# BORA4-PTS: experimental reproduction of a Pressurized Thermal Shock, and building of numerical simulation with the CATHARE Code

Alexis Berny, Cécile Demathieu, Joël Nibas, Alain Ungar

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Alexis Berny, Cécile Demathieu, Joël Nibas, Alain Ungar. BORA4-PTS: experimental reproduction of a Pressurized Thermal Shock, and building of numerical simulation with the CATHARE Code. Nuclear Engineering and Design, 2024, 428, pp.113497. 10.1016/j.nucengdes.2024.113497. cea-04669431

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# BORA4-PTS: Experimental reproduction of a Pressurized Thermal Shock, and building of numerical simulation with the CATHARE Code

Alexis Berny<sup>a,*</sup>, Cécile Demathieu<sup>b</sup>, Joël Nibas<sup>b</sup>, Alain Ungar<sup>b</sup>

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

### Keywords:

Pressurized Thermal Shock

BORA4-PTS

CATHARE 3

Experiment

Numerical simulation

Downcomer

## ABSTRACT

When a break occurs in a nuclear reactor, a fast cooldown has to be down to prevent the melting of the core. This is done by the injection of cold water at 7 °C, in a pressurized vessel at 295 °C. This is a Pressurized Thermal Shock. To improve the safety of the nuclear reactor, an experimental facility was built to analyze the mix of hot and cold water in the downcomer of the vessel. This is the BORA4-PTS experiment. Salt water at 45 °C is injected into stagnant pure water at 20 °C, to represent the injection of cold water in hot water. Through this experiment, a scaling was established to compare it with the reactor case. We then made a numerical simulation of this experimental facility with the CATHARE code. With this simulation come another scaling, in order to properly compare the numerical and the experimental results. The numerical simulations give results that are very similar to the experimental ones. With this experiment, we show the excellent capacity of CATHARE to simulate and model the complex thermohydraulic inside a downcomer.

## Contents

<table><tr><td>1.</td><td>Introduction</td><td>2</td></tr><tr><td>2.</td><td>The BORA4-PTS experiment</td><td>2</td></tr><tr><td>2.1.</td><td>Experimental setup</td><td>2</td></tr><tr><td>2.2.</td><td>Experimental scaling with the reactor case</td><td>3</td></tr><tr><td>2.2.1.</td><td>Geometrical scaling</td><td>3</td></tr><tr><td>2.2.2.</td><td>Time scaling</td><td>4</td></tr><tr><td>2.2.3.</td><td>Advection-diffusion scaling</td><td>4</td></tr><tr><td>2.2.4.</td><td>Numerical application</td><td>4</td></tr><tr><td>2.3.</td><td>Description of the experiment</td><td>5</td></tr><tr><td>3.</td><td>Simulation of the BORA4-PTS experiment with CATHARE</td><td>5</td></tr><tr><td>3.1.</td><td>The CATHARE code</td><td>5</td></tr><tr><td>3.2.</td><td>Inlet condition</td><td>6</td></tr><tr><td>3.3.</td><td>Thermodynamic scaling</td><td>6</td></tr><tr><td>3.4.</td><td>Time scaling</td><td>7</td></tr><tr><td>3.5.</td><td>Numerical setup</td><td>7</td></tr><tr><td>4.</td><td>Comparison between the simulations and the experiments</td><td>9</td></tr><tr><td>4.1.</td><td>Validation of the method on one sensor</td><td>9</td></tr><tr><td>4.2.</td><td>Confrontation between the complete experiment and the simulation</td><td>10</td></tr><tr><td>5.</td><td>Conclusions</td><td>11</td></tr><tr><td></td><td>CRediT authorship contribution statement</td><td>11</td></tr><tr><td></td><td>Declaration of competing interest</td><td>11</td></tr><tr><td></td><td>Data availability</td><td>11</td></tr><tr><td></td><td>Acknowledgments</td><td>11</td></tr><tr><td></td><td>Appendix. Equations of states of salt water</td><td>11</td></tr><tr><td></td><td>References</td><td>11</td></tr></table>

<footnote><sup>a</sup> Université Paris Saclay, CEA, Service de Thermo-hydraulique et de Mécanique des Fluides, 91191 Gif-sur-Yvette, France</footnote>

<footnote><sup>b</sup> EDF R&D Lab Chatou, Département de mécanique des Fluides, Énergie et Environnement, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: alexis.berny@cea.fr (A. Berny).</footnote>

<footnote>https://doi.org/10.1016/j.nucengdes.2024.113497</footnote>

<footnote>Received 8 February 2024; Received in revised form 18 July 2024; Accepted 21 July 2024</footnote>

<footnote>Available online 31 July 2024</footnote>

<footnote>0029-5493/© 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).</footnote>
# Nomenclature

## Greek Letters

$\lambda$ Conductivity (W m⁻¹ K⁻¹).

$\alpha$ Proportion of salt liquid in the mix.

$\mu$ Dynamic viscosity (kg m⁻¹ s⁻¹).

$\nu$ Kinematic viscosity (m² s⁻¹).

$\rho$ Density (kg m⁻³).

$\tau$ Characteristic time scale of the viscous diffusion (s).

## Roman Letters

$C_p$ Heat capacity at constant pressure (J kg⁻¹ K⁻¹).

$c_{sel}$ Salt concentration (10⁶ ppm).

$Q_v$ Volumetric flowrate (m³ s⁻¹).

$D$ Diameter (m).

$D$ Diffusivity or diffusion coefficient (m² s⁻¹).

$U$ Internal volumic energy of the liquid (J m⁻³).

$Fr$ Densimetric FROUDE number.

$g$ Gravity component.

$L_c$ Characteristic length scale (m).

$Pe_m$ PECLET number for mass diffusion ReSc.

$Pe_{th}$ PECLET number for thermal diffusion RePr.

$Pr$ PRANDTL number $\left[ \frac{\mu_k \cdot C_p k}{\lambda_k} \right]$.

$P$ Pressure (Pa).

$Re$ REYNOLDS number $\left[ \frac{\rho V L_c}{\mu_k} \right]$.

$Sc$ SCHMIDT number $\left[ \frac{\mu_k}{\rho_k \cdot D} \right]$.

$S_r$ STROUHAL number.

$T$ Temperature (°C).

$t$ Time (s).

$V$ Velocity (m s⁻¹).

# Subscripts and Superscripts

$exp$ Refer to the BORA4-PTS experiment.

$init$ Refer to the state at the beginning of the experiment or of the simulation in the vessel.

$inj$ Refer to the state in the safety injectors.

$k$ Relative to the kth phase.

$L$ Relative to the liquid.

$num$ Refer to the CATHARE3 simulation.

$0$ Fluid of reference.

# 1. Introduction

In France, nuclear energy is an important source of electricity with 56 nuclear reactors, representing 61.4 GW of low carbon installed electric power. In order to keep those reactor running, Électricité de France (EDF), FRAMATOME and the CEA are conducting research in the field of the nuclear safety. Within this field, the Pressurized Thermal Shock (PTS) is an important topic.

