Current status and outlook of thermomechanics research and development for blanket pebble beds

1. Current status and outlook of thermomechanics research and development for blanket pebble beds Jon Van Lew Ph.D. Student UCLA Fusion Science and Technology Center Ratna Kumar Annabattula Institute for Applied Materials KIT, Germany

2. Outline • Introduction to thermomechanic properties • Experimental work • Lithium ceramics • Beryllium • Discussion Topics № 1 • Modeling • Discussion Topics № 2 • Discussion Topics № 3

3. Introduction – most important physical properties • Interface conductance • Effective thermal conductivity • Modulus of deformation • Creep • Coefficient of thermal expansion

4. Experimental work review Lithium ceramics

5. State of Li4SiO4 and Li2TiO3 pebble bed characterization • Mechanical behavior of Li4SiO4 on temperature ranges up to 900°C[6-8,18] and data for Li2TiO3up to 850°C[15] • Modulus of deformation fit to • Creep strain given to fit A,B,C,n,m,p determined experimentally[7,18] • Many experiments of uncompressed Li4SiO4[2-4]and Li2TiO3[3,10-13] pebble beds a and b determined experimentally

6. Thermal conductivities of compressed pebble beds[9] Li4SiO4 • a With: Li2TiO3 • bEnoeda, et al.[3]: SBZ model fit with

7. Tanigawa, et al.[14] have done experiments on meta-titanite to show thermal conductivity at low temperature is affected by annealing After annealing at 973 K increased Before annealing • Piazza, et al.[32] note a decrease in crush load after long-term annealing • Still above acceptable blanket design values

8. Experimental work review Beryllium

9. Beryllium pebble bed thermomechanics and heat transfer characterization • Modulus of deformation relationship[7,8,18] C, m determined experimentally[18] • Creep is pronounced at temps above 650°C A,B,n,pdetermined experimentally[8] • Compressed beryllium beds[16-19] determined experimentally[19] Thermal conductivity of 1 mm beryllium pebbles as a function of strain.[18]

10. Discussion Points № 1 • Are the history effects of thermo-mechanical cycles accounted for in models? We think “Yes” to some extent Any comments/inputs? • What other physical properties are also important? Such as friction coefficient of pebbles, crush loads under multiple contacts…. • Irradiated material properties and similar correlations deduced for un-irradiated pebbles? Any other suggestions? • What confidence do we have on wall interface interactions?

11. Review of two, mature continuum models (FEM) for pebble beds Pebble bed modeling

12. Model benchmarking with HEXCALIBER results • Dell’Orco, et al., with DIN’s 3D FEM model performed benchmarking tests of the HEXCALIBER experimental setup[27]

13. FZK Model[22] Benchmarking • Applied their model to simulate the HELICA (shown) and HEXCALIBER[24,25] • Did not validate against HEXCALIBER • Small gap formation is detected in the analysis • In the range of 0.25–0.38 mm

14. Discussion Points № 2 • Constitutive relationships have been provided from experimental data • Phenomenological models built upon experimental fits. • Develop continuum level constitutive relations from discrete element • models– any work under progress or suggestions? • Benchmarking begun for European models (KIT and DIN) • DIN models have obtained good agreement with experiments on temperature calculations • Disagreement between models concerning gap formation • No direct benchmarking/validation of KIT model

15. Discussion Points № 3 • Do we have enough confidence of the impact of pebble bed thermomechanics on the design during beginning of life (BOF)? • What is the maximum allowable stress that the pebbles can be exposed during the operations? • Can this be related to pebble properties during fabrication? • What, if any, are the design criteria to which the pebble bed should be imposed? • If we would develop a roadmap for the pebble bed thermomechanics how would it look? • What criteria inform each step? • Where we are with respect to this roadmap? 

16. References • A.R. Raffray. R&D Plan for Addressing the Thermomechanical Behavior of Lithium Ceramic and Beryllium Pebble Beds in Fusion Blankets. University of California, San Diego, UCSD-ENG-095. • Dalle Donne et al., Measurements of the effective thermal conductivity of a Li4SiO4 pebble bed, Fusion Engineering and Design 49-50, November 2000. • M. Enoeda, Y. Ohara, N. Roux, A. Ying, S. Malang, Effective thermal conductivity measurements of the ceramic breeder pebble beds using the hot wire method under IEA collaboration program, CBBI-8, Colorado Springs, CA, Oct.6-8, 1999. • M. Enoeda, K.H. Furuya, S. Takatsu, T. Kikuchi, Hatano, Effective thermal conductivity measurements of the binary pebble beds by hot wire method for the breeding blanket, Fusion Technology 34, November, 1998. • L. Giancarli, V. Chuyanov, M. Abdou, M. Akiba, B. Hong, R. Lasser, C. Pan, and Y. Strebkov. Test blanket modules in ITER: An overview on proposed designs and required DEMO-relevant materials. Journal of Nuclear Materials 367-370:1271–1280, August 2007. • A.Y. Ying, Z. Lu, M. Abdou, Mechanical behavior and design database of packed beds for blanket designs, Fusion Engineering and Design 39-40, 1998 • Reimann, J., Arbogast, E., Behnke, M., Müller, S., Thomauske, K., Thermomechanical behaviour of ceramic breeder and beryllium pebble beds. Fusion Engineering and Design 49-50, 643-649, 2000. • Reimann, J., Wörner, G., Thermal creep of Li4SiO4 pebble beds. Fusion Engineering and Design 58-59, 647-651, Nov. 2001. • Reimann, J., Hermsmeyer, S., Nov. 2002. Thermal conductivity of compressed ceramic breeder pebble beds. Fusion Engineering and Design 61-62, 345-351. • Saito, S., Tsuchiya, K., Kawamura, H., Terai, T., Tanaka, S., Mar. 1998. Density dependence on thermal properties of Li2TiO3 pellets. Journal of Nuclear Materials 253 (1-3), 213-218.

