Verification and Validation 

of Selected Fire Models for 

Nuclear Power Plant 

Applications 

Volume 2: 

Fire Dynamics Tools (FDTs

) 

January 2006 

U.S. Nuclear Regulatory Commission Electric Power Research Institute 

Office of Nuclear Regulatory Research 3412 Hillview Avenue 

Washington, DC 20555-0001 Palo Alto, CA 94303 

 

NUREG-1824 EPRI 1011999 

Draft for Comment Preliminary Report

Verification & Validation of Selected 

Fire Models for Nuclear Power Plant 

Applications 

Volume 2: Fire Dynamics Tools (FDTs) 

NUREG-1824 EPRI 1011999 

January 2006 

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

Office of Nuclear Regulatory Research (RES) 3412 Hillview Avenue 

Division of Risk Analysis and Applications Palo Alto, CA 94303 

Two White Flint North, 11545 Rockville Pike 

Rockville, MD 20852-2738 

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

M. H. Salley R. P. Kassawara 
DISCLAIMER OF WARRANTIES AND LIMITATION OF LIABILITIES 

THIS DOCUMENT WAS PREPARED BY THE ORGANIZATION(S) NAMED BELOW AS AN 

ACCOUNT OF WORK SPONSORED OR COSPONSORED BY THE ELECTRIC POWER RESEARCH 

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PROCESS, OR SIMILAR ITEM DISCLOSED IN THIS DOCUMENT. 

ORGANIZATION(S) THAT PREPARED THIS DOCUMENT: 

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Science Applications International Corporation 

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Requests for copies of this report should be directed to EPRI Orders and Conferences, 1355 Willow 

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iii 

COMMENTS ON DRAFT NUREG-1824 REPORT 

This report is being published jointly by the U.S. Nuclear Regulatory Commission (NRC) and 

the Electric Power Research Institute (EPRI). Any interested party may submit comments on 

this report for consideration by the NRC and EPRI staffs. Comments may be accompanied by 

additional relevant information or supporting data. Please specify both the report number (Draft 

NUREG-1824) and the volume number in your comments, and send them by March 31, 2006, to 

the following address: 

Chief Rules Review and Directives Branch 

U.S. Nuclear Regulatory Commission 

Mail Stop T-6D59 

Washington, DC 20555-0001 

For any questions about the material in this report, please contact: 

Mark Henry Salley 

Mail Stop T-10E50 

U.S. Nuclear Regulatory Commission 

Washington, DC 20555-0001 

Phone: (301) 415-2840 

Email: MXS3@nrc.gov

If EPRI members also wish to provide comments to EPRI, they may send them to the following 

address: 

R.P. Kassawara 

Electric Power Research Institute 

3412 Hillview Avenue 

Palo Alto, CA 94304 

Phone: (650) 855-2775 

Email: RKASSAWA@epri.com

v 

CITATIONS 

This report was prepared by 

U.S. Nuclear Regulatory Commission, 

Office of Nuclear Regulatory Research (RES) 

Two White Flint North, 11545 Rockville Pike 

Rockville, MD 20852-2738 

Principal Investigators: 

K. Hill 

J. Dreisbach 

Electric Power Research Institute (EPRI) 

3412 Hillview Avenue 

Palo Alto, CA 94303 

Science Applications International Corp (SAIC)

4920 El Camino Real 

Los Altos, CA 94022 

Principal Investigators: 

F. Joglar 

B. Najafi 

National Institute of Standards and Technology 

Building Fire Research Laboratory (BFRL) 

100 Bureau Drive, Stop 8600 

Gaithersburg, MD 20899-8600 

Principal Investigators: 

K McGrattan 

R. Peacock 

A. Hamins 

Volume 1, Main Report: B. Najafi, M.H. Salley, F. Joglar, J. Dreisbach 

Volume 2, FDTS

: K. Hill, J. Dreisbach 

Volume 3, FIVE-REV. 1: F. Joglar 

Volume 4, CFAST: R. Peacock, J. Dreisbach, P. Reneke (NIST) 

Volume 5, MAGIC: F. Joglar, B. Guatier (EdF), L. Gay (EdF), J. Texeraud (EdF) 

Volume 6, FDS: K. McGrattan, J. Dreisbach 

Volume 7, Experimental Uncertainty: A. Hamins, K. McGrattan 

This report describes research sponsored jointly by U.S. Nuclear Regulatory Commission, Office 

of Nuclear Regulatory Research (RES) and Electric Power Research Institute (EPRI). 

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

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

Volume 2: Fire Dynamics Tools (FDTS

), U.S. Nuclear Regulatory Commission, Office of 

Nuclear Regulatory Research (RES), Rockville, MD: 2005 and Electric Power Research Institute 

(EPRI), Palo Alto, CA. NUREG-1824 and EPRI 1011999.

vii 

ABSTRACT 

There is a movement to introduce risk- and performance-based analyses into fire protection 

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

protection community, as well as the nuclear power plant (NPP) fire protection community. 

In 2002, the National Fire Protection Association (NFPA) developed NFPA 805, PerformanceBased Standard for Fire Protection for Light-Water Reactor Electric Generating Plants, 2001 

Edition. In July 2004, the U.S. Nuclear Regulatory Commission (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 nuclear fire protection community wants to use risk-informed, performance-based 

(RI/PB) approaches and insights to support fire protection decision-making in general. 

One key tool needed to support RI/PB fire protection is the availability of verified and validated 

fire models that can reliably predict the consequences of fires. Section 2.4.1.2 of NFPA 805 

requires that only fire models acceptable to the Authority Having Jurisdiction (AHJ) shall be 

used in fire modeling calculations. Further, Sections 2.4.1.2.2 and 2.4.1.2.3 of NFPA 805 state 

that fire models shall only be applied within the limitations of the given model, and shall be 

verified and validated. 

This report is the first effort to document the verification and validation (V&V) of five fire models 

that are commonly used in NPP applications. The project was performed in accordance with the 

guidelines that the American Society for Testing and Materials (ASTM) set forth in Standard 

E1355-04, “Evaluating the Predictive Capability of Deterministic Fire Models.” The results of 

this V&V are reported in the form of ranges of accuracies for the fire model predictions. 

ix 

CONTENTS 

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

2 MODEL DEFINITION..............................................................................................................2-1

2.1 Name and Version of the Model ..................................................................................2-1

2.2 Type of Model ..............................................................................................................2-1

2.3 Model Developers........................................................................................................2-1

2.4 Relevant Publications ..................................................................................................2-1

2.5 Governing Equations and Assumptions.......................................................................2-2

2.6 Input Data Required to Run the Model ........................................................................2-2

2.7 Property Data...............................................................................................................2-2

2.8 Model Results ..............................................................................................................2-2

2.9 Uses and Limitations of the Model...............................................................................2-3

3 THEORETICAL BASIS FOR FDTS ........................................................................................3-1

3.1 Estimating Hot Gas Layer Temperature ......................................................................3-2

3.1.1 Natural Ventilation: Method of McCaffrey, Quintiere, and Harkleroad (MQH)........3-2

3.1.2 Natural Ventilation (Compartment Closed): Method of Beyler.................................3-5

3.1.3 Forced Ventilation: Method of Foote, Pagni, and Alvares (FPA)............................3-5

3.1.4 Forced Ventilation: Method of Deal and Beyler .......................................................3-6

3.2 Estimating Smoke Layer Height...................................................................................3-7

3.2.1 Natural Ventilation (Smoke Filling): The Non-Steady State Yamana 

and Tanaka Method..........................................................................................................3-7

3.3 Assumptions and Limitations for Hot Gas Layer Calculations .....................................3-9

3.4 Flame Height .............................................................................................................3-10

3.4.1 Assumptions and Limitations.................................................................................3-12

3.5 Estimating Radiant Heat Flux from Fire to a Target...................................................3-13

3.5.1 Point Source Radiation Model ...............................................................................3-13

3.5.2 Solid Flame Radiation Model with Target at and Above Ground Level .................3-15

3.5.3 Assumptions and Limitations.................................................................................3-16
x 

3.6 Estimating the Centerline Temperature of a Buoyant Plume.....................................3-17

3.6.1 Assumptions and Limitations.................................................................................3-20

4 MATHEMATICAL AND NUMERICAL ROBUSTNESS..........................................................4-1

5 MODEL SENSITIVITY ............................................................................................................5-1

5.1 Definition of Base Case Scenario for Sensitivity Analysis ...........................................5-1

5.2 Sensitivity Analysis for FDTs ........................................................................................5-2

5.3 Conclusions .................................................................................................................5-6

6 MODEL VALIDATION ............................................................................................................6-1

6.1 Hot Gas Layer Temperature and Height......................................................................6-3

6.2 Plume Temperature .....................................................................................................6-5

6.3 Flame Height ...............................................................................................................6-7

6.4 Target/Radiant Heat Flux.............................................................................................6-7

6.5 Summary .....................................................................................................................6-9

7 REFERENCES .......................................................................................................................7-1

Bibliography......................................................................................................................7-2

A TECHNICAL DETAILS OF THE FDTS VALIDATION STUDY ............................................. A-1

A.1 Hot Gas Layer Temperature and Height..................................................................... A-1

A.1.1 ICFMP BE # 2 ........................................................................................................ A-2

A.1.2 ICFMP BE # 3 ........................................................................................................ A-4

A.1.3 ICFMP BE # 4 ...................................................................................................... A-12

A.1.4 ICFMP BE # 5 ...................................................................................................... A-13

A.1.5 The FM-SNL Test Series ..................................................................................... A-15

A.1.6 The NBS Test Series ........................................................................................... A-17

A.1.7 Summary: Hot Gas Layer Temperature and Height............................................. A-19

A.2 Plume Temperature .................................................................................................. A-20

A.2.1 ICFMP BE # 2 ...................................................................................................... A-20

A.2.2 The FM-SNL Test Series ..................................................................................... A-22

A.3 Flame Height ............................................................................................................ A-25

A.3.1 ICFMP BE # 2 ...................................................................................................... A-25

A.3.1 ICFMP BE # 3 ...................................................................................................... A-26

A.4 Target Heat Flux ....................................................................................................... A-27
xi 

A.4.1 ICFMP BE #3 ....................................................................................................... A-27

A.4.2 Summary: Radiant Heat Flux ............................................................................... A-36

FIGURES 

Figure 3-1: Characteristics of Flame Height Fluctuations ........................................................3-11

Figure 3-2: Radiant Heat Flux from a Pool Fire to a Floor-Based Target Fuel 

(Point Source Model) .......................................................................................................3-14

Figure 3-3: Radiant Heat Flux from a Pool Fire to a Floor-Based Target Fuel (Point 

Source Model)..................................................................................................................3-16

Figure 3-4: Solid Flame Radiation Model with No Wind and Target at Ground Level..............3-16

Figure 3-5: Point Source Fire Plume........................................................................................3-19

Figure 5-1: Sensitivity Ratios for inputs to HGL Temperature in a Compartment with 

Natural Ventilation..............................................................................................................5-3

Figure 5-2: Sensitivity Ratios for Inputs to HGL Temperature in Compartment with 

Forced Ventilation ..............................................................................................................5-3

Figure 5-3: Sensitivity Ratios for Inputs to HGL Temperature in a Closed Compartment..........5-4

Figure 5-4: Sensitivity Ratios for Inputs to HRR Algorithm ........................................................5-4

Figure 5-5: Sensitivity Ratios for Inputs to Burning Duration Algorithm .....................................5-5

Figure 5-6: Sensitivity Ratios for Inputs to Heskestad’s Flame Height Algorithm ......................5-5

Figure 5-7: Sensitivity Ratios for Inputs to Plume Temperature Algorithm ................................5-6

Figure 6-1: Relative Differences for HGL Temperature .............................................................6-5

Figure 6-2: Relative Differences for Plume Temperature ..........................................................6-7

Figure 6-3: Relative Differences for Radiant Heat Flux .............................................................6-9

Figure A-1: Hot Gas Layer Temperature, ICFMP BE #2, Cases 1, 2, and 3 ............................ A-4

Figure A-2: Hot Gas Layer Temperature, ICFMP BE #3, closed door tests ............................. A-8

Figure A-3: Hot Gas Layer Temperature, ICFMP BE #3, closed door tests (cont.) .................. A-9

Figure A-4: Hot Gas Layer Temperature, ICFMP BE #3, open door tests.............................. A-10

Figure A-5: Hot Gas Layer Height, ICFMP BE #3, open door tests w/o ventilation ................ A-11

Figure A-6: Hot Gas Layer Temperature, ICFMP BE #4 ........................................................ A-13

Figure A-7: Hot Gas Layer Temperature, ICFMP BE #5 ........................................................ A-15

Figure A-8: Hot Gas Layer Temperature, FM/SNL tests......................................................... A-17

Figure A-9: Hot Gas Layer Temperature, NBS tests .............................................................. A-19

Figure A-10: Plume Temperature, ICFMP BE #2, Cases 1, 2, and 3 ..................................... A-22

Figure A-11: Plume Temperature, FM/SNL tests.................................................................... A-24
xii 

Figure A-12: Photographs of heptane pan fires, ICFMP BE #2, Case 2. Courtesy, Simo 

Hostikka, VTT Building and Transport, Espoo, Finland................................................... A-26

Figure A-13: Photograph and simulation of ICFMP BE #3, Test 3, as seen through the 2 

m by 2 m doorway. Photo courtesy of Francisco Joglar, SAIC. ..................................... A-27

Figure A-14: Radiant Heat Flux, ICFMP BE #3, Tests 1 and 7............................................... A-29

