DEM simulations in nuclear engineering: a review of recent progress

References

• Gui N, Yang X, Tu J, et al. Effect of bed configuration on pebble flow uniformity and stagnation in the pebble bed reactor. Nucl Eng Des. 2014;270:295–301. doi:10.1016/j.nucengdes.2013.12.055
   Web of Science ®Google Scholar
• Wu M, Gui N, Wu H, et al. Numerical study of mixing pebble flow with different density in circulating packed bed. Ann Nucl Energy. 2019;130:483–492. doi:10.1016/j.anucene.2019.03.020
   Web of Science ®Google Scholar
• Gui N, Huang X, Yang X, et al. HTR-PM-based 3D pebble flow simulation on the effects of base angle, recirculation mode and coefficient of friction. Ann Nucl Energy. 2020;143. doi:10.1016/j.anucene.2020.107442.
   Web of Science ®Google Scholar
• Li Y, Gui N, Yang X, et al. Effect of a flow-corrective insert on the flow pattern in a pebble bed reactor. Nucl Eng Des. 2016;300:495–505. doi:10.1016/j.nucengdes.2016.02.002
   Web of Science ®Google Scholar
• Li Y, Gui N, Yang X, et al. Effect of friction on pebble flow pattern in pebble bed reactor. Ann Nucl Energy. 2016;94:32–43. doi:10.1016/j.anucene.2016.02.022
   Web of Science ®Google Scholar
• Jiang SY, Yang XT, Tang ZW, et al. Experimental and numerical validation of a two-region-designed pebble bed reactor with dynamic core. Nucl Eng Des. 2012;246:277–285. doi:10.1016/j.nucengdes.2012.02.005
   Web of Science ®Google Scholar
• Rycroft CH, Dehbi A, Lind T, et al. Granular flow in pebble-bed nuclear reactors: Scaling, dust generation, and stress. Nucl Eng Des. 2013;265:69–84. doi:10.1016/j.nucengdes.2013.07.010
   Web of Science ®Google Scholar
• Luo X, Wang X, Shi L, et al. Nuclear graphite wear properties and estimation of graphite dust production in HTR-10. Nucl Eng Des. 2017;315:35–41. doi:10.1016/j.nucengdes.2017.02.016
   Web of Science ®Google Scholar
• Tang YS, Yin ZZ, Zhang LG, et al. The application of the DEM-based burnup construction method in the pebble burnup history analysis in HTR-10. Nucl Eng Des. 2019;349:1–7. doi:10.1016/j.nucengdes.2019.04.013
   Web of Science ®Google Scholar
• Liu M, Liu R, Liu B, et al. Preparation of the Coated Nuclear Fuel Particle Using the Fluidized Bed-chemical Vapor Deposition (FB-CVD) Method. Procedia Eng. 2015;102:1890–1895. doi:10.1016/j.proeng.2015.01.328
   Google Scholar
• Liu M, Liu R, Chen M, et al. Preliminary simulation study of particle coating process by FB-CVD method using a CFD-DEM-PBM model. Nucl Eng Des. 2018;329:53–59. doi:10.1016/j.nucengdes.2017.11.047
   Web of Science ®Google Scholar
• Liu M, Chen M, Li T, et al. CFD–DEM–CVD multi-physical field coupling model for simulating particle coating process in spout bed. Particuology. 2019;42:67–78. doi:10.1016/j.partic.2018.03.011
   Web of Science ®Google Scholar
• Duan G, Yamaji A, Sakai M. A multiphase MPS method coupling fluid–solid interaction/phase-change models with application to debris remelting in reactor lower plenum. Ann Nucl Energy. 2022;166:108697. doi: 10.1016/j.anucene.2021.108697
   Web of Science ®Google Scholar
• Li G, Wen P, Feng H, et al. Study on melt stratification and migration in debris bed using the moving particle semi-implicit method. Nucl Eng Des. 2020;360:110459. doi:10.1016/j.nucengdes.2019.110459
   Web of Science ®Google Scholar
• Chen R, Guo K, Zhang Y, et al. Numerical analysis of the granular flow and heat transfer in the ADS granular spallation target. Nucl Eng Des. 2018;330:59–71. doi:10.1016/j.nucengdes.2018.01.019
   Web of Science ®Google Scholar
• Ma L, Zhang X, Zhang S, et al. Validation of the idea of granular flow target: A beam coupling test. Nucl Eng Des. 2018;330:289–296. doi:10.1016/j.nucengdes.2017.12.023
   Web of Science ®Google Scholar
• Zhang Z, Wu Z, Sun Y, et al. Design aspects of the Chinese modular high-temperature gas-cooled reactor HTR-PM. Nucl Eng Des. 2006;236(5–6):485–490. doi: 10.1016/j.nucengdes.2005.11.024
   Web of Science ®Google Scholar
• Liu FR, Chen XW, Li Z, et al. DEM–CFD simulation of modular PB-FHR core with two-grid method. Nucl Sci Tech. 2017;28(7):28. doi: 10.1007/s41365-017-0246-3
   Web of Science ®Google Scholar
• Cundall PA, Strack ODL. A discrete numerical model for granular assemblies. Géotechnique. 1979;29(1):47–65. doi: 10.1680/geot.1979.29.1.47
   Web of Science ®Google Scholar
• Jordam Caserta A, Navarro HA, Cabezas-Gómez L. Damping coefficient and contact duration relations for continuous nonlinear spring-dashpot contact model in DEM. Powder Technol. 2016;302:462–479. doi: 10.1016/j.powtec.2016.07.032
   Web of Science ®Google Scholar
• Moukalled F, Mangani L, Darwish M. The Finite Volume Method in Computational Fluid Dynamics. Springer; 2016;103–135.
