domain: phys chim

text:
Dr Yiran Zhao

Prof. N Julie Descamps

Soraya Ababou-Girard

Jean-François Bergamini

Lionel Santinacci

Dr Yoan Léger
email: yoan.leger@insa-rennes.fr

Neso Sojic
email: neso.sojic@enscbp.fr

Gabriel Loget
email: gabriel.loget@univ-rennes1.fr

Dr J.-F Bergamini

Sojic

Prof. S Ababou-Girard

Metal-Insulator-Semiconductor Anodes for Ultrastable and Site-Selective Upconversion Photoinduced Electrochemiluminescence

Keywords: localized electrochemistry, luminescence, photoelectrochemistry, silicon, upconversion

Photoinduced electrochemiluminescence (PECL) allows the electrochemically assisted conversion of low-energy photons into high-energy photons at an electrode surface. This concept is expected to have important implications, however, it is dramatically limited by the stability of the surface, impeding future developments. Here, a series of metal-insulator-semiconductor junctions, using photoactive n-type Si (n-Si) as a light absorber covered by a fewnanometer-thick protective SiOx/metal (SiOx/M, with M = Ru, Pt, and Ir) overlayers are investigated for upconversion PECL of the model co-reactant system involving the simultaneous oxidation of tris(bipyridine)ruthenium(II) and tri-n-propylamine. We show that n-Si/SiOx/Pt and n-Si/SiOx/Ir exhibit high photovoltages and record stabilities in operation (35 h for n-Si/SiOx/Ir) for the generation of intense PECL with an anti-Stokes shift of 218 nm. We also demonstrate that these surfaces can be employed for spatially localized PECL. These unprecedented performances are extremely promising for future applications of PECL.

Introduction

Photoinduced electrochemiluminescence (PECL) is a growing field of research that combines charge transfer at the semiconductor/electrolyte interface and electrochemiluminescence (ECL). [1][2][3][4][5][6] ECL is a well-known phenomenon that involves an electrochemical reaction generating the excited state of a luminophore at an electrode surface leading to light emission. [7,[START_REF] Sojic | Analytical Electrogenerated Chemiluminescence: From Fundamentals to Bioassays[END_REF] A model ECL system that has become widely used in medical diagnosis [START_REF] Faatz | Anal. Electrogenerated Chemilumin. From Fundam. to Bioassays[END_REF][START_REF] Zanut | [END_REF] and currently attracts considerable attention for sensing, [11][12][13] imaging, [14][15][16][17] and microscopy, [18][19][20][21][22] involves the simultaneous oxidation of tris(bipyridine)ruthenium(II) ([Ru(bpy)3] 2+ ) and tri-n-propylamine (TPrA) in an aqueous electrolyte at physiological pH. In PECL, this co-reactant ECL system can be employed with Si photoanodes to perform an electrochemically-assisted upconversion process [3] where the absorption of infrared (IR) photons (>800 nm) results in the emission of visible photons (632 nm) at the electrode vicinity, as shown in Figure 1a. Another remarkable aspect of PECL is the considerable decrease of the ECL onset potential, which is caused by the photovoltage at the semiconductor interface and allows for triggering photon emission at record low potentials [3][4][5] even if ECL reactions are always highly exergonic and typically require the application of high potentials. [23,24] PECL systems are extremely promising for ultrasensitive detection, microscopy, light-addressable devices, and IR imaging. [1][2][3][4][5][6] However, as for all photoelectrochemical processes, they are strongly limited by the poor stability of the photoelectrode. [25] The advantages of PECL and the challenges in this field have been discussed in a recent review. [26] So far, upconversion PECL could be demonstrated in water and was reported for short durations, typically in the minute scale (Table S1) for Si-based photoanodes protected with a covalentlyattached organic monolayer, [4], [27] and n-Si/SiOx/Ni metalinsulator-semiconductor (MIS) photoanodes. [3] These operation times are obviously too short to allow a prospect of practical application. A possible solution to this bottleneck is the use of oxide-based photoanodes, known to exhibit higher stabilities. This strategy, which has been recently explored with BiVO4 [5] and α-Fe2O3, [6] resulted in considerably improved PECL stability of 2 h (Table S1). [5] However, the wide bandgaps of oxide-based semiconductors do not allow absorption of low-energy photons and strictly prohibit their use in upconversion PECL processes (allowing only Stokestype PECL). [5,6] Consequently, future developments in upconversion PECL crucially rely on the development of stable narrow-bandgap photoanodes. Silicon is established as the material of choice in many lightconversion applications due to its abundancy, nontoxicity, and narrow bandgap (Eg = 1.1 eV) which makes it active from IR to UV regions. For these reasons, it is undeniably the most important semiconductor in the photovoltaic industry, [28,29] a highly promising material for photonics, [30,31] and a prime candidate for photoelectrochemical devices. [32][33][34] However, manufacturing stable Si photoelectrodes is still a major challenge [35], [36] because of its low intrinsic activity and poor stability in aqueous solutions. [START_REF] Zhang | Electrochemistry of Silicon and Its Oxide[END_REF] This issue is even more pronounced on photoanodes as photocorrosion generates an electrically insulating SiOx layer that inhibits charge transfer at the solid/electrolyte interface. In this respect, Si photoanodes based on the MIS junction, a key architecture of modern electronics, are attracting considerable attention because of their remarkable properties. [START_REF] Scheuermann | [END_REF][39][40][41][42][43][44][45] Specifically, it has been reported that MIS photoanodes made on n-type Si (n-Si) wafers can be used to efficiently and durably oxidize water in harsh conditions. [46][47][48][49][50][51][52] In typical MIS photoanodes, the metal thin film is a key element that must have a thickness in the nanometer range to enable light transmission that ensures electron/hole (e -/h + ) pair photogeneration in the semiconductor. [35][36][START_REF] Zhang | Electrochemistry of Silicon and Its Oxide[END_REF][START_REF] Scheuermann | [END_REF][39][40][41][42][43][44][45][46][47][48][49] Besides, it plays a crucial role by i) protecting the semiconductor by avoiding its corrosion, [35][36][START_REF] Zhang | Electrochemistry of Silicon and Its Oxide[END_REF] ii) ensuring the efficient collection of charge carriers through the insulator tunnel layer, [START_REF] Scheuermann | [END_REF]39] iii) granting fast kinetics of the electrochemical reaction, [53] and iv) ensuring a high barrier Schottky junction to promote high photovoltage. [41,54] In this article, we report on our investigations of three Si/SiOx/metal (Si/SiOx/M, with M = Ru, Pt, and Ir) MIS electrodes for the upconversion PECL of the [Ru(bpy)3] 2+ /(TPrA) model system. Ru, Pt, and Ir were chosen as potential candidates because, according to their Pourbaix diagrams, they are expected to exhibit higher stability [START_REF] Pourbaix | Atlas of Electrochemical Equilibria in Aqueous Solutions[END_REF] in PECL conditions (pH = 7.4) than the previously-used Ni thin films. [3] In addition, these metals are known for their good electrocatalytic activities and possess high work functions (4.7 eV < WM < 5.9 eV), [START_REF] Hölzl | Solid Surf. Physics. Springer Tracts Mod. Physics[END_REF][START_REF] Derry | [END_REF] essential for creating a photoactive junction with n-Si and producing high photovoltages. [54] Our results demonstrate that, while Si/SiOx/Ru fails in promoting PECL, n-Si/SiOx/Pt and n-Si/SiOx/Ir photoelectrodes exhibit unprecedented performances, enabling long-term PECL generation with ultrathin film thicknesses (3 nm), opening exciting opportunities for PECL.

Results and Discussion

Preparation and characterization of the surfaces The Si/SiOx/M MIS junctions were prepared, first, by chemically oxidizing cleaned Si (100) wafers to create a 1.5-to-2 nm-thick SiOx tunnel layer, as we previously reported. [50,58] After that, a 3 nm-thick metal layer was deposited on SiOx by direct current magnetron sputtering onto 1.5x1.5 cm² Si/SiOx surfaces. During deposition, the thickness of the coating was monitored in-situ using a quartz crystal microbalance (QCM) and monitored ex-situ by atomic force microscopy (AFM). This low thickness value was specifically chosen because previous research in the field of Sibased MIS anodes has revealed that ultralow metal thicknesses (< 5 nm) promote the highest photoelectrochemical performance. [3,40,47] AFM and scanning electron microscopy (SEM) were performed on the so-prepared Si/SiOx/M surfaces and revealed high uniformity and planarity of the metal films, which is demonstrated by the absence of observable features on the high-magnification SEM pictures of Figure S1 and the low root mean square (RMS) roughness values of 0.36, 0.28, and 0.33 nm determined from the AFM pictures of Si/SiOx/Ru, Si/SiOx/Pt, and Si/SiOx/Ir presented in Figure 2a,b, and Figure S2. The composition of the outermost surface of the electrodes was analyzed by X-ray photoelectron spectroscopy (XPS), as shown in Figure 2c. The grey spectrum, measured for Si/SiOx, indicates that, before deposition, the surface is only constituted of Si and O atoms, with a low content of adventitious carbon. The colored spectra, acquired after the deposition of the metal thin films, confirm the presence of the deposited metals with characteristic Pt 4f peaks at 71.5 and 74.9 eV, Ru 3d peak at 280.5 and 284.6 eV, and Ir 4f peaks at 61.0 and 63.9 eV. These spectra also feature a strong disappearance of the Si 2s and 2p peaks, which is in good agreement with dense and conformal metal thin films. The presence of oxygen, which can be observed by its 1s peak localized between 530 and 534 eV, originates from the native oxide/hydroxide phase at each metal surface and the underlying SiOx layer.

