# Experimentation and simulation of ablated surface by jet impingement for core-catcher safety issue

Antoine Avrit, Nathalie Seiler, Alexandre Lecoanet, Asma Djermoune, Nicolas

Rimbert, Michel Gradeck

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## To cite this version:

Antoine Avrit, Nathalie Seiler, Alexandre Lecoanet, Asma Djermoune, Nicolas Rimbert, et al. Experimentation and simulation of ablated surface by jet impingement for core-catcher safety issue. ERMSAR 2024 - the 11th European Review Meeting on Severe Accident Research Conference, May 2024, Stockholm, Sweden. cea-05504173

HAL Id: cea-05504173

https://cea.hal.science/cea-05504173v1

Submitted on 10 Feb 2026

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# EXPERIMENTATION & SIMULATION OF SURFACE ABLATION BY A JET FOR CORE-CATCHER SAFETY ISSUE

Avrit A, Seiler N<fnref n="1" />, Lecoanet A and Djermoune A

CEA, DES, IRESNE, DTN, SMTA

F-13108 Saint-Paul-Lez-Durance, France

nathalie.seiler@cea.f, alexandre.lecoanet@cea.fr, asma.djermoune@cea.fr

Rimbert N, Gradeck M

Université de Lorraine, CNRS, LEMTA

F-54000, Nancy, France

nicolas.rimbert@univ-lorraine.fr, michel.gradeck@univ-lorraine.fr

## ABSTRACT

These coupled experimental and numerical studies support the safety demonstration of Sodium Fast Reactors SFR severe accident mitigation features. In order to limit potential power excursion in SFR core in the case of hypothetical severe accident, the implementation of the mitigation devices called transfer tubes was planned into the ASTRID core design. More specifically, they connect the core to the core-catcher and enable the early discharge of the corium towards the core-catcher. However, these devices, which effectively reduce the probability of reactivity excursions in the core, accentuate the issue of core-catcher resistance to corium inflow. Differing from past reactor core designs, the presence of these tubes could lead to coherent corium jets impinging on the core-catcher surface. In the past, numerous studies dedicated to thermal ablation of a solid by a jet have been carried out to characterize the maximum ablated depth. Although these experiments are very valuable at a macroscopic scale, they do not give information about the local physical phenomena governing heat transfer and melting. Keeping this final goal in mind, this study followed a R&D methodology based on an analytical situation using simulant materials enabling direct visualization. In this paper, the ablation of an ice block by an immersed water jet and a free surface jet are investigated in conditions shown to be close to the reactor case. Associated to the experimental part, CFD simulations of these tests are performed to validate the calculation methodology (mesh, turbulence models and interface melting...).

In this paper, the physical analysis of the heat transfer at jet impingement and in its vicinity is characterized for immersed jet conditions.

## KEYWORDS

RNR Na, core-catcher, jet ablation, experiment, simulation, CFD

## 1. INTRODUCTION

As part of the ongoing drive to improve nuclear reactor safety, innovative concepts are being proposed for 4th generation nuclear reactors. Among these nuclear reactor concepts, those with a fast neutron spectrum are not in their maximum reactive neutron configuration, and may experience further reactivity insertion. To cope with this situation, in the event of a hypothetical severe accident (i.e. in the case of a core meltdown configuration), innovative mitigation designs have been developed. During the ASTRID project (Advanced

<footnote n="1">¹ Corresponding author</footnote>
Sodium Technological Reactor for Industrial Demonstration), which was a liquid sodium-cooled fast reactor demonstrator, transfer tubes (or mitigation tubes - Figure 1) were installed inside the core to transfer molten fuel (and hence corium) outside the core to the lower plenum [1]. Corium accumulation and compaction in the core is thus prevented, but these devices entail other safety issues. Indeed, as can be seen from Figure 1, the mitigation tubes positioned in the core pass through diagrid with a small section restriction. In the case of a hypothetical severe accident, this new core design leads to the arrival of a coherent jet of very hot corium onto the core-catcher. This issue was not relevant for previous Sodium Fast Reactor (SFR) designs, for which the corium did not have a preferred path and all the more fragmented in contact with the sodium, leading to scattered debris bed as its arrival in the lower plenum was diverted.