Figure A-15: Radiant Heat Flux, ICFMP BE #3, Tests 2 and 8............................................... A-30

Figure A-16: Radiant Heat Flux, ICFMP BE #3, Tests 3 and 9............................................... A-31

Figure A-17: Radiant Heat Flux, ICFMP BE #3, Tests 4 and 10............................................. A-32

Figure A-18: Radiant Heat Flux, ICFMP BE #3, Tests 5 and 14............................................. A-33

Figure A-19: Radiant Heat Flux, ICFMP BE #3, Tests 5 and 14............................................. A-34

Figure A-20: Radiant Heat Flux, ICFMP BE #3, Tests 15 and 18........................................... A-35

Figure A-21: Radiant Heat Flux, ICFMP BE #3, Test 17 ........................................................ A-36
xiii 

TABLES 

Table 3-1: Spreadsheets included in the V&V Study ................................................................3-1

Table 5-1: Technical Details for Base Case...............................................................................5-2

Table A-1: Input Values for ICFMP BE # 2 Case 1 and 2......................................................... A-2

Table A-2: Input Values for ICFMP BE # 2 Case 3.................................................................. A-3

Table A-3: Input values for ICFMP BE#3 Closed Compartment Tests ..................................... A-5

Table A-4: Input values for ICFMP BE # 3 No Ventilation Tests............................................... A-6

Table A-5: Input values for ICFMP BE # 3 Forced Ventilation Tests ........................................ A-7

Table A-6: Input Values for ICFMP BE # 4 ............................................................................. A-12

Table A-7: Input Values for ICFMP BE # 5 ............................................................................. A-14

Table A-8: Input values for FM/SNL Tests.............................................................................. A-16

Table A-9: Input Values for NBS Tests ................................................................................... A-18

Table A-10: Hot Gas Layer Temperature Relative Differences .............................................. A-20

Table A-11: Input values for ICFMP BE # 2 Plume Temperature Calculations ...................... A-21

Table A-12: ICFMP BE #2 Heat Release Rates ..................................................................... A-21

Table A-13: Input values for FM/SNL Tests Plume Temperature Calculations ...................... A-23

Table A-14: Plume Temperature Relative Differences ........................................................... A-24

Table A-15: Distance from Fire to Radiant Heat Flux Gauges, meters................................... A-28

Table A-16: Relative Differences, Radiant Heat Flux ............................................................. A-36

xv 

REPORT SUMMARY 

This report documents the verification and validation (V&V) of five selected fire models 

commonly used in support of risk-informed and performance-based (RI/PB) fire protection at 

nuclear power plants (NPPs). 

Background 

Over the past decade, there has been a considerable movement in the nuclear power industry to 

transition from prescriptive rules and practices towards the use of risk information to supplement 

decision-making. In the area of fire protection, this movement is evidenced by numerous 

initiatives by the U.S. Nuclear Regulatory Commission (NRC) and the nuclear community 

worldwide. In 2001, the National Fire Protection Association (NFPA) completed the 

development of NFPA Standard 805, “Performance-Based Standard for Fire Protection for Light 

Water Reactor Electric Generating Plants 2001 Edition.” Effective July, 16, 2004, the NRC 

amended its fire protection requirements in 10 CFR 50.48(c) 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. RI/PB fire protection relies on fire modeling 

for determining the consequence of fires. NFPA 805 requires that the “fire models shall be 

verified and validated,” and “only fire models that are acceptable to the Authority Having 

Jurisdiction (AHJ) shall be used in fire modeling calculations.” 

Objectives 

The objective of this project is to examine the predictive capabilities of selected fire models. 

These models may be used to demonstrate compliance with the requirements of 10 CFR 50.48(c) 

and the referenced NFPA 805, or support other performance-based evaluations in NPP fire 

protection applications. In addition to NFPA 805 requiring that only verified and validated fire 

models acceptable to the AHJ be used, the standard also requires that fire models only be applied 

within their limitations. The V&V of specific models is important in establishing acceptable 

uses and limitations of fire models. Specific objectives of this project are: 

• Perform V&V study of selected fire models using a consistent methodology (ASTM E1355) 

and issue a report to be prepared by U.S. Nuclear Regulatory Commission Office of Nuclear 

Regulatory Research (RES) and Electric Power Research Institute (EPRI). 

• Investigate the specific fire modeling issues of interest to the NPP fire protection 

applications. 

• Quantify fire model predictive capabilities to the extent that can be supported by comparison 

with selected and available experimental data. 
xvi 

The following fire models were selected for this evaluation: (i) NRC’s NUREG-1805 Fire 

Dynamics Tools (FDTs), (ii) EPRI’s Fire-Induced Vulnerability Evaluation Revision 1 (FIVERev. 1), (iii) National Institute of Standards and Technology’s (NIST) Consolidated Model of 

Fire Growth and Smoke Transport (CFAST), (iv) Electricite de France’s (EdF) MAGIC, and (v) 

NIST’s Fire Dynamics Simulator (FDS). 

Approach 

This program is based on the guidelines of the ASTM E1355, “Evaluating the Predictive 

Capability of Deterministic Fire Models,” for verification and validation of the selected fire 

models. The guide provides four areas of evaluation: 

• Defining the model and scenarios for which the evaluation is to be conducted, 

• Assessing the appropriateness of the theoretical basis and assumptions used in the model, 

• Assessing the mathematical and numerical robustness of the model, and 

• Validating a model by quantifying the accuracy of the model results in predicting the course 

of events for specific fire scenarios. 

Traditionally, a V&V study reports the comparison of model results with experimental data, and 

therefore, the V&V of the fire model is for the specific fire scenarios of the test series. While 

V&V studies for the selected fire models exist, it is necessary to ensure that technical issues 

specific to the use of these fire models in NPP applications are investigated. The approach 

below was followed to fulfill this objective. 

1. A set of fire scenarios were developed. These fire scenarios establish the “ranges of 

conditions” for which fire models will be applied in NPPs. 

2. The next step summarizes the same attributes or “range of conditions” of the “fire 

scenarios” in test series available for fire model benchmarking and validation exercises. 

3. Once the above two pieces of information were available, the validation test series, or 

tests within a series, that represent the “range of conditions” was mapped for the fire 

scenarios developed in Step 1. The range of uncertainties in the output variable of 

interest as predicted by the model for a specific “range of conditions” or “fire scenario” 

are calculated and reported. 

The scope of this V&V study is limited to the capabilities of the selected fire models. There are 

potential fire scenarios in NPP fire modeling applications that do not fall within the capabilities 

of these fire models and therefore are not covered by this V&V study. 

Results 

The results of this study are presented in the form of relative differences between fire model 

predictions and experimental data for fire modeling attributes important to NPP fire modeling 

applications, e.g., plume temperature. The relative differences sometimes show agreement, but 

may also show both under-prediction and over-prediction. These relative differences are 

affected by the capabilities of the models, the availability of accurate applicable experimental 

data, and the experimental uncertainty of this data. The relative differences were used, in 

combination with some engineering judgment as to the appropriateness of the model and the 
xvii 

agreement between model and experiment, to produce a graded characterization of the fire 

model’s capability to predict attributes important to NPP fire modeling applications. 

This report does not provide relative differences for all known fire scenarios in NPP applications. 

This incompleteness is due to a combination of model capability and lack of relevant 

experimental data. The first can be addressed by improving the fire models while the second 

needs more applicable fire experiments. 

EPRI Perspective 

The use of fire models to support fire protection decision-making requires that their limitations 

and confidence in their predictive capability is well understood. While this report makes 

considerable progress towards that goal, it also points to ranges of accuracies in the predictive 

capability of these fire models that could limit their use in fire modeling applications. Use of 

these fire models present challenges that should be addressed if the fire protection community is 

to realize the full benefit of fire modeling and performance-based fire protection. This requires 

both short term and long term solutions. In the short term a methodology will be to educate the 

users on how the results of this work may affect known applications of fire modeling. This may 

be accomplished through pilot application of the findings of this report and documentation of the 

insights as they may influence decision-making. Note that the intent is not to describe how a 

decision is to be made, but rather to offer insights as to where and how these results may, or may 

not be used as the technical basis for a decision. In the long term, additional work on improving 

the models and performing additional experiments should be considered. 

Keywords 

Fire Fire Modeling Verification and Validation (V&V) 

Performance-based Risk-informed regulation Fire Hazard Analysis (FHA) 

Fire safety Fire protection Nuclear Power Plant 

Fire Probabilistic Risk Assessment (PRA) Fire Probabilistic Safety Assessment 

 (PSA)

xix 

PREFACE 

This report is presented in seven volumes. Volume 1, the Main Report, provides general 

background information, programmatic and technical overviews, and project insights and 

conclusions. Volumes 2 through 6 provide detailed discussions of the verification and validation 

(V&V) of the following five fire models: 

Volume 2 Fire Dynamics Tools (FDTS

) 

Volume 3 Fire-Induced Vulnerability Evaluation, Revision 1 (FIVE-Rev1) 

Volume 4 Consolidated Model of Fire Growth and Smoke Transport (CFAST) 

Volume 5 MAGIC 

Volume 6 Fire Dynamics Simulator (FDS) 

Finally, Volume 7 quantifies the uncertainty of the experiments used in the V&V study of these 

five fire models. 

xxi 

FOREWORD 

Fire modeling and fire dynamics calculations are used in a number of fire hazards analysis (FHA) studies and 

documents, including fire risk analysis (FRA) calculations; compliance with, and exemptions to the regulatory 

requirements for fire protection in 10 CFR Part 50; “Specific Exemptions”; the Significance Determination 

Process (SDP) used in the inspection program conducted by the U.S. Nuclear Regulatory Commission (NRC); 

and, most recently, the risk-informed performance-based (RI/PB) voluntary fire protection licensing basis 

established under 10 CFR 50.48(c). The RI/PB method is based on the National Fire Protection Association 

(NFPA) Standard 805, “Performance-Based Standard for Fire Protection for Light-Water Reactor Generating 

Plants.” 

The seven volumes of this NUREG-series report provide technical documentation concerning the predictive 

capabilities of a specific set of fire dynamics calculation tools and fire models for the analysis of fire hazards in 

nuclear power plant (NPP) scenarios. Under a joint memorandum of understanding (MOU), the NRC Office of 

Nuclear Regulatory Research (RES) and the Electric Power Research Institute (EPRI) agreed to develop this 

technical document for NPP application of these fire modeling tools. The objectives of this agreement include 

creating a library of typical NPP fire scenarios and providing information on the ability of specific fire models to 

predict the consequences of those typical NPP fire scenarios. To meet these objectives, RES and EPRI initiated 

this collaborative project to provide an evaluation, in the form of verification and validation (V&V), for a set of five 

commonly available fire modeling tools. 

The road map for this project was derived from NFPA 805 and the American Society for Testing and Materials 

(ASTM) Standard E1355-04, “Evaluating the Predictive Capability of Deterministic Fire Models.” These 

industry standards form the methodology and process used to perform this study. Technical review of fire 

models is also necessary to ensure that those using the models can accurately assess the adequacy of the scientific and 

technical bases for the models, select models that are appropriate for a desired use, and understand the levels 

of confidence that can be attributed to the results predicted by the models. This work was performed using 

state-of-the-art fire dynamics calculation methods/models and the most applicable fire test data. Future 

improvements in the fire dynamics calculation methods/models and additional fire test data may impact the results 

presented in the seven volumes of this report. 

This document does not constitute regulatory requirements, and RES participation in this study neither 

constitutes nor implies regulatory approval of applications based on the analysis contained in this text. The 

analyses documented in this report represent the combined efforts of individuals from RES and EPRI, both of 

which provided specialists in the use of fire models and other FHA tools. The results from this combined 

effort do not constitute either a regulatory position or regulatory guidance. Rather, these results are intended 

to provide technical analysis, and they may also help to identify areas where further research and analysis are 

needed. 

 _________________________________

 Carl J. Paperiello, Director 

 Office of Nuclear Regulatory Research 

 U.S. Nuclear Regulatory Commission

xxiii 

ACKNOWLEDGMENTS 

The work documented in this report benefited from contributions and considerable technical support 

from several organizations. 

The verification and validation (V&V) studies for FDTS (Volume 2), CFAST (Volume 4), and 

FDS (Volume 6) were conducted in collaboration with the U.S. Department of Commerce, 

National Institute of Standards and Technology (NIST), Building and Fire Research Laboratory 

(BFRL). Since the inception of this project in 1999, the NRC has collaborated with NIST 

through an interagency memorandum of understanding (MOU) and conducted research to provide 

the necessary technical data and tools to support the use of fire models in nuclear power plant 

fire hazard analysis (FHA). 

We appreciate the efforts of Doug Carpenter and Rob Schmidt of Combustion Science 

Engineers, Inc. for their comments and contribution to Volume 2. 

In addition, we acknowledge and appreciate the extensive contributions of Electricité de France 

(EdF) in preparing Volume 5 for MAGIC. 

We also appreciate the efforts of organizations participating in the International Collaborative 

Fire Model Project (ICFMP) to Evaluate Fire Models for Nuclear Power Plant Applications, 

which provided experimental data, problem specifications, and insights and peer comment for 

the international fire model benchmarking and validation exercises, and jointly prepared the 

panel reports used and referred to in this study. We specifically appreciate the efforts of the 

Building Research Establishment (BRE) and the Nuclear Installations Inspectorate in the United 

Kingdom, which provided leadership for ICFMP Benchmark Exercise (BE) #2, as well as 

Gesellschaft fuer Anlagen-und Reaktorsicherheit (GRS) and Institut fuer Baustoffe, Massivbau 

und Brandschutz (iBMB) in Germany, which provided leadership and valuable experimental data 

for ICFMP BE #4 and BE #5. In particular, ICFMP BE #2 was led by Stewart Miles at BRE; 

ICFMP BE #4 was led by Walter Klein-Hessling and Marina Rowekamp at GRS, and R. 

