Influence of Concrete Properties on Molten Core-Concrete Interaction : A Simulation Study

In a severe nuclear power plant accident, the molten core can be released into the reactor pit and interact with sacrificial concrete. In this paper, a simulation study is presented that aims to address the influence of sacrificial concrete properties on molten coreconcrete interaction (MCCI). In particular, based on theMELCORCode, the ferrosiliceous concrete used in European Pressurized Water Reactor (EPR) is taken into account with respect to the different ablation enthalpy and Fe 2 O 3 and H 2 O contents. Results indicate that the concrete ablation rate as well as the hydrogen generation rate depends much on the concrete ablation enthalpy and Fe 2 O 3 and H 2 O contents. In practice, the ablation enthalpy of sacrificial concrete is the higher the better, while the Fe 2 O 3 and H 2 O content of sacrificial concrete is the lower the better.


Introduction
In a simulated core melt accident of nuclear power plant (NPP), a molten pool called corium can melt through the reactor pressure vessel (RPV) and be released to the containment basemat.Driven by the decay power of the fission products and the high temperature, the basemat concrete, which is the last barrier that prevents leakage of the radioactive products into environment in the secondgeneration NPPs, starts to ablate [1,2].Thus, the molten coreconcrete interaction (MCCI) is of great importance in NPP because it may result in leakage of fission products.Previous studies show that the concrete properties have significant impact on MCCI [1][2][3][4][5][6].In the third-generation NPPs, such as European Pressurized Water Reactor (EPR) [7], a core catcher is introduced to encase the corium, through which the integrity of the containment is preserved.Moreover, a specific ferrosiliceous sacrificial concrete containing both siliceous and hematite aggregates is employed in the reactor pit of EPR.The role of the sacrificial concrete is to adjust the properties of the corium released from RPV in terms of the interaction between them (MCCI).An investigation carried out by Chu et al. [8] has recently presented a systematic study on thermal properties of ferrosiliceous sacrificial concrete subjected to high temperatures, and another report focusing on the mechanical and physicochemical properties of ferrosiliceous concrete at high temperatures has also been recently published [9].However, the ablation behavior or MCCI of ferrosiliceous concrete has not been studied in these literatures.
Wang et al. [10] have conducted a simulation investigation on core thermal response during a station blackout initiated severe accident in China pressurized reactor (CPR1000) using MELCOR Code, and the safety of the reactor core has been assessed.Nie [11] has made a systematic research on temporary melt retention in the reactor pit of EPR and has pointed out that, for a large breach loss of coolant accident scenario in the EPR, 1.20 × 10 5 kg of metallic melt and 1.85 × 10 5 kg of oxidic melt are released in the reactor pit, and the decay heat decreases from 32 MW (3 h after scram) to 20 MW (30 h after scram).Nevertheless, the concrete used in the CPR1000 was not the ferrosiliceous sacrificial concrete.Due to the complexity of MCCI, information on this phenomenon is still limited and needs to be updated.This paper focuses on the influence of ferrosiliceous concrete properties on the MCCI, including the concrete ablation enthalpy and the Fe 2 O 3 and H 2 O contents.In the work, a simulation study is performed based on the MELCOR Code used for CPR1000.The calculation model is established by replacing the concrete cavity of a 1000 MW pressurized reactor (CPR1000) by the EPR reactor pit which employed the special ferrosiliceous sacrificial concrete.In essence, it is assumed that the interaction is induced by a typical small break loss of coolant severe accident sequence (SBLOCA) of the CPR1000, but the concrete cavity in the current study has been replaced by the ferrosiliceous sacrificial concrete cavity.

