2.1 Sacrificial Material

A reactor safety system is designed to prevent various phenomena, including the direct heating of the reactor containment due to the injection of high-pressure molten corium into the cavity, vapor explosion, and MCCIs. The molten corium material enters the CC system and combines with the sacrificial material to reduce the molten temperature. Within the CC system, the six roles of the sacrificial material are as follows [2]:

• Decreases the melt corium temperature by the endothermic effect during the corium–sacrificial material reaction;

• increases the molten volume and provides a greater heat transfer level between the corium and cooling water; reduces the thermal flux in the walls and increases the safety margin of the critical thermal flux;

• decreases the corium chemical activity due to the oxidation of its elements by the oxides of the sacrificial material;

• minimizes hydrogen production during the oxidation of zirconium in the corium to prevent hydrogen explosion;

• ensures the subcriticality of the molten corium;

• inverses the oxide and steel layers in the corium pool.

It is noteworthy that a few CC designs for VVER- and EPR-type reactors have been realized based on two different approaches. Fig. 1 shows the CC designs for both reactor types.

Fig. 1Full-screen View

(Color online) Schemes of CC for VVER and EPR reactors. (a) Cooling method of corium in VVER reactors. (b) Cooling method of corium in EPR reactors [13].

In the VVER design, the CC is crucible-type system that contains the sacrificial material and is located under the RPV. In this case, the corium combines with the sacrificial material, and its temperature decreases owing to the abovementioned six roles of the sacrificial material. In addition, the water flow around the CC can be considered as an additional decay heat removal system.

The first practical design of these systems was developed by the Russians for VVER-1000-type reactors at the Tyanvan China Power Plant and the Indian Kudankulam Power Plant [9], where the CC of the Tyanvan China reactor was initially built.

Another case is a CC for the EPR, which comprises a core melt stabilization system located on the lateral side of the RPV. The stabilization system is intended to first spread the melt and then execute cooling operations. The EPR CC was held under the reactor vessel designed by Fischer et al. [13]. Fig. 1b shows a schematic view of the EPR CC. In this case, the corium was transferred into a flat and wide area to reduce its temperature and avoid its neutronics criticality.

2.2 Current Case Study: VVER-V528

The current operational Bushehr nuclear power plant (BNPP) is of the VVER-1000-v446 type. The VVER-1000-V528 reactor is associated with the second phase of the BNPP and is currently under investigation and pre-construction for future operation. It is noteworthy that the first phase of the BNPP, which is currently operating, comprises a VVER-1000/v446 reactor without a core catcher system, and the second phase of this power plant, which is under development, will comprise a VVER-1000/v528 reactor including a CC system. Based on the similarity between both VVERs (except for minor cases in the core, such as fuel rod enrichment, dimensions, mixed Gd, and control rod patterns), the first and second circuits of the VVER-1000/V446 as well as the reactor containment were modeled.

2.2.2 Dimensions of Primary-Loop Pipelines

The primary circuit of the BNPP comprises one pressurizer and four coolant loops. Each loop comprises one steam generator, a main coolant pump, and 300 mm pipe lines. Figure 2 shows the layout of the primary circuit, which was applied in the current study. For more details regarding the steady-state data, one can refer to [16-18].

Fig. 2Full-screen View

(Color online) Primary circuit pipelines of BNPP.

2.3 MELCOR code

In our study, we used the MELCOR code to evaluate the CC system and perform a TH analysis.

MELCOR is a fully integrated, engineering-level computer code that models the progression of severe accidents in LWRs; it was developed by Sandia National Laboratories for the U.S. Nuclear Regulatory Commission [20]. The MELCOR code models a wide range of physical phenomena, including thermal hydraulics, heat transfer, aerosol physics, heat-up, degradation, relocation of reactor cores, ex-vessel debris behavior, fission product release, and H2 production.