Electrochemiluminescence (ECL)

The junctions were then investigated for ECL of the co-reactant [Ru(bpy)3] 2+ /TPrA system. In the first experiments, the MIS electrodes were manufactured onto degenerate p ++ -Si. This type of silicon, characterized by a high concentration of dopants and low resistivity (ρ = 0.001 -0.005 Ω cm), is non-photoactive, which allows straightforward assessment of the ECL performance for each MIS electrode in the dark. The effects of the ECL reagents dissolved in phosphate-buffered saline (PBS) were investigated on p ++ -Si/SiOx/Ir. Figure 3a presents the cyclic voltammograms (CVs, top panel) and the corresponding ECL intensity vs potential curves (bottom panel). This figure shows that, when studied individually, TPrA (black curves) and [Ru(bpy)3] 2+ (blue curves) are oxidized at potentials higher than 0.9 V and 1 V, respectively (all potentials reported in this article are referred vs Ag/AgCl (3 M KCl)), and do not emit detectable ECL. However, when they are present together in the electrolyte, their concomitant oxidation produces ECL from 1 V, showing the suitability of the p ++ -Si/SiOx/Ir anode for triggering [Ru(bpy)3] 2+ /TPrA ECL. Next, the effect of the metal thin film was investigated. The electrochemical and corresponding ECL responses for the three p ++ -Si/SiOx/M anodes in the ECL electrolyte (100 mM TPrA and 5 mM [Ru(bpy)3] 2+ in PBS) are presented in Figure 3b. Here, we can observe a strong similarity between p ++ -Si/SiOx/Ir (red curves) and p ++ -Si/SiOx/Pt (blue curves) that both granted ECL emission from 1 V and stable voltammograms. However, p ++ -Si/SiOx/Ru exhibited a completely different behavior. First, it only produced measurable ECL at potentials higher than 1.35 V (detailed data for this anode is presented in Figure S3) and its CV features changed drastically during cycling. The first cycle, shown as a thin green line in Figure 3b, exhibits a large oxidation wave with a current density (j) as high as 8.7 mA cm -2 , while subsequent cycles are associated with smaller values (j <1.7 mA cm -2 ) and decaying ECL intensity (Figure S3). Similar behavior was observed in the absence of the ECL reagents (in an electrolyte consisting only of PBS, Figure S4a), which suggests that the large current observed during the first forward scan is mainly caused by the oxidation of the Ru thin film and the oxidation of water. The higher ECL onset potential is attributed to the low activity of this anode and the evolution of the CVs during cycling is consistent with strong damage of the Ru thin film during the first cycle, leading to its deactivation. This is in good agreement with the AFM measurements presented in Figure S4c, which shows a considerable increase in the surface roughness after the CV study. The stability was assessed by galvanostatic experiments in which a current density of 1 mA cm -2 was applied and the anode potential was monitored. In these tests, the electrolyte was circulated in the cell using a peristaltic pump (flow rate = 0.7 mL s -1 ), which ensures efficient mass transport of the ECL reactants at the solid/liquid interface leading to homogenous and brighter ECL emission for a long duration. [59] The chronoamperograms (CPs) of Figure 3c shows that freshly hydrogenated p ++ -Si (p ++ -Si-H, pink), uncoated p ++ -Si/SiOx (grey), and p ++ -Si/SiOx/Ru (green) rapidly failed. It is evidenced by the strong potential increase (resulting from the degradation of the electrode interface) occurring a few minutes after the beginning of the test. Compared to these anodes, p ++ -Si/SiOx/Pt exhibited a considerable stability improvement and operated at a potential lower than 2 V for almost 2 h. However, after 160 min, its degradation led to a dramatic potential increase. Conversely, p ++ -Si/SiOx/Ir outperformed all studied anodes and could be used for 3 h without potential variation. In these conditions, p ++ -Si/SiOx/Ir and p ++ -Si/SiOx/Pt produced a bright ECL emission during the entire experiment (circles in Figure 3c) that was visible with naked eyes.

Photoinduced electrochemiluminescence (PECL)

After having identified the best interfaces for ECL, we tested them for PECL. For that, MIS structures were prepared on moderately doped n-Si (ρ = 0.3-0.7 Ω cm) to yield photoactive n-Si/SiOx/Pt and n-Si/SiOx/Ir anodes (i.e., photoanodes). The typical emission responses obtained for ECL with a non-photoactive MIS surface and PECL for its photoactive equivalent can be compared in Figure 4a. This 3D plot presents the emission spectra as a function of potential recorded: i) in the dark on a non-photoactive p ++ -Si/SiOx/Ir producing ECL (left) and ii) under 850 nm illumination on a n-Si/SiOx/Ir producing PECL (right). We now discuss the characteristic PECL features of the n-Si/SiOx/M photoanodes. In the CV (top part) of Figure 4b, it can be observed that both n-Si/SiOx/Pt and n-Si/SiOx/Ir are inactive in the dark, revealing their rectifying nature. However, when illuminated with λexc = 850 nm they afford photocurrents and PECL. While both non-photoactive anodes (p ++ -Si/SiOx/Ir and p ++ -Si/SiOx/Pt) triggered ECL at similar onset potential (vide supra, Figure 3b), the photoelectrochemical data presented in Figure 4b reveals that both photoanodes generates PECL at distinct potentials, which is characteristic of a different photovoltage (Voc) at each photoactive MIS junctions. Subtraction of the onset potential values of ECL (p ++ -Si/SiOx/M in the dark) with that of PECL (illuminated n-Si/SiOx/M) gives Voc values of 485 and 280 mV for n-Si/SiOx/Pt and n-Si/SiOx/Ir photoanodes, respectively (arrows in Figure 4b). Remarkably, the photovoltage for n-Si/SiOx/Pt corresponds to state-of-the-art performance for n-Si-based photoanodes [START_REF] Scheuermann | [END_REF]41,50] and is higher than that reported for n-Si/SiOx/Ni (Voc = 410 mV) in similar conditions. [3] Voc values are correlated with the Schottky barrier height of the MIS device, which is theoretically controlled by the work function of the metal (Figure S5). However, in practice, the effective Shottky barrier height is also strongly affected by other parameters such as the interface quality and homogeneity. [54] If Ir and Pt have reported WM values lying in the same range (5.1 eV < WM < 5.9 eV), [START_REF] Hölzl | Solid Surf. Physics. Springer Tracts Mod. Physics[END_REF][START_REF] Derry | [END_REF] in our case, Pt produces a higher Schottky barrier at n-Si/SiOx. This finding is well in line with a recent work where 2 nm-thick Pt thin films were employed as Schottky contact to considerably enhance the photovoltage of n-Si-based MIS photoanodes for water splitting. [41] In this regard, it is also known that the thickness of the metal thin film often affects photovoltage on MIS photoanodes, which we experimentally verified for n-Si/SiOx/Ir, as shown in Figure S6. Long-term stability was tested for both photoanodes at a photocurrent density of 1 mA cm -2 in the same conditions as that previously described, except that, in this case, the entire electrode surface was homogeneously illuminated at 850 nm. As presented in Figure 4c, n-Si/SiOx/Pt exhibited a stability profile very close to that previously determined for its p ++ -Si-based counterpart (both CP curves are plotted in Figure S7). The photoanode operated below 2 V for 140 min, then, a strong increase of its potential followed. Comparatively, n-Si/SiOx/Ir exhibited exceptional stability and generated strong PECL over 35 h of operation with a minimal potential increase (red curve in Figure 4c). At the end of the test, the photoanode was still operating at a potential of 0.95 V, with a PECL intensity of 60% of the initial value, demonstrating the outstanding performance of n-Si/SiOx/Ir. Four independently prepared n-Si/SiOx/Ir were tested for at least 6 h and all promoted PECL identically, without noticeable performance decrease. After the stability test, the surface of n-Si/SiOx/Ir was analyzed ex-situ by XPS (Figure S8) that revealed strong Ir 4f and 4d bands and weak Si 2s and 2p bands, demonstrating that the Ir film was still present and densely covered the Si/SiOx surface. An increase of the O 1s peak can also be noticed on the spectrum, which is correlated with the oxidation of the surface during the photoelectrochemical experiment. Finally, AFM analysis performed on this surface (Figure S9) showed the apparition of bigger particles which may be correlated with the precipitation of insoluble species onto the photoanode, in good agreement with the increase of the carbon content observed on the XPS spectrum and the decrease of PECL intensity (Figure 4c). These results demonstrate that Pt and Ir thin films allow the promotion of upconversion PECL in water with record stabilities. So far, this phenomenon was only reported for 15 min [3] (Table S1), while our results show that n-Si/SiOx/Pt and especially n-Si/SiOx/Ir allow promoting PECL for tens of hours without any surface regeneration or re-activation treatments, as usually performed in classic ECL imaging or bioassays. [START_REF] Faatz | Anal. Electrogenerated Chemilumin. From Fundam. to Bioassays[END_REF]60] This remarkable emission stability opens new technological perspectives. Finally, the most promising surface, namely, n-Si/SiOx/Ir was tested for site-selective upconversion in proof-of-principle experiments. For that, the setup of Figure 1b was adapted for an 840 nm single-mode laser that was employed for locally illuminating a 30 µm-diameter spot on the photoanode, that was constantly polarized at an applied potential (Eapp) of 0.85 V. Localized illumination of the surface with the invisible (for the human eye) IR laser beam induced the appearance of a bright light spot at the surface of the n-Si/SiOx/Ir that could be easily observed by naked eyes and recorded with a digital camera. This PECL spot could be moved instantaneously over the photoanode surface by displacing the laser beam. This can be observed in the movie provided in Supplementary information (and the snapshots of Figure 4d) showing the displacement of the PECL spot in the photoelectrochemical cell when the incident laser spot is moved horizontally on the surface. The laser and the PECL spots could be localized and measured using a homemade hyperspectral confocal apparatus (see Methods section). As shown in Figure 4e, the excitation (i.e., the laser spot) and emission maxima (i.e., the PECL spot) are localized at the same location. These curves also show that the PECL spot size is much larger than the laser beam diameter, which is a direct consequence of the physical parameters of crystalline Si. Due to its indirect bandgap and its high charge transport capabilities, photogenerated holes have a long lifetime and a diffusion length. These results are in good agreement with the decay of the PECL profile (Figure S10), the calculation of hole diffusion length (Section 3 in Supplementary Information), and previous literature on light-addressable electrochemistry. [4,[61][62][63]

Conclusion

Si/SiOx/M (M = Ru, Pt, and Ir) MIS anodes were investigated for upconversion PECL of the aqueous [Ru(bpy)3] 2+ /(TPrA) model system at physiological pH. The performance of the anodes was first assessed for ECL in the dark, with non-photoactive p ++ -Si substrates, and, then, under IR illumination, with photoactive n-Si substrates. We found that while Si/SiOx/Ru fails in the anodic regime due to dramatic oxidation, Si/SiOx/Pt and Si/SiOx/Ir exhibit outstanding performance. Specifically, n-Si/SiOx/Pt generates PECL with an unprecedented photovoltage of 480 mV and n-Si/SiOx/Ir allows to generate bright PECL for 35 h. This is remarkable when considering the low stability of Si photoanodes and previous reports achieving a maximum operation time for upconversion PECL of only 15 min (Table S1). [3] This anti-Stokes PECL process allows to convert IR irradiation (λexc = 850 nm) in a visible signal (λem = 632 nm) onto the whole surface of the MIS photoanode or at a specifically-chosen location when an IR beam with a small spot size is used, which was demonstrated on proofof-principle experiments. As the spatial resolution is mainly controlled by the high performance of crystalline Si, we anticipate that the resolution for site-selective PECL will be improved soon by semiconductor engineering. These results provide solutions to break the wall of instability, which hindered the application of PECL for technological issues and open exciting opportunities in IR imaging, (bio)analysis, and microscopy.

