• International Journal of Technology (IJTech)
  • Vol 14, No 4 (2023)

Numerical Study on Relocation Process of Al, Fe, and Pb by Using the Moving Particle Semi-Implicit Method During Severe Accident of Reactor

Numerical Study on Relocation Process of Al, Fe, and Pb by Using the Moving Particle Semi-Implicit Method During Severe Accident of Reactor

Title: Numerical Study on Relocation Process of Al, Fe, and Pb by Using the Moving Particle Semi-Implicit Method During Severe Accident of Reactor
Yacobus Yulianto, Asril Pramutadi Andi Mustari

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Cite this article as:
Yulianto, Y., Mustari, A.P.A., 2023. Numerical Study on Relocation Process of Al, Fe, and Pb by Using the Moving Particle Semi-Implicit Method During Severe Accident of Reactor. International Journal of Technology. Volume 14(4), pp. 800-810

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Yacobus Yulianto Physics Department, Halu Oleo University, Jl. H.E.A. Mokodompit, Kendari 93232, Indonesia
Asril Pramutadi Andi Mustari Physics Department, Bandung Institute of Technology, Jl. Ganesha 10, Bandung 40132, Indonesia
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Abstract
Numerical Study on Relocation Process of Al, Fe, and Pb by Using the Moving Particle Semi-Implicit Method During Severe Accident of Reactor

Reactor safety is one of the essential parts of reactor research, especially to appropriately respond when melts down occurred during a severe accident. In this study, the relocation process of Al, Fe, and Pb was simulated by using the Moving Particle Semi-Implicit method to study the relocation mechanism of the liquids when they experienced an interaction between liquids at high temperatures. It is obtained that, to reach the stratified condition, Pb-Al needs 0.63 seconds, Al-Fe and Al-Pb need 1.14 seconds, and Fe-Al needs more than three seconds. Overall, the results indicate that the difference in viscosity and density between two liquids influences the time to reach the stratified condition. The greater the density difference between two liquids, the faster the stratification process.

Liquid flow; Moving particle semi-implicit; Relocation process; Severe accident of a reactor

Introduction

      Reactor safety is one of the substantial matters that should be concerned in the study of the reactor. The reactor accidents of Three Miles Island, Chernobyl, and Fukushima have warned nuclear researchers to care about the importance of reactor safety. Information about the behavior of some reactor materials (Talaat et al., 2019; Chandran et al., 2018) is very urgent to be provided. The relocation of melting material during a severe accident is an important phenomenon due to its influence on the heat transfer to the lower plenum of the reactor, which may affect the breaching of the reactor.
        Several studies have been conducted regarding the relocation of molten corium. Moreover, stratification during the accident is also important to be understood to predict the failure of the reactor pressure vessel (Li et al., 2013). During a severe accident, the variation of materials may lead to several combinations of interaction between two materials. In the research reactor, Fe-Al interaction may need to be understood since Al is the main material with parts of Fe (Hainoun, Ghazi, and Alhabit, 2019; Farrell, 2012). On the other hand, in the LFR (Lead-cooled Fast Reactor), a study of Pb-Fe interaction in the liquid phase is needed. The reason is that Pb is the main coolant and Fe is the main structural material (Mustari and Takahashi, 2011; Machut et al., 2007), where Al is proposed as the outer layer of structural material (Knebel et al., 2000) in the Accelerator Driven System (ADS). Unfortunately, investigations on these material combinations in the liquid phase are very limited.
        Some experiments about reactor core accidents are complicated or costly to be performed. Although experiments are still principal for some cases, computational simulations (Aliffrananda et al., 2022; Utama et al., 2021) can be an alternative to reduce the complexity or the cost of experiments. On the other hand, the conventional mesh methods face difficulty in explaining several melted core phenomena, i.e. stratification case, free-surface flow, and phase transitions. The Moving Particle Semi-Implicit (MPS) method introduced first by Koshizuka and Oka (1996) is one of the alternative mesh-free methods utilized to simulate the relocation process of some nuclear materials. This method has been applied successfully (Duan, Yamaji, and Sakai, 2022; Masumura, Yamaji, and Furuya 2015; Mustari et al., 2015; Li, Oka, and Furuya, 2014; Kawahara and Oka, 2012) as reviewed by Li et al. (2020).
        While there are many studies analyzing melting interactions between the melted core and solid materials during reactor core melting, there is still limited simulation on the relocation of molten fluids. Studies of the relocation process of some liquids were performed by some researchers, such as Li et al. (2013) with silicon oil and salt water, Ilham et al. (2018) with freshwater, and Hidayati et al. (2021) with cooking oil and freshwater. In this study, the liquids of Al, Fe, and Pb are utilized. The simulation of the relocation process is one of the visible solutions for understanding the phenomena in the reactor accident. Therefore, the study of the relocation process is utterly substantial to be performed for nuclear materials. Due to the lack of study on the materials in the case of a severe accident, where most materials are in the liquid phase, the objective of this study is to simulate the relocation process of some liquids of nuclear materials (Al, Fe, and Pb) and the contact process between two liquids with various temperatures.

Experimental Methods

2.1. Mathematical Model and Numerical Method
      The Moving Particle Semi-Implicit method assumes that a particle only exercises an interaction with a limited number of its nearest particles as shown in Figure 1. To accommodating this assumption, the weight function exists as described well in the paper of Koshizuka and Oka (1996), including the explanation of the particle number density, the gradient, the divergence, and the Laplacian models. All equations in the MPS method follow the mass and the momentum conservation equations as the commonly used governing equations for incompressible flow where (Koshizuka and Oka, 1996).