This new design raises a new issue: the thermomechanical resistance of the core-catcher to the potential impact of this jet. To study this problem in the most penalizing case for safety, a coherent liquid steel jet is considered without fragmentation, which would be due to the boiling of sodium at its interface, and without the formation of a possible crust reducing thermal transfers.

<figure><img src="image_3.png" /><figcaption>Figure 1: Accidental scenario and corium discharge through mitigation tubes</figcaption></figure>

This issue was recently tackled in the framework of ESFR-SMART and ESFR-SIMPLE European projects [2][3]. Two prototypical experiments were conducted in KIT with the JIMEC facility [4][5] where a 1 ton metallic melt, produced by thermite reaction, impacted an instrumented cylindrical formed stainless steel block (thickness, 416 mm and diameter, 425 mm). In these tests, the metallic melt had the same composition as the metallic test substrate. Indeed, as explained by Lecoanet [6], this configuration, which does not lead to the formation of a thermally protective solid crust at the interface (like it would have been the case with oxide fuel impacting a metal core-catcher), results in maximum ablation of metal core-catcher.

Under these macroscopic conditions, it is difficult to investigate in detail the local phenomenology of the interaction of the hot jet with the metal, which results in its thermal ablation. That's why, as part of these European projects, it was also decided to carry out small-scale laboratory experiments with simulating materials, with proven representativeness. In this context, instrumented experiments involving the impact of a free surface water jet on a block of ice were carried out [7][8]. The ranges of the dimensionless numbers characteristic of this problem are given in Table 1. For comparison, these numbers are also given for a hypothetical case of a severe accident on an SFR such as ASTRID.

<table><caption>Table 1: Dimensionless numbers</caption><thead><tr><td></td><td>Experimental HAnSoLO set up</td><td>Severe Accident case</td></tr></thead><tbody><tr><td>Reynolds : Re<sub>j</sub></td><td>1.2 x 10<sup>4</sup> - 1.5 x 10<sup>5</sup></td><td>~ 10<sup>6</sup></td></tr><tr><td>Prandtl : Pr<sub>j</sub></td><td>2.5 - 5.5</td><td>~ 0.1 - 0.6</td></tr><tr><td>Melting : B</td><td>0.3 - 0.9</td><td>~ 0.25 - 0.95</td></tr></tbody></table>
This table shows that the Reynolds range of the hot fluid impacting, defined as $Re_j = \frac{D_j v_j}{v_j}$ where $v_j$ is the cinematic viscosity of the jet, $D_j$ its diameter and $v_j$ its velocity evaluated at the nozzle exit, is one order of magnitude less than in severe accident circumstances but the fluid flow remains turbulent in both cases (i.e. the transition to turbulence for a jet is considered to be $Re_j > 4 000$ [9]). Furthermore, the range of the melting number $B$ is well covered. This number stands for the ratio between the energy supplied by the jet to the energy required to bring the solid to its melting temperature and melt it:

$$B = \frac{c_{p,j} (T_j - T_m)}{L + c_{p,s} (T_m - T_{s,ini})}$$

where $j$ stands for jet, $s$ for solid, $m$ for melting and $ini$ for initial. $c_p$ and $L$ are the specific and latent heat respectively. Scaling is discussed in detail in [6]. But, Table 1 raises the point that, using water/ice to simulate corium on a metal core-catcher, the main representativeness issue is about the range of fluid Prandtl number $Pr_j$ which is more than unity for water and less for liquid metal/corium. This influences the thermal and dynamic boundary layer behaviors and will have some consequences on heat transfer between the jet and the solid. Li et al. [10][11] studied numerically the ablation by a free-surface jet with the reactor case material, using a particle method, showing an ablation dynamic quite different from what was observed for the water-ice case.

