COOLABILITY OF A CORIUM POOL IN A DEBRIS
BED-CALCULATION OF CRITICAL HEAT FLUX
(CHF) TESTS WITH THE ASTEC CODE

J.-A. Zambaux, C. Sartoris

► To cite this version:

J.-A. Zambaux, C. Sartoris. COOLABILITY OF A CORIUM POOL IN A DEBRIS BED-CALCULATION OF CRITICAL HEAT FLUX (CHF) TESTS WITH THE ASTEC CODE. ERMSAR 2024 - 11th European Review Meeting on Severe Accident Research Conference, May 2024, Stockholm, Sweden. 10.5445/IR/1000174165. [hal-04969014](https://hal.science/hal-04969014v1)

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# COOLABILITY OF A CORIUM POOL IN A DEBRIS BED –
CALCULATION OF CRITICAL HEAT FLUX (CHF) TESTS WITH THE
ASTEC CODE

Zambaux J-A. and Sartoris C.

Institut de Radioprotection et de Sureté Nucléaire

Cadarache, 13115, BP3, Saint Paul lez Durance

julie-anne.zambaux@irsn.fr; christine.sartoris@irsn.fr

## ABSTRACT

In case of severe accident in a light water reactor, a debris bed may form in the core and possibly melt, as it happened in TMI-2. Knowledge about the coolability of such molten pool surrounded by debris is crucial to investigate the possibility of stabilizing a part of the fuel inside the vessel. Based on experimental tests conducted at IRSN investigating the effect of debris size, steam and liquid flowrate, inclination and pressure, some numerical simulations have been conducted with the severe accident system code ASTEC. Some global conclusions could be drawn: the surface temperature evolution is well reproduced and the pool boiling CHF value is correctly calculated except in presence of debris. Pressure and liquid flowrate are satisfactorily evaluated but differences are shown as concerns the debris diameter impact, the inclination impact and the gas flowrate impact. The observed discrepancies are analyzed here and prospects for improvements of CHF and void fraction modelling are provided.

## KEYWORDS

Severe accident, Corium coolability, Critical Heat Flux, ASTEC code

## 1. INTRODUCTION

In case of a severe accident in a nuclear reactor, a large debris bed may be created in the core. If, in some part of this debris bed, the temperature keeps on rising up to the melting point, it may form a molten pool of corium, as it happened in TMI-2 [1]). The molten pool is expected to become less and less coolable as it grows larger because the heat flux at the periphery of the pool increases linearly with the pool diameter. Therefore, it is of primary interest to determine the maximum size of a molten pool surrounded by debris which may be stabilized under water after reflooding the vessel (as in TMI-2) or in case of a debris bed formed in a flooded reactor pit where the presence of denser zones may limit the coolability ([2], [3]). The maximum heat flux that may be extracted, or Critical Heat Flux (CHF), is a key parameter for that issue. Severe accident codes are a needed tool for safety analysis and should be able to correctly assess this degraded core cooling capability in case of reflooding scenarios. The ASTEC v3.1.1 code is a severe accident system code developed by IRSN [4], used for safety analysis and source term evaluation studies. ASTEC is organized in different coupled independent modules, each for a different type of physics, therefore allowing dedicated studies and validation (see [5] for the main validation elements). In the frame of this paper, the ASTEC code has been used for CHF evaluation validation. Only the system thermal-hydraulic module CESAR (based on 1D two-fluid model approach [6]) and the core degradation module ICARE (evaluating the heat transfer and mechanical state of the core) were activated.

In most of studies for thermal-hydraulic system codes, CHF evaluation experiments have been performed in small diameters and high length vertical tube geometries in order to represent the fuel assembly
configuration. Among the different experimental data available, the Groeneveld look-up table [7] is widely
used in thermal-hydraulic system codes, for example in the CATHARE code [8] or the TRACE and the
RELAP 5 codes [9]. Severe accident system codes follow the same approach. However, core configuration
can be strongly modified during the degradation process, as stated in [10]. The use of CHF correlation
established for intact core geometries is often extended for partially degraded core geometries, as it is the
case in the ASTEC code. The global evolution for degraded core reflooding can be reasonably reproduced
(see [11] for an assessment of the ASTEC code ability to calculate the TMI-2 accident for example).
Nevertheless, these global validation studies involve important uncertainties and potential compensating
effects. Therefore, specific validation of each phenomenon such as the boiling crisis is still needed to
improve code reliability.

