# Strategy Evaluation for Cavity Flooding during an ESBO Initiated Severe Accident

Authors: Nan Jiang; Minjun Peng; Wei Wei; Tenglong Cong
Journal: Science and Technology of Nuclear Installations
 (2018)

---

## Abstract

Intentional depressurization and cavity flooding are two important measures in current severe accident management guidelines (SAMGs). An extreme scenario of an extended station blackout (ESBO), when electric power is unavailable for more than 24 hours, actually occurred in the Fukushima Daiichi accident and attracted lots of attention. In an ESBO, the containment spray cannot be activated for condensation, and, thus, cavity flooding will generate a large amount of steam, which, ironically, overpressurizes the containment to failure before the reactor vessel is melted through. Therefore, consideration of these conflicting issues and the ways in which plants operate is crucial for strengthening the strategies outlined in SAMGs. In this paper, the effects of intentional depressurization and cavity flooding in an ESBO for a representative 900 MW second-generation pressurized water reactor (PWR) are simulated with MAAP4 code. Diverse scenarios with different starting times of depressurization and water injection are also compared to summarize the positive and negative impacts for accident mitigation. The phenomena associated with creep ruptures, hydrogen combustion, corium stratification, and cavity boiling are also analyzed in detail to strengthen our understanding of severe accident mechanisms. The results point out the facility limitations of second-generation PWRs which can improve existing SAMGs.


---

## Body

## 1. Introduction

After the Fukushima Daiichi nuclear accident, national regulators put forward higher requirements for severe accident management guidelines (SAMGs) in nuclear power plants. In addition to designing more advanced and safer reactors, improving present SAMGs for in-service plants also requires attention. Because the concepts and methods in SAMGs are unique to a particular facility’s layout and cannot be easily applied to other plants, there are many challenges related to applicability that must be addressed when a specific plant tries to optimize its own SAMGs.Fukushima Daiichi was a serious accident that involved, as a result of a large tsunami, an extended station blackout (ESBO) situation, which caused the loss of all AC power. Then the cooling of the reactor gradually deteriorated. Hydrogen generated from the zirconium-water reaction finally exploded in the containment [1]. When a second-generation pressurized water reactor (PWR) deals with a similarly severe SBO incident, most of the active safety facilities, such as the containment spray and auxiliary feed-water pumps, will be disabled. If the operator misses the best timing for external intervention or makes a mistake, the core components may melt and the reactor pressure vessel (RPV) consequently fails.Intentional depressurization of the RCS is the most direct method of preventing high-pressure melt ejection (HPME). The present SAMGs [2] explicitly point out that the operator should manually open the pressurizer safety valves (PSVs) to depressurize the RCS to a regulation safe level when the core exit temperature exceeds 922 K. The low pressure in the primary system can provide a favorable condition for preventing HPME and launching the low pressure injection (LPI) when the supply of electric power is recovered. Since RCS injection is the most effective strategy of mitigating core degradation, much previous research has optimistically assumed that the LPI can be recovered within 24 hours and the hydrogen discharged from the PSVs is stable in the containment [3–5]; thus, intentional RCS depressurization is a safe decision for accident mitigation under this condition. However, in actual scenarios, external power may not be recovered for more than 24 hours, and depressurizing will merely accelerate the loss of coolant and pressurization of the containment, akin to a leakage in the RCS. Moreover, the phenomenon associated with creep ruptures, hydrogen combustion, will make the consequences of depressurization more complicated and should else be considered. Therefore, the consequences of depressurization require careful consideration in such an extreme condition.In addition, many experimental studies indicate that the growth of the molten pool still cannot be effectively stopped even after the depressurization and reflooding under some extreme scenarios [6]. In fact, it was observed in the TMI-2 accident that the molten pool still continued to grow even after the core had been totally covered with water [7]. Thus, advanced third-generation PWRs are equipped with a passive reactor cavity flooding system to provide cooling of the external reactor vessel in case reflooding fails, a method known as in-vessel retention via external reactor vessel cooling (IVR-ERVC). IVR-ERVC is an important concept in advanced SAMGs that involves injecting water into the reactor cavity before the core debris relocates to the lower head. The decay heat can be conducted from molten corium to the wall of the reactor and removed through the convection of outside water. Then the molten pool will be stabilized, and the integrity of the RPV will be maintained [8].For IVR-ERVC in high-power PWRs, like AP1000, there is a special flow path between the reactor insulation and RPV, which is carefully designed to enhance the heat transfer to water outside of the RPV. A natural circulation with flow boiling can then be established to remove heat without any subsequent operation after flooding the cavity. The additional steam generated from the cavity can also be condensed passively by the double containment structure [9–11]. However, applying IVR-ERVC in second-generation PWRs continues to be challenging, because they are not designed with similar passive facilities, that is, special flow path and double containment. Previous studies have indicated that continuously injecting the cavity is possible to keep the boiling stable [12–14]. However, these studies mostly aim to maintain the integrity of the RPV in the initial stage of the accident. The negative effect of pressurization during the long-term cooling of the containment is often ignored. In SBO scenarios, the containment spray is disabled. Although flooding the cavity early is more conducive to RPV cooling, it also accelerates the accumulation of steam and can even overpressurize the containment before the vessel is melted through. Therefore, the starting time of injecting water into cavity will significantly affect inner heat dissipation and containment pressurization. Terminating water injection at an appropriate time may be able to solve the issue of steam accumulating in the containment during cavity flooding.In summary, previous research on SBO scenarios has mainly focused on recovering RCS injection after a short period of depressurization. However, the RCS injection may not be recovered in 24 h and the cooling that results from reflooding the core may not be effective in actual accidents. Thus, it is necessary to reconsider the effectiveness of intentional depressurization with cavity flooding. Besides, the reactor and containment structures of in-service plants are difficult to rebuild, so inevitable contradictions regarding the behaviors of the core and containment will also exist when applying IVR-ERVC to the second-generation PWRs. Therefore, the insufficient consideration of accident scenarios and the facility limitations both require further research. In addition, investigations of the starting times for depressurization and water injection should be carried out to balance the positive and negative impacts of these two strategies, since they are crucial for accident mitigation.In this paper, the mitigation of intentional depressurization and cavity flooding in SBO scenarios for a typical 900 MW second-generation PWR are simulated with the MAAP4 code. Diverse scenarios with different starting times of depressurization and water injection are also compared to summarize the positive and negative impacts for accident mitigation. The simulation adequately considers the uncertainties of creep rupture, cavity boiling, and steam pressurization and finally proposes advices to minimize the negative effects. This study can provide insights for improving existing SAMGs.