   Google Scholar
• Koshizuka S, Oka Y. Moving-particle semi-implicit method for fragmentation of incompressible fluid. Nucl Sci Eng. 1996;123(3):421–434. doi: 10.13182/NSE96-A24205
   Web of Science ®Google Scholar
• Aidun CK, Clausen JR. Lattice-Boltzmann method for complex flows. Annu Rev Fluid Mech. 2010;42(1):439–472. doi: 10.1146/annurev-fluid-121108-145519
   Web of Science ®Google Scholar
• Peskin CS. Flow patterns around heart valves: A numerical method. J Comput Phys. 1972;10(2):252–271. doi: 10.1016/0021-9991(72)90065-4
   Web of Science ®Google Scholar
• Koshizuka S, Nobe A, Oka Y. Numerical analysis of breaking waves using the moving particle semi-implicit method. Int J Numer Methods Fluids. 1998;26(7):751–769. doi: 10.1002/(SICI)1097-0363(19980415)26:7<751:AID-FLD671>3.0.CO;2-C
   Web of Science ®Google Scholar
• Zhong W, Yu A, Liu X, et al. DEM/CFD-DEM modelling of non-spherical particulate systems: theoretical developments and applications. Powder Technol. 2016;302:108–152. doi:10.1016/j.powtec.2016.07.010
   Web of Science ®Google Scholar
• Wang T, Zhang F, Furtney J, et al. A review of methods, applications and limitations for incorporating fluid flow in the discrete element method. J Rock Mech Geotech Eng. 2022;14(3):1005–1024. doi: 10.1016/j.jrmge.2021.10.015
   Web of Science ®Google Scholar
• Coetzee CJ. Review: Calibration of the discrete element method. Powder Technol. 2017;310:104–142. doi: 10.1016/j.powtec.2017.01.015
   Web of Science ®Google Scholar
• Sakai M. How should the discrete element method be applied in industrial systems?: A review. KONA Powder Particle J. 2016;33:169–178. Hosokawa Powder Technology Foundation. doi: 10.14356/kona.2016023
   Google Scholar
• Shi Q, Sakai M. Recent progress on the discrete element method simulations for powder transport systems: A review. Adv Powder Technol. 2022;33(8):103664. doi: 10.1016/j.apt.2022.103664
   Web of Science ®Google Scholar
• Golshan S, Sotudeh-Gharebagh R, Zarghami R, et al. Review and implementation of CFD-DEM applied to chemical process systems. Chem Eng Sci. 2020;221:115646. doi:10.1016/j.ces.2020.115646
   Web of Science ®Google Scholar
• Horabik J, Molenda M. Parameters and contact models for DEM simulations of agricultural granular materials: A review. Biosyst Eng. 2016;147:206–225. doi: 10.1016/j.biosystemseng.2016.02.017
   Web of Science ®Google Scholar
• Qiu X DEM simulations in mining and mineral processing. Proceedings of the 7th International Conference on Discrete Element Methods. Dalian, China; 2016. p. 37–43.
   Google Scholar
• Di Maio FP, Di Renzo A. Analytical solution for the problem of frictional-elastic collisions of spherical particles using the linear model. Chem Eng Sci. 2004;59(16):3461–3475. doi: 10.1016/j.ces.2004.05.014
   Web of Science ®Google Scholar
• Di Renzo A, Di Maio FP. An improved integral non-linear model for the contact of particles in distinct element simulations. Chem Eng Sci. 2005;60(5):1303–1312. doi: 10.1016/j.ces.2004.10.004
   Web of Science ®Google Scholar
• Di Renzo A, Di Maio FP. Comparison of contact-force models for the simulation of collisions in DEM-based granular flow codes. Chem Eng Sci. 2004;59(3):525–541. doi: 10.1016/j.ces.2003.09.037
   Web of Science ®Google Scholar
• Hertz VHH. Ueber die Berührung fester elastischer Körper (On contact between elastic bodies). Crll. 1882;1882(92):156–171. doi: 10.1515/crll.1882.92.156
   Google Scholar
• Mindlin RD. Compliance of elastic bodies in contact. J Appl Mech. 1949;16(3):259–268. doi: 10.1115/1.4009973
   Web of Science ®Google Scholar
• Mindlin RD, Deresiewicz H. Elastic spheres in contact under varying oblique forces. J Appl Mech. 1953;20(3):327–344. doi: 10.1115/1.4010702
   Web of Science ®Google Scholar
• Kruggel‐Emden H, Simsek E, Rickelt S, et al. Review and extension of normal force models for the discrete element method. Powder Technol. 2007;171(3):157–173. doi: 10.1016/j.powtec.2006.10.004
   Web of Science ®Google Scholar
• Kruggel-Emden H, Wirtz S, Scherer V. A study on tangential force laws applicable to the discrete element method (DEM) for materials with viscoelastic or plastic behavior. Chem Eng Sci. 2008;63(6):1523–1541. doi: 10.1016/j.ces.2007.11.025
   Web of Science ®Google Scholar
• Stevens AB, Hrenya CM. Comparison of soft-sphere models to measurements of collision properties during normal impacts. Powder Technol. 2005;154(2–3):99–109. doi: 10.1016/j.powtec.2005.04.033
   Web of Science ®Google Scholar
• Langston PAA, Tüzün U, Heyes DMM. Continuous potential discrete particle simulations of stress and velocity fields in hoppers: transition from fluid to granular flow. Chem Eng Sci. 1994;49(8):1259–1275. doi: 10.1016/0009-2509(94)85095-X
   Web of Science ®Google Scholar
• Langston PA, Tüzün U, Heyes DM. Discrete element simulation of granular flow in 2D and 3D hoppers: Dependence of discharge rate and wall stress on particle interactions. Chem Eng Sci. 1995;50(6):967–987. doi: 10.1016/0009-2509(94)00467-6
   Web of Science ®Google Scholar
• Kuwabara G, Kono K. Restitution coefficient in a collision between two spheres. Jpn J Appl Phys. 1987;26(8R):1219–1223. doi: 10.1143/JJAP.26.1230
   Google Scholar
• Thornton C, Cummins SJ, Cleary PW. An investigation of the comparative behaviour of alternative contact force models during inelastic collisions. Powder Technol. 2013;233:30–46. doi: 10.1016/j.powtec.2012.08.012
   Web of Science ®Google Scholar
• Tsuji Y, Tanaka T, Ishida T. Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technol. 1992;71(3):239–250. doi: 10.1016/0032-5910(92)88030-L
   Web of Science ®Google Scholar
• Antypov D, Elliott JA. On an analytical solution for the damped Hertzian spring. EPL (Europhysics Letters). 2011;94(5):50004. doi: 10.1209/0295-5075/94/50004
   Google Scholar
• Shamsuzzaman M, Horie T, Fuke F, et al. Experimental evaluation of debris bed characteristics in particulate debris sedimentation behaviour. Volume 6: beyond design basis events. Student Paper Competition. American Society of Mechanical Engineers; 2013.
