Nuclear Power Plant 

Fire Modeling Analysis 

Guidelines 

(NPP FIRE MAG) 

Final Report 

U.S. Nuclear Regulatory Commission Electric Power Research Institute 

Office of Nuclear Regulatory Research 3412 Hillview Avenue 

Washington, D.C. 20555-0001 Palo Alto, CA 94303 

 

NUREG-1934 EPRI 1023259 

 Final Report
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Nuclear Power Plant 

Fire Modeling Analysis 

Guidelines 

(NPP FIRE MAG) 

NUREG-1934 EPRI 1023259

Final Report 

November 2012 

U.S. Nuclear Regulatory Commission Electric Power Research Institute (EPRI) 

Office of Nuclear Regulatory Research (RES) 3420 Hillview Avenue 

Washington, D.C. 20555-0001 Palo Alto, CA 94304-1338 

U.S. NRC-RES Project Manager EPRI Project Manager 

M.H. Salley R. Wachowiak 

 
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Copyright © 2012 Electric Power Research Institute. All rights reserved.
iii 

ABSTRACT 

There is a movement to introduce risk-informed and performance-based (RI/PB) analyses into 

fire protection engineering practice, both domestically and worldwide. This movement exists in 

both the general fire protection and the nuclear power plant (NPP) fire protection communities. 

The U.S. Nuclear Regulatory Commission (NRC) has used risk-informed insights as a part of its 

regulatory decision making since the 1990s. 

In 2001, the National Fire Protection Association (NFPA) issued NFPA 805, Performance-Based 

Standard for Fire Protection for Light-Water Reactor Electric Generating Plants, 2001 Edition. 

In July 2004, the NRC amended its fire protection requirements in Title 10, Section 50.48 of the 

Code of Federal Regulations (10 CFR 50.48) to permit existing reactor licensees to voluntarily 

adopt fire protection requirements contained in NFPA 805 as an alternative to the existing 

deterministic fire protection requirements. In addition, the NPP fire protection community has 

been using RI/PB approaches and insights to support fire hazard analysis in general. 

One key element in RI/PB fire protection is the availability of verified and validated (V&V) fire 

models that can reliably estimate the effects of fires. The U.S. NRC, together with the Electric 

Power Research Institute (EPRI) and the National Institute of Standards and Technology 

(NIST), conducted a research project to verify and validate five fire models that have been used 

for NPP applications. The results of this effort are documented in a seven-volume NUREG 

report, NUREG-1824 (EPRI 1011999), Verification & Validation of Selected Fire Models for 

Nuclear Power Plant Applications. 

This report describes the implications of the V&V results for fire model users. The features and 

limitations of the five fire models documented in NUREG-1824 (EPRI 1011999) are discussed 

relative to NPP fire hazard analysis (FHA). Finally, the report provides information on the use of 

fire models in support of various commercial NPP fire hazard analysis applications. 

 

v 

CONTENTS 

ABSTRACT ................................................................................................................................. iii

CONTENTS .................................................................................................................................. v

FIGURES ..................................................................................................................................... xi

TABLES ...................................................................................................................................... xv

REPORT SUMMARY ............................................................................................................... xvii

PREFACE .................................................................................................................................. xix

CITATIONS ................................................................................................................................ xxi

ACKNOWLEDGEMENTS ....................................................................................................... xxiii

LIST OF ACRONYMS .............................................................................................................. xxv

NOMENCLATURE ................................................................................................................. xxvii

1 INTRODUCTION .................................................................................................................... 1-1

1.1 Background ..................................................................................................................... 1-1

1.2 Objective ......................................................................................................................... 1-2

1.3 Scope .............................................................................................................................. 1-2

1.3.1 User Capabilities ..................................................................................................... 1-2

1.3.2 Training Resources ................................................................................................. 1-3

1.4 Fire Modeling Theory ...................................................................................................... 1-4

1.5 Fire Modeling Tools ......................................................................................................... 1-7

1.5.1 Algebraic Models ..................................................................................................... 1-7

1.5.2 Zone Models ............................................................................................................ 1-7

1.5.3 CFD Models ............................................................................................................. 1-9

1.5.4 Fire Model Verification and Validation (V&V) ........................................................ 1-11

1.6 Fire Modeling Applications ............................................................................................ 1-11

1.6.1 License Amendments and Exemptions ................................................................. 1-11

1.6.2 Fire Induced Circuit Failures .................................................................................. 1-11

1.6.2.1 Deterministic Application ............................................................................. 1-12

1.6.2.2 Risk-Informed, Performance-Based Application .......................................... 1-12

1.6.3 NFPA 805 Performance-Based Applications ......................................................... 1-12

1.6.3.1 Fire Modeling ............................................................................................... 1-13

1.6.3.2 Fire Risk Evaluations ................................................................................... 1-14

1.6.4 Fire Modeling in Support of Fire PRA .................................................................... 1-14

1.7 Organization of the Guide ............................................................................................. 1-15

2 THE FIRE MODELING PROCESS ......................................................................................... 2-1

2.1 Step 1: Define Fire Modeling Goals and Objectives ........................................................ 2-2

2.2 Step 2: Characterize Fire Scenarios ............................................................................... 2-4

2.2.1 General Considerations ........................................................................................... 2-4

2.2.2 Enclosure Details ..................................................................................................... 2-5

2.2.3 Fire Location ............................................................................................................ 2-6

2.2.4 Credited Fire Protection ........................................................................................... 2-7

2.2.5 Ventilation Conditions .............................................................................................. 2-8

2.2.6 Target Locations ...................................................................................................... 2-8

2.2.7 Secondary Combustibles ......................................................................................... 2-9

2.2.8 Source Fire .............................................................................................................. 2-9

2.3 Step 3: Select Fire Models ............................................................................................ 2-10

2.3.1 Fire Dynamics Tools (FDTs

) .................................................................................. 2-14

2.3.2 Fire Induced Vulnerability Evaluation (FIVE-Rev1) ............................................... 2-16
vi 

2.3.3 Consolidated Fire Growth and Smoke Transport (CFAST) Model ........................ 2-18

2.3.4 MAGIC ................................................................................................................... 2-19

2.3.5 Fire Dynamics Simulator (FDS) ............................................................................. 2-19

2.3.6 Verification and Validation (V&V) .......................................................................... 2-22

2.3.7 Fire Modeling Parameters Outside the Validation Range ..................................... 2-28

2.3.7.1 Sensitivity Analysis ...................................................................................... 2-29

2.3.7.2 Additional Validation Studies ....................................................................... 2-31

2.4 Step 4: Calculate Fire-Generated Conditions ................................................................ 2-32

2.5 Step 5: Conduct Sensitivity and Uncertainty Analyses .................................................. 2-33

2.6 Step 6: Document the Analysis ..................................................................................... 2-34

2.7 Summary ....................................................................................................................... 2-35

3 GUIDANCE ON FIRE MODEL SELECTION AND IMPLEMENTATION ................................ 3-1

3.1 Model Implementation of Fire Scenario Elements ........................................................... 3-1

3.1.1 Heat Release Rate .................................................................................................. 3-1

3.1.2 Plant Area Configuration ......................................................................................... 3-2

3.1.3 Ventilation Effects .................................................................................................... 3-3

3.1.4 Targets .................................................................................................................... 3-4

3.1.5 Intervening Combustibles ........................................................................................ 3-5

3.2 Guidance on Model Selection and Analysis .................................................................... 3-5

3.2.1 Targets in the Flames or Plume .............................................................................. 3-8

3.2.1.1 General Objective .......................................................................................... 3-8

3.2.1.2 Modeling Strategy .......................................................................................... 3-8

3.2.1.3 Recommended Models .................................................................................. 3-9

3.2.1.4 Detailed Examples ....................................................................................... 3-10

3.2.2 Scenario 2: Targets Inside or Outside the Hot Gas Layer ..................................... 3-11

3.2.2.1 General Objective ........................................................................................ 3-11

3.2.2.2 Modeling Strategy ........................................................................................ 3-11

3.2.2.3 Recommended Modeling Tools ................................................................... 3-12

3.2.2.4 Detailed Examples ....................................................................................... 3-13

3.2.3 Scenario 3: Targets Located in Adjacent Rooms .................................................. 3-14

3.2.3.1 General Objective ........................................................................................ 3-14

3.2.3.2 Modeling Strategy ........................................................................................ 3-14

3.2.3.3 Recommended Modeling Tools ................................................................... 3-15

3.2.3.4 Detailed Examples ....................................................................................... 3-15

3.2.4 Scenario 4: Targets in Rooms with Complex Geometries ..................................... 3-16

3.2.4.1 General Objective ........................................................................................ 3-16

3.2.4.2 Modeling Strategy ........................................................................................ 3-16

3.2.4.3 Recommended Modeling Tools ................................................................... 3-17

3.2.4.4 Detailed Examples ....................................................................................... 3-17

3.2.5 Scenario 5: Main Control Room Abandonment ..................................................... 3-18

3.2.5.1 General Objective ........................................................................................ 3-18

3.2.5.2 Modeling Strategy ........................................................................................ 3-18

3.2.5.3 Recommended Modeling Tools ................................................................... 3-18

3.2.5.4 Detailed Examples ....................................................................................... 3-19

3.2.6 Scenario 6: Smoke Detection and Sprinkler Activation ......................................... 3-20

3.2.6.1 General Objective ........................................................................................ 3-20

3.2.6.2 Modeling Strategy ........................................................................................ 3-20

3.2.6.3 Recommended Modeling Tools ................................................................... 3-21

3.2.6.4 Detailed Examples ....................................................................................... 3-21

3.2.7 Scenario 7: Fire Impacting Structural Elements .................................................... 3-22

3.2.7.1 General Objective ........................................................................................ 3-22
vii 

3.2.7.2 Modeling Strategy ........................................................................................ 3-22

3.2.7.3 Recommended Modeling Tools ................................................................... 3-23

3.2.7.4 Detailed Examples ....................................................................................... 3-23

4 UNCERTAINTY AND SENSITIVITY ...................................................................................... 4-1

4.1 Validation of Fire Models ................................................................................................. 4-2

4.2 Derivation of the Model Uncertainty Statistics ................................................................. 4-6

4.3 Calculation of Model Uncertainty ..................................................................................... 4-8

4.3.1 Example 1: Target Temperature .............................................................................. 4-8

4.3.2 Example 2: Critical Heat Flux .................................................................................. 4-9

4.4 Parameter Uncertainty .................................................................................................. 4-10

4.4.1 Parameter Uncertainty Propagation ...................................................................... 4-10

4.4.2 Sensitivity Analysis ................................................................................................ 4-13

4.5 Chapter Summary ......................................................................................................... 4-17

5 REFERENCES ....................................................................................................................... 5-1

6 INTRODUCTION TO THE APPENDICES .............................................................................. 6-1

APPENDIX A CABINET FIRE IN MAIN CONTROL ROOM .................................................... A-1

A.1 Modeling Objective ........................................................................................................ A-1

A.2 Description of the Fire Scenario ..................................................................................... A-1

A.3 Selection and Evaluation of Fire Models ........................................................................ A-6

A.3.1 Temperature Criterion ............................................................................................ A-6

A.3.2 Heat Flux Criterion ................................................................................................. A-6

A.3.3 Visibility Criterion .................................................................................................... A-6

A.3.4 Validation ............................................................................................................... A-7

A.4 Estimation of Fire-Generated Conditions ..................................................................... A-10

A.4.1 Algebraic Models .................................................................................................. A-10

A.4.2 Zone Model .......................................................................................................... A-13

A.4.3 CFD Model ........................................................................................................... A-16

A.5 Evaluation of Results ................................................................................................... A-17

A.5.1 Temperature Criterion .......................................................................................... A-18

A.5.2 Heat Flux Criterion ............................................................................................... A-19

A.5.3 Visibility Criterion .................................................................................................. A-20

A.6 Conclusion ................................................................................................................... A-21

A.7 References................................................................................................................... A-22

A.8 Attachments (on CD) ................................................................................................... A-22

APPENDIX B CABINET FIRE IN SWITCHGEAR ROOM........................................................ B-1

B.1 Modeling Objective ........................................................................................................ B-1

B.2 Description of the Fire Scenario ..................................................................................... B-1

B.3 Selection and Evaluation of Fire Models ........................................................................ B-6

B.3.1 Temperature Criterion ............................................................................................ B-6

B.3.2 Heat Flux Criterion ................................................................................................. B-6

B.3.3 Validation ............................................................................................................... B-6

B.4 Estimation of Fire-Generated Conditions ....................................................................... B-9

B.4.1 Algebraic Models .................................................................................................... B-9

B.4.2 Zone Model .......................................................................................................... B-12

B.4.3 CFD Model ........................................................................................................... B-16

B.5 Evaluation of Results ................................................................................................... B-19

B.5.1 Cable Ignition and Damage .................................................................................. B-19

B.5.2 Cabinet Damage .................................................................................................. B-21

B.5.3 Parameter Uncertainty Propagation ..................................................................... B-22
viii 

B.6 Conclusion ................................................................................................................... B-24

B.7 References................................................................................................................... B-24

B.8 Attachments (on CD) ................................................................................................... B-24

APPENDIX C LUBRICATING OIL FIRE IN PUMP COMPARTMENT ..................................... C-1

C.1 Modeling Objective ........................................................................................................ C-1

C.2 Description of the Fire Scenario .................................................................................... C-1

C.3 Selection and Evaluation of Models ............................................................................... C-5

C.3.1 Fire Sustainability ................................................................................................... C-5

C.3.2 Temperature Criterion ............................................................................................ C-5

C.3.3 Validation ............................................................................................................... C-5

C.4 Estimation of Fire-Generated Conditions ....................................................................... C-7

C.4.1 Calculation of Oxygen Availability .......................................................................... C-7

C.4.2 Zone Model ............................................................................................................ C-8

C.4.3 CFD Model ........................................................................................................... C-14

C.5 Evaluation of Results ................................................................................................... C-16

C.5.1 The Fire ................................................................................................................ C-16

C.5.2 Temperature Criterion .......................................................................................... C-17

C.6 Conclusion ................................................................................................................... C-23

C.7 References .................................................................................................................. C-23

C.8 Attachments (on CD) ................................................................................................... C-24

APPENDIX D MOTOR CONTROL CENTER FIRE IN A SWITCHGEAR ROOM .................... D-1

D.1 Modeling Objective ........................................................................................................ D-1

D.2 Description of the Fire Scenario .................................................................................... D-1

D.3 Selection and Evaluation of Fire Models ....................................................................... D-5

D.3.1 Temperature Criterion ............................................................................................ D-5

D.3.2 Heat Flux Criterion ................................................................................................. D-5

D.3.3 Validation ............................................................................................................... D-5

D.4 Estimation of Fire-Generated Conditions ....................................................................... D-8

D.4.1 Algebraic Models ................................................................................................... D-8

D.4.2 Zone Models .......................................................................................................... D-8

D.4.3 CFD Model ........................................................................................................... D-12

D.5 Evaluation of Results ................................................................................................... D-14

D.5.1 Damage to Cabinet .............................................................................................. D-14

D.5.2 Cable Damage Based on Temperature Alone ..................................................... D-15

D.5.3 Cable Damage Based on Incident Heat Flux ....................................................... D-16

D.6 Conclusion ................................................................................................................... D-17

D.7 References .................................................................................................................. D-17

D.8 Attachments (on CD) ................................................................................................... D-18

APPENDIX E TRANSIENT FIRE IN CABLE SPREADING ROOM ......................................... E-1

E.1 Modeling Objective ........................................................................................................ E-1

E.2 Description of the Fire Scenario ..................................................................................... E-1

E.3 Selection and Evaluation of Fire Models ........................................................................ E-6

E.3.1 Temperature Criterion ............................................................................................ E-6

E.3.2 Heat Flux Criterion ................................................................................................. E-6

E.3.3 Validation ............................................................................................................... E-6

E.4 Estimation of Fire-Generated Conditions ....................................................................... E-9

E.4.1 Algebraic Models .................................................................................................... E-9
ix 

E.4.2 Zone Model .......................................................................................................... E-11

E.4.3 CFD Model ........................................................................................................... E-17

E.5 Evaluation of Results ................................................................................................... E-19

E.5.1 Smoke Detection .................................................................................................. E-20

E.5.2 Temperature Criterion .......................................................................................... E-20

E.5.3 Heat Flux Criterion ............................................................................................... E-21

E.5.4 Parameter Uncertainty Propagation ..................................................................... E-23

E.6 Conclusion ................................................................................................................... E-24

E.7 References................................................................................................................... E-25

E.8 Attachments (on CD) ................................................................................................... E-25

APPENDIX F LUBRICATING OIL FIRE IN A TURBINE BUILDING ........................................ F-1

F.1 Modeling Objective......................................................................................................... F-1

F.2 Description of the Fire Scenario ..................................................................................... F-1

F.3 Selection and Evaluation of Fire Models ........................................................................ F-6

F.3.1 Heat Flux and Target Temperature Algorithms ...................................................... F-6

F.3.2 Validation ................................................................................................................ F-6

F.4 Estimation of Fire-Generated Conditions ....................................................................... F-9

F.4.1 Algebraic Models .................................................................................................... F-9

F.4.2 CFD Model ........................................................................................................... F-13

F.5 Evaluation of Results ................................................................................................... F-14

F.5.1 Column Heat Flux and Column Temperature ....................................................... F-14

F.6 Conclusion ................................................................................................................... F-17

F.7 References ................................................................................................................... F-17

F.8 Attachments (on CD) .................................................................................................... F-18

APPENDIX G TRANSIENT FIRE IN A MULTI-COMPARTMENT CORRIDOR ....................... G-1

G.1 Modeling Objective ........................................................................................................ G-1

G.2 Description of the Fire Scenario .................................................................................... G-1

G.3 Selection and Evaluation of Models .............................................................................. G-5

G.3.1 Temperature Criterion ............................................................................................ G-5

G.3.2 Validation ............................................................................................................... G-5

G.4 Estimation of Fire-Generated Conditions ...................................................................... G-7

G.4.1 Algebraic Models ................................................................................................... G-7

G.4.2 Zone Model ............................................................................................................ G-7

G.5 Evaluation of Results ................................................................................................... G-13

G.5.1 Temperature Criterion .......................................................................................... G-13

G.5.2 Smoke Detection ................................................................................................. G-15

G.6 Conclusion ................................................................................................................... G-16

G.7 References .................................................................................................................. G-17

G.8 Attachments (on CD) ................................................................................................... G-17

APPENDIX H CABLE TRAY FIRE IN ANNULUS.................................................................... H-1

H.1 Modeling Objective ........................................................................................................ H-1

H.2 Description of the Fire Scenario .................................................................................... H-1

H.3 Selection and Evaluation of Fire Models ....................................................................... H-5

H.3.1 Damage to Cables ................................................................................................. H-5

H.3.2 Sprinkler Activation ................................................................................................ H-6

H.3.3 Validation ............................................................................................................... H-6

H.4 Estimation of Fire-Generated Conditions ....................................................................... H-7
x 

H.4.1 Algebraic Models ................................................................................................... H-7

H.4.2 CFD Model ............................................................................................................. H-8

H.5 Evaluation of Results ................................................................................................... H-11

H.5.1 Heat Flux and Temperature ................................................................................. H-11

H.5.2 Fire Protection Systems ....................................................................................... H-12

H.6 Conclusion ................................................................................................................... H-13

H.7 References .................................................................................................................. H-13

H.8 Attachments (on CD) ................................................................................................... H-13

INDEX ................................................................................................................................ Index-1

 
xi 

FIGURES 

Figure 1-1. Characteristics of compartment fires. ................................................................... 1-5

Figure 1-2. A two-zone enclosure fire with an HGL above and a cool lower layer 

below. ................................................................................................................... 1-8

Figure 1-3. A Smokeview visualization of a CFD model of a compartment fire 

experiment. ........................................................................................................ 1-10

Figure 2-1. Fire modeling process. ......................................................................................... 2-1

Figure 3-1. Pictorial representation of the fire scenario and corresponding technical 

elements described in this section. ...................................................................... 3-6

Figure 3-2. Legend for fire modeling sketches presented in this chapter. .............................. 3-7

Figure 3-3. Pictorial representation of scenario 1. .................................................................. 3-8

Figure 3-4. Pictorial representation of scenario 2. ................................................................ 3-11

Figure 3-5. Pictorial representation of scenario 3. ................................................................ 3-14

Figure 3-6. Pictorial representation of scenario 4. ................................................................ 3-16

Figure 3-7. Pictorial representation of scenario 5. ................................................................ 3-18

Figure 3-8. Pictorial representation of scenario 6. ................................................................ 3-20

Figure 3-9. Pictorial representation of scenario 7. ................................................................ 3-22

Figure 4-1. Sample set of results from NUREG-1824 (EPRI 1011999). ................................ 4-4

Figure 4-2. Two examples demonstrating how the validation data is tested for 

normality............................................................................................................... 4-8

Figure 4-3. Normal distribution of the “true” value of the cable temperature in a 

hypothetical fire. ................................................................................................... 4-9

Figure 4-4. Distribution of HRR for an electrical cabinet fire. ............................................... 4-12

Figure 4-5. Distribution of flame heights for the entire range of cabinet fires. ...................... 4-13

Figure 4-6. FDS predictions of HGL Temperature as a function of time due to a 

1,000 kW fire (solid line) and a 1,150 kW fire (dashed). .................................... 4-15

Figure A-1. Geometry of the main control room. .................................................................... A-2

Figure A-2. Main control room details. ................................................................................... A-3

Figure A-3. Photograph of a typical open-grate ceiling. ......................................................... A-4

Figure A-4. Photograph of a typical control cabinet. .............................................................. A-4

Figure A-5. Time history of the HRR used by all models in the MCR scenario. .................... A-5

Figure A-6. Schematic diagram of the FPA calculation for the MCR smoke purge 

scenario............................................................................................................. A-11

Figure A-7. Compartment geometry and surface material selection in CFAST for the 

MCR Fire. .......................................................................................................... A-13

Figure A-8. Specification of the fire in CFAST for the MCR Fire. ......................................... A-14

Figure A-9. Mechanical ventilation inputs in CFAST for the MCR fire. ................................ A-15

Figure A-10. Smokeview rendering of the CFAST simulation of the MCR fire with 

mechanical ventilation. ...................................................................................... A-15

Figure A-11. FDS/Smokeview rendering of the MCR, as viewed from above. ...................... A-17

Figure A-12. Hot Gas Layer Temperature and Height for the MCR scenario. ....................... A-19

Figure A-13. Predicted heat flux at the location of the operator. ............................................ A-20

Figure A-14. Optical density predictions for the MCR scenario. ............................................ A-21

Figure B-1. Geometry of the switchgear room. ...................................................................... B-5

Figure B-2. Schematic diagram of cabinet fire in switchgear room. ....................................... B-9

Figure B-3. Plume temperatures at cable trays located above a cabinet fire. ..................... B-10
xii 

Figure B-4. Average HGL temperature (red line) from FPA correlation and HRR (blue 

line) for SWGR cabinet fire scenario. ................................................................ B-12

Figure B-5. Average CFAST/Smokeview rendering of SWGR. ........................................... B-12

Figure B-6. CFAST inputs for compartment geometry in SWGR scenario. ......................... B-13

Figure B-7. CFAST fire specification inputs for the SWGR scenario. .................................. B-14

Figure B-8. CFAST mechanical ventilation inputs for the SWGR scenario. ........................ B-15

Figure B-9. CFAST inputs for cabinet and cable targets for the SWGR scenario. .............. B-16

Figure B-10. FDS/Smokeview rendering of the SWGR. ........................................................ B-18

Figure B-11. FDS/Smokeview rendering of the SWGR fire showing localized ignition of 

extinction of secondary cable fires resulting from initial cabinet fire. ................ B-18

Figure B-12. Heat release rate inputs to CFAST and FDS for a SWGR cabinet fire 

scenario............................................................................................................. B-20

Figure B-13. Estimated temperatures for Cable Tray A directly above the fire source for 

a SWGR cabinet fire scenario. .......................................................................... B-21

Figure B-14. Estimated temperature and heat flux to a cabinet adjacent to the fire 

source in a SWGR cabinet fire scenario. .......................................................... B-22

Figure B-15. Distribution of HRR for an electrical cabinet fire. .............................................. B-23

Figure B-16. Distribution of flame heights for the entire range of cabinet fires. ..................... B-23

Figure C-1. Geometry of the pump room. .............................................................................. C-2

Figure C-2. MAGIC view of the pump room. .......................................................................... C-9

Figure C-3. Heat release rate curve for lubricating oil fire. ................................................... C-10

Figure C-4. MAGIC fire input screen for pump fire. .............................................................. C-11

Figure C-5. Modeling multi-conductor cables in MAGIC. Source: NUREG-1824 

(EPRI 1011999), Volume 6, Figure 3-3. ............................................................ C-12

Figure C-6. Representation of the ERFBS protected cable raceway for MAGIC. ................ C-13

Figure C-7. MAGIC input screen for ERFBS layers. ............................................................ C-13

Figure C-8. MAGIC input screen for ventilation through door. ............................................. C-14

Figure C-9. FDS/Smokeview rendering of the pump room scenario at the early stage of 

the fire, before the compartment becomes under-ventilated. ............................ C-15

Figure C-10. HRR predicted by algebraic methods, MAGIC, and FDS for the pump room 

fire scenario....................................................................................................... C-17

Figure C-11. HGL Temperature Predicted by MAGIC and FDS for the pump room fire 

scenario............................................................................................................. C-17

Figure C-12. Cable surface temperature predicted by MAGIC and FDS for the pump 

room fire scenario. ............................................................................................ C-19

Figure C-13. Cable surface temperature predicted by MAGIC for changes to insulation 

wrapping............................................................................................................ C-20

Figure C-14. Temperature predicted by MAGIC for increased door size. .............................. C-21

Figure C-15. HRR for base case and HRR sensitivity case. .................................................. C-22

Figure C-16. Temperature for base case and HRR sensitivity case. ..................................... C-22

Figure D-1. Geometry of the MCC/SWGR in a BWR. ............................................................ D-3

Figure D-2. Typical electrical cabinet in the lower part of the SWGR. ................................... D-4

Figure D-3. View of the high ceiling space. ............................................................................ D-4

Figure D-4. Smokeview rendering of the geometry of two-height ceiling SWGR, as 

modeled in CFAST. ............................................................................................. D-9

Figure D-5. CFAST inputs for compartment geometry for SWGR. ...................................... D-10

Figure D-6. CFAST fire inputs for two-height ceiling SWGR scenario. ................................ D-10

Figure D-7. CFAST target inputs for two-height ceiling SWGR scenario. ............................ D-11

Figure D-8. CFAST inputs for vents connections in two-height ceiling SWGR scenario. .... D-12

Figure D-9. FDS/Smokeview representation of the MCC/SWGR scenario. ......................... D-13

Figure D-10. Heat flux and temperature predictions for the adjacent cabinet. ....................... D-15
xiii 

Figure D-11. Summary of the cable temperature and heat flux predictions for the 

MCC/SWGR. ..................................................................................................... D-16

Figure E-1. Geometry of the CSR. ......................................................................................... E-4

Figure E-2. Photograph of the CSR used for analysis. Note that the cables are located 

in the trays in the overhead. ................................................................................ E-5

Figure E-3. Geometric detail of the CSR. .............................................................................. E-5

Figure E-4. Schematic diagram of transient trash fire in CSR (not to scale). ........................ E-9

Figure E-5. Plume temperatures at cable trays located above a transient trash fire. .......... E-10

Figure E-6. Average HGL temperature (red line) from FPA correlation and heat release 

rate (blue line) for the CSR trash fire scenario. ................................................. E-11

Figure E-7. CFAST/Smokeview rendering of the CSR scenario. ......................................... E-12

Figure E-8. CFAST inputs for compartment geometry for the CSR scenario. ..................... E-13

Figure E-9. CFAST inputs for the fire in the CSR scenario. ................................................. E-14

Figure E-10. CFAST inputs for cable targets above the fire source in the CSR scenario. .... E-15

Figure E-11. CFAST inputs for natural ventilation for the CSR scenario. Note the 

opening of the doorway at 170 s, the time estimated for smoke detectors to 

activate. ............................................................................................................. E-16

Figure E-12. CFAST inputs for smoke detectors in the CSR scenario. ................................. E-17

Figure E-13. FDS/Smokeview rendering of the CSR scenario. ............................................. E-17

Figure E-14. HRR and estimated HGL temperature for CSR scenario. ................................. E-19

Figure E-15. Estimated cable conditions for the CSR. ........................................................... E-22

Figure E-16. Distribution of HRR for a trash fire. ................................................................... E-23

Figure E-17. Distribution of plume temperatures at Trays 3 and 6, respectively. .................. E-24

Figure F-1. Geometry of the turbine building. ......................................................................... F-2

Figure F-2. Main turbine lubricating oil tanks in the turbine building. ...................................... F-3

Figure F-3. Typical steel column in the turbine building. ........................................................ F-3

Figure F-4. Schematic diagram of the fire impinging on the ceiling. ..................................... F-10

Figure F-5. Detail from Figure F-1 with estimated flame extension beneath ceiling 

superimposed..................................................................................................... F-11

Figure F-6. FDS geometry for the turbine building fire scenario. .......................................... F-13

Figure F-7. Temperatures of columns for Curb Location 1. .................................................. F-15

Figure F-8. Temperatures of columns for Curb Location 2. .................................................. F-16

Figure G-1. Geometry of the multi-compartment corridor. ..................................................... G-2

Figure G-2. Geometry details of the multi-compartment corridor. .......................................... G-3

Figure G-3. HRR for the corridor fire scenario. ...................................................................... G-4

Figure G-4. Effective corridor layout for implementation in zone models (not to scale). ........ G-8

Figure G-5. MAGIC rendering of the corridor scenario. ......................................................... G-9

Figure G-6. MAGIC screen capture of the fire in corridor scenario. ..................................... G-10

Figure G-7. MAGIC screen capture for supply vent specification. ....................................... G-11

Figure G-8. MAGIC screen capture of the smoke detector specification. ............................ G-12

Figure G-9. HGL temperature predictions by MAGIC for the corridor scenario. .................. G-14

Figure G-10. HGL temperature for reduced ceiling height by MAGIC. ................................... G-15

Figure G-11. Detector temperature prediction by MAGIC for fire corridor. ............................. G-15

Figure G-12. Detector temperature for two radial distances predicted by MAGIC. ................ G-16

Figure H-1. Geometry of the annulus. .................................................................................... H-3

Figure H-2. Geometry details of redundant cable trays located in the annulus. .................... H-4

Figure H-3. HRR for a cable fire in the annulus. .................................................................... H-5

Figure H-4. FDS/Smokeview rendering of the annulus fire scenario. .................................. H-10

Figure H-5. Summary of simulation results for the annulus. ................................................ H-12

Figure H-6. Predicted sprinkler link temperature for the annulus fire scenario. ................... H-12

xv 

TABLES 

Table 2-1. Summary of common fire model tools. ............................................................... 2-13

Table 2-2. Routines included in the FDTs

. ........................................................................... 2-14

Table 2-3. Routines included in FIVE-Rev1. ....................................................................... 2-17

Table 2-4. Fire modeling attributes included in NUREG 1824/EPRI 1011999 (2007). ........ 2-23

Table 2-5. Summary of selected normalized parameters for application of the 

validation results to NPP fire scenarios (NUREG-1824/EPRI 1011999, 

2007). ................................................................................................................. 2-24

Table 3-1. Material properties. .............................................................................................. 3-3

Table 3-2. Listing of generic scenarios described in this chapter. ......................................... 3-5

Table 4-1. Results of the V&V study, NUREG-1824 (EPRI 1011999). ................................. 4-2

Table 4-2. Experimental uncertainty of the experiments performed as part of the 

validation study in NUREG-1824 (EPRI 1011999). .............................................. 4-7

Table 4-3. Sensitivity of model outputs from Volume 2 of NUREG-1824 (EPRI 

1011999). ........................................................................................................... 4-14

Table 6-1. Appendix fire scenario descriptions and cross-index. .......................................... 6-1

Table A-1. Data for MCR fire based on XPE/neoprene electrical cable. .............................. A-5

Table A-2. Normalized parameter calculations for the MCR fire scenario. See Table 

2-5 for further details. .......................................................................................... A-9

Table A-3. Summary of input parameters for the FPA calculation of the MCR. ................. A-10

Table A-4. Summary of the model predictions of the MCR scenario. ................................. A-18

Table B-1. Products of combustion for switchgear room cabinet and cable fire. .................. B-4

Table B-2. Normalized parameters and their ranges of applicability to NUREG-1824 

(EPRI 1011999). ................................................................................................. B-8

Table B-3. Summary of input parameters for FPA analysis of switchgear room 

scenario............................................................................................................. B-11

Table B-4. Summary of the model predictions of the cabinet fire scenario. ....................... B-19

Table B-5. Estimated time to ignition of lowest cable tray by CFAST for the SWGR 

cabinet fire......................................................................................................... B-20

Table C-1. Data for ERFBS and cable insulation. ................................................................. C-3

Table C-2. Data for lubricating oil fire. .................................................................................. C-4

Table C-3. Normalized parameter calculations for the pump room fire scenario. ................. C-6

Table C-4. Calculated input for lubricating oil fire. ................................................................ C-8

Table C-5. Summary of the model predictions of the pump room scenario. ....................... C-16

Table C-6. Integrated thermal exposure of an object subjected to the ASTM E119 

temperature curve. ............................................................................................ C-19

Table D-1. Products of combustion for the MCC fire. ........................................................... D-2

Table D-2. Normalized parameter calculations for the MCC fire scenario. ........................... D-7

Table D-3. Summary of the model predictions of the MCC fire scenario. ........................... D-14

Table E-1. Products of combustion for CSR fire. .................................................................. E-3

Table E-2. Normalized parameters and their ranges of applicability to NUREG-1824. ........ E-8

Table E-3. Summary of input parameters for FPA analysis of CSR scenario. ................... E-10

Table E-4. Cross-sectional area as a function of height used for CFAST calculation. ....... E-12

Table E-5. Summary of the model predictions for the CSR scenario. ................................ E-20

Table E-6. Smoke detector activation times, CSR. ............................................................. E-20

Table F-1. Structural steel failure criteria (ASTM E119-10a). ................................................ F-4

Table F-2. Data for lubricating oil fire. ................................................................................... F-5

Table F-3. Normalized Parameter Calculations for the Turbine Building Fire Scenario. ....... F-8
xvi 

Table F-4. Summary of results for the turbine building fire scenarios. ................................ F-14

Table G-1. Products of combustion for a wood pallet fire. .................................................... G-4

Table G-2. Normalized parameter calculations for the multi-compartment corridor fire 

scenario............................................................................................................... G-6

Table G-3. Compartment dimensions for corridor scenario. ................................................. G-8

Table G-4. Summary of the model predictions of the corridor scenario. ............................. G-13

Table H-1. Products of combustion for a PE/PVC cable fire. ................................................ H-2

Table H-2. Normalized parameter calculations for the annulus fire scenario. ...................... H-7

Table H-3. Summary of model predictions for the annulus fire scenario. ........................... H-11
xvii 

REPORT SUMMARY 

Background 

Beginning in the 1990s, when the U.S. Nuclear Regulatory Commission (NRC) adopted the 

policy of using risk-informed methods to make regulatory decisions whenever possible, the 

nuclear power industry has been moving from prescriptive rules and practices toward the use of 

risk information to supplement decision making. Several initiatives have furthered this transition 

within the fire protection field, including risk-informed, performance-based fire protection 

programs (FPPs) compliant with Title 10, Section 50.48(c) of the Code of Federal Regulations 

(10 CFR 50.48(c)) and FPP change evaluation under the existing Title 10 Section 50.48 and 

Regulatory Guide 1.189, Fire Protection for Nuclear Power Plants, October 2009. RI/PB fire 

protection often relies on fire modeling to estimate the effects of fires. 

Objectives 

 To provide guidance on the proper application of fire models to NPP fire scenarios 

 To fulfill the need as a teaching tool and support the NRC/EPRI Fire PRA training 

Approach 

There were five different fire models evaluated in NUREG-1824 (EPRI 1011999), Verification 

and Validation of Selected Fire Models for Nuclear Power Plant Applications: (1) the NRC’s Fire 

Dynamics Tools (FDTs

), (2) the Electric Power Research Institute’s (EPRI) Fire-Induced 

Vulnerability Evaluation Revision 1 (FIVE-Rev1), (3) the National Institute of Standards and 

Technology’s (NIST) Consolidated Model of Fire Growth and Smoke Transport (CFAST), 

(4) Electricité de France’s (EdF) MAGIC, and (5) NIST’s Fire Dynamics Simulator (FDS). To 

support consistency, the same fire models were used in the development of this report. The 

project team developed guidance on the selection and application of each model and treatment 

of uncertainty and/or sensitivity as part of the fire modeling analysis. Based on this guidance, 

the project team selected appropriate models and conducted fire modeling analyses of eight 

different fire scenarios of interest in nuclear power plants (NPPs). The results of each analysis 

were to be documented in a format appropriate for fire model calculation submittals. 

Results 

This report presents a step-by-step process for using fire modeling in NPP applications. The 

recommended methodology consists of a six step process: (1) define fire modeling goals, (2) 

characterize fire scenarios, (3) select fire models, (4) calculate fire-generated conditions, (5) 

conduct sensitivity and uncertainty analyses, and (6) document the results. 

This report is designed to assist fire model users in applying this technology in the NPP 

environment. There are a number of unique construction and fire hazard attributes associated 

with NPPs. It was the authors’ goal to explore and demonstrate the use of different models for 

this application. In addition, a fifth module, “Advanced Fire Modeling”, has been added to the 

annual NRC/EPRI Fire PRA training workshop in 2011. This report expands upon the 

information provided in NUREG/CR-6850 (EPRI 1011989), EPRI/NRC-RES Fire PRA 

Methodology for Nuclear Power Facilities, and will serve as the training material for the 

Advanced Fire Modeling module. 
xviii 

The report contains a CD to assist the reader in reproducing the examples discussed in the 

appendices. The CD contains the installation files for CFAST and FDS. It also contains the 

latest versions (November 2012) of the NUREG-1805 spreadsheets. The CD also contains the 

input files for each model used to analyze the eight fire scenarios. 

EPRI Perspective 

The use of fire models requires a good understanding of their limitations and predictive 

capabilities, and also presents challenges that should be addressed if the fire protection 

community is to realize the full benefit of fire modeling and performance-based fire protection. 

EPRI, in partnership with NRC under a Memorandum of Understanding (MOU), will continue to 

provide training to the fire protection community, using this document to promote fire modeling 

and gain feedback on how the results of this work may affect known applications of fire 

modeling. In the long term, model improvement and additional experiments should be 

considered. 

This report supersedes EPRI 10002981, Fire Modeling Guide for Nuclear Power Plant 

Applications, August 2002, as guidance for fire modeling practitioners in NPPs. The report has 

benefited from the insights gained since 2002 on the predictive capability of selected fire models 

in improving confidence in the use of fire modeling in NPP applications. 

Note: Due to EPRI limitations on distribution of software, the FDTs

 spreadsheets, CFAST, and 

FDS are not included on the EPRI version of the CD. The FDTs can be obtained from the NRC 

web site (www.nrc.gov), and CFAST and FDS can be obtained from the NIST web site 

(www.nist.gov). 

Keywords 

Fire 

Verification and Validation (V&V) 

Risk-Informed Regulation 

Fire Safety 

Nuclear Power Plant (NPP) 

Fire Modeling 

Performance-Based 

Fire Hazard Analysis (FHA) 

Fire Protection 

Probabilistic Risk Assessment (PRA) 
xix

PREFACE 

This report describes research sponsored jointly by EPRI and U.S. Nuclear Regulatory 

Commission, Office of Nuclear Regulatory Research (RES). The main purpose of this report is 

to provide guidance on the application of fire models to nuclear power plant (NPP) fire scenarios 

and to serve as a teaching tool and support the Advanced Fire Modeling module of the NRCRES/EPRI Fire PRA Course. The fire modeling analyses presented in this report represent the 

combined efforts of individuals from RES and EPRI. Both organizations provided specialists in 

the use of fire models/fire hazard analysis tools to support this work. These results are intended 

to provide technical analysis of the predictive capabilities of five fire modeling calculation tools. 

This report is the fifth in a series designed to assist those responsible for performing fire 

modeling in NPP applications. 

In August 2002, EPRI published EPRI 1002981, Fire Modeling Guide for Nuclear Power Plant 

Applications. This report offered step-by-step guidance that analysts could follow when using 

fire modeling to support nuclear power plant fire protection applications. It also included FIVERev1, an Excel-based library of fire models previously documented by EPRI, and additional 

models from fire protection literature. 

In December 2004, the NRC published NUREG-1805, Fire Dynamics Tools (FDTs

) Quantitative 

Fire Hazard Analysis Methods for the U.S. Nuclear Regulatory Commission Fire Protection 

Inspection Program. This report provided an introduction to the principles of fire dynamics, and 

included an Excel-based library of fire models comparable to EPRI FIVE-Rev1. 

In a follow-up effort as a part of the NRC/RES-EPRI Memorandum of Understanding (MOU), 

NRC/RES and EPRI jointly conducted a verification and validation of selected fire models for 

use in nuclear power plant fire modeling to gain insight into the predictive capabilities of these 

models. The results of this work were published in NUREG-1824 (EPRI 1011999), Verification 

and Validation of Selected Fire Models for Nuclear Power Plant Applications, May 2007. Using, 

in part, the findings of this work, the NRC conducted a Phenomena Identification and Ranking 

Table (PIRT) study to evaluate the current state of knowledge for fire modeling for NPP 

applications. The results of this work were published in NUREG/CR-6978, A Phenomena 

Identification and Ranking Table (PIRT) Exercise for Nuclear Power Plant Fire Modeling 

Applications, November 2008. 

This document does not constitute regulatory requirements. RES participation in this 

study does not constitute or imply regulatory approval of applications based upon this 

methodology. 

 

xxi

CITATIONS 

This report was prepared by: 

U.S. Nuclear Regulatory Commission, 

Office of Nuclear Regulatory Research (RES) 

Washington, D.C. 20555-0001 

Principal Investigator: 

D. Stroup 

Electric Power Research Institute (EPRI) 

3412 Hillview Avenue 

Palo Alto, CA 94303 

Principal Investigator: 

R. Wachowiak 

National Institute of Standards and 

Technology 

Principal Investigators: 

K. McGrattan 

R. Peacock 

University of Maryland 

Principal Investigator: 

J. Milke 

Kleinsorg Group Risk Services 

Division of Hughes Associates, Inc. 

Principal Investigator: 

F. Joglar 

S. LeStrange 

B. Najafi 

California Polytechnic State University 

Principal Investigator: 

F. Mowrer 

Hughes Associates, Inc. 

Principal Investigator: 

S. Hunt 

Westinghouse Electric Company 

Principal Investigator: 

C. Worrell 

Science Applications International Corp (SAIC) 

Principal Investigators: 

D. Birk 

ERIN Engineering 

Principal Investigator: 

K. Zee 

This report describes research sponsored jointly by the U.S. Nuclear Regulatory Commission’s 

(NRC) Office of Nuclear Regulatory Research (RES) and the Electric Power Research Institute 

(EPRI). 

The report is a corporate document that should be cited in the literature in the following manner: 

Nuclear Power Plant Fire Modeling Analysis Guidelines (NPP FIRE MAG), U.S. Nuclear 

Regulatory Commission, Office of Nuclear Regulatory Research (RES), Washington, D.C., 

2012, and Electric Power Research Institute (EPRI), Palo Alto, CA, NUREG-1934 and EPRI 

1023259. 

xxiii

ACKNOWLEDGEMENTS 

This report is the result of a multi-year effort by the authors, during which it has been 

significantly rewritten in response to comments from various reviewers. The authors wish to 

thank those reviewers for taking the time to provide their thoughts on this document. The 

authors express appreciation to the members of the peer review panel who provided comments 

on the original draft of this document in 2009: Professor Jose L. Torero and his students at BRE 

Centre for Fire Safety Engineering, The University of Edinburgh, Scotland; Professor Frederick 

Mowrer, formerly of the Department of Fire Protection Engineering, University of Maryland, and 

currently with the Department of Fire Protection Engineering, California Polytechnic State 

University; Mr. Patrick Finney, NRC Resident Inspector at Susquehanna Nuclear Plant; 

Mr. Naeem Iqbal, Fire Protection Engineer, Office of Nuclear Reactor Regulation (NRR), NRC; 

and Mr. Thomas Gorman, Project Manager, Pennsylvania Power and Light, Susquehanna 

Nuclear Plant. 

Drafts of this report were Noticed twice in the Federal Register for public comment: first on 

December 29, 2009 (74 FR 68873), and second on August 2, 2011 (76 FR 46331). The authors 

thank those members of the public who provided comments during the two public comment 

periods, specifically Robert M. Brady, Schirmer Engineering Corporation; Patricia L. Campbell, 

GE Hitachi Nuclear Energy; Jason E. Floyd, Hughes Associates, Inc.; Pablo Guardado, Entergy; 

Michael D. Jesse, Excelon Nuclear; Daeil Kang, Korea Atomic Energy Research Institute; 

Nancy McNabb, National Fire Protection Association; Daniel Orr, NRC, Region 1; Mark 

Schairer, Engineering Planning and Management (EPM); and Robert Webster, AREVA, all of 

whom provided insightful comments on the two drafts of the document. 

This report was used as a textbook for pilot offerings of an advanced fire modeling course held 

as part of the annual NRC/EPRI Fire PRA training in 2011 and 2012. The authors would like to 

thank the students in those two classes for their many constructive comments that significantly 

improved the final report. 

Meetings were held before the Reliability and PRA Subcommittee of the Advisory Committee on 

Reactor Safeguards (ACRS) and before the full ACRS committee on March 21, 2012 and 

July 11, 2012, respectively. We would like to thank the members of the ACRS for their time and 

efforts in supporting the meetings and reviewing and providing comments and suggestions for 

improvements to the final report. 

Finally, the authors express their thanks to Laurent Gay and Eric Wizenne, Electricité de France 

(EdF), for reviewing the MAGIC calculations. The authors would also like to acknowledge Mr. 

Bryan Klein of Thunderhead Engineering and Drs. Nathan Siu and Raymond Gallucci of the 

NRC for their valuable contributions to this report. The authors also express appreciation to Ms. 

Aixa Belen, Mr. Ken Canavan, Mr. Stuart Lewis, Mr. Nicholas Melly, Ms. Carolyn Siu, and Mr. 

Robert Vettori for their reviews of and comments on various drafts of this document. Publication 

of this document would not have been possible without assistance from the NRC’s Office of 

Administration. Specifically, the authors thank Tojuana Fortune-Grasty and Guy Beltz for their 

efforts in publishing this report. 

 

xxv

LIST OF ACRONYMS 

ACH Air Changes per Hour 

ACRS Advisory Committee on Reactor Safeguards 

AGA American Gas Association 

AHJ Authority Having Jurisdiction 

ANS American Nuclear Society 

ASET Advanced Science and Engineering Technologies 

ASME American Society of Mechanical Engineers 

ASTM American Society for Testing and Materials 

ATF Bureau of Alcohol, Tobacco, and Firearms 

BE Benchmark Exercise 

BFRL Building and Fire Research Laboratory 

BRE Building Research Establishment 

BWR Boiling Water Reactor 

CAROLFIRE Cable Response to Live Fire 

CDF Core Damage Frequency 

CFAST Consolidated Fire Growth and Smoke Transport Model 

CFD Computational Fluid Dynamics 

CFR Code of Federal Regulations 

CHRISTIFIRE Cable Heat Release, Ignition, and Spread in Tray Installations during Fire 

COR Code of Record 

CSR Cable Spreading Room 

DBD Design Basis Document 

ECCS Emergency Core Cooling Systems 

EdF Electricité de France 

EPRI Electric Power Research Institute 

ERFBS Electrical Raceway Fire Barrier System 

FDS Fire Dynamics Simulator 

FDTs

 Fire Dynamics Tools (NUREG-1805) 

FHA Fire Hazard Analysis 

FIVE-Rev1 Fire-Induced Vulnerability Evaluation, Revision 1 

FFT Fast Fourier Transform 

FLASH-CAT Flame Spread over Horizontal Cable Trays 

FM/SNL Factory Mutual & Sandia National Laboratories 

FPA Foote, Pagni, and Alvares 

FPRA Fire Probabilistic Risk Assessment 

FRA Fire Risk Analysis 

GRS Gesellschaft für Anlagen- und Reaktorsicherheit (Germany) 

HGL Hot Gas Layer 

HRR Heat Release Rate 

HRRPUA Heat Release Rate Per Unit Area 

HVAC Heating, Ventilation, and Air Conditioning 

IAFSS International Association of Fire Safety Science 

iBMB Institut für Baustoffe, Massivbau und Brandschutz 

ICFMP International Collaborative Fire Model Project 

ID Identification 

IEEE Institute of Electrical and Electronics Engineers 
xxvi 

IPEEE Individual Plant Examination of External Events 

LERF Large Early Release Frequency 

LES Large Eddy Simulation 

LFS Limiting Fire Scenario 

LLNL Lawrence Livermore National Laboratory 

LOL Low Oxygen Limit 

MCC Motor Control Center 

MCR Main Control Room 

MEFS Maximum Expected Fire Scenario 

MOVs Motor-Operated Valves 

MQH McCaffrey, Quintiere, and Harkleroad 

MOU Memorandum of Understanding 

NBS National Bureau of Standards (now NIST) 

NEI Nuclear Energy Institute 

NFPA National Fire Protection Association 

NIST National Institute of Standards and Technology 

NPP Nuclear Power Plant 

NRC U.S. Nuclear Regulatory Commission 

NRR Office of Nuclear Reactor Regulation (NRC) 

PE Polyethylene 

PMMA Polymethyl-Methacrylate 

PRA Probabilistic Risk Assessment 

PVC Polyvinyl Chloride 

PWR Pressurized Water Reactor 

RCP Reactor Coolant Pump 

RES Office of Nuclear Regulatory Research (NRC) 

RG Regulatory Guide 

RI/PB Risk-Informed, Performance-Based 

RIS Regulatory Issue Summary 

RTE Radiation Transport Equation 

RTI Response Time Index 

SBDG Stand-By Diesel Generator 

SDP Significance Determination Process 

SFPE Society of Fire Protection Engineers 

SNL Sandia National Laboratory 

SWGR Switchgear Room 

THIEF Thermally-Induced Electrical Failure 

TP Thermoplastic 

TS Thermoset 

UL Underwriters Laboratory 

V&V Verification & Validation 

WTC World Trade Center 

XPE Cross-Linked Polyethylene and Neoprene 

ZOI Zone of Influence 
xxvii

NOMENCLATURE 

ܣ area (m2) 

ܣ ௟௙floor area (m2

) 

ܣ ௢opening area (m2

) 

ܣ் surface area of enclosure boundary (m2

) 

ܿ specific heat, solid material (kJ/kg/K) 

ܿ௣ specific heat, gas, constant pressure (kJ/kg/K) 

ܦ fire diameter (m) or optical density (m-1) 

כܦ characteristic diameter 

ܧ experimental measurement 

݃ acceleration of gravity (m/s2

) 

݄௞ heat transfer coefficient (kW/m2

/K) 

ܪ ௖ceiling height (m) 

ܪ ௙height of fire base above floor (m) 

ܪ ௢opening height (m) 

݇ thermal conductivity (kW/m/K) 

݇௠ constant 

݇௩ volumetric entrainment coefficient 

ܭ light extinction coefficient (m-1) 

ܭ ௠mass-specific extinction coefficient (m2

/kg) 

ܮ compartment length (m) 

ܮ ௙flame height (m) 

݉ᇱ

 total mass per unit length of a single cable (kg/m) 

݉௖

ᇱᇱ combustible mass per unit area of tray (kg/m2

) 

݉ሶ mass loss or flow rate (kg/s) 

݉ሶ

ᇱᇱ mass loss rate per unit area (kg/s/m2

) 

ܯ model prediction 

݊ number of cables per tray 

ܲ probability, wall perimeter (m) 

ሶݍ

ᇱᇱ heat flux (kW/m2

) 

ሶݍ

௖

ᇱᇱ critical heat flux (kW/m2

) 

ܳሶ heat release rate (kW) 

ܳሶ

כ fire Froude number 

ݎ radial distance (m) 

ݎ ௝௖ceiling jet distance (m) 

ݏ specific area (m2

/g) 

∆ݐ burnout time (s) 

ݐ time (s) 

ܶ temperature (°C) 

ܸ volume (m3

) 

ܸሶ volume flow rate (m3

/s) 

ܹ compartment width (m), width of tray (m) 

ݔ cell dimension (m) 

ݔ ௖critical value 

ݕ product yield (kg/kg) 

ܻ mass fraction (kg/kg) 
xxviii 

ݖ ௜smoke layer interface position above base of fire (m) 

Greek: 

ߙ fire growth coefficient (kW/s2

) 

ߜ model bias factor, difference operator 

∆ܪ heat of combustion (kJ/kg) 

∆݌ pressure difference (Pa) 

߮ equivalence ratio 

Ψ stoichiometric oxygen to fuel ratio 

 mean ߤ

ߩ density (kg/m3

) 

ߪ standard deviation 

ߪ෤ா relative standard deviation, experiment 

ߪ෤ெ relative standard deviation, model 

߭ stoichiometric coefficient, residue yield (kg/kg) 

Subscripts: 

∞, ܽ ambient 

 average ݃ݒܽ

݀ݏ݌ distributed point source 

݁ effective 

݂ fuel or fire 

݂݈ floor 

݅ i

th element in set 

 leakage ܮ

݊ total number of elements in a set 

 opening ݋

ܱଶ relating to oxygen 

 plastic ݌

ݏ݌ point source 

 required ݍ݁ݎ

ݏ soot or smoke 

ݐ݁݊ tenability limit 

 total ݐ݋ݐ
1-1 

1 

INTRODUCTION 

1.1 Background 

In 2001, the National Fire Protection Association (NFPA) issued the first edition of NFPA 805, 

Performance-Based Standard for Fire Protection for Light-Water Reactor Electric Generating 

Plants, 2001 Edition1

. Effective July 16, 2004, the U.S. Nuclear Regulatory Commission (NRC) 

amended its fire protection requirements in Title 10, Section 50.48(c) of the Code of Federal 

Regulations (10 CFR 50.48(c)) to permit existing reactor licensees to voluntarily adopt fire 

protection requirements contained in NFPA 805 following a performance-based approach as an 

alternative to the existing deterministic2

 fire protection requirements. One important element in 

a performance-based approach is the estimation of fire hazard using mathematical fire models. 

Fire modeling is often used in constructing Fire PRAs to determine the effects of fire hazard so 

that the associated risk can be quantified. 

As part of its fire modeling requirements, NFPA 805 states that “fire models shall be verified and 

validated” (section 2.4.1.2.3) and that “only fire models that are acceptable to the authority 

having jurisdiction (AHJ) shall be used in fire modeling calculations” (section 2.4.1.2.1). This is 

an important requirement because the verification and validation (V&V) of fire models is 

intended to ensure the correctness, suitability, and overall quality of the method. Specifically, 

verification is the process used to determine whether a model correctly represents the 

developer’s conceptual description (i.e., whether it was “built” correctly), while validation is used 

to determine whether a model is a suitable representation of the real world and is capable of 

reproducing phenomena of interest (i.e., whether the correct model was “built”). 

In 2007, the NRC’s Office of Nuclear Regulatory Research (RES) and the Electric Power 

Research Institute (EPRI) completed a collaborative project for the V&V of five select fire 

modeling tools. The results of this study, which was performed under the NRC/RES-EPRI 

Memorandum of Understanding (MOU), are documented in NUREG-1824 (EPRI 1011999), 

Verification and Validation of Selected Fire Models for Nuclear Power Plant Applications. The 

National Institute of Standards and Technology (NIST) was also an important partner in 

developing this publication, providing extensive fire modeling and experimentation expertise. 

The V&V effort is intended to support the use of fire modeling for various NPP fire hazard 

analysis applications. 

This report builds on the V&V research described earlier by incorporating the results into a set 

of guidelines and recommendations for conducting fire modeling studies in support of 

 

1

 All references in this report to NFPA 805 are specific to the 2001 edition of the standard, which is the code of record (COR) 

required by 10 CFR 50.48(c). 

2

 In nuclear fire protection, the term “deterministic” is typically used to refer to prescriptive requirements while “deterministic” is often 

used as an adjective with “fire model” in the general fire protection field. Within this report, the usage should be clear from the 

context in which the word is used. 
INTRODUCTION 

1-2 

commercial nuclear industry applications. When the NRC’s Advisory Committee on Reactor 

Safeguards (ACRS) issued a letter to Luis Reyes, Executive Director for Operations, 

recommending publication of NUREG-1824 (EPRI 1011999), they identified two major items to 

be included in the user’s guide (Wallis, 2006). Specifically, the ACRS recommended that the 

user’s guide include: 

 Estimates of the ranges of normalized parameters to be expected in nuclear plant 

applications 

 Quantitative estimates of the uncertainties associated with each model’s predictions, 

preferably in the form of probability distributions 

The ACRS indicated that quantitative estimates of the “intrinsic model uncertainty” would be a 

valuable input in risk-informed as well as non-risk-informed applications. Chapters 2 and 3 

address the first ACRS recommendation. Chapter 4 specifically addresses the second ACRS 

recommendation, that is, the development of V&V results into quantitative estimates of model 

uncertainty. Finally, the appendices contain examples that illustrate the entire process for 

several nuclear power plant (NPP) scenarios. 

1.2 Objective 

The objective of this guide is to describe the process of conducting a fire modeling analysis, 

principally for commercial NPP applications. The process described in this guide addresses 

most of the technical elements relevant to fire modeling analysis, such as the selection and 

definition of fire scenarios and the determination and implementation of input values, sensitivity 

analysis, uncertainty quantification, and documentation. In addition, requirements associated 

with fire modeling analyses and analytical fire modeling tools are addressed through generic 

guidance, recommended best practices, and example applications. 

1.3 Scope 

1.3.1 User Capabilities 

This guide should be used as a complement to, not a substitute for, “user’s manuals” for specific 

fire modeling tools, fire dynamics textbooks, technical references, education, and training. This 

guide only compiles information and organizes it procedurally for NPP applications. Analysts 

are encouraged to review the references identified throughout the guide for in-depth coverage of 

the advantages and the range of applicability of specific models. Once a fire scenario has been 

selected, this guide will help the fire model user define the necessary modeling parameters, 

select an appropriate model, and properly interpret the fire modeling results. Since all models 

are merely approximations of reality, this guide also provides useful insights for translating real 

configurations into modeling scenarios. Due to the technical nature of this guide, users with the 

following areas of expertise will benefit the most from it: 

 General knowledge of the behavior of compartment fires 

 General knowledge of basic engineering principles, specifically thermodynamics, heat 

transfer, and fluid mechanics 
INTRODUCTION

1-3

 Ability to understanding the basis of mathematical models involving algebraic and 

differential equations 

This guide focuses on the capabilities of the models selected for V&V. However, some generic 

guidance is also provided, and most of the discussion is applicable to any fire model of the 

respective type (algebraic model, zone model, or computational fluid dynamics (CFD) model). 

Five specific models are discussed in this guide: 

(1) The NRC’s Fire Dynamics Tools (FDTS

), NUREG-1805 and Supplements 

(2) EPRI’s Fire-Induced Vulnerability Evaluation, Revision 1 (FIVE-Rev1) 

(3) NIST’s Consolidated Model of Fire Growth and Smoke Transport (CFAST) Version (6) 

(4) Electricité de France’s (EdF) MAGIC code Version (4.1.1) 

(5) NIST’s Fire Dynamics Simulator (FDS) Version (5) 

Finally, the user of this document would benefit from a familiarity with the use of fire modeling in 

a fire protection performance-based approach and NUREG/CR-6850 (EPRI 1011989), 

EPRI/NRC-RES Fire PRA Methodology for Nuclear Power Facilities. 

1.3.2 Training Resources 

For individuals seeking to enhance or update their expertise in the areas noted in section 1.3.1, 

there are several resources available, including academic courses, short courses, and written 

materials. 

Information on academic institutions with degree programs or single classes in fire protection 

engineering can be found at the Society of Fire Protection Engineers (SFPE) web site: 

http://www.careersinfireprotectionengineering.com/career_types.htm

A background in engineering fundamentals is essential for fire modelers, especially in the areas 

of fluid mechanics, thermodynamics, and heat transfer. These subjects are offered at virtually 

any academic institution with programs in fire protection and/or mechanical, aerospace, civil, 

and chemical engineering. While general courses provide basic background discussions, 

courses involving fire applications are preferable, and would be provided by the institutions 

offering courses or degree programs in fire protection engineering. 

In addition to the academic programs, short courses in fire behavior and fire modeling are 

available through professional and industry associations, such as the SFPE 

(http://www.sfpe.org) and EPRI (http://www.epri.com). 

Key written references on fire behavior and fire modeling include: 
INTRODUCTION 

1-4 

ASTM E1355–05a (2005), Standard Guide for Evaluating the Predictive Capability of 

Deterministic Fire Models, American Society for Testing and Materials, West 

Conshohocken, PA, 2005. 

Buchanan, A. H. (2001), Structural Design for Fire Safety, John Wiley and Sons, LTD, 

Chichester, England, 2001. 

Babrauskas, V., Ignition Handbook, Fire Science Publishers/Society of Fire Protection 

Engineers, Issaquah WA (2003). 

Drysdale, D., An Introduction to Fire Dynamics, 3rd Ed., John Wiley, 2011. 

Karlsson, B. and Quintiere, J.G., Enclosure Fire Dynamics, CRC Press, 2000 

Quintiere, J.G., Principles of Fire Behavior, Delmar Publishers, 1998. 

Quintiere, J.G., Fundamentals of Fire Phenomena, John Wiley, 2006. 

NFPA, Fire Protection Handbook, National Fire Protection Association, 20th Ed., A.E. 

Cote, (Editor) 2008. 

NUREG-1824 (EPRI 1011999), Verification and Validation of Selected Fire Models for 

Nuclear Power Plant Applications, Nuclear Regulatory Commission, 2007. 

SFPE, SFPE Engineering Guide to Assessing Flame Radiation to External Targets from 

Pool Fires, SFPE Engineering Guide, Society of Fire Protection Engineers, 

Bethesda, MD, March, 1999. 

SFPE, SFPE Engineering Guide to Fire Exposures to Structural Elements, SFPE 

Engineering Guide, Society of Fire Protection Engineers, Bethesda, MD, 

November, 2005. 

SFPE, SFPE Engineering Guide to Piloted Ignition of Solid Materials Under Radiant 

Exposure, SFPE Engineering Guide, Society of Fire Protection Engineers, 

Bethesda, MD, January, 2002. 

SFPE, SFPE Engineering Guide to Predicting Room of Origin Fire Hazards, SFPE 

Engineering Guide, Society of Fire Protection Engineers, Bethesda, MD, 

November, 2007. 

SFPE, SFPE Handbook of Fire Protection Engineering, 4th Ed., P. DiNenno (Editor), 

National Fire Protection Association, 2008. 

1.4 Fire Modeling Theory 

Fire development in compartments is often divided into phases depending on the dominant 

processes at any given stage of development. Ignition is dictated by the characteristics of the 

fuel item being ignited (i.e., ignition temperature, geometry, orientation, and thermophysical 

properties3

) and the strength of the ignition source. Once the flames are sustained on a burning 

fuel item, a smoke plume develops, transporting mass and heat vertically as a result of the 

buoyancy of the smoke (see Figure 1-1). The plume will entrain air as it rises, thereby causing 

the smoke to cool and become diluted; as a result, the quantity of smoke being transported will 

increase with increasing elevation. After a smoke plume strikes the ceiling, the smoke travels 

horizontally under the ceiling in a relatively thin layer, referred to as a ceiling jet. As the ceiling 

jet travels, the smoke cools with increasing distance from the plume impingement point, in part 

because of air entrainment into the ceiling jet as well as heat losses from the ceiling jet to the 

solid ceiling boundary. 

 

3

 Thermophysical properties include thermal conductivity, specific heat, and density. 
INTRODUCTION

1-5

In an ideal situation, once the ceiling jet reaches the enclosing walls, a Hot Gas Layer4

 (HGL) 

develops. As a result of the continuing supply of smoke mass and heat via the plume, the HGL 

becomes deeper, and its temperature increases. Other properties of the smoke in the HGL also 

increase (including concentration of gas species and solid particulates). 

Radiant heat from the HGL to other combustibles not involved in the fire increases their 

temperature. Similarly, the temperature of non-burning combustibles will also increase as a 

result of receiving thermal radiation from the burning item(s). As the other combustibles reach 

their respective ignition temperatures, they will also ignite. In some cases, the ignition of many 

other combustibles in the space caused by heating from the HGL occurs within a very short time 

span. This is commonly referred to as flashover. 

Several aspects of fire behavior may be of interest when applying fire models, depending on the 

purpose of the modeling application. Analysts may seek to determine the effects associated 

with heating of targets submerged in smoke or receiving radiant heat from the flames, the 

response of ceiling-mounted detectors or sprinklers to the fire environment, or other 

phenomena. 

Figure 1-1. Characteristics of compartment fires. 

 

4

 Hot Gas Layer or HGL is also called “smoke layer” or “hot upper layer” in other publications in fire protection engineering. 
INTRODUCTION 

1-6 

The most common aspects of fire behavior that typically are of interest in such analyses include, 

but are not limited to: 

 Rate of smoke production 

 Rate of smoke filling 

 Properties of the ceiling jet 

 Properties of the HGL 

 Target response to incident heat flux via either thermal radiation or convection 

A detailed review of each of these aspects is provided in texts on fire dynamics. A brief review 

of each is provided here. 

Rate of smoke production 

Smoke is defined as a combination of the gaseous and solid particulates resulting from the 

combustion process, plus the air that is entrained into the flame and/or smoke plume. 

Consequently, the rate of smoke production at a particular height in the plume is the 

combination of the generation rate of combustion products and air entrainment rate into the 

flame and/or smoke plume between the top of the fuel and the height of interest. In most cases, 

the air entrainment rate greatly exceeds the generation rate of fuel volatiles. Thus, the 

correlations used to estimate the rate of smoke production are usually taken from experimental 

research on entrained air. 

Rate of smoke filling 

The rate of smoke filling is dependent on the rate of smoke production, the heat release rate 

(HRR), floor area, height and configuration of the space, and time from ignition. For a fire with a 

steady HRR, the rate of smoke filling in a compartment will decrease with time due to a 

decrease in the smoke production rate, which decreases as the height available to entrain air 

decreases when the HGL deepens. 

Properties of the ceiling jet 

The ceiling jet transports smoke and heat horizontally away from the plume after it impacts with 

the ceiling. The response of ceiling-mounted fire detectors or sprinklers is governed primarily by 

their interaction with a ceiling jet. The temperature and concentration of smoke in a ceiling jet is 

principally dependent on the height and configuration of the space, distance to the ceiling 

impact point of the smoke plume, and the HRR of the fire. 

Properties of the HGL 

As smoke and heat are transported to the HGL via the smoke and fire plumes, the properties of 

the HGL will change. The principal properties of interest include the depth, temperature, and 

gas concentrations in the HGL. The magnitude of the properties depends on the HRR of the 

fire, geometry of the space, ventilation openings (permitting material from the HGL to leave the 

space, providing air to the fire, and/or causing a stirring action), yields of combustion products, 
INTRODUCTION

1-7

and the elapsed time after ignition. These changes can be tracked by considering the 

conservation of energy, mass, and species relative to the HGL. 

Target response to incident heat flux via either thermal radiation or convection 

The targets’ temperature will increase as a result of receiving heat via either thermal radiation or 

convection. Radiation heat transfer is dependent on the intensity of thermal radiation emitted by 

a source, the size of the source, and the proximity of the target to the source. For this 

application, the flame height, the portion of heat released from the fire as radiation, and the 

distance separating the target from the flame are the dominant parameters. Convective heating 

occurs whenever the target is submerged in the smoke plume or HGL. 

1.5 Fire Modeling Tools 

1.5.1 Algebraic Models 

Algebraic models may be standalone equations found in literature or may be contained within 

spreadsheets (such as the NRC’s FDTs

), and can help give a general understanding of one of 

the fire environment phenomena. These equations are typically closed-form algebraic 

expressions, many of which were developed as correlations from empirical data. In some 

cases, they may take the form of a first-order ordinary differential equation, and, when used 

properly, can provide an estimate of fire variables, such as; HGL temperature, heat flux from 

flames or the HGL, smoke production rate, depth of the HGL, and the actuation time for 

detectors. 

Algebraic models are helpful because they require minimal computational time and a limited 

number of input variables. When applying the results of the algebraic models, users need to be 

aware that the development of most equations involved approximations to simplify the analysis. 

Algebraic models are useful primarily as screening tools (i.e., to provide a rough approximation 

for an analysis, perhaps as a check of an aspect of the results of the computer-based models), 

and are also applicable when only one phenomenon can be treated in isolation: for instance, 

plume or ceiling jet correlations are not applicable if there is a significant HGL unless they are 

modified to account for this effect. 

1.5.2 Zone Models 

A zone model, such as the Consolidated Fire Growth and Smoke Transport Model (CFAST) or 

MAGIC, calculates fire environment variables using control volumes, or zones, of a space. The 

zones correspond to a cooler lower layer and a HGL, as depicted in Figure 1-2. The 

fundamental idea behind a zone model is that each zone is well-mixed and that all fire 

environment variables (temperature, smoke concentration, etc.) are therefore uniform 

throughout the zone. Conditions in each zone are calculated by applying conservation 

equations and the ideal gas law. The variables in each zone change as a function of time and 

rely on the initial conditions specified by the user. There is a well-defined boundary separating 

the two zones, though this boundary may move up or down throughout the simulation. 
INTRODUCTION 

1-8 

Figure 1-2. A two-zone enclosure fire with an HGL above and a cool lower layer below.