## 2. Method and Model

### 2.1. Analysis Method and Plant Model

Models of the reactor and containment are built by the modular severe accident analysis code MAAP4. This code can sufficiently simulate the entire spectrum of various severe accidents on a system-wide level. The computational accuracy is enough to deal with the coupled behaviors of the facility and complex phenomena of the accident.(
1
) The model of the 900 MW plant consists of a reactor, three coolant circuits, and a large dry containment. The detailed nodalization is illustrated in Figure 1. Three safety valves are installed on the top of the pressurizer, which can be deployed either automatically or manually according to the trigger limit. Three accumulators (ACCs) are also modeled to provide passive water injection.Figure 1
Primary system nodalization.(
2
) The core and lower head are divided into concentric radial rings and axial levels, as shown in Figure 2. Since the in-vessel retention stage is an emphasis of this research, the lower head of the RPV is further divided into five radial rings with five axial levels on the symmetrical hemisphere. The power of the reactor decay heat is calculated by the standard ANSI equation, which is a function of fuel enrichment and shutdown time.Figure 2
Nodalization of the core and lower head.Consider an accident state in which molten core debris slumps into the lower head. Molten debris with internal heat will form a circulation pattern, as shown in Figure3. Based on the experimentally determined values from Jahn and Reineke [15], the average heat flux of the molten pool for upward (u), downward (d), and sideward (s) circulation can be expressed as shown in Figure 3.(1)qu=0.345kpxΔTR1pRa0.233.qd=0.54kpxΔTR1pRa0.18z1pR1p0.26qs=0.85kpxΔTR1pRa0.19Figure 3
Arrangement of the molten pool in the lower head.The Rayleigh number of a developing molten pool was defined by the maximum height as(2)Ra=gβqυR1p5αυkpx.(
3
) The structure of the large dry containment is provided in Figure 4. When an SBO occurs, water is injected from the bottom to flood the cavity and cool the vessel. The volume of the cavity is shown in Figure 5. The steam and water released from the PSVs are directed to the lower compartment atmosphere (volume 2) and then pressurize the entire containment.Figure 4
Containment structure.Figure 5
Cavity nodalization.(
4
) In coupling calculation of the cavity boiling, the nodal dynamic model of debris is shown in Figure 6. The model is a one-dimensional heat conduction in a moving boundary slab control volume.Figure 6
Nodal dynamic model of debris.The equations for energy of the crust and the metal can be expanded as follows:Metal wall:(3)dUmdt=qo′′-qwo′′A+dmmdth.Crust:(4)dUxdt=qL′′+qVL-qo′′A+dmxdth.The cavity of 900 MW reactor is dry, and there is no special flow path outside RPV like AP1000. Therefore, when the cavity is flooded, the cooling mechanism should be the pool boiling under the heating of RPV external wall. The failure mechanism should be the soaring of wall temperature caused by boiling crisis. In the thermal hydraulic models of MAAP4, the heat flux of pool boilingqwo′′ is calculated by the difference between wall temperature and saturation temperature as follows:(5)qwo′′=hΔT.The boiling coefficienth is a function of temperature and pressure. In the thermal hydraulic models of MAAP4, the boiling heat transfer coefficients are calculated by different correlations for various boiling regimes, including the nucleate boiling, transition boiling, and film boiling. MAAP4 code has also been used in the existing publications [12, 13] to simulate the pool boiling in reactor cavity, and the predicted results by MAAP4 code are reasonable. According to the above analysis, the model is applicable to simulating cavity boiling of the 900 MW reactor.


### 2.2. Steady-State Calculation

Before simulating an ESBO, this research selects the key parameters of the primary system and the containment for steady-state calibration. The calculation time is 2000 s. The results of the steady-state simulation are presented in Table1. All the steady-state parameters are in good agreement with operating conditions (relative errors less than 2%). The subsequent accident scenarios described in this research are all based on this steady-state as the initial condition.Table 1
Key parameters under the steady-state for comparison.
Parameter
Unit
Plant design value
Steady state calculation
Rated thermal power
MW
2895.0
2895.0
Hot leg average water temperature
K
599.75
600.01
Pressure of primary system
MPa
15.5
15.4
Containment pressure
MPa
0.101
0.102
Initial UO2 mass in core
ton
82.11
82.11
Initial Zr mass in core
ton
18.21
18.21


## 2.1. Analysis Method and Plant Model

Models of the reactor and containment are built by the modular severe accident analysis code MAAP4. This code can sufficiently simulate the entire spectrum of various severe accidents on a system-wide level. The computational accuracy is enough to deal with the coupled behaviors of the facility and complex phenomena of the accident.(
1
) The model of the 900 MW plant consists of a reactor, three coolant circuits, and a large dry containment. The detailed nodalization is illustrated in Figure 1. Three safety valves are installed on the top of the pressurizer, which can be deployed either automatically or manually according to the trigger limit. Three accumulators (ACCs) are also modeled to provide passive water injection.Figure 1
Primary system nodalization.(
2
) The core and lower head are divided into concentric radial rings and axial levels, as shown in Figure 2. Since the in-vessel retention stage is an emphasis of this research, the lower head of the RPV is further divided into five radial rings with five axial levels on the symmetrical hemisphere. The power of the reactor decay heat is calculated by the standard ANSI equation, which is a function of fuel enrichment and shutdown time.Figure 2
Nodalization of the core and lower head.Consider an accident state in which molten core debris slumps into the lower head. Molten debris with internal heat will form a circulation pattern, as shown in Figure3. Based on the experimentally determined values from Jahn and Reineke [15], the average heat flux of the molten pool for upward (u), downward (d), and sideward (s) circulation can be expressed as shown in Figure 3.(1)qu=0.345kpxΔTR1pRa0.233.qd=0.54kpxΔTR1pRa0.18z1pR1p0.26qs=0.85kpxΔTR1pRa0.19Figure 3
Arrangement of the molten pool in the lower head.The Rayleigh number of a developing molten pool was defined by the maximum height as(2)Ra=gβqυR1p5αυkpx.(
3
) The structure of the large dry containment is provided in Figure 4. When an SBO occurs, water is injected from the bottom to flood the cavity and cool the vessel. The volume of the cavity is shown in Figure 5. The steam and water released from the PSVs are directed to the lower compartment atmosphere (volume 2) and then pressurize the entire containment.Figure 4
Containment structure.Figure 5
Cavity nodalization.(
4
) In coupling calculation of the cavity boiling, the nodal dynamic model of debris is shown in Figure 6. The model is a one-dimensional heat conduction in a moving boundary slab control volume.Figure 6
Nodal dynamic model of debris.The equations for energy of the crust and the metal can be expanded as follows:Metal wall:(3)dUmdt=qo′′-qwo′′A+dmmdth.Crust:(4)dUxdt=qL′′+qVL-qo′′A+dmxdth.The cavity of 900 MW reactor is dry, and there is no special flow path outside RPV like AP1000. Therefore, when the cavity is flooded, the cooling mechanism should be the pool boiling under the heating of RPV external wall. The failure mechanism should be the soaring of wall temperature caused by boiling crisis. In the thermal hydraulic models of MAAP4, the heat flux of pool boilingqwo′′ is calculated by the difference between wall temperature and saturation temperature as follows:(5)qwo′′=hΔT.The boiling coefficienth is a function of temperature and pressure. In the thermal hydraulic models of MAAP4, the boiling heat transfer coefficients are calculated by different correlations for various boiling regimes, including the nucleate boiling, transition boiling, and film boiling. MAAP4 code has also been used in the existing publications [12, 13] to simulate the pool boiling in reactor cavity, and the predicted results by MAAP4 code are reasonable. According to the above analysis, the model is applicable to simulating cavity boiling of the 900 MW reactor.