When there is a break in the primary circuit of the reactor, cold water is injected to cool down the reactor, in order to prevent to core to melt down. This cold water is at 7 °C and is injected in hot water at 295 °C and 85 bars. Such temperature difference create a thermal shock in the reactor vessel. It is then important to analyze the mix between hot and cold water in order to know how the cold water will reach the vessel and how it will interact with it, in order to estimate the mechanical load due to the thermal shock in the vessel. This is

the context of the present study. We want to analyze the hydrolic mix between hot and cold water during a PTS event.

The present study is in the continuity of previous work (Martin et al., 2010; Raynaud et al., 2013; Moutin et al., 2015). The work of Martin et al. (2010) was based on the experimental facility UPTF (Weiss et al., 1986). Its goal was to assess the capacity of code saturne to analyze the thermohydraulic mix during a PTS event in the vessel of the UPTF facility. The work of Raynaud et al. (2013) was based on the HYBISCUS II facility, an experimental loop belongings to EDF and modeling the thermal mix in the downcomer of a French 1300 MWe PWR. Last, the work of Moutin et al. (2015) was based on the TOPFLOW facility (Schaffrath et al., 2002). Their goal was to assess a new model for the CATHARE code for a PTS event.

Of course, the PTS event is the object of research by other team, with for example the work of Scheuerer et al. (2005) which consist of a European benchmark for the use of different CFD code to model a PTS event, the work of Pasichnyk et al. (2011) which consist of the use of the system code ATHLET to model the UPTF-TRAM C1 experiment, the work of Trewin et al. (2023) which is an uncertainties analysis on a PTS event, made in the framework of the APAL European project. Closer to our work, Orea et al. (2020) build a 80 cm height experiment using salt water and ethanol to introduce density differences to observe the mixing in the cold leg and 10 cm below it in the downcomer using PIV.

The present work consist in a new step in the research regarding the PTS event, in the context of the nuclear safety. This work is based on a new experimental facility belonging to EDF, named BORA4-PTS. The present work is organized as follow: first we will present the BORA4-PTS facility, with a focus on the scaling method used to move from a full scale french 1300 MWe reactor, to the experimental facility. Secondly, we will model this experiment with the CATHARE code. In particular, we will present a method to compare the numerical results obtained with the CATHARE code, with the experimental results. Then, we will validate our method and our numerical simulations, using the experimental results. Last, we will evaluate the quality of the numerical simulations compare to the BORA4-PTS experiment.

# 2. The BORA4-PTS experiment

## 2.1. Experimental setup

The BORA4-PTS experiment is located in Chatou, in the facility of EDF R&D. This experiment represents, on a 1:5 scale, the vessel of a French 1300 MWe PWR, all the details over 1 mm are accurately represented. A photo of the experiment is shown on Fig. 1. We can see the different elements of the experiment. There are 4 cold loops connected to the vessel. On each loop, we can observe an injection with a conical shape that represent the SIS (Safety Injection System), a U-tube (coming from the steam generator in PWR), a box and the cold leg going to the downcomer. The boxes represent, by a volume, the Reactor Coolant Pumps (RCP) used in the reactor to move the water. After the downcomer, we have a lower plenum: bottom of the vessel with internals, instrumentation and lower core plate, which links the downcomer to the core of the experiment (fuel assemblies are not represented here). The water exits the facility at the top of the core. The 4 hot loops are not present and are represented by black cylinders.

This facility has been designed to study the PTS in a French 1300 MWe PWR. More specifically, this experiment will help to understand how cold water, injected through the safety injection, will propagate into the downcomer, and impact the temperature of the downcomer wall. This experiment was also designed to analyze the convective effect between hot and cold water into the downcomer.

The BORA4-PTS experiment can also be cut in half. Some walls can be added into the experiment between the “hot-legs” in the downcomer and in the lower plenum. This then gives us two separate experiments, close to the HYBISCUS II configuration (Raynaud et al., 2013)
<figure><img src="image_4.png" /><figcaption>Fig. 1. Photo of the experimental setup of BORA4-PTS, in the experimental lobby of EDF R&D in Chatou. Crédits photos: EDF-Jacques Witt.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 2. Instrumentation of the BORA4-PTS experiment. On the left, we show the sensors location on the outside wall of the downcomer. On the right, we show the sensors location on the inside wall of the downcomer.</figcaption></figure>

On Fig. 2, we display the instrumentation of the downcomer in the BORA4-PTS experiment. On the Left Hand Side (LHS) of the figure, we show the location of the temperature sensors on the outside wall of the downcomer. There are 5 lines of 18 sensors. On the Right Hand Side (RHS), we show the location of the temperature sensors on the inside wall of the downcomer. There are 3 lines of 10 sensors. On the inside wall, the sensors are located under the cold legs, where the mix between the hot and the cold water would be the most important.

The EDF R&D team has established that, for the entire measurement chain, the precision of the measured temperature is 1 °C. In other words, we have a precision of ± 1 °C for a given sensor, at a given time.

We can also observe, on Fig. 2 the location of the inside wall that allows the compartmentalization of the downcomer in 2. Each half experiment has the following disposition: one hot leg (crossing the downcomer), two cold legs and again, one hot leg.

On Fig. 3, we show the location of the sample carrier in the BORA4-PTS experiment. They reproduce the location of the sample carrier in the 1300 MWe French PWR. They are located between the cold legs 1 and 4 (LHS photo) and under the cold leg 3 (RHS photo).

On the different pictures, we can see that the BORA4-PTS experiment is made of plexiglass. It is a material that cannot handle the temperature and pressure conditions of a PTS event. Some modifications in the fluid in action have to be made. In the reactor case, we have hot water at 295 °C and at 85 Bars in the vessel and we inject cold

water at 7 °C. In the experiment, we need to have two miscible fluids, with enough density difference. The choice has been made to represent the initial hot water with pure water. The injected cold water will be represented by saturated salty water. These two fluids are miscible with a good density difference. To follow the propagation of the salt water in the vessel, we choose to heat it up at 46 °C, and to keep the clear water at room temperature (15 to 20 °C depending on the experimental hall temperature). We will then use the thermocouples of the BORA4-PTS experiment to follow the propagation of the hot salt water in the clear cold water, since the temperature will have very little impact on the density of the fluids.

The use of a mix of salt and pure water to simulate a PTS event also assume that the salt diffusion and the temperature diffusion are similar, or are at least taken into account in the experimental scaling of the facility.

