UNITED STATES 

NUCLEAR REGULATORY COMMISSION 

TECHNICAL TRAINING CENTER 

POWER PLANT 

ENGINEERING 

COURSE MANUAL
Power Plant Engineering Course Manual 

TABLE OF CONTENTS 

LIST OF TABLES ................................................................... xv 

LIST OF ILLUSTRATIONS ........................................... xvi 

1.0 BASIC PLANT CYCLES ...................................... 1-1 

1.1 Boiling Water Reactor Overview ............................................... ......................... 1-1 

1.1.1 1.1.1 BWrR Product Lines ............ ........ .. . . . . BW • R Prod~u t Lin s .............. ....2•..... :. ... ................ ......... : ...-......•. .......... :. 1-2 

1.1.2 Primary and Auxiliary Systems ...............- ..1-2 2.........................

1-1.3 ._ Control System s .......................................................................- ............ ...... :......:.. 1-4 

1.1.4 " Emergency Core Cooling Systems........................................... ..... 1-5 

11.5 -Plant Startup ...................................................................................... .... .... .: I-6 

1.1.6 Plant Shutdown ............................................. 1-7 

-1.2 Pressurized Water Reactor Overview ......... ............ ......... 1-8 

1.2.1 Primary Systems - PWR .............. ..... 1..-.........................

1-9 

,1.2.2 Secondary Systems ................................................................. ............. 1-12 

.1.2.3 Control Systems ............. .......... ..................... 1-13 

1.2.4 -.. Emergency Systems ............................................................. ............ 1-14 

1.2.5 'Plant Startup - PW R ............................................................................................ 1-15 

1.2.6. Plant Shutdown - PW R ............... ............. ......................................................... 1-16 

" .Barriers ".1.3 to Release of Fission Products . : ............................ -17 

1.3.1 BWR Plant Fission Product Barriers ............................................. ..... 117 

1.3.2 PWR Plant Fission Product Barriers ................................. .. 1.1............ 1-17 7...........7... 

1.4 . Summary ..................................................................................... ...... 1.17 

2.0 REACTOR PHYSICS ......................................................................................... 2-1 

2.1 Introduction ....................................................................................................... 2-1 

2.2 Fission Process ................................................................................................. 2-1 

2.3'-- Nuclear Cross Section ......................................................................................... 2-2 

2.4 Slowing Down of Neutrons............................. ; ............ ................................ 2-3. 

. Mu-ltiplication Factor............................. ............... 2-4 

,2.5.1 Fast Fission Factor (c)'.............. .............................. 2-5 

-2.5.2 Fast Nonleakage Factor (Lf).... ................................................................... ..2-5 

.2.5.3 ý Resonance Escape Probability (p) ................................ 2-5 

2.5.4 Thermal Nonleakage Factor (ui.) ........................................................................ 2-5 

USNRC Technical Training Center - -Rev. 1295
Power Plant Engineering Course Manual 

2.5.5 Therm al Utilization Factor (f) ................................................................................ 2-5 

2.5.6 Reproduction Factor (i) ......................................................................................... 2-6 

2.6 Reactivity (p) .......................................................................................................... 2-6 

2.7 Reactor Period and Startup Rate ............................................................................ 2-6

2.8 Reactivity Coefficients ........................................................................................... 2-7 

2.8.1 M oderator Temperature Coefficient (M TC) ........................................................ 2-7 

2.8.2 M oderator Void Coefficient (Exv) .......................... ................................................ 2-8 

2.8.3. Pressure Coefficient ............................................................................................... 2-8 

2.8.4 Fuel Tem perature (Doppler) Coefficient (FTC) ..................................................... 2-9 

2.8.5 Power Coefficient. .................................................................................................. 2-10 

2.8.6 Reactivity Coefficient Values ................................................................................ 2-10 

2.9 Behavior of Reactivity Coefficients in a BW R ...................................................... 2-10 

2.9.1 M oderator.Tem perature Coefficient - BW R ......................................................... 2-10 

2.9.2 M oderator Void Coefficient - BW R ....................................................................... 2-11 

2.9.3 Fuel Tem perature (Doppler) Coefficient - BW R ................................................... 2-11 

2.9.4 Power Coefficient - BW R ...................................................................................... 2-11 

2.10 Behavior of Reactivity Coefficients in a PWR .......................................................... 2-11 

2.10.1 M oderator Temperature Coefficient - PW R .......................................................... 2-11 

2.10.2 M oderator Void Coeffi cient - PW R ....................................................................... 2-12 

2.10.3 Fuel Tem perature (Doppler) Coefficient - PW R .................................................... 2-12 

2.10.4 Power Coefficient - PW R ....................................................................................... 2-12 

2.11 Control Rod W orth ................................................................................................. 2-12 

2.12 Boron W orth ........................................................................................................... 2-13 

2.13 Fis~ion Product Poisons ......................................................................................... 2-14 

2.14 Burnable Poisons .................................................................................................... 2-16 

2.15 Subcritical M ultiplication ....................................................................................... 2-16 

2.16 Neutron Production ................................................................................................ 2-17 

2.16.1 Effect of Delayed Neutrons on Reactor Control ........................ 2-18 

2.17 Reactor Startup - BW R .......................................................................................... 2-19 

2.17.1 -The Source Range .................................................................................................. 2-19 

2.17.2 The Interm ediate Range and Reactor Heatup ........................................................ 2-19 

2.17.3 The Power Range .................................................................................................. 2-19

USNRC Technical Training Center ii Rev. 1295
Power Plant Engineering Course Manual

2.18 Reactor Startup - PWR ............................................................................ ,. ......... 2-20 

2.18.1 Source and Intermediate Ranges ............................................................................ 2-20 

2.18.2 Power Range ....................................................................................................... 2-21 

2:19 Decay Heat Production After Shutdown ............................. 2-21 

3.0 HEAT TRANSFER AND THERMAL HYDRAULICS ....................................... 3-1 

3.1 Introduction ........................................................................................................... 3-1 

3.2 Steam Power Cycle ................................................................... ....... 3-1 

3.2.1 Overview of the Steam Power Cycle ............................... I 3-1 

3.2.2 The First Law of Thermodynamics ........................................................................ 3-2 

3.2.3 . The Second Law of Thermodynamics ............................... 3-3

3.2.4 Thermodynamic Cycle Efficiency .......................................................................... 3-3 

•3.2.5 T-S and H-S Cycle Diagrams ................................................................................. 3-4 

3.2.6 Steam Power Cycle Analysis ................................................................................. 3-6 

3.2.7 Example Cycle Analysis .................................................. ............. 3-7 

.3.2.8 Improving Cycle Efficiency ............................... ...... 3-9. 

"3.3 . Basic Heat Transfer Mechanisms and Principles.:: ........................... 3-10 

,_3.3.1.. Conduction ..................................................................................................... .3-0 

3.3.2 Radiation ..................................................... 3-12 

3.3.3 Convection ..................................................-................................................... 3-12 

'3.4 Practical Applications of Heat Transfer in the Plant....................... 3-13 

3.4.1 -Physical Parameters of Basic Heat Transfer .. ý ................. .-. .3-13 

3.4.2 Heat Transfer in Heat Exchangers ......... .................... :................ ......................... 3-15 

,3.5 Boiling Heat Transfer .................................... ................. 3-16 

3.5.1 Physical Parameters of Boiling Heat Transfer ....................................................... 3-17 

3.5.2 Steam Generation Characteristics .......................................................................... 3-19 

3.6 Reactor Thermal and Hydraulic Performance ....................................................... 3-20 

3.6.1 Performance Objectives ........................................................................................ 3-20 

3.6.2 Departure from Nucleate Boiling ........................................................................... 3-22 

3.7 Reactor Plant Heat Balances ............................................ 3-24 

3.7.1 .PWR Heat Balance ............................................ -3-24 

3.7.2 BWR Heat Balance ............................................................ .............. 3-26 

3.8. Natural Circulation in Reactors ............................ ....... I 3-27

:-USNRC Technical Training Center .7 !11 Rev. 1295
Power Plant Engineering Course Manual

PROCESS CH EM ISTRY ...................................................................................... 4-1

4.1 Acids and Bases ..................................................................................................... 4-1 

4.2 Conductivity ........................................................................................................... 4-3 

4.3 Radiolysis of W ater ................................................................................................ 4-5 

4.4 Voltaic Cells ........................................................................................................... 4- 6

Corrosion ................................................................................................................ 4-7 

Corrosion of Iron .................................................................................................... 4-7 

Corrosion Rate ........................................................................................................ 4-9

4.6 Types of Corrosion ................................................................................................. 4-9 

4.7 Crud ........................................................................................................................ 4-11

4.8 

4.8.1 

4.8.2 

4.8.3 

4.8.4

Sources of Radioactivity in Reactor Coolant ......................................................... 4-14 

Activation of Corrosion Products ........................................................................... 4-14 

Activation of W ater. .............................................................................................. 4-14 

Activation of W ater Im purities .............................................................................. 4-15 

Fission Products ..................................................................................................... 4-16

4.9 Detection of Fuel Cladding Failures ...................................................................... 4- 16

4.10 

4.10.1 

4.10.2

Ion Exchangers and Demineralizers ....................................................................... 4- 18 

Deep Bed Demineralizers ....................................................................................... 4-20 

Powdered Resin Filter Demineralizers ................................................................... 4-20

4.11 Basic W ater Chemistry Requirements ................................................................... 4-21

PRINT READ ING ................................................................................................. 5-1

5.1 Introduction ............................................................................................................ 5-1

Categories of Drawings .......................................................................................... 5-1 

Drafting Organization ............................................................................................ 5-2 

Status of M odifications .......................................................................................... 5-2 

Controlled vs. Inform ation Only ............................................................................ 5-2

Print Reading Fundam entals .................................................................................. 5-3 

Indexes ................................................................................................................... 5-3 

Title Block .............................................................................................................. 5-3

USNRC Technical Training Center

4.0

4.5 

4.5.1 

4.5.2

5.0

5.2 

5.2;1 

5.2.2 

5.2.3

5.31 

5.3.1 

5.3.2

Rev. 1295 iv
Power Plant Engineering Course Manual 

5.3.3 Numbering Systems ........................................ 5.. 5-3 

5.3.4 G rids ....................................................................................................................... 5-4 

5.3.5 Revisions................................................... 5-4 

5.4' --Piping and Instrumentation Diagrams ................................ ......... :.......,,...... 5 

5.4.1--- P&ID Symbols ................................ ,............................................. 5-4 

5.4.2 P& ID Examples ..................................................................................................... 5-4 

5.5 One-Line Electrical Diagrams and Control Wiring Diagrams ............. 5-6 

5.5.1- Purposes ................................................ ............... 5-6 

5.5.2 Symbols and Notation ................. .............................................. ......... 5-7 

5.5.3 Exam ples . .8............................................. ............................ ...................... ......... -8 

5.-6-- Logic Diagrams .. .......... .... ............... ................. 5-9 

5.6.1 Logic Logic.Diag......ra.......... Diagram Symbols ............................... ............ 5-9 

5.6.2 Logic Diagram Examples .................................... 5-'10 

5.7 ' Sum m ary ........................................................... ..... .......................... 5..................... 5 

APPENDIX 5A STANDARD ELECTRICAL DEVICE NUMBERS 

AND FUNCTIONS ............................................................ 5A-1 

5A, I Purpose of Device Function Number ............................................................ 5A-1 

5A,2 Standard Device Function Numbers .................................. ....................... 5A-1 

5A.3 Supervisory Control and Indication ............ ........................................................... 5A-7 

5A :4 Suffix Letters ............................. ........................... .. ................ ............. .... 5A-7 S........... 

5A,4.1 Letters for Separate Auxiliary Devices .................................. ,........................ 5A-8 

5AA.2 Letters for Condition/Electrical Quantity ............................................................... 5A-8 

5A.4.3 Letters for Location of Main Device in the Circuit .......................... 5A-9 

5A.4.4 Letters for Parts of the Main Device ......... :.........................................., .. 5A-9 

5A.4.5 Other Letter Designations ...................................................................................... 5A--12 

5A•4.6 Lower Case Letters ........................................ 5A-12 

5A.5 Suffix Numbers ..................................... . ............................. .... 5A-12 

5A:6 Devices Performing More Than One Function ................................... _... . S......5A-12 

5A.7 - Representation of Device Contacts on Electrical Diagrams ........................... 5A-1i3 

USNRC Technical Training Center V Rev. 0197
Power Plant Engineering Course Manual

6.0 BASIC ELECTRICAL ........................................................................................... 6-1 

6.1 Electrical Fundam entals ......................................................................................... 6-1 

6.1.1 Voltage ................................................................................................................... 6-1 

6.1.2 Current .................................................................................................................... 6-2 

6.1.3 Resistance ............................................................................................................... 6-2 

6.2 Electricity and M agnetism ..................................................................................... 6-3 

6.2.1 Electric Current Produces a M agnetic Field .......................................................... 6-3 

6.2.2 Sim ple Relay ......................................................................................................... 6-3 

6.2.3 Electrom agnetic Induction ..................................................................................... 6-4 

6.2.4 Two Pole A C Generator .................................................................................... 64 

6.3 Real, Apparent and Reactive Power ................................................................. 6-4 

6.3.1 Root Mean Square or Effective Values of Voltage and Current. ........................... 6-5 

6.3.2 Real Power and Reactive Power in AC Circuits .................................................... 6-6 

6.3.3 Real Power in Com plex Circuits ............................................................................ 6-9 

6.3.4 Reactive Power in Com plex Circuits ..................................................................... 6-10 

6.3.5 Im pedance .............................................................................................................. 6-10 

6.3.6 Power Triangles ...................................................................................................... 6-10 

6.3.7 Leading and Lagging Power Factors ................................................................. 6-il 

6.4 Three Phase System s .............................................................................................. 6-11 

6.4.1 Phase and Line Relationships in Three-Phase Systems ......................................... 6-12 

6.4.2 Power in Three-Phase Systems .............................................................................. 6-13 

6.4.3 Grounded Three-Phase Systems ............................................................................. 6-13 

6.5 Transform ers .......................................................................................................... 6-14 

6.5.1 Theory of Operation ........................................................................................... 6- 14 

6.5.2 Ideal Transform ers ................................................................................................. 6-15 

6.5.3 The Autotransform er .............................................................................................. 6-16 

7.0 GENERATORS ..................................................................................................... 7-1 

7.1 Introduction ....................................................................................................... 7.-1 

7.2 Polyphase and M ultiple Pole Generators ............................................................... 7-1 

7.3 Generator Construction .......................................................................................... 7-2 

7.3.1 The Stator (or Arm ature) ........................................................................................ 7-2 

7.3.2 The Rotor ............................................................................................................. 7-3 

7.3.3 Exciter .................................................................................................................... 7-3 

7.3.4 Brushless Exciter .................................................................................................... 7-4

USNRC Technical Training vi Center Rev. 0197 USNRC Technical Training Center" Ai Rev. 0197
Power Plant Engineering Course Manual 

- Page 

7.4 Generator Auxiliary Systems ................................................................... ............. 7-4 

7.4.1 Stator Water Cooling System ............................. . t ....... 7-4

7.4.2 Hydrogen Cooling System .......................................................... 7-4 

7.4.3 Generator Core Monitor ..................................................-............................. ...... 7-4 

7.4.4 Gas Control System ................................................................................................ 7-5 

7.4.5 Hydrogen Seal Oil System ..................................................................................... 7-5 

7.5 Generator Operation ............................................................................................... 7-5 

7.5.1 Speed and Voltage Regulation .................................................................... ..7-5 

7.5.2 Single Generator Supplying an Isolated Load ........................................................ 7-6 

7.5.3' .The Infinite Bus .............................................. 7-7..

7.5.4 .Paralleling Generators .............................................................. .......... 7-8 

7.6- -Generator Limitations .......................................... 7-8' 

8.0 AC MOTORS ....................................................... .......................................... 8- 

8.1 - Introduction ..................................................................................... ...... 8

8.2' AC Motor Theory ............................................-................................. ........ .... 8-1 

8.2.1 Development of a Rotating Field .................................................................... 8-'I 

8.2.2 Motor Synchronous Speed ..................................................................................... 8-2 

8.2.3 AC Motor Losses and Efficiency .......................................................... 2 

8.3 . Three-Phase Induction Motors ........... 8-3............................

8.3.1-'. Induction Motor Construction .................................................... .... 8-3 

8.3.2 Induction Motor Operation 1 .1 -.. . 8-................................

8.3.3 "Induction Motor Response to an Increase in Load ..................... .. 8-4 

8.4 Single-Phase AC Motors ........................................ 8-4 

8.4.1 Shaded Pole Single-Phase Motors ................................. 8-4, 

8.4.2 Induction-Start Single-Phase Motors ......... ........................... 8-4 

8.4.3' Capacitor-Start Single-Phase Motors ......................................... 8-5 

8.5 Synchronous Motors ........................................................................................ . 8-5 

8.5.1 Synchronous Motor Operation ........................................ 8-5 

8.5.2 Synchronous Motor Speed ...................................................... .....................- : ........ 8-5 

8.5.3 Overexcited Synchronous Motors .......................................................................... 8-6 

8.5.4 Synchronous Motor Applications ............ ................ .................... ...... ..... * 8-6'-6 

8.6 Motor Starting Current ...................................... .8-6 

8.6.1-' No-Load Starting ........................................................................................ 8-7 

8.7 Starting Circuits ...................................................................................................... 8-7 

USNRC Technical Training Center vii - Rev. 0197
Power Plant Engineering Course Manual 

8.7.1 General ................................................................................................................... 8-7 

8.7.2 Full-Voltage Starters .............................................................................................. 8-8 

8.7.3 Prim ary-Resistor Starters ....................................................................................... 8-8 

8.7.4 Autotransform er Starters ........................................................................................ 8-8 

9.0 ELECTRICAL DISTRIBUTION EQUIPMENT .................................................. 9-1 

9.1 General D iscussion ................................................................................................. 9-1 

9.2 Generic Distribution System ............................................................................... .. 9-1 

9.2.1 Power Distribution Grid ......................................................................................... 9-2 

9.2.2 Switchyard Bus Arrangem ents ............................................................................... 9-3 

9.2.3 Electrical System Design Requirements ................................................................ 9-3 

9.2.4 Offsite (Preferred) Power Connections ............................................................ 9-4 

9.2.5 Onsite Power System Term s ............................................................................. 9-4 

9.2.6 Vital and Nonvital Subsystems .............................................................................. 9-6 

9.3 Switchyard Connection Com ponents ..................................................................... 9-7 

9.3.1 Switchyard Transform ers ....................................................................................... 9-7 

9.3.2 High Voltage Buses and Bus Ducts ....................................................................... 9-7 

9.3.3 Disconnects ............................................................................................................ 9-7 

9.4 Circuit Breakers and Breaker Control .................................................................... 9-8 

9.4.1 Air Circuit Breakers ............................................................................................... 9-9 

9.4.2 Air-Blast Circuit Breakers ...................................................................................... 9-9 

9.4.3 Oil Circuit Breakers ............................................................................................... 9-10 

9.4.4 Vacuum Circuit Breakers ....................................................................................... 9-10 

9.4.5 Breaker Control ...................................................................................................... 9-11 

9.5 Protective Relays .................................................................................................... 9-11 

9.5.1 Instantaneous or High-speed .................................................................................. 9-12 

9.5.2 Definite Tim e Delay .............................................................................................. 9-12 

9.5.3 Inverse Tim e Delay ................................................................................................ 9-12 

9.6 Fuses ....................................................................................................................... 9-12 

9.6.1 Low-Voltage. Cartridge Fuse .................................................................................. 9-13 

9.6.2 High-Voltage Fuses ................................................................................................ 9-13 

9.7 Special Onsite Distribution Equipment .................................................................. 9-13 

9.7.1 Autom atic Bus Transfer Devices ........................................................................... 9-13 

9.7.2 Inverters and Battery Chargers ............................................................................... 9-13 

9.7.3 M otor-Generator Sets ............................................................................................. 9-13 

9.7.4 Uninterruptible Power Supplies ............................................................................. 9-14

USNRC Technical Training Center viii Rev. 0197
Power Plant Engineering Course Manual . 

P~am 

9.8 Batteries ............................................ ': . 9-14 

9.8.1 Cells and Batteries ......... ........................................... .9-14 

S9.82 Construction of a Lead-Acid Storage Battery ....................... .......................... 9-14 

9.8.3 -Storage Battery Operation ...................................................................................... 9-15 

9.8.4 Hydrom eter. ........................................................................................................ 9-17 

9.8.5 Potential Difference and Current ............................... 9-17 

9.8.6 Cell Capacity ................................... ......................................................................... 9 17 

9.8.7 Battery Charges ...................................................................................................... 9-18 

-9.9 . Emergenc esponses.. . ............................................................................ 9-18 

9.91 Plant geiy Responses...................................9-18 

9.9. PatTrip P............................................. ...... ...... 98 

9.9.2 Lbss of Offsite Power ............................................................................................. 9-19 

S9.9.3 Safety Injection Actuation .................................... 9-19 

10.0 PIPIN G ..................... .... ........................................... . .............. l.................... 

10.1 General Description ........................................ 10-1 

10.2 Pipe .........-...................................................................................................... 10-1 

10.2.1 Piping Standards .......................................................................................... 10-1 

-10.2.2 Pipe Size and Schedule ................................... ...... :..................................... 10-2 

i0.2.3 Pipe Matieiials and Applications ................. .................. 10-3 

10.3 Pipl Hangers, Supports, and Snubbers ........................... 10-3 

10.3.1' Adjui table Hangers ................................................................................................ 10-4 

,10.3.2 Variable Spring Hangers ..................................... ............... ..... 1.0....................-...... 10-4 

-10.3.3 Consiant- S.ipporis ................................ ....................................... -.......... ................. 10-4 

10.3.4 RolleSan Supo................ . .........................................10-4 

1O3ARolr Stand Supports ................. ............... 1

10.3.5 Snubbers................................................................................................................. 10-4 

10.4 Valves......................................................................... .. . : .... 10-5 

10.4.1 Common Valve Parts.......... ................ ......... ........... 10-5 

10.4.2 G ate V alves .......................................................................................................... 10-7 

10.4.3 Globe Valves ............................................ 10-7 

i0.4.A Check Valves ............ .. .......................... :.....10-9 

10.4.5 Butterfly Valves .............. I ........................ 10-10 

'10.4.6 Safety a. d R6& Valves ................ .......... ........................................ ..... 10-10 

10.4.7 Sp6cialty Valves ............................ ....... ............... 10-12 

10.4.8 VValve Packing ............................................. ............................10-16 

10.4.4.9" G askets ................................................................................................................ : ......10-16 

10.5 Valve Operators ..... ............. .......- o ......- ..... ............. .... :.....)...... ............. _10-17 

"10.5.1 Manual Operators ....... .................................. 10-17 

USNIRC Technical Traifiing'Cent-& .x ., -.. Rev. 1295
Power Plant Engineering Course Manual 

Page 

10.5.2 Electric Operators ................................................................................................... 10-17 

10.5.3 Pneum atic Operators .............................................................................................. 10-24 

10.5.4 Hydraulic Operators ............................................................................................... 10-25 

11.0 TURBINES '"'"""'"""-------------------'-----------------......---................................................. 11-1 

11.1 Introduction ............................................................................................................ 11-1 

11.2 Turbine Design Types ............................................................................................ 11-1 

11.2.1 Im pulse Turbines .................................................................................................... 11-1 

11.2.2 Reaction Turbines.............................................11-2 

11.3 Turbine Staging ...................................................................................................... 11-2 

11.3.1 Im pulse Turbine Compounding ............................................................................. 11-2 

11.3.2 Reaction Turbine Com pounding ............................................................................ 11-3 

11.3.3 Stage Efficiencies in Practical Turbines ................................................................. 11-3 

11.4 Construction Details .......................................................................................... 11-4 

11.4.1 Stage Sealing .......................................................................................................... 11-4 

11.5 Axial Thrust Loading ............................................................................................. 11-4 

11.5.1 Rotor Designs ........................................................................................................ 11-5 

11.5.2 Shaft Sealing System ....................................................... 11-5 

11.5.3 Rotor Glands ................................................ 11-5 

11.5.4 Gland Steam Condenser ......................................................................................... 11-6 

11.6 Practical Turbine Types ......................................................................................... 11-6 

11.6.1 Condensing vs. Noncondensing ............................................................................. 11-6 

11.6.2 Extraction vs. Nonextraction .................................................................................. 11-6 

11.7 Reheat vs. Nonreheat .............................................................................................. 11-6 

11.7.1 Single Casing vs. Compound Turbines .................................................................. 11-7 

11.7.2 ........................................................................................ 11-7 

11.8 M odem Power Plant Turbines ................................................................................ 11-7 

11.8.1 Turbine Valves ....................................................................................................... 11-8 

11.8.2 Electro-hydraulic Control System .......................................................................... 11-8 

11.8.3 Lube Oil System .............................................. 11-8 

11.8.4 Turbine Bearings .................................................................................................... 11-9 

11.8.5 Extraction Steam ..................................................................................................... 11-10 

11.8.6 Exhaust Hood Spray ............................................................................................... 11-11 

11.8.7 Turning Gear .......................................................................................................... 11-11 

1.8.8 FrontStandard ........................................................................................................ 11-11 

11.8.9 Turbine Governor -. 1r-11 

USNRC Technical Training Center x Rev. 1295
Power Plant Engineering Course Manual 

11.9 Turbine Operational Problems .................................. _...11-12 

11.9.1 Vibration 11.9.1 V bration............................................... 11-12 ................................................................................................................. 11-12 

11.9.2 Critical Speeds ........................................................................................................ 11-13 

11.9.3 Water Induction ............................................................ 11-.14 

11.9.4 Overspeed ............................................................................................................... 11-14 

.11.9.5 Low Lube Oil Pressure/High Thrust Bearing Wear ........................... 1 15 

11.9.6 Reactor Trip ........................................................................................................... 11-15 

,11.10 Standby Auxiliary Turbines ....................................... 11-15 

12.0 PUMPS ................................................................................................ ....... ..... 12-1 

"12.1 Introduction ................................................................................................ ........ 12-1 

12.1.1 Head ...............................................................................................-............... I.. .12-1 

"-12.2 Principles of Liquid Pumping ......................................................................... ... 12-2 

S12.2.1 Centrifugal Force .............................................................................................. ..12-2 

12.2.2 Volumetric Displacement ....................................................................................... 12-3 

,12.2.3 Transference of Momentum ...................................... 1 2-3 

,12.3 " Centrifugal Pumps ......................................................... ............. ................. ' ..... 12-3 

12.3.1 Casings ................................................................................................................... 12-4 

12.3.2 Impellers ................................................................................................................. 12-4 

12.3.3 Pump Shafts .......................................................................... ... ........... 12-5 

12.3.4 Stuffing Boxes ........................................................................................................ 12-6 

"12.3.5 Mechanical Seals 12-7..........................

12.3.6 Bearings .................................................................................................................. 12-8 

12.3.7 Cavitation ...................................... ........................ . 12-8 

12.3.8 Suction Head .......................................................................................................... 12-9 

,12.4 Positive Displacement Pumps .......................... .......... 12-10 

12.4.1 Liquid End Construction ................................................................................. ...... 12-11 

12.4.2 Pulsations ..... : . ....... 12-12 

12.4.3 Flow Characteristics ............................................................................................... 12-12 

12.4.4 Net Positive Suction Head Requirements ............................. 12-12 

12.5 Jet Pumps ............................................................................................................. 12-12 

12.6 Operating Characteristics of a Centrifugal Pump .................................................. 12-13 

12.6.1 Single Pump Operations .................................... ; ....... :.............. ............ ...... 12-13 

.12.6.2 Centrifugal Pump Laws ............................................... ... ............................... ...... 12-13 

12.6.3 Operating Point ........................................................... ... . ................ 12 3........... 

12.6.4 Shutoff Head and Runout Conditions .................................... ........ 12-14 

12.6.5 .Multiple Pump Operations ...................................................................... ............... 12-15 

USNRC Technical Training Center " -.' Rev. 1295
Power Plant Engineering Course Manual 

12.7 Operating Characteristics of a Positive Displacement Pump ....................................... 12-15 

13.0 D IESEL GENERA TORS ....................................................................................... 13-1 

13.1 Introduction ............................................. 13-1 

13.2 G eneral ................................................................................................................... 13-1 

13.2.1 Four-Stroke D iesel Engine ..................................................................................... 13-1 

13.2.2 Tw o-Stroke D iesel Engine ..................................................................................... 13-2 

13.3 D iesel System s ....................................................................................................... 13-2 

13.3.1 Starting System ...................................................................................................... 13-3 

13.3.2 Fuel System s .......................................................................................................... 13-3 

13.3.3 D iesel Engine Lube Oil System ............................................................................. 13-5 

13.3.4 Cooling System s ..................................................................................................... 13-6 

13.3.5 Scavenging Air, Supercharging, and Turbocharging Systems ............................... 13-6 

13.3.6 G overnor System s .................................................................................................. 13-8 

13.4 Em ergency Starts .................................................................................................... 13-11 

13.5 Em ergency Responses ............................................................................................ 13-11 

14.0 PROCESS INSTRUMENTATION ...................................................................... 14-1 

14.1 Introduction ............................................................................................................ 14- 1 

14.2 Basic Instrum ent Channels ..................................................................................... 14-1 

14.3 Tenmperature ........................................................................................................... 14-2 

14.3.1 Therm ocouples ....................................................................................................... 14-2 

14.3.2 Resistance Tem perature Detector ........................................................................... 14-4 

14.4 Pressure .................................................................................................................. 14-6 

14.4.1 Bourdon Tube ......................................................................................................... 14-7 

14.4.2 Bellow s ................................................................................................................... 14-7 

14.4.3 D iaphragm .............................................................................................................. 14-7 

14.5 M echanical - Electrical Conversion ....................................................................... 14-7 

14.5.1 Force Balance Transm itter ..................................................................................... 14-7 

14.5.2 M ovable Core Transmitter ..................................................................................... 14-8 

14.5.3 V ariable Capacitance Transm itter .......................................................................... 14-8 

14.5.4 Strain G auge ........................................................................................................... 14-8

USNRC Technical Training Center xii Rev. 1295
Power Plant Engineering Course Manual 

14.6 Flow Rate Measurement ........................................ 14-9 

14.6.1 Orifice Plate ............................................................................................................ 14-9 

14.6.2 Flow Nozzle ......................................................................................................... . 14-9 

14.6.3 Flow Venturi .......................................................................................................... 14-10 

14.6.4 ElbowFlow Measuring Device ........... ......................... . 14-10 14.6.5 Pitom eter ................................................................................... .......................... ... 14-10 

-14.7 . Flow Sensors ........................................................................................................ 14-11 

14.7.1 Bellows Flow Sensor ............................................ 14-11 

14.7.2 Diaphragm Flow Sensor .......... ............................ .. 14-11 

J. 14.7.3 Magnetic Flow Sensor ......................................... 14-11 

-_,.14.8 Level .................................................................... I... .. .......... 1.1................... 14 11 

14.8.1 Level Error ............................................................................................................. 14-12 

14.9 Signal Processing ................................................................................................... 14-13 

-:14.10 Calibration .................................................................... .. ............... ........ 14-13 

14.11 Environm ental Qualification .................................................................................. 14-14 

.14.12 Compensating Measures for Adverse Environment ..................... 14-14 

14.13 Summ ary ................................................................... ................. ....................... 14-15 

15.0 CONTROLLERS ................................................................................................... 15-1 

15.1 Introduction ............................................................................................................ 15-1 

15.2 Controller Term inology .......................................................................................... 15-1 

15.3 Exam ples of Feedback Control .............................................................................. 15-2 

15.4 Controller Operation .............................................................................................. 15-3 

15.4.1 Bistable Control ...................................................................................................... 15-4 

15.4.2 Proportional Control ............................................................................................... 15-5 

15.4.3 Proportional Integral Control ................................................................................. 15-6 

15.4.4 Proportional Derivative Control ............................................................................. 15-7 

15.4.5 Proportional Integral Derivative Control ............................................................... 15-8 

15.5 Com parison of Control M odes ............................................................................... 15-9 

15.6 Summ ary ................................................................................................................ 15-9

USNRC Technical Training Center Xiii . T Rev. 1295
Power Plant Engineering Course Manual 

Page 

16.0 N U CLEAR INSTRUM ENTATION ...................................................................... 16-1 

16.1 Introduction .................................................. ..... .... 16-1 

16.2 N uclear Ionization .................................................................................................. 16-2 

16.3 N uclear Ionization Detectors .................................................................................. 16-3 

16.3.1 Recom bination Region ........................................................................................... 16-3 

16.3.2 Ionization Region ................................................................................................... 16-4 

16.3.3 Proportional Region ............................................................................................... 16-4 

16.3.4 Lim ited Proportional Region .................................................................................. 16-4 

16.3.5 G eiger-M ueller Region .......................................................................................... 16-5 

16.3.6 Continuous Discharge Region ................................................................................ 16-5 

16.4 N eutron D etection .................................................................................................. 16-5 

16.5 Proportional Type D etectors .................................................................................. 16-6 

16.5.1 BF3 Proportional Counter ...................................................................................... 16-6 

16.5.2 Source Range/Startup Channel Gamma Compensation ......................................... 16-7 

166 Ionization Type D etectors ...................................................................................... 16-8 

16.6.1 Fission Cham ber ..................................................................................................... 16-8 

16.6.2 Com pensated Ion Cham ber (CIC) .......................................................................... 16-9 

16.6.3 Uncom pensated Ion Cham ber ................................................................................ 16-10 

16.7 Self-Powered D etectors (SPND ) ............................................................................ 16-10

USNRC Technical Training Center xiv Rev. 1295

USNRC Technical Training Center xiv SRev. 1295
Power Plant Engineering Course Manual 

LIST OF TABLES 

Table 

1-1 GE BWR Product Lines ................................................ ...... ....... 1-19 

2-1 Neutrons From Fission ......... ............................ 2-23 

2-2 Microscopic Cross Sectioni (a) Valuesi....... ........................... 2-25 

2-3 Ineffective Subcritical Multiplication ................................................................. 2-27 

-2-4 . Subcritical Multiplication ........ ..................... ........... 2-29 

2-5 Delayed Neutron Fraction for Various Fuels .............................. 2-31 

2-6 'Delayed Heat Production Fo116oing Reactor Shutdown From Full Power........ 2-33 

4-1 'pH and Ion Concentrations......... ................................... ............................. 4-23 

4-2 Activated Corrosion Products ................................ 4.25 

"4-3 Radioiodines .............. : .............. .......... .... 4..: 4-27 27......................

-4-4 Fission Gases ...... .......................................... 4-29 

4-5 'Soluble Metal Ions ............. . ........ ........................................... 4-31 

4-6 Resin Affinity .................................................................................................... 4-33 

8-1 Synchronous Motor Characteristics and Applications.......................... 8-9, 

9-1 Definitions............................................................................ 9-21 

r,10-1 Pipe Data ...................................................................................................... 10-27 

10-2 Allowable Stress Values for Temperatures 650 to 1150 0F................................. 10-29 

- , -, " £ : " =4

USNRC Technical Training Center xv Rev1295

USNRC Technical Training Center Ixv .' Rev.-1295
Power Plant Engineering Course Manual 

LIST OF ILLUSTRATIONS 

Figure Pg 

1-1 Boiling W ater Reactors in Various Systems ......................................................... 1-21 

1-2 Basic BW R Power Plant ........................................................................................ 1-23 

1-3 Simplified BWR Primary and Auxiliary Systems ................................................. 1-25 

1-4 BW R Reactor Vessel ............................................................................................. 1-27 

1-5 BW R Control System s .......................................................................................... 1-29 

1-6 Emergency Core Cooling System .......................................................................... 1-31 

1-7 Basic PW R Power Plant ........................................................................................ 1-33 

1-8 Sim plified PW R System Composite ...................................................................... 1-35 

1-9 PW R Reactor Vessel ............................................................................................. 1-37 

1-10 Sim plified Reactor Vessel ...................................................................................... 1-39 

1-11 Typical PW R Fuel Assem bly ................................................................................. 1-41 

1-12 W estinghouse Steam Generator ............................................................................. 1-4 3 

1-13 Steam Generator Secondary-side Flowpaths .......................................................... 1-4 5 

1-14 PW R Control System s ............................................................................................ 1-47 

1-15 Emergency Core Cooling System Simplified Composite ...................................... 1-49 

2-1 Fission Neutron Energy .......................................................................................... 2-35 

2-2 U-235 Absorption Cross-Section Vs. Energy ........................................................ 2-37 

2-3 Neutron Cycle in a Therm al Reactor ...................................................................... 2-39 

2-4 M oderator Tem perature Coefficient ....................................................................... 2-4 1 

2-5 Void Coefficient ..................................................................................................... 2-43 

2-6 Resonance Absorption (Stationary Nucleus) ......................................................... 2-4 5 

USNRC Technical Training Center xvi Rev. 1295
Power Plant Engineering Course Manual 

Figue -Page 

,2-7 Resonance Capture ............................................ 2-47 

2-8 U-238 Cross Section Curve ..................... ... 2:........................ 2-49 :.4................9...