Entry for the Table of Contents

n-Si/SiOx/Pt and n-Si/SiOx/Ir exhibit high photovoltages and record stabilities in operation (up to 35 h) for the generation of intense anti-Stokes photoinduced electrochemiluminescence onto the whole surface of the MIS photoanode or at a specifically-chosen location. These results provide solutions for overcoming the instability that has hampered the practical application of upconversion PECL.

Institute and/or researcher Twitter usernames: @chimie_ISCR

Figure 1 .

 1 Figure 1. Upconversion PECL and MIS structures. a) Scheme showing the photoinduced charge transfer process occurring at the MIS photoanode initiated by the absorption of IR light (λexc) and leading to the emission of visible light (λem) by PECL (the side product of the TPrA radicals formed during the ECL process is denoted by P). b) Scheme of the photoelectrochemical setup employed for studying PECL. c) Normalized spectra of the electrolyte absorption (orange curve), emission of the LED used in this work (brown), PECL emission (red curve), and bandgap position of Si (blue dashed line).

Figure 2 .

 2 Figure 2. Characterization of the MIS surfaces. a,b) AFM pictures of the p ++ -Si/SiOx surface before coating (a), and p ++ -Si/SiOx/Ir after Ir coating (b). c) XPS spectra of the p ++ -Si/SiOx surface before coating (grey) and the p ++ -Si/SiOx/M surfaces with M = Pt (blue), M = Ru (green), and M = Ir (red).

Figure 3 .

 3 Figure 3. ECL at non-photoactive MIS electrodes. a) CVs measured in the dark (top) and corresponding ECL intensity profiles (bottom) measured on p ++ -Si/SiOx/Ir in the presence of 100 mM TPrA (green), 5 mM [Ru(bpy)3] 2+ (purple), and 100 mM TPrA + 5 mM [Ru(bpy)3] 2+ (red). b) CVs measured in the dark (top) and corresponding ECL intensity profiles (bottom) measured in the presence of 100 mM TPrA + 5 mM [Ru(bpy)3] 2+ on p ++ -Si/SiOx/Ir (red), p ++ -Si/SiOx/Pt (blue), and p ++ -Si/SiOx/Ru (green). The first cycle measured on p ++ -Si/SiOx/Ru is shown by a thin green line. The ECL intensity shown for p ++ -Si/SiOx/Ru corresponds to the second CV cycle. c) CP curves (lines) recorded at 1 mA cm -2 on p ++ -Si/SiOx/Ru (green), p ++ -Si-H (pink), p ++ -Si/SiOx (black), p ++ -Si/SiOx/Pt (blue), and p ++ -Si/SiOx/Ir (red). The ECL intensity is shown by circles for p ++ -Si/SiOx/Pt (blue circles) and p ++ -Si/SiOx/Ir (red circles). These experiments were performed in PBS (pH 7.4), CVs were recorded at 50 mV s -1 .

Figure 4 .

 4 Figure 4. PECL at photoactive MIS electrodes. a) Consecutive ECL emission spectra recorded in the dark on p ++ -Si/SiOx/Ir (left) and illuminated n-Si/SiOx/Ir (right) during linear sweep voltammetry. b) CVs (top) measured on n-Si/SiOx/Ir (red) and n-Si/SiOx/Pt (blue) in the dark and under 850 nm illumination. Corresponding PECL intensity profiles (bottom) measured on n-Si/SiOx/Ir (red) and n-Si/SiOx/Pt (blue) in the dark (full lines) and under 850 nm illumination (circles). The ECL measured in the dark on p ++ -Si/SiOx/Ir (red) and p ++ -Si/SiOx/Pt (blue) is also shown by dotted lines. c) CP curves (lines) recorded at 1 mA cm -2 on n-Si/SiOx/Pt (blue), and n-Si/SiOx/Ir (red) under 850 nm illumination. PECL intensity is shown by circles. The electrolyte was replaced at the time indicated by dashed vertical lines. d) Optical images showing the displacement of the PECL spot on n-Si/SiOx/Ir by moving an 840 nm laser beam on that surface when a potential of 0.85 V is imposed, the white dashed line indicates the boundary of the electrode surface. These images were extracted from the movie available in the Supplementary file. e) Normalized intensity profile of the IR excitation pattern (green) and the PECL emission pattern (red) recorded at two different positions. This data was measured in the presence of 100 mM TPrA + 5 mM [Ru(bpy)3] 2+ in PBS (pH 7.4), CVs were recorded at 50 mV s -1 .

Acknowledgements

This work was funded by ANR (LiCORN, ANR-20-CE29-0006). Loïc Joanny and Francis Gouttefangeas from ScanMAT/CMEBA are acknowledged for SEM analyses.


Riccardo Cocci
email: riccardo.cocci@cea.fr

Alberto Ghione
email: alberto.ghione@cea.fr

Lucia Sargentini
email: lucia.sargentini@cea.fr

Guillaume Damblin
email: guillaume.damblin@cea.fr

Didier Lucor
email: didier.lucor@lisn.upsaclay.fr

MODEL ASSESSMENT FOR DIRECT CONTACT CONDENSATION INDUCED BY A SUB-COOLED WATER JET IN A CIRCULAR PIPE

In this paper, the condensation induced by a sub-cooled water injection in a circular horizontal pipe with a two-phase stratified flow is investigated. The focus of the work is to review the physical models or correlations predicting the condensation heat transfer coefficient and assess them against an experimental database.

Three experiments, namely COSI, TOPFLOW-PTS and UPTF, are consolidated in a substantial database. They have different configurations and complexity, covering a wide range of injection mass flowrate, temperature and pressure. A thermal-hydraulic analysis is performed, resulting in reliable and coherent experimental data.

The condensation models found in the literature are based on the modelling of the Nusselt number through several dimensionless numbers. The assessment of these correlations against the experimental database provides poor results. Thus, a new approach is proposed.

The cold jet is modelled as a heat exchanger, which is described by a condensation potential.

The analytical formula of the potential is found starting from an energy balance at the injection, showing that the condensation depends on the jet geometrical shape and a parameter 𝜂.

A new correlation for the parameter 𝜂 is calibrated against the COSI and TOPFLOW-PTS experiments, significantly reducing the average standard deviation between evaluations and experimental data. The new correlation is then applied to an independent database, i.e. the UPTF experiments. The results show good agreement between the calculated and

experimental values, proving the capability of the new model to accurately predict the condensation at the injection.

Keywords

Introduction

Direct Contact Condensation (DCC) phenomena between steam and sub-cooled water are of great importance in various industrial fields such as nuclear [START_REF] Aksan | Thermal-hydraulic phenomena for water cooled nuclear reactors[END_REF], chemical [START_REF] Finkelstein | Interfacial Heat Transfer Coefficients of Various Vapors in Direct Contact Condensation[END_REF] and manufacturing [START_REF] Maćkowiak | Modelling of combined direct-contact condensation and reactive absorption in packed columns[END_REF].

In the literature, two main configurations for the occurrence of DCC have been widely investigated: the injection of steam in large liquid pools (e.g. [START_REF] Aya | Evaluation of heat-transfer coefficient at direct-contact condensation of cold water and steam[END_REF], [START_REF] Yang | Thermal hydraulic characteristics of unstable bubbling of direct contact condensation of steam in subcooled water[END_REF], [START_REF] Zu | Experimental study on direct contact condensation of stable steam jet in water flow in a vertical pipe[END_REF], [START_REF] Gregu | Experimental study on steam chugging phenomenon in a vertical sparger[END_REF], [START_REF] Song | Steam Jet Condensation in a Pool: From Fundamental Understanding to Engineering Scale Analysis[END_REF]) and the injection of sub-cooled water in large volumes of steam (e.g. [START_REF] Celata | A comprehensive analysis of direct contact condensation of saturated steam on subcooled liquid jets[END_REF], [START_REF] Seidel | Experimental studies on high-pressure hightemperature contact-condensation at falling jets in the TOPFLOW pressure-tank[END_REF], [START_REF] Takahashi | Heat Transfer in Direct Contact Condensation of Steam to Subcooled Water Spray[END_REF]). On the contrary, the DCC induced by a sub-cooled water injection in a circular horizontal pipe with a two-phase stratified flow was studied in a limited number of articles. In Fig. 1, the phenomenon is briefly illustrated. There, the cold water (in light blue) flows mainly from the left to the right of the pipe. The gas phase (in yellow) consists of pure steam without non-condensable gases that can flow in either a co-current or counter-current way.

Fig. 1 Main phenomena occurring at a sub-cooled injection into a two-phase flow.

Two main condensation zones are identified: the jet and the stratified condensation. The former is due to the contact of the cylindrical jet with the steam and then its impact in the liquid flow, the latter to the contact of the steam and the liquid at the interface in the stratified flow far away from the jet. In this article, we are interested on studying and modelling the condensation at the injection in the framework of system codes development.

In Fig. 2, the main local DCC phenomena in the injection region are represented [START_REF] Liao | Cold leg condensation model for analysing loss-of-coolant accident in PWR[END_REF]. The cold water is injected in the pipe, plunging in a two-phase flow of hot water (in dark blue) and pure steam.

Fig. 2 Main local DCC phenomena occurring at the injection.

Different local condensation phenomena are identified. Before the impact with the hot water, the steam condensates over the rough cold jet surface. After the impact, the condensation is mostly driven by the steam entrainment in the liquid phase [START_REF] Petrovic De With | Three-dimensional condensation regime diagram for direct contact condensation of steam injected into water[END_REF] and the induced turbulence enhances the heat exchange mechanism. In the liquid phase, mixing phenomena take place between the cold water rebounding the walls and the hot water [START_REF] Naik-Nimbalkar | Thermal mixing in T-junctions[END_REF]. Moreover, the injection itself and the lateral rebounds create a wavy liquid-steam surface, enhancing the steam condensation [START_REF] Hughes | Direct Contact Condensation and Momentum Transfer in Turbulent Separated Flows[END_REF].