However, as the main advantage of water/ice experiments is that they allow visualization of the ablated interface evolution, this fluid was selected for tests aiming at better understanding the ablation phenomenology. The experimental water/ice set-up HANSoLO is widely described in [7] for free surface jet. Interpretation of the results enabled us to distinguish two flow regimes, and hence heat transfers: the film regime, occurring when only a liquid film flows to the bottom of the cavity created by ablation, and the pool regime when this cavity is filled with water. Based on previous results [12-15], the phenomenology characteristic of both the regime change at jet impact (where heat transfer is maximal) and heat exchange along the wall (which determines the shape of the cavity) has been physically explained and correlated [4] [6-8]

As it is not possible to guarantee the representativeness of these heat exchanges for $Pr_j < 1$, a numerical approach was pursued. On the strength of the predictivity of CFD simulation tools whatever the Prandtl number, the validation of a CFD solver on a water/ice case is performed before using this solver for steel liquid jet on a metal core-catcher. To follow this methodology and to ensure the validity of the calculation results, the simulated configuration is of increasing complexity. Due to the very high complexity of simulating a turbulent jet impacting with ablation of the wall and its free surface with the surrounding air, the study began with an immersed jet. Furthermore, regarding safety issue, the case of an immersed jet is another limiting case, when liquid corium is already on the core-catcher or when the pool-effect is reached. To validate these initial simulations, the experimental set-up HANSoLO has been adapted to immersed jets by [16] (Figure 2) in order to obtain an experimental database for validation. 20 immersed jet tests with a diameter of 6 mm and an initial jet/ice height of 10 mm were carried out with initial temperatures and speeds of: $V_j \in \{1.1, 2.5, 5.0, 7.5, 10.\}$ m/s & $T_j \in \{30, 50, 70\}$ °C

This experimental work led to local investigation (Figure 3), particularly at the stagnation point. We estimated the melt velocity, which led to the first establishment of a macroscopic heat transfer correlation at immersed jet impact in a form based on a literature review [16]. A macroscopic heat transfer correlation was proposed, where $Nu$ is the Nusselt number:

$$Nu_0 = Nu(r = 0) = Nu_0 = 0.054 \exp(-0.0775 \frac{y_0}{D_j}) Re_j^{0.65} Pr_j^{0.73} \frac{\ln(1+B)}{B} \quad (1)$$

with $y_0(t)$ the depth of the cavity at the stagnation point.

Heat transfer and ablation velocity (local velocity of the cavity surface) were characterized at the stagnation point by picture analysis (i.e. during cavity formation).
Moreover, the results of these experimental tests enabled to carry out local analysis of the ablation dynamics, investigating why the shape of the obtained cavity features a shoulder.

An empirical law giving the evolution of depth as a function of time has been derived from the previous law on $Nu_0$:

$$ \frac{y_0(t)}{D_j} = \frac{1}{0.0775} \ln \left( \frac{4.18 \times 10^{-3} B \lambda_j Re_j^{0.65} Pr_j^{0.73} \ln (1+B)}{\rho_s D_j^2 c_{p,j}} t + 1 \right) \quad (2) $$

<figure><img src="image_4.png" /><figcaption>Figure 2: (a) HAnSoLO set up for immersed jets and (b) high speed camera visualization at the initial time [16]</figcaption></figure>

Finally, in this paper, we present the preliminary validation of the CFD code OpenFOAM® on the simulated ablation obtained in two experimental tests ($Re_j = 11.6 \times 10^3$ and $Re_j = 26.10^3$). Validation of the simulation methodology for a non-melting case is first presented, taking jet turbulence into account, followed by a discussion on the ablation results at jet impact.

## 2. PRELIMINARY RESULTS : IMMERSED JET WITHOUT MELTING

In the solver OpenFOAM® "buoyantPimpleFoam" [17], which is devoted to non-isothermal turbulent flow undergoing buoyancy, the LES approach has been selected to simulate ablation by an immersed jet. With reasonable calculation costs, it enables better resolution of near-wall turbulence and heat transfer. The LES approach also makes it possible to simulate fluctuating and unsteady flow. First, a study of the problem without melting is carried out with validation on literature results in order to ensure the validity of the methodology (turbulence resolution according to the initial jet turbulence model, which influences melting, mesh size and boundary conditions...).

The parameters for the considered case are a $Re_j = 11.6 \times 10^3$ (i.e. $V_j = 1.1m.s^{-1}$) and $Pr = 3.55$ (i.e. $T_j = 50°C$), corresponding to experiment with the lowest $Re_j$ value in order to reduce the simulation time. At this Reynolds level, the flow is fully turbulent at the jet exit.

### 2.1 Initial jet turbulence

To generate a realistic fluctuating velocity field at the jet output, without performing a preliminary DNS for the establishment of flow in the tube, two methods are considered: Divergence-Free Synthetic Eddy Method (DFSEM) and Forward-Stepwise Method (FSM).

