Transient thermal analysis for optimal armor material in upgraded mockup for PST using MOOSE Framework
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Habib Ur Rahman
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Shahab Ud-Din Khan
Abstract
The divertor mockup design for the Pakistan Spherical Tokamak (PST) needs several improvements. These include reducing the total number of upper and lower divertors to 32 and enhancing the heat load capacity to 1 MW/m2. This study involves a thermal analysis of the upgraded divertor design for PST through simulation using MOOSE Framework. The simulation involves two steps – validation and thermal analysis. Validation is achieved by modeling 1D and 2D conduction problems in MOOSE Framework and comparing the results with the analytical solutions. The thermal analysis of a mockup of the upgraded PST divertor configurations with tungsten and graphite as armor materials under peak thermal heat load conditions of 1 MW/m2 is performed. The results of the transient thermal analysis reveal that the mockup surface temperature rise for tungsten remains lower than that for graphite. The findings of the study indicate that both tungsten and graphite mockups can sustain a specific heat flux of 1 MW/m2 for up to 3 s. However, even being a good conductor of heat, tungsten’s high atomic number (Z) poses challenges in plasma stability. On the other hand, graphite when paired with an efficient cooling system for controlling surface temperature rise is a superior armor material due to its affordability, ease of availability, and better compatibility with plasma environments. It is recommended as the preferred armor material for the upgraded divertor mockup in the PST system.
Acknowledgments
The authors acknowledge the support extended by the Pakistan Tokamak Plasma Research Institute (PTPRI) in conducting this research work. The computational resources provided by the Pakistan Institute of Engineering and Applied Sciences (PIEAS) are highly appreciated.
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Research ethics: The authors are strong advocates of the research ethics.
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Informed consent: Informed consent was obtained from all individuals included in this study.
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Author contributions: All authors have contributed to this research work. They accept the responsibility for the entire content of this manuscript and have approved its submission.
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Use of Large Language Models, AI and Machine Learning Tools: None declared.
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Conflict of interest: The authors have no conflict of interest with the editors and reviewers.
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Research funding: None declared.
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Data availability: Not applicable.
References
Alam, A., Khan, S.U.D., Abdullah, M., Khan, R., Ilyas, M., Chaudri, K.S., Ali, A., Shakir, S., Rehman, Z.U., Zahid, S., et al.. (2023). Optimization of divertor design for Pakistan spherical tokamak. Kerntechnik 88: 437–445, https://doi.org/10.1515/kern-2022-0105.Search in Google Scholar
Bamber, R., Iglesias, D., Asunta, O., Bunting, P., Daughtry, S., Dunbar, G., Hanks, S., Horozaniecki, A., Moore, P., Lockley, D., et al.. (2021). The ST40 IVC1 divertor project: procurement and installation in times of COVID-19. Fusion Eng. Des. 168: 112378, https://doi.org/10.1016/j.fusengdes.2021.112378.Search in Google Scholar
Chen, X., Du, P., Tian, R., Li, Z., Lian, H., Zhuang, K., and Wang, S. (2023). Study on heat transfer characteristics and structural parameter effects of heat pipe with fins based on MOOSE platform. Nucl. Eng. Technol. 55: 364–372, https://doi.org/10.1016/j.net.2022.09.022.Search in Google Scholar
De Monte, F. (2000). Transient heat conduction in one-dimensional composite slab. A ‘natural’ analytic approach. Int. J. Heat Mass Transfer 43: 3607–3619, https://doi.org/10.1016/S0017-9310(00)00008-9.Search in Google Scholar
De Monte, F. (2003). Unsteady heat conduction in two-dimensional two slab-shaped regions. Exact closed-form solution and results. Int. J. Heat Mass Transfer 46: 1455–1469, https://doi.org/10.1016/S0017-9310(02)00417-9.Search in Google Scholar
Fedrigucci, A., Marzari, N., and Ricci, P. (2024). Comprehensive screening of plasma-facing Materials for nuclear fusion. PRX Energy 3: 043002(1)–043002(44), https://doi.org/10.48550/arXiv.2407.00858.Search in Google Scholar