In 1989, Bestion and Gros d'Aillon [START_REF] Bestion | Condensation tests analysis and correlation for the CATHARE code[END_REF] An improvement of this initial correlation was later proposed by Janicot and Bestion [START_REF] Janicot | Condensation modelling for ECC injection[END_REF] in 1993. This model is based on the liquid height in the test section H as the turbulence length (e.g. the characteristic length associated to the Nusselt and Reynolds numbers) and the heat exchange area as function of the void fraction in the test section and the injection pipe diameter.

In 2015, Liao et al. [START_REF] Liao | Cold leg condensation model for analysing loss-of-coolant accident in PWR[END_REF] developed a new DCC model based on the same dimensionless numbers but an undefined function of the liquid height f(H) to define the turbulence length.

This length was then used to calculate the heat exchange area. They decided to fit the correlation using another subset of COSI experiments: the Westinghouse configuration, characterised by a vertical injection. Good results were also shown for the prediction of the condensation in another test facility UPTF (Upper Plenum Test Facility) [START_REF] Weiss | UPTF experiments: Principal full-scale test results for enhanced knowledge of large break LOCA scenarios in PWR's[END_REF].

In the same year, Ren et al. [START_REF] Ren | Experiment of Condensation in T-junction: Steam-water Flow in Water-injected Condition[END_REF] described the ECCS (Emergency Core Cooling System) facility, which has a test section similar to the COSI one. Once described the phenomenology in the test section, the authors proposed different models based on the same dimensionless numbers and selected the best-fitting one. Gaillard and Rodio [START_REF] Gaillard | A general thermal stratification criterion for single and two-phase flows in a pipe after subcooled injection[END_REF], in 2018, proposed a stratification criterion for single and two-phase flows in presence of a sub-cooled injection. In their paper, a new condensation model at the jet is used for the validation of the criterion. Nevertheless, the authors do not specify which experiments they used to fit the model. In this new correlation, the Froude number, the void fraction and the ratio of the injection diameter over the test section diameter were added to the historical three dimensionless numbers. According to the authors, these parameters take into account the free surface disruption of the jet. Moreover, the heat exchange area is defined as the jet cross section.

In Table 1, the characteristic lengths, reference temperature and temperature difference are These models are mainly calibrated using different subset data from the same experiment (e.g. COSI) or a very similar one (e.g. ECCS). However, they do not seem consistent with each other. Moreover, the experimental database can be improved and enlarged with other experiments.

In order to better understand the DCC phenomenon induced by a water injection in a circular horizontal pipe and to improve its modelling, three experiments named COSI, TOPFLOW-PTS [START_REF] Péturaud | General overview of the TOPFLOW-PTS experimental program[END_REF], [START_REF] Prasser | TOPFLOW pressure chamber -Versatile techniques to simplify design and instrumentation of therml fluid dynamic experiments at high pressure[END_REF] and UPTF are analysed in this work. These tests were carried out respectively at CEA-Grenoble, HZDR and BMFT-KWU. A reliable and wide experimental database is prepared so that the correlations from the literature can be properly assessed. Eventually, a new correlation is developed and validated.

The paper is organised as follows: in the following section, the experimental databases and their thermal-hydraulic analysis are presented. In Section 3, the experimental database is tested against the physical models from the literature. Section 4 is dedicated to the development and the validation of a new condensation correlation. In Section 5 conclusions are drawn.

Experimental database

The correlations found in the literature and reviewed in the introduction must be assessed against experimental data. The assessment process is important to evaluate the predictive capabilities of the models to reproduce the experimental data. If the correlations do not show good results, a new model must be calibrated against the assessment database. The new bestestimate correlation is then tested against an independent database not used to tune the model [START_REF] Thacker | Concepts of model verification and validation[END_REF]. This validation phase quantifies the model accuracy in predicting the data when the experimental conditions differ from the calibration ones.

In Table In the following three sections, the experiments are introduced. Section 2.4. presents the experimental uncertainties. In Section 2.5., a detailed thermal-hydraulic analysis of the experimental database is performed. Finally, Section 2.6 illustrates the methodology used for the quantification of the condensation rate.

The COSI experiments

The COSI experiment was carried out at CEA Grenoble in the 80s. The goal was to obtain a reliable database to develop a condensation model at the injection [START_REF] Janicot | Condensation modelling for ECC injection[END_REF].

Two test sections were built to simulate the cold leg of a French (Framatome, from now on shortened Fra) and American (Westinghouse, from now on shortened West) nuclear Pressurised Water Reactor (PWR). In Fig. 3, the two configurations consist of:

 A horizontal pipe of 0.118 m in diameter and of 1.4 m in length for Fra and 3.77 m for West;

 An inlet pipe for the steam coming from the boiler and an outlet pipe going to the condenser;

 A vertical pipe to evacuate the water and keep the liquid level constant. This pipe is from now on called downcomer (DC);

 Different injection pipes, welded to the horizontal pipe. The arrows show the direction of the liquid (blue) and of the steam (orange). In Fig. 3, the steam is depicted co-current with the liquid. Nevertheless, for both configurations, there are tests with steam in co-current and counter-current flow.

The test sections are equipped with the following instrumentation:

 Thermocouple rakes, assemblies of thermocouples used to measure the temperature in precise points in space. The geometry of a rake can be found below the Fra test section in Fig. 3. There are 8 rakes for Fra and 5 for West, of 16 thermocouples each.

One injection pipe in the West configuration is also equipped with 3 rakes;

 A thermocouple in the downcomer;

 A weir of adjustable height (0, 0.3, 0.5 times the diameter D for Fra and 0, 0.5 times for West) to keep the liquid level constant in the horizontal pipe.

In Fig. 4 and Table 3, the different injection pipe configurations are shown. The first one being the Fra injection and the two on the right respectively the West injections of type Accumulator (Acc) and High Pressure (HP). Only the HP injection is equipped with thermocouple rakes.

Table 3 COSI injection pipe angles and diameters.

In Fig. 5, a representation of the phenomenology in the COSI experiment is shown. The steam is sent from a boiler into the test section and the phenomenology due to the jet injection is highlighted.

Fig. 5 Phenomenology in the COSI test section.

Four different zones can be identified. The injection zone, where the jet impacts the liquid and the steam bubbles may be entrained in the liquid phase. Upstream the jet, large temperature gradients and strong interfacial shears lead to a recirculation zone. Downstream the jet, thermal stratification is observed. The presence of the weir may produce a "standing water" effect, creating a small recirculation zone in the surroundings. After the weir, the water falls in the downcomer generating a cascade.

The COSI database consists of 219 Fra tests and 96 West tests.

The TOPFLOW-PTS experiments

The TOPFLOW-PTS (Pressurised Thermal Shock) experiment was carried out in Helmholtz-Zentrum of Dresden-Rossendorf (HZDR) in 2010-2012. The goal was to study and better understand the phenomena behind the Pressurised Thermal Shock (PTS), namely the thermal shock phenomena possibly occurring in nuclear reactors due to cold-water injection at high pressure. Data were obtained, mainly to validate Computational Fluid Dynamics (CFD) codes [START_REF] Lucas | TOPFLOW-experiments, development and validation of CFD models for steam-water flows with phase transfer[END_REF].

In Fig. 6, the test section is composed by:  A pump simulator (PS) with two pipes for water injection and extraction;

 A horizontal pipe of 0.2792 m in diameter and 2.95 m in length;

 An annular space to simulate the DC;

 An injection pipe of 0.0531 m in diameter and welded at 30° in the vertical plane, as shown in Fig. 7. The test section is equipped with:

 4 thermocouple rakes of 25 thermocouples each;

 Several thermocouple rakes in the downcomer.

The phenomenology during the experiments is the same as COSI, with the exception of the cascade zone. In TOPFLOW-PTS, the liquid free level is kept constant thanks to a feed & bleed (F&B) system placed at the bottom of the DC. This system extracts a quantity of water equal to the injection and condensed steam mass flowrates, holding always a constant level in the DC.

Two typologies of tests have been realised during the experimental campaign:

The UPTF experiments

The UPTF (Upper Plenum Test Facility) experiment has been carried out by Siemens/KWU in the 80s in Germany. It is composed of all the thermal-hydraulic components of a PWR, as described in [START_REF] Weiss | UPTF experiments: Principal full-scale test results for enhanced knowledge of large break LOCA scenarios in PWR's[END_REF].

Only the tests with a stratified flow in the test section are retained for this analysis, namely UPTF 8, UPTF 25, UPTF 27 and UPTF TRAM C2 6a.

In Fig. 8, the test section is schematised. For the selected tests, it is composed by:  A PS with no water injection;

 A horizontal pipe of 0.75 m in diameter and 9.48 m in length;

 An annular space to simulate the DC;

 An injection pipe of 0.2225 m in diameter and welded at 60° in the horizontal plane, as shown in Fig. 9. The test section is equipped with:

 4 thermocouple rakes of 6 thermocouples each (8 in TRAM configuration);

The phenomenology during the experiments is slightly different with respect to COSI and TOPFLOW-PTS. In UPTF, the liquid flow is directed towards the DC thanks to the injection angle, thus no recirculation zone is present. Moreover, the free level is not maintained constant.

In UPTF 8, 25 and 27, the steam comes from the PS. In TRAM configuration, the PS is full of water and the steam comes from the DC in counter-current direction with respect to the liquid flow.

The UPTF database consists of 24 tests.

Experimental uncertainties

The experimental uncertainties on the measurements are reported in

Experimental analysis

The experimental data must be reliable and coherent. A thermal-hydraulic analysis is then performed.

During the experimental campaigns, several tests presented problems such as: no available data, defective instrumentations, incoherent measurements, no sub-cooled injections, no stabilised tests, presence of overheated steam, repeated tests, tests without condensation and calibration tests. Suppressed those tests from the databases, an experimental analysis is carried out on the 198 tests left.

Visualisation and analysis of the jet dynamics

In the TOPFLOW-PTS experiment, a camera is pointing over the jet [22] [25]. The experimental image of a typical sssw test is shown in Fig. 10, in which pressure and temperature are representative to those in a reactor.

Fig. 10

Experimental image of a typical TOPFLOW-PTS sssw test injection [START_REF] Coste | Two-phase CFD validation: TOPFLOW-PTS steady-state steamwater tests 3-16, 3-17, 3[END_REF].