## 2.2. Experimental scaling with the reactor case

### 2.2.1. Geometrical scaling

As we saw, the BORA4-PTS experiment is a 1:5 reactor vessel where the hot water is replaced by pure cold water and where the cold water is replaced by hot saturated salty water. Therefore, we have to do a scaling analysis, to determine the input parameters of the experiment and the duration of each test. This will ensure that we can compare the experiments with the reactor case.
<figure><img src="image_6.png" /><figcaption>Fig. 3. Photos of the BORA4-PTS downcomer. These photos show the locations of the sample carrier located into the real reactor and reproduced here in the BORA4-PTS downcomer. There are two samples carriers. One between the cold legs 1 and 4, and one under the cold leg 3.</figcaption></figure>

The choice has been made to preserve the densimetric Froude number between BORA4-PTS and the reactor case. This number is defined by:

$$Fr = \frac{V_{\text{inj}}}{\sqrt{\frac{\Delta\rho}{\rho_0} g L_c}} \qquad (1)$$

In this number, the densities are already fixed, and so is the characteristic length $L_c$. Therefore, the only way to preserve $Fr$ is to correctly select the injection velocity $V_{\text{inj}}$. To help us fixing the injection velocity, lets introduce the hat notation that compares the parameters between the reactor case and the BORA4-PTS case. For a $G$ parameter, we note:

$$\hat{G} = \frac{G_{\text{experiment}}}{G_{\text{reactor}}} \qquad (2)$$

With this notation, we have, for example,

$$\hat{L}_c = \frac{L_{c\text{experiment}}}{L_{c\text{reactor}}} = \frac{1}{5} \qquad (3)$$

which corresponds to the ratio between the characteristic length of the experiment and the one of the reactor. In order to preserve the densimetric Froude number, using the introduced notation, we have:

$$\frac{\hat{V}_{\text{inj}}}{\sqrt{\left(\frac{\Delta\rho}{\rho_0}\right) \hat{L}_c}} = 1 \qquad (4)$$

In the reactor (or in the experiment), we do not have a direct control on the injected velocity. We are indeed controlling the initial flow rate. We have $Q_v = V_{\text{inj}} D_{\text{inj}}^2 \pi/4$, which gives, by substitution, the relationship between the injection and the other parameters:

$$\hat{Q}_v = \left(\frac{\Delta\rho}{\rho_0}\right)^{\frac{1}{2}} \hat{L}_c^{\frac{5}{2}} \qquad (5)$$

### 2.2.2. Time scaling

The time scale has been determined using the Strouhal number. This number is defined by:

$$S_r = \frac{V_t}{L_c} \qquad (6)$$

For the BORA4-PTS experiment we also want to preserve the Strouhal number. Therefore, it implies that $\hat{S}_r = 1$. By using the already defined hat notation, and the relationship between velocity and flow rate, we have:

$$\hat{t} = \hat{L}_c^3 \hat{Q}_v^{-1} = \left(\frac{\Delta\rho}{\rho_0}\right)^{-\frac{1}{2}} \hat{L}_c^{\frac{1}{2}} \qquad (7)$$

<caption>Table 1</caption>

Density values for the reactor and the experiment. Depending on the conditions in the experimental hall (namely the temperature in the experimental hall which cannot be controlled), the density of the salt water may vary from 1175 kg m⁻³ up to 1190 kg m⁻³.

<table><thead><tr><th>Parameter</th><th>Reactor</th><th colspan="2">BORA4-PTS</th></tr></thead><tbody><tr><td>ρ<sub>injection</sub></td><td>1002.89 kg m<sup>-3</sup></td><td>1175 kg m<sup>-3</sup></td><td>1190 kg m<sup>-3</sup></td></tr><tr><td>ρ<sub>vessel</sub></td><td>734.32 kg m<sup>-3</sup></td><td colspan="2">998 kg m<sup>-3</sup></td></tr><tr><td>Δρ/ρ<sub>0</sub></td><td>0.366</td><td>0.1773</td><td>0.1923</td></tr></tbody></table>

### 2.2.3. Advection-diffusion scaling

The mass diffusivity of salt in water is different than the thermal diffusivity. However, the BORA4-PTS experiment is designed to analyze the advection of salt water in pure water. Therefore, we have to be sure that the reactor case and the BORA4-PTS case are both dominated by the advection, and therefore that the diffusion effects can be neglected.

The effects of diffusion and advection can be compared by the Peclet number. For the reactor case, where we have a thermal diffusion, we will use a thermal Peclet number. This number is defined as:

$$Pe_{th} = RePr = \frac{\rho_{\text{inj}} V_{\text{inj}} L_c C p_{\text{inj}}}{\lambda_L} = \frac{\rho_{\text{inj}} C p_{\text{inj}} Q_v}{L_c \lambda_L} \qquad (8)$$

For the BORA4-PTS case, where we have a mass diffusion, we will use a mass Peclet number. This number is defined as:

$$Pe_m = ReSc = \frac{V_{\text{inj}} L_c}{D} = \frac{Q_v}{L_c D} \qquad (9)$$

We will have to check that both Peclet number are great compare to one, to validate our assumption regarding the dominance of the effect of the advection compare to the diffusion effects.

### 2.2.4. Numerical application

With the ratios we just defined, we can compute the ratio linking the scaling parameters between the BORA4-PTS experiment and the reactor case. The density values are summed up in the Table 1. The density of salt water may vary upon the conditions in which it was prepared (as we will explain in Section 2.3).

The data for the BORA4-PTS experiment are taken for saturated salt water (with a concentration of salt of approximately 250 kg of salt for 1000 kg of water) at 45 °C. They are issued from Company and United States. Office of Saline Water (1971). The data for the reactor case are taken from the CATHARE 3 EOS library. We can now compute the hat variables, using a density of 1175 kg m⁻³ for the salt water. We have

$$\left(\frac{\Delta\rho}{\rho_0}\right) = 0.4849 \text{ and } \hat{L}_c = 0.2. \text{ This gives us:}$$

$$\hat{Q}_v = 0.01246 \qquad \hat{t} = 0.64 \qquad (10)$$
<figure><img src="image_7.png" /><figcaption>Fig. 4. Example of an experiment with the addition of eosin in the salt water.</figcaption></figure>

<table><caption>**Table 2**

Physical parameter used for the computation of the Peclet number in the reactor case, and in the BORA4-PTS case.</caption><thead><tr><th>Parameter</th><th>Reactor</th><th>BORA4-PTS</th></tr></thead><tbody><tr><td>Debit of injection</td><td>36.9 L/s</td><td>0.46 L/s</td></tr><tr><td>Diffusion</td><td>0.57 W m<sup>-1</sup> K<sup>-1</sup></td><td>1.4 &times; 10<sup>-9</sup> m<sup>2</sup> s<sup>-1</sup></td></tr><tr><td>Heat capacity</td><td>4120 J kg<sup>-1</sup> K<sup>-1</sup></td><td>5651 J kg<sup>-1</sup> K<sup>-1</sup></td></tr><tr><td>Characteristic length</td><td>7.5 m</td><td>1.5 m</td></tr><tr><td>Peclet number</td><td>&asymp;268 &times; 10<sup>3</sup></td><td>&asymp;3 &times; 10<sup>6</sup></td></tr></tbody></table>

Regarding the Peclet number, we have to use data that directly come from the experimental setup or the reactor case. We chose, as characteristic length, the height of the downcomer. It is approximately 1.5 m height for the BORA4-PTS experiment, and so 7.5 m height for the reactor case. For the experiment we will use in this paper (see Section 2.3), the water injection is at 0.46 L/s for the BORA4-PTS case, so 36.9 L/s for the reactor case.