Main Assumptions for the Calculation
MELCOR is a fully integrated, engineering-level computer code that consists of various modules and packages [12].The MELCOR Cavity (CAV) package models the attack of hot (often molten) core materials on the basemat concrete [14], and the cavity contents and boundary conditions are shown in Figure 1.
In the CAV package, two modes can be selected for the configuration of the core melt, that is, enforced mixing or enforced stratification.The enforced mixing is the simplest mode which considers the melt being a single layer.For the enforced stratification mode, the configuration of the melt is determined by the specific density of each layer.The most common structure is a three-layer configuration, where a metallic layer (MET) exists between the light oxide layer (LOX) and the heavy oxide layer (HOX).Another factor influencing the configuration of core melt is the rising gas bubbles generated by concrete decomposition, which promotes the mixing of different layers.In Sections 3.1 and 3.2, the configurations of core melt are assumed to be enforced mixing.In Section 3.3, with respect to the impact of rising gas bubbles, the configuration of core melt is assumed to be enforced stratification that shall address the influence of H 2 O content.The ablation behavior of sacrificial concrete depends on the heat transferred from melt to it.The heat in the cavity comes from two sources, that is, the decay power from fission products (FP) and the chemical reaction taking place in the melt.The heat is transferred either through the top surface of the debris or to the concrete basemat and sidewalls, as determined by the thermal resistances.
In regard to the thermal resistance at MCCI, there are also two models to be selected, that is, the gas film model and the slag film model.For the gas film model, the dominant heat transfer mode is bubble-enhanced heat transfer determined by Greene correlation [15].For the slag film model, intermittent melt-concrete contact results in periodic growth and removal of slag from the interface, and thus a modified version of the Kutateladze correlation [16] is used for bubbling heat transfer coefficient.In addition, a solid crust may be formed at the interface between sacrificial concrete and melt with heat transfer by thermal conduction.The solid crust hinders the contact of melt with concrete and decreases the heat transfer from melt to sacrificial concrete.In the paper, the slag film model is selected for both bottom and radial thermal resistance, because, under the postulated severe accident, superficial gas velocity is much lower and cannot form a stable gas film [17].
Another important parameter that affects sacrificial concrete ablation is the temperature at MCCI, which is defined as the ablation temperature of sacrificial concrete in MELCOR.The ablation temperature of ferrosiliceous sacrificial concrete used in the study is 1453 K, according to [1].
A typical small break loss of coolant severe accident sequence (SBLOCA) of the 1000 MW EPR NPP is assumed in this study.Before the accident, the EPR operates at full power with the thermal power of 3426 MW and the average coolant temperature of 566 K. Time zero in the calculation corresponds to the time of the reactor scram.Upon a stable calculation, that is, −550∼0 s, the break initiates.No safety intervention is applied during the accident process.At 4360 s, the RPV was melted through.After that, the corium was poured into the sacrificial concrete pit mainly at two periods, 4360∼5000 s and 7455∼9767 s, and the mass of the corium in these two periods is 0.72 × 10 5 and 0.54 × 10 5 kg, respectively.The total mass of corium released to the reactor pit is about 1.26 × 10 5 kg.
The MELCOR decay heat package models the decay heat power resulting from the radioactive decay of fission products.In the study, the whole decay heat power was set according the CPR1000.The evolution of decay heat, heat loss to sacrificial concrete, and heat loss from debris surface is shown in Figure 2.And the decay heat, heat loss to sacrificial concrete, and heat loss from debris surface are not changed after 14500 s.
The material in reactor pit is made up of the ferrosiliceous sacrificial concrete with high content of Fe 2 O 3 .The composition and properties of sacrificial concrete input for calculation are shown in Tables 1 and 2, respectively.The geometry of the initial concrete cavity is cylindrical with a height of 4.95 m, radius of 3.075 m, basemat axial thickness of 0.45 m, and radial thicknesses of 0.55 m.The calculations are processed until axial melt-through.In addition, the maximum radius ablation depth is around 0.31 m.
In the paper, we supposed that the ablation behavior of sacrificial concrete was isotropic.An investigation by Sevón  et al. [2] has shown that an anisotropic ablation pattern is observed for ferrosiliceous sacrificial concrete, but this result is based on small scale of MCCI.On the whole, however, the isotropic assumption was reasonably taken to evaluate the MCCI as it maximizes basemat ablation.