2-9, FTC Vs. Fuel Temperature .................................................................................. 2-51 

2-10 Total Power Defect ............................................................................................. 2-53 

2-11 Moderaior Temperature Coefficient.................................................................... 2-55 

2-12- Differenjial Rod Worth Curve ........................................................................... 2-57 

2-13 Integral Rod Worth Curve.................................................................................... 2-59 

2-14 Boron Worth Vs. Moderator Temperature ............................................................. 2-61 

2:15 Fission Yield Curve ............................................. ...................................... 2-63 

216 Xenon Reactivity Vs. Reactor Power as Function of Time ............. ........... 2-65 

2-17" XenonPealdng ...................................................... .......................................... 2-67 

2-18 Samiairium Buildup............................................... 2-69 

2-19 Samarium Peaking............................................................................................. 2-71 

2-20 Subcritical Multiplication ....................................................................................... 2-73 

2-21 Delayed Neutron Production ................................................................................ 2-75 

2-22 Delayed Neutron Effects .................................................................................. 2-77 

3-1 Basic Steam-Water Power Cycle ..................................... 3-29 

3-2 Simple Power Cycle ........................................................................................... 3-31 

3-3 Temperature-Entropy Diagram for Analysis of Simple Steam Cycle .................... 3-33 

3-4 Mollier Dia'gram ........................................................... ................................ 3-35 

3-5 Basic Steam Cycle........................................................................................... 3-37 

3-6 T-S Diagram for Basic Steam Cycle .............................................................. 3-39 

3-7 H-S Diagram for Basic Steam Cycle .................................... ............................... 3-41 

USNRC Technical Training Center xvii . Rev. 1295
3-8 

3-9

t1xln. I ecnmcal I raining Center

x v ' e v 1 9

Power Plant Engineering Course Manual 

Fimr

3-10 

3-11 

3-12 

3-13 

3-14 

3-15 

3-16 

3-17 

3-18 

3-19 

3-20 

3-21 

3-22 

3-23 

3-24 

3-25 

3-26 

4-1 

4-2 

4-3

Page 

Steam Cycle with Feedwater Heating and Steam Reheating ................................. 3-43 

T-S Diagram for Steam Cycle (Ideal) with Feedwater Heating and Steam 

Reheating ............................................................................................................ 3-45 

Heat Conduction Through a Plane W all ................................................................ 3-47 

Convection Heat Transfer From a Surface ...................................................... 3-49 

Heat Transfer Curve ............................................................................................... 3-51 

Effects of Flow on Convection Heat Transfer ....................... 3-53 

Heat Transfer for a Typical Heat Exchanger .......................................................... 3-55 

Boiling Heat Transfer ....................................................................................... 3-57 

Transition Boiling ........................................................................................... 3-59 

Effect of a Pressure Increase on Boiling Heat Transfer ......................................... 3-61 

Effect of a Pressure Decrease on Boiling Heat Transfer ........................................ 3-63 

Effect of a Flow Increase on Boiling Heat Transfer .............................................. 3-65 

Cyclone-Type Moisture Separator ......................................................................... 3-67 

Chevron-Type M oisture Separator ......................................................................... 3-69 

Fuel Arrangement Showing Centerline .................................................................. 3-71 

Fuel Channel Boiling Conditions ........................................................................... 3-73 

PW R Reactor Core Heat Balance Diagram ............................................................ 3-75 

BW R Reactor Core Heat Balance Diagram ........................................................... 3-77 

Natural Circulation .............................................................................................. 3-79 

Voltaic Cell Operation .................................................................................... 4-35 

Corrosion of Iron .............................................................................................. 4-37 

Crevice Corrosion ........................................................................................... 4-39

Xvii Rev. 1295

J
Power Plant Engineering Course Manual 

Figure Pa=e 

4-4 Factors Affecting Crevice Corrosion ................................................................. 4-41 

4-5 Pitting ................................................................................................. Corrosion 4-43 

4-6 Cu-Zn Galvanic Cell .................................................... .......................................... 4-45 

4-7 Intergranular Corrosion ............................... ....I.......................... .................. ..4-47 

4-8 Recoil Range .................................................... 4-49 

4-9 Basic Resin Structure ........................................... . .......... . ..... 4-51 

4-10 Common Resin Representations .................................. 4-53 

4-11 Deep Bed Demineralizer ...................................... ...................... .................. 4-55 

4-12 Typical Filter/Demineralizer Unit ...................................... 4-57 

5-1 Partial Print Index ........................................................................-.... ................ .:5-13 

5-2 Typical P&ID Symbol List .................................... : .................................. 5-15 

5-3 P&ID Symbol List - Part 1. ...................................... 5.-17 

-5-4 MID Symbol List- Part 2 ............................. .......................... :....... ................ .5-19 

5-5 Diesel Air Start System Sketch ........................................................................... 5-21 

5-6 Diesel Air Start System P&ID .......... :-2......3......................................................... .5-23 

---5-7 Auxiliary Feedwater and Steam Generator (Partial) ...................................... 5-25 

5-8 Auxiliary Feedwater and Steam Generator Blowdown Systems (Partial) ............. 5-27 

5-9 Elementary Electrical (Three-Line) Diagram ....... ............... .................... 5-29 

.5-10 Typical.One-Line Diagram Legend ....................................................................... 5-31 

5-11 Diesel Generator Tie.Breaker Control Wiring Diagram . .......... 5-33 

5-12 Electrical Distribution System Sketch .............................. 5-35 

5-13 Electrical Distribution System One-Line Diagram ............ ............. ....... ...5-37 

5-14 .... Logic Functions .............................................. 5-39 

USNRC Technical Training Center -xix -Rev.'1295
Power Plant Engineering Course Manual 

Figure= 

5-15 Miscellaneous Logic Diagram Symbols ................................................................ 5-41 

5-16 Typical Logic Diagram Symbols ........................................................................... 5-43 

5-17 Training Sketch of Reactor Trip Logic ................................... 5-45 

5-18 Pressurizer Pressure Logic Diagram ................................................................... 5-47 

6-1 Graph of Alternating Current in an AC Circuit ...................................................... 6-17 

6-2A Resistors in Series ....................................................... .................................... 6-19 

6-2B Resistors in Parallel ................................................................................................ 6-19 

6-3 Direction of Magnetic Field is from North to South Pole ...................................... 6-21 

6-4 Schematic Presentation of Relay and Associated Circuits ..................................... 6-23 

6-5 Two-Pole AC Generator ...................................... 6-25 

6-6 Generation of a Sine Wave ..................................................................................... 6-27 

6-7 Determining the Effective Value of an Alternating Current .................................. 6-29 

6-8 Real Power in a Purely Resistive Circuit ............................................................... 6-31 

6-9 Reactive Power in a Purely Inductive Circuit ........................................................ 6-33 

6-10 Principle of Parallel Plate Capacitor ................................................................ 6-35 

6-11 Reactive Power in a Purely Capacitive Circuit.......................6-37 

6-12 Complex AC Circuit ......... ..................................................... 6-39 

6-13 Impedance in AC Circuits ........................................ 6-41 

6-14A General Plot of Power Components.............................................. 6-43 

6-14B Power Triangle AC................. ....... .................. .... 6-43 

6-15 Application of Power Triangle. ....................................................................... 6-45 

6-16A Three-phase Source................................................................................................ 6-47 

6-16B Wye Connection...............................................................6-47 

USNRC Technical Training Center xx Rev. 1295
Power Plant Engineering Course Manual 

Figure 

6-16C Delta Connection ............................................. 6-47 

6-17 Instantaneous Power in a Three-Phase System ......................... 6-49 

6-18 Elements of Simple Transformer ........... ....................... 6-51 

-6-19 Schematic Diagram of Step-Down Autotransformer- &...........: ..... ..................... 6-53 

1 Revolving Field Generator and Resultant Output .............. :......... :...................... S7= 7-11 

-7-2 Three-Phase Generator and Resultant Output ............ .......................................... * 7-13 

,7-3 Four-Pole, Three-Phase AC Generator and SchematicDiagram for ---

Y-Connected Armature W indings ....................................................................... 7-15 

7-4 Generator Stator or Armature ............................................................................... 7-17 

7-5 'ýStator Bar Assemblies in Stator Core Slots ............................................................ 7-19 

-7-6 SimplifiedRotor Assembly ........................................ ........ ................. 7-21 

7-7 Exciter System ................................. .............. 7-23 

7-8 Brushless Exciter System ....................................... 7-25 

.7-9A Speed Regulator Characteristic ................................... 7-27 

7-9B Voltage Regulator Characteristic .................................... .................................. 7-27 

7-10A Generator Supplying Isolated Loads................................ 7-29 

7-10B Power Triangles .................. .......... . : ....... ...... . . .... ..................... 7-29, 

7-10C Regulator Characteristic for Generator .Supply'g Isolated Loads ........................ 7-29 

,7- 11 Effect of Increasing No-Load Frmuency and Voltage Setpoints to ... 

Generator Supplying Isolated Loads .................................................................. 7-31 

7-12 Frequency and Voltage Characteristics of an Infinite Bus ................................ 7-33 

7-13 Generator in Parallel with an Infinite Bus ............................... 7-35 

7-14 Load Sharing Between a Generator and an Infinite Bus ...................................... 7-37 

7-15 Frequency Requirements for Paralleling Generators ..................... ................ 7-39 

USNR-C Technical Training Center . ... V. 1295
Power Plant Engineering Course Manual

Figure 

7-16 

7-17 

7-18 

8-1 

8-2 

8-3 

8-4 

8-5 

8-6 

8-7

USNRC Technical Training xxii Center Rev. 1295

Pawge 

Synchroscope ......................................................................................................... 7-41 

Operating Quadrants ......................................................................................... 7-43 

Generator Capability Curves ............................................................................. 7-45 

Developm ent of a Rotating Field ........................................................................... 8-11 

Squirrel Cage Induction M otor .............................................................................. 8-13 

W ound Rotor Induction M otor ............................................................................... 8-15 

Shaded-Pole Single-Phase M otor ........................................................................... 8-17 

Induction-Start Single-Phase M otor ....................................................................... 8-19 

Capacitor-Start Single-Phase M otor ....................................................................... 8-21 

Indicating the General Areas of Application of Synchronous and 

Induction Motors ............................................ 8-23 

AC M otor Starting Current Curve .......................................................................... 8-25 

M agnetic Across-The-Line Starter ......................................................................... 8-27 

Prim ary Resistor Starter Diagram ......................................................................... 8-29 

Autotransform er Starting Diagram ......................................................................... 8-31 

Sim plified Grid System ......................................................................................... 9-23 

Ty'pical Distribution System ................................................................................... 9-25 

In-Plant Load Tripping ........................................................................................... 9-27 

Switchyard Bus Arrangem ent ................................................................................ 9-29 

Parallel Bus Arrangem ent ...................................................................................... 9-31 

Ring Bus Arrangement ..................................................................................... 9-33 

Typical Onsite Electrical Distribution System ....................................................... 9-35 

Vital and Nonvital Subsystems .............................................................................. 9-37

8-8 

8-9 

8-10 

8-11 

9-1 

9-2 

9-3 

9-4 

9-5 

9-6 

9-7 

9-8

Rev. 1295

USNRC Technical Training Center xxii
Power Plant Engineering Course Manual 

Figure -

9-9 In-Plant'Protective Bus Ducts .................................... 9-39 

9-10 Solenoid-Operated Circuit Breaker Operating Mechanism :..,....:. ........................ 9-41 

9-11 Air Circuit Breaker Operation .................................... 9-43 

9-12 Load Center With Air Circuit Breakers ................................ ........................ 9-45 

9-13 Cam-Operated Breaker Sequence .............................................. ,, .............. 9-47 

Air-Blast Circuit Breaker ....................................... 9•49 

9-15 Oil Circuit Breaker ............................................................... .. ............ ..9-51 

9-16 Vacuum Circuit Breaker .............................................................. .........9-53 

9-17 Breaker Control Circuit ........................... ............... 9-55 

9-18 Protective Relays ............................................. 9-57 

9-19 Typical Fuses ................................................................................. ....................... 9-59 

-9-20 Uninterruptible Power Supply .................................... 9-61 

9-21 Lead-Acid Battery Construction ................................... 9-63 

"9-22 Basic Chemical Action of a Lead-Acid Storage Battery.,.:..,.:.........................9-65 

.10-1 Common Adjustable Hangers ......................................................................... 10-31 

-10-2 Variable Spring Hanger ........................................ 10-33 

10-3 Constant Support ........................... .............................. 10-35 

10-4 Roller Stands .......................................................................................................... 10-37 

10-5 Hydraulic Snubber Basic Arrangement ............................... 10-39 

10-6 Basic Components of GateValves ..... ............................... .... 10-41 

10-7 Typical Globe Valve ............................................ ; ....... .................. .10-43 

10-8 Globe Valve with Conventional Disk and Conical Seat ................................... :...10-45 

10-9 Angle Globe Valve .............. ......................................................................... ,. 10-47 

USNRC Technical Training Center - .xxiii Rev. 1295
Power Plant Engineering Course Manual 

Fi gure Page 

10-10 Needle Valve ...................................................................................................... 10-49 

10-11 Swing - Check Valve ........................................................................................... 10-51 

10-12 Lift - Check Valve ............................................................................................... 10-53 

10-13 Stop - Lift - Check Valve .................................................................................... 10-55 

10-14 Butterfly Valve .................................................................................................... 10-57 

10-15 Nozzle Reaction Safety Valve ............................................................................. 10-59 

10-16 Huddling Cham ber Safety Valve ........................................................................ 10-61 

10-17 Relief Valve ......................................................................................................... 10-63 

10-18 Direct-Acting and Pilot-Operated Solenoid Valves ............................................ 10-65 

10-19 Two Types of Plug Valves .................................................................................. 10-67 

10-20 Ball Valve ............................................................................................................ 10-69 

10-21 Diaphragm Valves ............................................................................................... 10-71 

10-22 Air-Operated Single-Seated Control Valve ......................................................... 10-73 

10-23 Double-Seated Control Valve ............................................................................. 10-75 

10-24 Self-Contained Pressure-Reducing Valve ........................................................... 10-77 

10-25 Three-W ay Valve for Diverting Service ............................................................. 10-79 

10-26 Three-W ay Valve for Combining Service .......................................................... 10-81 

10-27 Deluge Valve ....................................................................................................... 10-83 

10-28 Electric Valve Operator ....................................................................................... 10-85 

10-29 Cutaway View of a SMB-0 Limitorque Operator ............................................... 10-87 

10-30 SM B-0 Lim itorque Operator ............................................................................... 10- 89 

10-31 Sim plified W orm Operation Diagram ................................................................. 10- 91 

10-32 SMB-0 Limitorque Operator (Exploded View) ................................................. 10-93 

USNRC Technical Training Center xdi Rev. 1295
Power Plant Engineering Course Manual 

Fieur _Page 

10-33 SMB-000/00 Limitorque Operator ................................ 10-95 

10-34 SMB-000 Limitorque Operator (Exploded View) ..................... . 10-97 

10-35 Basic MOV Valve Control Circuit with Seal-in ............................................ 10-99 

10-36 Basic MOV Throttle Valve Control Circuit ......................... 10-101 

10-37 Diaphragm Operators ......................................... 10-103 

10-38 Simple E/P Converter ......................................... 10-105 

10-39 HydraulicOperators .......................................... 10-107 

11-1 Impulse Turbine Principle ............................................ : ........ . ....... 11-17 

11-2 Ieal~ubines......................................... 11-19 

11-2 Ideal Turbines ............................ :. :.:.:. ............................. , ..... .:....... :...... ,.... '............. 11-'19

11-3:1 Reaction Turbine Principle ...... ................. ,........... 11-21.....................

lI-211 

11-4: Velocity Compound Staging (Curtis Stage) Pressure-Vel6city Diagramii ..... 11-23

11-5-, Pressure Compound Staging Pressure-Velocity Diagram............. ....... 11P25 

11-6 Reaction and Impulse Efficiencies ................................ 11-27 

11-7 Interstage Sealing ............................................................................................... 11-29: 

11-8 , D ouble-Flow Rotor ..................................................................... ": .......................... ' 11-31 , 

11-8 : Doule-Row Rotr........................................1-1 

11-9 *Rotor Types ............................. ... ....... . ......... 11-33 

11-10 Shaft Gland Sealing System ................................. ....... ...... ........................... 11-35 

11-11 Labyrinth Seals 11-37 11-37....................

11;-12 Gland Seal Steam Distribution .............- .13..................9............................. ....... 11-39 

11-13' Turbine Types ............ .... .............. ......... ..... 11-. 11-41 4.41.....4...........

11-14 Four Cylinder Nuclear Unit...:.................................................. 11-45 

1115 1 Four Cylinder Turbine, Cross Section .....................- ..................................... 11-47 

11-16 M ain Steam System ......................................................................................... 11-49_ 

USNRC Technical Training Center xxv . :- Rev. 1295
Power Plant Engineering Course Manual 

Figzure Page 

11-17 EHC System Hydraulic Power Unit .................................................................... 11-51 

11-18 Turbine Lube Oil System .................................................................................... 11-53 

11-19 Typical Journal Bearing ...................................................................................... 11-55 

11-20 Thrust Bearing ..................................................................................................... 11-57 

11-21 Side-M ounted Turning Gear ............................................................................... 11-59 

11-22 Flyweight Governor System ................................................................................ 11-61 

11-23 Rotor Critical Speeds .......................................................................................... 11-63 

12-1 Volute Casing Pump ............................................................................................ 12-17 

12-2 Multistage (Three) Pump Impeller and Shaft Assembly ..................................... 12-19 

12-3 Radial Reaction Forces in Pumps ........................................................................ 12-21 

12-4 Radial Reaction Forces in Single-Volute Versus Double-Volute Pumps ........... 12-23 

12-5 Double-Volute Casing Pump .............................................................................. 12-25 

12-6 Double-Suction Impeller ..................................................................................... 12-27 

12-7 Conventional Stuffing Box with Bottoming Ring .............................................. 12-29 

12-8 Seal Cage Arrangement ....................................................................................... 12-31 

12-9 Typical M echanical Pump Seal Construction ..................................................... 12-33 

12-10 Internal Versus External Pump M echanical Seal Assemblies ............................ 12-35 

12-11 Double M echanical Seal ...................................................................................... 12-37 

12-12 Displacement of a Solid in a Liquid .................................................................... 12-39 

12-13 Suction and Discharge Strokes of a Reciprocating Pump ................................... 12-41 

12-14 Schematic of a Double-Acting Liquid End Reciprocating Pump ....................... 12-43 

12-15 Liquid End, Vertical Pump ............................................................................. 12-45 

12-16 Stuffing Box ........................................................................................................ 12-47 

USNRC Technical Training Center xxvi Rev. 1295
12-17 

12"18 

12-19 

12-19 

12-20 

12-21 

12-22 

12-24 

12-24 

12-25 

12-26

USNRC Technical Training Center xxvii - Rev.1295

Power Plant Engineering Course Manual 

Figure

Discharge Rates for Single Double-Acting and Triplex Single-Acting' 

Pum ps ............................................................................................................... 12-49 

Flow Characteristics of Simple and Duplex Pumps .................... 12-51 

Required NPSH for a Triplex Pump .................................................................... 12-53 

Jet Pum p .............................................................................................................. 12-55 

Centrifugal Pump Characteristic Curve .............................................................. 12-57 

Changing Speeds for Centrifugal Pump ............................ 12-59 

Characteristic Curves for a Three-Stage Centrifugal Pump ................................ 12-6 1 

Operating Point for a Centrifugal Pump .............................................................. 12-63 

Change in Operating Point Due to Pump Wear ...................... 12-65 

Pump Characteristic Curve for Two Identical Centrifugal Pumps Used in 

Parallel .............................................. :................................. 12-67 

Operating Point for Two Centrifugal Pumps in Parallel ..... :................. I .......... 12-69 

Pump Characteristic Curve for Two Identical Centrifugal Pumps Used 

in Series .......................................................................................................... 12-71 

Operating Point for Two Centrifugal Pumps in Series .... .............. 12-73 

Positive Displacement Pump Characteristic Curve ............................................. 12-75 

Four-Stroke Diesel Engine Cycle ........................................ : ............. : ........... 13-13 

Two-Stroke Diesel Engine Cycle : ............................ 1.-15.......................

13-15 

Typical Diesel Air Starting System ........... . I . - ' 13-17 

s................................ .............. :.........K. 13-19 

Air Start Valves ................................................. ;..:; ..... :. ..... .. ;.:...... ......... .. :.............. 13-19 

Diesel Fuel Oil System ........................................ 13-21 

Diesel Generator Lube Oil System.......................................................... ....... 13-23 

Diesel Cooling System ........................................ 13-25

12-27 

12-28 

-12-29 

12-30 

13-1, 

13-2 

:13-3 

13-4 

13-5 

13-6 

13-7

." Xxvii '"•Rev. 1295 • USNRC Technical Training Center
Power Plan t Engineering Course Manual

Figure 

13-8 

13-9 

13-10 

13-11 

13-12 

13-13 

13-14 

13-15 

14-1 

14-2 

14-3 

14-4

USINKC; I ecnmcal I raining Center TYn,nn Pr. . . . - . .

xxiiii 

Rev. 1295

Page 

Diesel Cycle Tim ing ............................................................................................ 13-27 

Roots Blower Scavenging System ...................................................................... 13-29 

Turbocharger System .......................................................................................... 13-31 

Simple Mechanical Governor ................................ 13-33 

Hydraulic.Governor...................................... 13-33 Hydraulic G overnor ............................................................................................. 13-35 

Hydraulic Governor with Feedback .................................................................... 13-37 

Hydraulic G overnor with Compensating Device ................................................ 13-39 

Electric Governor ................................................................................................ 13-41 

Basic Instrument Channel ................................................................................... 14-17 

Basic Therm ocouple Diagrams ........................................................................... 14- 19 

Detailed Therm ocouple Circuit ........................................................................... 14- 21 

Resistance - Temperature Characteristics of Metals at Elevated 

Tem peratures ................................................................................................... 14-23 

Resistance Tem perature Detector ........................................................................ 14-25 

W heatstone-Bridge Circuit .................................................................................. 14-27 

Rem ote ................................................................................. 14-29 

Pressure Units .......................................................... : ........................................... 14- 31 

Bourdon Tube Pressure Gauge ............................................................................ 14-33 

Diaphragm/Bellows Pressure Sensors ................................................................. 14-35 

Force Balance Transmitter .................................................................................. 14-37 

M ovable Core Transmitter .................................................................................. 14- 39 

Variable Capacitance Differential Pressure Sensor ............................................ 14-41 

Strain Gauge ........................................................................................................ 14-43

14-5 

14-6 

14-7 

14-8 

14-9 

14-10 

14-11 

14-12 

14-13 

14-14

xxvii Rev. 1295
Power Plant I 

Figure 

14-15 

--14-16 

14-17 

14-18 

14-19 

14-20 

14-21 

14-22 

14-23 

14-24 

14-25 

15-1 

15-2 

15-3 

15-4 

15-5 

15-6 

15-7 

15-8 

15-9 

15-10 

15-11

;ngineering Course Manual

Pa=e 

Primary Elements ................................................................................................ 14-45 

Elbow Flow Measuring Device .................................. 14-47 

Pitometer Flow Tube ......................................................... 1.............................. 14-49 

Bello ws Fl Sesor._................. .....: .............................. ............................ 14-51 

Bellows Flow Sensor..................................14-1 

Diaphragm Flow Sensor ...................................................................................... 14-53 

Magnetic Flow Sensor ......................................................................................... 14-55 

Level Measuring Device for Tank Open to Atmospheric Pressure .................... 14-57 

Differential Pressure Level Detector ................................................................... 14-59 

Reference Leg Differential Pressure System ..................................................... 14-61 

Pressurizer Differential Pressure Level Detector ................................................ 14-63 

Current Loop ....................................................................................................... 14-65 

Block Diagram of Feedback Control System ...................................................... 15-11 

Control System Response .................................................................................... 15-13 

Manual and Automatic Feedback Controls for Thermal Systems ...................... 15-15 

Steam Generator Water Level Control System ....................... 15-17 

Simple Bistable Control ................................................................................ 15-19 

Bistable Control with Deadband Reaction to Decrease in Steam Demand ........ 15-21 

Bistable Response to Step Change in Input ........................................................ 15-23 

Proportional Band ................................................................................................ 15-25 

Response of Proportional Controller to Decrease in Steam Demand ................. 15-27 

Proportional Controller Response to Step Change in Input (Gain = 1) .............. 15-29 

Proportional Integral Control .............................................................................. 15-31

I- Rev. 1295 - USNRC Technical Training Center xUxi
Power Plant Engineering Course Manual

Fi15

15-12 

15-13 

15-14 

15-15

USNRC Technical Training xxx Center Rev. 1295

Page 

Response of Proportional Integral Controller to Decrease in Steam Demand .... 15-33 

Proportional Integral Controller Response to Step Change in Level Setpoint .... 15-35 

Proportional Derivative Control .......................................................................... 15-37 

Response of Proportional Derivative Controller to Decrease in Steam 

Demand ............................................................................................................ 15-39 

Response of Proportional Derivative Controller to Step Change in Setpoint ..... 15-41 

Proportional Integral Derivative Control ............................................................ 15-43 

PID Controller Characteristics ............................................................................ 15-45 

Effects of Change in Demand ............................................................................. 15-47 

Neutron Detector Operational Ranges ................................................................ 16-11 

Gas-Filled Detector ............................................................................................. 16-13 

Gas Ionization Curves for Constant Incident Radiation Fields ........................... 16-15 

BF3 Proportional Counter ................................................................................... 16-17 

Startup Channel ................................................................................................... 16-19 

Fission Chamber .................................................................................................. 16-21 

Compensated Ion Chamber ................................................................................. 16-23 

Uncompensated Ion Chamber ............................................................................. 16-25 

Self-Powered Neutron Detector .......................................................................... 16-27

15-16 

15-17 

15-18 

15-19 

16-1 

16-2 

16-3 

16-4 

16-5 

16-6 

16-7 

16-8 

16-9

xxx USNRC Technical Training Center Rev. 1295
Power Plant Engineering Course Manual Basic Plant Cycles

1.0 BASIC PLANT CYCLES 

Learning Objectives 

After studying this chapter, you should be able 

to perform the following for PWR and BWR 

"plants' 

I. Describe the basic flowpaths for the major 

heat transfer cycle(s). 

a. Primary 

b. Secondary (PWR only) 

2. Describe the functions and basic operation 

of major plant systems and components. 

a. Primary 

b. Secondary (PWR only) 

c. Emergency 

d. Control 

3. Describe the sequence of basic operations 

necessary to perform a plant startup and 

plant shutdown.

4. List the principal barriers io the release of 

radioactive fission products.

1.1 - Boiling Water Reactor Overview 

Commercial nulearpJ'werplants in the United 

States'fall into two6broad design categories. Spe

cifically, these design categories are dual-cycle , 

plants and'diret-cyclk plants. D'ual-c•yle plants' 

are characte'rihzd by ti'o pjhysicallyi iidep~ndent 

fluid systems which separate the high pressure 

radioactive react6r'c6olant (priinarysy'stem)'from 

the low press•ure non-radioactive steamnconden

sate systems (secondary system). Pressurized' 

water reactors are exampleý: of dual-cycle sys

tems. r . 

Direct cycle ilants iie'fundamentally daffer-' 

ent from dual-cycle plants. Direct-cycle plants 

generate steam in the 'reactor and pass the steam 

directly to-the turbine.- Boiling'water reactors are 

examples of direct-cycle plants. As show'n in" 

Figure 1-1, there is no distinction between primary

or secondary systems.as 'tere is in a PWR. -The 

direct-cycle design used in commercial boiling 

water reactor's offers niumerous operational and 

maintenance advantages for the owner-utilities. 

The basic operatioh of a foic6ed-circula'tion 

direct-cycle BWR is shown in Figure 1-2. Inside 

the BWR vessel (A), a steam-water n.ixtu~re is 

producedas coolant water removes heat from the 

reactor core (B)." The steani-water mixture moves 

Upward and into the moisture separator (C), where 

water droplets are removed before the',-tiam is 

allowed to enter the-steam line I(D). The steam 

turns the turbine (E), which turns the electrical 

generator (F). The steam then enters the con

denser (G), where it is condensed into water. The 

water is pumped by the feedivater pump (H) from 

the condenser back into the reactor vessel. The 

recirculation pump (I) and jet pump (J) allow the 

operator to vary. the coolant flow rate (and thus 

change reactor power). 

The fluid flow rates and reactivity levels! in a 

forced-circulation direct-ccleiBWR require close 

control of steam flow from the reactor, feedwater 

flow into the reactor, recirculation flow fthough 

the reactor, and control rod positions. The design' 

of the control systems considers conventional 

power generation objectives, such isreliability, 

ease of operation, response times of the ci6otr0l-. 

ling parameters, etc Beyondthe' iraditional power 

generation objectives, 'the control systems must 

incorporate featuresspecific to reacti vity control, 

and nuclear plant safety. ',These c6insiderations, 

involve -effects on moderator? temperature, fuel 

temperature, iad mioderator void content (amount 

of steam in the'waier) -as a fuictimn of steam 

pressure; steain generation and feedwater input;, 

fuel exposure; and automatic shutdown of the 

nuclear chain reaction-during unsafe oi-po'lientially 

unsafe conditions. 

The BWRR material presented here is based onz 

a single facility and is n'bt intended to represent a 

complete discussion'of all BWR' facilities"-and 

systems. For a more complete and detailed treat

ment of the material presented here, the reader

USNRC TecliDical Training Center 1-1 Rev. 0197

Power Plant Engineering Course Manual Basic Plant Cycles

USNRC Technical Training Center 1-1 Rev. 0197
Power Plant Engineering Course Manual

Basic Plant Cycles should refer to a BWR technology manual or a 

BWR systems manual. Informatiofi about a spe cific plant can be found in its Final Safety Analysis 

Report (FSAR). 

1.1.1 BWR Product Lines 

Different product lines or classes ofB WRs are 

designated numerically. There are'currently six 

product lines: BWR/1, 2, 3, 4, 5, and 6. Table I

1 gives some basic information on the'different 

product lines. The descriptions in this chapter are 

based on the BWR/4 pioduct line. Plants of this 

product line became fully operational during the 

1980's. Note that the BWR/4 product line does not 

reflect the state of the art in industry today, but 

fairly represents the typical designs, systems, and 

circuits that would be found in most commercial 

boiling water reactors. 

1.1.2 Primary and Auxiliary Systems 

The BWR primary and auxiliary systems are 

those that are immediately involved in the direct

cycle BWR concept as part of the steam cycle, or 

that provide an auxiliary function for the direct

cycle system. These systems are shown in Figure 

1-3. The BWR direct steam cycle starts with the 

reactor vessel, which is part of the-reactor coolant 

pressure boundary and contains the rektor core. 

The reactor core provides the heat source for steam 

generation, consisting primarily of the nuclear 

fuel and control rods for regulating the fission 

process: The steam generated in the reactor vessel 

is routed to thie steam loads and then 6ondensed 

into water. The water is then purified, heated, and 

pumped back to the reactor vessel to be reheated. 

Water from the reactor vessel is circul ate'd through 

external pumping loops and is then returned to the 

reactorvessel to provide forced circulation of flow 

through the reactor core. Reactor water is contiiu

ously purified to minimize impuriiies. Should the 

reactor become isolated from its main heat sink, an 

auxiliary system auiomatically keeps the reactor 

core covered with water. The BWR primary and 

auxiliary systems are discussed in the paragraphs 

which follow.

1.1.2.1 Reactor Vessel 

The Reactor Vessel 

* houses the reactor core, 

serves as part of the reactor coolant pres

sure boundary, 

supports and aligns the fuel and control 

rods, 

* provides a flow path for the circulation of 

coolant past the fuel, 

* removes moisture from the steam exiting 

the reactor vessel, 

a provides an internal floodable volume to 

allow for reflooding the reactor core fol

lowing a loss-of-coolant accident, and 

0 limits downward control rod motion fol

lowing a postulated failure of the control 

rod drive housing. 

A typical BWR reactor vessel is shown in 

Figure 1-4. The reactor vessel is mounted verti

cally within thi pima-ry containment (drywell); it 

comprises a cylindrical shell with rounded bottom 

head. The top head is also rounded but it can be 

removed to facilitate refueling operations. The 

vessel assembly is supported by a support skirt that 

is mounted to the reactor vessel support pedestal. 

The base material of the reactor vessel and the 

top and bottom heads is a low carbon steel alloy. 

The insidewall of the cylindrical shell and bottom 

head is clad with stainless steel to provide corro

sion resistance. The inside of the top head is not 

clad with stainless steel because it is exposed to the 

less corrosive steam environment. 

The internal components of the reactor vessel 

are supported from the bottom head and/or the 

reactor vessel walls. The reactor core is made up 

of the fuel assemblies, control rods, and nuclear

IW .1r'' L . -

b z%- I -cuumca. I rammg tcenter 1-2 Rev. 0197

Basic Plant Cycles
Power PIint Engineering Course Manual Basic Plant Cycles

instrumentation arranged roughly .as 'a vertical 

cylinder within the reactor vessel. The structure 

surrounding the reactor core consists of, a core 

shroud, core plate, and top guide. 

The components making up the remainder of 

the reactor-vessel internals are the jet pumps, 

"control rod guide tubes and housing, steam sepa

rators, steam dryers, feedwaterspargers, core spray 

spargers, standby liquid control injection line, and 

incore monitors. Except for the zirconium all6y 

used in the fuel cladding and channels, the reactor 

internals are made of stainless steel or other corro

'sion-resistant alloys. 

L1.2.2 Fuel and Control Rods 

The fuel generates energy from the nuclear 

fission reaction to provide heat for steam genera

tion.-The control rods control reactor power level, 

-both axially and radially, to optimize core perfor

mance. -They also provide adequate excess nega

tive reactivity3 to shut down the reactor from any 

normal operating or accident condition at the most 

reactive time in core life. 

Note that the control rods penetrate the reactor 

yessel from the bottom, a design that is unique to 

BWRs.. Bottom penetrating control rods offer 

,several advantages during maintenance. -Less 

time is required during refueling outages to re

move and reinstall the reactor vessel, head since 

control rod-drives are not a factor as they are in 

PWR refueling operations. Control rods remain 

operable when the reactor vessel head is removed. 

Internal moisture removal and steam separation 

can be more easily accomplished without interfer

ence from any top-mounted control rods. In a 

BWR, a large percentage of voids in the upper part 

of the core significantly reduces the power in this 

area. If control rods entered from the top of the 

core, those rods, which arepartially inserted, would 

, severely depress the flux in the upper part of the 

,core. The control rods are also used for axial 

power shaping by leaving some of them partially 

inserted in the power portion of the core which 

helps to control flux peaking 4 in local areas of the

core and yields an optimum fuel burnup. Bottom 

entry control rods allow maximum use of water as 

a neutron shield for control rod drive mechanism 

components. 

The'reactor'core is'arranged into fuel cells. 

!-Ech fuel cell consists of a control iod and the four 

fuel assemblies that immediately surround it. The 

four fuel assemblies are supported by a fuel

support piece. Around the outer edge of the core, 

certain fuel assemblies not immediately adjacent 

to a controliod are supported by individual pen'iph

eral fuel-support pieces. . 

A fuel assembly consists of a fuel bundle and 

,the' fuel channel that surrounds it. .A'fuel bundle 

-contains 62 fuel r6ds and 2 water rods arranged in 

a square 8 by 8 array. 

A fuel rod consists of uranium dioxide (UO2) 

pellets and a ,irconium alloy clidding tube. A fuel 

rod is made by stacking pellets in a cladding tube 

that is evacuat&l, back-filled with helium, and 

sealed by welding plugs in-each end of the iube' 

The pellets are stacked to an active length of 150 

inches leaving about 10 inches to act as a fission 

gas 5 plenum. The water rods are tubes of zirco

nium alloy cladding without fuel. They have small 

holes at both the upper and lower ends to allow 

water to be driven through the rods. 

"A control rod consists of a sheathed, cruciform 

array of vertical neutron absorber rods.- The ab

sorber rods are small stainless-steel tubes filled 

with boron carbide (B4C) powder:' The control 

rods can be positioned at 6-inch steps and have -a 

normal withdrawal and insertion speed of 3 inches 

per second.' -

1.1.2.3 Control Rod Drive System 

The Control Rod Drive (CRD) system makes 

gross changes in core reactivity by pogitioning the 

neutron absorbing control rods in response to 

Reactor Manual Control system (RMCS) signals 

and by rapidly~inserting all control rods to 'shut 

down the reactor in response to Reactor Protection

USNRC Technical Training Center 1-3 Rev. 0195

Power Plant. FEnieering Course Manual basic Plant Cycles

-USNRC Technical Training Center 1-3 I ,- Rev. 0195;
Power Plant Engineering Course Manual Basic Plant Cycles

system (RPS) signals.

1.1.2.4 Recirculation System 

The Recirculation system provides forced cir

culation of water through the reactor core, thereby 

allowing a higher power level to be achieved than 

with natural circulation alone. 

1.1.2.5 Main Steam System and Main Turbine 

The Main Steam (MS) system directs steam 

from the reactor vessel to certain safety-related 

systems and selectedbalance-of-plant (BOP) loads. 

The safety-related systems include theReactor 

Core Isolation Cooling (RCIC) system, the High 

Pressure Coolant Injection (HPCI) system, and the 

safety/relief valves. The selected BOP loads in

cdude the main turbine and turbine bypass valves, 

reactor feed pump turbines;, and steam jet air 

ejectors. The main turbine accomplishes the pri

mary plant task of converting the steam (heat) 

energy into the rotational-kinetic energy of the 

turbine shaft, which is physically connected to the 

rotor of the main generator, where the kinetic 

energy is converted to electrical output. 

1.1.2.6 Condensate and Feedwater System 

The Condensate and Feedwater system con

denses turbine exhaust and bypass steam, removes 

impurities, heats the feedwater, and delivers the 

water back to the reactor vessel at the'required rate 

to maintain correct inventory. The feedwater 

piping also provides a means for the Reactor 

Water Cleanup (RWCU) system, the Reactor Core 

Isolation Cooling (RCIC) system, and the High 

Pressure Coolant Injection (HPCI) system to dis

charge water to the reactor vessel. 

1.1.2.7 Reactor Core Isolation Cooling System 

The RCIC system supplies high pressure 

makeup water to the reactor vessel when the reac

tor is isolated from the main condenser and/or the 

reactor feed pumps have been lost.

1.1.2.8 Reactor Water Cleanup System 

The RWCU system maintains reactor water 

quality by removing corrosion products, fission 

products, and other impurities that end up in the 

reactor coolant. The RWCU system also provides 

a path for the removal of reactor coolant from the 

reactor vessel during reactor startup and shut

down. 

1.1.2.9 Residual Heat Removal System 

The Residual Heat Removal system comprises 

several subsystems. Two of the subsystems of 

particular interest at this time are the Low Pressure 

Coolant Injection (LPCI) mode and the Shutdown 

Cooling (SDC) mode. The LPCI mode will be 

discussed in the Emergency Core Cooling section 

that follows. The SDC mode of operation pro

vides a means of removing decay heat from the 

core following a reactor shutdown. SDC takes a 

suction from one of the recirculation loops, passes 

the water through aheat exchanger, and returns the 

water to the reactor via the recirculation loops. 

1.1.3 Control Systems 

The systems described in the subsections be

low are used for control of core reactivity under 

normal, abnormal, and emergency conditions and 

for process control. The control systems are 

shown in simplified form in Figure 1-5. 

1.1.3.1 Reactor Manual Control System 

The RMCS provides rod movement control 

signals to the control rod drive system to vary core 

power level and power distribution. 

1.1.3.2 Reactor Protection System 

The RPS automatically initiates arapid reactor 

shutdown (scram) by inserting control rods to 

preserve the integrity of the fuel cladding and 

reactor coolant pressure boundary.

USNRC Technica] Training Center 1-4 Rev. 0195

Power Plant Engineering Course Manual Basic Plant Cycles

USNRC Techical Training Center 1-4 Rev. 0195
Power Plant Engineering Course Manual Basic Plant Cycles

1.1.3.3 Standby Liquid Control System 

The Standby Liquid Control System (SLCS) 

injects a neutron-absorbing poison solution into 

the reactor vessel during an emergency when the 

control rods are unable to shut down the reactor. 

The SLCS functions independently of any control 

rod movement and can maintain the reactor suib

critical under all plant conditions. 

1.1.3.4 Recirculation Flow Control System 

The Recirculation Flow Control system 

(RFCS) provides a means for' control' of core 

power level, over a limited range, by controlling 

recirculation system flow, which, in turn, deter

mines the flow rate of water through the reactor 

core. 

1.1.3.5 Electro-Hydraulic Control System 

The Electro-Hydraulic Control (EHC) system 

provides reactor vessel pressure control by posi

tioning the turbine control'valves and/or turbine 

bypass valves to pass an amount of steam flow 

consistent with the amount being generated in the 

reactor. The EHC system also controls the-speed 

and/or electrical load on the turbine generator 

during p-ower operations, and controls reactor pres

sue dur-ingistartup, heaitup, and cooldown evolu

tions. 

1.1.3.6 Feedwater Conirol System. 

The Feedwater Control sstem (FWCS) regu-: 

lates the flow of feedwater to the reiactor vessel to 

maintain reactor water level. The FWCS mea

sures and uses total steam flow, total feedwater 

flow, and reactor vessel water level signals to

carry out its function. 

1.1.4 Emergency Core Cooling Systems 

The 'iurpose of the Emergency Core Cooling 

systems (ECCS) is to proivide core cooling under 

loss-of-coolant accide'nt (LOCA) 'conditions to 

limit fuel cladding damage. The Code of Federal

Regulations requires the ECCS to be designed so 

that after auiy LOCA the reactor core remains in a 

'geometrical configuration amenable to cooling. 

The basic criteria are to limit fuel cladding tem

perature and oxidation to minimize clad fragmen

tation, 'and to minimize the hydrogen generation 

from clad oxidation to protect the containment. 

The ECCS, shown in Figure 1-6, consists of 

two high-pressure systems and two lo•w'-pressure 

systems. The high-pressure systems are the HPCI 

system and the Automatic Depressurization sys

tern (ADS). The low pressure systems' ae the Low 

Pressure Coolant Injection (LPCI) m6de of the 

Residual Heat Removal (RHR) system and the 

Core'Spray (CS) system.. 

1.1.4.1 High Pressure Cooiant Injection 

System 

The HPCI system maintains adequate reactor 

vessel water inventory for core cooling on small

break LOCAs, depressurizes the reactor vessel to 

allow the low pressure ECCS to inject on interfre

diate-break LOCAs,' and backs'up th6 function-of 

the Reactor Core Isolation Co'oling" (RCIC) s ys-_ 

tern underreactor vessel isolation conditions. 

i.1.42 Automatic Depressurizatiio System 

The ADS serves asa abac'kbp' to the HPCI 

system to depressurize the reactor-vessel so that 

the low pressure ECCS can inject water into the 

reactor vessel following small- or intermediate

break LOCAs. The ADS provides an autoniatic; 

actuation signal to approximately half of the safity/ 

relief valves causing these valves, to,.discharge 

steam from the reactor vessel/main steam lines to 

the suppressiofi pool.

1.1.4.3 Core Sprmay'System 

The CS system provides spray cooling to the 

reactor core to help mitigate the consequences of 

the large-break LOCAs when reactor pressure is 

low enough for the system to inject water into the 

reactor vessel.

USNRC Technical Training Center 15 Rev. 0197

-,Basic Plant Cycles Power Plant Engineering Course Manual

USNRC Technical Training Center Re-. 0197 1--5
Power Plant Engineering Course Manual Basic Plant Cycles

1.1.4.4 Low Pressure Coolant Injection 

The LPCI mode of the RHR systein restores 

and maintains water level in the reactor vessel 

following large-break LOCAs when reactor pres

sure is low enough for the system to inject water. 

