain, UAE[END_REF]. It runs diagonally across the site and neither its source nor destination is clear. ENR {108} has a steep 'V'-shaped profile, c. 1.5 m deep with a maximum upper width of c. 80 cm and lower width of c. 10 cm. A crack tapering from c. 6 to 3 cm wide continues down to an uncertain depth, probably created by the water as it eroded away the soft natural conglomerate during its period of use. This feature may therefore be interpreted as the primary surface channel of a falaj. Its 'V'-shaped profile is however unparalleled and highlights the diversity of falaj morphology. This putative falaj cuts through the underlying phases of agricultural activity associated with a well feeding channels watering tree pits, constituting the latest agricultural feature in the stratigraphic sequence of the Iron Age II phases, which might further be interpreted as an intensification of agricultural practices from well to falaj irrigation.

The gardens fed by falaj Hili-15 are at least partly preserved but have not been fully investigated. Along the primary channel, a few secondary and tertiary earthen channels have been excavated, which branch off at right angles from each other. At Masafi-1 the remains of three successive irrigation systems could be partly explored to the north of the collective building on both sides of a stone-built fence wall that separated the settlement area, where the building was standing from a garden area located more to the north (fig. 6). The oldest system (System A in Level 4A) included a primary channel which took the shape of a small earthenmade channel 10 cm deep with a crescent-shaped profile, reinforced on the western side by a row of stones. The bottom of the channel, c. 7 cm in thickness, was made of compact fine silt, light-beige in colour with nodules of carbonates, small oxide, micro-charcoals and a few small gravels. Silty-clay sediments, orange in colour deposited at the bottom of the channel (Charbonnier et al., 2017: 17-18).

System A crossed the fence wall enclosing the garden area via a small opening that was later closed by a stone and fed a subsidiary channel. Built above the ground, this channel had a 'U'shaped section and was delimited by earthen borders. The junction between the primary and the secondary channel was destroyed. The hypothesis of their connexion is based on the similarity of the deposits at the bottom of their filling. To the east the primary channel System A, a portion of a further channel coming from the east was partly excavated, which might have belonged to this first phase. This channel measured 15 to 23 cm in width and 5 cm in depth, with a 'U'-shaped profile. This structure was running in the direction of the primary channel, at a slightly higher altitude, but their respective fillings indicate that they were not connected. A second irrigation system was later rebuilt in the same area (System B1 in Level 4B). It included a primary channel oriented SE-NW, which was bringing water from the NE. This new channel was 20-25 cm wide and 30 cm deep and was delimited by walls vertical or slightly inclined, made of stone blocks and pebbles of irregular size and shape arranged in irregular courses assembled without mortar. To the north, at its downstream end, the channel was running below the level of the ground. It was partly covered by 2 groups of 3 to 4 stone slabs around 50-70 x 20 cm to 40 x 20 cm, laid transversally across the channel. They were probably meant to protect the water from evaporation. An opening was separating the two groups of slabs, probably used to clean the channel (Charbonnier et al., 2017: 18).

The channel was distributing water into a earthen-made subsidiary channel, heading toward the east and located north of the fence wall, via a small 'V'-shaped opening between two stones.

Later (System B2 in Level 4B), this initial channel was replaced by three channels that were probably delivering water to different agricultural plots: two going to the east, a second one to the north-east, a third one to the west. All these channels were built of simple earth over the floor (Charbonnier et al., 2017: 18-19). A 14C dating was obtained from a charcoal sampled in a layer directly associated to the latest secondary channels. It yielded a dating of 2680+30BP (897-801 BC after calibration) thus showing that System B2 was in used in the middle of the Iron Age II (Charbonnier et al., 2017: 19).

A small basin or water tank dug into the ground was built at the corner of two subsidiary channels. It was only partly preserved as it has been damaged to the north by the digging of a modern channel. The basin is bordered by a low and slightly curved earthen levee. Initially, the basin may have been oval or circular in shape and c. 3 m in diameter. It is only preserved on a length of 1.7 m. A thin layer of clayey orange sediments, forming a sub-circular patch of c. 60 cm in diameter, was noticed at the bottom of the basin. It was most probably filled through a small opening on the western subsidiary channel. This basin could have surrounded a palm or a fruit tree but neither remains of roots nor any organic material were recovered during the excavation. Alternatively, the basin could have been used to store water or as a drinking place for animals.

Distributing water

We have evidence for sluices regulating and orienting the flow of water in both AM-2 and Hili-15 (al-Tikriti, 2002b: Figs. 31 & 32). Sluices gates were made of stone slabs or, in the case of AM-2, large potsherds. Two stone slabs, one still in situ, were found along AM-2 channels (Del Cerro, 2015: 251-252). One has to keep in mind that perishable material might have been used as well. In Hili, some of these sluices were implemented along a water distributor as indicated by vertical jambs located on each sides of its outlets. This structure is named shari'a by al-Tikriti although it mainly distributed water into sub-channels. The distributor corresponds to a broader section of the main channel, reaching a width of c. 1 m and paved with large stone slabs, which feeds three secondary channels: one aligned with the main channel and two branching-off at right angles, toward the northwest and the southeast (al-Tikriti, 2002b: 120).

Many Iron Age sherds were found inside this structure. Combined with the stone pavement, this would suggest its use for domestic activities. The stone slabs could however also have been placed to prevent scouring when water was diverted to either channel.

