Modelling of fast neutron transients in an accelerator driven system [Elektronische Ressource] / vorgelegt von Cristian Rabiti

Crabiti

Informations

• Publié par: universitat_stuttgart
• Publié le: 01 janvier 2007
• Nombre de lectures: 24
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Institut für Kernenergetik
und Energiesysteme



Modelling of Fast Neutron

Transients in an Accelerator

Driven System






Cristian Rabiti


Universität Stuttgart IKE 6-202








MODELLING OF FAST NEUTRON TRANSIENTS IN
AN ACCELERATOR DRIVEN SYSTEM
Von der Fakultät für Maschinenbau der Universität Stuttgart zur
Erlangung der Würde eines
Doktor-Ingenieurs (Dr.-Ing.) genehmigte Abhandlung

vorgelegt von

Cristian Rabiti
aus Forlì (FC), Italien

Hauptberichter: Prof. G. Lohnert, Ph. D.
Mitberichter: Frau Prof. Dr. rer. nat. B. Wohlmuth


Tag der mündlichen Prüfung: 10. November 2006


Institut für Kernenergetik und Energiesysteme der Universität Stuttgart

2007










Acknowledgment
The number of people I wish to thank is very large. This tells me that I was fortunate in my
professional life to meet such good people. I wish to start with my thesis from which
everything has originated which significant credit is due to Dr. Richard Sanchez. From my
discussions with him I attribute my passion for applied mathematics in the field of neutron
transport where by I would not be at this point, thus I thank Dr. Sanchez.
After my graduation, I took a doctoral position in Germany. In Germany I met with Dr. Werner
Maschek who believed in me and accepted me in his team. Sometimes I think that he still
estimates me more than I do and even if I am not for sure the best worker: forgetting meetings,
being late at deadlines is one of my specialties, his door was always open for any help and
suggestions: thanks Werner.
Now it comes the time of the person that, of course after me, has the greatest responsibility in
this thesis: Dr. Andrei Rineiski. He has made the choice of the subject and he lead me during
these three years by means of long discussions, I believe that not a day passed without I
knocked at his door, may be just to say everything is going on. But this is not the place only for
technical thanks therefore a special thank to Andrei because he was always able to bring me
back to calm when the code was not running and I got no other explanation that some kind of
evil magic.
There is another unforgettable person: Dr. Edgar Kiefhaber; first of all I should apologize to
him about not having been able to read all the articles and references he gave me. Discussing
with him was always a pleasure and not only about work but also about historical aspects of
nuclear technology. Thanks also for having spent so much time correcting my presentations
and papers, I believe that when I would have finished he would have felt eased too, forgive me
again and thank Edgar.
Now, even when I was always speaking about how it is possible to divide the ‘world’ in even
and odd functions but only in time scales with so many zeros after the comma that a normal
engineer would laugh about, one person in Stuttgart decided that I could get a Ph.D. in
mechanical engineering anyway. Thanks Professor Günter Lohnert: it was a pleasure being one
of your students. I have to say that I always appreciated your comments. I got the feeling that
every paper approved by you was a step towards the final goal and this was for me important.
I want to thank all the ‘Partition and transmutation’ team at Forschungszentrum Karlsruhe. It,
was a lovely place where to work, I felt well with you all; you helped me with the German
language (especially Claudia), and also how to forget the smoker community: no one is without
if someone has some.
Thanks also to Dr. Thomas Schulenberg, director of the Institute for Nuclear and Energy
Technologies, and to the Forschungszentrum Karlsruhe for offering me the opportunity of
performing this thesis work.
I wish to thank also Dr. Michael A. Smith who helped me reviewing this work especially the
English correctness.
There is a person that followed me since a long time. When we met for the first time, neutrons
were not yet in my life, but she followed me when ever possible, and allowed me to go around
in Europe for my job and passion. I cannot imagine a better support for me and I know that it
was not always easy at all sharing me with my work. Thanks Anna, you have a great part.
There is also a lady that probably is still wondering if she has done a good job growing me up,
for the moment it seems yes even if it means that I am always far from her and she misses me;
thanks for all, dear mother.
Now I have to carry out a reverential duty that I’m glad to be able to fulfill: this thesis is
dedicated to my father that I lost too early but he is of course part of me.





II

CONTENTS

Acknowledgment...............................................................................................................II
Abstract ..........................................................................................................................V
Chapter I. INTRODUCTION .....................................................................................1
I.1. Background .................................................................................................1
I.2. Motivations..................................................................................................4
I.3. The Neutron Transport Equation ..................................................................8
I.4. The Steady State Second Order Transport Equation....................................15
Chapter II. DISCRETIZATION OF THE NEUTRON TRANSPORT EQUATION
..................................................................................................................20
II.1. The Multi-Group Approximation and Spatial Homogenization ...................20
II.2. The Spatial Discretization ..........................................................................26
II.3. The Angular Discretization by the Method of Spherical Harmonics ............30
II.4. The Angular Discretization by the Method of Simplified Spherical
Harmonics .............................................................................................33
II.5. The Multi-Group Strategy ..........................................................................37
II.6. Time Discretization by the Direct Method ..................................................39
Chapter III. EXTENSIONS OF THE DIRECT METHOD FOR THE TIME
DISCRETIZATION ................................................................................47
III.1. The New Direct Scheme Equations (P Case).............................................47 N
III.2. The New Direct Scheme Equations (SP Case) ..........................................58 N
III.3. Comparison of the Two Schemes ...............................................................60
III.4. Estimations of the Error .............................................................................63
III.5. Higher Time Discretization Scheme ...........................................................67
III.6. Time Step Control Options.........................................................................69
III Chapter IV. NUMERICAL SIMULATION RESULTS AND CONCLUSIONS........74
IV.1. One-Dimensional Analytic Benchmark ......................................................74
IV.2. Two Dimensional Muse Transient Analysis................................................79
IV.3. Adaptive Time Step Control Two Dimensional Test ...................................86
IV.4. PDS-XADS Transient Analysis..................................................................93
IV.5. Conclusions .............................................................................................108




IV Abstract
There are several alternatives under consideration for energy production aiming at reducing
the dependence upon oil, coal, and natural gas. The underlying goal of course is a future in
which oil, coal, and natural gas will play a far less important role in energy supply. One such
alternative is nuclear energy derived from nuclear fission. This power source, similar to oil,
coal, and natural gas is backed up by years of engineering experience. Increasing its role
should increase its public acceptance, especially in Europe, where its use is strongly under
discussion. The key factor that will decide the role of nuclear power in the future lies in the
proof of a safe way to handle nuclear waste. For this reason, several alternative approaches
for treating nuclear waste have been proposed and are investigated. Every idea proposed is, of
course, a trade off between the public acceptance, costs, and technological capabilities. One of
the most challenging approaches, from the technological point of view, is the strategy based on
burning the most dangerous part of nuclear waste in dedicated reactors such as the one studied
in this work. This alternative introduces a new class of reactor behavior which needs to be
carefully studied. The analysis work inevitably relies upon high precision simulation using
numeri