For the diffusion, the mass diffusion of salt in water will vary from approximately 1.3 and $1.5 \times 10^{-9} \text{ m}^2 \text{ s}^{-1}$. The thermal diffusion in cold (7 °C) or hot water (295 °C) at 75 bar is approximately at 0.57 W m$^{-1}$ K$^{-1}$. Last, the heat capacity vary from 4120 J kg$^{-1}$ K$^{-1}$ at 7 °C to 5651 J kg$^{-1}$ K$^{-1}$ at 295 °C. We summarize all the value and the results in the Table 2.

The Peclet number for the thermal diffusion or the salt diffusion, regarding the advection effects are both high compare to 1. This shows that the advection effects are dominant either

The Peclet number for the thermal or the salt diffusion, are both high compare to 1. This shows that the advection effects are dominant on both the reactor and the experiment scale. We can then neglect the effect of thermal or salt diffusion, to only focus on the advection effects.

## 2.3. Description of the experiment

In this study, we will only present one experiment, named “C2”. However, all the experiment are run with the same method.

We first starts by filling up the experiment with clear water. This water has an initial temperature between 15 and 20 °C. This variation is linked to the environmental condition in the experimental lobby.

In the meantime, we prepare the saturated salt water. Salt basket are placed in a water reservoir at room temperature. 5 to 7 tonnes of salt are diluted in the liquid. A pump force the circulation of the water, to ensure a good homogenization of the liquid. Again, depending of the season, the water temperature in the reservoir may slightly change, which may impact the amount of salt that is diluted in the reservoir.

In the rest of this study, we will assume that there is 250 kg of salt diluted in 1000 kg of water. We then heat the water to 46 °C. To qualitatively follow the results, some eosin is added into the water and video can be made to follow the plume formation in the downcomer. The eosin act as a passive tracer, it does not impact the physical parameters of the salt water. An example of an ongoing experiment is shown on picture 4.

The experiment start when we begin the injection of salt water in the safety injector. We can control the volume of water that is injected this way. During the experiment, clear water can also be injected in the cold legs. It plays the role of the water coming from a residual recirculation.

In the C2 experiment, we inject the salt water in the 4 safety injector, at 0.46 L/s and at 45 °C. There is no injection flow in the cold legs. The water is then extract through the core, in the middle of the experiment. The experiment is run for 30 min. It is repeated 6 times.

# 3. Simulation of the BORA4-PTS experiment with CATHARE

## 3.1. The CATHARE code

The CATHARE code (Code for Analysis of Thermal-Hydraulics during an Accident of Reactor and safety Evaluation) is a French thermal-hydraulic system code. It is owned and developed since 1979 by the CEA, EDF, FRAMATOME and the French radio-protection and nuclear safety institute (IRSN). This code is validated through the extensive use of experimental facilities (Barre and Bernard, 1990). The latest major release, CATHARE 3 starts its development in 2006 (Emonot et al., 2011; Préa et al., 2020) and the first industrial version, CATHARE 3 V2.1.0 was released in 2019.

The modeling of a circuit within CATHARE is done by assembling different hydraulic elements. They are either represented by a Volume (0-D mesh), an axial (1-D mesh) or a threeD (3-D mesh). For each element, CATHARE consider a mean flux and the main variable are in the center of the cells. In an hydraulic circuit, the code is able to simulate different flow regimes (in one or two phase flow) and fluids (water, hydrogen or sodium for example). To do that, CATHARE use a two-phase flow six equations model (mass, energy and momentum balance equation for each phase) closed by physical closure laws. It used a Newton-Raphson solving iterative method (Bestion, 1990). It is important to note that water mixed with salt is not in the list of available fluids in CATHARE.

In the present study, we will use the CATHARE 3-V2.3.191 version to simulate the BORA4-PTS experiment. This version is in the continuity of the CATHARE 3-V2.1.0 version presented in Préa et al. (2020).
<table><caption>**Table 3**
Parameters for our numerical simulations compared to the BORA4-PTS conditions.</caption><thead><tr><th>Parameter</th><th>BORA4-PTS</th><th>Scaling law from Company and United States. Office of Saline Water (1971)</th><th>CATHARE simulations</th></tr></thead><tbody><tr><td>T<sub>inj</sub></td><td>Between 45 and 46 °C</td><td>45 °C</td><td>7 °C</td></tr><tr><td>ρ<sub>inj</sub></td><td>Between 1175 and 1190 kg m<sup>-3</sup></td><td>1172 kg m<sup>-3</sup></td><td>1000 kg m<sup>-3</sup></td></tr><tr><td>T<sub>vessel</sub></td><td>Between 15 and 20 °C</td><td>20 °C</td><td>212 °C</td></tr><tr><td>ρ<sub>vessel</sub></td><td>Between 996 and 998 kg m<sup>-3</sup></td><td>998 kg m<sup>-3</sup></td><td>850 kg m<sup>-3</sup></td></tr><tr><td>Δρ/ρ<sub>0</sub></td><td>0.158</td><td>0.149</td><td>0.150</td></tr></tbody></table>

## 3.2. Inlet condition

The CATHARE code is not able to simulate a mix of salt and pure water. For this reason, we have to work with equivalent fluids. We choose to work with hot water in the vessel and cold water in the safety injection.

We choose to keep similar injections conditions between the CATHARE simulation and the BORA4-PTS experiment, with the same densimetric Froude number. Our choices implies that we keep the same flow rate for the two injections, with the same Froude number. In other words, $Q_{vexp} = Q_{vsimu}$ and $Fr_{exp} = Fr_{simu}$. In the Froude number, our choices lead to an imposed length scale and injection velocity. The density ratio between the cold and the hot water will then have to correspond to the density ratio in the BORA4-PTS experiment. Our modeling choices lead us to work in condition that are similar to a reactor case. We choose a flow at 7 °C in the safety injection. Then to keep the same $\Delta\rho/\rho_0$ value, this force us to work with a vessel at 212 °C and at 25 Bar. The pressure was selected to prevent the flashing of water in the vessel. We summarize the conditions on Table 3, with the reminder of the BORA4-PTS conditions. We add an extra column. The density of the hot salt water are indeed different depending on the source. Either we consider the value from the experiment, varying from 1175 to 1190 kg m⁻³ or we consider the law from Company and United States. Office of Saline Water (1971) as a reference. We chose to compare the hot and cold water density ratio with the value from the Company and United States. Office of Saline Water (1971). As we can see on Table 3, this slightly change the density ratio. We will later see in Section 3.5 that we have a very coarse mesh to describe the BORA4-PTS experiment and especially the downcomer (21 cells for 1.5 m height, which gives approximately 8 cm per cell). This means that we are making a lot of approximation regarding the physical behavior of a liquid flow (see Préa et al. (2020) for a more precise description of the CATHARE 3 code). Therefore, the slight variations we observe on the density ratio are neglectable regarding the approximations made due to the mesh discretization.