Irrigated spaces

The excavation of AM-2 by the Spanish team led by J. Córdoba and M. Del Cerro has provided unprecedented and invaluable information regarding Iron Age field systems. Preserved under the sand dunes and entirely cut into the upper, and decayed, substratum, the irrigation system of AM-2 is estimated to extend over about 15 hectares (fig. 5) (Del Cerro & Córdoba, 2018: 85). Large elongated basins or small circular ones, cut into the substratum, are aligned along the secondary channels, and are interpreted as planting holes. These basins and the channels were infilled with sand and no trace of organic matter is reported. Only a few date stones were discovered (Del Cerro & Córdoba, 2018: 96), suggesting the cultivation of date palms in at least some of these basins. Other basins, perhaps the elongated ones, could also have been dedicated

to annual crops such as wheat and barley. The absence of organic matter could be explained by its poor conservation in sandy soil.

The study of the channel systems provide indication on water distribution during the Iron Age.

The presence of sluices, along channels and distributors, indicate that water flow was regulated and thus that plots were irrigated sequentially. Some sort of rotation must have been established.

In the absence of any text, we do not know if water shares were owned by individuals, lineage groups or tribes. The absence of plot boundaries in al-Madam could argue for community-based land management. Be that as it may, the spatial setting of AM-2, a primary channel running along the entire oasis with secondary channels at right-angle, has no modern parallel.

Contemporary water systems tend to adopt an arborescent spatial pattern: this reinforces the impression that one is dealing with a very old landscape. At Masafi-1 the distribution of the water inside the garden area (or at least the small excavated portion of it) also suggests the irrigation of several plots but does not seem to follow a mapping as regular as in al-Madam.

Conclusion

Falaj AM-2 constitutes one of the most important in South East Arabia largely owing to the careful documentation of J. Córdoba and his team. This allows us to compare and contrast Falaj AM-2 with the other reasonably well-documented aflaj discussed above. Two of these (Hili 15, 13 BBS) appear to be ghayl aflaj tapping shallow ground water; one was fed by runoffs (Masafi-1); the forth is the only one which might have tapped a deep aquifer, as it was cut through calcareous bedrock (AM-2). The schematic diagram of a Dawudi falaj tapping mountain aquifers that usually accompanies most books and articles dealing with Iron Age aflaj (e.g. Cleuziou & Tosi, 2007: p. 152, Fig. 162;Magee, 2014: p. 216, Fig. 8.2) is as such inappropriate and possibly anachronous. The known Iron Age II aflaj therefore appear to broadly correspond to the 'water draining galleries' previously discussed by Rémy [START_REF] Boucharlat | Iron Age water drainig galleries and the Iranian 'Qanāt[END_REF]. Similarly, the 'cut-and-cover' section of the falaj is absent from AM-2 and all other well-documented Iron Age aflaj with the exception of Hili-15. The primary surface channels of AM-2, Masafi-1 and Bin Ati were all open. It thus seems that the 'cut-and-cover' section of the Hili-15 falaj cannot be considered archetypal. These disparities raise questions that still await an answer, regarding the geographical extension, the magnitude, the relation with technical aspects of falaj construction, the possible different cultural response to, and the ultimate geo-hydrological reasons for their development. Nevertheless, significant progresses have been made in the study of these phenomena, and a relevant part of these are owed to the great effort put by J. Cordoba and his team in the large-scale investigation of its development in the al-Madam plain.

Bibliography

  to reach a height of 8 m. The German team supposed the gallery to have been deepened several times over a long period of useor in occasion of several moments of re-useextending from the Iron Age up to the Late Islamic period (see also Yule 2017: fig. 10). This suggests a possible first construction during the Iron Age II. Also excluded from our description of Iron Age falaj morphology and techniques should be the aflaj of al-Ayaay, Dhahret al-Hasa and al-Jabeeb, only surveyed and mentioned by al-Tikriti (2010) in Abu Dhabi Emirate; the falaj at Muweilah in the Sharjah Emirate published by M.

  Al-Ghafri, A. (2004), Study on Water Distribution Management of Aflaj Irrigation Systems of Oman. (Doctoral Thesis, Hokkaido University, Sapporo, Japan). Al-Sulaimani, Z. bin K., Helmi, T. and Nash, H. (2007), The Social Importance and Continuity of Falaj Use in Northern Oman, International History Seminar on Irrigation and Drainage, Tehran-Iran May 2-5, 2007. The Iranian National Committee on Irrigation and Drainage (IRNCID). Available at: https://ore.exeter.ac.uk/repository/handle/10036/15174 (Accessed: 16 October 2018). Al-Tikriti, W. Y. (2002a), "The south-east Arabian origin of the falaj system", Proceedings of the Seminar for Arabian Studies, 32, 117-138. ISSN: 0308-8421. Available at: http://www.jstor.org/stable/41223728.

FiguresFigure 1 .

 1 Figures

  Figure 1. Map of Southeast Arabia indicating the location of aflaj discussed in the text (© J. Charbonnier).

Figure 2 .

 2 Figure 2. Archetypal section of a falaj (© J. Charbonnier).

Figure 3 .

 3 Figure 3. Map of falaj Hili-15 and associated archaeological sites (© J. Charbonnier). Top left: photo of Area H (©T. Power)

Figure 5 .Figure 6 .

 56 Figure 5. Map of Al-Madam aflaj associated archaeological site (© J. Charbonnier). Top left: aerial view of the irrigation area associated with falaj AM-2 (courtesy C. Del Cerro and J. Córdoba, © Spanish archaeological mission in the UAE).