Experiments such as PEARL and PRELUDE [12] have given important insight about the reflooding process
in a heated debris bed. They have given validation elements for the porous media approach in ASTEC [13].
More recently, other experiments were performed, in order to evaluate the CHF in a geometry representative
of a degraded core [14,15]. These experiments have explored the influence of several geometrical and flow
parameters on the CHF. They provide an important addition to the very limited available data for CHF
evaluation in those porous media geometries.

The current paper aims at assessing the validation status of the current version of the ASTEC v3.1.1 code
using these new CHF evaluation experiments [14,15]. A brief reminder of the experimental facility and
performed tests for CHF evaluation in degraded core configuration is first given. Then the ASTEC code
modelling proposed, and results analysis is presented. As in the experimental work, different simulations
have been performed, varying different parameters that are expected to influence the CHF in porous media
configuration. The influence of each parameter is specifically studied in the last section of the paper.

## 2. EXPERIMENTAL DEVICE

The CHF tests are performed in a test section (see Figure 1, left) mainly composed of a tank filled with steel balls and deionized water at saturation temperature. A 50 mm diameter copper cylinder is positioned, one of its ends abutting this debris bed and its other end heated by electrical cartridges. The test section is possibly equipped with another electrically heated copper block used as a steam generator and can be connected to a deionized water loop to inject liquid water at the debris bed bottom. A connection is also possible to a water tank situated above the test section to achieve higher pressure in the test section thanks to the water column weight (connections not shown here). All the external surfaces are thermally insulated.

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Test Section (left) and Implantation of the Thermocouples inside the Heated Cylinder (right).</figcaption></figure>
The thermal heat flux is calculated by Fourier's law thanks to measurements of thermocouples inserted in the heated copper cylinder (see Figure 1, right). The copper cylinder is slowly heated until the CHF achievement signaled by a dramatic increase of the cylinder temperature. Then the power is shut down. Detailed descriptions of devices, instrumentation, uncertainties calculations, heated plate surface preparation and detailed heating procedure are given in [14] and [15].

The following parameters impacts are experimentally investigated and compared to numerical simulations in the next paragraphs:

- Ball size of 2, 3 and 4 mm,

- Different inclinable test sections are used to study inclinations from 0° (horizontal plate) up to 150° (nearly downward facing plate) to simulate different local zones of a corium mass,

- Pressure from atmospheric pressure up to 2.5 absolute bar.

# 3. CALCULATIONS PRESENTATION

## 3.1. ASTEC v3.1.1 Modelling

The ASTEC code can be used in 2D for axi-symmetrical domains. In the 2D modelling, internal reactor structures can be considered and impact the flow and the heat transfer. These structures can be used to represent an intact core but also a degraded core with highly viscous liquid magma or debris. Debris are considered as spherical monodisperse and are assimilated to a porous media. This approach in the ASTEC code has been validated for flow in a porous media with the results of the PEARL experiments [11].

The heat transfer between core elements and the fluid phase is evaluated depending on local flow conditions in the considered mesh. The heat transfer is distributed into three contributions, one to the liquid phase, one to the gas phase and one to the interface, directly used for the mass transfer (by vaporization/condensation). This last contribution depends mainly on the water subcooling. At saturation conditions, all the heat flux is directed to the interface.

Depending on the value of the void fraction in the considered mesh, the heat transfer happens preferentially with the liquid phase or with the gas phase (the dry-out condition is set in the code for a void fraction above 0.999). In the case of a heated wall or object in presence of liquid, the heat transfer regime depends on the wall temperature:

- If the wall temperature is below the fluid saturation temperature: this is the liquid convection regime, the wall exchanges energy with the liquid phase.

- When wall temperature becomes higher than saturation conditions: this is the boiling regime. Nucleate boiling is first observed. Depending on the water subcooling, most of the heat flux is directly used for mass change in this regime. It is assumed that the regime remains nucleate boiling as long as the calculated heat transfer due to nucleate boiling remains below the calculated CHF value and the void fraction does not exceed 0.999.