Zone models are most applicable in situations involving simple geometries or where spatial 

resolution within a compartment is not important. The preparation of input for a zone model, the 

computation time, and the amount of output data generated are slightly more extensive than a 

simple algebraic model; however, the overall computational time cost is still low. 

Zone models can easily analyze conditions resulting from fires involving single compartments or 

compartments with adjacent spaces, and are often used to compute the HGL temperature, HGL 

composition, and target heat fluxes. They are also capable of modeling some effects of natural 

and mechanical ventilation in both horizontal and vertical directions. Some zone models allow 

the user to select a thermal plume model, which may assist in better characterization of a known 

fire scenario, while others use an axisymmetric smoke plume. Other features of a zone model 

may include a user-specified single zone or multiple fire plumes. 

Simulations of spaces with complex ceilings or numerous compartments can be challenging 

with a zone model. Because zone models specify uniform conditions in the HGL and lower 

layer, results cannot be distinguished between locations at different distances from the fire. Due 

to the zone approach, smoke transport time lags are not considered in the simulation, which is 

an acceptable approximation in relatively small spaces but may lead to significant error in largevolume spaces or spaces with large aspect ratios. 

Smoke production, fire plume dynamics, ceiling jet characteristics, heat transfer, and ventilation 

flows are all algebraic models embedded within zone models. Other parameters that can be 

calculated with a zone model include thermal behavior, detection response, and suppression 

response. The output of a zone model is typically simple to understand and is generally 

presented through an automatic user interface. 

HGL 

Mass 

outflow 

Mass inflow 

Plume mass 

flow 
INTRODUCTION

1-9

Most zone models have default values that must be recognized and adjusted as necessary to 

obtain an accurate solution. The model user must understand and justify the relevance of the 

default values used in any application. Fire model users are expected to assess the 

appropriateness of default values provided in the fire models and make changes or adjust 

values as necessary. User manuals and technical references for each zone model outline such 

values and may provide recommended ranges for the parameters. 

1.5.3 CFD Models 

A computational fluid dynamics (CFD) model is often useful when trying to determine fire 

variables at a specific location or when there are geometric features that are expected to play a 

significant role in the results beyond what can be calculated in a zone model approximation. A 

typical CFD model consists of a preprocessor, a solver, and a postprocessor. CFD models can 

provide a detailed analysis in both simple and complex geometries. 

CFD models essentially apply a series of conservation and state equations across multiple cell 

boundaries in a space. The number of cell boundaries depends on the mesh size, which breaks 

the geometry into three-dimensional subvolumes called cells. Solutions to the conservation 

equations of mass, momentum, and energy are updated as a function of time within each 

numerical grid cell, with the solutions in all cells collectively describing the fire environment 

within the geometry at the cell resolution. 

The number of grid cells defines the type of mesh. A fine mesh is made up of numerous grid 

cells. Since the equations are applied at each cell’s boundaries, a more detailed distribution of 

fire parameters is characterized. A coarse mesh is made up of fewer grid cells and can result in 

less accurate results. The type of mesh and number of grid cells should be based on the 

geometry and the desired results. If a more detailed simulation is needed, then a finer mesh 

should be used. Be aware that a finer mesh significantly increases the computational running 

time of the model as well as the quantity of output data. 

CFD models have much better spatial fidelity than zone models, being able to distinguish 

conditions in one part of the space from another. Because of the appreciable amount of time 

and effort required to apply CFD models as compared to zone models or algebraic models, CFD 

models are generally applied when: 

 Spatial resolution is important, relative to either the locations of fuel packages or targets. 

 Large compartments relative to the fire size are involved. 

 Compartments have complex geometries, flow connections, or numerous obstructions in 

the upper part of the compartment. 

 Large numbers of compartments are within the area of interest and the presence of each 

compartment is expected to affect the fire environment in the area of interest. 

An example of a CFD simulation of a fire experiment is shown in Figure 1-3. The purpose of the 

calculation was to simulate an experiment that was part of the validation study described in 

NUREG-1824 (EPRI 1011999). In the experiment, a pan fire was placed in a relatively small 
INTRODUCTION 

1-10 

compartment, and temperatures and heat fluxes were measured at various locations. The CFD 

simulation is able to describe the changing behavior of the fire as it interacts with its 

surroundings. 

Figure 1-3. A Smokeview visualization of a CFD model of a compartment fire experiment.

While CFD models provide a detailed analysis of a space, they are costly to create, simulate, 

and maintain. The input files created in the preprocessing stage require a significant effort to 

create. The user must understand the code syntax and the implications and approximations 

embedded in the model. A firm understanding of fire dynamics is important in providing input 

data that is relevant to the application. Most CFD models have default values that must be 

recognized and adjusted as necessary to obtain an accurate solution. The model user must 

understand and justify the relevance of the default values used in any application. Fire model 

users are expected to assess the appropriateness of default values provided in the fire models 

and make changes or adjust values as necessary. User manuals and technical references for 

each CFD model outline such values and may provide recommended ranges for the 

parameters. 

Depending on the complexity of the scenario and the computer’s computational power, the 

solver within the model can take anywhere from a few hours to weeks to complete all the 

calculations. This time cost depends on the measured parameters, the size of the geometry, 

and the mesh size of the calculations. Outputs of CFD models are visualized through a post-
INTRODUCTION

1-11

processing program. The CFD model developed at NIST, Fire Dynamics Simulator (FDS), 

employs the program “Smokeview” to represent distributions of temperature, mass, heat flux, 

burning rate, etc. throughout the geometry. These parameters can be described through point 

locations, isocontours, or vector diagrams. Output data may also be stored in a commaseparated value file format that can be read by a standard spreadsheet program. 

1.5.4 Fire Model Verification and Validation (V&V) 

The use of fire models requires a good understanding of their limitations and predictive 

capabilities. For example, NFPA 805 states that fire models shall only be applied within the 

limitations of that fire model (section 2.4.1.2.2). ASTM E 1355, Standard Guide for Evaluating 

the Predictive Capability of Deterministic Fire Models, provides definitions of the terms model 

verification and model validation. 

Model Verification is the process of determining that the implementation of a calculation method 

accurately represents the developer’s conceptual description of the calculation method and the 

solution to the calculation method. The fundamental strategy of verification of computational 

models is the identification and quantification of error in the computational model and its 

solution. 

Model Validation is the process of determining the degree to which a calculation method is an 

accurate representation of the real world from the perspective of the intended uses of the 

calculation method. The fundamental strategy of validation is the identification and 

quantification of error and uncertainty in the conceptual and computational models with respect 

to intended uses. 

As noted in Section 1.1, NRC/RES and EPRI conducted a collaborative project for V&V of five 

fire models. The results of this project were documented in NUREG-1824 (EPRI 1011999), 

Verification and Validation of Selected Fire Models for Nuclear Power Plant Applications. 

1.6 Fire Modeling Applications 

Fire modeling is used in a variety of NPP applications. Examples include license amendments 

or exemption requests, fire induced circuit failure analyses, NFPA 805 performance based 

applications, and fire PRA support. This section provides a brief overview of common fire 

modeling applications. 

1.6.1 License Amendments and Exemptions 

Fire modeling has been used to justify requests for changes from the deterministic requirements 

contained in 10 CFR 50.48 and Appendix R of 10 CFR 50. License amendments and 

exemption requests are evaluated by NRC staff on a case by case basis. 

1.6.2 Fire Induced Circuit Failures 

The disposition of certain fire-induced circuit failures, such as multiple spurious operations 

(MSOs), is another accepted fire modeling application used in commercial NPPs. MSOs 

typically involve one or more fire-induced component failures that include spurious operation 

due to hot shorts, shorts to ground, or open circuits as a result of fire damage to electrical 

cables. 
INTRODUCTION 

1-12 

1.6.2.1 Deterministic Application 

When one of the redundant safe-shutdown trains in a fire area is maintained free of fire damage 

by one of the specified means in Regulatory Position 5.3.1.1 of Regulatory Guide (RG) 1.189, 

Revision 2, then fire modeling may be used to demonstrate that components important to safe 

shutdown, including systems, structures, and components (SSCs) that are not part of the 

success path, are protected from fire damage. When fire modeling is used to demonstrate that 

components important to safe shutdown are protected from fire damage, the analysis would 

consider all in situ and transient fire sources in the area and all targets that involve components 

important to safe shutdown. Variations in fire compartment configuration (e.g., doors open or 

closed, ventilation system on or off, etc.) are to be included in this fire modeling analysis. The 

analysis needs to clearly demonstrate that the largest expected fire will not damage 

components important to safe shutdown. The phrase “largest expected” defines a fire that is 

consistent with the characteristics of the ignition sources and other combustibles in the area 

where the fire can propagate. 

1.6.2.2 Risk-Informed, Performance-Based Application 

RG 1.205 provides regulatory guidance on the evaluation of fire-induced circuit failures when 

used in applications that support risk-informed, performance-based decision making. Within a 

risk-informed, performance-based NFPA-805 license basis, fire-induced circuit failure5

 scenarios 

can be evaluated using a fire PRA. When applicable, the fire-induced circuit failure scenarios 

are included in the plant response model. Chapter 5 of NUREG/CR-6850 provides information 

on the definition of and methods for developing plant response models, such that the fireinduced circuit failure contribution is included in the quantification of core damage and large 

early release frequencies. The model needs to address both the possible plant impact caused 

by spurious operation(s) and the inability to restore equipment operability as a result of fire 

damage. With the applicable fire-induced circuit failure scenarios modeled in the risk 

assessment, quantitative risk calculations could be used to show that the scenarios present 

acceptable risk contributions within the overall plant fire risk profile, as discussed in RG 1.205. 

Fire modeling can be used within the framework of the fire PRA to characterize the risk 

associated with fire scenarios. Determining the risk associated with fire scenarios may include 

such evaluations as developing a range of fire sizes that may damage cables at varying 

distances from an ignition source, with the corresponding times that it would take a fire to grow 

to those damaging sizes. In this context, the fire modeling objective is to predict the fire 

conditions that could induce cable damage and thus trigger fire-induced circuit failure scenarios, 

so that the corresponding risk contribution is captured in the analysis. If the fire-induced circuit 

failure is successfully resolved using fire modeling in a probabilistic approach, it must 

demonstrate that the damage necessary to cause the fire-induced circuit failure would not occur 

for the postulated fire scenario (e.g., a specific ignition source is screened from the analysis), or 

that the risk associated with the fire-induced circuit failure condition is acceptable, given the 

specific characteristics of the fire necessary to produce the postulated condition. 

1.6.3 NFPA 805 Performance-Based Applications 

NFPA 805 allows the use of either fire modeling or fire risk evaluations to demonstrate that 

performance based requirements are satisfied. 

 

5

 The term fire-induced circuit failure is intended to address loss of function due to fire damage to cables and equipment as well as 

spurious operation(s) of that equipment either singly or in multiples. 
INTRODUCTION

1-13

1.6.3.1 Fire Modeling 

The NFPA 805 requirements associated with fire modeling are organized into two sections, 

Section 2.4.1 and Section 4.2.4.1. Section 2.4.1 describes the requirements associated with the 

fire modeling calculations and analysis. Section 4.2.4.1 describes the requirements for the 

implementation of a performance-based fire modeling analysis. 

Section 2.4.1.2 of NFPA 805 describes the requirements for the use of fire models, which 

include: 

 The use of fire models acceptable to the authority having jurisdiction (AHJ), i.e., the U.S. 

Nuclear Regulatory Commission 

 The application of fire models within their range and limitations 

 Fire models shall be verified and validated 

In the context of this application, the specific analytical capabilities within the fire model need to 

be verified and validated. Model capabilities not invoked in a specific calculation are outside the 

scope of this requirement. NUREG-1824 (EPRI 1011999) is an example of a verification and 

validation study for fire models specifically developed for NPP applications. 

Section 4.2.4.1 is subdivided by process element as follows: 

Identify Targets (NFPA 805 § 4.2.4.1.1): This subsection requires the description of the 

targets (e.g., equipment or cables) and target locations (specific locations of raceways/conduits 

containing the cables, electrical cabinets, or equipment) associated with them needed to 

achieve the nuclear safety performance criteria. 

Establish Damage Thresholds (NFPA 805 § 4.2.4.1.2): This subsection requires the 

description of damage thresholds for the equipment and cables needed to achieve the nuclear 

safety performance criteria. The damage threshold (i.e., target vulnerability) for cables exposed 

to fire is expressed in most cases in the form of an incident heat flux on the cables or the cables’ 

surface temperature shall be established in accordance with Section 2.5 of NFPA 805. 

Determine Limiting Conditions (NFPA 805 § 4.2.4.1.3): This subsection requires the 

description of the combination of equipment or required cables with the highest susceptibility to 

any fire environment. 

Establish Fire Scenarios (NFPA 805 § 4.2.4.1.4): This subsection requires the description of 

a given area’s fire conditions resulting from the identified and analyzed fire scenarios. It should 

be noted that the scenario definition is consistent with the requirements listed under § 2.4.1.3 of 

NFPA 805. Appendix C of NFPA 805 provides two categories of fire scenarios used in the 

standard as follows: 

Maximum Expected Fire Scenario: The maximum expected fire scenario (MEFS) is 

defined in NFPA 805 Section C.3.2, as the scenario that is used to determine by fire 

modeling whether the performance criteria are met in the fire area being analyzed. The 

input data for the fire modeling of the MEFS should be based on the following: 

 Existing in-situ combustibles in the fire area 
INTRODUCTION 

1-14 

 Types and amounts of transient combustibles that industry experience and 

specific plant conditions indicate can reasonably be anticipated in the fire area 

 Heat release and fire growth rates for actual in-situ and transient combustibles 

that are realistic and conservative based on available test data and applicable 

fire experience 

 Ventilation within normal operating parameters with doors in the open or closed 

position 

 Active and passive fire protection features operating as designed 

Limiting Fire Scenario: The limiting fire scenario (LFS) is defined in NFPA 805 Section 

C.3.3 as fire scenario(s) in which one or more of the inputs to the fire modeling 

calculation (e.g., heat release rate, initiation location, or ventilation rate) are varied to the 

point that the performance criterion is not met. The intent of this scenario(s) is to 

determine that there is a reasonable margin between the expected fire scenario 

conditions and the point of failure ... [T]he LFS can be based on a maximum possible, 

though unlikely, value for one input variable or an unlikely combination of input variables. 

... The values used for LFS input should remain within the range of possibility but can 

exceed that determined or judged to be likely or even possible. 

For each fire scenario, the environmental conditions resulting from each MEFS are compared to 

the damage thresholds for the targets in the fire area. If damage thresholds are not exceeded, 

the targets in the fire area can be considered free of fire damage under the conditions of the 

postulated MEFS. 

By definition, the effects of the LFS include damage to the targets in the fire area under 

consideration. Fire modeling parameters that have been varied to establish the LFS conditions 

are identified and described. 

1.6.3.2 Fire Risk Evaluations 

A fire risk evaluation for the NFPA 805 performance-based approach uses fire PRA methods, 

tools, and data to compare the risk associated with implementation of the proposed alternative. 

Sections 2.4.3 and 4.2.4.2 of NFPA 805 contain specific requirements for the use of fire risk 

evaluations. The fire PRA methods, tools, and data must be acceptable to the AHJ, and they 

should be appropriate for the nature and scope of the evaluation, be based on the as-built and 

as-operated and maintained plant, and reflect the operating experience at the plant. The 

evaluation uses core damage frequency (CDF) and large early release frequency (LERF) as 

measures for risk. The proposed alternative must ensure that the philosophies of defense in 

depth and sufficient safety margin are maintained. Section 1.6.4 of this report provides 

information on using fire modeling in support of fire PRA. 

1.6.4 Fire Modeling in Support of Fire PRA 

Fire PRA often applies fire modeling in the fire scenario development and analysis process. A 

fire scenario in a Fire PRA is often modeled as a progression of damage states over time, which 

is initiated by a postulated fire resulting from an ignition source. Each damage state is 

characterized by a time and a set of targets damaged within that time. Fire modeling is 

commonly used to determine the targets affected in each damage state and the associated time 

at which this occurs. The first damage state usually consists of damage only to the ignition 

source itself. Depending on the characteristics and configuration of the scenario, the last 

damage state may consist of an HGL formation that leads to full room damage by exceeding 
INTRODUCTION

1-15

predetermined damage criteria. Damage states between the first and final states capture target 

sets compromised as the fire propagates through intervening combustibles. 

Each scenario progression postulated in a Fire PRA is quantified to determine its contribution to 

fire risk. The most common fire risk metrics are the reactor Core Damage Frequency (CDF) 

and Large Early Release Frequency (LERF) of radioactive material. NUREG/CR-6850 provides 

guidance on the quantification of fire risk. 

The Fire PRA standard (ASME/ANS RA-Sa-2008 and Addenda RA-Sa-2009) lists requirements 

for all the technical elements associated with a Fire PRA, includes specific requirements for the 

use of fire models. The standard addresses: (1) the selection of appropriate fire modeling tools 

for estimating fire growth and damage behavior, considering the physical behaviors relevant to 

the selected fire scenarios, and (2) the application of fire models that are sufficiently capable of 

modeling the conditions of interest within known limits of applicability. In the case of analytical 

fire models, the standard requires the use of appropriate fire modeling tools with the ability to 

model the conditions of interest within known limits of applicability. 

1.7 Organization of the Guide 

The guidance material provided in this document is divided into five chapters and a number of 

appendices, as outlined below. 

 Chapter 2 presents a qualitative overview of the process for conducting fire modeling, 

including the basic principles of fire simulation, advantages and limitations of the 

technology, and brief descriptions of the five models 

 Chapter 3 provides specific guidance on selecting models to address typical scenarios in 

commercial NPPs 

 Chapter 4 contains information on determining the sensitivity and uncertainty associated 

with fire modeling calculations 

 Chapter 5 contains the list of references identified throughout this document 

 Chapter 6 contains general information on the eight scenarios documented in the 

appendices 

 Appendices A through H provide detailed examples of fire modeling analyses of typical 

NPP scenarios: 

o Appendix A – Cabinet Fire in Main Control Room 

o Appendix B – Cabinet Fire in Switchgear Room 

o Appendix C – Lubricating Oil Fire in Pump Compartment 

o Appendix D – Motor Control Center Fire in Switchgear Room 

o Appendix E – Trash Fire in Cable Spreading Room 

o Appendix F – Lubricating Oil Fire in Turbine Room 

o Appendix G – Transient Fire in Multi-Compartment Corridor 

o Appendix H – Cable Tray Fire in Annulus 

 CD containing the following files: 

o Appendix A Files 

 Algebraic models 

 CFAST and FDS input files 

o Appendix B Files 
INTRODUCTION 

1-16 

 Algebraic models 

 CFAST and FDS input files 

o Appendix C Files 

 FDS and MAGIC input files 

o Appendix D Files 

 CFAST and FDS input files 

o Appendix E Files 

 Algebraic models 

 CFAST and FDS input files 

o Appendix F Files 

 Algebraic model files 

 FDS files 

o Appendix G Files 

 Algebraic model files 

 MAGIC input files 

o Appendix H Files 

 FDS input files 

o Fire Modeling Software 

 CFAST Software Guides 

 FDS Software Guides 

 NUREG-1805 Spreadsheets 

o Related Publications 

 
2-1 

2 

THE FIRE MODELING PROCESS 

This chapter provides a general step-by-step process for modeling fires in commercial nuclear 

power plants (NPPs). The recommended methodology comprises six steps: (1) define fire 

modeling goals and objectives, (2) characterize the fire scenarios, (3) select fire models, 

(4) calculate fire-generated conditions, (5) conduct sensitivity and uncertainty analyses, and (6) 

document the analysis. A simplified process involving the six steps is shown in Figure 2-1. 

 

Start

Define fire modeling goals

and objectives (Section 2.1)

Characterize the fire

scenarios(Section 2.2)

Selectthe fire model(s)

(Section 2.3)

Can the

problem

be

redefined

?

Is

another

model

available

?

Isthe

model

suitable?

An alternate analysis may be

required

End

Calculate the fire generated

conditions(Section 2.4)

Conduct a sensitivity and

uncertainty analysis (Section

2.5)

Are the

goals and

objective

satisfied?

Document the analysis

(Section 2.6)

End

Yes

Yes

Yes Yes

No

No No

No

Figure 2-1. Fire modeling process. 
THE FIRE MODELING PROCESS 

2-2 

2.1 Step 1: Define Fire Modeling Goals and Objectives 

The first step in a fire model analysis is to identify and state the fire modeling goals and 

objectives. A fire modeling goal is a broad statement of what needs to be accomplished using 

fire modeling (SFPE, 2007). The goal(s) should also identify whether the analysis results are 

intended to help resolve a deterministic issue or are intended as input for a probabilistic risk 

assessment (PRA). 

The objectives are more specific and describe in engineering terms how the goal(s) will be met 

(SFPE, 2007). Clearly defined objectives provide focus and are needed to correctly select the 

fire scenarios that will be evaluated and the fire modeling tools that will be used. In order to 

define the objectives, some understanding of the conditions by which success or failure are 

measured (i.e., the performance criteria) is necessary at the analysis outset. Any fire modeling 

objective may thus be viewed as a statement defining what needs to be accomplished, which 

criteria will be used to define success or failure, and which analysis process will be followed. 

The criteria should be stated in terms that can be achieved by the fire modeling analysis. 

Some common situations in commercial NPPs where fire modeling may be used to determine 

which goals and objectives would be developed include, but are not limited to: 

 Evaluating whether or when a fire could damage a single electrical cable or component 

 Evaluating whether or when a fire could damage multiple electrical cables or 

components 

 Evaluating whether conditions are habitable in an enclosure 

 Evaluating the potential for fire propagation through or across a fire barrier 

 Evaluating detection or sprinkler actuation 

 Evaluating the potential for fire propagation between fire zones or fire areas, or to 

secondary combustibles 

 Evaluating the structural response under fire conditions 

The performance criteria are an important aspect for developing the fire modeling objectives 

and will be specific to the fire modeling application. The performance criteria will often include, 

but are not limited to one or more of the following: 

 Maximum acceptable surface temperature or jacket-insulation interface temperature for 

a cable, component, secondary combustible, structural element, or fire-rated 

construction 

 Maximum acceptable incident heat flux for a cable, component, structural element, or 

secondary combustible 

 Maximum acceptable exposure temperature for a cable, component, structural element, 

or secondary combustible 

 Maximum acceptable enclosure or key structural element temperatures 
THE FIRE MODELING PROCESS

2-3

 Maximum smoke concentration or minimum visibility 

 Maximum or minimum concentration of one or more gas constituents, such as carbon 

monoxide, oxygen, hydrogen cyanide, etc. 

The performance criteria may also involve sequences of events, such as “detection or sprinkler 

actuation before cable damage, which occurs when the surface temperature exceeds a 

specified threshold value.” NUREG/CR-6850 (EPRI 1011989) provides some performance 

thresholds for common NPP targets (see Appendix H) as well as for habitability (see Section 

11.5.2.11). 

A few simple examples will illustrate the various ways in which a fire modeling goal may be 

stated. In many NPP fire modeling applications, the motivation for a fire modeling analysis is a 

need to know whether or not an electrical cable or a component remains free of damage from a 

fire. This could be very specific (i.e., a particular exposure fire exposing a particular cable) or 

general (i.e., the maximum distance from which a particular type of fire could damage cables). 

In addition, it may only be necessary for a single fire to damage a single cable, or it may be 

necessary to simultaneously damage two particular cables with a known separation. The 

following are examples of goals that would lead to a fire modeling analysis: 

 “Ensure that Panel ‘X’ and Cable ‘Y’ are not subject to failure given a fire in Room ‘Z.’” 

 “Tabulate the distance through which an electrical cabinet ignition source could 

adversely affect electrical targets for use as a screening tool in support of a PRA.” 

 “Ensure that Cable ‘X’ and Cable ‘Y’ both do not fail in Room ‘Z’ when exposed to a 

single transient fuel package fire.” 

 “Quantify the potential benefit of the sprinkler system in Room ‘X’ for preventing damage 

to Cable ‘Y’.” 

Each of the goals explicitly states the purpose of the analysis and the means by which success 

is determined in terms that can be achieved by a fire modeling analysis. The objectives are 

more specific and may include specific steps that will be followed to satisfy the goal. Some 

examples of objectives that support the previously cited example goals are as follows: 

 “Perform a calculation to determine if a fire in Fire Area ‘X’ involving Panel ‘Y’ could 

cause the surface temperature of Cable ‘Z’ to exceed a specified threshold value.” 

 “Evaluate the maximum distance from any surface of an electrical cabinet at which a 98th

percentile heat release rate (HRR) fire in Fire Zone ‘X’ could cause the surface 

temperature of a cable to exceed a specified threshold value.” 

 “Perform a calculation to determine if a fire in Fire Area ‘X’ involving a transient fuel 

package could simultaneously cause the surface temperature of both Cables ‘Y’ and ‘Z’ 

to exceed a specified threshold value.” 

 “Determine if any ignition sources in Fire Zone ‘X’ could damage cables in Raceway ‘Y’ 

by causing the surface temperature of any cables in the raceway to exceed a specified 

threshold value before the sprinkler system actuates.” 
THE FIRE MODELING PROCESS 

2-4 

Thus, the objectives define in specific terms the means by which a goal will be fulfilled and the 

means by which success is determined. 

2.2 Step 2: Characterize Fire Scenarios 

The second step in the fire modeling process is to characterize the relevant fire scenarios that 

capture those technical elements necessary to address the goals. A fire scenario is defined 

within this guide as a set of elements needed to describe a fire event. These elements usually 

include the following: 

 the enclosure details (i.e., compartment) 

 the fire location within the enclosure 

 the fire protection features that will be credited 

 the ventilation conditions 

 the target locations 

 the secondary combustibles 

 the fire, which is sometimes referred to as the “ignition source” 

A number of the fire scenario elements may also be viewed as fire model input. This section 

provides a broad perspective on the considerations that apply when formulating the appropriate 

fire scenario, given a fire modeling goal. Chapter 3 provides additional guidance on specific fire 

scenario elements as they apply to various fire modeling goals and objectives evaluated with a 

particular fire model. 

Note that when characterizing the fire scenarios, preliminary consideration should also be given 

to how many scenarios are needed to address a particular goal and which specific fire event 

characteristics each scenario should capture (i.e., which scenarios are needed). In general, at 

least one fire scenario would be necessary to assess the effects for a single ignition sourcetarget set pair. The analyst should become familiar with the information necessary to develop 

input files for the fire modeling tools. In practice, this information should be collected during the 

process of selecting and describing fire scenarios to minimize the number of walkdowns and 

document/drawing reviews. 

2.2.1 General Considerations 

Various documents provide guidance for describing fire scenarios from a technical and 

regulatory perspective. Most of these documents are “application”-specific; for instance, NFPA 

805 defines two general categories of fire scenarios, limiting fire scenarios (LFSs) and 

maximum expected fire scenarios (MEFSs). According to NFPA 805, the input values 

necessary to determine the MEFS are those that lead to the “most challenging fire that could 

reasonably be anticipated for the occupancy type and conditions in the space.” For LFSs, “one 

or more of the inputs to the fire modeling calculation (e.g., heat release rate, initiation location, 

or ventilation rate) are varied to the point that the performance criterion is not met.” If there is a 
THE FIRE MODELING PROCESS

2-5

“sufficiently large" margin between the MEFS and the LFS, then the fire scenario can be 

screened from the risk assessment (Gallucci, 2011). 

In a Fire PRA, the goal is to quantify the risk contribution from individual scenarios and to 

identify potential risk-contributing scenarios (e.g., fires impacting important targets in the 

compartment). Although specific elements in the scenario selection process are “standardized” 

for guidance and completeness purposes, a certain degree of fire protection engineering 

judgment is also necessary. NUREG/CR-6850 (EPRI 1011989) contains information on fire 

frequency, cable (target) selection, HRR, damage criteria, and other information that is useful in 

developing fire scenarios. 

Selected scenarios should represent a complete set of fire conditions that are important to the 

fire modeling goal. For example, if the goal of the fire modeling analysis is to estimate whether 

specific cable(s) will remain free of fire damage, the analyst should consider exposures that are 

close to the cables as well as exposures that are farther away. A small, localized fire exposure 

could be a greater challenge than a larger fire that is farther away, or vice versa. It may not 

always be appropriate to select, or at times even possible to define, the worst case fire scenario 

prior to conducting the analysis, due to the different exposure mechanisms associated with 

various ignition sources. In large enclosures with a limited number of targets to protect, such as 

a turbine building in an NPP when the protection of a safety-related circuit is the fire modeling 

goal, it is easier to locate the targets of interest and then identify those fire sources capable of 

affecting that target. 

When attempting to characterize the fire scenario, plant walkdowns should be an essential 

aspect of the scenario selection. Many key decisions relevant to fire modeling, including those 

related to model selection and input parameters, are influenced by observations made during 

walkdowns. The occupants, the access level to a particular area, and the fire brigade/fire 

department access should be observed during the walkdowns, as applicable. 

It should also be noted that not all the elements associated with a commercial NPP fire scenario 

can be directly modeled using the tools within the scope of this guide (e.g., the effect of 

suppression activities by the fire brigade or the conditions in a space after a sprinkler system 

has actuated). It is important, however, not to limit the scenario selection and description to 

those elements that can be modeled. 

2.2.2 Enclosure Details 

The enclosure details include the identity of the enclosures that belong in the fire model 

analysis, the physical dimensions of the enclosures included in the fire model, and the boundary 

materials of each enclosure. The enclosure(s) that belong in the fire model may depend on the 

fire modeling goal, the complexity and connectivity of the spaces in the general area of interest, 

the type of analysis conducted, and the type of fire model selected. It is possible that no 

enclosure may be involved, as would be the case for an exterior transformer fire. As a 

minimum, the space containing the fire would normally be included in the fire model, though 

treatments involving algebraic plume temperature or flame height correlations would not model 

the enclosure effects per se. Multiple enclosures might be necessary if there are flow 

connections (natural or forced) to adjacent areas and if the conditions in both areas could affect 

the analysis results or are of interest. Care should be taken to consider the potential effects of 

fires in adjacent areas on the targets of interest. In some cases, a heating, ventilation, and air 

conditioning (HVAC) recirculation system may involve areas that are fairly remote from the area 

of interest. Depending on the type of analysis conducted, the conditions within either or both 

areas may be of interest, and the fire model would thus include both spaces. 
THE FIRE MODELING PROCESS 

2-6 

The physical dimensions of the enclosure and the boundary materials are model input and 

should be determined once the fire model has been selected, since the level of detail varies 

considerably among the fire models. One-zone models may only require a volume and 

boundary area; two-zone models will typically require the length, width, and height; and 

computational fluid dynamics (CFD)-type models will require details commensurate with the 

model grid resolution. The determination of the correct physical dimensions and boundary 

materials are described in Chapter 3 for various types of NPP fire scenarios. 

2.2.3 Fire Location 

The location of the fire will depend strongly on the fire modeling goal, the target location, and 

the fire modeling tool selected. For example, when evaluating the performance of a fire barrier 

system, fire scenarios challenging the barriers are of interest; when conducting a risk analysis, 

fire scenarios impacting safety-related circuits may be of primary interest. The selected 

scenarios for these two applications may not be the same. 

When selecting the fire location, the fire scenario should challenge the conditions being 

estimated. For example, if the goal is to evaluate flame radiation to a target, locating the ignition 

source relatively far from the target may not provide the best representation of the fire hazards. 

If the goal is to determine whether a fire can cause two circuits in different raceways to fail, it 

may be appropriate to locate the fire between the two raceways. There will be situations in 

which the target location is fixed within the plan area of a space, but there is some flexibility in 

the vertical placement. A good example of this is an electrical cabinet fire. For a given 

electrical cabinet, the floor position is fixed; however, the base of the fire is not. Depending on 

the type of cabinet, it may be appropriate to locate the fire base at the cabinet floor (e.g., open 

back and containing thermoplastic (TP) cables), at the top (open top and no side vents), or 

somewhere in between. NUREG/CR-6850 Supplement 1 (EPRI 1019259), Fire Probabilistic 

Risk Assessment Methods Enhancements, recommends a fire elevation equal to the top of the 

upper vent or 0.3 m (1 ft) below the cabinet top for cabinets meeting certain physical 

constraints. 

In the case of transient fuel package fires or other types of fires that are not fixed, some 

consideration of the effects of the wall or corner on the upper gas layer temperature is 

necessary. If the primary exposure mechanism is the Hot Gas Layer (HGL), then locating the 

fire in a corner or near a vertical boundary will produce higher HGL temperatures. However, the 

type of analysis may dictate that multiple locations be postulated not necessarily yielding the 

worst fire effects. Other features that affect the fire location could include the presence or slope 

of a floor, particularly when a melting plastic or liquid hydrocarbon fuel is considered and 

transient fuel packages may be staged on mezzanine levels, scaffolding, or platforms. The 

October 19, 1989, turbine lubricating oil fire at the Vandellos NPP in Spain illustrated this 

problem. Additional information can be found in NUREG/CR-6738, Risk Methods Insights 

Gained from Fire Incidents. 

The following general guidelines and considerations for locating the fire for different fire 

exposure mechanisms may be followed as applicable: 

 Targets in the fire plume or ceiling jet. Locating a source on top of a cabinet ignition 

source usually results in the most severe fire conditions, since the cabinet walls will not 

affect fire-generated conditions. Furthermore, since the fire is located in the highest 

possible position, flames are expected to be higher, and temperatures in the plume and 

ceiling jet will also be high. The user should judge whether this is conservative based on 
THE FIRE MODELING PROCESS

2-7

the goal of the analysis. For example, this would not necessarily be conservative if 

detection of the fire was a critical aspect of the analysis. 

 Targets affected by flame radiation. Combustible materials that are not fixed, such as 

transient fuel packages and unconfined liquid spills, should be located so that there is an 

unobstructed (when no passive fire protection system is credited) view between the 

source and the target. A horizontal path between flame and target provides the highest 

heat flux to the target. 

 Targets engulfed in flames. Flame height calculations should be performed to determine 

whether the selected location will result in targets engulfed in flames. Proper justification 

should be provided as to the location of the fire to ensure that the target is out of the 

flames. For example, consider the case where the analyst locates the fire on top of an 

enclosed cabinet, resulting in a cable tray engulfed in flames. This would represent the 

most severe exposure for the cable tray since the fire is expected to start somewhere 

inside the cabinet. The analyst may choose to lower the fire’s position and ignore the 

cabinet walls after a visual examination identifies the actual location of the combustibles. 

 Targets immersed in the HGL. The fire’s elevation may influence how far down the HGL 

will develop as predicted by some fire models, although other important scenario 

characteristics will also be influential. 

2.2.4 Credited Fire Protection 

The fire protection features that will be credited in a fire modeling analysis usually require a fire 

protection engineering evaluation of the system’s effectiveness in performing its design 

objectives. This may include both an assessment of the system compliance with applicable 

codes, including maintenance and inspection, and an assessment of the system performance 

against the particular fire scenario considered. The evaluation should determine whether the 

detection, suppression, and/or passive systems can protect the selected target from firegenerated conditions. Once the decision to credit a fire protection system is made, the analyst 

should specify the type of system selected for the scenario. 

There are several common fire protection features that may be present in a typical NPP area: 

 Fire detection systems. These include smoke detectors, heat detectors, or high 

sensitivity detection systems 

 Fire suppression systems. These include automatic or manually activated fixed 

systems, fire extinguishers, and fire brigades 

 Passive fire protection systems. These include structural fire barriers, fire doors, 

Electrical Raceway Fire Barrier Systems (ERFBSs), radiant shields, and fire stops 

 Administrative controls. These include combustible or transient-free zones, combustible 

fuel load limits, and hotwork procedures 

When assessing the performance of a system against the postulated fire hazard, it is necessary 

to consider the conditions under which the system is designed (fire size, fuel load, exposure 

temperature, plant operation mode, etc.). For example, an ordinary hazard sprinkler system 

may not have a sufficient water spray delivery to protect against a large hydrocarbon pool fire. 

Another example would be passive fire protection systems that are rated against an ASTM 
THE FIRE MODELING PROCESS 

2-8 

E119 (2008) fire exposure. Under some exposure conditions, such as prolonged flame 

impingement or large hydrocarbon pool fire scenarios, such systems may not provide sufficient 

fire resistance. There may be circumstances in which the thermal material properties are well 

defined, such that the response of the passive systems can be analytically determined. In other 

situations, it may be necessary to specify at the start of the fire modeling analysis that the 

passive systems do not protect the target or prevent fire propagation because the exposure 

exceeds the design capability of the passive fire protection feature. 

When considering the effect of active fire protection features, a valid set of response 

characteristics of the system is needed. For manually actuated fixed suppression systems or 

manual intervention in the fire modeling analysis, additional information relating to the 

occupants, the fire brigade, and the fire department are usually necessary. This may include 

the means of access to the area considered, the presence of a fire watch, the potential for plant 

personnel to be in the area, etc. Notice that the fire modeling tools within the scope of this 

guide may not be capable of modeling the impact of some of the fire protection features that 

may be credited in a given scenario. Credit for active fire suppression may thus be limited to 

preventing further increases in the HRR or alteration of the HRR profile using suppression 

curves such as those described in Appendix P of NUREG/CR-6850 (EPRI 1011989) and 

Chapter 14 of NUREG/CR-6850 Supplement 1 (EPRI 1019259). Nevertheless, fire protection 

features are designed to impact the outcome of a scenario, so their effects should be included in 

the analysis. 

2.2.5 Ventilation Conditions 

Ventilation conditions collectively refer to the operation of the mechanical ventilation system 

(e.g., the system will continue in normal operational mode, the system will transfer to smoke 

purge mode, the system will transfer off with closed dampers, etc.) and the position of doors or 

other openings during the fire event (e.g., doors closed, doors open, doors opening at fire 

brigade arrival, etc.). Typically, both normal and off-normal ventilation conditions are 

considered. Spaces in which doors are normally closed may have the doors propped open or 

opened during the fire by plant personnel, or damaged during the fire. HVAC flows that are 

normally present in a space may change during the fire due to dampers closing, activation of 

purge modes, filter plugging, or fan damage by the hot gases. Characterization of the flow field 

from mechanical devices may be important in some scenarios, especially if the inlet or outlet of 

the mechanical system is in close proximity to the fire or target. 

2.2.6 Target Locations 

The target location refers to the physical dimensions of the target relative to the source fire or 

the fire model coordinate system. These could include its horizontal and vertical distances from 

the ignition source or source fire, or its spatial position within the room itself. It may be 

necessary to further specify the location of a vulnerable portion of a target, such as the junction 

box on a service water pump motor. The orientation of the target with respect to the exposure 

fire may be of interest as well. An elevated target that is exposed only in the vertically upward 

direction may be susceptible to thermal radiation from an HGL, but possibly shielded from 

thermal radiation from the source fire itself. Note that in some types of analyses (e.g., a control 

room abandonment calculation), occupants may be a target. 

The fire exposure mechanisms should also be assessed when quantifying the target location. 

Fire exposure mechanisms, such as flame impingement, fire plume, ceiling jets, HGLs, and 

flame radiation, should be considered based on the relative location of the ignition source, 
THE FIRE MODELING PROCESS

2-9

intervening combustibles, and the targets. The subsequent fire model analysis should quantify 

relevant fire conditions and include a discussion of the proper disposition of those that are not 

expected to affect the target. 

2.2.7 Secondary Combustibles 

Secondary combustibles include any combustible materials that, if ignited, could affect the 

exposure conditions of the target set considered. Intervening combustibles, which are typically 

those combustibles that are located between the ignition source or source fire and the target, 

are examples of secondary combustibles. However, secondary combustibles would also 

include combustible materials that are not between the fire and the target but are exposed to the 

fire effects. In this case, if the secondary combustibles were to ignite, the total HRR in the 

enclosure (if applicable) would increase, resulting in a hotter gas layer, and the radiant energy 

from the burning secondary combustible would augment the exposure from the initial source 

fire, regardless of its location. 

Secondary combustibles would include both fixed and transient materials. Typical fixed 

combustibles include exposed cable jackets or cable insulation, combustible thermal insulation, 

and combustible wall lining materials. Transient combustibles vary considerably from plant to 

plant and plant area to plant area, but they may include trash containers, waste accumulations, 

hoses, hand tools, cleaners and solvents, protective clothing, plastic containers, and so on. It is 

essential to perform a visual survey of an area to obtain an understanding of the types of 

combustibles present and the activities in the space, which can provide insight into the types of 

combustibles that may be present from time to time. The combustible load calculations, fire 

protection procedures, and fire hazards analysis could provide additional details on the nature of 

fixed and transient fuel packages in a particular plant area. 

Combustible materials in sealed or rated containers may be excluded from consideration if the 

container is capable of resisting the effects of the fire. Some examples include cabinets 

containing flammable liquids, solid bottom cable trays with fixed top covers, and bus ducts. 

Secondary combustibles will take on the characteristics of a target prior to their ignition (see 

Section 2.2.6). In this regard, the physical location and orientation of the secondary 

combustibles with respect to both the ignition source and the target set are determined. The 

performance criterion for a secondary combustible target is the ignition condition, which will 

usually be a critical radiant heat flux or exposure temperature or an integrated heat flux. Unlike 

a true target, once the performance criterion has been met, the secondary combustible is ignited 

and then takes on the characteristics of a second source fire (see Section 2.2.8). 

2.2.8 Source Fire 

The source fire is the forcing function for the fire scenario. As all fire effects are directly related 

to the characterization of the source fire, great care must be taken in characterizing it. A source 

fire is often described as the “ignition source,” which introduces the concept of having both a 

fuel package and a credible ignition mechanism. There are many ignition mechanisms in a 

nuclear power plant; however, ignition sources are typically grouped by component or item such 

as into electrical cabinets, transient fuel packages, self-ignited cable trays, hotwork-ignited cable 

fires, and overheated motors. 
THE FIRE MODELING PROCESS 

2-10 

The source fire is typically characterized by a HRR, though other important aspects include the 

physical dimensions of the burning object, its composition, and its behavior when burning. The 

HRR may be specified as a continuous function of time (e.g., proportional to the square of time 

or a t

2

 fire), or it may be an array of HRR and time data. Algebraic models may only permit a 

constant HRR. There may be situations in which the HRR is a function of the ventilation rather 

than the object burning. Burning behaviors that may need consideration include whether the 

material can melt and form a liquid pool, whether it can spread by dripping, and where a liquid 

could pool. The HRR for many common ignition sources may be developed using the guidance 

provided in both NUREG/CR-6850 (EPRI 1011989) and NUREG/CR-6850 Supplement 1 (EPRI 

1019259). A summary of the information contained in these documents that may be used to 

develop HRR profiles is as follows: 

 Appendix E of NUREG/CR-6850 (EPRI 1011989) provides distributions of peak HRR 

values as a function of the types (qualified vs. unqualified) and amounts (single vs. 

multiple bundles) of cables inside vertical electrical cabinets 

 Appendix G of NUREG/CR-6850 (EPRI 1011989) provides guidance on defining the 

transient HRR profiles for electrical cabinets, transient combustible materials, and 

flammable/combustible liquids 

 Appendix R of NUREG/CR-6850 (EPRI 1011989) provides guidance on calculating the 

flame spread and HRR from cable fires 

 Appendix S of NUREG/CR-6850 (EPRI 1011989) provides guidance on estimating fire 

propagation times between electrical cabinets, which would affect the total HRR profile 

for a given area 

 Chapter 8 of NUREG/CR-6850 Supplement 1 (EPRI 1019259) provides further guidance 

on fire propagation among groups of electrical cabinets 

 Chapter 11 of NUREG/CR-6850 Supplement 1 (EPRI 1019259) provides further 

guidance on cable tray fires, including applicability of the Appendix R of NUREG/CR6850 cable fire parameters 

 Chapter 17 of NUREG/CR-6850 Supplement 1 (EPRI 1019259) provides further 

guidance on the fire growth rate for transient combustible materials 

When fire modeling is used to support a Fire PRA, the HRR for a source fire may be 

represented as a conditional probability distribution. In this case, depending on the type of 

analysis, a screening value may be selected (e.g., a 98th percentile peak HRR as recommended 

in NUREG/CR-6850), or the effects may be represented using multiple points on the conditional 

probability distribution. 

As was the case with secondary combustibles, combustible materials in sealed or rated 

containers may be excluded from consideration if the container is capable of resisting the 

effects of the fire. In addition, self-ignited cable fires are generally postulated only for non-IEEE383 qualified power cables (NUREG/CR-6850/EPRI 1011989). 

2.3 Step 3: Select Fire Models 

A number of models are available for performing fire simulations. These models range from 

algebraic models to sophisticated CFD computer codes that require days to set up a scenario 

and perform the associated calculations. Given the availability of different models, the analyst is 
THE FIRE MODELING PROCESS

2-11

responsible for understanding the advantages and limitations of a particular model in a specific 

situation in order to achieve the established goals. In general, fire models can be classified into 

three groups: (1) algebraic models, (2) zone models, and (3) CFD models. The level of effort 

required to describe a scenario and the computational time consumed by each group increase 

in the order in which they are listed. Table 2-1 provides a summary of the three groups of 

models, their advantages and disadvantages, and typical applications. 

In practical fire modeling applications, it is likely that a combination of all three types of models 

would be useful for analyzing a specific problem. For example, algebraic models might be used 

to estimate the radiative flux to a target for determination of a zone of influence (ZOI) or 

minimum separation distance. A zone model would provide the temperature of the HGL and 

height as a function of time for evaluating cable temperatures. CFD model calculations could be 

used to provide more detailed information on fire-induced conditions in areas where the 

algebraic models and zone models are not conclusive. Complex models can also be used as a 

means of estimating the degree of conservatism in a simple model analysis. 

The first step in selecting a model is to determine whether the scenario can be analyzed using 

algebraic models, zone models, or CFD models. This guide focuses on the following five fire 

models: Fire Dynamics Tools (FDTs

) (NUREG-1805, 2004), Fire Induced Vulnerability 

Evaluation (FIVE-Rev1) (EPRI 1002981, 2002), Consolidated Fire Growth and Smoke Transport 

(CFAST) model (Jones et al., 2004), MAGIC (Gay et al., 2005), and Fire Dynamics Simulator 

(FDS) (McGrattan et al., 2009). The FDTs

 and FIVE-Rev1 are a set of relatively simple 

algebraic models codified in the form of electronic spreadsheets. CFAST and MAGIC represent 

the class of fire models commonly referred to as zone models, which divide a compartment of 

interest into two zones, an elevated temperature upper layer and a cool lower layer. FDS is an 

example of a CFD model, which divides each compartment into thousands or millions of cells. 

Temperatures and other quantities of interest are calculated for each cell. 

Algebraic models can be performed by hand with relatively little computational effort. Karlsson 

and Quintiere (2000) classify algebraic models into three categories: (1) those that deal with 

combustion, (2) those that estimate resultant environmental conditions, and (3) those that 

address heat transfer. Algebraic models related to the combustion process estimate fire 

intensity based on the flammability characteristics of the fuel. Equations that estimate firegenerated conditions include plume, ceiling jet, and compartment temperatures. Heat transfer 

equations deal with target temperatures and heat fluxes in the plume, ceiling jet, and lower and 

upper layer regions. 

Zone models are computer algorithms that solve conservation equations for energy and mass. 

The fundamental approximation associated with zone models is that the enclosure is divided 

into a limited number of distinct gas zones of uniform properties. In fire applications, the 

enclosure is usually divided into two zones. The HGL is the volume of smoke generated by the 

fire and accumulated below the ceiling of the enclosure. This layer is modeled as 

homogeneous and will have uniform density and temperature. Its temperature and depth are 

affected by the amount of mass and energy entering or leaving the volume in each time step 

during the simulation. The lower layer, which can also experience a temperature increase, is 

characterized by colder fresh air between the floor and the bottom of the HGL. This layer will 

also have uniform density and temperature. 

CFD models are sophisticated algorithms that solve a simplified version of the Navier-Stokes 

equations. To run CFD codes, the enclosure must be divided into a large number of control 

volumes (perhaps several million), and the equations solved for each control volume. CFD 

models then provide a detailed estimate of temperature profiles because calculations are 
THE FIRE MODELING PROCESS 

2-12 

performed for each control volume specified in the enclosure. CFD models also handle 

turbulent gas flows. Another advantage of CFD models is their ability to simulate fire conditions 

in geometries other than rectangular floor compartments with flat ceilings. Some CFD models 

also attempt to estimate HRR values based on fuel flammability properties provided by the 

analyst. The drawback of CFD models is the computational time and the level of effort required 

to set up a scenario, as computational times are usually on the order of days. The time required 

to set up a problem usually depends on the complexity of the geometry. 

Another consideration when selecting a CFD-type model is that the amount of detail supplied to 

the model is significantly greater than it is for the simpler empirical and zone models. Given the 

large amount of information required for input, there is an intrinsically higher likelihood of errors 

being introduced into the input, which is different from the model uncertainty and parameter 

uncertainty described in Chapter 4. Furthermore, the features that may be described in the 

input could include ductwork, cable trays, electrical cabinets, and other fixed contents that may 

later be modified, relocated, or removed. New cabinets, cable trays, or other fixed contents that 

would have been included in the fire model had they been present may be added to an area. 

Although these changes may be minor, at the very least they would require an assessment by a 

fire modeler as to whether the original analysis is still applicable or whether the model needs to 

be adapted for the change. In some situations, such as the determination of a sprinkler 

actuation time, such small modifications could have a significant effect on the model results. 

 
THE FIRE MODELING PROCESS

2-13

Table 2-1. Summary of common fire model tools. 

Fire Model 

Class Examples Typical Applications Advantages Disadvantages 

Algebraic 

models 

FDTS

FIVERev1 

Screening calculations; 

ZOI; target damage by 

thermal radiation, HGL, 

or thermal plume acting 

in isolation. 

Simple to use; minimal 

inputs; quick results; 

ability to perform 

multiple parameter 

sensitivity studies. 

Limited 

application range; 

treats phenomena 

in isolation; 

typically 

applicable only to 

steady state or 

simply defined 

transient fires 

(e.g., proportional 

to the square of 

time or t2 fires). 

Zone Model CFAST 

MAGIC 

Detailed fire modeling 

in simple geometries; 

often used to compute 

HGL temperatures and 

target heat fluxes. 

Simple to use; couples 

HGL and localized 

effects; quick results; 

ability to perform 

multiple parameter 

sensitivity studies. 

Error increases 

with increasing 

deviation from a 

rectangular 

enclosure; large 

horizontal flow 

paths not well 

treated. 

Computation 

Fluid 

Dynamics 

Model 

FDS Detailed fire modeling 

in complex geometries, 

including computing 

time to target damage 

and habitability (main 

control room (MCR) 

abandonment or 

manual action 

feasibility). 

Ability to simulate fire 

conditions in complex 

geometries and with 

complex vent 

conditions. 

Significant effort 

to create input 

files and postprocess the 

results; long 

simulation times; 

difficult to model 

curved geometry, 

smoke detector 

performance, and 

conditions after 

sprinkler 

actuation. 

An important consideration in the fire model selection process is the type of analysis performed. 

Because of the large number of potential scenarios in a typical NPP, it is usually not practical to 

default to the most sophisticated tool available. The analysis typically begins with a series of 

screening analyses (NUREG/CR-6850/EPRI 1011989) performed to identify a subset of fire 

scenarios and targets that require further analysis with greater resolution. The screening 

process will typically use fairly simple fire modeling tools, such as algebraic models or generic 

solutions. When such screening is conducted, it is important to remain within the model 

limitations and the verification and validation (V&V) basis for the screening model. Section 2.3.6 

and Chapter 4 provide additional guidance on the significance of the fire model V&V basis and 

steps that the user should take to ensure that the fire model is used within acceptable limits. 
THE FIRE MODELING PROCESS 

2-14 

2.3.1 Fire Dynamics Tools (FDTs) 

Fire Dynamics Tools (FDTs) is a set of algebraic models preprogrammed into Microsoft® Excel®

spreadsheets. The FDTs

 library is documented in NUREG-1805, Fire Dynamics Tools (FDTs): 

Quantitative Fire Hazard Analysis Methods for the U.S. Nuclear Regulatory Commission Fire 

Protection Inspection Program (NUREG-1805, 2004) and Supplement 1 (NUREG-1805 

Supplement 1, 2012). The primary objective of the FDTs

 library and the accompanying 

documentation is to provide a methodology for U.S. Nuclear Regulatory Commission (NRC) fire 

protection inspectors to use in assessing potential fire hazards in NRC-licensed NPPs. The 

methodology uses simplified, quantitative fire hazard analysis techniques to evaluate the 

potential hazard associated with credible fire scenarios. 

The FDTs

 library includes a suite of spreadsheets that can be used to calculate various fire 

parameters under varying conditions. Documentation of the theoretical bases underlying the 

equations used in the FDTs spreadsheets helps to ensure that users understand the 

significance of the inputs that each spreadsheet requires, and why a particular spreadsheet 

should (or should not) be selected for a specific analysis. The governing equations for FDTs

 are 

well established within the fire science community and are documented in handbooks and 

scientific publications, such as the NFPA Fire Protection Handbook (NFPA Handbook, 2008), 

the SFPE Handbook of Fire Protection Engineering (SFPE Handbook, 2008), and other fire 

science literature. 

The complete list of spreadsheets included in the FDTs

 library is shown in Table 2-2. A number 

of the calculation methods included in the FDTs

 were part of the V&V study conducted by the 

NRC, the Electric Power Research Institute (EPRI), and the National Institute of Standards and 

Technology (NIST) (NUREG-1824 Volume 3, EPRI 1011999, 2007). These spreadsheets are 

identified in Table 2-2. The NRC maintains a website at http://www.nrc.gov/reading-rm/doccollections/nuregs/staff/sr1805/final-report/index.html, where both new and updated 

spreadsheets are posted. 

Table 2-2. Routines included in the FDTs

. 

FDTS Spreadsheet 

Function Name 

NUREG-1805 Chapter and Function 

Description 

NUREG-1824 

Verification 

and Validation 

Status 

02.1_Temperature_NV.xls 

Chapter 2. Predicting Hot Gas Layer Temperature and 

Smoke Layer Height in a Compartment Fire with Natural 

Ventilation (Compartment with Thermally Thick/Thin 

Boundaries): Method of McCaffrey, Quintiere, and 

Harkleroad (MQH) 

V&V provided 

02.2_Temperature_FV.xls 

Chapter 2. Predicting Hot Gas Layer Temperature in a 

Compartment Fire with Forced Ventilation 

(Compartment with Thermally Thick/Thin Boundaries): 

Method of Foote, Pagni, and Alvares (FPA) and 

Method of Deal and Beyler 

V&V provided 

02.3_Temperature_CC.xls 

Chapter 2. Predicting Hot Gas Layer Temperature in a 

Compartment Fire with Door Closed (Compartment has 

Sufficient Leaks to Prevent Pressure Buildup; leakage is 

Ignored): Method of Beyler 

V&V provided 

03_HRR_Flame_Height_ 

Burning_Duration_Calculation.

xls 

Chapter 3. Estimating Burning Characteristics of Liquid 

Pool Fire, HRR, Burning Duration, and Flame Height 

V&V provided for 

flame height only 
THE FIRE MODELING PROCESS

2-15

FDTS Spreadsheet 

Function Name 

NUREG-1805 Chapter and Function 

Description 

NUREG-1824 

Verification 

and Validation 

Status 

04_Flame_Height_Calculations

.xls 

Chapter 4. Estimating Wall Fire Flame Height, Line 

Fire Flame Height Against the Wall, and Corner Fire 

Flame Height 

V&V not provided 

05.1_Heat_Flux_Calculations_ 

Wind_Free.xls 

Chapter 5. Estimating Radiant Heat Flux from Fire to a 

Target Fuel (Wind-Free Condition):

Point Source Radiation Model (Target at Ground Level); 

Solid Flame Radiation Model (Target at Ground Level); 

and Solid Flame Radiation Model (Target Above 

Ground Level) 

V&V provided for 

the point source 

model and the 

solid flame 

radiation model 

(above ground) 

only 

05.2_Heat_Flux_Calculations_ 

Wind.xls 

Chapter 5. Estimating Radiant Heat Flux from Fire to a 

Target Fuel (Presence of Wind): Solid Flame Radiation 

Model (Target at Ground Level); and Solid Flame 

Radiation Model (Target Above Ground Level) 

V&V not provided 

05.3_Thermal_Radiation_From

_Hydrocarbon_Fireballs.xls 

Chapter 5. Estimating Radiant Heat Flux from Fire to a 

Target Fuel: Estimating Thermal Radiation from 

Hydrocarbon Fireballs 

V&V not provided 

06_Ignition_Time_Calculations.

xls 

Chapter 6. Estimating the Ignition Time of a Target 

Fuel Exposed to a Constant Radiative Heat Flux 

Method of Estimating Piloted Ignition Time of Solid 

Materials Under Radiant Exposures Method of: 

(1) Mikkola and Wichman; 

(2) Quintiere and Harkleroad; 

(3) Janssens; 

(4) Method of Toal, Silcock, and Shields; and 

(5) Method of Tewarson

V&V not provided 

07_Cable_HRR_ 

Calculations.xls 

Chapter 7. Estimating Full-Scale Heat Release Rate of 

a Cable Tray Fire V&V not provided 

08_Burning_Duration_Soild.xls Chapter 8. Estimating Burning Duration of Solid 

Combustibles V&V not provided 

09_Plume_Temperature_ 

Calculations.xls 

Chapter 9. Estimating Centerline Temperature of a 

Buoyant Fire Plume V&V provided 

10_Detector_Activation_ 

Time.xls 

Estimating Detector Response Times: 

Chapter 10. Estimating Sprinkler Response Time 

Chapter 11. Estimating Smoke Detector Response 

Time 

Chapter 12. Estimating Heat Detector Response Time

V&V not provided 

13_Compartment_Flashover_ 

Calculations.xls 

Chapter 13. Predicting Compartment Flashover 

Compartment Post-Flashover Temperature: Method of 

Law 

Minimum Heat Release Rate Required to Compartment 

Flashover: 

(1) Method of McCaffrey, Quintiere, and Harkleroad 

(MQH); 

(2) Method of Babrauskas; and 

(3) Method of Thomas

V&V not provided 

14_Compartment_Over_ 

Pressure_Calculations.xls 

Chapter 14. Estimating Pressure Rise Attributable to a 

Fire in a Closed Compartment V&V not provided 

15_Explosion_Claculations.xls Chapter 15. Estimating the Pressure Increase and 

Explosive Energy Release Associated with Explosions V&V not provided 
THE FIRE MODELING PROCESS 

2-16 

FDTS Spreadsheet 

Function Name 

NUREG-1805 Chapter and Function 

Description 

NUREG-1824 

Verification 

and Validation 

Status 

16_Battery_Compartment_ 

Flammable_Gas_Conc.xls 

Chapter 16. Calculating the Rate of Hydrogen Gas 

Generation in Battery Compartments: 

Method of Estimating Hydrogen Gas Generation Rate in 

Battery Compartments; 

Method of Estimating Flammable Gas and Vapor 

Concentration Buildup in Enclosed Spaces; and 

Method of Estimating Flammable Gas and Vapor 

Concentration Buildup Time in Enclosed Spaces 

V&V not provided 

17.1_FR_Beams_Columns_ 

Substitution_Correlation.xls 

Chapter 17. Calculating the Fire Resistance of 

Structural Steel Members (Algebraic Models): 

Beam Substitution Correlation (Spray-Applied 

Materials); and 

Column Substitution Correlation (Spray-Applied 

Materials) 

V&V not provided 

17.2_FR_Beams_Columns_ 

Quasi_Steady_State_Spray_ 

Insulated.xls 

Chapter 17. Calculating the Fire Resistance of 

Structural Steel Members (Algebraic Models): Heat 

Transfer Analysis using Numerical Methods Protected; 

and Steel Beams and Columns (Spray-Applied) 

V&V not provided 

17.3_FR_Beams_Columns_ 

Quasi_Steady_State_Board_ 

Insulated.xls 

Chapter 17. Calculating the Fire Resistance of 

Structural Steel Members: Heat Transfer Analysis using 

Numerical Methods Protected Steel Beams and 

Columns (Board Materials) 

V&V not provided 

17.4_FR_Beams_Columns_ 

Quasi_Steady_State_ 

Uninsulated.xls 

Chapter 17. Calculating the Fire Resistance of 

Structural Steel Members: Heat Transfer Analysis using 

Numerical Methods Unprotected Steel Beams and 

Columns 

V&V not provided 

18_Visibility_Through_Smoke.

xls Chapter 18. Estimating Visibility Through Smoke V&V not provided 

2.3.2 Fire Induced Vulnerability Evaluation (FIVE-Rev1)6

In August 2002, EPRI published the Fire Modeling Guide for Nuclear Power Plant Applications

(EPRI 1002981, 2002) for the first time. Since then, it has provided fire protection engineers in 

the commercial nuclear industry with a broad overview of fire modeling theory and applications, 

including representative calculations performed with various state-of-the-art fire models. With 

this guide, EPRI included a library of preprogrammed Microsoft® Excel® equations, which are 

used to estimate some aspects of fire-induced conditions. This collection of algebraic models is 

referred to as the Fire Induced Vulnerability Evaluation model (FIVE-Rev1). In general, the 

equations in the library are closed-form analytical expressions that can be solved by hand. The 

capabilities of the various equations in the library include predicting temperature and convective 

heat fluxes in the fire plume or ceiling jet, radiation heat flux, upper-layer temperature, time to 

detection, and target heating, among others. Some of the equations in FIVE-Rev1 were 

included in the V&V study (NUREG-1824 Volume 4, EPRI 1011999, 2007). Like the FDTs

, 

several of the equations used in the examples have not been subject to V&V. Subsequent 

efforts will be directed at the V&V of these equations and models. The calculations included in 

the FIVE-Rev1 are summarized in Table 2-3. 

 

 

6

 FIVE-Rev1 is a proprietary software package available to EPRI members (www.epri.com). 
THE FIRE MODELING PROCESS

2-17

Table 2-3. Routines included in FIVE-Rev1. 

FIVE-Rev1 

Function Function Description 

NUREG-1824 

Verification 

and Validation 

Status 

Qf Heat release rate profile considering t2 growth and four stages. V&V not provided 

Firr Estimates flame irradiation at distance r from the fire source. 

Point source approximation for REMOTE targets. V&V provided 

FHeight Flame height based on Heskestad flame height correlation. V&V provided 

TpAlpert Plume temperature at a specific height based on Alpert plume 

temperature correlation. V&V not provided 

TpMcCaffrey Plume temperature at a specific height based on McCaffrey plume 

temperature correlation. V&V not provided 

TpHeskestad Plume temperature at a specific height based on Heskestad 

plume temperature correlation. V&V not provided 

Plcflux Estimates convective heat flux in the fire plume. V&V not provided 

VpAlpert Plume velocity at a specific height based on Alpert's plume 

temperature correlation. V&V not provided 

VpMcCaffrey Plume velocity at a specific height based on McCaffrey plume 

temperature correlation. V&V provided 

VpHeskestad Plume velocity at a specific height based on Heskestad plume 

temperature correlation. V&V provided 

EpZukoski Air entrainment into plume based on Zukoski plume entrainment 

correlation. V&V not provided 

EpThomas Air entrainment into plume based on Thomas plume entrainment 

correlation. V&V not provided 

EpHeskestad Air entrainment into plume based on Heskestad plume 

entrainment correlation. V&V not provided 

PdHeskestad Estimates plume diameter based on Heskestad plume correlation. V&V not provided 

TcjAlpert Unconfined ceiling jet temperature based on Alpert ceiling jet 

correlation. V&V provided 

TcjDelichatsios Confined ceiling jet temperature based on Delichatsios ceiling jet 

correlation. V&V not provided 

Cjcflux Estimates convective heat flux in the ceiling jet. V&V not provided 

VcjAlpert Unconfined ceiling jet velocity based on Alpert ceiling jet 

correlation. V&V not provided 

MQHTemperature Compartment temperature after a specified time, given a steady 

HRR based on MQH approach. V&V provided 

MQHFlashover Heat release rate required for flashover after a specified time 

based on MQH approach. V&V not provided 

FiveTemp Estimates compartment temperature based on FIVE-Rev1. V&V provided 

Detact Activation time of heat detection devices based on heat release 

rate profiles. V&V not provided 

Aset 

Time required by Hot Gas Layer to reach a specific height based 

on heat release rate profiles and openings at the bottom of the 

enclosure. 

V&V not provided 

CThrr 

Estimates heat release rate from cable trays. The correlation is 

based on 14 experiments with a stack of 12 horizontal cable trays 

and 2 experiments with a combination of 12 horizontal cable trays 

and 3 vertical trays. 

V&V not provided 
THE FIRE MODELING PROCESS 

2-18 

FIVE-Rev1 

Function Function Description 

NUREG-1824 

Verification 

and Validation 

Status 

Visib Estimates the length of a visible path in a smoke environment. 

The correlation applies to light-reflecting signs. V&V not provided 

Ttar Estimates target temperature under constant heat flux. V&V not provided 

Ttdam Time to target damage under constant heat flux. V&V not provided 

2.3.3 Consolidated Fire Growth and Smoke Transport (CFAST) Model 

The Consolidated Fire Growth and Smoke Transport (CFAST) model is a two-zone computer 

fire model. For a given fire scenario, the model subdivides a compartment into two control 

volumes, which include a relatively hot upper layer (i.e., the HGL) and a relatively cool lower 

layer. Mass and energy are transported between the layers via the fire plume and mixing at the 

vents. Combustion products accumulate via the plume in the HGL. Each layer has its own 

energy and mass balances. The most important approximation for the model is that each zone 

has uniform properties, that is, that the temperature and gas concentrations are constant 

throughout the zone, only changing as a function of time. The CFAST model describes the 

conditions in each zone by solving equations for conservation of mass, species, and energy, 

along with the ideal gas law. The Technical Reference Guide for CFAST (Jones et al., 2004) 

provides a detailed discussion concerning the specific derivation of these conservation laws. 

Documentation for CFAST also includes a User’s Guide (Peacock et al., 2008b), which details 

the use of the model, and a Model Development and Evaluation Guide (Peacock et al., 2008a), 

which presents the latest model V&V results. 

For some applications, including long hallways or tall shafts, the two-zone approximation may 

not be appropriate. To address this, CFAST includes empirical algorithms to simulate smoke 

flow and filling in long corridors and for a single well-mixed volume in tall shafts. CFAST also 

includes several correlations (as sub-models), based on experimental data that are used to 

calculate various physical processes during a fire scenario: smoke production, fire plume 

dynamics, heat transfer by radiation, convection, conduction, natural flows through openings 

(vertical and horizontal), forced or natural ventilation, thermal behavior of targets, heat 

detectors, and water spray from sprinklers. 

CFAST models horizontal flow through vertical vents (doors, windows, wall vents, etc.), vertical 

flow through horizontal vents (ceiling holes, hatches, roof vents, etc.), and mechanical 

ventilation through fans and ductwork. Natural flow is determined by the pressure difference 

across a vent, using Bernoulli’s law for horizontal vent flow, and by algebraic models for vertical 

vent flow. Mechanical ventilation is based on an analogy to electrical current flow in series and 

parallel paths where flow is split in parallel paths proportional to the flow resistance in each path 

and resistance to flow is additive for paths in series. 

CFAST includes algorithms to account for radiation, convection, and conduction within a 

modeled structure. Radiative transfer occurs among the fire(s), gas layers, and compartment 

surfaces (ceiling, walls, and floor). It is a function of the temperature differences and emissivity 

of the gas layers, as well as the compartment surfaces. Convective heat transfer between gas 

layers and compartment or target surfaces is based on typical correlations available in the 

literature. The V&V results for CFAST are documented in Volume 5 of NUREG-1824 (EPRI 

1011999). Additional validation results, particularly for plume temperature predictions that were 

not included in the NUREG-1824 (EPRI 1011999) Volume 5 results, are included in the CFAST 

Model Development and Evaluation Guide (Peacock et al., 2008a). 
THE FIRE MODELING PROCESS

2-19

2.3.4 MAGIC7

MAGIC is another two-zone computer fire model, developed and maintained by Electricité de 

France (EdF) specifically for use in NPP analysis. MAGIC is supported by three EdF 

publications, including: (1) the technical manual, which provides a mathematical description of 

the model (Gay et al., 2005b); (2) the user’s manual, which details how to use the graphical 

interface (Gay et al., 2005a); and (3) the validation studies, which compare MAGIC’s results to 

experimental measurements (Gay et al., 2005c). These three proprietary publications and the 

MAGIC software are available through EPRI to EPRI members. Additional V&V results for 

MAGIC are documented in Volume 6 of NUREG-1824 (EPRI 1011999). 

MAGIC is fundamentally the same type of model as CFAST and thus solves the same basic set 

of differential equations. The combustion model and vent flow models are similar as well. 

Despite this, MAGIC differs from CFAST in that it does not have the corridor or shaft submodels, and the ceiling jet and wall jet treatments are different. The user should consult the 

technical manual for a complete description of the MAGIC sub-models (Gay et al., 2005b). 

Once a given simulation is completed, MAGIC generates an output file with all of the solution 

variables. Through a “post-processor” interface, the user selects the relevant output variables 

for the analysis. Typical outputs include the temperatures of hot and cold zones, concentrations 

of oxygen and unburned gases, smoke migration into each compartment, the mass flow rates of 

air and smoke through the openings and vents, the pressures at the floor level of each 

compartment, the temperatures at the surfaces of the walls, and the thermal fluxes (radiative 

and total) exchanged by the targets placed by the user. 