Gaston, D., Newman, C., Hansen, G., and Lebrun-Grandié, D. (2009). MOOSE: a parallel computational framework for coupled systems of nonlinear equations. Nucl. Eng. Des. 239: 1768–1778, https://doi.org/10.1016/j.nucengdes.2009.05.021.Search in Google Scholar
Gaston, D.R., Permann, C.J., Peterson, J.W., Slaughter, A.E., Andrš, D., Wang, Y., Short, M.P., Perez, D.M., Tonks, M.R., Ortensi, J., et al.. (2015). Physics-based multiscale coupling for full core nuclear reactor simulation. Ann. Nucl. Energy 84: 45–54, https://doi.org/10.1016/j.anucene.2014.09.060.Search in Google Scholar
Khan, S.U.-D., Danish, S.N., Haider, S., and Khan, S.U.-D. (2015). Theoretical calculation simulation studies of ABV nuclear reactor coupled with desalination system: coupled nuclear reactor and desalination system analysis. Int. J. Energy Res. 39: 1554–1563, https://doi.org/10.1002/er.3363.Search in Google Scholar
Khan, S.U.-D., Wang, J., Song, Y., Khan, S.U.-D., Rana, U.A., and Khan, R. (2018). Steady state and transient analysis of novel design helium cooled ceramic blanket (HCCB) system of China fusion engineering test reactor (CFETR). J. Fusion Energy 37: 308–316, https://doi.org/10.1007/s10894-018-0191-0.Search in Google Scholar
Khan, S.U.-D., Khan, S.U.-D., Alaswad, S.O., Song, Y., Hussain, S., and Khan, R. (2020). Impurity transport and halo current effects on tungsten divertor system. J. Radiat. Res. Appl. Sci. 13: 309–317, https://doi.org/10.1080/16878507.2020.1738090.Search in Google Scholar
Hansel, J., Andrs, D., Charlot, L., and Giudicelli, G. (2024). The MOOSE thermal hydraulics module. J. Open Source Software 9: 6146(1)–6146(6), https://doi.org/10.21105/joss.06146.Search in Google Scholar
Khan, S.U.-D., Abdullah, M., Ali, A., Khan, R., Shakir, S., Rehman, Z.U., Zahid, S., and Ali, R. (2023). Determination of limiter design and material composition of MT-II spherical tokamak. Kerntechnik 88: 54–62, https://doi.org/10.1515/kern-2022-0073.Search in Google Scholar
Lindsay, A., Ridley, G., Rykhlevskii, A., and Huff, K. (2018). Introduction to moltres: an application for simulation of molten salt reactors. Ann. Nucl. Energy 114: 530–540, https://doi.org/10.1016/j.anucene.2017.12.025.Search in Google Scholar
Linke, J., Du, J., Loewenhoff, T., Pintsuk, G., Spilker, B., Steudel, I., and Wirtz, M. (2019). Challenges for plasma-facing components in nuclear fusion. Matter Radiat. Extremes 4: 056201, https://doi.org/10.1063/1.5090100.Search in Google Scholar
Litnovsky, A., Hellwig, M., Matveev, D., Komm, M., Van Den Berg, M., De Temmerman, G., Rudakov, D., Ding, F., Luo, G.-N., Krieger, K., et al.. (2015). Optimization of tungsten castellated structures for the ITER divertor. J. Nucl. Mater. 463: 174–179, https://doi.org/10.1016/j.jnucmat.2014.11.009.Search in Google Scholar
Mancini, A., Ayllon-Guerola, J., Doyle, S.J., Agredano-Torres, M., Lopez-Aires, D., Toledo-Garrido, J., Viezzer, E., Garcia-Muñoz, M., Buxton, P.F., Chung, K.J., et al.. (2021). Mechanical and electromagnetic design of the vacuum vessel of the SMART tokamak. Fusion Eng. Des. 171: 112542, https://doi.org/10.1016/j.fusengdes.2021.112542.Search in Google Scholar
Meier, E.T., Gerhardt, S., Menard, J.E., Rognlien, T.D., and Soukhanovskii, V.A. (2015). Modeling divertor concepts for spherical tokamaks NSTX-U and ST-FNSF. Nucl. Fusion 55: 086002, https://doi.org/10.1088/0029-5515/55/8/086002.Search in Google Scholar
Menard, J. and Fonck, R. (2024). U.S. spherical tokamak program initiatives for the next decade. FESAC Whitepaper, Available at: https://www.burningplasma.org/resources/ref/fspp/whitepapers/FESAC_whitepaper_Spherical_Tokamak_initiatives.pdf.Search in Google Scholar
Permann, C.J., Gaston, D.R., Andrš, D., Carlsen, R.W., Kong, F., Lindsay, A.D., Miller, J.M., Peterson, J.W., Slaughter, A.E., Stogner, R.H., et al.. (2020). MOOSE: enabling massively parallel multiphysics simulation. SoftwareX 11: 100430, https://doi.org/10.1016/j.softx.2020.100430.Search in Google Scholar
Rubel, M.J., Coad, J.P., and Pitts, R.A. (2007). Overview of co-deposition and fuel inventory in castellated divertor structures at JET. J. Nucl. Mater. 367–370: 1432–1437, https://doi.org/10.1016/j.jnucmat.2007.04.007.Search in Google Scholar
Sakharov, N.V. (2001). Spherical tokamak globus-m construction and operation. Plasma Devices Oper. 9: 25–37, https://doi.org/10.1080/10519990108224485.Search in Google Scholar
Sengupta, A. and Ranjan, P. (2000). Forecasting disruptions in the ADITYA tokamak using neural networks. Nucl. Fusion 30: 1993–2008, https://doi.org/10.1088/0029-5515/40/12/304.Search in Google Scholar