MELCOR is executed in two parts [20]: The first part is known as MELGEN, in which the majority of the input is specified, verified, and processed. When the input verification is satisfied, a restart file is written for the initial conditions. The second part is the MELCOR program, which solves the time-dependent problem using MELGEN and any other boundaries. Finally, post-processing graphics are provided by the HISPLT module.

It is noteworthy that because VER-type reactors are Russian-type reactors, most related studies thus far have been conducted by modeling severe power plant accidents using MELCOR. For instance, in recent studies [15, 21-24], the Bulgarian VVER-1000/v320 reactor can be cited as a MELCOR simulation [25-28].

2.3.1 Containment Modeling

The containment building was partitioned into 23 cells, of which each included 33 engineering-VENTS, as shown in Fig. 3. As presented in Fig. 3, each cell can be connected to the other cells. For instance, cells 2 and 8, cells 2 and 9, cells 2 and 21, cells 3 and 10, cells 3 and 11, and cells 3 and 21 are defined as VALVE. The details of each cell are listed in Table 4. In this study, the containment structure and its instruments were modeled using 509 heat structures, which included walls, roofs, and floors, as described in Table 4.

Table 4:Full-screen View

BNPP containment cell specifications.

Cell number	Description of cell	Free volume (m3)
1	Room for leakage collection	620
2	Rooms of SG compartment, pressurizer, and filters	4938
3	Rooms of SG compartment, bubbler, and filters	5050
4	Reactor vault	345
5	Reactor vault, reactor internal pool	925
6	Vaults of steam pipelines, feed water pipelines, and adjoining rooms	233
7	Vaults of steam pipelines, feed water pipelines, and adjoining rooms	265
8	RCP room	197
9	RCP room	214
10	RCP room	205
11	RCP room	205
12	Fuel cooling pool and cask storage pool	1467
13	Fresh fuel storage facility	600
14	Room of filtering installation and air recirculation	645
15	Room of filtering installation and air recirculation	645
16	TF system valve chambers	443
17	Staircases, adjoining rooms under fuel cooling pool, TU system valve chamber, and pumps of RCP oil cooling system. Chamber of process monitoring transducers. Oil cooler pump of fourth loop	1350
18	Staircases, adjoining rooms, chamber of backup converter. Pumps of RCP oil cooling system, pipelines	660
19	TA system valve chambers	930
20	Passage along containment perimeter	139
21	Room of TA system high-pressure cooler	21,100
22	Reactor hall space inside cylindrical wall	14,480
23	Reactor hall space between cylindrical wall and steel containment	16,000
	Reactor hall space above cylindrical wall

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Fig. 3:Full-screen View

Definition of CELL, VENT, and VALVE in MELCOR.

2.3.2 Modeling of Primary–Secondary Circuits, Lower Plenum, and Core

In the nodalization diagram and based on symmetry, the plant is simplified to a one-equivalent loop. The nodalizations of the primary and secondary loops are shown in Fig. 4a, whereas those of the core and lower plenum are shown in Fig. 4b. The nodalization scheme of the core (including the lower plenum) was segmented into four concentric radial rings and 24 axial levels. Axial levels 9–24 represent the active core region, and levels 1–7 correspond to the lower plenum. The support plate was located at level 8. In addition, the lower plenum was segmented into four concentric radial rings.

Fig. 4Full-screen View

(Color online) Nodalizations of primary loop, secondary loop, and core. (a) Primary and secondary loops; (b) core and lower plenum.

2.3.3 Cavity and CC Modeling

Figure 5 shows the cavity, CC, and in-containment refueling water storage tank (IRWST), which were modeled using the MELCOR code. In this study; the cavity, CC system, and IRWST were modeled as follows:

Fig. 5Full-screen View

(Color online) Schematic illustration of cavity, CC, and IRWSRT from MELCOR.

• The cavity was modeled using CV806 including the concrete inside, the materials of which are listed in Table 5;

Table 5Full-screen View

Composition of concrete cavity materials used in BNPP [21].