With the selected condition, we have a difference of 0.6% between the Froude number of reference (obtained using the scaling law from Company and United States. Office of Saline Water (1971)) and the one from the CATHARE simulation. Now we need to establish the thermodynamic scaling between the numerical simulation and the experiment, in order to compare them correctly.

## 3.3. Thermodynamic scaling

The numerical simulation and the experiment do not operate at the same temperatures. For this reason, we will have to transform the temperature obtained from the CATHARE simulation. We start by determining the mix rate $\alpha$. To do that, we first consider that we work at constant pressure, either in the simulation or in the experiment. We also assume that there is no thermal loss on the wall on both case. We consider the state of injection as a referent state. Then, using internal energy, at constant pressure, we have:

$$U_{\text{mix}} = \int_{T_{\text{inj}}}^{T_{\text{mix}}} C_p(T) \rho(T) dT \qquad (11)$$

The energy mix is also equal to

$$U_{\text{mix}} = \alpha \int_{T_{\text{inj}}}^{T_{\text{init}}} C_p(T) \rho(T) dT \qquad (12)$$

Where the “inj” index refer to the injected liquid in the safety injection and the “init” index refer to the liquid that is present at the origin into the vessel. This equation is valid, either for the BORA4-PTS experiment or for the CATHARE simulation. Using Eqs. (11) and (12), we can express the mix $\alpha$:

$$\alpha = \frac{\int_{T_{\text{inj}}}^{T_{\text{mix}}} C_p(T) \rho(T) dT}{\int_{T_{\text{inj}}}^{T_{\text{init}}} C_p(T) \rho(T) dT} \qquad (13)$$

In our cathare simulation, we know the initial condition (temperature and pressure). From the EOS library, we can compute the density and the heat capacity. Since the pressure remains constant during the simulation (at 25 Bar), from the measured mix temperature, we can compute the mix heat capacity and the mix density. For the cathare simulation, we do the following assumptions:

$$\bullet \rho_{\text{num}}(T, P) = \rho_{\text{num}}(T)$$

$$\bullet C_{p\text{num}}(T, P) = C_{p\text{num}}(T)$$

The pressure variation has been neglect, since the original pressure (25 Bar) is high compare to the variation in the hydrostatic pressure (≈0.1 Bar because the BORA4-PTS vessel is ≈1 m high).

We now move on to the conditions of the BORA4-PTS experiment. According to the law available from Company and United States. Office of Saline Water (1971), for the BORA4-PTS experimental conditions (injection of saturated salted water at 45 °C in pure water at 15 °C), we assume that:

$$\bullet \rho_{\text{exp}}(T, c_{\text{sel}}) = \rho_{\text{exp}}(c_{\text{sel}})$$

$$\bullet C_{p\text{exp}}(T, c_{\text{sel}}) = C_{p\text{exp}}(c_{\text{sel}})$$

$$\bullet c_{\text{sel inj}} \approx c_{\text{sel sat}}$$

We also assume that the salt concentration of the mix has a linear evolution, which gives us:

$$c_{\text{selexp}} = \alpha c_{\text{selsat}} \qquad (14)$$

where $c_{\text{selsat}} = 0.25 \times 10^6$ ppm. The concentration of salt, express in ppm, means that, for 1000 kg of water, we have 250 kg of salt.

On Eq. (13), we can assume that $C_p(T)\rho(T)$ is constant, between 7 and 212 °C. We represent on Fig. 5(a) the variation of $C_p(T)\rho(T)$ as a function of the temperature, divided by the mean value of $C_p(T)\rho(T)$ between 7 and 212 °C. We can observe a variation between +2% and -3% around the mean value.

On Fig. 5(b), we plot the evolution of $C_p(T, c_{\text{sel}})\rho(T, c_{\text{sel}})$ for a salt concentration varying between 0 and $0.25 \times 10^6$ ppm at 15, 30 and 45 °C. As for Fig. 5(a), we have divided all the evolution by the mean value of $C_p(30 \,^\circ\text{C}, c_{\text{sel}})\rho(30 \,^\circ\text{C}, c_{\text{sel}})$. As we can see, all the value are close to the mean value, with a variation between +5% and -2%. We can then, again, make the assumption that $C_p(T, c_{\text{sel}})\rho(T, c_{\text{sel}})$ is constant.

We can then simplify Eqs. (12) and (13) to get:

$$U_{\text{mix}} = \rho_{\text{mix}} C_p \rho_{\text{mix}} T_{\text{mix}} \qquad (15)$$
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** (a) variation of $\rho(T)C_p(T)$ between 7 and 212 °C, divided by its mean value. (b) variation of $\rho(T, C_{sel})C_p(T, C_{sel})$ for a salt concentration between 0 and 0.25 × 10⁶ ppm at 15, 30 and 45 °C.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Table 4**
Fluid properties at the injection for the experiment and the simulation.</figcaption></figure>

<table><thead><tr><th>Parameter</th><th>BORA4-PTS</th><th>Simulation</th></tr></thead><tbody><tr><td>ρ<sub>inj</sub></td><td>1172 kg m<sup>-3</sup></td><td>1000 kg m<sup>-3</sup></td></tr><tr><td>μ<sub>inj</sub></td><td>1.12 × 10<sup>-3</sup> kg m<sup>-1</sup> s<sup>-1</sup></td><td>1.41 × 10<sup>-3</sup> kg m<sup>-1</sup> s<sup>-1</sup></td></tr><tr><td>ν<sub>inj</sub></td><td>0.956 × 10<sup>-6</sup> m<sup>2</sup> s<sup>-1</sup></td><td>1.41 × 10<sup>-6</sup> m<sup>2</sup> s<sup>-1</sup></td></tr></tbody></table>

$$U_{\text{mix}} = \alpha \rho_{\text{inj}} C_p T_{\text{inj}} + (1 - \alpha) \rho_{\text{init}} C_p T_{\text{init}} \quad (16)$$

$$\alpha = \frac{\rho_{\text{mix}} C_p T_{\text{mix}} - \rho_{\text{init}} C_p T_{\text{init}} T_{\text{init}}}{\rho_{\text{inj}} C_p T_{\text{inj}} - \rho_{\text{init}} C_p T_{\text{init}} T_{\text{init}}} \quad (17)$$

From the BORA4-PTS experiment, we know the temperature in the downcomer. Using Eqs. (15) and (16), we can express this temperature, as a function of the thermodynamic parameters $\rho$ and $C_p$ and of the mix parameter $\alpha$. We get:

$$T_{\text{exp}} = \frac{(1 - \alpha)\rho_{\text{init}} C_p T_{\text{init}} T_{\text{inj}} + \alpha \rho_{\text{inj}} C_p T_{\text{inj}} T_{\text{inj}}}{\rho_{\text{exp}} (c_{\text{sel}}) C_p \rho_{\text{exp}} (c_{\text{sel}})} \quad (18)$$

From our simulation, we measure the temperature in the downcomer and we use this information to compute $\alpha$, using Eq. (13). We then get the equivalent salt concentration in the BORA4-PTS experiment, using Eq. (14). Last, we use Eq. (18) to get the equivalent temperature in the BORA4-PTS experiment of our simulation. For $\rho_{\text{exp}}$ and $C_p_{\text{exp}}$, we use the law from Company and United States. Office of Saline Water (1971), that link the thermodynamic variables to the salt concentration.

