Clément Beust

Erwin Franquet
email: erwin.franquet@univ-pau.fr

Jean-Pierre Bédécarrats

Pierre Garcia

Predictive approach of heat transfer for the modeling of large-scale latent heat storages

Keywords: Thermal energy storage, liquid-vapor, solid-liquid, model reduction, non-dimensional correlation, heat transfer Highlights

Thermal energy storage systems based on phase change materials are interesting candidates to handle the difficulties raised by intermittent renewable sources or by batch processes. Among these systems, many rely on the use of steam, as for instance in concentrating solar power plants or district heating, or in the pharmaceutical or food industries. Today, there is no systematic method to design such systems quickly and easily since complex heat transfer is observed due to the influence of the geometry and to the dual characteristics associated with solid/liquid and liquid/gas transitions. The aim of the present work is thus to propose a multi-scale modelling methodology of a latent heat storage system for the storage of steam. It mainly involves two different simulation models with different scales for the heat transfer fluid and the phase change material. Furthermore, it relies on the use of a heat transfer correlation based on specific non-dimensional numbers, which is deduced from previous simulations of the phase change material's behavior, obtained with fine 3D computational fluid dynamics calculations. Consequently, a reduced model is built to simulate the whole system. This model does not need to be tuned against experiments. This model is then directly used to compare the numerical results with measurements coming from a prototype scale latent heat storage available at CEA Grenoble. The results are very promising and show that an a priori approach that is more physically consistent and not based on any model tuning can lead to acceptable results. Moreover, the computational time can be divided by 10 to 40, thus allowing future design and real performance evaluations of latent heat storage modules.

2

Nomenclature

Latin letters

A

factor in the damping term of the momentum equation (kg.m -3 .s -1 ) Amush mushy zone constant (kg.m -3 .s -1 ) b constant term in the damping term c tube perimeter (m) cp heat capacity at constant pressure (J.kg - Greek symbols α heat transfer coefficient (W.m -2 .K -1 ) β ρ µ ν thermal expansion coefficient (K -1 ) density (kg. m -3 ) dynamic viscosity (kg. m -1 .s -1 ) kinematic viscosity (m 2 .s -1 ) ε void fraction (-) λ thermal conductivity (W.m -1 .K -1 ) λeq equivalent thermal conductivity (W.m - Thermal energy storage systems are known to be key components of solar thermal power plants, principally because they reduce the probabilities of breakdown [START_REF]Technology Roadmap -Solar Thermal Electricity[END_REF], [START_REF] Medrano | State of the art on high-temperature thermal energy storage for power generation. Part 2-Case studies[END_REF] and thus lead to more stable regimes. At the same time, many industrial applications make a huge use of steam, as for example in Direct Steam Generation (DSG) concentrating solar power (CSP) plants, where the two-phase heat transfer fluid (HTF) avoids the installation of heat exchangers and extends the 400°C limit usually associated with common thermal oils. Again, this simplifies the design and operations, and increases overall efficiency [START_REF] Fernández-García | Parabolic-trough solar collectors and their applications[END_REF], [START_REF] Birnbaum | A concept for future parabolic trough based solar thermal power plants[END_REF]. Nonetheless, the thermal storage of DSG-CSP must be adapted to the twophase feature of the HTF. Generally, a steam accumulator is used and the water vapor is stored in pressurized vessels, in a saturated state in thermal equilibrium with a saturated liquid water volume [START_REF] Steinmann | Buffer storage for direct steam generation[END_REF]. Unfortunately, such technologies are rather expensive when large capacities are needed [START_REF] Laing | Thermal energy storage for direct steam generation[END_REF], [START_REF] Ju | Numerical analysis of thermal storage performance with high-temperature phase change materials operated by condensing steam[END_REF]. Therefore, the underlying research question of the present contribution concerns the development of latent heat storages (LHSs), using phase change materials (PCMs) to store the thermal energy of the steam in the latent heat of a solid-liquid phase transition. In such storage systems where the phase change occurs in a narrow temperature range, the steam pressure drop between charge and discharge cycles is minimized compared to sensible storages [START_REF] Garcia | Design and modelling of an innovative three-stage thermal storage system for direct steam generation CSP plants[END_REF]. The most mature steam storage technology with PCM is the shell-and-tube concept [START_REF] Caron-Soupart | Performance analysis of thermal energy storage systems using phase change material[END_REF], [START_REF] Martinelli | Experimental study of a phase change thermal energy storage with copper foam[END_REF], where the HTF flows in tubes that go through a PCM-filled tank. During the charge, the steam condenses inside the tubes and the initially solid PCM progressively melts, while during the discharge, liquid water fed to the tubes evaporates and regenerates steam due to the heat released during the solidification of the PCM. Practically, metallic or graphite fins are often disposed around these tubes to enhance the heat transfer, in order to cope with the low thermal conductivities of usual PCM [START_REF] Do Couto Aktay | Thermal Conductivity of High-Temperature Multicomponent Materials with Phase Change[END_REF]. Moreover, the PCM shell does not need to be pressurized, which simplifies the storage design and reduces its costs. Generally, there are two materials that are regularly used as PCMs with storages designed for CSP applications, namely sodium nitrate NaNO3 [START_REF] Laing | Thermal energy storage for direct steam generation[END_REF]- [START_REF] Garcia | Design and modelling of an innovative three-stage thermal storage system for direct steam generation CSP plants[END_REF], [START_REF] Garcia | Experimental and Numerical Investigation of a Pilot Scale Latent Heat Thermal Energy Storage for CSP Power Plant[END_REF], [START_REF] Johnson | Design of high temperature thermal energy storage for high power levels[END_REF] and a eutectic mixture of potassium nitrate and sodium nitrate KNO3/NaNO3. [START_REF] Do Couto Aktay | Thermal Conductivity of High-Temperature Multicomponent Materials with Phase Change[END_REF], [START_REF] Fornarelli | CFD analysis of melting process in a shell-and-tube latent heat storage for concentrated solar power plants[END_REF]. For prototypes or laboratory scale bench-top modules, all kinds of PCM can be found, such as for instance RT35-HC [START_REF] Caron-Soupart | Performance analysis of thermal energy storage systems using phase change material[END_REF]- [START_REF] Martinelli | Experimental study of a phase change thermal energy storage with copper foam[END_REF] or n-octadecane [START_REF] Lacroix | Numerical simulation of a shell-and-tube latent heat thermal energy storage unit[END_REF]- [START_REF] Adine | Numerical analysis of the thermal behaviour of a shell-and-tube heat storage unit using phase change materials[END_REF], as well as salt hydrates [START_REF] Zondag | Performance analysis of industrial PCM heat storage lab prototype[END_REF]. Several prototype-scale shell-and-tube LHS modules involving a two-phase liquid water -steam HTF have been built and successfully operated by several teams around the world [START_REF] Laing | Thermal energy storage for direct steam generation[END_REF], [START_REF] Garcia | Experimental and Numerical Investigation of a Pilot Scale Latent Heat Thermal Energy Storage for CSP Power Plant[END_REF], [START_REF] Bayón | Analysis of the experimental behaviour of a 100 kWth latent heat storage system for direct steam generation in solar thermal power plants[END_REF], demonstrating the feasibility and the relevance of this concept for the storage of steam. Among numerical studies, a few 1D or 2D simulation models intended for module design or quick performance estimation can be found in the literature [START_REF] Ju | Numerical analysis of thermal storage performance with high-temperature phase change materials operated by condensing steam[END_REF], [START_REF] Garcia | Design and modelling of an innovative three-stage thermal storage system for direct steam generation CSP plants[END_REF], [START_REF] Johnson | Design of high temperature thermal energy storage for high power levels[END_REF]. Due to the small number of large-scale modules being built, and to the complexity of the heat transfer phenomena inside a module, no design model has yet been validated on experimental data from large-scale modules. In summary, since the selection of a PCM is known to be strongly oriented by the storage application, DSG-CSP plants require a PCM whose phase transition is around 300°C (saturation temperature of steam at a pressure level suitable for turbine operations). In this temperature range, inorganic salts (such as sodium nitrate) are an interesting solution thanks to their favorable physical and chemical properties (stable, non-corrosive) and low cost. Their major drawback is their low thermal conductivity, which implies either very low charging and discharging thermal powers, or a small distance between tubes. To achieve acceptable charge and discharge times (typically about six hours for CSP applications), without increasing the number of tubes and thus the cost of the heat exchanger, an improvement in the heat transfers is needed.