   Google Scholar
• Ma H, Zhou L, Liu Z, et al. A review of recent development for the CFD-DEM investigations of non-spherical particles. Powder Technol. 2022;412:117972. doi:10.1016/j.powtec.2022.117972
   Web of Science ®Google Scholar
• Lu G, Third JR, Müller CR. Discrete element models for non-spherical particle systems: from theoretical developments to applications. Chem Eng Sci. 2015;127:425–465. doi: 10.1016/j.ces.2014.11.050
   Web of Science ®Google Scholar
• WILLIAMS JR, PENTLAND AP. Superquadrics and modal dynamics for discrete elements in interactive design. Eng Comput (Swansea). 1992;9(2):115–127. doi: 10.1108/eb023852
   Google Scholar
• Ning Z, Boerefijn R, Ghadiri M, et al. Distinct element simulation of impact breakage of lactose agglomerates. Adv Powder Technol. 1997;8(1):15–37. doi: 10.1016/S0921-8831(08)60477-X
   Web of Science ®Google Scholar
• Nassauer B, Liedke T, Kuna M. Polyhedral particles for the discrete element method. Granul Matter. 2013;15(1):85–93. doi: 10.1007/s10035-012-0381-9
   Web of Science ®Google Scholar
• Sakai M, Yamada Y, Shigeto Y, et al. Large-scale discrete element modeling in a fluidized bed. Int J Numer Methods Fluids. 2010;64(10–12):1319–1335. doi: 10.1002/fld.2364
   Web of Science ®Google Scholar
• Sakai M, Takahashi H, Pain CC, et al. Study on a large-scale discrete element model for fine particles in a fluidized bed. Adv Powder Technol. 2012;23(5):673–681. doi: 10.1016/j.apt.2011.08.006
   Web of Science ®Google Scholar
• Yokoi K. Numerical method for interaction between multiparticle and complex structures. Phys Rev E. 2005;72(4):046713. doi: 10.1103/PhysRevE.72.046713
   Web of Science ®Google Scholar
• Shigeto Y, Sakai M. Arbitrary-shaped wall boundary modeling based on signed distance functions for granular flow simulations. Chem Eng J. 2013;231:464–476. doi: 10.1016/j.cej.2013.07.073
   Web of Science ®Google Scholar
• Sakai M, Takabatake K, Tamura K, et al. Why do wet-particles adhere to a high-speed roll in a three-roll mill? Phys Fluids. 2019;31(3):31. doi: 10.1063/1.5085693
   Web of Science ®Google Scholar
• Sakai M, Shigeto Y, Basinskas G, et al. Discrete element simulation for the evaluation of solid mixing in an industrial blender. Chem Eng J. 2015;279:821–839. doi:10.1016/j.cej.2015.04.130
   Web of Science ®Google Scholar
• Basinskas G, Sakai M. Numerical study of the mixing efficiency of a ribbon mixer using the discrete element method. Powder Technol. 2016;287:380–394. doi: 10.1016/j.powtec.2015.10.017
   Web of Science ®Google Scholar
• Tsunazawa Y, Shigeto Y, Tokoro C, et al. Numerical simulation of industrial die filling using the discrete element method. Chem Eng Sci. 2015;138:791–809. doi:10.1016/j.ces.2015.09.014
   Web of Science ®Google Scholar
• Tsugeno Y, Sakai M, Yamazaki S, et al. DEM simulation for optimal design of powder mixing in a ribbon mixer. Adv Powder Technol. 2021;32(5):1735–1749. doi: 10.1016/j.apt.2021.03.026
   Web of Science ®Google Scholar
• Tsory T, Ben-Jacob N, Brosh T, et al. Thermal DEM–CFD modeling and simulation of heat transfer through packed bed. Powder Technol. 2013;244:52–60. doi:10.1016/j.powtec.2013.04.013
   Web of Science ®Google Scholar
• Wu H, Gui N, Yang X, et al. Numerical simulation of heat transfer in packed pebble beds: CFD-DEM coupled with particle thermal radiation. Int J Heat Mass Transf. 2017;110:393–405. doi:10.1016/j.ijheatmasstransfer.2017.03.035
   Web of Science ®Google Scholar
• Wu H, Gui N, Yang X, et al. Effect of scale on the modeling of radiation heat transfer in packed pebble beds. Int J Heat Mass Transf. 2016;101:562–569. doi:10.1016/j.ijheatmasstransfer.2016.05.090
   Web of Science ®Google Scholar
• Wu H, Gui N, Yang X, et al. An approximation function model for solving effective radiative heat transfer in packed bed. Ann Nucl Energy. 2020;135:107000. doi:10.1016/j.anucene.2019.107000
   Web of Science ®Google Scholar
• Wu H, Gui N, Yang X, et al. Analysis and evaluations of four models of thermal radiation for densely packed granular systems. Chem Eng Sci. 2020;211:115309. doi:10.1016/j.ces.2019.115309
   Web of Science ®Google Scholar
• Sotiropoulos F, Yang X. Immersed boundary methods for simulating fluid–structure interaction. Prog Aerosp Sci. 2014;65:1–21. doi: 10.1016/j.paerosci.2013.09.003
   Web of Science ®Google Scholar
• Liao C-C, Chang Y-W, Lin C-A, et al. Simulating flows with moving rigid boundary using immersed-boundary method. Comput Fluids. 2010;39(1):152–167. doi: 10.1016/j.compfluid.2009.07.011
   Web of Science ®Google Scholar
• Kim J, Kim D, Choi H. An immersed-boundary finite-volume method for simulations of flow in complex geometries. J Comput Phys. 2001;171(1):132–150. doi: 10.1006/jcph.2001.6778
   Web of Science ®Google Scholar
• Uhlmann M. An immersed boundary method with direct forcing for the simulation of particulate flows. J Comput Phys. 2005;209(2):448–476. doi: 10.1016/j.jcp.2005.03.017
   Web of Science ®Google Scholar
• Su S-W, Lai M-C, Lin C-A. An immersed boundary technique for simulating complex flows with rigid boundary. Comput Fluids. 2007;36(2):313–324. doi: 10.1016/j.compfluid.2005.09.004
   Web of Science ®Google Scholar
• d’Humières D, Ginzburg I, d’Humières D. Viscosity independent numerical errors for Lattice Boltzmann models: from recurrence equations to “magic” collision numbers. Comput Math Appl. 2009;58(5):823–840. doi: 10.1016/j.camwa.2009.02.008
   Web of Science ®Google Scholar
• Ginzburg I. Equilibrium-type and link-type lattice Boltzmann models for generic advection and anisotropic-dispersion equation. Adv Water Resour. 2005;28(11):1171–1195. doi: 10.1016/j.advwatres.2005.03.004
   Web of Science ®Google Scholar
• D’Humières D. Generalized Lattice-Boltzmann equations. rarefied gas dynamics: theory and simulations. Washington DC: American Institute of Aeronautics and Astronautics; 1994. p. 450–458.