The Divergence-Free Synthetic Eddy Method [18] consists in generating velocity fluctuations, or eddies/turbulent structures, and superimpose them on the mean velocity on the inlet of the tube. This method considers as input parameter the mean velocity field, the Reynolds tensor and the local turbulent
characteristic scale (which is derived from the turbulent kinetic energy and the turbulent energy dissipation rate) on the inlet surface.

The concept of Forward-Stepwise Method [19] is to use a filter to obtain a velocity field from random signals with the desired turbulence statistics. Like the DFSEM, the FSM takes as input turbulent statistics, namely the mean velocity profile and the components of the Reynolds tensor. These data could be obtained from a RANS simulation of the jet established in the tube. RANS simulation of a velocity flow, similar to that imposed experimentally, is carried out in a 6mm tube, $40D_j$ long, with a no-slip wall condition to ensure fully developed turbulent flow [9].

<figure><img src="image_5.png" /><figcaption>**Figure 3 : Evolution of cavity shape from high-speed camera visualization ($V_j = 5 \text{ m s}^{-1} - Re_j \sim 5.3 \times 10^4$ and $T_j = 323 \text{ K} - Pr_j = 3.55$) [16]**</figcaption></figure>

Sensitivity studies on radial mesh refinement and the size of the first mesh cell at the wall as well as the turbulence model considered for the RANS calculation were carried out. The RANS calculation (models standard k-ε [20], realizable k-ε [21] and k-ε RNG [22] and their associated wall law) have been carried out with sensitivity studies to radial mesh refinement and the size of the first wall mesh and turbulence model. These results have been compared with DNS studies giving fluctuating radial velocity profiles at the nozzle outlet [23]. The influence of the turbulence model was less than that of the mesh, and a mesh such as $y^+ = 6.1$ ($y^+$ is the dimensionless size of the first mesh cell at the wall) provided initial data for the DFSEM and FSM. For the FSM, whose characteristic length is more complex to determine than that used in the DFSEM, a study concluded that the simulation considering an anisotropic reference length with $L_{u,x} = L_{u,y} = 10^{-3} \text{m}$ and $L_{u,z} = 10^{-4} \text{m}$ led to a Reynolds stresses tensor very close to the desired
tensor. This suggests that velocity fluctuations are correlated more with each other in the x-y plane than
along the z axis.

Based on this data at the nozzle outlet, a simulation of a jet impinging a plate but without melting was carried
out to validate the heat transfers.

## 2.2 Validation of heat transfer at jet impingement on a solid wall

A turbulent velocity field is imposed at the inlet of the domain either by the DFSEM or FSM method. The
mesh used is three-dimensional (and not 2D axisymmetric, to catch 3D phenomena).

A half-cylinder is used for the domain to halve the calculation cost. The domain and boundary conditions considered for the impinging immersed jet are shown in Figure 4. The axis of the jet is placed at r = 0 and its height is 10 $D_j$.

<figure><img src="image_6.png" /><figcaption>Figure 4: Domain and boundary conditions for immersed jet</figcaption></figure>

In order to simply model fluid entrainment around the nozzle with negligible influence on jet dynamics,
Aillaud et al. [24] suggest the use of a fixed velocity condition $u_z = 0.05V_j$. The pressure is fixed at the
atmospheric pressure at the outlet surface, located far enough from the jet to reduced boundary influence. A
constant heat flow condition is imposed on the bottom surface to derived Nusselt number. Simulations are
performed using a LES (large Eddy Simulation) approach, with the WALE (Wall Adapting Local Eddy
viscosity) model for turbulence [25]. This approach, which leads to a more realistic prediction of near-wall
turbulent quantities, imposes mesh constraints. The characteristic cut-off length of the filter used in the LES
approach corresponds to the mesh size, which must correspond to the turbulent Taylor scale length so that
dissipative scales are filtered, and inertial scales are resolved. Estimates of turbulent scales have led to the
definition of a progressive axial mesh of $N_z = 340$ cells and a wall cell size such that $z_1^+ = 0.001D_j$
($z_1^+$ being the dimensionless cell size, in the z direction). Sensitivity to mesh refinement confirmed these
estimates, and results consistent with those of Lee and Lee [26], who obtained Nusselt profiles as a function
of radial distance from the stagnation point for values of $Re_j$ between $1.0 \times 10^4$ and $3.0 \times 10^4$, were obtained
for $N_z \ge 500$ cells and $z_1^+ \le 0.002D_j$. The mesh used for the simulations contains up to around $5 \times 10^6$ cells;
a simulation requires around $10^5$s using 192 processors.