In general, the heat transfer coefficient between the condensing/evaporating HTF and the inner tube wall is high. Consequently, the heat transfer dynamics are mainly driven by the phenomena occurring on the PCM side. Here, heat transfer is influenced by both the geometric shape and dimensions of the fins, and by the possible natural convection movements inside the PCM liquid phase. Indeed, several studies have shown that natural convection could have a non-negligible influence on the thermal performances of a storage module [START_REF] Garcia | Experimental and Numerical Investigation of a Pilot Scale Latent Heat Thermal Energy Storage for CSP Power Plant[END_REF]- [START_REF] Mostafavi Tehrani | The error of neglecting natural convection in high temperature vertical shell-and-tube latent heat thermal energy storage systems[END_REF]. Since computational fluid dynamics (CFD) calculations, which are capable of representing this kind of problem, are often too long and/or expensive, one needs simpler engineering tools to perform fast and multiple computations. Generally, one tries to rely on heat transfer correlations [START_REF] Lacroix | Numerical simulation of a shell-and-tube latent heat thermal energy storage unit[END_REF]- [START_REF] Adine | Numerical analysis of the thermal behaviour of a shell-and-tube heat storage unit using phase change materials[END_REF]; however, these correlations often lack generality and show caveats when they are simply fitted on experimental data [START_REF] Lacroix | Numerical simulation of a shell-and-tube latent heat thermal energy storage unit[END_REF]- [START_REF] Zondag | Performance analysis of industrial PCM heat storage lab prototype[END_REF]. In contrast, other studies propose to use CFD simulations to estimate a non-dimensional correlation, which can then be used later on in a reduced system model. Thus, Garcia et al. [START_REF] Garcia | Experimental and Numerical Investigation of a Pilot Scale Latent Heat Thermal Energy Storage for CSP Power Plant[END_REF] and Johnson et al. [START_REF] Johnson | Design of high temperature thermal energy storage for high power levels[END_REF] implemented such a technique in a 3D purely conductive regime of fusion/solidification to account for the role of fins and inserts. Another similar approach can be found in Mostafavi Tehrani et al. [START_REF] Mostafavi Tehrani | An improved, generalized effective thermal conductivity method for rapid design of high temperature shell-and-tube latent heat thermal energy storage systems[END_REF] who modeled the convective-driven melting of a PCM around a single tube without fins and inserts. They deduced from these simulations a non-dimensional correlation for the heat transfer, which was then used in a reduced system model. In fact, the underlying goals of these analyses are to allow for better predictions of the main features of the storages, namely their energy capacity and associated efficiency and their charging/discharging times. These characteristics are of paramount importance, yet they are singularly different from one case to another. For instance, in [START_REF] Laing | Thermal energy storage for direct steam generation[END_REF][START_REF] Laing | Development of high temperature phasechange-material storages[END_REF] a NaNO3based storage system with an average storage capacity of 700 kWh and a discharge thermal power of 200 to 500 kW was investigated both experimentally and numerically. Its charging time was around 1-3h. The same PCM, with the same methodology, were used in the LHASSA module [START_REF] Garcia | Experimental and Numerical Investigation of a Pilot Scale Latent Heat Thermal Energy Storage for CSP Power Plant[END_REF] where full cycles for the charge and discharge lasted approximately 8 h and 6 h respectively, with a storage efficiency of 90%. The equivalent powers were thus around 35 kW and 47 kW. Along the same lines, [START_REF] Pirasaci | Influence of design on performance of a latent heat storage system for a direct steam generation power plant[END_REF] performed a numerical study of the effectiveness of a multi-tube storage, with a NaCl-MgCl2 eutectic mixture as a PCM, where the length and diameter were varied (between 10 to 150 m, and between 1 and 2 inches and 1 and 2 and 3 inches for the inner diameter of the tubes and the space between them).

Results showed a variation in the efficiency of the order of 70%. With an insulated steel container housing a fin-tube heat exchanger filled with HDPE, [START_REF] Zauner | Experimental characteri-zation and simulation of a fin-tube latent heat storage using high density polyethylene as PCM[END_REF] demonstrated experimentally and numerically the achievement of a 20-25 kWh storage in 1-2 h. In the case of smaller volumes or with preliminary prototype modules, the same research questions regularly arise. In [START_REF] Al-Abidi | Experimental study of melting and solidification of PCM in a triplex tube heat exchanger with fins[END_REF], three 0.5 m concentric tubes with internal fins containing a tube with internal fins, and PCM between them, was experimentally investigated, to show that charging could occur in 60 to 160 min. In [START_REF] Mostafavi Tehrani | The error of neglecting natural convection in high temperature vertical shell-and-tube latent heat thermal energy storage systems[END_REF], concentric tubes, with varying lengths and radii for the PCM zone, were tested together with three different PCM (H325, H425 and H525). Whatever the PCM, the charging (respectively discharging) time was shown to vary up to three (resp. 2) times depending on the conditions, while the maximum variation between the various PCM could go up to six in both modes. In [START_REF] Zondag | Performance analysis of industrial PCM heat storage lab prototype[END_REF], a prototype of a 140 L shell-and-tube storage permitted to measure a 5 kW power charge and 2-3.5 kW power discharge with RT70, and a 3.55 kW power charge and 2-3 kW power discharge with MgCl2•6H2O.

Lastly, an interesting concept of a new fin design, for a shell containing extended finned tubes surrounded by NaNO3 as PCM, was simulated in [START_REF] Johnson | Design of high temperature thermal energy storage for high power levels[END_REF]. The discharge thermal power per tube length varied from 3 to 10 kWm -1 , to fulfill the 15 min constraint initially set in their project.

Novelty of the study

This work presents the development of a reduced multi-scale modelling approach for the charge of a steam storage module involving a PCM. Similarly to what was proposed by Mostafavi Tehrani et al. [START_REF] Mostafavi Tehrani | An improved, generalized effective thermal conductivity method for rapid design of high temperature shell-and-tube latent heat thermal energy storage systems[END_REF], a heat transfer correlation during the melting is deduced on the PCM side from fine 3D CFD computations. Indeed, as it is judiciously highlighted in [sec. 1.2 p. 4, 21], prior correlations too often rely on experimental fitting. The contributions of this paper are threefold. First, it proposes to continue apace the development of such a methodology since it has the potential to avoid any experimental tuning and to overcome the limits of corresponding methods. In fact, the implicit goal is to further improve the knowledge concerning heat transfer correlations for solid/liquid phase change, since it still lags far behind what can be found for liquid/gas phase change, e.g. [START_REF] Kandlikar | Handbook of phase change: Boiling and condensation[END_REF]. Secondly, to the authors' knowledge, this is the first time ever that such a method is used for multi-tubes with fins and inserts, and for a dual two-phase storage with liquid/gas HTF inside the tubes and solid/liquid PCM outside. Thirdly, a local correlation is built, and not an average one. Since phase changes, from both the HTF and PCM, can occupy only part of the tube's length, the heat transfer is indeed far from being homogeneous. Here again, this is the first time that such a procedure is considered.

Methodology

As stated above, the current situation deals with a prototype shell-and-tube latent heat steam storage module available at CEA Grenoble [START_REF] Beust | Modélisation multi-échelles d'un système de stockage thermique de vapeur par Matériau à Changement de Phase (MCP)[END_REF][START_REF] Olcese | Design methodology and experimental platform for the validation of PCM storage modules for DSG solar plants[END_REF]. This module is made of a cylindrical shell, containing a bundle of 19 finned tubes (see Figure 1-(a)), with melded rectangular fins following a helical pattern (see Figure 1-(b)). This storage design does not include any inserts. Both tubes and fins are made of carbon steel SA334 Grade 6. To be cost competitive, storage modules are designed using off-the-shelf standard fins. The closer the tubes or the higher the heat exchange surface of the fins, the higher the thermal performances of the storage system and the higher its cost: consequently, the spacing between the tubes is logically a trade-off between system performances and costs. The HTF flows inside the tubes, whereas the shell is filled with approximately 1700 kg of sodium nitrate (NaNO3). The immerged tube length is 4.08 m when the PCM is fully liquid. Schematically, the present problem is summarized in Figure 2. The two-phase HTF (liquid water / steam) and the PCM (solid / liquid) exchange heat and three thermal resistances can be identified, which need to be assessed. First, a convective heat exchange takes place between the flowing HTF and the inner tube wall. Second, the heat flow goes through the tube wall by thermal conduction. Third, heat is 10 exchanged between the external tube wall and the PCM, 11

either by the fins or directly at the tube's surface. [START_REF] Garcia | Experimental and Numerical Investigation of a Pilot Scale Latent Heat Thermal Energy Storage for CSP Power Plant[END_REF] Generally, the main difficulty comes from this last thermal 13 resistance, involving the PCM, and, consequently, this will 14 be one of the cornerstones of the present paper. Firstly, a 3D CFD model is used to simulate the phase transition of the PCM, in presence of conductive and convective heat transfer. Then, several simulations are performed to build a non-dimensional correlation for the heat transfer, considering both the presence of fins and the phase change. Following the classic approach for non-reactive convective-only flows, this correlation is searched under the following form [START_REF] Wright | A Correlation to Quantify Convective Heat Transfer Between Vertical Window Glazings[END_REF], [START_REF] Churchill | Correlating equations for laminar and turbulent free convection from a vertical plate[END_REF]:

(1)

Here, the Rayleigh and Nusselt numbers need to be properly defined, since their expression is not unequivocal [START_REF] Hirata | An analysis of heat transfer using equivalent thermal conductivity of liquid phase during melting inside an isothermally heated horizontal cylinder[END_REF], [START_REF] Lacroix | Numerical simulation of a shell-and-tube latent heat thermal energy storage unit[END_REF], [START_REF] Adine | Numerical analysis of the thermal behaviour of a shell-and-tube heat storage unit using phase change materials[END_REF], [START_REF] Wang | The energy efficiency ratio of heat storage in one shell-and-one tube phase change thermal energy storage unit[END_REF], [START_REF] Mostafavi Tehrani | An improved, generalized effective thermal conductivity method for rapid design of high temperature shell-and-tube latent heat thermal energy storage systems[END_REF], [START_REF] Yang | Numerical analysis of phase-change material melting in triplex tube heat exchanger[END_REF]:

(

There are indeed various possible definitions for the characteristic length and the mean PCM temperature . Besides, these definitions must be local since a local correlation is searched for; so, they should involve the altitude inside the tube. Several possibilities will be discussed and compared, as shown in section 3.2.

