IENCE SC • VTT SCIENCE • T S E Development of a stochastic temperature treatment N C O H I N technique for Monte Carlo neutron tracking S O I V Dissertation L • O S G Nuclear fission reactors are based on a self-sustaining fission T 84 Y H • R G chain reaction, carried on by neutrons. Since the reaction I E L S H 84 E G A probabilities and scattering kinematics of neutrons are strongly I R H C affected by the thermal motion of target nuclides, the temperatures H of nuclear reactor materials need to be taken into account in all reactor physical analyses. Detailed modeling of the temperature distributions within operating nuclear reactors is often problematic when using traditional neutron transport methods, which require the interaction probability data to be stored in the computer memory separately at each temperature appearing in the system. Development of a stochastic temperature treatment... Consequently, the feasible level of detail in the temperature distributions is always restricted by the memory capacity of computers. This thesis covers the previous development of the Target Motion Sampling (TMS) temperature treatment technique, which is capable of taking the effects of thermal motion on interaction probabilities into account on-the-fly during Monte Carlo neutron transport calculation. With the TMS method, arbitrary temperature distributions can be modeled based on interaction probability data at one temperature only, which significantly facilitates high-fidelity neutron transport calculations. The results suggest that the TMS method is both accurate and well-feasible in terms of performance, and thus it can be considered a practical temperature treatment technique for Monte Carlo neutron tracking. Development of a stochastic temperature treatment technique for Monte Carlo neutron ISBN 978-951-38-8242-6 (Soft back ed.) ISBN 978-951-38-8243-3 (URL: http://www.vtt.fi/publications/index.jsp) tracking ISSN-L 2242-119X ISSN 2242-119X (Print) ISSN 2242-1203 (Online) Tuomas Viitanen VTT SCIENCE 84 Development of a stochastic temperature treatment technique for Monte Carlo neutron tracking Tuomas Viitanen Thesis for the degree of Doctor of Science to be presented with due permission for public examination and criticism in Auditorium E, at Aalto University (Otakaari 1, Espoo, Finland), on the 8th of May, 2015, at 1 p.m. ISBN 978-951-38-8242-6 (Soft back ed.) ISBN 978-951-38-8243-3 (URL: http://www.vtt.fi/publications/index.jsp) VTT Science 84 ISSN-L 2242-119X ISSN 2242-119X (Print) ISSN 2242-1203 (Online) Copyright © VTT 2015 JULKAISIJA – UTGIVARE – PUBLISHER Teknologian tutkimuskeskus VTT Oy PL 1000 (Tekniikantie 4 A, Espoo) 02044 VTT Puh. 020 722 111, faksi 020 722 7001 Teknologiska forskningscentralen VTT Ab PB 1000 (Teknikvägen 4 A, Esbo) FI-02044 VTT Tfn +358 20 722 111, telefax +358 20 722 7001 VTT Technical Research Centre of Finland Ltd P.O. Box 1000 (Tekniikantie 4 A, Espoo) FI-02044 VTT, Finland Tel. +358 20 722 111, fax +358 20 722 7001 Grano Oy, Kuopio 2015 Development of a stochastic temperature treatment technique for Monte Carlo neutron tracking Tuomas Viitanen. Espoo 2015. Abstract Thermal motion of nuclides has a significant effect on the reaction probabilities and scattering kinematics of neutrons. Since also the nuclides in nuclear reactor materi- als are in constant thermal motion, the temperature-induced effects need to be taken into account in all neutron transport calculations. This task is notably complicated by the fact that the temperature distributions within operating power reactors are always non-uniform. With conventional transport methods, accurate modeling of temperature distribu- tions within a reactor is cumbersome. The temperature distributions that are in reality continuous in space need to be approximated with regions of uniform temperature. More importantly, pre-generated temperature-dependent data on reaction probabil- ities must be stored in the computer memory at each temperature appearing in the system, which restricts the feasible level of detail in the modeling of temperature distributions. This thesis covers the previous development of a temperature treatment technique for modeling the effects of thermal motion on-the-fly during Monte Carlo neutron transport calculation. Thus, the Target Motion Sampling (TMS) temperature treat- ment technique is capable of modeling arbitrary temperature distributions such that the memory footprint of the interaction data is unaffected by the resolution of the tem- perature discretization. As a very convenient additional feature the TMS technique also provides for modeling of continuous temperature distributions as-is, making the discretization of temperature distributions unnecessary altogether. The basic idea of the TMS technique is introduced, and