- When nucleate boiling is left, a transition regime is assumed during which the heat flux remains at the CHF value. As in the nucleate boiling regime, this heat flux is distributed between the interface and the liquid phase. Film boiling regime is entered when the wall temperature reaches minimum temperature for a stable film condition.

In ASTEC v3.1.1, the CHF is assessed by the code with the Zuber correlation for pool flow [16], using the correcting coefficient proposed by Lienhard and Dhir [17] with additional correction factors. The complete expression is given by:

$$ \phi_{CHF} = F_l C_{sub} 0.149 \left( \frac{g\gamma(\rho_L - \rho_G)}{\rho_G^2} \right)^{\frac{1}{4}} \rho_G h_{LG} \quad (1) $$
$$ \text{with } C_{sub} = 1 + 0.1 \frac{1}{h_{LG}} C p_L (T_{sat} - T_L) \left(\frac{\rho_L}{\rho_G}\right)^{\frac{3}{4}} (2) \text{ and } F_l = \begin{cases} 1.259 & \text{if } L_c < 4 \text{ mm} \\ \left(\frac{8}{L_c(\text{mm})}\right)^{\frac{1}{3}} & \text{if } L_c < 16 \text{ mm} \\ 0.79 & \text{otherwise} \end{cases} \quad (3) $$

In this expression (1), $h_{LG}$ is the latent heat needed to vaporize water, $\rho_L$ and $\rho_G$ are respectively the steam and the liquid water density, $\gamma$ is the surface tension and $g$ is the gravity. The first coefficient correction factor $C_{sub}$ is a correction coefficient proposed by Ivey and Morris [18] for subcooled flow. The second correction factor $F_l$ has been introduced for degraded core configuration, where a porous media is assumed with small characteristic length. It is based on the correction advised by Groeneveld et al. [7] to take into account variation in flow characteristic length $L_c$ is here applied.

## 3.2. ASTEC v3.1.1 Dataset and Meshing

The complete experimental set-up presented in paragraph 2 cannot be simulated as only 2D geometries can be represented by the code. Since the 2D ASTEC meshing is axi-symmetrical, the heated surface is modelled as a crown whose height corresponds to the experimental heated surface diameter and whose internal radius corresponds to the total fluid domain width (see Figure 2, left). In the calculation, a domain width of 50 cm is considered. After verification, that it is not too narrow to impact the steam flow around the heated surface. In the experiments, the heated device is a long full copper cylinder whereas in the calculations, its thickness corresponds to the thickness of the rest of the wall. The height of the domain is kept the same as in the experiments, to have the same hydrostatic pressure.

<figure><img src="image_3.png" /><figcaption>Figure 2. Numerical representation of the experimental set-up (left) and domain discretization considered for the study</figcaption></figure>

ASTEC is a system code using correlations and transitions between regime parameters based on mean values in control volumes (for example, dry-out condition is based on the void fraction value in the considered mesh which is directly dependent on the mesh volume). After a preliminary meshing dependency study, the discretization presented on Figure 2, right is retained. On this figure, the fluid domain is in blue while the solid wall is in grey. The red part on the wall indicates the location of the heating condition. The heated level and the vicinity of the wall are refined to give a good insight on the flow close to the wall and on the void fraction evolution in the domain. In the fluid domain, the porosity is imposed to 0.34, from the
experimental data measurement [14]. At the top of the domain, an imposed pressure boundary condition is set with water being allowed to flow back. A mass source inlet condition can be set at the bottom of the domain for both water and steam. A heat flux is imposed on the red part of the wall while an adiabatic condition is considered on the rest.

### 3.3. Reference Case

This reference calculation considers no inlet liquid nor gas mass flow rate at the bottom, the imposed pressure is set at 1.08 bar at the top of the domain, the test section is vertical (90° angle) and the balls have a 4 mm diameter. In the experiments, an increasing heat flux was applied on the heated copper mass with an increase slope of 0.09 W/s. The numerical imposed slope takes into account the 30% heat losses estimated in the experiments on the copper cylinder length. Moreover, in order to keep the same heat flux density as in the experiment, the imposed numerical heat flux also considers the geometry modification and heat surface modification. Figure 3 presents the detail of the calculated temperature of each heated wall element along with the void fraction in the cells facing each element.