We now have to build the time analogy between our simulation and the BORA4-PTS experiment.

### 3.4. Time scaling

We have preserved the densimetric Froude number between the numerical simulations and the experiment. However, we do not have the same mechanism that drives the mix in the vessel. For the BORA4-PTS, the mix of salt and pure water is characterized by the Schmidt number. This number compare the viscosity of a fluid with the diffusivity of a species in this fluid. The mix of hot and cold water is characterized by the Prandtl number. It compares the viscosity of a fluid with its thermal diffusion. These two numbers are defined as:

$$S_c = \frac{\mu_{\text{salt water}}}{\rho_{\text{salt water}} D_{\text{salt in water}}} \quad (19)$$

$$Pr = \frac{\mu_{\text{inj}} C_p T_{\text{inj}}}{\lambda_L} \quad (20)$$

where $\mu_{\text{salt water}}$ is the viscosity of the injected salt water, $D_{\text{salt in water}}$ is the diffusion coefficient of salt in water and $\lambda_L$ is the thermal diffusion in pure water.

For the experiment, we have $S_c \approx 650$. For the simulation, we have $Pr \approx 10$. Both of them are great compared to one. For the BORA4-PTS experiment, a Schmidt number above 1 means that the viscosity is the driving phenomenon for the propagation of the salt water in the experiment. For the simulation, a Prandtl number above 1 indicates that the viscosity drives the propagation of hot water in the vessel.

The parameters are summed up on Table 4. In this table, we can clearly see that the dynamic viscosities differs between the experiments and the simulations. They also differ in their kinematic viscosities. This means that the simulations and the experiments will not have the same characteristic time scale. We cannot use the time scale build earlier to compare the BORA4-PTS experiment and the reactor case (see Eq. (7)), due to the modeling choices we made (same size, same injection flow rate, same density ratio).

It is important to note that the kinematic viscosity are also different between the BORA4-PTS experiment and the reactor case, with the same order of magnitude than between the BORA4-PTS experiment and the CATHARE simulation. However, this difference has been neglected for the comparison between the experiment and a reactor case.

Since the main differences between the experiments and the simulations lies in the physical parameters of the fluid, namely the dynamic viscosity and the density, we use them to build a characteristic time scale. We introduce $\tau$ define as:

$$\tau = \frac{L_c^2 \rho_{\text{inj}}}{\mu_{\text{inj}}} = \frac{L_c^2}{\nu_{\text{inj}}} \quad (21)$$

To move from the simulation to the experiment, we have to change the time scale:

$$\frac{t_{\text{exp}}}{\tau_{\text{exp}}} = \frac{t_{\text{simu}}}{\tau_{\text{simu}}} \quad (22)$$

Which gives us the following link between the time in the experiment and the time in the simulation:

$$t_{\text{exp}} = t_{\text{simu}} \times \frac{\nu_{\text{simu}}}{\nu_{\text{exp}}} \approx 1.47 \times t_{\text{simu}} \quad (23)$$

### 3.5. Numerical setup

Now that we have selected the operating conditions, we describe the CATHARE simulation of the BORA4-PTS experiment.

In our simulations, the cold legs are modeled by axial elements. They are connected to the downcomer, represented by a 3D CATHARE element. Then, the bottom of the vessel is modeled by a 0D. The safety injections used in the experiment are modeled by piquages in the cold legs. At the origin of each cold leg, we impose a flow rate boundary condition. For the exit condition, instead of imposing a condition at the top of the core, we choose to impose it at the bottom of the vessel.
<figure><img src="image_10.png" /><figcaption>**Fig. 6.** View of the CATHARE simulation setup. The difference between the two pictures lies in the representation of the downcomer. On the left, there is 8 junction between the 3D representation of the downcomer and the lower plenum. On the right, there is 18 links between the lower plenum and the 3D downcomer. See Fig. 8 for the unrolled mesh of the downcomer.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Fig. 7.** View of the mesh for the downcomer. On the left, it has 8 azimuthal cells and is 21 cells height. On the right, it has 18 azimuthal cells and is 21 cells height.</figcaption></figure>

This condition is a pressure condition. At the bottom of the vessel, the pressure is imposed at 25 Bar plus the hydrostatic pressure coming from the downcomer height.

On Fig. 6, we show the 2 meshes we will use for our CATHARE simulations. In the simulations, we will only model the cold leg from the safety injection to the downcomer. We also will only model the downcomer and the bottom of the vessel, without the core (that is present in the experiment).

On Fig. 7, we display the meshes we use for the modeling of the downcomer. In general, the downcomer is represented by cathare 3D cylindrical elements, with only one cell in the radial direction. The LHS picture shows a mesh made of 8 azimuthal cells and 21 cells high. The RHS one shows a mesh with 18 azimuthal cells, and 21 cells high.

The heights of the cells are chosen so that each sensors will be on the center of a cell (regarding to their height).

The azimuthal size is chosen so that the cold legs end up in the middle of a cell. On the mesh with 8 azimuthal cells (Fig. 7, left), they all have the same azimuthal size (or represent the same angle on the cylinder), which correspond to one eighth (1/8th) of a cylinder. On the mesh with 18 azimuthal cells, the columns below the hot and cold leg represent 1/12th of a cylinder. The other columns are 1/24th of a cylinder, except for the one where we cut the downcomer in 2. For those, they represent 1/48th of a cylinder.

The downcomer has a reduction of his section on the top. We represent it by a porosity in the cells. In other words, all the cells have the same thickness and we use the porosity to represent the change

in the downcomer section. We also change, in accordance with the geometry, the hydraulic parameters for the top of the downcomer.

The downcomer of BORA4-PTS contains caps that represent the path of the hot legs. They are also modeled by changing the porosity and the other hydraulic parameters of the cells.

Last, there is a 2 sample carriers in the vessel. We also modeled them by changing the porosity and the other hydraulic parameters in the affected cells (hydraulic diameters, cross section, etc.).

On Fig. 8, we show the unrolled meshes we will use for the modeling of the downcomer. The top one corresponds to the 8 × 21 mesh. The bottom one corresponds to the 18 × 21 mesh. On those meshes, we indicate through a point the locations of the thermal sensors. We also mark them with the corresponding sensor in the experiment coming from the outside wall. When a sensor's name is an integer, it means that we will compare the result of CATHARE with one sensor from the experiment. When the name is the following form “xx_5”, it means that the center of the cell falls in between two sensors. We will then compare the result of cathare with two sensors, the sensor number “xx” and the sensor number “xx + 1”.