2.3.5 Fire Dynamics Simulator (FDS) 

Fire Dynamics Simulator (FDS) (McGrattan et al., 2007) is a CFD model of fire-driven fluid flow. 

The model numerically solves a form of the Navier-Stokes equations appropriate for low-speed, 

thermally driven flow, with an emphasis on smoke and heat transport from fires. The partial 

derivatives of the equations for conservation of mass, momentum, and energy are approximated 

as finite differences, and the solution is updated in time on a three-dimensional, rectilinear grid. 

Thermal radiation is computed using a finite volume technique on the same grid as the flow 

solver. Lagrangian particles are used to simulate smoke movement and sprinkler discharge. 

FDS computes the temperature, density, pressure, velocity, and chemical composition within 

each numerical grid cell at each discrete time step. There are typically hundreds of thousands 

to several million grid cells, and thousands to hundreds of thousands of time steps. In addition, 

FDS computes the temperature, heat flux, mass loss rate, and various other quantities at solid 

surfaces. 

Time histories of various quantities at a single point in space, or global quantities, such as the 

fire’s HRR, are saved in simple, comma-delimited text files that can be plotted in a spreadsheet 

program. Some output quantities typically used to assess the conditions in a space or to 

compare against measured data are not inherently calculated in a CFD-type model, such as the 

HGL temperature and interface height. FDS does provide an estimate of these types of 

parameters using the continuous vertical temperature distribution and an integrated averaging 

scheme, as described by McGrattan et al. (2007). 

Most field or surface data are visualized with a program called Smokeview, a tool specifically 

designed to help analyze results generated by FDS. FDS and Smokeview are used in concert 

 

7

 MAGIC is a software package available to EPRI members (www.epri.com). 
THE FIRE MODELING PROCESS 

2-20 

to model and visualize fire phenomena. Smokeview does this by presenting animated tracer 

particle flows, animated contour slices of computed gas variables, and animated surface data, 

and also presents contours and vector plots of static data anywhere within a scene at a fixed 

time. The FDS User’s Guide (McGrattan et al., 2007) provides a complete list of FDS output 

quantities and formats, while the Smokeview User’s Guide (Forney, 2008) explains how to 

visualize the results of an FDS simulation. Volume 7 of NUREG-1824 (EPRI 1011999) contains 

the results of V&V efforts for FDS. Additional V&V results for FDS are contained in the FDS 

documentation series (McGrattan et al., 2007). 

FDS solves conservation equations of mass, momentum, and energy for an expandable mixture 

of ideal gases in the low Mach number limit. This means that the equations do not permit 

acoustic waves, the result of which is that the time step for the numerical solution is bounded by 

the flow speed, rather than the sound speed. Situations in which this limitation may be 

encountered include jet fires, deflagrations, and detonations. This limitation also reduces the 

number of unknowns by one, as density and temperature can be related to a known background 

pressure. Flow turbulence is treated by large eddy simulation. 

For most simulations, FDS uses a mixture fraction combustion model. The mixture fraction is a 

conserved scalar that represents, at a given point, the mass fraction of gases originating in the 

fuel stream. In short, the combustion is controlled by the rate at which fuel and oxygen mix. 

Unlike versions of FDS prior to version 5, the reaction of fuel and oxygen is not necessarily 

instantaneous and complete, and there are several optional schemes that are designed to 

estimate the extent of combustion in under-ventilated spaces. The mass fractions of all of the 

major reactants and products can be derived from the mixture fraction by means of “state 

relations,” expressions achieved through a combination of simplified analysis and measurement. 

The combustion model used by FDS is an area of active development. Consequently, FDS 

users should consult the latest code documentation for a description of new features or submodels. 

Numerical parameters play a very important role in a CFD model like FDS. A numerical 

parameter is any input value that is needed for the mathematical solution of the equations, but 

has little or no physical meaning. For example, the time step with which the numerical solution 

of the HGL temperature is computed does have units of seconds, but it is not a value that has 

meaning outside of that particular algorithm; nevertheless, these numerical parameters can 

affect the solution, and their sensitivity should be assessed in some way. For the spreadsheet 

and zone models, this procedure is relatively straightforward because the calculations run in 

less than a minute. One simply varies the value and ensures that the solution does not change 

appreciably. Specifically, one should simply demonstrate that the solution converges towards a 

particular value as the parameter is varied; for instance, using a smaller and smaller time step 

ought to lead to convergence of any evolution equation. 

In FDS, the numerical parameter with the greatest importance is cell size. CFD models solve 

an approximate form of the conservation equations of mass, momentum, and energy on a 

numerical grid. The error associated with the discretization of the partial derivatives is a function 

of the size of the grid cells and the type of differencing used. FDS uses second-order accurate 

approximations of both the temporal and spatial derivatives of the Navier-Stokes equations, 

meaning that the discretization error is proportional to the square of the time step or cell size. In 

theory, reducing the grid cell size by a factor of two reduces the discretization error by a factor 

of four; however, it also increases the computing time by a factor of at least sixteen (a factor of 

two for the temporal and each spatial dimension). Clearly, there is a point in diminishing returns 
THE FIRE MODELING PROCESS

2-21

as one refines the numerical mesh. Determining which size grid cell to use in any given 

calculation is known as a grid sensitivity study.

Determining an optimal grid size in FDS is usually a matter of assessing the size of the fire. The 

physical diameter of the fire is not always a well-defined property; a compartment fire does not 

have a well-defined diameter, whereas a circular pan filled with a burning liquid fuel has an 

obvious diameter. Regardless, it is not the physical diameter of the fire that matters when 

assessing the “size” of the fire, but rather its characteristic diameter, כܦ: 

כܦ ൌ ቆ ܳሶ

݃ඥ∞ܶ௣ܿ∞ߩ

ቇ

ଶ/ହ

(2-1) 

where ܳሶ is the fire HRR (kW), ߩ ∞is the ambient density of air (kg/m3

), ܿ௣ is the specific heat of 

air (kJ/kg/K), ܶ∞ is the ambient air temperature (K), and ݃ is the acceleration of gravity (m/s2

). 

In many instances, כܦ is comparable to the physical diameter of the fire. FDS employs a 

numerical technique known as large eddy simulation (LES) to model the unresolvable or “subgrid” motion of the hot gases. The effectiveness of the technique is largely a function of the ratio of 

the fire’s characteristic diameter, כܦ, to the size of a grid cell, ݔߜ. In short, the greater the ratio 

כܦ/ݔߜ, the more the fire dynamics are resolved directly, and the more accurate the simulation. 

Past experience has shown that a ratio of 5 to 10 usually produces favorable results at a 

moderate computational cost for problems where gross smoke movement is of interest. 

As an example, suppose the HRR of the fire were 700 kW. The characteristic diameter may 

then be calculated as follows: 

כܦ ൌ ቆ 700 kW

1.2 kg/mଷ ۭ 1.012 kJ/kg/K ۭ 293 K ۭ√9.81 m/sଶ

ቇ

ଶ/ହ

ൌ 0.83 m (2-2) 

To perform a grid sensitivity analysis, a good place to start might be a cell resolution of 15 cm 

(6 in), which means that כܦ/ݔߜ ൌ 5.5. Then choose a grid of 10 cm (4 in), and then 5 cm (2 in). 

At this point, the calculation time will have increased by a factor of roughly three hundred, 

making it potentially impractical to compute; however, if it can be shown that there is little 

difference between the 5 cm (2 in) and 10 cm (4 in) grids, then the objective has been achieved. 

The meaning of “little difference” can be interpreted in several ways. Given that NUREG-1824 

(EPRI 1011999), the fire model V&V study, lists the relative error expected of the various 

models for the various quantities, it is reasonable to interpret the difference in results on 

different grids in light of what is expected of the model accuracy. 

Although the fire size and dimensions often determine the optimum grid resolution, there are 

other factors that can influence the selection of the grid resolution. These include the number of 

cells used to resolve a flow path dimension, the number of cells used to describe the fire 

dimension, and the number of cells used to resolve the conditions in a partially isolated volume. 

These considerations are related in that it is generally advisable to include at least three cells 

across any flow path, such as a door or a window, and fire dimension, regardless of the 

minimum number of cells computed using the fire characteristic diameter. In some cases, 

partially isolated volumes are created by various obstructions; if the temperature and flow 

conditions are of interest in these areas, a minimum of three cells across any dimension should 

be provided. Another consideration that could influence the grid resolution is the dimension of 
THE FIRE MODELING PROCESS 

2-22 

the obstructions that are expected to influence the result. For example, if it is necessary to 

quantitatively assess the effect that various conduits and light fixtures may have on the 

actuation time of a nearby sprinkler, the maximum grid resolution would be comparable to the 

dimensions of the smallest distinct obstruction included in the model. 

FDS input files are frequently created with the assistance of preprocessing software, which may 

include commercial software packages that can create input files for FDS or spreadsheet tools 

created by users to insert obstructions or create stair-step approximations to curved geometries. 

This type of software can reduce the tediousness of creating the geometric representation of a 

space, but is not part of the FDS model. Any input files created by such software should be 

carefully checked by the user to ensure that the geometry or boundary data are exactly as 

intended. 

2.3.6 Verification and Validation (V&V) 

The use of fire models requires a good understanding of their limitations and predictive 

capabilities. NFPA 805, for example, states that fire models shall only be applied within the 

limitations of the given model and shall be verified and validated. Previously, the NRC’s Office 

of Nuclear Regulatory Research (RES) and EPRI conducted a collaborative project for the V&V 

of the five selected fire models described in Sections 2.3.1 through 2.3.5. NIST was also an 

important partner in this project. The results of this project were documented in the seven 

volumes of NUREG-1824 (EPRI 1011999), Verification and Validation of Selected Fire Models 

for Nuclear Power Plant Applications. 

The parameters for which NUREG-1824 (EPRI 1011999) provides V&V information are shown 

in Table 2-4. Not all output parameters are available in all models. The information in Table 2-4 

may be a useful element to consider when selecting the appropriate fire model tool; for 

example, it is clear that the libraries of algebraic models (FDTs

, FIVE-Rev1) have limited 

capabilities when compared to the zone and CFD models. These libraries do not have 

appropriate methods for estimating many of the fire scenario attributes evaluated in this study. 

The correlations that the libraries do contain are typically empirically deduced from a broad 

database of experiments; they are based on fundamental conservation laws, and have gained a 

considerable degree of acceptance in the fire protection engineering community. However, 

because of their empirical nature, they are subject to many limiting approximations. The user 

must be cautious when using these tools. 

CFD model predictions can be more accurate in complex scenarios; however, the time it takes 

to obtain and understand a prediction may also be an important consideration in the decision to 

use a particular model for a specific scenario. FDS is computationally expensive in all respects 

(preprocessing, simulation, and post-processing), and, while the two-zone models produce 

answers in seconds to minutes, FDS provides comparable answers in days to weeks. In 

general, FDS is better suited to estimate fire environments within more complex configurations. 

The fire experiments selected for inclusion in the V&V were limited to high-quality, real-scale 

experiments with direct applicability to NPP applications. As it was not possible to consider all 

possible NPP applications, a method for determining the applicability of validation results to 

other specific NPP fire scenarios has been described in NUREG-1824 Volume 1 (EPRI 

1011999). The applicability of the validation results is determined using normalized parameters 

traditionally used in fire modeling applications. Normalized parameters allow users to compare 

results from scenarios of different scales by normalizing the physical characteristics of the 

scenarios. 
THE FIRE MODELING PROCESS

2-23

Table 2-4. Fire modeling attributes included in NUREG 1824/EPRI 1011999 (2007). 

Fire Modeling Attributes 

Fire Model 

FDTs FIVE-Rev1 CFAST MAGIC FDS 

Hot Gas Layer (HGL) Temperature YES YES YES YES YES 

Hot Gas Layer (HGL) Height NO NO YES YES YES 

Ceiling Jet Temperature NO YES YES YES YES 

Plume Temperature YES YES NO YES YES 

Flame Height YES YES YES YES YES 

Radiated Heat Flux to Targets YES YES YES YES YES 

Total Heat Flux to Targets NO NO YES YES YES 

Total Heat Flux to Walls NO NO YES YES YES 

Wall Temperature NO NO YES YES YES 

Target Temperature NO NO YES YES YES 

Smoke Concentration NO NO YES YES YES 

Oxygen Concentration NO NO YES YES YES 

Room Pressure NO NO YES YES YES 

Table 2-5 identifies normalized parameters that may be used to compare NPP fire scenarios 

with validation experiments. A full description of each parameter follows Table 2-5. The 

validation range for the normalized parameters shown in Table 2-5 were derived from NUREG1824 (EPRI 1011999), Table 2-4, and are intended to provide guidance on which groups of 

validation experiments to consider when evaluating a certain attribute based on the validation 

results. These parameters may not be the only ones appropriate for evaluating the applicability 

of a specific experiment; Table 2-5 of NUREG-1824 (EPRI 1011999) Volume 1 lists the ranges 

of values for different physical characteristics and normalized parameters based on the 

experiments considered in the validation study. 

It is seen in Table 2-5 that the fire diameter plays a role in three of the normalized parameters: 

the fire Froude Number, the flame length ratio, and the radial distance ratio. The fire diameter 

may be estimated from the total plan area of the burning fuel using the following equation 

(SFPE, 2011): 

ܣ4ඨ ൌ ܦ

ߨ

(2-3) 

where ܦ is the effective fire diameter (m) and ܣ is the plan area of the burning fuel (m2) equal to 

the fuel package length dimension multiplied by the width dimension. Equation 2-3 produces a 

diameter of a circle having an equivalent area to that of the burning fuel and is therefore 
THE FIRE MODELING PROCESS 

2-24 

applicable to fires with a plan area that is nearly circular. When the aspect ratio of a source fire 

with a rectangular plan or footprint (i.e., the ratio of the long dimension to the short dimension) 

becomes large, the flame length and thermal plume take on characteristics of a line type fire 

(Grove et al., 2002). There is no clearly defined aspect ratio limit; however, a value of up to 

about five is shown to be reasonable for using the effective diameter (Grove et al., 2002). Note 

that the form of the Froude Number for a line type source fire is nearly the same as the 

axisymmetric source, with the exception that the source area is used in place of the diameter 

(Yuan et al., 1996). The fire tests used to V&V the various fire models in NUREG-1824 all had 

aspect ratios below two. 

Table 2-5. Summary of selected normalized parameters for application of the validation results to 

NPP fire scenarios (NUREG-1824/EPRI 1011999, 2007). 

Quantity Normalized Parameter General Guidance 

NUREG1824 

Validation 

Range 

Fire Froude 

Number ܳሶ

כ ൌ ܳሶ

ܦ݃ଶඥܦ∞ܶ௣ܿ∞ߩ

Ratio of characteristic 

velocities. A typical accidental 

fire has a Froude number of 

order 1. Momentum-driven fire 

plumes, like jet flares, have 

relatively high values. 

Buoyancy-driven fire plumes 

have relatively low values. 

0.4 – 2.4 

Flame Length 

Ratio 

௙ܮ ൅ ௙ܪ

௖ܪ

௙ܮ

ܦ ൌ 3.7 ܳሶ

כଶ/ହ െ 1.02

A convenient parameter for 

expressing the “size” of the fire 

relative to the height of the 

compartment. A value of 1 

means that the flames reach 

the ceiling. 

0.2 – 1.0 

Ceiling Jet 

Distance Ratio 

cjݎ

௙ܪ െ௖ ܪ

Ceiling jet temperature and 

velocity correlations use this 

ratio to express the horizontal 

distance from target to plume. 

1.2 – 1.7 

Equivalence 

Ratio 

߮ ൌ

ܳሶ

∆ܪைమ݉ሶ Oమ

݉ሶ Oమ ൌ ቐ

0.23 ൈ

1

(Natural଴ (ܪඥ଴ܣ 2

0.23 ߩஶܸሶ ሺMechanicalሻ

The equivalence ratio relates 

the energy release rate of the 

fire to the energy release that 

can be supported by the mass 

flow rate of oxygen into the 

compartment, ݉ሶ Oమ. The fire is 

considered over- or underventilated based on whether ߮

is less than or greater than 1, 

respectively. 

0.04 – 0.6 

Compartment 

௖ܪܹ/ or௖ ܪ/ܮ Ratio Aspect

This parameter indicates the 

general shape of the 

compartment.

0.6 – 5.7

Radial Distance 

Ratio 

ݎ

ܦ

This ratio is the relative 

distance from a target to the 

fire. It is important when 

calculating the radiative heat 

flux. 

2.2 – 5.7 
THE FIRE MODELING PROCESS

2-25

Froude Number

The Froude Number is a measure of the buoyant strength of the fire plume. A large Froude 

Number indicates a strong source, and, given a sufficiently high Froude Number, the fire plume 

may take on characteristics of a jet fire. The Froude Number is determined through the 

following equation: 

ܳሶ

כ ൌ ܳሶ

 (2-4) ܦ݃ଶඥܦ∞ܶ௣ܿ∞ߩ

where ܳሶ

כ is the Fire Froude number (non-dimensional), ܳሶ

 is the fire heat release rate (kW), ߩ∞

is the density of ambient air (kg/m3), ܿ௣ is the heat capacity at constant pressure for ambient air 

(kJ/kg-°C), ܶ∞ is the ambient temperature (K), ܦ is the fire diameter or the effective fire diameter 

(m2), and ݃ is the acceleration of gravity (9.81 m/s2). The heat release rate that is used to 

generate the validation range is the peak heat release rate; thus, when comparing the model 

application range to these values, the peak heat release rate should be used. The effective fire 

diameter may be computed using Equation 2-3. The ambient density and temperature are 

typically coupled through the following equation: 

ߩஶ ൌ 352

ܶஶ

 (2-5) 

where all terms have been defined. The heat capacity for air varies slightly with temperature, 

and, at 298 K, it is equal to about 1.012 kJ/kg-°C. 

Flame Length Ratio

The flame length ratio is a measure of the flame height relative to the upper horizontal boundary 

(ceiling). The NUREG-1824 validation tests all involved fires with a flame height that was at or 

below the ceiling. In situations where the flame height is greater than the ceiling, the flames will 

extend radially outward from the impingement point. This configuration is not well characterized 

by simple algebraic models, or even by zone models that use plume and flame height 

correlations. 

Flame Length Ratio ൌ

௙ܮ ൅ ௙ܪ

௖ܪ

(2-6) 

where ܪ ௙is the base height of the fire (m), ܮ ௙is the flame height (m), and ܪ ௖is the enclosure 

height (m). Note that the flame length ratio does not apply to fires modeled outside an 

enclosure. The flame height is computed using the following equation: 

௙ܮ

ܦ ൌ 3.7 ܳሶ

כଶ/ହ െ 1.02 (2-7) 

where ܦ is the fire diameter or the effective fire diameter (m2) and ܳሶ

כ is the fire Froude Number 

calculated using Equation 2-4 (non-dimensional). The effective fire diameter may be computed 

using Equation 2-3. 
THE FIRE MODELING PROCESS 

2-26 

Ceiling Jet Distance Ratio

The ceiling jet distance ratio is a measure of the ceiling jet position at which data is sought 

relative to the enclosure height and is applicable primarily when the temperature and velocity of 

the ceiling jet are quantities of interest. A low ceiling jet distance ratio indicates that the position 

is within the impingement zone and that the conditions would be dominated by the thermal 

plume. A high ceiling jet position ratio suggests that the position is approaching the edge of the 

ceiling jet, at least as idealized by algebraic correlations. A high ceiling jet ratio also suggests 

that a considerable portion of the ceiling would need to be free of obstructions in order to 

conform to the underlying approximations of the ceiling jet models. The ceiling jet ratio is given 

by the following equation: 

Ceiling Jet Ratio ൌ

௝௖ݎ

௙ܪ െ௖ ܪ

(2-8) 

where ݎcj is the horizontal distance within the ceiling jet from the fire centerline (m), ܪ ௖is the 

enclosure height (m), and ܪ ௙is the base height of the fire (m). The ceiling jet ratio is applicable 

primarily when sprinkler or heat detector actuation is calculated. It is not applicable when the 

fire is modeled outside an enclosure. 

Equivalence Ratio

This quantity is the ratio of the generation rate of fuel to the supply rate of oxygen. When the 

equivalence ratio is equal to one, the exact amount of oxygen required for complete combustion 

is available. When the ratio is greater than one, the environment is fuel rich and the fire is 

considered to be under-ventilated. The reverse is true when the ratio is less than one. The 

upper limit for the equivalence ratio in enclosure fires is about three (Gottuk et al., 2008). 

Modeling under-ventilated fires is challenging in part because the fuel mass loss rate is typically 

specified by the user and is not adjusted by the fire models to the conditions actually present. 

The equivalence ratio may be estimated for natural and forced ventilation by the expression: 

߮ ൌ

ܳሶ

∆ܪைమ݉ሶ Oమ

(2-10)

where ߮ is the equivalence ratio (non-dimensional), ܳሶ is the heat release rate of the fire (kW), 

∆ܪைమ is the “heat of combustion” for oxygen (kJ/kg), and ݉ሶ Oమ is the mass flow rate of oxygen 

into the enclosure (kg/s). The “heat of combustion” for oxygen is the energy released per unit 

mass of oxygen and varies by less than five percent among nearly all carbon-based fuels 

(Janssens, SFPE Handbook, 4th edition). The value for ∆ܪைమis typically taken to be 13,100 

kJ/kg, an average value over a wide range of common fuels. A notable exception to this 

convention is hydrogen, whose heat of combustion based on oxygen consumption is 

approximately 18,000 kJ/kg. For other pure fuels, it is possible to calculate a more accurate 

value than 13,100 kJ/kg, in which case Eq. (2-10) can be modified accordingly. 

The mass flow rate of oxygen into the enclosure is given by the following equation: 

݉ሶ Oమ ൌ ቐ

0.23 ൈ

1

(Natural଴ (ܪඥ଴ܣ 2

0.23 ߩஶܸሶ ሺMechanicalሻ

 (2-11)
THE FIRE MODELING PROCESS

2-27

where ܣ ଴is the effective area of the openings (m2), ܪ ଴is the effective height of the openings 

(m), ߩ ∞is the density of ambient air given by Equation 2-5 (kg/m3), and ܸሶ

 is the volumetric flow 

rate of air into the enclosure (m3/s). In the case of natural ventilation, Equation 2-11 is 

applicable only to enclosures with one or more vertical openings. Note that the oxygen mass 

flow parameter is the oxygen flow into an enclosure; if the enclosure has forced exhaust only, 

the mass flow rate during the fire will likely change as the temperature of the enclosure 

increases. The mass flow that corresponds to the heated environment should be used when 

computing the equivalence ratio. An alternate means of estimating the mass flow rate of 

oxygen into the enclosure is necessary if there are horizontal openings, which could include 

using the model-predicted vent flow rates. This approach may also be used for enclosures in 

which there is only forced exhaust. If there are multiple vertical openings, the effective opening 

height (ܪ (଴is given by the following equation (Buchanan, 2001): 

௡ ௜ܪ௜ܣ ∑ ൌ௢ ܪ

௜ୀଵ

௡ ௜ܣ ∑

௜ୀଵ

 (2-12)

where ܣ ௜is the area of the i

th opening (m2), ܪ ௜is the height of the ith opening, and ݊ is the total 

number of openings. The effective opening area (ܣ଴ሻ is given by the following equation 

(Buchanan, 2001): 

௜ܣ ෍ ൌ௢ ܣ

௡

௜ୀଵ

(2-13)

where ܣ ௜is the area of the i

th opening (m2). 

In many compartments, both natural and forced ventilation is present. The recommended 

procedure to follow in this case is to select the dominant ventilation mode (i.e., the mode that 

produces the highest mass flow of oxygen). If the two modes are comparable, the oxygen 

masses may be added. As was the case for the ceiling jet ratio and the flame length ratio, the 

equivalence ratio applies only to fires that are modeled within an enclosure. 

Compartment Aspect Ratio

The compartment aspect ratio is a measure of the deviation of the enclosure dimensions from a 

cube. When at least one of the compartment aspect ratios is large, the enclosure takes on the 

characteristics of a corridor. In such cases, the transport time of the combustion products and a 

non-uniform layer can both become significant parameters that require consideration. When at 

least one of the compartment aspect ratios is low, the enclosure takes on the characteristics of 

a shaft. In these cases, stratification of the combustion products, the interaction of the fire 

plume and the enclosure boundaries, or choked flow could become parameters that influence 

the results. These situations may lie outside the development basis for algebraic and zone fire 

models. The compartment aspect ratio is computed using the following equation: 

Compartment Aspect Ratio ൌ 

ە

ۖ

۔

ۖ

ܮ ۓ

௖ܪ

ܹ

௖ܪ

 (2-14)
THE FIRE MODELING PROCESS 

2-28 

where ܮ is the compartment length (m), ܹ is the compartment width (m), and ܪ ௖is the 

compartment height (m). The compartment aspect ratio is applicable to fires evaluated within 

an enclosure. 

Radial Distance Ratio

The radial distance ratio is a measure of the distance from the center of the source fire at which 

a heat flux quantity is predicted. It is applicable only when the heat flux parameter is computed. 

A low radial distance ratio indicates that the target location is close to the fire and that near-field 

thermal radiation effects could be significant. Large radial distance ratios indicate that the target 

is located far from the fire. The radiant heat flux at high radial distance ratios will approach that 

predicted from a point heat source, barring other sources of external thermal radiation or 

geometric factors (flame deflections under a ceiling or boundary re-radiation). 

The radial distance ratio is given by the following equation: 

Radial Distance Ratio ൌ

ݎ

(2-15) ܦ

where ݎ is the actual distance between the target and the center of the fire base (m) and ܦ is 

the fire diameter as computed using Equation 2-3. 

For a given set of experiments and NPP fire scenarios, the user can calculate the relevant 

normalized parameters. If the fire scenario parameters fall within the ranges evaluated in the 

study, then the results of the study offer appropriate validation for the scenario. If they fall 

outside the range, then a validation determination cannot be made based on the results from 

the study. For any given fire scenario, more than one normalized parameter may be necessary 

for determining the applicability of the validation results. 

The V&V study provides valuable insight into the predictive capability of the five fire models. 

This insight is ultimately characterized in terms of a bias and a standard deviation for a number 

of output parameters. The closer the bias is to unity, the more accurate the fire model tends to 

be in predicting the given parameter; the smaller the standard deviation, the smaller the 

expected scatter around the mean bias. Chapter 4 of this guide describes how the V&V 

uncertainty information can be used to assign a probability function to the output data. 

NUREG-1824 (EPRI 1011999) provides V&V documentation for specific versions of fire models. 

Because the fire models considered are under active development, new releases are expected 

to and do occur. The user has the option of using the model version that has been verified and 

validated in NUREG-1824 (EPRI 1011999) or re-evaluating cases in NUREG-1824 (EPRI 

1011999) to demonstrate that the predictive capability of the model has not decreased for the 

application at hand. It is expected that NUREG-1824 (EPRI 1011999) will be updated from time 

to time, as the need arises. 

2.3.7 Fire Modeling Parameters Outside the Validation Range 

The development of the sample problems documented in the appendices to this report suggests 

that many commercial NPP fire modeling applications can fall outside the range of applicability 

of the validation study documented in NUREG-1824 (EPRI 1011999). The primary reason for 

this is that the range of applicability, as defined by the dimensionless parameters, is governed 

by the experiments selected for the validation study. The selected experiments are 

representative of various types of spaces in commercial NPPs, but do not encompass all 

possible geometries or applications. Accordingly, the analyst will encounter many areas or 
THE FIRE MODELING PROCESS

2-29

applications that will fall outside this application range. The predictive capabilities of the fire 

models in specific scenarios can extend beyond the range of applicability defined in NUREG1824 (EPRI 1011999). Additional analysis and justification is required by the analyst to address 

situations where some or all of the analysis parameters fall outside the range of applicability 

defined in NUREG-1824 (EPRI 1011999). The additional analysis and justification should 

address the applicability of fire modeling results generated by input parameters outside the 

validation range to support the conclusions of the study. This section describes the 

recommended strategies for addressing this situation. 

2.3.7.1 Sensitivity Analysis 

In the context of applicability of validation results, sensitivity analysis refers to varying selected 

input parameters in the “conservative” direction so that they fall within the applicability range. If 

the fire modeling conclusions are not affected by the variations in the parameters, the analyst 

may use the sensitivity analysis results to further justify the conclusions. Based on the 

dimensionless terms listed above, the following sensitivities could be evaluated: 

 Froude number: The two parameters that can be practically varied are the fire diameter 

and the HRR. For fire sizes (i.e., HRR) that are small for the postulated diameter, the 

resulting Froude number can fall under the low end of the applicability range. Similarly, 

for fires that are relatively large for the postulated diameter, the Froude number can fall 

above the applicability range. In the former situation, the analysts may consider 

reducing the fire diameter and keeping the HRR profile unchanged. In most fire 

modeling tools, the fire diameter is simply used to determine HRRs or to calculate the 

fire plume conditions, such as the flame height or plume temperature. Considering that 

the HRR is “fixed” in this sensitivity study, the fire diameter may not be a relevant 

parameter in the analysis, with the important exception of scenarios where the fire plume 

conditions are relevant. A similar approach could be used for the latter situation. 

Increasing the fire diameter can “force” the dimensionless term into range. It should be 

stressed that fire diameter is often a parameter that influences predicted flame height 

and fire plume conditions, and that the effects of diameter variations should be explicitly 

addressed in the analysis. This includes other dimensionless terms where the fire 

diameter is a key input (e.g., target distance to diameter (r/D), etc.). 

 Flame length relative to ceiling height: This is a convenient parameter for expressing the 

“size” of the fire relative to the height of the compartment. A value of 1 means that the 

flames reach the ceiling. The validation range extends up to a value of 1.0, which 

should cover most of the scenarios of interest in commercial NPPs. Scenarios that are 

expected to fall out of the range are: 

o Those associated with relatively short flames. Typical ceiling heights in NPP 

scenarios range from about 3 to 6.1 m (10 to 20 ft), excluding the containment and 

turbine buildings, which have relatively large openings between elevations. 

Consequently, flame lengths shorter than 0.6 to 1.2 m (2 to 4 ft) will be considered 

outside of validation range. A sensitivity analysis increasing the HRR values should 

provide a conservative estimate of fire conditions within the validation range. In 

cases where the conclusion of the analysis does not change given the increased fire 

intensity (e.g., no damage within the flame length of fire plume), the suggested 

sensitivity analysis can be used as the justification for the evaluation of a 

compartment that falls outside the validation range. 
THE FIRE MODELING PROCESS 

2-30 

o Flame extensions under ceilings. In this particular case, not only are such flame 

lengths out of the range of validation, but also the models for predicting this 

phenomenon have not been verified or validated with a process similar to the one 

documented in NUREG-1824 (EPRI 1011999). 

 Ceiling jet radial distance relative to the ceiling height: Ceiling jet temperature and 

velocity correlations use this ratio to express the horizontal distance from target to 

plume. Ceiling jet applications in commercial NPPs should be carefully evaluated due to 

the numerous obstructions near the ceiling (e.g., cable trays, HVAC ducts, piping, etc.). 

Most of its applications include determination of time to detection and sprinkler 

activation, in which the ceiling jet velocity is a sub-model in the analysis. An alternative 

option is a sensitivity analysis consisting of moving the fire location to distances that 

would fall within the validation range; it is recognized, however, that in many situations 

the fire location cannot be altered, particularly in the case of fixed ignition sources or 

transient fires postulated near areas where redundant targets are in close proximity 

(pinch-points). In general, longer horizontal distances will result in longer activation time 

results; by contrast, shorter horizontal distances would result in “conservative” time-todamage results. In situations where the ceiling jet geometry deviates significantly from 

the idealized flat horizontal surface, as may be the case when there are large numbers 

of obstructions or bays, a CFD model may be the better choice for calculating detector 

response times. 

 Equivalence ratio as an indicator of the ventilation rate: The validation available is for 

well-ventilated fires: that is, no model validation information is available for underventilated compartment fires, including fire extinction due to lack of oxygen. In general, 

fires that are considered well ventilated in the enclosure should result in bounding 

conditions as long as the HRR profile is appropriate. Conditions in the enclosure are not 

expected to be worse in a fire where the combustion process is affected by lack of 

oxygen than they would be under fire conditions where the combustion process is 

unaffected. However, under-ventilated fire conditions should be considered carefully as 

sudden air inflows into compartments with under-ventilated fire conditions could produce 

relatively severe fire conditions. 

 Compartment aspect ratio: It is expected that some compartments in commercial NPPs 

would have geometric characteristics outside the validation range (e.g., relatively long, 

narrow corridors with high ceilings, etc.). These parameters are important in fire 

scenarios involving HGL calculations, as the size and configuration of the compartment 

are important input parameters. Clearly, these parameters should not be applicable in 

scenarios where the enclosure conditions are not considered, such as flame radiation 

calculations using the point source model and plume temperature calculations using 

algebraic models where it has been determined that enclosure conditions are not a 

factor. As part of the sensitivity analysis, the analyst may consider “shortening” the 

length, width, or height of the compartment to values that fall within the validation range, 

with the expectation that this will result in an elevated level of hazardous fire-generated 

conditions, as predicted by the model (i.e., a conservative calculation). In cases where 

the conclusion of the analysis does not change given the “smaller” compartment (e.g., 

the HGL temperature does not exceed damage threshold of cables in either case), the 
THE FIRE MODELING PROCESS

2-31

suggested sensitivity analysis can be used as the justification for the evaluation of a 

compartment that falls outside the validation range. 

 Radial distance relative to the fire diameter: This ratio is the relative distance from a 

target to the fire, and is important when calculating the radiative heat flux. Note that the 

validation range starts at a distance approximately twice the fire diameter. In practice, 

targets at a very close distance to the fire (approximately two fire diameters or less) 

should be expected to fail, given the relatively low damage threshold levels for cables. 

An alternative option is a sensitivity analysis, which consists of moving the fire location to 

distances that would fall within the validation range; it is recognized, however, that in 

many situations the fire location cannot be altered, particularly in the case of fixed 

ignition sources or transients fires postulated near “pinch-points.” In general, shorter 

horizontal distances will result in higher heat flux levels. 

2.3.7.2 Additional Validation Studies 

There are other fire model validation studies besides NUREG-1824 (EPRI 1011999) that can 

serve as a basis for establishing the applicability of fire modeling results. In developing the 

examples documented in the appendices of this report, the research team identified relevant 

validation studies outside of NUREG-1824 (EPRI 1011999), as summarized below: 

 Scenarios involving targets within the fire plumes: A useful discussion of fire plumes is 

contained in Gunnar Heskestad’s chapter in the SFPE Handbook of Fire Protection 

Engineering, 4th ed., “Fire Plumes, Flame Height, and Air Entrainment.” The plume 

correlations used in the empirical and zone models are described, as well as their range 

of applicability. NUREG-1824 (EPRI 1011999) contains experimental measurements of 

fire plumes, but the range is somewhat limited. The plume correlations used by the 

models have a much wider range of applicability than that exercised in NUREG-1824 

(EPRI 1011999). 

 Scenarios involving targets within the ceiling jet: Similarly, Ronald Alpert’s chapter 

“Ceiling Jet Flows” in the SFPE Handbook contains a description of the various 

correlations used to estimate the temperature and gas velocity of ceiling jets. There are 

extensive references to the original experimental test reports from which the correlations 

were derived. 

 Scenarios involving targets exposed to flame radiation: A useful collection of techniques 

and validation data for thermal radiation calculations is found in the SFPE Engineering 

Guide for Assessing Flame Radiation to External Targets from Pool Fires, written by the 

SFPE Task Group on Engineering Practices, 1999. 

 Scenarios involving flashover/post-flashover conditions: A series of experiments was 

conducted at NIST as part of an investigation of the collapse of the World Trade Center 

towers. Validation calculations with FDS are described in the report NIST NCSTAR 1-

5F, Federal Building and Fire Safety Investigation of the World Trade Center Disaster: 

Computer Simulation of the Fires in the WTC Towers, September 2005. 

 Scenarios involving electrical failure of cables: The Cable Response to Live FIRE 

(CAROLFIRE) program led to the development and validation of the Thermally-Induced 
THE FIRE MODELING PROCESS 

2-32 

Electrical Failure (THIEF) model (NUREG/CR-6931, Volume 3). This model can be 

used to estimate the temperature within an electrical cable that is exposed to an 

elevated temperature or heat flux. 

 Scenarios involving cable burning: The Cable Heat Release, Ignition, and Spread in 

Tray Installations in Fire (CHRISTIFIRE) program led to the development and validation 

of the Flame Spread in Horizontal Cable Trays (FLASH-CAT) model (NUREG/CR-7010, 

Volume 1). This model addresses the growth and spread of fire within vertical stacks of 

horizontal, open-back cable trays. 

In addition to NUREG-1824 (EPRI 1011999) and the various documents cited above, the 

individual model developers typically maintain a collection of validation cases that are included 

as part of the model documentation. The algebraic spreadsheet models, FDTs

 and FIVE-Rev1, 

are based directly on experimental correlations. Validation of these models is typically not part 

of the model documentation; rather, there are references to source material like the SFPE 

Handbook or the original test reports. Validation studies by the CFAST and FDS developers are 

contained within: 

NIST Special Publication 1086, CFAST – Consolidated Model of Fire Growth and Smoke 

Transport, Software Development and Model Evaluation Guide, 2008. 

NIST Special Publication 1018, Fire Dynamics Simulator, Technical Reference Guide, 

Volume 3, Validation, 2007. 

In summary, the purpose of the sensitivity analysis is to “re-shape” the scenario with parameters 

that fall within the V&V range and result in more severe fire generated conditions (e.g., higher 

HGL or plume temperature, higher incident heat flux, etc.). Depending on the application, one 

or more parameters may need to be varied affecting multiple dimensionless parameters. It is 

recommended that the results from the sensitivity calculations always be compared to those 

resulting from the base case to ensure that the input parameter manipulation produces more 

severe fire generated conditions. 

2.4 Step 4: Calculate Fire-Generated Conditions 

This step involves running the model(s) and interpreting the results. When running a computer 

model, the following general steps are recommended: 

1. Determine the output parameters of interest. If the goal of the simulation is to estimate 

wall temperatures, for example, the analyst should be interested in internal and external 

wall temperatures. The analyst should ensure that the model will provide the output of 

interest, or at least the fire conditions that can help achieve the objectives of the 

analysis. The output file should be labeled with a distinctive file name. 

2. Prepare the input file. In this step, the analyst enters the input parameters into the 

model. The best way to enter input parameters is to follow the same guidelines 

described in the scenario description section. Each model has a user’s manual with 

instructions on creating the respective input file. These files are created either through 

user-friendly menus and screens or through a text editor. If a text editor is used, it is 

strongly recommended that the analyst start with an example case prepared by code 

developers, and make appropriate changes to that file. 
THE FIRE MODELING PROCESS

2-33

3. Run the computer model. The running time for zone models is on the order of minutes, 

depending on the complexity of the scenario and the speed of the computer. 

Calculations using a CFD model may take up to days or weeks in complex scenarios, 

including multiple compartments, multiple fires, and mechanical ventilation systems. 

4. Interpret the model results. Check that the results are intuitively consistent with the input 

and expectations. Check that the output results accurately reflect the desired input; 

common verifications would include the fire size and location, the location and status of 

any doors or boundary openings, and the forced ventilation flow rate and location. The 

model output should be checked for indications of a solution error. For example, the 

pressure and the HGL should fall within the ranges observed in test data; the HGL 

temperature should be greater than the lower gas layer temperature; and there should 

not be anomalous areas of flow acceleration or temperature change. Determine whether 

or not the fire scenario resulted in conditions that exceed the performance criteria, as 

applicable. 

5. Organize the results in a form that answers the question(s) and allows the calculations to 

be reproduced. If the results are used in a PRA screening analysis, this may take the 

form of a ZOI dimension or a maximum HGL temperature. If the results are part of a 

deterministic analysis, the output form may be a conclusion with regard to the 

performance of some component and an associated safety margin if the component is 

predicted to be free of damage. 

For the FDTs

 and FIVE-Rev1, the input data is entered directly into a spreadsheet, and the 

results are presented in the spreadsheet. Some of the FDTs

 spreadsheets include graphical 

and tabular results. FIVE-Rev1 typically provides a single result for a given set of input data; 

however, many of the calculations in FIVE-Rev1 are implemented as Microsoft Excel functions. 

These functions can be called from any cell in the spreadsheet, and can be used to easily 

calculate the plume temperature at a specific location above the fire as a function of time for a 

fire with a time-varying HRR. 

CFAST, MAGIC, and FDS can handle user-specified transient heat release rates, as they 

calculate the results for each zone or cell at each time step. The time step required to maintain 

stable calculations is typically determined by the model. The interval at which results are 

presented is a user-specified value. CFAST, MAGIC, and FDS can output results as text files, 

which can be read or plotted using commercially available spreadsheet programs; CFAST and 

FDS can also output their results in a form appropriate for SMOKEVIEW (Forney, 2010). 

SMOKEVIEW is a software tool that visualizes smoke and other attributes of the fire using 

traditional scientific methods, such as displaying tracer particle flow, two- or three-dimensional 

shaded contours of gas flow data (e.g., temperature), and flow vectors showing flow direction 

and magnitude. MAGIC includes its own post-processor for visually analyzing the results of a 

simulation. Post-processing may also be performed using other graphical or graphical 

animation software. If using a software package that is not designed for viewing the particular 

fire model results, the user should check that the output parameters are interpreted and 

displayed as intended. 

2.5 Step 5: Conduct Sensitivity and Uncertainty Analyses 

This document recommends a comprehensive treatment of uncertainty and/or sensitivity 

analysis as part of a fire modeling analysis for the following reasons: 
THE FIRE MODELING PROCESS 

2-34 

 Models are developed based on idealizations of the physical phenomena and simplifying 

approximations, which unavoidably introduces the concept of model uncertainty (i.e., 

model error) into the analysis. 

 A number of input parameters are based on available or generic data or on fire 

protection engineering judgment, which introduces the concept of parameter uncertainty 

into the analysis. 

The concepts of model and parameter uncertainty have traditionally been addressed in fire 

modeling using uncertainty and/or sensitivity analysis. The uncertainty in a variable represents 

the lack of knowledge about the variable, and is often represented with probability distributions. 

Its objective is to assess the variability in the model output, that is, how uncertain the output is 

given the uncertainties related to the inputs and structure of the model. By contrast, the 

sensitivity of a variable in a model is defined as the rate of change in the model output with 

respect to changes in the variable. A model may be insensitive to an uncertain variable. 

Conversely, a parameter to which a model is very sensitive may not be uncertain. 

Details of the uncertainty and sensitivity analysis are included in Chapter 4. 

2.6 Step 6: Document the Analysis 

The amount of information required and generated by a fire modeling analysis can vary widely. 

Simple algebraic models may not require a large number of inputs, and the complete analysis, 

including output results, can be documented on a single piece of paper. On the other hand, 

some fire modeling exercises may require use of multiple computer models, where outputs from 

one are inputs to others. These cases, for the most part, will require a significant number of 

input parameters and will produce outputs requiring documentation. Regardless of the amount 

of information required or generated by the analysis, proper documentation is vital to identifying 

the important findings of the exercise and providing clear, focused conclusions. 

Documentation of the fire scenario selection and description process should include enough 

information so that the final report is useful in current and future applications. This is particularly 

relevant in the commercial nuclear industry, where compartment and equipment layouts or 

processes do not change much over time. It is likely that fire scenarios analyzed for one 

application may be useful for other applications as well; the key, however, is to develop and 

maintain good documentation of the selected fire scenarios, including all the technical elements 

discussed in this section. The SFPE Engineering Guide to Substantiating a Fire Model for a 

Given Application (SFPE, 2010) provides general guidance on information to be included in fire 

modeling analyses. 

It is likely that the information necessary for documenting the fire scenario selection will be 

gathered from a combination of observations made during engineering walkdowns and a review 

of existing plant documents and/or drawings. The documentation process then involves 

compiling the information from different sources into a well-organized package that can be used 

in future applications and for NRC regional inspections. The documentation package may 

consist of: 

 Marked-up plant drawings. Plant layout, detection, suppression, cable tray, HVAC, and 

conduit drawings are often marked to highlight the location of the compartment, the 

ignition sources, the targets, the ventilation flow paths, and the fire protection features. 

The drawings also serve as sources of fire model input values, such as compartment 
THE FIRE MODELING PROCESS

2-35

dimensions, ventilation flow rates, and relative locations of fire protection systems or 

targets. 

 Design basis documents (DBDs). Design basis documents (DBDs) provide in-depth 

assessments of plant features in various operation modes, such as the HVAC system. 

 Sketches. Sketches are perhaps one of the most useful ways of documenting a fire 

scenario. A sketch typically consists of a drawing illustrating the ignition source, 

intervening combustibles, targets, and fire protection features. A first draft of the sketch 

is usually prepared during walkdowns. The analyst should take the opportunity to 

include details such as raceways and conduit identifications (IDs), and other information 

relevant to the fire modeling analysis. Pictures often supplement sketches. 

 Write-ups and input tables. Write-ups and input tables are used to compile the 

information collected from drawings and walkdowns in an organized way. The write-up 

should include a brief scenario description and detailed documentation supporting 

quantitative inputs to the fire modeling analysis, as well as any relevant sketches or 

pictures associated with each scenario. 

 Software versions, descriptions, and input files. The documentation package should 

include the version numbers of any software, brief descriptions of the software, and 

copies of the input files. 

The examples presented in Appendices A through H of this guide illustrate techniques for the 

proper documentation of fire modeling calculations using the format described. In conclusion, a 

properly documented analysis should enable someone else to reproduce the results from the 

information contained within the documentation. 

2.7 Summary 

This chapter described a recommended process for conducting and documenting a fire 

modeling analysis. Chapter 3 provides guidance on selecting the appropriate fire modeling tool 

and input parameters for typical commercial NPP applications. Fire model uncertainty is 

addressed in Chapter 4 of this document. Specific fire modeling examples evaluated using the 

process described in this Chapter are provided in Appendices A through H. 

 
THE FIRE MODELING PROCESS 

2-36 

 
3-1 

3 

GUIDANCE ON FIRE MODEL SELECTION AND 

IMPLEMENTATION 

This chapter contains a catalogue of typical nuclear power plant (NPP) fire scenarios, including 

relevant physical phenomena, model selection criteria, and suggested modeling strategies. In 

particular, the chapter provides recommendations as to the appropriate use of empirical 

correlations, zone models, and CFD calculations. 

3.1 Model Implementation of Fire Scenario Elements 

This section provides a description of fire modeling elements typically present in commercial 

NPP scenarios. The following fire modeling elements are described: 

 Heat Release Rate 

 Plant Area Configuration 

 Ventilation Parameters 

 Targets 

 Intervening Combustibles 

3.1.1 Heat Release Rate 

For most fire model applications, the heat release rate (HRR) is the most important parameter to 

specify. All enclosure fire models solve some form of the energy conservation equation (i.e., the 

energy from the fire increases the temperature and drives hot air out and cold air into the 

enclosure). The models essentially redistribute the energy from the fire throughout the 

enclosure. For most NPP applications, the HRR is specified by the analyst in the form of a time 

history. This time versus HRR curve typically has four stages: incipient, growth, steady burning 

at peak intensity, and decay. 

During the incipient stage, the fire burns at a low intensity (i.e., smoldering insulation or a small 

trash can fire). The duration of this stage may vary from seconds to hours, and the energy 

release is relatively low. Because of the uncertainty in the intensity of the fire during this stage, 

and the exact time that the fire will transition to a significant fire, the incipient stage is often not 

considered in the analysis. 

Depending on the combustible and its arrangement, the growth to a fully developed fire will vary 

from seconds to minutes. Unless experimental data is available, the HRR is usually specified to 

increase following a so-called t2

 growth profile (Karlsson and Quintiere, 2000). The basic idea 

behind this approximation is that the burning surface area of a growing fire increases as the 

square of the time from the beginning of the growth period. 

The steady burning phase occurs when the fuel reaches its maximum burning rate. In most 

cases, the peak HRR is obtained from experimental data. Alternatively, it can be estimated by 

multiplying the heat of combustion by the maximum burning rate of the fuel, if known. The peak 
GUIDANCE ON FIRE MODEL SELECTION AND IMPLEMENTATION 

3-2 

HRR may be limited by the available air supply. Estimates of the maximum HRR inside a 

compartment with a given ventilation rate are available in fire protection engineering handbooks. 

Following the steady burning phase, the HRR is usually specified to decrease to zero linearly. 

The duration of this phase depends on the amount of fuel available. In fact, the integral of the 

entire HRR time profile (in units of kJ) divided by the heat of combustion of the fuel (in units of 

kJ/kg) should equal to the mass of combustibles (in units of kg). 

In addition to the HRR time history, the following parameters may be important depending on 

the model or the scenario. 

 Fire elevation: The elevation of the base of the fire, measured from the floor. It is important 

in scenarios involving targets in the fire plume where the relative distance between the fire 

and the target strongly influences the exposing temperature. It is also important because 

the height of the fire relative to the hot gas layer (HGL) influences the air entrainment into 

the plume, the position of the HGL, and, potentially, the actual HRR (since air entrained from 

the HGL is oxygen-depleted). 

 Fire location: In scenarios where the fire is located near a wall or corner, the plume is 

expected to entrain less air, resulting in higher plume temperatures (Karlsson and Quintiere, 

2000, p. 72). 

 Fuel mass: This parameter is an important factor in determining the burning duration 

 Soot and product yields: The yield of a combustion product is the mass of the product 

generated per unit mass of fuel consumed. In particular, the soot yield is an important factor 

in radiative heat transfer (e.g., targets immersed in the HGL), visibility calculations, and 

smoke detector response estimates. The yields of toxic gases can also be important in 

habitability calculations 

 Radiative fraction: The fraction of energy emitted in the form of thermal radiation. For most 

materials, the radiative fraction is approximately one third. That is, one third of the total 

HRR radiates in all directions and two thirds is convected upwards into the smoke plume 

3.1.2 Plant Area Configuration 

The plant area configuration refers to the geometrical layout and construction of the enclosure. 

Each of these elements is described in detail next. 

Compartment Geometry 

Compartment geometry refers to the physical layout of the volume in which the fire is 

postulated. The length, width, and height of the room are the typical inputs required by the 

model. The size of a compartment is an important factor in the volume, and is used to solve the 

fundamental conservation equations. Algebraic and zone models employ considerable 

simplifications of the geometry, while CFD models attempt to replicate as much of the geometry 

as possible. 

Compartment Boundary Materials 

Boundary (e.g., wall or ceiling) materials are characterized with thermophysical properties, 

which include the density, specific heat, and thermal conductivity of the material. In the majority 

of commercial nuclear power plant (NPP) applications, the wall material is concrete. Other 

materials may include steel, gypsum board, etc. Properties for these materials are often 
GUIDANCE ON FIRE MODEL SELECTION AND IMPLEMENTATION

3-3

available in “drop down” menus in the fire models or in fire protection engineering handbooks. 

Table 3-1 provides typical properties for materials commonly found in NPPs. These properties 

were used in the examples described later in this Guide. It should be noted that these 

properties, as input parameters to the models, may also be available from sources other than 

the ones listed in Table 3-1. Regardless of the source of the information, users should always 

check that the material property values are appropriate for their specific application, as the 

resulting fire conditions may be sensitive to these parameters.

Table 3-1. Material properties. 

Material 

Thermal 

Conductivity 

(W/m/K) 

Density 

(kg/m3) 

Specific Heat

(kJ/kg/K) Source 

Brick 0.8 2600 0.8 NUREG-1805, Table 2-3 

Concrete 1.6 2400 0.75 NUREG-1805, Table 2-3 

Copper 386 8954 0.38 SFPE Handbook, Table B.6 

Gypsum 0.17 960 1.1 NUREG-1805, Table 2-3 

Plywood 0.12 540 2.5 NUREG-1805, Table 2-3 

PVC 0.192 1380 1.289 NUREG/CR-6850, Appendix R 

Steel 54 7850 0.465 NUREG-1805, Table 2-3 

XLP 0.235 1375 1.390 NUREG/CR-6850, Appendix R 

3.1.3 Ventilation Effects 

Ventilation effects include natural ventilation through vertical or horizontal openings, the effects 

of leakage paths, and/or the effects of mechanical ventilation. Each of these elements is 

described next. 

Vertical Openings 

Vertical openings are usually doors, but they can also be other wall openings, such as windows 

or passive ventilation ducts. In some cases, a compartment will have more vertical openings 

than the number that can be specified in a simplified model. For example, the McCaffrey, 

Quintiere, and Harkleroad (MQH) correlation for calculating HGL temperature uses only one 

opening when calculating the ventilation factor which, is defined as the product of the opening 

area and the square root of the opening height ܣ௢ඥܪ) ௢Karlsson et al., 2000; Drysdale, 2011). 

Buchanan (2001) suggests the following method for calculating an effective height and area: 

௜,௢ܪ௜,௢ܣ ௜∑ ൌ௢ ܪ

௢ܣ

ؠ

௜,௢ܪ௜,௢ܣ ௜∑

௜,௢ܣ ௜∑

(3-1) 

Here Ao,i and Ho,i are the individual door areas and heights. The effective width of multiple 

vertical openings can be estimated by the ratio Ao/Ho. 

Regarding doors (and other operable openings), consideration should be given to the doors 

being opened (or closed) during a fire. For example, when the fire brigade arrives, they will 

open the doors to the fire area to gain access, which will affect the ventilation and possibly 

result in smoke spread. 
GUIDANCE ON FIRE MODEL SELECTION AND IMPLEMENTATION 

3-4 

Leakage Paths 

The doors of most compartments in commercial NPPs are normally closed, but are not perfectly 

sealed. Consequently, the resulting pressure and the rate of pressure increase are often kept 

very small by gas leaks through openings in the walls and cracks around doors, or “leakage 

paths.” Leakage paths must be specified in compartments with closed doors during the fire 

event unless the analysis considers a completely sealed enclosure where pressure rise is an 

important variable. By contrast, compartments with at least one open door or window can 

maintain pressure close to ambient during the fire event. Leakage paths therefore do not need 

to be specified, since the leakage opening area is negligible when compared with the opening 

areas of doors and windows. 

Horizontal Openings 

Horizontal openings consist of hatches or stairwells. For modeling purposes, the areas of 

horizontal openings can simply be added. Any zone model should provide similar answers with 

single or multiple horizontal openings as long as the total opening area is the same. Note that 

the Consolidated Fire Growth and Smoke Transport (CFAST) model only allows for a single 

connection between any pair of compartments included in a simulation. For a CFD model, no 

special provisions are necessary to describe a horizontal opening. 

Mechanical Ventilation 

Mechanical ventilation refers to any air injected into or extracted from a compartment by 

mechanical means. This has a number of practical applications, such as extracting smoke from 

the HGL (e.g., a smoke purge system). The ventilation rate and the vent position are the two 

most important mechanical ventilation parameters. For some applications, the velocity of the 

airflow may also be important. These mechanically induced flows have the potential to alter the 

fire-induced flows. Mechanical ventilation often consists of a supply and an exhaust system that 

are maintained to achieve a certain pressure level. 

3.1.4 Targets 

A target is an object of interest that can be affected by the fire-generated conditions and 

typically consists of cables in conduits, cables in raceways, or plant equipment. Targets are 

characterized by their location, damage criteria, and thermophysical properties. 

A target’s location simply refers to its location relative to the fire. The location is represented by 

three-dimensional coordinates within the volume of the room in which the fire conditions are 

simulated. Where the target faces in a particular direction, an orientation vector to indicate that 

direction needs to be entered. 

The damage criteria refer primarily to a damage/response threshold. In general, the damage 

criteria for scenarios involving cable damage is expressed in terms of damage temperature or 

incident heat flux. 

The models within the scope of this Guide require specification of the target’s thermophysical 

properties, primarily the density, specific heat, and thermal conductivity, for the analysis. These 

parameters are used to estimate heat conducted into the targets. The predicted time for the gas 

temperature surrounding a target to reach a specific limit is usually less than the time it takes 

the target to reach the same limit because the heat conduction inside the target will delay the 

temperature rise at the surface during the heating process. 
GUIDANCE ON FIRE MODEL SELECTION AND IMPLEMENTATION

3-5

Information on target damage thresholds and target thermophysical properties can be found in 

documents such as NUREG-1805, NUREG/CR-6931, and NUREG/CR-6850 (EPRI 1011989). 

3.1.5 Intervening Combustibles 

In many cases, commercial NPP fire scenarios do not require burning targets to be modeled 

because it is sufficient to determine only when the target is damaged. This is clearly not the 

case with intervening combustibles, whose flammability characteristics need to be incorporated 

into the model so that the fire progression is considered. Therefore, the intervening 

combustibles should be described not only in terms of their proximity to the fire and the targets, 

but also in terms of their relevant thermophysical and flammability properties. 

In many cases, intervening combustibles consist of cables in ladder back trays. Representing 

intervening combustibles, like cables, in fire models presents technical challenges that the 

analyst should consider, including (1) obtaining the necessary geometric and thermophysical 

properties representing the intervening combustible and (2) the ability of the computer tools to 

model the fire phenomena (e.g., fire propagation). Because of these challenges, simplified 

models for determining the contribution to the HRR due to flame spread and fire propagation 

through cable trays have been developed. Appendix R of NUREG/CR-6850 (EPRI 1011989) 

provides guidance on the calculation of fire spread and HRRs for cable trays. Additionally, 

research is underway to develop improved methods for predicting the HRR and flame spread of 

electrical cables. A simple model, Flame Spread over Horizontal Cable Trays (FLASH-CAT) 

which predicts flame spread over cables, has been developed as part of the Cable Heat 

Release, Ignition, and Spread in Tray Installations during Fire (CHRISTIFIRE) project 

(NUREG/CR-7010, vol. 1, 2012), sponsored by the U.S. Nuclear Regulatory Commission (NRC) 

and conducted by the National Institute of Standards and Technology (NIST). 

3.2 Guidance on Model Selection and Analysis 

This section provides guidance on model selection and analysis of specific fire scenarios. Each 

subsection is devoted to a specific fire scenario, as listed in Table 3-2. In addition, Figure 3-1 

provides a pictorial representation of each of these scenarios. The circled numbers are 

intended to direct the reader to the section in which the scenario is described. Please note: 

these pictorial representations are not drawn to scale and are used for illustrative purposes only. 

Table 3-2. Listing of generic scenarios described in this chapter. 

Number Chapter Section Scenario Description 

1 3.2.1 Scenarios consisting of determining time to damage of cables above the ignition 

source located inside the flames or the fire plume. 

2 3.2.2 

Scenarios consisting of determining time to damage of cables located inside or 

outside the HGL. This scenario also includes a secondary fuel source (i.e., 

propagation to cable trays). 

3 3.2.3 Scenarios consisting of determining time to damage of cables located in a room 

adjacent to the room of fire origin. 

4 3.2.4 Scenarios consisting of determining time to damage of cables located inside or 

outside the HGL in rooms with complex geometries. 

5 3.2.5 Scenarios consisting of determining time to loss of habitability of the main control 

room. 

6 3.2.6 Scenarios consisting of determining time to smoke or heat detector activation. 

7 3.2.7 Scenarios consisting of determining temperature of structural elements. 
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Each of the sections listed above is organized as follows: 

 A sketch capturing most of the technical elements relevant to the analysis. A legend 

summarizing the different elements presented in the sketches is provided in Figure 3-2. 

 A scenario objective stating the purpose of the modeling exercise in engineering terms. 

 A description of the relevant technical fire scenario elements, such as mechanical 

ventilation, room geometry, etc. Recall that fire scenario elements refer to the different 

characteristics of the fire scenario that are relevant to the analysis, and should be properly 

represented in the model. 

 A modeling strategy section summarizing the recommended steps for performing the 

calculation. 

 A section listing fire model recommendations for the analysis. 

 A section referencing relevant detailed fire modeling examples documented in the Appendix 

section of this guide. 

Figure 3-1. Pictorial representation of the fire scenario and corresponding technical 

elements described in this section. 

1

2

3

4

5

6

7
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 Figure 3-2. Legend for fire modeling sketches presented in this chapter. 

 

HVAC

1. Supply 

2. Exhaust

Smoke 

Detector

Cable 

Tray

1. Exposed 

2. Target

Junction 

Box and 

Conduit

Electrical 

Cabinet

Fire

Sprinkler

Open 

Door

Closed 

Door

Pump

Plant 

Employee

Control 

Board

1.

2.

1.

2.

Structural 

Element Obstruction 
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3.2.1 Targets in the Flames or Plume 

Figure 3-3. Pictorial representation of scenario 1.

3.2.1.1 General Objective 

The objective of this scenario is to calculate the time to damage for a target immediately above 

a fire, as indicated by the dashed circle in Figure 3-3. For this scenario, the target is an 

electrical raceway and the fire source is an electrical cabinet. This scenario is often 

encountered as the initial part of a progression of target damage (i.e., the first item ignited, aside 

from the ignition source). Consequently, the characterization of the first item ignited after the 

ignition source is important in subsequent estimations of fire propagation through other 

intermediate combustibles. 

3.2.1.2 Modeling Strategy 

The recommended modeling strategy is summarized in the following steps: 

1. Determine whether the target cable, which is directly above the fire, is within the flame zone 

or within the fire plume. The target should be considered inside the flame zone if it is 

located directly above the base of the fire and its distance from the base of the fire is less 

than the flame height. If the target is above the fire but is not within the flame zone, then it is 

considered to be within the fire plume. It should be noted that unobstructed fire plumes will 

increase in diameter as a function of height. Consequently, a target does not need to be 

directly above the ignition source to be immersed in the fire plume. 

2. Calculate the time to damage by finding the minimum of either: 

a. The time at which the flame reaches the target. This is achieved by calculating the 

flame height as a function of time using the HRR profile (HRR vs. time) and fire 

diameter as input. 

b. The time it takes the fire plume temperature to exceed the target damage 

temperature. This is achieved by calculating the plume temperature at the specified 

height as a function of time, using the HRR profile as an input. This approach can be 
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considered conservative, as it predicts cable damage occurs when the gas 

temperature surrounding the target reaches the damage temperature (i.e., heating of 

the cable is ignored). As an alternative, a potentially more accurate time to damage 

can be obtained by calculating the surface temperature of the cable as a function of 

time, given a heat flux profile generated by the flame or plume. 

If non-target raceways are located between the ignition source and the target, the contributions 

of intervening combustibles need to be considered in the analysis. For example, consider a 

cabinet fire that ignites the first of a stack of trays overhead. The fire involving the combination 

of the cabinet and first tray may then ignite the second tray in the stack, and the fire may 

progress to damaging the target raceway. Considerations of the intervening combustibles in the 

analysis include the HRR contribution and the corresponding effects on the target heating time. 

Section 3.2.2 (Scenario 2) provides guidance on treatment of intervening combustibles. 

In addition to the guidance provided above, the analyst should determine whether HGL effects 

are relevant to the scenario. The portion of the fire plume immersed in the HGL entrains air at 

higher temperatures (i.e., the HGL temperature) and is expected to have increased 

temperatures when compared with portions of the fire plume outside the HGL. In scenarios 

consisting of targets located relatively close to the ignition source (which is the case for the 

scenario discussed in this section), the HGL effects on the plume temperature are generally not 

considered, as the time to target damage is expected to be relatively short. For scenarios 

involving targets in the fire plume, located relatively far from the ignition source, the HGL effects 

on target heating should be considered. In the latter case, the room’s geometry and ventilation 

(both natural and mechanical) conditions should be captured by the analysis. 

3.2.1.3 Recommended Models 

Algebraic Models 

Both the FDTs

 and FIVE-Rev1 have models that can be useful for this scenario, provided that 

the configuration is within the correlation basis and that there are no significant HGL effects. 

Heskestad’s flame height correlation is an alternative for determining flame height. Similarly, 

Heskestad’s fire plume temperature correlation is an alternative for determining plume 

temperature and diameter (Heskestad, 2002). 

The correlations listed above are particularly applicable for scenarios consisting of targets 

relatively close to the ignition source, where HGL effects are not considered in the analysis. 

As noted above, the time to damage is the minimum of either the time at which the flame 

reaches the target, or the time it takes the fire plume temperature to exceed the target damage 

temperature. This is simply the time at which the HRR reaches the value required for either of 

the failure criteria. In both cases, the correlations are solved for a specific HRR at a specific 

time up to when the fire conditions suggest target damage (e.g., flames reach the location of the 

raceway or the plume temperature exceeds the damage temperature of the cables). 

Another option, for scenarios where the flames do not reach the cables, would be to use the 

Thermally-Induced Electrical Failure (THIEF) model (NUREG/CR-6931, volume 3) to determine 

the surface temperature at the target. The THIEF model is included in NUREG-1805, 

Supplement 1 (2012). 
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Zone Models 

Zone models can be used for this scenario. To do so, set up the necessary input file, which 

should include a “target” in the location of the electrical cable of interest, along with the 

corresponding thermophysical properties, so that the surface temperature of the cable can be 

tracked. Zone models have the ability to include HGL effects in their calculation of plume 

temperature, and are thus particularly appropriate for scenarios where the HGL temperature 

interacts with the fire plume at the location of the target. 

Again, the time to damage is the minimum of either the time at which the flame reaches the 

target or the time it takes the fire plume temperature to exceed the target damage temperature. 

The zone models routinely calculate and report these values. 

CFD Model 

Although a CFD model could be used to analyze this scenario, the level of detail and resolution 

offered by a CFD calculation is generally not necessary. On the other hand, the CFD model 

would be particularly applicable if the scenario involved obstructions between the fire and the 

target inside the fire plume or if HGL effects are significant. The effects of these obstructions on 

the exposure conditions are not captured by algebraic models or zone models. 

3.2.1.4 Detailed Examples 

Readers are referred to Appendix B, which describes the analysis of an electrical cabinet fire in 

the switchgear room, and Appendix E, which describes the analysis of a transient fire in a cable 

spreading room. 

 
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3.2.2 Scenario 2: Targets Inside or Outside the Hot Gas Layer 

Figure 3-4. Pictorial representation of scenario 2.

3.2.2.1 General Objective 

The objective of this scenario is to calculate the time to damage for a target inside or outside the 

HGL produced by a fire. The time to ignition of a secondary fuel source and the resulting 

contribution to the total HRR can also be determined. For the case shown in Figure 3-4, the 

target is a cable in an electrical raceway and the fire source is an electrical cabinet. 

3.2.2.2 Modeling Strategy 

Two levels of analysis can be employed: (1) algebraic models for the average room temperature 

as an indicator of the gas temperature surrounding the target, or (2) detailed heat transfer 

analysis for determining the target temperature. 

The first strategy consists of determining the overall room temperature using an algebraic model 

(e.g., the MQH room temperature model) (McCaffrey et al., 1981). Such a calculation will 

indicate whether the target may be subjected to damaging temperatures and the time at which 

such temperatures may be observed. It should be noted that the room needs to be represented 

as a rectangular parallelepiped and the area of all the surfaces in the room must be conserved. 

In addition, if the target cable tray is relatively close, the target may be damaged by radiant 

heating. This can be assessed with simple point source estimates that only require the HRR of 

the fire, the separation distance between the fire and the target, and the damage criteria (i.e., 

critical heat flux for damage). The point source model may lead to over-predictions when used 

to predict heat flux to targets in very close proximity to the fire. In many applications, the overpredictions will clearly suggest target damage or ignition. 

The second strategy is best addressed with a model capable of including detailed heat transfer 

analysis for determining the target’s temperature. A raceway outside the fire plume may be 

exposed to HGL conditions if the smoke accumulating in the upper part of the room descends to 
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the location of the raceway. Consequently, targets outside the fire plume are initially exposed to 

“lower layer” conditions. As the smoke continues to accumulate, the target is immersed in HGL 

conditions. As heat transfer conditions will be different for each case, a model with the ability to 

track the relevant/applicable heat transfer interaction and calculations as a function of time, 

such as a zone model or a CFD model, should be selected to handle this scenario at the 

desired level of resolution. 

With regard to the secondary fuel source, three distinct additional analyses must be made to 

determine: 

 time at which the secondary fuel source ignites, 

 HRR of the secondary fuel source, and 

 combined HRR of the primary and secondary fires. 

The more detailed models, such as FDS, can handle the ignition and contribution of multiple 

fires, provided that the ignition criteria and source HRR characteristics are provided as input. 

Other models, especially the algebraic models, only accept the total HRR as a function of time, 

which is found by summing up the individual HRRs. 

In the present example, consider a cable tray directly above the fire. The time to ignition of the 

cable tray can be determined via algebraic models that estimate the flame height and plume 

temperature as a function of time for the initial cabinet fire (see scenario previously discussed). 

Once the flames from the cabinet reach the cable tray, the cable ignites. The same is true when 

the plume temperature at the elevation of the cable tray reaches the ignition temperature of the 

cables. Both calculations should be completed, and the shorter time used as the ignition time. 

The HRR from the cable tray can be added to the HRR of the cabinet to determine a combined 

HRR as a function of time. The resulting HRR profile can take into consideration both the fuel 

consumption and propagation to additional intervening combustibles as a function of time. In 

cases where fuel consumption is not considered, the resulting HRR profile is expected to 

overestimate the fire intensity. This total rate can then be used in the various models as an 

approximation of the HRR profile. 

Appendix R of NUREG/CR-6850 (EPRI 1011989) addresses cable fires, including methods for 

calculating the HRR for a variety of cable configurations. 

It should be noted that the simple summation of the two HRRs is a simplification of a complex 

phenomenon and only provides an approximation of the conditions created by the two separate 

fires. 