   Google Scholar
• Latt J, Chopard B. Lattice Boltzmann method with regularized pre-collision distribution functions. Math Comput Simul. 2006;72(2–6):165–168. doi: 10.1016/j.matcom.2006.05.017
   Web of Science ®Google Scholar
• Boghosian BM, Yepez J, Coveney PV, et al. Correction for Boghosian et al., entropic lattice Boltzmann methods. Proc R Soc London A: Math Phys EngSci. 2001;457(2016):3052–3052. doi: 10.1098/rspa.2001.2003
   Web of Science ®Google Scholar
• Krüger T, Kusumaatmaja H, Kuzmin A, et al. The Lattice Boltzmann method [Internet]. 1st. Springer Cham; 2017. 10.1007/978-3-319-44649-3.
   Google Scholar
• He Y-L, Liu Q, Li Q, et al. Lattice Boltzmann methods for single-phase and solid-liquid phase-change heat transfer in porous media: A review. Int J Heat Mass Transf. 2019;129:160–197. doi:10.1016/j.ijheatmasstransfer.2018.08.135
   Web of Science ®Google Scholar
• Gingold RA, Monaghan JJ. Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc. 1977;181(3):375–389. doi: 10.1093/mnras/181.3.375
   Web of Science ®Google Scholar
• Wang Z, Hu F, Duan G, et al. Numerical modeling of floating bodies transport for flooding analysis in nuclear reactor building. Nucl Eng Des. 2019;341:390–405. doi:10.1016/j.nucengdes.2018.11.031
   Web of Science ®Google Scholar
• Duan G, Chen B, Zhang X, et al. A multiphase MPS solver for modeling multi-fluid interaction with free surface and its application in oil spill. Comput Methods Appl Mech Eng. 2017;320:133–161. doi:10.1016/j.cma.2017.03.014
   Web of Science ®Google Scholar
• Xiao X, Cai Q, Chen R, et al. An improved MPS-DEM numerical model for fluid–solid coupling problem in nuclear reactor. Nucl Eng Des. 2022;396:111875. doi:10.1016/j.nucengdes.2022.111875
   Web of Science ®Google Scholar
• Tamai T, Koshizuka S. Least squares moving particle semi-implicit method. Comp Part Mech. 2014;1(3):277–305. doi: 10.1007/s40571-014-0027-2
   Web of Science ®Google Scholar
• Chen J-S, Pan C, Wu C-T, et al. Reproducing Kernel Particle methods for large deformation analysis of non-linear structures. Comput Methods Appl Mech Eng. 1996;139(1–4):195–227. doi: 10.1016/S0045-7825(96)01083-3
   Web of Science ®Google Scholar
• Duan G, Matsunaga T, Yamaji A, et al. Imposing accurate wall boundary conditions in corrective‐matrix‐based moving particle semi‐implicit method for free surface flow. Int J Numer Methods Fluids. 2021;93(1):148–175. doi: 10.1002/fld.4878
   Web of Science ®Google Scholar
• Duan G, Yamaji A, Koshizuka S, et al. The truncation and stabilization error in multiphase moving particle semi-implicit method based on corrective matrix: Which is dominant? Comput Fluids. 2019;190:254–273. doi:10.1016/j.compfluid.2019.06.023
   Web of Science ®Google Scholar
• Duan G, Matsunaga T, Koshizuka S, et al. New insights into error accumulation due to biased particle distribution in semi-implicit particle methods. Comput Methods Appl Mech Eng. 2022;388:114219. doi:10.1016/j.cma.2021.114219
   Web of Science ®Google Scholar
• Duan G, Sakai M. An enhanced semi-implicit particle method for simulating the flow of droplets with free surfaces. Comput Methods Appl Mech Eng. 2022;389:114338. doi: 10.1016/j.cma.2021.114338
   Web of Science ®Google Scholar
• Anderson TB, Jackson ROY. A fluid mechanical description of fluidized beds. Indus Eng Chem Fundamental. 1967;6(4):527–539. doi: 10.1021/i160024a007
   Web of Science ®Google Scholar
• Li M, Kong D, Guo Q, et al. Investigation of movement and deposition behaviors of solid particles in hydraulic water reservoir via the CFD-DEM coupling method. Chin J Mech Eng. 2022;35(1):118. doi: 10.1186/s10033-022-00788-z
   Web of Science ®Google Scholar
• Li L, Remmelgas J, van Wachem BGM, et al. Effect of drag models on residence time distributions of particles in a Wurster fluidized bed: a DEM-CFD study. KONA Powder Part J. 2016;33:264–277. doi: 10.14356/kona.2016008
   Google Scholar
• Ergun S, Orning AA. Fluid Flow through randomly packed columns and fluidized beds. Ind Eng Chem. 1949;41(6):1179–1184. doi: 10.1021/ie50474a011
   Web of Science ®Google Scholar
• Wen CY, Yu YH. A generalized method for predicting the minimum fluidization velocity. AIChE J. 1966;12(3):610–612. doi: 10.1002/aic.690120343
   Web of Science ®Google Scholar
• Di Felice R. The voidage function for fluid-particle interaction systems. Int J Multiphase Flow. 1994;20(1):153–159. doi: 10.1016/0301-9322(94)90011-6
   Web of Science ®Google Scholar
• Mori Y, Sakai M. Development of a robust Eulerian–Lagrangian model for the simulation of an industrial solid–fluid system. Chem Eng J. 2021;406:126841. doi: 10.1016/j.cej.2020.126841
   Web of Science ®Google Scholar
• Maramizonouz S, Nadimi S. Drag force acting on ellipsoidal particles with different shape characteristics. Powder Technol. 2022;412:117964. doi: 10.1016/j.powtec.2022.117964
   Web of Science ®Google Scholar
• Sun X, Sakai M. Three-dimensional simulation of gas–solid–liquid flows using the DEM–VOF method. Chem Eng Sci. 2015;134:531–548. doi: 10.1016/j.ces.2015.05.059
   Web of Science ®Google Scholar
• Washino K, Chan EL, Kaji T, et al. On large scale CFD–DEM simulation for gas–liquid–solid three-phase flows. Particuology. 2021;59:2–15. doi:10.1016/j.partic.2020.05.006
   Web of Science ®Google Scholar
• Hirt CW, Nichols BD. Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys. 1981;39(1):201–225. doi: 10.1016/0021-9991(81)90145-5
   Web of Science ®Google Scholar
• Noh WF, Woodward P. SLIC (Simple Line Interface Calculation). Proceedings of the Fifth International Conference on Numerical Methods in Fluid Dynamics. Twente University, Enschede; 1976 p.330–340.
