Ceramic breeder pebble beds undergo complex thermo-mechanical interactions during blanket operations due to stress build-up and relaxation under the effects of confined thermal expansion, thermal cycling, and creep. Understanding the evolution of such processes can aid in guiding blanket design/assembly, breeder materials developments, predicting performance and possible failure modes identification and remedy. Experimental efforts on ceramic pebble beds and their associated constitutive equations have been derived from single effect tests where one parameter is varied and its effects are isolated and studied separately (e.g. using constant temperatures and externally applied loads). These experiments are incapable of reproducing the true multiple/synergistic effects of the physics that occur in real blankets, and the phenomena arising from the interactions of single effects are yet to be discovered. For example, it is unclear whether the combined effect of plasticity and creep under reactor-relevant loading conditions will either enable the altered pebble bed packing configuration to reach an acceptable self-regulating temperature state, or significantly deteriorate its heat transfer efficiency and subsequent tritium release. Therefore, studying the isolated thermal and mechanical effects is not sufficient to predict pebble bed behavior; it is the coupling and interdependence between the dynamic thermal and mechanical fields, as well as the synergistic effects between the various modes of deformation that is key to fully understand and predict the pebble bed behavior in a realistic fusion environment.
Previous mock-up experimental campaigns thus far have suffered from critical shortfalls which severely hamstringed their scientific impact. The lack of experimental data that incorporates multiple-effects interaction in addition to the complexity of building a full-scaled breeder unit mock-up triggered the need for this experimental and modeling effort. The body of work presented in this document served the following key points: (1) established and validated the practicality of various volumetric heating simulation techniques for representative thermo-mechanics study, (2) recreated prototypical breeder unit’s thermal-hydraulic behavior using a scaled-down reduced activation ferretic steel box with optimized manifold design connected to oil cooling loop facility, (3) evaluated the pebble bed thermo-mechanics using a novel non-intrusive in-situ tactile pressure sensing technology capable of generating real-time contact pressure maps that reveal the spatial and temporal stress evolution with emphasis on understanding the roles that each of the thermo-mechanical forces play in dictating the pebble bed’s equilibrium operating conditions, and (4) developed and benchmarked thermo-mechanical Finite Element Method (FEM) code that is able to predict the pebble bed’s thermo-mechanical evolution under the effects of creep and thermal cycling, in addition to providing useful extrapolations beyond the experimental limitations. Accordingly, this study introduces first-of-a-kind experimental techniques that enable us to both create as well as investigate an environment in which the pebble bed stresses are organically generated as a result of relevant temperature gradients and magnitudes that allows for observing the combined thermo-mechanical interaction effects on contact pressure rise and fall, as well as temperature fluctuations.
A comprehensive picture of the stress distribution and evolution with time and thermal cycling inside the pebble bed was captured and carefully investigated. The real-time in-situ spatial and temporal thermo-mechanical interactions and evolution were captured under reactor-relevant conditions for the first time using the novel tactile pressure sensor technology. Two types of bed-wall contact pressure drop were recorded: (1) within the subsequent cycles due to pebbles irreversible rearrangements, and (2) within the cycle itself as a result of creep/stress-relaxation. The measured stresses were self-generated, unlike previous experiments where an external force has to be applied on the bed. Similarly, two mechanisms of self-regulation that contributed to the bed’s thermo-mechanical stability were identified and studied: (1) stress self-regulation as a result of pressure rise and fall due to thermal expansion and creep/thermal cycling, respectively, and (2) temperature self-regulation as the rise in temperatures caused by the deteriorated interface conductance and loosely packed pebbles with thermal cycling in the non-creep region is balanced by the temperature reduction in the core creep zone due to the locally enhanced thermal conductivity. These two mechanisms are highly desirable as they lower the probability of the events of pebbles crushing/further sintering and thermal runaways under high temperatures and poor heat extraction. The results also showed that the use of effective bed thermal conductivity, that is widely used in the solid breeder pebble bed community, needs to be reevaluated since the thermal conductivity is not only a function of temperature and pressure, but it also varies greatly with the spatial distribution in the bed. Moreover, the positive effects of creep have been experimentally verified and new effects have been discovered. In addition to stress relief after the build-up caused by confined thermal expansion and irradiation-induced swelling, creep flattens out the temperature profile by locally enhanced thermal conductivity at the hottest core region (gradient smoothing) which not only reduces chances of thermal runaways by staying within the design temperature window, but may also allow the possibility of operating at higher Neutron Wall Load (NWL) after the first 24 hours of operation which could yield tremendous benefits for power extraction. Pebble bed pre-conditioning mechanisms have been investigated as part of the filling procedure and shown high promise of improving packing density and hence Tritium Breeding Ratio (TBR) and thermo-mechanical stability which would enable us to reach an optimal initial packing configuration that allows for safe operation within the design margins.
The phenomenological model developed and validated in this work assumes a pebble bed is a continuum medium and describes the typical overall behavior of the material under fusion-relevant conditions. The modeling incorporates previously derived constitutive equations and described the thermo-mechanical response of a pebble bed by a nonlinear elasticity law, a modified Drucker-Prager plasticity model, a creep model and temperature-dependent physical properties. Finally, a benchmark exercise has been carried out on the basis of the present phenomenological model. The results from the simulation have been compared to the experimental data, showing that the present modelling is suitable for thermo-mechanical analyses of fusion blankets. The model is able to quantify and map out the spatial and temporal stress distributions and evolution of the first thermal cycle as well as for continuous operation, which is experimentally proven to capture the maximum stress the bed will experience during operation. It can also extrapolate the stress results to every point in the bed after validating the interface stress distributions with experiments, which can (1) guide blanket designers in determining geometrical features, sizing components and selecting materials, and (2) predict failure of pebbles. The model can also predict the spatial and temporal creep strain/stress relaxation evolution, which enables locating regions with high propensity of sintering and correlate creep strain with the volume % of sintered pebbles from experiments in order to assess what percentage of creep strain can be tolerated.
Furthermore, the findings of this work provide a comprehensive framework and guiding objectives to pave the way for “Next-Generation” ceramic breeder mock-up experiments. On the experimental side, test article dimensions’ optimization recommendations were provided to account for incorporating various complex flange connections, minimizing packing disturbances, and allowing low wall temperature operation (300 C at a minimum) for safe sensor operation. Further experimental enhancements that are necessary for a more fusion relevant environment have also been discusses in later chapters of this work. As for the modeling front, all the limitations were outlined and recommendations for using advanced techniques such as adaptive meshing, DEM/FEM coupling, and direct thermo-mechanical coupling were provided for use when the modeling technology and computational resources reach feasible levels. The work presented in this document not only provides novel experimental techniques and data that enhance our understanding of synergistic thermo-mechanical interactions and effects, but it also offers models that, through the validation presented in this work, can now be used to predict the first cycle and continuous operation thermo-mechanics characteristics critical to the success of breeder operations.