Results and Discussion
3.1.Ablation Enthalpy.Sacrificial concrete ablation enthalpy quantifies the heat required to convert a unit mass of virgin sacrificial concrete into condensed and gaseous decomposition products at the specified ablation temperature.Ablation enthalpy not only modifies the sacrificial concrete ablation heat but also changes the energy balance of ablation.For ferrosiliceous sacrificial concrete, the value of 1730 kJ/kg could be assigned as its ablation enthalpy, according to literature [18].In this study, an increased ablation enthalpy of 10%, 20%, and 30% shall be performed to address its effect on the MCCI behavior.As shown in Figure 3, the sacrificial concrete ablation rate shows a "peak-valley" tendency which may result from a "form-melt-reform-remelt" process of the crust.As the sacrificial concrete ablation enthalpy increases, the ablation rate decreases.In consequence, the melt-through time increases.At the elapsed time of 4360∼5800 s and 7300∼8700 s, the low and stable ablation rate of 2.2 × 10 −5 m/s can be detected, which is attributed to the crust formed at the interface.Thereafter, the ablation rate increases rapidly.The maximum ablation rate of the initial (control) sacrificial concrete is 7.0 × 10 −5 m/s.When the ablation enthalpy increases by 30%, the value of that is 4.7 × 10 −5 m/s.Besides that, the melt-through time of the initial sacrificial concrete is 9442 s.When the ablation enthalpy increases by 10%, 20%, and 30%, the meltthrough time is 10332 s, 11283 s, and 12245 s, respectively.As the melt is released from RPV to the pit, the melt temperature displays a rapid increase, as shown in Figure 4, the result of which is due to the decay heat released by fission products.The temperature decreases gradually after 5800 s upon the mixing of cold sacrificial concrete decomposition products with the melt.Similar to the sacrificial concrete ablation rate, the hydrogen generation rate also shows a "peak-valley" tendency, as illustrated in Figure 5. Minor discrepancies can be detected for the sacrificial concretes with varying ablation enthalpy.It might be due to the longer melt-through time for sacrificial concrete with larger ablation enthalpy.Thus, if the ablation enthalpy of sacrificial concrete is increased through mix design, then the melt-through time is prolonged, which is paramount for nuclear accident mitigation.Past studies have suggested that concrete ablation in essence depends on the heat transfer from the melt pool to concrete.In this way, the concrete ablation rate can be expressed as follows [13]:

Advances in Materials Science and Engineering
where Q is the heat flux to concrete,  is the concrete density, Δ is the concrete decomposition enthalpy, and  is the area of the ablating concrete.In practice, the heat conducted into concrete can be ignored with respect to the low thermal conductivity of concrete.Equation (1) suggests that when the concrete decomposition enthalpy increases, the concrete ablation rate decreases.In other words, upon the same heat flux, the concrete will be ablated more for the concrete with smaller decomposition enthalpy.Thus, as the mixed cold concrete decomposition products increase, the melt temperature decreases faster.Meanwhile, since H 2 O is produced from the concrete decomposition, the hydrogen generation rate is closely related.As shown in Figure 5(b), the tendency of hydrogen generation rate is similar to the sacrificial concrete ablation rate.As shown in Figures 6-8, with the increased Fe 2 O 3 content, both the sacrificial concrete ablation rate and the hydrogen generation rate increase, while the melt temperature decreases faster.In particular, the maximum sacrificial concrete ablation rate for the 48% Fe 2 O 3 content is about 1.4 times that for the 32.3% Fe 2 O 3 content.The melt-through time of sacrificial concrete decreases from 9442 s to 9131 s to 8193 s.In addition, the maximum temperature difference reaches 223 K, as compared to the concretes of 32.3% and 48% Fe 2 O 3 contents.The mass of generated hydrogen is 102.6 kg for the sacrificial concrete with 32.3% Fe 2 O 3 content.However, sacrificial concrete with 48% Fe 2 O 3 content generates slightly less hydrogen, that is, 96.9 kg, the result of which is in line with literature [3].

Fe
Figure 9 indicates that the heat loss to sacrificial concrete increases with the increase of Fe 2 O 3 content.Also, it reveals the reason why the sacrificial concrete ablation rate increases with the increase of Fe 2 O 3 content.Above 2143 K, the SiO 2 -Zr reaction is endothermic and the Fe 2 O 3 -Zr reaction is exothermic.Below 2143 K, the heat released from the Fe 2 O 3 -Zr reaction is higher than the SiO 2 -Zr reaction upon the oxidation of same amount of Zr.It should be noted that, in the calculation except the very last instants of MCCI, SiO 2 -Zr interaction is endothermal in the bulk of the pool, as shown in Figures 4 and 7 (the horizontal full line at 2143 K).Thus, the higher Fe 2 O 3 content leads to the higher heat loss to sacrificial concrete.Figure 10 presents that the enthalpy of SiO 2 is higher than that of Fe 2 O 3 .At the ablation temperature of 1453 K, the ablation enthalpy shall be lower for the sacrificial concrete with higher Fe 2 O 3 content.It is another reason for the faster ablation of the sacrificial concrete with higher Fe 2 O 3 content.Therefore, the melt-through time can be extended by decreasing the Fe 2 O 3 content in ferrosiliceous sacrificial concrete.