   Google Scholar
• Youngs D. Time-dependent multi-material flow with large fluid distortion. In: Morton K, and M Baines, editors Numerical methods in fluid dynamics. San Diego, California: Academic Press Inc.; 1982. p. 273–285.
   Google Scholar
• Martinez J-M, Chesneau X, Zeghmati B. A new curvature technique calculation for surface tension contribution in PLIC-VOF method. Computational Mechanics. 2006;37(2):182–193. doi: 10.1007/s00466-005-0689-y
   Web of Science ®Google Scholar
• Yokoi K. Efficient implementation of THINC scheme: A simple and practical smoothed VOF algorithm. J Comput Phys. 2007;226(2):1985–2002. doi: 10.1016/j.jcp.2007.06.020
   Web of Science ®Google Scholar
• Norouzi HR, Zarghami R, Sotudeh-Gharebagh R, et al. Coupled CFD-DEM Modeling. Chichester, UK: John Wiley & Sons, Ltd; 2016. doi: 10.1002/9781119005315
   Google Scholar
• Mori Y, Sakai M. Advanced DEM simulation on powder mixing for ellipsoidal particles in an industrial mixer. Chem Eng J. 2022;429:132415. doi: 10.1016/j.cej.2021.132415
   Web of Science ®Google Scholar
• Sun X, Sakai M. A liquid bridge model for spherical particles applicable to asymmetric configurations. Chem Eng Sci. 2018;182:28–43. doi: 10.1016/j.ces.2018.02.034
   Web of Science ®Google Scholar
• Basinskas G, Sakai M. Numerical study of the mixing efficiency of a batch mixer using the discrete element method. Powder Technol. 2016;301:815–829. doi: 10.1016/j.powtec.2016.07.017
   Web of Science ®Google Scholar
• Tamura K, Mori Y, Takabatake K, et al. Validation study on a toroidal approximation-based capillary force model in the discrete element method simulation. Phys Fluids. 2022;34(2):023319. doi: 10.1063/5.0080792
   Web of Science ®Google Scholar
• Sun X, Sakai M. Immersed boundary method with artificial density in pressure equation for modeling flows confined by wall boundaries. J Chem Eng Jpn. 2017;50(3):161–169. doi: 10.1252/jcej.16we115
   Web of Science ®Google Scholar
• Mori Y, Takabatake K, Tsugeno Y, et al. On artificial density treatment for the pressure Poisson equation in the DEM-CFD simulations. Powder Technol. 2020;372:48–58. doi:10.1016/j.powtec.2020.05.116
   Web of Science ®Google Scholar
• Takabatake K, Sakai M. Flexible discretization technique for DEM-CFD simulations including thin walls. Adv Powder Technol. 2020;31(5):1825–1837. doi: 10.1016/j.apt.2020.02.017
   Web of Science ®Google Scholar
• Sun X, Sakai M, Yamada Y. Three-dimensional simulation of a solid–liquid flow by the DEM–SPH method. J Comput Phys. 2013;248:147–176. doi: 10.1016/j.jcp.2013.04.019
   Web of Science ®Google Scholar
• Sun X, Sakai M, Sakai M-T, et al. A Lagrangian–Lagrangian coupled method for three-dimensional solid–liquid flows involving free surfaces in a rotating cylindrical tank. Chem Eng J. 2014;246:122–141. doi:10.1016/j.cej.2014.02.049
   Web of Science ®Google Scholar
• Yamada Y, Sakai M. Lagrangian-Lagrangian simulations of solid-liquid flows in a bead mill. Powder Technol. 2013;239:105–114. doi: 10.1016/j.powtec.2013.01.030
   Web of Science ®Google Scholar
• Sakai M, Abe M, Shigeto Y, et al. Verification and validation of a coarse grain model of the DEM in a bubbling fluidized bed. Chem Eng J. 2014;244:33–43. doi:10.1016/j.cej.2014.01.029
   Web of Science ®Google Scholar
• Sakai M, Mori Y, Sun X, et al. Recent Progress on Mesh-free Particle Methods for Simulations of Multi-phase Flows: A Review. KONA Powder Part J. 2020;37:132–144. doi: 10.14356/kona.2020017
   Google Scholar
• Yao H, Mori Y, Takabatake K, et al. Numerical investigation on the influence of air flow in a die filling process. J Taiwan Inst Chem Eng. 2018;90:9–17. doi:10.1016/j.jtice.2017.11.031
   Web of Science ®Google Scholar
• Al Falahi F, Mueller G, Al-Dahhan M. Pebble bed nuclear reactor structure study: A comparison of the experimental and calculated void fraction distribution. Prog Nucl Energy. 2018;106:153–161. doi: 10.1016/j.pnucene.2018.03.006
   Web of Science ®Google Scholar
• Li Z, Feng K, Zhao Z, et al. Neutronics study on HCCB blanket for CFETR. Fusion Eng Des. 2017;124:1273–1276. doi:10.1016/j.fusengdes.2017.02.027
   Web of Science ®Google Scholar
• Gámez Rodríguez A, Rojas Mazaira LY, García Hernández CR, et al. An integral 3D full-scale steady-state thermohydraulic calculation of the high temperature pebble bed gas-cooled reactor HTR-10. Nucl Eng Des. 2021;373:111011. doi:10.1016/j.nucengdes.2020.111011
   Web of Science ®Google Scholar
• van der Laan J, Fedorov A, van Til S, et al. Ceramic breeder materials. Compr Nucl Mater. 2012;463–510. Elsevier.