Secondly, a reduced system model is built to represent the whole dual two-phase storage module. The goal being to develop a fast and stand-alone tool, the outside of the tube (PCM, fins, inserts if any) is approximated as a homogeneous material, and natural convection inside the PCM is handled through an effective thermal conductivity. Practically, this latter is based on the previous Nusselt correlation, built from prior numerical experiments with the previous CFD model.

Eventually, the proposed methodology was then used for the prototype shell-and-tube latent heat steam storage module presented in Figure 1, to carry out three simulations of charging mode.

3 Determination of the heat transfer correlation

CFD modelling

In the present calculations, for the sake of limiting the computational time, only an angular sector of 22.5° and a tube length of 0.54 m (27 fins) are represented (see Figure 3-(a)). For the associated boundary conditions, a fixed temperature is set at the inner tube wall and a symmetry condition for the lateral and outer boundaries, while a wall condition is imposed for the others. The entire mesh is composed of 539 046 cells, whose mean size is 0.83 mm, and its maximum skewness is 0.81 (see Figure 3-(b)). Grid independence was verified by comparing punctual PCM temperature evolutions at several distances from the external tube wall to those obtained with a finer mesh containing 774 098 cells, for a mean size of 0.63 mm. The coarser mesh was found to give acceptable results, and furthermore, its features are similar to those used in [START_REF] Fornarelli | CFD analysis of melting process in a shell-and-tube latent heat storage for concentrated solar power plants[END_REF][START_REF] Mostafavi Tehrani | The error of neglecting natural convection in high temperature vertical shell-and-tube latent heat thermal energy storage systems[END_REF]. The time step adopted is 0.025 s or 0.05 s, depending on the simulations, and, here again, the independence of the results on the time step was checked by dividing it regularly by 2. Next, the PCM is modelled using the enthalpy-porosity approach, described by Voller and Prakash [START_REF] Voller | A fixed grid numerical modelling methodology for convection-diffusion mushy region phase-change problems[END_REF], which assumes an incompressible regime and uses the Boussinesq approximation to account for the buoyancy forces. The balance equations for mass, momentum and energy conservations are written:

(4) (5) (6)
The porosity approach consists in adding a damping term at the end of the right-hand side of the momentum equation, whose role is to cancel the velocity field in solid phase. It expresses: [START_REF] Ju | Numerical analysis of thermal storage performance with high-temperature phase change materials operated by condensing steam[END_REF] with b = 10 -3 .

In the tube wall and fins, only the energy equation applies: [START_REF] Garcia | Design and modelling of an innovative three-stage thermal storage system for direct steam generation CSP plants[END_REF] The physical properties of the PCM and the steel are given in Table 1, and in Figure 4 and Figure 5. The value of the mushy zone constant was set to Amush = 10 8 kg.m -3 .s -1 , using a prior experiment where the temperature field was compared with corresponding measurements [START_REF] Beust | Modélisation multi-échelles d'un système de stockage thermique de vapeur par Matériau à Changement de Phase (MCP)[END_REF][START_REF] Beust | A numerical investigation of some key factors for the simulation of convection-dominated melting[END_REF]. For the specific heat capacities and the thermal conductivities, linear regressions were performed. The numerical experiments were performed with ANSYS Fluent® v. 17.2 software. Due to the incompressible feature of the partial differential equations system (4-6), a pressure-based formulation was chosen. Then, the PISO scheme was adopted for the pressure-velocity coupling together with, respectively, a second order upwind scheme for the convective terms in the momentum and energy equations and a least-square cell-based scheme for the diffusive terms. Finally, the pressure equation was discretized with the PRESTO! approach; for the residuals' convergence, relative decrease values of 10 -3 were taken for the continuity and momentum equations but the energy residual was set to 10 -11 [91].

Non-dimensional relation

Three CFD computations were performed with an imposed temperature Tw = 310, 318 and 328°C respectively at the inner tube wall. The PCM is initially solid at 290°C. The meshed domain was then divided into 27 representative volumes, centered on the individual fins (the boundaries between these volumes can be seen on Figure 3-(a)).

Regularly, the heat flow-rate entering the PCM was recorded as a function of time, along with associated physical variables, e.g. temperature field, molten fraction… From these values, expressions were investigated for the characteristic length and the mean PCM temperature involved in Eqs. (2-3). Thus, four and three different relations were tested for and respectively:

• Characteristic length 1. Altitude, taken at the center of the representative volume considered:

2. Thickness of the annular space outside the tube:

3. Local thickness of the liquid PCM layer: [START_REF] Do Couto Aktay | Thermal Conductivity of High-Temperature Multicomponent Materials with Phase Change[END_REF] where is the mean mass liquid fraction in the representative volume considered:

4. Present complete thickness of the liquid PCM layer on the whole tube height: [START_REF] Tiari | Numerical study of finned heat pipe-assisted thermal energy storage system with high temperature phase change material[END_REF] where is computed in the same way as , but by averaging the liquid fraction on the whole computational domain, and not only on the representative volume considered. This enabled 12 scatter plots to be drawn, to assess whether or not the above expressions allow the Rayleigh and Nusselt numbers to correlate. The corresponding graphs are shown in Figure 7. From the results available on Figure 7, one can easily note that some definitions for the characteristic length and the mean PCM temperature do not lead to a good correlation between the Rayleigh and Nusselt numbers. This is especially the case for Eq. ( 14), whatever the definition of , and similarly for Eq. ( 9), whatever the definition of . For the six remaining candidates, two behaviors can be observed. Either the points gather relatively well around a single curve, except at the beginning of melting, or two curves are to be found (one for the lowest Nusselt numbers at the beginning of melting -in blue -, and then another one for the highest Nusselt numbers at the end of melting -in green -). Given that the heat transfer should go from a mainly conductive regime to a convection-dominated one, it is preferable to select the latter case. Therefore, one can use either Eqs. [START_REF] Do Couto Aktay | Thermal Conductivity of High-Temperature Multicomponent Materials with Phase Change[END_REF] or [START_REF] Tiari | Numerical study of finned heat pipe-assisted thermal energy storage system with high temperature phase change material[END_REF] for the characteristic length and the mean PCM temperature should be taken as that of the liquid layer Eq. ( 15) at the given height.

• Mean

(a) Characteristic length given by Eq. ( 9) (b) Characteristic length given by Eq. ( 10) (c) Characteristic length given by Eq. ( 11) (d) Characteristic length given by Eq. ( 13) To further highlight this difference between low and high Nusselt numbers, for a given similar Rayleigh number, it is proposed to look at the temperature and velocity fields at a time when the 27 representative volumes are split between both curves. Figure 8 presents the corresponding results in these two zones, in a vertical plane situated in the middle of the domain. Depending on the vertical position in the tube, the Nusselt number can either undergo small values, corresponding to a velocity maximum at 17 mm.s -1 (see Figure 8.a), or high values, for an equivalent maximum velocity at 9 mm.s -1 (see Figure 8.b).

Then, it can be noted that melting is still ongoing in volumes whose (Ra, Nu) values gather around the first curve, whereas melting of the PCM is complete in volumes whose (Ra, Nu) couples follow the second curve. Besides, one can remark the highest velocity magnitudes in the first case. This is due to the higher temperature gradient inside the PCM, between the phase front remaining at the melting temperature and the inner wall (also at a fixed temperature).

When the PCM is molten, heat transfer is singularly reduced since this temperature gradient is reduced. Finally, these two situations just entail two different regimes of convective heat transfer, logically associated with two different scaling laws. Last but not least, it was verified that points lying between these two asymptotic behaviors show liquid fraction values between 0 and 1 at the external boundary of the domain.

(a) lower portion of the tube with ongoing melting (b) higher portion of the tube where fusion is over (only liquid phase here) Figure 8: Temperature and velocity fields at t = 2390 s for the case Tw = 328°C In summary, using Eqs. ( 11) or ( 13) and Eq. ( 15) for, respectively, the characteristic length and the mean PCM temperature gives to obtain a scaling law between the Nusselt and Rayleigh numbers. Depending on the time and the altitude, that is to say depending on the completeness of the phase change, this scaling law will be bounded by two asymptotic behaviors. In this respect, a local heat transfer correlation will be preferred for Eq. ( 1) and, consequently, final choices will rely on Eqs. [START_REF] Do Couto Aktay | Thermal Conductivity of High-Temperature Multicomponent Materials with Phase Change[END_REF] or [START_REF] Mostafavi Tehrani | The error of neglecting natural convection in high temperature vertical shell-and-tube latent heat thermal energy storage systems[END_REF]. It leads to the following scaling laws for the two limiting cases:

(16) (17)
As can be seen on Figure 9, a very good agreement with the numerical results is observed. 11) and ( 15) for the definitions of lc and TPCM, with correlations ( 16) and ( 17) for the heat transfer From a practical point of view, one will need a criterion to know when to go from one expression to the other. Indeed, a continuous formulation is required since the real physical heat transfer is not discontinuous and, second, because it is more suitable in a reduced model to avoid oscillations and unstable behaviors. As the proper definition of this threshold is beyond the scope of the present article, the following definition was chosen: [START_REF] Waser | Fast and experimentally validated model of a latent thermal energy storage device for system level simulations[END_REF] 4 Application As mentioned in Section 2, the idea is now to use the Nusselt correlation thus obtained to build an effective thermal conductivity that can be implemented in the reduced model, as summarized in Figure 10. The proposed methodology will be tested on the three previous fusion experiments.