17. References (continued) • Hoshino, T., Dokiya, M., Terai, T., Takahashi, Y., Yamawaki, M., Nov. 2002. Non-stoichiometry and its effect on thermal properties of Li2TiO3. Fusion Engineering and Design 61-62, 353-360. • Piazza, G., Enoeda, M., Ying, A., Nov. 2001. Measurements of effective thermal conductivity of ceramic breeder pebble beds. Fusion Engineering and Design 58-59, 661-666. • Abou-Sena, A., Ying, A., Abdou, M., Jan. 2007. Experimental measurements of the effective thermal conductivity of a lithium titanate (Li2TiO3) pebbles-packed bed. Journal of Materials Processing Technology 181 (1-3), 206-212. • Tanigawa, H., Hatano, T., Enoeda, M., Akiba, M., 2005. Effective thermal conductivity of a compressed Li2TiO3 pebble bed. Fusion Engineering and Design 75-79, 801-805. • Lulewicz, J. D., Roux, N., Piazza, G., Reimann, J., van der Laan, J., Dec. 2000. Behaviour of Li2ZrO3 and Li2TiO3 pebbles relevant to their utilization as ceramic breeder for the HCPB blanket. Journal of Nuclear Materials 283-287, 1361-1365. • Tanigawa, H., Tanaka, Y., Enoeda, M., Dec. 2010. Packing behaviour of a Li2TiO3 pebble bed under cyclic loads. Journal of Nuclear Materials. • Piazza, G., Reimann, J., Hofmann, G., Malang, S., Goraieb, A. A., Harsch, H., Sep. 2003. Heat transfer in compressed beryllium pebble beds. Fusion Engineering and Design 69 (1-4), 227-231. • Reimann, J., Boccaccini, L., Enoeda, M., Ying, A. Y., Nov. 2002. Thermomechanics of solid breeder and Be pebble bed materials. Fusion Engineering and Design 61-62, 319-331. • Reimann, J., Piazza, G., Harsch, H., Feb. 2006. Thermal conductivity of compressed beryllium pebble beds. Fusion Engineering and Design 81 (1-7), 449-454.

18. References (continued) • Dell'Orco, G., Maio, P. A. D., Giammusso, R., Tincani, A., Vella, G., 2007. A constitutive model for the thermo-mechanical behaviour of fusion-relevant pebble beds and its application to the simulation of HELICA mock-up experimental results. Fusion Engineering and Design 82 (15-24), 2366-2374. • DiMaio2008 • Gan, Y., Kamlah, M., 2007. Identification of material parameters of a thermo-mechanical model for pebble beds in fusion blankets. Fusion Engineering and Design 82 (2), 189-206. • Di Maio, P.A., R. Giammusso, G. Vella, Sezione di prova HELICA. Analisitermomeccaniche, Rapporto del Dipartimento di IngegneriaNucleare per lENEA-Brasimone, Universita di Palermo, Giugno, 2005 • Gan, Y., Kamlah, M., Dec. 2008. Thermo-mechanical analysis of pebble beds in HELICA mock-up experiments. Fusion Engineering and Design 83 (7-9), 1313-1316. • Gan, Y., Kamlah, M., Apr. 2009. Thermo-mechanical analyses of HELICA and HEXCALIBER mock-ups. Journal of Nuclear Materials 386-388, 1060-1064. • Gan, Y., Kamlah, M., Jan. 2010. Thermo-mechanical modelling of pebble bed–wall interfaces. Fusion Engineering and Design 85 (1), 24-32. • Dell'Orco, G., Di Maio, P. A., Giammusso, R., Tincani, A., Vella, G., Aug. 2010. On the theoretical–numerical study of the HEXCALIBER mock-up thermo-mechanical behaviour. Fusion Engineering and Design 85 (5), 694-706. • Zhao, Z., Feng, K. M., Feng, Y. J., Dec. 2010. Theoretical calculation and analysis modeling for the effective thermal conductivity of Li4SiO4 pebble bed. Fusion Engineering and Design 85 (10-12), 1975-1980. • Poitevin, Y., Boccaccini, L. V., Zmitko, M., Ricapito, I., Salavy, J. F., Diegele, E., Gabriel, F., Magnani, E., Neuberger, H., Lässer, R., Dec. 2010. Tritium breeder blankets design and technologies in europe: Development status of ITER test blanket modules, test & qualification strategy and roadmap towards DEMO. Fusion Engineering and Design 85 (10-12), 2340-2347.

19. References (continued) • An, Z., Ying, A., Abdou, M., 2007. Application of discrete element method to study mechanical behaviors of ceramic breeder pebble beds. Fusion Engineering and Design 82 (15-24), 2233-2238. • Gan, Y., Kamlah, M., Feb. 2010. Discrete element modelling of pebble beds: With application to uniaxial compression tests of ceramic breeder pebble beds. Journal of the Mechanics and Physics of Solids 58 (2), 129-144. • Piazza, G., Reimann, J., Günther, E., Knitter, R., Roux, N., Lulewicz, J. D., Dec. 2002. Characterisation of ceramic breeder materials for the helium cooled pebble bed blanket. Journal of Nuclear Materials 307-311, 811-816.