The same main local phenomena described in Fig. 2 can be found. The jet seems regular and has a quasi-cylindrical shape. At the impact, steam bubbles are entrained in the liquid phase and reflect the light coming from the top of the test section. The lateral rebound is small and the liquid-steam interface does not seem very wavy.

Stratified flow in the injection pipe

In all three experiments (COSI, TOPFLOW-PTS and UPTF), a stratification in the injection pipe was sometimes observed, as shown in Fig. 11. This occurred at low injection mass flowrates.

Fig. 11 Representation of a stratified flow in the injection pipe at 30°.

This phenomenon affects the injection surface, thus the heat exchange area 𝐴 𝑒𝑥 and the jet velocity 𝑢 𝑖𝑛𝑗 . Therefore, these quantities strongly impacting the condensation are either impossible to calculate or, with our simple modelling approach, affected by great uncertainty.

It was then decided to exclude the tests with stratified injection from the assessment and validation databases.

In the TOPFLOW-PTS experiment, the experimenters [START_REF] Seidel | TOPFLOW-PTS air-water experiments on the stratification in the ECC nozzle and the ECC water mixing during PTS scenarios[END_REF] discovered the presence of a stratified flow in the injection pipe for mass flowrates below 1.7 kg/s. Thus, 2 sssw and 1 tsw tests are not considered in our database.

Also in the COSI experiment, a stratification is observed in the HP injection of the West configuration. In this experiment there is no camera, however the thermocouple rake 8 shows a stratified flow. This phenomenon occurs at every injection mass flowrate. This is probably explained by the injection diameter 𝑑 𝑖𝑛𝑗 being the biggest one among the possible injection pipe configurations.

The UPTF experimenters wrote in technical reports [START_REF] Siemens | Division Production d'Energie, Essai C1/C2 Refroidissement par panache et par lame de la paroi de la cuve[END_REF] that a stratified flow may occur in the injection pipe, as shown in Fig. 12.

Fig. [START_REF] Liao | Cold leg condensation model for analysing loss-of-coolant accident in PWR[END_REF] Stratified flow in the UPTF injection pipe.

In the experiment, there is no camera nor thermocouple rakes in the injection pipe. However, the experimenters proposed the Schröder formula [START_REF] Press | Hydrodynamik im Wasserbau (Hydrodynamic in hydraulic structures[END_REF]. It calculates the liquid height of a twophase flow inside a low inclined pipe and reads:

{ (𝜓 𝑖𝑛𝑗 -sin(𝜓 𝑖𝑛𝑗 )) 3 sin ( 𝜓 𝑖𝑛𝑗 2 ⁄ ) = 512 • 𝑄 ̇𝑖𝑛𝑗 2 • 𝜌 𝑖𝑛𝑗 𝑔 • 𝑑 𝑖𝑛𝑗 5 • (𝜌 𝑖𝑛𝑗 -𝜌 𝑔 ) 𝐻 𝑖𝑛𝑗 = 𝑑 𝑖𝑛𝑗 • 𝑠𝑖𝑛 2 ( 𝜓 𝑖𝑛𝑗 4 ⁄ ) (1)
This formula predicts the occurrence of the stratification phenomenon in all the COSI and TOPFLOW-PTS tests where stratification was experimentally observed. Since Eqn. ( 1) is validated, it can be used as a stratification criterion. It is applied to the whole database,

showing that stratification occurs in 13 UPTF tests and 46 COSI tests. Thus, these 59 tests are not considered in the following analyses. The application range of this study is then limited to fully filled injection pipes. In future works, it would be interesting to take into account the stratification inside the injection pipe and its impact on the modelling of the condensation.

Injection in the liquid

In TOPFLOW-PTS, the camera shows that when the free level is too high the jet enters directly into the liquid.

This phenomenon may occur also in COSI. The tests with the highest weir (0.6 •D) are assumed to behave like in Fig. 13.

Fig. [START_REF] Petrovic De With | Three-dimensional condensation regime diagram for direct contact condensation of steam injected into water[END_REF] Assumed behaviour of COSI tests with a 0.6 weir.

Those tests are characterised by a short jet, which may lead to small or no condensation rate.

Thus, the condensation mass flowrate computation is not reliable in this configuration. 2 tests TOPFLOW-PTS and 6 COSI are then eliminated from the assessment database.

Hot injections in TOPFLOW-PTS

Several TOPFLOW-PTS tests, namely the ones with enabled PS, have a hot water injection. The sub-cooling (𝑇 𝑠𝑎𝑡 -𝑇 𝑖𝑛𝑗 ) is low, between 27 and 80 °C. In these conditions, the calculated condensation mass flowrate is extremely low and its computation is not reliable due to the strong impact of the experimental uncertainties.

In order to avoid any bias in the assessment of the model, these tests are moved to the validation database.

Reduced database

On the basis of the experimental analysis, it was decided to include the COSI and TOPFLOW experiments in the assessment database. These two experiments are simpler and easier to interpret, so that they are more suitable to assess and develop the condensation model. On the contrary, the UPTF tests are more complex, so that they are used exclusively in the validation phase. As already explained in Section 2.5.3, the TOPFLOW tests with hot injection are also moved to the validation database.

In Table 5, the revised database is shown. Total number of tests 110 18

Table 5 Reduced database after the experimental analysis.

At the end of the thermal-hydraulic analysis, the assessment database is composed of 110 tests and the validation database of 18 tests. The experimental conditions range between 0.3 and 7 MPa for the pressure, 0.2-161 kg/s for the injection flowrate and between 20 and 220 °C for the injection temperature.

Methodology for the quantification of the condensation rate

As already seen in the literature, the condensation in the jet region is modelled through dimensionless numbers. In order to calculate these numbers and properly assess the correlations in Table 1, the following physical quantities must be evaluated from the experimental data:

1. The liquid level height in the test section;

2. The mean liquid temperature 𝑇 ̅ 𝑟,𝑖 from the rake of thermocouples;

3. The condensation mass flowrate at the injection 𝑚̇𝑐 𝑜𝑛𝑑 .

A methodology for each of these quantities is here below presented.

Evaluation of the liquid level height and of the mean liquid temperature

For the calculation of the condensation mass flowrate and the heat exchange area, respectively the mean liquid temperature of each rake and the liquid level height in the test section must be estimated (e.g. the interface between the two phases must be identified).

The impact of the jet in the circular test section creates waves at the interface between the gas and liquid phases.

In the TOPFLOW-PTS experiment, the thermocouple temperature profiles in time are The thermocouple at the interface is in the steam and it is wetted regularly by the waves. Thus, it is not representative of the liquid temperature.

A typical rake time-averaged temperature profile is shown in Fig. 15. There, the normalised temperature is plotted against the dimensionless height of the thermocouple in the test section. The black line marks the saturation temperature 𝑇 𝑠𝑎𝑡 , the red one 𝑇 𝑠𝑎𝑡 -5 °C. where the temperature is higher than 𝑇 𝑠𝑎𝑡 -5 °C). In particular, three thermocouples are identified at the liquid-steam interface (black crosses in Fig. 15) since they are characterised by significant temperature fluctuations in the experiment.

Based on these experimental observations on the TOPFLOW-PTS tests, a criterion to identify the thermocouples in the liquid and the liquid-steam interface has been developed and validated. Starting from the bottom of the rake, the first thermocouple is always supposed in the liquid. Proceeding up the rake, the increase of temperature between two successive thermocouples is compared to the sub-cooling of the thermocouple (i.e. the difference between the saturation and the thermocouple temperature). If the temperature increase is larger than 80 % of the sub-cooling, then the thermocouple is considered at the liquid-steam interface. All other thermocouples at higher z/D are then supposed in the steam and neglected when evaluating the average liquid temperature of the rake.

The free level in the test section is computed as the halfway distance between the last thermocouple in the liquid and the first one detected at the interface.

The COSI and the UPTF experiments have very similar time-averaged temperature profiles to the TOPFLOW-PTS one in Fig. 15. However, the time evolution of the temperatures are not available. The new developed criterion is then applied and the thermocouples in the liquid are identified.

In the end, for all the experiments, the rake mean liquid temperature is calculated. Assuming a uniform liquid velocity field, the weighted mean of those temperatures with the associated surfaces (shown in Fig. 16) gives the mean liquid temperature:

𝑇 ̅ 𝑟 = ∑ 𝑇 𝑘 • 𝑆 𝑘 𝑘=𝑙𝑎𝑠𝑡 𝑇𝐶 𝑖𝑛 𝑡ℎ𝑒 𝑙𝑖𝑞𝑢𝑖𝑑 𝑘=1 ∑ 𝑆 𝑘 𝑘=𝑙𝑎𝑠𝑡 𝑇𝐶 𝑖𝑛 𝑡ℎ𝑒 𝑙𝑖𝑞𝑢𝑖𝑑 𝑘=1
(2)

Fig. [START_REF] Bestion | Condensation tests analysis and correlation for the CATHARE code[END_REF] Thermocouple associated surfaces estimation for a COSI rake.

Several experimental uncertainties (see Table 4) may influence the calculation of the mean liquid temperature. A Monte-Carlo propagation of these uncertainties is performed to estimate the experimental uncertainty on the mean liquid temperature. Two main hypothesis are made. First, no uncertainty on which is the last TC in the liquid is considered. Second, the uncertainty on the liquid height in the test section H is equal to the half space between the last thermocouple in the liquid and the first in the steam.

The rake mean liquid temperature is then estimated to have an uncertainty up to ±6 °C for COSI, ±4 °C for TOPFLOW-PTS and ±3.5 °C for UPTF experiments.

Quantification of the condensation mass flowrate

Historically, the correlations based on the COSI experiments were obtained calculating the condensation mass flowrate applying an energy balance over the whole COSI test section (from the jet to the thermocouple in the DC). Defining the control volume in this way, the condensation due to the cascade and to the stratification is accounted as due to the jet. To separate the effects, a new methodology for the quantification of the jet condensation has been developed. The condensation mass flowrate is quantified defining a control volume (shown in Fig. 17) between the injection and a thermocouple rake whose mean liquid temperature is calculated according to the previous section.

Fig. 17 Control volume between the injection and a thermocouple rake.

Applying an energy balance to the control volume in terms of enthalpy, the steam mass flowrate condensing in the liquid phase is computed as:

𝑚̇𝑐 𝑜𝑛𝑑 = 𝑚̇𝑖 𝑛𝑗 • 𝑖̅ 𝑟,𝑖 -𝑖 𝑖𝑛𝑗 𝑖 𝑔,𝑠𝑎𝑡 -𝑖̅ 𝑟,𝑖 (3)
Assuming that the condensation in the stratification zone is negligible, due to the reduced test section length between the injection and the DC, Eqn. (3) can be applied:  Between the jet and the rake 8 for COSI-Fra (5 for COSI-West), to quantify the condensation occurring at the jet.