1.1.5 Plant Startup 

Startup of a commercial nuclear power plant is 

a complex evolution which requires coordination 

between control room and p!ant personnel, atten

tion to detail, adherence to plant procedures, and a 

thorough understanding of integrated plant opera

tions. The plant startup can be more readily 

analyzed by subdividing the procedur6 into four 

distinct phases, namely prestartup checks, ap

proach to critical, heatup and pressurization, and 

increase to rated power. 

1.1.5.1 Prestartup Checklists 

Prestartup checklists are conducted to ensure 

that all plant systems' are operational and are 

properly' aligned for plant startup. The startup 

checks are typically commenced one week in 

advanice of startup and are conducted by the plant 

operations and maintenance department person

nel. Valve lineups are verified in accordance with 

the startup procedures, and operational tests, called 

surveillances, are performed on plant systems to 

ensure that they will function as designed when 

required. 

The typical plant status prior to a cold startup 

is as follows:

Reactor Auxiliary Systems 

Reactor water temperature 

Reactor water level 

Control rods 

Recirculation pumps 

RWCU system 

RHR-Shutdown Cooling 

Main Steam Isolation 

Valves 

Reactor Head Vent

approximately 125°F 

normal 

fully inserted 

ready for operation 

in operation 

in operation 

closed 

open

Turbine Generator and Auxiliary Systems

Turbine 

Stop, control, and 

intercept valve 

Hotwell level 

Condensate and Feedwater

on turning gear 

closed 

normal 

shutdown

Emergency Core Cooling Systems 

HPCI in standby 

LPC in standby 

Core Spray in standby 

ADS in standby 

Electrical.Systems: 

Electrical system supplied from offsite 

Each system is started and brought online as 

required to support the plant startup. The first 

systems to be started are typically the condensate 

and feedwatersystems, and the reactor recirculation 

system. The condensate and feedwater systems 

are required to provide a source of water to the 

reactor. The recirculation system is started as a 

source of forced'cooling to the core in preparation 

for reactor startup. 

1.1.5.2 Approach to Critical6 

The approach to critical portion of the plant 

startup procedure involves the withdrawal of con

trol rods to achieve reactor criticality. First, the 

mode selector switch is moved from the SHUT

DOWN position to the STARTUP/HOT 

STANDBY position. This position enables the 

control rods to be withdrawn and enforces reactor 

protective system scram limits that are reserved 

for reactor startup conditions. The control rods are 

withdrawn in the order and sequence specified by 

the nuclear engineering department. This ensures 

that reactor thermal limits are not exceeded and 

that the core is not placed in a condition that has not 

been thoroughly analyzed by the engineering staff. 

The approach to critical is conducted in a slow, 

deliberate manner. The operators closely monitor 

control rod movements, reactor power, and reac

tor period7 to verify that the reactor is under

USNRC Technical Training Center 1-6 Rev. 0197

t__________

USNRC Technical Training Center 1-6 Rev. 0197
Power Plant Engineering Course Manual Basic Plant Cycles

control and is res'pohding as expected. The reactor 

operator will declare the reactor critical when 'a 

stable, positive reactor period is attained with no 

additional'control rod movement. Once' the rea'c

tor has been brought to citicial,;the reactor opei'a

tor will continue to increase reactor power in a 

slow, controlled manner. Typically, the operators 

wvill maintain reactor period beiween-60 to 100 

seconds. At this point in the startup, control room 

personnel -will start to draw a vacuum in the main 

condenser to establish a heat sink forithe steam that 

will be produced during the heatup and pressuriza

tion phase of the startup. 

1.1.5.3 Heatup and Pressurization 

The heatup and pressurization phase of 'ih 

staitup commences when reactor power is suffi

ciently high io 'increase the temperature of the 

water in the'reactor. This point is referied to ai the 

point of adding heat'(POAH). Once at the POAH, 

control rods are-withdrawn from the core as re

qiiired it maintain i'constant heatup rate. 

The water in the reactor will eventually reach 

saturation temperatu're and will start to boil. The 

steam will be directed down the main steam lines 

to warmup the'piping and the main turbine. 'Con

densed steam is driained frbm the steam lines and, 

is directed to the minn condenser. As more energy 

is added to the reactor coolant, the boiling rate will 

increase. If steam 'iss'being pirduced at a rate 

greater than'it is being removed from the reaetor,_ 

reactor pressure will increase. The operators will, 

therefore, restrict the flow of steam thrdugh'the' 

main steam lines to increase reactor pressure and 

will continue to raik-e reactor pressure until it is 

approximately 1000 piig. 

:At'this point in the plant st"artup, reaciorp6wer 

is approximately 5%, reactor pressure is, 1000 

psig, a vacuum exists in the main condenser, one 

feedwaterpump is pr6vidirig water to the reactor, 

the mode switch 'is in- the STARTUP/HOT 

STANDBYposition, and the main turbine is in the 

process of warming up. The operators are now 

ready to commence the increase to rated power

phase of the plant startup. 

1.1.5.4 Increase to Rated Power 

The operators next place the Mode Selector 

Switch to' RUN. This "Establishes the reactor 

protective system scram setpoints at their normal 

values for full power 6peration. Control rods are 

then witidiawn to increase reactor power to ap

proximately 30%: The turbin&egenerator, which 

by this time has been completely warmed, is 

placed on line. Additionalffeedwater pumps are 

started as required to support the increased steam 

demand 6f the'turbine. The electrical generator 

attached to the turbine can now besyr ebronized to 

the electric grid and power canfi be increased to 

100% or as specified by thelo'ad dispatcher. 

1.1.6 Plant Shutdown 

"Over the course of a plant's lifetime, it will 

become necessary to conduct normal, controlled 

shutdowns fromrated power forrefueling or main

tenance. Note that shutdown procedures cannot 

possibly provide for every contingency that might 

exist andl that'some degree of flexibility must be 

permitted. Therefore; some steps of a shutdown 

procedure may be performed simultaneously or, 

depending on the existiing c6nidition's;some steps 

may be conducted prior to the- shutdown itself.: 

Therefore. the student should focusrfi ithe under

lying logic and reason for the steps that are taken 

as- opposed to the exact oider' of the steps as 

outlined in the following text. For the purposes of 

this discussion of plant shutdown, assume that the 

plant'is operating at 100% pokwer. 

The plant shutdown' procedure involves'-re-` 

ducing reactor'power,-divorcing the generator 

fromi the electric grid, shutting the reactor dov& 

(subcritical), and'cooling' down -an depressuzii

ing the 'reactor.'- Each of these; phases 'will bý' 

discussed in more detail. ..

.1.6.1 Pre-shutdown Checklists

The first step in a-plant -shutdown' requires

USNRC Technical Training Center 1-7 Rev. 0197

USNRC Technical Training Center

Power Plant Engineering Course Manual Basic Plant Cycles

v-7 " " Rev. 0197
Power Plant Engineering Course Manual Basic Plant Cycles

plant personnel to complete-pre-shutdown check

lists. Among other actions, the operators will 

verify that the lube oil systems associated with the 

turbine turning gear are operational, the Source 

Range Monitors (SRMs) and Intermediate Range 

Monitors (IRMs) are calibrated, and that the Shut

down Cooling mode of the Residual Heat Re

moval system is operational. Control room per

sonnel will also call the Load Dispatcher to inform 

him of the planned power reduction. 

1.1.6.2 Normal Shutdown 

When all preparations have been completed, 

the control room personnel will commence the 

power reduction by reducing recirculation flow. 

The flow reduction increases the void fraction in 

the core, thereby adding negative reactivity and 

reducing reactor power. When reactor power has 

been reduced to approximately 55%, the operators 

will remove one of the two feedwater pumps from 

service. 

Power reduction using recirculation flow will 

continue until power is approximately 45%. At 

this point, the reactor operator will drive control 

rods into the core in accordance with approved 

procedures to reduce reactor power further. As 

power decreases, the operators will fully insert the 

IRMs and SRMs into the core so that power can be 

adequately monitored through, the intermediate 

range and the source range. The IRMs will typi

cally be fully inserted by the time reactor power 

has decreased to 10%. 

When reactor power is approximately 5%, the 

operators will remove the generator from the elec

tric grid. They will then start the auxiliary turbine 

oil systems and the bearing lift pump and remove 

the turbine from service. The turbine bypass 

valves are used to dump steam to the main con

denser to remove heat from the reactor and control 

reactor power. At this time, the control room 

operators will place the Mode Selector Switch to 

the STARTUP/HOT STANDBY position. This 

enforces a more conservative set of scram setpoints 

during the plant startup section.

The reactor operator will continue to insert 

control rods to further reduce reactor power. The 

other control room personnel will commence to 

cooldown and depressurize the reactor by bleed

ing steam to the main condenser via the turbine 

bypass valves. Because the water in the core is at 

saturation conditions, as system pressure decreases, 

water temperature also decreases. When system 

pressure has decreased to 250 psig, the demand for 

feedwater to the reactor will be sufficiently small 

that the remaining feedwater pump can be se

cured. The condensate pumps will now provide 

the motive force for feeding water into the reactor 

vessel. 

Eventually, steam pressure will be so low that 

continued cooldown with the main condenser is 

inefficient. The cooldown will be completed 

using the shutdown cooling mode of the Residual 

Heat Removal system. Once SDC is in operation, 

the operators can shut the turbine bypass valves, 

break vacuum on the main condenser, and shut the 

system down. The plant is now in a shutdown, 

cooled down, and depressurized condition. 

1.2 Pressurized Water Reactor Overview 

Most of the operating commercial nuclear 

power plants use pressurized water reactors 

(PWRs). Westinghouse supplies about two-thirds 

of the PWRs in the United States, with the remain

der supplied by Combustion Engineering and 

Babcock & Wilcox. Many of the details of PWRs 

vary from one vendor to another and even from 

one reactor to the next of the same vendor design. 

The PWR descriptions that follow are based on a 

Westinghouse design. However, the fundamental 

characteristic of all PWRs remains the same: the 

primary coolant raises the temperature of feedwater 

to produce steam in a heat exchanger called a 

steam generator and this steam drives the turbine. 

A simplified schematic of a PWR plant is 

shown in Figure 1-7. The PWR differs fundamen

tally from the BWR in that the PWR is a dual-cycle 

system.

USNRC Technical Training Center 1-8 Rev. 0197

Power Plant Engineering Course Manual Basic Plant Cycles

USNRC Technical Training Center 1-8 Rev. 0197
Power Plant Engineering Course Manual Basic Plant Cycles

The primaiy 1

6op- contains the heat source 

consisting of a nuclear fueled core within a reactor 

vessel where the heat resulting from the controlled 

fission reaction is transferred to the reactor cool

ant. The coolant is pumped to the sieam generator 

where the heat is transferred to a secondary loop 

- -through a number of U-shaped tubes. -Thereactor 

coolant returns back to the reactor vessel-to con

tinue the process. An electrically heated pressur

,-izer is connected to the primary loop to maintain 

pressure above the saturation pressure to prevent 

bulk boiling of the reactor coolant. 

The secondary loop is the heat utilization cir

"cuit where dry steam produced in the steam gen

erator- flows %to a -turbine generator where the 

thermal energy of the steam is converted to me

- chanical energy in the turbine to produce electrical 

energy from the generator. The exiting steam is 

exhausted to a condenser where it is condensed. 

*The condensate is pumped back to the steam 

generator to continue the cycle. 

The purpose of the dual cycle is to reduce the 

level of radioactive materials (contamination) in 

the plant's turbines, condensers, and other second

ary system components. The primary system 

-serves as a barrier to the release of radioactive 

-materials. 

-The PWR material presented here is generally 

based on a-single facility and is not intendedto 

represent a complete discussion of all PWR facili

ties and systems.- For a more complete and de

tailed treatment of the material presented here, the 

-reader should refer to a PWR technology manual 

.or PWR systems manual. Information about a 

specific plant design can be found in its final safety 

analysis report (FSAR). , , - ; I 

1.2.1 Primary Systems - PWR 

The major PWR primary systems are shown in 

Figure 1-8. The Reactor Coolant system (RCS), or 

primary system, consists of the reactor, where the 

heat from fission is transferred to the light water 

coolant; the steam generator(s), where the hot

reactor coolant is circulated through tubes to pro

-duce steami; and the reactor c6olant pump that 

circulates the coolant through the heat transfer 

loop(s). The rated thermal output of a PWR is 

determined by the size of the reactor and the 

number of heat transfer loops in the primary sys

-tem. 

1.2.11 Reactor Coolait System" 

"The RCS (primar system) consists of -a reac

tor and two, three,'or four reactor coolant'loops. 

Each loop contains one steam generator, one or 

two reactor coolantpumps, stfinless steel piping, 

and instrumentation. The major function of the 

RCS is to transport heated coolant from the reactor 

'through the steam generators -andr back to the 

"reactor for reheating: The primary system also 

contains an' electrically heated pressurizer con

nected to one of the reactor coolant loops. The 

pressurizer is a cylindrical vessel that is kept about 

*half full of coolant (water) that is mintit ed in a 

saturated (or boiling) 9tate. The hijlh-temperat.re 

steam volume in the top half iof the pre.surizer is 

kept at a high pressure to keep the circulating 

coolant in the RCS in a liquid state. i

1.2.1.2 Reactor Vessel 

The'reactor vessel encloses and supports the 

:reactor core components"and directi the flow of 

'coolant from the RCS loops through the core and 

back to the RCS loops.- 

The reactor vessel is a heavy-willed cylindri

cal tank with a rounded bottom and a removable 

rounded top. The top (head) is bolted tothe reactor 

vessel during all plant operations except refueling 

and special inaintenanced. The side of ihe reactor 

vessel has connectionpoints (called nozzles) for 

reactor coolant piping. Figure 1 -9 shows atypical 

PWR reactor vessel. The reactor 'vessel has two 

removable internal assemblies: the lower core 

support structure and the upper core support struc

i The lower core support structure isýalso known

USNRC Technical Training Center 1-9 Rev.0195

Basic Plant Cycles Power Plant Engineering Course Manual

USNRC Technical Training Center °" Rev.;019$ ' 1-9
Power Plant Engineering Course Manual

Basic Plant Cycles

as the "core basket" or-core barreL." Its purpose is to support the reactor fuel assemblies and direct 

reactor coolant flow past the fuel for heat removal. 

All major portions of this structure are made of 

stainless steel. 

The upper core support structure is also known 

as the upper internals package or upper plenum assembly. Its purpose is to properly align the top portions of reactor fuel assemblies within the 

reactor vessel, and to guide and protect control rod 

cluster assemblies that have been withdrawn from 

the reactor core. The upper core support structure 

is primarily made of stainless steel. 

The reactor core consists of fuel assemblies, 

control rods, and a number of neutron source rods 

and special poison rods. The core is located inside 

the lower core support structure, which is inside 

the reactor vessel. The upper core support struc

ture holds the fuel assemblies in their proper location within the vessel as thousands of gallons 

per minute of coolant water are forced through the 

core for heat removal. 

Figure 1-10 shows a simplified view of a 

reactor vessel. Reactor coolant enters the reactor 

vessel via the inlet nozzles. The water flows 

downward between the core barrel and the vessel 

wall into the bottom of the vessel. The coolant is 

then forced upward through flow distribution holes 

into the core where fuel heat is removed. Upon exiting the core, the coolant mixes in the outlet 

plenum and exits the reactor vessel through the 

outlet nozzles. 

1.2.1.3 Reactor Fuel 

The function of the reactor fuel is to provide fissile atoms to support the nuclear fission pro

cess, which produces the thermal energy required 

to heat the coolant for subsequent use in the steam 

generators. 

Figure 1-11 illustrates a typical PWR fuel 

assembly. PWRs use slightly enriched uranium 

dioxide pellets for nuclear fuel. "Enrichment"

T7?Yr. -........

1-10 

Rev. 0195 •raining ICIechn•ca Center 1-10 Rev. 0195

refers to the percentage of fissionable uranium

235 that is combined with the more abundant and 

less reactive uranium-238. Common PWR fuel 

enrichments range from about 2.0% to 3.5% ura

nium-235. The uranium dioxide fuel pellets are 

sealed inside a cylindrical metal tube called a fuel 

rod (or fuel pin). Fuel rods are made of a zirco

nium alloy. 

A number of fuel rods are grouped together to 

form a fuel assembly (also known as a fuel element 

or fuel bundle), which is shown in figure 1-11. The 

number of fuel rods per assembly varies slightly 

from vendor to vendor. The typical PWR fuel 

assembly is a square grouping of fuel rods with 15, 

16, or 17 rods per side and is 12 feet in length. 

All PWR fuel assemblies have a number of 

tubes that do not contain uranium fuel pellets. 

These tubes (called control rod guide tubes or 

thimble tubes) are open at the top, and allow 

insertion of control rods or instrumentation. 

1.2.14 Control Rods 

The function of the control rod system is to 

control the nuclear fission process by inserting 

strong neutron absorbers (control rods) into the 

reactor core. These neutron absorbers can be 

slowly removed from the core to "start up" the 

nuclear fission process, or they can be fully in

serted into the core to "shut down" the reactor. 

The control rods consist of a silver-indium

cadmium or boron carbide mixture sealed inside 

stainless-steel tubes. The tubes are connected to a 

cluster assembly. Control rod cluster assemblies 

are moved up and down within the control rod 

guide tubes to control reactor power level. 

The control rod drive mechanisms (CRDMs) 

are located above the removable reactor vessel 

head. The CRDMs are used to withdraw and insert 

control rods and latch them in.the desired position 

during plant operations. The CRDMs are electro

magnetic jacking devices.

Basic Plant Cycles
Power Plant Engineering Course Manual Basic Plant Cycles

When an electric current ig directed through 

the CRDMs, the control rod drive shafts will be 

either raised, lowered, or held in their present 

location. The interruption of current flow to the 

CRDMs releases all control rod drive shifts and 

allows the control rods to drop into the core (reac

tor trip or scram).

1.2.1.5 Reactor Coolant Pump (RCP) 

The reactor coolant pump (RCP) is an electri

cally driven mechanical device that draws reactor 

coolant from the steam generator and discharges 

the coolant into the reactor vessel for removal of 

heat generated in the reactor fuel. Each 

Westinghouse reactor coolant loop will have onie 

RCP. -Other PWR designs use two RCPs per loop. 

Typical RCPs are capable of producing 100,000 

gpm reactor coolant flow rate. 

1.2.1.6 Pressurizer 

The pressurizer is a cylindrical tank with a 

rounded top and bottom. It is made of carbon steel 

and lined with stainless steel. The pressurizer has 

two purposes: 

1. It establishes and maintains the high pres

sure (2235 psig) that keeps the circulating 

coolant from boiling at normal operating 

temperatures between 530' and 595°F. 

2. It serves as a surge volume for the Reactor 

- Coolant system. The pressurizer receives 

water from the RCS piping as increasing 

temperatures cause water molecules to ex

pand (insurge). Similarly, the pressurizer 

serves as a source (insurge) ofwater for the 

RCS as decreasing temperatures cause 

water molecules to contract (outsurge). 

The bottom portion of the pressurizer contains 

a bank of electric heaters that will increase-pres

sure when energized. The top section contains a 

spray nozzle and pressure relief valve connections 

that can lower pressure.

1.2.1.7 Steam Generator-Primary Side 

Each reactor coolant loop of the primary sys

tem has one steam generator to transfer heat from 

the reactor coolant to the secondary system. Fig

ure 1-12 shows a typical Westinghouse U-tube 

steam generator.

Reactor coolant enters the steam generator 

inlet channel and is directed upward into thou

sands of metal U-shaped tubes. The coolant trans

fers some of its heat- through the tubes to the 

secondary system. Coolant water exits the tubes, 

passes through the outlet channel, and enters the 

intermediate leg (6r crossover leg) piping to pro

vide suction for the reactor coolant pump. (Note: 

The Babcock and Wilcox'design PWRs use steam 

"generators with stiraight tubes vice U-tubes.) 

1.2.1.8 Chemical and Volume Control System 

The Chemical -and Volume Control system 

(CVCS) provides'the following functions: 

Provides a method for primary system 

cleanup (removal of corrosion- products 

and chemical impurities) and to add chemi

cals for corrosion control.' 

* Automatically maintains the volume of 

the Reactor-Coolant -system at a desired 

level by adding water (charging) to or 

draining water (letdown) from the RCS. 

"Provides a method to increase or decrease 

'the 'concentration of boric acid (neutron 

absorber) in the reactor coolant for re'actor 

"power changes. 

' Provides seal water to the reactor coolant 

pumps. ' 

* . Provides an aliernate source of spray water 

* - for the RCS pressurizer if normal pressur

izer spray is unavailable.' 

* Provides part-of the plant's emergency

USNRC Technical Training Center 1-11 Rev. 0195

,USNRC Technical Training Center

BasicPl~ant Cycles Power Plant Engineering Cours Manual

-1-11 , Rev. 0195
Power Plant Engineering Course Manual

core cooling system (high pressure safety Basic Plant Cvdes 

core cooling system (high pressure safety 

injection). 

1.2-1.9 Residual Heat Removal System 

The RHR system (also known as the decay heat removal system) provides a means for the 

transfer of heat energy out of the reactor coolant 

system during plant shutdowns and emergency 

conditions. 

During a normal- reactor shutdown and 

cooldown, the RHR system transfers reactor de

cay heat into a separate fluid system (the compo nent cooling water system) and ultimately to the 

environment. This is accomplished by pumping the hot RCS water from the hot leg through a heat 

exchanger and back into the RCS via the cold leg. 

During plant emergencies, portions of the RHR 

system are used to inject emergency cooling water 

into the RCS. The refueling water storage tank 

(RWST) supplies the source of borated injection 

water. 

1.2.2 Secondary Systems 

1.2.2.1 Steam Generator - Secondary Side 

Density differences cause the circulation of 

water inside a PWR steam generator. Figure 1-13 

shows a cutaway section of the secondary side of 

a steam generator. Feedwater enters the steam 

generator through a feed nozzle and is distributed 

by a feed ring. Water leaving the feed ring mixes 

with water extracted from the exiting steam. The 

resultant mixture flows downward into the 

downcomer region between the steam generator shell and the tube bundle wrapper (shroud). The 

feedwater flows under the shroud and upward around the tube bundle absorbing heat from the 

primary coolant flowing through the tubes. As the 

water inside the shroud is heated, steam bubbles 

form and the water becomes less dense.. Prior to 

exiting the tube bundle region, most of the 

feedwater boils to steam. The emerging steam is 

channeled through moisture separators that remove entrained moisture to produce dry steam at 

the steam generator outlet. The extracted water is 

recirculated (directed outside the shroud where it 

mixes with incoming feedwater) to produce a 

good circulation flow within the steam generator. 

1.2.2.2 Main Steam System 

The Main Steam (MS) system receives heat 

from the RCS via the steam generators. In the 

steam generators, feedwater is heated to produce high pressure saturated steam. The MS system 

transfers the steam to the main turbine where the 

energy of the steam is extracted to turn the turbine 

rotor and its attached electrical generator. Auxil

iary uses for main steam include steam dump, reheat steam, feedwater pump turbine supply, air 

ejector operating steam, etc. 

1.2.2.3 Main Turbine - Generator 

The main turbine-generator receives the steam 

from the main steam system. Nozzles increase the 

kinetic energy (velocity) of the steam and directs 

it toward the turbine rotor blades, thereby turning the rotor. Being connected to the same shaft, the 

generator rotor also turns and produces an electri

cal output. Both high-pressure and low-pressure 

turbines are used to maximize turbine efficiency and work output. 

1,2.2.4 Condensate and Feedwater System 

The Condensate and Feedwater system con

denses turbine exhaust or bypass steam, removes 

impurities, heats the feedwater, and delivers the 

water back to the steam generators at the required rate to remove heat from the RCS. 

Steam exiting the low pressure turbines enters 

the main condenser where it passes over tubes 

containing circulating cooling water. As the steam 

condenses, it is collected in the bottom of the 

condenser in the hotwell. 

The condensate pumps draw the condensate 

out of the main condenser hotwell and supply the

USNRU Technical Training Center Rev. 0195 1-42

Basic Plant Cycles
Power Plant Engineering Course Manual Basic Plant Cycles

booster pumps that increase the pressure of the 

condensate supplies to the main feedwater pumps. 

Prior to reaching the main feedwater pumps, the 

condensate passes through feedwater heaters that 

add heat to the condensate to increase the overall 

,efficiency of the secondary plant. A portion of the 

condensate is also directed through a filtration and 

ionexchange system consisting of condensate 

demineralizers. 

The feedwater pumps draw in the condensate 

and develop a system pressure sufficient to force 

*the water. (now called feedwater) through addi

tional feedwater heaters and into the steamn genera: 

tors. 

1.2.3 Control Systems 

The basic function of apowerplant is to supply 

electrical energy to the power distribution net

work on demand. To meet this demand (load), the 

nucleai core must provide heat generation propor

tional to the demand (eltrical power output), and 

the steam gene rators must respond with the correct 

flow of low-moisture steam to the turbine-genera

tor. This is normally accomplished automatically 

by the coordinated action of several control sys

tems. These systems also provide for the control 

of rapid disturbances arising from abnormal con

ditions and for control of processes that maintain 

the ,plant in an economical operating condition. 

The ba-sic .control systems are shown in block 

-diagram form in Figure 1-14. 

1.2.3.1 Pressurizer Control System 

The Pressurizer Control system matintains RCS 

presiure within design limits by automatically 

actuatingpressurizerheaters and spray valves, and 

maintains reactor coolant inventory (pressurizer 

level) by automatically adjusting CVCS letdown 

and charging flow rates., 

1.2.3.2 Rod Conti-ol.System 

The Rod Contol siystem automatically adjusts 

the power level of the reactor to match the power

demanded by the turbine. The direction and speed 

of control rod movement is based on the reactor 

coolant temperature needed to meet the turbine 

power demand, the nuclear.power (neutron flux 

level) rate of change, and the measured reactor 

coolant temperature.

The Rod Control system -has provisions for 

manual and automatic control rod operation. In an 

emergency, the Reactor Protection system (RPS) 

will remove power from the control rod drive 

mechanisms, causing the control rods to fall into 

the core and shut down the reactor. 

1.2.3.3 Steam Dump (Turbine Bypass) 

Control System 

The steam dumps (turbine bypass valves) are 

automatically actuated to remove steam from the 

steam generator (and heat from the RCS) when a 

large turbine load reduction or turbine trip occurs. 

Steam is dumped directly to the main condenser to 

maintain a preset temperature in the RCS. 

1.2.34 Turbine Control System 

The Turbine Control systempositions the steam 

admission valves of the main turbine to control 

turbine speed and load and to automatically shut

down the turbine when operating setpoints are 

exceeded. High-pressure hydraulic fluid is sup-: 

plied to or dumped from valve operators to posi-, 

tion the valves. If a turbine trip is required, the 

entire control system will depressurize causing all 

turbine steam valves to close quickly. 

L2.3.5 Feedwater Control System 

The Feedwater Control system (FWCS), also 

called the Steam Generator Water Level Control 

system (SGWLCS),regulates the flow offeedwater 

to the steam generators to-maintain the desired 

water leveL The FWCS monitors steamr.flow, 

feelwater flow, and steam generator water level. 

and positions feedwater control valves to ensure 

an adequate steam generator level is maintained.

USNRC Technical Training Center 1-13 - Rev. 0195

Power Plant Engineering Course Manual I - Basic Plant Cycles

USNRC Technical Training Center " 1-13 S_ Rev. 0195
Power Plant Engineering Course Manual Basic Plant Cycles

1.2.3.6 Reactor Protectiori System, 

The Reactor Protection system (RPS) pro

vides the following functions: 

1. Monitors the plant for abnormal condi

tions and alerts the operator to take appro

priate action. 

2. Automatically provides 

"* reactor trip (shutdown) signals and 

"* engineered safeguards actuation sig

nals when plant conditions reach es

tablished safety limits. 

Variables that are monitored by the RPS as 

part of its trip function include: 

1. The process variables that are directly re

lated to equipment mechanical limitations, 

such as pressurizer pressure -and water 

level (to prevent water discharge through 

safety valves and uncovering of heaters). 

2. The process parameters that directly affect 

the heat transfer capabilities of the reactor, 

such as steam generator water lev'el, RCS 

flow rate, and RCS temperature. 

Whenever a safety, setpoint is exceeded, the 

reactor Will be shut down (1) to ýrevent fuel rod 

damage for an anticipated transient (2) to limit 

core damage for infrequent faults and (3) to protect 

the reactor coolant pressure boundary. The RPS 

also provides for manual initiation of a reactor trip 

in the control room. 

1.2.4 Emergency Systems 

The PWR emergency systems are also known 

as the Engineered Safety Feature (ESF) systems. 

The purpose of the ESF systems is to protect 

public health and safety by mitigating the'conse

quences of accidents that could otherwise lead to 

failure of the PWRs fission product barriers. Sev

eral PWR emergency systems are discussed in the 

following sections.

1.2.4.1 Emergency Core Cooling Systems 

The Emergency Core Cooling systems (ECCS) 

supply borated vater to the reactor core in the 

event of a loss-of-coolant accident to maintain 

heat removal from the reactor fuel. These systems 

also ensure that the reactor remains in a shutdown 

condition during the cooldown accompanying a 

steamline-break accident. 

A simplified composite of the ECCS is shown 

in Figure 1-15. The ECCS is divided into four 

subsystems, which are described below. Some of 

these subsystems or their components are also 

used during normal plant operations. 

1.2-4.1.1 Low Pressure Safety Injection 

(LPSI) System 

The LPSI system is used as the low pressure, 

high volume portion of the ECCS. During normal 

plant operation, the LPSI pumps are aligned to 

take suction from the RWST and discharge into 

the RCS cold legs. All that is necessary for LPSI 

injection is that the pumps start and RCS pressure 

drops below the maximum discharge pressure 

(200 psig) of the LPSI pumps. 

1.±4.1.2 Accumulator System 

The accumulators (often referred to as cold leg 

accumulators, safety injection tanks, or core flood 

tanks) are tanks that are filled with borated water 

and are pressurized to approximately 600 psig 

with nitrogen gas. During normal plant opera

tions, each accumulator is isolated from its respec

tive RCS loop cold leg by two check valves. 

If the RCS pressure decreases below accumu

lator pressure (e.g., during a LOCA), the check 

valves will open and the nitrogen gas pressure will 

force the borated water into the RCS. The accu

mulators are considered to be passive engineered 

safety features because no external power source 

or initiation signal is needed to.obtain a fast acting, 

high injection flow rate.

USNRC Technical Training Center 1-14 Rev. 0195

Rev. 0195

Poweir Plant Engineering Course Manual Basic Plant Cycles

USNRC Technical Training Center 1-14
Power Plant Engineering Course Manual Basic Plant Cycles

1.2.4.1.3 Safety Injection System 

The Safety Injection (SI) system is used as the 

intermediate pressure, intermediate volume por

tion of the ECCS. During normal plant operation, 

the SI-pumps are aligned to take suction from the 

RWST and discharge into, the RCS cold legs 

through the same penetrations used by the LPSI 

system and the accumulators. All that is necessary 

for SI pump injection during a LOCA is for the 

pumps to start and RCS pressure to decrease below 

the maximum discharge pressure (approximately 

1500 psig) of the pimups. 

1.21.4. igh Pressure Safety Injection, 

... .. (HPSE System 

-The HPSI system provides the highest pres

.sure and lowest flow rate of all the ECCS. The 

HPSI pumps perform dual purpose as the centrifu

gal charging pumps in the CVCS. 

The HPSI pumps will automatically start and 

align to inject borated water from the RWST into 

the RCS.,-The HPSI system provides makeup 

water to the RCS'during a small LOCA when the 

.RCS remains at a relatively high pressure (> 1500 

psig). 

1.2.4.1•_ . Refueling Water Storage Tank 

(RWST). 

The RWST provides the source of injection 

water that is used during the initial stages of a 

LOCA: -This water is supplied to the suctions of 

"the HPSI, LPSI, SL and containment spray pumps. 

This water is highly borated to ensure the reactor 

remaiis shutdown while-the core is cooled. 

1.2.4.2 Auxiliary Feedwater System 

The primary function of the Auxiliary 

Feedwater (AFW) system is to supply an emer

gency source of feedwater to the steam generators 

following accident or transient conditions when 

the mrnini feedwatir system is not available. The 

AFW system thereby maintains the capability of

the steam generators to remove the stored RCS 

heat and core decay heat by converting the auxil

iary feedwater to steam, which is then discharged 

to the condenser or to the atmosphere. 'A second

ary function of the AFW system is to provide the 

normal source'of feedwater to the steam genera

tors during shutdown, startup, and low power 

levels., 

1.2.4.3 Containment Spray/Cooling System 

The Containment Spray system is designed to 

spray the containment volume with relatively cool 

-water following a LOCA or steam-line break to 

prevent overpressurization. The RWST supplies 

the suction of the containment spray pumps. In 

addition-to reducing containment pressure and 

temperature, the spray water will absorb free io

dine, thereby reducing the magnitude of the radio

activity release if the containment is breached. 

"The Containment Cooling system consists of 

large forced flow air-to-liquid heat exchangers 

located inside the containment. The ,coolers are 

supplied cooling water from an ESF cooling water 

system (such as the Component Cooling Water 

system) and are also designed to reduce contain

ment pressure and temperature. Both the Contain

ment Spray and Containment Cooling systems 

will actuate on high containment pressure. 

1.7-4.4 -,--Component Cooling Water (CCW) 

'System -, 

The CCW system supplies the cooling waterto 

the ECCS and ESF systems to provide a heat sink 

and to prevent overheating of system equipment 

during long-term operation.- The system is nor

mally in operation to ensure immediate cooling of 

systems required for plant and public safety.

1.2.5 Plant Startup - PWR

1.2.5.1 Plant Heatup. 

-A plant startup commences with filling and 

venting the RCS and.pressurizer. RCPs are operUSNRC Technical Training Center - - 1-15 Rev. 0195

Power Plant Engineering Course Manual Basic Plant Cycles

USNRC Technical Training Center Rev. 0195
Power Plant Engineering Course Manual

Basic Plant Cycles

ated intermittently to sweep away air pockets and 

vent their own seals., Condensate and feedwater 

systems are recirculated through the condensate 

demineralizers to adjust chemistry and to remove 

contaminants. The operability of all ESF equip

ment is verified prior to heatup of the RCS. 

Heatup of the RCS occurs by operating one or 

more RCPs. Pressurizer heaters are energized to 

begin steam bubble formation in the pressurizer. 

When a pressurizer steam bubble exists, pressur

izer level is lowered to the normal operating range. 

When RCS temperature increases to approxi'

mately 300*F, RHR is removed from service and 

aligned for low pressure iafety injection. Pressur

izer pressure is increased during the heatup to 

ensure the RCS remains subcooled. 

Steam generators are drained to their normal 

operatinglevels and the auxiliary feedwaterpumps 

are operated to maintain SG level. The RCS 

continues to heat up until normal temperature is 

achieved (approximately 5501F). At this time, the 

Steam Dump Control system will begin dumping 

steam from the steam generators to the main con

denser to stabilize RCS temperature. 

1.2.5.2 Approach to Criti~al 

Upon completion of the RCS heatup, the reac

tor is taken critical by withdrawal of the control 

rods. The control rods are withdrawn in a speci

fied order and sequence to ensure the safest and 

most efficient use of the reactor fuel. Control rod 

withdrawal is performed in aý slow, delib'erate 

manner while the operator continuously monitors 

the reactorpowerlevel. The reactor will be critical 

when reactor power continues to increase with no 

control rod movement. 

1.2.5.3 Increase to Rated Power 

Reactor power is increased until it begins to 

add heat to the RCS. Reactor power is stabilized 

at approximately 3% with the Steam Dump Con

trol system still maintaining a stable RCS ternyr.y.,nn........................

1-16 

Rev. 0195

perature. A main feedwater pump is started for SG 

water level control, and the auxiliary feedwater 

pump is stopped. The main turbine is warmed and 

rolled with steam until it reaches its normal oper

ating speed of 1800 rpm. The main generator is 

then started electrically and connected to the elec

trical grid to begin supplying electrical loads. 

Main generator load is controlled by using the 

Turbine Control system.' As more steam flow is 

directed to the main turbine, main generator load 

increases and the steam dump valves will throttle 

closed. When the steam dump valves have fully 

closed, reactor power will increase as generator 

load increases. Heieafter, the reactor is a slave to 

the turbine. As turbine-generator load increases, 

reactor power will automatically increase to keep 

pace. Full power is reached when the generator 

reaches its design load or the reactor is operating 

at 100%. 

1.2.6 Plant Shutdown - PWR 

Prior to commencing a plant shutdown, the 

electrical system load dispatcher is notified that 

main generator electrical load will be reduced. If 

the RCS will be opened for maintenance after 

shutdown, then RCS hydrogen concentration will 

be reduced. Instrumentation required for monitor

ing shutdown conditions (e.g., source range nuclear 

instrumentation) will have surveillances performed 

to ensure operability. 

Electrical 0oad is reduced by gradually lower

ing the Turbine Control system load setpoint which 

slowly closes' the main turbine control valves. 

RCS temperature, pres'suizer pressure and level, 

and steam generator level will be maintained at 

their programmed setpoints. Control rods will be 

slowly inserted and/or RCS boron concentration 

will be slowly increased as main generator load 

and reactor power decrease. 

At approximately 15% loadtheFWCS is placed 

in manual control. At approximately 10)% load, 

onsite electrical loads are switched to offsite power. 

At approximately 1% load, the main generator

USN-UC I ecnnical I ramnng Center

Basic Plant Cycles

1-16 Rev. 0195
Power Plant Engineering Course Manual Basic Plant Cycles

output breaker is opened to disconnect the genera

tor from the electrical grid and the main turbine is 

manually tripped. The reactor is then shut down 

by manually inserting all control rods. 

If an RCS cooldown is desired, then the opera

tors will dump steam to the main condenser. RCS 

pressure is reduced by manually opening the pres

surizer spray valves. When RCS temperature 

decreases below 300TF and RCS pressure de

creases below 350 psig, the RHR system will be 

placed in service to remove decay heat. The RCS 

can now be cooled down below 200TF. If RCS 

maintenance is to be performed, the RCS will be 

completely depressurized and partially drained. 

L.3 Barriers to Release of MiLssion Produor 

When nuclear'fuel undergoes fission, highly 

radioactive fission products are produced. Some 

fission products decay quickly, thereby losing 

their radioactivity and posing little hazard to the 

public. Others remain radioactive for many years 

and must be contained within the reactor fuel until 

they can be disposed of properly. 

1.3.1 BWR Plant Fission Product Barriers 

The first and most important barrier to fission 

product release in a BWR power plant is the fuel 

cladding. Restrictions are imposed on reactor 

operation to ensure the integrity of the clad. How

ever, even with proper operation, fuel clad perfo

ration sometimes occurs. During accident condi

tions (e.g., loss of reactor coolant), the margin to 

fuel clad failure is significantly decreased. 

Once fission products have escaped through 

the fuel clad, the BWR primary and auxiliary 

system boundaries provide the next barrier. These 

systems comprise the reactor vessel, main steam 

piping, turbine, condensate, and feedwater sys

tems. The primary and auxiliary systems form a 

closed loop and should contain the released fission 

products. Under accident conditions, however, a 

rupture of one of the system boundaries may occur 

which would compromise the integrity of the

fission product barrier. 

The third and final barrier to fission product 

release are the primary and secondary contain

ment buildings. The primary containment will 

condense steam and contain fission products re

leased from aLOCA. The secondary containment 

is the physical boundary which encloses the pri

mary containment boundary, those systems exter-" 

nal to-the primary containment which would con

tain reactor coolant after a LOCA and, the areas in 

which spent fuel is stored and handled. 

13.2 PWR Plant Fission Product Barriers 

The first and most important barrier to fission 

product release in a PWR power plant is the fuel 

cladding. Restrictions are imposed on reactor 

operation to ensure the integrity of the clad.- How

ever, even with proper operation, fuel clad perfo

ration sometimes occurs. During accident conditions,(e.g., loss of reactor coolant), the margin to 

fuel clad failure is significantly, decreased. - j; 

Once fission products have escaped through 

the fuel clad, the RCS piping walls provide the 

next barrier. The RCS is a closed system and

should contain the released fission products.-How

ever, under accident conditions the RCS piping 

may become breached. 

The third and final barrier to fission product 

release is the reactor containment building. The 

containment is a large building surrounding the 

RCS that is designed to contain the heat energy 

from an RCS blowdown. Containment building 

walls are normally made of thick, reinforced con

crete that is sheathed and sealed on the inside with 

quarter-inch thick steel plate. 