Sensitivity to the methods of establishing turbulent fluctuations at the jet outlet has been carried out.
In order to characterize these fluctuations, the maximum of $mag(R_{ij})$ defined as
$mag(R_{ij}) = \sqrt{\sum_{i,j} R_{ij}^2}$ (magnitude of the Reynolds stresses tensor) is closer to the Lee & Lee experiments
in the FSM simulation than in the DFSEM simulation (Figure 5). Mixing-induced turbulence reaches the
center of the jet at a shorter distance from the nozzle outlet in the FSM simulation (Figure 6 left). The literature review [27] indicates that the mixing-induced turbulence should reach the center of the jet at a distance from the nozzle of ~5D~j ~−~6D~j. The behavior observed for the DFSEM method is therefore consistent unlike the FSM method.

<figure><img src="image_7.png" /><figcaption>Figure 5: Mag(Rij) obtained by FSM (left) and DFSEM (right) methods (related legend on the right)</figcaption></figure>

Since the maximum fluctuations occur further from the wall in the FSM simulation, there is a decrease in transfer to the wall compared with the DFSEM simulation. This is confirmed by the evolution of the Nusselt numbers along the heated wall (obtained in our simulation for Re_j = 11.6 × 10^3) with the results of Lee and Lee (obtained at Re_j = 1.0 – 1.5 × 10^4) (Figure 6- right). The results presented in Figure 6 also show that results obtained without considering turbulent fluctuations (labelled “uniform”) at the jet outlet lead to underestimate the potential core length and the heat flux extracted at the wall. Predictive simulation of the turbulence that develops in the jet, due to its stagnant fluid environment, is essential, but is not sufficient to correctly simulate wall heat transfer; the turbulence of the flow at the jet outlet must be simulated. It is demonstrated that the use of a uniform velocity field at the nozzle outlet produces results far from those found in the literature.

<figure><img src="image_8.png" /><figcaption>Figure 6: <u>u</u>_z at the jet center along the height (left), <u>Nu</u>_0 along the solid plate (right)</figcaption></figure>

3. NUMERICAL RESULTS FOR IMMERSED JET ABLATION

The simulation parameters obtained in the previous preliminary study for the case without melting are applied to simulations with ablation. It requires much more numerical resources. The DFSEM method has been selected and the results are compared with the experimental results obtained on HAnSoLO.

3.1 Liquid/solid interface simulation method: enthalpy - porosity

To simulate the liquid/solid interface motion induced by thermal ablation, the enthalpy-porosity approach proposed by Voller and Prakash [28] is used. This method was developed to simulate the melting or
solidification of a non-pure material (typically an alloy) using a fixed mesh. It consists in describing the liquid-solid system with a presence volume fraction $g_l$ such that $g_l=1$ in the liquid and $g_l=0$ in the solid. The principle is similar to the VOF method with the $g_l$ fraction controlled by temperature. In this method, considering a single fluid with two phases characterized by the function $g_l$, the balance equations for momentum and enthalpy are solved with additional source terms, to consider the energy associated with the phase change for the enthalpy equation, and friction in a porous medium (according to Darcy's law) for the momentum equation. This term in the momentum equation is such that $S_m = -A \nu$ with $\nu$ the velocity and A a coefficient, which derives from the Carman-Kozeny equation, and can be written in the following form:

$$A = C_{\text{voller}} \frac{1-g_l^2}{g_l^3+\epsilon} \qquad (3)$$

With $C_{\text{voller}}$ representing the porous terms magnitude, which cancels out the velocity in the solid, and $\epsilon$ a numerical residue to avoid division by zero.

This method, adapted by Brent et al. [29] for a pure material in OpenFOAM, is used for these simulations. It is worth noting that this method does not consider the density jump at the liquid/solid interface. In a recent work, Faden et al. [30] obtained a formulation with the density jump, but this formulation is not yet available in OpenFOAM.