Rate	Parameter
Average temperature (K)	1470
Fe (%)	16.2
H20 evap (%)	3.1
SiO2 (%)	47.4
CaO (%)	20.0
CO2 (%)	6.76
Al2O3 (%)	1.76
Fe2O3	2.0
MgO	1.1
Total density (kg/m3)	2600

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• the CC system was modeled using CV807, including the CV806 volume; the sacrificial materials were layered in the CC volume;

• the IRWST is used to supply water around the CC and was modeled according to CV 808.

Table 6 lists the sacrificial materials used in the CC system. It is noteworthy that the composition of the sacrificial material was selected based on the optimal composition obtained from the Komlev project [12], in which the new sacrificial material was analyzed. In this study, 160 tons of SM in a CC system was assumed.

Table 6Full-screen View

Composition of sacrificial material for modeling CC system.

Compositions	Mass fraction of material (%)	Mass (Kg)
Fe2O3	60	96,000
Al2O3	28	44,800
SiO2	2	3200
SrO	5	8000
CaO	5	8000

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4.1 Containment Pressure Validation based on LB-LOCA and ECCS

To validate the containment model, LB-LOCA was performed in cold-leg pipelines (diameter = 850 mm), and emergency core cooling systems (ECCS including KWUs and ACC emergency tanks) were used to manage the accident. Fig. 6 shows a comparison of the pressure in the reactor containment for both the FSAR and current model; as shown, similar trends are presented.

Fig. 6:Full-screen View

Containment pressure after LB-LOCA accident and including ECCS.

The parameter settings used in the current simulation were as follows:

• The total containment air volume was Vtot = 71040 m3, based on Table 5.

• The containment contained heat sources, such as SGs and pipelines. Therefore, the effective temperature was within 55–70 °C at a pressure close to the atmospheric pressure (in the steady-state condition before the accident). In this case, the effective air density was 1.07 kg/m3. The volume of each containment room is shown in Table 5. Therefore, the total mass of air in the containment can be computed easily, i.e., Ma = 76012 kg.

• Consider a rupture of 850 mm in one loop. The four-loop was simulated as the average one-loop, where the water flow rate in the four-loop primary side was 84,800 m3/h (in the steady state of the four-loop). A one-average-loop was assumed to simulate the four-loop. In this LB-LOCA case, $\frac{84800}{4}$= 21200 m3/h was the flow rate (source term) of hot water ejected from and injected into the containment. For instance, three hours after an accident, the amount of ejected water would be 63600 m3.

• The nominal reactor power was 3000 MWt in the steady-state condition before the accident onset.

Based on the initial conditions above, immediately after the LOCA, the resulting pressure and steam quality increased in the containment. The ECCS (including eight KWUs tanks and four ACC, c.f., Table 3) injects water into the primary system and core cooling after the accident. The fission fragment decay heat and the boiling crisis are two major heat sources in the containment. In addition, the ECCS is a heat sink that decreases the ejected water temperature. Based on the MELCOR simulations, the containment pressure was obtained, as shown in Fig. 6.

4.2 Primary and Secondary Loop Validation in Steady State

The main parameters of the BNPP under steady-state conditions are summarized in Table 8, and they were verified in the current study. The relative errors obtained were less than the accepted criteria [31].

4.3 SBO Validation

Although we have proposed innovative operational procedures for SBO management [18], the formal FSAR document was used for SBO benchmarking (c.f., Table 7). Using the SBO sequences provided in Table 7 and the MELCOR input, the primary pressure was obtained. Figure 7 shows the primary pressure following the SBO accident, with and without the ECCS.

Fig.7Full-screen View

Primary pressure with/without ECCS: (a) With ECCS; (b) without ECCS.