In the equations above, the density is represented by  the time is represented by t, the velocity vector is represented by  the gradient is represented by  the gravity is represented by the pressure is represented by P, and the kinematic viscosity is represented by  To assist the calculation process, the numerical calculations are proceeded explicitly by using the finite difference method and implicitly by using the Crank-Nicholson method (Koshizuka and Oka, 1996). Here are the references that explained the MPS method clearly, including the algorithm (Li et al., 2020; Kawahara and Oka, 2012; Koshizuka and Oka, 1996).

2.2. Simulation
        In this study, two types of liquids were used, namely, the fallen liquid placed inside the 2D containment and the target liquid placed inside a bottle located 102 mm above the surface of the target liquid. Both liquids are chemically miscible, and it was assumed that the stratification process in thermal-hydraulic is faster than in the chemical process, as supported by references (Mustari et al., 2015; Mustari and Oka, 2014), these liquids can be considered as an immiscible liquid. The temperature, density, and kinematic viscosity of each used liquid can be seen in Table 1. The simulation was performed by using 4139 particles and a similar code of these references (Yulianto et al., 2019; Ilham et al., 2018).

Figure 1 Boundary (a) and initial (b) condition (in mm)

Table 1 The parameters of each liquid (IAEA, 2008)

Component

Tmelting (°C)

Tboiling (°C)

Tsimulation (°C)

Density

(kg m-3)

Kinematic

viscosity (m2 s-1)

Al

660

2,519

1,600

2.084890 × 103

7.382931 × 10-4

1,800

2.022690 × 103

7.083604 × 10-4

2,000

1.960490 × 103

6.846094 × 10-4

Fe

1,538

2,861

1,600

6.977548 × 103

2.050208 × 10-3

1,800

5.115362 × 103

1.784475 × 10-3

2,000

4.930162 × 103

1.591594 × 10-3

Al

660

2,519

1,200

2.209290 × 103

8.295089 × 10-4

1,400

2.147090 × 103

7.771429 × 10-4

1,600

2.084890 × 103

7.382931 × 10-4

Pb

327

1,745

1,200

9.590534 × 103

8.123931 × 10-8

1,400

9.342134 × 103

6.835953 × 10-8

1,600

9.093734 × 103

5.823038 × 10-8

Results and Discussion

3.1. The Relocation Profiles

       The relocation process of Fe-Al can be seen in Figure 2 where all temperatures have a similar pattern, where Fe made a contact with Al, broke through the Al layer, dived, created a layer under the Al layer, and reached the stratified condition. When colliding with the target liquid, Fe could break through Al as presumed that Fe has a greater density than Al. The relocation process of Al-Fe can be seen in Figure 3 where all temperatures have a similarity in its pattern where Al made a contact with Fe, floated above the Fe layer, made a layer in that position, and finally reached the stratified condition. When colliding with the target liquids, Al cannot equalize the buoyancies of Fe. It forces Al to move on top of Fe and create a layer above that liquid. It is because Al has a lower density than Fe. It is presumed that the liquid with greater density needs more effort to break the layer of the target liquid and dives under that layer. In the stratification process, the lower density moves down gradually to form a layer under the higher density. The higher viscous force that dominates the stratification process is expected as the reason for this phenomenon. The collision time and the time to reach the stratified condition for all used temperatures are similar. The collision time was reached in 0.16 seconds and the stratified condition was reached in 1.30 seconds.

       The relocation process of Al-Fe can be seen in Figure 4. The relocation process in this case has a similar pattern to the relocation process of Al-Fe. The time collision and the time to reach the stratified condition are similar to those of Al-Fe, except for the collision time at 1,400°C where Al-Pb reached it in 0.17 seconds. The relocation process of Al-Fe can be seen in Figure 5 where Pb collided with Al in 0.13 seconds and made splashes that reached up to the height of the containment. These splashes were gone out at 0.37 seconds. After that, Pb formed gradually a layer below Al and commenced the stratification process at 0.37 seconds. The stratified condition of Pb-Al is achieved at about a second for all temperatures. These obtained results are similar to the cases of Pb-Al although the temperature was different.
        From those results above, compared to Al and Fe, Pb left the bottle and reached the surface of the target liquid in the fastest time among the used combinations. It results because, still as the presumption, the density of Pb is the greatest among them. Besides, the kinematic viscosity of Pb is the smallest among them. It makes Pb flow out of the bottle container easily. However, it still needs further study for verification. Next, the focus is targeted at the collision between liquids. In this study, the relocation process without splashes has been found in the cases of Fe-Al, Al-Fe, and Al-Pb. The relocation process with splashes has been found in the Pb-Al. When Pb-Al was run, the splashes were obtained. When switching to Al-Pb, the splashes were not obtained. It means that the splash will arise if the fallen liquid has a higher density when the difference in density between the two is great enough. The time duration was counted as follows. The timing of collision started when the two liquids made direct contact. Both liquids are considered to reach the stratified state if two layers have formed along the length of the container. The summary of time, for all cases, is performed in Figure 6 where at 2,000°C, to make a contact and to reach the stratified condition, Al has the fastest time among the other temperatures.


Figure 2 Relocation process of Fe-Al