   Google Scholar
• Gong B, Feng Y, Liao H, et al. Discrete element modeling of pebble bed packing structures for HCCB TBM. Fusion Eng Des. 2017;121:256–264. doi:10.1016/j.fusengdes.2017.08.002
   Web of Science ®Google Scholar
• Feng Y, Gong B, Cheng H, et al. Effects of bed dimension, friction coefficient and pebble size distribution on the packing structures of the pebble bed for solid tritium breeder blanket. Fusion Eng Des. 2021;163:112156. doi:10.1016/j.fusengdes.2020.112156
   Web of Science ®Google Scholar
• Wu Q, Lei M, Wang J, et al. Packing characteristics of pebble beds for fusion reactors under different friction coefficients. Fusion Eng Des. 2022;176:113051. doi:10.1016/j.fusengdes.2022.113051
   Web of Science ®Google Scholar
• Sohn D, Lee Y, Ahn M-Y, et al. Numerical prediction of packing behavior and thermal conductivity of pebble beds according to pebble size distributions and friction coefficients. Fusion Eng Des. 2018;137:182–190. doi:10.1016/j.fusengdes.2018.09.012
   Web of Science ®Google Scholar
• Desu RK, Moorthy A, Annabattula RK. DEM simulation of packing mono-sized pebbles into prismatic containers through different filling strategies. Fusion Eng Des. 2018;127:259–266. doi: 10.1016/j.fusengdes.2018.01.005
   Web of Science ®Google Scholar
• Li Y, Huang T, Xu S, et al. Study on the perturbation effect of the different vibration frequency and amplitude to the fusion pebble bed. Fusion Eng Des. 2019;138:358–363. doi:10.1016/j.fusengdes.2018.12.041
   Web of Science ®Google Scholar
• Dai W, Reimann J, Hanaor D, et al. Modes of wall induced granular crystallisation in vibrational packing. Granul Matter. 2019;21(2):26. doi: 10.1007/s10035-019-0876-8
   Web of Science ®Google Scholar
• Feng Y, Gong B, Cheng H, et al. Effects of fixed wall and pebble size ratio on packing properties and contact force distribution in binary-sized pebble mixed beds at the maximum packing efficiency state. Powder Technol. 2021;390:504–520. doi:10.1016/j.powtec.2021.05.099
   Web of Science ®Google Scholar
• Almusafir RS, Jasim AA, Al-Dahhan MH. Review of the fluid dynamics and heat transport phenomena in packed pebble bed nuclear reactors. Nucl Sci Eng. 2023;197(6):1001–1037. doi: 10.1080/00295639.2022.2146993
   Web of Science ®Google Scholar
• Gong B, Feng Y, Liao H, et al. Numerical investigation of the pebble bed structures for HCCB TBM. Fusion Eng Des. 2018;136:1444–1451. doi:10.1016/j.fusengdes.2018.05.033
   Web of Science ®Google Scholar
• Potgieter MC, du Toit CG. The porosity distribution in the HTTU annular packed bed of spheres. Nucl Eng Des. 2023;402:112124. doi: 10.1016/j.nucengdes.2022.112124
   Web of Science ®Google Scholar
• Gong B, Cheng H, Yan J, et al. Effects of the aspect ratio and cross-sectional area of rectangular tubes on packing characteristics of mono-sized pebble beds. Energies (Basel). 2023;16(1):570. doi: 10.3390/en16010570
   Web of Science ®Google Scholar
• De Beer M, Du Toit CG, Rousseau PG. A methodology to investigate the contribution of conduction and radiation heat transfer to the effective thermal conductivity of packed graphite pebble beds, including the wall effect. Nucl Eng Des. 2017;314:67–81. doi: 10.1016/j.nucengdes.2017.01.010
   Web of Science ®Google Scholar
• Wang J, Lei M, Yang H, et al. Effects of coefficient of friction and coefficient of restitution on static packing characteristics of polydisperse spherical pebble bed. Particuology. 2021;57:1–9. doi:10.1016/j.partic.2020.12.013
   Web of Science ®Google Scholar
• Kim D-O, Hwang S-P, Sohn D. DEM study of packing and connectivity of binary-sized pebbles according to their size and mixing ratios under vibration conditions. Fusion Eng Des. 2021;168:112648. doi: 10.1016/j.fusengdes.2021.112648
   Web of Science ®Google Scholar
• Panchal M, Chaudhuri P, Van Lew JT, et al. Numerical modelling for the effective thermal conductivity of lithium meta titanate pebble bed with different packing structures. Fusion Eng Des. 2016;112:303–310. doi:10.1016/j.fusengdes.2016.08.027
   Web of Science ®Google Scholar
• Chen L, Wang C, Moscardini M, et al. A DEM-based heat transfer model for the evaluation of effective thermal conductivity of packed beds filled with stagnant fluid: Thermal contact theory and numerical simulation. Int J Heat Mass Transf. 2019;132:331–346. doi:10.1016/j.ijheatmasstransfer.2018.12.005
   Web of Science ®Google Scholar
• Wu M, Liu X, Gui N, et al. Prediction of the remaining time and time interval of pebbles in pebble bed HTGRs aided by CNN via DEM datasets. Nucl Eng Technol. 2023;55(1):339–352. doi: 10.1016/j.net.2022.09.019
   Web of Science ®Google Scholar
• Wu M, Gui N, Yang X, et al. Effects of 3D contraction on pebble flow uniformity and stagnation in pebble beds. Nucl Eng Technol. 2021;53(5):1416–1428. doi: 10.1016/j.net.2020.10.022
   Web of Science ®Google Scholar
• Li Y, Gui N, Yang X, et al. Experimental research and DEM simulations on stagnant region in pebble bed reactor. International Conference on Nuclear Engineering American Society of Mechanical Engineers. Chengdu, China. 2013. p. 55799:V002T03A012.
   Google Scholar
• Wu M, Gui N, Liu X, et al. Numerical analysis of the effects of different outlet sizes on pebble flows in HTR-10 pebble beds. Nucl Eng Des. 2022;387:111620. doi:10.1016/j.nucengdes.2021.111620
   Web of Science ®Google Scholar
• Li Y, Gui N, Yang X, et al. Effect of wall structure on pebble stagnation behavior in pebble bed reactor. Ann Nucl Energy. 2015;80:195–202. doi:10.1016/j.anucene.2015.02.011
   Web of Science ®Google Scholar
• Qi H, Gui N, Yang X, et al. Effects of restitution coefficient on pebble motion in a thin pebble bed – Lagrangian analysis. Ann Nucl Energy. 2020;145:145. doi:10.1016/j.anucene.2020.107549
   Web of Science ®Google Scholar
• Li B, Gui N, Wu H, et al. Effects of the 3-D wall structures on the flow and mixing characteristics of pebbles in pebble beds in HTR-10. Ann Nucl Energy. 2021;164:108607. doi:10.1016/j.anucene.2021.108607
   Web of Science ®Google Scholar
• Tang Y, Zhang L, Guo Q, et al. Analysis of the pebble burnup profile in a pebble-bed nuclear reactor. Nucl Eng Des. 2019;345:233–251. doi:10.1016/j.nucengdes.2019.01.030
   Web of Science ®Google Scholar
• Stronge WJ. Rigid body collisions with friction. Proc R Soc Lond A Math Phys Sci. 1990;431:169–181.
