nuci 887 study guide

8/8/2019 Nuci 887 Study Guide

1/21

NUCLEAR REATOR ANALYSISSTUDY GUIDE FOR

NUCI 887 EB*NUCI887EB*FACULTY OF ENGINEERING


2/21


3/21

Study unit 1

Study guide compiled by:

Kostadin N. Ivanov

Page layout by Janine Jansen van Vuuren, graphikos .

Printing arrangements and distribution by Department Logistics (Distribution Centre).

Printed by The Platinum Press (018) 299-4226.

Copyright 2010 edition. Date of revision: September 8, 2010.

North-West University, Potchefstroom Campus.

No part of this book may be reproduced in any form or by any means without writtenpermission from the publisher.


4/21

Study unit 1

2

MODULE CONTENTSWord of welcome ................................................................................................................... 3

Contact information ................................................................................................................ 3

Prerequisites .......................................................................................................................... 3

Study material ........................................................................................................................ 3How to study .......................................................................................................................... 3

Assessment ........................................................................................................................... 4

Time schedule ....................................................................................................................... 4

Module outcome .................................................................................................................... 4

Warning against plagiarism .................................................................................................... 5

Study unit 1 Neutron nuclear reactions ............................................................. 6

Study unit 2 Nuclear fission chain reaction ........................................................ 3

Study unit 3 Neutron transport theory ............................................................... 5

Study unit 4 Neutron diffusion theory ................................................................. 7

Study unit 5 Neutron energy distribution ............................................................ 9

Study unit 6 Nuclear reactor dynamics ............................................................. 11

Study unit 7 Fuel burnup .................................................................................... 18


5/21

Study unit 1

WORD OF WELCOME

This module in Nuclear Reactor Analysis is the most fundamental topic of nuclearengineering. As it is covered at an introductory level, it is almost self contained and requiresonly some basic knowledge and skills of engineering mathematics and physics. For those

engineers who intend to continue with the advanced reactor physics, the course provides thevery first step, for others it will remain to be the essential knowledge of a lifetime throughouttheir professional career.

The major objective of this course is to provide the student with an understanding of the mostfundamental physical principles underlying the safe operation of a nuclear reactor. It isexpected that by the end of this course the student will acquire enough knowledge and skillsto analyse and estimate the behavior of neutrons inside the reactor in a quick andapproximate way, and consequently the student will be able to understand the majorneutronic aspects of in-core power generation, and to identify the most salient parametersrelated to reactor safety. Nuclear reactor physics with its advanced computational tools is amatured topic, and this course will provide an insight to the physical principles, andcomputational methods for reactor design and analysis.

CONTACT INFORMATION

Prof. Kostadin N. Ivanov

Office:

e-Mail: [email protected]

PREREQUISITES

A sound knowledge of Engineering Mathematics, and basic principles of Nuclear Physics.

STUDY MATERIAL

The following study materials are recommended and are essential for the course:

1. Textbook (requested):

1a. J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis , Wiley (1976).

or

1b. W. M. Stacey, Nuclear Reactor Physics , John Wiley&Sons, Inc. (2001).

2. Reference (optional):

2a. J. R. Lamarsh and A. Baratta, Introduction to Nuclear Reactor Theory , ThirdEdition, Addison-Wesley

2b. E. E. Lewis, Fundamentals of Nuclear Reactor Physics , Academic PressElsevier (2008).

3. Supplementary study guidelines, herein.

HOW TO STUDY

Please read:Chapters 2 through 8 and Chapter 15 of Textbook 1a


6/21

Study unit 1

4

or

Chapters 1 through 6 and Chapter 9 (Sections 1 and 7) of Textbook 1b

Also it is optional to read Chapters 1 to 7 from Reference 2a and/or Chapters 1 to 10 ofReference 2b.

ASSESSMENT

The mark for the course is comprised of 25% of the participation and 75% of the finalexamination marks. Please turn in the answer sheets on the day of the final examination.