1.4 Summary 

The preceding text has presented a basic de

scription of the systems, components, and 

flowpaths in BWR and PWR commercial nuclear 

plants. Although there are several vendors of 

nuclear plants, the systems discussed in this chapUSNRC Technical Training Center 1.177 Rev. 0195

Power Plant Engineering Comrse Manual Basic Plant Cycles.,

USNRC Technica Training Center 1-17-t- __ ptii--Om
Power ter are Plant generic Engineering and applicable Course to Manual most commercial Basic Plant Cycles 

ter are generic and applicable to most commercial 

nuclear plants in the country. 

FOOTNOTES 

IReactivity is a measure of the change in neutron 

population from one neutron generation to the 

next. 

2 Moderator is the light water coolant that is 

circulated through the core to remove the heat 

generated by fission. 

3 Negative reactivity implies that the neutron popu

lation is decreasing from one generation to the 

next (i.e., power is decreasing). 

4 Flux peaking refers to the phenomena in which 

the neutron flux (power) in one location of the core 

is significantly higher than the neutron flux in the 

immediate surrounding area. 

5 Fzssion-gases, primarily krypton and xenon, are 

released as byproducts of the fission process. 

6 The reactor is said to be "critical" when the 

neutron chain reaction is self-sustaining (i.e., 

enough neutrons are being produced by fission to 

maintain a steady neutron population). 

7 Reactor period is a measure of the a of change 

in reactor power. Specifically, it is the time 

required for reactor power to change by a factor of 

"e" (-2.72). 

USNRC Technical Training Center .18 Rey. 0195

Power Plant Engineering Course Manual Basic Plant Cycles

-18 Re.v. 0195
Power Plant Engineering Course Manual Basic Plant Cycles

Table 1-1. GE BWR Product Lines

Year-of Characteristic 

Product Line Introduction Plants 

BWR/1 1955 Dresden 1, Big 

Rock Point, 

Humboldt Bay 

* First commercial BWRs 

* First internal steam separation 

BWR/2 1963 Oyster Creek 

• First turnkey plant 

* Eliminated dual cycle 

BWR/3 1965 Dresden 2 

• First jet pump application 

* Improved Emergency Core 

Cooling system 

BWR/4 1966 Browns Ferry 

* Increased power density 10% 

BWR/5 1969 Lasalle 

"* Improved Recirculation system 

performance 

"* Improved Emergency Core 

Cooling system performance 

"* Mark H containment 

BWR/6 1972 Grand Gulf 

"* Improved cbre performance 

* Improved Rod Control systems 

"* Mark III containment

USNRC Technical Training Center 1-19 Rev. 0195

Power Plant Engineering Course Manual Basic Plant Cycles

USNRC Technical Training Center 1-19 Rev. 0195
Power Plant Engineering Course Manual Basic Plant Cycles

HUMBOLDT BAY (BWR/1)

NATURAL CIRCULATION, DIRECT CYCLE

BIG ROCK POINT (BWRI1) 

OYSTER CREEK (BWRI2) 

DRESDEN 2&3 (BWR/3) 

BROWNS FERRY (BWRI4) 

LASALLE 1&2 (BWRI5) 

GRAND GULF 1&2 (BWR/6)

FORCED CIRCULATION, DIRECT CYCLE

Figure 1 - 1. Boiling Water Reactors in Various Systems

USNRC Technical Tr4ining Center 1-21 Rev. 0892

Power Plant Engineering Course Manual Basic Plant Cycles

USNRC Technical Training Center 1-21 Rev. 0892
=z REACTOR 0 A VESSEL 

o STEAMLINE VALVE 

-•. ~MOISTURE • 

S, SEPARATOR .... .. .. 

STURBINE C ........ 