<figure><img src="image_4.png" /><figcaption>Figure 3. Detailed evolution of the void fraction close to the heated surface (left) And wall temperature (right)</figcaption></figure>

As expected, the void fraction increases with height but always remains in this case lower than the dry-out condition set in the code (void fraction of 0.999) and thus does not impact the heat transfer evaluation. Surface temperature behaviour is interesting to note here as it increases faster for cells located in the middle of the heated surface compared with the bottom and top elements. This is in fact due to conduction to the rest of the cold wall on the sides of the heated part of the wall. This conduction in the experiments was limited due to insulation but it was not taken into account in the calculations. During the nucleate boiling regime, when the cooling by the fluid is very efficient, this conduction heat flux is very limited (amounting around 5% of the total imposed heat flux). In the transition regime, when the heat flux extracted by the fluid is limited, this conductive heat transfer increases up to 20% of the total imposed heat flux and limits the temperature increase of the heated part of the surface. This conductive heat transfer introduces a small bias in the calculations compared with the experimental set-up.

For the nucleate boiling process to be sustained, vapour needs to get away from the heating wall so liquid water can access it. When this process is no longer possible and vapour accumulates in the vicinity of the heated wall, efficient cooling is no longer possible and CHF condition is reached.

The cooling process in the nucleate boiling regime in the porous media is illustrated on Figure 4. This figure presents the fields of liquid superficial velocity $j_L$ and the gas superficial velocity $j_G$ close to the heated part
of the wall at 15 060 s, when the nucleate boiling regime is established. Arrows indicate the direction and magnitude of the flow. It shows that the vapor flow remains contained on a thin layer close to the wall (up to two radial meshes, i. e. 5 cm). The strong vapor flow seems to drive the liquid flow: the water is accessing the heated part of the wall from below and not radially. Direct radial liquid flow to the heated surface is prevented by the vapour layer and a loop develops, fed by water coming from the lower part of the fluid domain.

<figure><img src="image_5.png" /><figcaption>Figure 4. Liquid (left) and vapor (right) superficial velocity map (m/s) close to the heated wall during the nucleate boiling regime</figcaption></figure>

The numerical results can be compared with the experimental data. On Figure 5 (left), it is interesting to note that at the beginning, the time needed by the surface to reach nucleate boiling conditions (fluid saturation temperature) is well reproduced by the calculation, validating the imposed numerical heat flux. During the nucleate boiling phase, both calculated wall temperature and estimated heat flux increases are comparable to experimental ones. However, the calculated departure from the nucleate boiling regime and subsequent temperature increase happens significantly later than the experimental ones (Figure 5 right). Moreover, after CHF, the experimental flux drops drastically while the numerical simulation keeps a nearly constant heat flux (in consistency with the transition regime modelling limiting the heat flux by the CHF estimated by correlation). The drastic drop is only observed when the minimum stable film temperature is reached.

In all experiments performed in the same conditions as the reference case, the CHF was evaluated around 200 kW/m² (+-24 kW/m²). This uncertainty does not take into account strong scattering of the experimental results, partially due to the difficulty to control the surface state as stated in [15]. However, this would not explain the difference with the calculated CHF of 756 kW/m². This shows that the current evaluation of the CHF with the correlations defined in the code in not satisfactorily in this configuration. A verification has been made in pool boiling configuration (no porous media, free volume), the other parameters being kept the same. The calculated CHF is then 1346 kW/m² whereas experiments performed in these conditions give a CHF around 1275 kW/m² (+-166 kW/m²). So, in pool boiling conditions, the agreement between the code and the experiments is rather good. Consequently, it is the evaluation of the CHF for porous media with small porosity and small particle size that is not adequately predicted.
<figure><img src="image_6.png" /><figcaption>Figure 5. Comparison between the experimental and the numerical results</figcaption></figure>

## 4. INFLUENCE OF THE MAIN PARAMETERS

Vapor and liquid flowrate impacts are not presented here. Study has shown that influence of liquid flowrate was satisfactorily calculated in the narrow experimental liquid flowrate range. The strong impact of steam flowrate was not observed on the calculations results. More complete numerical calculations will be considered in future work to better understand this discrepancy.