## 2.2. Steady-State Calculation

Before simulating an ESBO, this research selects the key parameters of the primary system and the containment for steady-state calibration. The calculation time is 2000 s. The results of the steady-state simulation are presented in Table1. All the steady-state parameters are in good agreement with operating conditions (relative errors less than 2%). The subsequent accident scenarios described in this research are all based on this steady-state as the initial condition.Table 1
Key parameters under the steady-state for comparison.
Parameter
Unit
Plant design value
Steady state calculation
Rated thermal power
MW
2895.0
2895.0
Hot leg average water temperature
K
599.75
600.01
Pressure of primary system
MPa
15.5
15.4
Containment pressure
MPa
0.101
0.102
Initial UO2 mass in core
ton
82.11
82.11
Initial Zr mass in core
ton
18.21
18.21


## 3. Accident Description and Sequences Condition

### 3.1. Description of an ESBO

An ESBO is a beyond design-basis accident (BDBA) that is most often caused by multiple failures. For example, the plant system loses all on-site and off-site electric power during an extreme natural disaster. In addition, most of the engineered safeguards are not operable. This study conservatively assumes that external electric power is not recovered for at least 72 h.Generally speaking, an SBO is usually identified as a high-pressure accident. However, a new mechanism has recently been developed that has changed our understanding. In high-pressure conditions, after the core is uncovered, if the primary system is equipped with U-tube SGs, high-temperature steam between the upper plenum of the reactor and the inlet plenum of the SG will form a natural circulation [16]. The steam may cause a creep rupture on hot leg, pressurizer surge line, or SG tube before RPV failure. The primary system is then depressurized passively by the rupture. Passive depressurization may help prevent HPME, but the size and location of the creep rupture remain uncertain variables during the actual accidents. Therefore, this mechanism of steam circulation should be considered as an uncertain phenomenon instead of an accident management strategy.


### 3.2. Sequences Assumption

Considering the uncertainties associated with steam circulation described above, the base sequence for the present work is an ESBO with no operator action and a creep rupture occurs on the hot leg of the RCS. Then diverse cases with different assumptions for intentional depressurization and cavity flooding are compared. The starting times of depressurization and water injection are adjusted as the key factors to simulate the consequences of an accident. The detailed sequences are described as follows:(1)
Effect of intentional depressurization
Case 1.1: no operationCase 1.2: early depressurization, when SG is dryCase 1.3: late depressurization when the exit temperature of the core exceeds 922 K(2)
Effect of cavity flooding
Case 2.1: no injectionCase 2.2: early injection when the exit temperature of the core exceeds 922 KCase 2.3: late injection, delay of 5000 s later than in Case 2.2(3)
Effect of terminating injection
Case 3.1: continuously injecting the cavityCase 3.2: early termination, stopping the injection at 50,000 sCase 3.3: late termination, stopping the injection at 100,000 sThe cases in the first group consider the effects of intentional depressurization. The schemes of RCS depressurization can be divided into two types [2]: early depressurization and late depressurization. Early depressurization requires an operator to open the PSVs when the SG dries up. Late depressurization describes the initiation of depressurization when the exit temperature of the core exceeds 922 K. This scheme is referred to the present work. The times at which PSVs are opened are considered for early depressurization and late depressurization as in Case 1.2 and Case 1.3, respectively. The base sequence is set as Case 1.1: an SBO without any operator action and a passive depressurization caused by a 0.0005-m2 creep rupture on the hot leg. The only safeguard that can be launched during depressurization is the passive ACCs.The cases in the second group consider the effects associated with the timing of the water injection. According to the SAMGs [17] for AP1000, the cavity flooding should be initiated when the core exit temperature exceeds 922 K. When an SBO occurs in a second-generation PWR, the feasible solution for injecting water into the cavity is taking water from the fire pool with mobile fire pumps. The early injection in Case 2.2 is set as a full flow rate (86 kg/s) when the temperature in the core exit exceeds 922 K. After two hours, the flow rate is adjusted to 8 kg/s to maintain flooding and save water for a longer continuous injection. Considering that the external water may not be delivered on time in an extreme situation, the late injection in Case 2.3 is set at a 5000-s delay. The flow regulation of the water injection is the same as in Case 2.2. Because the primary system has to be depressurized (a precondition for cavity flooding), the PSVs in Case 2.1, Case 2.2, and Case 2.3 are similar to the assumption in Case 1.2, expected to open when the core exit temperature exceeds 922 K. Case 2.1 is set as the base sequence without external water injection.The cases in the third group consider the effects of continuous injection and terminating the injection. The continuous generation of steam pressurizes the containment since the containment spray is disabled in an SBO. Thus, a new method of terminating the injection by stopping the fire pumps is proposed to balance this conflict. Under the same premise as inCase 2.2, Case 3.2 is set as early termination to stop the water injection at 50,000 s after an SBO occurs. Case 3.3 is set as late termination at 100,000 s. Case 3.1 is set as the base sequence with the continuous injection. After terminating the injection, the condensed water that reflows from the containment is expected to maintain the flooding of the cavity.


## 3.1. Description of an ESBO

An ESBO is a beyond design-basis accident (BDBA) that is most often caused by multiple failures. For example, the plant system loses all on-site and off-site electric power during an extreme natural disaster. In addition, most of the engineered safeguards are not operable. This study conservatively assumes that external electric power is not recovered for at least 72 h.Generally speaking, an SBO is usually identified as a high-pressure accident. However, a new mechanism has recently been developed that has changed our understanding. In high-pressure conditions, after the core is uncovered, if the primary system is equipped with U-tube SGs, high-temperature steam between the upper plenum of the reactor and the inlet plenum of the SG will form a natural circulation [16]. The steam may cause a creep rupture on hot leg, pressurizer surge line, or SG tube before RPV failure. The primary system is then depressurized passively by the rupture. Passive depressurization may help prevent HPME, but the size and location of the creep rupture remain uncertain variables during the actual accidents. Therefore, this mechanism of steam circulation should be considered as an uncertain phenomenon instead of an accident management strategy.