REACTOR al ,1 ...... .. • 

SJET PUMP 

ELECTRICAL 

CONDENSER GENERATOR 

~~~RECIRC EIC 

PUMP PUMP 

Figure 1 -2. Basic BWR Power Plant
EAr PRIMARY) MOISTURE SEPARATORS (1) ) 

222 

AO ý oo Ioo UWE 

RIVE AA ! F ER S 

:rM SEPV SIMV STM 

RECICULWIO COlRO ECIRCULATION P 

on, OROWIRS FROM c 

P O RIVER M A Im N gN5a WL ICWATER PUMdP 431 

POOL : 

REICTH PRESUR PRESSUREIZS(9 FIOWE 

VESSEL "SOTWELL CONO 

EEATPUMP IRS 

PRlIMARY IM01SARU 

CONTAINMEINT RECIRC S4 LINES LINE 

toH HEAEER DRAINS 

ORcs 

SidM SEP 1114 Slid Sli 

RIECIRCULATIONI CONTROL RECIRCULATIlON 

PUMP REOD DRIVEE PUMP I P 

RWCU • PUP 

00 1 6 rFiEDWATER FEEdWATER CONDANSAyE F FOHEATER HtEATERS BOOSTER PUMP 131 

NRHX I(EJECI WATER 

N R H N 10 C S T • 

IFIDEWATER PUMP |3) 

*11 Figure 1-3. Simuplified BWR Primary and Auxiliary Systems
Power Plant Engineering Course Manual Basic Plant Ccles

Figure 1-4. BWR Reactor Vessel

USNRC Technical Training Center 1-27 

Rev. 0892

Rev. 0892 1-27
CONTROL (EHC) 

MSIVII 

M=V'S[•Ho STOP • ! [ , ! VALVES • 

" • ! .YP•' . •7CONTROL 

RECIRCULATION I 

STANDBY PUMP ERAO] LIQUID TURBIN 

CONTROLMOR 

SYSTEM • 

(SLCS) 

_• CONDENSER 

II 

H 

IAN 

PROTECION [FLOW ONTRO MNUAL 

SYST CONTROL 

-- H FCID) WGo r SystEms A 

COD FEEDWHATERSCNTO 

SSE COTO SYSTEM HIHFRESCE8EATO 

(,-' SYTM(Figur oto SystemFEED HEATE 
Power Plant Engineering Course Manual Basic Plant Cycles

Core Spray 

Pumps

50%/o

Figure 1-6. Emergency Core Cooling System 

USNRC Technical Training Center 1-31

To Turbine 

From Reactor 

Feed Pump

Rev. 0195

Power Plant Engineering Course Manual Basic Plant Cycles
'PRIMARY LOOP +,._[•, SECONDARYLOOP C,, 

p-I 

==. 

,,-) 

ft

CONDENSER 

CIRCULATING 

WATER

",I CONDENSATE 

CONTAINMENT PUMP 

WALL

Figure 1 - 7. Basic PWR Power Plant

7

GENERATOR

ftI

n 

C-) 

n

0 

-I 

m 

a 

C-, 

0
CST SAFETY VALVES & F RELIEF VALVE 

MSIV SEE 

DETAIL FUEL HANDLING •: '•- I"m- BUILDING . 

FRV pM13

HP FEED SURGE TANK 

TURBINE HEATING S 

STEAM PUMP SECONDARY 

STEAM MFPPENETRATION 

DUMP ROOM 

MS 

COND CONTAINMENT 

SoHTRS 

TURBINE BUILDING MPENETRATION AREA 

_AUXILIARY BUILDING 

ne 

. Figure 1-8. Simplified PWR System Composite

I' |
Power Plant Engineering Course Manual Basic Plant Cycles

CONTROL ROD 

DRIVE MECHANISM 

UPPER SUPPORT 

PLATE 

INTERNALS 

SUPPORT 

LEDGE

CORE BARREL 

SUPPORT COLUMN 

UPPER CORE 

PLATE 

OUTLET NOZZLE 

BAFFLE RADIAL 

SUPPORT 

BAFFLE 

CORE SUPPORT 

COLUMNS 

INSTRUMENTATION 

THIMBLE GUIDES 

RADIAL SUPPORT

BOTTOM SUPPORT 

C•STING

INSTRUMENTATION 

PORTS 

THERMAL SLEEVE 

LIFTING LUG 

CLOSURE HEAD 

ASSEMBLY 

HOLD-DOVWN SPRING 

CONTROL ROO 

GUIDE TUBE 

CON"ROL ROO 

DRIVE SHAFT 

INLET NOZZLE 

CONTROL ROD 

CLUSTER tWITHDRAWN) 

ACCESS PORT 

REACTOR VESSEL 

LOWER CORE PLATE

Figure 1-9. PWR Reactor Vessel

USNRC Technical Tr4ining Center 1-37 Rev. 0892

USNRC Technical Training Center 1-37 Rev. 0892
Power Plant Engineering Course Manual Basic Plant Cycles

REACTOR INTERNAL ARRANGEMENT 

CEDM 

NOZZLE 

"INSTRUMENT 

NOZZLE 

EXPANSION 

I--RING 

24" ID 

UEL IINLET 

IBLY " NOZZLE 

"THERMAL 

SHIELD 

WIE ,,, GT- " CORE 

-T .1 SHROUD lt1!' -T • CORE 

SUPPORT "---• .............•:"BARREL 

FLOW 

SKIRT

Figure 1-10. Simplified Reactor Vessel

USNRC Technical Training Center 1-39 Rev. 0892

Power Plant Engineering Course Manual Basic Plant Cycles

USNRC Technical Training Center 1-39 Rev. 0892
Power Plant Engineering Course Manual Basic Plant Cycles

Rod Cluster 

Control Assembly

Top Nozzle Control Rod

Fuel Rod

Grid Assembly

Top View

Bottom View

Bottom Nozzle

Figure 1-11. Typical PWR Fuel Assembly

USNRC Technical Training Center 1-41 Rev. 0892

Power Plant Engineering Course Manual Basic Plant Cycles

USNRC Technical Training Center 1-41 Rev. 0892
Power Plant Engineering Course Manual Basic Plant Cycles

ANTI-VIBRATION 

BARS 

PARTITION 

MANWAY 

SUPPORT FOOT * " 

PRIMARY 

COOLANT . 

INLET

Figure 1-12.

STEAM OUTLET 

TO TURBINE 

GENERATOR

- MOISTURE 

SEPARATOR 

MANWAY (2) 180o APART 

SWIRL VANE 

- MOISTURE 

SEPARATOR 

UPPER SHELL 

- TUBE BUNDLE 

TUBE SUPPORTS 

LOWER SHELL 

- FEEDWATER INLET 

TUBE PLATE 

CHANNEL HEAD 

PRIMARY 

COOLANT 

OUTLET

Westinghouse Steam Generator

USNRC Technical Training Center 1-43 Rev. 0892

Power Plant Engineering Course Manual Basic Plant Cycles

USNRC Technical Training Center 1-43 Rev. 0892
Power Plant Engineering Course Manual Basic Plant Cycles

STEAM OUTLET

NORMAL WATER 

LEVEL 

AT 100% POWER 

FEEDWATER 

INLET 

NOZZLE 

STEAM 

WATER 

MIXTURE

REACTOR 

COOLANT 

INLET 

Figure 1-13.

SECONDARY SEPARATORS 

- (MIST EXTRACTORS) 

(CHEVRON) 

CIRCULATING WATER

REACTOR 

COOLANT 

OUTLET

Steam Generator Secondary-side Flowpaths

USNRC Technical Training Center 1-45 Rev. 0892

I

Power Plant Engineering Course Manual Basic Plant Cycles

USNRC Technical Training Center 1-45 Rev. 0892
Power Plant Engineering Course Manual Basic Plant Cycles

STEAM 

BYPASS 

CONTROL 

SYSTEM

REACTOR 

PROTECTION 

SYSTEM

TURBINE 

ELECTRO

HYDRAULIC 

CONTROL 

(EHC) SYSTEM 

I

Figure 1-14. PWR Control Systems

USNRC Technical Training Center 1-47 Rev. 0194

Power Plant Engineering Course Manual Basic Plant Cycles

USNRC Technical Training Center 1-47 Rev. 0194
z ACCUM. A9 

•"I •' HEAT 

RHR PUMP 

I I •NORMAL NORMAL 

I I ~~(cNo~te:nBcorocn I njection Tank may B.,, n"T. CHARGING SU CTION"[ 

.• ~Figure I - 15. Emergency Core Cooling System Simplifed Composite 

(o 

I-'U
Power Plant Engineering Course Manual Reactor Physics

+2.0 REACTOR PHYSICS

-Learning Objectives 

After studying this chapter, you should b6 able 

to: 

-' 1. Describe the basic fission process includ

-ing:* 

a. Reactor fuels capable of thermal/fast 

fission 

b. Probability of neutron absorption in a 

reactor fuel 

c. Conversion of fission energy into heat. 

-2. Define the following terms: 

a. Keff 

b." Reactivity 

c. --Startup rate . . 

-4- Reactor period 

,e. jControl rod worth 

f. Boron worth 

S3. Compare and contrast the following terms: 

a. Critical 

b. Subcritical 

.- c. Supercritical 

4. Using the factors from the six-factor for

mula, :describe a neutron life cycle from 

birth to absorption in a reactor fuel. 

5. Describe how each of the following coef

ficieints provides reactivity feedback to the 

reactor. 

a. Moderator temperature coefficient 

b. Moderator void coefficient

c. Fuel temperature (Doppler) coefficient 

d. Power coefficient . 

6. Compare and contrast differential and in

tegral rod worth. 

" 7. Describe how Xe-135 and Sm-149 affect 

- reactivity following a power change., 

8. Describe the effects of subcritical multiplication on reactor operation.' 

9: State the reasons for adding burnable poi

sons to a reactor core. -, 

10. State the purpose of 1/m plots during a 

reactor startup." 

11. Explain theeffects of delayed neutrons on 

reactor control and stability. 

12: Describe the source and efficts of decay 

heat following a reactor shutdown.

413., Descrile how the following methods of 

"-ie;ctivity control are used by the opera

tors:' 

a. Control rods 

b.', Soluble boron (PWR only) 

"-c. Core flow (BWR only)

2.1 Iatroduction 

This chapter contains a summary of basic 

nuclear physics and nuclear reactor design prini

ciples and terminology. The material presented is 

broader in scope than can be conveniently covered 

in the classroom time allotted; therefore, 'all the 

written material will not be covered in detail. 

Basic explanations and definitions of concepts 

will be given in the classroom. The purpose here 

is to provide a sound understanding of the basic 

nuclear processes involved in nuclear power gen

eration. 

2.2 Fissioin Process 

Nuclearfission is the splitting of the nucleus of 

an atom into two or more separate nuclei, accom

pani&l *by the releise of a large amount of energy. 

Nearly all of the fissions in the reactor are gener

ated in the fuel by neutron absorption, which 

results in the splitting of the fissionable a.iomsthat 

make upthefuel. Onlyafew of the heavy isotopes 

are available in quantities large enough and have 

a high enough probability of fissioning to be used 

as reactor fueL Commonly used fuels are ura7 USNRC Technical Training Center "- - "-;Rev. 0493

- Power Plant Engineering Course Manual .. .Reactor Physics

2-1
Power Plant Engineering Course Manual

Reactor Physics

nium-233 (U-233), uranium-235 (U-235), ura

nium-238 (U-238), plutonium-239 (Pu-239), and 

plutonium-241 (Pu-241). Several other isotopes 

also undergo fission, but their contribution is al

ways extremely small 

U-235 and U-238 are naturally occurring iso

topes with very long half-lives; they account for 

the majority of the fuel used in commercial reac

tors. Artificially produced fuels include U-233 

(produced by the irradiation of thorium-232 (Th

232) in areactor) andPu-239 (produced by irradia

tion ofU-238 in a reactor). Th-232 and U-238 are 

called fertile materials and are generally placed in 

the core or in a blanket surrounding, the core (in 

breederreactors) in order to produce fuel (fission

able material) as the original fuel is used up in 

fissioning. The ratio of the amount of fuel pro

duced in areactor to the amount that is used during 

any period of time is called the conversion ratio of 

the reactor. 

When a fuel nucleus absorbs a neutron, a 

fission occurs almost immediately. In the case of 

U-235, the reaction is represented by the follow

ing: 

92UM + 0N' -9 2U236 * --. X + "yA +2.43 on' 

+ Energy 

*IndieatLs that the isotope is unstable 

The total energy released per fission is about 

200 Mev for U-235 and is distributed as shown 

below:

Insnnus M 

K.E. of fission fragments 

Irstantaneous gamma ray energy 

K.E. of fission neutrons (prompt)

Spar•icles from fission products 

Gamma rays from fission products 

Neutrinos

v/Fission 

165.0 

7.0 

157 17"7n

7.0 

6.0 

23.0

The energy of the neutrinos, which accom

pany the radioactivity, is not available for produc

ing power because these particles do not interact 

appreciably with matter, thus, the net energy avail

able is still roughly 200 Mev per fission. 

Neutron production (neutrons per fission) var

ies with the different fissionable isotopes and with 

the energy at which the fission reaction is caused 

to take place. Table 2-1 shows some relative 

values for neutrons per fission for some of the 

common fuels that are now being used in reactors. 

Note that each fission does not produce the 

same number of neutrons. The neutrons per fis

sion given in Table 2-1 represent an average num

ber produced per fission when a large number of 

fissions are used to determine the statistics. From 

individual fissions of a nucleus some reactions 

produce only one neutron, possibly none, and 

some reactions produce as many as five neutrons 

per fission. 

The neutrons released from fission, vary in 

energy from essentially thermal energy up to about 

15 Mev. More than 98% of all the neutrons 

produced by fission are below 8 Mev. The energy 

distribution of these neutrons is shown in Figure 2

1. In section 2.3, -the slowing down of these 

neutrons to thermal equilibrium will be discussed. 

2.3 Nuclear Cross Section 

When a- neutron strikes a nucleus, several 

reactions can occur. One possibility is that the 

neutron Will bounce off a nucleus; this is termed 

elastic scatterin9.' A second possibility is that the 

neutron will' penetrate the nucleus and form an 

unstable compound nucleus. If the neutron is then 

ejected, this is called inelastic scattering. In both 

cases, the neutron usually will transfer some of its 

energy to the nucleus. If the nucleus keeps the 

neutron after the collision, this is called neutron 

=tngi. FinýUy, the captured neutron can cause 

the nucleus to fission. The probability that a 

neutron will undergo one of the aforementioned 

reactions with a nucleus is measured in units of

UNKL Technical Training Center 2-2

2-2 Rev. 0493

Reactor Physics

4 V

USNRC Technical Training Center
Power Plant Engineering Course Manual Reactor Physics

microscopic cross section. The unit of micro

scopic cross section, a, is the barn. (Note that 1 

barn = 10-24 cm2.) 

The cross sections are probabilities of interac

tion, and individual probabilities may be'summed 

to give the total probability. The total cross section 

at is the sum of the'absorption and scattering cross 

sections: 

ayt=a'+ as 

For fissionable material, the absorption cross sec

tion is the sum of the fission and capture cross 

sections: 

aa = ac + Of. 

" Microscopic cross sections are a function of 

the target nucleus (U-235, U-238, etc.) and the 

incident neutron's energy (thermal,'epithermalI 

resonance, or fast). In general, the probability of 

a given reaction will be increased for neutrons of 

lower energy and velocity. Typical values of 

microscopic cross sections for U-235 and B-10 

are given in Table 2-2. 

The absorption of neutrons tends to follow an 

inverse velocity trend. Figure 2-2 shows this 

general trend in U-:235- Certain isotopes (such as 

U-238 and Pu-240) exhibit a strong resonance 

capture phenomenon at certain incident neutron 

energy levels. A'qualitative explanation of the 

re-onance phenomenon is that certain nuclei have 

allowable excited states that are discrete. If the 

energy of the incident neutron is such that the 

energy of the resultant compound nucleus is equal 

to one of these states, then the neutron has a high 

probability of being captured. These excited states 

occur at certain energies which determine where 

these isotopes vwill have' an abupt increase in their 

capture cross section. Thesespikes in the cross 

section curve are referred to'as resonance peaks 

and are most prevalent in'the' heavier elements.

centimetei is referred to as the macroscopic, 

cross section-(): -(Q

Na,

where 

N = number of individual atoms (or nuclei) 

per cubic centimeter, and 

, - microscopic cross section in barns. 

The macroscopic cross section has dimen

sions of reciprocal length (cm-l). It is sometimes 

convenient to consider the macroscopic cross sec

tion as the probability of neutron interaction per 

unit track length. The reciprocal of is called the 

neutron'mean free path (denoted by •) and is a 

measure of the average distance a neutron will 

travel in a substance before it experiences the 

nuclear reaction under consideration. If a material 

contains several isotopes the effective macroscopic 

cross section is: 

X,= 1 +7-2 + .2. i=Noaj+N 2a 2 +...+Nia

The number of nuclei per cubic centimeter may be 

calculated as follows: 

N- =PN (gin 6.023(iO')atoms' atoms ' 

A ,cm gram atom ) cm3 

where 

"N ='number of nuclei per cm3, -

p- = density: 

A = atomic weight, and 

Na = Avogadro's number. 

2.4 Slowing Down of Neutrons

Tb e total effecie 

by all of the nuclei of z

cross section presented In -an operating reactor, the probability of 

fission for most reactor fuels is generally inversely given isotope in a cubic dependent on the energy of the incident neutrons.

USNRC Technical Training Center 2-3 Rev. 0195 t

- Power Plant Engineering Course Manual - :. .o :Reactor Physics

USNRC Technical Training Center 2-3 Rev. 0195
Power Plant Engineering Course Manual

leactMr Phvcim

Since fission neutrons are born 'at high energies 

(fast neutrons), the probability thatthey will cause 

a fission while at that energy is very small; there

fore, it is necessary to reduce this neutron energy 

to a value where the probability that it will cause 

fission is increased. This is accomplished by 

interposing relatively non-absorbing nuclei as 

collision media to reduce the kinetic energy of 

fission neutrons through the process of scattering. 

This medium is called the "moderator." It acts to 

moderate (slow down), or "thermalize" the fission 

neutrons. 

Typical moderators are hydrogen, beryllium, 

and carbon. Fewer collisions are necessary in a 

hydrogen medium to cause complete moderation 

than in carbon, since the atomic mass of hydrogen 

is smaller, and therefore, able to absorb more 

kinetic energy from the neutron during the scatter

ing process. The following description is analo

gous to this scattering process: 

If moving billiard ball A strikes stationary 

billiard ball B, ball B moves away and ball A 

will come to rest. If billiard ball B is replaced 

by a bowling ball, moving ball A bounces off, 

barely transferring any energy to the bowling 

ball. A neutron-proton collision is like a two

billiard ball collision and a neutron-carbon 

collision is like a billiard ball-bowling ball 

collision. 

The amount of moderator in a reactor greatly 

influences the slowing down process. If there is 

too little moderator, the neutrons are not adequately 

thermalized. Hence, the probability of fission is 

reduced as more neutrons will either leak out of the 

core or be absorbed in nonfissioning materials. If 

there is too much moderator, the probability that a 

thermal neutron will be captured by the moderator 

is greatly increased. 

2.5 Multiplication Factor 

The ratio of the number of thermal neutrons 

obtained at the end of the neutron cycle to the 

number of those initiating the cycle is called the

effective multiplication factor and is denoted by 

I&ff. It is a significant parameter of the nuclear 

chain reaction because its value determines the 

rate of neutron level multiplication. 

If Keff> 1, the reactor is supercritical; the 

neutron population, the fission rate, and energy 

production are increasing exponentially. 

If Keff = 1, the reactor is critical; the neutron 

population is constant, as is the fission rate and the 

energy production. The nuclear chain reaction is 

sustained and controlled. 

If Kf < 1, the reactor is subcritical; the neu

tron population, the fission rate, and the energy 

production are decreasing exponentially. 

The initial value of Keff is affected by the 

material composition and the geometry of the 

reactor core. Under normal operating conditions, 

a power reactor is kept critical; i.e., the equilib

riumvalue of Keffis 1.0 all the time. Subcriticality 

leads eventually to shutdown of the reactor. 

Supercritical operation is necessary during startup 

and power increase, but care must be taken not to 

let Keff become too large or else the reactor will be 

difficult to control. 

The multiplication factor is not a parameter 

that can be directly observed or measured. To 

understand how Keffis affected by changes in core 

parameters, a six factor formula will be used to 

illustrate the factori that must be considered when 

deriving Keff. Figure 2-3 illustrates these factors. 

Keff = E LfpLthfT , 

where

Keff 

Lf 

p Lth 

f 

11

effective multiplication factor, 

fast fission factor, 

fast nonleakage probability, 

resonance escape probability, 

thermal nonleakage probability, 

thermal utilization factor, and 

reproduction factor.

USNLC tchnical I Training Center 2-4 

Rev. 0195 2-4 Rev. 0195

R•a•1- Phvd•
Power Plant Engineering Course Manual Reactor Physics

2.5.1 Fast Fission Factor (c)' 

The fast fission factor (c) is the contribution to 

neutron multiplication from the fissions that occur 

at higher-than-thermal energies. This contribu

tion is mainly from fast fission of U-238. U-238 

will fission only ifi absorbs a neutron with kinetic-, 

energy aboye approximately 1.0 Mev. Below 1.0'. 

Mev, the neutron will be captured and will be lost' 

from the fission process. The probability of a 

fission reaction in U-238 is quite low, but there is 

so much 6f this isotope in the reactor core that 

there is a significant contribution to the multiplica

tion factor. -Appirximately 7% of the total reactor 

power is a result of fast fissions. The fast fission 

factor, e, is defined as follows: 

F, = Neutrons from all fission 

Neutrons from thermal fission 

As moderator temperature is increased,.the 

value of c increases because neutrons remain at 

higher'energies longer (because of the poorer' 

nmoderating properties of the water) and are more 

able to fission the U-238. There is only a slight 

(ailmost insignificant) change over the core life-" 

time as a result ofU-238 depletion. A typical value 

for c is 1.03. 

2.5.2 Fast Nonleakage Factor (Lf) 

"The fast nonleakage factor, Lf , is the fraction 

of neuitrons-that is ndt lost due td leakage from the 

core durýng.te slowing down process. It is'also 

the probability that a neutron will remain in the 

core and become a thermal neutron without being 

lost by fast leakage. 

As the temperature of the moderatorincreases, 

Lf decreases because of the increased slowing 

down time and increased leakage from the loss of 

water. 

2.5.3 Resonance Escape Probability (p) 

The resonance escape probability, symbolized 

by p, is the probability that a neutron will escape

resonance capture during the slowing down pro

cess. It is always less than 1.0 when there is any 

amount of U-238 prsentin the core, Whichmeans 

that resonance capture byU-238 always removes 

some of the neutrons. 

As the moderator temperature increases, the 

resonance escape probabily decreases because, 

as 'the slowing down time increises, more neu

trons are likely to exist at the energies susceptible.. 

to resonance capture. The resonance escape pr6ob 

ability changes over core life because of changes 

in fuel temperature required for full power opera

tion. Also, other isotopes that are resonance ab

sorbers are being produced., 

25A4 Thermal Nonleakage Factor (Lthb) 

The thermal nonleakage factor, Lth , is the 

fraction of the thermal neutrons-that do'not'leak 

out of the core ifter becoming thrmalized-but-" 

remain to conriibute to the chain reaction. Lth is 

also the probability that a thermal neutron Will remain and be utilized in the core. 

The value of Lth decreases as the temperature 

of the moderator increases for'the same reasons 

given for the fast nonleakage factor. 

2.5.5 Thermal Utilization Factor (f) 

The thermal utilizaiti6n factor, f, is the ratio of 

the probability that a ieitron',will beabsorbed in 

the fuel to the probability that the neutron will be 

absorbed in all the material in the core. It is 

described by the following equation: 

f= tud Ott"="", p.+Z 

Where la = macroscopic absorption cross section. 

An examination of f shows that the -a (fuel) 

comprises only the absorption by the U-235 at the 

beginning of core life. As Pu-239 begins to build 7 

up from the irradiation of U-238 in the core, it is

USNRC Technical Training Center 2-5 - Rev. 0195

S: ": • Rev. 0195

Power Plant Engineering Course Manual -Reacto~r Phjsics

USNRC Technical Training Center 2ý5-•
Power Plant Engineering Course Manual Reactor Physics

necessary to ýonsider the changeiin fuel'composi

tion in determining the value off k different times 

in the core lifetime. It'is estimated that Pu-239 

fissions account for 40% of full reactor power at 

end of core life. 

The plant operator has the greatest effect on 

this factor since he can control the amonunt of.a in 

the core by the insertion and withdrawal of control 

rods and the addition or dilution of soluble boron 

(in a PWR). A typical value of f is 0.83. 

2.5.6 Reproduction Factor (11) 

The reproduction factor, TI, is the average 

number of neutrons produced per thermal neutron 

absorbed in the fuel. It is based onphysical 

measurement of each type of fuel used in a reactor. 

The numerical value of T does not change with 

core temperature over the range considered for 

most reactors. There is essentially no change in ij 

over the lifetime of the reactor core because of the 

closeness of the values of T for U-235 and pluto

nium-239. A typical value for Ti is 2.05. 

As the reactor operates for a period of time, 

and Pu-239 begins to contribute to the neutron 

economy of the core, the average effect of Ti is 

expressed by: 

11- y~ : + V9 I•f2 

l=235 +7a239 + 

where 

U = average number of neutrons produced 

from fission and 

7 = macroscopic cross section. 

2.6 Reactivity (p) 

Reactivity is the measure of the fractional 

change in neutron population per generation in a 

reactor and is a measure of a reactor's departure 

from criticality. Reactivity is expressed as (p) and

mny be calculated by the formula: 

eff 

K- 1 - A 

K• K 

It can then be seen that in a critical reactor keff 

=1, p = 0. A supercritical reactor (Kff > 1) will 

have positive reactivity; a subcritical reactor (Keff 

< 1) will have negative reactivity. 

Although reactivity is unitless, it is assigned 

the units of AK/K for convenience. Because of the 

very small amount of reactivity usually present in 

a core, other units are also used. These are % AK/ 

K and PCM (percent millirho). 

The relationship between these units is: 

IAK/K = 100% AK/K = 105 PCM. 

Some of the factors that affect the reactivity of 

a reactor core throughout core life are fission 

product poisons, fuel depletion, moderator tem

perature, fuel temperature, steam void fraction, 

reactor pressure, control rods, and burnable poi

sons. 

2.7 Reactor Period and Startup Rate 

Reactor period is a measure of the rate of 

change of reactor power and is defined as the time 

required to chafige reactor power by a factor of e, 

the natural logarithm. The following equation 

describes thi effect of reactor period on power 

level as a function of time: 

P - Pet/ , 

where 

P - Power after elapsed time, t, 

P = Initial power, 

t = Elapsed time in seconds, and 

= Reactor period. 

Startup rate is another means of measuring the

USNRC Technical Training Center 2-6 Rev. 0195

Power P lant Engineering Course Manual Reactor Physics

USNRC Technical Training Center 2-6 Rev. 0195
Power Plani Engineering Course Manual Reactor Physics

rate of change of power in a reactor. The'startup 

rate (SUR) is the numbei'of decades (powers of 

"10) reactor power will change in 1 minute. 

As with period; an equation can rela.te SUR to 

power level as a functioh of time. 

P =P 0 OSUR(O 

;where 

P -'Power afterpsed time,'t, 

'P, = Initial power, 

t = Elapsed timein minutes, and 

SUR = Startup rate in decades per minute.

S tartup rate and period are related by the equation: 

SUR, 

Other useful relationships for reactor period are: 

1: =l.44 DT =1.44 HT, 

where

doubling time, DT = 

halving time, HT =

the time required for 

reactor power to 

double, and 

the time for power to 

halve.

2.8 Reactivity Coefficients

'When the operating conditions of the core 

-(coolant temperature,' coolant 'pressur,' reactor 

'power level, coolant void fraction', fuel tempera

tare, etc.) are changed, the critical status of ihe 

core is also changed.' A change in any of theabbve 

operating parameters'will add either positive"or 

negative reactivity to the core. The inherent fea

tures in a reactor system that automatically change 

,core reactivity upon a change of a core 6perating 

parameter are known as reactivity coefficients.

"Each' reactivity coefficient is defined as a 

change in ieactivity dividedl by a iinit'change in 

some operating- parametei of the reactor. The 

coefficients'that are' significaiit in reactor opera

tions 'are the Irroderator temperature coefficient 

(MTC), moderatofvoid coefficient (av),*fuel teim

perature coefficient (FTC), and power coefficient. 

The moderator, pressire'coeffi6ient is normally 

very small in PWR'plants; in'BWR plants,'pres

sure changes primarily affect the moderator void 

Sfraction so the pressure coefficient is included in 

the moderator void coefficient for BWR 'plants. 

2.8.1 Moderator Temperature Coefficient 

(MTC)

"The moderator temperature coefficient (MTC) 

is defined as the change in "-eactivit• that results 

from a change in the temperature 6f the m'odera

torin the core. It is measured in units of AK/K/0F, 

orchangein reactivity perdegree Fahrenheit change 

'in'the average moderator temperature*. 

When moderator temperature' incrases, the 

moderator density decreases', so fewer moderator 

molecules are 'available for slowing down ind 

thermiing the neutrons. This causes the neu

trons toremain at higherenergies longer and travel 

farther, which results in increased leakage and 

more nonpi'6ductive -capture. The effect of a 

moderator temperature increase on Keff can be 

determined by examinmg the effect on the-fast and 

'thermal nionleakaige probabilities (Lf and Lth) aid 

the resonance escape probability_ (p). As modera

tor temperature increases, each of these probabili

'ties (Lf, Lth, and p) decreases, which results in a 

"de6crase in Krjff.: Because negative reactivity- is 

normally added to the core by-an' increase in' 

moderator temperature, MTC is normally a ifiega

:tive valu'e. 

" Sme: eactor parameter changes cause the 

value of MTC to change. As moderator tempera

tureincreases, MTC becomes more negative. This 

"is' because a IF increase at a high moderator 

"temperature results in a larger density reduction 

'(laiger redtiction in'molecules available to therUSNUC Technical Training Center 2-7 Rev. 0493

Power Plant Engineering Course Manual .- Reactor Physics

1 

USNRC Technical Training Center -2 .7 ... - Rev. 0493
Power Plant Engineering Course Manual

Reactor Phvsi

malize neutrons) than a I T increase at a lower 

moderator temperature. Therefore, a 1 F increase 

at a high moderator temperture adds more nega tive reactivity than a 1 increase at a low modera

tor temperature. Conversely, a IT decrease at a 

high moderator temperature adds more positive reactivity than a IT decrease at a low moderator 

tempeaue. Figure*2-4 illustrates the effect of 

moderator temperature on MTc. 

The MTC should always be negative to con

tribute to "inherent reactor stability." This means 

negative reactivity must be inserted when the 

temperature of the moderator increases. Consid

ering only the reactivity effect of MTC, consider 

what would happen if the MTC were positive. 

With a positive MTC, a small increase in 

moderator temperature would add positive reac

tivity, causing reactor power to increase. As 

power increased, more heat'would be added to the 

moderator causing moderator temperature to in

crease. As the moderator trmpermtureý increased, 

with positive MTC more positive reactivity would 

be added, further increasing power, which would 

raise moderator temperature, etc. I• can be seen 

that reactor power would be self-escalating with a 

positive MTC. 

2.82 Moderator Void Coefficient (av) 

The moderator void coefficient of reactivity is 

defined as the change in reactivity produced by a 

1% change in-void fraction (AK/KV) and is 

illustrated in Figure 2-5. -As the moderator boils 

and the void fraction increases, the moderator 

density decreases resulting in a re-ctivity change 

involving several interacting mechanisms. A de

crease in moderator density results in less absorp

tion in the moderator, which causes the thermal 

utilization factor to increase. An increased dis

tance between moderator molecules means that 

the neutrons travel a greater distance while at 

higher energies and have a greater probability of 

being ciaptured in resonance regions of uranium or 

plutonium; thus, the resonance escape probability 

decreases. In addition, the distance a neutron

travels after theimalizing also increases, produc

ing a decrease in thermal nonleakage probability. 

The large negative effects of increased resonance 

capture and, to a lesser degree, increased thermal 

leakage outweigh, the positive effect of less ab

sorption in the moderator and result in a moderator 

void coefficient of reactivity which is strongly 

negative. 

The slope of the curve in Figure 2-5 is negative 

because resonance capture increases more rapidly 

at high void fraction than at low void fiaction. As 

previously explained, the increased resonance cap

ture results from the decrease in moderation in the 

steam bubbles. A 1% increase in voids at a high void content displaces a greater percentage of 

remaining moderator than a 1% increase in voids 

at a low void content. 

Consider two examples: 10% void fraction 

and 70% void fraction. At 10% void fraction (90% 

water fraction), a 1% increase in void fraction 

decreases water fraction from 90% to 89% or 

roughly 1.1%. At 70% void fraction (30% water 

fraction), however, a 1% increase in void fraction 

decreases the water fraction from 30% to 29% or 

a change of 3.45%. Thus, at higher void fractions, 

there is a greater percent change in moderator 

fraction fora given percent change in void fraction 

than occurs at low void fractions. Therefore, the 

negative reactivity added at higher void fractions 

is greater than at lower void fractions. 

2.8.3 Pressure Coefficient 

Some reactor kinetics texts also include a 

moderator pressure coefficient of reactivity with 

the other reactivity coefficients. The primary 

effect of increasing nmdertor pressure is to in

crease moderator density, both through compres

sion of the liquid and through compression/con

densing of the voids. When the moderator density 

increases, reactivity increases (as inversely de

scribed in section 2.8.1 for MTC). When the 

moderator pressure decreases, moderator density 

decreases, causing an insertion of negative reac

tivity similar to the affects of a temperature inwt.t..sn -........................-

2-8 

Rev. 0493 uvxaliK technical Training Center Rev. 0493

Reactor Physics 9

2-8
Power Plant Engineering Course Manual Reactor Physics

crease. -If there are no voids in the moderator, 

however, the moderator density increase per 100 

psig increase in pressure is very small (water is 

nearly inc6mpressible). Therefore, the pressure 

coefficient in a reactor with essentially single

phase moderator (all PWRs under normal condi

tions) is insignificant in relation to the other coef

ficients. 

If there are voids in the moderator, a change in 

pressure directly effects the moderator void frac

tion. Therefore, the reactivity effect of a pressure 

"-change on a moderator with a significant void 

fraction (all BWRs under normal 'conditions) is 

included in the moderator void coefficent of reac

tivity. 

Because the pressure coefficient is not a sig

nificant factor in PWR reactor operations; and 

because the effects of pressure in BWR plants are 

included in the moderator void coefficient, the 

pressure coefficient is notffurther discussed in this 

manual. 

- 2.8.4. FuelTemperature (Doppler) Coefficient 

(FTC) 

Another reactivity coefficient of majorimpor

tance is the fuel temperature (or Doppler) coeffi

cient of reactivity (FTC), which is defined as the 

"change in reactivity thai results from a unit change 

infuel temperature (AK/K/F). Like MTCFTC is 

negative, adding negative reactivity for an in

,,;crease in fuel temperature. Normally, FTC is the 

"coefficienthat acts first to terminate a iapid reac

tor power increase since a power increase will 

result in a fuel temperature increase before the 

• moderator can be heated or voids can be created. 

-An understanding of the FTC iequires an un

"derstanding of the mechanics of resonance ab

" sorption. Resonance absorption occurs when the 

kinetic energy of the neutron will raise the target 

nucleus (mainly U-238 and Pu-240) to an allow

able excited state. The probability for absorption 

of a neutron at any other energy is relatively low.

Figure 2-6 shows a simplified cross section 

versus neutron energy curve as discussed above. 

The resonance peaks are illustrated as straight 

"-vertical lines. 

- Figure 2-6 would be acorrectrepresentation of 

the resonance abs6rption peaks ifthe targetnucleus 

were stationary. HoweVer, the target nucleus is in 

'motion and its movement inciea6ss with increas

ing temrperature.-We measure neutron energy or 

velocity from an external point of view and not as 

the target nucleus sees the neutron velocity. 

The velocity of a neutron is propoitional to the 

square root of its kinetic energy (KE) so for a 

neutron with energy KE1 -we can say that it has a 

velocity V 1. Figure 2-7 shows that for a stationary 

target only a neutron with velocity Vj wiH un

dergo resonance absorption.: Because the tem

- perature of the target nucleus causes it to be~in 

motion; as shown on Figure 2-7, there is i biand of 

neutron velocities or energies where resonance 

absorption could occur. In this case, VelocitiesV2 

-and V3 look exactly like VI as far as the target 

nucleus is concerned." Elevating the temrperature 

of the target nucleus will broaden this absoiption 

band. Again, velocities V4 and V5 look exactly 

"like V1 as far as the target nucleus is concerned. 

-When the targetnucleusis in motionitsveloc

• ity will cause the- probability of absorption 'for 

- neutrons with velocity V1-to decrease. The de

crease in-the height of the resonance peak as well 

.as the increase in width is kriown-as Doppler 

broadening and is shown on 'Figure 2-8. If the 

temperature of the target material is increased 

more, the'resonance peaks will again broaden and 

decrease in height. 

Since neutrons are slowed down in steps, there 

is a probability that they will never enter the 

energy band where resonance absorption will take 

place., As the resonance band broadens due to a 

temperature increase, more neutrons will iriter the 

band as they are slowing down. With more neu

trons in the band, more of them will be absorbed. 

This increased absorption will reiult ina negative

USNRC Technical Training Center '2-9 Rev. 0493

Power Plant Engineering Course Manual Reactor Physics

USNRC Technical Training Center '2-9 •Rev. 0493
Power Plant Engineering Course Manual

Reactor Physics

reactivity addition. 

In case of a deliberate or inadvertent addition 

of a positive reactivity to a reactor core, the. FTC 

would be the first reactivity coefficient to respond. 

It is effective almost instantaneously because an 

increase in reactivity causes the fission rate to 

increase and produce more heat in the fuel, which 

in turn causes a decrease in reactivity. As quickly 

as the heating rate is increased, the FTC becomes 

effective. A graph of FTC versus fuel temperature 

is provided in Figure 2-9. 

2.85 Power Coefficient 

A change in reactor power normally causes or 

is accompanied by a change in fuel temperature, 

moderator temperature, and/or moderator void 

fraction. Therefore, it is frequently convenient to 

consider a power coefficient that combines the 

effects of the fuel temperature, moderator tem

perature, and void coefficients for changes in 

reactor power. Power coefficient is expressed as 

the change in reactivity per change in percent 

power, AK/K/% power, and is negative at all times 

in core life. 

As power is increased, negative reactivity will 

be added to the core because the power coefficient 

is negative. Therefore, an equal amount of posi

tive reactivity must be added to keep the reactor 

critical. When power is decreased quickly, as it is 

after a trip or scram, the power coefficient adds 

positive reactivity, and negative reactivity inser

tion is required to make and keep the reactor 

subcriticaL The total amount of reactivity added 

by a power change is called power defect Figure 

2-10 illustrates power defect as a function of 

reactor power. 

2.8.6 Reactivity Coefficient Values 

Approximate numerical values for the major 

reactivity coefficients are as follows: 

a, =_lxlO3 AK/K 

% voids

MTC=-1 x 104 AK/K 

° F moderator 

FTC =_lx IV. AK/K 

'F fuel 

Power Coefficient = -1 x 104 AK / K 

% power 

Note that all the significant coefficients are nega

tive. Therefore, if a change in some reactor con

dition makes a coefficient more negative in value, 

its absolute value increases. Conversely, if a 

change in some reactor condition makes a coeffi

cient less negative, its absolute value decreases. 

This relationship is important to remember. 

2.9 Behavior of Reactivity Coefficients in a 

2.9.1 Moderator Temperature Coefficient 

BWR 

The moderator temperanure coefficient of re

activity is affected by core age. As core age 

increases, the buildup of Pu-240 increases the 

chance of resonance absorption, causing the coef

ficient to become more negative (absolute value 

increases). As the fuel depletes, control rods are 

withdrawn to add positive reactivity. As control 

rods are withdrawn, the effective size of the core 

increases, resulting in decreased fast and thermal 

neutron leakage, thereby causing the coefficient to 

become less negative (absolute value decreases). 

In addition, as control rods are withdrawn, more 

thermal neutrons are utilized by the fuel, causing 

the coefficient to become less negative. However, 

the dominant effect is the increase in thermal 

neutron utilization resulting in a less negative 

moderator temperature coefficient at the end of 

core life, as shown in Figure 2-4. It must be noted 

that MTC plays an important role during reactor 

startup and heatup when large moderator tempera

ture changes occur. However, during normal 

power operation, moderator temperature stays esUSNRC Technical Training Center 2-10 Rev. 0493

Rev. 0493

Reactor Physics

USNRC Technical Training Center 2-10
Power sentially Plant constant Engineering and Course MTC has Manual little reactivirReactor Physics 

sentially constant and MTC has little-reactivity 

effect. 

2.9.2 Moderator Void Coefficient - BWR 

'The behavior of the void coefficient as core 

age increases is similar to the moderator tempera

ture coefficient. Depending on core design and 

exposure, the void coefficient may increase, de

crease, or remain approximately constant. In 

general,'the void coefficient is inversely propor

tional to the effective core size, which is deter

-" mined by the control rod density. As control rods 

are Withdrawn to offset fuel burnout, the effective 

ize of the core increases, resulting in fewer neu

"tronis leaking out of the core and fewer thermal 

neutroins being absorbed by control rods. 'Thus, 

the Vid coefficient becomes slightly less negative 

toward the end of core life when all of the control 

rods are fully withdrawn. 

2.9.3 Fuel Temperature (Doppler) Coefficient 

-BWR 

As shown in Fig re'2-9, FC becomes less 

negative as fuel temper increases. This de

-crease in ihe magnitude of FTC is caused by three 

key factors. First, the incremental broadening of 

a resbnant absoi-tion peak decreases as fuel tem

perature increases. Second, the elevate• fuel tem

perature increases the average neutron flux ener

"gies',causingi6e neutrons to move through nmaller 

resonance absorption peaks. (As can be seen' on 

Fi 2-8, the resonance absorption peaks are 

"significantly smaller at higher neutron energies.) 

- Third, as fuel 'iemperature increases, Doppler 

"broadening shifts toward the higher energy reso

nance absorption peaks. Beciuse these pealk are 

smaller and have aaiy broadeied at lower tern

"- peratures, the effect on'the neutrons that are slow

ing down will decrease. 

Any increase in either the moderator tempera

ture or thecore void fraction will'cause FTC to 

become more negative. Afn increase in either of 

these parameters will resut in longer neutron 

"slowing down lengths and times,'thus inraing

theprobability of resonance absorption. As reso

nance absorption increases, FTC becomes more 

negative.. 

As the core ages, FTC becomes more negative. 

'The'dominant factoirresulting in this change is the 

- buildup of Pu-240, which is a strong resonant 

neutron absorber. Pu-240 is produced when U

' 238 absorbs a neutron and through a chain of 

d6ecay results in Pu-239. When Pu-239 absorbs a 

neutron, it will either fission or decay to Pu-240. 

- As Pu-240 buildi into the core, the total resonance 

absorption increases, thereby ciusing FTC to be

come more negative. 

2.9.4 PoVwer'Coefficient- BWR 

The interaction of the recirculation pumps 

with reactor power- in BWR -plants makes the 

prediction of power coefficient trei dsmruch more 

complex in BWR plants than in-PWR plants. 

Normally, the fuel temperature coefficient and the 

moderator void coefficient are both large con

tributors to the power coefficien.t. .Any reactor 

parameter change that affects either of these coef

ficients also affects the power coefficient. 

2.10 Behavior of Reactivity Coefficients in a 

2.10.1 Moderator Temper ature Coefficient 

* - PWR 

-Over core life, soluble boron concentration 

can range anywhere from about 1200 ppm to 10 

ppm. As soluble boron concentration in the core 

decreases; MTC becomes rore negative. This is 

"because a ?0

F increase in rdioderator'temperature 

at a low' oluble boron concentration7 will expel 

fewer boron atoms (neutron'absorbers) from the 

core than a 1 °F increase n mloderator temperature 

at a high boron concentration. The expulsion of 

boron atoms from the core is a positive reactivity 

component to the MTC. As boron concentration 

'-'decreases, fewer boron-atoms will-be expelled 

from the core fora 1 ' moderator increase, thereby 

resulting in MTC becoming more negative at the

USNRC Technical Training Center 2-11 Rev. 0493

Power- Plant Engineering Course Manual Reactor Physics

:USNRC Technical Training Center - 2-11 Rev. 0493
Power Plant Engineering Course Manual

Reactor Physics

end-of-core life (EOL). Figure 2-11 illustrates the 

effect of boron concentration on MTC. 

During a reactor startup to full power, control 

rods are generally fully withdrawn. When control 

rods are partially inserted, more neutron absorber 

material is in the core. Under these conditions, a 

1 OF increase in moderator temperature will result 

in more neutrons being absorbed by the control 

rods than if the control rods were fully withdrawn. 

Therefore, control rod insertion results in a more 

negative MTC. Conversely, as control rods are 

withdrawn from the core, MTC becomes less 

negative. 

2.10.2 Moderator Void Coefficient - PWR 

Voiding of the moderator in a PWR occurs 

only at high power levels and usually does not 

exceed 0.5%. For this reason, the' effects of the 

void coefficient are negligible when compared 

with the other reactivity coefficients. 

2.10.3 Fuel Temperature (Doppler) Coefficient 

-PWR 

The fuel temperature coefficient for a PWR is 

primarily affected by:

S 

S

Fuel temperature, 

Moderator temperature, and 

Core age.

A discussion of how each of the above param

eters affects FTC is provided in section 2.9.3. 

Remember. As fuel temperatr increases, 

FTC becomes less negative. Ai core age or 

moderator temperature increases, FTC becomes 

more negative. The combinid effects result in a 

more negative FTC at end of core life. 

2.10.4 Power Coefficient - PWR 

At the beginning of core life mi a PWR, FTC is 

the largest contributor to the negative power coef

ficient, so power coefficient largely follows FTC

changes. As a PWR core ages, the absolute value 

of MTC increases significantly (becomes much 

more negative) so that at end of core life, the 

contributions of FTC and MTC are nearly equal. 

Therefore, the power coefficient becomes signifi

cantly more negative as the core ages, and is nearly 

doubled by the end of core life. 

2.11 Control Rod Worth 

Control'r6d worth is the amount of negative 

reactivity that a control rod or group of control 

rods can inseit into the core. The worth of a control 

rod is approximately equal to the fraction of core 

neutrons that it can absorb and is directly propor

tional to the square of the thermal neutron flux in 

the vicinity of the rod (or group of rods) and 

inversely proportional to the square of the core 

average thermal neutron flux. 

Rod Worth cc n flux2 ri 

n flux2 

Control rod worth is affected by a variety of 

factors. Any change in the reactor core that affects 

the thermal neutron flux will change rod worth. A 

control rod that is located in an area of the core that 

exposes it to a high thermal flux will have a greater 

rod worth. 

Changes in moderator temperature will affect 

control rod worth. As moderator temperature 

increases, the density of the moderator decreases. 

For the control rods, the major effect of the density 

change will be longer thermal neutron diffusion 

lengths. Therefore, neutrons from deeper within 

the fuel bundle will be able to travel to the vicinity 

of a control rod. Hence, the thermal flux at the 

control rod effectively increases as moderator 

temperature increases, resulting in an increased 

control rod worth. 

For BWRs a change in the core void fraction 

will'also result in a change in moderator density, 

thereby changing controlrod worth. However, the 

density change during voiding is much more proUN ICC Technical Training Center 2-12

Rev. 0493

Reactor Physics

USNRC Technical Training Center 2-12
nounced. Power Plant As Engineering Course Manual Reactor Physithe core void fraction increases, the

nounced. As the core void fraction increases, the 

"density of the moderator decreases significantly. 

With respect to control rod worth, the major effect. 

"is much longer neutron slowing down lengihs, 

meaning that more neutrons will be resonantly 

absorbed as the neutrons slow down, resulting in a 

lower thermal neutron flux at the control rod. 

Thereforie, as voids incr6ase in BWRs, the control 

rod worth decreases.

Fuel temperature also affects control rod worth 

but is small in magnitude compared to other pa

rameter changes in the core. As fuel temperature 

increases, theresonance absorption increases, caus

ing a decrease in the thermal flux surrounding the 

control rod and a decrease in control rod w6rth. 

The effect of core age on control rod worth is 

quite complex. In BWRs, control rod worth may 

increase or decrease as the core ages depending on 

the buildup of fission product poisons, burnable 

poison depletion, control rod position, fuel deple

tion, and depletion of the control rod boron. To

ward the end of core life, the fuel depletion and the 

control rod boron depletion are the dominant ef

fects and result in a decreased control rod worth. 

-In PWRs, as the core ages, soluble boron 

*-concentration is reduced. A higher neutron flux 

"exists as less neutrons are absorbed by the boron in 

the moderator. The neutrons travel farther as less 

fuel atoms are present and are more likely tobe 

absorbed in .a control rod. Therefore, in a PWR, 

control rod worth increases over core life. 

S, -Control rods and groups are sequenced and/or 

overlapped to make the reactivity addition rate 

smoother. The differential rod worth is the amount 

of reactivity added by a 1% insertion of a control 

rod or group and is illustrated in Figure 2-12. The 

integral rod worth is the total amount of reactivity 

added by a control rod or group as it moves from 