On Fig. 8, we also display the locations of the samples carriers into the downcomer. As we can see, in the 8 × 21 mesh, the samples carriers are wholly within a column.

This is no longer the case for the 18 × 21 mesh, where the sample carrier is, on one side, in the column below the cold leg 3, and on the other side in two columns, the one below the cold leg 4 and the one between the cold legs 4 and 1.
<figure><img src="image_12.png" /><figcaption>**Fig. 8.** Unrolled mesh of the downcomer. We show the mesh, and in each cells, we indicate the sensor we will refer to between the cathare simulation and the BORA4 experiment. A sensor number between two values (1.5 for example) means we will work with the previous and the next one (1 and 2 for our example). We also display the position of the samples carriers in the downcomer mesh. The picture on the top corresponds to the 8 × 21 mesh. The one on the bottom corresponds to the 18 × 21 mesh.</figcaption></figure>

# 4. Comparison between the simulations and the experiments

## 4.1. Validation of the method on one sensor

We run the CATHARE simulation, and we compare it with the experimental results. We first focus our attention to a single cell. We choose the cell 13 (see Fig. 8). This cell is located on the top of the downcomer, under the cold leg 2. We will compare the numerical results of this cell with the mean temperature of the sensor 13, on the outside wall of the downcomer, and the sensor 97, on the inside wall of the downcomer.

Fig. 9(a) shows the raw temperature with respect to time from CATHARE, for the two meshes (the fine one in green and the coarse one in orange). It evolves from 212 to 7 °C. For the two meshes, we observe oscillations in the evolution of the temperature. Those oscillations are not located at the same timestamps. However, they have the same intensity. We also show on this graph the temperature evolution within the BORA4-PTS facility. We plot in black the mean temperature between the sensor 13 and 97, for the 6 runs of the C2 experiment. In light blue, we draw the envelope of the experimental results between the minimal and the maximal value we measured for the sensors 13 and 97, and for the 6 runs of the experiment. For the BORA4-PTS experiment, the temperatures evolve between 20 and 45 °C.

We apply the method we described in Section 3.3. To apply this method, we need the initial temperature in the downcomer and in the safety injectors, in the experimental facility. The downcomer temperature is the mean temperature of all the sensors in the downcomer at the first timesteps of the experiment, on the 6 runs. The temperature at the injection is the mean temperature on the 4 injections, on the 6 runs. The results of the thermodynamic transformation is shown on Fig. 9(b). The CATHARE simulations now evolve between 22 and 45 °C. As we anticipated on Section 3.4, the CATHARE simulations are in advance compare to the experiment, the plots of the numerical results are indeed above the mean experimental temperature. This is in accordance with our assumptions on Section 3.4 where we established that the numerical simulation are approximately 1.47 times faster than the experiment (see Eq. (23)).

We then apply the time transformation we described in Section 3.4 regarding the time. The fully transformed results of our simulations are shown in Fig. 9(c). As for Fig. 9(a), the green and orange curves are respectively for the fine and the coarse downcomer 3D-mesh. In black, we have the mean experimental temperature, and in blue the min/max envelope. As we can see, there is a very good agreement between the experimental result and the one from the simulations. The two meshes give similar results, and no trend can be observe regarding the mesh convergency. The two CATHARE simulations are also within the experimental envelope practically all the time. This plot qualitatively validate our method, regarding the modeling of the BORA4-PTS experiments with CATHARE 3.

On Fig. 9(c) we can observe a mismatch between the experimental results and the numerical simulations, at the beginning of the transient. We do not have any explanation yet on this behavior, and this would be the scoop of a more detailed study since our interest in the present work was on the ability of CATHARE to reproduce the BORA4-PTS experiment globally.

To quantitatively observe the difference between the numerical simulation and the experiment, we plot, on Fig. 9(d) the difference between the numerical results, and the mean value of the 6 experimental runs of the test C2. We keep the same color code than on the previous plot (orange for the coarse mesh, green for the fine one and blue for the min/max experimental envelope). We also plot two others envelope to visually quantify the differences with the experimental mean. The dash line represent a ±1 °C difference with the experiment, and the dash-dotted line represent a ±2.5 °C difference.

As we can see, the simulation stays mostly within the 2.5 °C lines. At the beginning, for the first 60 s, CATHARE is colder than the experiments. After 230 s, the simulation is, in majority, within the 1 °C lines. A 1 °C difference between the experiment and the numerical simulation, on the BORA4-PTS temperature scale correspond to less than 10 °C of temperature difference between a reactor case and a CATHARE simulation.

Another important point to mention is that the simulation is, practically all the time within the experimental uncertainties. The temperature we get from CATHARE is indeed within the min/max experimental
<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 9. (a) Temperature evolution for the CATHARE simulations (orange and green) for the sensor at the position 13. We plot in black the mean temperature of the sensor 13 and 97 in the BORA4-PTS experiment, and in blue the min/max envelope of the experimental data. The temperature of the simulation evolve from 212 to 7 °C, while the BORA4-PTS temperature is between 20 and 45 °C. (b) Thermodynamic rescale of the numerical simulation. As expected, the simulation “heat up” faster than the experiment. (c) Full rescale of the numerical simulation. The liquid temperature follow the mean experimental temperature with a good agreement. The CATHARE simulation is also within the experimental envelope practically all the time. (d) Comparison of the liquid temperature between the numerical simulations and the mean experimental temperature. Both, the fine and the coarse mesh give good results that stay within a ±2.5 °C range.</figcaption></figure>

envelope, except at the beginning of the simulation. The small differ-
ence at the beginning of the simulation can be explain by the way
CATHARE model a flow, compare to the experiment. In BORA4-PTS,
we have a hot salty current that might be located only along a wall,
whereas in CATHARE we work with means flows. This is emphasize by
our modeling choice: our two downcommers meshes have only one cell
in their thickness.

Nevertheless, by having the CATHARE results within the experimen-
tal uncertainties (in the min/max experimental envelope, and in a ±
1 °C range), we can assume that our method and our simulation are
valid. We can now apply it to all the accessible sensors.

## 4.2. Confrontation between the complete experiment and the simulation

Now that we have validate our scaling method in one sensor, we
will apply it to all the sensors that can compare to a cell from the
numerical simulation. To compare all the data quantitatively, we build
a distribution of the temperature differences between the experiments
and the simulations. Roughly, this corresponds to a distribution of the
numerical error, regarding the mean experimental values. We take the
numerical data used to build the plot on Fig. 9-(d). We do that for all
the numerical cells containing sensors. From this dataset, we build a
normalized distribution, that will allow us to observe how far from the
mean experimental temperature our numerical simulation are, and how
they spread. Those distributions are plots on Fig. 10. We can call such
distributions “error”, since they show how far are the numerical (or
experimental) results to the mean experimental one.