3.2.2.3 Recommended Modeling Tools 

Algebraic Models 

Select the appropriate HGL (or room temperature) model and then collect the required inputs, 

including room size, opening sizes, boundary material properties, forced ventilation, and the 

HRR profiles for the initial and secondary fuel packages. For screening purposes, the use of 

algebraic models is recommended as long as the contributions of the first item ignited and 

intervening combustibles are considered. As was mentioned earlier, this approach will provide 

an approximation of the room temperature in which the target may be immersed. The methods 

used by algebraic models to address the secondary fire source are discussed above. Target 

damage due to radiant heating can be estimated using algebraic models; all that is required is 
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the HRR of the fire (as a function of time), the separation distance between the fire and the 

target, and damage criteria (i.e., critical flux for damage). 

Zone Models 

Zone models provide a good alternative for modeling this scenario, as they provide the incident 

heat flux profile, the surface temperature, and the internal temperature of the target in one 

simulation. Set up the necessary input file with the required inputs, including room size, 

opening sizes, boundary material properties, HRR, fire diameter, and a target and fire location 

so that the cable’s surface temperature can be predicted. 

Zone models also have the benefit of being able to handle secondary fire sources as separate 

entities. Secondary fires can be ignited at a prescribed time, temperature, or heat flux. 

However, zone models have limited capabilities for handling obstructions. 

Target damage due to radiant heating from the fire is easily handled by zone models, as long as 

there are no obstructions between the fire and the target that block radiant heat transfer. Zone 

models can also account for radiant heating of targets by the HGL. 

CFD Model 

The use of CFD models for this scenario is recommended for complex geometries capable of 

affecting the location of the HGL and the incident heat flux to the targets, or when greater 

accuracy of the ignition and contribution of secondary fires is warranted. For instance, 

obstructions between the ignition source and the target affect the heat balance at the surface of 

the target. The CFD model will require inputs similar to the ones collected for the zone models; 

however, the compartment geometry will need to be specified in greater detail. 

Due to their detailed calculations, CFD models are best able to model secondary fire sources, 

including their ignition and subsequent contribution to the HRR within the enclosure. 

Like zone models, CFD models can handle targets damaged by radiant heating from the fire 

and the HGL. CFD models can also include the effects of obstructions between the fire and the 

target. 

3.2.2.4 Detailed Examples 

Appendix C describes the analysis of a relatively large lubricating oil fire affecting a raceway in a 

pump room, and Appendix E describes the analysis of a transient fire in a cable spreading 

room. 
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3.2.3 Scenario 3: Targets Located in Adjacent Rooms 

Figure 3-5. Pictorial representation of scenario 3.

3.2.3.1 General Objective 

The objective of this scenario is to calculate the time to damage for a target in the HGL in a 

room adjacent to the room of fire origin. An opening connecting the room of origin to the 

adjacent room allows combustion products to enter the adjacent room. For the case shown in 

Figure 3-5, the target is a cable in an electrical raceway, the fire source is an electrical cabinet, 

and there is an unprotected opening in the wall. 

3.2.3.2 Modeling Strategy 

The recommended strategy for determining the temperature of targets located in a room 

adjacent to the room of fire origin consists of four basic steps: 

1. Determine the following characteristics for the HGL in the room of fire origin and the 

adjacent compartment: 

a. Temperature as a function of time 

b. Depth as a function of time 

2. Determine the incident heat flux surrounding the target cable. 

3. Determine the surface and internal temperature of the target cable. 

4. Compare the surface or internal temperature of the target with its damage temperature. 

One way to approach this (using algebraic models or zone models) is to first model the HGL 

temperature in the room of origin and the resulting effect on remote targets in the room. If this 

approach indicates that target damage/ignition is unlikely in the room of origin, there would 

probably be little benefit in evaluating similar targets in adjacent spaces. However, if target 

damage is possible in the room of origin, the next step would be to model the room of origin and 

the adjacent room and determine whether the resulting HGL is capable of causing 

damage/ignition of the target(s). 
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3.2.3.3 Recommended Modeling Tools 

Algebraic Models 

Generally, algebraic models are not suitable for this calculation, as a model capable of tracking 

fire conditions in adjacent rooms is necessary. Zone and CFD models can provide this 

capability. As a screening tool, algebraic models could be used to model the HGL temperatures 

in the room of fire origin. If the estimated fire conditions in the room of origin are determined not 

to generate damage or ignition of targets, it can be concluded that targets in adjacent rooms are 

also not expected to be damaged. 

Zone Models 

The zone model is an appropriate tool for addressing this scenario. Zone models are efficient 

tools for scenarios involving relatively simple geometries (i.e., geometries and openings that can 

be easily represented in rectangular parallelepipeds without compromising the technical 

elements in the analysis). Consequently, the room geometry should be represented as 

accurately as possible. One of the primary outputs of zone models is the height and 

temperature of the HGL versus time in each of the rooms specified in the computational domain. 

Zone models are also capable of determining target temperature (not just the temperature of the 

gases surrounding the target), given the boundary conditions generated by the fire and the 

thermophysical properties of the target. 

CFD Model 

A CFD model would be particularly appropriate for addressing targets located in adjacent rooms 

in scenarios with complex geometries (i.e., geometries that can’t be easily represented as 

rectangular parallelepipeds). CFD models can describe the geometry of the compartment in 

detail, including the opening(s) providing smoke migration paths to the adjacent room. 

3.2.3.4 Detailed Examples 

Readers are referred to Appendix G, which describes the analysis of targets in rooms remote 

from the fire room. 
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3.2.4 Scenario 4: Targets in Rooms with Complex Geometries 

Figure 3-6. Pictorial representation of scenario 4.

3.2.4.1 General Objective 

The objective of this scenario is to calculate the time to damage for a target in the HGL in a 

room with a complex geometry. For the case shown in Figure 3-6, the target is a cable in an 

electrical raceway and the fire source is an electrical cabinet. 

3.2.4.2 Modeling Strategy 

The first strategy involves using an algebraic or single compartment zone model to estimate the 

HGL temperature. This approach requires that the complex geometry be reduced to a single 

equivalent volume. In the case of two different ceiling heights, an empirical correlation or a 

single compartment zone model may underestimate the temperature of the smaller volume and 

overestimate the temperature of the larger. The fire’s energy is conserved, but it is not 

expected to be uniformly distributed. For this reason, it is suggested that the model only be 

applied to the portion of the compartment where the fire is postulated. This reduction in room 

volume will result in a higher predicted HGL temperature. This strategy should not be applied if 

the purpose of the calculation is to predict the activation of a sprinkler or smoke detector 

because an overestimate of the HGL temperature will lead to an underestimate of the activation 

time. 

The second strategy is to use a model capable of describing the complex geometry. A zone 

model can model the entire compartment as a collection of connected volumes. A CFD model 

can “block off” portions of the numerical grid to account for geometric obstructions. In complex 

geometries, HGL development can be significantly impacted by mixing associated with spilling 

and ventilation, and these can only be modeled by zone and CFD models. 
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3.2.4.3 Recommended Modeling Tools 

Algebraic Models 

Detailed analyses of complex geometries typically cannot be easily accomplished with algebraic 

models. However, for screening purposes, it is possible to use algebraic models. As mentioned 

earlier, this approach can provide an approximation of the HGL temperature in which the target 

may be immersed. To utilize this approach, first select the appropriate HGL (or room 

temperature) model and then collect the required inputs, including room size, opening sizes, 

boundary material properties, and HRR. Next, the complex geometry must be reduced to a 

single equivalent volume while maintaining total surface area (due to the importance of energy 

losses through the bounding surfaces) and ceiling height. It should be noted that the more 

complex the space, the less ideal the equivalent volume/area approximation becomes. Based 

on the estimates derived using the algebraic models, more detailed modeling may be indicated. 

Zone Models 

Zone models should also be used with caution when modeling this scenario. If the entire space 

is modeled, the interface between lower and upper compartments is treated as a big door. The 

entrainment correlations used by the zone model to handle vertical vents were not designed for 

such large, open “doors.” 

CFD Model 

CFD models may be required when detailed analyses of complex geometries capable of 

affecting fire development and the location of the HGL and the incident heat flux to the target 

are desired. CFD models are expected to better estimate the overall compartment 

temperatures, both upper and lower, because the basic methodology can handle non-uniform 

ceilings. 

3.2.4.4 Detailed Examples 

Readers are referred to Appendix D, which consists of a switchgear fire in a room with a 

complex geometry, and Appendix H, which consists of a fire inside the containment annulus. 
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3.2.5 Scenario 5: Main Control Room Abandonment 

Figure 3-7. Pictorial representation of scenario 5.

3.2.5.1 General Objective 

The objective of this scenario is to determine when control room operators will need to abandon 

the control room due to fire-generated conditions inside the room. This scenario consists of a 

fire, such as an electrical cabinet fire within the main control. A schematic diagram of this 

scenario is shown in Figure 3-7. Notice the presence of a suspended ceiling in the room. 

3.2.5.2 Modeling Strategy 

Main control room (MCR) abandonment is specified as being solely dependent on habitability 

conditions. As mentioned in the previous sections, control room operators are considered 

“targets” in this scenario, so it is necessary to establish the fire conditions that would force 

operators out of the control room. This can be considered the “abandonment criteria”; for 

example, visibility, temperature, heat flux, and toxicity are often the habitability indicators in 

these scenarios. Tracking these conditions can provide the time at which the operator may 

need to abandon the control room. Once the criteria have been established (see Chapter 11 of 

NUREG/CR-6850 (EPRI 1011989) for details on habitability conditions), the fire-generated 

conditions in the room can be calculated so that the abandonment time can be determined. 

For MCR analyses, two ventilation conditions should be taken into consideration: (1) the 

ventilation system is turned off, causing hot gases and smoke to accumulate inside the control 

room and (2) the ventilation system is operating in smoke-purge mode. 

3.2.5.3 Recommended Modeling Tools 

Algebraic models 

Algebraic models can be used to address individual abandonment criteria, but not all 

simultaneously. Algebraic models are typically based on empirical correlations, not the basic 

conservation laws of mass, momentum, and energy. For this reason, it is difficult to perform a 
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sensitivity analysis for a collection of correlations because they may not capture the 

interdependent relationships of the predicted quantities. 

Zone Models 

Unlike algebraic models, zone models are capable of simultaneously tracking a number of 

relevant output variables (e.g., habitability conditions) in this scenario. They are also capable of 

modeling the impact of the various ventilation configurations required for modeling MCR 

abandonment. Zone models are a good tool for modeling fires in the MCR as long as 

compartment or zonal average conditions within a given enclosure provide the necessary 

insights to support the conclusions. Localized radiation conditions can also be estimated using 

zone models. Questions, such as average temperature, visibility conditions in the control room, 

and smoke management, are well handled by zone models. In contrast, questions associated 

with temperature, heat flux levels and visibility at specific locations within the control room (e.g., 

near a panel) are best handled by CFD models. 

CFD Model 

CFD models are also a good alternative to address this scenario, particularly if complex 

geometries are involved or localized fire conditions are needed. CFD models have the added 

advantage of handling rooms with complex geometries, intervening combustibles and 

obstructions, and varying ventilation conditions. 

3.2.5.4 Detailed Examples 

Readers are referred to Appendix A, which describes the analysis of a fire in an MCR. 
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3.2.6 Scenario 6: Smoke Detection and Sprinkler Activation 

Figure 3-8. Pictorial representation of scenario 6.

3.2.6.1 General Objective 

The objective of this scenario is to calculate the response time of a smoke or heat detector. The 

flow of heat and smoke from the fire to the detector may be obstructed by ceiling beams, 

ventilation ducts, etc. Failure of a detector to actuate in response to a fire can delay the 

response of either the fire brigade or an automatic suppression system. Typical scenarios are 

shown in Figure 3-8. 

3.2.6.2 Modeling Strategy 

For scenarios involving unobstructed smoke detector devices: 

1. Determine the location of the detection device relative to the fire. 

2. Select the detector response (activation) criteria. Chapter 11 of NUREG/CR-1805 contains 

guidance on estimating smoke detector response times. 

3. Calculate the detection time using the appropriate model. 
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For scenarios involving obstructed smoke detector devices: 

1. Determine the following characteristics of the HGL using all the necessary inputs for an HGL 

calculation, as described earlier in this chapter. 

a. Temperature as a function of time. 

b. Depth as a function of time. The smoke detector is expected to activate shortly after 

the HGL reaches the bottom of the obstruction and spills into the location of the 

device. 

2. Select the detector response (activation) criteria. Chapter 11 of NUREG/CR-1805 contains 

guidance on estimating smoke detector response times. 

3. Calculate the response time of the given smoke detector once the combustion products 

reach the detector. 

For scenarios involving thermal devices (e.g., sprinklers, fusible links, or heat detectors), the 

process is similar. The only difference is that the thermal device needs to be characterized with 

relevant parameters, typically an activation temperature and the response time index (RTI). In 

addition, the selected model should account for the heating process of thermally thin elements 

(i.e., the heat detector device). 

3.2.6.3 Recommended Modeling Tools 

Algebraic models 

Algebraic models can be used to determine time to heat or smoke detection when the fireinduced flows are not obstructed before reaching the detection device. By contrast, algebraic 

models are typically not suitable when fire-induced flows, such as fire plumes or ceiling jets, will 

be obstructed before reaching the detection device. In some cases, algebraic models that 

estimate the HGL temperature as a function of time may be used for rough estimates of 

activation times. 

Zone Models 

Zone models can address the different scenario conditions presented above; for instance, 

CFAST and MAGIC are capable of determining time to smoke or heat detection when no 

obstructions are present, and can simultaneously calculate smoke accumulation so that the time 

for smoke detection activation can be estimated. This would provide an approximation, as zone 

models do not directly account for complex geometries, including obstructions. These models 

are not recommended for determining time to heat detection in obstructed geometries, since the 

velocity of the gases impacting the heat detector is not available in zone model calculations. As 

mentioned above, in some cases the HGL temperature alone may be used as a rough indicator 

of smoke and heat activation times. 

CFD Model 

CFD models are good tools for estimating time to fire detection in complex geometries, including 

obstructions, as they can describe the compartment’s complex geometries and mechanical 

ventilation conditions in detail. 

3.2.6.4 Detailed Examples 

Readers are referred to Appendices B and E, which discuss the calculation of the time to smoke 

and heat activation.
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3.2.7 Scenario 7: Fire Impacting Structural Elements 

Figure 3-9. Pictorial representation of scenario 7.

3.2.7.1 General Objective 

The objective of this scenario is to characterize the temperature of structural elements exposed 

to a nearby fire source. For the case shown in Figure 3-9, the exposure fire is an electrical 

cabinet. 

3.2.7.2 Modeling Strategy 

The fire modeling tools within the scope of this Guide should indicate whether the exposed 

structural element will reach damaging temperatures. However, this information is often not 

enough to determine whether the structural integrity of the compartment will be compromised by 

the exposing fire conditions. A more detailed structural analysis (i.e., one that involves complex 

temperature-dependent load-bearing calculations) may be needed if such a determination is 

necessary. 

Considering the limitations listed above, the following general guidance is provided: 

1. Determine whether the structural element is directly above the fire, within the ceiling jet, 

exposed to radiant heating, or within the HGL. The results of this determination will suggest 

which model or combination of models should be used. 

2. Calculate the temperature of the structural element based on the fire conditions affecting it. 

This will require an initial estimate of the fire-generating conditions surrounding the structural 

element, and, subsequently, the temperature of the element itself. 
GUIDANCE ON FIRE MODEL SELECTION AND IMPLEMENTATION

3-23

3.2.7.3 Recommended Modeling Tools 

Algebraic models 

Provided that the fire conditions affecting the structural element are appropriately identified 

(e.g., a fire plume, a ceiling jet, flame radiation, or an HGL exposure without significant 

contributions from any of the other three exposure mechanisms), algebraic models may be 

capable of determining whether the structural element will be exposed to damaging conditions. 

For example, plume temperature correlations can be used to determine the gas temperature 

surrounding an element inside the fire plume. MQH calculations can indicate whether 

compartment temperatures are near the critical temperature of structural elements; however, 

these may provide overly conservative estimates, as the algebraic models do not account for 

the heating of those structural elements that typically have large masses. Point source radiation 

calculations can be used to estimate the heat flux to structural elements that are not directly in 

the plume but close enough to the fire to become significantly heated. 

Zone Models 

Zone models are an appropriate tool to address this scenario, as the input file can be developed 

to capture the relative location of the fire and the structural element(s) as long as compartment 

or zonal average conditions within a given enclosure are appropriate to support the analysis. 

Localized conditions, such as flame radiation or radiation from surfaces, can also be handled by 

zone models. Structural elements can be represented as a target, and the incident fire 

conditions can be tracked during the fire. Zone models are also capable of performing 

conduction heat transfer calculations for the structural element, resulting in a prediction of the 

temperature of the element itself. 

CFD Model 

CFD models are good tools for estimating temperatures in structural elements of complex 

geometries, including obstructions, as they can handle the compartment’s complex geometries, 

fire development, and mechanical ventilation conditions in detail, as well as the localized 

heating of the structural elements. 

3.2.7.4 Detailed Examples 

Readers are referred to Appendix F, which describes the analysis of a lubricating oil fire’s effect 

on structural elements. 

 
GUIDANCE ON FIRE MODEL SELECTION AND IMPLEMENTATION 

3-24 
4-1 

4 

UNCERTAINTY AND SENSITIVITY 

The fire models discussed in this report are classified as deterministic to distinguish them from 

stochastic models. In essence, this means that each model takes as input a set of values, 

known as input parameters, that describe a specific fire scenario, and the model’s algorithms 

then calculate the fire conditions within the compartment. The output of the models usually 

takes the form of time histories of the various predicted quantities of interest, such as 

temperature, heat flux or smoke concentration. In a sense, the model calculation is a virtual 

experiment because the design of a model simulation often involves the same thought process 

as the design of a physical experiment. The results of the calculation are likewise expressed in 

terms similar to those of an experiment, including an estimate of the uncertainty. The sources 

of uncertainty in a model prediction are different than those in an experimental measurement. 

According to NUREG-1855, Volume 1, Guidance on the Treatment of Uncertainties Associated 

with PRAs in Risk-Informed Decision Making (2009), there are three types of uncertainty 

associated with a model prediction: 

Parameter Uncertainty: Input parameters are often chosen from statistical distributions or 

estimated from generic reference data. In either case, the uncertainty of these input parameters 

is propagated through the calculation, and the resulting uncertainty in the model prediction is 

known as the parameter uncertainty. The process of determining the extent to which the 

individual input parameters affect the results of the calculation is known as a sensitivity analysis. 

Model Uncertainty: Idealizations of physical phenomena lead to simplifying approximations in 

the formulation of the model equations. In addition, the numerical solution of equations that 

have no analytical solution can lead to inexact results. Model uncertainty is estimated via the 

processes of verification and validation (V&V). The first seeks to quantify the error associated 

with the mathematical solution of the governing equations, typically through numerical analysis, 

while the second seeks to quantify the error associated with the simplifying physical 

approximations, typically through comparison of model predictions and full-scale experiments. 

Completeness Uncertainty: This refers to the fact that a model may not be a complete 

description of the phenomena it is designed to predict. Some consider this a form of model 

uncertainty because most fire models neglect certain physical phenomena that are not 

considered important for a given application. For example, a model of sprinkler activation might 

neglect water condensation. 

The purpose of this chapter is to provide relatively simple methods to assess model and 

parameter uncertainty. Completeness uncertainty is addressed, indirectly, by the same process 

used to address the model uncertainty. Model uncertainty is based primarily on comparisons of 

model predictions with experimental measurements as documented in NUREG-1824 (EPRI 

1011999) and other model validation studies. Parameter uncertainty is addressed using simple 

techniques to propagate input parameter uncertainty and to conduct sensitivity analyses. 
UNCERTAINTY AND SENSITIVITY 

4-2 

4.1 Validation of Fire Models 

The use of fire models requires a good understanding of their limitations and predictive 

capabilities. For example, NFPA 805 (NFPA, 2001) states that fire models shall only be applied 

within the limitations of the given model and shall be verified and validated. The NRC Office of 

Nuclear Regulatory Research (RES) and the Electric Power Research Institute (EPRI) 

conducted a collaborative project for the V&V of the five selected fire models described in 

Chapter 2. The results of this project were documented in NUREG-1824 (EPRI 1011999), 

Verification and Validation of Selected Fire Models for Nuclear Power Plant Applications. 

Twenty-six full-scale fire experiments from six different test series were used to evaluate the 

models’ ability to estimate thirteen quantities of interest for fire scenarios that were judged to be 

typical of those that might occur in a nuclear power plant (NPP). The results of the study are 

summarized in Table 4-1. An explanation of this table is to follow. 

Table 4-1. Results of the V&V study, NUREG-1824 (EPRI 1011999). 

Output Quantity 

FDTs FIVE-Rev1 CFAST MAGIC FDS Exp 

ா෤ߪ ெ෤ߪ ߜ ெ෤ߪ ߜ ெ෤ߪ ߜ ெ෤ߪ ߜ ெ෤ߪ ߜ

HGL Temperature Rise* 1.44 0.25 1.56 0.32 1.06 0.12 1.01 0.07 1.03 0.07 0.07

HGL Depth* N/A N/A 1.04 0.14 1.12 0.21 0.99 0.07 0.07

Ceiling Jet Temp. Rise N/A 1.84 0.29 1.15 0.24 1.01 0.08 1.04 0.08 0.08

Plume Temperature Rise 0.73 0.24 0.94 0.49 1.25 0.28 1.01 0.07 1.15 0.11 0.07

Flame Height** I.D. I.D. I.D. I.D. I.D. I.D. I.D. I.D. I.D. I.D. I.D. 

Oxygen Concentration N/A N/A 0.91 0.15 0.90 0.18 1.08 0.14 0.05

Smoke Concentration N/A N/A 2.65 0.63 2.06 0.53 2.70 0.55 0.17

Room Pressure Rise N/A N/A 1.13 0.37 0.94 0.39 0.95 0.51 0.20

Target Temperature Rise N/A N/A 1.00 0.27 1.19 0.27 1.02 0.13 0.07

Radiant Heat Flux 2.02 0.59 1.42 0.55 1.32 0.54 1.07 0.36 1.10 0.17 0.10

Total Heat Flux N/A N/A 0.81 0.47 1.18 0.35 0.85 0.22 0.10

Wall Temperature Rise N/A N/A 1.25 0.48 1.38 0.45 1.13 0.20 0.07

Wall Heat Flux N/A N/A 1.05 0.43 1.09 0.34 1.04 0.21 0.10

I.D. indicates insufficient data for the statistical analysis. 

N/A indicates that the model does not have an algorithm to compute the given Output Quantity. 

Underlined values indicate that the data failed a normality test because of the relatively small sample size. 

* The algorithm used to compute the layer temperature and depth for the model FDS is described in NUREG-1824. 

** All of the models except FDS use the Heskestad Flame Height Correlation (Heskestad, SFPE Handbook). These models were 

shown to be in qualitative agreement with the experimental observations, but there was not enough data to further quantify this

assessment. 

Models: Five fire models were selected for the study, based on the fact that they are commonly 

used in fire analyses of NPPs in the U.S. Two of the models consist of simplified engineering 
UNCERTAINTY AND SENSITIVITY

4-3

correlations (Fire Dynamics Tools (FDTs) and Fire-Induced Vulnerability Evaluation (FIVERev1)), two are “zone” models (Consolidated Fire Growth and Smoke Transport (CFAST) model 

(CFAST) and MAGIC), and one is a computational fluid dynamics (CFD) model (Fire Dynamics 

Simulator (FDS)). 

Experiments: Six series of experiments (26 individual fire experiments in all) were selected for 

the NRC/EPRI fire model validation study (NUREG-1824/EPRI 1011999). Each series 

represented a typical fire scenario (for example, a fire in a switchgear room or turbine hall); 

however, the test parameters could not encompass every possible NPP fire scenario. Table 2-5 

lists various normalized parameters that can be used to characterize fire scenarios and the 

ranges of the validation experiments. These parameters express, for instance, the size of the 

fire relative to the size of the room, or the relative distance from the fire to critical equipment. 

This information is important because typical fire models are not designed for fires that are very 

small or very large in relation to the volume of the compartment or very large in relation to the 

ceiling height. 

For a given set of experiments and NPP fire scenarios, the user can calculate the relevant 

normalized parameters. These parameters will either be inside, outside, or on the margin of the 

validation parameter space. Consider each case in turn: 

1. If the parameters fall within the ranges that were evaluated in the validation study, then 

Table 4-1 can be referenced directly. 

2. If only some of the parameters fall within the range of the study, additional justification is 

necessary (see Section 2.3.7 for guidance). This is a common occurrence because realistic 

fire scenarios involve a variety of fire phenomena, some of which are easier to estimate than 

others. A case in point is the burning of electrical cabinets and cables. NUREG-1824 (EPRI 

1011999) does not address these fires directly, even though some of the experiments used 

in the study were intended as mock-ups of control or switchgear room fires. For scenarios 

involving these kinds of fires, the heat release rates (HRR) are often taken from experiments 

rather than being predicted by a model. It has been shown, in NUREG-1824 (EPRI 

1011999) and other validation studies, that the models can estimate the transport of smoke 

and heat with varying degrees of accuracy, but they have not been shown (at least not in 

NUREG-1824 (EPRI 1011999)) to estimate the details of the fire’s ignition and growth. 

While this does not eliminate the models from the analysis, it still restricts their applicability 

to only some of the phenomena. 

3. If the parameters fall outside the range of the study, a validation determination cannot be 

made based on the results from the study. The modeler needs to provide independent 

justification for using the particular model. For example, none of the experiments 

considered in NUREG-1824 (EPRI 1011999) were under-ventilated. However, several of 

the models have been independently compared to under-ventilated test data, and the results 

have been documented either in the literature or in the model documentation. As another 

example, suppose that the selected model uses a plume, ceiling jet, or flame height 

correlation outside the parameter space of NUREG-1824 (EPRI 1011999) but still within the 

parameter space for which the correlation was originally developed. In such cases, 

appropriate references are needed to demonstrate that the correlation is still appropriate, 

even if not explicitly validated in NUREG-1824 (EPRI 1011999). It is expected that the V&V 

effort, as documented in NUREG-1824 (EPRI 1011999), will be updated over time to include 

comparisons with additional test data and new versions of the models. These updates will 

expand the validation range shown in Table 2-5 and ensure the availability of V&V 

information for the latest versions of the models documented in this report. 
UNCERTAINTY AND SENSITIVITY 

4-4 

Predicted Quantities: The experimental data for the validation study consisted of 

measurements of one or more of the 13 physical quantities listed in the table. The FDTs

 and 

FIVE-Rev1 do not possess algorithms to estimate every quantity; in the cases in which there 

was no estimate, the table cell is labeled N/A. 

Statistics: For each model and output quantity, a summary plot of the results is presented in 

NUREG-1824 (EPRI 1011999). For example, Figure 4-1 compares the measured and predicted 

target temperatures for the model FDS. If a particular prediction and measurement are the 

same, the resulting point falls on the solid diagonal line. The longer-dashed off-diagonal lines 

indicate the experimental uncertainty. Roughly speaking, points within the longer dashed lines 

are said to be “within experimental uncertainty,” and in such cases it is not possible to further 

quantify the accuracy of the prediction. Points falling outside the experimental uncertainty 

bounds cannot be said to be free of model uncertainty. At the time of the publication of 

NUREG-1824 (EPRI 1011999), the writing team decided to use the colors green and yellow to 

indicate the degree to which the model predictions are inside or outside of the experimental 

uncertainty bounds. However, since the writing of NUREG-1824 (EPRI 1011999), it was 

decided to replace the color system with a more quantifiable metric of model accuracy. 

Figure 4-1. Sample set of results from NUREG-1824 (EPRI 1011999). 

Consider again Figure 4-1. To make better use of results such as these, two statistical 

parameters8

 have been calculated for each model and each predicted quantity. The first 

parameter, ߜ, is the bias factor. It indicates the extent to which the model, on average, underor over-predicts the measurements of a given quantity. For example, the bias factor for the data 

shown in Figure 4-1 is 1.02. This means that the model has been shown to slightly 

 

8

 The statistical parameters listed in Table 4-1 are based on the versions of the fire models used in the V&V study, circa 2006. As 

the models are improved and new validation data introduced, these values may change. 

FDS Target Temperature

Measured Temperature (°C)

0 100 200 300 400 500 600 700

Predicted Temperature (°C)

0

100

200

300

400

500

600

700
UNCERTAINTY AND SENSITIVITY

4-5

overestimate target temperatures by an average 2%, and this is represented by the red dashdot line just above the diagonal. The bias factor for each model and each output quantity is 

listed in Table 4-1. Results of the V&V study, NUREG-1824 (EPRI 1011999).. 

The second statistic9

 in Table 4-1 is the relative standard deviation of the model, ߪ෤ெ, and the 

experiments, ߪ෤ா. These indicate the uncertainty or degree of “scatter” of the model and the 

experiments, respectively. Referring again to Figure 4-1, there are two sets of off-diagonal 

lines. The first set, shown as long-dashed black lines, indicate the experimental uncertainty. 

The slopes of these lines are 1 േ 2ߪ෤ா (it is customary to express uncertainties in the form of “2-

sigma” or 95% confidence intervals). The second set of off-diagonal lines, shown as shortdashed red lines, indicates the model uncertainty. The slopes of these lines are ߜ േ 2ߪ෤ெ. If the 

model is as accurate as the measurements against which it is compared, the two sets of offdiagonal lines would merge. The extent to which the data scatters outside of the experimental 

bounds is an indication of the degree of model uncertainty. 

The derivation of the statistical parameters in Table 4-1 is provided in the next section, while 

their use is described here. Suppose that a model prediction is denoted as ܯ. The “true” value 

of the predicted quantity is specified as a normally distributed random variable with a mean, 

ߤ ൌ ܯ/ߜ, and a standard deviation, ߪൌߪ෤ெܯ/ߜ. Using these values, the probability of 

exceeding a critical value, ݔ௖, is: 

ܲሺݔ൐ݔ௖ሻ ൌ 1

2 erfc ൬

ߤ െ௖ ݔ

(4-1) ൰ 2√ߪ

Note that the complementary error function is defined as follows: 

erfcሺݔሻ= 2

√ߨ න ݁ି௧మ ஶ

௫

(4-2) ݐ݀

It is a standard function in mathematical or spreadsheet programs like Microsoft Excel10. 

To summarize, the procedure for determining the probability that a quantity predicted by a 

model could exceed a critical value is as follows: 

1. Express the model prediction as a rise above its ambient value. Call this number ܯ. Note 

that the ambient value of most output quantities is zero. Temperature, oxygen 

concentration, and smoke layer height are exceptions. For these quantities, express the 

predicted value as a temperature rise, oxygen decrease below ambient, and layer depth. 

2. Using the values of ߜ and ߪ෤ெ from Table 4-1, compute the mean, ߤ ൌ ܯ/ߜ, and standard 

deviation, ߪൌߪ෤ெܯ/ߜ, of the normal distribution for the quantity of interest. 

3. Use the equation to compute the probability that the predicted quantity could exceed a 

critical value, ݔ௖. Remember to also express this critical value as a rise above ambient in 

the same way as the predicted value, ܯ.

A few examples of this procedure are included in Section 4.3. 

 

9

 For some models/quantities, there was an insufficient amount of data to calculate the relative standard deviation of the distribution, 

in which case I.D. is shown in the Table. 

10 Excel 2007 does not evaluate erfcሺݔሻ for negative values of ݔ, even though the function is defined for all real ݔ. In such cases, 

use the identity erfcሺെݔሻ ൌ 2 െ erfcሺݔሻ.
UNCERTAINTY AND SENSITIVITY 

4-6 

4.2 Derivation of the Model Uncertainty Statistics 

This section describes the derivation of the statistics listed in Table 4-1. These values 

summarize the results of the NRC/EPRI fire model validation study documented in NUREG1824 (EPRI 1011999). This section is included for information only; there is no need for a 

model user to perform this type of calculation. McGrattan and Toman (2011) provide additional 

details on the development of these uncertainty calculations. 

For each of the fire models and each of the output quantities that were evaluated in the study, a 

plot similar to that shown in Figure 4-1. Sample set of results from NUREG-1824 (EPRI 

1011999). was produced. For each measurement point, a single experimental measurement 

was plotted against a single model prediction. The plot shows all the comparison points. The 

calculation of the statistics uses this set of measured and predicted values, along with an 

estimate of the experimental uncertainty. The purpose of the calculation is to “subtract off,” in a 

statistical sense, the experimental uncertainty so that the model uncertainty can be estimated. 

This calculation is subject to the following constraints: 

1. The experimental measurements are unbiased, and their uncertainty is normally distributed 

with a constant relative standard deviation, ߪ෤ா (that is, the standard deviation as a fraction of 

the measured value). Table 4-2 provides estimates of relative experimental uncertainties for 

the quantities of interest in terms of 2-sigma (95 percent) confidence intervals. 

2. The model error is normally distributed around the predicted value divided by a bias factor, 

ߜ. The relative standard deviation of the distribution is denoted as ߪ෤ெ. 

The computation of the estimated bias and scatter associated with model error proceeds as 

follows. Given a set of ݊ experimental measurements, ܧ௜, and a corresponding set of model 

predictions, ܯ௜, compute the following: 

lnሺܯ/ܧሻ തതതതതതതതതതത ൌ 1

ሻ௜ܧ/௜ܯlnሺ෍ ݊

௡

௜ୀଵ

(4-3)

The standard deviation of the model error, ߪ෤ெ, can be computed from the following equation: 

ටߪ෤ெ

ଶ ൅ ߪ෤ாଶ ؆ ඩ 1

݊െ1෍ൣlnሺܯ௜/ܧ௜ሻ െ lnሺܯ/ܧሻ തതതതതതതതതതത൧

ଶ

௡

௜ୀଵ

(4-4)

The bias factor is: 

ߜ ൌ exp ቆlnሺܯ/ܧሻ തതതതതതതതതതത ൅

ெ෤ߪ

ଶ െ ߪ෤ாଶ

2 ቇ (4-5)

For a given model prediction, ܯ, the “true” value of the quantity of interest, is a normally 

distributed random variable with a mean of ܯ/ߜ and a standard deviation of ߪ෤ெሺܯ/ߜሻ. 
UNCERTAINTY AND SENSITIVITY

4-7

Table 4-2. Experimental uncertainty of the experiments performed as part of the validation study 

in NUREG-1824 (EPRI 1011999). 

ࡱ෥࣌૛ Quantity

HGL Temperature Rise 0.14 

HGL Depth 0.13 

Ceiling Jet Temperature Rise 0.16 

Plume Temperature Rise 0.14 

Gas Concentration 0.09 

Smoke Concentration 0.33 

Pressure (no forced ventilation) 0.40 

Pressure (with forced ventilation) 0.80 

Heat Flux 0.20 

Surface or Target Temperature 0.14 

There are a few issues to consider when using this procedure: 

1. All values need to be positive, and each value needs to be expressed as an increase over 

its ambient value. For example, the oxygen concentration should be expressed as a 

positive number (i.e., the decrease in concentration below its ambient value). Thus, for an 

ambient oxygen concentration of 21 % and a predicted value of 14 %, the predicted 

decrease in oxygen concentration is 7 %. 

2. If the measurement uncertainty is overestimated, the model error will be underestimated. If 

the model error is less than the experimental uncertainty, the latter should be reevaluated. 

The model cannot be shown to have less error than the uncertainty of the experiment with 

which it is compared. 

3. The procedure requires that the quantity lnሺܯ ܧ⁄ ሻ is normally distributed. This is not 

necessarily true, especially in cases where there are an insufficient number of points in the 

sample. Figure 4-2 provides two examples in which the normality of the validation data is 

tested11. In cases where the data is not normally distributed, only the bias is reported. 

4. The validation data used to develop the accuracy statistics may be fairly sparse over a 

particular range. For example, in Figure 4-1, for temperatures below 300 C (570 F), there 

are a sufficient number of points to derive the statistics. For temperatures above 300 C 

(570 F), however, there are less data points and these few points do not necessarily follow 

the trend. In such cases, it is left to the discretion of the analyst to determine if it is 

appropriate to calculate the model uncertainty using the derived statistics if the temperature 

is clearly outside of the range. Depending on the application, it might be sufficient to 

indicate the model tends to over-predict these higher temperatures, as is this case, or the 

reviewer might request additional evidence that the model can be applied for this range of 

temperatures. 

 

11 The Kolmogorov-Smirnov test for normality has been applied using the software package SigmaPlot®

10, Systat Software, Inc. 

The default P value of 0.05 was used. 
UNCERTAINTY AND SENSITIVITY 

4-8 

Figure 4-2. Two examples demonstrating how the validation data is tested for normality. 

4.3 Calculation of Model Uncertainty 

This section contains a few exercises to explain the procedure for calculating model uncertainty. 

These examples consider model uncertainty only; that is, the input parameters are not subject 

to uncertainty. 

4.3.1 Example 1: Target Temperature 

Suppose that cables within a compartment fail if their surface temperature reaches 330 °C 

(625 °F). The model FDS predicts that the maximum cable temperature due to a fire in an 

electrical cabinet is 300 °C (570 °F). What is the probability that the cables could fail? For this 

exercise, the model input parameters are not subject to uncertainty, only the model itself. 

Step 1: Subtract the ambient value of the cable temperature, 20 °C (68 °F) to determine the 

predicted temperature rise. Refer to this value as the model prediction: 

ܯ ൌ 300 °C െ 20 °C ൌ 280 Ԩ (4-6)

Step 2: Refer to Table 4-1, which indicates that, on average, FDS over-predicts target 

temperatures with a bias factor, ߜ, of 1.02. Calculate the adjusted model prediction: 

ൌ ߤ

ܯ

ߜ ൌ 280 °C

1.02 ؆ 275 °C (4-7)

Referring again to Table 4-1, calculate the standard deviation of the distribution: 

ߪൌߪ෤ெ ൬

ܯ

ߜ ൰ ൌ 0.13 ൬

280 Ԩ

1.02 ൰ ؆ 36 °C (4-8)

Step 3: Calculate the probability that the actual cable temperature would exceed 330 °C12: 

 

12 In the result of Equation 4-9, the precise value for μ and σ were used rather than the rounded values shown. 

Interval Number

1 2 3 4 5 6 7 8 9 10

Number of Data Points

0

10

20

30

40

Wall Temperature

Normality Test: Pass

Plume Temperature, FDTs

Normality Test: Fail

Interval Number

1 2 3 4 5 6 7 8 9 10

Number of Data Points

0

1

2

3
UNCERTAINTY AND SENSITIVITY

4-9

ܲሺܶ ൐ 330 Ԩሻ ൌ 1

2 erfc ൬

ܶെܶ଴ െ ߤ

ߪ√2 ൰ ൌ 1

2 erfc ൬

330 Ԩ െ 20 Ԩ െ 275 Ԩ

36 Ԩ √2 ൰ ؆ 0.16 (4-9)

The process is shown graphically in Figure 4-3. The area under the “bell curve” for 

temperatures higher than 330 °C (625 °F) represents the probability that the actual cable 

temperature would exceed that value. Note that this estimate is based only on the model 

uncertainty. 

Figure 4-3. Normal distribution of the “true” value of the cable temperature in a 

hypothetical fire. 

4.3.2 Example 2: Critical Heat Flux 

As part of a screening analysis, the model MAGIC is used to estimate the radiant heat flux from 

a fire to a nearby group of thermoplastic (TP) cables. Using, for example purposes, data from 

NUREG/CR-6850 (EPRI 1011989), Appendix H, one of the damage criteria for TP cables is a 

radiant heat flux to the target cable that exceeds 6 kW/m2

. The model, by coincidence, predicts 

a heat flux of 6 kW/m2

. What is the probability that the actual heat flux from a fire will be 

6 kW/m2

 or greater? For this exercise, the model input parameters are not subject to 

uncertainty, only the model itself. 

Step 1: Unlike in the previous example, there is no need to subtract an ambient value of the 

heat flux (it is zero). Thus, the model prediction is: 

ܯ ൌ 6 kW/mଶ (4-10)

Step 2: Refer to Table 4-1, which indicates that, on average, MAGIC over-predicts radiant heat 

flux with a bias factor, ߜ, of 1.07. Calculate the adjusted model prediction: 

ൌ ߤ

ܯ

6 ൌ ߜ

1.07 ؆ 5.6 kW/mଶ (4-11)

Temperature (°C)

100 150 200 250 300 350 400 450 500

Probability Density Function

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

Model Prediction

Adjusted Model Prediction

P(T>330 °C)
UNCERTAINTY AND SENSITIVITY 

4-10 

Referring again to Table 4-1, calculate the standard deviation of the distribution: 

ߪൌߪ෤ெ ൬

ܯ

ߜ ൰ ൌ 0.36 ൬ 61.07൰ ؆ 2.0 kW/mଶ (4-12)

Step 3: Calculate the probability that the actual heat flux, ݍሶ

ᇱᇱ, will exceed the critical value of the 

heat flux, ݍሶ

௖

ᇱᇱ: 

ܲሺݍሶ

ᇱᇱ ൐ 6 kW/mଶሻ ൌ 1

2 erfc ቆݍሶ

௖

ᇱᇱ െ ߤ

ߪ√2 ቇ ൌ 1

2 erfc ቆ6 kW/mଶ െ 5.6 kW/mଶ

2.0 kW/mଶ √2 ቇ ؆ 0.42 (4-13)

Even though the model predicts a peak radiant heat flux equal to the critical value, there is only 

a 42% chance that the actual heat flux would exceed this value. This is mainly due to the fact 

that MAGIC has been shown to overestimate the heat flux by about 7%. 

It is important to note that this calculation of model uncertainty does not take into account the 

input parameters, such as the HRR of the fire. It is only an assessment of how well the model 

MAGIC can estimate the radiant heat flux to a target. Another key point is that the damage 

threshold, temperature in the first example and heat flux in the second, is known exactly, i.e., 

without uncertainty. 

4.4 Parameter Uncertainty 

The previous sections describe how to express the uncertainty of a model prediction resulting 

from the inherent limitations of the model itself. However, in most cases, the larger source of 

uncertainty is the input parameters of the model, not the model itself. This section suggests 

ways to assess the impact of this kind of uncertainty on the final prediction. 

Parameter uncertainty is addressed in this chapter in two ways: (1) parameter uncertainty 

propagation, and (2) sensitivity analysis. It is recognized that one or both approaches may be 

necessary for a given application. Depending on the complexity of the model, the number of 

input parameters will range from one to several dozen. The choice of which to analyze is based 

on (1) the importance of the parameter to the outcome, and (2) its degree of uncertainty. In 

almost all cases, the heat release rate of the fire dominates all other parameters in terms of 

these two criteria. 

The propagation of parameter uncertainty refers to the process of propagating the probability 

distributions of one or more input parameters through the model in order to determine the 

distributions of the model output quantities. Guidance on uncertainty propagation is provided in 

Section 4.4.1. 

Sensitivity analysis refers to the process of determining the "rate of change" of the model output 

with respect to variations in the magnitude in one or more of the model inputs, usually one 

parameter at a time. Guidance on sensitivity analysis is provided in section 4.4.2. 

4.4.1 Parameter Uncertainty Propagation

Typically, fire models are run using a discrete set of input parameters that describe a single, 

specific fire scenario. However, for some Fire PRA applications, it may be necessary to 

consider the range of consequences due to the variability that can result from that specific fire 

scenario within a particular compartment. If the key input parameters can be expressed in the 

form statistical distributions, then the model output quantities may also be expressed as 
UNCERTAINTY AND SENSITIVITY

4-11

distributions. In this way, it is possible to determine the probability of exceeding a critical 

temperature, heat flux, or some other critical value. 

Notarianni and Parry (SFPE Handbook, 4th edition) discuss a number of techniques for 

propagating parameter uncertainty. The most common are Monte Carlo methods in which the 

fire model is run repeatedly with randomly chosen input parameters, based on specified 

probability distributions. For simple algebraic models, this technique is relatively simple and 

there are various software packages available to help. For zone models, the technique 

becomes more complicated because it requires more time to set up and run the model, but it is 

still practical if the number of parameters is reduced and the ranges of the parameters are 

appropriately discretized into “bins”. For CFD models, the technique is not practical except in 

special cases where the number of model runs can be reduced to a relatively small number. 

The increased accuracy afforded by the CFD model is often unwarranted given that the 

uncertainty in the input parameters is typically greater than that of the models themselves. 

Because the HRR is the most important input parameter in most fire model analyses, and 

because NUREG/CR-6850 (EPRI 1011989) provides distributions of the HRR for a variety of 

combustibles within an NPP, parameter uncertainty propagation for fire modeling may involve 

only the HRR distribution applied within an algebraic model. In fact, Appendix E of NUREG/CR6850 (EPRI 1011989) provides data which can be used to illustrate a simple technique to 

propagate the HRR distribution. 

Suppose, for example, that as part of a Fire PRA the problem is to determine the probability of 

flames extending above an electrical cabinet to a particular height, threatening a cable tray. To 

answer this question, the flame height needs to be represented as a probability distribution. 

Figure 4-4 displays the distribution13 of peak heat release rates, ܳሶ

, for vertical cabinets with 

more than one bundle of unqualified cable (NUREG/CR-6850, Appendix E). The probability 

density function (pdf) is denoted ݃൫ܳሶ; ߙ, ߚ൯, where ߙ and ߚ) 2.6 and 67.8) are parameters of this 

particular gamma distribution. 

 

13 NUREG/CR-6850 specifies gamma distributions for the various types of combustibles found within an NPP. Microsoft Excel® 

provides a built-in function (GAMMA.DIST) that calculates the probability density function given the parameters ߙ and ߚ. 
UNCERTAINTY AND SENSITIVITY 

4-12 

Figure 4-4. Distribution of HRR for an electrical cabinet fire. 

For convenience, a spreadsheet can be used to take each value of ܳሶ, from 1 kW to 600 kW, 

and compute a corresponding flame height, ܮf (in meters), using Heskestad’s correlation: 

ܮf ൌ 0.235 ܳሶ

ଶ/ହ െ 1.02 ܦ) 4-14 (

The diameter of the fire, ܦ, is fixed at 0.48 m (1.6 ft), based on the equivalent diameter of the 

vent. Whereas Appendix E of NUREG/CR-6850 recommends dividing the range of ܳሶ into 15 

“bins”, it is just as easy for this example to compute the flame height for 600 values of ܳሶ (each 

bin has a width of 1 kW). The pdf for the flame height, ݂ሺܮfሻ, is related to the pdf for ܳሶ

 by the 

following expression: 

݂ሺܮfሻ ൌ ݃൫ܳሶ

൯ߚ ,ߙ ;

ฬ

fܮ݀

݀ܳሶ

ฬ

ൌ ݃൫ܳሶ

ሶܳ ൯ߚ ,ߙ ;

ଷ/ହ

0.094 (4-15)

This distribution is shown in Figure 4-5. Note that when the derivative in Equation (4-15) is not 

easily written in closed form, it is sufficient to calculate the bin width of the model output divided 

by that of the model input. In this example, the bin width of the model input parameter, ܳሶ, is 

1 kW and the bin width of the model output parameter is the difference in flame heights for two 

successive values of ܳሶ. 

HRR Distribution

Heat Release Rate (kW)

0 200 400 600

Probability Density Function

0.000

0.001

0.002

0.003

0.004

0.005
UNCERTAINTY AND SENSITIVITY

4-13

Figure 4-5. Distribution of flame heights for the entire range of cabinet fires. 

Once the pdf for the flame height is calculated, it can be used to determine the probability of the 

flames reaching a certain height. In this case, the cable tray is 1.5 m (4.9 ft) above the top of 

the cabinet. The probability that the flames from a randomly chosen fire will reach the cables is 

given by the area beneath the curve in Figure 4-5 for flame heights greater than 1.5 m (4.9 ft). 

In this example, it is approximately 0.31. 

4.4.2 Sensitivity Analysis 

The algebraic calculations described in this report are perhaps the models more amenable to 

parameter uncertainty studies in practical applications. The more complex fire models 

discussed in this report can require dozens of physical and numerical input parameters for a 

given fire scenario. However, only a few of these parameters, when varied over their plausible 

range of values, will significantly impact the results. For example, the thermal conductivity of 

the compartment walls will not significantly affect a predicted cable surface temperature. Table 

4-3 lists the input parameters whose impact on the given output quantity significantly outweighs 

all the other parameters. The HRR is almost always one of these. 

In Volume 2 of NUREG-1824 (EPRI 1011999), Hamins quantifies the functional dependence of 

these key input parameters (see Table 4-3). These relationships are based either on the 

governing mathematical equations or on algebraic models. The basic mathematical form of the 

relationship is: 

Output Quantity ൌ Constant × (Input Parameter)Power (4-16)

The exact value of the Constant is not important; rather, it is the Power that matters. The larger 

its absolute value, the more important the Input Parameter. According to the McCaffrey, 

Quintiere, and Harkleroad (MQH) correlation, for example, the hot gas layer (HGL) temperature 

rise in a compartment fire is proportional to the HRR raised to the two-thirds power: 

ܶെܶ଴ ൌ ܥܳሶ

ଶ/ଷ (4-17)

What is important here is the amount that the HGL temperature, ∆ܶ, changes due to a shift in 

the HRR, ∆ܳሶ. It is the two-thirds power dependence, as found in Table 4-3, that matters. To 

Flame Height Distribution

Flame Height (m)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Probability Density Function

0.0

0.2

0.4

0.6

0.8

1.0
UNCERTAINTY AND SENSITIVITY 

4-14 

see why, take the first derivative of ܶ with respect to ܳሶ and write the result in terms of 

differentials: 

∆ܶ

ܶെܶ଴

؆

2

3

∆ܳሶ

ܳሶ (4-18)

This is a simple formula with which one can readily estimate the relative change in the model 

output quantity, ∆ܶ/ሺܶ െ ܶ଴ሻ, due to the relative change in the model input parameter, ∆ܳሶ/ܳሶ. 

The uncertainty in a measured quantity is often expressed in relative terms14. Suppose that the 

uncertainty in the HRR of the fire, ∆ܳሶ/ܳሶ, is 0.15, or 15%. The expression above indicates that a 

15% increase in the HRR should lead to a 2/3 x 15 = 10% increase in the prediction of the HGL 

temperature. The result is equally valid for a reduction; if the HRR is reduced by 15%, the HGL 

temperature is reduced by 10%. 

Table 4-3. Sensitivity of model outputs from Volume 2 of NUREG-1824 (EPRI 1011999). 

Output Quantity Important Input 

Parameters Power Dependence 

HGL Temperature 

HRR 

Surface Area 

Wall Conductivity 

Ventilation Rate 

Door Height 

2/3 

-1/3 

-1/3 

-1/3 

-1/6 

HGL Depth Door Height 1 

Gas Concentration HRR 

Production Rate 

1/2 

1 

Smoke Concentration HRR 

Soot Yield 

1 

1 

Pressure 

HRR 

Leakage Rate 

Ventilation Rate 

2 

2 

2 

Heat Flux HRR 4/3 

Surface/Target 

Temperature HRR 2/3 

This relationship is based on experimental data, and has nothing to do with any particular 

model; however, an effective way to check a fire model is to take a simple compartment fire 

simulation, vary the HRR, and ensure that the change in the HGL temperature agrees with the 

correlation. Consider the two curves shown in Figure 4-6. For Benchmark Exercise #3 of the 

International Collaborative Fire Model Project (ICFMP), Test 3 was simulated with FDS, using 

HRR values of 1000 kW and 1150 kW. An examination of the peak values confirms that the 

relative change in the HGL temperature (10%) is two-thirds the relative change in the HRR 

 

14 Note that a differential relationship is only approximate. This method of relating input parameters to output quantities is valid for 

relative differences that are less than approximately 30% in absolute value. 
UNCERTAINTY AND SENSITIVITY

4-15

(15%), consistent with the empirical result of the MQH correlation. Even though FDS is a much 

more complicated model than the simple expression shown above, it still exhibits the same 

functional dependence on the HRR. 

Figure 4-6. FDS predictions of HGL Temperature as a function of time due to a 1,000 kW 

fire (solid line) and a 1,150 kW fire (dashed). 

This section illustrates the usefulness of sensitivity analysis. As an example, consider that 

NFPA 805 uses the term Maximum Expected Fire Scenario (MEFS) to describe a severe fire 

that could be “reasonably anticipated” to occur within a compartment and the term Limiting Fire 

Scenario (LFS) to describe a severe fire that exceeds one or more performance criteria. The 

analyst is often asked to determine the model inputs for both of these scenarios. For MEFS, 

input parameters can be chosen from distributions for a particular percentile value. Gallucci 

(2011) discusses the issues important in determining the appropriate choice of HRR distribution. 

The development of the LFS is essentially a sensitivity analysis performed to identify which 

combinations of input parameters or variables are critical to the analysis. The particular 

variables to be evaluated depend entirely on the problem being analyzed. At a minimum, the 

following parameters should be varied until failure conditions result: HRR, the fire growth rate or 

the flame spread rate, the flame radiative fraction or the radiative power, and the location of the 

fuel package relative to the target (if variable). 

Suppose, for example, that as part of an analysis the problem is to determine the minimum HRR 

needed to cause damage in a particular compartment whose HGL temperature is not to exceed 

500 °C (930 °F). The geometrical complexity of the compartment rules out the use of the 

algebraic and zone models, and that FDS has been selected for the simulation. 

Step 1: Determine a reasonable, but conservative, estimate of what might be the maximum fire 

that could occur in the compartment. Using data from NUREG/CR-6850, for this example, 

suppose that a 98th percentile HRR for the electrical cabinet fire, 702 kW, has been chosen for 

this representative estimate. Choose a model and calculate the peak HGL temperature. 

Step 2: The model chosen is FDS and it predicts 450 °C (840 °F) for the selected fire scenario. 

Adjust the prediction to account for the model bias, ߜ) see Table 4-1): 

Hot Gas Layer Temperature

ICFMP BE #3, Test 3

Time (min)

0 5 10 15 20 25 30

Temperature (°C)

0

100

200

300

400
UNCERTAINTY AND SENSITIVITY 

4-16 

ܶadj ൌ ܶ଴ ൅

ܶെܶ଴

൅ Ԩ 20 ൌ ߜ

450 Ԩ െ 20 Ԩ

1.03 ؆ 437 Ԩ (4-19)

Step 3: Calculate the change in HRR required to increase the HGL temperature to 500 °C 

(930 °F): 

∆ܳሶ ൎ 3

2ܳሶ ∆ܶ

ܶadj െ ܶ଴

ൌ 3

2 ൈ 702 kW ൈ

500 Ԩ െ 437 Ԩ

437 Ԩ െ 20 Ԩ ؆ 159 kW (4-20)

This calculation suggests that adding an additional 159 kW to the original 702 kW will produce 

an HGL temperature in the vicinity of 500 °C (930 °F). This result can be double-checked by rerunning the model with the modified input parameters. 

Table 4-3 lists several other parameters besides the HRR that can affect the HGL temperature. 

Following the example just discussed, similar calculations can be performed in which these 

other parameters are varied to determine how else the minimum damage threshold might be 

reached. For example, suppose that the surface area, ܣ, of the compartment is 400 m2

 (4300 

ft2

). How much would the surface area have to increase or decrease to raise the HGL 

temperature to 500 °C (930 °F)? If the thermal conductivity of the walls, ݇, is 0.1 W/m/K, how 

much would it have to change? If the ventilation rate is 1 m3

/s (2100 cfm), how much would it 

have to change? If the door height, ݄, is 2 m (6.6 ft), how much would it have to change? 

Following the example for the HRR, the required changes in these parameters can be 

calculated as follows: 

ܣ3െ ؆ ܣ∆

∆ܶ

ܶadj െ ܶ଴

ൌ െ3 ሺ400 mଶሻ 500 െ 437

417 ؆ െ181 mଶ (4-21)

∆݇ ؆ െ3݇

∆ܶ

ܶadj െ ܶ଴

ൌ െ3 ሺ0.1 W/m/Kሻ 500 െ 437

417 ؆ െ0.045 W/m/K (4-22)

∆ܸሶ ؆ െ3ܸሶ ∆ܶ

ܶadj െ ܶ଴

ൌ െ3 ሺ1 mଷ⁄ ሻs

500 െ 437

417 ؆ െ0.45 mଷ/s (4-23)

∆݄ ؆ െ6݄

∆ܶ

ܶadj െ ܶ଴

ൌ െ6 ሺ2 mሻ 500 െ 437

417 ؆ െ1.8 m (4-24)

For this example, to increase the HGL temperature by 63 °C (145 °F), one could increase the 

HRR by 159 kW, decrease the surface area of the compartment by 181 m2

 (1948 ft2), decrease 

the thermal conductivity of the walls by 0.045 W/m/K, decrease the ventilation rate by 0.45 m3

/s 

(950 cfm), or decrease the door height by 1.8 m (5.9 ft). Of course, some of these options are 

not physically possible. Room dimensions and thermal properties are not subject to significant 

change, but the HRR and ventilation rates can vary significantly. Also note that if the relative 

change in the parameter values exceeds 30 %, it is recommended that further calculations be 

performed to confirm the estimated quantity changes. 
UNCERTAINTY AND SENSITIVITY

4-17

4.5 Chapter Summary 

This chapter describes the three forms of uncertainty related to fire modeling: parameter, model, 

and completeness uncertainty. Model and completeness uncertainty are closely related, and it 

would be impractical to evaluate them separately. The most practical way to quantify their 

combined effect is to compare model predictions with as many experimental measurements as 

possible in order to develop a robust statistical description of the model’s accuracy. The five 

models considered in this repor underwent a validation study (NUREG-1824 (EPRI 1011999)) in 

which their predictions were compared with measurements from a variety of full-scale 

experiments. It is possible to take a given model’s prediction of a given quantity and determine 

a distribution for the “true” value of this quantity. Rather than reporting the result of a calculation 

as a single value, it is preferable to report the probability that the true value of a predicted 

quantity will exceed a given critical value. 

Treatment of parameter uncertainty is dependent on the application. Some analyses, 

probabilistic risk assessments (PRAs) for example, employ relatively simple techniques to 

propagate the distribution of the HRR through the model. More complex forms of PRAs can 

involve a broad statistical sampling of input parameters from specified distributions. From a fire 

modeling perspective, some modeling tools are more amenable to the evaluation of parameter 

uncertainty given the complexity and computational times of some of these tools. 

Deterministic applications usually consider “worst case” or “bounding” analyses, in which 

extreme, yet plausible, input parameters are used. In mathematical terms, all of these 

applications involve selecting parameters from relatively narrow or broad regions of the 

parameter “space.” It is often prohibitive to consider all possible combinations of input 

parameters, which is why a simple form of sensitivity analysis, outlined in this chapter, can be 

used to extend the range of outcomes. Algebraic models may initially be used to indicate the 

extent to which all of the output quantities of interest are sensitive to changes in the specified 

HRR, reducing the need to re-run model simulations for an extensive number of values. 

Over time, the V&V effort, documented in NUREG-1824 (EPRI 1011999), will be expanded to 

include comparisons with additional test data and new versions of the models. These updates 

will expand the validation range shown in Table 2-5 and ensure the availability of V&V 

information for the latest versions of the models documented in this report. Model users should 

refer to the latest version of the V&V when conducting their fire modeling analyses. In general, 

the techniques documented in this chapter for analyzing uncertainty and sensitivity will remain 

applicable regardless of the V&V version being used for the analysis. 

 
UNCERTAINTY AND SENSITIVITY 

4-18 
5-1 

5 

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2007. 

NUREG/CR-7010, Cable Heat Release, Ignition, and Spread in Tray Installations during Fire 

(CHRISTIFIRE), Phase 1: Horizontal Trays, National Institute of Standards and 

Technology, Gaithersburg, MD, 2012. 

Peacock, R., K. McGrattan, B. Klein, W. Jones, and P. Reneke, CFAST – Consolidated Model 

of Fire Growth and Smoke Transport (Version 6) – Software Development and Model 

Evaluation Guide, Special Publication 1086, National Institute of Standards and 

Technology, Gaithersburg, MD, 2008. 

Peacock, R., W. Jones, P. Reneke, and G. Forney, CFAST: An Engineering Tool for Estimating 

Fire Growth and Smoke Transport, Version 6 – User’s Guide, Special Publication 1041, 

National Institute of Standards and Technology, Gaithersburg, MD, 2008. 

Quintiere, J. G., Principles of Fire Behavior, Delmar Publishers, 1998. 

Quintiere, J. G., Fundamentals of Fire Phenomena, John Wiley, 2006. 

Salley, M.H., J. Dreisbach, K. Hill, R. Kassawara, B. Najafi, F. Joglar, A. Hamins, K. McGrattan, 

R. Peacock; and B. Gautier, “Verification and Validation--How to Determine the 

Accuracy of Fire Models,” Fire Protection Engineering, vol. 34, pp. 34 - 44, Spring 2007.

Schiffiliti, R., and W. Pucci, Fire Modeling, State of the Art, Fire Detection Institute, 1996. 

SFPE, SFPE Engineering Guide to Assessing Flame Radiation to External Targets from Pool 

Fires, SFPE Engineering Guide, Society of Fire Protection Engineers, Bethesda, MD, 

March 1999. 
REFERENCES

5-5

SFPE, SFPE Engineering Guide to Fire Exposures to Structural Elements, SFPE Engineering 

Guide, Society of Fire Protection Engineers, Bethesda, MD, November, 2005. 

SFPE, SFPE Engineering Guide to Piloted Ignition of Solid Materials Under Radiant Exposure, 

SFPE Engineering Guide, Society of Fire Protection Engineers, Bethesda, MD, January, 

2002. 

SFPE, SFPE Engineering Guide to Predicting Room of Origin Fire Hazards, SFPE Engineering 

Guide, Society of Fire Protection Engineers, Bethesda, MD, November, 2007. 

SFPE, SFPE Engineering Guide to Substantiating a Fire Model for a Given Application, SFPE 

Engineering Guide, Society of Fire Protection Engineers, Bethesda, MD, June, 2010. 

SFPE, SFPE Handbook of Fire Protection Engineering, 4th Edition (P. J. DiNenno, Editor-in-Chief), 

National Fire Protection Association and The Society of Fire Protection Engineers, Quincy, 

MA, 2008. 

SFPE, SFPE Engineering Standard on Calculating Fire Exposures to Structures, SFPE S.01.2001, 

Society of Fire Protection Engineers, Bethesda, MD, 2011. 

Underwriters’ Laboratories, Single Station Fire Alarm Device, UL 217, Underwriters’ Laboratories, 

Northbrook, Illinois. 

Wallis, G. B., “Draft Final NUREG-1824, Verification and Validation of Selected Fire Models for 

Nuclear Power Plant Applications,” Memorandum from Advisory Committee on Reactor 

Safeguards to Luis Reyes, ML062980154, U.S. Nuclear Regulatory Commission, October, 

2006. 

Yuan, L., and G. Cox, “An Experimental Study of Some Line Fires,” Fire Safety Journal, Volume 27, 

1996, pp. 123 – 139. 

 
REFERENCES 

5-6 
6-1 

6 

INTRODUCTION TO THE APPENDICES 

Eight unique fire scenarios that typify different fire modeling applications likely to be 

encountered in commercial nuclear power plants (NPP), have been evaluated using the process 

and guidance of Chapters 2 – 4 of this document. The analysis of the eight example fire 

scenarios is summarized in Appendices A through H. Table 6-1 provides a summary of the 

individual fire scenarios as well as a cross-index between the eight appendix fire scenarios and 

the seven generic fire scenarios described in Chapter 3. In the scenarios, one or more aspects 

of Chapter 3 generic fire scenarios are incorporated. For example, Appendix B considers both 

localized exposure effects near the fire (Chapter 3.2.1) and hot gas layer (HGL) effects in a 

simple room (Chapter 3.2.2). Default values for many quantities (e.g., material properties, 

numerical parameters, physical parameters, empirical constants, etc.) are referenced 

throughout these application examples. Fire model users must understand and justify the use 

of default values for their applications. Fire model users are expected to assess the 

appropriateness of default values provided in the fire models and make changes or adjust 

values as necessary. Fire model user guides, handbooks, and other technical documentation 

are useful for this purpose. 

Table 6-1. Appendix fire scenario descriptions and cross-index. 

Appendix Appendix Scenario Description 

Chapter 3 

Generic Fire 

Scenario 

A Determination of the time to main control room (MCR) abandonment given a low 

voltage panel fire. 3.2.5 

B Determination of the potential for a switchgear panel fire to damage cables above the 

fire and adjacent to the fire. 3.2.1, 3.2.2 

C Determination of the potential for a lubricant oil fire to damage cables protected with 

an electrical raceway fire barrier system (ERFBS). 3.2.2 

D Determination of the potential for an motor control center (MCC) panel fire to damage 

cables via the HGL in an irregularly shaped enclosure. 3.2.4 

E Determination of the potential for a transient trash fire to damage cables in a stack of 

horizontal cable trays located directly above the fire. 3.2.1 

F Determination of the potential for a lubricant oil fire to cause structural damage. 3.2.7 

G Determination of the potential for a large transient fuel package fire to damage cables 

in an adjacent space. 3.2.3 

H Determination of the potential for a cable tray fire to damage a nearby raceway with 

and without sprinklers. 3.2.1, 3.2.6 

The structure of each appendix reflects the analysis sequence as well as the recommended 

means by which to document each type of fire modeling analysis. In particular, the appendices 

use the following format 

 Fire modeling objective. This section clearly presents the issue that is being evaluated 

and the reason the analysis is being performed. 

 

 Description of the fire scenario. This section provides a detailed description of the fire 

scenario being evaluated, including important parameters such as the room geometry, 
INTRODUCTION TO THE APPENDICES 

6-2 

ventilation, fuel package data, material properties, and scenario specific information 

required for a successful analysis. 

 Selection of the fire models. This section presents the basis for selecting the different 

types of fire models used to address the fire modeling objective. This includes 

considerations of the model capability as well as the available verification and validation 

(V&V) basis. Generally, two or more models are selected in order to highlight the 

strengths and weaknesses of the models for the given application. The selected models 

are not necessarily the only models that can be used, but the basis provided is broadly 

applicable to a given class of fire models. 

 Estimation of the fire-generated conditions. This section presents model specific inputs 

and supporting calculations and identifies applicable model nuances for the scenario 

considered. 

 Evaluation of results. The results of the fire models are presented in terms of the data 

necessary to support the fire modeling objective in this section. Model sensitivity and 

uncertainty are also described for each output parameter and model considered. 

 Conclusions. A summary of the fire modeling analysis, including the outcome relative to 

the fire modeling goal is presented in this section. 

The authors strove to create fire scenarios based on actual commercial NPP configurations in 

order to provide realistic fire scenario development and results. Be cautioned that the fire 

modeling results are not generic, and different applications will require careful consideration of 

the various input parameters, the fire model applicability, and the dominant exposure 

mechanism(s). However, the structure presented is generic, and when followed it is expected to 

lead to a fire modeling analysis that could be used to support safety related applications. 

This report also contains a CD. On the CD you will find the complete NUREG-1934 final report 

in pdf format and the input files used for the fire model runs discussed in each appendix. In 

addition, the current versions of the FDTs

, CFAST and FDS that were used for each appendix 

are on the CD. The complete layout and contents of the CD are described in the README file 

included on the CD. 
A-1 

APPENDIX A 

CABINET FIRE IN MAIN CONTROL ROOM 

A.1 Modeling Objective 

The purpose of the calculations described in this appendix is to approximate the length of time 

that the main control room (MCR) remains habitable after the start of a fire within a low-voltage 

control cabinet. These calculations follow the guidance provided in NUREG/CR-6850 

(EPRI 1011989), Volume 2, Chapter 11, “Detailed Fire Modeling (Task 11).” MCR fire scenarios 

are treated differently than fires within other compartments, mainly because it is necessary to 

consider and evaluate forced abandonment in addition to equipment damage. 

A.2 Description of the Fire Scenario 

General Description: A fire ignites within a control cabinet containing XPE/neoprene cables. 

The door to the MCR is normally closed, and normal ventilation conditions are in place at the 

start of the fire. The typical ambient temperature is 20 C (68 F). Following guidance given in 

Chapter 11 of NUREG/CR-6850 (EPRI 1011989), two scenarios are considered, one in which 

the ventilation system is turned off and one in which the ventilation system is switched to 

smoke-purge mode at the start of the fire. 

Geometry: Drawings of the MCR are shown in Figure A-1 and Figure A-2. The compartment 

has a variety of control cabinets in addition to typical office equipment, such as computer 

monitors on table tops. There is an open-grate suspended ceiling above the floor, a photograph 

of which is shown in Figure A-3. This suspended ceiling is specified to be of noncombustible 

construction for this scenario, but the combustibility of such ceilings should be verified for other 

MCR scenarios. One wall of the compartment is made of 0.9 m (3 ft)-thick concrete with no 

additional lining material. The other bounding walls are constructed of 1.6 cm (5/8 in) gypsum 

board supported by steel studs. The floor is a slab of concrete covered with low-pile carpet that 

is nominally 1.25 cm (0.5 in) thick. The ceiling is concrete with the same thickness as the floor 

(0.5 m (1.6 ft)), but with no lining material. 

Materials: Thermal properties of various materials in the compartment are listed in Table 3-1. 

Carpet is not listed in the table, but, according to Table 6-5 of NUREG-1805, the thermal inertia 

(kρc) for “Carpet (Nylon/Wool Blend)” is 0.68 (kW/m2

/K)2 s, its ignition temperature is 412 °C 

(774 °F), and its minimum heat flux for ignition is 18 kW/m2

. The steel housing of the electrical 

cabinets is nominally 1.5 mm (0.06 in) thick. 

