Granular Dynamics in Pebble Bed Reactor Cores by Michael Robert Laufer A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Engineering – Nuclear Engineering in the Graduate Division of the University of California, Berkeley Committee in Charge: Professor Per Peterson, Chair Professor Brian Wirth Professor Tarek Zohdi Dr. Robert Budnitz Spring 2013 Granular Dynamics in Pebble Bed Reactor Cores Copyright 2013 by Michael Robert Laufer Abstract Granular Dynamics in Pebble Bed Reactor Cores by Michael Robert Laufer Doctor of Philosophy in Engineering – Nuclear Engineering University of California, Berkeley Professor Per F. Peterson, Chair This study focused on developing a better understanding of granular dynamics in pebble bed reactor cores through experimental work and computer simulations. The work completed includes analysis of pebble motion data from three scaled experiments based on the annular core of the Pebble Bed Fluoride Salt-Cooled High- Temperature Reactor (PB-FHR). The experiments are accompanied by the development of a new discrete element simulation code, GRECO, which is designed to offer a simple user interface and simplified two-dimensional system that can be used for iterative purposes in the preliminary phases of core design. The results of this study are focused on the PB-FHR, but can easily be extended for gas-cooled reactor designs. Experimental results are presented for three Pebble Recirculation Experiments (PREX). PREX 2 and 3.0 are conventional gravity-dominated granular systems based on the annular PB-FHR core design for a 900 MWth commercial prototype plant and a 16 MWth test reactor, respectively. Detailed results are presented for the pebble velocity field, mixing at the radial zone interfaces, and pebble residence times. A new Monte Carlo algorithm was developed to study the residence time distributions of pebbles in different radial zones. These dry experiments demonstrated the basic viability of radial pebble zoning in cores with diverging geometry before pebbles reach the active core. Results are also presented from PREX 3.1, a scaled facility that uses simulant materials to evaluate the impact of coupled fluid drag forces on the granular dynamics in the PB-FHR core. PREX 3.1 was used to collect first of a kind pebble motion data in a multidimensional porous media flow field. Pebble motion data were collected for a range of axial and cross fluid flow configurations where the drag forces range from half the buoyancy force up to ten times greater than the buoyancy force. Detailed analysis is presented for the pebble velocity field, mixing behavior, and residence time distributions for each fluid flow configuration. 1 The axial flow configurations in PREX 3.1 showed small changes in pebble motion compared to a reference case with no fluid flow and showed similar overall behavior to PREX 3.0. This suggests that dry experiments can be used for core designs with uniform one-dimensional coolant flow early in the design process at greatly reduced cost. Significant differences in pebble residence times were observed in the cross fluid flow configurations, but these were not accompanied by an overall horizontal diffusion bias. Radial zones showed only a small shift in position due to mixing in the diverging region and remained stable in the active core. The results from this study support the overall viability of the annular PB-FHR core by demonstrating consistent granular flow behavior in the presence of complex reflector geometries and multidimensional fluid flow fields. GRECO simulations were performed for each of the experiments in this study in order to develop a preliminary validation basis and to understand for which applications the code can provide useful analysis. Overall, the GRECO simulation results showed excellent agreement with the gravity-dominated PREX experiments. Local velocity errors were found to be generally within 10-15% of the experimental data. Average radial zone interface positions were predicted within two pebble diameters. GRECO simulations over predicted the amount of mixing around the average radial zone interface position and therefore can be treated as a conservative upper bound when used in neutronics analysis. Residence time distributions from the GRECO velocity data based on the Monte Carlo algorithm closely matched those derived from the experiment velocity statistics. GRECO simulation results for PREX 3.1 with coupled drag forces showed larger errors compared to the experimental data, particularly in the cases with cross fluid flow. The large discrepancies suggest that GRECO results in systems with coupled fluid drag forces cannot be used with high confidence at this point and future development work on coupled pebble and fluid dynamics with multidimensional fluid flow fields is required. 