fully withdrawn to fully inserted and is shown in 

Figure 2-13. -

2.12 Boron Worth 

Boron worth is the change in reactivity associ

ated with a ppm change in the soluble boron 

concentration of the moderator in a PWR core. 

The moderator in a PWR typically contains be

tween 10 and 1000 ppm of soluble boron in the 

form of boric acid. Boron-10 (B-10) has a very high absorption cross section for thermal neutrons 

that qualifies B-10,as a reactorpoison:. 

Figure 2-14 shows the boron worth versus 

,,moderator temperature for BOL and EOL. As 

moderator temperature increases, boron atoms are 

spread, farther apart, resulting in fewer boron at

oms present in the core. Increasing boron concen

tration by 1 ppm at a highermoderator temperature 

will add fewer boron atoms to the core.-, Thus, 

boron worth becomes less negative as moderator 

-temperature increases. 

Boron worth becomes more negative over 

core life. This is because fuel depletion and the 

reduction of the boron conceniration resultkin less 

competition within the core for thermal neutrons. 

The higher thermal neutron flux makes the boron 

worth more negative. The increase in the boron 

worth over core life is not as pronounced at higher 

moderator temperatures. This is due to the buildup 

of plutonium, whiclh competes with bor6n for 

neutrons. 

The boron worth is a ratio of neutrons ab

sorbed in the boron to neutrons absorbed in the 

fuel: 

B.W. = 

The reciprocal of this expression would be the 

inverse boron worth. 

1 N ',___ ,__ 

B.W. Nbo-bqrUW

USNRC Technical Training Center 2-13 Rev. 0493

..•Reactor Physics Plant Engineering Course Manual 

USNRC Technical Training Center 2-13 Rev. 0493
Power Plant Engineering Course Manual

Reactor Phvci.c

-2.13 Fission Product Poisons 

In the fission process, the nucleus absorbs a 

neutron and the resultiing nucleus breaks into two 

or more parts called fission fragments. A detailed 

investigation of the thermal neutron fission of U

235 has shown that the resultant nucleus splits in 

many different ways, yielding more than 350 

primary fission products (or fission fragments). In 

Figure 2-15, the percent fission yields of U-235 

are plotted against the mass niumbers. Note that 

each mass number represents several isotopes (different elements). During power operation, the 

isotope Xenon-135 (Xe- 135) is formed as a fission 

product. This isotope has an extýemely large 

capture cross section (2.6 million barns). The 

isotope is formed in two ways: directly s a fission 

product (0.3% of the total fission prodiucts) and 

indirectly from the radioctive decay of tellurium

135 (5.9% of the total"fission produ&ts). The 

radioactive decay chain of tellurium- 135 (Te- 135) 

is as follows: 

52-TeM --•) 5 -_ Xe3m ,cs3Ss 

(All decay by 03 emission) 

where 

Te-135"half-life = 2 rin:., 

1-135 half-life = 6.7 hr., 

Xe-135 half-life = 9.2 hr., and 

Cs-135 is stable. 

Xe-135 C'aptures a thermal neutron, forming 

Xe-136, which is stable and has a very small 

capture cross section. 

When the reactor is first brought to power, the 

Xe- 135 concentrations (atoms/cm3) is slowly built 

up to an equilibrium. This is due primarily to the 

relatively long half-lives of 1-135 (6.7 hours) and 

Xe-135 (9.2 hours). Because of the high thermal 

neutron cross section ofXe-135,'as the concentra

tion of the isotope increases, the macroscopic 

absorption cross section will also increase. Opera

tionally, as xenon builds up, other poisons in the

0n 1 + 92U235 U23 

(fission) 

SXen 

531135 

54 

(P decay)

Removal

IXe 1 3 6 

54 

(n absorption)

55Cs135 

(0 decay)

The equilibrium value for the xenon concen

tration is a function of the reactor neutron flux 

level (power level). Since Xe-135 absorbs ther

mal neutrons, its effect on the chain reaction can be 

described in terms of reactivity. The multiplica

tion factor is lowered primarily by the decrease in 

the thermal utilization factor. The reactivity effect 

can be shown to be approximately equal to the 

ratio of the macroscopic absorption cross section 

of the xenon to that of the fuel. 

A change in power will cause a change in 

xenon concentration. At the end of the trinsient 

(about 2 days) the xenon concentration will reach 

its new equilibrium, assuming that power is left 

constant after the change. 

Refer to Figure 2-16 at time 50 hours. *The 

reactor has reached an equilibrium xenon' coricen

tration for 50% power. Power is then increased io 

100%. Initially there is only a small increase in 

production of xenon because the production as a 

direct fission product is small (about 0.3%), and

USN3IM I ecnaic I raining Center 2-14 

Rev. 0493

Rev. 0493

core (contiol material such as control rods or boric 

acid) must be' removed to maintairin criticality. 

Provided there is enough control material to re

move during this xenon buildup, the xenon con

centration reaches equilibrium after approximately 

40 hours of power operation. 

Equilibrium isa point it which the production 

of Xe-135 is'equia to theremoval of Xe-135 by 

neutron capture plus the loss of Xe-135 through 

radioactive decay.

Reactor Phv•ie¢

2-14
Power Plant Engineering Course Manual

Reactor Physics

because the iodine-concentration does not changa 

very quickly, so the production by decay of iodini 

remains practically constant. However, remova 

of xenon is increased significantly because o 

increased burnout (xenon absorbs neutrons). Th 

decay of xenon to cesium remains almost constan 

initially. These are only the initial effects; but i 

can be seen that the removal of xenon has in 

creased more than the production; -herefore, xe 

non concentration decreases. This will continuc 

for a few hours until the iodine concentration ha., 

increased enough that xenon production by•iodinc 

decay is greater than xenon removal. Eventually. 

the xenon concentration will reach an equilibriuir 

value corresponding to 100% power. This will 

happen when production and removal rates are 

again equal. 

Refer to Figure 2-16 at time 150 hours. Power 

is decreased from 100% to 50%.: Xenon produc ;tion initially is changed very little. Because of the 

lower neutron population, burnout is rediced and 

xenon concentration increases. As iodine concen

tration decreases, production of xenon decreases 

until removal is greater than production. Then 

xenon concentration will decrease until equilib

rium for 50% power is reached. 

SA shutdown, shown in Figure 2-17, is similar 

to a power decrease but causes a greater change in 

xenon concentration. Production of xenon di

rectly from fission and removal by burnout almost - cease. Radioactive decay of iodine (to produce 

Sxenon) and radioactive decay of xenon (to remove 

i-.t) is left. Xenon concentration will increase 

initially, just as in the power decrease case. How

ever, due to-the difference in decay-'times, the 

increase will continue longer and reach much 

higher levels before a decrease occurs. The peak 

occurs about 8 or 9 hours after shutdown. The 

reactor will be considered xenon free in about 72 

hours. - - - f 

*. _ In some cases, Xe-135 presents moderately 

sensitive reactor operating conditions. Consider a 

reactor that has operated at power long enough to 

establish a high xenon concentration.

e_ Assume that the reactor trips and that a rapid 

e recovery to full power is achieved simultaneously 

1 with the point in time at which "peak" xenon 

f occurs (time 9.5 hours in Figure 2-17). 

e 

t In returning the reactor to power, the negative 

t reactivity associated with the xenon is overcome - by withdrawing the control rods to a higher posi - tion than normally requi With the high flux of 

full power operation acting to "burnout" the accu

mulated Xe- 135 and the decay ofXe- 135 resulting 

from the previous shutdown, the concentration 

quickly falls off, and the result is a relatively fast, 

positive reactivity insertion. It should be pointed 

, out that properly designed power reactors will 

overcome this xenon burnout adequately with the 

proper control rod system operation. 

* Another imp:crtant fission Pro'duct poison en

countered in reactor ope-ation is samarium-149 

(Sm-149). This stable'isotope has a capture cross 

section of aboiit5 x 104barns.It enterithiis system 

as the end product of ifie following decay chain: 

6ONdI, 9 "P', 14 9 ' , Sm'49 (stable), 2 hr. - -53 hr. 

.where,

Nd = 'neodymium and 

P.• = promethium. 

products occur in about -These 1.1% of U-235 

fissions. Because Sm-149 is stable, its equilib

rium value in any reactor produces about 1% AK/ 

K reactivity, independent of the neutron flux. The 

rate at which Sm-149 approaches this equilibrium 

is determined by the Pm-149 half-life (53 hours). 

As shown on Figure 2-18, equilibrium is reached 

in -about 60 days.-. -A -power increase reduces 

samarium concentration initially due to increaied 

burnout, but theconce-ntration returns to ihe same 

equilibrium value. Upon reactor shutdown, the 

Sm-149 builds up to an asymptotic Value depen

dent on the power history of the reactor. The 

promethium concentration-is power level depen

dent. Because the: only means of Sm-149

USNRC Technical Training Center Rev. 0194

" 2-15

.Reactor Physics

USNRC Technical Training Center Rev. 0194
Power Plant Engineering Course Manual

Reactor Ph-sics

removal (burnout) is- essentially removed on a 

reactor shutdown, 'the shutdown concentration 

varx (see Figure 2-19). 

2.14 Burnable Poisons 

A burnable poison is a neutron absorber that is 

loaded into the reactor at discrete locations during refueling. They are positioned within the core to 

maintain an optimum neuiron' flux distribution 

and to compensate for excess fuel while maintain

ing a negative MTC (PWR only). 

Burnable poisons are loaded into the core so. 

that more fuel can be loaded into the core at the 

beginning of life. By loading this excess reactivity 

at the b~ginning of core life, reactor p6wer opera tion at 100% power-can be extenided, thereby reducing the frequency of refueling outages. Bo

ron or gadolinium are often used as the poison material. Upon neutron abso rption,' the poison loses some of its reactivity. At end of core life, nearly all of the installed poisons will be depleted. 

In a BWR, control rods can also be inserted to 

allow more fuel to be loaded. However, by load

ing burnable poisons into the core more fuel can be 

loaded without increasing the number of control 

rods that must be designed into the reactor core. In 

addition, the gadolinium is loaded in varyifig axial 

concentrations to flatten the core thermal neutron 

flux to improve the fuel exposure shape in the core. 

This flux flattening results in a more even burnup of fuel ov:- core life and better margins to fuel 

limitations. 

2.15 Subcritical Multiolication' 

There is some spontaneous fission within the 

core material. For example, U-235; with a spon

taneous fission half-life of 1.8 x 1017 yrs., delivers 

8 x 10-4, n/sec/gm; U-238, with a spontaneous fission half-life of 8 x 1015 yrs., delivers 1.6 x 

10-2 n/sec/gra. 

The spontaneous fission process, however, is 

insufficient to appreciably register on the neutron

sensors of power- reactors. Previous experience 

with power reactors indicates a background neu

tron count of 1/6 cps, with the plant cold and a Keff 

of 0.97. The specification for startup requires a 

neutron count rate of at least 1/2 cps with the plant cold at a Keff of 0.97. To achieve this count rate, 

a startup neutron source is installed. 

When the reactor is operating in the source 

range, it is necessary to consider the effect of the 

addition of source neutrons as well as fission 

neutrons to understand what is happening to the 

total neutron density. The reason for this is that the 

factors included in the calculation of Keff do not 

account for source neutrons, which are insignifi

cant when compared with the number of fission 

neutrons at higher power levels. 

S ubcritical multiplication is the multiplication 

of source neutrons thatvoccurs as a result of fis

sions in the fuel of a subcritical reactor. Table 2

3 is discussed below for various reactor shutdown 

Cases. 

1. To understand subcritical multiplication 

first consider a condition in which there ts 

zero subcritical multiplication. If 100 neu

trons are inserted into a core with Keff = 0 

(no fuel), the neutron level will rapidly 

decrease to zero as they are absorbed in the 

water or leak out. 

2. As fuel is added to the core, Ieff will 

increase. In our second case assume Keff 

is now.0.5.o The neutron population will 

again decrease to zero, but the fuel will 

cause the rate of decrease to lengthen. 

In this case, as in the first case, we siarted with 

100 neutrons which were followed to absorption. 

Now consider a source that supplies 100 neutrons 

to the reactor at the beginning of each generation. 

1. Again we will assume Keff = 0. Because 

no multiplication is involved, the neutron 

population will be steady at 100 neutrons 

as a direct result of the source.

ait'•, I ecuiucai I raining Center 2-1 Re .0 9

Rev. 0194

Reactor Physics

2-16
Power Plant Engineering Course Manual Reactor Physics

2. The last -case (Table 2-4) represents the 

conditions that actually exist in a reactor. 

Assume Keff' =0.5. Also for convenience 

assume that a continuous source of 100 

neutrons are introduced at the beginning of 

each generation. This shows the effect of 

subcritical multiplication. 

An equation that yields the equilibrium neu

tron population is: 

1 S ' 

NT =Sx I - (only for Kef < 1), 

where 

NT = equilibrium neutron population and 

S = source. 

For this case the-results are: 

1 NT = 100 x-- = 200 (after multiplication). 

- Remember that subcritical multiplication is 

the equilibrium neutron population divided byithe 

source -populatio n. 'For more practical application 

consider subcritical multiplication to equal the 

equilibrium neutron population divided by an ini

tial neutron population following a change in Keff. 

This concept is utilized by operators to compare 

neutron population between different subcritical 

conditions.- -," 

The term M may be used to represent subcriti

cal multiplication: 

CR_ 1-Kfl

where 

CRI 

CR2

the initial count rate and 

the count rate following a change 

in Keff.

The time required for power to level off at 

some new value following a subcritical reactivity 

change is a function of the average generation time 

(e) and the numberof generations required to level 

off. 

t(sec) = N(generations) x £ (sec/generation) 

Figure 2-20 shows that when-Keff = 0.5, 

N =7 whereas when Keff = 0.9, N= 44. 

The l/M plot is a tool used in predicting the 

point at which a subcritical reictor will reach 

criticality as reactivity is added in positive incre

ments. The 1/M plot is tused because a plot of M 

would approach'infinity as Keff approaches 1. 

2.16 Neutron Production, 

The multiplication factor Keff was previously 

discussed in terms of its individual componrents. 

This section shows how the term is applied to the 

actual operating core. Consider a reactor in which 

Keff is exactly 1.0. -. 

With equilibrium established, the neutrons 

entering into the self-sustaining reaction are a 

mixture of prompt anddeliyed neutrons. Promrpi 

neutrons appear at approximately 10-14 seconds 

after a fissioning event, whereas delayed neutrons 

are not a direct result of a fission but rather a 

product of the decay of one of the fission products. 

These neutrons are produced at some time after the 

original fission and are dependent on the half lifU 

of the fission product. _-The fission products are 

referred to as delayed neutron precursors. Figure 

2-21 shows the decay scheme for. the delayed 

neutron precursor Bromine-87. 

The fraction of total fission neutrons that are 

delayed neutrons is known as the P3 fraction. As 

shown in Table 2-5, each fuel has a characteristic 

j3due to its yield of delayed neutron producers. 

The total P fraction for the fuel is a weighted 

average of the P's of the isotopes that combine to 

make up the fuel. . -

USNRC Technical Training Center -- - - -2-17 ReiCO 194

Power Plant Engineering Course Manual Reactor Physics

USNRC Technical Training Center _ ......- 2-17 ?-" Rev'.014
Power Plant Engineering Course Manual

Reactor Phvsiks

At BOL 93% of the power generated in the 

core is generated by the U-2351 7% is generated by the U-238. In a reactor at BOL the total 03 fraction 

would be: 

13 = (.9 3 )(13U-235) + (.0 7 )(13U-238) 

= (.93)(.0065) + (.07)(.0148) 

= .006045 +.001036 

- .0070 at BOL 

At EOL assume 40% of our power is now 

generated by Pu-239, 7% by U-238 and 53% by U

235. The total 13 fraction at EOL would be: 

13 = (.53 )(13U-235) + (.07 )(13U-238) + (.40)(13Pu-239) 

= (.53)(.0065) + (.07)(.0148) + (.40)(.0021) 

= .003445 + .001036+ .00084 

= .0053 at EOL. 

- Delayed neutrons are born at a lower energy level than the prompt neutrons (.5 Mev vs. 1-2 

Mev)., -This will cause the delayed neutrons to 

have a different value in the multiplication factor 

due to this lower energy effect on the fast fission 

factor and on fast leakage. 

Since the delayed neutrons are born at energy levels below the threshold for fast fission (U-238 

requires neutron energy z I Mev to fast fission), 

Peff will be less than 13. 

Being borne at this lower energy level also 

means that there will be less fast leakage of de

layed neutrons. This results in 13eff being greater than 13. The combined result of these two effects 

will be that p

3

eff is less than 13 due to the high value 

of fast fissions in the core. 

2.16.1 Effect of Delayed Neutrons on Reactor 

Control 

Even though the fraction of delayed neutrons 

is very low, 0.7% of all the fission neutrons have 

a large effect on the operation of the reactor. To 

illustraje this, consider d reactivity change using 

both prompt and delayed neutrons.

The following equation can be used to calcu

late a change in neutron population over a given 

period of time: 

N =Noe(Keff-1) t/i, 

where: 

N = Number of neutrons after time t, 

No= Number of neutrons at t = 0, 

t = time period (seconds), and 

i= generation time. 

The generation time (mean life time) is the 

time between the absorption of a neutron in the 

fuel and the absorption of the resulting fission 

neutron in some material. 

For a prompt neutron, the generation time (1p) is: 

tp = 10-14 see (absorption to fission/birth) 

+ 10-4 see (birth to absorption) = 10-4 sec. 

The average mean lifetime for delayed neu

tron precursors is about 10 seconds. This results in 

a delayed neutron generation time (2d) of: 

d = 10-14 see (absorption to fission) 

+ 10 see (fission to birth) 

+ 10-4 see (birth to absorption) = 10 see. 

The life cycle time or generation time is a 

weighed average of the lifetimes for prompt and 

delayed neutrons. Since the delayed neutron frac

tion is 13, then the prompt neutron fraction is (1-P3). 

These are used as the weighting factors. 

To compute a weighted generation time, com

pute a neutron population change using both prompt 

and delayed neutrons. 

I = (1-)p t (0) (7d) 

Assume BOL conditions P3 = .0070 

£ = (I-.007)(10-4) + (.007)(10)

U3SNIM. I ecnnicai I raining tLenter 2-18 

Rev. 0194 2-18 Rev. 0194
Power Plant Engineering Course Manual ReactorPhysics

I = .006693 +.07 

-= .0700993 seconds =. 07 seconds 

kFigure 2-22 shows that the reactor would be 

uncontrollable with a life cycle time due to prompt 

, neutrons alone, but with' the addition of delayed 

neutronfs the reactor is controllable. 

-2.17 R1actor Startiip - BWR 

2.17.1 The So'ur' Range 

The source range covers approximately 10-8% 

to 10"4% reactor power. Positive reactivity is 

added by control rod withdrawal to establish the 

reactor critical. Further control rod withdrawal 

will then etýblish arate ofpowerincrease into the 

intermediate range to commence a plant heatup. 

The operator verifies, before withdrawing any 

control rods, that there is a minimum count rate 

"indicated on the source range monitor. As the 

operator withdraws control rods (n6nfissioning 

neutron absorbers) from the core, he is increasing 

the thermal utilizationlfactor (f), and causing Keff 

to increase. The source range monitor indications 

'will show 'a slow increase in count rate. The 

"neutrons being counted are coming from incore 

neutron sources and subcritibal multiplication. 

Control rods are always withdrawn in a pro

cgrammed sequence. The sequencing of r&d with

drawal minimizes individual rod, worths, extends 

core life, and minimizes the effects of transients. 

"C6Cntrol rods are further withdrawn to achieve 

criticality. The reactor operator announces that 

the reactor is critical when he observes a continu

"ously increasiig power level and a sustairhed posi

tive period without control rod motion. The reac

"toi is actually slightly supercritical at this point. 

However, it would be difficult and time-consum

ing to determine when the reactor is first exactly 

criticalhin the 'source range. The operator then 

adjusts the period to about 100 seconds by control 

rod withdrawal and allows power to increase into 

the'intermediate range.

"2.17.2 'Thi Intermediate Range and Reactor 

Heatup

The intermediate range of reactor operation 

occ~urs from reactor power levels of about 

-0-% to about 10%. 'After criticality is attained, 

reactor power will continue to steadily increase 

until some effect turns reactor power. As power 

"mcreaises, the sourice range monitors Will approach 

the high end of their indicating'scale and will be 

withdrawn from the core when the intermediate 

range monitors aireon scale.' 

Reactor power will turn when 'the point' of 

adding heat (POAH)-)is reached. The POAB 

occurs when the heat produced by the fission 

process in the Core exc'ds the ambi6ntheatlosses 

from the core. At approximately 1% reactor 

power; the moderator will begin to heat up. As the 

temperature of the moderator increases, the MTC 

adds negative reactivity to the core, lengthening 

the reactor period 'and slowing the power increase 

rate. In addition, the fuel temperature is increasing 

so that the FIC is also adding negative reactivity. 

To continuedthe startup, the 0perator rfiusf'cbn

tinue to withdraw control rods to overcome this 

negative reactivity insertion. As 'the reactor is 

heated up, the ope-'ator will control the hetp rate 

(HUR) by rod withdrawal. The operat6r will 

maintain a HUR of l6ss than 100°F per hour to 

prevent inducing excessive theirmal stresses in the 

reactor pressure vessel. -When" moiderator tem-' 

perature reaches 212TF, reactorpressure ýwil be

gin increasing., The 6peiator will continue' fd 

withdrawal to heat up and pressurize the rector to 

"about 540 0F and 920 psig, respectively. 

2.17.3 The Power Range. 

The power range includes reactor operations 

from reactor power levels of about 1% to 100%. 

-As reactor 'power increases to about 3%, the-aver

age power range monitoring nuclear instrumenta

tion comes on scale, and at about 10% power, the 

intermediate range nuclear instruments are with

drawn from the core:

'USNRC Technical Training Center 2-19 Rev. 0195

Reactor Physics Power Plant Engineering Course Manual

",USNRC Technical Training Center ,2;19 Rev. 0195
Power Plant Engineering Course Manual Reactor Physics

Reactor pressure is maintained at- approxi

mately 920 psig by opening the main turbine 

bypass valves, which dump steam directly to the 

main condenser. The operator continues to with

draw rods to increase reactor power and steam 

production until enough -steam is being produced 

to place the main turbine generator in service. 

As the operator increases reactor power, the 

moderator temperature does not change signifi

cantly since the reactor is maintained at saturated 

conditions for 920 psig. Because the moderator 

temperature is no longer significantly changing, 

the MTC no longer provides any significant reac

tivity changes. However, as reactor power in

creases above 1%, steam bubbles or voids begin 

production in the core. As the core void fraction 

increases, the void coefficient (av) adds negative 

reactivity to the core, requiring the operator to 

continue to withdraw rods to increase power. 

-The fuel temperature is continuing to increase 

as reactor power is increased. As a result, the FTC 

is also adding negitive reactivity to the core, 

requiring additional control rod withdrawal. 

During reactor power .operation, another 

method of reactor power control is utilized on 

BWRs. The reactor core flow is increased to attain 

100% power. Increasing core flow increases the 

amount of heat that can be carried away from the 

fuel by the moderator.; As core flow is increased, 

the void fraction in the core is reduced. When the 

void fraction in the core is decreased, fewer neu

trons are resonantly absorbed while slowing down 

and fewer neutrons will leak out of the core; 

therefore, positive reactivity is added to the core. 

Hence, an increase in core flow results in a reactor 

power increase. 

The. operator continues- to increase reactor 

power with a combination of control rod with

drawal and core flow increases to ensure reactor 

operation within core limitations. -The operator 

will continue to increase reactorpower to increase 

the output of the main turbine generator. In a 

BWR, the main turbine is "slaved to the reactor."

Prior to 'a reactor startup in a PWR, all shut

down rods are withdrawn to ensure adequate shut

down capability. RCS boron concentration is 

adjusted to -a value that has been calculated to 

produce criticality at a desired rod position during 

the rod withdrawal.' The reactivity added by the 

boron change is determined using the boron worth. 

If the RCS is below normal operating tempera

ture, decay heat or reactor coolant pump operation 

will be used to raise reactor coolant temperature. 

This will be a negative reactivity addition as the 

MTC is negative. Source range count rate is 

logged on a l/M plot. The source range count rate 

is established by the neutron source strength and 

Keff. 

2.18.1 Source and Intermediate Ranges 

As control rods are withdrawn, positive reac

tivity is added causing neutron level to increase.

USNRC Technical Training Center 2-20 Rev. 0195

As reactor power is increased, steam production is 

increased. After the main turbine generator is 

placed in service, the main turbine electro-hydrau

lic control system opens the turbine control valves 

(and closes the turbine bypass valves) as necessary 

to maintain a constant 920 psig at the inlet to the 

turbine control valves. As steam production and 

steam flow increase with increasing reactorpower, 

the control valves must be opened more and more 

to maintain the valve inlet pressure at 920 psig. As 

more steam passes through the main turbine, more 

work is done and the main generator output in

creases. Therefore, the turbine load is controlled 

by the reactor power. 

The reactor steam pressure also increases as 

reactor power increases to offset the increasing 

friction losses caused by more steam flow in the 

main'steam lines between the react6r and the 

tuibine. At full power the reactor steam pressure 

in most BWR plants is stable at 985 to 1000 psig 

with turbine control valve inlet pressure main

tained at 920 psig. 

2.18 Reactor Startup - PWR

Power Plant Engineering Course Manual -- , Reactor Physics

USNRC Technical Training Center 2-20 Rev. 0195
'P-&v Plant"Pihw~neering Course ManualRecoPhss

After each withdrawal, the startup is paused to 

allow source range count rate to reach an equilib

rium value. These values are logged on the I/M 

plot and estimated critical rod positions are deter

mined. Once criticality is attained, neutron level 

continues to increase and the reactor is placed on 

a positive startup rate. As reactor power increases 

through the source range and intermediate range, 

reactivity in the core remains essentially constant. 

Fuel temperature and moderator temperature re

main unchanged until reactor power reaches the 

POAH. 

2.18.2 Power Range 

When reactor power enters the power range, 

the rate of fissions has increased sufficiently to 

produce heat in the fuel that is carried away by the 

moderator. As fuel and moderator temperatures 

increase, the FTC and MTC add negative reactiv

ity, thereby reducing the startup rate. Negative 

reactivity feedback will continue to reduce the 

startup rate until reactor power stabilizes. At this 

point, net reactivity is zero. 

As reactor power enters the power range, sur

plus heat is removed from the moderator by the 

steam generators. The steam generators are main

tained in a saturated condition at approximately 

1100 psig by automatic steam dumping. If reactor 

power increases, more steam is dumped to main

tain steam generator pressure and moderator tem

perature nearly constant. As control rods are 

further withdrawn, reactor power will increase 

and stabilize as FTC and MTC continue to provide 

negative reactivity feedback. 

When reactor power reaches approximately 

10%, the main turbine-generator is placed in ser

vice. The extra steam needed for the main turbine

generator causes a reduction in automatic steam 

dumping. Reactor power is now being controlled 

by the electrical load carried by the main turbine

generator. The turbine electro-hydraulic control 

system gradually opens the turbine control valves 

to increase the electrical output of the generator. 

As the turbine control valves are opened, more

steam is drawn from the steam generators, which 

decreases the coolant temperature. A negative 

MTC results inapositive reactivity addition,which 

increases reactor power. As fuel temperature 

increases with the increase in reactor power, nega

tive reactivity is added by the FTC until net reac

tivity is zero and reactor power stabilizes at a 

highervalue to match the increased electrical load. 

Unlike a BWR plant, in a PWR plant the reactor is 

said to be "slaved to the turbine" because reactor 

power changes follow the main turbine generator 

electrical load/steam flow changes. 

Additional electrical load increases will con

tinue to lower the coolant temperature until the 

resulting steam generator temperature is too low 

for efficient electrical power generation. To pre

vent the coolant temperature decrease when elec

trical load is increased, positive reactivity must be 

added by other means. The two methods com

monly used to add positive reactivity during an 

electrical load increase are control rod withdrawal 

and boron dilution. 

2.19 Decay Heat Production After 

Shutdown 

When the reactor is shut down, the fuel contin

ues to generate heat even though the fission rate 

decreases to the level sustained by subcritical 

multiplication. Highly radioactive fission prod

ucts continue to decay by emitting alpha, beta, 

gamma, and other forms of radiation. These 

emissions interact with the surrounding fuel and 

reactor materials, thereby transferring significant 

energy in the form of heat. Reactor cooling must 

be maintained after shutdown to remove this de

cay heat and prevent fuel melting. 

Decay heat is greatest immediately after a 

reactor shutdown. As the shorter-lived radioac

tive fission products complete their decay process, 

decay heat production tapers off. This accounts 

for an exponential decrease in decay heat after 

shutdown. Table 2-6 provides approximate levels 

of decay heat generation at various time intervals 

after a reactor shutdown from full rated power.

TAiAzev. ui,

USNRC Technical Training Center 2-21

USNRC Technical Training Center

Reactor Physics

Ire 0175 2-21
Powe Curs PlntMaualReactor ngieerig Phvsics

Chapter 2 Definitions

(EFFECTIVE MULTIPLICATION 

FACTOR) 

REACTIVHTY 

STARTUP RATE 

REACTOR PERIOD 

CONTROL ROD WORTH 

DIFFERENTIAL CONTROL ROD 

WORTH 

INTEGRATED CONTROL ROD 

WORTH 

BORON WORTH 

CRITICAL

SUBCRITICAL 

SUPERCRITICAL

The ratio of the number of thermal neutrons available 

at the end of a neutron cycle to the number of thermal 

neutrons initiating the cycle. 

The fractional change in neutron population per generation. It is a measure of a reactor's departure from criticality. 

The number of decades (powers of 10) reactor power changes in one minute. 

The number of seconds required to change reactor 

power by a factor of e, the base of the natural 

logarithm (2.718...). 

The amount of negative reactivity that a control rod or 

a group of control rods can insert into the core. 

- The amount of reactivity added by a unit (1 inch or 

1%) insertion of a control rod or control rod group into the core. 

- The total amount of reactivity added by a control rod 

or control rod group as it moves from fully withdrawn to fully inserted into the core. 

- The change in reactivity associated with a one ppm 

change in the soluble boron concentration in the 

reactor coolant in a PWR core. 

- KI equals 1.0 

- Kef is less than 1.0 

- Kf is greater than 1.0

USNRC Technical Training Center 2-i) Rev. 1295

Power Plant Engineering Course Manual Reactor Phv•ic•

USNRC Technical Training Center 2-D Rev. 1295
Power Plant Engineering Course Manual Reactor Physics

Table 2-1.

REACTOR FUEL

Neutrons From Fission

NEISIRON FISSION

U-235 2.43 

Pu-239 2.90 

U-233 2.50 

U-238 2.30

USNRC Technical Training Center 2-23 Rev. 0493

Power Plant Engineering Course Manual Reactor Physics

USNRC Technical Training Center 2-23 Rev. 0493
Power Plant Engineering Course Manual Reactor Physics

Table 2-2. Microscopic Cross Section (a) Values

NUCLIDE REACTIONS En C(barns)

Absorption .025 ev 690 

Scattering .025 ev 10 

Fission .025 ev 580 

Capture .025 ev 110 

Alpha emission .025 ev 0 

Absorption .025 ev 4010 

Capture .025 ev 0 

Alpha emission .025 ev 4010 

Scattering .025 ev 5 

Absorption 1 ev 665 

Absorption 10 ev 200 

Absorption 100 ev 66.5 

Absorption 1000 ev 20.0 

Absorption 10,000 ev 6.65

USNRC Technical Training Center 2-25 Rev. 0493

Power Plant Engineering Course Manual Reactor Physics

USNRC Technical Training Center 2-25 Rev. 0493
Power Plant Engineering Course Manual Reactor Physics

GENERATION 

NEUTRONS

Table 2-3. Ineffective Subcriticai Multiplication 

Keff =0 

(No Source) 

1 2 3 4 5 6 7 8 9 

100 0 0 0 0 0 0 0 0

Keff = 0.5 

(No Source) 

GENERATION 1 2 3 4 5 6 7 8 9 10 

NEUTRONS 100 50 25 13 6 3 0

Keff=0 

(Continuous Source - 100 neutrons/generation) 

GENERATION 1 2 3 4 5 6 7 8 9 10 

NEUTRONS 100 100 100 100 100 100 100 100 100 100

USNRC Technical Training Center 2-27 Rev. 0493

10 

0

2-27

Power Plant Engineering Course Manual Reactor Physics

USNRC Technical Training Center Rev. 0493
Table 2-4. Subcritical Multiplication 

Keff = 0.5 

(Continuous Source - 100 neutrons/generation) 

Generation 1 2 3 4 5 6 7 8 9 10 

Neutrons 100 150 175 188 194 197 198 200 200 200 

GENERATION 1 2 3 4 5 6 7 8 9 10 

100 50 25 13 6 3 2 1 0 0 

100 50 25 13 6 3 2 1 0 

100 50 25 13 6 3 2 1 

100 50 25 13 6 3 2 

100 50 25 13 6 3 

100 50 25 13 6 

100 50 25 13 

100 50 25 

100 50 

100 

TOTAL 100 150 175 188 194 197 199 200 200 200

USNRC Technical Training Center 2-29 Rev. 0493

Power Plant Engineering Course Manual Reactor Physics

USNRC Technical Training Center 2-29 Rev. 0493
Power Plant Engineering Course Manual Reactor Physics

Table 2-5. Delayed Neutron Fraction for Various Fuels

HALF LIFE DECAY CONSTANT YIELD FRACTION 

GROUP T1/2(SEC) X (SEC-1 ) (NEUTRONS/FISSION) 13 

1 55.72 0.0124 0.00052 0.000215 

2 22.72 0.0305 0.00346 0.001424 

U2 3 5 3 6.22 0.111 0.00310 0.001274 

4 2.30 0.301 0.00624 0.002568 

5 0.610 1.14 0.00182 0.000748 

6 0.230 3.01 0.00066 0,000273 

TOTAL YIELD: 0.0158 

TOTAL DELAYED NEUTRONS FRACTION (13): 0.0065 

HALF LIFE DECAY CONSTANT YIELD FRACTION 

GROUP TIt2(SEC) X (SEC"1) (NEUTRONS/FISSION) 13 

1 52.38 0.0132 0.00054 0.000192 

2 21.58 0.0321 0.00564 0.002028 

U2 3 8 3 5.00 0.139 0.00667 0.002398 

4 1.93 0.358 0.01599 0.005742 

5 0.490 1.41 0.00927 0.003330 

6 0.172 4.02 0.00309 0.001110 

TOTAL YIELD: 0.0412 

TOTAL DELAYED NEUTRONS FRACTION (13): 0.0148

GROUP 

1 

2 

pU2 39 3 

4 

5 

6

HALF LIFE 

TI/2(SEC) 

54.28 

23.04 

5.60 

2.13 

0.618 

0.257

DECAY CONSTANT 

X (SEC 1 ) 

0.0128 

0.0301 

0.124 

0.325 

1.12 

2.69

YIELD FRACTION 

(NEUTRONS/FISSION) I3

0.00021 

0.00182 

0.00129 

0.00199 

0.00052 

0-0277

0.000073 

0.000626 

0.000443 

0.000685 

0.000181 

0.000092

TOTAL YIELD: 0.0061 

TOTAL DELAYED NEUTRON FRACTION (13): 0.0021

USNRC Technical Training Center 2-31 Rev. 0493

Rev. 0493

Power Plant Engineering Course Manual Reactor Physics

USNRC Technical Training Center 2-31
Table 2-6. Delayed Heat Production Following Reactor Shutdown 

From Full Power 

TIME SINCE SH=OWN PERCENT OF FULL POWER 

1 second 6.0 

1 minute 4.5 

1 hour 1.6 

1 day 0.7 

1 week 0.5 

1 month 0.1

USNRC Technical Training Center 2-33 Rev. 0493

Power Plant Engineering Course Manual Reactor Physics

USNRC Technical Training Center 2-33 Rev. 0493
Power Plant Engineering Course Manual Reactor Physics

2 4 6 8 10 

FISSION NEUTRON ENERGY (En) 

Figure 2 - 1. Fmsion Neutron Energy

USNRC Technical Training Center 2-35 Rev. 0493

0.4 

0.3

C 

LU 

U

0 

I

m 

0 

0.

0.2

0.1

0 12 14

Power Plant Engineering Course Manual Reactor Phyvsics

USNRC Technical Training Center 2 -35 Rev. 0493
S ~10,000 1000 

; CF 1000 

10 

0.001 0.01 0.1 1.0 10 100 1000 10,000 

Neutron Energy, ev

Figure 2 - 2. U-235 Absorption Cross-Section Vs. Energy
Power Plant Engineering Course Manual Reactor Physics

Number of neutrons from 

thermal fissions in 

generation "N+I"

Number of neutrons from 

thermal fissions in 

generation "N"

Thermal neutrons 

absorbed in 

non-fuel material 

Thermal neutron 

leakage

Reproduction Factor 

TI 

The average number of 

neutrons produced per 

thermal neutron absorbed 

in the fuel 

Thermal Utilization Factor 

f 

The fraction of thermal 

neutrons absorbed in fuel 

Thermal Nonleakage Factor 

Lth 

The fraction of thermal 

neutrons that don't leak 

out of the core during 

thermal diffusion

Fast Fission Factor 

The neutron contribution 

from fissions at higher 

than thermal energies 

Fast Nonleakage Factor 

Lf 

The fraction of fast neutrons 

that are not lost due to 

leakage while slowing down 

to thermal energy 

Resonance Escape 

Probability 

p The probability that 

neutrons will escape 

resonance capture while 

slowing to thermal 

energy.

Fast neutron 

leakage 

aim Neutrons captured

Keff = ELf P 1-h fTI =

Number of neutrons in "N+l" generation 

Number of neutrons in "N" generation

When critical Ytff =I 

Figure 2-3. Neutron Cycle in a Thermal Reactor

USNRC Technical Training Center 2-39 Rev. 0197

Power Plant Engineering Course Manual Reactor Physics

USNRC Technical Training Center 2-39 Rev. 0197
Power Plant Engineering Course Manual Reactor Physics

0

-8 --

-12 1-.

-16 

-20-

0

100 200 300 400 500

I I I

II I

100 200

I

300

I I

400 500

600

0 

-4

-- -8

600

-12 

-16 

-20

Temperature (OF) 

Figure 2-4. Moderator Temperature Coefficient

USNRC Technical Training Center 2-41 Rev. 0493

0

-4

x

USNRC Technical Training Center 2-41 Rev. 0493

Power Plant Engineering Course Manual Reactor Physics

I I

I I
Power Plant Engineering Course Manual Reactor Physics

-4

-6 

-8 

-10 

x 

> -12 

-14 

-16 

-18 

-20 I I I I 1 

0 10 20 30 40 50 60 70 80 

CORE AVERAGE VOIDS (%) 

Figure 2-5. Void Coefficient

USNRC Technical Training Center 2-43 Rev. 0493

Power Plant Engineering Course Manual Reactor Physics

USNRC Technical Training Center Rev. 0493 2-43
CS 00 0 

PROBABILITY 

OF 

ABSORPTION 

J=b 

KE 1KE 2 

NEUTRON KINETIC ENERGY 

Figure 2 - 6. Resonance Absorption (Stationary Nucleus) 

¢t0 

.- I
Power Plant Engineering Course Manual Reactor Physics

NEUTRON 

VELOCITY

-l. 

RESONANCE 

ABSORPTION BAND

I -

TARGET 

NUCLEUS

STATIONARY 

MOVING DUE TO 

TEMPERATURE

TARGET VELOCITY 

MOVING FASTER 

"> DUE TO HIGHER 

TEMPERATURE

RESONANCE WIDTH 

DOUBLES WHEN 

TARGET VELOCITY 

DOUBLES 

Figure 2-7. Resonance Capture

USNRC Technical Training Center 2-47 Rev. 0493

V1

V2

V3

V4

Power Plant Engineering Course Manual Reactor Physics

f

USNRC Technical Training Center 2-47 Rev. 0493
Power Plant Engineering Course Manual Reactor Physics

10,000 

5,000 

1000 

500 

(BARNS) 

50 

10 

5 

2

Neutron Energy (ev) 

Figure 2 - 8. U - 238 Cross Section Curve

USNRC Technical Training Center 2-49 Rev. 0493

Power Plant Engineering Course Manual Reactor Physics

USNRC Technical Training Center 2-49 Rev. 0493
-2.0

N 

0 

-4~

-0.5 

300 500 1000 1500

FUEL TEMPERATURE, OF 

Figure 2-9. FTC Vs. Fuel Temperature

TI 

0 

1* 

x 

IL. 

0 

0 

0 

w

-1.5 

-1.0

'V 

0 

ft 

'1 

ft 

n 

-9 

0 

1 

'V

2000 2500
Power Plant Engineering Course Manual Reactor Physics

a. 

00 

-500 -1000 

E\ 

0 BI 

0 

-2000------------------ -

-2500 

0 20 40 60 80 100 

Power (% full power) 

Figure 2-10. Total Power Defect

USNRC Technical Training Center 2.53 Rev. 0493

Power Plant Engineering Course Manual Reactor Physics

USNRC Technical Training Center 2-53 Rev. 0493
I-' 

a. 

0 

3 

N 

U' 

El

+3 

+2 

+1

0

If 0 

x 

o.

460 480 500 520 540 

MODERATOR TEMPERATURE, OF 

Figure 2- 11. Moderator Temperature Coefficient

-1 

-2 

-3 

400

C) 

El 

to 

to. 

n 

r0

420 440 560 580 600
C! 

s.<

-12.0 

-11.0 

-10.0 

-9.0 

-8.0 

-7.0 

-6.0 

-5.0 

-4.0 

-3.0 

-2.0 

-1.0 

0

30 40 50 60 70 90 100

% GROUP INSERTION 

Figure 2-12. Differential Rod Worth Curve

80

IL 

cb 

,.,

0 10 20
-7.0 

S-6.0 3 

S,-5.0 

AK/K -4.0 

x 10 3

. 

x 10"3-3.0 

-2.0 

-1.0 1 

0 

0 10 20 30 40 50 60 70 80 90 100 

% GROUP INSERTION 

Figure 2-13. Integral Rod Worth Curve
S~0 

€12 

-6 " 

"-2 -8_ __ _ _ _ __ _ _ _ _ _ _ _ 

U1014 - -

S-12 -

-18 

-20 

-22 

0 100 200 300 400 500 600 700 

MODERATOR TEMPERATURE (OF) 

Figure 2-14. Boron Worth Vs. Moderator Temperature
Power Plant Engineering Course Manual Reactor Physics

100 120 140 

Mass Number 

Figure 2-15. Fission Yield Curve

USNRC Technical Training Center 2-63 Rev. 0493

10 

1 

-1• 

10-2

0 

A2 CO 

U-J

0-4

10"5

70

80

170

160

Power Plant Engineering Course Manual Reactor Physics

USNRC Rev. 0493 Technical Training Center 2-63
REACTOR POWER

50% 1 fll 0, -0 % r-100%

20 40 60 80 100 120 140 160 

HOURS 

Figure 2.16. Xenon Reactivity Vs. Reactor Power as Function of Time

c) 

('4 

Cm 

n=

-4 

-3

0

-5

N 

"U 

0 

'C

-2 

-1 

0 

0

100%

180 200

r: nf o/

C 

-V 

C) 

0 

n 

0 

9
5. 

ft 

0% 

ft 

ti)

30 40 50 60

HOURS 

Figure 2-17. Xenon Peaking

Ie

-6.0 

-5.5 

-5.0 

-4.5 

-4.0 

-3.5 

-3.0 

-2.5 

-2.0 

-1.5 

-1.0 

".5 

0

(% AK) VERSUS TIME IN HOURS 

K 

• 100% ii 

80 

50%,

0 10 20 70 80 '9 

0 

-I
AK 

% A- VERSUS TIME IN DAYS K

a 

S. 

C-, 

ft 

5 

1 

'C 

ft 

w

-1.2 

-1.0 

-.8

OR~-.6

30 40 50 60 70 

DAYS 

Figure 2 - 18. Samarimn Buildup

-.4 

"-.2 

0

ft 

t,,.

0 10 20 80 90
-1 .4 1 " 

c 75% M/%c 50%_ __ _ _ _0_

5.-1.2 

aq 

.. 

t,j ".8 

-.6 

-.4 

0 5 10 15 20 25 30 35 

DAYS 

S14 

Figure 2-19. Samarium Peaking
Power Plant Engineering Course Manual Reactor Physics

CONSIDER TWO CASES:

T=0 T--O

K=0.50

ADDED

LEVEL

K=0.90

-- - - - - ----- ------------------ I............ 

N=S(KK 2 3 2 3 Nt = So 0+KK+ K K+... Nt = S 0(1+K+K + K3 K4 ... Kr ) 

IERATION COUNT RATE GENERATION COUNT RATE 

1 100+50 1 100+90 

2 100+50+25 2 100+90+81 

3 100+50+25+12.5 3 100+90+81+73 

4 100+50+25+12.5+6.25 4 100+90+81+73+66 

The higher order terms It will take many more 

become small quickly. In fact, generations before the 

already by the 71h higher order terms becc 

-- generation less than one negligibly small. In fact 

neutron is added per not until the 44th genen 

generation. is less than one new nei 

added per generation.

ime 

ition 

utron

Figure 2-20. Subcritical Multiplication

USNRC Technical Training Center 2-73 Rev. 0493

GEIS

Power Plant Engineering Course Manual Reactor Physics

USNRC Technical Training Center 2-73 Rev. 0493
Power Plant Engineering Course Manual Reactor Physics

V

In

EMISSION

Rb 87

Sr 87 

STABLE

STABLE

Figure 2 - 21. Delayed Neutron Production

USNRC Technical Training Center 2-75 Rev. 0493

Rev. 0493

Power Plant Engineering Course Manual Reactor Physics

USNRC Technical Training Center 2,75
Power Plant Engineering Course Manual Reactor Physics

GIVEN: ND= 106 NEUTRONS 

t =5 SEC 

,p =10 SEC 

-&d = 10 SEC 

, =0.07 SEC 

Keff = 1.001

PROMPT N1 ONLY 

N = N. e (Keff -1) t /lp 

N=10s e (.oo1)5/10 

N=10O N=06 e50 e° 

N=10 x 5.184 x 10d& 

N = 5.18 x 1027 NEUTRONS

PROMPT + DELAYED N 

N = N e (Keff-l) tl/I 

N = 106 e(.0 0 1)

5 1 '

0 7 

N=10 6 e-0 714 

N=106 x 1.074 

N = 1.074 x 10 NEUTRONS

Figure 2-22. Delayed Neutron Effects

USNRC Technil Training Center 2-77 Rev. 0194

Power Plant Engineering Course Manual Reactor Physics

USNRC Technical Training Center 2-77 Rev. 0194
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

- 3.0 HEAT TRANSFER AND THERMAL 

HYDRAULICS

Learning Objectives 

After studying this chapter, you should be able 

to: 

1. Describe the mechanisms of heat transfer:. 

a. Conduction 

b. Convection 

c. Radiation 

2. Perform basic calculations associated with 

a plant cycle including: 

a. Plant efficiency , 

b. Determining work performed 

c. Determining heat rejected 

3. Describe the heat transfer across a typical 

reactor fuel rod. 

4. Define or explain the meaning of the fol

lowing terms and concepts: 

a. Subcooled nucleate boiling 

b. Bulk nucleate boiling 

c. Onset of transition boiling 

d. Critical heat flux 

5. Describe how boiling can improve or de

grade heat transfer ability. 

6. 'Describe how pressure, temperature, flow, 

andreactor power can affect the departure 

fromfiucleateboqing (DNB). _%' 

7. Describe how a heat balance is performed 

"on a PWR and a BWR. 

3.1 Introuc~nn 

In nuclear power plants water and steam are 

"the 'media most commonly used'to transfer heat 

Senergy from the heat production source (reactor) 

to the mechanical conversion devices (turbines) 

that drive the electric generators. This chapter 

discusses the application of fundamental thermo7 USNRC Technical Training Center 3-I * - 'Rev. 0194

3-1 . .-:. - ,-Re•;. 0 194

Power. Plant Engineering Course Manual Heat Tr~ansfer and Thermal Hydraulics

dynamic and heat transfer concepts used in reactor 

and steam plant energy conversion processes. The 

objective 6f the material presented in this chapter 

"is to provide a basic understafiding of the thermal 

and hydraulicprinciples that goveem normal op

eration and the'conditions that'can limit plant 

operation. 

3.2 Steam PowerCycle "' 

Thomas Savery, an English inventor, built the 

first steampowered fire engine in the late seven

teenth century. Before the beginning of the nine

.-teenth century a very simple steam engine was 

being used to pump -water out, of Scottish coal 

mines. Since those early times,-a whole area of 

scientific study has been developed aronfid the use 

of steam to produce power. This aira of study is 

called thermodylnamics (thermo, meaning heat; 

dynamics, meaning work), and'it dealh with the 

conversion of heat into work.-Theirmiodyfian'ics is 

important in the study of power plant performa-ice 

because, in a nuclear power plant, heat ii'used to 

produce steam to do work.' 

.3.2.1 Overview of the Steam Power Cycle 

The main components used in the process of 

converting heat into -'ork- are shown schemati

cally in Figure 3-1. ;The first compbnenf shown in 

Figure 3-1 is the reactor or steam generafor, where 

* heat enters the system and water is converted into 

-steam. ,In a nuclear power plant,ýthe heat used to 

boil water comes from the fiuclear energy'pro

duced by the fission process. When the water 

boils, it turns into steam, a high-temperature, high

pressure gas. 

The steam flows through a series Of pipes to 

"-the next component- the turbine.' In the turbine, 

some of the energy carried by the steam is ex

-,tracted and turned into useful work. The steam 

forces the turbine to rotate; and this action turns the 

generator, which produces electricity. The steam 

-loses some of its energy as it forces the turbine to 

rotate. When it leaves the turbine, the steam is at 

a lower pressure and a lower temperature than

7, U'SNRC Technical Training Center
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

when iit entered the turbine. 

Thie lower energy steam flows into the next 

system component- the condenser. The steam in 

the condenser is cooled by an external water sys

tem and changed into water called condensate. 

During this process the steam loses, more of its 

energy. The heat energy released by the steam is 

transferred to the cooling water where it is rejected 

from the system and lost fr-om the cycle. 

The condensate from the condenser, now at 

low pressure and low temperature, flows to the 

next system component - the pump. The pump 

increases the pressure of the water and forces it 

back into the reactor or steam generator so that the 

process can begin again. The pump increases the 

water pressure by putting work into the water. 

The cycle shown in Figure 3-1 and discussed 

in this chapter is called the steam-water cycle. It 

is a continuing cycle. , Water is heated until it 

becomes steam, which powers a turbine. The 

lower energy steam leaving the turbine passes to 

the condenser, where it becomes water again. The 

water is then pumped back into the boiler to restart 

the cycle. 

:The steam-water cycle is also a process of heat 

in/beat out and work in/work out. Heat enters or is 

added to the system in the reactor or steam genera

tor, and heat is rejected or leaves the system in the 

condenser. Work enters the system at the pump, 

and work leaves the system at the turbine. 

3.2.2 The First Law of Thermodynamics 

The first law of thermodynamics states that 

energy is neither created nordestroyed. The forms 

that energy takes may change, but the amount of 

energy remains constant. In a power plant, this 

law means that the plant cannot produce work 

unless energy is added. 

nThe concept of the first law is easily applied to 

the plant. When the energy into the plant equals 

the energy leaving the plant, the system is said to

be balanced. In this case, energy in equals energy 

out (Ein = Eout). The energy in the plant remains 

constant. 

If the plant becomes unbalanced, then energy 

in does not equal energy out. In the unbalanced 

plant there must be a change in the amount of 

energy stored in the plant .because energy cannot 

just appear or disappear. This relationship is 