Ventilation: During normal operation, the mechanical ventilation system provides five air 

changes per hour (ACH). As shown in Figure A-1, ventilation is provided through six supply 

diffusers and two return vents of nominally the same size. The supply air to the compartment is 

equally distributed among the six supply vents, and the return air is drawn equally from the two 

returns. A 120 Pa overpressure (relative to the adjacent compartments) is maintained in the 

MCR during normal operation. Leakage from the compartment occurs via a 1.3 cm (0.5 in) high 

crack under the 0.9 m (3 ft) wide door. All other penetrations are sealed. Smoke-purge mode 

provides 25 air changes per hour and is activated manually by an MCR operator in accordance 
CABINET FIRE IN MAIN CONTROL ROOM 

A-2 

with specified procedures, which is known for this control room to be 120 seconds after the start 

of a fire. 

Figure A-1. Geometry of the main control room. 
CABINET FIRE IN MAIN CONTROL ROOM

A-3

Figure A-2. Main control room details. 
CABINET FIRE IN MAIN CONTROL ROOM 

A-4 

Figure A-3. Photograph of a typical open-grate ceiling. 

Figure A-4. Photograph of a typical control cabinet. 

 
CABINET FIRE IN MAIN CONTROL ROOM

A-5

Fire: The fire ignites due to an electrical malfunction in bundles of qualified XPE/neoprene 

cables inside an isolated control cabinet (Figure A-4), designated as the Fire Origin Cabinet in 

Figure A-2. The fire grows according to a “t-squared” curve to a maximum value of 702 kW in 

12 min and remains steady for eight additional minutes, consistent with NUREG/CR-6850 (EPRI 

1011989), Appendix G, for a low-voltage cabinet fire involving more than one bundle of qualified 

cable. After 20 min, the fire’s heat release rate (HRR) decays linearly to zero in 19 min. A peak 

fire intensity of 702 kW represents the 98th percentile of the probability distribution for the HRR 

in cabinets of this general description. The HRR curve is shown in Figure A-5. 

Figure A-5. Time history of the HRR used by all models in the MCR scenario. 

Based on a physical assessment of the cabinet, it is determined that the exterior panels of the 

burning cabinet do not open before or during the fire. The smoke, heat, and flames are 

exhausted from an air vent in the side of the cabinet. The top of the air vent is 0.3 m (1 ft) below 

the top of the cabinet. The air vent is 0.6 m (2 ft) wide and 0.2 m (8 in) high. The cabinet is 

2.4 m (8 ft) tall. 

The heat of combustion and product yields for XPE/neoprene cable are taken from Table 3-4.16 

of the SFPE Handbook, 4th edition and are listed in Table A-1. When estimating the 

composition of the fire’s combustion products, the jacket and insulation material of the cable are 

taken as an equal-parts mixture of polyethylene (C2H4) and neoprene (C4H5Cl), with the 

effective chemical formula C3H4.5Cl0.5. 

Table A-1. Data for MCR fire based on XPE/neoprene electrical cable. 

Parameter Value Source 

Effective Fuel Formula C3H4.5Cl0.5 Combination of polyethylene and neoprene 

Peak HRR 702 kW NUREG/CR-6850 (EPRI 1011989), App. G 

Time to reach peak HRR 720 s NUREG/CR-6850 (EPRI 1011989), App. G 

Heat of Combustion 10,300 kJ/kg SFPE Handbook, 4th ed., Table 3-4.16 

CO2 Yield 0.63 kg/kg SFPE Handbook, 4th ed., Table 3-4.16 

Soot Yield 0.175 kg/kg SFPE Handbook, 4th ed., Table 3-4.16 

CO Yield 0.082 kg/kg SFPE Handbook, 4th ed., Table 3-4.16 

Radiative Fraction 0.53 SFPE Handbook, 4th ed., Table 3-4.16 

Mass Extinction Coefficient 8700 m2/kg Mulholland and Croarkin (2000) 

0

100

200

300

400

500

600

700

800

0 600 1200 1800 2400 3000 3600

HRR (kW)

Time (s)

Heat Release Rate
CABINET FIRE IN MAIN CONTROL ROOM 

A-6 

Habitability: The MCR is manned 24 hours per day during normal plant operations. To assess 

habitability of the compartment, the operator position indicated in Figure A-1 is used. According 

to NUREG/CR-6850 (EPRI 1011989), Volume 2, Chapter 11, “Detailed Fire Modeling,” a space 

is considered uninhabitable if at least one of the following occurs: 

1. The incident heat flux at 1.8 m (6 ft) exceeds 1 kW/m2

. A smoke layer temperature of 

approximately 95 °C (200 °F) generates this level of heat flux. 

2. The smoke layer descends below 1.8 m (6 ft) from the floor, and the optical density of the 

smoke is greater15 than 3 m-1. 

A.3 Selection and Evaluation of Fire Models 

This section discusses the overall modeling strategy. In particular, it describes the process of 

model selection, including a discussion of the validity of these models for the given fire scenario. 

A.3.1 Temperature Criterion 

The forced ventilation correlation of Foote, Pagni, and Alvares (FPA) that is incorporated in the 

Fire-Induced Vulnerability Evaluation (FIVE-Rev1) is used to estimate the compartment 

temperatures under smoke purge ventilation conditions. This correlation is not appropriate in 

the scenario without ventilation. The Consolidated Fire Growth and Smoke Transport Model 

(CFAST) and the Fire Dynamics Simulator (FDS) are used to estimate the hot gas layer (HGL) 

temperature for both the smoke purge and unventilated scenarios. One advantage of a 

Computational Fluid Dynamics (CFD) model like FDS for this fire scenario is that it can estimate 

habitability conditions at the specific location of the operator, whereas a zone model like CFAST 

can only estimate average conditions in the hot gas layer. 

A.3.2 Heat Flux Criterion 

The point source radiation heat flux model is first used to estimate the heat flux to the operator. 

FIVE-Rev1 and the Fire Dynamics Tools (FDTs

) both contain methods to estimate the heat flux 

from a fire to a target located a specified distance away. However, distant targets, including the 

operators, may not be exposed directly to the thermal radiation; it is also possible that the 

descending hot gas layer will be responsible for some fraction of the heat flux to which the 

operator is exposed. Neither FIVE-Rev1 nor the FDTs

 include calculation methods to account 

for this source of thermal radiation. CFAST and FDS will be used to determine whether the 

thermal radiation from the HGL reaches the critical value for tenability. 

A.3.3 Visibility Criterion 

FIVE-Rev1 and the FDTs do not include correlations to estimate visibility in a ventilated 

compartment, but correlations from the SFPE Handbook are applied to develop an estimate of 

smoke obscuration in the MCR under smoke purge conditions. With a smoke purge ventilation 

rate of 25 ACH, a well-mixed smoke environment is expected, and the average smoke 

concentration and visibility conditions can be calculated using these methods. CFAST and FDS 

are also used to address the visibility criterion. CFAST has an advantage over MAGIC for this 

 

15 The original edition of NUREG/CR-6850 (EPRI 1011989) contains an error in the specification of the optical density (NRC ADAMS 

Accession Number ML061630360). The value of 3 m-1 is correct. 
CABINET FIRE IN MAIN CONTROL ROOM

A-7

analysis because it computes the smoke obscuration. FDS is particularly useful because it 

does not require that the smoke is confined to a uniform descending layer. It is expected that 

air currents in the room will mix the smoke to the floor. Zone models typically do not allow the 

smoke layer to descend below the height of the base of the fire. 

The case of the unventilated enclosure fire scenario is addressed with CFAST and FDS to 

estimate the smoke layer interface position and smoke layer optical density as a function of 

time. One advantage of a CFD model like FDS for this fire scenario is that it can estimate 

habitability conditions at the specific location of the operator. 

A.3.4 Validation 

The principal source of validation data justifying the use of the fire models discussed above for 

this scenario is the U.S. Nuclear Regulatory Commission/Electric Power Research Institute 

(NRC/EPRI) verification and validation (V&V) study documented in NUREG-1824 (EPRI 

1011999). The National Institute of Standards and Technology (NIST) has expanded the 

NRC/EPRI V&V to include the latest versions of CFAST (6.1.1) (Peacock, 2008) and FDS 

(5.5.3) (McGrattan, 2010). In particular, a Factory Mutual/Sandia National Laboratories 

(FM/SNL) test series was designed specifically as a mock-up of a control room in a nuclear 

power plant (NPP). One of these experiments (Test 21) involves a fire within a hollow steel 

cabinet. 

Table A-2 lists the important non-dimensional parameters that characterize the fire scenario and 

the ranges for which the NRC/EPRI validation study is applicable. A few parameters fall outside 

the validation parameter space and are addressed individually: 

 The Fire Froude Number falls outside the range. This parameter is essentially a measure of 

the fire’s heat output relative to its base area. In this example, the fire is specified as 

emanating from the side of the cabinet, with the vent opening serving as its base. This 

leads to a higher value of ܳሶ

כ than would be calculated if the fire were burning completely 

outside of the cabinet. Thus, the high value of ܳሶ

כ is the represents more severe fire 

conditions than would be expected if the fire were specified as burning partially within the 

cabinet. 

 The relatively low Equivalence Ratio for the compartment is a result of the relatively large 

amount of air forced into the room during the smoke purge mode. Twenty-five air changes 

per hour is a considerable flow rate, and no validation experiment in NUREG-1824 (EPRI 

1011999) involved such a high ventilation rate. However, the results of all the model 

simulations indicate that the scenario in which the ventilation is turned off is most likely to 

compromise human habitability, and the presence of any level of ventilation reduces room 

temperature and heat flux and increases visibility. 

For the scenario with no ventilation, the classic definition of the Equivalence Ratio does not 

apply because there is no supply of oxygen in the room. However, it can be shown that 

there is sufficient oxygen in the room to sustain the specified fire. The total mass of oxygen 

in the room is the product of the density of air, ߩ, the volume of the room, ܸ, and the mass 

fraction of oxygen in the air, ܻOమ: 

݉Oమ,tot ൌ ߩܸܻOమ ൌ 1.2 kg/mଷ ൈ 1945 mଷ ൈ 0.23 ؆ 537 kg (A-1)
CABINET FIRE IN MAIN CONTROL ROOM 

A-8 

The mass of oxygen required to sustain the fire is equal to the total energy produced by the 

fire divided by the energy released per unit mass oxygen consumed: 

݉Oమ,req ൌ ܳ

Oమܪ∆

؆

702 kW ൈ 60 s/min ൈ ቀ

12

3 ൅8൅ 19

2 ቁ min

13,100 kJ/kg ؆ 69 kg (A-2)

These calculations show that the quantity of oxygen in the room would be able to sustain the 

specified cabinet fire. 

 The ratio of the Target Distance relative to the Fire Diameter, ݎ/ܦ, exceeds the range of the 

validation study. However, this parameter is only relevant to the point source radiation heat 

flux calculation, which is by definition more accurate, as the target moves further from the 

source. Thus, although the parameter is outside the validation range, it is not outside of the 

methodology’s range of validity. 

 
CABINET FIRE IN MAIN CONTROL ROOM

A-9

Table A-2. Normalized parameter calculations for the MCR fire scenario. See Table 2-5 for further 

details. 

Quantity Normalized Parameter Calculation 

NUREG1824 

Validation 

Range 

In 

Range? 

Fire Froude 

Number 

ܳሶ

כ ൌ ܳሶ

ߩஶܿ௣ܶஶܦଶ.ହඥ݃

ൌ 702 kW

ሺ1.2 kg/mଷሻሺ1.0 kJ/kg/Kሻሺ293 Kሻሺ0.4ଶ.ହ mଶ.ହሻඥ9.8 m/sଶ ؆ 6.2

0.4 – 2.4 No 

Flame 

Height, 

 ,௙ܮ ൅ ௙ܪ

relative to the 

Ceiling 

௖ܪ ,Height

௙ܮ ൅ ௙ܪ

௖ܪ

ൌ 2.1 m ൅ 2.7 m

5.2 m ؆ 0.9

ܮ ௙ൌ ܦ ቀ3.7 ܳሶ

כଶ/ହ െ 1.02ቁ ൌ 0.4 m ሺ3.7 ൈ 6.2଴.ସ െ 1.02ሻ ؆ 2.7 m

0.2 – 1.0 Yes 

Ceiling Jet 

Radial 

Distance, ݎcj, 

relative to the 

Ceiling 

௖ܪ ,Height

N/A – Ceiling jet targets are not included in simulation. 1.2 – 1.7 N/A 

Equivalence 

Ratio, φ, of 

the room, 

based on 

Forced 

Ventilation of 

Purge Mode 

߮ ൌ

ܳሶ

ΔܪOమ݉ሶ Oమ

ൌ 702 kW

13,100 kJ/kg ൈ 3.7 kg/s ؆ 0.014

݉ሶ Oమ ൌ ܻOమ ߩஶܸሶ ൌ 0.23 ൈ 1.2 kg/mଷ ൈ 13.4 mଷ/s ؆ 3.7 kg/s

0.04 – 0.6 No 

Compartment 

Aspect Ratio 

ܮ

௖ܪ

ൌ 24.6 m

5.2 m ؆ 4.7

ܹ

௖ܪ

ൌ 16.2 m

5.2 m ؆ 3.1 0.6 – 5.7 Yes 

Target 

 ,ݎ ,Distance

relative to the 

Fire 

ܦ ,Diameter

ݎ

ܦ ൌ 8.8 m0.4 m ؆ 22 2.2 – 5.7 No 

Notes: 

(1) The effective diameter of the base of the fire, ܦ, is calculated using ܦ ൌ ඥ4ܣ/ߨ, 

where ܣ is the area of the cabinet vent. 

(2) The Flame Height, ܪ ൅ ௙ܮ௙, is the sum of the height of the fire base above the 

floor and the fire’s flame length. 

 
CABINET FIRE IN MAIN CONTROL ROOM 

A-10 

A.4 Estimation of Fire-Generated Conditions 

This section provides details as to how each of the models was set up and run. 

A.4.1 Algebraic Models 

General: The forced ventilation correlation of FPA is used to estimate the HGL temperature of 

the MCR for the smoke purge scenario. The point source method is used to estimate the heat 

flux from the fire to the operator for both the smoke purge and non-ventilated scenarios. The 

smoke concentration and visibility are calculated for the smoke purge scenario based on quasisteady conditions, as described below. 

Temperature in the Smoke Purge Scenario 

Figure A-6 is a schematic diagram that illustrates the smoke purge scenario. The FPA 

correlation requires room dimensions to be specified in terms of length, width, and height. For 

this example, the selected compartment is not a rectangular parallelepiped, so it needs to be 

represented with an effective length, width, and height that provide the same volume and 

boundary surface area as the actual compartment. The effective compartment height is taken 

as the actual height of 5.2 m (17 ft) because it is important to maintain the same compartment 

height for smoke filling calculations. Next, the effective length and width are calculated to 

maintain the same volume and boundary surface area of the actual compartment. Because the 

actual and effective heights are the same, this is equivalent to maintaining the same floor area 

(ܣfl) and wall perimeter (ܲ) of the enclosure. From Figure A-1, the MCR floor area is 372 m2

(4004 ft2

), and the perimeter is 81.6 m (274 ft). Maintaining the total floor area and perimeter 

yields effective compartment dimensions of 27.1 m (89 ft) by 13.8 m (45 ft). This is calculated 

by solving the following two equations for the effective length and width, ܮ ௘and ܹ௘: 

ܣfl ൌ ܮ ௘ൈ ܹ௘ ; ܲൌ2ൈ ሺܮ ൅ ௘ܹ௘ሻ (A-3)

The parameters for the FIVE-Rev1 implementation of the FPA are listed in Table A-3. Note that 

the specified time-dependent HRR is used in the calculation, but that the calculation does not 

include either the fire’s elevation above the floor or any other information about the fire. The 

walls, ceiling, and floor are all specified as gypsum board rather than concrete because the FPA 

correlation only accounts for one type of lining material. Gypsum board was chosen because it 

has a lower thermal conductivity than concrete, which results in a slightly higher HGL 

temperature. 

Table A-3. Summary of input parameters for the FPA calculation of the MCR. 

Parameter Value Source 

Room height (H) 5.2 m Figure A-1 

Room effective length (Le) 27.1 m Equation (A-3) 

Room effective width (We) 13.8 m Equation (A-3) 

Room boundary material Gypsum board Table 3-1 

Mech. ventilation rate (ܸሶ) 13.4 m3

/s Specified (25 ACH) 

Ambient temperature (Ta) 20 °C Specified 

Fire parameters Table A-1 
CABINET FIRE IN MAIN CONTROL ROOM

A-11

Figure A-6. Schematic diagram of the FPA calculation for the MCR smoke purge scenario. 

Heat Flux 

The point source model is used to estimate the heat flux from the flames to the operator when 

the fire is at its peak HRR. The peak HRR, ܳሶ, is 702 kW, the radiative fraction, ߯௥, is 0.53, and 

the distance from the cabinet vent to the operator is approximately 8.8 m (29 ft). The heat flux 

is calculated: 

ሶݍ

ᇱᇱ ൌ ߯௥ ܳሶ

4ߨ ݎଶ ൌ 0.53 ൈ 702 kW

4ߨ ൈ 8.8ଶ mଶ ؆ 0.38 kW/mଶ (A-4)

While this heat flux prediction is well below the critical value of 1 kW/m2

, it does not account for 

the thermal radiation from the HGL. Thus, the point source method can be used as a screening 

tool, and further analysis can be performed by CFAST and FDS. 

Smoke concentration and visibility

Neither the FDTs

 nor FIVE-Rev1 include methods to calculate smoke concentrations or visibility 

in mechanically ventilated enclosure fires, but calculation methods provided in Section 3, 

Chapter 9, of the SFPE Handbook, 4th ed. are relatively simple to apply and are based on the 

same principles and concepts embodied in zone models. These hand calculations provide an 

estimate of the fire-generated smoke concentrations and visibility conditions for this scenario 

and will indicate whether more detailed modeling is warranted. 

The soot mass generation rate, ݉ሶ ௦, is the product of the soot yield, ݕ௦, and the mass burning 

rate of fuel, ݉ሶ

௙. The latter quantity is obtained by dividing the HRR, ܳሶ

, by the heat of 

 :ܪ∆ ,combustion

݉ሶ ௦ ൌ ݕ௦݉ሶ

௙ ൌ ݕ௦

ܳሶ

∆ܪ ൌ 0.175 ൈ

702 kW

10,300 kJ/kg ؆ 0.012 kg/s (A-5)

Point source fire with time ‐

dependent heat release rate

but no specified location or

height

Closed door Uniform

compartment

temperature

Constant exhaust in balance

with supply

Constant air supply

Uniform material properties and thickness

for walls, floor, and ceiling
CABINET FIRE IN MAIN CONTROL ROOM 

A-12 

The soot mass fraction in the smoke layer, ܻ௦, is then calculated: 

ܻ௦ ൌ ݉ሶ ௦

݉ሶtot

؆

݉ሶ ௦

݉ሶ ௔

ൌ ݉ሶ ௦

ሶܸߩ

ൌ 0.012 kg/s

1.2 kg/mଷ ൈ 13.4 mଷ⁄s ؆ 0.00075 kg/kg (A-6)

The extinction coefficient of the smoke, ܭ, is calculated: 

ܭൌܭ௠ߩܻ௦ ൌ 8700 mଶ⁄kg ൈ 1.2 kg mଷ ⁄ ൈ 0.00075 kg/kg ؆ 7.8 mିଵ (A-7)

Here ܭ ௠is the mass-specific extinction coefficient listed in Table A-1. By definition, the optical 

density of the smoke is related to the extinction coefficient via the expression: 

ൌ ܦ

ܭ

ln 10 ؆

7.8 mିଵ

2.3 ؆ 3.4 mିଵ (A-8)

This calculated optical density is then compared with the tenability limit, 3 m-1. This calculation 

indicates that the visibility criterion for tenability would be exceeded for the MCR smoke purge 

scenario based on the specified parameters and the MCR uniformly filling with smoke. 

However, because this analysis is based only on the peak rather than the time-dependent HRR, 

further modeling with zone and CFD models is warranted. 
CABINET FIRE IN MAIN CONTROL ROOM

A-13

A.4.2 Zone Model 

Geometry: CFAST divides the geometry into one or more compartments connected by vents. 

For this simulation, the entire compartment is modeled as a single compartment. As with the 

algebraic models, zone models simulate fires in compartments with rectangular floor areas. The 

strategy for selecting effective room dimensions is the same as for the FPA analysis described 

above. Figure A-7 shows the compartment geometry inputs to CFAST. 

Figure A-7. Compartment geometry and surface material selection in CFAST for the MCR 

Fire. 

While there are numerous cabinets and tables in the compartment, they do not significantly 

change the overall volume of the room and may be neglected as obstructions. There are no 

mechanisms within CFAST to account for the open-grate ceiling. This ceiling provides a 

negligible flow resistance to the heat and air that go through it, so it can be ignored. It is 

expected that neglecting it will lead to slightly higher HGL temperatures because there is less 

resistance for the rising smoke and hot gases. 

Fire: In CFAST, a fire is described as a source of heat placed at a specific point within a 

compartment that generates combustion products according to user-specified combustion 

chemistry. Consistent with typical practice for the use of zone fire models for electrical cabinet 

fires, the fire is positioned at the top of the air vent, 0.3 m (1 ft) below the top of the cabinet, at 
CABINET FIRE IN MAIN CONTROL ROOM 

A-14 

the center of the cabinet. The air vent dimensions are 0.6 m (2 ft) wide and 0.2 m (0.7 ft) high. 

The effective diameter of the fire is 0.4 m (1.3 ft), as noted in Table A-2. 

Combustion chemistry in CFAST is described, at a minimum, by the production rates of CO, 

CO2, and soot. The yield of HCl is calculated by the model based on the specified molecular 

formula and the conversion of all of the chlorine into hydrochloric acid. Inputs for the fire 

specification in CFAST, taken directly from Table A-1, are shown in Figure A-8. 

Note: Values for “Total Mass,” “Heat of Gasification,” and “Volatilization Temperature” are set at default values.

Figure A-8. Specification of the fire in CFAST for the MCR Fire. 

Materials: CFAST does not include the ability to model individual walls of different materials, 

but it can model different materials for walls, floors and ceilings. For this example, the 

compartment walls are specified as being entirely made of gypsum wallboard which has a 

thermal conductivity lower than the other wall materials. The floor and ceiling are modeled as 

0.5 m (1.6 ft) thick concrete. 

Ventilation: For the smoke-purge calculation, air is supplied to the MCR via the six supply 

vents and exhausted through the two returns. The total ventilation rate is 25 air changes per 

hour, or 13.4 m3

/s. Mechanical ventilation inputs for CFAST are shown in Figure A-9. A 

snapshot of the CFAST simulation is shown in Figure A-10. 
CABINET FIRE IN MAIN CONTROL ROOM

A-15

Note: Values for “Begin Dropoff At” and “Zero Flow At” are set at default values. 

Figure A-9. Mechanical ventilation inputs in CFAST for the MCR fire. 

Figure A-10. Smokeview rendering of the CFAST simulation of the MCR fire with 

mechanical ventilation. 
CABINET FIRE IN MAIN CONTROL ROOM 

A-16 

A.4.3 CFD Model 

Geometry: The entire compartment is included in the computational domain. The exterior 

concrete wall coincides with the boundary of the computational domain, meaning that the inside 

surface of the concrete wall is flush with the boundary of the computational domain, and the 

properties of concrete (including its thickness) are applied to this boundary. The tables (made 

out of wood) and the electrical cabinets (made out of steel) are included in the simulation. Note 

that the drop ceiling is not modeled because it is open and for this example provides a negligible 

resistance to the heat and air that go through it. An FDS/Smokeview rendering of the scenario 

is shown in Figure A-12. 

The computational mesh consists of a uniform grid of cells that are approximately 0.2 m (0.7 ft) 

on a side. A simple grid resolution study demonstrates that because the details of the fire (other 

than its specified heat and smoke production rates) within the cabinet are not relevant for this 

simulation, there is no need to further refine the grid in the vicinity of the cabinet. An 

explanation related to choosing the appropriate grid size can be found in NUREG-1824 (EPRI 

1011999), Vol. 7. 

Fire: Following the guidance in Chapter 12 of NUREG/CR-6850 (EPRI 1011989), 

Supplement 1, the fire is modeled as emanating from the upper vent of the burning cabinet. 

The fuel stoichiometry is input to the model as specified above. FDS requires the designation of 

a single gaseous fuel molecule via the number of carbon and hydrogen atoms in the surrogate 

fuel, plus the number of other atoms in the molecule that play no role in the reaction. The soot 

yield and heat of combustion are input directly from Table A-1. 

Materials: The cabinets are represented by closed boxes with the specified properties of steel. 

The tables are assigned the properties of plywood that is 5 cm (2 in) thick. The table legs are 

not modeled because they play little role in the fire or heat transfer calculation to the solids. 

Concrete and gypsum properties are applied to the applicable walls and ceiling. The floor is 

modeled as a 1 cm (0.4 in) thick carpet over a 0.5 m (1.6 ft) thick concrete slab. The concrete 

properties are taken directly as specified. The carpet properties are obtained by choosing 

individual values of the thermal conductivity, ݇, density, ߩ, and specific heat, ܿ, so that their 

product equals the given value of ݇ߩܿ. 

݇ߩܿ ൌ 0.0017 kW/m/K ൈ 200 kg/mଷ ൈ 2.0 kJ/kg/K ൌ 0.68 ሺkW/mଶ/Kሻଶ s

The ݇ߩܿ used to estimate the individual thermal parameters is derived from an empirical ignition 

model, and it may differ somewhat significantly from the true value. However, in this case, the 

heat losses to the carpet are not expected to play a significant role in the simulation and the 

choice of its thermal properties is not expected to affect the results. If the boundary is expected 

to be an important heat loss surface, then a more accurate determination of the thermal 

parameters is necessary. 

Ventilation: Air is supplied to the MCR via the six supply vents and exhausted through the two 

returns. The supply rate is divided equally among the six supply vents, and the return rate is 

divided equally among the two returns. The leakage from the compartment is modeled by 

specifying a small vent located at the base of the door through which air escapes at a rate 

determined by the pressure difference between the MCR and ambient. Note that the door crack 

itself is not modeled explicitly, as the numerical grid is not fine enough. Rather, the leak is 

spread over a slightly larger area. The volume flow through the leakage area, ܸሶ

௅, is estimated 

via the equation: 
CABINET FIRE IN MAIN CONTROL ROOM

A-17

ܸሶ

௅ ൌ ܣ ௅ඨ2 Δ݌

ߩஶ (A-9) 

where ܣ௅AL is the actual leakage area (0.9 m (3 ft) by 0.013 m (0.04 ft), or 0.0117 m2

 in this 

case), ∆݌ is the pressure difference between the inside and outside of the compartment (Pa), 

and ߩஶ is the ambient air density. 

A.5 Evaluation of Results 

The habitability of the MCR depends on the temperature, heat flux, and smoke concentration to 

which the operators would be exposed. According to NUREG/CR-6850 (EPRI 1011989), 

Volume 2, Chapter 11, abandonment of the MCR is occurs if the gas temperature 1.8 m (6 ft) 

above the floor exceeds 95°C (200°F) or if the heat flux exceeds 1.0 kW/m2

 or if the optical 

density exceeds 3 m-1. 

Table A-4 summarizes the results of all the models for the three tenability criteria. For each 

predicted value, a calculation is performed to determine the Probability of Exceeding the Critical 

Value. The procedure for calculating this probability is given in Chapter 4, and it accounts for 

the model bias and standard deviation. The purpose of this table is to highlight the criterion that 

is most likely to be exceeded, so that further analysis can be focused on this criterion and the 

model or models that predict it. Each criterion is discussed in greater detail in the following 

subsections. 

 

Figure A-11. FDS/Smokeview rendering of the MCR, as viewed from above. 
CABINET FIRE IN MAIN CONTROL ROOM 

A-18 

Table A-4. Summary of the model predictions of the MCR scenario. 

Model 

Bias 

Factor, 

ࢾ

Standard 

Deviation,

ࡹ෥࣌

Ventilation Predicted

Value 

Critical 

Value 

Probability 

of 

Exceeding 

Temperature (°C), Initial Value = 20 °C 

FIVE-Rev1 

(FPA) 1.56 0.32 

Purge 

70 95 0.000 

CFAST 1.06 0.12 61 95 0.000 

FDS 1.03 0.07 48 95 0.000 

CFAST 1.06 0.12 No Vent. 82 95 0.009 

FDS 1.03 0.07 70 95 0.000 

Heat Flux (kW/m2) 

FIVE-Rev1 1.42 0.55 

Purge 

0.4 1 0.000 

CFAST 0.81 0.47 0.1 1 0.000 

FDS 0.85 0.22 0.2 1 0.000 

CFAST 0.81 0.47 No Vent. 0.6 1 0.228 

FDS 0.85 0.22 0.4 1 0.000 

Optical Density (m-1) 

CFAST 2.65 0.63 Purge 7.6 3 0.471 

FDS 2.7 0.55 0.5 3 0.000 

CFAST 2.65 0.63 No Vent. 54 3 0.912 

FDS 2.7 0.55 31 3 0.909 

A.5.1 Temperature Criterion 

The HGL temperature and height predictions are summarized in Table A-4 and are shown in 

detail in Figure A-12. None of the analyses imply that the temperature tenability limit would be 

exceeded by a fire of this type, regardless of the ventilation system. It is important to note that 

neither the FPA correlation nor CFAST estimate the temperature at the operator location 

specifically. For the purpose of assessing habitability, the HGL temperature is used to 

approximate the flux condition to which the operator would be exposed, regardless of whether 

the HGL descends to the operator’s height. This means that the FPA and CFAST analyses 

have an extra level of conservatism built in for this particular case. 

The FPA correlation predicts a peak HGL temperature of 70 °C (158 °F) when the smoke purge 

system is on, but, based on the CFAST calculation, it is expected that the layer height would not 

descend to the operator level if the purge system were in operation. 

CFAST predicts that the HGL temperature reaches just above 80 °C (176 °F) in 20 min when 

the smoke purge system is off. The HGL descends to 2 m (6.6 ft) above the floor in 

approximately the same amount of time and thus remains above the head of the operator. 

When the smoke purge system is on, CFAST predicts that the peak HGL temperature reaches 
CABINET FIRE IN MAIN CONTROL ROOM

A-19

approximately 60 °C (140 °F), but that the smoke layer does not descend beyond a meter below 

the ceiling due to the operation of the smoke exhaust system. 

The FDS predictions of HGL temperature are lower than those of the other models because 

FDS accounts for the mixing of heat and smoke with ambient air due to the high purging flow, 

since it models flow within the compartment in detail. 

The HGL temperature is largely a function of the amount of energy from the fire that is carried 

aloft in the smoke plume. The model simulations have all used, based on data from the SFPE 

Handbook, 4th edition, a convective fraction of the HRR that is relatively low for the kind of 

cables under consideration. Typically, approximately 65% of the fire’s energy is lofted upwards 

in the plume, whereas in this case the models have all used a convective fraction of only 47% 

(one minus the radiative fraction). As a result, the HGL temperature might be lower than one 

would expect from a typical fire because a higher percentage of its energy is radiated away. 

Referring to Table 4-3, the HGL temperature rise is proportional to the HRR to the two-thirds 

power. For the purpose of this analysis, the HRR can be regarded as the convective HRR. If 

the convective HRR were increased by 38%, the HGL temperature rise would increase by 

approximately two-thirds of 38%, or 25%. This would have the effect of increasing the CFASTpredicted temperature rise from 60 °C (140 °F) to 75 °C (167 °F). Given an ambient 

temperature of 20 °C (68 °F), this means that if CFAST were to use the conventional 35% 

radiative fraction (65% convective fraction), its prediction16 of the HGL in the no-ventilation case 

would be approximately 95 °C (203 °F), the critical value for abandonment. A similar argument 

can be made for the other HGL predictions. 

Figure A-12. Hot Gas Layer Temperature and Height for the MCR scenario. 

A.5.2 Heat Flux Criterion 

In the fire scenario that includes the operation of the smoke purge system, none of the models 

predict that the heat flux to the operator exceeds the tenability criterion (see Figure A-13). In 

fact, CFAST and FDS estimate a peak flux of approximately 0.1 kW/m2

, a value that is one-tenth 

the critical value. With the smoke purge system turned off, FDS predicts a peak heat flux of 

 

16 The bias factor for the CFAST predictions of HGL temperature is 1.06. Taking this into account, the CFAST prediction of HGL 

temperature for the 35% radiative fraction case would be 90 °C (194 °F) rather than 95 °C (203 °F). This is close enough to the 

critical value to warrant further modeling. 

0

20

40

60

80

100

120

140

0 600 1200 1800 2400 3000 3600

Temperature (C)

Time (s)

Temperature near Operator

FPA (Purge)

CFAST (No Vent.)

CFAST (Purge)

FDS (No Vent.)

FDS (Purge)

0

1

2

3

4

5

6

0 600 1200 1800 2400 3000 3600

Height (m)

Time (s)

HGL Height

CFAST (No Ventilation)

FDS (No Ventilation)
CABINET FIRE IN MAIN CONTROL ROOM 

A-20 

0.4 kW/m2

 and CFAST predicts 0.6 kW/m2. However, as in the case of the HGL temperature 

criterion, it is important to consider the ramifications of the decision to use a radiative fraction of 

53% rather than a value more typical of most fires, 35%. Table 4-3 suggests that the heat flux 

is proportional to the HRR to the four-thirds power. If the models were to use a radiative fraction 

of 35% rather than 53%, the convective HRR would be 38% greater, in which case the heat flux 

from the HGL layer onto the operator could increase by as much as 4/3 times 38%, or 50%. 

Referring to Figure A-13, this would have the effect of increasing the CFAST prediction from 

0.6 kW/m2

 to 0.9 kW/m2, close to the critical value of 1 kW/m2. In fact, the validation study 

documented in NUREG-1824 (EPRI 1011999) indicates that CFAST tends to underpredict the 

total heat flux by 19%, on average. Given this fact and the discussion above on the HGL 

temperature, it should be noted that in the unventilated case, CFAST predicts that the HGL 

would descend to a level comparable in height to the operator (approximately 2 m), and it is 

reasonable to conclude that the operator would be exposed to a heat flux comparable to the 

habitability threshold. 

Figure A-13. Predicted heat flux at the location of the operator. 

A.5.3 Visibility Criterion 

The optical density results are shown in Figure A-14. As with temperature, the CFAST 

prediction is based on its upper layer smoke concentration calculation, whereas that of FDS is 

based on the actual operator location. The simple algebraic techniques described in A.4.1 and 

CFAST both predict that the optical density will exceed the critical threshold, even when the 

purge system is on. FDS, however, predicts a much lower optical density in the purge mode 

scenario for two reasons. First, FDS does not limit the transport of smoke to a descending layer 

like CFAST; and, second, FDS does not uniformly mix the smoke over the entire compartment 

volume like the simple algebraic model. As the operator stands relatively close to two supply 

vents, the supplied fresh air keeps this vicinity clearer than other areas. 

When the smoke purge system is off, FDS predicts that the visibility tenability criterion will be 

exceeded at the operator position in about 12 min. Such conditions would force abandonment 

of the MCR. CFAST predicts that the visibility tenability criterion would be exceeded in the 

smoke layer in approximately 7 min, but it also predicts that the smoke layer remains above the 

operator’s head throughout the fire simulation, which suggests that the MCR would not need to 

be abandoned. The fact that the HGL remains above 2 m (6.6 ft) is partially an artifact of the 

0.0

0.2

0.4

0.6

0.8

1.0

0 600 1200 1800 2400 3000 3600

Heat Flux (kW/m2)

Time (s)

Heat Flux to Operator

FIVE (Purge)

CFAST (No Vent.)

CFAST (Purge)

FDS (No Vent.)

FDS (Purge)
CABINET FIRE IN MAIN CONTROL ROOM

A-21

zone model. There is no mechanism in CFAST for the smoke layer to descend below the base 

of the fire; a fire with a lower base height could result in a lower HGL elevation. 

There is considerable uncertainty in the smoke yield of real fires, especially in cases where the 

fire might be under-ventilated inside of a cabinet. A value of 0.175 (kg soot per kg fuel 

consumed) was chosen for the smoke yield in the models, even though literature values range 

from 0.01 to 0.2 (kg soot per kg fuel consumed), depending on the fuel. In addition to the 

uncertainty in the specified input value of the smoke yield, the NRC/EPRI V&V study (NUREG1824 (EPRI 1011999)) indicates that both CFAST and FDS overestimate measured smoke 

concentrations, on average, by factors of 2.65 and 2.70, respectively. In light of these 

uncertainties in both models and in the input parameters, it is prudent to consider the sensitivity 

of the simulation results to the selected value of the smoke yield. Table 4-3 indicates that the 

optical density is directly proportional to the smoke yield. This means that if the smoke yield is 

doubled, the predicted optical density is doubled as well. The curves in Figure A-14 can easily 

be adjusted to show the effect of a variation in the smoke yield, but the predicted abandonment 

times in the unventilated scenario do not change significantly with changes in the smoke yield. 

Figure A-14. Optical density predictions for the MCR scenario. 

A.6 Conclusion 

A fire modeling analysis has been performed to assess the habitability of the MCR in the event 

of a fire within an isolated electrical cabinet. The fire is not expected to spread to other 

cabinets. Of the three MCR abandonment criteria, it is most likely that the operators would be 

forced to abandon the MCR because the optical density would surpass 3 m-1 approximately 12 

minutes after the fire ignites if the smoke purge system is not activated before this time, 

according to the FDS analysis. A simple analytical method and the zone model CFAST indicate 

that the optical density would exceed the critical value with the smoke purge system on and with 

the ventilation system turned off. However, these analyses are based on the use of several 

important conservative parameters. For the smoke purge case, the analytical method predicts 

that the smoke fills the entire compartment uniformly, even though the FDS analysis shows that 

the supply vents maintain visibility in the vicinity of the operator location. CFAST reports the 

optical density of the upper layer, but does not predict that the upper layer would descend to the 

level of the operator in either the purge or no-ventilation scenario based on the conservative 

specifications, at least for a fire having a base height of 2 m (6.6 ft). 

0.0

10.0

20.0

30.0

40.0

50.0

60.0

0 600 1200 1800 2400 3000 3600

Optical Density (1/m)

Time (s)

Optical Density near Operator

SFPE (Purge)

CFAST (No Vent.)

CFAST (Purge)

FDS (No Vent.)

FDS (Purge)
CABINET FIRE IN MAIN CONTROL ROOM 

A-22 

A.7 References 

1. Mulholland, G.W., and C. Croarkin, “Specific Extinction Coefficient of Flame Generated 

Smoke,” Fire and Materials, 24:227–230, 2000. 

2. NIST SP 1018-5, Fire Dynamics Simulator (Version 5), Technical Reference Guide, 

Volume 3, Experimental Validation, 2010. 

3. NIST SP 1030. CFAST: An Engineering Tool for Estimating Fire Growth and Smoke 

Transport, Version 5 - Technical Reference Guide, National Institute of Standards and 

Technology, Gaithersburg, Maryland, 2004. 

4. NUREG-1805, Fire Dynamics Tools (FDTs

) Quantitative Fire Hazard Analysis Methods for 

the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program, 2004.

5. NUREG-1824 (EPRI 1011999), Verification and Validation of Selected Fire Models for Nuclear 

Power Plant Applications, 2007. 

6. NUREG/CR-6850 (EPRI 1011989), EPRI/NRC-RES Fire PRA Methodology for Nuclear 

Power Facilities, 2005.

7. SFPE Handbook of Fire Protection Engineering, 4th edition, 2008. 

A.8 Attachments (on CD) 

1. FDS input files: 

a. Main_Control_Room_No_Purge.fds 

b. Main_Control_Room_Purge.fds 

2. CFAST input files: 

a. Cabinet fire in MCR No Ventilation.in 

b. Cabinet fire in MCR.in 

3. Algebraic calculation input files: 

a. FPA_AppA.xlsx 
B-1 

APPENDIX B 

CABINET FIRE IN SWITCHGEAR ROOM 

B.1 Modeling Objective 

The calculations described in this appendix estimate the effects of fire in a switchgear room 

electrical cabinet on overhead cables and other nearby cabinets (targets). These calculations 

are part of a larger fire analysis described in Chapter 11 of NUREG/CR-6850 (EPRI 1011989), 

Volume 2, “Detailed Fire Modeling (Task 11).” The switchgear room (SWGR) contains both 

Train A and Train B safety-related equipment that is not separated as required by 10 CFR 50, 

Appendix R. The lack of separation between the two has been identified as an unanalyzed 

condition. The purpose of the calculation is to analyze this condition and determine whether 

these targets fail, and, if so, at what time failure occurs. 

B.2 Description of the Fire Scenario 

General Description: The 4160 V SWGR is located in the auxiliary building and contains three 

banks of cabinets (labeled A, B, and C in Figure B-1). Cabinet banks A and C contain safetyrelated equipment. In addition to the cabinets, there are nine cable trays, with three stacks of 

three trays each located, directly above each of the cabinet banks. The lower two trays above 

the middle bank of cabinets contain control cables for safety-related equipment. The 

compartment is not normally occupied. Ambient temperature in the room is 20 °C (68 °F). 

Construction: Plan and section views of the SWGR are shown in Figure B-1. The 

compartment floor, ceiling, and walls are concrete, nominally 0.5 m (1.6 ft) thick. The cabinets, 

ventilation ducts, and cable trays are made of steel. The cabinet housings are 1.5 mm (0.06 in) 

thick. The ducts are 2 mm (0.08 in) thick. The cable tray steel is 3 mm (0.12 in) thick. The 

trays are stacked 0.5 m (20 in) apart, bottom to bottom. The tray width is 0.8 m (31 in). 

Materials: The thermal properties of the concrete and steel are listed in Table 3-1. The cable 

trays are filled with PE-insulated, PVC-jacketed control cables, which have a diameter of 

approximately 15 mm (0.6 in), a jacket thickness of approximately 1.5 mm (0.06 in), and seven 

conductors. The cable mass per unit length is 0.38 kg/m (0.25 lb/ft), and the mass fraction of 

copper is 0.68. The cables are contained in nine stacked cable trays. There are 50 cables in 

each tray. 

Thermoplastic (TP) cables are considered damaged when their interior17 temperature reaches 

205 °C (400 °F) or the exposure heat flux reaches 6 kW/m2

 (NUREG-1805, Appendix A). The 

damage criteria for the adjacent cabinet is taken to be equal to that for PE/PVC cable since the 

cables inside the cabinet are unqualified. 

Ventilation: There are three supply and three return vents located near the side walls, as 

shown in Figure B-1. Each vent is 0.5 m (1.6 ft) by 0.6 m (2.0 ft), and each has an airflow rate 

of 0.47 m3

/s (1000 cfm). The mechanical ventilation is normally on, and normal operations 

continue during the fire. The supply air to the compartment is equally distributed among the 

supply vents, and the return air is drawn equally from the returns. The compartment has only 

 

17 The cable interior temperature is taken to be that of the insulation material surrounding the conductors. 
CABINET FIRE IN SWITCHGEAR ROOM 

B-2 

one door, which is normally closed. The room temperature is maintained at 20 °C (68 °F), and 

the pressure is comparable to adjacent compartments. Leakage from the compartment occurs 

via a 2.5 cm (1 in) high crack under the 0.91 m (3 ft) wide door indicated on the drawing. All 

other penetrations are sealed. 

Fire: The fire ignites in one cabinet in the middle bank, as specified in Figure B-1. The cabinet 

door is closed, but there are vents on the top of the cabinet for air circulation. The cabinet 

contains more than one bundle of unqualified cable. The fire grows following a “t-squared” 

curve to a maximum value of 464 kW in 12 min and remains steady for eight additional min, 

consistent with NUREG/CR-6850 (EPRI 1011989), page G-5, for a cabinet with more than one 

bundle of unqualified cable. After 20 min, the fire heat release rate (HRR) decays linearly to 

zero in 12 min. A peak fire intensity of 464 kW represents the 98th percentile of the probability 

distribution for HRRs in cabinets with unqualified cable in scenarios where flames propagate 

through cable bundles. From a cabinet configuration perspective, this selection is appropriate 

for control cables where cable loading is typically higher than in other types of cabinets. From 

an applications perspective, the use of the 98th percentile is consistent with the guidance 

provided in NUREG/CR-6850 (EPRI 1011989) for evaluating fire conditions with different fire 

intensities (including the 98th percentile) within the probability distribution range. 

There is an air vent on the top the cabinet. The air vent is 0.6 m (2 ft) wide and 0.3 m (1 ft) long. 

The cabinet is 2.4 m (8 ft) tall. Consistent with NUREG/CR-6850 (EPRI 1011989), the fire burns 

within the interior of the cabinet, and the smoke, heat, and possibly flames exhaust from the air 

vent at the top of the cabinet. 

In this scenario, the cables above Cabinet B are not only targets, they are also “intervening 

combustibles” that may add to the overall HRR of the fire. Predicting the ignition and growth of 

a cable fire is challenging for all the models, which is why empirical models are used instead. In 

this case, the 464 kW cabinet fire described above is supplemented by additional heat from the 

cable fire. In this scenario, the cables are ignited by the cabinet fire, after which a relatively 

simple model for predicting the growth and spread of a fire within a vertical stack of horizontal 

cable trays is applied. The model is referred to as FLASH-CAT, short for Flame Spread over 

Horizontal Cable Trays. This scenario follows Appendix R of NUREG/CR-6850 (EPRI 

1011989), with some additional information provided by the small- and intermediate-scale 

experiments described in NUREG/CR-7010. The FLASH-CAT model makes use of the 

following information: 

 The cable trays are horizontal and stacked vertically. 

 There are no barriers separating the trays, and the tray tops and bottoms are open. 

 The cables are not protected with coatings, shielding, or thermal blankets. 

 There is a fire beneath the lowest tray. 

 Each tray has at least a single row of cables. 

In this scenario, the fire propagates upward through the array of cable trays according to an 

empirically determined timing sequence. First, ignition of the cables in the lowest tray occurs 

when the internal temperature of a target cable within that tray reaches the failure temperature 

of 205 °C (400 °F). This analysis is based on guidance provided in NUREG/CR-6850 (EPRI 

1011989), Appendix R. The calculation of the cable’s internal temperature is based on the 

Thermally-Induced Electrical Failure (THIEF) methodology (NUREG/CR-6931, Volume 3). 

Following ignition, the cables in the lowest tray burn at a rate of 250 kW/m2

, a value appropriate 

for TP cables (NUREG/CR-7010, Volume 1). The width of the burning cable is the same as the 
CABINET FIRE IN SWITCHGEAR ROOM

B-3

width of the trays (0.8 m). The lateral extent of burning cable in the lowest tray, before the onset 

of lateral spread, is equal to that of the ignition source. The lateral extent of the burning cable in 

upper trays, before the onset of lateral spread, is given by the formula: 

ܮ ௜ൌ ܮ௜ିଵ ൅2݄௜ tanሺ35°ሻ (B-1) 

where ܮ ௜is the length of tray ݅ and ݄௜ is the distance (bottom to bottom) between tray ݅െ1 and 

tray ݅. The 35° upward spread angle is described in NUREG/CR-6850 (EPRI 1011989), 

Appendix R. In this example, ܮଵ is equal to the length of the vent in the cabinet (0.6 m (2 ft)) 

and ݄௜ is the distance between trays (bottom to bottom). 

Following ignition, the fire in the first tray spreads laterally at a rate of 3.2 m/h (NUREG/CR6850 (EPRI 1011989), Appendix R). The fire in the second tray ignites 4 min after the first, and 

the lateral extent of the initial fire in the second tray is widened based on Equation (B-1) to 

1.3 m. The burning and spread rates of the fire in the second tray are the same as the first. 

The fire in the third tray ignites 3 min after the fire in the second, and the initial lateral extent of 

the fire is widened yet again following the 35° spread angle to 2.0 m. 

Local burnout of the fire occurs when the cable plastic is consumed. The time to burnout is 

calculated as follows. First, determine the combustible mass per unit area of tray, ݉௖

ᇱᇱ: 

݉௖

ᇱᇱ ൌ ݊ ܻ௣ ሺ1െߥሻ݉ᇱ

ܹ ൌ 50 ൈ 0.32 ൈ ሺ1െ0ሻ ൈ 0.38 kg/m

0.8 m ൌ 7.6 kg/mଶ (B-2) 

where ݊ is the number of cables per tray, ܻ௣ is the mass fraction of combustible (i.e., nonmetallic or plastic) material in the cable, ߥ is the residue yield, ݉ᇱ

 is the total mass per unit 

length of a single cable, and ܹ is the tray width. Next, calculate the burnout time, Δݐ: 

ൌ ݐ∆

݉௖

ܪ∆ ᇱᇱ

ሶݍ 5

avg

ᇱᇱ /6 ൌ 7.6 kg/mଶ ൈ 20,900 kJ/kg

5/6 ൈ 250 kW/mଶ ؆ 762 s (B-3) 

where ∆ܪ is the heat of combustion18, and ݍሶ

avg

ᇱᇱ is the average HRR per unit area of tray. The 

FLASH-CAT model asserts that the HRR per unit area ramps linearly to its average value over a 

time period of ∆ݐ/6, remains steady for a time period of 2 ∆ݐ/3, and then decreases linearly to 

zero over a time period of ∆ݐ/6. The linear ramp-up and ramp-down are typical ways of 

approximating the time history of an item’s HRR. Further details of the FLASH-CAT model are 

provided in NUREG/CR-7010, Volume 1. 

The heat of combustion and product yields for PE/PVC cables are taken from Table 3-4.16 of 

the SFPE Handbook, 4th edition. Note that five different types of PE/PVC cables are listed in 

the chapter. The values listed in Table B-1 are for a cable with relatively high soot and CO 

yields, typical of an under-ventilated fire burning within a closed cabinet. Note also that the nonmetallic components of the cables are a mixture of PE (C2H4) and PVC (C2H3Cl). Because the 

mixture consists of approximately the same mass of each, the cable materials with an effective 

chemical formula of C2H3.5Cl0.5 have been selected. Table B-1 summarizes the fuel and 

combustion parameters for this scenario. 

 

18 By default, the FLASH-CAT model uses a heat of combustion of 16,000 kJ/kg unless there is experimental data that is more 

appropriate. In this case, the chosen heat of combustion is based on a measurement of PE/PVC cable. 
CABINET FIRE IN SWITCHGEAR ROOM 

B-4 

Table B-1. Products of combustion for switchgear room cabinet and cable fire. 

Parameter Value Source 

Effective Fuel Formula C2H3.5Cl0.5 Combination of polyethylene and PVC 

Peak HRR 464 kW NUREG/CR-6850 (EPRI 1011989), App. G 

Heat of Combustion 20,900 kJ/kg SFPE Handbook, 4th Ed., Table 3-4.16 

CO2 Yield 1.29 kg/kg SFPE Handbook, 4th Ed., Table 3-4.16 

Soot Yield 0.136 kg/kg SFPE Handbook, 4th Ed., Table 3-4.16 

CO Yield 0.147 kg/kg SFPE Handbook, 4th Ed., Table 3-4.16 

Radiative Fraction 0.49 SFPE Handbook, 4th Ed., Table 3-4.16 
CABINET FIRE IN SWITCHGEAR ROOM

B-5

Figure B-1. Geometry of the switchgear room.
CABINET FIRE IN SWITCHGEAR ROOM 

B-6 

B.3 Selection and Evaluation of Fire Models 

This section discusses the overall modeling strategy. In particular, it describes the process of 

model selection, including a discussion of the validity of these models for the given fire scenario. 

B.3.1 Temperature Criterion 

The algebraic models are used in this scenario to estimate the flame height and plume 

temperatures from the cabinet fire, first to determine whether the overhead cable trays would be 

damaged by the cabinet fire and then to calculate the average hot gas layer (HGL) temperature 

using the Foote, Pagni, and Alvares (FPA) correlation to determine whether cables in the 

adjacent cabinets would be damaged by the cabinet fire only. Note that the Fire Dynamics 

Tools (FDTs

) do not allow the HRR to be input as a function of time. With a constant HRR, the 

FDTs

 are use a conservative approximation of an instantaneous, fully developed fire that 

remains at peak HRR for the duration of the fire scenario. Although this approach would be 

more likely to estimate a conservative shorter time to failure than tools that utilize a timedependent HRR, it is useful as a screening tool to determine whether failure is likely to occur at 

any time. The FPA correlation is used to estimate the average HGL temperature that would 

result from the initial cabinet fire alone; this analysis using the FPA correlation does not consider 

the potential ignition of cable trays, or their potential contribution to the fire’s HRR. 

The Consolidated Fire Growth and Smoke Transport Model (CFAST) and the Fire Dynamics 

Simulator (FDS) estimate damage to and ignition time of the overhead cable trays, and also use 

the development of elevated temperature and heat flux from the cabinet fire and any ignited 

overhead cables to estimate damage to the adjacent cabinets. CFAST provides timedependent conditions for the cable trays and cabinet, and uses a point source for radiation from 

the fire sources. FDS distributes the fire in a more realistic way, which should provide more 

accurate estimates of temperature and heat flux to adjacent cabinets. 

B.3.2 Heat Flux Criterion 

CFAST and FDS are used to estimate heat flux to the overhead cable trays and to the adjacent 

cabinets. The heat flux calculation in CFAST includes the contribution of radiation from the fire, 

upper and lower gas layers, and bounding surfaces, as well as convection from nearby gases. 

Radiation from the fire sources is based on a point source for the radiation calculation. 

The relative position of the cabinet fire and cable trays may provide a challenge because the 

algorithms used by the zone models to assess target damage are based on a fire radiation point 

source. FDS models the fire in much the same way as the zone models, with the fire on top of 

the cabinet. However, because it is a CFD model, FDS can estimate local conditions at the 

specific location of the target cables and adjacent cabinet. Thus, instead of locating the fire at a 

single point, FDS more naturally distributes the fire amongst the trays, and the resulting heat 

flux calculation is more realistic. 

B.3.3 Validation 

NUREG-1824 (EPRI 1011999) contains experimental validation results for CFAST and FDS that 

are appropriate for this scenario. The National Institute of Standards and Technology (NIST) 

has expanded the U.S. Nuclear Regulatory Commission/Electric Power Research Institute 
CABINET FIRE IN SWITCHGEAR ROOM

B-7

(NRC/EPRI) V&V to include the latest versions of CFAST (6.1.1) (Peacock, 2008) and FDS 

(5.5.3) (McGrattan, 2010). In particular, the International Collaborative Fire Model Project 

(ICFMP) Benchmark Exercise #3 test series was designed specifically as a mock-up of a real 

SWGR. These experiments include ventilation effects on, heat fluxes to, and temperatures of 

various targets, particularly cables. Fire sizes in these experiments bound those used in this 

scenario. Also, the cable failure and cable fire spread algorithms, THIEF and FLASH-CAT, are 

developed and validated in NUREG/CR-6931 (Vol. 3) and NUREG/CR-7010 (Vol. 1). 

Table B-2 below lists the important non-dimensionalized parameters that characterize this fire 

scenario. With the exception of the Fire Froude Number, all of the scenario parameters fall 

within the range of the NRC/EPRI fire model validation study (NUREG-1824 (EPRI 1011999)). 

The Fire Froude Number is essentially a measure of the fire’s heat output relative to its base 

area. In this example, the fire is located at the cabinet’s top vent, with the vent opening serving 

as the area of the base of the fire. This method leads to a higher value of ܳሶ

כ than would be 

calculated if the fire burns completely outside of the cabinet. Thus, the high value of ܳሶ

כ is the 

result of this method that will lead to more severe fire conditions than would be expected if the 

fire were to burn partially within the cabinet. Therefore, the model predictions should be valid 

for this scenario. Also, the Fire Froude Number is calculated to be within the validation range 

when the heat release rate for the initial cabinet fire and the burning cables are considered 

together with an average effective diameter of 1 m (3.2 ft). 

 
CABINET FIRE IN SWITCHGEAR ROOM 

B-8 

Table B-2. Normalized parameters and their ranges of applicability to NUREG-1824 (EPRI 

1011999). 

Quantity Normalized Parameter Calculation 

NUREG1824 

Validation 

Range 

In 

Range? 

Fire Froude 

Number 

ܳሶ

כ ൌ ܳሶ

ߩஶܿ௣ܶஶܦଶ.ହඥ݃

ൌ 464 kW

ሺ1.2 kg/mଷሻሺ1.0 kJ/kg/Kሻሺ293 Kሻሺ0.48ଶ.ହ mଶ.ହሻඥ9.8 m/sଶ ؆ 2.6

ܳሶ

כ ൌ ܳሶ

ߩஶܿ௣ܶஶܦଶ.ହඥ݃

ൌ 1600 kW

ሺ1.2 kg/mଷሻሺ1.0 kJ/kg/Kሻሺ293 Kሻሺ1ଶ.ହ mଶ.ହሻඥ9.8 m/sଶ ؆ 1.4

0.4 – 2.4 No 

Flame Length, Lf, 

relative to the 

Ceiling Height, Hc

௙ܮ ൅ ௙ܪ

௖ܪ

ൌ 2.4 m ൅ 2.1 m

6.1 m ؆ 0.7

ܮ ௙ൌ ܦ ቀ3.7 ܳሶ

כଶ/ହ െ 1.02ቁ ൌ 0.48 m ሺ3.7 ൈ 2.6଴.ସ െ 1.02ሻ ؆ 2.1 m

0.2 – 1.0 Yes 

Ceiling Jet Radial 

Distance,rcj, 

relative to the 

Ceiling Height, Hc

N/A – Ceiling jet targets are not included in simulation. 1.2 – 1.7 N/A 

Equivalence Ratio, 

φ, as an indicator of 

the Ventilation Rate 

߮ ൌ ொሶ

∆ுOమ ௠ሶ Oమ

ൌ ଵ,଺଴଴ kW

ଵଷ,ଵ଴଴ kJ/kgൈ଴.ସ kg/s ؆ 0.31 (based on peak fire size) 

݉ሶ Oమ ൌ 0.23 ߩஶܸሶ ൌ 0.23 ൈ 1.2 kg/mଷ ൈ 1.4 mଷ/s ؆ 0.4 kg/s

0.04 – 0.6 Yes 

Compartment 

Aspect Ratio 

ܮ

௖ܪ

ൌ 26.5 m

6.1 m ؆ 4.3

ܹ

௖ܪ

ൌ 18.5 m

6.1 m ؆ 3.0 0.6 – 5.7 Yes 

Target Distance, r, 

relative to the Fire 

Diameter, D

ݎ

ܦ ൌ 1.5 m0.48 m ؆ 3.1 2.2 – 5.7 Yes 

Notes: 

(1) The effective diameter of the fire is determined from the formula, ܦ ൌ ඥ4ܣ/ߨ, 

where ܣ is the area of the vent on the cabinet. Fire area varies for the cable fire; 

an area of 1 m2

 is typical at the peak heat release rate. 

(2) The Fire Height, ܪ ൅ ௙ܮ௙, is the sum of the height of the fire from the floor, plus 

the fire’s flame length. 
CABINET FIRE IN SWITCHGEAR ROOM

B-9

B.4 Estimation of Fire-Generated Conditions 

This section provides details specific to each model. 

B.4.1 Algebraic Models 

General: The general approach to using the algebraic models for this scenario is to first 

calculate the flame height of the cabinet fire to determine whether the flame reaches one or 

more of the overhead cable trays, then to calculate the plume temperatures from the cabinet fire 

to determine which of the overhead cable trays would be damaged by the cabinet fire, and 

finally to calculate the average hot gas layer temperature using the FPA correlation to determine 

whether the cables in the adjacent cable trays would be damaged by the cabinet fire only. The 

general scenario is depicted schematically in Figure B-2. 

Figure B-2. Schematic diagram of cabinet fire in switchgear room.

The first step in using algebraic models is to determine whether the cables in the cable trays 

located directly above the cabinet fire are likely to be damaged and potentially ignited by the 

cabinet fire. As shown in Figure B-1, the top of the cabinet is located at an elevation of 2.4 m 

(7.9 ft), and the lowest overhead cable tray is located at an elevation of 3.9 m (12.8 ft), which is 

1.5 m (4.9 ft) above the top of the cabinet. As shown in Table B-2, the flame length of the 

cabinet fire is calculated to be 2.1 m (6.9 ft) at the cabinet peak heat release rate of 464 kW, so 

this empirical correlation for flame length can be used to confirm that the overhead cables would 

likely be damaged in this scenario. This calculation supports the scenario that the overhead 

cable trays would be ignited by the cabinet fire, as discussed in Section B.2. 

The next step is to calculate the fire plume temperatures that develop from the cabinet fire to 

determine which of the three cable trays located above the cabinet would be damaged by the 

cabinet fire. The Heskestad plume temperature correlation included in the FDTs

 and the FireInduced Vulnerability Evaluation (FIVE-Rev1) was used to calculate the plume centerline 

temperature above the cabinet fire. The results of this calculation are shown in Figure B-3. 

These results show that the plume temperature at all three cable trays would exceed the cable 

damage threshold temperature of 205 °C (400 °F). However, the Heskestad plume temperature 

Bank A Bank B Bank C 

Cable 

Tray B 

Cable 

Tray A 

Cable 

Tray C 
CABINET FIRE IN SWITCHGEAR ROOM 

B-10 

correlation is based on an unobstructed plume. The obstruction caused by the position of the 

cable trays within the fire plume would alter the actual fire plume entrainment and temperatures. 

Nonetheless, these results demonstrate that the potential for damage and ignition of the cable 

trays as a result of the cabinet fire warrants more detailed analysis. 

Figure B-3. Plume temperatures at cable trays located above a cabinet fire. 

The FPA forced ventilation correlation is used to estimate the average HGL temperature of the 

SWGR resulting only from the cabinet fire only, based on the parameters described in the 

following subsections and summarized in Table B-3. 

Geometry: The FPA correlation requires room dimensions to be specified in terms of length, 

width, and height. For this example, the selected compartment is a rectangular parallelepiped, 

so its length, width, and height are specified directly from dimensions shown in Figure B-1. 

Fire: As applied to this scenario, the FPA correlation is used with the time-dependent HRR 

specified for the cabinet fire only. This HRR history is shown in Figure B-4. 

Materials: The walls, ceiling, and floor are all specified as concrete, with the thermal properties 

specified in Table 3-1. 

Ventilation: The ventilation rate of the smoke purge mode is 1.42 m3

/s (3,000 cfm). This value 

is used as a direct input parameter in the FPA correlation. 

 

0

100

200

300

400

500

600

700

800

900

1000

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

Plume temperatures ‐ Heskestad correlation

Bottom

Middle

Top
CABINET FIRE IN SWITCHGEAR ROOM

B-11

Table B-3. Summary of input parameters for FPA analysis of switchgear room scenario. 

Parameter Value Source 

Room height (H) 5.2 m Figure B-1 

Room length (L) 26.5 m Figure B-1 

Room effective width (We) 18.5 m Calculation 

Room boundary material Concrete Figure B-1. See Table 3-1 for properties. 

Mech. Ventilation rate (ܸሶ) 1.42 m3

/s From scenario description 

Fire elevation (Hf) 2.4 m From scenario description of cabinet height 

and vent location. 

Ambient temperature (Ta) 20°C Specified 

Fire parameters See Table B-1 

Temperature: The FPA HGL temperature correlation for mechanically ventilated spaces is 

expressed in non-dimensional terms as: 

∆ܶ௚

ܶஶ

ൌ 0.63 ቆ ܳሶ

݉ሶ ܿ௣ܶஶ

ቇ

଴.଻ଶ ቆ

்ܣ௞݄

݉ሶ ܿ௣

ቇ

ି଴.ଷ଺

(B-4) 

∆ܶ௚ is the HGL temperature rise above ambient, ܶஶ is the ambient air absolute temperature, ܳሶ

is the HRR of the fire compartment, ݉ሶ is the mass ventilation flow rate, ܿ௣ is the specific heat of 

air, ݄௞ is the heat transfer coefficient, and ܣ் is the total area of the compartment enclosing 

surfaces. The results for the cabinet fire are shown in Figure B-4, based on the input 

parameters specified in Table B-3 and the HRR history shown in Figure B-4. These results 

show that, for the specified parameters, the average HGL temperature reaches a maximum of 

approximately 65 °C (149 °F) at 20 minutes, based on the peak cabinet fire HRR of 464 kW. 

These results show that cables in the two adjacent cabinets would not be damaged by the initial 

cabinet fire alone. However, further analysis is required to determine the potential impact of 

overhead cable ignition on the potential for damage to cables in the adjacent cabinets. CFAST 

and FDS are used to perform this more detailed analysis. 
CABINET FIRE IN SWITCHGEAR ROOM 

B-12 

Figure B-4. Average HGL temperature (red line) from FPA correlation and HRR (blue line) 

for SWGR cabinet fire scenario. 

B.4.2 Zone Model 

Geometry: The CFAST analysis defines the compartment as a single rectangular 

parallelepiped with the specified dimensions. While there are a number of cable trays in the 

compartment, the compartment is large enough that the cable trays do not occupy a significant 

fraction of the total volume, so the compartment dimensions are taken directly from the scenario 

description and Figure B-1. Figure B-5 illustrates the scenario as modeled by CFAST. Figure 

B-6 shows the CFAST inputs for the geometry. 

Figure B-5. Average CFAST/Smokeview rendering of SWGR. 

0

50

100

150

200

250

300

350

400

450

500

0

10

20

30

40

50

60

70

0 600 1200 1800 2400 3000 3600

HRR (kW)

Temperature (°C)

Time (s)

HGL temperature calculation ‐ FPA correlation

FPA [°C]

HRR [kW]
CABINET FIRE IN SWITCHGEAR ROOM

B-13

Figure B-6. CFAST inputs for compartment geometry in SWGR scenario. 

Fire: CFAST requires a user-specified, time-dependent HRR and stoichiometry for the 

combustion of fuel and oxygen. The HRR is the combined cabinet/cable fire described above. 

Figure B-7 shows the CFAST inputs for the fire taken directly from Table B-1. 
CABINET FIRE IN SWITCHGEAR ROOM 

B-14 

Note: Values for “Lower Oxygen Limit” and “Gaseous Ignition Temperature are set at default values. 

Figure B-7. CFAST fire specification inputs for the SWGR scenario. 

Materials: The walls, floor, and ceiling are specified as concrete in CFAST with properties as 

previously described. The target properties are provided directly as input. 

Ventilation: Mechanical ventilation and leakage are specified as input to CFAST directly from 

the scenario description. CFAST uses three inlet and three outlet vents for the mechanical 

ventilation at the heights specified in the scenario description. Horizontal placement of the 

mechanical ventilation within the compartment does not affect the zone model calculation and is 

not part of the input. Figure B-8 shows the CFAST inputs for the mechanical ventilation. Since 

pressure for this scenario peaks approximately at the lower fan cutoff pressure threshold, 

default values for these pressures are used as they should not impact the calculations. 

 
CABINET FIRE IN SWITCHGEAR ROOM

B-15

Note: Values for “Begin Dropoff At” and “Zero Flow At” are set at default values. 

Figure B-8. CFAST mechanical ventilation inputs for the SWGR scenario. 

Cable Targets: In CFAST, target temperatures are calculated with a one-dimensional 

cylindrical heat transfer calculation based on the material properties and cable diameter, as 

specified in the scenario description. CFAST uses the THIEF methodology developed as part of 

the Cable Response to Live Fire (CAROLFIRE) program (NUREG/CR-6931, Vol. 3). Each of 

the target cables is specified directly in the model. Thermal properties are taken directly from 

NUREG/CR-6931. Cable density is calculated from the specified mass per unit length and the 

cross-sectional area of the cable as 0.38 kg/m /(π x 0.0075 m)2

 = 2150 kg/m3. Figure B-9 

shows the CFAST inputs for targets in the scenario. Ignition time for the target cables was 

calculated with an initial CFAST run with only the cabinet fire. This run estimated this ignition 

time (as the time flames reached the secondary cable target) as 480 s. 
CABINET FIRE IN SWITCHGEAR ROOM 

B-16 

Figure B-9. CFAST inputs for cabinet and cable targets for the SWGR scenario. 

B.4.3 CFD Model 

Geometry: The compartment has a simple rectangular geometry that coincides with the 

external boundary of the computational domain. In other words, the exterior walls are not 

explicitly declared, but are defined by default to be the external boundaries of the domain with 

the surface properties of concrete, given above. The cabinets are modeled simply as boxes 

constructed of steel, whose properties are specified above. No attempt is made to model the 

interior of the cabinets because the fire has been specified as originating at or near the top of 

one of the cabinets. Figure B-10 shows the compartment geometry used in FDS. 

The numerical mesh away from the fire consists of uniform grid cells, approximately 0.2 m (8 in) 

on a side. In the vicinity of the fire, the mesh cells are approximately 0.1 m (4 in) on a side. 

This refinement of the mesh is needed to better locate the actual tray locations. Further 

refinement of the mesh is unnecessary because the fire’s growth and spread are to be specified 

based on the empirical model FLASH-CAT. 

Materials: The material properties are applied directly as specified to the walls, floor, ceiling, 

and cabinet. The cabinets adjacent to the center bank are modeled as hollow steel boxes 

whose interiors remain at ambient temperature. For the cables, the thermal properties are 
CABINET FIRE IN SWITCHGEAR ROOM

B-17

superseded by the algebraic ignition and flame spread model called FLASH-CAT. In FDS, the 

model is applied as follows. First, each cable tray is declared an obstruction, the top and 

bottom of which are given the thermal properties of PVC cables from NUREG/CR-6850 (EPRI 

1011989), Volume 2, Appendix R.4.1.1 (k=0.192 W/m/K, ߩ=1,380 kg/m3

, c=1.289 kJ/kg/K). 

These properties are not particularly important because the cable failure, ignition, and fire 

spread are not dependent on them, but merely provide approximate thermal boundary 

conditions for those cables that are not burning. Next, the top surface of each tray is divided 

into three sections. The middle section ignites and burns according to the timing sequence of 

the FLASH-CAT model. The two adjacent sections ignite at the same time, but only at the edge 

abutting the middle section. The fire then spreads laterally at a rate specified by the FLASHCAT model, in this case, 0.9 mm/s. 