Dobbernack and Olaf Riese at iBMB; and ICFMP BE #5 was led by Olaf Riese and D. Hosser at 

iBMB, and Marina Rowekamp at GRS. We acknowledge and sincerely appreciate all of their 

efforts. 

We greatly appreciate Paula Garrity, Technical Editor for the Office of Nuclear Regulatory 

Research, and Linda Stevenson, agency Publication Specialist, for providing editorial and 

publishing support for this report. We also greatly appreciate Dariusz Szwarc, Nuclear Safety 

Professional Development Program participant, for his assistance finalizing this report. 

xxv 

LIST OF ACRONYMS 

AGA American Gas Association 

AHJ Authority Having Jurisdiction 

ASME American Society of Mechanical Engineers 

ASTM American Society for Testing and Materials 

BE Benchmark Exercise 

BFRL Building and Fire Research Laboratory 

BRE Building Research Establishment 

CFAST Consolidated Fire Growth and Smoke Transport Model 

CFR Code of Federal Regulations

EdF Electricité de France 

EPRI Electric Power Research Institute 

FDS Fire Dynamics Simulator 

FDTS Fire Dynamics Tools (NUREG-1805) 

FHA Fire Hazard Analysis 

FIVE-Rev1 Fire-Induced Vulnerability Evaluation, Revision 1 

FM-SNL Factory Mutual & Sandia National Laboratories 

FPA Foote, Pagni, and Alvares 

FRA Fire Risk Analysis 

GRS Gesellschaft fuer Anlagen-und Reaktorsicherheit (Germany) 

HRR Heat Release Rate 

IAFSS International Association of Fire Safety Science 

iBMB Institut für Baustoffe, Massivbau und Brandschutz 

ICFMP International Collaborative Fire Model Project 

IEEE Institute of Electrical and Electronics Engineers 

MCC Motor Control Center 

MQH McCaffrey, Quintiere, and Harkleroad 
xxvi 

MOU Memorandum of Understanding 

NBS National Bureau of Standards (now NIST) 

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) 

RES Office of Nuclear Regulatory Research (NRC) 

RI/PB Risk-Informed, Performance-Based 

SDP Significance Determination Process 

SFPE Society of Fire Protection Engineers 

V&V Verification & Validation
1-1 

1 

INTRODUCTION 

As the use of fire modeling tools increases in support of day-to-day nuclear power plant (NPP) 

applications including fire risk studies, the importance of verification and validation (V&V) 

studies for these tools also increases. V&V studies afford fire modeling analysts confidence 

in applying analytical tools by quantifying and discussing the performance of the given model 

in predicting the fire conditions measured in a particular experiment. The underlying assumptions, 

capabilities, and limitations of the model are discussed and evaluated as part of the V&V study. 

This volume documents the V&V study of the library of quantitative fire hazards analysis (FHA) 

models known as Fire Dynamics Tools (FDTS

). Quantitative FHA tools can be useful in 

predicting the risks of fire hazards in various settings within an NPP. Consequently, a number of 

quantitative FHA tools (including the FDTS library) have been developed — with varying 

capabilities and levels of complexity — to serve this purpose. 

The U.S. Nuclear Regulatory Commission (NRC), Office of Nuclear Reactor Regulation (NRR), 

Division of Systems Safety and Analysis (DSSA), Plant Systems Branch (SPLB), Fire Protection 

Engineering and Special Projects Section developed the FDTS [Ref. 1] library using state-of-the-art 

principles of fire dynamics to assist fire protection inspectors in performing risk-informed 

evaluations of credible fires that may cause critical damage to essential safe-shutdown 

equipment. Toward that end, the FDTS library comprises a series of Microsoft® Excel®

spreadsheets, which are pre-programmed with fire dynamics equations and correlations to assist 

inspectors in performing quick, first-order calculations for potential fire scenarios. The technical 

bases for the models included in the FDTS library were primarily derived from the Society of 

Fire Protection Engineers (SFPE) Handbook of Fire Protection Engineering, the National Fire 

Protection Association (NFPA) Fire Protection Handbook, and other fire science literature. 

This report describes the equations included in the spreadsheets that have been subjected to 

V&V, the technical bases of those equations, and evaluation of the sensitivities and predictive 

capabilities of the component spreadsheets. 

The V&V methodology employed in this report generally follows the guidelines outlined in 

ASTM E1355, “Standard Guide for Evaluating the Predictive Capability of Deterministic 

Fire Models” [Ref. 2]. These guidelines were put into effect by the American Society for Testing and 

Materials (ASTM). As such, this report presents the fire model evaluation methodology in terms of 

the following basic focuses of evaluation: 

Define the model and scenarios for which the evaluation is to be conducted. 

• Assess the appropriateness of the theoretical basis and assumptions used in the model. 

• Assess the mathematical and numerical robustness of the model. 

• Quantify the uncertainty and accuracy of the model results in predicting the course of events 

in similar fire scenarios. 
Introduction 

1-2 

In accordance with ASTM E1355, it is critical to evaluate fire models to establish their 

acceptable uses and limitations. Evaluation is also necessary to ensure that those using the models 

can assess the adequacy of their scientific and technical bases, select appropriate models for 

a desired use, and understand the levels of confidence that can be placed on the results predicted 

by the models. Adequate evaluation will also help to prevent unintended misuse of fire models. 

Evaluation of a fire model includes model verification and validation, which are commonly defined 

as follows: 

• Verification: The process of determining that the implementation of a calculation method 

accurately represents the developer’s conceptual description of the calculation method 

and its solution. The fundamental strategy of verifying computational models involves 

identifying and quantifying error in the computational model and its solution. 

• Validation: The process of determining the degree to which a calculation method accurately 

represents the real world from the perspective of its intended uses. The fundamental strategy 

of validating computational models involves identifying and quantifying error and uncertainty 

in the conceptual and computational models with respect to their intended uses. 

It is not possible to evaluate a fire model in its entirety. Thus, guidance such as that provided 

in ASTM E1355 is intended to define a methodology for evaluating the predictive capabilities 

for a specific use. Validation for one application does not indicate validation for a different scenario. 

In accordance with ASTM E1355, this report is structured as follows: 

• Chapter 2 provides qualitative background information about FDTS

 and the V&V process. 

• Chapter 3 describes the technical and theoretical bases of the FDTS models that were included 

in this V&V study. This chapter also discusses the assumptions and limitations associated 

with each of the evaluated models. 

• Chapter 4 discusses the mathematical and numerical robustness of the FDTS

 models. 

• Chapter 5 presents a sensitivity analysis, for which the researchers defined a base case scenario 

and varied selected input parameters in order to test each model’s response to changes in the 

input parameters. 

• Chapter 6 presents the results of the V&V study in the form of accuracies classified 

according to NPP configuration and relevant attributes of enclosure fires in NPPs. The calculated 

accuracies are based on both “blind” and “open” calculations. Blind calculations refer to those 

conducted before the experimental data were available. In contrast, open calculations refer to 

those conducted with the experimental data available. 

• Appendix A presents the technical details supporting the calculated accuracies discussed 

in Chapter 6.
2-1 

2 

MODEL DEFINITION 

This chapter provides qualitative background information about FDTS and the V&V process, as 

required by ASTM E1355. Sufficient documentation of calculation models is necessary to assess the 

adequacy of their scientific and technical bases, as well as the accuracy of the computational 

procedures for the scenarios of interest. In addition, adequate documentation will help to prevent 

the unintentional misuse of the models. 

This chapter briefly describes the FDTS library, following the framework suggested by ASTM 

E1355. As such, this chapter identifies the version of the library that was evaluated in this study; 

identifies its type, developers, and relevant publications; discusses its governing equations 

and assumptions, as well as the required input data, property data, and results; and outlines 

the uses and limitations of the library. Chapter 3 presents more detailed information concerning 

the equations and correlations that comprise each of the library’s component spreadsheets. 

2.1 Name and Version of the Model 

This study evaluated Version 1805.0 of the Fire Dynamics Tools (FDTS), which the NRC 

released in January 2005. 

2.2 Type of Model 

The FDTSs library comprises a series of Microsoft® Excel® spreadsheets, which are pre-programmed 

with fire dynamics equations and correlations to assist inspectors in performing quick, first-order 

calculations for potential fire scenarios. Each spreadsheet also contains a list of the physical 

and thermal properties of the materials commonly encountered in NPPs. 

2.3 Model Developers 

The FDTS library was developed by the U.S. Nuclear Regulatory Commission (NRC), 

Office of Nuclear Reactor Regulation (NRR), Division of Systems Safety and Analysis (DSSA), 

Plant Systems Branch (SPLB), Fire Protection Engineering and Special Projects Section. 

2.4 Relevant Publications 

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 comprises the FDTS

 Excel worksheet package and a 

detailed narrative describing the technical and theoretical bases for each of the fire dynamics 

tools included in the package. The narrative also discusses the uses and limitations of the 

spreadsheets and includes sample applications for each.

Other relevant texts include the SFPE Handbook of Fire Protection Engineering and the NFPA 

Fire Protection Handbook. 
Model Definition 

2-2 

2.5 Governing Equations and Assumptions 

The governing equations and assumptions used in the FDTS spreadsheets come primarily from 

the principles described in the SFPE Handbook of Fire Protection Engineering, the NFPA Fire 

Protection Handbook, and other fire science literature. Those governing equations and assumptions 

are generally accepted within the fire science community as the state-of-the-art in calculation methods 

for fire phenomena. Chapter 3 provides detailed descriptions of the equations programmed into 

the spreadsheets included in this V&V study. 

2.6 Input Data Required to Run the Model 

Each FDTS spreadsheet requires the user to input certain fire parameters that are necessary 

for the equations to compute the output of interest. For example, a spreadsheet may require 

information about the dimensions of the fire enclosure, the fire size, the ambient room conditions, 

and so forth. To reduce the chance of user error, the spreadsheets include drop-down selection 

menus for pre-programmed properties of various materials that are commonly found in NPPs. 

2.7 Property Data 

Some of the models in the FDTS library require the following property data: 

• thermal properties of enclosure surfaces: 

3⁄4 thermal inertia 

3⁄4 thermal conductivity 

3⁄4 specific heat 

3⁄4 density 

• fuel properties: 

3⁄4 mass burning rate 

3⁄4 effective heat of combustion 

3⁄4 density 

3⁄4 fuel vapor mass 

3⁄4 fuel vapor density 

• target properties: 

3⁄4 material thermal inertia 

3⁄4 material ignition temperature 

3⁄4 material critical heat flux for ignition 

2.8 Model Results 

The FDTS spreadsheets use simple algebraic calculations that require little or no computation time 

to produce first order results. The output generated by each FDTS spreadsheet is presented 

as either a single point value numerical result or a series of point values accompanied by a plot 

showing the trend in the results within the Excel spreadsheet. 
Model Definition 

2-3 

2.9 Uses and Limitations of the Model 

The primary objective of the FDTS library and the accompanying documentation (NUREG-1805) 

is to provide a methodology for NRC fire protection inspectors to use in assessing potential 

fire hazards in NRC-licensed NPPs. The methodology uses simplified, quantitative FHA techniques 

to evaluate the potential for credible fire scenarios. One purpose of these evaluations is to determine 

whether a potential fire can cause critical damage to safe-shutdown components. Its intent is to 

provide insights into fire dynamics, without using the sophisticated mathematics that are normally 

associated with the study of fire dynamics. Inspectors using these tools need a working knowledge 

of algebra, graphical interpretation, scientific notation, formulas, and use of some simple 

mathematics functions to understand the quantitative aspects of fire phenomena. 

Chapter 3 discusses the limitations and assumptions associated with each of the fire dynamics tools, 

within the context of its technical basis. 

3-1 

3 

THEORETICAL BASIS FOR FDTS

This chapter presents a technical description of the FDTS library, including theoretical background 

and the underlying physics and chemistry inherent in the component models. The discussion 

includes assumptions and approximations, an assessment of whether the open literature provides 

sufficient scientific evidence to justify the approaches and assumptions used, and an assessment 

of empirical or reference data used for constant or default values in the context of the model. 

In so doing, this chapter addresses the ASTM E1355 requirement to “verify the appropriateness 

of the theoretical basis and assumptions used in the model.” 

FDTS

 is not a model per se, but a set of algebraic hand calculations pre-programmed into 

Microsoft Excel spreadsheets and compiled into a package. The FDTS library includes 

23 distinct 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 

will help 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 particular analysis. 

This chapter explains the predictive equations used in the FDTS spreadsheets that were subjected 

to V&V in this study, as listed in Table 3-1. Note that some spreadsheets in the FDTS

 library 

have not been subjected to V&V in this study because of a lack of applicable experimental data 

for comparison. NUREG-1805 provides complete documentation of the equations 

and theoretical bases for the FDTS library. 