2 To my wife, Carolyn. You are the most caring and dedicated person that I know. Your support and encouragement made this possible. I love you with all of my heart. To my parents, Henry and Marsha. You inspire me to take on the big problems in the world. i Acknowledgements I am deeply grateful to many people who have helped to make this dissertation possible both in my time at U.C. Berkeley and before. I am sure that I will forget to acknowledge some of them here and I must apologize in advance for any oversight. First, I would like to express many thanks to my advisor, Per Peterson, who has been a constant source of support and interesting insights throughout this project. It is not an exaggeration to say that the origins of this project came from Per asking a supposedly simple question based on the results of the 2009 NE 270 Senior Design Project. I offered to investigate and four years later this dissertation is the answer. He also has been helpful in providing the critical pressure at the end of this process that has prevented me from spending too much time working on the many other interesting projects in our laboratory. I must also thank each of the other members of my dissertation committee. Brian Wirth was a reliable source of encouragement and provided important feedback early in this process on what scope of work I should pursue. Tarek Zohdi provided useful resources on particle simulations with coupled physics even more complicated than that covered in this thesis. Finally, Bob Budnitz from Lawrence Berkeley Laboratory provided a valuable outside perspective and an eye for detail that has improved this dissertation. He was also a source of great enthusiasm. Jeff Bickel has been invaluable throughout this process and the experimental components of this project would not have been possible without his help. Jeff built PREX 3.0 as part of his master’s project in 2010 and it was the first experiment that I used to produce data on the motion of pebbles at the visible surface. As a research engineer in our laboratory, Jeff is responsible for most of the detailed design and fabrication of PREX 3.1. A number of graduate students at U.C. Berkeley made valuable contributions to this project and have been a source of support through this process. I owe a great deal of gratitude to Ed Blandford, who provided me with great advice throughout my graduate studies and who I view as an important mentor. Jeff Powers, Raluca (Scarlat) Merric de Bellefon, and Tommy Cisneros all started with me in the same year and we have each studied different aspects of pebble fuel. Jeff and I had regular coffee outings that were a staple of my graduate school experience. I must also thank David Krumwiede for his help in keeping our exciting new granular flow projects in the Thermal-Hydraulics laboratory moving forward while I have been working hard to wrap up this thesis. Lisa Zemelman, the Graduate Student Affairs Officer for the ii Nuclear Engineering Department at U.C. Berkeley, has also been extremely helpful throughout my graduate program in navigating the university bureaucracy. The experimental results in this thesis were collected with the help of many U.C. Berkeley undergraduate students. I am thankful to all of the students who helped to build and run the PREX experiments, in addition to many hours of pebble sorting. The 2009 NE 170 Senior Design Class (Rada Hong, Steve Huber, Kenneth Lee, Patrick Purcell, Sahak Margossian, and John-David Seelig) built PREX 2 and I must acknowledge their role in helping me find this interesting topic. Kyle Chestnut, Sebastian Dionisio, and John Doojphibupol helped to collect data for this project from PREX 2 and 3.1. Andrew Serpa and Grant Buster did a meticulous job in their residence time studies with PREX 3.0. Alex Dixon also helped with the pebble projects in the lab, including the amazing task of figuring out how to get metal pins through the plastic pebbles for our future work in the X-PREX facility. My family has also been a great source of support and encouragement throughout my life. My parents provide constant inspiration to take on big challenges in life and are always cheering me on. I also owe a great deal of thanks to Jerry Cahill and Kathy King, who have welcomed me into their family and made me feel at home here in the Bay Area. I am also thankful for the love and support of my brothers and their families. I am incredibly grateful to my wife, Carolyn, who provided constant emotional support through both my undergraduate and graduate studies. I am in constant amazement of her tireless work ethic and she has helped to keep me on track throughout this process. She has also made sure that I take care of myself when I get absorbed in my work. I am looking forward to all of our future adventures in life together.