System modelling

The present model will stand for the two-phase HTF inside the tube, for the tube, and for the fins, inserts and PCM approximated together as a homogeneous material. For each of these materials, 1D and 2D discretization are adopted respectively.

On the HTF side, the flow has been shown to be in forced regime [START_REF] Martinelli | Experimental study of a phase change thermal energy storage with copper foam[END_REF]. Moreover, the liquid and vapor phases are assumed to be in thermal and dynamical equilibrium, i.e. with the same local velocity and temperature, and axial conduction is neglected. Therefore, the PDE system for the HTF, incorporating directly the wall boundary condition in the energy equation [START_REF] Bestion | Balance equations[END_REF], is written:

(19) (20)
To compute the HTF density, it is assumed that liquid and vapor phases are at saturation in the two-phase region:

Finally, the heat flux at the wall is calculated by means of a classic thermal resistance: [START_REF] Hirata | An analysis of heat transfer using equivalent thermal conductivity of liquid phase during melting inside an isothermally heated horizontal cylinder[END_REF] Next, the tube simply obeys the heat equation. Following the thermal resistance analogy of Eq. ( 24), the energy balance is written (using enthalpy for the sake of clarity with other PDE systems): [START_REF] Wang | The energy efficiency ratio of heat storage in one shell-and-one tube phase change thermal energy storage unit[END_REF] and logically, one gets for the outer heat flux: [START_REF] Yang | Numerical analysis of phase-change material melting in triplex tube heat exchanger[END_REF] Last but not least, one needs to write the modelling of the homogeneous material. Since natural convection is accounted for by means of an effective thermal conductivity, it only relies on the energy balance equation. To handle the latent term, the previous source term approach [START_REF] Voller | Fixed grid techniques for phase change problems: A review[END_REF] is still considered. For the sake of simplicity, the heat transfer in the axial direction is neglected and thermal losses are also assumed to be negligible. Thus, the energy equation can be written: [START_REF] Beust | Influence of the Modeling Parameters on the Numerical CFD Simulation of a Shell-and-Tube Latent Heat Storage System with Circular Fins[END_REF] where the average properties are given by: (28) [START_REF] Voller | Fixed grid techniques for phase change problems: A review[END_REF] Then, the paramount parameter that needs to be further detailed is the effective thermal conductivity. It is generally deduced from the Nusselt number, or equivalently, from the Rayleigh number. During melting, the situation encountered can be represented as depicted in Figure 11: thermal conductivity of the homogeneous material corresponds to the effective thermal conductivity λeff in the liquid molten layer and to the average thermal conductivity in the external solid part. By definition, the effective thermal conductivity is such that the total amount of heat is equal to the heat exchanged in the convective case: [START_REF] Voller | A fixed grid numerical modelling methodology for convection-diffusion mushy region phase-change problems[END_REF] To express the thickness of the liquid layer el, a mass balance is used, involving the mean mass liquid fraction at the considered altitude : (31) [START_REF] Nunes | Molten salts as engineering fluids -A review: Part I. Molten alkali nitrates[END_REF] In [START_REF] Nunes | Molten salts as engineering fluids -A review: Part I. Molten alkali nitrates[END_REF], Vj represents the volume of the j-th cell in the radial direction.

Then, at a given altitude z along the tube, the local Nusselt and Rayleigh numbers are expressed as follows: [START_REF] Kandlikar | Handbook of phase change: Boiling and condensation[END_REF] (34) By combining equations ( 30), ( 31), ( 33) and (34), one gets:

(35)
In the solid part, a classic mean calculation holds:

(36)
Finally, in each cell, the equivalent thermal conductivity λeq,j is computed with a weighted sum between the effective thermal conductivity in the liquid layer and the homogeneous equivalent thermal conductivity in the solid layer:

(37)

The values of all the other variables, and of the operational parameters, are provided in Table 2.

Results

The present computations deal with the same test cases as the ones presented in Section 3. In the current situation, the space steps are Δz = 54.0 mm and Δr = 1.85 mm. The HTF pressure is chosen so that the saturation temperature is equal to the desired wall temperature, and accordingly, the internal heat transfer coefficient is set to αtint = 10 6 W.m -

2

.K -1 . Water vapor, with a slight superheating of 0.1°C, is injected at the top with a 0.05 kg.s -1 mass flow-rate.

The whole system is solved with an in-house code, in Scilab language. For Eqs. ( 19), ( 20), ( 25) and ( 27), a classic finite volume method is used. The temporal integration is fully implicit. The numerical resolution is done separately for the HTF on the one hand, and for the tube thickness and the homogeneous material on the other hand. For these two blocks, the convergence criterion is based on the variation of the solved quantities from one iteration to another. On the HTF side, convergence is reached when the relative variation of mass enthalpy and mass flow in each mesh cell is below 10 -12 . For the second block, the total mass enthalpy is normalized by its initial value, and convergence is assumed to be reached when the variation of this normalized mass enthalpy is below 10 -8 .

The main focus is very much on the ability to reproduce the storage behavior, that is to say to represent the variation of energy inside the module. Therefore, the temporal evolution of the energy accumulated by the PCM is represented on Figure 12 for the three cases, for both the CFD model and the reduced model. Overall, the agreement between the system model and the CFD results is good: the mean discrepancy between the two models is 4.8% for Tw = 328°C, 6.8% for Tw = 318°C, and 14% for Tw = 310°C. In the latter case, it is important to mention that this discrepancy probably comes from the intrinsic limit of the Nusselt correlation that fundamentally holds only for the liquid region. However, as can be seen in Figure 13, the mushy region is far more pronounced for the lower HTF temperature. As a consequence, the method is here less reliable. All in all, the overall agreement between the reduced model and the complete CFD model is relatively good, and these results are very promising. Finally, to further highlight the assets of the present method, comparisons of the computational times needed to obtain the results are presented in Table 3. It is straightforward to notice that a considerable reduction can be achieved, resulting in 10 to 40 times lower CPU costs.

Conclusion

A reduced model has been built to carry out fast and accurate simulations of a dual two-phase storage of steam, composed of a shell containing a PCM crossed by several finned tubes containing a liquid/vapor heat transfer fluid.

The corresponding system is based on an effective thermal conductivity which is determined using a heat transfer correlation with specific non-dimensional numbers. This correlation mainly involves the Nusselt and Rayleigh numbers which are linked from previous simulations of the phase change material's behavior, obtained with fine 3D computational fluid dynamics calculations. A specific study was made to determine the best suited definitions for the characteristic length and the mean PCM temperature involved in the Nusselt and Rayleigh numbers. In summary, the present method proposes to avoid the usual tuning of endogenous parameters; instead, a Nusselt correlation is determined and then used directly in the system model without any other a posteriori calibration. When comparing the results of the two approaches, the agreement obtained is rather good for the three test cases considered (three different temperatures of the inner tube wall Tw = 310, 318 and 328°C with the PCM initially solid at 290°C). The evolution of the accumulated energy over time is predicted by the system model with an average deviation of 4 to 14% from the CFD results. The time required for the simulation of a melting is 10 to 40 times less for the reduced model than for the CFD model. Thus, the current method appears to be very promising, making it possible to consider future easy and fast designs of latent heat storage systems, and/or multiple sensitivity analysis that would be too prohibitive otherwise. In the near future, it is planned to consolidate first the determination of the Nusselt correlation. Then, the reduced model will be further developed to remove its basic assumptions, that can easily be avoided; at the same time, it will be validated on numerous test cases in order to bound its precision, together with the savings in computational cost.

Figure 1 :

 1 Figure 1: Description of the prototype storage module

16

 16

Figure 2 :

 2 Figure 2 : Schematic view of the physical phenomena occurring in a shell-and-tube steam storage system based on LHS

  a) fraction of the prototype simulated (b) details of the mesh in the wall and fins Figure 3 : Description of the geometry and mesh retained

Figure 5 :

 5 Figure 5 : Thermal conductivity of NaNO3

2 . 15 ) 3 .

 2153 Mean temperature of the liquid PCM layer in the representative volume considered:(Temperature of the first mesh cells near the outer tube wall. It is computed as the mean temperature of six PCM cells and one fine mesh cell near the wall, as shown on Figure6.

Figure 6 :

 6 Figure 6: Mesh cells near the outer wall of the inner tube (yellow: PCM cells; red: fin cells)

Figure 7 :

 7 Figure 7: Accuracy of the correlation between the Rayleigh and Nusselt numbers depending on the definitions taken for and : phase change temperature (left), mean liquid temperature at the considered height (middle), mean temperature near the wall (right)

Figure 9 :

 9 Figure 9: Comparisons of the (Ra, Nu) scatter plot obtained from the CFD results, using Eqs. (11) and (15) for the definitions of lc and TPCM, with

Figure 10 :

 10 Figure 10 : Structure and characteristics of the proposed multi-scale model

Figure 11 :

 11 Figure 11: General case for the definition of the effective thermal conductivity

Figure 12 :

 12 Figure 12: Comparisons of the energy accumulated in the PCM, the tube and the fins during melting at a constant and uniform wall temperature, for the CFD and system models

Figure 13 :

 13 Figure 13: Liquid fraction and velocity fields in a vertical plane for the three CFD computations

Figure 14 :

 14 Figure 14: Comparisons of the phase fronts predicted by the CFD and system models for Tw = 328°C (black lines represent the boundaries of the PCM domain. Left: outer tube wall. Right: external domain boundary.)