### 4.1. Pressure Effect

Experimentally, several operating pressures have been studied by varying the height of the water column on top of the test section. In the calculation, the pressure is imposed at the top of the domain (corresponding to the top of the section filled with steel balls). Four calculations are performed at 1.08 bar (reference case), 1.51 bar, 1.85 bar and 2.49 bar. All the other initial and boundary conditions are kept the same as in the reference calculation presented in the above section. Figure 6 presents the CHF ratio between the pressured case CHF and the reference one for the numerical and experimental results. A dependence around $P^{0.5}$ has been found in the experiments (in agreement with literature) while it is slightly lower, closer to $P^{0.4}$ in the calculations. Nevertheless, the current evolution given in the code does seem rather reasonable.

<figure><img src="image_7.png" /><figcaption>Figure 6. CHF ratio evolution with pressure (coefficient $R = \frac{\sum (x - \bar{x})(y - \bar{y})}{\sqrt{\sum (x - \bar{x})^2 (y - \bar{y})^2}}$)</figcaption></figure>
## 4.2. Steel Ball Diameter

The experiments involved 2 mm, 3 mm and 4 mm balls (reference case). The porosity remains the same. Table 1 presents experimental and numerical CHF ratios (CHF/CHF_4 mm).

<table><caption>Table I. CHF evolution with steel balls diameter $D_p$</caption><thead><tr><td>Ball diameter Dp (mm)</td><td>Numerical CHF (kW/m²)</td><td>Numerical CHF ratio</td><td>Experimental CHF ratio</td></tr></thead><tbody><tr><td>2</td><td>614</td><td>0.810</td><td>0.630</td></tr><tr><td>3</td><td>760</td><td>1.005</td><td>0.740</td></tr><tr><td>4</td><td>756</td><td>1.000</td><td>1.000</td></tr></tbody></table>

Although experimental results show an increasing CHF with ball diameter, the numerical results do not follow a regular trend. For the 3 mm ball diameter, the CHF ratio is slightly increased compared with the 4 mm reference case. This can be explained by the Groeneveld correction [7] for flows with small characteristic length – ball diameter – currently used in CHF ASTEC modelling. This correction, established for flows in pipes, predicts an increase for the CHF when the characteristic length decreases (with a $D_p^{-1/3}$ dependency) for diameters greater than 4 mm. It is kept constant for lower diameters. Therefore a very slight increase in CHF correlation for the 3 mm case is expected compared with the 4 mm case. To verify the trend of the numerical results, an additional calculation was performed with 11 mm balls and lead to a CHF of 410 kW/m², confirming the CHF decrease trend with diameter increase. This evolution is opposite to the experimental findings, where a $D_p^{0.5}-D_p^{0.7}$ dependency of the CHF was observed, in accordance with other literature findings [14]. It is concluded that the Groeneveld correction currently used in ASTEC is not fit to represent flow effects on the CHF correlation in porous media.

For 2 mm balls, a lower numerical CHF was reached as in the experiments (see Figure 7). This can be explained by a local drying observed on the top of the surface: due to the small characteristic length and capillarity effect, it is more difficult for vapor to leave the heated surface vicinity and void accumulates until reaching the dry-out condition (void fraction of 0.999). Then the top of the surface starts heating a lot and makes the rest of the surface also heat-up. Figure 8 presents the evolutions of the void fraction and the surface temperature for each heated wall element and the adjacent fluid meshes (to compare to Figure 3).

<figure><img src="image_8.png" /><figcaption>Figure 7. Evolution of the total heat flux from the heated wall to the ball bed for different ball diameters</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Figure 8. Local void fraction and surface temperature evolution for 2 mm balls diameter case</figcaption></figure>

Numerical results show that, with a fine enough nodalization, the flow in the porous media takes into account capillarity effect and can reproduce the experimentally results by reaching local dry-out conditions. However, this type of behavior is highly mesh dependent (as dry-out conditions is based on global void fraction value in a given mesh) and is not taken into account in the global CHF correlation. This one should be changed to involve this local void fraction effect.