H 2 O Content.
During MCCI, the generated H 2 O from concrete decomposition arises through the melt pool.On one hand, H 2 O can react with the metal in the melt to release H 2 .On the other hand, the gas bubble stirs the melt, which can facilitate to the heat transfer and the mixing of different layers.In this regard, the H 2 O content is another important factor for MCCI.In this paper, the H 2 O content is chosen at 2%, 4.4%, and 8% to investigate the related effect on MCCI.The other components are adjusted to maintain the sum of 100%.The enforced stratification is applied for the configuration of the pool.As shown in Figure 11(a), with the increase of H 2 O content, the ablation depth of sacrificial concrete decreases during most period of MCCI.It is noted that, at the elapsed time of 11698∼14446 s, the sacrificial concrete ablation depth for the 4.4% H 2 O content is larger than that for the 2% H 2 O content.As shown in Figure 11(b), little difference can be detected for the sacrificial concrete ablation rate before 7730 s.After 7730 s, however, the ablation rate varies sharply after a period of slow ablation due to the appearance and disappearance of the LOX layer.For the sacrificial concrete with 2% H 2 O, the ablation rate increases sharply  content.After 15343 s, the ablation rate is 1.9∼3.6 × 10 −5 m/s and is also lower than that of concrete with 2% H 2 O content.In addition, the ablation rate with 8% H 2 O content is always at a low value of 1.33∼1.70× 10 −5 m/s till 23480 s.It increases sharply till the sacrificial concrete is melted through due to the disappearance of the LOX layers after 23480 s.The meltthrough time increases from 16005 s to 18130 s to 23622 s for the sacrificial concrete with 2%, 4.4%, and 8% H 2 O content, respectively.Similar results were reported by Gencheva et al. [19].On the whole, with the increase of H 2 O content, the ablation rate of sacrificial concrete was decreased.Maybe that was because the bubbling caused by the higher H 2 O content could result in mixing and thus lead to an even slower axial ablation rate [20].
In addition, the temperatures of HOX and MET decrease with the increase of H 2 O content in sacrificial concrete, as illustrated in Figure 12.
As shown in Figure 13, the hydrogen mass and the generation rate of concrete with 8% H 2 O content are both higher than those of concrete with 2% and 4.4% H 2 O content, which differs from its ablation depth and rate.The total mass of hydrogen generated for the 8% H 2 O content is 389.42 kg, and it is 3.6 times of that generated for the 2% H 2 O content.Therefore, the higher H 2 O content could lead to the increase of H 2 explosion possibility in reactor, which affects the safety of NPP.As shown in Figure 14, the small thickness of LOX varies mildly with the H 2 O content before 7300 s.As the sacrificial concrete ablates, the thickness of LOX for the sacrificial concrete with 2% H 2 O content increases rapidly at 11698∼144258 s.The related elapsed time is at 9500∼13231 s for the sacrificial concrete with 4.4% H 2 O content, while no LOX layer can be detected until 23480 s for the sacrificial concrete with 8% H 2 O content.It might be attributed to the larger mass of heavy ZrO 2 generated by the Zr-H 2 O reaction.The gas mass generated during MCCI increases with the increase of H 2 O content, which results in more heat loss to surface and less heat loss to sacrificial concrete, as can be seen in Figures 15 and 16.Most of all, for the sacrificial concrete with 8% H 2 O content, the heat loss to surface by generated gas is about 10 times of that to sacrificial concrete ablation.In this regard, the ablation rate decreases with the decrease of H 2 O content.In addition, the LOX MET and HOX hinder heat loss through the surface of melt, as illustrated in Figure 16.The ablation rate increases sharply when the LOX exists.Consequently, the H 2 O content has a big effect on the ablation rate and hydrogen production of MCCI, and the H 2 O content of sacrificial concrete is the lower the better for the safety of nuclear power plant.
In a word, the properties of sacrificial concrete have a crucial impact on the MCCI.In practice, the ablation enthalpy of sacrificial concrete is the higher the better, while the H 2 O and Fe 2 O 3 content of sacrificial concrete is the lower the better for the safety of NPP and for the nuclear accident mitigation.The simulation investigation has important consulting meaning to the mixture design of the ferrosiliceous sacrificial concrete.