TIME SCHEDULE

A tentative time schedule is presented below:

Morning Afternoon

October 11 Unit 1 Unit 1 Unit 2 Unit 2





MODULE OUTCOME

Upon successful completion of the module, the student should have acquired basicknowledge of Nuclear Reactor Analysis, which includes the following topics:

physics of neutron-nuclear interactions and fission chain reaction;

neutron transport model and diffusion theory;

neutron energy distribution including slowing down, resonance absorption, and groupenergy method;

nuclear reactor dynamics;

fuel burnup.

This level of knowledge would enable the student to understand physical principles and applycomputational methods for reactor design and analysis such as the calculation of neutronflux distribution in space and energy for simple homogenous geometries and heterogenouslattices.


7/21

Study unit 1

WARNING AGAINST PLAGIARISM

ASSIGNMENTS ARE INDIVIDUAL TASKS AND NOT GROUP ACTIVITIES. (UNLESSEXPLICITLY INDICATED AS GROUP ACTIVITIES)

Copying of text from other learners or from other sources (for instance the study guide,prescribed material or directly from the internet) is not allowed only brief quotations areallowed and then only if indicated as such.

You should reformulate existing text and use your own words to explain what you have read.It is not acceptable to retype existing text and just acknowledge the source in a footnote you should be able to relate the idea or concept, without repeating the original author to theletter.

The aim of the assignments is not the reproduction of existing material, but to ascertainwhether you have the ability to integrate existing texts, add your own interpretation and/orcritique of the texts and offer a creative solution to existing problems.

Be warned: students who submit copied text will obtain a mark of zero for theassignment and disciplinary steps may be taken by the Faculty and/or University. It isalso unacceptable to do somebody elses work, to lend your work to them or to makeyour work available to them to copy be careful and do not make your work availableto anyone!


8/21

Study unit 1

6

1. NEUTRON NUCLEARREACTIONS

Outcomes

After completing this study unit, you should have a thorough understanding of

Nuclear reaction fundamentals

Neutron interactionsNeutron-induced nuclear fission,

Neutron cross-sections,

Evaluated nuclear data files,

Kinematics of elastic scattering.

Learners should be able to:

Use neutron cross sections,

Differentiate between the various types of cross sections of various isotopes,Calculate the energy loss in scattering of neutrons from isotopes.

Diagnostic testIf you can successfully complete the assignments, exercises and self-assessment test, youmay continue to the next unit.

TimeThe study time proposed for Study Unit 1 is 15 hours including assignment, exercises and

the self-assessment test.

OverviewThe physics of nuclear reactors is determined by the transport of neutrons inside the core.The main parameters of the neutron transport phenomenon are the cross sections whichdetermine the outcomes of the neutron-nuclear interactions.


9/21


10/21


11/21


12/21

Study unit 3

10

3. NEUTRON TRANSPORTTHEORY

Outcomes

After completing this study unit you should have a thorough understanding of

Concepts of angular and scalar neutron densities, flux and current,

Neutron transport equation,

Transport theory methods,

Simplifications,

Diffusion approximation,


Describe different terms of the neutron transport equation including initial and boundaryconditions,

Classify and explain different methods used to solve the neutron transport equation,Introduce and derive common simplifications to the neutron transport equation,

Derive the diffusion approximation including the diffusion theory boundary conditions.

Diagnostic testIf you can successfully complete the assignment, you may continue to the next unit.

TimeThe study time proposed for Study Unit 3 is 15 hours. This includes the assignment,exercises and the self assessment test.

OverviewIn this unit an introduction to neutron transport theory is provided including concepts ofangular and scalar neutron densities, fluxes and currents. The neutron transport equation isdiscussed and the physics behind every term is explained along with initial and boundaryconditions. The methods used for solution of neutron transport equation are classified andanalysed. Common simplifications to neutron transport equation are introduced anddiscussed. The diffusion approximation to neutron transport equation is consistently derivedwith emphasis on utilized assumptions and their physical consequences.