Table 3-1: Spreadsheets included in the V&V Study

Spreadsheet Name Excel File Name 

Predicting Hot Gas Layer Temperature 

and Smoke Layer Height in a Room Fire 

With Natural Ventilation Compartment

02.1_Temperature_NV.xls

Predicting Hot Gas Layer Temperature in a Room Fire 

With Forced Ventilation Compartment 

02.2_Temperature_FV.xls

Predicting Hot Gas Layer Temperature in a Fire Room 

With Door Closed 

02.3_Temperature_CC.xls

Estimating Radiant Heat Flux From Fire to a Target Fuel 

at Ground Level Under Wind-Free Condition 

(Point Source Radiation Model)

05.1_Heat_Flux_Calculations_Wind_Free.xls

Estimating Centerline Temperature 

of a Buoyant Fire Plume

09_Plume_Temperature_Calculations.xls

Estimating Burning Characteristics of Liquid Pool Fire, 

Heat Release Rate, Burning Duration, and Flame Height 

(Flame Height Only)

03_HRR_Flame_Height_Burning_Duration_Calculations.xls
Theoretical Basis for FDTS 

3-2 

3.1 Estimating Hot Gas Layer Temperature 

The various FDTS spreadsheets include a number of correlations for estimating the hot gas layer 

temperature under varying conditions. The spreadsheet for calculating hot gas layer temperature 

in a compartment with natural ventilation also includes a calculation for hot gas layer or smoke layer 

height. This section discusses the predictive equations for each of the correlations for estimating 

hot gas layer temperature, while Section 3.2 discusses the correlations for smoke layer height. 

Section 3.3 augments this discussion by listing the assumptions and limitations that must be employed 

when using these spreadsheets. Chapter 2 of NUREG-1805 provides the following discussion 

on estimating hot gas layer temperature and smoke layer height. 

3.1.1 Natural Ventilation: Method of McCaffrey, Quintiere, and Harkleroad (MQH) 

The temperatures throughout a compartment in which a fire is burning are affected by the amount 

of air supplied to the fire and the location at which the air enters the compartment. Ventilationlimited fires produce different temperature profiles in a compartment than well-ventilated fires. 

A compartment with a single rectangular wall opening (such as a door or window) is commonly used 

for room fire experiments. Such compartments are also commonly involved in real fire scenarios, 

in which a single door or vent opening serves as the only path for fire-induced natural ventilation 

to the compartment. The hot gas layer that forms in compartment fires descends within the opening 

until a quasi-steady balance is struck between the rate of mass inflow to the layer and the rate 

of mass outflow from the layer. 

A complete solution of the mass flow rate in this scenario requires equating and solving two 

nonlinear equations describing the vent flow rate and the plume entrainment rate as a function 

of the layer interface height (the layer in a compartment that separates the smoke layer from 

the clear layer). If it is non-vented, the smoke layer gradually descends as the fire increases, 

thereby lowering the smoke interface and (possibly) eventually filling the compartment. 

McCaffrey, Quintiere, and Harkleroad (MQH) [Ref. 5] have developed a simple statistical 

dimensionless correlation for evaluating fire growth (hot gas layer temperature) in a compartment 

with natural ventilation (also reported by Walton and Thomas [Ref. 14]). This MQH correlation is 

based on 100 experimental fires (from 8 test series involving several types of fuel) 

in conventional-sized rooms with openings. The temperature differences varied from ∆T = 20  ̊C 

(68  ̊F) to 600  ̊C (1,112  ̊F). The fire source was away from walls (i.e., data was obtained 

from fires set in the center of the compartment). The larger the heat release rate (HRR) 

and the smaller the vent, the higher we expect the upper-layer gas temperature to increase. 
Theoretical Basis for FDTS 

3-3 

The approximate formula for the hot gas layer temperature increase, ∆Tg, above ambient (Tg - Ta) 

is as follows: 

( )( )

∆T Q

A h Ah g

v v Tk

=

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥ 6 85

2

1

3

. &

 (3-1) 

Where: 

∆Tg = upper layer gas temperature rise above ambient (Tg - Ta) (K) 

Q&

 = heat release rate of the fire (kW) 

Av = total area of ventilation opening(s) (m2) 

hv = height of ventilation opening (m) 

hk = heat transfer coefficient (kW/m2-K) 

AT = total area of the compartment enclosing surfaces (m2), excluding area of vent 

opening(s). 

The above equation can be used for multiple vents by summing the values, as follows: 

 A h v v

( ) A h v v

i

n

= i

∑

⎛

⎝

⎜ ⎞

⎠

⎟

1

Where n is the number of vents, and can be used for different construction materials by 

summing the AT values for the various wall, ceiling, and floor elements. 

The compartment interior surface area is calculated as follows: 

 AT = ceiling + floor = 2 (wc x lc) 

 + 2 large walls = 2 (hc x wc) 

 + 2 small walls = 2 (hc x lc) 

 - total area of vent opening(s) = (Av) 

 AT = [2 (wc x lc) + 2 (hc x wc) + 2 (hc x lc)] - Av (3-2) 

 Where: 

 AT = total compartment interior surface area (m2

), excluding area of vent opening(s) 

 wc = compartment width (m) 

 lc = compartment length (m) 

 hc = compartment height (m) 

 Av = total area of ventilation opening(s) (m2

)
Theoretical Basis for FDTS 

3-4 

For very thin solids, or for conduction through a solid that continues for a long time, the process 

of conduction becomes stationary (steady-state). The heat transfer coefficient, hk, after long 

heating times, can be written as follows: 

h k

k =

δ (3-3) 

Where: 

 k = thermal conductivity (kW/m-K) of the interior lining 

δ = thickness of the interior lining (m)

This equation is useful for steady-state applications in which the fire burns longer than the time 

required for the heat to be transferred through the material until it begins to be lost out the back 

(cold) side. This time is referred to as the thermal penetration time, tp, which can be calculated 

as follows: 

t

c

k p

p =

⎛

⎝

⎜ ⎞

⎠

⎟

⎛

⎝

⎜ ⎞

⎠

⎟ ρ δ

2

2

 (3-4) 

Where: 

ρ = density of the interior lining (kg/m3

)

cp = thermal capacity of the interior lining (kJ/kg-K) 

 k = thermal conductivity of the interior lining (kW/m-K) 

δ = thickness of the interior lining (m)

However, if the burning time is less than the thermal penetration time, tp, the boundary material 

retains most of the energy transferred to it and little will be lost out the non-fire (cold) side. 

In this case, the heat transfer coefficient, hk, can be estimated using the following equation 

for t < tp: 

h k c

t k = ρ

 (3-5) 

Where: 

 kρc = interior construction thermal inertia [(kW/m2

-K)2-sec] 

 (thermal property of the material responsible for the rate of temperature increase) 

 t = time after ignition in seconds (characteristic burning time) 

By contrast, for t ≥ tp, the heat transfer coefficient is estimated using Equation 3-3.As indicated 

above, the kρc parameter is a thermal property of the material responsible for the rate of 

temperature increase. This is the product of the material thermal conductivity (k), material 

density (ρ), and heat capacity (c). Collectively, kρc is known as the material thermal inertia. For 

most materials, c does not vary significantly, and the thermal conductivity is largely a function of 

material density. This means that density tends to be the most important material property. 
Theoretical Basis for FDTS 

3-5 

Low-density materials are excellent thermal insulators. Since heat does not pass through such materials, 

the surface of the material actually heats more rapidly and, as a result, can ignite more quickly. 

Good insulators (low-density materials), therefore, typically ignite more quickly than poor insulators 

(high-density materials). This is the primary reason that foamed plastics are so dangerous in fires; 

they heat rapidly and ignite in situations in which a poor insulator would be slower to ignite 

because of its slower response to the incident heat flux. The thermal response properties (kρc), 

for a variety of generic materials have been reported in the literature. These values have been 

derived from measurements in the small-scale lateral ignition and flame spread test (LIFT) apparatus 

[Ref. 4]. 

3.1.2 Natural Ventilation (Compartment Closed): Method of Beyler 

Beyler [Ref. 12] developed a correlation based on a non-steady energy balance to the closed 

compartment, by assuming that the compartment has sufficient leaks to prevent pressure buildup 

(also reported by Walton and Thomas [Ref. 14]).For constant HRR, the compartment hot gas 

layer temperature increase, ∆Tg, above ambient (Tg - Ta) is given by the following equation:

∆T TT ( ) K

K

Kt e g ga

k t = − = −+

2 − 1 2

1

2 1 1

 (3-6)

Where: 

( )

K

k c

mc

K Q

mc p p

1 2

2 04

= =

. & ρ

And: 

∆Tg = upper layer gas temperature rise above ambient (Tg - Ta) (K) 

 k = thermal conductivity of the interior lining (kW/m-K) 

ρ = density of the interior lining (kg/m3) 

 c = thermal capacity of the interior lining (kJ/kg-K) 

Q&

 = heat release rate of the fire (kW) 

 m = mass of the gas in the compartment (kg) 

 cp = specific heat of air (kJ/kg-k) 

 t = exposure time (sec) 

3.1.3 Forced Ventilation: Method of Foote, Pagni, and Alvares (FPA) 

Foote, Pagni, and Alvares [Ref. 16] developed another method that follows the basic correlations of the 

MQH method, but adds components for forced-ventilation fires (also reported in Refs. [13], 

[14]). This method is based on temperature data that were obtained from a series of tests 

conducted at Lawrence Livermore National Laboratory (LLNL), in which fresh air was 

introduced at the floor and pulled out the ceiling by an axial fan. Test fires from 150 to 490 kW 

were used, producing ceiling jet temperatures from 100 to 300 °C. The approximate constant 
Theoretical Basis for FDTS 

3-6 

HRR and ventilation rates were roughly between 200 and 575 cfm, which were chosen to be 

representative of possible fires in ventilation-controlled rooms with seven room air changes per 

hour.

The upper-layer gas temperature increase above ambient is given as a function of the fire HRR, 

compartment ventilation flow rate, gas-specific heat capacity, compartment surface area, and 

effective heat transfer coefficient. The non-dimensional form of the resulting temperature 

correlation is as follows: 

∆T

T

Q

mc T

h A

m c

g

a pa

k T

p

= ⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

−

0 63

0 72 0 36

. &

& &

. .

 (3-7) 

Where: 

∆Tg = hot gas layer temperature rise above ambient (Tg - Ta) (K) 

 Ta = ambient air temperature (K) 

Q&

 = HRR of the fire (kW) 

m& = compartment mass ventilation flow rate (kg/sec) 

 cp = specific heat of air (kJ/kg-K) 

 hk = heat transfer coefficient (kW/m2-K) 

 AT = total area of compartment enclosing surfaces (m2

) 

The above correlation for forced-ventilation fires can be used for different construction materials 

by summing the AT values for the various wall, ceiling, and floor elements. 

3.1.4 Forced Ventilation: Method of Deal and Beyler 

Deal and Beyler [Ref. 15] developed a simple model of forced-ventilation compartment fires 

(also reported in Ref. [14]). The model is based on a quasi-steady simplified energy equation 

with a simple wall heat loss model. The model is only valid for times up to 2,000 seconds. The 

approximate compartment hot gas layer temperature increase, ∆Tg, above ambient (Tg - Ta ) is 

given by the following equation: 

∆T TT Q

mc h A g ga

p kT

=−= +

&

& (3-8) 

Where: 

∆Tg = hot gas layer temperature rise above ambient (Tg - Ta) (K) 

 Ta = ambient air temperature (K) 

Q&

 = HRR of the fire (kW) 

m& = compartment mass ventilation flow rate (kg/sec) 

 cp = specific heat of air (kJ/kg-K) 

 hk = convective heat transfer coefficient (kW/m2

-K) 

 AT = total area of compartment enclosing surfaces (m2

) 
Theoretical Basis for FDTS 

3-7 

The convective heat transfer coefficient is given by the following expression: 

h k c

t

k k = ⎛

⎝

⎜ ⎞

⎠ 0 4. max , ⎟ ρ

δ

 (3-9) 

 Where: 

k = thermal conductivity of the interior lining (kW/m-K) 

ρ = density of the interior lining (kg/m3

) 

 c = thermal capacity of the interior lining (kJ/kg-K) 

 t = exposure time (sec) 

δ = thickness of the interior lining (m) 

3.2 Estimating Smoke Layer Height 

The smoke layer can be described as the accumulated thickness of smoke below a physical 

or thermal barrier (e.g., ceiling). The smoke layer is typically not a homogeneous mixture, 

and it does not typically have a uniform temperature. However, for first-order approximations, 

the calculation methods presented below assume homogeneous conditions. The smoke layer 

includes a transition zone that is non-homogeneous and separates the hot upper layer 

from the smoke-free air (i.e., two zones). 

3.2.1 Natural Ventilation (Smoke Filling): The Non-Steady State Yamana 

and Tanaka Method 

In a compartment with larger openings (windows or doors), there will be little or no buildup 

of pressure attributed to the volumetric expansion of hot gases, with the exception of rapid 

accumulation of mass or energy. Thus, for first-order approximations, pressure is assumed 

to remain at the ambient pressure. The opening flows are thus determined by the hydrostatic 

pressure differences across the openings, and mass flows out of and into the compartment. 

We also assume that the upper layer density (ρg) is some average constant value at all times 

throughout the smoke-filling process. 

Assuming a constant average density in the upper hot gas layer has the advantage that we can form 

an analytical solution of the smoke-filling rate, where the HRR does not need to be constant 

(that is, it can be allowed to change with time), and we can use the conservation of mass to arrive 

at the expression for the smoke-filling rate. When this is done, the height of the smoke layer 

as a function of time is known, and we can use the conservation of energy to check the stipulated 

value of ρg. 
Theoretical Basis for FDTS 

3-8 

Yamana and Tanaka [Ref. 19] developed an expression for the height of the smoke layer 

interface, z, in terms of time, as follows (also reported in Ref. [17]): 

z

kQ t

A c h c

= +

⎛

⎝

⎜

⎜

⎜

⎜

⎞

⎠

⎟

⎟

⎟

⎟

−

2

3

1

1

3

2

3

3

2

&

 (3-10) 

Where: 

 z = height (m) of the smoke layer interface above the floor 

Q&

 = heat release rate of the fire (kW) 

 t = time after ignition (sec) 

 Ac = compartment floor area (m2

) 

 hc = compartment height (m) 

 

 And: 

 k = a constant given by the following equation: 

 k g

g c T

a

p a

= ⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

0 21 2

1

3 .