the results are shown to be in accordance with reference solutions calculated with conventional neutron transport methods. The TMS method is developed further by optimizing its imple- mentation, and the performance is compared against conventional neutron trans- port methods in different reactor systems. The results show that the TMS method significantly facilitates the modeling of complex temperature distributions in nuclear reactors without compromising the accuracy of the calculations. The method also proves to be well-feasible in terms of performance, especially as long as the number of temperature-dependent nuclides remains relatively small. Keywords Monte Carlo, neutron tracking, temperature, Doppler-broadening, DBRC, Target motion sampling, TMS, temperature majorant cross section 3 Academic dissertation Supervising professor Prof. Filip Tuomisto Department of Applied Physics Aalto University, Finland Thesisadvisor Adj. Prof.JaakkoLeppänen Nuclear Energy VTT Technical Research Centre of Finland Ltd Preliminary examiners Prof. Brian Kiedrowski Nuclear Engineering and Radiological Sciences University of Michigan Prof. Kord Smith Nuclear Science & Engineering Massachusetts Institute of Technology Opponent Prof.SedatGoluoglu Department of Material Sciences & Engineering University of Florida 4 Acknowledgments I wish to express my special appreciation and thanks to my instructor and mentor, the Father of Serpent, Dr. Jaakko Leppänen, for the inspiring research topic and all the invaluable guidance and support during the process. Having the opportunity to test and implement the new method as a part of Serpent has been extremely motivating, and, of course, the thesis would not exist without the ambitious Serpent code development project. Working together has also been a lot of fun. I would like to thank my other colleagues at VTT for the great working atmosphere and for providing help whenever needed. I am especially grateful to our Team Leader, Dr. Petri Kotiluoto, and the Head of Research Area, Dr. Timo Vanttola, for their continuous support, and Dr. Maria Pusa for providing important comments on the key articles of the thesis. I am obliged to Prof. Filip Tuomisto of the Department of Applied Physics, Aalto University, for acting as my supervisor and for Prof. Sedat Goluoglu of the Depart- ment of Material Sciences & Engineering, University of Florida, for acting as my opponent in the defense of this thesis. I wish to express my gratitude to the pre- liminary examiners Prof. Brian Kiedrowski, University of Michigan, and Prof. Kord Smith, Massachusetts Institute of Technology (MIT), for their careful work and in- sightful views on the thesis. I would like to thank also Prof. Benoit Forget (MIT) for hosting a short but very efficient and educative visit to MIT in the fall of 2013, during which this thesis took a giant step forward. Finally, I want to thank the Polytech Choir for filling the musical void within for the past 9 years. Above all, I wish to thank thank my beloved wife Elina for her love and support during the long process. This work has been funded through the Finnish Research Programme on Nuclear Power Plant Safety SAFIR and the Academy of Finland research program NUMPS. 5 List of publications This thesis consists of the present article and the following seven publications. I T. Viitanen and J. Leppänen, “Explicit treatment of thermal motion in continuous-energy Monte Carlo tracking routines”, Nucl. Sci. Eng., 171, pp. 165- 173, (2012). II T. Viitanen and J. Leppänen, “Explicit temperature treatment in Monte Carlo neutron tracking routines — first results”, In proc. PHYSOR-2012, Knoxville, TN, Apr. 15-20 2012, (2012). III T. Viitanen and J. Leppänen, “Optimizing the implementation of the target mo- tion sampling temperature treatment technique — How fast can it get?”, In proc. M&C 2013, Sun Valley, ID, May 5-9 2013, (2013). IV T. Viitanen and J. Leppänen, “Target motion sampling temperature treatment technique with elevated basis cross-section temperatures”, Nucl. Sci. Eng., 177, pp. 77-89, (2014). V T. Viitanen and J. Leppänen, “Temperature majorant cross sections in Monte Carlo neutron tracking”, Nucl. Sci. Eng., Accepted for publication Aug 31. 2014. VI T. Viitanen and J. Leppänen “Effect of the target motion sampling temperature treatment method on the statistics and performance”, Ann. Nucl. Energy, Ac- cepted for publication Aug 21. 2014. VII T. Viitanen, J. Leppänen and B. Forget, “Target motion sampling temperature treatment technique with track-length estimators in OpenMC — Preliminary re- sults”, In proc. PHYSOR-2014, Kyoto, Japan, Sep. 28-Oct 3. 2014, (2014). 6 Author’s contribution Publication I: Explicit treatment of thermal motion in continuous-energy Monte Carlo tracking routines The author