Validation and Application of a Code for Three-Dimensional Analysis of Hydrogen–Steam Behavior in a Nuclear Reactor Containment during Severe Accidents

Response to Reviewer 1 Comments

1. Summary

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files

Comments 1: Please indicate which correlations (Table 1) were used in current simulations. Why?

Response 1: Thank you for pointing this out.

The current PAR analysis module contains 7 PAR models. Most of the PAR models are based on the vender-supplied correlations, and only the generic PAR model is based on the diffusion rates of the hydrogen and oxygen species.

Figure 1. PAR models implemented in contain3d code.

For the THAI HR2 benchmark simulation, the AREVA-correlation based model (hear areva model) was used. The NIS-correlation in table 1 was used for the THAI HR14 benchmark simulation. SPARC S8 and SP9 tests and APR1400 simulations were conducted by using the KNT PAR correlation-based model (knt model in the figure).

Figure 8 and 10 captions were changed as follows:

Figure 8. Hydrogen mass remaining in the test vessel and recombination rate of: (a) The HR2 test simulation with the AREVA correlation; (b) The HR14 test simulation with the NIS correlation.

Figure 10. Hydrogen mass remaining in the test vessel and recombination rate of: (a) The SPARC SP8 test; (b) The SP9 test simulation with the KNT correlation.

Comments 2: Please indicate the CFD results were mesh independent.

Response 2: Thank you for pointing this out

Normal mesh dependency tests were conducted for validation and accident analysis cases. The following figures and sentences are added in the manuscript for simple description of the mesh dependency test.

A computational mesh for the APR1400 containment was generated using snappyHexMesh which is an automatic mesh generator included in OpenFOAM. The numerical solution may be dependent on the mesh characteristics used, among which the number of cells, mesh skewness, and mesh topology were considered in the study. To evaluate the mesh dependency of the numerical solutions, three meshes were constructed. Figure 12 shows the three meshes tested for solution's mesh dependency. The meshes in Figure 12 (a) and (c) are generated based on a hexahedral background grid and consist of 680,000 and 1,150,000 cells, respectively. As can be expected, the containment outer wall is cylindrical. A cylindrical mesh can be an option. The mesh in Figure 12 (b) is generated based on a cylindrical background grid. This mesh is the coarsest among them because a 0.3 m annular gap between the containment wall and operating deck is easily resolved in the cylindrical background grid. A simple hydrogen injection and PAR recombination test was conducted to check the mesh dependency of the solution. In this study, mesh dependency was evaluated based on the hydrogen mass remaining in the containment at 1000 seconds. The difference among the meshes is less than 0.1%. So, Mesh-A was chosen for the accident analysis because it gives the fastest running time among the three meshes due to its smaller number of cells and better skewness.

1. (b) (c)

Figure 12. Computational mesh for the APR1400 containment: (a) Mesh-A with 680,000 cells using a hexahedral background grid; (b) Mesh-B with 540,000 cells using a cylindrical background mesh; (c) Mesh-C with 1,150,000 cells using a hexahedral background mesh.

Comments 3: If posssible, please compare the results of APR1400 to the safety analysis report.

Response 3: Thank you for pointing this out

As mentioned in response 4, the MELCOR PAR model requires PAR startup time for each PAR. If it is set to 0, the remaining hydrogen mass in the APR1400 containment over time is much smaller than the results of CFD simulation. It means that the MELCOR results are user dependent.

From a conservative point of view, we think that the comparison of the MELCOR and CFD analysis results is an issue that requires more effort.

Comments 4: How can the CFD models improve 1D lumped models in nuclear reactor system analysis?

Response 4: Thank you for pointing this out.

One of the CFD contributions is about PAR startup time. Current PAR model in the MELCOR code requires startup time.