## 3.2. Sequences Assumption

Considering the uncertainties associated with steam circulation described above, the base sequence for the present work is an ESBO with no operator action and a creep rupture occurs on the hot leg of the RCS. Then diverse cases with different assumptions for intentional depressurization and cavity flooding are compared. The starting times of depressurization and water injection are adjusted as the key factors to simulate the consequences of an accident. The detailed sequences are described as follows:(1)
Effect of intentional depressurization
Case 1.1: no operationCase 1.2: early depressurization, when SG is dryCase 1.3: late depressurization when the exit temperature of the core exceeds 922 K(2)
Effect of cavity flooding
Case 2.1: no injectionCase 2.2: early injection when the exit temperature of the core exceeds 922 KCase 2.3: late injection, delay of 5000 s later than in Case 2.2(3)
Effect of terminating injection
Case 3.1: continuously injecting the cavityCase 3.2: early termination, stopping the injection at 50,000 sCase 3.3: late termination, stopping the injection at 100,000 sThe cases in the first group consider the effects of intentional depressurization. The schemes of RCS depressurization can be divided into two types [2]: early depressurization and late depressurization. Early depressurization requires an operator to open the PSVs when the SG dries up. Late depressurization describes the initiation of depressurization when the exit temperature of the core exceeds 922 K. This scheme is referred to the present work. The times at which PSVs are opened are considered for early depressurization and late depressurization as in Case 1.2 and Case 1.3, respectively. The base sequence is set as Case 1.1: an SBO without any operator action and a passive depressurization caused by a 0.0005-m2 creep rupture on the hot leg. The only safeguard that can be launched during depressurization is the passive ACCs.The cases in the second group consider the effects associated with the timing of the water injection. According to the SAMGs [17] for AP1000, the cavity flooding should be initiated when the core exit temperature exceeds 922 K. When an SBO occurs in a second-generation PWR, the feasible solution for injecting water into the cavity is taking water from the fire pool with mobile fire pumps. The early injection in Case 2.2 is set as a full flow rate (86 kg/s) when the temperature in the core exit exceeds 922 K. After two hours, the flow rate is adjusted to 8 kg/s to maintain flooding and save water for a longer continuous injection. Considering that the external water may not be delivered on time in an extreme situation, the late injection in Case 2.3 is set at a 5000-s delay. The flow regulation of the water injection is the same as in Case 2.2. Because the primary system has to be depressurized (a precondition for cavity flooding), the PSVs in Case 2.1, Case 2.2, and Case 2.3 are similar to the assumption in Case 1.2, expected to open when the core exit temperature exceeds 922 K. Case 2.1 is set as the base sequence without external water injection.The cases in the third group consider the effects of continuous injection and terminating the injection. The continuous generation of steam pressurizes the containment since the containment spray is disabled in an SBO. Thus, a new method of terminating the injection by stopping the fire pumps is proposed to balance this conflict. Under the same premise as inCase 2.2, Case 3.2 is set as early termination to stop the water injection at 50,000 s after an SBO occurs. Case 3.3 is set as late termination at 100,000 s. Case 3.1 is set as the base sequence with the continuous injection. After terminating the injection, the condensed water that reflows from the containment is expected to maintain the flooding of the cavity.


## 4. Results and Discussion

### 4.1. Effect of Intentional Depressurization

This section analyzes the separate effects on depressurizing the RCS by opening the PSVs. The resulting sequences of these cases are presented in Table2.Table 2
Sequences of the scenario cases in seconds.
Analysis purpose
Effect of intentional depressurization
Effect of cavity flooding
Effect of injection termination
Scenario ID
Case 1.1
Case 1.2
Case 1.3
Case 2.1
Case 2.2
Case 2.3
Case 3.1
Case 3.2
Case3.3
Event description
No operation
Early opening of valves
Delayed opening of valves
No injection
Early injection of the cavity
Delayed injection of the cavity
Continuous injection
Early termination of the injection
Late termination of the injection
Opening safety valves
--
6248 s/SG dry
9790 s/Core exit 922 K
9790 s
9790 s
9790 s
9790 s
9790 s
9790 s
Accumulator delivery
16,193 s
7803 s
10,486 s
10,486 s
10,483 s
10,486 s
10,483 s
10,483 s
10,483 s
Accumulator depleted
16,219 s
19,645 s
23,131 s
23,131 s
22,729 s
22,786 s
22,729 s
22,729 s
22,729 s
Relocation
14,527 s
25,877 s
28,617 s
28,617 s
26,196 s
27,936 s
26,196 s
26,196 s
26,196 s
Cavity injection
--
--
--
--
9790 s/Core exit 922 K
14,790 s/Delay 5,000 s
9790 s/Core exit 922 K
9790 s
9790 s
Terminating injection
--
--
--
--
Continuous injection
Continuous injection
Continuous injection
50,000 s
100,000 s
RV failure
16,182 s
29,583 s
34,562 s
34,562 s
N/A
N/A
N/A
88,926 s
N/A
Containment failure
137,191 s
N/A
N/A
N/A
158,231 s
185,485 s
158,231 s
N/A
N/A
N/A: no failure for 72 hours (259,200 s).The ESBO sequence without any operator intervention is calculated inCase 1.1. The decay power causes pressurization of the primary system (Figure 7(a)). Then the PSVs begin cyclically opening around the limit to maintain a high pressure of the primary system. In addition, the coolant of the primary system is quickly lost (Figure 7(b)). Until the core is uncovered, cladding begins to oxidize, accelerating the rate of increase in core temperature (Figure 7(c)). The natural circulation of steam finally causes a creep rupture on the hot leg at 11,433 s, even before the exit temperature of the core reaching 922 K. The hydraulic area of this rupture is set as 0.0005 m2 to simulate a small break loss of coolant accident scenario. The small break slowly depressurizes the primary system, and, thus, the ACCs cannot be launched. The core degrades quickly, and then the corium melts through the lower support plate to relocate into the lower head (Figure 7(d)). Later, at 16,182 s, the RPV fails. Because of the high RCS pressure throughout the entire process of degradation, HPME occurs. Consequently, the pressure in the containment briefly peaks (Figure 7(f)). Meanwhile, RPV failure abruptly depressurizes the primary system to activate the ACCs, but the cooling water flows into the cavity through the location of the failure and vaporizes quickly (Figure 7(g)). Subsequent containment pressurization has two main causes. The first cause is the noncondensable gas and steam that comes from MCCI (Figure 7(e)), in which hydrogen is generated (Figure 7(h)). The second cause is the heating of residual water by granulated debris in other compartments of the containment, which causes additional vaporization.Figure 7
Effect of intentional depressurization timing.
(a)
Pressure of the primary system
(b)
Water level of the primary system
(c)
Temperature of core exit
(d)
Corium in the lower head
(e)
Corium in containment
(f)
Containment pressure
(g)
Water level of the cavity
(h)
Hydrogen in containmentInCase 1.2 and Case 1.3, the primary system is depressurized to launch ACCs before the corium relocation (Figure 7(a)). Thus, the water is injected into the core to significantly alleviate degradation. As illustrated in Figure 7(c), the peak temperature of the core exit is obviously lower than in Case 1.1. The quantity of water in the primary system remains low for longer until the ACCs are depleted (Figure 7(b)). Although the RPV inevitably fails in the end, the timing of the failure is significantly delayed to 29,583 s and 34,562 s. In addition, the RCS maintains a low-pressure condition to prevent HPME. Only MCCI contributes to the later pressurization of the containment. The growth of pressure in the containment in both cases is obviously slower than in Case 1.1, and the containment still maintains its integrity for 72 hours (Figure 7(f)).Furthermore, in the two cases of low-pressure degradation, the relative concentration of hydrogen, which is mixed in steam, is much higher than inCase 1.1. Until the relative concentrations of steam and hydrogen reach the point of combustion, hydrogen burns in containment at 42,102 s and 46,314 s (Figure 7(h)). In the simulation, hydrogen combustion is set to be steady due to the limitation of the models. However, the actual accumulation of hydrogen may cause an explosion to fail the containment before the late overpressure. In the base sequence with passive depressurization, ACC water is injected into the cavity after the RPV fails, which significantly slows MCCI and the release of hydrogen (Figures 7(e) and 7(h)). Meanwhile, although the HPME increases the amount of steam in the containment, thereby accelerating overpressure, the hydrogen is also maintained in an inert atmosphere, which prevents combustion.As the analysis above indicates, intentional depressurization has the positive effect of preventing HPME and delaying RPV failure. Opening PSVs before the corium relocation contributes to the timely launching of ACCs and to alleviating the degradation of core. For the large containment in second-generation PWR, the pressurization caused by the discharge of steam is also within the acceptable limit. If the restoration of cyclical safety injection can be predicted, early depressurization helps in reducing the damage done to core components. If the active LPI cannot be recovered, delaying depressurization can avoid depleting the ACC water prematurely and further defer RPV failure. However, late depressurization has the potentially negative effect of causing an uncontrollable creep rupture during the delay time. The uncertainty related to depressurization is the combustion of hydrogen. Although the generation of additional steam during HPME is avoided by depressurization, the risk of combustion also increases, since an inert atmosphere cannot form.