 Between the rake 8 for COSI-Fra (5 for COSI-West) and the thermocouple in the DC, to quantify the condensation at the cascade.

In this way, the condensation term at the cascade can be compared to the jet one (Fig. 18).

Fig. 18 Percentage of the condensation due to the cascade over the global condensation

for the COSI experiments.

The condensation at the cascade can go up to 60% of the total condensation for low injection mass flowrates. This proves that the choice of the control volume, to compute the jet condensation mass flowrate, is of great importance.

The same local energy balance is applied to TOPFLOW-PTS and UPTF. In these experiments, the stratified condensation is not negligible anymore. Thus, the condensation mass flowrate is calculated between the jet and rake 4 for TOPFLOW-PTS and rake 5 for UPTF.

Assessment of selected correlations from the literature

The accuracy associated to a thermal-hydraulic correlation must be quantified in a rigorous manner. It can be estimated through some statistical indicators which assess the model ability to calculate the output physical quantity. In this work, the indicators proposed in [START_REF] Cocci | A comprehensive Bayesian framework for the development, validation and uncertainty quantification of thermalhydraulic models[END_REF] are adopted.

Statistical indicators

From the comparison between experimental and calculated data, a relative and absolute residual can be defined. For an output quantity z, they read respectively:

{ 𝜀 𝑧,𝑟𝑒𝑙 = 1 𝑛 • ∑ 𝑧 𝑐𝑎𝑙𝑐,𝑖 -𝑧 𝑒𝑥𝑝,𝑖 𝑧 𝑒𝑥𝑝,𝑖 𝑛 𝑖=1 • 100 |𝜀 𝑧,𝑟𝑒𝑙 | = 1 𝑛 • ∑ | 𝑧 𝑐𝑎𝑙𝑐,𝑖 -𝑧 𝑒𝑥𝑝,𝑖 𝑧 𝑒𝑥𝑝,𝑖 | 𝑛 𝑖=1
• 100

(4) { 𝜀 𝑧,𝑎𝑏𝑠 = 1 𝑛 • ∑ 𝑧 𝑐𝑎𝑙𝑐,𝑖 -𝑧 𝑒𝑥𝑝,𝑖 𝑛 𝑖=1 |𝜀 𝑧,𝑎𝑏𝑠 | = 1 𝑛 • ∑|𝑧 𝑐𝑎𝑙𝑐,𝑖 -𝑧 𝑒𝑥𝑝,𝑖 | 𝑛 𝑖=1 (5)
where n is the number of tests.

In Eqns. ( 4) and ( 5), the mean and standard deviation of the first indicator (without absolute value) give respectively the accuracy and the precision of the model while the mean of the second one (with modulus) measures the average error of the prediction.

To measure the goodness of fit, the coefficient of determination R 2 defined in [START_REF] Kvålseth | Note on the R2 measure of goodness of fit for nonlinear models[END_REF] is selected.

The higher the prediction quality of the model is, the closer the coefficient is to one.

Results of the assessment

In Table 1, the physical models are shown together with their characteristic lengths.

In order to quantify their performances, these correlations are tested against the new revised assessment database. When the reference temperature 𝑇 𝑟𝑒𝑓 is unknown, it is supposed to be equal to the Liao et al. one. In Table 6, the residuals are quantified with Eqn. [START_REF] Yang | Thermal hydraulic characteristics of unstable bubbling of direct contact condensation of steam in subcooled water[END_REF]. The models do not show good results.

Name

the cold liquid that enters at 𝑇 𝑖𝑛𝑗 and leaves at 𝑇 ̅ 𝑟 (as already seen in Fig. 17). The secondary side is represented by the steam, at saturation temperature.

Fig. [START_REF] Ren | Experiment of Condensation in T-junction: Steam-water Flow in Water-injected Condition[END_REF] Visualisation of the jet as a heat exchanger.

Thus, the temperature difference representative of the heat exchange at the jet is the logarithmic mean temperature difference that reads:

∆𝑇 𝑙𝑛 = ∆𝑇 𝑖𝑛 -∆𝑇 𝑜𝑢𝑡 𝑙𝑛 ( ∆𝑇 𝑖𝑛 ∆𝑇 𝑜𝑢𝑡 ⁄ ) = 𝑇 ̅ 𝑟 -𝑇 𝑖𝑛𝑗 𝑙𝑛 ( (𝑇 𝑠𝑎𝑡 -𝑇 𝑖𝑛𝑗 ) (𝑇 𝑠𝑎𝑡 -𝑇 ̅ 𝑟 ) ⁄ ) (6)
The condensation heat flux can be then written as:

𝑞ċ 𝑜𝑛𝑑 = 𝑚̇𝑐 𝑜𝑛𝑑 • 𝑖 𝑙𝑔 = ℎ • 𝐴 𝑒𝑥 • ∆𝑇 𝑙𝑛 (7)

Modelling of the heat transfer area

The heat transfer area is difficult to model due to the turbulent and chaotic nature of the physical phenomenon. In Fig. 20, different heat exchange areas are illustrated for a vertical injection.

Fig. 20 Heat exchange areas for a vertical injection.

As already observed in Fig. 10, three different zones can be found:

1. A cylindrical zone, from the injection pipe outlet to the liquid phase;

2. An entrainment zone, due to the impact of the jet in the liquid;

3. A rebound zone, where the liquid is above the free level and the kinetic energy is transformed in potential energy.

As suggested in [START_REF] Iciek | The hydrodynamics of a free, liquid jet and their influence on direct contact heat transfer-III. Direct contact heating of a cylindrical, free falling liquid jet[END_REF], we suppose that most of the condensation occurs in the first zone. Due to this hypothesis, the heat transfer area can be approximated as:

𝐴 𝑒𝑥 = 𝜋 • 𝑑 𝑖𝑛𝑗 • 𝐿 (8)
For injection angles lower than 90°, the jet length L can be estimated using the Clausnitzer &

Hager formula [START_REF] Clausnitzer | Outflow Characteristics from Circular Pipe[END_REF] that allows to compute the lower trajectory (or lower nappe) of the jet.

The lower nappe is then described by the following equation in the reference system (x', y') in Fig. 21:

𝑦′ = 1 3 • 𝑥′ • 𝐹𝑟 -0.8 + 1 4 • 𝑑 𝑖𝑛𝑗 • 𝑥′ 2 • 𝐹𝑟 -1.6 (9)
The Froude number is defined by the velocity 𝑢 𝑖𝑛𝑗 and the diameter 𝑑 𝑖𝑛𝑗 of the jet. Thus, the trajectory is dependent on the jet geometry and kinetic energy.

Modelling of the condensation potential

The heat exchanger condensation potential R is defined as: 𝑅 = 𝑇 ̅ 𝑟 -𝑇 𝑖𝑛𝑗 𝑇 𝑠𝑎𝑡 -𝑇 𝑖𝑛𝑗 [START_REF] Seidel | Experimental studies on high-pressure hightemperature contact-condensation at falling jets in the TOPFLOW pressure-tank[END_REF] It measures how much the cold jet is exploited to condense the steam. If R=1, the cold jet condenses all the steam possible so that it reaches the saturation temperature. If R=0, the jet condenses no steam.

The condensation potential in Eqn. [START_REF] Seidel | Experimental studies on high-pressure hightemperature contact-condensation at falling jets in the TOPFLOW pressure-tank[END_REF] can be analytically modelled adapting the approach proposed for boiling in [START_REF] Whittle | A correlation for the Minima in Pressure Drop Versus Flow-rate Curves for Sub-cooled Water Flowing in Narrow Heated Channels[END_REF] and [START_REF] Stelling | The Onset of Flow Instability for Downward Flow in Vertical Channels[END_REF] to the condensation [START_REF] Buschman | Use of fundamental condensation heat transfer experiments for the development of a sub-grid liquid jet condensation model[END_REF]. Combining Eqn. [START_REF] Gregu | Experimental study on steam chugging phenomenon in a vertical sparger[END_REF] with Eqn.

(3) and using the ratio between the heat exchange and the jet cross sectional areas:

𝐴 𝑒𝑥 𝐴 𝑖𝑛𝑗 = 𝜋 • 𝑑 𝑖𝑛𝑗 • 𝐿 𝜋 4 ⁄ • 𝑑 𝑖𝑛𝑗 2 = 4 • 𝐿 𝑑 𝑖𝑛𝑗 (11)
The liquid temperature difference in the heat exchanger can be written as:

𝑇 ̅ 𝑟 -𝑇 𝑖𝑛𝑗 = 𝑞" 𝑐𝑜𝑛𝑑 𝐺 ̇𝑖𝑛𝑗 • 𝑐 𝑝,𝑟𝑒𝑓 • 4 • 𝐿 𝑑 𝑖𝑛𝑗 • 𝑖 𝑔,𝑠𝑎𝑡 -𝑖̅ 𝑟,𝑖 𝑖 𝑙𝑔 (12)
Supposing the characteristic lengths of Nusselt and Reynolds numbers to be equal, the Stanton number can be defined using the heat flux in Eqn. [START_REF] Gregu | Experimental study on steam chugging phenomenon in a vertical sparger[END_REF] as:

𝑆𝑡 = 𝑞" 𝑐𝑜𝑛𝑑 𝐺 ̇𝑖𝑛𝑗 • 𝑐 𝑝,𝑟𝑒𝑓 • 𝜌 𝑖𝑛𝑗 𝜌 𝑟𝑒𝑓 • 1 ∆𝑇 𝑙𝑛 (13)
Thus, combining Eqns. ( 12) and (1):

𝑇 ̅ 𝑟 -𝑇 𝑖𝑛𝑗 = 𝑆𝑡 • 𝜌 𝑟𝑒𝑓 𝜌 𝑖𝑛𝑗 • ∆𝑇 𝑙𝑛 • 4 • 𝐿 𝑑 𝑖𝑛𝑗 • 𝑖 𝑔,𝑠𝑎𝑡 -𝑖̅ 𝑟,𝑖 𝑖 𝑙𝑔 (14)
Eqn. ( 14) can be put in the definition of the condensation potential. Considering that the argument of the logarithm in Eqn. ( 6) can be rewritten as 1 (1 -𝑅) ⁄ , it follows:

𝑅 = 1 -𝑒𝑥𝑝 (-4 • 𝑆𝑡 • 𝜌 𝑟𝑒𝑓 𝜌 𝑖𝑛𝑗 • 𝑖 𝑔,𝑠𝑎𝑡 -𝑖̅ 𝑟 𝑖 𝑙𝑔 • 𝐿 𝑑 𝑖𝑛𝑗 ) (15)
For simplicity, Eqn. ( 15) can be rewritten as:

{ 𝑅 = 1 -𝑒𝑥𝑝 (-4 • 𝜂 • 𝐿 𝑑 𝑖𝑛𝑗 ) 𝜂 = 𝑆𝑡 • 𝜌 𝑟𝑒𝑓 𝜌 𝑖𝑛𝑗 • 𝑖 𝑔,𝑠𝑎𝑡 -𝑖̅ 𝑟 𝑖 𝑙𝑔 (16)
From Eqn. ( 16), the condensation potential is then a function of the geometrical feature of the jet 𝐿 𝑑 𝑖𝑛𝑗 (also called shape parameter) and a coefficient 𝜂. In Fig. 22, R is plotted against the shape parameter for both the assessment and the validation databases. It can be observed that the condensation potential R seems to depend exponentially to the shape parameter. The longer and thinner the jet is, the closer the condensation potential is to one.