## 3.2 Simulation domain

The simulation domain is close to that the one considered for simulations without ablation, with an additional finely meshed solid domain (with respect to the turbulent scale of the fluid) to be sufficiently resolved when fluid enters this domain (Figure 7). As in the experiments described by Avrit et al. [16] (with evaluation of associated uncertainties), the initial temperature of the stagnant fluid is 277.15K ($T_{\text{melting}} + 4K$) and a linear temperature profile along z is initially applied to the ice between 271K and 273.15K.

<figure><img src="image_9.png" /><figcaption>Figure 7: Simulation domain (left), sensitivity to $C_{\text{voller}}$ (right)</figcaption></figure>

Voller and Prakash recommend $C_{\text{voller}} = 1600$ to simulate the solidification of an alloy presenting a mushy zone between its liquidus and solidus temperature. As water is a pure material, three different $C_{\text{voller}}$ values were tested: $10^3$; $10^6$, $10^{10}$. The ablated depth is extracted from the $g_l$ field, assuming that the solid-liquid boundary is at $g_l=0.5$. Figure 7 (right) shows the curves of the evolution of $y_0/D_j$, where $y_0$ is the localization of the interface solid/liquid at the stagnation point for the different $C_{\text{voller}}$ values considered. The curve at $C_{\text{voller}} = 1000$ is extremely distant from the rest of the results which are converged. The correlation on $y_0/D_j$ (eq. (2)), issued from the experimental work, is also plotted in Figure 7, and is the reference curve for low ablated depths, since the first experimental points are only obtained for $t > 2s$. The simulation results obtained for $C_{\text{voller}} > 10^6$ are consistent with the correlation. Based on these results, $C_{\text{voller}} = 10^{10}$ is used in the following simulations.
## 3.3 Results and Comparisons

Two experimental tests were simulated. For the first, the conditions remain unchanged: $Re_j = 11.6 \times 10^3$ (i.e. $V_j = 1.1 \text{m.s}^{-1}$) and $Pr_j = 3.55$ (i.e. $T_j = 50^{\circ}\text{C}$). For the second, the Reynolds number and thus the jet velocity is increased ($e_j = 26.0 \times 10^3$; $V_j = 2.5 \text{m.s}^{-1}$). For this second case, the turbulent lengths were recalculated to build the mesh accordingly.

$$ \textit{First case: } Re_j = 11.6 \times 10^3 $$

The instantaneous temperature field $T$ at different time are shown in Figure 8, to provide visualizations of the jet and ablation obtained by numerical simulation.

<figure><img src="image_10.png" /><figcaption>**Figure 8:** Temperature evolution in the simulation of the experimental test $Re_j = 11.6 \times 10^3$</figcaption></figure>

The instantaneous temperature field enables instantaneous visualization of the jet, and observation of both mixing with the ambient fluid and the resulting temperature reduction as it moves away from the nozzle outlet. The solid-liquid boundary is well defined by the rapid temperature change in this region, particularly along the jet axis. The potential core can also be seen in Figure 8: the temperature remains constant at the center of the jet over a length consistent with literature (~5-6$D_j$) before mixing-induced turbulence reaches the center of the jet.

<figure><img src="image_11.png" /><figcaption>**Figure 9:** Ablation depth at the stagnation point (zoom at low instant on the right) $Re_j = 11.6 \times 10^3$</figcaption></figure>

The depth at the stagnation point is the most important data for the study of jet ablation, since it corresponds to the maximum ablation depth. Figure 9 shows the evolution of the cavity depth at the stagnation point and
compares the results of simulations (with DFSEM or FSM) with the experimental results and the correlation (eq. (2)), established from these results but allowing their domain to be extended to very low time (t < 6 s). As already observed, heat transfers are largely underestimated at the stagnation point using the FSM method. These calculations were not continued. In the case of simulation with the DFSEM method, we observe very good agreement of the ablation curve with the experimental points, and the correlation curve, even over the long term.

A good agreement is observed between the cavity shape obtained numerically and the experimental shape (Figure 10) at two different times. The same change in slope is observed around $\frac{r}{D_j} = 2.5$, which can be investigated by observing simulated local flows.