Fire: The initial fire source is modeled as a 0.6 m (2 ft) x 0.3 m (1 ft) “gas burner” atop the 

central cabinet with the specified HRR. This is meant to represent a fire that burns near the top 

of the cabinet and exhausts through the vent. The ignition and growth of the cable fire is based 

on the empirical FLASH-CAT model described above. Figure B-11 shows a snapshot of the 

burning cable during the simulation. 

Ventilation: The door is included in the calculation merely as a surface with different properties 

than the default concrete wall. The supply and return vents are specified according to the 

drawing and given volume flow rates. Note that because of the relative coarseness of the 

underlying numerical grid, the ventilation rate is input directly in terms of the volume flow 

rate (m3

/s) rather than as a separate vent area (m2) and velocity (m/s). The model automatically 

adjusts the dimensions of all objects to conform to the numerical mesh, and it also adjusts the 

velocity of the air stream to properly reflect the desired volume flow rate. 
CABINET FIRE IN SWITCHGEAR ROOM 

B-18 

Figure B-10. FDS/Smokeview rendering of the SWGR. 

Figure B-11. FDS/Smokeview rendering of the SWGR fire showing localized ignition of 

extinction of secondary cable fires resulting from initial cabinet fire. 

 
CABINET FIRE IN SWITCHGEAR ROOM

B-19

B.5 Evaluation of Results 

In this example, the objective of the calculations is to estimate the effects of fire in a cabinet in a 

SWGR on nearby cable and cabinet targets; that is, to determine whether and when 

temperatures and/or heat flux to the cable and adjacent cabinets exceed established critical 

values. Cables are considered damaged when the temperature of the cable reaches 205 °C 

(400 °F) or the exposure heat flux reaches 6 kW/m2

 (NUREG/CR 6850 (EPRI 1011989), 

Appendix H, Table H-1). These criteria are intended to be indicative of electrical failure, but, 

based on experimental observation, are routinely also used as ignition criteria. 

Table B-4 summarizes the results of all the models for the chosen failure criteria. For each 

Predicted Value, a calculation is performed to determine the Probability of Exceeding the Critical 

Value. The procedure for calculating this probability is given in Chapter 4, and it accounts for 

the model bias and scatter. The purpose of this table is to highlight the criterion that is most 

likely to be exceeded, so that further analysis can be focused on this criterion and the model or 

models that predict it. Each criterion is discussed in greater detail in the following subsections. 

Table B-4. Summary of the model predictions of the cabinet fire scenario. 

Model 

Bias 

Factor, 

ࢾ

Standard 

Deviation, 

ࡹ෥࣌

Location Predicted 

Value 

Critical 

Value 

Probability 

of 

Exceeding 

Temperature (°C), Initial Value = 20 °C 

CFAST 1.00 0.27 Cable Tray A 335 205 0.937 

FDS 1.02 0.13 755 205 1.000 

CFAST 1.00 0.27 Cabinet A 168 205 0.177 

FDS 1.02 0.13 136 205 0.000 

Heat Flux (kW/m2) 

CFAST 0.81 0.47 Cabinet A 5.3 6 0.576 

FDS 0.85 0.22 4.2 6 0.159 

B.5.1 Cable Ignition and Damage 

The algebraic models cannot be used in this case to accurately assess the damage to cables. 

FIVE-Rev1 does not have an algorithm that considers the thermal inertia of the cables. FDTs

does, but the model is only applicable when the exposing temperature is constant, which is not 

the case for this example. However, the algebraic models can be used for screening purposes, 

to show that the plume temperatures resulting from the specified cabinet fire are high enough to 

potentially cause damage to and ignition of cables located in cable trays directly above the 

cabinet. 

CFAST and FDS estimate conditions resulting from the ignition (based on initial model runs of 

the initial cabinet fire) and burning of the cables (based on calculations from the FLASH-CAT 

model). NUREG/CR-6850 (EPRI 1011989) contains some guidance on modeling cable ignition, 

flame spread, and the fire’s resulting heat release based on a limited set of fire test data. The 

differences in HRR between the models (Figure B-12) result from variations in the 

implementation of this guidance. Figure B-12(a) shows the HRR from the initial cabinet fire 
CABINET FIRE IN SWITCHGEAR ROOM 

B-20 

source only. Figure B-12(b) shows the overall HRR, including the initial cabinet fire source and 

the cables ignited by this initial fire. 

 

(a) Initial cabinet fire only (b) Initial cabinet fire and ignited cables 

Figure B-12. Heat release rate inputs to CFAST and FDS for a SWGR cabinet fire scenario. 

There are several ways to assess the initial fire source’s potential to ignite the lowest cable tray 

(Cable Tray A). Cables are considered damaged when the temperature reaches 205 °C 

(400 °F) or the exposure heat flux reaches 6 kW/m2

 (NUREG-1805, Appendix A). These criteria 

are intended to indicate electrical failure, but are routinely also applied as ignition criteria. In 

newer studies in NUREG/CR-7010, cable ignition was not observed at fluxes below 25 kW/m2

, 

and most often only with direct flame impingement. Handbook values for minimum ignition flux 

for power and communication cables are reported in the range of 15 kW/m2

 to 35 kW/m2 (SFPE 

Handbook, Table 3-4.2). For this scenario, CFAST predicts that the flame height reaches the 

cable tray in approximately 490 s, quite similar to the temperature-based prediction. Table B-5 

shows the lowest cable tray’s estimated time to ignition for a variety of ignition criteria. For this 

simulation, 490 s was chosen. 

Table B-5. Estimated time to ignition of lowest cable tray by CFAST for the SWGR cabinet fire. 

Ignition Criterion Time 

Gas temperature ≥ 205 oC 270 s 

Cable temperature ≥ 205 oC 860 s 

Heat flux ≥ 6 kW/m2 490 s 

Heat flux ≥ 15 kW/m2 740 s 

Flame impingement 490 s 

The CFAST and FDS temperature predictions for the Cable Tray A cables are shown in Figure 

B-13. FDS predicts cable failure in Tray A at about 495 s, CFAST in about 600 s. Peak 

temperatures from both models are well above the failure criteria for the cables, so it can be 

expected that the cables will ignite and provide an additional source of fire. 

0

50

100

150

200

250

300

350

400

450

500

0 600 1200 1800 2400 3000 3600

HRR (kW)

Time (s)

Heat Release Rate

CFAST

FDS

0

200

400

600

800

1000

1200

1400

1600

1800

0 600 1200 1800 2400 3000 3600

HRR (kW)

Time (s)

Heat Release Rate

CFAST

FDS
CABINET FIRE IN SWITCHGEAR ROOM

B-21

Figure B-13. Estimated temperatures for Cable Tray A directly above the fire source for a 

SWGR cabinet fire scenario. 

Qualitatively, the results of the CFAST and FDS predictions are quite different. The radiation 

from the fire source in CFAST is calculated based on a point source fire positioned at the base 

of the fire. Thus, once the fire grows and the flame height approaches the target cable tray, 

CFAST can be expected to underestimate the local cable temperature and heat flux, since the 

cable would actually be immersed within the flames. CFAST does include an estimate of the 

flame height, which can also be used as an indicator of damage to the cable. For this scenario, 

CFAST predicts that the flame height will reach the cable tray in approximately 490 s, quite 

similar to the temperature-based prediction. Past this point, CFAST estimates of the local target 

temperature are expected to be under-predictions. FDS predictions include the impact of direct 

flame impingement and immersion of the target in flames. Thus, the higher temperatures 

predicted by FDS are expected. 

Upon ignition of the bottom cable tray (Cable Tray A), the higher cable trays are ignited, 

consistent with the FLASH-CAT model. 

B.5.2 Cabinet Damage 

To assess potential damage to adjacent cabinets, both the predicted temperatures and heat 

fluxes are evaluated. Because the two adjacent cabinets are equidistant from the fire and have 

similar properties, only one is considered here. The critical damage thresholds are the same for 

these cabinets as for the cables in trays. Figure B-14 shows estimated temperature and heat 

flux on the cabinet surface. 

The algebraic models are not capable of estimating the temperature of a target such as an 

electrical cabinet, whereas the other models do provide this capability. CFAST and FDS 

estimate peak temperatures below 165 °C (330 °F), which is well below the threshold of 205 °C 

0

100

200

300

400

500

600

700

800

0 600 1200 1800 2400 3000 3600

Temperature (C)

Time (s)

Cable Tray A Temperature

CFAST

FDS
CABINET FIRE IN SWITCHGEAR ROOM 

B-22 

(400 °F). The somewhat higher cabinet temperature and heat flux predicted by CFAST is 

consistent with the point source radiation calculations for the CFAST simulation. CFAST and 

FDS both estimate an incident heat flux below about 5 kW/m2, with the difference caused by the 

more simple radiation calculation in CFAST. 

Figure B-14. Estimated temperature and heat flux to a cabinet adjacent to the fire source 

in a SWGR cabinet fire scenario. 

B.5.3 Parameter Uncertainty Propagation 

The analysis above has shown that a 98th percentile cabinet fire is very likely to ignite cables in 

the trays above the cabinet and could potentially damage adjacent cabinets. Within the context 

of a PRA, the next step is to calculate the probability of cable damage for any fire within the 

cabinet, not just the 98th percentile fire. 

Figure B-15 displays the distribution19 of peak heat release rates for cabinets with more than 

one bundle of unqualified cable (NUREG/CR-6850, Appendix G). The analysis described above 

made use of the 98th percentile fire from this distribution, with a peak of 464 kW. 

 

19 NUREG/CR-6850 specifies gamma distributions for the various types of combustibles found within an NPP. Microsoft Excel® 

provides a built-in function (GAMMA.DIST) that calculates the probability density function given the parameters ߙ and ߚ. In this 

case, these parameters are 2.6 and 67.8, respectively. 

0

20

40

60

80

100

120

140

160

180

0 600 1200 1800 2400 3000 3600

Temperature (C)

Time (s)

Cabinet A Temperature

CFAST

FDS

0

1

2

3

4

5

6

0 600 1200 1800 2400 3000 3600

Heat Flux (kW/m2)

Time (s)

Cabinet A Heat Flux

CFAST

FDS
CABINET FIRE IN SWITCHGEAR ROOM

B-23

Figure B-15. Distribution of HRR for an electrical cabinet fire. 

Applying Heskestad’s flame height correlation to the entire range of HRR, now taken as a 

random variable, leads to a distribution of flame height shown in Figure B-16. 

Figure B-16. Distribution of flame heights for the entire range of cabinet fires. 

The cable tray is 1.5 m (4.9 ft) above the top of the cabinet. The probability that the flames from 

a randomly chosen fire will reach the cables is equal to the area beneath the curve in Figure 

B-16 for flame heights greater than 1.5 m (4.9 ft), or approximately 0.31. Consistent with the 

guidance in NUREG/CR-6850, this resulting probability can be used as the severity factor for 

the quantification of corresponding fire ignition frequencies. It is interesting to note that an 

analysis that uses the 50th percentile fire would lead to the conclusion that the flame from the 

0.000

0.001

0.002

0.003

0.004

0.005

0 100 200 300 400 500 600

Probability Density Function

Heat Release Rate (kW)

HRR Distribution

0.0

0.2

0.4

0.6

0.8

1.0

0 0.5 1 1.5 2 2.5 3

Probability Density Function

Flame Height (m)

Flame Height Distribution
CABINET FIRE IN SWITCHGEAR ROOM 

B-24 

cabinet fire does not impinge on the cables and that ignition of the cables is not likely to occur. 

This changes the outcome of the analysis significantly because an analysis that uses only the 

mean HRR without explicit quantification of the uncertainty would result in an overly optimistic 

modeling conclusion and an inappropriate evaluation of the scenario within the integrated fire 

analysis. 

B.6 Conclusion 

This analysis has considered the potential that a fire in an electrical cabinet in a 4160 V SWGR 

will damage overhead cables and adjacent electrical cabinets. Algebraic equations from the 

FDTs and FIVE-Rev1, including the Heskestad flame height correlation and the Heskestad 

plume temperature correlation, were used for screening purposes, to evaluate the potential for 

damage as well as to determine whether more detailed analysis with CFAST and FDS was 

warranted. The algebraic equations demonstrate that the calculated flame height from the 

cabinet fire would be high enough to potentially ignite the lowest of the three horizontal cable 

trays located directly above the cabinet fire. They also demonstrate that the calculated fire 

plume temperatures are high enough at all three horizontal cable trays located directly above 

the cabinet fire to potentially damage cables in all three trays. As applied in this scenario, the 

algebraic equations demonstrate that a more detailed analysis with CFAST and FDS is 

warranted. 

The more detailed analyses with CFAST and FDS demonstrate that the cabinet fire is likely to 

ignite the electrical cables in the lowest cable tray directly above the cabinet fire in 

approximately 10 min. The additional cable trays directly above the lowest tray would then 

ignite in turn. In addition, the models indicate that it is possible that the combined cabinet and 

cable fire could damage adjacent cabinets. These conclusions are based on an analysis of a 

severe (i.e., 98th percentile) fire. A subsequent analysis involving the propagation of the entire 

HRR distribution through a simple flame height model indicates that 31 % of all possible fires 

within the cabinet would ignite the overhead trays and the resulting fire could damage adjacent 

cabinets. 

B.7 References 

1. Jones, W., R.D. Peacock, G.P. Forney, and P.A. Reneke, CFAST - Consolidated Model of 

Fire Growth and Smoke Transport (Version 6), Technical Reference Guide, SP 1026, 

National Institute of Standards and Technology, Gaithersburg, MD, 2009. 

2. NIST SP 1018-5, Fire Dynamics Simulator (Version 5), Technical Reference Guide, 

Volume 3, Experimental Validation, 2010. 

3. NUREG-1805, Fire Dynamics Tools (FDTs

) Quantitative Fire Hazard Analysis Methods for 

the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program, 2004.

4. NUREG-1824 (EPRI 1011999), Verification and Validation of Selected Fire Models for 

Nuclear Power Plant Applications, 2007. 

5. NUREG/CR-6850 (EPRI 1011989), EPRI/NRC-RES Fire PRA Methodology for Nuclear 

Power Facilities, 2005.

6. SFPE Handbook of Fire Protection Engineering, 4th edition, 2008. 

B.8 Attachments (on CD) 

1. FDS input file: Switchgear_Room_Cabinet.fds 
CABINET FIRE IN SWITCHGEAR ROOM

B-25

2. CFAST input files: 

a. Initial Fire Only.in 

b. Cabinet Fire in Switchgear.in 

3. Algebraic calculation input files: 

a. FPA_AppB.xlsx 

 
CABINET FIRE IN SWITCHGEAR ROOM 

B-26 
C-1 

APPENDIX C 

LUBRICATING OIL FIRE IN PUMP COMPARTMENT 

C.1 Modeling Objective 

The purpose of the calculations described in this appendix is to determine whether important 

safe-shutdown cables within a pump room will fail in the event of a lubricating oil fire, and, if so, 

at what time failure occurs. These cables are protected by an electrical raceway fire barrier 

system (ERFBS), but there is a concern that the existing barrier system will not provide the 

required protection. The impact of opening a door during the fire is also investigated. 

C.2 Description of the Fire Scenario 

General Description: The compartment is of fire-resistive construction and contains an 

emergency core cooling system pump and a single tray containing safe-shutdown cables that 

are protected by an ERFBS. The pump is surrounded by a dike designed to contain any 

lubricating oil that may leak or spill, with a maximum capacity of 190 L (50 gal). The 

compartment contains one smoke detector and one sprinkler. The compartment is 

mechanically ventilated. The fire occurs when pump oil leaks into the dike area and ignites. 

Large oil fires are likely to cause flashover conditions. Flashover refers to the rapid transition 

from the growth period of a fire (pre-flashover) to the fully developed fire (post-flashover). A 

flashover condition is typically expected when the hot gas layer (HGL) temperature reaches 

500 °C (932 °F) or greater. Post-flashover conditions are expected in this scenario. 

Geometry: The pump room is relatively small and has only one door. As shown in Figure C-1, 

the walls are 0.1 m (0.3 ft) thick. The floor and ceiling are 0.9 m (3 ft) thick. 
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-2 

Figure C-1. Geometry of the pump room. 
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-3 

Materials: The walls, ceiling, and floor are all constructed of concrete. Nominal values for the 

thermal properties of various materials in the compartment are listed in Table 3-1. The single 

cable tray in this compartment is filled with PE/PVC cables with copper conductors. The 

properties of the cables are listed in Table C-1. The damage criterion is taken to be the point at 

which the cable temperature reaches 205 °C (400 °F) (NUREG-1805, Appendix A). The cable 

tray is protected by an ERFBS, which is two layers of ceramic fiber insulation blankets, covered 

by 0.0254 mm (1 mil) foil. The properties of the insulation material and cables are listed in 

Table C-1. Note that the properties of the ceramic fiber material are typically dependent on 

temperature, and that this material undergoes a series of chemical reactions that are designed 

to absorb heat and protect the underlying cables. Detailed thermophysical properties for this 

particular material are not known. However, the ERFBS has undergone a fire endurance 

furnace test in which the average temperature of the electrical raceway was maintained below 

121 °C (250 °F) and the maximum temperature below 163 °C (325 °F) for an hour when 

exposed to the standard ASTM E 119 temperature curve. 

The damage criterion is taken to be when the cable surface temperature reaches 205 °C 

(400 °C) (NUREG-1805, Appendix A). Using the temperature on the cable surface rather than 

inside the cable jacket is conservative, but is chosen in this case to allow a comparison of 

results between MAGIC and FDS at equivalent positions in the two models. 

Table C-1. Data for ERFBS and cable insulation. 

Material Parameter Value* 

Ceramic Fiber 

Insulation 

Thickness (2 layers) 5 cm 

Thermal conductivity 0.06 W/m/K 

Density 128 kg/m3

Specific heat 1.07 kJ/kg/K 

Emissivity 0.9 

Cable 

Diameter 15 mm 

Jacket thickness 2 mm 

Insulation/jacket conductivity 0.192 W/m/K 

Insulation/jacket density 1380 kg/m3

Insulation/jacket specific heat 1.289 kJ/kg/K 

Mass per unit length 0.4 kg/m 

Conductor mass fractions 33% PE/PVC, 67% copper 

*Source: Product literature (ERFBS) and NUREG/CR-6850 (EPRI 1011989), Volume 2, Appendix R 

(PVC cable insulation).

Fire Protection Systems: As shown in Figure C-1, a smoke detector and a sprinkler are 

located in the pump room. However, to determine whether the barrier system alone will provide 

the required protection, the fire detection and suppression systems are not credited in the fire 

scenario under consideration. 

Ventilation: There is one supply and one return air vent, each with an area of 0.25 m2

 (2.7 ft2), 

providing a volume flow rate of 0.25 m3

/s (530 cfm). The locations are shown in Figure C-1. 

The ventilation system continues to operate during the fire, with no changes brought about by 

fire-related pressure effects. This does not imply that the fire does not impact the ventilation 

system, but rather that there is typically limited information about the ventilation network that 

connects to a given compartment. The pump compartment has one door; it is 1.1 m (3.6 ft) 

wide and 2.1 m (6.9 ft) tall. The door is normally closed, but it is opened 10 min after ignition by 
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-4 

the fire brigade. Before the door opens, leakage from the doorway occurs via a 1.3 cm (0.5 in) 

gap under the door. 

Fire: The fire starts following an accidental release of 190 L (50 gal) of lubricating oil. The spill 

is contained by the dike. Lubricating oil is a mixture of hydrocarbons, mostly alkanes, which 

have the chemical formula CnH2n+2 (with n ranging from 12 to 15). For the purpose of modeling, 

the fuel is specified to be C14H30. Fuel properties for the lubricating oil are summarized in Table 

C-2. The properties obtained from NUREG-1805 correspond to those for transformer oil, based 

on the statement in Table 3-4 in NUREG-1805 that lubricating and transformer oils are similar. 

Table C-2. Data for lubricating oil fire. 

Parameter Value Source 

Effective Fuel Formula CnH2n+2 Specified as C14H30

Mass burning rate 0.039 kg/s.m2 NUREG-1805 Table 3-4 

Fuel volume 190 L Specified 

Fuel density 760 kg/m3 NUREG-1805 Table 3-4 

Heat of Combustion 46,000 kJ/kg NUREG-1805 Table 3-4 

Heat of Combustion per unit 

mass of oxygen consumed 13,100 kJ/kg Huggett 1980, Average value

CO2 Yield 2.64 kg/kg SFPE Handbook, 4th ed., Table 3-4.16* 

Soot Yield 0.059 kg/kg SFPE Handbook, 4th ed., Table 3-4.16* 

CO Yield 0.019 kg/kg SFPE Handbook, 4th ed., Table 3-4.16* 

Radiative Fraction 0.34 SFPE Handbook, 4th ed., Table 3-4.16* 

Mass Extinction Coefficient 8700 m2/kg Mulholland and Croarkin (2000) 

*Material identified as “Hydrocarbon” in SFPE Handbook was used to derive the properties. 

 
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-5 

C.3 Selection and Evaluation of Models 

This section describes the applicability of the models to this scenario. 

C.3.1 Fire Sustainability 

This fire scenario involves a large fire in a ventilated room that may not have sufficient oxygen 

to sustain the fire. An algebraic model is used to determine the oxygen availability within the 

room with the door closed. 

C.3.2 Temperature Criterion 

Algebraic Models: Neither the Fire-Induced Vulnerability Evaluation (FIVE-Rev1) nor the Fire 

Dynamics Tools (FDTs

) contain correlations to estimate the hot gas layer (HGL) temperatures 

within a flashed-over, under-ventilated compartment. Also, the point source radiation heat flux 

calculation included within FIVE-Rev1 and the FDTs

 cannot account for the attenuation of 

thermal radiation by the smoke that fills the compartment. Consequently, neither model is used 

for this scenario. However, an algebraic calculation is used to examine the availability of 

oxygen. 

Zone Models: This fire scenario is not a typical application of a zone model because it involves 

post-flashover conditions, where the two layers essentially become one. Nevertheless, zone 

models can transition to this state when the HGL essentially descends all the way to the floor 

and the room becomes a well-stirred reactor. Conservation laws of mass and energy still apply 

within the single layer; additionally, the processes governing the heating of a target immersed in 

the HGL still apply, even when the HGL fills the entire compartment. The zone model MAGIC 

has been selected for this application. 

CFD Models: This fire scenario is a challenging application, even for a computational fluid 

dynamics (CFD) model. It involves relatively high temperatures, under-ventilated conditions, 

and flashover. The primary advantage of a CFD model for this fire scenario is that CFD models 

typically include combustion algorithms that estimate near- and post-flashover conditions. 

C.3.3 Validation 

Table C-3 lists various important non-dimensional parameters and the ranges for which the 

validation study NUREG-1824 (EPRI 1011999) is applicable. The only parameters that fall 

outside the validation parameter space are the equivalence ratios for the mechanically 

ventilated portion of the scenario (first 10 minutes, while the door is closed) and for the natural 

ventilation portion of the scenario (after 10 minutes when the door is opened). In both cases, 

the high equivalence ratios for the compartment are a result of the relatively large fire and low 

airflows. 

For MAGIC, a sensitivity case is run, in which double doors, rather than a single door, are 

opened after 10 minutes to determine whether an increase in airflow would cause higher 

temperatures in the room. With the enlarged opening, the equivalence ratio is 0.5, putting it 

within the verification and validation (V&V) range. The results of the sensitivity case, presented 

in Section C.5.2, show that the HGL temperatures predicted in the room are not sensitive to the 

size of the door opening. 
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-6 

As part of the work performed at the National Institute of Standards and Technology (NIST) for 

the investigation of the World Trade Center disaster, the Fire Dynamics Simulator (FDS) has 

been validated against large-scale fire experiments. The experiments involved fairly large fires 

in a relatively small compartment, limited ventilation, a liquid fuel spray fire, and the 

measurement of the heat flux to and temperatures of insulated steel (similar to the cables 

protected by ceramic fiber blankets). The large-scale tests with furniture had equivalence ratios 

of approximately 1.4, which provides a validation basis for FDS under conditions similar to the 

natural ventilation portion of the scenario (after the door has been opened). The NIST 

experiments and the FDS simulations are described in NIST NCSTAR 1-5F. 

Table C-3. Normalized parameter calculations for the pump room fire scenario. 

Quantity Normalized Parameter Calculation 

NUREG1824 

Validation 

Range 

In 

Range? 

Fire Froude 

Number 

ܳሶ

כ ൌ ܳሶ

ߩஶܿ௣ܶஶܦଶ.ହඥ݃

ൌ 4934 kW

ሺ1.2 kg/mଷሻሺ1.0 kJ/kg/Kሻሺ293 Kሻሺ1.9ଶ.ହ mଶ.ହሻඥ9.8 m/sଶ ؆ 0.9

0.4 – 2.4 Yes 

Flame Length, 

L୤, relative to the 

Ceiling Height, 

Hc

௙ܮ

௖ܪ

ൌ 4.8 m

4.9 m ؆ 0.99

ܮ ௙ൌ ܦ ቀ3.7 ܳሶ

כଶ/ହ െ 1.02ቁ ൌ 1.9 m ሺ3.7 ൈ 0. 93଴.ସ െ 1.02ሻ ؆ 4.8 m

0.2 – 1.0 Yes 

Ceiling Jet 

Radial 

Distance,rcj, 

relative to the 

Ceiling Height, 

Hc

N/A 1.2 – 1.7 N/A 

Equivalence 

Ratio, φ, based 

on the 

mechanical 

ventilation rate 

߮ ൌ

ܳሶ

∆ܪOమ ݉ሶ Oమ

ൌ 4934 kW

13,100 kJ/kg ൈ 0.07 kg/s ؆ 5.5

݉ሶ Oమ ൌ 0.23 ߩஶܸሶ ൌ 0.23 ൈ 1.2 kg/mଷ ൈ 0.25 mଷ/s ؆ 0.07 kg/s

0.04 – 0.6 No 

Equivalence 

Ratio, φ, based 

on natural 

ventilation 

߮ ൌ

ܳሶ

∆ܪOమ ݉ሶ Oమ

ൌ 4934 kW

13,100 kJ/kg ൈ 0.38 kg/s ؆ 0.99

݉ሶ Oమ ൌ 0.23 · 0.5ܣ௢ඥ݄௢ ൌ 0.23 ൈ 0.5 ൈ 2.31 mଶ √2.1 m ؆ 0.38 kg/s

0.04 – 0.6 No 

Compartment 

Aspect Ratios 

ܮ

௖ܪ

ൌ 9.4 m

4.9 m ؆ 1.9

ܹ

௖ܪ

ൌ 2.8 m

4.9 m ؆ 0.6 0.6 – 5.7 Yes 

Target Distance, 

r, relative to the 

Fire Diameter, D

N/A 2.2 – 5.7 N/A 

Notes: 

(1) The non-dimensional parameters are explained in Table 2-5. 
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-7 

(2) The equivalent fire diameter, ܦ ൌ ඥ4ܣ/ߨ, where ܣ is the area of the spilled 

lubricating oil. 

(3) The compartment aspect ratios are calculated using the equivalent length and 

width. 

C.4 Estimation of Fire-Generated Conditions 

This scenario is modeled using algebraic calculations, the zone model MAGIC, and the CFD 

model FDS. 

C.4.1 Calculation of Oxygen Availability 

At the start of the scenario, the mechanical ventilation is operational, the door is closed, and the 

fire output immediately jumps to the peak heat release rate (HRR) with a total spill area of 

approximately 2.75 m2

 (29.6 ft2), as shown in the hatched area of Figure C-1. The peak HRR, 

ܳሶ, is computed from the fuel mass burning rate, ݉ሶ

ᇱᇱ, the heat of combustion, ∆ܪ, and the 

specified area of the spill, ܣ: 

ܳሶ ൌ ݉ሶ

ᇱᇱ ∆ܪ ܣ ൌ 0.039 kg/mଶ s ൈ 46,000 kJ/kg ൈ 2.75 mଶ ⁄ ؆ 4,934 kW (C-1) 

The oxygen needed to sustain the fire is calculated from the following equation: 

ܳሶ

Oమܪ∆

ൌ 4934 kW

13,100 kJ/kg ൌ 0.377 kg/s (C-2) 

where ∆ܪைమ is the heat of combustion per unit mass of oxygen consumed. The quantity of 

oxygen provided by the ventilation system is calculated by multiplying the oxygen content (0.23) 

by the density and the ventilation rate of the air: 

 0.23 ߩஶܸ ሶ ൌ 0.23 ൈ 1.2 kg/mଷ ൈ 0.25 mଷ/s ൌ 0.069 kg/s (C-3) 

The oxygen provided by the ventilation system is much lower than the amount needed to 

sustain the fire. The oxygen initially in the room can provide the additional oxygen needed for 

combustion for a short time. The available oxygen in the room, calculated from the room 

dimensions (Table C-4), is: 

0.23 ߩஶܮܹܪ ௖ൌ 0.23 ൈ 1.2 kg/mଷ ൈ ሺ2.81 ൈ 9.39 ൈ 4.9ሻ mଷ ൌ 35.7 kg (C-4) 

The oxygen initially in the room can sustain the fire for an amount of time equal to the oxygen 

quantity in the room divided by the consumption rate minus the ventilation supply rate, as shown 

below: 

35.7 kg

ሺ0.377 kg/s െ 0.069 kg/sሻ ൌ 116 s (C-5) 
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-8 

Equation C-4 requires that all the oxygen within the room be consumed by the fire. This 

establishes an upper limit to the burning duration before the fire becomes ventilation-limited. 

After 116 s, the size of the fire is maintained only by the ventilation system and is limited to: 

0.069 kg/s ൈ 13,100 kJ/kg ൌ 904 kW (C-6) 

These results show that the oxygen supply available to the room will only allow a fire of reduced 

size to burn until the door is opened (under-ventilated condition). 

C.4.2 Zone Model 

The following paragraphs outline the data utilized to model the scenario using MAGIC. Figure 

C-2 provides an illustration of the scenario, as rendered by MAGIC. 

Geometry: To model this scenario with MAGIC, the pump compartment is modeled as a single 

compartment having the same total volume and surface area as the actual enclosure. This 

allows the volume in which the HGL develops and the surface area through which energy is 

transferred from the compartment to be maintained. Maintaining the total volume and surface 

area while leaving the ceiling height unchanged at 4.9 m (16 ft) yields an effective compartment 

size of 9.39 m (30.8 ft) by 2.81 m (9.2 ft). The modification to the geometry can be seen by 

comparing Figure C-1 and Figure C-2. All other aspects of the geometry are relatively 

unchanged. 

Table C-4. Calculated input for lubricating oil fire. 

Parameter Value 

Effective Length 2.81 m 

Effective Width 9.39 m 

Fire Diameter 1.87 m 

Peak Heat Release Rate 4,934 kW 

Fire Duration 1345 s 

Mass of Fuel (kg) 144.4 

Stoichiometric Mass-Oxygen 3.5 g/g 

Specific Area 513 m2/g 
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-9 

Figure C-2. MAGIC view of the pump room.

Fire: For this scenario, the lubricating oil is preheated prior to the spill, such that the HRR 

reaches the peak immediately upon fire initiation, as shown in the HRR curve plotted in Figure 

C-3. The lower oxygen level is specified to be 10%. Using the specified spill area and volume, 

the spill depth is calculated as 0.069 m (0.23 ft). 

The fire is modeled as a single circular area of equivalent diameter. The actual entrainment for 

the pool fire is proportional to the perimeter of the fire, which is significantly greater than the 

perimeter of the circular area. However, the enclosure is small and the smoke filling rates are 

expected to be short regardless of the fire shape. 

The fire duration, ∆ݐ, is determined from the pool depth, ߜ, density, ߩ, and burning rate, ݉ሶ

ᇱᇱ: 

ߩ ߜ ൌ ݐ∆

݉ሶ

ᇱᇱ ൌ 0.069 m ൈ 760 kg/mଷ

0.039 kg/mଶ/s ؆ 1345 s ሺ22.4 minሻ (C-7) 
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-10 

Figure C-3. Heat release rate curve for lubricating oil fire. 

The location of the fire is placed at the edge of the dike, closest to the target cable. The total 

mass of fuel is 144.4 kg, calculated from the volume multiplied by the density from Table C-2. 

The stoichiometric mass-oxygen-to-fuel ratio, ߰, is calculated using Equation 22 from Chapter 

3-4 of SFPE Handbook, 4th Edition and the values from Table C-1, as follows: 

߰ ൌ

்ܪ∆

Oమܪ∆

ൌ 46,000 kJ/kg

13,100 kJ/kg ൌ 3.5 kg/kg (C-8)

where ∆ܪ் is heat of combustion per unit mass of fuel consumed and ∆ܪOమ is the heat of 

combustion per unit mass of oxygen consumed. One of the inputs required by MAGIC is the 

specific area, s, a measure of the smoke generation, which is calculated as described in 

NUREG-1824 (EPRI 1011999), Volume 6, Section 3.2.7: 

ݏൌݕ௦݇௠ ൌ 0.059 ൈ 8,700 mଶ/kg ؆ 513 mଶ/kg (C-9)

where ݇௠ is the mass extinction coefficient and ݕ௦ is the soot yield, as listed in Table C-2. The 

pyrolysis rate (g/s) is calculated for input to MAGIC by dividing the HRR values (4934 kW) at 

each time step by the heat of combustion (46,000 kJ/kg). Other inputs needed for MAGIC are 

listed in Tables 3-1, C-1, C-2, and C-4. Figure C-4 is a screenshot of the source fire in the 

MAGIC input file. 

0

1000

2000

3000

4000

5000

6000

0 600 1200 1800 2400 3000 3600

HRR (kW)

Time (s)

Heat Release Rate

Input HRR
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-11 

Figure C-4. MAGIC fire input screen for pump fire. 

 
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-12 

In MAGIC, multi-conductor cables, composed of jacket, insulation, and conductor (copper, in 

this case), are modeled as single-conductor cables, as shown in Figure C-5. 

Figure C-5. Modeling multi-conductor cables in MAGIC. Source: NUREG-1824 

(EPRI 1011999), Volume 6, Figure 3-3. 

The radius of the conductor in an equivalent single-conductor cable is needed for input to 

MAGIC. The mass of the conductor per unit length is calculated from the mass fraction of the 

conductor multiplied by the mass per unit length of the multi-conductor cable: 0.67 x 0.4 kg/m = 

0.27 kg/m (values from Table C-1). To determine the conductor radius, ݎ௖, the mass per unit 

length (0.27 kg/m) is set equal to the cross-sectional area times the density of copper, 8954 

kg/m3

 (Table 3-1) or 0.27 ൌ ݎߨ௖

ଶߩ. Rearranging the equation to solve for conductor radius 

results in the following: 

ݎ ௖ൌ ඨ 0.27

ߨ ൈ 8954 ൌ 3.1 mm (C-10)

The insulation thickness is calculated by cable radius – jacket thickness – copper thickness = 

7.5 mm – 2 mm – 3.1 mm = 2.4 mm. Since the jacket and the insulation are both composed of 

PE/PVC, the thicknesses are added together for a total thickness of 4.4 mm. As a result, the 

ERFBS protected cable raceway is modeled with three layers (Figure C-6): ceramic fiber 

blanket (5 cm), PE/PVC (4.4 mm), and copper (3.1 mm). The input screen for the layers of the 

ERFBS and the cables is shown in Figure C-7. 

a

Jacket

Insulation

Conductor

a
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-13 

Figure C-6. Representation of the ERFBS protected cable raceway for MAGIC. 

Figure C-7. MAGIC input screen for ERFBS layers. 

Ventilation: Mechanical ventilation is maintained constantly during the simulation, using the 

values provided above. MAGIC uses circular ducts, so the rectangular ducts seen in Figure C-1 

are modeled as circular areas with equivalent diameter of 0.56 m (1.8 ft). As noted above, the 

door is normally closed, but it is opened 10 minutes after ignition by the arriving fire brigade. 

Before the door opens, leakage due to the doorway occurs via a 1.3 cm (0.5 in) gap under the 

door. The MAGIC input screen for the doorway is shown in Figure C-8. 

 

Cooper Conductor

Ceramic Fiber Blanket (ERFBS)

Combined Cable Jacket 
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-14 

Figure C-8. MAGIC input screen for ventilation through door. 

C.4.3 CFD Model 

The following paragraphs outline the data utilized to model the scenario using FDS. Figure C-9 

provides an illustration of the scenario, as rendered by Smokeview. 

Geometry: The compartment is modeled as shown in Figure C-1, except that the pump itself is 

modeled as two rectangular boxes. A single uniform, rectangular mesh spans the entire 

compartment, plus the hallway outside the door. The numerical mesh consists of approximately 

0.2 m (0.7 ft) grid cells. A finer calculation with 0.1 m (0.3 ft) cells was performed with similar 

results. The latter calculation requires roughly a week of computing time on a single processor 

computer (2008 vintage), whereas the more coarsely gridded calculation requires about 10 

hours. 

Materials: All material properties are as specified above. The protected cable tray is modeled 

as a rectangular box with the same dimensions as the tray wrapped in a blanket. The box is 

made solely of 5 cm (2 in) of ceramic fiber insulation. The tray is neglected. A cable target is 

positioned within the box pointing downwards, as this is the hottest surface of the box. The 

exact dimensions of the box are not an issue; what matters is that the cable within the box is 

exposed to the heat that penetrates the thermal blanket. The cable temperature is computed 

using the Thermally-Induced Electrical Failure (THIEF) methodology (NUREG/CR-6931). 
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-15 

Fire: Due to the limited amount of validation data available for scenarios of this type and the 

considerable uncertainties involved, the approach taken is to specify, rather than attempt to 

predict, the burning rate of the fuel, even though the FDS model does provide the physical 

mechanisms to estimate burning rates. The fire is specified in the diked area surrounding the 

pump. Although FDS has a liquid fuel burning model, it is not used here because there is not 

enough information about the fuel, and, more importantly, it lacks the exact geometry of the 

pump and diked area. Typically, FDS would expect that the oil has formed a relatively deep 

pool with relatively little influence by the surrounding solids. This is not the case here. Instead, 

the specified burning rate, 0.039 kg/m2

/s, is applied directly to the model over an area of 

2.75 m2

 (29.6 ft2), yielding a burning rate of 0.107 kg/s. The density of the oil is 0.76 kg/L, which 

means that the oil burns at a rate of 0.141 L/s. At this rate, 190 L (50 gal) will require 1,348 s to 

burn out. Note that this is slightly different from the burning duration of 1345 s computed for the 

MAGIC input. The fire duration computation for FDS converts the mass data to volumetric data, 

Figure C-9. FDS/Smokeview rendering of the pump room scenario at the 

early stage of the fire, before the compartment becomes under-ventilated. 
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-16 

thus introducing an additional step and some rounding. The slight difference in the burning 

durations is due to this additional rounding and is not significant. The vaporized fuel is a mixture 

of various hydrocarbons, but FDS uses only one fuel molecule in the combustion sub-model. 

For this calculation the fuel molecule is modeled as C14H30. 

Ventilation: The volume flow rates are applied as specified. 

C.5 Evaluation of Results 

The primary purpose of these calculations is to assess whether the Kaowool ERFBS applied to 

the critical cables within the pump room would be damaged in the event of a lubricating oil fire. 

The results of the zone model MAGIC and the CFD model FDS are consistent in their HRR and 

compartment temperatures. This is expected because the models use the same specified 

burning rate, the same fuel stoichiometry, and the same basic rules of gas phase flame 

extinction based on oxygen and temperature levels in the vicinity of the fire. 

Table C-5 summarizes the predicted cable temperatures from MAGIC and FDS, including an 

assessment of the model uncertainty. Note that the results are based only on a direct 

calculation of the cable temperature and do not include an assessment of the sensitivity studies 

that are discussed in the next section. 

Table C-5. Summary of the model predictions of the pump room scenario. 

Model 

Bias 

Factor, 

ࢾ

Standard 

Deviation,

ࡹ෥࣌

Predicted 

Value 

Critical 

Value 

Probability of

Exceeding 

Cable Temperature (°C) 

MAGIC 1.19 0.27 135 205 0.000 

FDS 1.02 0.13 145 205 0.000 

C.5.1 The Fire 

The HRR curves predicted by the hand calculations and the MAGIC and FDS models are 

shown in Figure C-10 for the entire simulation (first plot) and the first five minutes (second plot). 

The figures show the pronounced drop in the HRR soon after the start of the fire, which 

demonstrates that there is insufficient air (i.e., oxygen) within the compartment to sustain the 

postulated fire. Based on the calculations, the drop in HRR does not occur until after about 

120 s, which is later than the predictions by MAGIC and FDS because the algebraic calculations 

allow all of the oxygen in the room to be consumed. MAGIC uses a lower oxygen limit of 10%, 

and FDS uses a lower oxygen limit that depends on temperature. At high temperatures, FDS 

expects all of the oxygen is consumed. After 120 s, but before the door is opened at 600 s, the 

value of the HRR calculated by the algebraic calculations (approximately 900 kW) is higher than 

the values predicted by MAGIC and FDS (approximately 350 kW) due to the differences in the 

lower oxygen level. The sudden jump in the HRR, predicted by FDS at 600 seconds, is caused 

by the unburned fuel igniting as the door is opened. Note that none of the models has an 

algorithm capable of determining whether or not the fire would be sustained at this reduced 

burning rate until the time when the door is opened. 
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-17 

Figure C-10. HRR predicted by algebraic methods, MAGIC, and FDS for the pump room 

fire scenario. 

C.5.2 Temperature Criterion 

MAGIC and FDS estimate the temperature of the hot gas layer as a function of time, as shown 

in Figure C-11. As expected, the HGL temperature changes in accordance with the altered 

(oxygen-starved) HRR. Once the door opens at 600 seconds, the increased HRR causes the 

HGL temperature to rapidly increase until the fire consumes the available fuel. After the fire 

burns out, the HGL temperature slowly drops as heat leaves the HGL through the bounding 

surfaces and open door. 

Figure C-11. HGL Temperature Predicted by MAGIC and FDS for the pump room fire 

scenario. 

0

4000

8000

12000

16000

20000

0 600 1200 1800 2400 3000 3600

HRR (kW)

Time (s)

Heat Release Rate

Entire Simulation

MAGIC

FDS

0

1000

2000

3000

4000

5000

6000

0 30 60 90 120 150 180 210 240 270 300

HRR (kW)

Time (s)

Heat Release Rate

First 5 Minutes

MAGIC

FDS

Hand Calculation

0

100

200

300

400

500

600

700

800

900

1000

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

HGL Temperature

MAGIC

FDS

ASTM E-119
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-18 

There are two strategies for assessing the viability of the protected cables. The first is to 

compare the predicted HGL temperature to the standard fire endurance curve under which the 

ERFBS was tested to determine whether the predicted thermal exposure is comparable to the 

qualification test. The second is to calculate the temperature of the cable directly, using the 

nominal thermal properties of the fiber insulating blanket. Each strategy will be assessed in turn 

below. 

Comparison to the Standard Fire Endurance Temperature Curve 

Figure C-11 includes the standard ASTM E119 temperature curve to which the ERFBS was 

subjected during its qualification test. The predicted HGL temperatures of both MAGIC and 

FDS fall below this curve during most of the hour-long simulation, but there is a period near the 

beginning of the fire where the models’ predicted temperatures exceed the standard curve. In 

order to compare the relative exposure of the ERFBS, it is necessary to consider the integrated 

incident heat flux corresponding to the model HGL predictions and the ASTM E 119 

temperature curve. The integrated heat flux is given by the following formula: 

ݍᇱᇱ ൌ න ݍሶ

ᇱᇱ

௧భ

௧బ

ሺݐሻ ݀ݐ ൌ න ߪሺܶସ െ ܶ଴

ସሻ ൅ ݄ሺܶെܶ଴ሻ

ଷ଺଴଴

଴

 (-11C (ݐ݀

Here, ݍᇱᇱ is the integrated heat flux received by the ERFBS, ܶ is the HGL temperature, ܶ଴ is the 

ambient temperature (20 °C), ݄ is the convective heat transfer coefficient (about 0.025 kW/m2

/K 

in fully developed fires), and ߪ is the Stefan-Boltzmann constant (5.67 × 10-11 kW/m2

/K4). Note 

that Equation C-11 is the total energy transferred from a thermally thick (emissivity of 1) hot gas 

to a cold target. It is intended only to compare the different temperature curves. In reality, the 

net heat transferred to a target in the compartment decreases as the target heats up. 

Applying Equation (C-11) to each of the HGL temperature curves in Figure C-11 yields values of 

346 MJ/m2

 for the ASTM E119 curve and approximately 40 MJ/m2 for both FDS and MAGIC. 

This 40 MJ/m2

 exposure corresponds to an approximately 14 min exposure within the standard 

test furnace. Table C-6 lists the thermal exposure as a function of time in the standard test 

furnace. It is also significant to note that the maximum predicted exposure temperature remains 

lower than the maximum exposure temperature that the ERFBS protected raceway was 

exposed to during the ASTM E119 fire test. 

 
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-19 

Table C-6. Integrated thermal exposure of an object subjected to the ASTM E119 temperature 

curve. 

Time

(min)

Thermal

Exposure

(MJ/m2) 

5 6 

10 23 

15 47 

20 75 

25 104 

30 135 

35 167 

40 200 

45 235 

50 270 

55 307 

60 346 

Direct Calculation of Cable Temperature 

MAGIC and FDS have heat conduction algorithms to account for the multiple layers of insulation 

and cable materials. The surface temperature predictions of the cables protected by the 

ERFBS (ceramic fiber insulation in this case) are shown in Figure C-12. MAGIC predicts a 

maximum cable surface temperature of approximately 135 °C (275 °F). FDS predicts a 

maximum cable surface temperature of approximately 145 °C (293 °F). Note that although the 

HGL temperature drops and then increases dramatically when the door opens, as shown in 

Figure C-11, the cable temperature slowly rises. This is due to the thermal lag caused by the 

ERFBS. 

Figure C-12. Cable surface temperature predicted by MAGIC and FDS for the pump room 

fire scenario. 

0

20

40

60

80

100

120

140

160

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

Cable Surface Temperature

Inside ERFBS

MAGIC

FDS
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-20 

Sensitivity of the ERFBS Construction 

Comparing Figure C-11 and Figure C-12 shows that the ERFBS has a large impact on the 

temperature of the target cable. To determine the sensitivity of the target cable temperature to 

the insulation installation technique, two additional MAGIC cases are run. In the first case (file: 

Pump_Room_thinner_wrapping.cas.), the thickness of the ceramic insulation blanket is reduced 

by 25% to 0.0375 m. In the second case (file: Pump_Room_tighter_wrapping.cas.), the 

thickness of the ceramic insulation blanket is reduced by 25% while the density is increased to 

171 kg/m3

, such that the mass per area remains constant, which simulates a tighter installation 

of the insulation. The results, plotted in Figure C-13, show that both cases led to a higher cable 

temperature. 

Figure C-13. Cable surface temperature predicted by MAGIC for changes to insulation 

wrapping. 

Sensitivity of the Door Size 

As mentioned in Section C.3.3, the equivalence ratio for the pump room scenario falls outside of 

the validation range. As a sensitivity test, MAGIC was run with the door area doubled, such that 

the equivalence ratio falls within the applicable validation range (0.04 – 0.6) for the portion of the 

simulation when the doors are open (file: Pump_Room_2Doors.cas), as calculated below: 

݉ሶ Oమ ൌ 0.23 · 0.5ܣ௢ඥ݄௢ ൌ 0.23 ൈ 0.5 ൈ 4.62 mଶ √2.1 m ؆ 0.77 kg/s (C-12)

߮ ൌ

ܳሶ

∆ܪOమ ݉ሶ Oమ

ൌ 4934 kW

13,100 kJ/kg ൈ 0.77 kg/s ؆ 0.5 (C-13)

Figure C-14 shows the temperature comparison for the HGL and the cable surface temperature 

(measured inside the ERFBS) for the base case and for the case with double doors. The plots 

show that the results for both cases are very similar, indicating that the door size does not 

significantly affect the results. Nevertheless, it is consistent with experimental data that the 

scenario with the equivalence ratio closest to unity produces the highest enclosure temperature. 

0

20

40

60

80

100

120

140

160

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

Cable Surface Temperature

Inside ERFBS

MAGIC Base Case

25% Tighter

Wrapping

25% Thinner

Wrapping
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-21 

Figure C-14. Temperature predicted by MAGIC for increased door size. 

Sensitivity of HRR Profile 

As discussed in Section C.5.1, both MAGIC and FDS predict that the HRR decreases rapidly 

soon after the fire starts, due to an insufficient oxygen supply within the compartment. The 

models indicate that the HRR decreases from about 4900 kW to about 350 kW in approximately 

2 min (Figure C-10). When the oxygen is insufficient to maintain the fire, MAGIC continues to 

vaporize the unburned liquid fuel, but these fuel gases do not combust (Gay, 2005). FDS also 

continues to vaporize the unburned fuel, and it continues to transport the fuel gas until the door 

is opened after 10 min, at which time this excess fuel mixes with incoming air and burns. This 

rapid burning of built-up excess fuel gas in an under-ventilated compartment is known as a 

“backdraft,” and it is apparent from the HRR plot in Figure C-10. However, much of the heat 

from this rapid burning of fuel is immediately exhausted from the compartment and does not 

significantly affect the temperature of the ERFBS. 

During the period of underventilation, both models specify that the liquid fuel contained in the 

dike continues to evaporate at the specified rate. In reality, the reduced temperature and 

oxygen within the compartment will probably reduce the evaporation rate of the fuel, the extent 

of which is difficult to predict. To account for this possibility, the fuel evaporates at a constant 

rate can be changed so that the evaporation rate during the time period between 2 min and 

10 min is reduced to support a 350 kW fire only. The excess fuel that does not evaporate in this 

time period is added to the end of the specified burning period so that the total fuel mass is 

conserved. As shown in the plot to the right in Figure C-15, a revised HRR curve (labeled as 

Extended HRR) was specified as input for MAGIC. The HGL temperature for this case reaches 

640 °C (1184 °F), compared to 580 °C (1076 °F) for the base case (Figure C-14), which is still 

significantly lower than the ASTM E119 temperature curve (Figure C-11). However, the 

predicted cable surface temperature is 200 °C (392 °F), falling just below the failure criterion of 

205 °C (400 °F). This five-degree margin suggests that further validation may be needed to 

ensure that the thermal properties of the ERFBS are accurate. As shown in the previous 

sensitivity cases, changes in the thermal properties of the ERFBS led to an increase of more 

than 10 °C in ERFBS exposure temperature. Therefore, further validation of the thermal 

0

100

200

300

400

500

600

700

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

HGL Temperature

MAGIC Base Case

Double Doors

0

20

40

60

80

100

120

140

160

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

Cable Surface Temperature

Inside ERFBS

MAGIC Base Case

Double Doors
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-22 

properties of the ERFBS is needed in this case to reduce the impact of parameter uncertainty 

on the surface temperature calculation. 

The sensitivity case shows that (1) based on comparison to the ASTM E119 temperature curve, 

the ERFBS system is not expected to fail under the predicted exposure temperatures, and (2) 

based on the predicted cable surface temperature, further validation of the thermal properties of 

the ERFBS is warranted as the surface temperature of the cable is close to the damage criteria. 

Figure C-15. HRR for base case and HRR sensitivity case. 

Figure C-16. Temperature for base case and HRR sensitivity case. 

 

0

1000

2000

3000

4000

5000

6000

0 600 1200 1800 2400 3000 3600

HRR (kW)

Time (s)

Base Case Heat Release Rate

Input HRR

MAGIC

0

1000

2000

3000

4000

5000

6000

0 600 1200 1800 2400 3000 3600

HRR (kW)

Time (s)

Sensitivity Case Heat Release Rate

Extended 

HRR

MAGIC

0

100

200

300

400

500

600

700

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

HGL Temperature

MAGIC Base 

Case

Extended 

HRR

0

50

100

150

200

250

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

Cable Surface Temperature

Inside ERFBS

MAGIC Base Case

Extended HRR
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-23 

C.6 Conclusion 

This analysis has considered the potential for a relatively large lubricating oil spill fire in a 

relatively small enclosure to damage a cable tray protected by an ERFBS. Algebraic 

calculations, the zone model MAGIC, and the CFD model FDS were all used to evaluate the fire 

conditions within the enclosure. MAGIC and FDS were used to calculate the thermal response 

of the cables to these calculated fire conditions. 

Based on the specified lubricating oil spill area and burning characteristics, a fire of 

approximately 5 MW is expected. However, after the rapid consumption of the limited quantity 

of air in the room, the mechanical ventilation to the enclosure could only support a HRR of less 

than 1 MW before the door to the enclosure opens after 10 min. This analysis suggests that to 

avoid rapid fire escalation, doors to such rooms should not be opened until firefighters are 

prepared to suppress the fire, and, even then, the potential for rapid fire escalation should be 

considered. 

Two different strategies were applied to assess the integrity of the ERFBS. Because the 

thermal and chemical properties of the insulating material are only partially known, it is 

necessary to implement an alternative technical approach of comparing the predicted HGL 

temperatures from the models with the standard temperature curve under which the ERFBS 

received an hour rating. Since the predicted HGL temperatures do not lie completely within the 

standard curve, a simple integrated heat flux calculation was performed to demonstrate that the 

ERFBS received approximately 10 times the thermal exposure in the standard fire endurance 

test than is predicted by the two models. 

A second strategy for assessing the integrity of the ERFBS was to directly calculate the heat 

penetration through the insulating blankets using the thermal material properties of the cables 

and the ERFBS. Both models predicted cable temperatures below the reported critical values. 

Based on the two approaches to determine its performance, the ERFBS is expected to prevent 

the cables from reaching temperatures that would limit their functionality in the event of a fire 

involving burning spilled lubricating oil. This conclusion is based on certain expected burning 

behavior of the lubricating oil during the under-ventilated stages. A sensitivity study on the 

burning behavior of the lubricating oil concluded that the results could change if the burning rate 

decreases during the under-ventilated stage. The results are also shown to be sensitive to the 

thermal properties of the ERFBS material. Further research or testing of the ERFBS thermal 

properties may be necessary to confirm the initial conclusion. 

C.7 References 

1. Gay, L., C. Epiard, and B. Gautier, MAGIC Software Version 4.1.1: Mathematical Model, 

EdF HI82/04/024/B, Electricité de France, France, November 2005. 

2. Gay, L., and J. Frezabeu, Qualification File of Fire Code MAGIC version 4.1.1, EdF HI82/04/022/A, Electricité de France, France, December 2004. 

3. Hugget, C., “Estimation of Rate of Heat Release by Means of Oxygen Consumption 

Measurements,” Fire and Materials, 4:61-65, 1980. 

4. Mulholland, G. W., and Croarkin, C., “Specific Extinction Coefficient of Flame Generated 

Smoke,” Fire and Materials, 24:227–230, 2000. 
LUBRICATING OIL FIRE IN PUMP COMPARTMENT

C-24 

5. NIST NCSTAR 1-5F, Federal Building and Fire Safety Investigation of the World Trade 

Center Disaster: Computer Simulation of the Fires in the World Trade Center Towers, 2005. 

6. NIST SP 1018-5, Fire Dynamics Simulator (Version 5), Technical Reference Guide, Volume 

3, Experimental Validation, 2010. 

7. NUREG-1805, Fire Dynamics Tools (FDTs

) Quantitative Fire Hazard Analysis Methods for 

the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program, 2004. 

8. NUREG-1824 (EPRI 1011999), Verification and Validation of Selected Fire Models for 

Nuclear Power Plant Applications, 2007. 

9. NUREG/CR-6850 (EPRI 1011989), EPRI/NRC-RES Fire PRA Methodology for Nuclear 

Power Facilities, 2005. 

10. NUREG/CR-6931, Cable Response to Live Fire (CAROLFIRE), Volume 3, ThermallyInduced Electrical Failure (THIEF) Model, 2007. 

11. SFPE Handbook of Fire Protection Engineering, 4th edition, 2008. 

C.8 Attachments (on CD) 

1. FDS input file: Pump_Room.fds 

2. MAGIC input file: 

a. Pump_Room.cas 

b. Pump_Room_tighter_wrapping.cas 

c. Pump_Room_thinner_wrapping.cas 

d. Pump_Room_2Doors.cas 

e. Pump_Room_extendedHRR.cas 
D-1 

APPENDIX D 

MOTOR CONTROL CENTER FIRE IN A SWITCHGEAR 

ROOM 

D.1 Modeling Objective 

The calculations described in this appendix estimate the likelihood that a motor control cabinet 

(MCC) fire will damage various cables and an adjacent cabinet within a switchgear room 

(SWGR). 

D.2 Description of the Fire Scenario 

General Description: The SWGR is located in the reactor building for a Boiling Water Reactor 

(BWR). The compartment contains multiple MCCs and some other switchgear cabinets. 

Geometry: The layout of the compartment is shown in Figure D-1. Figure D-2 shows the 

equipment typically contained in the compartment, and Figure D-3 shows the large elevation 

change between the high and low ceiling areas. 

Materials: Property values for the relevant materials are listed in Table 3-1. The SWGR 

boundaries are made of concrete that is at least 0.6 m (2 ft) thick. The cabinet housing is 

1.5 mm (0.06 in) thick steel. 

Cables: The cable trays are filled with cross-linked polyethylene (XPE or XLPE) insulated 

cables with a neoprene jacket. These are considered thermoset (TS) materials. These cables 

have a diameter of approximately 1.5 cm (0.6 in), a jacket thickness of approximately 2 mm 

(0.79 in), 3 conductors, and a mass per unit length of 0.4 kg/m. Tray locations are shown in the 

compartment drawing. These particular cables have been shown to fail when the temperature 

just underneath the jacket reaches approximately 400 °C (750 °F) (NUREG/CR-6931, Vol. 2, 

Table 5.1020). A second criterion for damage is exposure to a heat flux that exceeds 11 kW/m2

(NUREG-1805, Appendix A, Section A.5.4). Damage criteria for the adjacent cabinet are the 

same as for the cable trays because the cables within the cabinet are subjected to similar 

thermal exposure conditions as the steel cabinet housing. 

Fire: A fire originates within a MCC cabinet. The cabinet is closed and contains more than one 

bundle of qualified cable. The fire grows following a “t-squared” curve to a maximum value of 

702 kW in 12 min and remains steady for 8 more minutes, consistent with NUREG/CR-6850 

(EPRI 1011989), Appendix G. After 20 min, the heat release rate (HRR) decays linearly to zero 

in 19 min. A peak fire intensity of 702 kW represents the 98th percentile of the probability 

distribution for HRR in cabinets of this general description. 

The top of the cabinet contains a louvered air vent, 0.6 m (2 ft) long and 0.3 m (1 ft) wide. The 

cabinet is 2.4 m (8 ft) tall. The fire burns within the interior of the cabinet, and the smoke and 

 

20 The cable failure temperature is based on experiments conducted with Cable #14, an XLPE/CSPE, 3 conductor control cable. 
MOTOR CONTROL CENTER FIRE IN A SWITCHGEAR ROOM

D-2 

flames exhaust from this vent, which has an area of 0.18 m2

 (2 ft2) and an effective diameter21 of 

0.48 m (1.6 ft). 

The heat of combustion and product yields for XLPE/neoprene cable are obtained from Table 3-

4.16 of the SFPE Handbook, 4th edition, and are listed in Table D-1. When estimating the 

composition of the fire’s exhaust products, the jacket and insulation material of the cable are 

taken as an equal-parts mixture of polyethylene (C2H4) and neoprene (C4H5Cl), with an effective 

chemical formula of C3H4.5Cl0.5. 

Table D-1. Products of combustion for the MCC fire. 

Parameter Value Source 

Effective Fuel Formula C3H4.5Cl0.5 Combination of polyethylene and neoprene 

Peak HRR 702 kW NUREG/CR-6850 (EPRI 1011989), App. G 

Time to reach peak HRR 720 s NUREG/CR-6850 (EPRI 1011989), App. G

Heat of Combustion 10,300 kJ/kg SFPE Handbook, 4th Ed., Table 3-4.16 

CO2 Yield 0.63 kg/kg SFPE Handbook, 4th Ed., Table 3-4.16 

Soot Yield 0.175 kg/kg SFPE Handbook, 4th Ed., Table 3-4.16 

CO Yield 0.082 kg/kg SFPE Handbook, 4th Ed., Table 3-4.16 

Radiative Fraction 0.53 SFPE Handbook, 4th Ed., Table 3-4.16 

Ventilation: The compartment is normally supplied with three air changes per hour (ACH). 

The supply and return vents are indicated on the drawing. The two doors are normally closed. 

Normal heating, ventilation, and air conditioning (HVAC) operations continue during the fire, and 

the doors remain closed. The volume of the compartment is 882 m3

 (31,150 ft3); thus, three air 

changes per hour is equivalent to a volume flow rate of 0.735 m3

/s. 

 

21 The effective diameter is calculated as ܦ ൌ ඥ4ܣ/ߨ, where ܣ is the area of the vent opening. 
MOTOR CONTROL CENTER FIRE IN A SWITCHGEAR ROOM

D-3 

Figure D-1. Geometry of the MCC/SWGR in a BWR. 
MOTOR CONTROL CENTER FIRE IN A SWITCHGEAR ROOM

D-4 

Figure D-2. Typical electrical cabinet in the lower part of the SWGR. 

Figure D-3. View of the high ceiling space. 
MOTOR CONTROL CENTER FIRE IN A SWITCHGEAR ROOM

D-5 

D.3 Selection and Evaluation of Fire Models 

This section describes the overall modeling strategy, the selection of models, and a discussion 

of the validation exercises justifying the use of these models for this scenario. The discussion 

also separately addresses the prediction of the temperature and heat flux to the cabinet and 

cable targets. 

D.3.1 Temperature Criterion 

The primary temperature criterion of interest for this scenario is the cable temperature in Tray A, 

which is located 0.2 m (8 in) directly above the specified cabinet fire. The Heskestad flame 

height correlation included in the Fire Dynamics Tools (FDTs

) and the Fire-Induced Vulnerability 

Evaluation (FIVE-Rev1) is used to show if the cables in Tray A would be engulfed in the cabinet 

fire flames, and would therefore be expected to fail. 

The hot gas layer (HGL) temperature correlations included in the FDTs

 and FIVE-Rev1 are 

based on compartment fire experiments with a relatively uniform ceiling height. They are also 

based on fires located near floor level without flame impingement on the ceiling. For these 

reasons, the McCaffrey, Quintiere, and Harkleroad (MQH) and Foote, Pagni, and Alvares (FPA) 

temperature correlations are not appropriate for this scenario. Because the zone models 

Consolidated Fire Growth and Smoke Transport Model (CFAST) and MAGIC are designed 

primarily for compartments with relatively flat ceilings, the Fire Dynamics Simulator (FDS) will be 

used as a check on these simpler models. The differing ceiling heights are not an issue for 

FDS; the compartment geometry is input as is, with no need for further simplification. In a case 

like this, it may be convenient to use two rectangular meshes instead of one. The two meshes 

conform well to the actual geometry and enable the calculation to be run in parallel on two 

processors instead of one if desired. 

D.3.2 Heat Flux Criterion 

For this application, the point source radiation model included in the FDTs and FIVE-Rev1 can 

be used to estimate the radiation heat flux to the adjacent cabinet. However, this heat flux 

calculation does not consider the influence of flame extension beneath the ceiling, so it is useful 

primarily for screening purposes. The zone and/or the computational fluid dynamics (CFD) 

model are needed to calculate the heat flux from the HGL in the lower ceiling space if the HGL 

temperature calculation of any model indicates that the temperature of the layer is sufficiently 

high to cause damage. 

D.3.3 Validation 

The principal source of validation data justifying the use of the above-listed fire models for this 

scenario is the U.S. Nuclear Regulatory Commission/Electric Power Research Institute 

(NRC/EPRI) verification and validation (V&V) study documented in NUREG-1824 (EPRI 

1011999). The National Institute of Standards and Technology (NIST) has expanded the 

NRC/EPRI V&V to include the latest versions of CFAST (6.1.1) (Peacock, 2008) and FDS 

(5.5.3) (McGrattan, 2010). Also, CFAST and FDS utilize the cable failure algorithm, THIEF, 

which was developed and validated in NUREG/CR-6931 (Vol. 3). 
MOTOR CONTROL CENTER FIRE IN A SWITCHGEAR ROOM

D-6 

Table D-2 lists various important model parameters and the ranges for which the validation 

study is applicable. Two of the parameters, the Fire Froude Number and the Fire Height to 

Ceiling Height ratio, fall outside the listed validation ranges. The Fire Froude Number is 

essentially a measure of the fire’s heat output relative to its base area. In this example, the fire 

is specified as originating at the top of the cabinet, with the vent opening serving as its base. ܳሶ

כ

for this scenario will be higher than would be calculated if the fire was burning completely 

outside of the cabinet. Thus, the high value of ܳሶ

כ is the result of specifying conditions that will 

produce a more severe fire conditions than would be expected if the fire were to burn partially 

within the cabinet. 

With the fire located on top of a 2.4 m (7.9 ft) high cabinet under a 3.0 m (9.8 ft) high ceiling, the 

flame impinges on the ceiling and consequently falls outside of the NUREG-1824 (EPRI 

1011999) validation range. The extension of the flame beneath the ceiling would have an 

influence on the heat flux to adjacent cabinets, which needs to be addressed. The plume 

correlations used within the spreadsheets and the zone models are not valid when the fire 

impinges on the ceiling. The MQH and FPA compartment temperature correlations do not 

explicitly address fire elevation, but are based on experiments in which the fire source was 

located near floor level; they have not been validated for scenarios like this one, which have 

significant flame impingement on the ceiling. Zone models use plume air entrainment 

correlations in estimating the temperature and depth of the HGL, so they have limited validity for 

scenarios with significant flame impingement. For this reason, FDS is used to check the results 

of the simpler models. 

The FDS Validation Guide (NIST SP 1018) lists two sets of experiments that involve flame 

impingement on the ceiling. The first set, performed in support of the NIST investigation of the 

collapse of the World Trade Center, involved 3 MW heptane spray fires under a 3.8 m (12.5 ft) 

ceiling. The value of ܳሶ

כ was 2.7, and the ratio of flame to ceiling height was 1.2. A second set 

of experiments was performed by the Swedish fire test laboratory SP. The HRR from the 

propane burner was 450 kW, and the burner was elevated 0.65 m off the floor. The burner area 

was only 0.3 m by 0.3 m (1 ft by 1 ft), and ܳሶ

כ was approximately 6. The flame to ceiling height 

ratio was 1.2, but, because the fire was in the corner, the degree of flame impingement was 

enhanced significantly. Predicted HGL temperatures for these experiments were within 10 % of 

the reported measurements. Predicted target temperatures were within 20 %. 

The second important issue in regard to model validation is the two-tiered ceiling. Although 

none of the experiments used in the NRC/EPRI validation study have a similar ceiling 

configuration, Benchmark Exercise #2 of this study provides validation data to evaluate the 

models’ ability to estimate the plume and HGL temperature/depth of smoke and hot gases filling 

a fairly large, open hall with an angled roof. Predicted temperatures were within approximately 

10 % of the reported measurements. 
MOTOR CONTROL CENTER FIRE IN A SWITCHGEAR ROOM

D-7 

Table D-2. Normalized parameter calculations for the MCC fire scenario. 

Quantity Normalized Parameter Calculation 

NUREG1824 

Validation 

Range 

In 

Range? 

Fire Froude 

Number 

ܳሶ

כ ൌ ܳሶ

ߩஶܿ௣ܶஶܦଶ.ହඥ݃

ൌ 702 kW

ሺ1.2 kg/mଷሻሺ1.0 kJ/kg/Kሻሺ293 Kሻሺ0.5ଶ.ହ mଶ.ହሻඥ9.8 m/sଶ ؆ 3.6

0.4 – 2.4 No 

Flame 

Length, 

 ,௙ܮ ൅ ௙ܪ

relative to the 

Ceiling 

௖ܪ ,Height

௙ܮ ൅ ௙ܪ

௖ܪ

ൌ 2.4 m ൅ 2.5 m

3.0 m ؆ 1.6

ܮ ௙ൌ ܦ ቀ3.7 ܳሶ

כଶ/ହ െ 1.02ቁ ൌ 0.48 m ሺ3.7 ൈ 3.6଴.ସ െ 1.02ሻ ؆ 2.5 m

0.2 – 1.0 No 

Ceiling Jet 

Radial 

Distance,rcj, 

relative to the 

Ceiling 

Height, Hc

N/A – There are no targets like sprinklers or smoke detectors under 

consideration in this example. 1.2 – 1.7 N/A 

Equivalence 

Ratio, φ, as 

an indicator 

of the 

Ventilation 

Rate 

߮ ൌ

ܳሶ

∆ܪOమ ݉ሶ Oమ

ൌ 702 kW

13,100 kJ/kg ൈ 0.2 kg/s ؆ 0.3

݉ሶ Oమ ൌ 0.23 ߩஶܸሶ ൌ 0.23 ൈ 1.2 kg/mଷ ൈ 0.735 mଷ/s ؆ 0.2 kg/s

0.04 – 0.6 Yes 

Compartment 

Aspect Ratio 

(Lower | 

Upper) 

ܮ

௖ܪ

ൌ 8.5 m

3.0 m ؆ 2.8 ; 

ܹ

௖ܪ

ൌ 8.5 m

3.0 m ؆ 2.8

ܮ

௖ܪ

ൌ 8.6 m

9.1 m ؆ 0.9 ; 

ܹ

௖ܪ

ൌ 8.5 m

9.1 m ؆ 0.9 0.6 – 5.7 Yes 

Target 

Distance, r, 

relative to the 

Fire 

Diameter, D

ݎ

ܦ ൌ 1.1 m

0.5 m ؆ 2.2 2.2 – 5.7 Yes 

Notes: 

(1) The effective diameter of the fire is determined from the formula, ܦ ൌ ඥ4ܣ/ߨ, 

where ܣ is the area of the vent on the cabinet. 