   Web of Science ®Google Scholar
• Hiruta M, Johnson G, Rostamian M, et al. Computational and experimental prediction of dust production in pebble bed reactors, Part II. Nucl Eng Des. 2013;263:509–514. doi:10.1016/j.nucengdes.2013.04.032
   Google Scholar
• Fachinger J, Barnert H, Kummer AP, et al. Examination of Dust in AVR Pipe Components. In: Fourth international topical meeting on high temperature reactor technology, volume 1. Washington: ASMEDC; 2008. p. 591–602.
   Google Scholar
• Gottaut H, Krüger K. Results of experiments at the AVR reactor. Nucl Eng Des. 1990;121(2):143–153. doi: 10.1016/0029-5493(90)90099-J
   Web of Science ®Google Scholar
• Cogliati JJ, Ougouag AM, Ortensi J. Survey of dust production in pebble bed reactor cores. Nucl Eng Des. 2011;241(6):2364–2369. doi: 10.1016/j.nucengdes.2011.03.023
   Web of Science ®Google Scholar
• Zhang H, Li Z, Guo H, et al. DEM-CFD simulation of purge gas flow in a solid breeder pebble bed. Fusion Eng Des. 2016;113:288–292. doi:10.1016/j.fusengdes.2016.06.045
   Web of Science ®Google Scholar
• Ding W, Xiao X, Cai Q, et al. Numerical investigation of fluid–solid interaction during debris bed formation based on MPS-DEM. Ann Nucl Energy. 2022;175:109244. doi:10.1016/j.anucene.2022.109244
   Web of Science ®Google Scholar
• Guo L, Morita K, Tobita Y. Numerical simulations on self-leveling behaviors with cylindrical debris bed. Nucl Eng Des. 2017;315:61–68. doi: 10.1016/j.nucengdes.2017.02.024
   Web of Science ®Google Scholar
• Mardus-Hall R, Ho M, Pastrello A, et al. 3-Way coupled thermohydraulic-discrete element-neutronic simulation of solid fuel, molten salt reactor. Ann Nucl Energy. 2020;135:106973. doi:10.1016/j.anucene.2019.106973
   Web of Science ®Google Scholar
• Wu Z, Wu Y, Tang S, et al. DEM-CFD simulation of helium flow characteristics in randomly packed bed for fusion reactors. Prog Nucl Energy. 2018;109:29–37. doi:10.1016/j.pnucene.2018.07.010
   Web of Science ®Google Scholar
• Chen Y, Chen L, Liu S, et al. Flow characteristics analysis of purge gas in unitary pebble beds by CFD simulation coupled with DEM geometry model for fusion blanket. Fusion Eng Des. 2017;114:84–90. doi:10.1016/j.fusengdes.2016.12.003
   Web of Science ®Google Scholar
• Yang J, Wu J, Zhou L, et al. Computational study of fluid flow and heat transfer in composite packed beds of spheres with low tube to particle diameter ratio. Nucl Eng Des. 2016;300:85–96. doi:10.1016/j.nucengdes.2015.10.030
   Web of Science ®Google Scholar
• van der Merwe WJS, du Toit CG, Kruger JH et al. Influence of the packing structure on the flow through packed beds with small cylinder diameter to particle diameter ratios. Nucl Eng Des. 2020;365:110700. doi: 10.1016/j.nucengdes.2020.110700
   Web of Science ®Google Scholar
• Sharma A, Thakur A, Saha SK, et al. Thermal-hydraulic characteristics of purge gas in a rectangular packed pebble bed of a fusion reactor using DEM-CFD and porous medium analyses. Fusion Eng Des. 2020;160:160. doi:10.1016/j.fusengdes.2020.111848
   Web of Science ®Google Scholar
• Zhang S, Zhao X, Yang Z. Flow Simulations in a Pebble Bed Reactor by a Combined DEM-CFD Approach. Nucl Sci Eng. 2018;189(2):135–151. doi: 10.1080/00295639.2017.1388090
   Web of Science ®Google Scholar
• Chen L, Chen Y, Huang K, et al. Investigation of effective thermal conductivity for pebble beds by one-way coupled CFD-DEM method for CFETR WCCB. Fusion Eng Des. 2016;106:1–8. doi:10.1016/j.fusengdes.2016.03.001
   Web of Science ®Google Scholar
• Gui N, Li Z, Zhang Z, et al. Numerical study of pebble recirculation in a two-dimensional pebble bed of stationary atmosphere using LB-IB-DEM coupled method. Ann Nucl Energy. 2019;124:58–68. doi:10.1016/j.anucene.2018.09.018
   Web of Science ®Google Scholar
• Takahashi N, Duan G, Yamaji A, et al. Development of MPS method and analytical approach for investigating RPV debris bed and lower head interaction in 1F Units-2 and 3. Nucl Eng Des. 2021;379:111244. doi:10.1016/j.nucengdes.2021.111244
   Web of Science ®Google Scholar
• Muramoto T, Nishiyama J, Obara T. Granular fuel debris shape modeling in MPS-DEM for the simulation of fuel debris bed formation in water. J Nucl Sci Technol. 2022;59(4):438–445. doi: 10.1080/00223131.2021.1975584
   Web of Science ®Google Scholar
• Albano R, Sole A, Mirauda D, et al. Modelling large floating bodies in urban area flash-floods via a Smoothed Particle Hydrodynamics model. J Hydrol (Amst). 2016;541:344–358. doi:10.1016/j.jhydrol.2016.02.009
   Web of Science ®Google Scholar
• Amicarelli A, Albano R, Mirauda D, et al. A Smoothed Particle Hydrodynamics model for 3D solid body transport in free surface flows. Comput Fluids. 2015;116:205–228. doi:10.1016/j.compfluid.2015.04.018
   Web of Science ®Google Scholar
• López-Honorato E, Meadows PJ, Xiao P. Fluidized bed chemical vapor deposition of pyrolytic carbon – I. Effect of deposition conditions on microstructure. Carbon N Y. 2009;47(2):396–410. doi: 10.1016/j.carbon.2008.10.023
   Web of Science ®Google Scholar