<figure><img src="image_12.png" /><figcaption>Figure 10: No dimensional localization of solid/liquid interface –Cavity profile -Re<sub>j</sub> = 11.6 × 10<sup>3</sup></figcaption></figure>

Second case: Re<sub>j</sub> = 26.0 × 10<sup>3</sup>

Because of the long computation time required for these high-Reynolds simulations (~ 10<sup>6</sup> CPU hours), only 3s of transient were simulated.

The instantaneous temperature field and the cavity profile at 2.5 s are shown in Figure 11 to visualize the jet and ablation obtained by numerical simulation.

<figure><img src="image_13.png" /><figcaption>Figure 11: Instantaneous temperature fields (left) and cavity profile (right) at t=2.5s Re<sub>j</sub> = 26.0 × 10<sup>3</sup></figcaption></figure>

Once again, we can observe the jet and cavity formation, as well as the potential core region for which the temperature does not decrease at the center of the jet. Jet mixing is more intense than in the previous case at lower Reynolds. There is an acceptable agreement between the two cavity shapes shown. As the cavity shape detection algorithm (for the experimental shape) is less accurate at low ablated depths, only a low
number of points and a low radial extension are available for the experimental contour. However, there is
still a cavity shape with an inflection point.

The ablation curve obtained by simulation, superimposed on the experimental points and the correlation (eq. (2)), is shown in the Figure 12 for the first instants. Once again, the curve obtained by simulation agrees very well with the results obtained from experiments.

**4. CONCLUSIONS AND PERSPECTIVES**

This experimental and numerical work are part of the design of mitigation devices defined in case of the
hypothetical severe accidents in sodium fast reactor of ASTRID style. Indeed, the final aim of this work is
to improve the safety of sodium-cooled fast reactors (RNR-Na). New devices are being studied for
introduction into the core to mitigate potential reactivity insertions in the event of severe accidents with core
meltdown.

<figure><img src="image_14.png" /><figcaption>Figure 12 : Ablation depth at the stagnation point - Re<sub>j</sub> = 26.0 × 10<sup>3</sup></figcaption></figure>

One of these devices uses transfer tubes to discharge corium (molten core and structural materials) directly onto the core-catcher, raising a new safety issue: the core-catcher's resistance to thermomechanical due to the ablation consecutive to the impact of a corium jet at ~2,000-3,000 K. In order to size this core-catcher accordingly, experiments were carried out with simulating materials (water/ice) under representative conditions on the HAnSoLO (Hot AblatioN of a Solid by a Liquid - Observations) facility. The new results have enabled to model ablation phenomenology on a local scale and derived a correlation of the evolution of the cavity depth at the stagnation point. Numerical simulations on a local scale (CFD) completed this study to take into account the representativeness bias due to the low Prandtl of the corium in relation to those of water. As part of a progressive approach, immersed jet experiments were carried out and simulated using OpenFOAM® code. A LES (Large Eddy Simulation) approach with the WALE (Wall Adapting Local Eddy viscosity) model was used to simulate turbulent jets. Studies were carried out to select the mesh consistent with the assumptions of this approach. The method DFSEM (Divergence-Free Synthetic Eddy Method) demonstrated its ability to deliver turbulent fluctuations at the nozzle outlet. Simulations of immersed jets impinging a solid without melting have been validated on experimental results. Based on these results, the ablation of the impacted wall was simulated using the enthalpy-porosity method. Simulation results are close to those observed experimentally for the two values of Re<sub>j</sub> considered (Re<sub>j</sub> = 11.6 × 10<sup>3</sup> and Re<sub>j</sub> = 26.0 × 10<sup>3</sup>). The OpenFOAM® code has therefore been validated for the case of immersed jet ablation.

Subsequently, in order to extend this validation to the case of a liquid water jet in air, an interface tracking
method will be selected to simulate the water/air interface. Free surface jet test simulations will be validated
on free surface jet experimental results obtained using HANSoLO in a similar way to the work already carried out for immersed jet. Once these free surface jet simulations will have been validated, simulations of steel jets impinging a steel structure will be carried out at low jet Prandtl numbers. The enthalpy-porosity method will have to be revised to simulate the melting of this non-pure material.

## ACKNOWLEDGMENTS

The ESFR-SIMPLE project is funded by the European Union under Grant Agreement 101059543. Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union. The European Union can't be held responsible for them.

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