### 4.3. Tilting Angle

The next effect that has been studied is the tilting angle of the heated surface and wall. In the experiments, the facility was inclined with different angles. In ASTEC v3.1.1, it is possible to tilt the 2D axi-symmetrical calculation domain by specifying a rotation angle that modifies the gravity term projection on the domain two axis. In the present ASTEC v3.1.1 release, only angles between 90° (vertical default configuration) and 180° (horizontal up facing configuration) can be considered. Boundary condition is also modified to take into account hydrostatic pressure variation on the domain outlet.

Three calculations with an inclination angle of 90° (reference), 120° and 150° are performed and compared with the experimental results. Evaluated numerical and experimental CHF ratios (CHF/CHF_90°) to the reference case are given in Table 2.

<table><caption>Table II. CHF evolution for different tilting angles</caption><thead><tr><td>Tilting angle (°)</td><td>Numerical CHF (kW/m²)</td><td>Numerical CHF ratio</td><td>Experimental CHF ratio</td></tr></thead><tbody><tr><td>90</td><td>756</td><td>1.000</td><td>1.000</td></tr><tr><td>120</td><td>757</td><td>1.003</td><td>0.850</td></tr><tr><td>150</td><td>497</td><td>0.650</td><td>0.65</td></tr></tbody></table>

As for the ball diameter effect, there is a difference in behavior between the 120° case, where no effect of the tilting angle is observed, compared with the 150° tilting angle case. Due to inclination, it is more difficult for the vapor to leave the domain as gravity effect is decreased and dry-out conditions are favored. As for 2 mm diameter case, this behavior would not be observed with a coarser meshing.

Figure 9 presents the axial profile of the gas superficial velocity and void fraction close to the domain wall during the nucleate boiling regime for the three studied tilting angle (profile along an axis parallel to the
wall). The profile is plotted at 10 060 s. In the three cases, at this time, the nucleate boiling regime is established while the CHF is not yet reached. Calculations do indicate that vapor accumulation is enhanced with tilting angle. For the 150° tilting angle, there is only vapor close to the wall above the heated surface.

<figure><img src="image_10.png" /><figcaption>Figure 9. Axial gas superficial velocity (left) and void fraction profile close to the wall (right) during nucleate boiling regime (t=10 060 s) for three tilting angles</figcaption></figure>

## 5. CONCLUSION

The severe accident system code ASTEC capacity to evaluate the CHF in degraded core configuration has been assessed using experimental data specifically designed for this type of configuration. The CHF achievement rests on two main mechanisms. The first one relies on the CHF correlation that is currently implemented in ASTEC v3.1.1 and stands as a maximum for the exchanged heat flux by nucleate boiling. Although the current correlation used was shown to give good results for CHF evaluation in free water configuration, the calculations performed in the frame of this study in porous media show that the code highly over-estimate the CHF in those cases. This study highlights the need to propose a more adequate correlation for heat transfer in porous media configuration. The relative effect of different parameters on the CHF was also investigated, giving important insight on missing elements in the current CHF correlation. Pressure and inlet liquid mass flow rate impacts are in a relatively good agreement with the experimental data, at least in the range of their experimental variation. Other parameters impact such as balls diameter, tilting angle or the inlet gas mass fraction were less well reproduced by the code. New correlations taking into account the void fraction and capillarity length effect as well as the gas mass flow rate effect are needed. Future work will use this assessment study as a validation basis.

For inclined cases and small balls, the vapor retention is well reproduced, proving the code ability to predict heat flux reduction due to flow modification. DNB was reached due to local void fraction high level. As dry-out condition is given by a void fraction threshold value, this behavior is strongly dependent on meshing size. Improving dry-out condition is thus another important part for future work, especially for a system code such as ASTEC that relies on very large meshing for reactor scale applications.

## ACKNOWLEDGMENTS

The authors acknowledge Electricité De France (EDF) for their financial support, Thierry Garcin for his involvement in experimental work, Florian Fichot for scientific discussions and Abdelmalek Ourabah (internship) for his participation in the numerical modelling.
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