Operational Reactor Safety
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1 Operational Reactor Safety / Professor Andrew C. Kadak Professor of the Practice Lecture 3 Reactor Kinetics and Control Page 1
2 Topics to Be Covered Time Dependent Diffusion Equation Prompt Neutrons Delayed Neutrons Point Kinetics Equation Reactivity Inhour Equation Feedback - Fuel-Doppler, Moderator, Power Reactor Control Page 2
3 Key Concepts Time Dependent Diffusion Equation Rate of change = rate of production rate of absorption rate of leakage Prompt neutron keff Reactivity ρ = (k -1)/k Mean neutron generation time l* = 10-7 sec Reactor Period T = l*/ρ Time to increase power by factor of e Page 3
4 Impact of Delayed Neutrons 99 % of Neutrons are Prompt released at time of fission Fission Products also release neutrons with some delay based on half life - Precursors 20 Precursors grouped into 6 groups with half lives ranging from 0.25 sec to 1 minute Delayed neutron fraction ß i = delayed neutrons from precursor group C i /v Page 4
5 Delayed Neutrons Figures Hemisphere. All rights reserved. This content is excluded from our Creative Commons license. For more information, see Page 5
6 Neutron Balance Prompt source Delayed source Time Dependent Neutron Balance Equation Page 6
7 Key Kinetics Equations Point Kinetics Equations Inhour Equation Page 7
8 Average Delayed Neutron from Uranium and Plutonium Delayed neutrons are produced at about ½ the energy of prompt neutrons Figures Hemisphere. All rights reserved. This content is excluded from our Creative Commons license. For more information, see Page 8
9 Reactivity Insertions Reactor follows point kinetics equations Prompt jump drop Asymptotic Period considering delayed neutrons Prompt critical transition to prompt from delayed control ρ = ß Period of core used to start up reactor 80 sec. Page 9
10 $ = ρ/ß Page 10 Figures Hemisphere. All rights reserved. This content is excluded from our Creative Commons license. For more information, see
11 Reactivity Feedbacks Fuel Temperature Thermal expansion Doppler Moderator/Coolant Fuel Motion bowing Page 11
12 Reactivity Coefficients Fuel Temperature Moderator Temperature Moderator Density Void Coefficient Power Coefficient Page 12
13 Doppler Broadening Figures Hemisphere. All rights reserved. This content is excluded from our Creative Commons license. For more information, see Page 13
14 Reactivity Feedback Figures Hemisphere. All rights reserved. This content is excluded from our Creative Commons license. For more information, see Page 14
15 Page 15 Figures Hemisphere. All rights reserved. This content is excluded from our Creative Commons license. For more information, see
16 Reactor Control Inherent feedback mechanism Fast fuel Slow moderator Control Rods Relatively fast but rod worth an issue - Rod ejection - Rapid withdrawal Soluable Boron effect on Moderator Temp. Coefficient Page 16
17 Homework Assignment Knief Chapter 5 Problems: 1,4,6,9 Read Chapter 6 for next class Page 17
18 MIT OpenCourseWare Nuclear Reactor Safety Spring 2008 For information about citing these materials or our Terms of Use, visit:
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