### 4.2. Effect of Cavity Flooding

HPME is avoided by intentional depressurization, but the RPV still inevitably fails after exhausting all ACCs. Therefore, this section considers how continuously injecting the cavity provides a convection cooling outside of the vessel wall. The resulting sequences of these three cases are presented in Table2.For the base sequence inCase 2.1, molten debris relocates to the bottom of the lower head and results in a sharp increase in the temperature of the RPV wall (Figure 8(a)). But the wall temperature at axial node 4, the location of which does not directly contact the debris, is obviously lower (Figure 8(b)). High temperatures finally cause a creep to fail the RPV at the bottom of the lower head (axial node 1). This creep develops relatively quickly, before molten corium becomes stable enough to form a pool (Figures 8(c) and 8(d)). After the RPV fails, MCCI in the cavity become the main reason for the subsequent pressurization of the containment. The entire process is illustrated in Figure 9.Figure 8
Effect of cavity injection timing.
(a)
Temperature of the lower head surface (node 1)
(b)
Temperature of the lower head surface (node 4)
(c)
Mass of the lower crust
(d)
Mass of the metal layer
(e)
Water level of the cavity
(f)
Containment pressure
(g)
Steam in containment
(h)
Hydrogen in containmentFigure 9
RPV failure without cavity flooding.InCase 2.2 and Case 2.3, the cavity is injected and a large amount of internal heat is removed through the surface convection of external water. When the debris relocates into the lower head, the peak temperature of the inner wall is significantly reduced (Figure 8(a)). The failure at the bottom, which is similar to Case 2.1, is avoided. With consecutive relocation of the debris, a stable molten pool of geometric structure gradually forms (Figures 8(c) and 8(d)). The difference of density and the internal convection of the pool create a two-layer structure. A solid crust should form at the interface between the bottom of the corium and the inner wall of the lower head, which can prevent the direct penetration of the RPV, as illustrated in Figure 10. In fact, the current research conservatively recognizes this type of stratification as the most common.Figure 10
The hot focus during the stratification.In the simulation of long-term in-vessel retention, a stable molten pool gradually forms and remains in a state of heat balance (a quasi-steady-state, in fact). According to the theory by Theofanous et al. [18], the critical heat flux (CHF) between the surface of the lower head and the water in the cavity can be a conservative criterion for RPV failure. When the heat flux of the vessel surface is high enough to cause a boiling crisis, the sharp rise in wall temperature causes a creep failure on the RPV. The CHF of the present work is calculated by the transform formula of the analysis code, and the distribution of heat flux on the vessel is associated with the axial angle of the lower head. According to the simulation, the risk of RPV failure in Case 2.2 and Case 2.3 mainly comes from the effect of heat on the metal layer, also called the “focusing effect,” which may subsequently cause a high-temperature creep on the lower head, as indicated in Figure 10. The comparison in Figures 8(a) and 8(b) also indicates that an additional peak occurs in the temperature of the surface wall at the height of the metal layer (axial node 4). In Case 2.3, the molten pool accumulates more sensible heat due to the late injection, thus resulting in a stronger focusing effect during stratification. The higher temperature in Case 2.3 also subsequently melts the bottom crust and the inner wall of the lower head (Figures 8(c) and 8(d)). However, the decay heat of the molten pool is finally removed by continuous cooling from the cavity. The oxide layer is resolidified to form a crust, and the temperature gradually decreases. Thus, the reactor begins trending toward a safer condition.For the responses of the containment inCase 2.2 and Case 2.3, cold water is continuously injected into the cavity to maintain the full water level (Figure 8(e)). Being continuously supplemented with cold water is an effective way of stabilizing the convection boiling. The average temperature of the cavity inlet is maintained at nearly 320 K (Figure 11(a)), which is cool enough to avoid the boiling crisis during the entire process, and the RPV maintains its integrity for 72 h. Hydrogen in the containment is also stable (Figure 8(h)). The subsequent pressure response in the containment is mainly controlled by the steam generated from the vaporization of water in the cavity (Figures 8(f) and 8(g)). Without spraying or venting, the containment fails at 158,231 s and 185,485 s. The internal heat of the pool dissipates less in Case 2.3 than in Case 2.2 due to the late flooding of the cavity; thus, the total amount of steam is less and the overpressure failure is significantly delayed by about 30,000 s. The pressure response in the containment is consistent with the temperature response of molten pool.Figure 11
Effect of injection termination.
(a)
Average temperature of water in the cavity inlet
(b)
Water level of the cavity
(c)
Surface temperature of the lower head (node 4)
(d)
Heat transfer rate through the RV
(e)
Mass of the metal layer
(f)
Containment pressure
(g)
Steam in containment
(h)
Hydrogen in containmentIn summary, the positive effects of cavity injection are to maintain the integrity of the RPV. Therefore, the foundation ablation by MCCI and the subsequent combustion of hydrogen are both avoided, but the negative effect is an increase in steam generation in the containment. Corium stratification and containment pressurization are greatly affected by the timing of water injection. Early injection is conducive to stabilizing the molten pool in a shorter time and the lower head stays in a relatively safe condition with the lower temperature. However, early injection also accelerates the overpressure failure of the containment. Late injection delays the dissipation of internal heat, and, thus, the pool remains unstable for the duration of long-term cooling. Although pressurization of the containment is delayed and the pool finally begins trending toward a steady-state, the RPV faces a greater threat of failure. The risk of RPV failure mainly comes from the focusing effect of the metal layer, which is most intense in the maximum thermal-steady stage during the stratification of the molten pool. Conversely, the risk of containment failure is caused mainly by the accumulation of steam in the later period of long-term cooling. Therefore, with the premise that the molten pool becomes stable and the temperature of the lower head becomes relatively cool, it is possible to mitigate the pressurization of steam by slowing the extraction of heat through the vessel. However, this decision is risky.