The exponential dependence analytically derived in Eqn. ( 15) is suitable to fit the experimental data. Properly assessing a model for 𝜂 allows us to interpolate the data through Eqn. ( 16).

Modelling of 𝜼

The 𝜂 can be modelled through different dimensionless parameters. After a long work of analysis, the best-suited ones were identified as: the steam potential Nusselt, the injection Reynolds and the reference Prandtl dimensionless numbers. The correlation is introduced here below:

𝜂 = 𝜃 0 • 𝑁𝑢 𝑝𝑜𝑡 𝜃 1 • 𝑅𝑒 𝑖𝑛𝑗 𝜃 2 • 𝑃𝑟 𝑟𝑒𝑓 𝜃 3 (17)
where the steam potential Nusselt number is defined as:

𝑁𝑢 𝑝𝑜𝑡 = 𝑚̇𝑣 𝑎𝑝 • 𝑖 𝑙𝑔 • 𝑙 𝑐,𝑁𝑢𝑝𝑜𝑡 𝐴 𝑒𝑥 • 𝑘 𝑟𝑒𝑓 • (𝑇 𝑠𝑎𝑡 -𝑇 𝑖𝑛𝑗 ) (18)
It is defined as potential since it is calculated as if all the steam flowrate reaching the jet condensed, with the maximum temperature difference possible (i.e. T sat -T inj ). It is important to model the effect of the steam flowrate on the condensation, as observed for the DCC in other configurations (e.g. [36] [37]).

The characteristic lengths are summarised in Table 7.

Scales Definition

Reynolds velocity 𝑢 𝑖𝑛𝑗

Characteristic lengths 𝑙 𝑁𝑢,𝑝𝑜𝑡 = 𝑙 𝑅𝑒 = 𝑑 𝑖𝑛𝑗 Reference temperature 𝑇 𝑟𝑒𝑓 = 𝑇 𝑠𝑎𝑡 + 𝑇 𝑖𝑛𝑗 2 Table 7 Characteristic lengths for the new correlation.

Development of the correlation

The coefficients 𝜃, introduced in Eqn. [START_REF] Janicot | Condensation modelling for ECC injection[END_REF], are simultaneously optimised using the calibration methodology proposed in [START_REF] Cocci | A comprehensive Bayesian framework for the development, validation and uncertainty quantification of thermalhydraulic models[END_REF]. This procedure is applied to the assessment database.

The correlation then reads:

𝜂 = 0.014 • 𝑁𝑢 𝑝𝑜𝑡 0.58 • 𝑅𝑒 𝑖𝑛𝑗 -0.33 • 𝑃𝑟 𝑟𝑒𝑓 -1.2 (19)
The coefficient of determination 𝑅 2 (see Section 3.1.) associated to this model is equal to 0.82.

Thus, the correlation ability to reproduce the experimental data is good.

Eqn. [START_REF] Ren | Experiment of Condensation in T-junction: Steam-water Flow in Water-injected Condition[END_REF] leads to good predictions, as shown in Fig. 23 and Table 8 where the errors are quantified and summarised. 8 Relative error prediction on η for the new correlation.

The prediction of η is centred with a dispersion of 2𝜎 = 30.8 %. The relative error values show good results. The experiment-model discrepancy is on average equal to 12.3 %.

Once calculated the 𝜂 with the model in Eqn. [START_REF] Ren | Experiment of Condensation in T-junction: Steam-water Flow in Water-injected Condition[END_REF], Eqns. ( 16) and ( 10) can be applied to derive the mean liquid temperature 𝑇 ̅ 𝑟 .

In Fig. 24, the experimental temperatures are plotted against the calculated temperatures.

Two error bands in red show an error of ±30 °C. The indicators in Eqn. [START_REF] Yang | Thermal hydraulic characteristics of unstable bubbling of direct contact condensation of steam in subcooled water[END_REF] are computed with respect to the assessment database and presented in Table 9. 9 Absolute errors on the temperature with respect to the assessment database.

The model gives centred predictions with a dispersion of 2𝜎 = 26 °C. The min and max are almost the same, not showing a trend of the model to systematically under-or over-predict the condensation. Moreover, the mean absolute errors (both for COSI and TOPFLOW-PTS) are comparable to the measurement errors quantified in Section 2.6.1., emphasising the model capability to reproduce the experimental data.

Validation of the correlation

The mean liquid temperature 𝑇 ̅ 𝑟 is calculated for the validation database, composed by 7 UPTF tests and 11 TOPFLOW-PTS tests with a hot injection. In Fig. 25, the experimental temperatures are plotted against the calculated temperatures. In Table 10, the indicators in Eqn. Table 10 Absolute errors on the temperature with respect to the validation database.

The discrepancies have the same order of magnitude with respect to the results in Table 9,

showing a good capability of the model to predict the jet condensation when applied to the validation database and, in particular, to the UPTF tests (not used to develop the new correlation).

Thus, the model can be considered validated.

Conclusions

Three experiments with different geometrical configurations, namely COSI, TOPFLOW-PTS and UPTF, are studied to better understand the condensation phenomena occurring during the injection of a sub-cooled water jet in a circular pipe with a two-phase stratified flow.

  described the DCC phenomenology induced by a water jet in a circular horizontal pipe based on the experimental results obtained in the facility COSI (COndensation at Safety Injection). They found out that the biggest contribution to the global condensation in the test section was associated to the jet impact into the two-phase stratified flow and supposed that the main DCC mechanism was due to turbulence generated by impact of the water jet into the stratified water. To predict the steam condensation in the injection zone, they developed a correlation based on three experimental series of the COSI experiments carried out with the Framatome configuration of the test section (see description of the test facility in Section 2.1). The dimensionless numbers, Nusselt, Reynolds and Prandtl, were employed.

  summarised for every cited correlation. The reference temperature is the temperature at which the thermodynamic properties of the liquid water are calculated. The temperature difference defines the condensation heat flux 𝑞ċ 𝑜𝑛𝑑 = 𝑚̇𝑐 𝑜𝑛𝑑 • 𝑐 𝑝 • ∆𝑇. 𝑙 𝑁𝑢 = 𝑙 𝑅𝑒 = 𝐻 𝑢 𝑅𝑒 = 𝑢 𝑖𝑛𝑗 𝐴 𝑒𝑥 = 𝑑 𝑗𝑒𝑡 • √(1 -𝛼) • 𝛼 • 𝐷 𝑇 𝑟𝑒𝑓 = 𝑢𝑛𝑘𝑛𝑜𝑤𝑛 ∆𝑇 = 𝑇 𝑠𝑎𝑡 -𝑇 𝑖𝑛𝑗 Liao et al. [12] 𝑁𝑢 = 0.245 • 𝑅𝑒 1.1 • 𝑃𝑟 0.6 𝑙 𝑁𝑢 = 𝑓(𝐻) • 𝐷 𝑙 𝑅𝑒 = 𝑑 𝑖𝑛𝑗 𝑢 𝑅𝑒 = 𝑢 𝑖𝑛𝑗 𝐴 𝑒𝑥 = 𝑑 𝑖𝑛𝑗 • 𝑓(𝐻)

[ 20 ]

 20 𝑁𝑢 = 𝑅𝑒 • 𝑃𝑟 • 𝐹𝑟 0.5 • 𝛼 • 𝑑 𝑗𝑒𝑡 𝐷 𝑙 𝑁𝑢 = 𝑙 𝑅𝑒 = 𝑙 𝐹𝑟 = 𝐻 𝑢 𝑅𝑒 = 𝑢 𝐹𝑟 = 𝑢 𝑖𝑛𝑗 𝐴 𝑒𝑥 = 𝑑 𝑖𝑛𝑗 2 𝑇 𝑟𝑒𝑓 = 𝑢𝑛𝑘𝑛𝑜𝑤𝑛 ∆𝑇 = 𝑇 𝑠𝑎𝑡 -𝑇 𝑖𝑛𝑗

Fig. 3

 3 Fig. 3 Framatome (at the top) and Westinghouse (at the bottom) test sections in the COSI experiment.

Fig. 4

 4 Fig. 4 Geometrical configurations of the injection pipe in the COSI experiments. COSI-Fra COSI-West Acc COSI-West HP Inclination in the vertical plane 𝜃 𝑖𝑛𝑗 30 90 90 Inclination in the horizontal plane 𝜑 𝑖𝑛𝑗 0 0 45 Diameter 𝑑 𝑖𝑛𝑗 [𝑚𝑚] 22 5.6, 23 38

Fig. 6

 6 Fig. 6 TOPFLOW-PTS test section.

Fig. 7

 7 Fig. 7 TOPFLOW-PTS injection pipe geometrical configuration.

Fig. 8

 8 Fig. 8 UPTF loop II test section.

  recorded and plotted in Fig.14. There, the normalised temperature (with respect to the saturation temperature plus a random small constant 𝜉) is plotted against the time. Three thermocouples are shown: one in the steam (in yellow) at the saturation temperature, one in the liquid (in light blue) and one at the interface (in grey).