Table 1 :

 1 Material properties for the CFD model

	Material	NaNO3 [9], [10],[31],[32]	Steel
	ρ (kg.m -3 )	1927	7764
	β (K -1 )	3.8 10 -4	--
	cp (J.kg -1 .K -1 )
	solid	Variable	542.8
	liquid	1704
	λ (W.m -1 .K -1 )
	solid	Variable	50.33
	liquid	Variable
	μ (Pa.s)	2.8 10 -3	--
	L (kJ.kg -1 )	173.3	--
	Tsol (°C)	303.3	--
	Tliq (°C)	306.6	--
		Figure 4 : Specific heat capacity of NaNO3

Table 2 :

 2 Material and operational properties for the system model

	Geometrical configuration
	Total PCM volume fraction	0.936
	Total PCM mass fraction	0.785
	Material properties
	ρh	2299 kg.m -3
	cp,h
	solid	1540 J.kg. -1 .K -1
	liquid	1454 J.kg. -1 .K -1
	λPCM
	solid	0.720 W.m -1 .K -1
	liquid	0.515 W.m -1 .K -1
	λeq,s
	Rtext < r < Rtext + 10 mm	6.92 W.m -1 .K -1
	Rtext + 10 mm < r < Rtext + 30 mm	Variable (bounded values: 5.61 -3.48 W.m -1 .K -1 )
	r > Rtext + 30 mm	0.720 W.m -1 .K -1
	Mesh properties
	Number of cells
	axial direction	10
	radial direction	9
	total	110

Table 3 :

 3 Computational times for the CFD model and the reduced system model

		Tw = 310°C	Tw = 318°C	Tw = 328°C
	CFD model	289 h (≈12 days)	132 h (5.5 days)	158 h (≈ 7 days)
	System model	29 h	8 h	4 h

20

Last but not least, an important prospect will be the development of a similar multi-scale methodology for steam discharge, involving PCM solidification, and boiling of the heat transfer fluid. During solidification in a PCM heat storage module, the heat transfers are generally mainly conductive. The reduced model will have to be adapted.


Marc Laine
email: marc.laine@ap-hm.fr

Gilles Lemesle

Stéphane Burtey

Guillaume Cayla

Grégoire Range

Gonzalo Quaino

Matthias Canault

Mathieu Pankert

Franck Paganelli

Etienne Puymirat

MD Laine Marc

MD, PhD Lemesle Gilles

MD, PhD Burtey Stéphane

MD, PhD Cayla Guillaume

MD, PhD Range Grégoire

MD Quaino Gonzalo

PhD Canault Matthias

MD Pankert Mathieu

MD, PhD Paganelli Franck

MD, PhD Puymirat Etienne

MD, PhD Bonello Laurent

TicagRelor Or Clopidogrel in severe or terminal chronic kidney patients Undergoing PERcutaneous coronary intervention for acute coronary syndrome: The TROUPER trial

Keywords: Acute coronary syndrome, percutaneous coronary intervention, thrombosis, chronic kidney disease, P2Y12-ADP-receptor inhibitor Highlights

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

Introduction

Chronic kidney disease (CKD) is a major public health issue with a stable prevalence in developed countries of approximately 15% of the general population [START_REF] Levey | The definition, classification, and prognosis of chronic kidney disease: a KDIGO Controversies Conference report[END_REF][START_REF] Hallan | International comparison of the relationship of chronic kidney disease prevalence and ESRD risk[END_REF][START_REF] Murphy | Trends in Prevalence of Chronic Kidney Disease in the United States[END_REF]. This prevalence is increasing with age and reaches 30% in the elderly [START_REF] Stengel | Epidemiology and prognostic significance of chronic kidney disease in the elderly--the Three-City prospective cohort study[END_REF]. CKD is associated with an increased risk of major adverse cardiovascular events (MACE), including cardiovascular death [START_REF] Sarnak | Kidney disease as a risk factor for development of cardiovascular disease: a statement from the American Heart Association Councils on Kidney in Cardiovascular Disease, High Blood Pressure Research, Clinical Cardiology, and Epidemiology and Prevention[END_REF][START_REF] Foster | Cardiovascular risk factor burden, treatment, and control among adults with chronic kidney disease in the United States[END_REF]. Moreover, CKD patients are more likely to die of cardiovascular events, including acute coronary syndrome (ACS), than to develop end-stage renal failure [START_REF] Foster | Cardiovascular risk factor burden, treatment, and control among adults with chronic kidney disease in the United States[END_REF][START_REF] Keith | Longitudinal follow-up and outcomes among a population with chronic kidney disease in a large managed care organization[END_REF][START_REF] Shulman | Prognostic value of serum creatinine and effect of treatment of hypertension on renal function. Results from the hypertension detection and follow-up program. The Hypertension Detection and Follow-up Program Cooperative Group[END_REF]. In contrast, CKD is encountered in up to 40% of patients admitted for ACS. Furthermore, the prognosis is poor: the 1-year rate of MACE can reach 40% in CKD patients with ACS, while they have a threefold in-hospital mortality rate compared to patients with normal renal function [START_REF] Parikh | Impact of severity of renal dysfunction on determinants of in-hospital mortality among patients undergoing percutaneous coronary intervention[END_REF][START_REF] Lin | Impact of impaired glomerular filtration rate and revascularization strategy on one-year cardiovascular events in acute coronary syndrome: data from Taiwan acute coronary syndrome full spectrum registry[END_REF][START_REF] Wong | Temporal management patterns and outcomes of non-ST elevation acute coronary syndromes in patients with kidney dysfunction[END_REF][START_REF] Fox | Use of evidence-based therapies in short-term outcomes of ST-segment elevation myocardial infarction and non-ST-segment elevation myocardial infarction in patients with chronic kidney disease: a report from the National Cardiovascular Data Acute Coronary Treatment and Intervention Outcomes Network registry[END_REF]. Thus, CKD patients comprise a very high-risk population regarding thrombotic events.

The rupture of an atherosclerotic plaque that leads to thrombosis of a coronary artery is the leading cause of ACS. Therefore, platelet inhibition is of the utmost importance to prevent recurrences. Dual antiplatelet therapy (DAPT) (which combines aspirin with a platelet P2Y12 ADP-receptor inhibitor) is the cornerstone of the therapeutic strategy for the management of patients with ACS undergoing PCI [START_REF] Ibanez | ESC Guidelines for the management of acute myocardial infarction in patients presenting with ST-segment elevation: The Task Force for the management of acute myocardial infarction in patients presenting with ST-segment elevation of the European Society of Cardiology (ESC)[END_REF][START_REF] Roffi | ESC Guidelines for the management of acute coronary syndromes in patients presenting without persistent ST-segment elevationTask Force for the Management of Acute Coronary Syndromes in Patients Presenting without Persistent ST-Segment Elevation of the European Society of Cardiology (ESC)[END_REF][START_REF] Mehta | Effects of pretreatment with clopidogrel and aspirin followed by long-term therapy in patients undergoing percutaneous coronary intervention: the PCI-CURE study[END_REF].

Clopidogrel has major limitations: a mild level of platelet inhibition, delayed onset of action, particularly in ACS patients, and a wide interindividual variability in its biological efficacy, leading to a 40% rate of high on-treatment platelet reactivity (HTPR) [START_REF] Bonello | Consensus and Future Directions on the Definition of High On-Treatment Platelet Reactivity to Adenosine Diphosphate[END_REF]. Of importance, CKD patients have a higher rate of HTPR than the general population. HTPR in CKD patients was shown to correlate with thrombotic events and CV death in those undergoing PCI [START_REF] Dj | Impact of chronic kidney disease on platelet function profiles in diabetes mellitus patients with coronary artery disease taking dual antiplatelet therapy[END_REF][START_REF] Barragan | Resistance to thienopyridines: Clinical detection of coronary stent thrombosis by monitoring of vasodilator-stimulated phosphoprotein phosphorylation[END_REF]. Ticagrelor, a platelet P2Y12 ADP-platelet receptor inhibitor, has been developed to overcome the limitations of clopidogrel. From a biological point of view, ticagrelor has a more rapid onset of action and induces a more potent and reproducible platelet inhibition than clopidogrel, including in CKD patients [START_REF] Husted | Pharmacokinetics and pharmacodynamics of ticagrelor in patients with stable coronary artery disease: results from the ONSET-OFFSET and RESPOND studies[END_REF][START_REF] Bliden | The effect of ticagrelor versus clopidogrel on high on-treatment platelet reactivity: Combined analysis of the ONSET/OFFSET and RESPOND studies[END_REF][START_REF] Gurbel | Randomized double-blind assessment of the ONSET and OFFSET of the antiplatelet effects of ticagrelor versus clopidogrel in patients with stable coronary artery disease: the ONSET/OFFSET study[END_REF][START_REF] Laine | Platelet reactivity evaluated with the VASP assay following ticagrelor loading dose in acute coronary syndrome patients undergoing percutaneous coronary intervention[END_REF]. Pharmacodynamic and pharmacokinetic studies have demonstrated that ticagrelor could be safely used in patients with kidney failure, including patients under dialysis [START_REF] Butler | Pharmacokinetics, pharmacodynamics, and safety of ticagrelor in volunteers with severe renal impairment[END_REF][START_REF] Jeong | Platelet reactivity after receiving clopidogrel compared with ticagrelor in patients with kidney failure treated with hemodialysis: a randomized crossover study[END_REF]. In the PLATO trial, focused on ACS patients, ticagrelor demonstrated superiority over clopidogrel regarding ischemic recurrences and mortality. Although major bleedings were similar in the two study arms, there was a higher rate of non-CABG-related major bleeding in the ticagrelor group according to the study criteria (4.5% vs. 3.8%, p =0.03) and the TIMI criteria (2.8% vs. 2.2%, p =0.03) [START_REF] Wallentin | Ticagrelor versus Clopidogrel in Patients with Acute Coronary Syndromes[END_REF]. However, a limited number of patients with stage >3b CKD (glomerular filtration rate (GFR) < 45 mL/min or dialysis) were included (21%), and dialysis patients were excluded. Moreover, CKD is associated with an increased rate of bleeding events; therefore, the particular ratio of thrombotic and bleeding risk in CKD patients is likely to differ from patients without CKD and remains to be determined [START_REF] Herzog | Atherosclerotic versus nonatherosclerotic evaluation: the Yin and Yang of cardiovascular imaging in advanced chronic kidney disease[END_REF][START_REF] Desai | Contemporary Time Trends in Use of Antiplatelet Agents Among Patients with Acute Coronary Syndrome and Comorbid Diabetes Mellitus or Chronic Kidney Disease[END_REF][START_REF] Ocak | Chronic kidney disease and bleeding risk in patients at high cardiovascular risk: a cohort study[END_REF]. Frequently, CKD patients do not receive up-todate management in relation to both therapeutic nihilism and the paucity of data regarding new therapies [START_REF] Rhee | Clinical features, use of evidence-based therapies, and cardiovascular outcomes among patients with chronic kidney disease following non-ST-elevation acute coronary syndrome[END_REF]. To fill this gap in evidence, we designed the TicagRelor Or Clopidogrel in severe or terminal chronic kidney patients Undergoing PERcutaneous coronary intervention for acute coronary syndrome (TROUPER) trial to compare the efficacy of ticagrelor and clopidogrel in ACS patients with stage ≥3b CKD intended for an invasive strategy.