(2) The Flame Length, ܪ ൅ ௙ܮ௙, is the sum of the height of the fire from the floor and 

the fire’s calculated flame length. 

(3) The ceiling height, ܪ௖, is the lower of the two ceiling heights. 

 
MOTOR CONTROL CENTER FIRE IN A SWITCHGEAR ROOM

D-8 

D.4 Estimation of Fire-Generated Conditions 

This section describes how each of the models is used in the analysis, including specific 

approximations unique to the particular model. 

D.4.1 Algebraic Models 

Fire: The FDTs use a steady-state HRR in both the flame height and radiation heat flux 

calculation. A constant HRR of 702 kW is used for both. A fire diameter of 0.48 m (1.6 ft) is 

calculated from the effective vent area atop the cabinet of 0.18 m2

 (2 ft2). Table D-2 indicates 

that the Heskestad flame height correlation yields a calculated flame height of 2.5 m (8.2 ft). 

Consequently, the cables located directly above the cabinet would be engulfed in flame and 

would therefore be expected to fail. This flame height calculation also shows that there would 

be significant flame extension beneath the ceiling, which is located just 0.6 m (2 ft) above the 

base of the fire. 

The point source radiation model predicts the peak heat flux to the side of the adjacent cabinet, 

which is approximately 1.1 m (3.6 ft) from the center of the vent on top of the burning cabinet: 

ሶݍ

ᇱᇱ ൌ ߯௥ ܳሶ

4ߨ ݎଶ ൌ 0.53 ൈ 702 kW

4ߨ ൈ ሺ1.1 ݉ሻଶ ؆ 24.5 kW/mଶ (D-1)

This estimate does not include any contributions to the heat flux by the HGL or by the flame 

extension beneath the ceiling. However, it does indicate that the heat flux to the adjacent 

cabinet could exceed the critical heat flux by a relatively large margin. Consequently, this 

scenario would warrant more detailed analysis with either a zone model or a CFD model. 

D.4.2 Zone Models 

Geometry: Zone fire models subdivide the space of interest into one or more compartments 

connected by vents. With CFAST, the single, large compartment is modeled as two adjacent 

compartments, connected by a vertical vent. Figure D-4 and Figure D-5 show the geometry and 

input parameters of the CFAST calculation. 

Fire: Following guidance in NUREG/CR-6850 (EPRI 1011989), the fire is placed near the top of 

the cabinet. It is positioned directly below Cable Tray A to maximize exposure. The current 

version of CFAST only uses the plume centerline temperature. The specified fire area, HRR, 

and species yields are input directly into the model. Figure D-6 shows the fire inputs for the 

CFAST calculation. 

Cables: CFAST uses the Thermally-Induced Electrical Failure (THIEF) methodology developed 

as part of the Cable Response to Live Fire (CAROLFIRE) program (NUREG/CR-6931, Vol. 3). 

The thermal conductivity and specific heat are fixed constants. Cable density is calculated from 

the specified mass per unit length, ݉ᇱ

, and the cross-sectional area of the cable, ܣ: 

ൌ ߩ

݉ᇱ

ܣ ൌ 0.4 kg/m

ߨ ൈ ሺ0.015/2ሻଶ mଶ ؆ 2264 kg/mଷ (D-2)
MOTOR CONTROL CENTER FIRE IN A SWITCHGEAR ROOM

D-9 

Electrical functionality is lost when the temperature just inside of the 2 mm (0.08 in) jacket 

reaches 400 °C (752 °F). Figure D-7 shows the target inputs for the CFAST calculation. 

Figure D-4. Smokeview rendering of the geometry of two-height ceiling SWGR, as 

modeled in CFAST. 
MOTOR CONTROL CENTER FIRE IN A SWITCHGEAR ROOM

D-10 

Figure D-5. CFAST inputs for compartment geometry for SWGR. 

Figure D-6. CFAST fire inputs for two-height ceiling SWGR scenario. 
MOTOR CONTROL CENTER FIRE IN A SWITCHGEAR ROOM

D-11 

Figure D-7. CFAST target inputs for two-height ceiling SWGR scenario. 

Ventilation: The two individual compartments used to model the entire room are connected by 

a single large vent. Although the size of this vent relative to the compartment size is not typical 

of a zone model application, the simple two-compartment geometry of the space and the more 

dominant mechanical ventilation flow from one side of the SWGR to the other should minimize 

any uncertainty in the calculation resulting from the large connecting vent. Mechanical 

ventilation is included at the specified height and with the specified volume flow applied to the 

single supply (in the low-ceiling space) and return (in the high-ceiling space). Additionally, since 

zone fire models use compartments that are completely sealed unless otherwise specified, a 

typical leakage vent, 13 mm (0.5 in) in height, is included at the bottom of each closed doorway 

to reflect the fact that the doorways are not totally airtight. Figure D-8 shows the CFAST inputs 

for these natural vents. 
MOTOR CONTROL CENTER FIRE IN A SWITCHGEAR ROOM

D-12 

Figure D-8. CFAST inputs for vents connections in two-height ceiling SWGR scenario. 

D.4.3 CFD Model 

Geometry: The entire compartment is included in the computational domain. Multiple meshes 

are used, one for the low-ceiling space and three for the high-ceiling space. The FDS User’s 

Guide (NIST SP 1019) contains detailed instructions for running the simulation on multiple 

computers. The concrete walls are essentially the boundaries of these two meshes. The 

electrical cabinets and cables are included in the simulation as simple rectangular solids, and 

their dimensions have been approximated to the nearest 10 cm (4 in). There is no attempt to 

model the details of either the cable trays or cabinets because the grid resolution is not fine 

enough. This is appropriate because the cables and cabinets are merely targets for which it is 

sufficient to know their bulk thermal properties. An FDS/Smokeview rendering of the scenario is 

shown in Figure D-9. 

The numerical mesh consists of uniform grid cells, 10 cm (4 in) on a side. Even with this 

relatively fine grid, there is considerable uncertainty in the exact nature of the fire relative to the 

cabinet and the cables just above. This uncertainty mainly has to do with specifying that the fire 

originates at the top of the cabinet rather than from within. 

Fire: The fire burns over an area of 0.6 m (2 ft) by 0.3 m (1 ft) on top of the cabinet, with a 

maximum HRR per unit area of 3,900 kW/m2

, yielding a peak HRR of 702 kW. 

Cables: The cables are modeled as 1.5 cm (0.6 in) cylinders with uniform thermal properties. 

Following the THIEF methodology in NUREG/CR-6931, Vol. 3, electrical functionality is lost 
MOTOR CONTROL CENTER FIRE IN A SWITCHGEAR ROOM

D-13 

when the temperature just inside of the 2 mm (0.08 in) jacket reaches 400 °C (752 °F). Note 

that no attempt is made in the simulation to predict ignition and spread of the fire over the 

cables, which is why the in-depth heat penetration calculation is focused on a single cable. For 

this scenario, at least one cable per tray is expected to be relatively free of its neighbors and 

would heat up more rapidly than those buried deeper within the pile. This is conservative and 

simplifies the heat transfer calculation. 

Ventilation: Three ACH are achieved with a volume flow of 0.735 m3

/s applied to the single 

supply and return vents. No other penetrations are included in the model. 

Figure D-9. FDS/Smokeview representation of the MCC/SWGR scenario. 
MOTOR CONTROL CENTER FIRE IN A SWITCHGEAR ROOM

D-14 

D.5 Evaluation of Results 

The purpose of the calculations described above is to predict if and when various components 

within the compartment become damaged due to a fire in the MCC. XLPE cables are expected 

to be damaged when their internal temperature exceeds 400 °C (750 °F) or the exposing heat 

flux exceeds 11 kW/m2

. Damage criteria for the adjacent cabinet are equivalent to those for the 

cables because the cables within the cabinet come in contact with the heated metal housing, 

and are therefore exposed to similar thermal conditions. The targets of interest are three cable 

trays, labeled A, B, and C, and a single electrical cabinet adjacent to the burning MCC (Figure 

D-1). 

Table D-1 summarizes the model predictions of the target temperature and heat flux. Chapter 4 

describes how to calculate the probability of exceeding the critical value. The purpose of the 

model summary is to readily identify the most likely targets to be damaged, and the model 

inputs underlying that assessment. 

Table D-3. Summary of the model predictions of the MCC fire scenario. 

Model Bias 

ࢾ ,Factor

Standard 

ࡹ෥࣌ ,Deviation

Target Predicted 

Value 

Critical 

Value 

Probability of 

Exceeding 

Surface Temperature (°C), Initial Value = 20 °C 

CFAST 1 0.27 Cabinet 390 400 0.460 

FDS 1.02 0.13 170 400 0.000* 

CFAST 1 0.27 Cable A 705 400 0.950 

FDS 1.02 0.13 620 400 0.997 

CFAST 1 0.27 Cable B 305 400 0.112 

FDS 1.02 0.13 280 400 0.000 

CFAST 1 0.27 Cable C 40 400 0.000 

FDS 1.02 0.13 65 400 0.000 

Heat Flux (kW/m2) 

CFAST 0.81 0.47 Cabinet 24.3 11 0.911 

FDS 0.85 0.22 6.0 11 0.006* 

CFAST 0.81 0.47 Cable A 104 11 0.974 

FDS 0.85 0.22 75.0 11 1.000 

CFAST 0.81 0.47 Cable B 15.8 11 0.823 

FDS 0.85 0.22 23.0 11 0.997 

CFAST 0.81 0.47 Cable C 0.2 11 0.000 

FDS 0.85 0.22 2.5 11 0.000 

* These results require closer scrutiny. See discussion below. 

D.5.1 Damage to Cabinet 

The predicted heat flux to and temperatures of the cabinet adjacent to the MCC are shown in 

Figure D-10. The cabinet is located approximately 1.1 m (3.6 ft) from the center of the flaming 

vent. The point source radiation calculation included in CFAST and the FDTs

 predicts a peak 

heat flux of 24.5 kW/m2 to the nearest point on the cabinet. FDS predicts the peak heat flux 
MOTOR CONTROL CENTER FIRE IN A SWITCHGEAR ROOM

D-15 

(and resulting surface temperature) to be significantly lower because the fire is partially 

obscured by the overhead cable tray and the burning MCC. FDS also accounts for the 

orientation of the adjacent cabinet top and side relative to the fire’s location. However, the heat 

flux to the top of the MCC near the adjacent cabinet is substantially greater than the critical 

value, and a small change in the position of the fire could result in a much higher heat flux to the 

target. Given the sensitivity of the predicted heat flux and surface temperature to a minor 

change in the fire dynamics, the FDS prediction for the cabinet ought to be discounted in this 

case. 

Figure D-10. Heat flux and temperature predictions for the adjacent cabinet. 

D.5.2 Cable Damage Based on Temperature Alone 

The predicted cable temperatures for the three trays are shown in Figure D-11. CFAST and 

FDS estimate cable temperatures using the THIEF methodology (NUREG/CR-6931, Vol. 3). 

Both models predict that the cables in Tray A are likely to fail. 

Neither model predicts that the cables in Tray B will reach the failure temperature of 400 °C 

(750 °F), but the CFAST prediction of 300 °C (572 °F) suggests that there is a 9% probability 

that the cable temperature could be as high as the critical value. Note that these predictions are 

sensitive to the exact location of the target cable within the tray, its view of the fire, and the HGL 

temperature. In this case, the cables in Tray B are heated primarily by convection and radiation 

from the HGL. Given that the HRR is the most important parameter controlling the temperature 

of the HGL, how much would the HRR have to increase to increase the CFAST prediction from 

300 °C (572 °F) to 400 °C (752 °F)? Table 4-3 indicates that the rise in the HGL temperature is 

proportional to the HRR to the 2/3 power. Following the methodology in Section 4.4.1, in order 

to increase the predicted HGL temperature by 100 °C (212 °F), the peak HRR, ܳሶ, must increase 

by approximately: 

∆ܳሶ ൌ 3

2ܳሶ ∆ܶ

ܶെܶ଴

ൌ 3

2 702 kW ൈ 

100 °C

300 °C െ 20 °C ؆ 376 kW (D-3) 

Both FDS and CFAST predicted cable temperatures for Tray C indicate that the cables are 

unlikely to fail. 

0

5

10

15

20

25

30

0 600 1200 1800 2400 3000 3600

Heat Flux (kW/m2)

Time (s)

Cabinet Heat Flux

CFAST

FDS

FDTs

0

100

200

300

400

500

0 600 1200 1800 2400 3000 3600

Temperature (C)

Time (s)

Cabinet Temperature

CFAST

FDS
MOTOR CONTROL CENTER FIRE IN A SWITCHGEAR ROOM

D-16 

D.5.3 Cable Damage Based on Incident Heat Flux 

The predictions of heat flux to the cables in the three trays are shown in Figure D-11. The 

critical value is 11 kW/m2. Flame height correlations predict that the fire will impinge on Tray A, 

and both CFAST and FDS indicate that the heat flux to these cables would be well in excess of 

the critical value. 

Figure D-11. Summary of the cable temperature and heat flux predictions for the 

MCC/SWGR. 

0

200

400

600

800

0 600 1200 1800 2400 3000 3600

Temperature (C)

Time (s)

Cable A Temperature

CFAST

FDS

0

20

40

60

80

100

120

0 600 1200 1800 2400 3000 3600

Heat Flux (kW/m2)

Time (s)

Cable A Heat Flux

CFAST

FDS

0

100

200

300

400

0 600 1200 1800 2400 3000 3600

Temperature (C)

Time (s)

Cable B Temperature

CFAST

FDS

0

5

10

15

20

25

0 600 1200 1800 2400 3000 3600

Heat Flux (kW/m2)

Time (s)

Cable B Heat Flux

CFAST

FDS

0

20

40

60

80

100

0 600 1200 1800 2400 3000 3600

Temperature (C)

Time (s)

Cable C Temperature

CFAST

FDS

0.0

0.5

1.0

1.5

2.0

2.5

0 600 1200 1800 2400 3000 3600

Heat Flux (kW/m2)

Time (s)

Cable C Heat Flux

CFAST

FDS
MOTOR CONTROL CENTER FIRE IN A SWITCHGEAR ROOM

D-17 

For the cables in Tray B, both FDS and CFAST indicate a relatively high probability of failure, 

based partly on the fact that both models have been shown to under-predict heat flux in the 

NRC/EPRI fire model validation study (NUREG-1824). 

For the cables in Tray C, none of the models predicts a heat flux that approaches the critical 

value. Note that the significant difference between FDS and CFAST is based on the fact that 

FDS outputs the maximum heat flux and cable temperature over the entire tray of cables, 

whereas CFAST predicts these values at a single target location. 

D.6 Conclusion 

The purpose of the calculations in this example is to predict if and when various components 

within a compartment will become damaged due to a fire in the MCC. The fire model analyses 

performed for this scenario indicate that the fire would damage the cables in Tray A because all 

the models (FDTs

, CFAST, FDS) predict that the flames would directly impinge on the cables 

themselves. 

 CFAST and FDS predict that the cables in Tray B are likely to be damaged based on the 

heat flux criterion. However, neither model predicts that the interior cable temperatures are 

likely to be high enough to cause failure. 

 Neither FDS nor CFAST predicts that the cables in Tray C would be damaged. 

 A point source heat flux analysis indicates that the adjacent cabinet housing would be 

exposed to a heat flux that would cause damage. Even though FDS does not predict 

damage, its predictions of heat flux to surfaces very near the adjacent cabinet are 

sufficiently high to cast doubt on the conclusion that the cabinet would not be damaged. 

Small changes in the positions of various obstructions could easily change the predicted 

heat flux by an order of magnitude. Even though the point source method tends to overpredict the heat flux to targets close to the fire, there is too much uncertainty in the 

geometric configuration to accept the validity of the more detailed calculation. 

D.7 References 

1. NIST SP 1018-5, Fire Dynamics Simulator (Version 5), Technical Reference Guide, Volume 

3, Experimental Validation, 2010. 

2. NIST SP 1019, Fire Dynamics Simulator (Version 5) User’s Guide, 2007. 

3. NIST SP 1086, CFAST – Consolidated Model of Fire Growth and Smoke Transport (Version 

6), Software Development and Model Evaluation Guide, 2008. 

4. NUREG-1805, Fire Dynamics Tools (FDTs

) Quantitative Fire Hazard Analysis Methods for 

the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program, 2004.

5. NUREG-1824 (EPRI 1011999), Verification and Validation of Selected Fire Models for 

Nuclear Power Plant Applications, 2007.

6. NUREG/CR-6850 (EPRI 1011989), EPRI/NRC-RES Fire PRA Methodology for Nuclear 

Power Facilities, 2005. 

7. NUREG/CR-6931, Cable Response to Live Fire (CAROLFIRE), Volume 2: Cable Fire 

Response Data for Fire Model Improvement, 2007. 

8. NUREG/CR-6931, Cable Response to Live Fire (CAROLFIRE), Volume 3: ThermallyInduced Electrical Failure (THIEF) Model, 2007.
MOTOR CONTROL CENTER FIRE IN A SWITCHGEAR ROOM

D-18 

9. SFPE Handbook of Fire Protection Engineering, 4th edition, 2008. 

D.8 Attachments (on CD) 

1. FDS input file: Switchgear_Room_MCC.fds 

2. CFAST input files: 

a. MCC in Switchgear.in 
E-1 

APPENDIX E 

TRANSIENT FIRE IN CABLE SPREADING ROOM 

E.1 Modeling Objective 

The calculations in this appendix estimate the impact that a fire in a trash receptacle inside a 

Cable Spreading Room (CSR) would have on safe-shutdown cables. These calculations are 

part of a larger fire analysis described in Chapter 11 of NUREG/CR-6850 (EPRI 1011989), 

Volume 2, “Detailed Fire Modeling (Task 11).” The CSR contains a large quantity of redundant 

instrumentation and control cables needed for plant operation. Transient combustibles have 

been identified as a possible source of fire that may impact the cables. The purpose of the 

calculation is to analyze this condition and determine whether the cable targets will fail, and, if 

so, at what time failure occurs. The time to smoke detector activation is also estimated. The 

calculation will provide information for a decision on the hazard and risk for this scenario. 

E.2 Description of the Fire Scenario 

General Description: The CSR contains a large quantity of redundant instrumentation and 

control cables needed for plant operation. The cables are installed in either ladder-back trays or 

conduits. 

Geometry: Figure E-1 illustrates the geometry of the CSR; Figure E-2 shows a photograph of 

the CSR. In addition to cables, the CSR contains a fully enclosed computer compartment, 

ductwork, and large structural beams. There is no high- or medium-voltage equipment 

(switchgears or transformers) in the compartment. As shown in Figure E-3, the top 2.2 m 

(7.2 ft) of the compartment is filled with cable trays containing cables, or ductwork, or large 

structural beams. 

Construction: The walls, floor, and ceiling of the CSR are constructed of normal-weight 

concrete. The ductwork is made of 2 mm (0.08 in) thick steel. 

Materials: Thermal properties of various materials in the compartment have been taken from 

Table 2-3 of NUREG-1805 and are listed in Table 3-1. The important cables for this calculation 

are located in the third and sixth trays above the fire source, which are filled with PE-insulated, 

PVC-jacketed control cables important to safe shutdown. These cables have a diameter of 

approximately 1.5 cm (0.6 in), a jacket thickness of approximately 1.5 mm (0.06 in), and 7 

conductors. The cable mass per unit length is 0.4 kg/m. There are approximately two rows of 

cables per tray. These cables are damaged when the internal cable temperature reaches 

205 °C (400 °F) or the exposure heat flux reaches 6 kW/m2

 (NUREG-1805, Appendix A). Cable 

insulation thermal properties are as follows: the density is 1380 kg/m3

, the thermal conductivity 

is 0.192 W/m/K, and the specific heat is 1.289 kJ/kg-K (NUREG/CR-6850, Volume 2, 

Appendix R). The copper in the cables has the following properties: the density is 8954 kg/m3

, 

the thermal conductivity is 386 W/m/K, and the specific heat is 0.3831 kJ/kg-K (SFPE 

Handbook, 4th Edition). The copper mass fraction of the cable is 0.67. 
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-2 

The bottom cable tray is protected on the lower surface by a solid metal barrier. The bottom 

and side surfaces of all cable trays in the CSR are of solid metal construction; top surfaces are 

open. The tray steel thickness is 3 mm (0.12 in). 

Detection System: Smoke detectors are located on the ceiling at locations shown in Figure 

E-1. The detectors are UL-listed with a nominal sensitivity of 4.9 %/m. 

Suppression System: A total flooding CO2 fire suppression system is initiated automatically by 

cross-zoned smoke detection in the compartment, or can be operated manually. In order to 

maintain a proper concentration of suppression agent, CO2 discharge causes fire dampers to 

close and mechanical ventilation fans to stop. Activation of the CO2 system is not modeled in 

this example. 

Ventilation: The CSR has two doors on the east wall that are normally closed. Each door is 

2 m (6.6 ft) wide by 2 m (6.6 ft) tall, with a 1 cm (0.4 in) gap along the floor. Standard procedure 

calls for an operator to investigate the fire within 600 s (10 min) of an alarm condition. For this 

reason, the door that is farthest from the fire is opened for this investigation. 

There are two supply and two return vents for mechanical ventilation, each with an area of 

0.25 m2

 (2.7 ft2). The total air supply rate is 1.4 m3/s (3,000 cfm). All vents are located 2.4 m 

(8 ft) above the floor. Upon smoke detector activation, the mechanical ventilation fans stop and 

the dampers close. 

Fire: A trash fire ignites within a cylindrical steel waste bin, 0.8 m (2.6 ft) high and 0.6 m (2.0 ft) 

in diameter, containing 5 kg (11 lb) of trash. The heat release rate (HRR) of the transient fire is 

estimated using NUREG/CR-6850 (EPRI 1011989). The fire grows following a “t-squared” 

curve to a maximum value of 317 kW (the 98th percentile value from Table G-1 in NUREG/CR6850 (EPRI 1011989)) in 480 s (consistent with NUREG/CR-6850 (EPRI 1011989) Supplement 

1 for a transient fire growth rate contained within a trash can). The fire burns at its maximum 

HRR value until the trash is consumed. To determine the duration of the fire, the total energy of 

the fuel, ܳ, is calculated as the product of the fuel mass and the heat of combustion: 

(5 kg)×(30,400 kJ/kg) = 152,000 kJ. The heat of combustion is described below. The time to 

consume the fuel is found by integrating the heat release rate over the time of the burn: 

ܳ ؠ 152,000 kJ ൌ න ܳ௣

ሶ ൬ ݐ

480൰

ସ଼଴ ଶ

଴

݀ݐ ൅ න ܳሶݐ݀ ௣

௧೑

ସ଼଴ ൌ 317 kW ቆ480 s

3 ൅ ൫ݐ ௙െ 480 s൯ቇ (E-1) 

Here, ܳሶ

௣ is the peak HRR of 317 kW, which is reached following a t-squared growth curve in 

480 s. Solving for ݐ ௙yields a total burning time of 799 s, which is rounded up to 800 s. 

While the exact composition of the trash is unknown, typical waste at the plant includes wood 

scraps and polyethylene protective suits. For this scenario, the trash is specified as being 

comprised of equal parts of each. The radiative fraction22 and product yields, like the heat of 

combustion, are taken to be averages of values for red oak and polyethylene (SFPE Handbook, 

4th ed., Table 3-4.16) and shown in Table E-1. For the purpose of modeling, the fuel molecule is 

specified as C4H7O2.5. 

 

22 The fraction of the fire’s total energy emitted as thermal radiation. 
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-3 

Table E-1. Products of combustion for CSR fire. 

Parameter Value Source 

Effective Fuel Formula C4H7O2.5 Specified 

Peak HRR 317 kW NUREG/CR-6850 (EPRI 1011989), App. G 

Time to reach peak HRR 480 s NUREG/CR-6850 (EPRI 1011989), App. G 

Heat of Combustion 30,400 kJ/kg SFPE Handbook, 4th ed., Table 3-4.16 

CO2 Yield 2.0 kg/kg SFPE Handbook, 4th ed., Table 3-4.16 

Soot Yield 0.038 kg/kg SFPE Handbook, 4th ed., Table 3-4.16 

CO Yield 0.014 kg/kg SFPE Handbook, 4th ed., Table 3-4.16 

Radiative Fraction 0.40 SFPE Handbook, 4th ed., Table 3-4.16 
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-4 

Figure E-1. Geometry of the CSR.
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-5 

Figure E-2. Photograph of the CSR used for analysis. Note that the cables are located in 

the trays in the overhead. 

Figure E-3. Geometric detail of the CSR. 
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-6 

E.3 Selection and Evaluation of Fire Models 

This section discusses the overall modeling strategy. In particular, it describes the process of 

model selection, including a discussion of the validity of these models for the given fire scenario. 

This scenario is a typical application of both zone models and computational fluid dynamics 

(CFD) models. With a single fire contained within a rectangular compartment, the application is 

straightforward. The general strategy is to use a plume correlation to estimate temperature at 

the height of the important cables. If this result indicates that the cables are likely to fail, a more 

detailed estimate of cable temperature will be made with zone and CFD models. 

Cable failure is typically judged on both elevated temperature and heat flux criteria. These 

cables are damaged when the internal cable temperature reaches 205 °C (400 °F) or the 

exposure heat flux reaches 6 kW/m2

 (NUREG-1805, Appendix A). 

E.3.1 Temperature Criterion 

The algebraic models are used in this scenario to estimate the flame height and plume 

temperatures from the transient trash can fire to determine whether the overhead cable trays 

would be damaged by the trash fire. The Foote, Pagni, and Alvares (FPA) correlation is used to 

estimate the average hot gas layer (HGL) temperature that would result from the trash fire 

alone; this analysis does not consider either the potential ignition of cable trays or their potential 

contribution to the fire HRR. 

The Consolidated Fire Growth and Smoke Transport Model (CFAST) and the Fire Dynamics 

Simulator (FDS) are used to estimate damage to the overhead cable trays and development of 

elevated temperature and heat flux from the fire and any ignited overhead cables to estimate 

damage to adjacent cables. CFAST imposes time-dependent conditions on the cable trays, but 

uses a point source for radiation from the fire sources. FDS will spread the fire in a more 

realistic way, which should provide more accurate estimates of temperature and heat flux to 

adjacent cables. 

E.3.2 Heat Flux Criterion 

CFAST and FDS are used to estimate heat flux to the overhead cable. The heat flux calculation 

in CFAST includes the radiation from the fire, upper and lower gas layers, and bounding 

surfaces, as well as the convection from nearby gases. Radiation from the fire sources uses a 

point source for the radiation calculation. 

FDS models the fire in much the same way as the zone models, with the fire at the top of the 

trash receptacle. However, because it is a CFD model, FDS can estimate local conditions at 

the specific location of the target cables. 

E.3.3 Validation 

NUREG-1824 (EPRI 1011999) contains experimental validation results for CFAST and FDS that 

are appropriate for this scenario. These experiments include ventilation effects on, heat fluxes 

to, and temperatures of various targets, particularly cables. Fire sizes in these experiments 
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-7 

bound those used in this scenario. For CFAST, the Software Development and Model 

Evaluation Guide, NIST SP 1086, includes updated validation results for the newest version of 

the model used for this calculation. This includes all of the validation comparisons from 

NUREG-1824 (EPRI 1011999), plus additional comparisons for experiments not included in the 

U.S. Nuclear Regulatory Commission (NRC) guide. Plume temperature calculations have been 

validated for a broad range of fire sizes and distances above the fire source in NIST SP 1086. 

Also, CFAST and FDS use the cable failure algorithm, THIEF, developed and validated in 

NUREG/CR-6931 (Vol. 3). 

Table 2-5 of Volume 1 of NUREG-1824 (EPRI 1011999) lists various important model 

parameters and the ranges for which the validation study is applicable. Table E-2 below lists 

the values of these parameters for this fire scenario, along with their ranges of applicability. 

Of these parameters, only the compartment aspect ratio is outside the range of tests included in 

NUREG-1824 (EPRI 1011999). In this scenario, the compartment width to height ratio is well 

within limits, but the length to height ratio is higher than those included in NUREG-1824 (EPRI 

1011999). For a zone model, this “longer than typical” compartment is mainly a concern early in 

the fire development, before a reasonably uniform layer has formed. Thus, predictions of 

events that occur early in the fire (such as smoke detection) may be expected to have a higher 

uncertainty if they are located farther from the fire source than those that occur later in the fire 

(such as ignition of cables above the initiating fire source) once the fire is more fully developed. 

For this scenario, smoke detectors are included throughout the compartment, but the primary 

ones of concern are those which would naturally respond faster (i.e., those nearest the fire). 

 
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-8 

Table E-2. Normalized parameters and their ranges of applicability to NUREG-1824. 

Quantity Normalized Parameter Calculation 

NUREG1824 

Validation 

Range 

In 

Range? 

Fire Froude 

Number 

ܳሶ

כ ൌ ܳሶ

ߩஶܿ௣ܶஶܦଶ.ହඥ݃

ൌ 317 kW

ሺ1.2 kg/mଷሻሺ1.0 kJ/kg/Kሻሺ293 Kሻሺ0.6ଶ.ହ mଶ.ହሻඥ9.8 m/sଶ ؆ 1.0

0.4 – 2.4 Yes 

Flame Length, 

Lf, relative to the 

Ceiling Height, 

Hc

௙ܮ ൅ ௙ܪ

௖ܪ

ൌ 0.8 m ൅ 1.6 m

4.0 m ൌ 0.6

ܮ ௙ൌ ܦ ቀ3.7 ܳሶ

כଶ/ହ െ 1.02ቁ ൌ 0.6 m ሺ3.7 ൈ 1.0଴.ସ െ 1.02ሻ ؆ 1.6 m

0.2 – 1.0 Yes 

Ceiling Jet 

Radial 

Distance,rcj, 

relative to the 

Ceiling Height, 

Hc

N/A – Ceiling jet targets are not included in simulation. 1.2 – 1.7 N/A 

Equivalence 

Ratio, φ, as an 

indicator of the 

Ventilation Rate 

߮ ൌ

ܳሶ

∆ܪOమ ݉ሶ Oమ

ൌ 317 kW

13,100 kJ/kg ൈ 0.4 kg/s ؆ 0.06

݉ሶ Oమ ൌ 0.23 ߩஶܸሶ ൌ 0.23 ൈ 1.2 kg/mଷ ൈ 1.4 mଷ/s ؆ 0.4 kg/s

0.04 – 0.6 Yes 

Compartment 

Aspect Ratio 

ܮ

௖ܪ

ൌ 40 m

4.0 m ൌ 10

ܹ

௖ܪ

ൌ 18.5 m

4.0 m ؆ 4.6 0.6 – 5.7 No 

Target Distance, 

r, relative to the 

Fire Diameter, D

ݎ

ܦ ൌ 2.3 m

0.6 m ؆ 3.8 2.2 – 5.7 Yes 

Notes: 

(1) The “Fire Height,” ܪ ൅ ௙ܮ௙, is the sum of the height of the fire from the floor and 

the fire’s flame length. 

 
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-9 

E.4 Estimation of Fire-Generated Conditions 

This section provides details specific to each model. 

E.4.1 Algebraic Models 

General: The general approach to using the algebraic models for this scenario is to first 

calculate the flame height of the transient trash fire to determine whether the flame reaches one 

or more of the overhead cable trays, then to calculate the plume temperatures from the trash 

fire to determine which of the overhead cable trays would be damaged by the trash fire alone. 

The general scenario is depicted schematically in Figure E-4. 

Figure E-4. Schematic diagram of transient trash fire in CSR (not to scale). 

The first step to estimate the fire-generated conditions using algebraic models is to determine 

whether the cables in the cable trays located directly above the trash fire are likely to be 

damaged and potentially ignited by the trash fire. As shown in Figure E-3, the top of the trash 

receptacle is located at an elevation of 0.8 m (2.6 ft), and the lowest overhead cable tray is 

located at an elevation of 1.8 m (5.9 ft), which is 1.0 m (3.3 ft) above the top of the trash 

receptacle. As shown in Table E-2, the flame length of the cabinet fire is calculated to be 1.6 m 

(5.2 ft) at the peak heat release rate of 317 kW, so this empirical correlation for flame length can 

be used to confirm that at least some of the overhead cables would likely be damaged in this 

scenario. However, due to the metal barrier on the bottom of the lowest cable tray, algebraic 

models cannot be used to predict whether the cables in the lowest cable tray would ignite. 

The next step is to calculate the fire plume temperatures that develop from the trash fire to 

determine whether cable trays A or B located above the trash fire would be damaged by the 

trash fire alone. The Heskestad plume temperature correlation included in the Fire Dynamics 

Tools (FDTs

) and the Fire-Induced Vulnerability Evaluation (FIVE-Rev1) was used to calculate 

the plume centerline temperature above the trash fire. The results, shown in Figure E-5, show 

that the plume temperature of all the cable trays would exceed the cable damage threshold 

temperature of 205 °C (400 °F). However, the Heskestad plume temperature correlation is 

based on an unobstructed plume. The obstruction caused by the position of the cable trays 

within the fire plume would alter the actual fire plume entrainment and temperatures. 

Nonetheless, these results demonstrate that the potential for damage and ignition of the cable 

trays located above the transient trash fire warrants more detailed analysis. 

Tray A

Tray B

Bottom

Smoke 

Detector

Air Supply 

(2 Vents)

Air Return 

(2 Vents) 
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-10 

Figure E-5. Plume temperatures at cable trays located above a transient trash fire. 

The FPA forced ventilation correlation is used to estimate the average HGL temperature of the 

CSR resulting only from the transient trash fire, based on the parameters described in the 

following subsections. 

Geometry: The FPA correlation requires room dimensions to be specified in terms of length, 

width, and height. For this example, the selected compartment is a rectangular parallelepiped, 

as shown in Figure E-1, so its length, width, and height are specified directly. 

Fire: As applied to this scenario, the FPA correlation is used with the time-dependent HRR 

specified for the transient trash fire. This HRR history is shown in Figure E-6. 

Materials: The walls, ceiling, and floor are all specified as concrete, with the thermal properties 

specified in Table 3-1. 

Ventilation: The ventilation rate in the smoke purge mode is 1.4 m3

/s (3,000 cfm). This value 

is used as a direct input parameter in the FPA correlation. 

Table E-3. Summary of input parameters for FPA analysis of CSR scenario. 

Parameter Value Source 

Room height (H) 4.0 m Figure E-1 

Room length (L) 40.0 m Figure E-1 

Room width (W) 18.5 m Figure E-1 

Room boundary material Concrete Figure E-1 See Table 3-1 for properties. 

Mech. Ventilation rate (ܸሶ) 1.4 m3

/s From scenario description 

Fire elevation (Hf) 0.8 m From scenario description 

Ambient temperature (Ta) 20°C Specified 

Fire parameters See Table E-1 

0

200

400

600

800

1000

1200

1400

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

Plume temperatures ‐ Heskestad correlation

Bottom

Tray A

Tray B
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-11 

Temperature: The FPA HGL temperature correlation for mechanically ventilated spaces is 

included in both the FDTs

 and FIVE-Rev1. The FPA results for the trash fire alone are shown in 

Figure E-6, based on the input parameters specified in Table E-3 and the HRR history shown in 

Figure E-6. These results show that, for the specified parameters, the average HGL 

temperature reaches a maximum of approximately 49 °C (120 °F) at 800 seconds, based on the 

peak trash fire HRR of 317 kW. These results show that cables in adjacent cable trays would 

not be damaged by the trash can fire alone. However, further analysis is required to determine 

the potential impact of overhead cable ignition on the potential for damage to cables in the 

adjacent cable trays. CFAST and FDS are used to perform this more detailed analysis. 

Figure E-6. Average HGL temperature (red line) from FPA correlation and heat release rate (blue 

line) for the CSR trash fire scenario. 

E.4.2 Zone Model 

General: In CFAST, the CSR is modeled as a single compartment with obstructions accounted 

for by modifying the cross-sectional area of the compartment as a function of height, as 

described in the geometry section below. Figure E-7 shows the scenario, as modeled by 

CFAST. 

0

50

100

150

200

250

300

350

0

10

20

30

40

50

60

0 600 1200 1800 2400 3000 3600

HRR (kW)

Temperature (°C)

Time (s)

HGL temperature calculation ‐ FPA correlation

FPA [°C]

HRR [kW]
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-12 

Figure E-7. CFAST/Smokeview rendering of the CSR scenario. 

Geometry: Since zone models are concerned with volumes and not physical length and width, 

the volume of the computer compartment, as well as the numerous cable trays, ductwork, and 

beams, was modeled in CFAST with a cross-sectional area that varies with height. Table E-4 

shows the cross-sectional area as a function of the height calculated from the compartment 

geometry shown in Figure E-1. Figure E-8 shows the CFAST inputs for compartment geometry. 

Table E-4. Cross-sectional area as a function of height used for CFAST calculation. 

Height 

(m) 

Area 

(m2) 

Floor Level 0 700.04 

Bottom of Cable Trays 1.8 635.74 

Bottom of Obstructions 2.2 483.74 

HVAC Ductwork 2.4 514.89 

Top of Obstructions 2.8 634.74 

Top of Cable Trays 3.2 699.04 

Ceiling Level Obstructions 3.6 291.46 

Ceiling Level 4 291.46 
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-13 

Figure E-8. CFAST inputs for compartment geometry for the CSR scenario. 

Fire: The specified fire is input directly. The combustion chemistry in CFAST is described, at a 

minimum, by the production rates of CO and soot. Figure E-9 shows the CFAST inputs for the 

fire location in the scenario taken directly from Table E-1. 

Cables: In CFAST, target temperatures are calculated using a one-dimensional cylindrical heat 

transfer calculation based on the material properties and cable diameter, as specified in the 

scenario description. Following the Thermally-Induced Electrical Failure (THIEF) methodology 

in NUREG/CR-6931, Vol. 3, electrical functionality is lost when the temperature just inside the 

jacket of a thermoplastic cable reaches 205 °C (400 °F). Specific heat and thermal conductivity 

for the cables are taken to be 1.5 kJ/kg/K and 0.2 W/m/K, as specified in the THIEF model. 

Cable density is determined from the mass per unit length and cross-sectional area of the cable 

from the scenario description,   0.4  0.015 2

2

 2264kg/m3

. To account for the shielding 

of the cables on the lower surface of the cable tray, the CFAST input for the normal vector from 

the cable surface is directed upwards. This effectively shields the cables from the fire below 

while exposing them to the surrounding gas temperature for convection and to the hot upper 

gas layer for radiation. Figure E-10 shows the CFAST inputs for the three cable targets above 

the fire. 
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-14 

Figure E-9. CFAST inputs for the fire in the CSR scenario. 
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-15 

Figure E-10. CFAST inputs for cable targets above the fire source in the CSR scenario. 

Ventilation: The supply and return airflow rates are input directly into CFAST. Upon smoke 

detector activation, mechanical ventilation fans stop and dampers are closed. Thus, before a 

stop time for the fans can be specified, the time to smoke detector activation is needed. This 

requires that CFAST be run with the fans on for the entire time to find the first smoke detector 

activation. The model is then re-run using the smoke detector activation time as the fan stop 

time. Figure E-11 shows the CFAST inputs for the natural ventilation. 
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-16 

Figure E-11. CFAST inputs for natural ventilation for the CSR scenario. Note the opening of the 

doorway at 170 s, the time estimated for smoke detectors to activate. 

Fire Detection: Although there are multiple smoke detectors in the space, the closest detector 

is the only one that needs to be modeled to determine time to detection, based on the fact that 

the nearest detector will be exposed to the greatest concentration of smoke products and the 

highest gas temperatures, thus leading to the earliest response. There are no geometric or 

ventilation features that would prevent this from being the case in the example considered. In 

CFAST, there is no direct way of calculating smoke density for smoke detector activation. 

Instead, the smoke detector is modeled as a sprinkler with a very low activation temperature 

and response time index (RTI). An activation temperature of 30 o

C (86 oF) and an RTI of 

5 (m/s)1/2 were used for this scenario. Figure E-12 shows the CFAST inputs for the detectors in 

the scenario. 
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-17 

Figure E-12. CFAST inputs for smoke detectors in the CSR scenario. 

E.4.3 CFD Model 

General: This scenario is notable because it includes a considerable amount of “clutter,” that 

is, the space has a relatively large number of obstructions. Figure E-13 illustrates the FDS 

simulation with all the blockages. Because the cable trays are regularly spaced in both the 

horizontal and vertical directions, it is easy in FDS to simply replicate a single tray as many 

times as necessary. Another interesting feature of the scenario is the automatic shutdown of 

the ventilation system at the time of any smoke detector activation. FDS models this by 

associating the creation or removal of obstructions or the activation/deactivation of a vent with 

actions taken by any number of fire protection devices. 

Figure E-13. FDS/Smokeview rendering of the CSR scenario. 

Geometry: The interior of the compartment is modeled, and all obstructions have been 

included. To get increased resolution in the area of interest, multiple meshes are used. The 

finest mesh has a 10 cm (4 in) resolution and spans a volume surrounding the trash can, which 
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-18 

is 6 m (20 ft) long, 3 m (10 ft) wide, and 4 m (13 ft) high. Coarse meshes cover the remainder of 

the compartment and adjacent hallway with cells of 20 cm (8 in). Because the objective of the 

calculation is to estimate time to failure for cables within stacked trays, it is important to have at 

least a 10 cm (4 in) resolution, the typical dimension of the rails of conventional cable trays. 

Fire: The trash can is modeled with a square, rather than round, cross section with an 

equivalent area to the round cross section and a height equal to the height of the trash can. 

The local flow features around the fire are not capable of affecting the outcome of this example 

calculation; therefore, the transformed square geometry is appropriate for this application. The 

specified HRR is applied to the top of the trash can. The duration of the fire is 635 s, as was 

computed for the zone model input. There is no need to model the interior of the can. 

Materials: The thermal properties of the walls are applied directly, as specified. 

Cables: The primary objective of the calculation is to estimate the potential damage to the 

cables within the trays. FDS is limited to only 1-D heat transfer into either a rectangular or 

cylindrical obstruction. In this simulation, the cables are modeled as 1.5 cm (0.6 in) cylinders 

with uniform thermal properties, given above. Following the THIEF methodology in 

NUREG/CR-6931, Vol. 3, electrical functionality is lost when the temperature just inside the 

jacket of a thermoplastic (TP) cable reaches 205 °C (400 °F). Note that no attempt is made in 

the simulation to estimate ignition and spread of the fire over the cables. The THIEF 

methodology does not account for the effects of bundled cables, which may reduce the overall 

heat-up of a single cable. 

For the bottommost cable tray, the bottom surface of the tray is protected by a solid metal 

surface. To model this in FDS, which models the trays as rectangular obstructions, individual 

properties for the top, sides, and bottom are specified. The top has the same properties as the 

cables; the sides and bottom are specified as having the same metal properties. 

Detection: FDS has a smoke detection algorithm that predicts the smoke obscuration within 

the detection chamber based on the smoke concentration and air velocity in the grid cell in 

which the detector is located. The detector itself is not modeled, as it is merely a point within 

the computational domain. The two parameters needed for the model are the obscuration at 

alarm, which is given by the manufacturer, and an empirically determined length scale from 

which a smoke entry time lag is estimated from the outside air velocity. The SFPE Handbook, 

4th Edition, provides a nominal value of 1.8 m (5.9 ft) for this length scale. The obscuration at 

alarm is 4.9 %/m, a typical sensitivity for smoke detectors. 

Ventilation: The supply and return airflow rates are input directly into FDS. The ducts are 

represented by rectangular obstructions with thin plates just below (one grid cell) the vent itself 

to represent the diffusing effect of the grill. The resolution of the grid is not fine enough to 

capture this effect directly. FDS is capable of stopping the ventilation system upon the 

activation of any smoke detector. 
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-19 

E.5 Evaluation of Results 

The purpose of the calculations described above is to estimate smoke detector activation times 

and potential cable damage from a trash can fire in the CSR. 

The compartment itself is relatively large, and the relatively small fire (317 kW) does not 

substantially heat it up. Figure E-14 shows the HRR and estimated HGL temperature for the 

CSR scenario for CFAST and FDS. Differences between the two models likely result from 

FDS’s ability to locally account for all the blockages in the room. HGL temperature in CFAST is 

a spatially average value intended to represent the bulk conditions throughout the compartment, 

while the FDS values are calculated based on a single vertical profile of temperature at a fixed 

location within the room (in this scenario placed several meters away from the fire location to 

eliminate local effects of the fire plume on the temperature profile). 

Figure E-14. HRR and estimated HGL temperature for CSR scenario. 

Because of the uncertainty in all models’ smoke detector activation predictions and the 

uncertainty associated with the possible ignition of cables in the trays just above the fire, it is 

difficult to predict whether or not the CO2 suppression system would be activated in time to 

prevent possible cable ignition. No validation results are available that address time to detector 

activation. Thus, the analysis does not consider activation of the suppression system. 

Table E-5 summarizes the results of all the models for the chosen damage criteria. For each 

predicted value, a calculation is performed to determine the probability of exceeding the critical 

value. The procedure for calculating this probability is given in Chapter 4, and it accounts for 

the model bias and scatter. The purpose of this table is to highlight the criterion that is most 

likely to be exceeded so that further analysis can be focused on this criterion and the model or 

models that predict it. Each criterion is discussed in greater detail in the following subsections. 

0

100

200

300

400

0 600 1200 1800 2400 3000 3600

HRR (kW)

Time (s)

Heat Release Rate

CFAST

FDS

10

20

30

40

50

0 600 1200 1800 2400 3000 3600

Temperature (C)

Time (s)

HGL Temperature

CFAST

FDS
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-20 

Table E-5. Summary of the model predictions for the CSR scenario. 

Model 

Bias 

Factor, 

δ

Standard 

Deviation, 

σM 

Location Predicted 

Value 

Critical 

Value 

Probability 

of 

Exceeding 

 

Temperature (°C), Initial Value = 20 °C 

CFAST 1 0.27 Bottom 

Cable 

298 205 0.893 

FDS 1.02 0.13 54 205 0.000 

CFAST 1 0.27 Cable A 202 205 0.472 

FDS 1.02 0.13 36 205 0.000 

CFAST 1 0.27 Cable B 126 205 0.003 

FDS 1.02 0.13 61 205 0.000 

 

Heat Flux (kW/m2) 

CFAST 0.81 0.47 Bottom 

Cable 

4.2 6 0.367 

FDS 0.85 0.22 1.0 6 0.001 

CFAST 0.81 0.47 Cable A 3.0 6 0.091 

FDS 0.85 0.22 0.3 6 0.000 

CFAST 0.81 0.47 Cable B 2.0 6 0.000 

FDS 0.85 0.22 0.8 6 0.001 

E.5.1 Smoke Detection 

Table E-6 shows the models’ predictions for smoke detector activation. The models provide 

similar estimates of the detector activation time. CFAST models smoke detector actuation as a 

heat detector with a relatively low thermal inertia and activation temperature. However, there is 

no consensus in the fire literature for the appropriate RTI value and activation temperature. 

Given the presence of beam pockets and obstructions, even a CFD model like FDS, which uses 

actual smoke concentration rather than temperature in its detector algorithm, is subject to 

significant uncertainty. For this reason, no credit is given for smoke detection in the final design, 

and there is no need to consider either its uncertainty or any further impact on the design. 

Table E-6. Smoke detector activation times, CSR. 

Model Time (s) 

CFAST 170 s 

FDS 160 s 

E.5.2 Temperature Criterion 

Figure E-15 shows the estimated impact of the fire on the cable trays above the fire. The 

bottom cable is located at least 1 m (3.3 ft) above the base of the waste bin fire. With an 

estimated flame height of 1.7 m (5.7 ft), ignition may occur from flame impingement. The 

algebraic tools and CFAST both predict a temperature well above the cable failure temperature. 

The plume temperature estimated by the algebraic tool is naturally higher than the CFAST 
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-21 

calculation, since CFAST is able to account for the heat transfer into the cable and thus provide 

an estimate of the actual cable temperature. However, both of these calculations are based on 

the cable being directly exposed to the high gas temperature of the fire plume directly above the 

fire and do not account for the protection afforded by the solid metal lower surface of the cable 

tray. FDS calculations take this into account and show a much lower temperature of the 

bottommost cable. 

For the upper cables, CFAST’s predicted temperature and heat flux are higher than FDS’s 

because CFAST does not account for the fact that the cable trays of interest are shielded by 

trays below or that the burning spreads outward from the ignition point. 

E.5.3 Heat Flux Criterion 

Heat flux estimates for both CFAST and FDS in Figure E-15 show values well below the critical 

value of 6 kW/m2

. Still, the CFAST-estimated heat flux to the bottom cable tray of 4.2 kW/m2

(Table E-5), combined with the estimated flame height (Figure E-15), does show the importance 

of the solid lower surface of the cable tray. 

It should also be noted that these damage criteria are intended to indicate electrical failure, but 

are routinely used as ignition criteria. In newer studies in NUREG/CR-7010, cable ignition was 

not observed at fluxes below 25 kW/m2

, and most often only with direct flame impingement. 

Handbook values for minimum ignition flux for power and communication cables are reported in 

the range of 15 kW/m2

 to 35 kW/m2 (SFPE Handbook, 4th ed., Table 3-4.2). 

 
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-22 

Figure E-15. Estimated cable conditions for the CSR. 

 

0

50

100

150

200

250

300

350

0 600 1200 1800 2400 3000 3600

Temperature (C)

Time (s)

Bottom CableTemperature

CFAST

FDS

0.0

0.5

1.0

1.5

2.0

0 600 1200 1800 2400 3000 3600

Flame Height (m)

Time (s)

Flame Height

CFAST

0

50

100

150

200

250

0 600 1200 1800 2400 3000 3600

Temperature (C)

Time (s)

Cable A Temperature

CFAST

FDS

0

1

2

3

4

5

0 600 1200 1800 2400 3000 3600

Heat Flux (kW/m2)

Time (s)

Cable A Heat Flux

CFAST

FDS

0

20

40

60

80

100

120

140

0 600 1200 1800 2400 3000 3600

Temperature (C)

Time (s)

Cable B Temperature

CFAST

FDS

0.0

0.5

1.0

1.5

2.0

0 600 1200 1800 2400 3000 3600

Heat Flux (kW/m2)

Time (s)

Cable B Heat Flux

CFAST

FDS
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-23 

E.5.4 Parameter Uncertainty Propagation 

The analysis above has shown that a 98th percentile trash fire is unlikely to damage cables in 

certain trays overhead because of the presence of a protective barrier beneath the lowest tray. 

However, for some PRA applications, it may be necessary to calculate the probability of cable 

damage for any fire, not just the 98th percentile fire, with or without a protective barrier. To 

illustrate this concept, let’s consider a simple plume temperature correlation. 

Figure E-16 displays the distribution23 of peak heat release rates for transient combustibles 

(NUREG/CR-6850, Appendix E). The analysis described above made use of the 98th percentile 

fire from this distribution, whose peak is 317 kW. 

Figure E-16. Distribution of HRR for a trash fire. 

Following the methodology described in Chapter 4 and Appendix E of NUREG/CR-6850, 

Heskestad’s plume temperature correlation24 is applied to the entire range of HRR, resulting in 

distributions of plume temperatures at the locations of Tray A and Tray B, as shown in Figure 

E-17. Tray A is 1.5 m above the top of the trash bin. The probability that the plume 

temperature at this height from a randomly chosen fire will exceed the cable failure temperature 

(205 °C; 400 °F) is equal to the area beneath the left hand curve in Figure E-17 for 

temperatures greater than 205 °C, or approximately 0.42. Similarly, the probability that the 

plume temperature at Cable Tray B (2.3 m above the bin) will exceed 205 °C is approximately 

0.08. Consistent with the guidance in NUREG/CR-6850, this resulting probability can be used 

as the "severity factor" for the quantification of corresponding fire ignition frequencies. 

Note that this analysis neglects the effect of the protective barrier or cable mass. It just 

estimates the likelihood that gas temperatures in the vicinity of the critical components could 

reach levels that might cause damage. 

 

23 NUREG/CR-6850 specifies gamma distributions for the various types of combustibles found within an NPP. Microsoft Excel® 

provides a built-in function (GAMMA.DIST) that calculates the probability density function given the parameters ߙ and ߚ. In this 

case, these parameters are 1.8 and 57.4, respectively. 

24 A value of 0.35 was used for the radiative fraction in determining the convective heat release rate. 

0.000

0.002

0.004

0.006

0.008

0.010

0 100 200 300 400 500

Probability Density Function

Heat Release Rate (kW)

HRR Distribution
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-24 

Figure E-17. Distribution of plume temperatures at Trays 3 and 6, respectively. 

E.6 Conclusion 

This analysis considers the potential impact of a transient trash fire on a stack of horizontal 

cable trays located directly above the transient fire source; it also considers the potential for the 

cables in these trays to ignite. 

Algebraic equations from the FDTs

 and FIVE-Rev1, including the Heskestad flame height 

correlation and the Heskestad fire plume temperature correlation, were used to evaluate the 

potential for the transient trash fire to ignite or damage cables in the cable trays located directly 

above this fire source. These calculations showed that the unobstructed flame height would 

reach multiple cable trays at the bottom of the stack; they also showed that the unobstructed 

plume temperatures would exceed the cable damage temperature in all trays located above the 

fire source. However, these calculations do not account for the impact of the cable trays on the 

actual flame height and plume temperatures, so more detailed analysis with CFAST and FDS is 

needed. 

The FPA correlation included in the FDTs

 and FIVE-Rev1 was used to evaluate whether the 

transient trash fire alone would cause damage to cable trays not located directly above this fire 

source. This calculation showed that the HGL temperature from the transient trash fire alone is 

well below the damage temperatures for the cables. 

The more detailed analysis with CFAST and FDS shows that a 317 kW waste bin fire beneath a 

vertical array of horizontal cable trays is unlikely to damage cables in the trays located three 

(Tray A) and six (Tray B) levels above the fire. Both CFAST and FDS estimate peak 

temperatures and heat fluxes below the failure criteria for cables in the third tray from the 

bottom. Based on FDS calculations, temperatures and heat fluxes for the protected lowest 

cable tray are well below critical values. Estimates from CFAST for unprotected cables 

demonstrate the importance of the protection afforded by the solid metal lower surface of the 

cable trays. 

0.000

0.002

0.004

0.006

0.008

0.010

0 100 200 300 400 500 600

Probability Density Function

Plume Temperature (C)

Plume Temperature Distribution at Tray A

0.000

0.002

0.004

0.006

0.008

0.010

0 100 200 300 400 500 600

Probability Density Function

Plume Temperature (C)

Plume Temperature Distribution at Tray B
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-25 

E.7 References 

1. NIST SP 1086, Consolidated Model of Fire Growth and Smoke Transport, CFAST (Version 

6), Software Development and Model Evaluation Guide, 2008. 

2. NUREG-1805, Fire Dynamics Tools (FDTs

) Quantitative Fire Hazard Analysis Methods for 

the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program, 2004. 

3. NUREG-1824 (EPRI 1011999), Verification and Validation of Selected Fire Models for 

Nuclear Power Plant Applications, 2007. 

4. NUREG/CR-6850 (EPRI 1011989), EPRI/NRC-RES Fire PRA Methodology for Nuclear 

Power Facilities, 2005. 

5. NUREG/CR-6931, Cable Response to Live Fire (CAROLFIRE) Volume 3: ThermallyInduced Electrical Failure (THIEF) Model, 2008. 

6. SFPE Handbook of Fire Protection Engineering, 4th edition, 2008. 

E.8 Attachments (on CD) 

1. FDS input files: Cable_Spreading_Room.fds 

2. CFAST input files: 

a. Trash Fire In Cable Spreading Room.in 

3. Algebraic model input files: 

a. FPA_AppE.xlsx 

 
TRANSIENT FIRE IN CABLE SPREADING ROOM

E-26 
F-1 

APPENDIX F 

LUBRICATING OIL FIRE IN A TURBINE BUILDING 

F.1 Modeling Objective 

The purpose of the calculations described in this appendix is to estimate the temperatures of 

unprotected structural steel members due to a large lubricating oil fire in a turbine building. For 

this scenario, a catastrophic failure of the turbine results in a large lubricating oil spill fire. The 

purpose of this example is to evaluate the turbine building structural steel response to internal 

lubricating oil fire in one of two potential curbed locations in the turbine building. The 

calculations provide information for a decision on the hazard posed to the structural steel for 

each potential fire location, thus serving as a basis for a plant modification. 

F.2 Description of the Fire Scenario 

General Description: The turbine building is a large structure that is approximately 100.3 m 

(329 ft) long by 99.5 m (326 ft) wide by 21 m (69 ft) tall, as shown in Figure F-1. The ambient 

temperature is 36 °C (97 °F), inside and outside the building. Although the building has multiple 

levels, for this example, only two levels the main turbine deck and the level just below it are 

evaluated. The lowest portion of the lower level floor is about 1.2 m (4 ft) below grade in the 

area near the fire, but most of the lower level floor elevation is at the 0 m elevation. The ceiling 

height of the lower level is 4.6 m (15 ft) above grade. The floor of the turbine deck is at the 

5.6 m (18 ft) elevation, and the ceiling for this upper level is at the 19.8 m (65 ft) elevation. The 

turbine deck has a smaller floor area than the lower level; the turbine deck level is 

approximately 90 m (295 ft) long by 70 m (230 ft) wide. The building contains the turbine 

generators (see Figure F-1) and a heating, ventilating, and air conditioning (HVAC) room. 

Each turbine generator contains about 3,000 L (792.5 gal) of lubricating oil in a single tank, as 

illustrated in Figure F-2. The proposed curbed is 6.1 m (20 ft) long by 4.6 m (15 ft) wide. Two 

potential locations have been identified on the lower level where the curbing could be installed. 

These locations are shown in Figure F-1. Either of the curbed areas would be designed to 

contain the entire volume of 3,000 L (792.5 gal) from one of the turbine generators main 

lubricating oil tanks. 

There are 40 unprotected steel support columns in a rectangular configuration (four rows of ten 

each) around the lubricating oil tank. Figure F-3 shows a typical unprotected steel column. The 

columns are all W14ۭ145 standard wide flange members, as shown in Detail A of Figure F-1 

(American Institute of Steel Construction, 2006). The six columns identified for analysis are 

denoted in Figure F-1 as A, B, C, D, E, and F. A structural analysis indicates that the loss of 

any of these six columns could lead to partial collapse of the turbine building. 

 
LUBRICATING OIL FIRE IN A TURBINE BUILDING

F-2 

Figure F-1. Geometry of the turbine building. 

 
LUBRICATING OIL FIRE IN A TURBINE BUILDING

F-3 

Figure F-2. Main turbine lubricating oil tanks in the turbine building. 

Figure F-3. Typical steel column in the turbine building. 
LUBRICATING OIL FIRE IN A TURBINE BUILDING

F-4 

Geometry: Plan and elevation views of the turbine building are shown in Figure F-1. The area 

of interest involves the two levels shown in Figure F-1, which are separated by the concrete 

turbine deck. There are several stairwell, hatch, and exhaust vent penetrations throughout the 

turbine deck. These penetrations are identified in Figure F-1 by the H symbol for a hatch and 

the S symbol for a stairwell. 

Construction: The turbine deck is made of 1 m (3.3 ft) thick normal-weight concrete. The floor 

and walls of the lower level are constructed of 0.3 m (1 ft) thick normal-weight concrete. 

Numerous areas and landings in the turbine building are made of metal grating. The floor in the 

area of the lubricating oil tank is 1 m (3.3 ft) thick normal-weight concrete. The walls and ceiling 

of the upper level of the turbine building are made of 3 mm (0.12 in) thick corrugated steel. The 

structural columns, steel grating, and corrugated steel are fabricated from steel containing 

0.5 percent carbon. 

Materials: Thermal properties of the normal-weight concrete and steel are listed in Table 3-1. 

The damage criteria for the structural steel are listed in Table F-1; these criteria are based on 

the acceptance criteria for a standard fire resistance test (ASTM E119-10a, 2010). The 

maximum cross-sectional temperature threshold normally applies to unprotected structural steel 

because of its high thermal conductivity. 

Table F-1. Structural steel failure criteria (ASTM E119-10a). 

Member 

Maximum Cross-Section 

Average Temperature 

°C (°F) 

Beam 593 (1,099) 

Column 538 (1,000) 

Detection System: There is no safety-related equipment in the turbine building, thus, no 

detection or suppression systems are credited for this analysis. If under-deck sprinklers were 

installed, they would not be credited when considering the potential for worst-case structural 

failure and the possible need for passive structural fire protection. 

Ventilation: The turbine building is an open area configuration with all forced ventilation 

intentionally shut down at the start of the fire for reasons unrelated to the fire. There are 

eighteen roof-mounted horizontal exhaust vents around the perimeter of the turbine deck level, 

as shown in Figure F-1. The exhaust vents each measure 5.0 m (16.4 ft) long by 2.5 m (8.2 ft) 

wide. There are no other internal or external openings beyond those already noted in the 

drawings. 

Fire: A large, confined spill fire involving 3,000 L (792.5 gal) of lubricating oil from the main 

turbine lubricating oil tank is postulated on the lower level. The lubricating oil has been 

preheated prior to the spill, such that the growth rate of the fire would be relatively short 

compared to the total time required to burn the spill volume. The total spill area is 

approximately 28.1 m2

 (300 ft2), as shown in Figure F-1; the spill depth is calculated to be 

0.11 m (0.35 ft), based on the specified spill area and fuel volume. 

The lubricating oil is dominated by alkanes, that have the chemical formulae of CnH2n+2, where n

ranges between 12 and 15 (centered around 14) and a soot yield of 0.059. Fuel properties for 
LUBRICATING OIL FIRE IN A TURBINE BUILDING

F-5 

the lubricating oil, obtained from Tables 3-2 and 3-4 of NUREG-1805 and from Table 3-4.16 of 

the SFPE Handbook, 4th edition, are summarized in Table F-2. The Handbook identifies the fuel 

as a “Hydrocarbon.” NUREG-1805 lists properties and states that lubricating and transformer 

oils are similar. 

Table F-2. Data for lubricating oil fire. 

Parameter Value Source 

Effective Fuel Formula CnH2n+2 Developed from fuel chemistry (n in range of 

12-15) 

Mass burning rate 0.039 kg/s.m2 NUREG-1805 Table 3-4 

Fuel volume 3,000 L Specified 

Density 760 kg/m3 NUREG-1805 Table 3-4 

Heat of Combustion 46,000 kJ/kg NUREG-1805 Table 3-4 

CO2 Yield 2.64 kg/kg SFPE Handbook, 4th ed., Table 3-4.16 

Soot Yield 0.059 kg/kg SFPE Handbook, 4th ed., Table 3-4.16 

CO Yield 0.019 kg/kg SFPE Handbook, 4th ed., Table 3-4.16 

Radiative Fraction 0.34 SFPE Handbook, 4th ed., Table 3-4.16 

Mass Extinction Coefficient 8,700 m2/kg Mulholland and Croarkin (2000) 

The peak heat release rate (HRR), ܳሶ, is computed from the fuel mass burning rate, ݉ሶ

ᇱᇱ, the heat 

of combustion, ∆ܪ, and the specified area of the spill, ܣ: 

ܳሶ ൌ ݉ሶ

ᇱᇱ ∆ܪ ܣ ൌ 0.039 kg/mଶ s ൈ 46,000 kJ/kg ൈ 28.1 mଶ ⁄ ؆ 50,400 kW (F-1)

The fire duration, ∆ݐ, is determined from the pool depth, ߜ, density, ߩ, and burning rate, ݉ሶ

ᇱᇱ: 

ߩ ߜ ൌ ݐ∆

݉ሶ

ᇱᇱ ൌ 0.11 m ൈ 760 kg/mଷ

0.039 kg/mଶ/s ؆ 2,144 s ሺ35.7 minሻ (F-2)
LUBRICATING OIL FIRE IN A TURBINE BUILDING

F-6 

F.3 Selection and Evaluation of Fire Models 

This section describes the process of model selection, including a discussion of their validity for 

this scenario. To the temperature of the steel it is necessary to calculate the heat flux from the 

fire to and the resulting temperature of the steel. It is also necessary to determine whether 

flame extension beneath the ceiling or a hot gas layer (HGL) would develop and contribute 

significantly to the column heating. 

F.3.1 Heat Flux and Target Temperature Algorithms 

The turbine building fire under consideration is not a typical compartment fire scenario because 

it exhibits both pre- and post- flashover conditions simultaneously. The 50 MW fire is expected 

to fully engulf the lower deck from floor to ceiling in the vicinity of the curbed areas and 

resemble a compartment fire after the onset of flashover. Away from the curbed areas, a 

distinct smoke layer is expected to form and the space would exhibit pre-flashover fire 

conditions. The empirical correlations and zone models are only capable of modeling one or the 

other condition, not both. However, the heat flux and target temperature algorithms used by 

these simpler models may be applicable. In particular, the point source and solid flame radiant 

heat flux models can be used to estimate the thermal exposure condition to the near-field and 

far-field columns, respectively. 

The CFD model, FDS, does have the necessary physics to model the scenario, but it is 

necessary first to assess if it has been validated for such conditions. 

F.3.2 Validation 

Table F-3 provides a summary of the normalized parameter calculations for the turbine building 

fire scenario. A number of parameters fall outside of the parameter space of the NRC/EPRI 

V&V study (NUREG-1824 (EPRI 1011999)), including the flame length/ceiling height ratio, the 

compartment aspect ratios and some of the target distance to fire diameter ratios. In addition, 

the equivalence ratio cannot be calculated with the simple equations that have been used for 

various other examples. 

The calculation of the equivalence ratio is challenging because natural ventilation is provided 

through the 18 roof vents located around the perimeter of the turbine deck level. To evaluate 

the potential impact of ventilation on the fire for this scenario, the quantity of oxygen available in 

the turbine building is compared to the amount of oxygen that would be consumed by the 

specified lubricating oil fire. Given a total volume of approximately 209,600 m3

, the mass of 

oxygen within the turbine building is estimated to be: 

݉Oమ,tot ൌ ߩܸܻOమ ൌ 1.1 kg/mଷ ൈ 209,600 mଷ ൈ 0.23 ؆ 53,030 kg (F-3)

The mass of oxygen required to burn all the fuel is estimated to be: 

݉Oమ,req ൌ ܳ ሶ ∆ݐ

Oమܪ∆

ൌ 50,400 kW ൈ 2,144 s

13,100 kJ/kg ؆ൌ 8,249 kg (F-4)
LUBRICATING OIL FIRE IN A TURBINE BUILDING

F-7 

Thus, the specified fire would consume less than 16% of the oxygen available within the turbine 

building. Consequently, the fire would not be expected to be ventilation-limited on a global 

basis, even without ventilation from the outside environment through the roof vents. 
Table F-3. Normalized Parameter Calculations for the Turbine Building Fire Scenario. 

Quantity Normalized Parameter Calculation 

NUREG1824 

Validation 

Range 

In 

Range? 

Fire Froude 

Number 

ܳכሶ ൌ

ܳሶ

ߩ

ஶܿ௣ܶஶ

ܦଶ.ହ

ඥ݃

ൌ

50,400 kW

ሺ1.1 kg/mଷሻሺ1.0 kJ/kg/

Kሻሺ309 

Kሻሺ6.0ଶ.ହ mଶ.ହሻඥ9.8 m/sଶ ؆ 0.524 0.4 – 2.4 Yes 

Flame length, 

Lf, relative to 

ceiling height, 

Hc

௙ܮ

௖ܪ

ൌ

11.0 m

4.6 m ؆ 2.4

ܮ ௙ൌ ܦ ቀ3.7 ܳכሶ ଶ/ହ െ 1.02ቁ ൌ 6.0 m ሺ3.7 ൈ 0. 52଴.ସ െ 1.02ሻ ؆ 11 m

0.2 – 1.0 No 

Ceiling jet 

radius 

relative to the 

ceiling height, 

Hc

N/A 1.2 – 1.7 N/A 

Equivalence 

ratio based on opening 

area 

See Section F.3.2 for discussion of this parameter. 0.04 – 0.6 Yes 

Compartment 

aspect ratios 

ܮ

௖ܪ

ൌ

100.3 m

4.6 m ؆ 21.8 ;

ܹ

௖ܪ

ൌ

99.5 m

4.6 m ؆ 21.6 0.6 – 5.7 No 

Target 

distance to 

fire diameter 

(Columns 

A,B,C,D,E,F) 

8.5 m6.0 m ؆ 1.4

7.2 m6.0 m ؆ 1.2

18.8 m

6.0 m ؆ 3.1

18.3 m

6.0 m ؆ 3.1

36.5 m

6.0 m ؆ 6.1

78. m6.0 m ؆ 13.1 2.2 – 5.7 Yes/No 

28.0 m

6.0 m ؆ 4.7

26.9 m

6.0 m ؆ 4.5

8.8 m6.0 m ؆ 1.5

3.9 m6.0 m ؆ 0.7

43.3 m

6.0 m ؆ 7.2

80. m6.0 m ؆ 13.5

Notes: The effective diameter of the fire is determined from the formula, ܦ ൌ

 where ,ߨ/ܣ4ඥ

ܣ is the curbed area of the dike. 

F-8

LUBRICATING OIL FIRE IN A TURBINE BUILDING 
LUBRICATING OIL FIRE IN A TURBINE BUILDING

F-9 

The flame length to ceiling height ratio of 2.4 calculated for this scenario indicates that the 

flames would be impinging on the ceiling and spreading out over a relatively large distance 

beneath the ceiling. This configuration is beyond the capability of the FDTs

, FIVE-Rev1, and 

CFAST, and could affect the plume entrainment, the HGL temperature and depth, and the 

radiant heat flux to a target. In fact, the fire in this scenario is so large that for columns within a 

few (say 3) fire diameters, the fire can be taken as fully-engulfing the columns. For columns at 

greater distances, the fire can be viewed as a point source of radiation. 