### 4.3. New Strategy of Terminating Injection

As the previous section demonstrated, the late overpressure of containment is caused by continuous vaporization in the cavity. Therefore, a new method for terminating the water injection of the cavity, after the molten pool is stable, is considered to limit the maximum amount of steam in the containment. Then a circulating cooling of vaporization and condensation should be established in the containment to retain the cooling of the external vessel and stabilize the pressure. The water supplement in the cavity relies on the backflow of condensate water from other compartments of the containment to keep the RPV submerged. This section analyzes the effects of continuous injection and terminating injection in long-term cooling. The resulting sequences of the three cases are presented in Table2.When water injection is terminated at 50,000 s inCase 3.2, the boiling in the cavity is gradually intensified with continued heating by the molten pool. The average temperature of cavity inlet increases (Figure 11(a)). Meanwhile, the water level in the cavity drops rapidly due to continuous vaporization. Until vaporization and condensation reach a relative balance in the containment, the water level remains constant (Figure 11(b)). Although the decline of the water level reduces the wetted area of the RPV, the intensification of boiling significantly enhances the convection of heat through the surface of the vessel (Figure 11(d)). The backflow of condensate water in the containment is sufficient to keep the lower head submerged after terminating the injection, but the stability of boiling in the cavity is difficult to maintain. When boiling is intensified to the point that the balance between vaporization and condensation is broken, the water level in cavity begins to decline again. At nearly 80,000 s, the surface convection of the lower head reaches a crisis point of boiling, and the wall temperature of the metal layer suddenly soars (Figure 11(c)). This temperature increase also undermines the stability of the molten pool and causes further melting of the inner wall (Figure 11(e)). Then the lower head quickly fails at 88,926 s due to the high-temperature creep located at the height of the metal layer (axial node 4). However, it is worth noting that even though the residual water in the cavity is completely vaporized by the molten debris in a short time, the maximum pressure load of steam does not cause containment overpressure, because water injection has been terminated (Figure 11(f)). The subsequent response of the containment after the RPV failure is mainly controlled by MCCI (Figures 11(g) and 11(h)).Water injection inCase 3.3 is terminated later than in Case 3.2, and, thus, the intensification of cavity boiling also occurs later (Figure 11(a)). The subsequent response of the containment is similar to Case 3.2: vaporization and condensation gradually reach a relative balance (Figure 11(b)). However, the difference is that the intensification of boiling in Case 3.2 is more assuasive than in Case 3.3 because most of the sensible heat in corium is removed by stable convection before the late termination. Thus, the boiling crisis in cavity is prevented and the stratification of molten pool remains relatively steady (Figure 11(e)). The surface convection in cavity is mainly affected by the decline of water level instead of the intensification of boiling, thus the dissipation of heat through the vessel wall decreases slightly more than in Case 3.1 (Figure 11(d)). Therefore, containment pressure is gradually stabilized by the decrease of steam generation, and the integrity of containment is maintained for 72 h (Figure 11(f)). However, the temperature of water in cavity rises slowly in the later period, meaning that the intensification of boiling slowly increases as well (Figure 11(a)). Therefore, the risk of a boiling crisis still exists.In summary, continuously injecting the cavity is important for long-term cooling. In addition to maintaining the maximum submergence of the RPV, continuous injection helps supplement cold water to reduce the average temperature in the cavity. Thus, the development of boiling can be prevented in the crisis. For second-generation PWRs, the cavity is not similar to the AP1000, which contains a special construction to strengthen the heat transfer and to stabilize the two-phase convection. Therefore, when continuous injection is stopped, the uncertainty of boiling in the cavity is the main reason to increase the risk of RPV failure. However, since the condensation in containment is limited after the active spraying is disabled, the positive impacts of terminating injection are slowing the heat dissipation of molten pool and reducing the steam load of containment. Late termination is more conducive to balancing the conflict between the cooling of the vessel and overpressure of the containment. Because late termination staggers the stage of maximum heat load during the stratification of the molten pool, cavity boiling is less intense and the dissipation of internal heat is limited to maintaining the balance of steam generation for longer. Besides, the backflow of condensate water is also sufficient to maintain the RPV submerged. According to the specific calculation results inCase 3.3, the steam temperature at core exit falls below 470 K and the containment pressure exceeding 0.65 MPa can be the criteria for the late termination. However, late termination of cavity injection is still not entirely safe. Although the containment pressure remains relatively stable in the end, the risk of a boiling crisis still exists. In addition, because the late pressure in containment remains high once the RPV fails, the pressurization induced by the vaporization of water in the cavity can be predicted to cause overpressure in containment in a short time.


## 4.1. Effect of Intentional Depressurization

This section analyzes the separate effects on depressurizing the RCS by opening the PSVs. The resulting sequences of these cases are presented in Table2.Table 2
Sequences of the scenario cases in seconds.
Analysis purpose
Effect of intentional depressurization
Effect of cavity flooding
Effect of injection termination
Scenario ID
Case 1.1
Case 1.2
Case 1.3
Case 2.1
Case 2.2
Case 2.3
Case 3.1
Case 3.2
Case3.3
Event description
No operation
Early opening of valves
Delayed opening of valves
No injection
Early injection of the cavity
Delayed injection of the cavity
Continuous injection
Early termination of the injection
Late termination of the injection
Opening safety valves
--
6248 s/SG dry
9790 s/Core exit 922 K
9790 s
9790 s
9790 s
9790 s
9790 s
9790 s
Accumulator delivery
16,193 s
7803 s
10,486 s
10,486 s
10,483 s
10,486 s
10,483 s
10,483 s
10,483 s
Accumulator depleted
16,219 s
19,645 s
23,131 s
23,131 s
22,729 s
22,786 s
22,729 s
22,729 s
22,729 s
Relocation
14,527 s
25,877 s
28,617 s
28,617 s
26,196 s
27,936 s
26,196 s
26,196 s
26,196 s
Cavity injection
--
--
--
--
9790 s/Core exit 922 K
14,790 s/Delay 5,000 s
9790 s/Core exit 922 K
9790 s
9790 s
Terminating injection
--
--
--
--
Continuous injection
Continuous injection
Continuous injection
50,000 s
100,000 s
RV failure
16,182 s
29,583 s
34,562 s
34,562 s
N/A
N/A
N/A
88,926 s
N/A
Containment failure
137,191 s
N/A
N/A
N/A
158,231 s
185,485 s
158,231 s
N/A
N/A
N/A: no failure for 72 hours (259,200 s).The ESBO sequence without any operator intervention is calculated inCase 1.1. The decay power causes pressurization of the primary system (Figure 7(a)). Then the PSVs begin cyclically opening around the limit to maintain a high pressure of the primary system. In addition, the coolant of the primary system is quickly lost (Figure 7(b)). Until the core is uncovered, cladding begins to oxidize, accelerating the rate of increase in core temperature (Figure 7(c)). The natural circulation of steam finally causes a creep rupture on the hot leg at 11,433 s, even before the exit temperature of the core reaching 922 K. The hydraulic area of this rupture is set as 0.0005 m2 to simulate a small break loss of coolant accident scenario. The small break slowly depressurizes the primary system, and, thus, the ACCs cannot be launched. The core degrades quickly, and then the corium melts through the lower support plate to relocate into the lower head (Figure 7(d)). Later, at 16,182 s, the RPV fails. Because of the high RCS pressure throughout the entire process of degradation, HPME occurs. Consequently, the pressure in the containment briefly peaks (Figure 7(f)). Meanwhile, RPV failure abruptly depressurizes the primary system to activate the ACCs, but the cooling water flows into the cavity through the location of the failure and vaporizes quickly (Figure 7(g)). Subsequent containment pressurization has two main causes. The first cause is the noncondensable gas and steam that comes from MCCI (Figure 7(e)), in which hydrogen is generated (Figure 7(h)). The second cause is the heating of residual water by granulated debris in other compartments of the containment, which causes additional vaporization.Figure 7
Effect of intentional depressurization timing.
(a)
Pressure of the primary system
(b)
Water level of the primary system
(c)
Temperature of core exit
(d)
Corium in the lower head
(e)
Corium in containment
(f)
Containment pressure
(g)
Water level of the cavity
(h)
Hydrogen in containmentInCase 1.2 and Case 1.3, the primary system is depressurized to launch ACCs before the corium relocation (Figure 7(a)). Thus, the water is injected into the core to significantly alleviate degradation. As illustrated in Figure 7(c), the peak temperature of the core exit is obviously lower than in Case 1.1. The quantity of water in the primary system remains low for longer until the ACCs are depleted (Figure 7(b)). Although the RPV inevitably fails in the end, the timing of the failure is significantly delayed to 29,583 s and 34,562 s. In addition, the RCS maintains a low-pressure condition to prevent HPME. Only MCCI contributes to the later pressurization of the containment. The growth of pressure in the containment in both cases is obviously slower than in Case 1.1, and the containment still maintains its integrity for 72 hours (Figure 7(f)).Furthermore, in the two cases of low-pressure degradation, the relative concentration of hydrogen, which is mixed in steam, is much higher than inCase 1.1. Until the relative concentrations of steam and hydrogen reach the point of combustion, hydrogen burns in containment at 42,102 s and 46,314 s (Figure 7(h)). In the simulation, hydrogen combustion is set to be steady due to the limitation of the models. However, the actual accumulation of hydrogen may cause an explosion to fail the containment before the late overpressure. In the base sequence with passive depressurization, ACC water is injected into the cavity after the RPV fails, which significantly slows MCCI and the release of hydrogen (Figures 7(e) and 7(h)). Meanwhile, although the HPME increases the amount of steam in the containment, thereby accelerating overpressure, the hydrogen is also maintained in an inert atmosphere, which prevents combustion.As the analysis above indicates, intentional depressurization has the positive effect of preventing HPME and delaying RPV failure. Opening PSVs before the corium relocation contributes to the timely launching of ACCs and to alleviating the degradation of core. For the large containment in second-generation PWR, the pressurization caused by the discharge of steam is also within the acceptable limit. If the restoration of cyclical safety injection can be predicted, early depressurization helps in reducing the damage done to core components. If the active LPI cannot be recovered, delaying depressurization can avoid depleting the ACC water prematurely and further defer RPV failure. However, late depressurization has the potentially negative effect of causing an uncontrollable creep rupture during the delay time. The uncertainty related to depressurization is the combustion of hydrogen. Although the generation of additional steam during HPME is avoided by depressurization, the risk of combustion also increases, since an inert atmosphere cannot form.