Methods

Study design

The TROUPER study is a prospective, multicenter, randomized, controlled, openlabel, 2 parallel-group study. The study design was recorded in clinicaltrial.gov (database: NCT03357874). The overall study design is summarized in Figure 1. This study includes 20 centers in France.

Patients with ACS with or without ST segment elevation intended for an invasive strategy will be eligible. They will be included if all inclusion criteria are met and in the absence of non-inclusion criteria after an informed consent is signed. Following inclusion, patients will be randomized in a 1:1 ratio to receive clopidogrel or ticagrelor. In the control group, patients will receive a 600 mg loading dose of clopidogrel after randomization followed by a 75 mg od regimen for 1 year after PCI.

In the ticagrelor group, patients will receive a 180 mg loading dose of ticagrelor after randomization followed by a 90 mg bid for 1 year. Treatment with a loading dose of the platelet P2Y12 ADP-receptor inhibitor could be administered as soon as the diagnosis of ACS is made, with randomization performed until the end of PCI.

Patients already treated with a P2Y12 antagonist before randomization will receive a loading dose of the allocated treatment following the consensus recommendations on switching between oral P2Y12 inhibitors if required [START_REF] Angiolillo | International Expert Consensus on Switching Platelet P2Y12 Receptor-Inhibiting Therapies[END_REF]. Of note, patients undergoing coronary angiography and medically managed without PCI will also be included in the study. The study will be performed in accordance with ethical principles consistent with the Declaration of Helsinki. The final study protocol and informed consent have been reviewed and approved by the health authorities and institutional review boards for all participating sites.

Participants

The aim of the TROUPER study is to include a representative population of CKD patients (stages 3b, 4 and 5). The glomerular filtration rate will be estimated with the Modification of Diet in Renal Disease (MDRD) formula. Only patients with a creatinine clearance <45 ml/kg/min will be eligible. Patients will be included if CKD is already known. Patients with acute kidney failure are not eligible.

Of importance, the delays of medical strategies will not be affected by the protocol.

Information obtained as part of routine care will be reviewed to determine eligibility for enrollment, including 12 lead electrocardiograms (ECG) and a physical exam, cardiac biomarkers and all means considered necessary for the diagnosis of STE-ACS and intermediate, high-risk and very high-risk NSTE-ACS [START_REF] Ibanez | ESC Guidelines for the management of acute myocardial infarction in patients presenting with ST-segment elevation: The Task Force for the management of acute myocardial infarction in patients presenting with ST-segment elevation of the European Society of Cardiology (ESC)[END_REF].

Patients must be intended for primary PCI for STE ACS or an invasive strategy in the case of NSTE ACS according to the ESC definition [START_REF] Ibanez | ESC Guidelines for the management of acute myocardial infarction in patients presenting with ST-segment elevation: The Task Force for the management of acute myocardial infarction in patients presenting with ST-segment elevation of the European Society of Cardiology (ESC)[END_REF][START_REF] Roffi | ESC Guidelines for the management of acute coronary syndromes in patients presenting without persistent ST-segment elevationTask Force for the Management of Acute Coronary Syndromes in Patients Presenting without Persistent ST-Segment Elevation of the European Society of Cardiology (ESC)[END_REF] (Table 1). Non-inclusion criteria are listed Table 1. The only exclusion criterion is a subject wishing to interrupt his/her participation during the study. After delivery of oral information regarding the study (e.g., objectives, schedule, benefits and risks), written consent will be obtained from all patients before inclusion.

Treatment protocol

Coronary revascularization

In the 2 groups, PCI will be performed according to international guidelines and at the discretion of the operator. The use of a drug-eluting stent and state-of-the-art intervention will be encouraged in both groups. The anticoagulant used during PCI is left to the physician's discretion between the drugs listed in the guidelines [START_REF] Ibanez | ESC Guidelines for the management of acute myocardial infarction in patients presenting with ST-segment elevation: The Task Force for the management of acute myocardial infarction in patients presenting with ST-segment elevation of the European Society of Cardiology (ESC)[END_REF][START_REF] Roffi | ESC Guidelines for the management of acute coronary syndromes in patients presenting without persistent ST-segment elevationTask Force for the Management of Acute Coronary Syndromes in Patients Presenting without Persistent ST-Segment Elevation of the European Society of Cardiology (ESC)[END_REF].

Culprit PCI is recommended during the initial procedure and in the case of multivessel PCI; non-culprit vessels could be treated in the same setting or in a staged fashion, according to the investigator's preferences.

The use of glycoprotein 2b/3a inhibitors will be left to the physician's decision; however, it must not be started before angiography.

Other care management

Aspirin Therapy

Adjunctive aspirin (ASA) is required for all patients. Aspirin (150 to 300 mg IV) can be administered as soon as the diagnosis is made. Daily maintenance therapy should be taken with 75 mg to 100 mg ASA [START_REF] Ibanez | ESC Guidelines for the management of acute myocardial infarction in patients presenting with ST-segment elevation: The Task Force for the management of acute myocardial infarction in patients presenting with ST-segment elevation of the European Society of Cardiology (ESC)[END_REF][START_REF] Roffi | ESC Guidelines for the management of acute coronary syndromes in patients presenting without persistent ST-segment elevationTask Force for the Management of Acute Coronary Syndromes in Patients Presenting without Persistent ST-Segment Elevation of the European Society of Cardiology (ESC)[END_REF].

Other permitted medications include, but are not limited to, histamine 2 receptor (H2) blockers; proton pump inhibitors (PPI); oral, sublingual, or intravenous nitrates; calcium channel blockers; beta blockers; angiotensin converting enzyme inhibitors (ACEIs); angiotensin receptor blockers (ARBs); 3-hydroxy-3-methylglutaryl coenzyme A (HMG Co-A) reductase inhibitors (statins); anti-arrhythmic drugs; vasodilators; and intravenous vasopressor agents.

Subjects will be treated with concomitant long-term therapies according to current guideline recommendations [START_REF] Ibanez | ESC Guidelines for the management of acute myocardial infarction in patients presenting with ST-segment elevation: The Task Force for the management of acute myocardial infarction in patients presenting with ST-segment elevation of the European Society of Cardiology (ESC)[END_REF][START_REF] Roffi | ESC Guidelines for the management of acute coronary syndromes in patients presenting without persistent ST-segment elevationTask Force for the Management of Acute Coronary Syndromes in Patients Presenting without Persistent ST-Segment Elevation of the European Society of Cardiology (ESC)[END_REF]. The use of all concomitant medications will be recorded on the CRF. Concomitant medications will be summarized by the treatment cohort. Following PCI, there will be no difference between the 2 groups in the therapeutic strategy and medical care with the exception of the P2Y12-ADP-receptor inhibitor used. Blood sampling will be performed, including usual tests and troponin measures, at each recurrent chest pain during the hospital stay to detect ongoing necrosis and peri-procedural myocardial infarction (MI).

During the hospital stay, patients will be monitored for recurrent myocardial ischemia with ECG monitoring and daily clinical examination.