As part of the work performed at NIST for the investigation of the World Trade Center (WTC) 

disaster, FDS was validated against large-scale fire experiments involving liquid fuel fires 

impinging on the ceiling of a large compartment with a flat ceiling. Measurements included the 

heat flux to and the temperatures of bare and insulated steel structural members. The NIST 

experiments and the FDS simulations are described in NIST NCSTAR 1-5F. The WTC 

validation work did not involve a compartment with aspect ratios as large as those in the 

scenario under consideration here, but other validation exercises have shown that the model 

can handle hallway flows with comparable length to height ratios. The FDS Validation Guide 

(NIST Special Publication 1018-5) includes the details of these validation studies, including the 

Bureau of Alcohol, Tobacco and Firearms (ATF) Corridor Experiments and the National Bureau 

of Standards (NBS) Multi-room Experiments. 

F.4 Estimation of Fire-Generated Conditions 

This section provides details of how the different models are applied to the scenario. 

F.4.1 Algebraic Models 

General: The fire is depicted schematically in Figure F-4. As discussed in Section F.3, the 

flame length is expected to be approximately 2.4 times the ceiling height, indicating that 

significant flame extension will occur beneath the turbine deck. 

The concept of ceiling flame impingement is illustrated in Figure 3-8 of NUREG-1805 and is 

discussed in Karlsson and Quintiere (2000). This reference indicates that the radial length of 

flame beneath a ceiling is approximately equal to the length of flame truncated by the ceiling, as 

illustrated in Figure F-4. This estimate is based on data from Heskestad and Hamada (1993). 

With a calculated flame length of 11 m (36 ft) and a ceiling height of 4.6 m (15 ft), this suggests 

that the flame beneath the ceiling would have a radial extension of approximately 6.4 m (21 ft) 

from the centerline of the fire. 
LUBRICATING OIL FIRE IN A TURBINE BUILDING

F-10 

Figure F-5 shows the approximate radial flame extension of 6.4 m (21 ft) superimposed (yellow 

circle) on a detail of Figure F-1 near the two proposed curb locations. As shown in Figure F-5, 

Column B is at the edge of the estimated flame extension for Curb Location 1, and Column D is 

well within the estimated flame extension for Curb Location 2, which means that the upper part 

of Column D would be engulfed in flames. Column A is near the edge of the estimated flame 

extension for Curb Location 1, and Column C is near the edge of the estimated flame extension 

for Curb Location 2. 

Unobstructed 

flame height 

Effective flame 

length beneath 

ceiling 

Figure F-4. Schematic diagram of the fire impinging on the ceiling. 
LUBRICATING OIL FIRE IN A TURBINE BUILDING

F-11 

Figure F-5. Detail from Figure F-1 with estimated flame extension beneath ceiling 

superimposed. 

The heat flux from the fire to a nearby column can be estimated using one of the FDTs

(NUREG-1805, 2005), specifically: 

 05.1_Heat_Flux_Calculations_Wind_Free.xls (Point Source) 

 05.1_Heat_Flux_Calculations_Wind_Free.xls (Solid Flame 1) 

For the point source method, the estimated peak HRR is 50,400 kW, the radiative fraction is 

0.33, and the horizontal distance from the center of the lubricating oil pool to the nearest column 

(Column D) is approximately 4.2 m (13.8 ft): 

ሶݍ

௥

ᇱᇱ ൌ ߯௥ ܳሶ

4ߨ ݎଶ ൌ 0.34 ൈ 50,400 kW

4ߨ ൈ 4.2ଶ mଶ ؆ 75.0 kW/mଶ (F-5) 

The solid flame calculation in the FDTs

 is based on the flame being approximated as “a 

cylindrical, blackbody, homogeneous radiator with an average emissive power” (Beyler, SFPE 

Handbook, 4th edition). However, Beyler points out that the solid flame calculation “represents 

the average emissive power over the whole flame and is significantly less than the emissive 

power that can be attained locally. Thus, the solid flame calculation is inappropriate for 

estimating the heat flux to columns that are potentially engulfed in flames. In fact, neither 

calculation is appropriate for estimating the heat flux to columns that are potentially in flames. 

Neither of these simple radiation calculations account for the flame extension beneath the 

ceiling, so it is likely that they underestimate the actual heat flux at the column, particularly for 

the case of the solid flame heat flux calculation. 
LUBRICATING OIL FIRE IN A TURBINE BUILDING

F-12 

Even though the simple heat flux calculation methods are questionable for close targets, it is still 

worthwhile to estimate the time for the column to heat up to temperatures that could potentially 

cause it to fail. If so, then it makes sense to continue analysis with a more detailed model like 

FDS. 

In order to estimate an approximate time for a column to reach the specified failure temperature 

of 538 °C (1,000 °F) when subjected to a given radiant heat flux, a simple energy balance is 

used to calculate the steel’s rate of temperature: 

ߩ௦ܿ௦ܸ௦

݀ܶ௦

ሶݍ ൌ ݐ݀

௥

ᇱᇱ ܣ௦ (F-6) 

The subscript ݏ refers to steel. The temperature of the steel is modeled as changing uniformly 

through the steel cross-section due to its relatively high thermal conductivity. This is sometimes 

called a “lumped capacitance” or “low Biot number” approximation. For a constant net heat flux, 

this differential equation can be readily integrated to yield the steel temperature as a function of 

time: 

ܶ௦ െ ܶ଴ ൌ ݍሶ

௥

ݐ ᇱᇱ

ߩ௦ܿ௦ሺܸ௦/ܣ௦ሻ (F-7) 

To calculate the time, ݐcrit, when the steel failure temperature is reached, this equation is 

rearranged, with the critical steel temperature, ܶcrit, inserted for the steel temperature. 

ݐcrit ൌ ߩ௦ܿ௦ሺܸ௦/ܣ௦ሻሺܶcrit െ ܶ଴ሻ

ሶݍ

௥

ᇱᇱ ൌ ܿ௦ሺܹ/ܦሻሺܶcrit െ ܶ଴ሻ

ሶݍ

௥

ᇱᇱ (F-8) 

The term ܸ௦/ܣ௦ is sometimes called the section factor, and is the effective thickness of the steel 

member; it is calculated as the cross-sectional area of a steel member divided by the heated 

perimeter of the member. In the U.S., it is more common to use a parameter referred to as the 

W/D ratio, which is simply the section factor multiplied by the steel density. For a W14x145 

steel column, the W/D ratio has a value of approximately 96.2 kg/m2

 (1.64 lb/ft/in). Using this 

value for the W/D ratio, the time to reach the critical steel temperature for the column can be 

estimated using the radiant heat flux estimated in Equation F-5: 

ݐcrit ൌ ሺ0.465 kJ/kg/°Cሻሺ96.2 kg/mଶሻሺ538 °C െ 36 °Cሻ

75.0 kW/mଶ ؆ 300 s (F-9) 

Because this time is much shorter than the estimated burning duration of the lubricating oil fire 

(~2,100 s), this analysis suggests that it may be necessary to protect the columns nearest the 

proposed curb locations with fire resistant coatings to prevent the columns from reaching the 

specified steel failure temperature. 

Because a number of conservative approximations were used for this analysis using algebraic 

models, FDS is also used to analyze this scenario. 
LUBRICATING OIL FIRE IN A TURBINE BUILDING

F-13 

F.4.2 CFD Model 

Geometry: The entire turbine hall is included in the simulation (see Figure F-6). One mesh 

covers the lower deck, and one covers the upper turbine deck. The numerical mesh consists of 

uniform grid cells with a resolution of 1 m (3.3 ft). While this mesh appears to be fairly coarse, 

the fire is so large that the ratio of כܦ) the characteristic fire diameter) to the cell size is about 

five. 

The columns cannot be resolved on the relatively coarse grid, and are approximated as steel 

plates with the given thickness of the actual columns. The column obstructions are one cell 

thick, which allows the boundary on the surface opposite the fire to be exposed to the room 

conditions. Even though the column obstruction is one cell thick in the domain mesh, the 

thickness of the steel surface through which heat is transferred is equal to the thickness of the 

column web. Note that FDS only performs a one-dimensional heat transfer calculation within 

solid obstructions, which is why there is little to be gained by resolving the column further. The 

neglect of lateral heat conduction within the solid tends to produce a slight over-prediction of the 

average column cross section temperature, but, because the heat flux from the fire is expected 

to be fairly uniform over the width of the column, a more detailed thermal conduction calculation 

is not warranted. 

Figure F-6. FDS geometry for the turbine building fire scenario. 

Materials: The material properties are applied directly as specified to the walls, floor, and 

ceiling. 

Upperlevel Hatches and stairs

between levels

HVAC room

Ventsto exterior

Lower level

Stair opening

Plant

north

Curb

Location 1

Curb

Location 2

Column A

Column B

Column C

Column D

Column E
LUBRICATING OIL FIRE IN A TURBINE BUILDING

F-14 

Fire: The fire is specified in the curbed areas, as described in Section F.2. The HRR, soot 

yield, and molecular weight are as described in Section F.2, and are provided directly as inputs 

to FDS. A ten-second growth rate is used to allow the flows to develop over a finite time 

interval. 

Ventilation: The openings to the exterior and between the upper and lower level are modeled 

at the locations, as shown in Figure F-6. It should be noted that the point of including the lower 

and upper levels of the turbine building in the simulation is to check whether there would be 

sufficient make-up air drawn through the various vents to sustain a steady-state 50 MW fire. 

F.5 Evaluation of Results 

The purpose of the calculations described above is to estimate the steel temperature of six large 

columns in the turbine building to determine whether any would lose the ability to carry their 

design load in the event of a large fire in the curbed area around a tank of lubricating oil. A 

structural steel column is considered to fail if the average cross section temperature of the steel 

exceeds 538 °C (1,000 °F), as described in Section F.2. The results of the FDS simulations are 

summarized in Table F-4. 

Table F-4. Summary of results for the turbine building fire scenarios. 

Model 

Bias 

Factor, 

ࢾ

Standard 

Deviation, 

ࡹ෥࣌

Target Predicted 

Value 

Critical 

Value 

Probability of 

Exceeding 

Surface Temperature (°C), Initial Value = 36 °C 

Curb Location 1 

FDS 1.02 0.13 Column A 270 538 0.000 

FDS 1.02 0.13 Column B 260 538 0.000 

FDS 1.02 0.13 Column C 170 538 0.000 

FDS 1.02 0.13 Column D 150 538 0.000 

FDS 1.02 0.13 Column E 90 538 0.000 

FDS 1.02 0.13 Column F 50 538 0.000 

Curb Location 2 

FDS 1.02 0.13 Column A 130 538 0.000 

FDS 1.02 0.13 Column B 120 538 0.000 

FDS 1.02 0.13 Column C 400 538 0.001 

FDS 1.02 0.13 Column D 620 538 0.828 

FDS 1.02 0.13 Column E 75 538 0.000 

FDS 1.02 0.13 Column F 50 538 0.000 

F.5.1 Column Heat Flux and Column Temperature 

The predicted column temperatures for Curb Location 1 and Curb Location 2 are shown in 

Figure F-7 and Figure F-8. According to the FDS analyses, only Column D is threatened 

significantly by a fire at Curb Location 2. 
LUBRICATING OIL FIRE IN A TURBINE BUILDING

F-15 

Figure F-7. Temperatures of columns for Curb Location 1. 

 

0

50

100

150

200

250

300

350

400

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

Temperature of Column A

FDS

0

50

100

150

200

250

300

350

400

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

Temperature of Column B

FDS

0

50

100

150

200

250

300

350

400

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

Temperature of Column C

FDS

0

50

100

150

200

250

300

350

400

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

Temperature of Column D

FDS

0

50

100

150

200

250

300

350

400

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

Temperature of Column E

FDS

0

50

100

150

200

250

300

350

400

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

Temperature of Column F

FDS
LUBRICATING OIL FIRE IN A TURBINE BUILDING

F-16 

Figure F-8. Temperatures of columns for Curb Location 2. 

 

0

100

200

300

400

500

600

700

800

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

Temperature of Column A

FDS

0

100

200

300

400

500

600

700

800

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

Temperature of Column B

FDS

0

100

200

300

400

500

600

700

800

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

Temperature of Column C

FDS

0

100

200

300

400

500

600

700

800

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

Temperature of Column D

FDS

0

100

200

300

400

500

600

700

800

0 600 1200 1800 2400 3000 3600

Temperature (°C)

Time (s)

Temperature of Column E

FDS

0

100

200

300

400

500

600

700

800

0 600 1200 1800 2400 3000 3600

Temperature (°C)

°

Temperature of Column F

FDS
LUBRICATING OIL FIRE IN A TURBINE BUILDING

F-17 

F.6 Conclusion 

This analysis has addressed the potential for a relatively large lubricating oil fire to damage 

exposed structural steel in a turbine building. The analysis is complicated by the significant 

flame impingement on the ceiling caused by an oil fire spread over a relatively large area. This 

type of fire behavior is beyond the validation range addressed in NUREG-1824 (EPRI 1011999). 

Algebraic calculations were performed to estimate the extent of flame extension beneath the 

ceiling. These algebraic calculations indicate that at least one of the columns (Column D) would 

be engulfed in the flames extending from the fire at Curb Location 2 These calculations also 

indicate that other columns would be located near the outer extent of flames from Curb 

Locations 1 and 2. Algebraic calculations were also performed to estimate the time to reach the 

critical steel temperature of the nearest column. These calculations indicate that damage could 

occur within a time frame of approximately five minutes. These calculations indicate that a more 

detailed analysis is warranted. The CFD model, FDS, was used to perform this more detailed 

analysis because zone models do not have the necessary physical models to simulate the 

postulated fire. 

Based on the FDS simulation of this scenario, a 50 MW lubricating oil fire in Curb Location 1 is 

not predicted to cause the steel columns to exceed a temperature of 538 °C (1,000 °F). This is 

not the case for the proposed Curb Location 2, which is located closer to Column D. 

Consequently, the recommendation for the design package is to install the curbed area at Curb 

Location 1. 

F.7 References 

1. American Institute of Steel Construction, Steel Construction Manual, 13th Edition, New York, 

2006. 

2. ASTM E119-10a. Standard Test Methods for Fire Tests of Building Construction Materials, 

American Society for Testing and Materials, West Conshohocken, PA, 2010. 

3. Heskestad, G., and Hamada, T., “Ceiling jets of strong fire plumes,” Fire Safety Journal, Vol. 

21, No. 1, pp. 69-82, 1993. 

4. Karlsson, B., and J.G. Quintiere, Enclosure Fire Dynamics, CRC Press LLC, Boca Raton, 

FL, 2000. 

5. Mulholland, G.W., and C. Croarkin, “Specific Extinction Coefficient of Flame Generated 

Smoke,” Fire and Materials, 24:227-230, 2000. 

6. NIST NCSTAR 1-5F, Federal Building and Fire Safety Investigation of the World Trade 

Center Disaster: Computer Simulation of the Fires in the World Trade Center Towers, 2005. 

7. NIST SP 1018-5, Fire Dynamics Simulator (Version 5), Technical Reference Guide, Vol. 3, 

Experimental Validation, 2010. 

8. NUREG-1805, Fire Dynamics Tools (FDTs

) Quantitative Fire Hazard Analysis Methods for 

the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program, 2004. 

9. NUREG-1824 (EPRI 1011999), Verification and Validation of Selected Fire Models for 

Nuclear Power Plant Applications, 2007. 

10. SFPE Handbook of Fire Protection Engineering, 4th edition, 2008. 
LUBRICATING OIL FIRE IN A TURBINE BUILDING

F-18 

F.8 Attachments (on CD) 

1. FDS input files: 

a. Lube_oil_fire_in_TB_Location_1.fds 

b. Lube_oil_fire_in_TB_Location_2.fds 

2. Algebraic model files: 

a. 05.1_Heat_Flux_Calculations_Wind_Free_AppF.xls (Point Source) 

b. 05.1_Heat_Flux_Calculations_Wind_Free_AppF.xls (Solid Flame 1) 
G-1 

APPENDIX G 

TRANSIENT FIRE IN A MULTI-COMPARTMENT 

CORRIDOR 

G.1 Modeling Objective 

The calculations described in this appendix predict room temperatures in a multi-compartment 

corridor after the accidental start of a transient fire in a stack of burning pallets with two trash 

bags on top that were left after a plant modification. The purpose of the calculation is to 

determine whether cables in adjacent compartments will fail, and, if so, at what time failure 

occurs. The time to smoke detector activation is also estimated. 

G.2 Description of the Fire Scenario 

General Description: After a plant modification, a fire ignites in a stack of pallets with two trash 

bags on top, in a corner of a corridor containing multiple compartments, with different door 

heights and soffits. Various important cables are routed through the corridor compartments. 

Geometry: This area consists of interconnected compartments and corridors on the same 

level. All boundary surfaces are 0.5 m (1.6 ft) thick, as shown in Figure G-1. Figure G-1 and 

Figure G-2 illustrate the geometry. 

Materials: The walls, ceiling, and floor are made of concrete. The thermal properties of the 

materials in the compartment are listed in Table 3-1. The cable trays contain cross-linked 

polyethylene (XPE or XLPE)-insulated cables with a Neoprene jacket. These thermoset (TS) 

type cables are considered damaged when the internal temperature just underneath the jacket 

reaches 330 °C (625 °F) (NUREG-6850 (EPRI 1011989), Table H-1). The tray locations are 

shown in Figure G-2. 

Fire Protection Systems: There are nine smoke detectors, located as shown in Figure G-1. 

The detectors are Underwriters Laboratory (UL) listed, with a sensitivity of 4.9%/m (UL 217, 

2006). There is no automatic fire suppression. 

Ventilation: The ventilation system supplies the combined space at a rate of 1.67 m3

/s 

(3,54 ft3

/min). The supply and return vents are shown in the drawing. There are three doors 

leading into the space, all of which are closed during normal operation but each has a 1.3 cm 

(0.5 in) gap between the floor and its base. 
TRANSIENT FIRE IN A MULTI-COMPARTMENT CORRIDOR

G-2 

Figure G-1. Geometry of the multi-compartment corridor. 
TRANSIENT FIRE IN A MULTI-COMPARTMENT CORRIDOR

G-3 

Figure G-2. Geometry details of the multi-compartment corridor. 
TRANSIENT FIRE IN A MULTI-COMPARTMENT CORRIDOR

G-4 

Fire: The fire, a stack of four wood pallets with two trash bags, is located in the corner, as 

shown in Figure G-1 and Figure G-2. The pallet stack is 0.44 m (1.4 ft) tall. The fire HRR 

follows a “t-squared” curve to a maximum value of 2,500 kW in seven minutes and remains 

steady for eight additional minutes. The heat release rate (HRR) is estimated by combining 

separate estimates for the stack of wood pallets and the trash bags and using data from the 

SFPE Handbook, 4th edition. After that, the fire’s HRR decays linearly to zero in eight minutes. 

The heat of combustion and product yields are based on values for red oak, and are listed in 

Table G-1. The HRR curve is shown in Figure G-3. 

Table G-1. Products of combustion for a wood pallet fire. 

Parameter Value Source 

Effective Fuel Formula C6H10O5 Cellulose 

Peak HRR 2,500 kW SFPE Handbook, 4th Ed., Figs. 3-1.65, 3-1.100

Time to reach peak HRR 420 s SFPE Handbook, 4th Ed., Figs. 3-1.64 

Heat of Combustion 17,100 kJ/kg SFPE Handbook, 4th Ed., Table 3-4.16

Heat of Combustion per unit 

mass of oxygen consumed 

13,100 kJ/kg Hugget 1980, Average value 

CO2 Yield 1.27 kg/kg SFPE Handbook, 4th Ed., Table 3-4.16 

Soot Yield 0.015 kg/kg SFPE Handbook, 4th Ed., Table 3-4.16 

CO Yield 0.004 kg/kg SFPE Handbook, 4th Ed., Table 3-4.16 

Radiative Fraction 0.37 SFPE Handbook, 4th Ed., Table 3-4.16 

Figure G-3. HRR for the corridor fire scenario. 

 

0

500

1000

1500

2000

2500

3000

0 600 1200 1800 2400 3000 3600

HRR (kW)

Time (s)

Heat Release Rate
TRANSIENT FIRE IN A MULTI-COMPARTMENT CORRIDOR

G-5 

G.3 Selection and Evaluation of Models 

This section discusses the overall modeling strategy. In particular, it describes the process of 

model selection, including a discussion of the validity of these models for the given fire scenario. 

G.3.1 Temperature Criterion 

The McCaffrey, Quintiere, and Harkleroad (MQH) correlation incorporated in the Fire-Induced 

Vulnerability Evaluation (FIVE-Rev1) is used to estimate the hot gas layer (HGL) temperature in 

the fire room. The correlation applies only to a single room; however, if the temperature in the 

fire room is less than the damage temperature, the conclusion can be made that the 

temperature will be even lower in the adjacent compartment, where the closest cable tray is 

located. 

The time to smoke detection can be calculated using FIVE-Rev1 with the ceiling jet temperature 

unconfined flow correlation of Alpert and the confined flow correlation of Delichatsios. 

Zone models can calculate the time-dependent HGL properties in multi-compartment scenarios, 

as well as the activation times of smoke detectors. Although the geometry in this scenario is 

somewhat complex, it can be handled by zone modeling, since it is largely a group of 

interconnected compartments. The zone model MAGIC is used in this scenario. 

G.3.2 Validation 

A source of validation data justifying the use of the fire models discussed above for this scenario 

is the U.S. Nuclear Regulatory Commission/Electric Power Research Institute (NRC/EPRI) 

verification and validation (V&V) study documented in NUREG-1824 (EPRI 1011999). The 

National Bureau of Standards (NBS, now the National Institute of Standards and Technology 

(NIST)) Multi-Room Test Series consists of 45 fire experiments in two relatively small rooms 

connected via a relatively long corridor. The fire source, a gas burner, was located against the 

rear wall of one of the small compartments, and fire tests of 100 kW, 300 kW, and 500 kW were 

conducted. The present scenario has a larger fire in a larger, longer compartment. The V&V 

study assessed the MQH HGL temperature correlation, the Alpert ceiling jet correlation, and the 

zone model, MAGIC. The unconfined ceiling jet correlation of Delichatsios is included in this 

analysis to assess the sensitivity of various input parameters. 

Table G-2 lists various important model parameters and the ranges for which the NRC/EPRI 

validation study is applicable. The calculations in Table G-2 are for the fire room 

(compartment 8, as shown in Figure G-4). The ceiling jet radial distance relative to the ceiling 

height is not within the range of validation. As a sensitivity case, an additional detector was 

added at a distance that would fall within the validation range (6.8 m (22.3 ft)). In addition, the 

room-width geometry is not within the range of validation. A sensitivity case with the height 

reduced to a value within the validation range (5 m (16.4 ft)) was performed. The remaining 

model parameters are within the applicable validation ranges. 

 
TRANSIENT FIRE IN A MULTI-COMPARTMENT CORRIDOR

G-6 

Table G-2. Normalized parameter calculations for the multi-compartment corridor fire scenario. 

Quantity Normalized Parameter Calculation 

NUREG1824 

Validation 

Range 

In 

Range? 

Fire Froude 

Number 

ܳሶ

כ ൌ ܳሶ

ߩஶܿ௣ܶஶܦଶ.ହඥ݃

ൌ 2500 kW

ሺ1.2 kg/mଷሻሺ1.0 kJ/kg/Kሻሺ293 Kሻሺ1.29ଶ.ହ mଶ.ହሻඥ9.8 m/sଶ ൌ 1.2

0.4 – 2.4 Yes 

Flame Length, 

L୤, relative to 

the Ceiling 

Height, Hc

௙ܮ ൅ ௙ܪ

௖ܪ

ൌ 0.44 m ൅ 3.8 m

6.1 m ൌ 0.7

ܮ ௙ൌ ܦ ቀ3.7 ܳሶ

כଶ/ହ െ 1.02ቁ ൌ 1.29 m ሺ3.7 ൈ 1.2଴.ସ െ 1.02ሻ ൌ 3.8 m

0.2 – 1.0 Yes 

Ceiling Jet 

Horizontal 

Radial 

Distance,rcj, 

relative to the 

Ceiling Height, 

Hc

௝௖ݎ

௙ܪ െ௖ ܪ

ൌ 4.46 m

6.1 m – 0.44 m ൌ 0.8 1.2 – 1.7 No 

Equivalence 

Ratio, φ, as an 

indicator of the 

Ventilation Rate 

߮ ൌ

ܳሶ

ΔܪOమ݉ሶ Oమ

ൌ 2500 kW

13,100 kJ/kg ൈ 0.46 kg/s ൌ 0.4

݉ሶ Oమ ൌ 0.23 ߩஶܸሶ ൌ 0.23 ൈ 1.2 kg/mଷ ൈ 1.67 mଷ/s ؆ 0.46 kg/s

0.04 – 0.6 Yes 

Compartment 

Aspect Ratios 

ܮ

௖ܪ

ൌ 15.2 m

6.1 m ൌ 2.49 ; 

ܹ

௖ܪ

ൌ 3.0 m

6.1 m ൌ 0.49 0.6 – 5.7 No 

Target 

Distance, r, 

relative to the 

Fire Diameter, 

D

N/A 2.2 – 5.7 N/A 

Notes: 

(1) The non-dimensional parameters are explained in Table 2-5. 

(2) The effective diameter of the base of the fire, ܦ, is calculated using ܦ ൌ ඥ4ܣ/ߨ, 

where ܣ is the area of the pallets. 

(3) The “Fire Height,” ܪ ൅ ௙ܮ௙, is the sum of the height of the fire from the floor and the 

fire’s flame length. 

 
TRANSIENT FIRE IN A MULTI-COMPARTMENT CORRIDOR

G-7 

G.4 Estimation of Fire-Generated Conditions 

G.4.1 Algebraic Models 

This scenario concerns the prediction of cable damage at a location outside the compartment of 

fire origin. The temperature of the HGL in the compartment of fire origin can be modeled as a 

potential screening tool. If the HGL temperature within the compartment of origin is not likely to 

cause damage to cables in that compartment, damage to cables outside the fire compartment is 

even more unlikely. As a part of this approach, the cable surface temperature is modeled as 

exactly matching the HGL temperature (i.e., heat-up of the cable is immediate). 

FIVE-Rev1 was used for the MQH room temperature analysis. The inputs to the model are 

found in Table 3-1, Table G-1, and Table G-3. The calculation is applied to the fire room only, 

with the opening to the next compartment treated as an opening with an area (height × width) 

equal to 6.1 × 3 = 18.3 m2

 (197 ft2). To correct the MQH temperature correlation for a fire in the 

corner, the results from FIVE-Rev1 are multiplied by a factor of 1.7, as suggested by Karlsson 

and Quintiere (Equation 6.23). 

For the time to detection, the Alpert ceiling jet temperature calculation is used. The approach is 

to calculate the time at which the ceiling jet temperature at the heat detector is 30 °C (86 °F). 

The additional inputs for this correlation are the horizontal radial distance from the centerline of 

the fire plume to the detector, which is 4.5 m (14.8 ft), and the fire location factor of 4, because 

of the fire in the corner. Because the fire room is corridor-shaped, the flow is likely to be 

confined; therefore, the confined flow correlation by Delichatsios is also used. The additional 

input is the corridor half-width of 1.5 m (4.9 ft). 

G.4.2 Zone Model 

This is a classic application of a zone fire model with a fire in one compartment connected to a 

number of additional compartments with doorway-like vents. Outputs of primary interest in the 

simulation include temperatures in the compartments, activation of smoke detectors in the 

compartments, and the temperature of cable targets in the compartments. This scenario was 

modeled using the zone model MAGIC (Gay et. al., 2005). 

Geometry: To simplify the process of modeling the multi-compartment geometry, the layout 

was divided into eight areas, as illustrated in Figure G-4. Note that the small indentation in 

compartment 1 was ignored for the MAGIC calculations. Compartments were connected by a 

door (compartments 5 to 6), a soffit (compartments 2 to 3), or were left open by using a full-wall 

opening (compartments 1 to 2, 3 to 4, 4 to 5, 3 to 7, and 7 to 8). 

Table G-3 summarizes the compartment dimensions used for zone modeling. A graphical 

depiction of the scenario, as modeled in MAGIC, is shown in Figure G-5. 
TRANSIENT FIRE IN A MULTI-COMPARTMENT CORRIDOR

G-8 

Figure G-4. Effective corridor layout for implementation in zone models (not to scale). 

Table G-3. Compartment dimensions for corridor scenario. 

Comp. Length 

m (ft) 

Width 

m (ft) 

Area 

m2 (ft2) 

1 8.1 (26.6) 4.1 (13.5) 33.2 (357) 

2 2.0 (6.6) 23.4 (76.8) 46.8 (504) 

3 45.1 (148) 4.1 (13.5) 184.9 (1990) 

4 8.1 (26.6) 6.0 (19.7) 48.6 (523) 

5 10.3 (33.8) 6.6 (21.7) 68.0 (732) 

6 10.3 (33.8) 6.6 (21.7) 68.0 (732) 

7 12.2 (40) 8.2 (26.9) 100.0 (1076) 

8 3 (9.8) 15.2 (49.9) 45.6 (491) 

1 

2 

3 

8 

4 

5 

6 

7 
TRANSIENT FIRE IN A MULTI-COMPARTMENT CORRIDOR

G-9 

Figure G-5. MAGIC rendering of the corridor scenario. 

Fire: The fire is modeled as a 1.3 m2 (14 ft2) source (equivalent diameter of 1.29 m (4.2 ft)) at 

an elevation of 0.44 m (1.4 ft) (see Figure G-2). The stoichiometric oxygen to fuel ratio, ߰, is 

calculated using Equation 22 from Chapter 4 in Section 3 of the SFPE Handbook, 4th edition

and the values from Table G-1, as follows: 

߰ ൌ

ܪ∆

Oమܪ∆

ൌ 17.1 kJ/g

13.1 kJ/g ؆ 1.3 g/g (G-1)

where ∆ܪ is heat of combustion per unit mass of fuel consumed and ∆ܪOమ is the heat of 

combustion per unit mass of oxygen consumed. One of the inputs required by MAGIC is the 

specific area, ݏ) NUREG-1824, Volume 6, Section 3.2.7): 

ݏൌݕ௦݇௠ ൌ 0.015 ൈ 7,600 mଶ

g

ൌ 114 mଶ/g (G-2)

where ݇௠ is a constant and ݕ௦ is the soot yield, as listed in Table G-1. Products of combustion 

for a wood pallet fire.. The pyrolysis rate (g/s) is calculated for input to MAGIC by dividing the 

HRR values (kW) at each time step (as shown in Figure G-3) by the heat of combustion 
TRANSIENT FIRE IN A MULTI-COMPARTMENT CORRIDOR

G-10 

(17.1 kJ/g). Other inputs needed for MAGIC are listed in Table G-1. Products of combustion for 

a wood pallet fire.. Figure G-6 is a screenshot of the source fire in the MAGIC input file. 

Figure G-6. MAGIC screen capture of the fire in corridor scenario. 
TRANSIENT FIRE IN A MULTI-COMPARTMENT CORRIDOR

G-11 

Ventilation: The ventilation rate is given in Section G.2. The vents in Figure G-1 are square, 

but, because MAGIC uses round vents, an equivalent diameter of 1.13 m (3.7 ft) was used as 

input. In room-to-room connections with the same ceiling height, a shallow (0.1 m) soffit was 

added to allow smoother model execution. Finally, the only leakage from the space occurs via a 

1.3 cm (0.5 in) crack under each of the three doors. The inputs for the supply air vent are 

shown in Figure G-7. 

Figure G-7. MAGIC screen capture for supply vent specification.

 
TRANSIENT FIRE IN A MULTI-COMPARTMENT CORRIDOR

G-12 

Fire Protection Systems: In MAGIC, there is no direct way of calculating smoke density for 

smoke detector activation. Consistent with NUREG-1805, the recommended approach given by 

the developers is to model the smoke detector as a sprinkler with a very low activation 

temperature and response time index (RTI). An activation temperature of 30 °C (86 °F) and an 

RTI of 5 (m/s)1/2 was selected. The location of the smoke detector closest to the fire was 

entered into the input file, as shown in Figure G-8. 

Figure G-8. MAGIC screen capture of the smoke detector specification. 
TRANSIENT FIRE IN A MULTI-COMPARTMENT CORRIDOR

G-13 

G.5 Evaluation of Results 

The purpose of the calculations is to determine whether a stack of burning pallets plus two trash 

bags in a corridor could generate gas temperatures in adjacent compartments that are capable 

of damaging cables and electrical equipment. Smoke detector activation is also estimated. The 

algebraic model FIVE-Rev1 and the zone model MAGIC were used for this scenario. In 

general, the results demonstrate that the fire is not capable of generating damaging conditions, 

even in the compartment of fire origin; as a result, there is no need for detailed modeling of the 

targets in remote locations. The following sections describe the results in greater detail. 

Table G-4 summarizes the results of the models for the damage criteria. For each predicted 

value, a calculation is performed to determine the probability of exceeding the critical value. 

The procedure for calculating this probability is given in Chapter 4, and it accounts for the model 

bias and scatter. The purpose of this table is to highlight the criterion that is most likely to be 

exceeded so that further analysis can be focused on this criterion and on the model or models 

that predict it. The criterion is discussed in greater detail in the following subsections. 

Table G-4. Summary of the model predictions of the corridor scenario. 

Model 

Bias 

Factor, 

ࢾ

Standard 

Deviation,

ࡹ෥࣌

Ventilation Predicted

Value 

Critical 

Value 

Probability 

of 

Exceeding 

HGL Temperature (°C), Initial Value = 20 °C 

FIVE-Rev1 

(MQH) 1.56 0.32 Natural 256 330 0.001 

MAGIC 1.01 0.07 Mechanical 240 330 0.000 

G.5.1 Temperature Criterion 

The MQH correlation in FIVE-Rev1 predicts a peak temperature of 256 °C (493 °F) in the 

corridor where the fire is located. MAGIC predicts 240 °C (464 °F) (see Figure G-9). Both 

predictions are below the cable damage temperature threshold of 330 °C (625 °F). MAGIC 

results show that the HGL temperatures for the other corridors are substantially lower; for 

example, the next closest corridor (compartment 7) reaches a peak temperature of 160 °C 

(320 °F), as shown in Figure G-9. A comparison of Figure G-9 and Figure G-3 shows that the 

timing and the shape of the HGL temperature curve closely follows the HRR curve. The HRR 

produced by MAGIC is unmodified from the one based on the input (i.e., there is no oxygen 

starvation). 
TRANSIENT FIRE IN A MULTI-COMPARTMENT CORRIDOR

G-14 

Figure G-9. HGL temperature predictions by MAGIC for the corridor scenario. 

Chapter 4, Model Uncertainty, provides guidance on how to express the uncertainty of the 

MAGIC predictions. MAGIC predicted a temperature rise of M = 240 – 20 = 220 °C (428 °F). 

As shown in Table 4-1, the NRC/EPRI V&V study (NUREG-1824 (EPRI 1011999)) found that 

MAGIC predictions of HGL temperature rise are, on average, 1% greater than corresponding 

measurements, with a relative standard deviation of 7%. The adjusted model prediction is μ = 

220/1.01 = 218, and the standard deviation is σ = 0.07 × (220/1.01) = 15.2 °C. Therefore, the 

probability that the cable temperature would exceed 330 °C (625 °F) is: 

ܲሺܶ ൐ 330ሻ ൌ 1

2 erfc ൬

330 െ 20 െ 218

15.2√2 ൰ ؆ 0 (G-3)

The same uncertainty calculation for the MQH correlation in FIVE-Rev1 results in a probability 

of exceeding the damage temperature of 0.001, or 0.1%. In other words, there is a near-zero 

probability of exceeding the damage temperature threshold for cables within the compartment of 

fire origin based on a surrounding HGL temperature, according to the FIVE-Rev1 and MAGIC 

predictions. This demonstrates that detailed analyses of the cables outside the compartment of 

origin are not warranted. 

Sensitivity of the Room Width to Height Ratio 

As shown in Table G-2, the room width to height ratio is not within the validation bounds. A 

sensitivity case is run in which the room height is reduced until the ratio is within the bounds. All 

inputs are the same, except that the height is reduced from 6.1 m (20 ft) to 5 m (16.4 ft) in the 

fire room. The results, plotted in Figure G-10, show that although the temperatures are slightly 

higher in the fire room, there is no change in the adjacent room, which contains the target. This 

shows that the room width to height ratio is not a significant influence on the results in this 

scenario and that the MAGIC results are applicable, even though the ratio falls outside of the 

validation bounds. 

0

50

100

150

200

250

300

0 600 1200 1800 2400

Temperature (C)

Time (s)

HGL Temperature Fire 

Room 

MAGIC

FIVE (MQH)

0

40

80

120

160

200

0 600 1200 1800 2400

Temperature (C)

Time (s)

HGL Temperature Compartment 7 
TRANSIENT FIRE IN A MULTI-COMPARTMENT CORRIDOR

G-15 

Figure G-10. HGL temperature for reduced ceiling height by MAGIC. 

G.5.2 Smoke Detection 

The smoke detector activation time in the corridor containing the fire is based on the time for the 

ceiling jet temperature to reach 30 °C (86 °F) at the detector location. The results, plotted in 

Figure G-11, show that the two correlations from FIVE-Rev1 produce identical results of 50 s, 

and MAGIC predicts 40 s. 

Figure G-11. Detector temperature prediction by MAGIC for fire corridor. 

0

50

100

150

200

250

300

0 600 1200 1800 2400

Temperature (C)

Time (s)

HGL Temperature Fire 

Room 

Base Case 

(H=6.1 m)

Ceiling 

Height=5 m

0

40

80

120

160

200

0 600 1200 1800 2400

Temperature (C)

Time (s)

HGL Temperature Compartment 7 

Base Case 

(H=6.1)

Height=5 m 

Fire Room

0

10

20

30

40

50

60

70

80

0 50 100 150

Temperature (C)

Time (s)

Ceiling Jet Temperature

FIVE (Alpert)

FIVE (Delichatsios)

MAGIC
TRANSIENT FIRE IN A MULTI-COMPARTMENT CORRIDOR

G-16 

Sensitivity of the Ceiling Jet Radial Distance Relative to the Ceiling Height 

As shown in Table G-2, the ceiling jet radial distance relative to the ceiling height is not within 

the validation bounds. A sensitivity case is performed in which a detector is placed at a further 

distance so that the ratio is within the validation bounds. The results, plotted in Figure G-12, 

show that the difference in time to detection varies from 40 s for the base case to 50 s for the 

detector located slightly further away. This small difference in time indicates that for this 

scenario, the results are valid, even though the ratio of radius to ceiling height falls outside of 

the validation bounds. 

Figure G-12. Detector temperature for two radial distances predicted by MAGIC. 

G.6 Conclusion 

This analysis addresses a transient fire in a relatively long, narrow room, identified as a corridor, 

which is connected with other rooms in a multi-room arrangement. The targets include cables in 

rooms located beyond the corridor where the fire is specified to occur. The MQH correlation 

included in FIVE-Rev1 was used to estimate temperature conditions within the corridor, and it 

was found that the HGL temperature predicted by the MQH correlation was lower than the cable 

damage temperature. Because the cables are located in rooms beyond the corridor where the 

fire occurs and it can be reasoned that the temperatures in these rooms will be lower than in the 

corridor, cable damage would not be expected. 

The zone model MAGIC was used to predict the HGL temperatures in all of the interconnected 

compartments, resulting from the stack of burning pallets and trash bags. These MAGIC 

calculations also demonstrate that the HGL temperature is not high enough to cause cable 

damage in any compartment or corridor, including the corridor of fire origin. These predictions 

account for model uncertainty in the temperature predictions and the sensitivity to variations in 

the heat release rate. Based on a simplified method for smoke detector activation, smoke 

detector operation is expected to occur between 40 s and 50 s after the ignition of the fire. 

0

10

20

30

40

50

60

70

80

0 50 100 150

Temperature (C)

Time (s)

Ceiling Jet Temperature

Base Case (r=4.5)

Radial distance=6.8 m
TRANSIENT FIRE IN A MULTI-COMPARTMENT CORRIDOR

G-17 

G.7 References 

1. Gay, L., C. Epiard, and B. Gautier, MAGIC Software Version 4.1.1: Mathematical Model, 

EdF HI82/04/024/B, Electricité de France, France, November 2005. 

2. Huggett, C., “Estimation of Rate of Heat Release by Means of Oxygen Consumption 

Measurements,” Fire and Materials, 4:61-65, 1980. 

3. Karlsson, B., and Quintiere, J. G., Enclosure Fire Dynamics, CRC Press, Boca Raton, 2000. 

4. NUREG-1805, Fire Dynamics Tools (FDTs) Quantitative Fire Hazard Analysis Methods for 

the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program, 2004. 

5. NUREG-1824 (EPRI 1011999), Verification and Validation of Selected Fire Models for 

Nuclear Power Plant Applications, 2007. 

6. NUREG/CR-6850 (EPRI 1011999), EPRI/NRC-RES Fire PRA Methodology for Nuclear 

Power Facilities, 2005. 

7. SFPE Handbook of Fire Protection Engineering, 4th edition, 2008. 

8. UL 217, Single and Multiple Station Smoke Alarms, 6th edition, Underwriters Laboratories, 

Inc., 2006. 

G.8 Attachments (on CD) 

1. Algebraic model file: 

a. Appendix G FIVE.xlsm 

b. MQH_AppG.xlsx 

2. MAGIC input files: 

a. Corridor.cas 

b. Corridor_reduced_H.cas 

 
TRANSIENT FIRE IN A MULTI-COMPARTMENT CORRIDOR

G-18 

 
H-1 

APPENDIX H 

CABLE TRAY FIRE IN ANNULUS 

H.1 Modeling Objective 

The calculations described in this appendix assess the potential for damage to redundant safeshutdown cables due to a fire in an adjacent cable tray in the annulus region of a pressurized 

water reactor (PWR) containment building. In addition, the calculations provide information on 

the effectiveness of a sprinkler system installed in a non-standard configuration. 

H.2 Description of the Fire Scenario 

General Description: The annulus is the region between the primary containment steel 

structure and the secondary concrete containment (shield) building. The primary and secondary 

containments are cylindrical with domes on top. The annulus space contains a variety of 

penetrations from the reactor to the external support systems. One of these penetrations 

contains two trays with redundant cables that control systems in both trains of safety equipment. 

A fire starts in one tray and spreads vertically and horizontally. The purpose of the calculation is 

to determine if a fire in one train of a cable tray (e.g., Train A) can damage the redundant train 

of equipment (e.g., Train B). 

Geometry: The layout of the annulus is shown in Figure H-1. The exterior wall is made of 

concrete, while the interior wall and cable trays are made of steel. The cable tray locations are 

shown in Figure H-2. The trays are 0.6 m (2 ft) wide. 

Materials: Property values for the relevant materials are listed in Table 3-1. The annulus wall 

thicknesses are indicated in the drawing. The cable tray steel is approximately 2 mm (0.079 in) 

thick. 

Cables: The cable trays are filled with PE-insulated, PVC-jacketed control cables. These 

cables have a diameter of approximately 1.5 cm (0.6 in), a jacket thickness of approximately 

1.5 mm (0.06 in), and 7 conductors. There are approximately 120 cables in each tray. The 

mass of each cable is 0.4 kg/m. The mass fraction of copper is 0.67. These cables fail when 

the internal temperature just underneath the jacket reaches approximately 205 °C (400 °F) or 

when the exposure heat flux exceeds 6 kW/m2

 (NUREG-1805, Appendix A). 

Fire: The heat of combustion and product yields for PE/PVC cables are taken from Table 3-

4.16 of the SFPE Handbook, 4th edition and listed in Table H-1. Note that the non-metallic 

components of the cables are a mixture of PE (C2H4) and PVC (C2H3Cl). Because the mixture 

consists of approximately the same mass of each, the cable materials are modeled using an 

effective chemical formula of C2H3.5Cl0.5. 

The fire ignites at the base of the lower cable train in the vicinity of the bend at the inner wall. 

From the results of the CHRISTIFIRE project (NUREG/CR-7010, Vol. 1), the heat release rate 

(HRR) per unit area of this thermoplastic (TP) cable is estimated to be 250 kW/m2

. The fire 

spreads vertically at a rate of 258 mm/s (10 in/s) and horizontally at a rate of 0.9 mm/s 
CABLE TRAY FIRE IN ANNULUS

H-2 

(0.035 in/s) (NUREG/CR-6850 (EPRI 1011989), Appendix R). The peak HRR is 945 kW once 

all of the cables in the first tray are burning (see Figure H-3). 

Table H-1. Products of combustion for a PE/PVC cable fire. 

Parameter Value Source 

Heat of Combustion 20,900 kJ/kg SFPE Handbook, 4th ed., Table 3-4.16 

CO2 Yield 1.29 kg/kg SFPE Handbook, 4th ed., Table 3-4.16 

Soot Yield 0.136 kg/kg SFPE Handbook, 4th ed., Table 3-4.16 

CO Yield 0.147 kg/kg SFPE Handbook, 4th ed., Table 3-4.16 

Radiative Fraction 0.49 SFPE Handbook, 4th ed., Table 3-4.16 

Local burnout of the fire occurs when the cable plastic is consumed. The time to burnout is 

calculated as follows. First, determine the combustible mass per unit area of tray, ݉௖

ᇱᇱ: 

݉௖

ᇱᇱ ൌ ݊ ܻ௣ ሺ1െߥሻ݉ᇱ

ܹ ൌ 120 ൈ 0.33 ൈ ሺ1െ0ሻ ൈ 0.4 kg/m

0.6 m ؆ 26.4 kg/mଶ (H-1)

where ݊ is the number of cables per tray, ܻ௣ is the mass fraction of combustible (i.e., nonmetallic or plastic) material in the cable, ߥ is the residue yield (which is conservatively set to 

zero in this calculation), ݉ᇱ

 is the total mass per unit length of a single cable, and ܹ is the tray 

width. Next, calculate the burnout time, Δݐ: 

ൌ ݐ∆

݉௖

ܪ∆ ᇱᇱ

ሶݍ 5

avg

ᇱᇱ /6 ൌ 26.4 kg/mଶ ൈ 20,900 kJ/kg

5/6 ൈ 250 kW/mଶ ؆ 2648 s (H-2)

where ∆ܪ is the heat of combustion and ݍሶ

avg

ᇱᇱ is the average HRR per unit area of tray. The HRR 

per unit area ramps linearly to its average value over a time period of ∆ݐ/6, remains steady for a 

time period of 2 ∆ݐ/3, and then decreases linearly to zero over a time period of ∆ݐ/6. The linear 

ramp-up and ramp-down are typical ways of approximating the time history of an item’s HRR. 

 
CABLE TRAY FIRE IN ANNULUS

H-3 

Figure H-1. Geometry of the annulus. 
CABLE TRAY FIRE IN ANNULUS

H-4 

Figure H-2. Geometry details of redundant cable trays located in the annulus. 
CABLE TRAY FIRE IN ANNULUS

H-5 

Figure H-3. HRR for a cable fire in the annulus. 

Suppression System: Standard response sprinklers are located on the inner wall, as shown in 

Figure H-2. The sprinklers have a response time index (RTI) of 130 (m·s)1/2 and activate at a 

temperature of 100 °C (212 °F) (NUREG-1805, Chap. 10). Each sprinkler is topped by heat 

collectors designed to trap heat from a fire. The ambient temperature within the annulus region 

is typically 35 °C (95 °F). 

H.3 Selection and Evaluation of Fire Models 

This section describes the overall modeling strategy, the selection of models, and a discussion 

of the validation exercises justifying the use of these models for this scenario. The discussion 

separately addresses the prediction of the heat flux to and temperature of the cable targets, and 

the sprinkler activation. 

H.3.1 Damage to Cables 

The point source radiation heat flux model included in the Fire Dynamics Tools (FDTs) and FireInduced Vulnerability Evaluation (FIVE-Rev1) provides useful screening estimates for cable 

damage. A simple extension of the point source heat flux model, in which the sources of heat 

are distributed at discrete points within the burning tray, provides a refinement of the single point 

source method. Given the close proximity of the two cable trays, the distributed point source 

model is expected to provide a more accurate estimate of the heat flux to the adjacent cable 

tray. 

This fire scenario can be categorized as an open rather than a compartment fire. For this 

reason, zone models are not particularly useful. Computational Fluid Dynamics (CFD) can 

refine the estimates of the simple heat flux calculations to account for tray geometry and 

orientation. 

0

100

200

300

400

500

600

700

800

900

1000

0 600 1200 1800 2400 3000 3600

HRR (kW)

Time (s)

Heat Release Rate
CABLE TRAY FIRE IN ANNULUS

H-6 

H.3.2 Sprinkler Activation 

Although the geometry of this scenario is unlike the mostly rectangular compartments found in a 

nuclear power plant (NPP), it is not particularly difficult to model in the Fire Dynamics Simulator 

(FDS). In fact, the containment building is so large that the curvature of the walls has little effect 

on the results of the calculation. For this reason, FDS can provide an estimate of the sprinkler 

link temperature to determine its potential for activation. Empirical correlations are not reliable 

because the fire burns along a horizontal and a vertical tray and thus has no well-defined 

circular base, and the plume abuts the cylindrical wall. 

H.3.3 Validation 

Only one of the non-dimensional parameters that have been used to characterize the fire 

scenarios is applicable here (Table H-2), mainly because the other parameters address 

phenomena unique to compartment fires. The only relevant parameter, ݎ/ܦ, indicates the 

relative distance separating the fire from the target cables. However, the effective fire diameter, 

ܦ, is not well-defined when the fire is expected to spread vertically and horizontally within the 

cable trays. The lateral distance between the burning tray and the target tray is 1.7 m (5.6 ft). 

The trays are each 0.6 m (2 ft) wide. For International Collaborative Fire Model Project (ICFMP) 

Benchmark Exercise #3, which is described in NUREG-1824, the relative distance between the 

fire and the heat flux gauges in some of the tests was similar to this scenario. However, the 

accuracy of the solid flame and point source algorithms included in the FDTs

 varied 

considerably in the validation study. The point source heat flux model loses accuracy when the 

target is relatively close to the fire. The solid flame model is designed to improve the accuracy 

in the near-field. However, the implementation within the FDTs

 is based on the fire being 

modeled as a pool fire with a nearly circular base and cylindrical shape. This is not the case in 

the scenario under consideration. In short, the simple heat flux models included in the FDTs

have been assessed in NUREG-1824 for experiments of comparable scope to the given 

scenario, but the models have not been demonstrated to be particularly accurate. For this 

reason, the models will be used to provide screening estimates, but the predictions will be 

supplemented by CFD calculations. 

The FDS sprinkler activation algorithm was validated using a variety of experimental test series 

(NIST SP 1018-5). The plume algorithm was also assessed in NUREG-1824. The cable failure 

algorithm, THIEF, was developed and validated in NUREG/CR-6931 (Vol. 3). 
CABLE TRAY FIRE IN ANNULUS

H-7 

Table H-2. Normalized parameter calculations for the annulus fire scenario. 

Quantity Normalized Parameter Calculation 

NUREG-1824 

Validation 

Range 

In 

Range? 

Fire Froude 

Number N/A – The fire does not conform to classic fire plume theory. 0.4 – 2.4 N/A 

Fire Height, 

 relative ,௙ܮ ൅ ௙ܪ

to the Ceiling 

௖ܪ ,Height

N/A – The fire does not conform to classic fire plume theory. 0.2 – 1.0 N/A 

Ceiling Jet Radial 

Distance, rcj, 

relative to the 

Ceiling Height, Hc

N/A – The ceiling height is essentially infinite. 1.2 – 1.7 N/A 

Equivalence Ratio, 

φ, as an indicator 

of the Ventilation 

Rate 

N/A – The scenario is outside of a clearly defined 

compartment. 0.04 – 0.6 N/A 

Compartment 

Aspect Ratio 

N/A – The scenario is outside of a clearly defined 

compartment. 0.6 – 5.7 N/A 

Target Distance, r, 

relative to the Fire 

Diameter, D

See discussion in Section H.3.3. 2.2 – 5.7 Yes 

H.4 Estimation of Fire-Generated Conditions 

This section provides specific details on how each model is set up and run. 

H.4.1 Algebraic Models 

The FDTs contain several correlations for estimating the heat flux at a fixed distance from a fire: 

 05.1_Heat_Flux_Calculations_Wind_Free.xls (Point Source) 

 05.1_Heat_Flux_Calculations_Wind_Free.xls (Solid Flame 1) 

For the point source method, the estimated peak HRR, ܳሶ, is 945 kW, the radiative fraction, ߯௥, 

is 0.49, and the horizontal distance from the center of the burning tray to the edge of the target 

tray, ݎ, is 2 m (6.6 ft). The calculated heat flux is: 

ሶݍ

ps

ᇱᇱ ൌ ߯௥ ܳሶ

4ߨ ݎଶ ൌ 0.49 ൈ 945 kW

4ߨ ൈ 2.0ଶ mଶ ؆ 9.2 kW/mଶ (H-3) 

The solid flame calculation is based on the fire having a roughly circular base with which it 

employs a flame height correlation to estimate the vertical extent of the luminous flame region. 
CABLE TRAY FIRE IN ANNULUS

H-8 

This is not the case for the vertical and horizontal trays filled with burning cables. However, it is 

possible to use a variation of the point source method to get a refined heat flux estimate that is 

similar in scope to a solid flame model. Essentially, the fire can be divided into several point 

sources along the length of the burning cable tray so that the radiative energy is not emanating 

from just one point. Suppose that the 4.6 m (15 ft) vertical tray segment is divided into four 

segments, each one 1.15 m (3.8 ft) long and 0.6 m (2 ft) wide. The horizontal tray is the fifth 

segment, 1.7 m (5.6 ft) long and 0.6 m (2 ft) wide. Each segment generates energy at a rate of 

250 kW/m2

. This leads to 172.5 kW for each of the four vertical segments and 255 kW for the 

horizontal segment. The sum is 945 kW. The distance between the center points of the 

segments and a point at the intersection of the horizontal and vertical trays nearest to the 

burning cable trays can be calculated, and the combined heat flux from this set of distributed 

sources can be calculated: 

ሶݍ

dps

ᇱᇱ ൌ ߯௥

ሶܳ෍ ߨ4

௜

௜ݎ

ଶ

௜

ൌ 0.49

൬ ߨ4

255

2.9ଶ ൅

172.5

2.4ଶ ൅

172.5

2.0ଶ ൅

172.5

2.2ଶ ൅

172.5

2.9ଶ ൰

kW

mଶ ؆ 6.2 kW/mଶ (H-4) 

Much like the solid flame method, the distributed point source method provides a refined 

estimate of the heat flux, based on the fact that the fire is distributed over the two parts of the 

tray and is not concentrated at a single point. The end result is a lower estimate of the heat flux 

to a given target point. The fire could be distributed over more than five points, but the answer 

would not significantly change. Neither the point source nor the distributed point source method 

accounts for changes in the orientation of the target. The target cables are modeled as having 

a direct view of the fire with no obstructions, such as the sides of the trays, that can reduce the 

heat flux to the target cables. The CFD model can provide a more refined estimate. 

H.4.2 CFD Model 

Geometry: Only the section of the annulus encompassing the cables and relevant targets is 

included in the computational domain. This volume is 9.6 m (31.5 ft) wide, 2.5 m (8.2 ft) deep, 

and 12.8 m (42 ft) high. Extra depth is needed to accommodate the slight curvature of the 

bounding walls. The top, bottom, and sides of the computational domain are specified as open, 

that is, open to an infinitely large volume. Since the volume of the annulus is very large, neither 

smoke build-up nor pressure effects would influence the region near the cables. Both the 

internal and external walls of the annulus are included in the model. Since FDS only allows 

rectilinear obstructions, a series of obstructions approximately 20 cm (7.9 in) thick approximate 

the curved walls. The numerical grid conforms to this “stair-stepped” geometry. 

Fire: The fire ignites near the base of the vertical portion of the cable tray attached to the inner 

wall. The spread rates of 258 mm/s (10 in/s) in the vertical direction and 0.9 mm/s (0.035 in/s) 

in the horizontal are input by using an FDS feature in which a surface is designated as having a 

fire spread over it at a designated rate. In this case, a surface is specified along the side of the 

vertical tray and along the top of the horizontal tray with the respective spread rates. The HRR 

per fire unit area is specified directly and not predicted by the model. A Smokeview rendering of 

the FDS simulation is shown in Figure H-4. 

Cables: One of the objectives of the calculation is to estimate the potential damage to the 

cables within the redundant train. FDS is limited to only 1-D heat transfer into either a 

rectangular or cylindrical obstruction. In this simulation, the cables are modeled as 1.5 cm 
CABLE TRAY FIRE IN ANNULUS

H-9 

(5.9 in) cylinders. Following the Thermally-Induced Electrical Failure (THIEF) methodology in 

NUREG/CR-6931, Vol. 3, electrical functionality is lost when the temperature just inside the 

1.5 mm (0.06 in) jacket reaches 205 °C (400 °F). Since the objective of this calculation is to 

estimate time to failure of the redundant cables, ignition and spread of the fire over the second 

set of cables is not considered. The in-depth heat penetration calculation is focused on a single 

cable that is relatively free of its neighbors and that would heat up more rapidly than those 

buried deeper within the pile. 

Sprinkler Activation: FDS uses the conventional RTI concept to predict sprinkler activation. 

In this scenario, a steel plate has also been added just above the location of the sprinkler to 

simulate the effect of the actual deflector. Note that the sprinkler itself is just a point in the 

model, and its activation is determined by the time history of the temperature and the velocity of 

the hot gases within the numerical grid cell in which the sprinkler is located. 
CABLE TRAY FIRE IN ANNULUS

H-10 

Figure H-4. FDS/Smokeview rendering of the annulus fire scenario. 
CABLE TRAY FIRE IN ANNULUS

H-11 

H.5 Evaluation of Results 

The calculations described above assess the potential for damage to redundant safe-shutdown 

cables due to a fire in an adjacent tray in the annulus region of the containment building. In 

addition, a CFD calculation is used to determine whether the fire would activate a sprinkler. The 

results of the calculations are summarized in Table H-3. 

Table H-3. Summary of model predictions for the annulus fire scenario. 

Model 

Bias 

Factor, 

ࢾ

Standard 

Deviation,

ࡹ෥࣌

Target Predicted 

Value 

Critical 

Value 

Probability 

of 

Exceeding

Heat Flux (kW/m2) 

Point Source 1.42 0.55 

Cables 

9.2 6.0 0.553 

Distributed Point 

Source 1.42 0.55 6.2 6.0 0.248 

FDS 1.10 0.17 2.5 6.0 0.000 

Target Temperature (°C) 

FDS 1.02 0.13 Cables 120.0 205.0 0.000 

Plume Temperature (°C) 

FDS 1.15 0.11 Sprinkler 90.0 100.0 0.001 

H.5.1 Heat Flux and Temperature 

The simple point source heat flux calculations are used as part of a screening analysis to 

determine whether more detailed calculations are warranted. Using the peak HRR as a 

constant input, the point source model estimates the heat flux to be 9.2 kW/m2

. A slightly more 

refined estimate using distributed point sources decreases this estimate to 6.2 kW/m2

. Both of 

these estimates suggest a potential for damage to the redundant train of cables. 

A more detailed calculation is performed with FDS, which yields a predicted peak heat flux of 

approximately 2.5 kW/m2

 (see Figure H-5). The reason that the FDS prediction of heat flux is 

significantly lower than the point source method predictions is that (1) FDS accounts for the side 

of the tray that blocks much of the thermal radiation, and (2) the radiation transport equation 

solved by FDS accounts for the orientation of the target tray relative to the fire. In other words, 

FDS does not model the target cables as directly facing the fire, whereas the point source 

models implicitly do. 

As with the heat flux, the predicted interior cable temperatures predicted by FDS indicate a very 

low probability for cable damage. However, it should be noted that these low probabilities are 

based on the particular configuration of the cables within the trays. If some of the target cables 

were to have a direct view of the fire, the heat flux would more likely be comparable to that 

predicted by the distributed point source model. 
CABLE TRAY FIRE IN ANNULUS

H-12 

Figure H-5. Summary of simulation results for the annulus. 

H.5.2 Fire Protection Systems 

The sprinkler link temperature predicted by FDS is shown in Figure H-6. The sprinkler is not 

predicted to activate in this scenario because the link temperature is predicted to increase to 

approximately 90 °C (194 °F), less than the activation temperature of 100 °C (212 °F). It should 

be noted, however, that the sprinkler is located just outside the fire plume. It is expected that for 

a real fire of this type, the natural air movements within such a large space as the containment 

annulus would almost certainly bend the plume from the vertical in a way that would be difficult 

to replicate with a model that is not accounting for the air movements throughout the entire 

facility. A slight lean in the plume towards the sprinkler could result in activation. 

Figure H-6. Predicted sprinkler link temperature for the annulus fire scenario. 

It is possible to determine how large a fire is needed to increase the plume temperature by 

10 °C. Table 4-3 indicates that the HGL temperature rise is proportional to the HRR to the 2/3 

power. The plume temperature behaves similarly. Following the methodology in Section 4.4, in 

0

30

60

90

120

150

0 600 1200 1800 2400 3000 3600

Temperature (C)

Time (s)

Redundant Cable Temperature

FDS

0

1

2

3

4

5

6

7

8

9

10

0 600 1200 1800 2400 3000 3600

Heat Flux (kW)

Time (s)

Redundant Cable Heat Flux

Point Source

Distributed Point Source

FDS

0

20

40

60

80

100

120

0 600 1200 1800 2400 3000 3600

Temperature (C)

Time (s)

Sprinkler Link Temperature

FDS
CABLE TRAY FIRE IN ANNULUS

H-13 

order to increase the predicted plume temperature by 10 °C, the peak HRR, ܳሶ, must increase 

by approximately: 

∆ܳሶ ൌ 3

2ܳሶ ∆ܶ

ܶെܶ଴

ൌ 3

2 945 kW ൈ 

10 °C

90 °C ‐ 35 °C ؆ 258 kW (H-5) 

In other words, the peak HRR of the fire would have to be approximately 945 + 258 = 1203 kW 

to bring the plume temperature into a range to cause sprinkler activation. 

H.6 Conclusion 

Simple point source heat flux calculations indicate that a fire in one of the cable trays within the 

annulus region of the containment building might damage the cables in an adjacent tray. 

However, an additional analysis using FDS indicates that cable damage is unlikely due to the 

orientation of the target cables and the blockage of thermal radiation by the cable tray itself. 

This suggests that the details of the cable tray location, orientation, and configuration can 

significantly impact potential for damage. 

FDS predicts that sprinkler activation above the fire is unlikely. However, its prediction is 

sensitive to the exact location of the sprinkler relative to a fire plume that may be subject to 

unpredictable air movements throughout the entire facility. Alternative protection strategies, 

such as shielding between trays or other thermal barriers, should be considered to ensure the 

protection of the redundant cables. 

H.7 References 

1. NIST SP 1018-5, Fire Dynamics Simulator (Version 5), Technical Reference Guide, Volume 

3, Experimental Validation, 2010. 

2. NUREG-1805, Fire Dynamics Tools (FDTs

) Quantitative Fire Hazard Analysis Methods for 

the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program, 2004. 

3. NUREG-1824 (EPRI 1011999), Verification and Validation of Selected Fire Models for 

Nuclear Power Plant Applications, 2007.

4. NUREG/CR-6850 (EPRI 1011989), EPRI/NRC-RES Fire PRA Methodology for Nuclear 

Power Facilities, 2005. 

5. NUREG/CR-6931, Cable Response to Live Fire (CAROLFIRE), Volume 3: ThermallyInduced Electrical Failure (THIEF) Model, 2008. 

6. NUREG/CR-7010, Cable Heat Release, Ignition, and Spread In Tray Installations during 

Fire (CHRISTIFIRE), Volume 1: Horizontal Trays, 2012. 

7. SFPE Handbook of Fire Protection Engineering, 4th edition, 2008.

H.8 Attachments (on CD) 

1. FDS input file: Annulus.fds 

 
CABLE TRAY FIRE IN ANNULUS

H-14 

 
Index-1 

INDEX 

Administrative controls ............................................................................................................... 2-7 

Algebraic models .................................... 1-7, 1-15, 1-16, 2-10, 2-11, 2-13, 3-18, 3-21, 3-23, 4-17 

ASTM E1355 ...................................................................................................................... 1-4, 5-1

Ceiling jet ................................................................................ 2-24, 2-30, A-9, B-8, E-8, F-8, F-17 

CFAST . xvii, xviii, xxv, 1-3, 1-7, 1-15, 1-16, 2-11, 2-13, 2-18, 2-19, 2-23, 2-32, 2-33, 3-4, 3-21, 4-

2, 4-3, 5-2, 5-3, 5-4, 6-2, A-6, A-7, A-11, A-13, A-14, A-15, A-18, A-19, A-20, A-21, A-22, B-6, 

B-11, B-12, B-13, B-14, B-15, B-16, B-19, B-20, B-21, B-24, B-25, D-5, D-8, D-9, D-10, D-11, 

D-12, D-14, D-15, D-16, D-17, D-18, E-6, E-11, E-12, E-13, E-14, E-15, E-16, E-17, E-19, E20, E-21, E-24, E-25, F-9 

CFD model ... 1-9, 1-10, 2-11, 2-19, 2-20, 2-22, 2-30, 2-33, 3-2, 3-4, 3-10, 3-12, 3-13, 3-15, 3-16, 

3-17, 3-19, 3-21, 3-23, 4-11, A-7, A-12, B-6, C-5, C-7, C-16, C-23, D-8, E-6, E-20, F-6, F-17, 

H-8 

Compartment aspect ratio ................................................................................................ 2-30, F-8 

Compartment geometry ................................................................................................... 3-2, A-13 

Detection ..................................................................... 3-20, 5-4, E-2, E-16, E-18, E-20, F-4, G-15 

Documentation ...................................................................................................... 2-14, 2-18, 2-34 

Equivalence ratio ............................................................................................................. 2-30, F-8 

Fire Dynamics Simulator (FDS) . xvii, 1-3, 1-11, 2-11, 2-19, 4-3, 5-3, A-6, B-6, C-6, D-5, E-6, H-6 

Fire Froude number ................................................................................................................. 2-25 

Fire location ............................................................................................................................... 3-2 

Fire PRA ... xvii, xix, xxiii, 1-1, 1-3, 1-14, 1-15, 2-5, 2-10, 4-10, 4-11, 5-4, A-22, B-24, C-24, D-17, 

E-25, G-17, H-13 

Heat release rate ................................................................................................. 2-17, B-20, C-10 

Hot Gas Layer (HGL) ....................................................................................................... 2-6, 2-23 

Intervening combustibles ........................................................................................................... 2-9 

Limiting Fire Scenario (LFS) .................................................................................................... 4-15 

MAGIC .. xvii, xxiii, 1-3, 1-7, 1-16, 2-11, 2-13, 2-19, 2-23, 2-33, 3-21, 4-2, 4-3, 4-9, 4-10, 5-1, 5-3, 

A-6, C-3, C-5, C-7, C-8, C-9, C-10, C-11, C-12, C-13, C-14, C-15, C-16, C-17, C-18, C-19, C20, C-21, C-23, C-24, D-5, G-5, G-7, G-9, G-10, G-11, G-12, G-13, G-14, G-15, G-16, G-17 

Main control room .................................................................................................. xxvi, 1-15, 3-18 

Maximum Expected Fire Scenario (MEFS) .............................................................................. 4-15 

Model uncertainty ....................................................................................................................... 4-1 

NFPA 805 ................................................ iii, 1-1, 1-11, 1-12, 1-13, 1-14, 2-4, 2-22, 4-2, 4-15, 5-2 

Normalized parameter .......................................................2-22, A-9, B-8, C-6, D-7, E-8, G-6, H-7 

Parameter uncertainty ...................................................................................................... 4-1, 4-10 

Plume .......................................................... 2-15, 2-17, 2-23, 3-8, 4-2, 4-7, B-10, E-7, E-10, H-11 

Secondary combustibles ............................................................................................................ 2-9 

Sensitivity analysis ................................................................................................................... 4-10 

Smoke production ...................................................................................................................... 1-8 

Smokeview . 1-10, 1-11, 2-19, 5-1, A-15, A-16, B-12, B-18, C-14, D-9, D-12, D-13, E-12, E-17, H8 

Structural steel .......................................................................................................................... F-4 

Suppression ...................................................................................................................... E-2, H-5 
INDEX

Index-2 

Target . 1-6, 1-7, 2-8, 2-15, 2-23, 3-12, 3-13, 4-2, 4-7, 4-8, 4-14, A-8, A-9, B-8, C-6, D-7, D-14, E8, F-6, F-8, F-14, G-6, H-7, H-11 

Uncertainty ................................................................... 2-33, 4-1, 4-6, 4-8, 4-10, B-22, E-23, G-14 

Ventilationxxv, 1-14, 2-8, 2-14, 3-1, 3-3, 3-4, 4-14, A-1, A-9, A-14, A-16, A-18, A-22, B-1, B-8, B10, B-11, B-14, B-17, C-3, C-13, C-16, D-2, D-7, D-11, D-13, E-2, E-8, E-10, E-15, E-18, F-4, 

F-14, G-1, G-6, G-11, G-13, H-7 

Zone model ............................... 1-8, 2-11, 3-10, 3-13, 3-15, 3-17, 3-19, 3-21, 3-23, A-7, D-6, G-5 
BIBLIOGRAPHIC DATA SHEET

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