13/21

Study unit 3

11

Study materialStudy Chapter 4 of Textbook 1a

or

study Chapter 9 of Textbook 1b (Sections 9.1, 9.6, 9.7, 9.8, 9.9 and 9.10).

If you have any problems or questions, contact the lecturer.

AssignmentRead the study material and solve problems:

from Textbook 1a: 4-1, 4-5, 4-9, 4-11, 4-13, 4-25, 4-27

or

from Textbook 1b: 9.7, 9.8, 9.9, 9.10, 9.15. Review ordinary and partial differential equation solution methods as well as specialfunctions and their properties.

Self-assessment testDerive in intermediary steps the one-group 1-D diffusion equations starting from 1-Denergy-dependent transport equation in slab geometry.

Compare discrete ordinates (S n) and spherical harmonics (P n) methods and discusstheir differences, strengths and deficiencies.


14/21

Study unit 3

12

4. NEUTRON DIFFUSION THEORY

Outcomes


One speed diffusion theory and its limitations,

Initial and boundary conditions,

Neutron diffusion in non-multiplying media ,

Bare homogeneous reactors,

Reflected cores,

Heterogeneous reactors,

Numerical solutions to diffusion equation,Nodal methods.


Solve neutron diffusion equation for various geometries and source conditions,

Solve some criticality problems based on the diffusion theory,

Calculate the neutron flux distribution within a bare homogeneous reactor for variousgeometries,

Calculate the flux distribution within a reflected reactor,

Calculate criticality parameters of a heterogeneous reactor,

Find numerical solution to the diffusion equation.


TimeThe study time proposed for Study Unit 4 is 35 hours. This includes the assignment,

exercises and the self assessment test.


15/21

Study unit 3

13

OverviewIn this unit one-speed neutron diffusion equation is derived once using arguments based onbasic principles. In practice one speed refers to a one-energy group of neutrons, neglectingthe slowing down. Analytical and numerical methods for solving the one-group diffusionequations are introduced and discussed. Although the neutron diffusion theory has itsshortcomings and limitations, it is the workhorse of computational nuclear reactor physics.


or

Study Chapter 3 of Textbook 1b.



from Textbook 1a: 5-2, 5-6, 5-8, 5-13, 5-14, 5-15, 5-30, 5-31, 5-34

or

from Textbook 1b: 3.1 -3.3, 3.5-3.8, 3.12, 3.14-3.21. Review ordinary and partial differential equation solution methods.

Self-assessment testFill out the intermediary steps in the solutions of diffusion equation for variousgeometries and boundary conditions explained in the textbooks.

Outline and discuss the inner/outer calculation scheme utilized in the numericalsolution of the diffusion equation


16/21

Study unit 4

14

5. NEUTRON ENERGYDISTRIBUTION

Outcomes


Neutron spectrum calculations in infinite medium,

Multi-group calculations of neutron energy distribution in an infinite medium,

Resonance absorption,

Multi-group diffusion theory.


Calculate neutron energy distribution in infinite medium and finite media,

Solve multi-group equations,

Perform resonance absorption calculations,

Solve multi-group diffusion equations.



OverviewIn this unit, the one energy group model of mathematical description of nuclear reactors ismodified to account for slowing down of neutrons born from a fission event due to scatteringreactions and resonance absorption. The neutron density (flux) distribution in a nuclearreactor as a function of energy is called neutron spectrum.

The presence of resonance absorbers makes it difficult for high energy fission neutrons toreach thermal energies and induce further fissions. Therefore resonance escape is animportant parameter that controls the reactor criticality and hence reactor safety especiallyfor thermal reactors. In addition to neutron spectrum the nuclide cross-sections are alsofunctions of energy of incoming neutron (depending on the nuclide and type of reaction). Theusual approach for addressing energy dependence of neutron flux and cross-sections in


17/21


18/21

Study unit 5

16

6. NUCLEAR REACTORDYNAMICS

Outcomes


Delayed fission neutrons,

Point reactor kinetics model,

Solution to point reactor kinetics equation,

Reactivity feedback and reactor dynamics,

Reactivity temperature coefficients,

Experimental determination of reactor kinetics parameters,

Spatial effects in reactor kinetics.