ρ

ρ (3-11) 

Where: 

ρg = hot gas density kg/m3

ρa = ambient density = 1.20 kg/m3

g = acceleration of gravity = 9.81 m/sec2

 cp = specific heat of air = 1.0 kJ/kg-K 

 Ta = ambient air temperature = 298 K 

Substituting the above numerical values in Equation 3-11, we get the following expression: 

k 0.076

g

= ρ (3-12) 

Where density of the hot gas layer (ρg) is given by: 

 

ρg Tg= 353

 (3-13) 

Where: 

 Tg = hot gas layer temperature (K) calculated from Equation 3-1 

Calculation Procedure 
Theoretical Basis for FDTS 

3-9 

• Calculate ρg from Equation 3-13. 

• Calculate the constant k from Equation 3-12. 

• Calculate the smoke layer height (z) at the some time (t) from Equation 3-10 given HRR. 

3.3 Assumptions and Limitations for Hot Gas Layer Calculations 

The methods discussed in this chapter have several underlying assumptions and limitations. 

The following assumptions and limitations apply to all forced and natural convection situations:

(1) These methods best apply to conventional-sized compartments; they should be used 

with caution for large compartments. 

(2) These methods apply to both transient and steady-state fire growth. 

(3) The HRR must be known; it does not need to be constant, and can be allowed to change 

with time. 

(4) Compartment geometry assumes that a given space can be analyzed as a rectangular space 

with no beam pockets. This assumption affects the smoke filling rate within a space 

if the space has beam pockets. For irregularly shaped compartments, equivalent 

compartment dimensions (length, width, and height) must be calculated and should yield 

slightly higher layer temperatures than would actually be expected from a fire 

in the given compartment. 

(5) These methods predict average temperatures and do not apply to cases in which 

prediction of local temperature is desired. For example, this method should not be used 

to predict detector or sprinkler actuation or the material temperatures resulting from 

direct flame impingement. 

(6) Caution should be exercised when the compartment overhead are highly congested 

with obstructions such as cable trays, conduits, ducts, and so forth. 

(7) A single heat transfer coefficient may be used for the entire inner surface of the compartment. 

(8) The heat flow to and through the compartment boundaries is unidimensional 

(i.e., corners and edges are ignored, and the boundaries are assumed to be infinite slabs). 

(9) These methods assume that heat loss occurs as a result of mass flowing out through openings. 

Consequently, these methods do not apply to situations in which significant time passes 

before hot gases begin leaving the compartment through openings. This may occur 

in large enclosures (e.g., turbine building), where it may take considerable time 

for the smoke layer to reach the height of the opening. 
Theoretical Basis for FDTS 

3-10 

The following assumptions and limitations apply only to natural convection situations:

(1) The correlations hold for compartment upper-layer gas temperatures up to approximately 

600 °C (1,112 °F) only for naturally ventilated spaces in which a quasi-steady balance 

develops between the rates of mass inflow and outflow from the hot gas layer. 

(2) These correlations assume that the fire is located in the center of the compartment 

or away from the walls. If the fire is flush with a wall or in a corner of the compartment, 

the MQH correlation is not valid with coefficient 6.85. The smoke layer height correlation 

assumes an average constant value of upper-layer density throughout the smoke-filling 

process. At the EPRI Fire Modeling Workshop in Seattle, Washington on August 26, 2002, 

Mark Salley asked Professor James G. Quintiere (one of the authors of the MQH method) 

what limits apply to compartment size when using the MQH equation. Professor Quintiere 

replied that the correlation will work for any size compartment, since it is a dimensionless 

equation, but Q& should be limited by the following expressions: 

m H & . kJ

kg

or A h kJ

kg fc vv ∆≤ ≤ 3000 0 5 3000

Where: 

m& f = mass loss rate of fuel (kg/sec) 

∆Hc = heat of combustion (kJ/kg) 

 Av = area of ventilation opening (m2

) 

 hv = Height of ventilation opening (m) 

The following assumptions and limitations apply only to forced convection situations:

(1) These correlations assume that the test compartment is open to the outside at the inlet, 

and its pressure is fixed near 1 atmosphere. 

(2) These correlations do not explicitly account for evaluation of the fire source, and they 

assume that the fire is located in the center of the compartment or away from the walls. 

If the fire is flush with a wall or in a corner of the compartment, the FPA correlation 

is not valid with coefficient 0.63. 

3.4 Flame Height 

As documented in Chapter 3 of NUREG-1805, the height of a flame is a significant indicator 

of the hazard posed by the flame. Flame height directly relates to flame heat transfer 

and the propensity of the flame to impact surrounding objects. As a plume of hot gases rises 

above a flame, the temperature, velocity, and width of the plume changes as the plume mixes 

with its surroundings. The size (height) and temperature of the flame are important in estimating 

the ignition of adjacent combustibles. Figure 3-1 shows a characteristic sketch of the flame height 

fluctuations associated with the highly intermittent pulsing structure of a flame, particularly 

along its perimeter and near its top. This intermittence is driven largely by the turbulent mixing 

of air and subsequent combustion, and the pulsing behavior, in turn, affects the temperature 

of the flame. Thus, the temperature at a fixed position fluctuates widely, particularly around 

the edges and near the top of the flame. This is why flame temperature is usually reported 

in terms of the centerline temperature or average flame temperature. 
Theoretical Basis for FDTS 

3-11 

Figure 3-1: Characteristics of Flame Height Fluctuations 

Researchers define flame height as the height at which the flame is observed at least 50 percent 

of the time. Above the fuel source, the flaming region is characterized by high temperature 

and is generally luminous. Flames from pool fires fluctuate periodically so that the tip of the flame 

is significantly different from the length of the continuous combustion (or luminous) region. 

Consequently, flame height has been defined by various criteria in order to correlate data. 

The flame height is an important quantitative characteristic of a fire and may affect fire detection 

and suppression system design, fire heating of building structures, smoke filling rates, and fire ventilation. 

Flame height typically depends on whether the flame is laminar or turbulent. In general, laminar flames 

are short, while turbulent flames are tall. The following two correlations are widely used 

to determine the flame height of pool fires (Heskestad [Ref. 9] and Thomas [Ref. 11]), 

respectively: 

H QD f = − 0 235 1 02

2

5 . & . (3-14) 

Where: 

 Hf = flame height (m) 

 Q& = heat release rate of the fire (kW) 

 D = diameter of the fire (m) 

H D m

gD f

a

= ⎛ ′′

⎝

⎜

⎜

⎞

⎠

⎟

⎟ 42

0 61

& .

ρ (3-15) 

Where: 

 Hf = flame height (m) 

 D = diameter of the fire (m) 

m&′′ = burning or mass loss rate per unit area per unit time (kg/m2

-sec) 

ρa = ambient air density (kg/m3

) 

 g = gravitational acceleration (m/sec2

) 
Theoretical Basis for FDTS 

3-12 

The above correlations can also be used to determine the length of the flame extension 

along the ceiling and to estimate radiative heat transfer to objects in the enclosure. 

The HRR of the fire can be determined by laboratory or field testing. In the absence 

of experimental data, the maximum HRR for the fire is given by the following equation: 

& & QmH A = c ,eff f ′′∆ (3-16) 

Where: 

 m&′′ = burning or mass loss rate per unit area per unit time (kg/m2-sec) 

∆Hc,eff = effective heat of combustion (kJ/kg) 

 Af = horizontal burning area of the fuel (m2) 

For non-circular pools, the effective diameter is defined as the diameter of a circular pool 

with an area equal to the actual pool area given by the following equation: 

D A f = 4

π (3-17) 

Where: 

 Af is the surface area of the non-circular pool 

3.4.1 Assumptions and Limitations 

(1) The flame height correlation described in this chapter was developed for horizontal pool fire 

sources in the center or away from the center of the compartment. The turbulent diffusion flames 

produced by fires burning near or close to a wall or in a corner configuration of a compartment 

affect the spread of the fire. Chapter 4 presents the flame height correlations for fires 

burning near walls and corners. 

(2) The size of the fire (flame height) depends on the diameter of the fuel and the HRR 

attributable to the combustion. 

(3) This correlation is developed for two-dimensional sources (primarily pool fires), 

and this method assumes that the pool is circular or nearly circular. 

(4) There is no fire growth period. (As stated above, real liquid pool fires grow very quickly, 

and it is realistic to assume that the pool fire instantaneously reaches its maximum HRR.) 
Theoretical Basis for FDTS 

3-13 

3.5 Estimating Radiant Heat Flux from Fire to a Target 

Chapter 5 of NUREG-1805 provides a complete discussion on the methods FDTS uses to 

estimate radiant heat flux from fire to a target. The method used in this V&V study is 

summarized below. 

3.5.1 Point Source Radiation Model 

A point source estimate of radiant flux is conceptually the simplest configurational model 

of a radiant source used in calculating the heat flux from a flame to target located outside the flame. 

To predict the thermal radiation field of flames, it is customary to model the flame based on 

the point source located at the center of a flame1. The point source model provides a simple 

relationship that varies as the inverse square of the distance, R. For an actual point source 

of radiation or a spherical source of radiation, the distance, R, is simply the distance from 

the point or from the center of the sphere to the target. 

The thermal radiation hazard from a fire depends on a number of parameters, including the composition 

of the fuel, size and shape of the fire, its duration, proximity to the object at risk, and thermal 

characteristics of the object exposed to the fire. The point source method may be used for either 

fixed or transient combustibles. They may involve an electrical cabinet, pump, liquid spill, 

or intervening combustible at some elevation above the floor. For example, the top of a switchgear 

or motor control center (MCC) cabinet is a potential location for the point source of a postulated 

fire in this type of equipment. By contrast, the point source of a transient combustible liquid spill 

or pump fire is at the floor. 

The point source model assumes that radiant energy is released at a point located at the center 

of the fire. The radiant heat flux at any distance from the source fire is inversely related to 

the horizontal separation distance (R), by the following equation [Ref. 7]:

& & q ′′ = Q

R

χr

4π 2 (3-18)

Where: 

q&′′= radiant heat flux (kW/m2)

Q&

 = heat release rate of the fire (kW) 

 R = radial distance from the center of the flame to the edge of the target (m) 

χr = fraction of total energy radiated 

In general, χr depends on the fuel, flame size, and flame configuration, and can vary from 

approximately 0.15 for low-sooting fuels (e.g., alcohol) to 0.60 for high sooting fuels 

(e.g., hydrocarbons). For large fires (several meters in diameter), cold soot enveloping 

the luminous flames can reduce χr considerably. 

 

1 More realistic radiator shapes give rise to very complex configuration factor equations.
Theoretical Basis for FDTS 

3-14 

Figure 3-2: Radiant Heat Flux from a Pool Fire to a Floor-Based Target Fuel 

(Point Source Model) 

The HRR of a fire can be determined by laboratory or field testing. In the absence of 

experimental data, the maximum HRR for the fire ( ) Q& , is given by the following equation [Ref. 

6]: 

& & QmH A = c ,eff f ′′∆

 (3-19) 

 Where: 

Q&

 = heat release rate of the fire (kW) 

m& " = burning or mass loss rate per unit area per unit time (kg/m2

-sec) 

∆Hc,eff = effective heat of combustion (kJ/kg) 

 Af = horizontal burning area of the fuel (m2

)
Theoretical Basis for FDTS 

3-15 

For non-circular pools, the effective diameter is defined as the diameter of a circular pool with an 

area equal to the actual pool area, given by the following equation: 

D A f = 4

π (3-20) 

Where: 

 Af = surface area of the non-circular pool (m2

) 

 D = diameter of the fire (m) 

3.5.2 Solid Flame Radiation Model with Target at and Above Ground Level 

The solid flame spreadsheet associated with this chapter provides a detailed method for assessing 

the impact of radiation from pool fires to potential targets using configuration factor algebra. 

This method covers a range of detailed calculations, some of which are most appropriate 

for first-order initial hazard assessments, while others are capable of more accurate predictions. 

The solid flame model assumes that (1) the fire can be represented by a solid body of a simple 

geometrical shape, (2) thermal radiation is emitted from its surface, and (3) non-visible gases 

do not emit much radiation. (See Figures 3-3 and 3-4 for general nomenclature.) To ensure that 

the fire volume is not neglected, the model must account for the volume, because a portion 

of the fire may be obscured as seen from the target. The intensity of thermal radiation 

from the pool fire to an element outside the flame envelope for no-wind conditions and 

windblown flames is given by the following equation [Ref. 8]: 

′′ = → q& EF1 2 (3-21) 

Where: 

q&′′ = incident radiative heat flux (kW/m2

) 

 E = average emissive power at flame surface (kW/m2) 

 F1→2 = configuration factor 
Theoretical Basis for FDTS 

3-16 

Figure 3-3: Radiant Heat Flux from a Pool Fire to a Floor-Based Target Fuel (Point Source 

Model) 

Figure 3-4: Solid Flame Radiation Model with No Wind and Target at Ground Level 

3.5.3 Assumptions and Limitations 

The methods discussed in this chapter are subject to several assumptions and limitations. 

For all radiation models, we assume that the pool is circular or nearly circular. 