Fig. 14

 14 Fig. 14 Typical temperature profiles in time in a TOPFLOW-PTS test.

Fig. 15

 15 Fig. 15 Typical time-averaged temperature profile of a rake in a TOPFLOW-PTS test. Three different zones can be identified. All the thermocouples below z/D=0.4 are most likely in the liquid. The other thermocouples are either positioned at the liquid-steam interface (e.g. the zone in the middle, 0.4 < z/D < 0.5 and 𝑇 < 𝑇 𝑠𝑎𝑡 -5 °C) or in the steam (e.g. the right zone,

2 ⁄

 2 A faster and thinner jet (high Froude) describes a longer nappe. The Clausnitzer & Hager correlation was originally developed for horizontal injection pipes at atmospheric pressure. Its application for inclined pipes at high pressure is validated thanks to the TOPFLOW-PTS tests images. In Fig. 21, the dimensionless experimental nappes (in light blue) of a TOPFLOW-PTS test are plotted. The lower nappe (in green) is computed applying Eqn. (9) and rotating it counter clockwise of the injection angle 𝜃 𝑖𝑛𝑗 , showing really good results. The centred trajectory of the jet (in black) is then obtained translating the parabola of 𝑑 𝑖𝑛𝑗 towards the jet centre of symmetry and adding the segment between the injection pipe exit and the parabola first point (the thin black segment). This rotated Clausnitzer & Hager formula is validated for all the TOPFLOW-PTS test images and is then applied to the whole database.The jet length is finally obtained integrating the centred trajectory of the jet.

Fig. 21

 21 Fig. 21 Application of the Clausnitzer & Hager formula to compute the lower nappe of the jet and its centred trajectory in a TOPFLOW-PTS test.

Fig. 22

 22 Fig. 22 Condensation potential R plotted against the jet length over diameter ratio. The triangles are the validation tests (also marked as * in the legend).

Fig. 23

 23 Fig.[START_REF] Thacker | Concepts of model verification and validation[END_REF] Fitting of the new condensation correlation over the assessment database.

Fig. 24

 24 Fig.[START_REF] Lucas | TOPFLOW-experiments, development and validation of CFD models for steam-water flows with phase transfer[END_REF] Prediction of the mean liquid temperature against the assessment database.

  Mean [°C] Standard deviation 𝜎 [°C] Min [°C] Max [°C]

Fig. 25

 25 Fig.[START_REF] Coste | Two-phase CFD validation: TOPFLOW-PTS steady-state steamwater tests 3-16, 3-17, 3[END_REF] Prediction of the mean liquid temperature against the validation database.

:

  Direct Contact Condensation, Liquid jet, Physical model assessment, Stratified flow

	𝑚̇	mass flowrate [	𝑘𝑔 𝑠 ⁄ ]
	Nu g	Nusselt number gas	𝑘 ℎ•𝑙 𝑁𝑢
	Pr inj	Prandtl number injection	𝑘 𝜇•𝑐 𝑝
	Nomenclature 𝑄 ̇ l	𝑠 ⁄ ] volumetric flowrate [ 𝑚 3 liquid
	pot	potential
	A 𝑞̇	area [𝑚 2 ] heat flux [𝑊]
	ps	pump simulator
	cp 𝑞̇" ref	specific heat capacity at constant pressure [ specific heat flux [ 𝑊 ⁄ ] 𝑚 2 calculated at the reference temperature	𝐽 ⁄ 𝑘𝑔 • 𝐾	]
	d Re sat	diameter [𝑚] Reynolds number saturation	𝜌•𝑢•𝑙 𝑅𝑒 𝜇
	D St	test section diameter [𝑚] Stanton number 𝑁𝑢 (𝑅𝑒 • 𝑃𝑟) ⁄
	Fr T	Froude number √ 𝑔•𝑙 𝐹𝑟 𝑢 2 temperature [𝐾]
	𝐺 ̇ u	specific mass flowrate [ velocity [ 𝑚 𝑠 ⁄ ]	𝑘𝑔 ⁄ 𝑠 • 𝑚 2	]
	g Greek symbols	gravity constant [ 𝑚 ⁄ ] 𝑠 2
	h 𝛼	heat transfer coefficient [ 𝑊 ⁄ 𝑚 2 • 𝐾 void fraction	]
	H 𝜇	liquid height in the test section [𝑚] dynamic viscosity [𝑃𝑎 • 𝑠]
	i 𝜌	specific enthalpy [ density [ 𝑘𝑔 𝑚 3 ⁄ ]	𝐽 ⁄ ] 𝑘𝑔
	ilg 𝜎	latent heat of condensation [ standard deviation	𝑘𝑔 ⁄ ] 𝐽
	k Subscripts	thermal conductivity [ 𝑊 𝑚 • 𝐾 ⁄	]
	l cond	characteristic length [𝑚] condensation
	L ex	jet length [𝑚] exchange

  Ren et al. defined the same heat exchange area as Liao et al., even if the characteristic length is unknown.

Table 1

 1 Jet condensation correlations found in the literature.

Table 2

 2 2, the main characteristics of the experiments are summarised. Main characteristics of the experiments.

		COSI	TOPFLOW-PTS	UPTF
	Number of tests	315	42	24

  The TOPFLOW-PTS database consists of 28 sssw tests with PS enabled, 9 sssw tests with PS disabled and 3 tsw tests.

	period, all the thermal-hydraulic parameters are approximately constant, so that they
	can be considered as steady-state. The PS is always disabled (i.e. no
	injection/extraction of water). These tests are indicated as tsw (Transient Steam
	Water).

1. Steady-state: after a stabilisation transient, the steady-state conditions are reached inside the test section and the jet condensation can be evaluated. Only the final steadystate conditions are registered for 60 seconds. Tests with and without injection/extraction of water in the PS are performed. These tests are indicated as sssw (Steady State Steam Water). 2. Transient state: in this typology, the whole transient is registered from the start of the water injection until the steady-state conditions are obtained. The last 100 seconds of each transient are used to evaluate the jet condensation after a time-averaging. In that The test conditions vary according to different parameters: pressure, steam mass flowrate, free liquid level, jet mass flowrate and temperature.

Table 4

 4

		COSI	TOPFLOW-PTS	UPTF
	Diameter	±0.5 mm	±0.5 mm	±0.5 mm
	Fluid temperature	±0.5 °C	±1 °C	±2.9 °C
	Flowrate	±0.005 kg/s	±0.5 %	±1.5 %
	Pressure	±0.5 %	±0.5%	±0.146 bar

. These uncertainties are associated to the geometries of the pipes (both the test section and the injection) and the measurements of temperature, mass flowrate and pressure.

Table 4

 4 Experimental uncertainties.

Table 6

 6 |𝜀 𝑇,𝑎𝑏𝑠 | 𝐶𝑂𝑆𝐼 [°C] |𝜀 𝑇,𝑎𝑏𝑠 | 𝑇𝑂𝑃𝐹𝐿𝑂𝑊-𝑃𝑇𝑆 [°C] Correlation errors against the new revised database.

	Janicot et al.	53	87
	Liao et al.	48	86
	Gaillard et al.	72	20
	Ren et al.	71	89

Acknowledgements

The current research project was conducted within a cooperation agreement between CEA (Commisariat à l'Energie Atomique et aux Energies Alternatives), EDF (Electricité de France), and Framatome. The authors gratefully acknowledge their financial support.

The Janicot and Liao correlations overestimate the condensation mass flowrate in both the COSI and TOPFLOW-PTS experiments, resulting in hotter calculated mean liquid temperatures 𝑇 ̅ 𝑟 . This may be due to the wrong control volume (e.g. from the jet to the DC) used to quantify the experimental condensation mass flowrate in the two articles. These flowrates were overestimated since the condensation due to the cascade and to the stratification was accounted to the jet.

The Ren et al. model behaves similarly, overestimating the jet condensation. This may be due to the same reason (e.g. the wrong definition of the control volume over the ECCS test section).

These three models show the worst results when applied to the TOPFLOW-PTS database, showing on average an absolute residual of ~90 °C. These poor predictions may be due to the model not scaling well with bigger jet dimensions, which characterise the TOPFLOW-PTS injection.

The Gaillard et al. correlation systematically underestimates the condensation. However, this model performs the best against the TOPFLOW-PTS tests. This may be due to the shape factor 𝑑 𝑗𝑒𝑡 𝐷 , which takes into account the bigger jet dimension with respect to the COSI one.

Development and validation of a new jet condensation model

In Section 3, the correlations found in the literature have been assessed against our experimental database. The condensation modelling through the Nusselt number, as often suggested in the literature, is not satisfactory. Thus, a new approach is presented in this section.

Modelling of the jet as an heat exchanger

The jet can be seen as a concentric heat exchanger. The heat exchange between the liquid and the steam varies with the position along the jet length. In Fig. 19, the primary side consists of After a thermal-hydraulic analysis, a total number of 110 tests are retained for the assessment of a new jet condensation model and 18 tests for its validation. The experimental conditions range between 0.3 and 7 MPa for the pressure, 0.06-161 kg/s for the injection flowrate and between 20 and 220 °C for the injection temperature. During the analysis of the experiments, it was found that a stratification can occur in the injection pipe which can have a strong impact on the calculation of the jet condensation. Thus, this study is limited to fully filled injection pipes.

New methodologies to average the mean liquid temperature of a thermocouple rake and for the estimation of the jet condensation mass flowrate were developed. The former identifies the last thermocouple in the liquid and averages the temperatures under the hypothesis of a uniform velocity field. The latter is based on the calculation of local heat balances between different thermocouple rakes and allows to determine the distribution of the condensation in the different zones of the test sections. It is then proven that most of the condensation occurs in the jet region, as usually assumed in the literature. The estimation of the heat exchange area is improved with respect to the other models found in the literature.

The correlations found in the literature modelled the condensation heat transfer coefficient through the Nusselt number. They were tested against the new revised assessment database, showing poor results. Thus, a new jet condensation model was developed with a different approach.

The jet is modelled as a heat exchanger and the condensation potential is defined. Its equation is analytically derived. It is shown that the condensation potential should follow an exponential function of a parameter 𝜂 and of the shape factor 𝐿 𝑑 𝑖𝑛𝑗 ⁄ , which is proportional to the ratio between the heat exchange and jet cross section areas.

A correlation for 𝜂 is assessed as function of a steam potential Nusselt, an injection Reynolds and a Prandtl number. The steam potential Nusselt number takes into account the effect of the steam flowrate on the condensation.

The newly developed correlation shows good results. The mean liquid temperature is predicted with a mean error of 10 °C on the assessment database. Good predictions are also obtained on the 18 validation tests not used for the development of the model.