<MELCOR PAR model>

Recombination rate:

τ = characteristic heat-up time (~1800s)

t0 = time of PAR initiation

t = time after PAR initiation

The biggest factor in the PAR startup time is the time it takes for hydrogen to reach the PAR inlet by convection. It is judged that the reliability of MELCOR analysis can be increased if the hydrogen arrival times according to the installation locations of the PARs are obtained from CFD analysis and assigned to the MELCOR input parameters.

Another contribution of CFD for LP analysis is node/CV construction. From the CFD analysis, it can be understood how the flow in the reactor containment is developed. Then LP nodalization can consider the flow structure to make CVs.

Response to Reviewer 3 Comments

1. Summary

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files

Comments 1: In the introduction: "Generally, it is divided into lumped parameter (LP) and 3-dimensional (3D) code depending on the method of discretizing the volume of the containment." Please check if this statement is sufficient. If yes, please find a reference to support it.

Response 1: Thank you for pointing this out.

As far as we know, the nodalization (similar to mesh generation for CFD) of a lumped-parameter code is conducted by assigning hand-calculated geometric data such as node volumes, node elevations, flow path area, and distance for each node and flow path. On the other hand, CFD mesh generator generates coordinates of cell vertices and cell connectivity.

The CFD code extracts necessary geometric information such as cell volumes and areas from the mesh file.

Currently, some LP codes such as RELAP-3D as GOTHIC contain 3-D modules. But their LP module requires user-specified geometric data.

A comparison of LP and 3-D is described in the reference an IAEA Tecdoc.

To help reader’s understanding, the reference is added.

Generally, it is divided into lumped parameter (LP) and 3-dimensional (3D) code depending on the method of discretizing the volume of the containment [5].

5. IAEA. Developments in the Analysis and Management of Combustible Gases in Severe Accidents in Water Cooled Reactors following the Fukushima Daiichi Accident; IAEA-TECDOC-1939, 2020.

Comments 2: Please find a reference to support this statement: "However, 3D codes can be of great help in assessing the conservativity of LP code analysis results or selecting conservative values for LP code model parameters".

Response 2: Thank you for pointing this out.

In principle, LP code does not calculate gradient-based transport such as thermal diffusion, mass diffusion, and shear transport. So It gives volume averaged or homogeneous solution. In a channel or pipe flow, this approach is very efficient. But it the case of a large open volume such as a reactor containment, LP code predicts well-mixed gas distributions. For the hydrogen safety in a containment, hydrogen stratification or inhomogeneous distribution is very important.

In an accident simulation by a LP code, hydrogen in a containment is easily mixed and quickly arrives at the PAR locations installed in the containment. It is under study how to transfer the hydrogen arrival information to the PAR model in a LP code.

To help reader’s understanding, the following reference is added which describes conservative results in a hydrogen distribution in a containment.

However, 3D codes can be of great help in assessing the conservativity of LP code analysis results or selecting conservative values for LP code model parameters [6].

6. Papini, D.; Andreani, M.; Niceno, B.; Prasser, H.-M.; Steiner, P.; Klugel, J.-U. Simulation of hydrogen distribution in the containment during a severe accident with fast hydrogen-steam release, International topical meeting on nuclear reactor thermal hydraulics, Chicago, USA, August 30 - September 4, 2015.

Comments 3: Please find and replace the citation of CFD tools such as FLUENT, CFX, and STAR-CCM+. Do not use links as references. They should be cited in accessible documents. Furthermore, revise other references originally cited by links.

Response 3: Thank you for pointing this out.

The references you mentioned are modified as follows:

7. ANSYS, Inc. FLUENT User’s Guide, Release 13.0, 2010.

8. ANSYS, Inc. CFX-Solver Theory Guide, Release 12.1, 2009.

9. Siemens Industries Digital Software. Simcenter STAR-CCM+, version 2023, Siemens, 2023.

13. OpenCFD Limited. OpenFOAM: The Open Source CFD Toolbox User Guide version v2312, 2023.

Comments 4: All abbreviations should be explained the first time they are used and not explained again once readers are familiar. For example, FLUENT, CFX, STAR-CD, GASFLOW, GOTHIC, etc.