On Fig. 10, the numerical normalized distributions are shown in
blue and orange for respectively the coarse and the fine mesh of

the downcomer. In black, we plot the normalized distribution of the
experimental data. For a given sensor, at a given timesteps, we take
the temperature of the 6 C2 experiments. We then take the difference
between those 6 values and their mean value. This third construction
is then, by construction, centered on 0, since we are comparing how
far the temperature distribution are compare to the mean experimental
value. This can be seen on Fig. 10.

The experimental distribution shows a large spread of datas. We ob-
serve here a standard deviation of 1.00 °C. This spread is in adequation
with the min/max envelope we could observe on Fig. 9. It is also in
adequation with the precision of the sensors that has been established
at ± 1 °C.

The coarse mesh gives results with a mean difference of 0.35 °C.
The distribution of the data has a smaller spread than the experimental
one (a standard deviation of 0.79 °C compare to 1 °C). The same
observations can be made for the fine mesh. The mean difference is
smaller (0.17 °C), but the spread of the data is bigger (0.88 °C).

For the whole experiment, the CATHARE simulations give results
that are in a very good agreement with the experimental ones, as we
can observe on Fig. 10. If we compare the numerical results, we can
observe that the two meshes give results that are very similar. The two
distributions look the same. Base on this observation, we can assume
that the results are numerically converge.

Regarding the shape of the numerical error, they present a high peak
around 0.3 °C. This “mean error” is within the range of validity of the
thermal sensors (the whole measure chain gives a results at ± 1 °C).
Furthermore, the numerical error present a smaller spread compare
to the experimental one, as we can see on Fig. 10. This confirm then
the capabilities of CATHARE to simulate with hot and cold water an
experiment made with pure and salt water.
<figure><img src="image_17.png" /><figcaption>Fig. 10. Normalized distribution of the temperature error for all the data point and all the timesteps. We take the data used to plot the graph on Fig. 9-(d), for all the available sensors. Those distributions are shown in blue and orange. In black, we plot the normalized distribution of the experimental temperature. For a given sensor, at a given timesteps, we take the temperature of the 6 C2 experiments. We then take the difference between those 6 values and their mean value. By construction, the experimental distribution is centered on 0. The two simulation have a mean difference of 0.35 °C for the coarse mesh and 0.17 °C for the fine one. The standard deviation of the experimental data is 1.00 °C, 0.79 °C for the coarse mesh and 0.88 °C for the fine one.</figcaption></figure>

## 5. Conclusions

In this article, we have presented a new experiment, BORA4-PTS, developed by the EDF R&D team. This experiments is used to analyze the propagation of water in the downcomer of a french 1300 MWe PWR reactor, during a pressurized thermal shock scenario. This experiment inject hot salted water (at 45 °C) in cold pure water (around 20 °C), instead of the injection of cold water at 7 °C in hot water at 295 °C. With this experiment, we also presented the scaling method used to move from the original reactor to the BORA4-PTS scale.

We then build a numerical simulation of the BORA4-PTS setup. We choose the CATHARE code. Since CATHARE is not able to simulate a mix of salt and pure water, we had to used only pure water. We then build a scaling method to be able to compare the numerical results we got from the CATHARE simulations with the BORA4-PTS results. This method give excellent results. The CATHARE simulations are in very good agreements with the BORA4-PTS experiment. The difference between the numerical results and the experimental one is below the uncertainties of the thermal sensors.

The next steps of the study will be the modeling of the HYBISCUS II experimental setup (Raynaud et al., 2013). We will build a numerical simulation with CATHARE and apply the scaling method we developed here. Since HYBISCUS II and BORA4-PTS are based on the same type of reactor, we expect to have good results too.

If the modeling of HYBISCUS II end up successfully, we will then move on to a scaling analysis, using the method developed by Ciechocki et al. (2022b,a), and that analyze the distortion coming from the different scale, between a reduce experimental setup and a full size reactor.

## CRediT authorship contribution statement

**Alexis Berny:** Writing – original draft, Validation, Software, Resources, Methodology, Investigation, Formal analysis, Data curation.
**Cécile Demathieu:** Writing – review & editing, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization.
**Joël Nibas:** Resources, Methodology, Investigation, Formal analysis,

Data curation, Conceptualization. **Alain Ungar:** Writing – review & editing, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization.

## Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Alexis Berny reports was provided by French Alternative Energies and Atomic Energy Commission. Cécile Demathieu, Joël Nibas, and Alain Ungar reports where provided by Electricité de France

## Data availability

The data that has been used is confidential.

## Acknowledgments

The authors want to thank L. Sargentini, A. Ghione and J-M Labit for fruitful discussions. This work has been done under the agreement CEA-EDF-FRAMATOME F35158.

## Appendix. Equations of states of salt water

In this section, we explain our method to get the equation of state of the salt water, between 15 and 50 °C.

From Company and United States. Office of Saline Water (1971), we numerise the plot regarding the physical parameter (the density ρ, the viscosity μ, the thermal capacity Cp) as a function of the temperature and of the salt concentration. We then use the software PlotDigitizer V2.1 to convert the plot into numerical value. Then, using the least square algorithm of gnuplot V4.4.3, we get the evolution of the physical parameter as a function of the temperature and the salt concentration.

The original datasets are given for a temperature between 0 and 200 °C, and for a salt concentration between 0 and 0.25.10⁶ ppm. We restricted the least-square algorithm to temperatures between 5 and 50 °C.

This gives the following equations of state:

$$ 
\begin{aligned}
\rho &=999.932 + 714.844c_{sel} - 9.96652 \times 10^{-2}T \\
&\quad + 273.633c_{sel}^2 - 3.43947 \times 10^{-3}T^2 \\
&\quad - 1.03359c_{sel}T
\end{aligned} 
\quad (24) 
$$

$$ 
\begin{aligned}
\mu &=1.77496 \times 10^{-3} + 1.61537 \times 10^{-3} c_{sel} - 5.53297 \times 10^{-5} T \\
&\quad + 1.16554 \times 10^{-2} c_{sel}^2 + 9.70441 \times 10^{-7} T^2 \\
&\quad - 5.63543 \times 10^{-5} c_{sel} T \\
&\quad + 1.46111 \times 10^{-2} c_{sel}^3 - 7.09377 \times 10^{-9} T^3 \\
&\quad - 2.18975 \times 10^{-4} c_{sel}^2 T + 8.03745 \times 10^{-7} c_{sel} T^2
\end{aligned} 
\quad (25) 
$$

$$ 
\begin{aligned}
C_p &=4184.61 - 5616.8c_{sel} - 0.30817T \\
&\quad + 9018.66c_{sel}^2 + 7.24171 \times 10^{-3}T^2 \\
&\quad + 13.6592c_{sel}T \\
&\quad - 5479.49c_{sel}^3 - 1.09587 \times 10^{-5}T^3 \\
&\quad - 13.2538c_{sel}^2T - 9.95106 \times 10^{-2}c_{sel}T^2
\end{aligned} 
\quad (26) 
$$

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