The following assumptions and limitations apply to point source radiation models:

(1) Except near the base of pool fires, radiation to the surroundings can be approximated 

as being isotropic or emanating from a point source. 

(2) The point source model overestimates the intensity of thermal radiation at the observer’s (target) 

locations close to the fire. This is primarily because the near-field radiation is greatly influenced 

by the flame size, shape, and tilt, as well as the relative orientation of the observer (target). 
Theoretical Basis for FDTS 

3-17 

(3) A theoretical analysis of radiation from small pool fire by Modak [Ref. 10] indicated that 

the point source model is within 5 percent of the correct incident heat flux when L/D > 2.5. 

(4) The energy radiated from the flame is a specified fraction of the energy released during combustion. 

(5) The model can be used to determine thermal radiation hazards in scenarios for which 

a conservative estimate of the hazard is generally acceptable. 

The following limitation applies to solid flame radiation models at and above ground level:

• The correlation of emissive power was developed on the basis of data from experiments 

that included kerosene, fuel oil, gasoline, JP-4, JP-52

, and liquified natural gas (LNG). 

With the exception of the LNG, these are quite luminous flames, so the correlation should be 

suitable for most fuels. The pool diameters ranged from 1 to 50 m. 

3.6 Estimating the Centerline Temperature of a Buoyant Plume 

As discussed in Chapter 9 of NUREG-1805, the peak temperature is found in the plume centerline, 

and decreases toward the edge of the plume where more ambient air is entrained to cool the plume. 

The centerline temperature, denoted as Tp(centerline), varies with height. In the continuous flame region, 

for example, the centerline temperature is roughly constant and represents the mean flame temperature. 

By contrast, the temperature decreases sharply above the flames as an increasing amount 

of ambient air is entrained into the plume. The symbol ∆Tp(centerline) describes the increase 

in centerline plume temperature above the ambient temperature, Ta, as shown in the following equation: 

∆TTT p ( )( ) centerline = p centerline − a (3-22) 

Numerous correlations are available to estimate the plume centerline temperature. These correlations 

relate the temperature as a function of HRR and of height above the source. For example, 

consider a region of a ceiling jet at radial distance from the fire axis equal to the vertical distance 

from the fire source to the ceiling. In this region, the maximum velocity in the jet drops to half 

the value near the fire axis, and the temperature (relative to ambient) drops to about 40 percent 

of the value near the fire axis. The maximum velocity and temperature exist at a distance below 

the ceiling equal to about 1 percent of the distance from the fire source to the ceiling. If the walls 

are much farther away than this, the temperature and velocity of the ceiling jet decay to negligibly 

low values before the jet encounters the nearest wall. However, if the nearest wall is not far away, 

a reflection occurs when the jet reaches the wall, and the reflected jet moves back toward the fire 

axis just under the original jet. Thus, the hot layer under the ceiling becomes thicker. 

If the compartment has an opening and fire continues, the hot layer ultimately becomes thick enough 

to extend below the top of the opening, after which the hot, smoke-laden gases begin to exit 

from the compartment. 

 

2 Common jet fuel. 
Theoretical Basis for FDTS 

3-18 

Heskestad [Ref. 9] provided a simple correlation for estimating the maximum centerline temperature 

of a fire plume as a function of ceiling height and HRR: 

( )

T T

T

g c

Q

z z

p centerline a

a

p a

c

( )

. &

− =

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

−

9 1 2 2

1

3 2

3

0

5

3

ρ

 (3-23) 

Where: 

 Tp(centerline) = plume centerline temperature (K) 

 Ta = ambient air temperature (K) 

Q&

c = convective HRR (kW) 

 g = acceleration of gravity (m/sec2) 

 cp = specific heat of air (kJ/Kg-K) 

ρa = ambient air density (kg/m3) 

 z = elevation above the fire source (m) 

 z0 = hypothetical virtual origin of the fire (m) 

The virtual origin is the equivalent point source height of a finite area fire (Figure 3-5). 

The location of the virtual origin is needed to calculate the thermal plume temperature for fires 

that originate in an area heat source. The thermal plume calculations are based on the assumption 

that the plume originates in a point heat source. Area heat sources include pool fires and burning 

three-dimensional objects such as cabinets and cable trays. The use of a point heat source model 

for area sources is accomplished by calculating the thermal plume parameters at the virtual point 

source elevation, rather than the actual area source elevation. 
Theoretical Basis for FDTS 

3-19 

Figure 3-5: Point Source Fire Plume 

The virtual origin, z0, depends on the diameter of the fire source and the total energy released, 

as follows: 

z

D

Q

D

0

2

5

=− + 1. . 02 0 083 &

 (3-24) 

Where: 

 z0 = virtual origin (m) 

 D = diameter of fire source (m) 

Q& = total HRR (kW) 

For non-circular pools, the effective diameter is defined as the diameter of a circular pool 

with an area equal to the actual area given by the following equation: 

D A f = 4

π (3-25) 

Where: 

 D = diameter of the fire (m) 

 Af = fuel spill area or curb area (m2

) 

Total HRR Q& is used when calculating the mean flame height and position of the virtual origin. 

However, the convective HRR Q&

c is used when estimating other plume properties, since this is 

the part of the energy release rate that causes buoyancy. The energy losses attributable to 

radiation from the flame are typically on the order of 20 to 40 percent of the total HRR Q& . 

The higher of these values is valid for the sootier and more luminous flames, often from fuels 
Theoretical Basis for FDTS 

3-20 

that burn with a low combustion efficiency. The convective HRR is, therefore, often in the range 

0.6 Q& to 0.8 Q& where Q& is the total HRR. 

3.6.1 Assumptions and Limitations 

The methods discussed in this chapter are subject to several assumptions and limitations: 

(1) All heat energy is released at a point. 

(2) The correlation was developed for two-dimensional area sources. 

(3) If the surrounding air is at an elevated temperature, the temperature difference between 

the plume and the surrounding environment is small. In this situation, the thermal plume 

cools less effectively, so Equation 3-23 will underestimate the temperature. 

(4) The thermal plume equation is not valid when the momentum forces in a plume are more 

significant than the buoyant forces, as in a jet fire. If this type of situation is encountered, 

specialized calculation approaches should be used. 
4-1 

4 

 MATHEMATICAL AND NUMERICAL ROBUSTNESS 

This chapter documents the mathematical and numerical robustness of the FDTS library, 

which involves verifying that the implementation of the model matches the stated documentation. 

A model’s mathematical and numerical robustness refers to its stability and ability to reliably 

produce the results that the model developers intended it to produce. Specifically, ASTM E1355 

requires the following analyses to address the mathematical and numerical robustness of models: 

• Analytical tests involve testing the correct functioning of the model. In other words, these tests 

use the code to solve a problem with a known mathematical solution. However, analytical 

tests cannot be applied to FDTS because there are no known mathematical solutions to which 

the results can be compared for the problems addressed by FDTS

. 

• Code checking refers to verifying the computer code on a structural basis. This verification 

can be achieved manually or by using a code-checking program to detect irregularities 

and inconsistencies within the computer code. Code checking can increase the level of confidence 

in the program’s ability to correctly process the data to the program; however, it does not 

give any indication of the likely adequacy or accuracy of the program in use. The FDTS library 

comprises relatively simple closed form equations that are pre-programmed into Excel 

spreadsheets. Each function requires a set of inputs and returns either a single point value 

or a series of values showing a trend. Problems related to irregularities and inconsistencies 

within the computer code are not expected; therefore, code checking in this sense is not 

necessary for the FDTS library. The calculations within each of the FDTS spreadsheets 

have been verified by comparison with the results of hand calculations. 

• Numerical tests investigate the magnitude of the residuals from the solution of a numerically 

solved system of equations employed in the model (as an indicator of numerical accuracy) 

and the reduction in residuals (as an indicator of numerical convergence). The models 

in the FDTS

 library are closed form mathematical expressions that are not solved using 

numerical methods. As a result, there are no numerical instabilities or convergence issues 

associated with the solutions to the models. 

In general, the analyses for numerical and mathematical robustness suggested by ASTM E1355 

do not apply to the FDTS

 library. Because the equations are generally solvable by hand 

calculations, there is little concern about model stability or program reliability. The equations used 

in the FDTS

 spreadsheets are primarily derived from the principles described in the SFPE 

Handbook of Fire Protection Engineering [Ref. 20], the NFPA Fire Protection Handbook [Ref. 

21], and other fire science literature. They are generally accepted within the fire science 

community as the state-of-the-art in calculation methods for fire phenomena. 

In FDTS version 1805.0, an error was identified in the algorithm for estimating the hot gas layer 

temperature in a closed compartment. The error was identified because it was found that the 

output for this algorithm was not consistent with the conceptual basis for this calculation. The 
 Mathematical and Numerical Robustness 

4-2 

algorithm was subsequently corrected and re-released in version 1805.1 on the NRC fire 

protection website. 
5-1 

5 

MODEL SENSITIVITY 

This chapter discusses sensitivity analysis, which ASTM 1355 defines as a study of how changes 

in model parameters affect the results. In other words, sensitivity refers to the rate of change 

of the model output with respect to input variations. The standard also indicates that model predictions 

may be sensitive to (1) uncertainties in input data, (2) the level of rigor employed in modeling 

the relevant physics and chemistry, and (3) the accuracy of numerical treatments. Thus, the purpose 

of a sensitivity analysis is to assess the extent to which uncertainty in the model inputs 

is manifested as uncertainty in the model results of interest. The information obtained can be used 

to determine the dominant variables in the models, define the acceptable range of values for each 

input variable, quantify the sensitivity of output variables to variations in input data and inform 

and caution any potential users about the degree and level of care that should be taken in 

selecting inputs and running the model. 

When an input parameter is changed there will also be a relative magnitude change in the output, 

a sensitivity analysis is conducted to determine and examine this relative magnitude change. 

These changes will vary with each input. Some might have a greater effect on the output then 

others. 

The goal, when examining the results obtained from the sensitivity analysis, is to determine 

which inputs cause the greatest changes in the final output. In order to stay consistent, a base 

case must be established. The inputs for each base case will be set at a value, and then each 

input will be varied over a defined percentage change. If the percentage change in the output is 

greater than the percentage change in the input then the model is more sensitive to the input 

parameter. Conversely, if the relative change in output is less than the relative change in input, 

the model is not as sensitive to the parameter that was changed. 

In the case of this study the inputs were varied by 10%, therefore if the output deviated by more 

than 10% from the base case output then the model has a higher sensitivity to that input. If the 

output deviates less than 10% then the model has a lower sensitivity to the input. 

5.1 Definition of Base Case Scenario for Sensitivity Analysis 

A sensitivity analysis involves defining a base case scenario, and varying selected input 

parameters. The resultant variations in the model output are then measured with respect to the base 

case scenario, in order to consider the extent to which uncertainty in model inputs influences 

model output. The inputs for the base case scenario used in this study are listed in the table that 

follows. 
Model Sensitivity 

5-2 

Table 5-1: Technical Details for Base Case 

Room Material properties Interior Lining 

Length 5 m Specific heat 1.1 kJ/kg-K 

Width 5 m Thermal conductivity 0.00017 kW/m-K 

Height 5 m Density 960 kg/m3

Vent Size 1 m x 2 m Target

Mech. ventilation 0.28 kg/s Elevation 5 m 

Top of Vent From Floor 2 m Fire (Heat release rate)

Ambient conditions HRR 200 KW 

Temperature 24.85 °C 298 K Fuel Spill Area 1 m2

Ambient Air Density 1.18 kg/m3 Fuel Spill Volume 0.0189 

Specific Heat of Air 1 kJ/kg-K Heat of combustion 44600 kJ/kg 

5.2 Sensitivity Analysis for FDTs

FDTS contains a number of algorithms, however, for this study, only the models included in the 

validation were analyzed. The models included were a natural ventilation compartment, a forced 

ventilation compartment via the FPA method, a forced ventilation via the method of Deal & 

Beyler, a closed compartment, the heat release rate from a pool fire, the burning duration of a 

pool fire, the flame height of a pool fire via the method of Heskestad, the flame height via the 

method of Thomas, and the center line plume temperature. The radiation model was not 

included in the sensitivity analysis. Most of the correlations are linear, therefore it is expected 

that a small change in input will not result in a large change in output. For this study each input 

was varied by +10% and -10% from the base case. The sensitivity ratio refers to the percentage 

change in output over the percentage change in the input. A ratio of greater than one (1.0) means 

that the model is sensitive to the input. Below are charts showing the inputs changed along with 

corresponding sensitivity ratio, the maximum, minimum, and average values for each ratio. 
Model Sensitivity 

5-3 

Natural Ventilation

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Length

Width

Height

Vent Width

Vent Height

Top of Vent From Floor

Ambient Air Temperature

Interior Lining Thermal Conductivity

Interior Lining Specific Heat

Interior Lining Density

Heat Relase Rate

Time After Ignition

Input Changed

Sensitivity Ratio

High

Low

Avg

Figure 5-1: Sensitivity Ratios for inputs to HGL Temperature in a Compartment with 

Natural Ventilation 

Forced Ventilation - Deal & Beyler

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Length

Width

Height

Forced Ventilation Flow Rate

Specific Heat of Air

Ambient Air Temperature

Interior Lining Thermal Conductivity

Interior Lining Specific Heat

Interior Lining Density

Heat Relase Rate

Time After Ignition

Input Changed

Sensitivity Ratio

High

Low

Avg

Figure 5-2: Sensitivity Ratios for Inputs to HGL Temperature in Compartment with Forced 