Response 4: Thank you for pointing this out.

Currently, those names have been used as proper nouns over the past several decades, and no explanation of the abbreviation can be found in any literature. Please understand this.

Comments 5: In the introduction: "..., but no papers have yet been found on its application to actual NPP containment analysis." Please confirm if this statement is correct. I found some papers which examined 3D analysis for the VVER-1000 containment.

Response 5: Thank you for pointing this out.

We know that VVER-1000 containment has been simulated by using GOTHIC, FLUENT et al. So, we added Kanik et al.’s work in the manuscript.

We think it is good to explain that the code developed by Kelm based on OpenFOAM was not applied for real containments yet. Until writing this reply to the comment, we could not find any papers for reactor containment analysis by the Kelm’s code.

We expect that the main reason is a parallelization of the PAR model implemented in the code. But soon the problem will be solved.

Kanik et al. [19] also used GOTHIC to 3-dimensionally simulate hydrogen distribution in the VVER-1000 containment.

19. Kanik, M.E.; Noori-kalkhoran, O.; Fernandez-Cosials, K.; Gei, M. 3D Analysis of Hydrogen Distribution and Its Mitigation Using Passive Autocatalytic Recombiners (PARs) Inside VVER-1000 Containment. Energies 2023, 16, 6612. doi.org/10.3390/en16186612.

Comments 6: Please rewrite the last paragraphs in the introduction to clearly indicate the research gap and the objective of this paper: "The hydrogen recombination rate ... were discussed in this study."

Response 6: Thank you for pointing this out.

The paragraph was change to the following sentences.

In this paper, we introduce the analytic models implemented in the code, with a particular focus on an enhanced PAR model that accounts for the pressure drop across the porous catalyst and the heat transfer between the catalyst body and the exhaust gas. The PAR and wall vapor condensation models are validated through benchmark test simulations. To streamline the time-consuming process of placing multiple PARs in the containment digital geometry model, we developed and applied a Python program to generate the APR1400 mesh. The contain3D code is used to study hydrogen behavior influenced by water vapor condensation and hydrogen recombination by PARs installed in the APR1400 containment [24]. Through these analyses, the hydrogen removal performance of PARs in the containment building is evaluated, along with the assessment of any uneven or stratified distribution of hydrogen.

Comments 7: Please check if Figures 3, 4, 5 need to be cited with reference [19]. Be careful if using the same or similar figures, equations, and tables as the published paper without sufficient citation.

Response 7: Thank you for pointing this out.

The figures 3, 4, 5 has been changed, and the reference was cited

Comments 8: All terms in the equations must be explained.

Response 8: Thank you for pointing this out.

All the variables in the equations listed in Appendix A Nomenclature.

Please check it.

Comments 9: The characteristics of APR1400 design need to be cited to an accessible document since Reference 20 is unavailable.

Response 9: Thank you for pointing this out.

The reference is changed with the followings:

24. KHNP. Status report 83 – Advanced Power Reactor 1400 MWe (APR1400), 2011.

Comments 10: Please check the clarity of this sentence: "What is important in modeling the geometry of a containment building is how detailed the shape is modeled."

Response 10: Thank you for pointing this out.

The sentence is changed as follows:

An important factor when modeling a containment building is the level of detail that can be resolved.

Comments 11: In the conclusion, the most important result of this paper is that this 3D developed code can simulate and compare well with experiments. The authors should focus on the outcomes of this paper and future work.

Response 11: Thank you for pointing this out.

The paper template provided includes a discussion chapter for discussion of issues and future work. Based on the provided template structure, issues regarding the use of 3-D codes, which are the subject of this study, and future work to be done are described in the discussion chapter.

The Conclusion chapter describes important findings as a result of analysis of hydrogen distribution during the accidents of APR1400 using 3-D code.

The model validation and containment applicability of the 3-D code are included in the discussion chapter.

We would like to seek the reviewer's understanding of this structure.