Calculate transients using point kinetics equations,

Calculate kinetics parameters with various methods,

Model and analyze the reactivity feedback and feedback coeffcients,

Calculate the reactor fast excursions.



OverviewIt is of prime importance for modelling time-dependent behaviour of a nuclear reactor tocalculate in an accurate manner the reactivity (measure of reactor off-criticality) changes. Indifference of steady state reactor analysis during transients the fact that there are two typesof neutrons (prompt and delayed) released during fission reactions pays a major role andhave to be taken into account explicitly. If not for the delayed neutrons it would have been


19/21

Study unit 5

17

impossible to control nuclear reactors. Point kinetics reactor model enables us to predictchanges in the reactor reactivity as function of time.

Reactors must have negative reactivity temperature feedback in order for them to operateunder stable conditions. Reactor dynamics is defined as reactor kinetics (time-dependentneutronics) with feedback mechanisms modelled. The dynamic response of a nuclear reactorto various perturbations has to be evaluated with a special emphasis on fast reactivity-

initiated excursions.


or

study Chapter 5 (sections 5.1-5.4, 5.6-5.7, 5.11-5.13) of Textbook 1b.



from Textbook 1a: 6-3, 6-4, 6-15, 6-16, 6-21, 6-30, 6-31, 6-32.

or

from Textbook 1b: 5.3, 5.5, 5.8, 5.11, 5.16, 5.17, 5.18, 5.19.

ExercisesReview Laplace transforms and complex analysis.

Self-assessment testDiscuss the difference between physical and effective delayed neutron fractions andmethods for their calculation?

What are the assumptions and limitations of the point kinetics reactor model?

Define prompt-jump and prompt-critical approximations.

Describe the techniques for measurement of kinetics parameters and reactivity.

How the feedback effects are taken into account in: a) the point kinetics equation (pointdynamics model); b) the three-dimensional multi-group kinetics equations.


20/21

Study unit 6

18

7. FUEL BURNUP

Outcomes


Changes in fuel composition,

Fission product poisoning,Fuel depletion analysis,

Nuclear fuel management.


Calculate the amount of fission products in spent fuel,

Understand reactivity control mechanisms during reactor core lifetime (cycle),

Evaluate effects of fuel depletion on power distribution.

Diagnostic testIf you can successfully complete the assignment, this module is completed.

TimeThe study time proposed for Study Unit 7 is 15 hours. This includes the assignment and theself assessment test.

OverviewThe economics of a nuclear power plant is dependent on the efficient use of the nuclear fuel.The fission chain reaction produces about 500 fission products. Some of these fissionproducts have very high absorption cross sections and interfere with the operation of thereactor. Also reduction of fissile isotopes during reactor core cycle has to be taken intoaccount to keep the reactor critical at all times. Conversion and breeding of new fuel isotopeshas to be considered. Thus, depletion calculations are an essential part of reactor analysis.

Study materialStudy Chapter 15 from Textbook 1a

or

study Chapter 6 from the Textbook 1b.


21/21

Study unit 6

19



From Textbook 1a: 15-2, 15-3, 15-7, 15-8, 15-14, 15-18

orfrom Textbook 1b: 6.1 , 6.2, 6.6, 6.11, 6.13, 6.14.

ExercisesNone for this unit.

Self-assessment testDifferentiate between conversion and breeding.

Compare the conversion cycles and conversion ratios of LWR, PHWR, HTGR, andLMFBR.

What does neutron economy and low-leakage loading pattern imply?

What are the units in which exposure is measured? What is difference between burnupand exposure?

Define Effective Full Power Days (EFPDs).

nuci 887 study guide

Documents