Ventilation 
Model Sensitivity 

5-4 

Closed Compartment

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Length

Width

Height

Specific Heat of Air

Ambient Air Temperature

Interior Lining Thermal Conductivity

Interior Lining Specific Heat

Interior Lining Density

Heat Relase Rate

Time After Ignition

Input Changed

Sensitivity Ratio

High

Low

Avg

Figure 5-3: Sensitivity Ratios for Inputs to HGL Temperature in a Closed Compartment 

HRR

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Fuel Spill Volume Fuel Spill Area or

Dike Area

Mass Burning

Rate of Fuel

Effective Heat of

Combustion of

Fuel

Fuel Density Empirical

Constant

Ambient Air

Temperature

Input Changed

Sensitivity Ratio

High

Low

Avg

Figure 5-4: Sensitivity Ratios for Inputs to HRR Algorithm 
Model Sensitivity 

5-5 

Burning Duration

0

0.2

0.4

0.6

0.8

1

1.2

Fuel Spill Volume Fuel Spill Area or

Dike Area

Mass Burning

Rate of Fuel

Effective Heat of

Combustion of

Fuel

Fuel Density Empirical

Constant

Ambient Air

Temperature

Input Changed

Sensitivity Ratio

High

Low

Avg

Figure 5-5: Sensitivity Ratios for Inputs to Burning Duration Algorithm 

Flame Height - Heskestad

0

0.1

0.2

0.3

0.4

0.5

0.6

Fuel Spill Volume Fuel Spill Area or

Dike Area

Mass Burning

Rate of Fuel

Effective Heat of

Combustion of

Fuel

Fuel Density Empirical

Constant

Ambient Air

Temperature

Input Changed

Sensitivity Ratio

High

Low

Avg

Figure 5-6: Sensitivity Ratios for Inputs to Heskestad’s Flame Height Algorithm 
Model Sensitivity 

5-6 

Plume Temperature

0

0.001

0.002

0.003

0.004

0.005

0.006

Heat Release Rate

of the Fire

Elevation Above the

Fire Source

Area of Combustible

Fuel

Ambient Air

Temperature

Ambient Air Density Convective Heat

Release Fraction

Input Changed

Sensitivity Ratio

High

Low

Avg

Figure 5-7: Sensitivity Ratios for Inputs to Plume Temperature Algorithm 

5.3 Conclusions 

As can be seen in the previous charts, the change in output is less than the change in input for the 

majority of the models. The only places where we see sensitivity ratio above one (1.0) is in the 

calculation of the heat release rate (HRR) and the burning duration of a pool fire. 

The three inputs that bring the ratio above one (1.0) for the HRR are the fuel spill area, mass 

burning rate of the fuel, and the effective heat of combustion for the fuel. Both the mass burning 

rate and the effective heat of combustion keep the change in output very close to the change in 

input. On the other hand, a 10% change in fuel spill area results in a 12% change in output. It is 

easy to see how the mass burning rate and effective heat of combustion effect the change in 

output, if both these go up, then the total HRR should also go up with the same magnitude. 

The burning duration output is sensitive to the fuel spill volume, fuel spill area, the mass burning 

rate, and the density of the fuel. All the averages of these sensitivity ratios fall very close to one 

(1.0). Therefore the relative change in the input variable will be very close to the relative change 

in the output. The effect the volume has on the burning duration is almost trivial, if you have 

10% more fuel then it should take 10% longer to burn off completely. For the area if your area is 

10% bigger then it should take around 10% less time to burn off. The same holds true for the 

burning rate, if the burning rate increases, then the burning duration should also fall respectively. 

Changing the density will in turn change the mass of fuel that occupies the volume being burned, 

therefore there is less mass in the same volume, resulting in a shorter burning duration. 
Model Sensitivity 

5-7 

Although there are some inputs that affect the model with a sensitivity ratio of greater than one 

(1.0), all in all, these results show that all the correlations are stable and their sensitivity to a 

particular input is typically low. 

6-1 

6 

MODEL VALIDATION 

Consistent with Section 11 of ASTM E1355, “Model Evaluation,” this chapter summarizes the 

results of the validation study conducted for the FDTS library. Appendix A presents the 

technical details supporting the validation, including model output and comparison with 

experimental data. 

Six experimental test series have been used in the V&V study. A brief description of each is 

given here. Further details can be found in Volume 7 and in the individual test reports. 

ICFMP BE #2: Benchmark Exercise #2 consists of 8 experiments, representing 3 sets of 

conditions, to study the movement of smoke in a large hall with a sloped ceiling. The results of 

the experiments were contributed to the International Collaborative Fire Model Project (ICFMP) 

for use in evaluating model predictions of fires in larger volumes representative of turbine halls 

in NPPs. The tests were conducted inside the VTT Fire Test Hall, which has dimensions of 19 m 

high by 27 m long by 14 m wide. Each case involved a single heptane pool fire, ranging from 2 

MW to 4 MW. 

ICFMP BE #3: Benchmark Exercise #3, conducted as part of the International Collaborative 

Fire Model Project (ICFMP) and sponsored by the US NRC, consists of 15 large-scale tests performed 

at NIST in June, 2003. The fire sizes range from 350 kW to 2.2 MW in a compartment with 

dimensions 21.7 m x 7.1 m x 3.8 m, designed to represent a variety of spaces in a NPP containing 

power and control cables. The walls and ceiling are covered with two layers of 25 mm thick 

marinate boards, while the floor is covered with two layers of 25 mm thick gypsum boards. The 

room has one 2 m x 2 m door and a mechanical air injection and extraction system. Ventilation 

conditions and fire size and location are varied, and the numerous experimental measurements 

include gas and surface temperatures, heat fluxes, and gas velocities. 

ICFMP BE #4: Benchmark Exercise #4 consists of kerosene pool fire experiments conducted at 

the Institut für Baustoffe, Massivbau und Brandschutz (iBMB) of the Braunschweig University 

of Technology in Germany. The results of two experiments were contributed to the International 

Collaborative Fire Model Project (ICFMP). These fire experiments involve relatively large fires 

in a relatively small (3.6 m x 3.6 m x 5.7 m high) concrete enclosure. Only one of the two 

experiments was selected for the present V&V study (Test 1). 

ICFMP BE #5: Benchmark Exercise #5 consists of fire experiments conducted with realistically 

routed cable trays in the same test compartment as BE #4. Only one test (Test 4) was selected 

for the present evaluation, and only the first 20 min during which time an ethanol pool fire preheats the compartment. 

FM/SNL Series: The Factory Mutual & Sandia National Laboratories (FM/SNL) Test Series is a 

series of 25 fire tests conducted for the NRC by Factory Mutual Research Corporation (FMRC), 

under the direction of Sandia National Laboratories (SNL). The primary purpose of these tests 

was to provide data with which to validate computer models for various types of NPP 
Model Validation 

6-2 

compartments. The experiments were conducted in an enclosure measuring 60 ft long x 40 ft wide 

x 20 ft high (18 m x 12 m x 6 m), constructed at the FMRC fire test facility in Rhode Island. All of 

the tests involved forced ventilation to simulate typical NPP installation practices. The fires 

consist of a simple gas burner, a heptane pool, a methanol pool, or a polymethyl-methacrylate 

(PMMA) solid fire. Four of these tests were conducted with a full-scale control room mockup in 

place. Parameters varied during testing were fire intensity, enclosure ventilation rate, and fire 

location. Only three of these tests have been used in the present evaluation (Tests 4, 5 and 21). 

Test 21 involves the full-scale mock-up. All are gas burner fires. 

NBS Multi-Room Series: The National Bureau of Standards (NBS, now the National Institute of 

Standards and Technology, NIST) Multi-Compartment Test Series consists of 45 fire tests 

representing 9 different sets of conditions, with multiple replicates of each set, which were 

conducted in a three-room suite. The suite consists of two relatively small rooms, connected via a 

relatively long corridor. The fire source, a gas burner, is located against the rear wall of one of the 

small compartments. Fire tests of 100, 300 and 500 kW were conducted, but for the current 

V&V study, only three 100 kW fire experiments have been used (Test 100A, 100O, and 100Z). 

The results for FDTS

 comparisons are organized by the following quantities: 

• Hot Gas Layer Temperature and Height 

• Plume Temperature 

• Flame Height 

• Target/Radiant Heat Flux 

As previously defined, validation is the process of determining the degree to which a calculation 

method accurately represents the real world from the perspective of its intended uses. To fulfill 

the need for validation, the experiments described above were modeled using the appropriate 

FDTS spreadsheets, and the results from the FDTS computations were then compared to the 

experimental measurements and presented in the form of relative differences. Peak values were 

compared from both the model predictions and the experimental data. For the comparison, the 

researchers used the following equation for relative difference between model and experiment: 

( ) ( )

( ) p o

p o p o

E E

M M E E

E

M E

−

− − − = ∆

∆ − ∆

ε =

where ∆M is the difference between the modeled peak value (Mp) of the evaluated parameter and 

its original value (Mo), and ∆E is the difference between the experimental observation (Ep) and 

its original value (Eo). Appendix A lists the calculated relative differences for the fire modeling 

parameters listed above using FDTS

. 

The measure of model “accuracy” used throughout this study is related to experimental 

uncertainty. Volume 7 discusses this issue in detail. In brief, the accuracy of a measurement, 

e.g. gas temperature, is related to the measurement device, e.g. a thermocouple. In addition, the 

accuracy of the model prediction of the gas temperature is related to the simplified physical 

description of the fire and to the accuracy of the input parameters, e.g. the specified heat release 

rate, which is based on experimental measurements. Ideally, the purpose of a validation study is 

to determine the accuracy of the model in the absence of any errors related to the measurement 

of both its inputs and outputs. Because it is impossible to eliminate experimental uncertainty, at 
Model Validation 

6-3 

the very least a combination of the uncertainty in the measurement of model inputs and output 

can be used as a yard stick. If the numerical prediction falls within the range of uncertainty due 

to both the measurement of the input parameters and the output quantities, it is not possible to 

quantify its accuracy further. At this stage, it is said that the prediction is within experimental 

uncertainty.

Each section in this chapter contains a scatter plot that summarizes the relative difference results 

for all of the predictions and measurements of the quantity under consideration. Details of the 

calculations, the input assumptions, and the time histories of the predicted and measured output 

are included in Appendix A. Only a brief discussion of the results is included in this chapter. 

Included in the scatter plots are an estimate of the combined uncertainty for the experimental 

measurements and uncertainty in the model inputs. It is important to understand that these are 

simply estimates of the lower bounds of random uncertainty and do not include systematic 

uncertainty in either the experimental measurements or model predictions. Along with expert 

engineering judgment of the project team, these uncertainty bounds serve as guidelines to judge 

the predictive capability of the model. 

At the end of each section, a color rating is assigned to each of the output categories, indicating, 

in a very broad sense, how well the model treats that particular quantity. A detailed discussion of 

this rating system is included in Volume 1. For FDTS, the Green, Yellow+, and Yellow ratings 

have been assigned to 4 of the 13 quantities of interest because these quantities fall within the 

capability of the FDTS

 library. The color Green indicates that the research team concluded the 

physics of the model accurately represent the experimental conditions and the calculated relative 

differences comparing the model and the experimental are consistent with the combined 

experimental and input uncertainty. The color Yellow+ indicates that the research team 

concluded the physics of the model accurately represent the experimental conditions and the 

model consistently over predicted the experimental measurements outside the combined 

experimental and input uncertainty. The user should take care and use caution when interpreting 

the results of the model for these parameters. The color Yellow suggests that one exercise 

caution when using the model to evaluate this quantity – consider carefully the assumptions 

made by the model, how the model has been applied, and the accuracy of its results. There is 

specific discussion of model limitations for the quantities assigned a Yellow rating. Parameters 

that are not given a color rating indicate that the model does not include output to be able to 

evaluate that parameter in its as-tested version. 

6.1 Hot Gas Layer Temperature and Height 

The single most important prediction a fire model can make is the temperature of the hot gas 

layer (HGL). After all, the impact of the fire is not so much a function of the heat release rate, 

but rather the temperature of the compartment. Following is a summary of the accuracy 

assessment for the HGL temperature predictions of the six test series. HGL Height calculations 

were not evaluated because FDTS

 does not contain a method applicable to any of the test series. 

ICFMP BE #2: FDTS

, using the methods of Beyler and Foote, Pagni, and Alvares, overpredicted the HGL temperature for all three cases. None of the predictions fell within the 

combined uncertainty bands. For the closed compartment predictions, the relative differences 

probably stem from an imprecise accounting of leakage in the model. The forced ventilation 

relative differences for case 3 might be a result of the fact that the spreadsheet used does not 
Model Validation 

6-4 

account for natural flow through open doorways. The model calculations were performed with 

mineral wool as the wall material because it is much less conductive than steel and results in 

more realistic model results. In the actual experiment the walls were made up of a 1 mm (0.04 

in) thick layer of sheet metal covering a 0.05 m (2 in) layer of mineral wool. 

ICFMP BE #3: FDTS

 over-predicted the HGL temperature for all fifteen tests. The open doors 

tests (Tests 3, 5, 9, 14, 15, and 18) using the method of McCaffrey, Quintiere, and Harkleroad 

are closer to experimental data than the closed door tests, with the exception of Test 5. In this 

test, the combination of open doors and mechanical ventilation (using the method of Foote, 

Pagni, and Alvares) led to experimental temperatures that were lower than similar tests without 

mechanical ventilation. None of the predictions fell within the combined uncertainty bands. For 

the closed compartment predictions where the method of Beyler was used, the relative 

differences probably stem may be the result of actual leakage. Beyler’s correlation for closed 

compartments only assumes a small leakage rate that will prevent a pressure buildup in the 

compartment. Therefore, if significant leakage did exist during the actual tests it could have 

contributed to lower temperatures by allowing the hot gases inside the compartment to escape. 