• Hwang B, Park HS, Jung WH, et al. Numerical validation and investigation for the sedimentation of solid particles in liquid pool using the CFD-DEM coupling algorithm. Nucl Eng Des. 2019;355:110364. doi:10.1016/j.nucengdes.2019.110364
   Web of Science ®Google Scholar
• Ding W, Chen R, Tian W, et al. Numerical investigation of dynamic characteristics of debris bed formation based on CFD-DEM method. Ann Nucl Energy. 2023;180:109492. doi:10.1016/j.anucene.2022.109492
   Web of Science ®Google Scholar
• Ma W, Dinh T-N. The effects of debris bed’s prototypical characteristics on corium coolability in a LWR severe accident. Nucl Eng Des. 2010;240(3):598–608. doi: 10.1016/j.nucengdes.2009.10.026
   Web of Science ®Google Scholar
• Rashid M, Kulenovic R, Laurien E, et al. Experimental results on the coolability of a debris bed with multidimensional cooling effects. Nucl Eng Des. 2011;241(11):4537–4543. doi: 10.1016/j.nucengdes.2010.11.023
   Web of Science ®Google Scholar
• Guo L, Morita K, Tobita Y. Numerical simulation of gas–solid fluidized beds by coupling a fluid-dynamics model with the discrete element method. Ann Nucl Energy. 2014;72:31–38. doi: 10.1016/j.anucene.2014.04.031
   Web of Science ®Google Scholar
• Sakai M, Koshizuka S. Large-scale discrete element modeling in pneumatic conveying. Chem Eng Sci. 2009;64(3):533–539. doi: 10.1016/j.ces.2008.10.003
   Web of Science ®Google Scholar
• Govender N. A DEM study on the thermal conduction of granular material in a rotating drum using polyhedral particles on GPUs. Chem Eng Sci. 2022;252:117491. doi: 10.1016/j.ces.2022.117491
   Web of Science ®Google Scholar
• Xie Z, Shen Y, Takabatake K, et al. Coarse-grained DEM study of solids sedimentation in water. Powder Technol. 2020;361:21–32. doi:10.1016/j.powtec.2019.11.034
   Web of Science ®Google Scholar
• Mori Y, Wu CY, Sakai M. Validation study on a scaling law model of the DEM in industrial gas-solid flows. Powder Technol. 2019;343:101–112. doi: 10.1016/j.powtec.2018.11.015
   Web of Science ®Google Scholar
• Widartiningsih PM, Mori Y, Takabatake K, et al. Coarse graining DEM simulations of a powder die-filling system. Powder Technol. 2020;371:83–95. doi:10.1016/j.powtec.2020.05.063
   Web of Science ®Google Scholar
• Di Renzo A, Napolitano E, Di Maio F. Coarse-Grain DEM Modelling in Fluidized Bed Simulation: A Review. Processes. 2021;9(2):279. doi: 10.3390/pr9020279
   Web of Science ®Google Scholar
• Markauskas D, Kačeniauskas A, Maknickas A. Dynamic domain decomposition applied to hopper discharge simulation by discrete element method. Inf Technol Control. 2011;40(4). doi: 10.5755/j01.itc.40.4.978
   Web of Science ®Google Scholar
• Gan JQ, Zhou ZY, Yu AB. A GPU-based DEM approach for modelling of particulate systems. Powder Technol. 2016;301:1172–1182. doi: 10.1016/j.powtec.2016.07.072
   Web of Science ®Google Scholar
• He Y, Muller F, Hassanpour A, et al. A CPU-GPU cross-platform coupled CFD-DEM approach for complex particle-fluid flows. Chem Eng Sci. 2020;223:115712. doi:10.1016/j.ces.2020.115712
   Web of Science ®Google Scholar
• Gan J, Evans T, Yu A. Application of GPU-DEM simulation on large-scale granular handling and processing in ironmaking related industries. Powder Technol. 2020;361:258–273. doi: 10.1016/j.powtec.2019.08.043
   Web of Science ®Google Scholar
• Kureck H, Govender N, Siegmann E, et al. Industrial scale simulations of tablet coating using GPU based DEM: A validation study. Chem Eng Sci. 2019;202:462–480. doi:10.1016/j.ces.2019.03.029
   Web of Science ®Google Scholar
• Herman AP, Gan J, Yu A. GPU-based DEM simulation for scale-up of bladed mixers. Powder Technol. 2021;382:300–317. doi: 10.1016/j.powtec.2020.12.045
   Web of Science ®Google Scholar
• Sun Q, Peng W, Yu S, et al. A review of HTGR graphite dust transport research. Nucl Eng Des. 2020;360:110477. doi:10.1016/j.nucengdes.2019.110477
   Web of Science ®Google Scholar
• Aissa A, Abdelouahab M, Noureddine A, et al. Ranz and Marshall correlations limits on heat flow between a sphere and its surrounding gas at high temperature. Therm Sci. 2015;19(5):1521–1528. doi: 10.2298/TSCI120912090A
   Web of Science ®Google Scholar
• Li J, Mason DJ. A computational investigation of transient heat transfer in pneumatic transport of granular particles. Powder Technol. 2000;112(3):273–282. doi: 10.1016/S0032-5910(00)00302-8
   Web of Science ®Google Scholar
• Sun B, Tenneti S, Subramaniam S. Modeling average gas–solid heat transfer using particle-resolved direct numerical simulation. Int J Heat Mass Transf. 2015;86:898–913. doi: 10.1016/j.ijheatmasstransfer.2015.03.046
   Web of Science ®Google Scholar
• Chen L, Lee J. Effects of inserted sphere on thermal field and heat-transfer characteristics of face-centered-cubic-structured pebble bed. Appl Therm Eng. 2020;172:115151. doi: 10.1016/j.applthermaleng.2020.115151
   Web of Science ®Google Scholar
• Wakao N, Kaguei S, Funazkri T. Effect of fluid dispersion coefficients on particle-to-fluid heat transfer coefficients in packed beds. Chem Eng Sci. 1979;34(3):325–336. doi: 10.1016/0009-2509(79)85064-2
   Web of Science ®Google Scholar