## 4.2. Effect of Cavity Flooding

HPME is avoided by intentional depressurization, but the RPV still inevitably fails after exhausting all ACCs. Therefore, this section considers how continuously injecting the cavity provides a convection cooling outside of the vessel wall. The resulting sequences of these three cases are presented in Table2.For the base sequence inCase 2.1, molten debris relocates to the bottom of the lower head and results in a sharp increase in the temperature of the RPV wall (Figure 8(a)). But the wall temperature at axial node 4, the location of which does not directly contact the debris, is obviously lower (Figure 8(b)). High temperatures finally cause a creep to fail the RPV at the bottom of the lower head (axial node 1). This creep develops relatively quickly, before molten corium becomes stable enough to form a pool (Figures 8(c) and 8(d)). After the RPV fails, MCCI in the cavity become the main reason for the subsequent pressurization of the containment. The entire process is illustrated in Figure 9.Figure 8
Effect of cavity injection timing.
(a)
Temperature of the lower head surface (node 1)
(b)
Temperature of the lower head surface (node 4)
(c)
Mass of the lower crust
(d)
Mass of the metal layer
(e)
Water level of the cavity
(f)
Containment pressure
(g)
Steam in containment
(h)
Hydrogen in containmentFigure 9
RPV failure without cavity flooding.InCase 2.2 and Case 2.3, the cavity is injected and a large amount of internal heat is removed through the surface convection of external water. When the debris relocates into the lower head, the peak temperature of the inner wall is significantly reduced (Figure 8(a)). The failure at the bottom, which is similar to Case 2.1, is avoided. With consecutive relocation of the debris, a stable molten pool of geometric structure gradually forms (Figures 8(c) and 8(d)). The difference of density and the internal convection of the pool create a two-layer structure. A solid crust should form at the interface between the bottom of the corium and the inner wall of the lower head, which can prevent the direct penetration of the RPV, as illustrated in Figure 10. In fact, the current research conservatively recognizes this type of stratification as the most common.Figure 10
The hot focus during the stratification.In the simulation of long-term in-vessel retention, a stable molten pool gradually forms and remains in a state of heat balance (a quasi-steady-state, in fact). According to the theory by Theofanous et al. [18], the critical heat flux (CHF) between the surface of the lower head and the water in the cavity can be a conservative criterion for RPV failure. When the heat flux of the vessel surface is high enough to cause a boiling crisis, the sharp rise in wall temperature causes a creep failure on the RPV. The CHF of the present work is calculated by the transform formula of the analysis code, and the distribution of heat flux on the vessel is associated with the axial angle of the lower head. According to the simulation, the risk of RPV failure in Case 2.2 and Case 2.3 mainly comes from the effect of heat on the metal layer, also called the “focusing effect,” which may subsequently cause a high-temperature creep on the lower head, as indicated in Figure 10. The comparison in Figures 8(a) and 8(b) also indicates that an additional peak occurs in the temperature of the surface wall at the height of the metal layer (axial node 4). In Case 2.3, the molten pool accumulates more sensible heat due to the late injection, thus resulting in a stronger focusing effect during stratification. The higher temperature in Case 2.3 also subsequently melts the bottom crust and the inner wall of the lower head (Figures 8(c) and 8(d)). However, the decay heat of the molten pool is finally removed by continuous cooling from the cavity. The oxide layer is resolidified to form a crust, and the temperature gradually decreases. Thus, the reactor begins trending toward a safer condition.For the responses of the containment inCase 2.2 and Case 2.3, cold water is continuously injected into the cavity to maintain the full water level (Figure 8(e)). Being continuously supplemented with cold water is an effective way of stabilizing the convection boiling. The average temperature of the cavity inlet is maintained at nearly 320 K (Figure 11(a)), which is cool enough to avoid the boiling crisis during the entire process, and the RPV maintains its integrity for 72 h. Hydrogen in the containment is also stable (Figure 8(h)). The subsequent pressure response in the containment is mainly controlled by the steam generated from the vaporization of water in the cavity (Figures 8(f) and 8(g)). Without spraying or venting, the containment fails at 158,231 s and 185,485 s. The internal heat of the pool dissipates less in Case 2.3 than in Case 2.2 due to the late flooding of the cavity; thus, the total amount of steam is less and the overpressure failure is significantly delayed by about 30,000 s. The pressure response in the containment is consistent with the temperature response of molten pool.Figure 11
Effect of injection termination.
(a)
Average temperature of water in the cavity inlet
(b)
Water level of the cavity
(c)
Surface temperature of the lower head (node 4)
(d)
Heat transfer rate through the RV
(e)
Mass of the metal layer
(f)
Containment pressure
(g)
Steam in containment
(h)
Hydrogen in containmentIn summary, the positive effects of cavity injection are to maintain the integrity of the RPV. Therefore, the foundation ablation by MCCI and the subsequent combustion of hydrogen are both avoided, but the negative effect is an increase in steam generation in the containment. Corium stratification and containment pressurization are greatly affected by the timing of water injection. Early injection is conducive to stabilizing the molten pool in a shorter time and the lower head stays in a relatively safe condition with the lower temperature. However, early injection also accelerates the overpressure failure of the containment. Late injection delays the dissipation of internal heat, and, thus, the pool remains unstable for the duration of long-term cooling. Although pressurization of the containment is delayed and the pool finally begins trending toward a steady-state, the RPV faces a greater threat of failure. The risk of RPV failure mainly comes from the focusing effect of the metal layer, which is most intense in the maximum thermal-steady stage during the stratification of the molten pool. Conversely, the risk of containment failure is caused mainly by the accumulation of steam in the later period of long-term cooling. Therefore, with the premise that the molten pool becomes stable and the temperature of the lower head becomes relatively cool, it is possible to mitigate the pressurization of steam by slowing the extraction of heat through the vessel. However, this decision is risky.