5.1 Materials Produced in Lower Plenum

Based on the current scenario, if the SBO accident cannot be efficiently managed, then the core will melt and the molten corium is transferred to the reactor’s lower plenum; subsequently, it enters the cavity and CC. Table 10 lists the molten material provided in the lower plenum based on two cases, i.e., with/without the ECCS. Fig. 8 shows the amount of molten corium transferred to the dry cavity, without a CC (state 1).

Fig. 8:Full-screen View

Comparison of amount of corium provided in lower plenum and transferred to dry cavity, without CC.

As shown in Fig. 8, the core melted at 16430 s when the ECCS was not used, whereas the heart melted at 28630 s when the ECCS was used.

The total amount of molten corium transferred into “state 1” was less in the case without the ECCS compared with that with the ECCS (c.f., Table 10). In addition, the molten UO2 was much lower in the case without the ECCS. The total amount of hydrogen was a major concern, and it was greater in the case without the ECCS. The details of the suggested material are shown clearly for both cases.

5.2 Materials Formed in Cavity

The total mass formed in the cavity based on the time-dependent conditions is shown in Fig. 9a, and the amount of hydrogen produced is shown in Fig. 9b.

Fig. 9Full-screen View

Total mass formed in cavity in different states for both with/without ECCS. (a) Mass formed in cavity (including corium + concrete); (b) amount of hydrogen.

5.3 Ablation Depth of Cavity

The axial and radial ablation depths of the cavity concrete are directly related to the corium mass. Generally, the higher the corium mass and temperature, the more significant is the ablation of the concrete cavity, which causes a larger radial depth, as shown in. Fig. 10.

Fig. 10Full-screen View

(Color online) Cavity radius and height changes during accident.

Figure 11 shows the ablation depth of the concrete in the radial and axial directions and for different states. As shown in Fig. 11a, the largest concrete ablation depth in the radial direction was obtained in the dry cavity and “without ECCS” case, whereas the smallest in the wet cavity and without ECCS case. The same behaviors were observed in the axial direction, as shown in Fig. 11b.

Fig. 11Full-screen View

Comparison of radial and axial ablation depths of concrete cavity in dry and wet states, with/without ECCS. (a) Radial ablation; (b) axial ablation.

5.4 Containment Pressure and Temperature

Figure 12a shows the computation results for the pressure of the containment (for 4 d after the SBO accident), in which different states without the ECCS were considered. Figure 12b shows the containment pressure with the ECCS. As shown in Fig. 12a, the highest and lowest containment pressures occurred in states 2 and 4, respectively. In addition, as shown in Fig. 12b, the highest and lowest pressures in the containment occurred in states 1 and 4, respectively. When the ECCS system was activated, the molten temperature was lower than that of the without ECCS case; meanwhile, when the corium entered the water pool, less steam was produce. Therefore, the dry cavity yielded the highest pressure owing to the MCCI. The current phenomena resulted in more voids owing to the corium being deposited into the water, and this may result in steam explosion.

Fig. 12Full-screen View

Containment pressure and temperature with/without ECCS for different states. (a) Pressure without ECCS; (b) pressure with ECCS; (c) temperature without ECCS; (d) temperature with ECCS.

The containment temperatures for cases without and with the ECCS are shown in Figs. 12c and 12d, respectively. It is clear that the highest containment temperature was in state 1, whereas the lowest was in state 4. If the ECCS is activated, then the highest and lowest temperatures will be recorded in states 6 and 8, respectively (c.f., Fig. 12d).

5.5 Gases in Containment

In this section, the amounts of gases such as hydrogen, carbon, carbon dioxide, and nitrogen produced by the MCCI are explained.

The decrease in the hydrogen explosion probability of the containment is an important issue. Hence, we focused on the hydrogen production amount of the containment, which is illustrated in Figs. 13a and 13b for different states. The highest and lowest production amounts were recorded in states 2 and 4, respectively. Fig. 13b shows that the highest and lowest hydrogen production amounts were recorded in states 5 and 8, respectively. Figs. 13c–13h show other gases that were produced in the containment.