shown by Equation 3-1:

Ein = AEstored + Eout. (3-1)

Energy is usually stored in the plant as heat that has 

increased the iemp erature of some part of the 

plant. Energy can be stored in other forms. One 

example is water stored in a reservoir behind a 

dam. In this case, energy is stored as potential 

energy. 

During steady-state plant operation, the sys

tem is balanced, and energy in equals energy out. 

This is not the case during startup and shutdown. 

During startup, the energy coming into'the plant is 

greater than the energy leaving the plIant. When 

this occurs, there is an increase in stored energy, 

and the plant heats up. During shutdown, the 

energy coming into the plant is less than the energy 

leaving the plant. In this situation, the stored 

energy decreaseý, and the plant cools down. 

The first law of thermodynamics can be used 

to account f6r many things that take place during 

plant operation. First, however, Equation 3-1 

must be expanded to include the various forms of 

energy that can exist in the plant. For a more 

detailed breakdown, Equation 3-1 can be expanded 

as follows: 

(PE +IKE + PV +W+Q)in 

= A(PE + KE + U + PV + W + Q)stord 

+ (PE + KE + U + PV + W + Q)out. (3-2)

USNRC Technical Training Center 3-2 

Rev. 0194

Rev. 0194

Power Plant EngineeringCourse Manual Heat Transfer and Thermlal Hydraul~ics

3-2
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

The following forms of energy are included in 

Equation 3-2: " 

'Potential energy (PE) - energy' due to an 

obje6t's vertical position 

* Kinetic energy (KE) - energy due to an 

object's inotion 

* Internal energy (U) - energy due to the 

motion of an object's molecules 

• Flow work (PV) - energy due to pressure 

- times volume 

• Mechanical work (W) - energy due to a 

force acting through a distance

• Heat (Q) - the'transfer of internal energy 

into or out of an object 

Energy is the potential to do work. In a power 

plant, a certain amount of energy is added to the 

plant, and some part of this energy is turned into 

work. The amount of energy turned into work 

compared to the 6nergy added is a measure of the 

power plant efficiency.

engines had to reject some heat to the environment 

to produce work. The rejected 'heat is lost or 

wasted energy from the viewpoint of the power 

cycle. 

3.2.4 Thermodynamic Cycle Efficiency 

Experiments have shown that the efficiency of 

a steam plant cannot exceed a definite limit that 

depends on the temperature at which heat is added 

to the cycle and the temperature at which heat is 

rejected from the cycle. As mentioned above, only 

some of the heat supplied to a power cycle can be 

converted to work. Thus, even if the equipment in 

the ,plant operated ideally (i.e., perfect perfor

mance with no heat loss and no friction), the plant 

could not achieve 100% thermodynamic efficiency.

This principle can be Iinderstood by examin

ing a simple power cycle such as the one shown in 

Figure 3-2. In the simple cycle, the work done by 

the cycle is the difference between the heat added 

-in the PWR steam generator (orB WR reactor) and 

-the heat rejected in the condenser. 

W=Q.MQ&. ..-

Further, the thermodynamic efficiency of a plant "3.2.3 The Second Law of.Thermodynamics is defined as the ratio of the work t6the heit added. 

-The second law of thermodynamics can be W 

divided into two parts. ,The first part states that E = 

heat naturally flows downhill, that is, from a high Q " 

temperature region to a low temperature region. A 

consequ ence of this phenomenon'is that work is Since the simple cycle is based on reversible 

_required to move heat from a low temperature (ideal) processes, another charicteristic is that the 

regi6n-to a high temperature region. This part of change in entropy during the heat addition process 

the second law is easily observed nis the same as the change of entropy during the heat 

Hot objects natraly lose heat to cooler objects, rejection process. 

"-but ork is needed to move heat frorinthe low 

temperature air in a refrigerator • o, the higher, =-- or Q- - = 

"temperature ouiside air. ,. Q. . 

The second part of the law states that not all - Combining these relationships yields Equa heat added to a system can be changed into work. tion 3-3, which can be used-to determine the 

".This was discovered by the" early experimenters theoretical maximum efficiency of a heat power 

with steam engines, who' found that all steam cycle. -

USNRC Technical Training Center .3-3 - Rev. 0194

Power Plant Engineering Course Manual •,"Heat Transfer and Therniaa!Hydr~aulics

USNRC Technical Training Center "'" • Rev. 0194 -.3-3
Power Plant Enginering Course Manual Heat Transfer and Thermal Hydraulics

E Q1 Q .ý.' T EUn=zX = - -- 'Qi Q. Q. T", 

T 

E• 1 = I ct (3-3) 

In this equation, Tout is the absolute temperature at 

which heat is rejected from the cycle, and Tin is the 

absolute temperature at which heat is added to the 

cycle. 

This expression shows why power plants are 

designed for the highest practical temperature for 

heat addition and the lowest possible temperature 

for heat rejection because achieving either or both 

will increase plant efficiency. 

As an example, the temperatures at which a 

plant operates can be usedto calculate the theoreti

cal maximum efficiency for the planit. Assume 

that all heat is added in the PWR steam generator 

(or BWR-reactor) at 5401F and all heat is rejected 

in the condenser at 800F. 1The maximum theoreti

cal efficiency of the cycle can be calculated using 

absolute temperatures as follows:-'

T_

= .46 or46% 

On the basis of this calculation, the maximum 

theoretical efficiency of this plant cycle is 46%. 

This limit can be used as a point of comparison for 

the actual efficiency. The actual efficiency of a 

real plant cycle is always less than the theoretical 

maximum thermodynamic efficiency. There are a 

number of reasons for this. First, not all heat is 

added at the maximum temperature of the plant. 

This has the effect of reducing the effective ternperature forheat addition to the plant. Second, the 

components and equipment in the plant are not 

perfectly insulated and some heat is lost from the 

components and pipes. This heat never has an 

opportunity to do real work. Third, power cycle 

components such as pumps and turbines are not 

frictionless.- Friction reduces the amount of work 

produced by the turbine and increases the amount 

of work required by the pump. Lastly, not all heat 

is rejected at the minimum plant temperature. This 

has the effect of increasing the temperature for 

heat rejection. 

As an example, assume heat addition occurs 

at 440'F. If 440'F is used for the thermodynamic 

efficiency calculation, then: 

Eth.•x = 1 T_ 

T. 

S(460+80 

ELU = 1 (460+440) 

E = 1 - .6 =.4 or 40% 

In practice, heat is added over a range of tempera

tures between 440'F and 540'F. Therefore, the 

effective temperature for heat additioni for the 

cycle would be between 440°F and 540'F, result

ing in a maximum theoretical efficiency some

where between'.40 and .46.

3.2.5 T-S and H-S Cycle Diagrams

To operate a power plant at the best effi

ciency, an understanding of what is happeni ng in 

each phase of the heat power cycle is needed. A 

graph called a temperature-entropy (T-S) diagram 

can be used to investigate plant processes. This 

diagram is useful for understanding heat, work, 

and cycle efficiencies. 

Figure 3-3 is a T-S diagram for a PWR steam 

power cycle: Theccurve shown on the diagram is 

called the saturation dome. Points on the cuive on 

the left portion of the dome represent waterjust as

USNRC Technical Training Center 3-4 Rev. 0194

Power Plant Engineiring Course Manual S, Heat Transfer and Thermal Hydraulics

E 60+80

_USNRC Technical Training Center 3-4 IRev. 0194
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

it is ready to boil at various temperatures (i.e., a 

saturated liquid). Points on the curve on the right 

portion of the dome represent steam just as it is 

ready to condense at various temperatures (i.e., a 

saturated vapor).' The area to the left' of the 

saturation dome represents liquid water. The area 

to the right of the dome represents steam with no 

water. The area under the dome represents a 

steam-water mixture. The path or processes in the 

steam cycle are shown on the diagram. Note the 

positions of-the fourbasic PWR components 

steam generator, turbine, condenser, and pump. 

At point'I on the diagram, water is heated at 

a constant pressure, and the water temperature 

increases until the saturated liquid curve is reached. 

At this point, the water starts to become steam. 

"Boiling occurs at a constant temperature (isother

mal process) and constant pressure (isobaric pro

cess) under the steam dome until point 2 on the 

saturated vapor curve is reached where all water 

has changed to steam. 

At point 2 the steam enters the turbine.7 'Be

cause some of the steam's energy is converted into 

work in the turbine, the steam loses some tempera

ture and pressure. If the turbine is assumed to be 

an ideal -or a perfect machine, the steam will 

expand in the turbine along the vertical line until 

point 3 is reached where the steam enters the 

condenser at condenser pressure. A perfect ma

chine is an idealized concept of a machine that can 

operate -without friction and without -heat loss 

(adiabatic Process). I 

Recall that steam expansion along the verti

cal line in the turbine means that entropy of the 

steam remains constant (isentropic) in the turbine. 

This is only true for an ideal turbine. -In a real 

turbine, entropy actually increases during the steam 

expansion process and point 3 will lie somewhat to 

the right of the isentropic expansion point. Be

cause the real steam expansion process is not 

,isentropic, less work is extracted from expansion 

through a real turbine than an ideal turbine. The 

mechanical efficiency of a turbine is the ratio of 

the real turbine work to the ideal turbine work, as

,shown in Equation 3-4: 

ET = W(3-4) 

In the condenser, heat is removed-fromr the steamat constant temperature and pressue until 

point 4 is reached, Where'all steam cofideiises to 

water. 

The pump'th'en increases the pressure of ihe 

-water to point 1 and forces'the water back t6o the 

steam generator. (Some heat is also added to the 

water by the feedwate preheaters.) If the pump is 

assuried to be an ideal or perfect pump (no friction 

or heat loss), the pump will compress the water 

along a vertical line, and the entropy will remain 

constant (isentropic)'during the pumping process. 

In a real pump, entropy actually increases during 

Sthe pump compression process, and point 1 will lie somewhat to the ight of the isenpc o -' tropic compres

"sion poinrti. -'Because the tcompression process is 

not'isentropic, more work 7is required to compress 

water in a real pump than in an ideal pump. The 

mechanical efficiency of a pump is theratio of the 

ideal pump work io the real pump work, as shown 

in Equation 3-5:

"E =W'dea, WP• 

PUM (3-5)

The T-S diagram is a useful tool for explaining 

•how a steam pjower cycle works. However, actual 

calculations are more straightforward if the en

thalpy is known at each of the four points in the 

"cycle:" Enthailpy-'is not usually found on a'T-S 

ýdiagiram, buit the required values can be obtained 

,froi the stearn tabiles if the state of eac' ,point is 

kno i.'For ilI ust roh purposes, i nes of constant 

enthalpy have been drawn onfFigure 3-3. 

'Another way of finding the enihalpy ai each of 

the foir'opinis is to use an H-S 6orMollier diagram. 

The Mollier diagram 'shown'in Figure 3-4 is an 

abbreviated H-S diagram for steam and water. An

USNRC Technical Training Center 3-5 Rev. 0194

Power IPlant Engineering Coui'se Manual -Heat Transfer and T~hermal Hydraulics

USNRC Technical Training Center 3-5 Rev. 0194
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

"advantage of the Mollierdiagram is that values of 

enthalpy can be read directly from the'diagram if 

the state of a point is known. 

An inspection of Figure 3-3 shows that some 

processes in the steam plant cycle are ideally 

isentropic (steam expansion in the turbine, pres

sure increase in the feed pump) and some are 

isothermal (boiling, condensation); however, no 

steam cycle events are isentialpic, or constant 

enthalpy, processes. One process that occurs in a 

steam plant that is isenthalpic is steam expansion 

throughathrottlingdevice, such as leakage through 

a safety/relief valve or throttling through a pres

sure reducing valve. A Mollier diagram is useful 

for determining the downstream conditions after 

this isenthalpic steam expansion occurs. 

3.2.6 Steam Power Cycle Analysis 

A basic steam cycle similar to those employed by, nuclear power plants is shown in Figure 3-5. 

Included in the system are a reactor or steam 

generator, a turbine, a condenser, and a feed pump. 

This cycle is also shown on a T-S diagram in 

Figureý 3-6. To summarize the cycle: 

1-2: Heat addition at constant pressure in 

the reactor or steam generator. 2-3S: Isentropic expansion of the steam 

through an ideal turbine. 

3S-4: Heat rejection at constant pressure in 

the condenser. 

4-1: Isentropic compression in an ideal 

pump. 

The line 2-3 shows the effect of a non-ideal tur

bine.. Notice the increase in entropy, As, which 

reduces the actual work output of the turbine. In 

this case, heat rejection in the condenser would 

occur along line 3-4. 

Quantities of energy and work can. be calcu

lated directly by plottinig the steam cycle on the H

S'diagram in Figure 3-7. .The important relation

ships for these calculations are:

1. Heat added: 

qadded = q1-2 = h2 - hl BTU/bm 

2. Energy converted to work in the ideal 

turbine is: 

BTU 

WzdV = W2 -3S = h; - h3s 

Energy converted to work in the real turbine is: 

W = h2 - h3 = ET(h-hS) BTU 

Ibm 

where ET is the real turbine efficiency and is 

given by: 

ET = h- h3 E h2 - h3s 

ET is a characteristic of the specific turbine and the 

value is provided by the manufacturer., A typical 

value for ET is 85%. 

3. Heat rejected in the condenser following 

an ideal steam expansion is: 

qrejected = %&4 = h4- h3s BTU/lbm. 

Since the turbine is not ideal, the actual 

energy rejected in the condenser is: 

qrejected = q3-- h4 -h 3 BTU/lbm. 

Because h3 is greater than h3s, the absolute 

value of q3-4 is greater than the absolute 

value of q3s-4- The negative sign simply 

indicates heat rejection rather than, heat 

addition. 

4. Work used by the feed pump to increase 

feedwater pressure is: 

Wp'ideal =W41 = h4 - hI BTU/Ibm

USNRC Technical Training Center 3-6 Rev. 0194

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center 3-6 Rev. 0194
'P-w~ Plant Engineering Course ManualHetTafradThrlHyaui

Wp ideal Ep x Wp actual 

Wp ideal Wp actual 

, A typical value for Ep = 90%. In practice, 

Wpaa and Wpidg are assumed to be the same 

since the error introduced by this assumption has 

little effect on overall plant performance calcula

tions. 

3.2.7 Example Cycle Analysis 

For the purpose of an example, the following 

quantities will be determined assuming the mass 

flow'rate (fm) in the plant is 2 x 106 ibm/hr. 

* Heat added in the reactor or steam genera

tor (in a PWR, the heat added in the steam 

- generator is approximately equal to the 

heat obtained from the reactor), 

* Useful work out of the turbine, 

"* Heat rejected in the condenser, 

* Work required to drive the feed pump, and 

"I The cycle efficiency. 

3.2.7.1 Turbine Work 

Refer to Figure 3-7, where the analysis starts at 

point 2 in the cycle. This point is the outlet'of- the 

reactor or steam generator and the inlet to the 

turbine. The assumption 'is made that the 'steam 

supplied to the turbine is a saturated vapor with no 

superheat. The reactor br steaim generator outlet 

steam pressure is 1015 psia (1000 psig) and the 

steam mass flow rate is 2 x 106 lbm/hr. 

From the steam tables or directly from the 

Mollieridiagram,'the specific enthaipy of saturated 

vapor, hg, at 1015 psia is about 1191 BTU/Ibm. 

'This enthalpy corresponds to point 2 on Figure 3

7. 

The steam expands through the turbine anc 

exhausts at the same pressure as the condenser (it

"1 this instance, 2 in. Hg absolute). Solving for the 

point 3S enthalpy can be done 6n a Mollier dia

gram. With an isentropic expansion, the steam 

expands through the turbine along the constant 

entropy line until point 3S is reached where the 

"-,constant pressure line f6r 2 iin Hg is intersected. 

From the Mollier diagram enthalpy axis, h3s is 

determined to be approximately 774 BTU/Ibm. 

To determine h3,ý-th -actual enthally of the 

ekhaust steam, the turbine efficiency relati6ixship 

and an' assumed efficiency of 85% is used. 

ET h2 h2 -h 35 - h3sh2. 

ET x (h2 - h3S) =h2 - h3 • -•.

h3 = h 2 - ET x (h2 - h3s)

h3 = 1191 -. 85 x (1191- 7 7 4 ) BTU/lbm

h3 =836BTU/Ibnm 

h3 is plotted'on the Mollier diagram at the 

intersection of the 2 in Hg constant pressure line 

-and the 836 BTU/lbm constant enthalpy line. 

The actual turbine work output per lbm of 

steam is: 

W2.3 =h2 - h3 

1191-•8 - 36= 355- BTU/Ibm 

The turbine power can be found by multiply

ing W2-3 by the steamii flow rate:

Turbine Power = rh x W2x3

Turbine Power =2 x 106 lbm/hr x 355 BTU/ 

. "Ibm 

Turbine Power = 7.1 x 108 BTU/hr 

Turbine power can be converted to ft-lbf/hr,

Key. V1

USNRC Technical Training Center 3.7

3-7

Heait Transfer and Thermal Hydraulics

I Rev. 0195 "USNRC Teclumical Training Center
Power Plant Engineering Course Manual horsepower, (M ~ )aCeieSyHa ~ ~ ~ ~ ~ ~ ~ or ~meaats ~ rn~p.~, ~ ~ ~ h.mtT...U. ~ -. 

horsepower, Or megawatts- (MW) as desired by using the proper conversion factors. 

3.2.7.2 Condenser Heat Rejection 

The heat rejected in the condenser is given by: 

q3-4 = h4 - h3

The pressure at point 4 is2 in-Hg absolute or 

.98 psia. The saturation temperature is 101 OF. The 

saturated steam tables show that point 4 corre

sponds to a saturated liquid with an enthalpy, hf, 

of about 69 BTU/Ibm. Using this value for h4, the 

amount of heat rejected in the condenser per Ibm 

of steam is: 

q34 = 69 - 836 = -767 BTU/lbm 

The negative sign means a loss of heat from the 

system. The rate of heat rejection is this value 

multiplied by the exhaust flow'rate: 

(ý 3-4 = -767 BTU/1bm 2x 106 lbm/hr 

Q 3-4 = -1.53 x 109 BTU/hr 

Note that more 'han twice as much heat is rejected in the condenser as is extacted by the 

turbine. 

3.2.7.3 Feed Pump Work 

Work is required to drive the feed puip which 

increases the pressure of the feedwater to 1015 

psia. This work is given by: 

W4ý1 h4 - hi BTU/Ibm 

Since the saturation temperature correspond

ing to 1015 psia is about 546°F, the pump dis

charge is subcooled water. From subcooled water 

tables, the enthalpy for hl, compressed water at 

101 TF and a pressure of about 1000 psia, is about 

71.7 BTU/Ibm. Therefore, the pump work is: 

W4- = 69 - 71.7 = -2.7 BTUIlbm

The negative sign arises because this is work 

that must be put into the cycle or done on the 

system. The pump work load or pumping power 

is determined by multiplying W4 -1 by the mass 

flow rate: 

Pumping Power = rh x W4 _1 

Pumping Power = 2 x 106 lbm/hr 

x (-2.7 BTU/Ibm) 

Pumping Power = -5.4 x 106 BTU/hr 

The pumping power can be converted to horse

power, ft-lbf/hr, or megawatts as desired by using 

the proper conversion factor. 

Neglecting the minus sign, the magnitude of 

the ratio of the pumping power to the turbine 

power is: 

Pumping Power 5.4 x 10 6 BTU / hr 6 

Turbine Power 7.1 x lO BTU / hr 

Thus, the ratio of the required pumping power 

to the turbine power is less than 1%. This, small 

ratio is the primaryjtxstification forignoring pump 

efficiency in the overall analysis as discussed 

earlier. 

3.2.7.4 Heat Addition 

The heat added to the cycle is: 

qadded = ql-2 = h2 - hi. 

The values of h2 and hl were determined 

earlier so: 

q1-2" 1191 - 71.7 = 1119 BTU/Ibm. 

The heat added to the cycle, which is about 

equal to the reactor thermal power, is found by multiplying ql-2 by the steam flow rate: 

Reactor Thermal Power _ in = ii q1-2

flflttnnn. . . . - - -

3.8 

Rev. 0195

oUSt I Lectnncal Training Center Rev. 0195

I Heat Transfe-r anAr h.• t..~

3-8
Power Reactor Plant Thermal Engineering Power Course =2 x Manual 106 ibm/hr x 1119 Heat Transfer and Thermal Hydraulics 

Reactor Thermal Power = 2 x 106 Ibm/hr x 1119 

BTU/Ibm 

Reactor Thermal Po~wer = 2.24 x 109 BTU/hr 

"Sinc' I mdgaw'itt equals 3'.413 x' 106 BTU/hr, 

reactor thermal'p0iver canr be& given as: 

Reactor . 

Thenhal T 

Power 2.24x109T X .... 1M 

hr 3.4 13x 106 BTU 

"hr 

Reactor Thermal Power = 656 MW 

3.2.7.5 Cycle Efficiency 

The actual cycle efficiency is given by: 

E W_& 

QiD 

Watt is the net work of the .cycle which is the 

difference between the turbine and pump work. If 

pump work is neglected, the net workis the turbine 

work.'_ 

".355 BTU/lbm 

-1119 BTU/lbmr 

Ea.= 31.7%, which is representative of the 

actual cycle efficiency of modemr 

nucleariplants. 

The actual efficiency cani be compared to the

maximum theoretical efficiency' foir this' 6y'cle 

which is given by: :- -

E = 1 

T.

Tout = (Saturation Temperature in Condenser) 

,=10lF=5610R 

tin= (Saturation Temperature in reactor/steam 

generator) 546*F = I(06°R

"10061_ 

E, •= A42=-44.2%, ; 

As expected, the actual efficiency is less than 

the theoretical maximum efficiency.. 

3.2.8M Improving Cycle Efficiency 

Any improvements that can be made in cycle 

efficiency will increase the amount of electric 

power that can be generated from a given amount: 

of nuclear fuel. As discussed in section 3.2.4, 

either increasing the effective temperature duing, 

heat addition or decreasing the effective tempera-. 

ture during heat rejection will improve cycle effi

ciency. Various methods are used to improve the 

efficiency of the steam plant cycle. Two methods 

commonly used in nuclear power plants are dis

cussed in the following sections. 

3.2.8.1 Feedwater Heating 

Feedwater heating is. used to -preheat the 

feedwater prior to, entering the reactor/steam gen

erator. Feedwater heating is accomplished by 

directing the feedwater through a series of heat 

exchangers called feedwater -heaters. A steam 

cycle incorporating feedwater heating is shown in 

Figure 3-8. . . 

The heatingmedium for the feedwater heaters 

is typically turbine'extraction steam. Extraction 

steam from the turbines has a high moisture content and is removed from various turbine stages to 

prevent erosion of the latter-stage blades. After 

transferring heat to the. feedwater, the extraction 

steam remnants exiting the feedwater heaters are 

drahiri to the ?condensate system or sent to the 

main condensei.' - . 

Preheatingthe feedwaterwiti extraction steam 

uses energy that would otherwise be rejected or 

lost from the steam cycle. Essentially, heating 

increases the effective temperature for heat addi

tion during steam generation. With warmer

USNRC Technical Training Center 3-9 Rev. 0195

Beat Transfer" and Thermal Hydraulics Power Plant Engineering Course Manual

USNRC Technical Training Center 3-9 I Rev. 0195
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

feedwater-entering the- reactor/steam generator, 

less reactor heat is required to change each pound 

of feedwater to steam. The overall effect is an 

improvement in cycle efficiency. The effect of 

feedwater heating on the steam plant cycle is 

shown on a T-S diagram in Figure 3-9. 

3.2.8.2 Steam Reheating 

Steam reheating is used to dry and slightly 

superheat (reheat) the steam that has been partially 

expanded in the turbine. -In nucl6ar power plants, 

reheating is typically accomplished by diretiiiig 

the high pressure turbine exhatist through a- heat 

exchanger called a moismre-separator/reheater 

(MSR). The dried and'reheated steam is then 

directed to the low pressure turbine for more 

expansion. A steam- plant cycle incorporating 

reheating is shown in Figure 3-8. 

The heating medium for the MSR is typically 

main steam or high temperature turbine extraction 

steam. After transferring heat to the cooler high 

pressure turbine exhaust in the MSR, the heating 

medium steam remnants are drained to the con

densate system or sent to the main condenser. In 

some plants with feedwaier heating, the heating 

medium steam remnants may also be used in the 

feedwater heaters. 

Removing the moisture from and reheating the 

high pressure turbine exhaust steam prior to send

ing it to the low pressure turbine allows the steam 

expansion to continue to a lower pressure/tem

peature and thereby reduces the effective tern

peratuire for heat rejection during steam condensa

tion. 'The lower heat rejection temperature is 

manifested in a lower condenser pressure that 

peirnits greater steami expansion in the turbines. A 

greater steam expansion extracts more work from 

each pound of steam, which iesults in an improve

ment in cycle efficiency. The effect of reheating 

on the steam plant cycle is shown on aT-S diagram 

in Figure 3-9.

3.3 Basic Heat Transfer Mechansmsaýndd 

Principles 

There are two primary mechanisms of heat 

transfer. conduction and radiation. Convection, 

sometimes referred to as separate mechanism, is 

actually a combination of conduction, radiation, 

and mass transfer. Conduction heat transfer is a 

flow of heat through a body or between bodies in 

direct contact. It results from the transfer of 

kinetic energy by molecular motion. Radiation 

heat transfer occurs when energy is exchanged 

between bodies through an intervening space by 

electromagnetic waves. Convection is the transfer 

of heat between a fluid and a surface by circulation 

or mixing of the fluid. Because convection, de

pends on the fluid's direct contact with the surface, 

the heat transfer between the fluid molecules and 

the associated surface involves the mechanism of 

conduction. 

3.3.1 Conduction 

Conduction is the basic method of heat trans

fer through any solid material, such as th cladding 

around fuel elements or the wall ofa steam genera

tor tube. Conduction is heat transfer from one 

molecule to another molecule. Figure 3-10 shows 

the cladding of a fuel element, with the heat source 

on one side and water on the other. For simplicity, 

the cladding is modeled as a wall. 

The molecules in the metal wall are constantly 

vibrating. As the temperature of the metal in

creases, the energy of the molecules increases and 

the vibrations become stronger. When a hot mol

ecule strikes a cool molecule, energy transfers to 

the cool molecule. This cool molecule, in turn, 

will transfer energy to a still cooler molecule. The 

process continues until a flow of energy or heat 

across the metal wall is achieved. 

The transfer of energy from hot molecules to 

cool molecules is the fundamental pniinciple of 

conduction heat transfer. Therefore, if heat is to be 

conducted, there must be a temperatuie differeince 

between the molecules. If there is no temlperature

USNRC Technical Training Center 3-10 Rev. 0195

Rev. OM9

Power Plant Engineering Course Manual . Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center 3-10
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

difference, no heat will flow. In mathematical terms, 

comes Equation 3-6: 

The fundamental principles of conduction heat 

,transfer can be •~k summarized as follows: (T . T2 

• There must be a temperature gradient (AT) X 

for heat to be transferred through a mate- wheire " 

rial.

The amount of heat transferred per unit 

time will depend upon the thickness (X) of 

the material. If the material is very thick, 

little orno heat will be transferred through 

the wall. .

.* The amount of heat transferred per unit 

time will depend on the area (A)of the 

.-material., 

- -The amount of heat transferred per unit 

time will depend upon the thermal conduc

tivity(k)ofthematerial. A material that is 

a poor conductor of heat or a good insula

torwill have a small k. A material that is 

- - a good conductor of heat or a poor insula

tor will have a large k. 

, With these principles, a-word and a math

ematical equation can be written to describe con

duction heat transfer. The amount of heat trans

ferred is directly proportional to the temperature 

gradient and total area, and inversely proportional 

to the material thickness." 

Heat transfer rate - area x temperature gradient 

material thickness 

To make this proportionality an equality, a 

constant of proportionality can be introduced. 

This constant is the "coefficientof. thermal con

ductivity" or "thermal conductivity'! of the mate

"rial. The expression then becomes: 

"Heat transfer rate = " " , 

thermal conductivity x area x temp. gradient 

. material thickness . -.

this 'expression be

-, "(3-6)

Q = rate of heat transfer (BTU/hr), 

"k = coefficient of thermal conductivity 

(BTU/hr-ft-oF), 

"- - A = areaofsurface (ft2), 

" T1 =higher temperature (OF),* 

"T= lower temperature (OF), and 

X material thickness (ft). 

Equation 3-6 is called Fourier's Law for -time 

independent, steady-state heat flow. 

Thermal conductivity of different materials 

: varies greatly. Metals and alloys have high values 

of k, while most insulatingmaterials such as glass 

wool, cork, and kapok have low values' In actual

ity, thermal conductivity-is somewhat dep6endnt 

upon temperature, and generally increases with 

'increasing temperature. The variation of k with 

temperature in metals-is small, however, aind for 

many crystalline substances the thermal conduc

"*tivity decreases 'with temperature. For most prac

tical purposes, k can be assumed to be constant. 

However, At high temperatures such as those exi t

_ing in reactor fuel, this assumption cfin'tit6duce 

;-substantial error. 

An6ther frequently used term is "heat flux" 

(QIA). Heat flux is the heat flow rate per unit area 

.'rand its units are BTU/hr-ft2. H-Ieat flux is a conve

nient way of expressing heat tranisfer rate on a per 

unit basis. 

Fourier's LaUw is'readily adalpted to-produce 

results in terms of heat flux b'dividinig both sides 

by the area (A), as shown in Equation 3-7:

Q k(T -T 2 )- 

- -A .I-X " .- . - (3-7)

USNRC Technical Training Cenier - - - - 3-11 *Rev. 0195

Power Plant Engineering Course Manual Hint Trzier and Thermal HydrauIlics

USNRC Technical Training ceniiei- .3-11 I Rev. 0195
.Power Plant Engineering Course Manaud

Heat Transfer and The-Ad alr

3.3.2 Radiation 

Radiation is the transmission of energy by electromagnetic waves across an intervening space. 

A body emits electromagnetic waves by virtue of 

its absolute temperature. In general, the body must 

be extremely hot for a substantial amount of en

ergy to be emitted in this form. 

A body having a temperature above absolute 

zero radiates energy. Electromagnetic waves 

emitted by such a body are similar to light waves 

but usually have longer wave lengths. These 

waves may either be absorbed, transmitted, or 

reflected by objects which they strike. In turn, the 

body receives energy from other radiating bodies 

and either absorbs, transmits, or reflects these 

waves. 

Radiation heat transfer can be a significant 

method of energy. transfer wherever very high 

temperatmes are found. Radiation heat transfer is 

quite important in high temperature furnaces and 

internal combustion engines. 

Radiation heat transfer from a body depends 

upon the absolute temperature, of the body, the 

shape of the surface of the body, and a term called 

the, emissivity (ability to, emit) of a body., In 

general, radiation heat transfer from a body can be 

quite difficult to calculate because the net radia

tion heat transferrate is the difference between the 

energy being radiated by a body and the energy 

being absorbed by the body. An important point to 

remember about radiation heat transfer is that the 

radiation heat transfer between two bodies at tem

peratures T1 and T2 is proportional to T1

4 - T2

4, not T1 - T2 as for conduction and convection. 

Radiation heat transfer is not an especially 

_important heat transfer mechanism during normal 

plant operation. One place where radiation heat 

transfer can be important for nuclear reactors is 

following a loss-of-coolant accidents (LOCA) 

when the nuclear fuel is uncovered. Under these 

conditions, the primary means by which the high 

temperature fuel element can cool itself prior to

initiation of Emergency Core Cooling Systems 

(ECCS) is by heat radiation to cooler fuel rods and 

surroundings., Prevention of this condition is one 

reason for the thermal safety limits provided for all 

power reactors. 

3.3.3 Convection' 

Convection is the transfer of heat between a 

fluid and a surface by the'circulation or mixing of 

a fluid. Figure 3-11 shows the convection process. 

In Figure 3-11, a fluid is flowring overa heated wall 

surface. Whenever fluid is in contact with a wall, 

a very thin layer of stagnant fluid exists immedi

ately next to the surface. Such a layer is known as 

a' stagnant- (or fluid) film. The film contains 

several slowly moving layers of fluid only a few 

molecules thick. Any heat passing from the wall 

to the bulk fluid must pass through this film. The 

film's thermal properties are the same as the fluid, 

but thei film's thickness depends on fluid viscosity 

and the fluid flow conditions. The film is thickest 

for free convection and laminar flow. It is thinnest 

during turbulent flow ;ad forced convection. A 

typical film thickness for free convection is 0.04 

inch. 

Heat is transferred across the fluid film in a 

process similar to-conduction. The process'is 

slightly different in that there is a mechanical 

motion of the fli- (albeit slow). Hence, heat "energy is canried away from the surface by two 

mechanisms as follows: 

The physical collision of fluid molecules 

and wall material, thereby transferring heat 

energy in a manner identical to conduc

tion, and 

* The inecham6ical movement of fluid mol

eculeg away from the surface andot iu* into 

the fluid;, where stbied energy is trans

ferred through random collisions with other 

fluid molecules. 

Convection heat trnsfer from the heated sur

face, through the film, and into the bulk fluid, is

%i . ecanum~ A raming Lenter 3--,.Rev. 019.

3-12 Rev. 0195
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

described by the same fundamental relationships 

as conduction heat transfer. The rate at which heat 

"is transferred across the film is proportional to the 

temperature gradient, the thermal conductivity of 

the stagnant film, and the total area from which the 

.heat is transferred.-oThe heat -transfer rate is in

versely proportional to the thickness of the fluid 

film. Fourier's law can be written for the heat 

transfer across the film as Equation 3-8:

- kfA(T. - Tf) 

Xf ,1 (3-8)

where

kf= 

A

Tw= 

Tf

Xftotal heat transfer rate (BTU/hr), 

thermal conductivity of the stagnant 

film (BTU/hr-ft-°F), 

total surface area (ft2), 

wall surface temperattire (-F), 

bulk fluid temperature (OF), and 

stagnant film thickness (ft).

/A hf(rw - Tf) (BTU/hr-ft2). 

If the bulk fluid temperature (Tf) is higher than 

the surface temperature, the heat flux calculated 

by this equation will be negative. This indicates 

that the heat flow is from the fluid to the surface 

(i.e., the fluid is losing heat). 

3.4 Practical Applications of Heat Transfer 

in the Plant 

3.4.1 Physical Parameters of Basic Heat 

Transfer 

Conduction and convection are'the impbrtant 

heat transfer mechanisms in power plants. The 

key factors affecting conduction andc'6fivection 

are temperature difference across the transferring 

material, the thickness of the material, the surface 

area of the transferring material, the iype of mate

rial, and the flow of fluid along the heated surface.

The heat flux equation is Equation 3-9: 

" "Q/A =k 'w-T) , (3-9) Xf 

where Q/A = heat flux (BTU/hr - ft2). 

The use of this on would be simple if not 

for the extreme difficulty of determining actual 

film thickniess (Xf) which depends on 

"Fluid velocity, 

* Fluid viscosity, 

* Heat flux, 

Surface roughness, and 

Type of flow (single- or two-phase flow). 

Because of these difficulties, it is customary to 

combine kf/Xf and call this new term the film heat 

transfer coefficient, (hf). Film heat transfer coef

ficients are normally determined empirically and 

"have units of BTU/hr-ft2 'F. The basic equation 

for heat convection from a surface then becomes:

3.4.1.1 Temperature Difference -',

Heat flows from a high temperature to low 

temperature. This high to low temperature differ

ence is represented by AT. For conduction and 

convection, heat flow is proportional to AT.' The 

relationship between heat flow and AT can be 

expressed mathematically as follows: 

&o T 

Q=KT AT, - " 

where KT is a constant of proportionality. 

Example: 

Heat is being transferred from a source through 

a wall. Assume that 10 BTUs per hour are trans

ferred when the AT across the wall is 50F. How 

much AT is required to transfer 12 BTUs per hour? 

Q cc AT = KT AT

USNRC Technical Training Center 3-13 Rev. 0195

- Power Plant Engineering Course Manual _• •...- .... Beat Transfer and Thermial Hydraulics

USNRC Technical Training Center '3-13 Rev. 0195
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

Q 3.4.1.3 Area 1 AT! 

Q2 AT2 

10 BTU / hr 

12 BTU / hr

AT2 = (50F) 

AT2 = 6*F 

3.4.1.2 Material Thickness 

The heat transfer rate is approximately in

versely proportional to the material thickness. 

This relationship can be, expressed mathemati

cally as follows:

1 Q

Qý=I~SL I 

x 

where KX is a constant of proportionality. 

Example: 

Heat is being transferred at a 20 BTU/hr rate 

through a wall. If the AT across the 'wall rem-ain 

constant, what will be the heat transfer rate if the 

wall thickness is halved? 

X 

Qx, = Q2 X2 ; X2 , 2 

Q=Q ,- 1X I -Q,-, .(2X1 " 2 (20) (2)=40BTU/hr

50F 

"AT2

USNRC Technical Training Center - 3-14 Rev. 0195

The heat transfer rate is proportional to the 

heat traisfer area. If ey6ry other factor involved in 

the heat transfer process remains constant when 

the heat transfer-surface area doubles, the total 

heat traiisfer would also double. Changing'heit 

transfer area is s6methingithat is actually donie in 

the plant. For example, different numbers of 

feedwater heaters are used for operation at differ

ent power levels, as are different numbers of lube 

oil coolers. 

The mathematical relationship is: 

QO=A 

S= KAA, 

where KA is a constant of proportionality. 

3.4.1.4 Material 

The metals in the plant are good conductors. 

An obvious poor conductor is the insulation used 

on the piping and turbine. This insulation keeps 

excess heat from being wasted and keeps the 

building from becoming unbearably hot. 

Other poor conductors are deposits that can 

build up on the walls of heat transfer surfaces in the 

reactor, steam generator, or condenser. If deposits 

build up on heat transfer surfaces, the temperature 

of the heat source mu.st increase to provide the 

larger AT that is necessary to maintain the same 

heat transfer rate. If the heat source is the reactor 

fuel, the higher temperature could cause fuel dam

age unless power levels are decreased. If the heat 

source is the steam ii'thie condenser, an increase in 

the steam temperature would result in a snmaller 

temperature drop across the turbine and reduced 

plant efficiency. 

Heat transfer rate is proportional to thermal 

conductivity. Mathematically, this relationship 

is:

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

USNRC Tecluical Training Center " 3-14 Rev. 0195
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

O= Kkk, 

where K& is a constant of proportionality. 

3.4.1.5 Flow 

Heat is transferred from the walls of the steam 

generator to the water by convection, which in

cludes conduction through the fluid film before 

-the heat enters the moving water. The thicker the 

film, the more- difficult it is for the heat to be 

carnied away from the heated surface.

Water flowing past a surface strips off the 

heated watermolecules sticking tothe surface. An 

-increase in the flow rate causes the removal of 

more water molecules. Thus, an increase in flow 

rate decreases the thickness of the film, which 

decreases the required temperature drop from the 

wall to the moving water. The result is either a 

larger amount of heat transfer or a smaller AT. 

The effects of flow on heat transfer from a heat 

transfer surface into water can be shown on a heat 

transfer curve as in Figure 3-12. Both of the axes 

on the graph are logarithmic because the graph has 

to cover such a wide range. The vertical axis is the 

heat flux (Q /A), the amount of heat transferred per 

-unit time.- The horizontal axis is the AT between 

the surface of the wall and the'bulk of the water. 

The heat transfer curve assumes that pressure, 

flow, and enthalpy are all constant.'If any of ihese 

properties change, the curve will change. 

The solid line A in Figure 3-13 is-a closeup of 

- the convection part of thdeheat transfer curve in 

Figure 3-12. Because the slope of line A is 1; the 

heat transfer rate' doubles if the AT is doubled. -If 

flow is increased, the curve shifts left to line B. If 

- the flow is decreased, the curve shifts right to line 

.C. Thus, for a constant heat transfer rate line D, the 

'.higher flow rate will have a smaller AT.','

-3.4.2 Heat Transfer in Heat Exchangers 

The main area of difficulty in calculating heat 

transferrates in heat exchangers is determining the 

--heat transfer coefficient (h). -The heat -transfer 

coefficient is normally determined empirically for 

different fluids, fluid viscosities, heat flux rates, 

surface roughnesses, and -fluid flow rates. By 

-measuring heat flux and temperature differences, 

values of hf can be found using the heat flux 

equation discussed earlier. These values are then 

tabulated in engineering manuals forconditions of 

common interest. In addition, research has pro

duced formulas that can be used to calculate ap

proximate values ofhf if conditions such as viscos

ity and surface roughness are known. 

In many heat exchanger applications,_ a need 

exists to transfer heat from one fluid, across a solid 

divider surface (a wall or tube), toanother fluid. In 

"1this instance, twIo stagnaint films must be consid

ered. In addition, it is quite common that the fluids 

and their thermal properties differ. ,,Some ex

Saiples of this application .r. thieturbine lube oil 

heat exchangers (oil to water) and the generator 

',hydrogen gas coolers (hydrogen to water). 

Figure 3-14 is a simple sketch of heat transfer 

"in atypical heat exchanger. Fluid I is'hotter than 

flui- 2 'and releases its stored 'energy by heat 

transfer to fluid'2 (note the' thermal gradients). 

For simplicity, most heat exchanger calcula

tions are performed for steady-state conditions. 

Under steady-state conditions the same amount'of 

heat flows through each fluid' stagnant fim-m'as 

flows through the heat exchanger tube Wall. Be

cause most fluids have smaller thermal conduc

tivities than metals, the thermal gradient is'greater 

across ,the fluid films ,than the tube wall. The 

temperature gradients shown.in Figure 3-14 are 

characteristic of all heat exchangers. 

3.4.2.1 Heat-Transfer Across Tube Walls 

To facifitate heat exchanger calculations, an 

overall heat transfer coefficient (U)'is defined.

'."USNRC T&Iiiiical TrainingCenter - <'3-15 Rev. 0195

-Heat Transfer and Thermal Hydraulics Power Plant Engineering Course Manual

-USNRC Techimical TrhiuneinCnter Rev. 0195
Power Plaiit Engineering Course Mnual Heat Transfer and Thermal Hydraulics

The overall heat transfer coefficient is used for 

heat transferbetween two fluids across atube wall 

or several tube walls.: U is an inclusive thermal 

conductivity factor that can be determined for a 

specified combination of fluids; flows, andoperat

ing conditions. By using previously developed 

equations forconduction and convection heat trans

fer, Equation 3-10 that describes the rate of heat 

transfer from fluid 1 to fluid 2 across several tube 

wails can be written:

Q = rh Cp AT, (3-11)

where

0 •= total heat transfer rate (BTU/hr), 

Mh = mass flow rate (Ibm/hr), 

Cp = heat capacity ofthe fluid (BTU/lbm-°F) 

AT = temperature change within the fluid (°F) 

AT = Tout - Tin (within the one fluid).

0 = UA(TI - T2),, 

where

A 

TI 

T2 

U

total heat transfer rate (BTU/hr),' 

total tube wall surface area (ft2), 

fluid 1.temperature (OF)," 

fluid 2 temperature (OF), and 

overall heat transfer coefficient (BTU/ 

hr-ft2-*F).

Equation 3-10 is used to calcul.ate the heat 

transfer rate across a tube wall, or several tube 

walls, as from the reactor coolant to the feedwater 

across the tube walls of a PWR steam generator. 

The value of U incorpo raes the heat transfer 

coefficients -of the fluid films and the' thermal 

conductivity, of the tube wall fiiterial. Typical 

values of U for various heat exchangers found in a 

power plant are: 

6Component U 

Condenser and Feedwater 600 BTU/hr-ft2 -F 

Heaters 

Lube Oil Cooler 40 BTU/hr-ft2-OF 

Air Preheater 5 BTU/hr-ft2-OF 

3.4.2.2 Heat Transfer Within One Fluid 

The heat transfer within one fluid in a heat 

exchanger can be determined using a mass and 

energy approach. The heat transferred by or to a 

single-phase fluid within a heat exchanger can be 

calculat&t -using Equation 3-11:

Equation 3-11 'does not depend upon the area 

(3-10) of the heat exchanger or the heat transfer coeffi

cient. The heat capacity term, Cp, refers to the 

amount of heat contained in each pound-maiss of 

the fluid per OF.

Equation 3-11 is used only for single-phase 

fluid (when there is no change in state within the 

fluid). The variation of Equation 3-Il, used when 

the fluid changes state (boils to steam orcondenses 

to condensate), is Equation 3-12:

(3-12)

where 

h = specific enthalpy of the fluid (BTU/Ibm), 

and enthalpy hour and hin represent the energy 

contained in each pound-mass of the fluid at the 

exiting state and the'entering state. 

3.5 Boiling Heat Transfer 

Boiling heat transfer is heat transferred by the 

boiling of water.. 'Boiling- occurs in the BWR 

reactor and in the PWR steam generator by design. 

During an unusual, transient, large amounts of 

additional core boiling' could occur and safety 

limits could be exceeded; therefore, boiling heat 

transfer is an extremely important topic for acci

dent considerations. Boiling heat transfer is not a 

fourth method of heat transfer, but it is considered 

separately because of its importance. 

Figure 3-15 is the heat transfer curve that was

USNRC Technical Training Center 3-16

Rev. 0195

Power Plint Engineering Course Manual "-Heat Transfer and Thermal Hydraulics

- I - -

rh= (hout - hhn,

USNRC Technical Training Center 3-16
Power Plant Enaineerina Course Manual Heat Transfer and Thermal Hydraulics

-introduced earlier. The area of concentration this 

time is the region above the dotted line that is the 

boiling heat transfer region. The boiling heat 

transfer portion of the curve is steeper than the 

convection portion of the curve. This means that 

more heat is transferred per AT, and heat transfer 

is more effective.- In convection heat transfer, heat 

flow is proporti0nal 'to AT. IFor bo iling heat 

transfer, however, heat flow is" proportional to AT 

to approximately the 4.5 power. 

A microc-opic look at a typical heat transfeir 

surface shows small irregularities called nuele

ation points. Heat is being trinsferred all along the 

"surface, but the heat at a nucleation point is con'

centrated into a small amount of water. When the 

surface temperature gets high enough,. a steam 

-bubble foims, grows, and finally breaks awaiy 

from ihe surface. This is called nucleate boiling. 

Unlike single-phase convection, boiling heattrans

fer is a fast process. During nucleýte boiling thie 

"water absorbs its latent heat of vaporization and 

then moves quickly from the heated surface. 

'There are two requirements for nucleate boil

ing. First, there must be nucleation points so that 

steam bubbles'can form. Second, the 'surface 

temperature must bý about 8 to 10 degreieshigher 

than the saturation temperature of the liquid. If the 

surface is not hoi enough, there will be no boiling, 

and the heat transfer will be only by convection. 

-As each steam bubble is formed, it moves 

away from the wall. If the bulk of the water is at 

a temperature less than saturaton, the bubble will 

cool -and -condense. This is called sub6ooled 

nucleate boiling because the bulk of the water is 

subcooled below the saturation temperature. If the 

bulk of the water is at saturation temperature, 

however, the steam bubble will not cool and con

dense as it moves away. It will remain as a steam 

bubble mixed in the bulk water. This process is 

commonly called bulk boiling or fully, develbped 

-nucleate boiling. 

Convection 'heat transfer, subcoolid nucleate 

'boiling, and bulk boiling are the normal modes of

heat transfer expected during normal plant opera

tion. Another mode of boiling heat transfer is film 

boiling. Film boiling occurs when so much boil

ing takes place that all of the steam cannot be 

removed from the heated surface. NWhen'this 

happens a film of steam forms on the heat transfer 

surface or wall. The steam acts as an insulator and 

"further impedes heat transfer from the wall, result

ing-in an immediate jump in wall temperatuýe. 

.Experiments with film boiling have shown that the 

wall temperature can jump by 25 degrees almost 

instantaneously. Film boiling is an undesirable 

mode of heat transfer in nuclear power reactors. 

The process of going from nucleate boiling to 

fllmboilingis called transitibn boiling. Transition 

bling is shown as a- dot•td line on the heat 

transfer curve in Figure 3-16. The line is dotted 

Ibecause the processis so unstable that the heat 

'transfer process actuallymoves back and forth 

'between nucleate boiling and film boiling. ,The 

amount of heat required to cause transition boiling 

is called the critical heat flux (CHF). This pointis 

also called-the depaiture from"nucleate boiling 

(DNB) point. At DNB, the heat transfer literally 

departs from nucleate boiling. . -. 

"Figure , 3-16 shOws the change in AT that oc-. 

cuirs b6tween nucleate and filmi boiling at DNB. 

Most of the time, the heaitproduc-ed in the reactor 