## 4.3. New Strategy of Terminating Injection

As the previous section demonstrated, the late overpressure of containment is caused by continuous vaporization in the cavity. Therefore, a new method for terminating the water injection of the cavity, after the molten pool is stable, is considered to limit the maximum amount of steam in the containment. Then a circulating cooling of vaporization and condensation should be established in the containment to retain the cooling of the external vessel and stabilize the pressure. The water supplement in the cavity relies on the backflow of condensate water from other compartments of the containment to keep the RPV submerged. This section analyzes the effects of continuous injection and terminating injection in long-term cooling. The resulting sequences of the three cases are presented in Table2.When water injection is terminated at 50,000 s inCase 3.2, the boiling in the cavity is gradually intensified with continued heating by the molten pool. The average temperature of cavity inlet increases (Figure 11(a)). Meanwhile, the water level in the cavity drops rapidly due to continuous vaporization. Until vaporization and condensation reach a relative balance in the containment, the water level remains constant (Figure 11(b)). Although the decline of the water level reduces the wetted area of the RPV, the intensification of boiling significantly enhances the convection of heat through the surface of the vessel (Figure 11(d)). The backflow of condensate water in the containment is sufficient to keep the lower head submerged after terminating the injection, but the stability of boiling in the cavity is difficult to maintain. When boiling is intensified to the point that the balance between vaporization and condensation is broken, the water level in cavity begins to decline again. At nearly 80,000 s, the surface convection of the lower head reaches a crisis point of boiling, and the wall temperature of the metal layer suddenly soars (Figure 11(c)). This temperature increase also undermines the stability of the molten pool and causes further melting of the inner wall (Figure 11(e)). Then the lower head quickly fails at 88,926 s due to the high-temperature creep located at the height of the metal layer (axial node 4). However, it is worth noting that even though the residual water in the cavity is completely vaporized by the molten debris in a short time, the maximum pressure load of steam does not cause containment overpressure, because water injection has been terminated (Figure 11(f)). The subsequent response of the containment after the RPV failure is mainly controlled by MCCI (Figures 11(g) and 11(h)).Water injection inCase 3.3 is terminated later than in Case 3.2, and, thus, the intensification of cavity boiling also occurs later (Figure 11(a)). The subsequent response of the containment is similar to Case 3.2: vaporization and condensation gradually reach a relative balance (Figure 11(b)). However, the difference is that the intensification of boiling in Case 3.2 is more assuasive than in Case 3.3 because most of the sensible heat in corium is removed by stable convection before the late termination. Thus, the boiling crisis in cavity is prevented and the stratification of molten pool remains relatively steady (Figure 11(e)). The surface convection in cavity is mainly affected by the decline of water level instead of the intensification of boiling, thus the dissipation of heat through the vessel wall decreases slightly more than in Case 3.1 (Figure 11(d)). Therefore, containment pressure is gradually stabilized by the decrease of steam generation, and the integrity of containment is maintained for 72 h (Figure 11(f)). However, the temperature of water in cavity rises slowly in the later period, meaning that the intensification of boiling slowly increases as well (Figure 11(a)). Therefore, the risk of a boiling crisis still exists.In summary, continuously injecting the cavity is important for long-term cooling. In addition to maintaining the maximum submergence of the RPV, continuous injection helps supplement cold water to reduce the average temperature in the cavity. Thus, the development of boiling can be prevented in the crisis. For second-generation PWRs, the cavity is not similar to the AP1000, which contains a special construction to strengthen the heat transfer and to stabilize the two-phase convection. Therefore, when continuous injection is stopped, the uncertainty of boiling in the cavity is the main reason to increase the risk of RPV failure. However, since the condensation in containment is limited after the active spraying is disabled, the positive impacts of terminating injection are slowing the heat dissipation of molten pool and reducing the steam load of containment. Late termination is more conducive to balancing the conflict between the cooling of the vessel and overpressure of the containment. Because late termination staggers the stage of maximum heat load during the stratification of the molten pool, cavity boiling is less intense and the dissipation of internal heat is limited to maintaining the balance of steam generation for longer. Besides, the backflow of condensate water is also sufficient to maintain the RPV submerged. According to the specific calculation results inCase 3.3, the steam temperature at core exit falls below 470 K and the containment pressure exceeding 0.65 MPa can be the criteria for the late termination. However, late termination of cavity injection is still not entirely safe. Although the containment pressure remains relatively stable in the end, the risk of a boiling crisis still exists. In addition, because the late pressure in containment remains high once the RPV fails, the pressurization induced by the vaporization of water in the cavity can be predicted to cause overpressure in containment in a short time.


## 5. Conclusion

In this paper, the severe accident sequences induced by an ESBO are simulated for a 900 MW second-generation PWR. Diverse scenarios with different assumptions for the starting times of intentional depressurization and cavity flooding are also compared to point out their positive and negative impacts for accident mitigation. The uncertainties related to creep rupture, cavity boiling, and steam pressurization are considered in the simulation which aims to propose some pieces of advice to minimize these negative effects. Besides, the limitations of IVR-ERVC caused by the facilities of second-generation PWR are evaluated and a new strategy for terminating cavity injection in late period is proposed. This study can be a reference to improve existing SAMGs.(
1
) The positive impacts of intentional depressurization are the prevention of HPME and the delay of RPV failure. Early depressurization helps launch the ACCs to reduce the damage of core components. However, if it is uncertain whether the LPI can be recovered, delaying depressurization to late period can avoid the premature consumption of ACC water and help further delay RPV failure. The risk after RPV failure mainly comes from hydrogen combustion and steam overpressure.(
2
) The positive impacts of cavity flooding are to retain the integrity of the RPV. The negative impact is that it pressurizes the containment. Corium stratification and steam generation are greatly affected by the timing of water injection. Early water injection is more conducive to removing the inner heat of the molten pool; thus, the lower head remains at a lower temperature. Late injection increases the risk of RPV failure but slows the rate of steam generation and delays containment failure. The risk of RPV failure mainly comes from the focusing effect of the metal layer during the stratification of the molten pool; instead, the risk of containment failure mainly comes from the accumulation of steam in the later period of long-term cooling.(
3
) Considering the facility limitations of second-generation PWRs, continuously injecting the cavity is crucial for stabilizing the convection boiling on the vessel surface. The positive impact of terminating the injection in long-term cooling is that it effectively reduces the steam load in the containment. However, the negative impact is that boiling in the cavity intensifies, breaking the cyclical cooling with the balance of vaporization and condensation. Although late termination can slow the dissipation of internal heat in the cavity and thereby maintain a stable pressure in the containment for longer, the risk of a boiling crisis still exists.



---

*Source: 8680406-2018-02-01.xml*