Follow-up and study outcomes

The primary endpoint is defined by the rate of MACE, including death, myocardial infarction, urgent revascularization and stroke, at the one-year follow-up [START_REF] Hicks | ACC/AHA Key Data Elements and Definitions for Cardiovascular Endpoint Events in Clinical Trials: A Report of the American College of Cardiology/American Heart Association Task Force on Clinical Data Standards (Writing Committee to Develop Cardiovascular Endpoints Data Standards)[END_REF]. MI will be defined according to the universal definition, including type 1 to 3 MI [START_REF] Thygesen | Fourth Universal Definition of Myocardial Infarction[END_REF]. Urgent revascularization will be defined as all unplanned revascularization during follow-up by PCI or coronary artery bypass graft. Stroke, transient or definitive, as diagnosed by a neurologist will be based on the following:

-a transient episode of focal neurological dysfunction caused by brain, spinal cord, or retinal ischemia, without acute infarction; -a definite stroke is defined by the occurrence of neurological dysfunction as diagnosed by a neurologist (>24 h duration) and/or the presence of acute infarction as demonstrated by imaging.

The secondary objectives are to assess the 2 strategies in terms of efficacy and tolerance through in-person visits at discharge, one month and one year. Secondary endpoints are listed in Table 2 and include bleeding events, dyspnea, requirement of hemodialysis and ischemic events. For all events, the date of the occurrence will be obtained. The delay will be calculated from the randomization day and the date of the occurrence. A subject would be considered lost to follow-up if he or she fails to return or is unable to be contacted by the site for the 30-day and 12-month visits. Site staff are expected to make diligent attempts to contact subjects who fail to return for a scheduled visit. Survival status will be obtained within legal and ethical boundaries for all randomized subjects, including those who did not receive study drug. The status of "lost to followup" should only be determined at the conclusion of the trial. A blinded clinical endpoint committee will review clinical events.

Sample size

The sample size calculation was performed on the hypothesis formulated on the primary endpoint, i.e., the one-year rate of major adverse cardiovascular events (MACE), including all-cause mortality, myocardial infarction, urgent revascularization and stroke.

According to the literature, ischemic recurrences are more frequent in CKD patients and increases when creatinine clearance decreases [START_REF] Lee | Chronic Kidney Disease in the Second-Generation Drug-Eluting Stent Era: Pooled Analysis of the Korean Multicenter Drug-Eluting Stent Registry[END_REF][START_REF] Go | Chronic kidney disease and the risks of death, cardiovascular events, and hospitalization[END_REF][START_REF] Natanzon | Statin therapy among chronic kidney disease patients presenting with acute coronary syndrome[END_REF][START_REF] Cardi | Prognostic Value of Incomplete Revascularization after Percutaneous Coronary Intervention Following Acute Coronary Syndrome: Focus on CKD Patients[END_REF][START_REF] Gowdak | Screening for significant coronary artery disease in high-risk renal transplant candidates[END_REF][START_REF] Scholz | One-year clinical outcomes in patients with renal insufficiency after contemporary PCI: data from a multicenter registry[END_REF][START_REF] Sato | Comparison of clinical outcomes of coronary artery stent implantation in patients with end-stage chronic kidney disease including hemodialysis for three everolimus eluting (EES) stent designs: Bioresorbable polymer-EES, platinum chromium-EES, and cobalt chrome-EES[END_REF][START_REF] Edfors | Outcomes in patients treated with ticagrelor versus clopidogrel after acute myocardial infarction stratified by renal function[END_REF][START_REF] Szummer | Influence of renal function on the effects of early revascularization in non-ST-elevation myocardial infarction: data from the Swedish Web-System for Enhancement and Development of Evidence-Based Care in Heart Disease Evaluated According to Recommended Therapies (SWEDEHEART)[END_REF]. Therefore, it is estimated that the rate of the primary endpoint (MACE) at 12 months will be 40% in the control group and 28% in the ticagrelor group (relative risk reduction of 30%) [START_REF] Go | Chronic kidney disease and the risks of death, cardiovascular events, and hospitalization[END_REF][START_REF] Natanzon | Statin therapy among chronic kidney disease patients presenting with acute coronary syndrome[END_REF][START_REF] Gowdak | Screening for significant coronary artery disease in high-risk renal transplant candidates[END_REF][START_REF] James | Ticagrelor versus clopidogrel in acute coronary syndromes in relation to renal function: results from the Platelet Inhibition and Patient Outcomes (PLATO) trial[END_REF][START_REF] Saltzman | Long-term impact of chronic kidney disease in patients with ST-segment elevation myocardial infarction treated with primary percutaneous coronary intervention: the HORIZONS-AMI (Harmonizing Outcomes With Revascularization and Stents in Acute Myocardial Infarction) trial[END_REF][START_REF] Morel | Impaired platelet P2Y12 inhibition by thienopyridines in chronic kidney disease: mechanisms, clinical relevance and pharmacological options[END_REF].

Therefore, to show a significant difference with a power of 80% and an alpha risk of 5% between 40% and 28%, 244 patients are required in each group. With a 5% lost to follow-up rate, we plan to enroll 257 patients in each group. A 2-year inclusion period is scheduled. Recruitment began in November 2018, and 40 patients have been randomized.

Randomization

Computer-generated randomized lists have been created using a permuted block design (stratified on center). Each center has a specific list.

Statistical analysis

The data will be analyzed using SPSS version 17.0 software (IBM) or a later version.

All tests will be two-sided. Statistical significance is defined as p<0.05. The methodology will be based on the Consolidated Standards of Reporting Trials Statement [START_REF] Schulz | CONSORT 2010 statement: updated guidelines for reporting parallel group randomised trials[END_REF]. The full analysis population (including subjects who will be at least evaluated at baseline and randomized) will be used in the primary analysis. In this intention-to-treat analysis, all patients will remain in the group to which they were allocated. The per-protocol population (including all subjects who will be randomized and will not have major protocol deviations) will be used in the secondary analysis to assess the robustness of the results. No interim analysis is planned. The time from randomization to the first occurrence of a MACE during the 1-year follow-up will be compared between the 2 groups using a two-sided log-rank test. The Kaplan-Meier method will be used to depict this comparison and estimate the median survival times and one-year event rates. A hazard ratio and its 95% confidence interval will be estimated using a Cox proportional-hazards model after determining that the treatment effect is not time-dependent. A secondary adjusted analysis will include prespecified baseline variables of prognostic value. A per-protocol analysis will then be conducted using the same procedure. The rates of the secondary endpoints will be compared between the 2 groups using the same procedure. Multivariate approaches will be performed according to the procedure described for the primary endpoint. If the exact date of some endpoints cannot be determined with sufficient confidence, one-month and one-year rates will be compared using χ 2 tests and logistic regression models.

Adverse events (AEs) will be summarized by frequency and proportion. The characteristics of AEs, the maximum grade, the incidence of deaths and the primary cause of death will be summarized. The results of scheduled assessments will be described. An independent Clinical Endpoints Committee (CEC), blinded to the treatment, will adjudicate all death, recurrent ischemia, MI, stroke, recurrent and all BARC bleeds. Primary analyses will be conducted on CEC-adjudicated endpoints.

monitoring will be conducted under the auspices of an independent, external data monitoring committee (DMC) assigned to this study. The primary endpoint analysis and all other key efficacy and safety analyses will be conducted using the two-sided log-rank test from a time-to-first event analysis, unless otherwise specified.

Funding and conduct of the study

This academic study is entirely funded by the French Ministry of Health. The authors are solely responsible for the design and conduct of this study, all study analyses, the drafting and editing of the paper and its final contents.

Discussion

CKD patients have a high incidence of ACS with a worse outcome than the general population [START_REF] Parikh | Impact of severity of renal dysfunction on determinants of in-hospital mortality among patients undergoing percutaneous coronary intervention[END_REF][START_REF] Lin | Impact of impaired glomerular filtration rate and revascularization strategy on one-year cardiovascular events in acute coronary syndrome: data from Taiwan acute coronary syndrome full spectrum registry[END_REF][START_REF] Wong | Temporal management patterns and outcomes of non-ST elevation acute coronary syndromes in patients with kidney dysfunction[END_REF][START_REF] Fox | Use of evidence-based therapies in short-term outcomes of ST-segment elevation myocardial infarction and non-ST-segment elevation myocardial infarction in patients with chronic kidney disease: a report from the National Cardiovascular Data Acute Coronary Treatment and Intervention Outcomes Network registry[END_REF]. These patients have a high thrombotic risk related to 3 main factors: i) alteration of the coagulation cascade; ii) endothelial injury; and iii) platelet alteration. Platelets play a key role in thrombotic events that affect CKD patients and in atherothrombotic events, thus emphasizing the importance of an adequate antiplatelet strategy in secondary prevention in this specific population. Platelet reactivity and platelet-leucocyte aggregation are stimulated due to increased fibrinogen receptor PAC-1 and P-selectin concentrations associated with higher platelet susceptibility to thrombin [START_REF] Bonello | P2Y12-ADP Receptor Blockade in Chronic Kidney Disease Patients With Acute Coronary Syndromes[END_REF]. This high thrombotic phenotype of platelets in CKD is critical to their higher risk of recurrent thrombotic events following ACS. However, at the same time, CKD is also associated with an increased bleeding risk [START_REF] Herzog | Atherosclerotic versus nonatherosclerotic evaluation: the Yin and Yang of cardiovascular imaging in advanced chronic kidney disease[END_REF][START_REF] Desai | Contemporary Time Trends in Use of Antiplatelet Agents Among Patients with Acute Coronary Syndrome and Comorbid Diabetes Mellitus or Chronic Kidney Disease[END_REF][START_REF] Ocak | Chronic kidney disease and bleeding risk in patients at high cardiovascular risk: a cohort study[END_REF]. Of importance, bleedings are major adverse events associated with death in ACS patients [START_REF] Eikelboom | Adverse impact of bleeding on prognosis in patients with acute coronary syndromes[END_REF]. Various mechanisms come into play in CKD patients and can be responsible for altered platelet adhesion and aggregation leading to hemorrhages: reduced ADP release, deregulation of acid and prostaglandin metabolism, disturbance of alpha-granules, changes in intraplatelet calcium flux, and circulating fibrinogen fragments that interfere with glycoprotein IIb/IIIa [START_REF] Bonello | P2Y12-ADP Receptor Blockade in Chronic Kidney Disease Patients With Acute Coronary Syndromes[END_REF]. Furthermore, anemia that is common in CKD patients increases the NO level and therefore amplifies the alteration of platelet aggregation [START_REF] Viganò | Hyperparathyroidism does not influence the abnormal primary haemostasis in patients with chronic renal failure[END_REF][START_REF] Moal | Impaired expression of glycoproteins on resting and stimulated platelets in uraemic patients[END_REF][START_REF] Benigni | Reversible activation defect of the platelet glycoprotein IIb-IIIa complex in patients with uremia[END_REF]. The specific and complex alteration of platelet physiology are responsible for a particular risk profile of CKD patients suffering from ACS. This specific thrombotic and bleeding risk ratio may influence the optimal antiplatelet regimen particularly if PCI is performed [START_REF] Ocak | Chronic kidney disease and bleeding risk in patients at high cardiovascular risk: a cohort study[END_REF].