core' will remain 6onst.int. Therefore, if the film 

biling stage is reached du.ring some transient, the 

wall temperaturewill increase rapidly. This could 

cause the fuel to overheat or "bum out." For this 

"rasdn, niany Safety limiits are included during 

"plant design to prevent film boiling.' 

3.5.1 Physical Prameters of Boiling Heat 

Triinser' 

The plant operator has control overkpressure, 

temnperature, and flow in the plant. A'-hange 'in 

-any 'of 'thesie phys'ic-al pa-ra-meters "can" have' an 

'effect on boiling heat transfer. 

St'-

USNRC Technical Training Center 3-17 Rev. 0195

USNRC Tedinical Training Center 3-17

SHeat Transfer and Thermal Hydraulics Power Plant Engineering Course Manual ... .

Rev. 0195
Power Plant Engineering Course Manual

Heat Transfer and Thermal Hvdranlics

3-5.1.1 Pressure 

If the piressure increases' wile nucleate boil

ing heat tiinfer is taking "place, the saturation 

temperature of the water increases and more heat 

is required for nucleate boilirig to continue.- If 

additional heat is not provided, nucleate boiling 

heat transfer will stop and convection will become 

the primary means of heat transfer. Since nucleate 

boilinig promotes more effective heat transfer, a 

sudden increase in pressure could cause, a corre

sponding increase in the temperature of the heat 

source. 

Figure 3-17 shows the effect of an increase in 

pressure on the heat tramsfeir curve.; Points on 

cuve'A indicate the initial boiling curve. An 

increase in pressure shifts the curve to the right to 

the new boiling curve line B. If heat flux is 

constant in the nucleate boiling region (Q/A)I, a 

higher AT is needed because nucleate boiling has 

been suppiessedby the pressure increase. On the 

other hand, if heat flux is constant in the convec

tion'heat' transfer region (Q/A) 2, a change in 

pressure has little effect on AT. 

If nucleate boiling is takihg place'and the 

pressure suddenly decreases, the saturation tem

peratur decreases, and more boii Wi occur. 

Depeinding upon the initial heat transfer rate, such 

a chanige could improve the heat transfer or could 

cause filni boiling to occur, resultingin a large 

increase in the temperature of the heat source. The 

effect of a pressUre decrease on boiling heat trans

fer is shown in, Figure 3-18. Points on curve A 

represent the in boiling curve. Decreasing 

pressure shifts the curve to the left as indicated by 

curve B. If the initial boiling point is low on the 

nucleate boiling curve such as point C, and heat 

flux remains constant during the pressure de

crease, a AT decrease will occur as point C moves 

to curve B. In this-case' the heat transfer improves, 

and the tempebrature of the heat source is reduced. 

On tIe otherihand, ifthe initial boiling point is high 

on the nucleate boiling curve, such as point D, and 

heat flux remains constant during the pressure 

decrease, a large AT increase will occur as point D

moves to curve B. This shift represent imme

diate departure from nucleate boiling, which will 

cause rapid overheating of the heat source. 

Therefore, a loss of pressure may be a major 

concern for plant safety. A loss of pressure could 

cause immediate film boiling and consequent dam

age to the reactor fuel. For normal plant opera

tions, it is best t6 maiktain a constant pressure and 

make only slow changes in power level. 

3.5.1.2 Temperature and Reactor Power 

The principal direct effect of temperature on 

heat transfer is through AT.' The greater the AT 

between the wall and the bulk fluid, the greater the 

heat transer rate and vice-versa. The temperature 

of the bulk fluid relative to the saturation tempera

ture of the fluid will also influence heat transfer 

because of the differences 'that occur between 

convectidn and boiling heat transfer. The maxi

mum fluid bulk temperature for saturated condi

tions is limited by the fluid saturation temperature. 

An increase in reactor power level will in

crease the fuel temperature. The'resulting in

creased wall temperature will increase the AT, 

increasing the heat transfer rate. 

If nucleate boiling is occurring prior to the 

reactor power increase, additionial nucleate boil

ing and increased heat transfer will occur. If 

parýameters such as pressure and flow remain un

changed, the bulk fluid temperature and heiattans

fer rate will increase as the boiling point moves up 

the heat transfer curve and closer to DNB. IfDNB 

is reached, the heat 'transfer rate will decrease 

rapidly causing a corresponding rapid increase in 

fuel temperature. 

3.5.1.3 Flow. 

If the flow of water is suddenly increased 

during heat transfer, the wall temperature .will 

decrease, which could decrease the amount of 

nucleate boiling.. If the flow is suddenly de

creased, the wall temperature will increase, which

U3L'CAL. l ecnical I raining Lenter 3-18 Rev. 0195

S.............d
Power~~_ Pln Eninern CoreMnaIetTaseradTemlHdal

could cause film boiling dependinig upon the ini

tial heat transfer rate. During plant operations, it 

is best to make only gradual changes to the flow 

rate through the reactor. 

Figure 3-19 shows the effects of a flow in' 

crease on boiling heat transfer. The solid line 

represents the boiling heat transfer curve for the 

initial flow. The dotted line shows the heat trans

fer curve for an increased flow. In the convection 

heat•iransfer region, an'incrase in flow at a 

constant heat flux (Q/A)f results in a decrease in 

AT. This decrease is due to a larger heat tanifer 

coefficient for the higher'flow. An increase in 

flow'also increases the critical heat flux for the 

respective boiling 'cuirve.' This increase occurs 

because the increased flow more readily sweeps 

steam bubbles from the heat transfer surface so 

that a higher heat tiansfeir rate is need for a steam' 

film to form. 

3.5.1.4 Summary of Parameter Effects on 

Margin to DNB 

As indicated in section 3.5, one of the require

ments for reactor safety is the prevention of reach

ing DNB conditions on the reactor heat transfer 

curve. An important duty of the plant operator is 

to contr6l plant parameters such that a safe margin 

to DNB (or distance fromnDNB on the heat transfer 

curve) is maintained. Any sudden, large change in 

the following plant parameter.i/directions will 

DECREASE the margin to DNB: 

• Decrease in reactor coolant pressure,. 

* Decrease in reactor coolant flow rate, 

* Increase in reactor power, -` 'I - ." 

* Increase in reactor coolant inlet tempera

ture. 

Therefore, the function of the operators and the 

plant design is to prevent i suddenilarge change in 

these plant parameters/difections. - ' '

3.5.2 Steam Generation Characteristics 

3.5.2.1 Steam Moisture Content and Removal 

Boiling is the principal heat trahsfer mecha

nisminBWRreactori andPWRstain generators. 

The steam produced may contain a smrall quantity 

of water.' This water is referred to as carryover. 

Carryover has the potential for causing 'erosion of 

steam piping and turbine rotor blading.' 

To prevent canryover, the steain-water mix

ture flows through separators. There are two basic 

types of steam-water separators in use:'

0e Cyclone moisture separator and 

Chevron moisture'separators

Figure 3-20 shows a cross-section of a" cy

clone-type moisture separator. The mixture of 

water and steam flows through fan-shaped blades. 

The higher-density water is thrown to the outside, 

and the steam flows through the middle. The 

cyclone moisture -separator is a v-ery common 

piece of equipment. Several cyclone separators 

are located on top of the heat transferpbrtion 6fthe 

BWR reactor and PWR steam generator, and vir

tually all exiting steam flows through them. The 

Wateris returned to mix wvith the entering feedwater. 

"-'Figure 3-21 shows'a top'view of a chevron

type moisture separator, which is used when there 

are smaller amounts of water in the steam. The 

chevron separator gets its name from the shape of 

its plates. Steam and water pass throughithe 

separator horizontally. The steam flows through 

easily, but the water hits the sides and drains down.' 

This action causes the water and steam to separate. 

The 'steam exits the separator and the water is 

returned to mix with the incoming feedwater. 

The quality of the exiting steam-water mixture 

is used to measure the efficiency of the moisture 

separators. If the quality is 100%, then only steam 

is present; if the quality is 0%, only water is 

present. The BWR and PWR steam separation 

devices provide dry steam with-a quality of 99% or

USNRC Technical Training Center 3-19 Rev. 0195

Power Plant Engineering Course Manual Heai Ti'ansfer ani d Thermal Hydraulics

USNRC Technical Training Center 3-19 S.. .•Revy. 0195
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

greater. 

Sometimes excessive moisture carryover can 

occur. One cause is improper water chemistry. A 

high concentration of impurities will cause large 

bubbles to form when steam is produced. When 

these bubbles collapse, more moisture droplets are 

carried along. Another cause of sudden carryover 

is steam-separator flooding, which can occurif the 

water level is too high. 

3.5.2.2 Water Level Changes 

Two types of sudden level changes occur in 

BWR reactors and PWR steam generators. These 

sudden level changes are called "swell" and 

"shrink." Swell occurs when there is a sudden 

decrease in steam pressure, and shrink occurs 

when there is a sudden increase in steam pressure. 

If the turbine control valves are suddenly 

opened more, the amount of steam supplied to the 

turbine is rapidly increased. This increase in the 

supply of steam to the turbine means that more 

steam is removed from the BWR reactor or PWR 

steam generator than is being produced at the 

moment. This results in a rapid decrease in pres

sure. When the pressure drops, the steam bubbles 

in the water increase in size and some of the hot 

water flashes into steam, creating more steam 

bubbles. Additionally, the temperature is de

creased which. produces a greater AT for heat 

transfer, so more heat is transferred to the water to 

produce more steam. All of these factors cause an 

apparent expansion of the amount of steam-water 

present. This expansion causes a sudden level 

increase called swell. 

If the steam supply to the turbine is suddenly 

reduced, an increase in pressure occurs in the 

BWR reactor or PWR steam generator. Some of 

the steam bubbles in the water collapse resulting in 

a contraction of the steam-water mixture. -The 

contraction causes a sudden level decrease called 

shrink

Swell and shrink are important because a rapid

power change might result in sudden high or low 

water levels.. The feedwater system can compen

sate for these conditions by maintaining a pro

grammed level. Program level is usually high for 

high power and low for low power to account for 

a certain amount of shrink and swell. 

3.6 Reactor Thermal and Hydraulic 

Performance 

The principles associated with heat, work, and 

the movement of water will be applied to the study 

of thermal and hydraulic performance in the reac

tor. Thermal and hydraulic. performance is the 

relationship between the heat that is produced in 

the reactor and the water that flows through the 

reactor and carries the heat to the steam cycle. 

3.6.1 Performance Objectives 

The reactor core consists of a large number of 

vertical tubes made of Zircaloy. These tubes 

enclose (clad) the nuclear fuel, which is in the form 

of ceramic pellets of uranium dioxide. These 

pellets produce the heat in the plant. 

When the reactor is operating, wateris pumped 

through the core, and it flows around the Zircaloy 

tubes. Nuclear fission occurs in the fuel pellets, 

and energy (primarily in the form of heat) is 

released. The heat is transferred from the ceramic 

pellet, through the Zircaloy tube, and into water. 

To begin to understand thermal and hydraulic 

performance, it is necessary to look at heat genera

tion and heat removal in the core and the ways that 

fuel might be damaged during these processes. 

This information will determine the basis of many 

of the technical specification operating limits that 

are designed to protect the plant as well as provide 

the basis for understanding much of the material 

on accidents that is included in the Final Safety 

Analysis Report (FSAR)." 

The basic consideration of reactor core design 

is for water to remove the heat generated by the 

core. One performance goal is to have as much

USNRC Technical Training Center 3-20 Rev. 0195

a

Power Plant Engin,ýring Course Manual , Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center 3-20 Rev. 0195
Power Plant Enginering Course Manual Heat Transfer and Thermal Hydraulics

heat as possible transferred fr6In the fuel to the 

water in the most efficient way. There are, how

ever, certain objectives that must be met in achiev

ing the best possible performance level and ensur

ing fuel integrity. 

The first objective of thermal and hydraulic 

design is to ensure that the fuel will not melt. In 

formal terms, the thermal and hydraulic design of 

•-the plant shouid ensure that the center of the 

-hottest fuel pellet does not melt. Figure 3-22 

shows a line drawn through the middle of the fuel 

* pellets called a "centerline." The highest tempera

ture reached in this area is called the,"peak 

centerline temperature." If this temperature ex

ceeds approximately 5000°F, the fuel will melt. 

(The exact melting temperature will vary slightly 

over core life.) 

SThe second objective of thermal and hydraulic 

design of the core is to ensure that the fuel clad is 

not damaged because the fuel clad is the first 

.barrier against release of fission products to the 

environment. The reactor design should ensure 

that the temperature of.the clad is not too high 

because excessive temperature itself can weaken 

the clad, and because excessive temperature can 

-damage the clad by raising the internal gas pres

sure in the fuel tube. This pressure, in conjunction 

with the high temperature, causes the clad-to 

stretch (strain) slightly. If the strain becomes too 

great, the clad can rupture and release fission 

products. --Normally, the thermal and hydraulic 

design limits the strain of the fuel clad to less than 

1% . ... 

Because fuel and clad damage can occur if 

reactor core temperatures are too high, reactor 

designers have to consider the causes of excessive 

'temperature. The two pri mary causes of excessive 

temperature are excessive peak power and film 

boiling. - .

If too much power is produced, that is, if the 

nuclear fuel produces too much heat, the tempera

ture of the clad and the fuel rise to the point where 

they can be damaged. Damage from too much

power is prevented by establishing design limits 

that are defined in terms of power produced. 

Film boiling can cause excessive fuel tem

perature. As described earlier, water goes through 

a transition just after the departure from DNB 

-point, and film boiling occurs., Thus, to prevent 

damage from film boiling, additional limits are set 

for heat and temperature in the reactor core water 

in terms of DNB. The overall objective is that the 

water should not approach the conditions at which 

the transition to film boiling occurs. 

One of the causes of film boiling is the produc

tion of too much heat in the fuel. To understand 

how excessive heat creates excessive temperature 

and affects core design, it is necessary to examine 

how heat is generated and'distributed in the core. 

-Heat is produced by uranium fissions in the fuel, 

but this heat is not produced evenly throughout the 

core. This means that local power ,levels vary 

-throughout the core.: Thus, the local power in the 

core is determined along the vertical and -radial 

axis of the core. The distribution of power levels at 

different points in the core is called power distri

bution, and the variance from average power is 

called power peaking. 

Power peaking involves a factor called the 

nuclear peaking -factor (NPF). The NPF is the 

power of any local point in the core divided by the 

average power of the entire core as described in 

Equation 3-13: ° - , .. - . 

NPF = local power (3-13) 

- average power --

Another factor is the maximum nuclear peak

ýing factor (MNPF). The MNPFis the highest local 

power divided by the average power. -This is 

shown in Equation 3-14. 

MNPF = highest local power (3-14) 

- - average power * 

- The MNPF represents the power being gener

ated at the hottest point in the core compared with

USNRC Technical Training Center 3-21 Rev. 0195

-Heat Transfer and Thermal Hydraulics Poirer Plant Engineiering Course Man"a

USNRC Technical Training Center 3-21 Rev. 0195
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

an average point. .I the MNPF gets too high, the 

fuel could be damaged. Even though the average 

power generation might be well within the limits 

for fuel safety, the local power at one point in the 

reactor might be high enough to cause damage. 

The power in the reactor is measured in units 

of kilowatts. Using these units, the arerage power 

generated per foot in the core can be calculated as 

shown in the following example. 

The first step in calculating the average power 

per foot is to multiply the total reactor power in 

megawatts by 1000 -to obtain the total reactor 

power in kilowatts. 

(reactor power in MW) x: (1000 kWIMW) 

"= (reactor power in kW) 

The total reactor powerin kilowatts divided by 

the number of fuel rods in the core yields the 

average power in kilowatts produced by each rod. 

(total power in kW) + (number of rods) 

- (average kW per rod) 

The final step is to divide the kilowatts per rod 

by the length in feet of each rod. This yields the 

average heat generation rate in kilowatts per foot 

of fuel rod. 

(average kW per rod) + (length of iod in ft) 

= (average kW per ft) 

Because power is not produced evenly in the 

reactor, it is also necessary to determine the maxi

mumn heat that will be generated locally. This is 

done by multiplying the average kilowatts per foot 

by the MNPF. 

(average kW per ft) x (MNPF) = (peak kW per ft) 

The result of this calculation is the maximum 

local heat generation rate or the peak kilowatts that 

will be produced in one foot of fuel rod.' These

calculations can be used to determine how much 

heat the hottest part of the reactor will be generat

ing. Reactor designers use the same relationships 

to determine limits in the reactor to avoid damage 

to the clad and the fuel. 

Fuel damage will occur when the centerline 

temperature of the fuel exceeds approximately 

50000F. To determine: how much heat must be 

generated to produce this temperature, reactor 

designers must consider more than just the highest 

I6cal power generated. Other considerations in

clude heat transfer factors specifically, the thermal 

conductivity of the fuel, the conductivity of the gas 

between the fuel and the clad, the conductivity of 

the clad, and the efficiency of the heat transfer 

from the fuel to the water. 

A major difficulty in considering safety limits 

for heat generation in the core is that the factors 

involved in heat transfer do not remain constant 

over the life of the fuel. The conductivity of the 

fuel changes during irradiationi. Cracks that form 

on the surface of the fuel pellets tend to decrease 

their heat transfer capability. Fuel pellets swell as 

time passes. This swelling decreases the gap 

between the pellets and the clad and tends to 

improve heat transfer. Thus, it is not only the 

factors involved in heat transfer, but also the 

changes in these factors' that must be taken° into 

account in reactor design. 

3.6.2 Depart e from Nucleate Boiling 

Reactor designers must set thermal limits that 

will prevent film boiling. Excessive temperatures 

in the reactor core can be caused by the generation 

of too much heat and/or film boiling. 

To accountlfor the possibility of film boiling, 

reactor designers have developed a ratio called ihe 

departure from nucleate boiling ratio (DNBR) as 

shown in Equation 3-15: 

DNBR'= critical local heat flux at DNB ioint 

actual local heat flux (3-15)

USNRC Technical Training Center 3-22 Rev. 0195

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center 3-22 -Rev. 01I95
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

The DNBR establishes howhigh local hea 

eration in the reactor can be before film b 

occurs. In actuality, the reactor is desigi 

ensure that the departure from nucleate b 

point is never reached. 

-•Exgample: 

Assume that enough heat will be generi 

'reach the DNB point when the local power n 

27 kilowatts per foot. Calculate the DNBR 

the actual local power is 9 kilowatts per fo 

DNBR - critical local heat flux 

actual local heat flux 

DNBR-= 2,7 2- g. 

at gen

oiling 

ned to 

*oiling 

ited to 

caches 

when 

Ot.

9

DNBR= 3,

Filmboiling does not occurwhen the DNBRis 

--3. However, if the actual local power increases to 

27 kilowatts per foot, theDNBRwill drop to l, and 

film boiling is just about to occur. 

DNBR= 27= 1 

--27 

'In many plants a limit for the DNBR is set at a 

value greater than 1.0 to provide amargin of safety 

and to ensure that DNB will never be reached by 

excessive heat generation. Maintaining the rec

ommended DNBR is one of the most iniportant 

thermal and hydraulic aspects of safe reactor op

eration. 

Excessiveheat gen Ieation is not the only cause 

of film boiling. Other causes depend on whether 

or not certain factors exceed their design" limits. 

Some of these factors are related to the water 

properties,, the flow, the'pjressure;-the inlet tem

perature, etc. Additional factors are related to the 

"physical design of the water flow passagei. Thus, 

factors such as manufacturing tolerances in all 

parts of the reactor must be considered. In many 

cases, all of the water-related factors are consid-

-ered in relation to the amount of heat generated 

(the nuclear factor). It is important "to include 

every consideration in the reactor design calcula

tions to ensure that film boiling does not occur in 

,the core. 

As has been mentioned, film boiling can occur 

. in different ways and can involve different factors. 

; The examination of some of these processes can 

begin with a look at the flow of water past the fuel 

rods as shown in Figure 3-23. Water enters the 

reactor core where heat is produced and flows 

-.between the fuel rods. It is subcooled, and heat is 

transferred by convection. As the water moves 

past the fuelrods, its temperature rises. Subcooled 

- nucleate boiling and then bulk nucleate boiling 

occur.-The flow at this point is often called bubbly 

flow because bubbles flow with the water., If the 

total flow is low, film boiling may occur. During 

film boiling a layer of bubbles (not actually a film) 

forms along the fuel rod and prevents water from 

contacting with the wall of the fuel rod. The 

-:.temperature of the rod and the fuel increase, and 

both can be damaged. With normal heat transfer 

rates, this condition only occurs when the flow-of 

water through the reactor is very low.- Normal 

operating conditions provide sufficient flow to 

prevent film boiling.. . 

Heat is constantly added as the water-steam 

-bubbles move along the fuel rod, and the bubbles 

:join together to form larger and larger bubbles. -If 

:the flow is reduced or if the heat being transferred 

"is too high, the bubbles may become large enough 

to fill the whole area between the fuel rods. The 

rods are alternately wet and dry as these bubbles, 

followed by slugs of water, pass by. This is called 

slug flow. - ,.. 

If boiling creates so much steam that the steam 

fills the whole central area and the only water left 

is a thin layer between the walls of the fuel rods, 

rthe flow is called annular flow.' A phenomenon 

called dryout occurs when all the.water has been 

boiled farther up in the core and heat can only be 

transferred to steam. If this happens, the heat 

transferred rate is reduced, the temperature of the

USNRC Technical Training Ceiter 3-23 Rev. 0195

3-23

"-Powier Plant Enigineering Course Manual Heat Transfer and Thermal Hydraulics

."USNRC Teciiial& Training Ceif'ter Rev. 0195
Power Plant Engineering Couzse Manual Heat Transfer and Thermal Hydraulics

clad increases', and the clad and the fuel may be 

dmaged. 

Since dryout and film boiling have the same 

effect on the fuel and the clad, the two are usually 

grouped together. The two most important vari

ables involved are heat transferrate and flow. Any 

time that the heat generated is too great or the flow 

is too low, the DNB point can be reached and film 

boiling may follow. 

Other factors that are important in limiting the 

approach to the DNB point include the pressure 

and the inlet temperature of the water. During 

routine operations, thereisusuallynotmuch change 

in these factors. However, during some accidents, 

the pressure and inlet temperature may change 

enough to reach the DNB point. 

During steady-state operations, the water in 

the core is hot and at high pressure. if the pressure 

drops suddenly, as is possible during an accident, 

an occurrence similar to the, "swelr" that was 

described earlier would occur. As previously 

discussed, the pressure drop in itself is enough to 

cause film boiling. In addition, the decreasing 

pressure would also cause large amounts 6f steam 

to form, and this cotld lead to dryout. 

The water that enters the core contains consid

erable hea. If the temperature of the inlet-water is 

too high, the heat added by the fuel in the reactor 

will'cause too much boiling in the ieactor., This 

excessive boiling could, again, lead'to dryout and 

fuel "bum out." 

The conditions at each point in the reactor core 

are unique and, therefore, the calculation of the 

CHF is difficult. The CIIF must be calculated for 

every poi't with the expected operating condi

tions at that point. The point used for determining 

plant operating limits Will be the one that reaches 

the DNB point first.' Of course, the ifmbsf critical 

location iii the reactor may vary with changing 

ope"dihig conditions. Norimlly, however, plant 

safety analyses and operating procedures will give 

the values for only the worst case, and the point

itself will not be located. 

3.7 Reactor Plant Heat Balances 

A reactor plant heat balance, which is also 

called a primary plant calorimetric, is performed 

to determine the thermal power being produced by 

the reactor core. A calorimetric is done frequently 

in a nuclear plant to provide a reliable point of 

comparison fornuclearinstrumentation. Although 

nuclear power levels can be read directly from 

nuclear instrumentation, nuclear instrumentation 

has a tendency to drift. The reactor plant calori

metric is used to keep the nuclear instrumentation 

accurate. 

Heat balances are often done by the unit com

puter, but operators must know how to do them by 

hand. This is necessary for several reasons. (1) 

Hand calculations provide a backup to the com

puter, if it fails. (2) Hand calculations are often 

done to ensure that operation is within the techni

cal specifications limit. (3) The reactor heat lial

ance is a basic concept of power plant operation. 

3.7.1 PWR Heat Balance 

Figure 3-24 shows a typical PWR reactor 

system and identifies the important parameters 

used fora PWR heat balance. The heat bilance for 

this PWR is give n by the following equation: 

QC= Og+Q Q b 

where 

C = core thermal power (BTU/hr) 

Q sg = heat delivered to the steam 

generator (BTU/hr) 

Q rais = miscellaneous heat losses 

Qp = heatinputfrommain coolantpumps 

(BTU/hr). 

(•bh = heat input from pressurizerbackup 

heaters (BTU/hr)

USNRC Technical Training Center 3-24 Rev. 0195

Power Plant Engineering Course Manual I Heat Transfer and Thermal Hydraulics

USNRC Techical Training Center 3-24 Rev. 0195
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

The first important point to note is that a 

calorimetric must be performed while the reactor 

plant is at steady state power. This is necessary to 

ensure that a transient condition does not lead to a 

false calculation. 

In a typical PWR heat balance, several factors 

are either assumed to be constant or are considered 

to be insignificant. -The power input from the 

reactor coolant pumps ((&p) is typically consid

ered to be a known constant that has been deter

mined from pri6i plant testing. Similarly, the 

miscellaneous heat loss is considered to be another 

known constant determined from prior plant test

ing. Another assumption is that the plant is oper

ated in such a manner that only the pressurizer 

backup heaters are energized. The backup heater 

heat input (( bb) is then determined from the time 

the backup heaters are energized during the heat 

balance. Lastly, the above expression is based on 

the assumption that steam generator blowdown is 

secured during the heat balance. 

"As an example, assume the following average 

temperatures and pressures were determined dur

"ing a heat balance.

P _ sg = 000 psia 

"=15x1O6 lbm/hr (total for all 

steam generators)Y

= 440°F

Backup hiaters are energized 50% of the time. 

The enthalpy of the main steam (hms) from the 

steam generators can be determined using the 

saturated steam tables (assuming 100% quality): 

h• =tg at 1000 psia 1193 BTU/Ibm 

The enthalpy of the feedwater (hfw) entering 

the steam generators can also be determined using 

the steam tables: 

h- " hf at 440 F =419 BTU/lbm

Therefore- -the heat delivered to the steam 

' generator (• sg) can be calculated using Equation 

3-12: %

Q3 =mfr (h,.'7 h.)

6 lb (1 3 19)BTU - - (19 Ibm 

hr =_1 1l,610.x10 BTUI_ . 

-Further, assume that (pand mscare- knio wn 

"from prior testing to be 64.1 x 106'BTU/hr 'and 

7.71 x i06 BTU/hr, respectively. Also, the input 

power of the pressurizer backup heaters is known 

to be 1200 KW while energized. Therefore, 

S= . 64.1 x 106 BTU/hr, 

Qmisc= 7.71 x 106 BTU/hr 

bb = (1200KW)(.5) 3 4 13 BTU/hr 

= 205 x 106 BTU/hr 

Therefore, the core thermal power (Q c) can be 

calculated: 

6= (1,610÷7.71-64.1-2.05) x-10 

- 11,55.5 x 10 BTU Lhr 

3.413 x 106 BTUIhr/MW

-.5

(QC = 3385 MW

Percent Reactor Power = (100%) 3752 

Percet Rector3385, Prcent Reactor Power= (- 100%) = 90.2% 

3752

'USNRC Technical Training Center 3-25 - Rev. 0195

Power Plant Engineering Course Manual Heat Transfer and Therinal Hydraulics

"I USNRC Technical Training Center - " ":'Rev. 0195 -'3-25
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydrauli.Correct performance of heat balance calculations 

is vital because a heat balance is the standard by 

which the nuclear instrumentation is calibrated. 

For example, suppose (hypothetically) that the 

levels in the steam generators were allowed to 

drop from a high level to a low level during 

performance of a heat balance. This would affect 

the calculations because the feedwater flow would 

be less than the steam flow. The calculated power 

production would be less than the true power 

production. Enthalpy rise is multiplied by 

feedwater flow to find power. In this case, 

feedwater flow would be artificially low, so calcu

lated power would also be low. If the nuclear 

instruments were indicating true power, they might 

be incorrectly adjusted to indicate a lower power. 

This is whY, heat balance 6alculations are checked 

and'double-checked. 

3.7.2 BWR Heat Baliaice 

Figure 3-25 shows a typical BWR reactor 

system and identifies the important parameters 

used for aBWR heat balance. The heat balance for 

this BWR is given by the following equation: 

QC - f,. (h= ,- hf.)+ iid (h= - hd) 

+n =(hi. - h.,) + (ýfl- Q 

where: 

Q€ C= core thermal power (BTU/hr) 

hms= hg = the enthalpy of the main steam 

(BTU/Ibm), 

io ¢C = the cleanup demineralizer flow 

(lbm/hr), 

h. = the enthalpy of the flow to the 

cleanup'demineralizer (BTU/Ibm),

"hCt =the enthalpy of the flow from the 

cleanup demineralizer (BTU/lbm),

(5fl = the fixed heat losses from the 

reactor (BTU/hr),

i f,, = the feedwater flow (Ibm/hr), 

hfw, = the enthalpy of the feedwater 

_ (BTU/Ibm), 

(ýp = the recirculation pump energy 

input (BTU/hr), 

rf rd = the control rod drive flow to the 

reactor (BTU/Ibm), and 

hrd = the enthalpy of the control rod 

drive flow to the reactor (BTU/ 

Ibm). 

The equation assumes that all of the cleanup 

flow is returned to the reactor. 

As was the case for the PWR, the calorimetric 

must be performed with the plant at steady state 

power to ensure a transient condition does not lead 

to a false calculation. 

The feedwater flow value is taken from a 

calibrated fl6w meter, which automatically com

pensates for temperature. This is the most impor

tant parameter in the heat balance, and extreme 

care must be taken to make sure that it is accurate. 

Recirculation pump power is obtained from cali

brated megawatt meters. 

In practice, several of the terms of the heat 

balance are treated as constants because system 

operation is nearly constant and because the terms 

themselves do not significantly affect the heat 

balance calculation. These terms are the control 

rod drive energy input, the cleanup demineralizer 

heat extraction, and heat losses from the reactor. 

Feedwater flow can be measured more accu

rately than steam flow. Thus, steam flow is evalu

ated by measuring the feedwater flow and the 

control rod drive flow to the reactor with a con

stant water level. The BWR heat balance equation

USNRC Technical Training Center 3-26 Rev. 0195

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydrauli'cs

USNRC Technical Training Center 3-26 Rev. 0195
includes more terms than the PWR, but the method distribution shape, and the suitability of the call

of solving proceeds in the Same manner. brating heat balance. The'main advantage of this 

-meth6d is the short response time of the nuclear

When core power is low, or when an approxi

mate core powervalue is needed quickly, a simpli

fied determination method can be used. These 

methods should be used cautiously, and it should 

be noted that they are only approximations of true 

core power. There are three methods for approxi

mating core power. 

The first method uses the following simplified 

equation: 

Q = m.f (hms - hN) + constant. 

The constant in the equation includes the heat 

losses and gains caused by the cleanup demineral

izer system, the recirculation pumps, and the con

trol rod drive flow. These and other fixed losses 

can be considered as a single combined fixed. 

quantity because all have a standard mode of 

operation. When this constant is used, the total 

operating condition of the plant must be consid

ered. Any nonstandard occurrences such as 

feedwater heaters being out of service must be 

considered before the core power value can be 

given any degree of reliability. 

With the second simplified method, core ther

mal power is related to plant electrical output. 

Core power and electric generator output are plot

ted on a graph, and then the graph can be used for 

a quick determination of core power for given 

generator outputs. Animprovement on this method 

involves the use of a family of curves with con

denser cooling water temperature as the other 

variable if there is a sizable seasonal variation in 

temperature. As with the first method, the total 

operating condition of the plant must be consid

ered. 

The third method determines core power from 

nuclear instrumentation. The accuracy of this 

method may depend on the number, type, location 

of neutron sensors, the stability of the power

instrumentation. 

3.8 Natural -Circulation in Reactors 

"Natural circulation flow can occur inPWR and 

"BWR iractbrs;- Natuial -circulation provides a 

capability for removing heat and prev enting ex

cessive fuel and cladding temper'atures when the 

"reactor cooling-pumps are not available tfoprbyide 

'forced circulation heat removal. The'conditions 

and places whire natural circulation occurs differ 

somewhat depending upon the reactotypei . How

ever,; the natural circulation'mechaniism is -the 

same. 

"Figure 3-26 is a schematic for the natural 

circulation that can occur betweenfa PWR'reactor 

and steam generator. Establishing natural circula

tion flow requires that a heat source and a heat sink 

.be present ifi the system and that the elevation of 

":the heat sink be higher than the eievatibn of the 

"heat source. The beat sink capacity must also 

match or exceed the heat source output.' 

In Figure 3-26 the driving head providing 

natural circulation in the primary system is pro

duced by the force of gravity and water density 

differences. As the coolant absorbs heat in the 

reactor, coolant temperature increases and coolant 

density decreases. In the steam generator, the 

coolant transfers its heat to the secondary system 

and reaches its minimum temperature (Tc). The 

colder, denser water then returns to the reactor. 

The difference between the density of the cold leg 

and the hot leg water produces the pressure differ

ential or driving head for the flow. 

The heat source" for natural circulation flow 

for PWR and BWR reactors is the reactor core. 

For PWRs the natural circulation heat sink is the 

steam generators, which transfer heat to make 

steam. The steam is dumped to the main con

denser through the turbine bypass valves, if pos

sible, or to atmosphere through the atmospheric

- USNRC Technical Training Center :3..27 - Rev. 0195

2

•:-:"2 : 2 --- " - ,Rev. 0195

', Power Plant Engineering Course Manual He~at Tranider and The-ina IHydraulics

SUSNRC Technical Training Center i3-27
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

dump valves. (The turbine bypass valves are 

preferred because this method maintains the sec

ondaiy water inventory, and the possibility of a 

radioactivity release to the environment is mini

mized.) 

Natural circulation plays a smaller, but still 

important, role in BWRs. If the reactor recircula

tion pumps trip during power operations, the reac

tor is scrammed, and the principle of natural circu

lation enables the cooler feedwater from the annu

lus to flow into the core, where it boils and cools 

the core. The steam then leaves the core and is 

replaced by more cool water from the annulus. 

When the reactor is in cold shutdown, a form of 

natural circulation may be used to prevent thermal 

stratification (lack of vertical mixing of the cool

ant in the core) and possible vessel pressurization 

if the shutdown cooling system is inoperable. To 

obtain this circulation, the vessel level is raised 

above the moisture separator skirt to allow natural 

circulation up through the core, into the annulus 

via the skirt drains, and then back into the core. 

With natural circulation established; an alternate 

heat sink, such as the Reactor Water Cleanup 

system, may be used to remove the heat from the 

core coolant.

UINKL lecimical Training Center 3-28

3-28 Rev. 0195

",.Power Plant Engineering Course• Manual. Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

Chapter 3 Definitions

SUBCOOLED NUCLEATE 

BOILING 

BULK NUCLEATE BOILING

ONSET OF TRANSITION 

BOILING 

CRITICAL HEAT FLUX

- Boiling characterized by the formation of steam 

bubbles on a heated surface that move away from the 

surface and collapse in the bulk stream, where the 

water is cooler than the saturation temperature. 

- Boiling characterized by the formation of steam 

bubbles on a heated surface that move away from the 

surface and mix with the bulk stream water, which is 

at saturation temperature. 

- That heat flux at which boiling begins to change from 

nucleate boiling to film boiling. 

- The heat flux at which transition boiling begins, 

which is also the heat flux at which the departure 

from nucleate boiling occurs.

USNRC Technical Training Center 3-D Rev. 1295

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center 3-D Rev. 1295
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

WORK 

OUT

E*> 

HEAT 

IN FROM 

REACTOR

WORK 

IN

HEAT 

OUT

Figure 3-1. Basic Steam-Water Power Cycle

USNRC Technical Training Center 3-29 Rev. 0493

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center 3-29 Rev. 0493
Power Plant Engineering Course Manual 

T 

I

o 0 STEAU G -

n

rr CONDIENSER• 

uJ 

L.U 

IHeat Transrer and Thermal Hydraulics

aIN

ENTROPY S

0 ADDED IN STEAM GENERATOR = 01-2 = % 

Q REJECTED IN CONDENSER = Q 3-4 OUT 

IN OUT 1-2 3-4 

Figure 3-2. Simple Power Cycle

USNRC Technical Training Center 3-31 Rev. 0493

USNRC Technical Training Center 3-31 Rev. 0493
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

h - ENTHALPY 

P-PRESSURE 

T - TEMPERATURE

SATURATION 

DOME .

h3 h2 

I I 

I I 

I 1 

I I

STEAM -WATER MIXTURE

ENTROPY S

THERMODYNAMIC PROCESSES

1-2: 

2-3: 

3-4: 

4-1:

HEAT ADDmON IN STEAM GENERATOR 

STEAM EXPANSION IN TURBINE 

HEAT REJECTION IN CONDENSER 

PRESSURE INCREASE IN PUMP

Figure 3-3. Temperature-Entropy Diagram 

for Analysis of Simple Steam Cycle

USNRC Technical Training Center 3-33 Rev. 0493

I

'U. 

0 

U)

- --. a

Heat Transfer and Thermal Hydraulics Power Plant Engineering Course Manual

USNRC Technical Training Center 3-33 Rev. 0493
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

II M7=7 

. • : 

-==• 4 

. -77

S

- .

-. 4 

-

... i 

a a t

U 

till! IiE

" , - 1MpI -- 'l.. I -" " 'j -

* .; z..fly..

U, - - . -

Mawr

Figure 3-4. Mollier Diagram

Rev. 9493 

USNRC Technical Training Center 3-35

W

Rev. 0493 USNRC Technical Training Center

& 5A . , .

>iF

. I ý; MT p- '5 '-! ý5,

m •

€

3-35

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

POINT 1 ubpl 

P = 1015 psla REACTOR 

SI ~OR STEAM 

GENERATOR 

WORK 

FEED 

PUMP 

POINT 4 

"P = 28 in. Hg Vacuum = 1 psia 

T= 101aF 

Figure 3-5. Basic Steam Cycle

USNRC Technical Training Center 3-37 Rev. 0195

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center 3-37 Rev. 0195
Power Plant Engineering Course Manual 

T 

0 

C 

t

'U 

0~ 

CfJ 

I

< 01-7

RITICAL 

POINT

ENTROPY - BTU/Ib - OR S

Figure 3-6. T-S Diagram for Basic Steam Cycle

vt-.-. t.Afl2 

USNRC Technical Training Center 3-39

Heat Transfer and Thermal Hydraulics 

,P = 1015 psia 

Ole = 28 In Hg VACUUM 

= 2 in Hg ABSOLUTE

Rev. V*993q 7

USNRC Technical Training Center 3-39
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

p = 1015 psla

SUPERHEATED 

VAPOR

I /

PCONDENSER 

= 28 In Hg Vacuum 

= 2 In Hg Absolute

3S LUQUID AND VAPOR

ENTROPY - BtUIb - OR 

Figure 3-7. H-S Diagram for Basic Steam Cycle

USNRC Technical Training Center 3-41 Rev. 0493

H

I

.0 

I

z LU

POINT

3

S

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center 3-41 Rev. 0493
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

FEED PUMP FEEDWATER CONDENSATE 

HEATER PUMP

Figure 3-8. Steam Cycle with Feedwater Heating and Reheating

USNRC Technical Training Center 3-43 Rev. 0194

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center 3-43 Rev. 0194
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

ENTROPY BTU/lb - OR

STEAM 

REHEATING

S

Figure 3-9. T-S Diagram for Steam Cycle (Ideal) with Feedwater 

Heating and Steam Reheating

USNRC Technical Training Center

C 

I

IUj 

tu 

II - -a

Power Plant Engineering Course Manual Heat Transfer and Thermal1 Hydraulics

Rev. 0194 3-45
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

T1 

HEAT 

SOURCE

INSIDE OUTSIDE

WATER

Ti = Inner Temperature 

T2 = Outer Temperature 

X = Material Thickness

DIRECTION OF 

HEAT FLOW 

Figure 3-10. Heat Conduction Through a Plane Wall

USNRC Technical Training Center 3-47 Rev. 0194

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center 3-47 Rev. 0194
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

STAGNANT FLUID 

FILM

A

INFINITE WALL

DIRECTION OF 

HEAT FLOW 

Figure 3-11. Convection Heat Transfer From a Surface

USNRC Technical Training Center

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

3-49 Rev. 0194
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

0 

.. I 

It 

'C 

-J 

LI

I

0 

-J

CONVECTION REGION (SINGLE PHASE)

LOG AT = LOG (TWALL - TBULK) 

Figure 3-12. Heat Transfer Curve

USNRC Technical Training Center 3-51 Rev. 0194

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center 3-51 Rev. 0194
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

HIGHER FLOW: 

SMALLER AT 

Ole 

.0e 

A //

3

0e

LOWER FLOW: 

HIGHER AT

LOG AT= (TWALL- TBULK) 

Figure 3-13. Effect of Flow on Convection Heat Transfer

USNRC Technical Training Center 3-53 Rev. 0195

.0 

0 

-J 

II 

-J

Heat Transfer and Thermal Hydraulics Power Plant Engineering Course Manual

USNRC Technical Training Center 3-53 Rev. 0195
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

IN 

II 

II 

II 

Ir~ 

Ilz•

WAL

T4 

FLUID 2 xw 

Xw X2

Fluid One Temperature 

Tube Inner Surface Temperature 

Tube Outer Surface Temperature 

Fluid Two Temperature 

Fluid One Film Thickness 

Tube Wall Thickness 

Fluid Two FilmThickness

DIRECTION OF 

HEAT FLOW 

Figure 3-14. Heat Transfer for a Typical Heat Exchanger

USNRC Technical Training Center 3-55 Rev. 0194

FLUID 1

I 

I I 

lI 

II 

Ix=! 

Iz 

I I

i I 

I 

Ix

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center 3-55 Rev. 0194
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

Bulk

/Boiling Heat Transfer (Two Phase) 

Convection Heat Transfer (Single Phase)

LOG AT= LOG(TWALL-TBULK) 

Figure 3-15. Boiling Heat Transfer

USNRC Technical Training Center 3-57 Rev. 0195

Subcooled 

Nucleate 

Boiling N

.0 

x 

LL

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center 3 -57 Rev. 0195
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

Change in AT 

Between 

Nucleate and 

Film Boiling

-O 

II 

-I 

IL. 

I

,-z

LOG AT= LOG( TWALL - TBULK) 

Figure 3-16. Transition Boiling

USNRC Technical Training Center 3-59 Rev. 0195

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center 3-59 Rev. 0195
Pnwer plant EFnoineering, Course Manual Ha rnfradTemlHdalc

AT INCREASE 

DUE TO PRESSURE 

INCREASE 

B 

J" A 

I . ' • 

I / 

-2 .-Z € -- -.-. -. - .- . .- .-.- . . -o-A) ..-.- 

L .. /CONSTANT HEAT FWX IN NUCLEATE 

_. _C.ON .ST A .NT _HE.AT FLUX I . 

BOUGHATTASE REGION2 

LOG AT = LOG (TWALL - TBULK) 

Figure 3-17. Effect of a Pressure Increase on Boiling Heat Transfer

USNRC Technical Training Center 3-61 Rev. 0195

Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center 3-61 Rev. 0195
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

AT INCREASE FOR 

/PRESSURE DECREASE

--J 

U 

-J 

LL.

AT DECREASE FOR 

PRESSURE INCREASE

LOG AT = LOG ( TWALL- TBULK) 

Figure 3-18. Effect of a Pressure Decrease on Boiling Heat Transfer

USNRC Technical Training Center 3-63 Rev. 0195

Power Plant Engineering Course Manual Beat Transfer and Thermal Hydraulics

3

! 1 

! 

I

/0'ý -,

USNRC Technical Training Center 3-63 Rev. 0195
Power Plant Engineerin~g Course Manual Ha rnfradTemlHdalc

INCREASE IN CRITICAL 

HEAT FLUX DUE TO 

INCREASE IN FLOW 

AT DECREASE 

DUETO FLOW ' 

INCREASE 

-j/ 

II 

x/ 

- - p CONSTANT HEAT FLUX IN - -1 

CONV*'EC•T"IVE HEA"T ITR"AlNS-FR RE'GION •'A 

0 

LOG AT= LOG (TWALL - TBULK) 

Figure 3-19. Effect of a Flow Increase on Boiling Heat Transfer

Rev. U19

USNRC Technical Training Center 3-65

3-65

Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center Rev. 0195
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

WATER STEAM WATER 

I i 

I I 

1 I 

1 I 

I 1 

STEAM AND WATER 

Figure 3-20. Cyclone-Type Moisture Separator

USNRC Technical Training Center 3-67 Rev. 0194

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center Rev. 0194 3-67
j4 

C4 

c-

'ti. 

"4 

0 

4J 

a' 

%0 a

4J 

U U

3... 

0 

4J 

I-. 

U, 

.5 

0 I

4., 

C", 

4., I-
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

I I 

I

CLAD 

__ _- FUEL PELLET 

_ _ CENTERUNE

I

Figure 3-22. Fuel Arrangement Showing Centerline

USNRC Technical Training Center 3-71 Rev. 0194

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center Rev. 0194 3-71
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

*. ANNULAR FLOW 

LIQUID"---" 

FUEL 

FUEL 

VAPOR. t

FUEL

sue U. 

FUEL

FUEL

t

FUEL

b. SUBCOOLED BOILING 

FUEL FUEL 

t.•,

1) VAPOR FORMS A CONTINUOUS 

PHASE IN THE SPACE BETWEEN 

FUEL ELEMENTS ISATURATED 

VAPOR) 

2) SLOWER MOVING LIQUID TRAVELS 

ALONG THE FUEL ELEMENT 

SURFACE 

3) EXPERIENCED NEAR CHANNEL 

EXIT IN HIGH POWER CHANNELS

1) BUBBLES ARE FORMING ON 

WALL AND COALESCING TO 

FORM VAPOR -SLUGS" IN 

MIDCHANNEL 

2) SIGNIFICANT VOID FRACTION 

3) IN HIGH POWER CHANNELS 

SLUG FLOW BEGINS BELOW 

CORE MIDPLANE 

1) BUBBLES FORM ON THE WALL BUT 

DO NOT COLLAPSE IN COOLANT 

STREAM. I.E.. -BULK BOILING

2) BULK COOLANT TEMPERATURE IS 

AT SATURATION TEMPERATURE 

3) BUBBLES ARE NOT YET COALESCING, 

LOW QUALITY

1I) BUBBLES FORM ON THE WALL BUT 

COLLAPSE IN THE BULK COOLANT 

STREAM 

2) NO NET VAPOR GENERATION 

3) A V•V' SMALL VOID FRACTION 

4) OCCURS ABOVE THE FORCED 

CONVECTION REGION

a. SINGLE PHASE FORCED CONVECTION

FUEL FUEL

1) NO BUBBLES ARE FORMED. THE 

COOLANT REMAINS IN A SINGLE 

PHASE (LIQUID) 

2) OCCURS AT VERY BOTTOM OF 

COOLANT CHANNEL

Figure 3-23. Fuel Channel Boiling Conditions

USNRC Technical Training Center 3-73 Rev. 0194

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center 3-73 Rev. 0194
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

PRESSURIZER

Figure 3-24. PWR Reactor Core Heat Balance Diagram

USNRC Technical Training Center 3-75 Rev. 0194

Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

USNRC Technical Training Center 3-75 Rev. 0194
Power Plant Engineering Course Manual Heat Transfer and Thermal Hydraulics

REGENERATIVE 

HX r

DEMINERALIZERI

Iicu

Figure 3-25. BWR Reactor Core Heat Balance Diagram

USNRC Technical Training Center 3-77 Rev. 0195

Power Plant Engineering Course Matnual] Beat Transfer and Thermal Hydraulics

USNRC Technical Training Center 3-77 Rev. 0195
Power Plant Engineering Course Manual

Heat Transfer and Thermal Hydraulics

STEAw 

GENERAMoR 

TOP OF 

TUDES.EET

RN* ITUam 

COLD LEG O&JECTION LINE

REA=MO COOLMI

REACTOR VESSEL

I I 

I I

HOT LEG A. Typical Natural Circulation Geometry COLD LEG 

HEAD (HHL) HEAD (HCL)

HCL= 2 Pcg+7pgg+12pcg=21PCg 

PAVG PH+PC 

HHL 12 ( -H-+P + 7N9 + 2Fkg = 15 Prg + 6pCg 

HKC = HCL- HHL = 21PCg-15Sg%-6%g = 15g%(C " ) 

B. Natural Circulation Driving Head 

Figure 3-26. Natural Circulation

USNKL i ecnnical Training Center 3-79 

Rev. 0194

Rev. 0194

Heat Transfer and Thermal Hydraulics

3-79