Soukhanovskii, V.A., Bell, R.E., Diallo, A., Gerhardt, S., Kaye, S., Kolemen, E., LeBlanc, B.P., McLean, A.G., Menard, J.E., Paul, S.F., et al.. (2012). Snowflake divertor configuration studies in national spherical Torus experiment. Phys. Plasmas 19: 082504, https://doi.org/10.1063/1.4737117.Search in Google Scholar
Sun, Y. and Wichman, I.S. (2004). On transient heat conduction in a one-dimensional composite slab. Int. J. Heat Mass Transfer 47: 1555–1559, https://doi.org/10.1016/j.ijheatmasstransfer.2003.09.011.Search in Google Scholar
Sykes, A., Ahn, J.-W., Akers, R., Arends, E., Carolan, P.G., Counsell, G.F., Fielding, S.J., Gryaznevich, M., Martin, R., Price, M., et al.. (2001). First physics results from the MAST mega-amp spherical tokamak. Phys. Plasmas 8: 2101–2106, https://doi.org/10.1063/1.1352595.Search in Google Scholar
Tabasso, A., Dowling, J., Ahn, J.-W., Cunningham, G., Kirk, A., McArdle, G., and Price, M., and The MAST Team (2003). Analysis of the progress to detachment in the divertor of the MAST tokamak. J. Nucl. Mater. 313–316: 936–940, https://doi.org/10.1016/S0022-3115(02)01480-0.Search in Google Scholar
Tanna, R.L., Macwan, T., Ghosh, J., Jadeja, K.A., Kumar, R., Aich, S., Patel, K.M., Raj, H., Singh, K., Dolui, S., et al.. (2022). Overview of recent experimental results from the ADITYA-U tokamak. Nucl. Fusion 62: 042017, https://doi.org/10.1088/1741-4326/ac31db.Search in Google Scholar
Thornton, A.J., Kirk, A., Chapman, I.T., and Harrison, J.R. (2013). Divertor heat fluxes and profiles during mitigated and unmitigated edge localised modes (ELMs) on the mega amp spherical tokamak (MAST). J. Nucl. Mater. 438: S199–S202, https://doi.org/10.1016/j.jnucmat.2013.01.026.Search in Google Scholar
Voss, G.M., Bond, A., Davis, S., Harte, M., and Watson, R. (2006). The cascading pebble divertor for the spherical tokamak power plant. Fusion Eng. Des. 81: 327–333, https://doi.org/10.1016/j.fusengdes.2005.08.090.Search in Google Scholar
Wang, H.M. and Liu, C.B. (2013). Analytical solution of two-dimensional transient heat conduction in fiber-reinforced cylindrical composites. Int. J. Therm. Sci. 69: 43–52, https://doi.org/10.1016/j.ijthermalsci.2013.02.001.Search in Google Scholar
Wu, X., Shi, J., Lei, H., Li, Y., and Okine, L. (2019). Analytical solutions of transient heat conduction in multilayered slabs and application to thermal analysis of landfills. J. Cent. South Univ. 26: 3175–3187, https://doi.org/10.1007/s11771-019-4244-y.Search in Google Scholar
Yang, B. and Liu, S. (2017). Closed-form analytical solutions of transient heat conduction in hollow composite cylinders with any number of layers. Int. J. Heat Mass Transfer 108: 907–917, https://doi.org/10.1016/j.ijheatmasstransfer.2016.12.020.Search in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Study of reliability prediction method and uncertainty analysis of the pump and valve of a floating nuclear power plant
- Thermal-hydraulic and safety analysis of alternative ceramic fuels in next generation of VVER-1000 reactor
- Transient thermal analysis for optimal armor material in upgraded mockup for PST using MOOSE Framework
- Analysis of hypothetical channel flow blockage of a tubular fuel assembly in a 10 MWth nuclear research reactor
- Preliminary neutronic analyses for annular VHTR with different coated fuel particle designs
- Improved intelligent model predictive controller for the nuclear power reactor system
- Monte Carlo simulation of photo-peak efficiency response function and calculation of total efficiency for a NaI (Tl) scintillator detector
- Calculation and application research on real-time source term diffusion in NPP auxiliary building under accident circumstances
- Calendar of events – issue 6 of KERN
Articles in the same Issue
- Frontmatter
- Study of reliability prediction method and uncertainty analysis of the pump and valve of a floating nuclear power plant
- Thermal-hydraulic and safety analysis of alternative ceramic fuels in next generation of VVER-1000 reactor
- Transient thermal analysis for optimal armor material in upgraded mockup for PST using MOOSE Framework
- Analysis of hypothetical channel flow blockage of a tubular fuel assembly in a 10 MWth nuclear research reactor
- Preliminary neutronic analyses for annular VHTR with different coated fuel particle designs
- Improved intelligent model predictive controller for the nuclear power reactor system
- Monte Carlo simulation of photo-peak efficiency response function and calculation of total efficiency for a NaI (Tl) scintillator detector
- Calculation and application research on real-time source term diffusion in NPP auxiliary building under accident circumstances
- Calendar of events – issue 6 of KERN