There is a major gap in evidence regarding the optimal P2Y12 ADP-receptor antagonists in this clinical setting. While CKD affects 20-40% of ACS patients, this population is deeply underrepresented in major clinical trials. In the PLATO trial that recruited more than 18,000 patients, 21% of the patients had an estimated creatinine clearance < 60 mL/min, while only 214 patients had a calculated clearance < 30 mL/min [START_REF] Wallentin | Ticagrelor versus Clopidogrel in Patients with Acute Coronary Syndromes[END_REF][START_REF] James | Ticagrelor versus clopidogrel in acute coronary syndromes in relation to renal function: results from the Platelet Inhibition and Patient Outcomes (PLATO) trial[END_REF]. According to the substudy dedicated to CKD patients, ticagrelor significantly reduced the rate of ischemic events and mortality without an increase in major bleedings [START_REF] James | Ticagrelor versus clopidogrel in acute coronary syndromes in relation to renal function: results from the Platelet Inhibition and Patient Outcomes (PLATO) trial[END_REF]. However, the limited sample of stage > 3 CKD patients included in the PLATO trial highlights the need for an adequately designed clinical trial that tests antiplatelet treatment in CKD patients with ACS. Similarly, the TRITON trial that compared prasugrel to clopidogrel in ACS included only 10.9% of patients with a creatinine clearance < 60 mL/min [START_REF] Wiviott | Prasugrel versus Clopidogrel in Patients with Acute Coronary Syndromes[END_REF]. Therefore, the benefit observed in the prasugrel group regarding ischemic events can hardly be extrapolated to the CKD population. Moreover, data are lacking in patients with a creatinine clearance less than 30 mL/min [START_REF] Bonello | P2Y12-ADP Receptor Blockade in Chronic Kidney Disease Patients With Acute Coronary Syndromes[END_REF].

We recently performed a meta-analysis that compared P2Y12 ADP-receptor antagonists with clopidogrel in patients with CKD suffering from ACS. In patients treated by PCI, there seemed to be a benefit with ticagrelor, although the number of patients with a creatinine clearance less than 45 mL/min was limited [START_REF] Bonello | Meta-Analysis of Potent P2Y12-ADP Receptor Antagonist Therapy Compared to Clopidogrel Therapy in Acute Coronary Syndrome Patients with Chronic Kidney Disease[END_REF]. With regard to prasugrel, in a propensity adjustment of the PROMETHEUS registry, prasugrel did not appear to be superior to clopidogrel regarding ischemic events in CKD patients [START_REF] Baber | Associations Between Chronic Kidney Disease and Outcomes With Use of Prasugrel Versus Clopidogrel in Patients With Acute Coronary Syndrome Undergoing Percutaneous Coronary Intervention: A Report From the PROMETHEUS Study[END_REF].

The limited available data in CKD patients leave practitioners helpless and jeopardize patient outcomes. Therefore, it is of the utmost importance to investigate the potential of ticagrelor compared to clopidogrel in CKD patients. The primary goal of the TROUPER trial is to test the hypothesis that ticagrelor is superior to clopidogrel regarding ischemic recurrences in stage 3a, 4 and 5 CKD patients (or patients undergoing chronic dialysis) suffering from ACS [START_REF] Hicks | ACC/AHA Key Data Elements and Definitions for Cardiovascular Endpoint Events in Clinical Trials: A Report of the American College of Cardiology/American Heart Association Task Force on Clinical Data Standards (Writing Committee to Develop Cardiovascular Endpoints Data Standards)[END_REF]. The primary endpoint was chosen considering the fact that MACE are the typical endpoint in trials focusing on ACS because of their major clinical interest. Furthermore, due to the higher bleeding rate in CKD patients, the safety of potent P2Y12 ADP-receptor inhibitors, such as ticagrelor, should be carefully assessed and monitored [START_REF] Ocak | Chronic kidney disease and bleeding risk in patients at high cardiovascular risk: a cohort study[END_REF][START_REF] Bonello | Impact of optimal medical therapy and revascularization on outcome of patients with chronic kidney disease and on dialysis who presented with acute coronary syndrome[END_REF][START_REF] Subherwal | Baseline risk of major bleeding in non-STsegment-elevation myocardial infarction: the CRUSADE (Can Rapid risk stratification of Unstable angina patients Suppress ADverse outcomes with Early implementation of the ACC/AHA Guidelines) Bleeding Score[END_REF]. The TROUPER study will help to unveil the potential interest of ticagrelor in CKD patients and analyze safety issues, including bleedings. The net clinical benefit (combining ischemic and bleeding events) will be assessed.

The determination of the optimal P2Y12-ADP receptor inhibitor in ACS patients with stage 3b, 4 and 5 CKD or under chronic hemodialysis is critical to improve their clinical outcome. The TROUPER trial will provide critical data in this regard, which could help physicians decide the optimal therapy this population and update the guidelines.

Challenges and limitations of the study design

We acknowledge that the open nature of the TROUPER study is a limitation.

However, the content of the primary endpoint (major adverse cardiovascular events, including death, myocardial infarction, urgent revascularization and stroke at oneyear follow-up) tends to reduce this bias given the low subjectivity in its adjudication.

In addition, all events will be adjudicated by a committee not involved in the study and blinded regarding the group assignment.

Conclusion

The TROUPER trial is a prospective, multicenter, randomized, controlled and open label study comparing the efficacy of ticagrelor with clopidogrel in stage 3b, 4 or 5 chronic kidney disease patients presenting with acute coronary syndrome and scheduled for an invasive strategy. The primary endpoint will be the rate of major adverse cardiovascular events, including death, myocardial infarction, urgent revascularization and stroke, at the one-year follow-up. Bleedings will also be recorded. The aim of this trial is to determine the optimal antiplatelet regimen in this very high-risk population that has been poorly studied in previous clinical trials. -the rate of BARC< 3 bleedings -the course of creatinin clearance between ticagrelor and clopidogrel during one-year follow-up including the requirement for hemodialysis Also, tolerance will be compared between the two groups: -dyspnea at one month and one year -compliance to P2Y12 ADP-receptor inhibitor at one month and one year

Figure 1. Study protocol Table 1. Inclusion and non-inclusion criteria

---- 5 (

 5 electrocardiographic ST-segment abnormalities (depression or transient elevation of at least 0.1 mV) or T-wave inversion in at least 2 contiguous leads, or (3) an elevated cardiac troponin value (above the upper limit of normal) or ST segment elevation ACS scheduled for primary PCI defined as a history of chest discomfort or ischemic symptoms of > 20 minutes duration at rest ≤ 14 days prior to entry into the study with one of the following present on at least one ECG prior to randomization: a) ST-segment elevation ≥1 mm in two or more contiguous ECG leads. Minors and pregnant or breastfeeding women Subject under chronic anticoagulant -Subject with thrombolytic therapy during the preceding 24 hours -Subject with bleeding diathesis -Subject participating in another research protocol -Subject does not agree to participate Subject or presumably new left bundle branch block (LBBB). c) ST-segment depression ≥1 mm in two anterior precordial leads (V1 through V4) with clinical history and evidence suggestive of true posterior infarction. Subject intended for an invasive strategy if NSTE-ACS or primary PCI if STE-ACS according to guidelines -Subject with CKD stage 3b, 4 and

Table 2 . Secondary endpoints

 2

	ARC: Academic Research Consortium
	BARC: Bleeding Academic Research Consortium
	MACE: Major Adverse Cardiovascular Events

Primary endpoint: MACE, including all cause death, myocardial infarction, urgent revascularization and stroke at 1 year

This academic study is entirely funded by the French Ministry of Health. Disclosures: Bonello and Laine received consulting and lecture fees from AstraZeneca and Boston Scientific; Bonello and Laine received research grants from Bayer, Biotronik, Boston Scientific, Abbott.