Conclusion
In this paper, based on the computer code MELCOR, we investigate the effects of sacrificial concrete properties on MCCI, including its ablation enthalpy and contents of Fe  EPR is examined upon a typical small break loss of coolant severe accident.Relevant parameters are discussed, including the sacrificial concrete ablation rate, the temperature of the melt, and the mass and generation rate of hydrogen.Some general conclusions can be drawn as follows: (1) As the sacrificial concrete ablation enthalpy increases, its ablation rate decreases, and meanwhile the meltthrough time of basemat increases.With the higher sacrificial concrete ablation enthalpy, the hydrogen generation rate is lower, and the temperature decreases faster.Besides that, little difference can be detected in the total hydrogen mass.
(2) The higher Fe 2 O 3 content leads to the larger ablation rate as well as hydrogen generation rate, but little difference exists for the total masses of hydrogen.A faster decrease of temperature is detected at the melt pool.(3) When LOX appears in the melt, the sacrificial concrete ablation rate increases rapidly.The quick decrease of heat to the surface results in the sharp increase of heat transmitted to sacrificial concrete.Most of all, the ablation rate of sacrificial concrete decreases with the increased H 2 O content.Compared with the 2% H 2 O content, the melt-through time and total hydrogen mass for the 8% H 2 O content are 0.48 and 2.6 times larger, respectively.
(4) In practice, the ablation enthalpy of sacrificial concrete is the higher the better, while the Fe 2 O 3 and H 2 O content of sacrificial concrete is the lower the better.
(5) The simulation study has significant consulting meaning to the mix proportion design of the ferrosiliceous sacrificial concrete.

Figure 2 :
Figure 2: The evolution of decay heat, heat loss to sacrificial concrete, and heat loss from debris surface in the calculation.

Figure 7 :
Figure 7: Temperature under different contents of Fe 2 O 3 .

Figure 8 :Figure 9 :
Figure 8: Hydrogen mass generation rate under different contents of Fe 2 O 3 .

Figure 11 :Figure 12 :
Figure 11: (a) Sacrificial concrete ablation depth and (b) ablation rate under different contents of H 2 O as a function of time.
2 O 3 and H 2 O.In particular, the ferrosiliceous concrete used in Advances in Materials Science and Engineering Hydrogen generation rate (×10 −2 kg/s) (b) Hydrogen generation rate

Figure 13 :Figure 14 :
Figure 13: Hydrogen mass and generation rate under different contents of H 2 O.

Figure 15 :
Figure 15: Heat loss to sacrificial concrete under different contents of H 2 O.

Figure 16 :
Figure 16: Heat loss to surface under different contents of H 2 O.
[3]]] Content.As aforementioned, the sacrificial concrete is critical to the core catcher in EPR pit.It mainly contains Fe 2 O 3 and SiO 2 with the total content reaching 76.7%[1,2].Previous studies indicated that heat released from the interactions of Fe 2 O 3 and SiO 2 with zirconium accounts for the ablation of concrete[17].For the sake of In the KAPOOL tests, this value was chosen at 48%[3].In this paper, the Fe 2 O 3 content is chosen at 32.3%, 36%, and 48%.Meanwhile, the SiO 2 content is adjusted to ensure the sum of Fe 2 O 3 and SiO 2 at 76.7%.Zr + SiO 2 → ZrO 2 + Si + 1.6 MJ/kg Zr [1]ustration, the reaction equations are presented, that is, (2)-(4).It can be noted that the heat with the Fe 2 O 3 -Zr reaction varies from that with the SiO 2 -Zr reaction, especially at the temperature above 2143 K. Thus, the Fe 2 O 3 content shall be of paramount importance for the MCCI.The Fe 2 O 3 content in ferrosiliceous sacrificial concrete is around 32∼36%[1].