Fig. 13Full-screen View

Gas production rates in containment with/without ECCS. (a) Hydrogen, without ECCS; (b) hydrogen, with ECCS; (c) CO, without ECCS; (d) CO, with ECCS; (e) CO2, without ECCS; (f) CO2, with ECCS; (g) N2, without ECCS; (h) N2, with ECCS.

Table 11 shows a summary of the results. The final results are indicated clearly. For instance, water around the CC resulted in a lower hydrogen production than the other states. Hence, we provided a (✓) mark for that case. A similar check-mark rule was applied for another case study and different states.

5.6 Theoretical Benchmarking of Best Result

Based on the MELCOR simulation, it was discovered that “Cavity+ CC including water around” provided the best result. It was clear that the corium, together with the vessel water, descended into the CC. The current section provides a theoretical investigation of the best simulation results, from which we developed a theoretical model.

First, consider a severe accident in which the core has completely melted and hence descends to the bottom of the pressure vessel. This situation is illustrated in Fig. 14. Subsequently, the corium together with the vessel water descend into the “Cavity+ CC including water around”. The molten mixture of fuel (UO2), fission products, clad (zircaloy), control rod material (B4C), and all core-supporting structures (steel) are known as the corium. In the case described, the corium melt fills the lower plenum and then moves to the CC system up to the hemispherical lower head. Water is present above the corium and outside the CC. The fuel decay heat is removed by boiling above the corium as well as by conduction through the CC wall (with boiling water outside the CC, which is the heat sink for the heat removal mechanism).

Fig. 14Full-screen View

(Color online) Illustration of corium entering from bottom of CC, resulting in two-phase fluid at the top and around the CC.

The corium temperature is denoted by Tc. Prior to the accident, the core thermal power was $P_0$ MWt. In this case, two-phase fluids occurred around the CC, and the temperature of the inside water (above the corium) is denoted as Twi.

The water in the abovementioned problem was in the film-boiling regime with radiation conflict. In this case, the film-boiling heat transfer correlations (in terms of W/m2 C) can be determined based on Berenson [32], as follows:

where the convection and radiation coefficients are expressed as

Here, $T_{\text{wi}}-T_{\text{sat}}=0.01\text{ K}$ is the difference between the corium two-phase water temperature above (at a constant pressure) and the saturated water. In this equation, $T_{\text{sat}}$ and $T_{\text{wi}}$ should be expressed in units of Kelvin.

where $\text{σ}$ is the surface tension.

Meanwhile, the energy balance for the corium melt is a combination of the decay heat as the source term and two removal terms, i.e., boiling in the water and conduction in the CC thickness. It can be expressed as shown in the following differential equation:

where c represents the corium. $P_{\text{decay}}$ is the fission fragment decay heat power t seconds after the scram and is a positive source term expressed as

where $P_0$ is the power before scramming in terms of MWt, and t should be expressed in units of seconds. The conduction heat transfer between the corium and CC thickness (including the steel and concrete parts) is determined based on the following approximation:

where $k_{\text{V}}\text{ represents }$ the effective CC conduction coefficient (steel + concrete), $T_{\text{Wo}}$ is the outside CC water temperature, and $\Delta$ is the effective CC thickness. The contact area is a hemispherical surface, $2\pi R_{\text{cc}}{}^2$, where $R_{\text{cc}}$ is as shown in Fig. 14.

Finally, the boiling term inside the CC (above the corium) is expressed as

The saturation temperature $T_{\text{sat}}$, upper disc-shaped area, and other related data are listed in Table 12.

The theory above was benchmarked with the best simulation result. Figure 15 shows a comparison of the results of the MELCOR calculations with those from theoretical investigation.

Fig. 15Full-screen View

Comparison of corium temperature for both theoretical and MELCOR calculations (t = 0 is the time at which all corium and water descended into the CC).