ICFMP BE #4: Using the Beyler method, FDTS

 under-predicted the HGL temperature for this 

test, outside of the combined uncertainty bands. The assumptions in the natural ventilation 

spreadsheet may not be appropriate for this test configuration due to the relatively large fire in a 

relative small compartment. The compartment likely allowed more energy to build into the HGL 

and not as much to be lost out of the opening, thus creating an imbalance and a hotter HGL. The 

experimental temperature also reached levels outside the bounds where this correlation is 

applicable. 

ICFMP BE #5: Test ICFMP BE #5 was conducted in the same compartment as test ICFMP BE 

#4 but utilized a smaller doorway and a smaller sized fire. As a result, the FDTS prediction, 

using Beyler’s method for a closed compartment with natural ventilation, fell within the 

combined experimental uncertainty. This is likely due to the smaller fire size. 

FM/SNL: The Foote, Pagni, and Alvares method was used to predict the HGL temperatures in 

the FM/SNL tests. FDTS

 over-predicted the HGL temperature for the three tests, well outside 

experimental uncertainty. Tests 4 and 21 had a ventilation rate of approximately 0.37 m3/s (800 

cfm), while Test 5 had a ventilation rate of approximately 3.7 m3

/s (8,000 cfm). As can be seen 

in Figure 6-1 the FM/SNL 5 test had the smallest relative difference (69%). The FPA model 

appears to work better with larger ventilation rates. 

NBS Multi-Room: Using the method of McCaffrey, Quintiere, and Harkleroad FDTS

 predicted 

the HGL temperature to within the experimental uncertainty for the three NBS tests. The model 

calculations were performed with a ceramic fiber as the wall material because it is less 

conductive than fire brick and results in more realistic model results. In the actual experiment 

the walls of the room of fire origin were made up of a 0.1 m (4 in) thick fire brick covered with a 

0.05 m (2 in) thick ceramic fiber. It is also important to note that the standard reduction method 

was not used to compute the experimental HGL temperature or height for this test series. Rather, 

the test director reduced the layer information individually for the eight thermocouple arrays 

using an alternative method [Ref. 16]. 

Summary: HGL Temperature—YELLOW+
Model Validation 

6-5 

• The FDTS models for HGL temperature capture the appropriate physics and are based on 

appropriate empirical data. 

• FDTS generally over-predicts HGL temperature, outside of uncertainty. 

FDTs HGL Temperature Predictions

-100%

-50%

0%

50%

100%

150%

200%

250%

BE 2-1BE 2-2BE 2-3BE 3-1BE 3-7BE 3-2BE 3-8BE 3-4

BE 3-10BE 3-13BE 3-16BE 3-17

BE 3-3BE 3-9BE 3-5

BE 3-14BE 3-15BE 3-18

BE 4-1BE 5-4

FM/SNL 4FM/SNL 5

FM/SNL 21

NBS 100A

NBS 100O

NBS 100Z

Relative Difference (%)

 

Figure 6-1: Relative Differences for HGL Temperature 

6.2 Plume Temperature 

Plume temperature data used to assess the accuracy of FDTS predictions were taken from ICFMP 

Benchmark Exercise #2 at 7 and 13 meters above the fire source and in the FM/SNL test at 5.66 

meters above the fire source. A total of 9 plume temperature data points were included in this 

study. The spreadsheet in the FDTS library used to estimate the centerline temperature of a 

buoyant plume is 09_Plume_Temperature_Calculations.xls. 

The primary user inputs to the plume temperature algorithm in FDTS

 are HRR, the ambient air 

temperature of the enclosure, the elevation above the fuel source, and the area of combustible 

fuel. The inputs and assumptions required for the spreadsheet in FDTS

 used to estimate the 

plume temperature are discussed in detail in Chapter 3, Section 3.7. 

ICFMP BE #2: Heskestad’s correlation in FDTS

 under-predicts the plume temperature in five of 

the six cases in this test series. At 12 meters above the fire source FDTS under-predicts by 

around 40% in all 3 cases. At 6 meters above the fire source, FDTS

 is more accurate, but it still 

under predicts in cases 1 and 2 and predicts within experimental uncertainty in case 3. However, 

upon observation of the plots in Figure A-9 in Appendix A, one can see that heat up of the plume 

is more closely modeled in cases 1 and 2. In cases 1 and 2 the doors to the compartment were 

closed, while in case 3, both natural and mechanical ventilation were present. The inaccurate 

FDTS plume temperature calculations can be attributed to the fact that the Heskestad plume 

temperature correlation is not valid at elevations where the plume enters a smoke layer. The 
Model Validation 

6-6 

HGL generally reached the 6 meter height within approximately two minutes for all three cases. 

This resulted in the inaccuracies of the model for the majority of each test. 

FM/SNL: In this test series FDTS

, using Heskestad’s correlation, under-predicts the plume 

temperature in tests 4 and 5 and predicts within experimental uncertainty in test 21. In tests 4 and 

5 the fire was located in the center of the compartment, while in test 21 the fire was located 

inside an electrical cabinet. It is possible that the model predictions came closer to those 

observed in the experiment for test 21 because some of the heat generated by the fire was 

absorbed by the walls of the cabinet, thus reducing the temperatures in the plume during the 

experiment. The FDTS

 algorithm has no way of taking this effect into account. The plots in 

Figure A-10 in Appendix A indicate that the transport lag effect is reduced somewhat, perhaps 

due to the shorter distance in question. 

The scatter plot shown below depicts the relative differences between the peak plume 

temperature recorded in the experiments and the predictions made by the FDTS algorithm. The 

red lines shown at -10% and 10% represent the approximate bounds to the combined uncertainty 

of the input values and the measurement of the experimental outputs. In these cases it appears 

that the maximum plume temperature estimates for the given conditions were always either 

under predicted or were predicted within experimental uncertainty. However, in both cases in 

which the temperature was predicted within experimental uncertainty it can be argued that the 

experimental temperatures were lowered due to test conditions that were not accounted for in the 

FDTS prediction. 

Summary: Plume Temperature – YELLOW 

• The FDTS model for plume temperature is based on appropriate empirical data and is 

physically appropriate. 

• FDTS

 generally under-predicts plume temperature, outside of uncertainty. 

• The FDTS model is not appropriate for predicting the plume temperatures at elevations within 

a hot gas layer. 
Model Validation 

6-7 

FDTs Plume Temperature Predictions

-100%

-80%

-60%

-40%

-20%

0%

20%

40%

60%

80%

100%

BE 2-1 TG1BE 2-1 TG2BE 2-2 TG1BE 2-2 TG2BE 2-3 TG1BE 2-3 TG2

BE 3-1BE 3-7BE 3-2BE 3-8BE 3-4

BE 3-10BE 3-13BE 3-16BE 3-17

BE 3-3BE 3-9BE 3-5

BE 3-14BE 3-15BE 3-18

BE 4-1BE 5-4

FM/SNL 4FM/SNL 5

FM/SNL 21

NBS 100A

NBS 100O

NBS 100Z

Relative Difference (%)

 

Figure 6-2: Relative Differences for Plume Temperature 

6.3 Flame Height 

Flame height is recorded by visual observations, photographs or video footage. Photographs 

from the ICFMP BE #2 test series and video from BE #3 test series are available. It is difficult to 

precisely measure the flame height, but the photos and videos allow one to make estimates 

accurate to within a pan diameter. Such observations can be compared with outputs from 

Heskestad’s flame height correlation. 

ICFMP BE #2: The height of the visible flame in these tests has been estimated to be between 

2.4 and 3 pan diameters (3.8 m (12.5 ft) to 4.8 m (15.7 ft)). From Heskestad’s flame height 

correlation in the FDTS

 the estimated flame height is 4.3 m (14.1 ft). 

ICFMP BE #3: During BE #3, Test 3, the peak flame height is estimated to be 2.8 m, roughly 

consistent with the view through the doorway in compartment. FDTS

 results in a flame height of 

3.0 m (9.8 ft) using Heskestad’s flame height prediction. 

Summary: Flame Height – GREEN 

• The FDTS

 model predicted flame heights consistent with visual test observations. 

6.4 Target/Radiant Heat Flux 

As described in Chapter 3, the FDTS library of correlations includes a radiation heat flux model 

that estimates heat flux at a specific distance away from a fire. This model, called the point 

source radiation model, was compared to radiant heat flux data from the ICFMP BE #3 

experiments. 
Model Validation 

6-8 

ICFMP BE #3: The FDTS

 spreadsheet used to calculate radiant heat flux is 

05.1_Heat_Flux_Calculations_Wind_Free.xls. This spreadsheet uses Drysdale’s equation for 

calculating the radiant heat flux. The graphs in Figures A-11 through A-18 in Appendix A and 

the scatterplot below do not indicate any specific trends about the accuracy of FDTS

 in 

calculating radiant heat flux using the point source model. For a number of tests the model 

predicts the peak radiant heat flux at the gauge within the uncertainty of the input parameters and 

the experimental measurements. For other tests the model both under-predicts and over-predicts 

the radiant heat flux at a target, outside uncertainty bands. The reason that the model predictions 

varied so greatly can be attributed to the fact that the point source radiation model is not meant to 

be used for locations within a hot gas layer. 

As can be seen in Figure 6-3 the majority of the under-predictions occurred at gauge 10, which 

was located at 1.8 m (5.9 ft) above the floor. Most of the over-predictions occurred at locations 

higher in the hot gas layer. Gauges 1, 3, and 7 were located at 2, 2.5, and 3 m (6.6, 8, and 9.8 ft) 

respectively above the floor. These gauges were immersed in smoke during all the tests by the 

time that the radiation measurements were selected for comparison. 

Summary: Radiant Heat Flux – YELLOW 

• The FDTS

 point source radiation model in general is based on appropriate empirical data and 

is physically appropriate with consideration of the simplifying assumptions. 

• The FDTS

 point source radiation model is not valid for elevations within a hot gas layer. 

• FDTS predictions had no clear trend. The model under- and over-predicted, outside 

uncertainty. 

• The point source radiation model is intended for predicting radiation from flames in an 

unobstructed and smoke-clear path between flames and targets. 
Model Validation 

6-9 

FDTs Radiant Heat Flux Predictions

-100%

-50%

0%

50%

100%

150%

200%

BE 2-1BE 2-2BE 2-3BE 3-1BE 3-7BE 3-2BE 3-8BE 3-4

BE 3-10BE 3-13BE 3-16BE 3-17

BE 3-3BE 3-9BE 3-5

BE 3-14BE 3-15BE 3-18

BE 4-1BE 5-4

FM/SNL 4FM/SNL 5

FM/SNL 21

NBS 100A

NBS 100O

NBS 100Z

Relative Difference (%)

Gauge 1 (2 m)

Gauge 3 (2.5 m)

Gauge 7 (3 m)

Gauge 10 (1.8 m)

Figure 6-3: Relative Differences for Radiant Heat Flux 

6.5 Summary 

This chapter presents a summary of numerous comparisons of the FDTS model with a range of 

experimental results conducted as part of this V&V effort. Four quantities were selected for 

comparison and a color rating assigned to each of the output categories, indicating, in a very 

broad sense, how well the model treats that particular quantity: 

• Hot Gas Layer (HGL) Temperature: Yellow+ 

• Plume Temperature: Yellow 

• Flame Height: Green 

• Radiant Heat Flux: Yellow 

One of the quantities (flame height) was assigned a green rating indicating that the research team 

concluded the physics of the model accurately represent the experimental conditions and the 

calculated relative differences comparing the model and the experimental are consistent with the 

combined experimental and input uncertainty. 

• FDTS

 predicts the flame height consistent with visual observations of flame height for the 

experiments. 

One of the quantities (hot gas layer temperature) was assigned a yellow+ rating indicating that 

the research team concluded the physics of the model accurately represent the experimental 

conditions, but the calculated relative differences comparing the model and the experimental 

results are not consistent with the combined experimental and input uncertainty. The yellow+ 

rating indicates that most of the results outside the relative uncertainty resulted in over-
Model Validation 

6-10 

predictions of the HGL temperatures. The user should take caution when using the model to 

evaluate HGL temperatures and should not automatically assume that the model will always over 

predict these values. 

Two of the quantities (plume temperature and radiant heat flux) were assigned a yellow rating 

indicating the user should take caution when using the model to evaluate that quantity. This 

typically indicates limitations in the use of the model. A few notes on the comparisons are 

appropriate: 

• The FDTS

 plume temperature and point source radiation models are not valid for elevations 

within a hot gas layer. 

• The point source radiation model is only intended for predicting radiation from flames in an 

unobstructed and smoke-clear path between flames and targets. 

• FDTS

 predictions had no clear trend for either parameter. The model under- and overpredicted, outside uncertainty. 

The FDTS predictions in this validation study used physically appropriate models but often 

resulted in predictions outside of the relative uncertainty. As such, it is important for the user to 

exercise caution when using the FDTS spreadsheets to model fire scenarios. Like all predictive 

models, the best predictions come with a clear understanding of the limitations of the model and 

of the inputs provided to do the calculations. 
7-1 

7 

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7-3 

Hasemi Y., and T.Tokunaga, “Some Experimental Aspects of Turbulent Diffusion Flames and 

Buoyant Plumes from Fire Sources Against a Wall and in Corner of Walls,” Combustion Science 

and Technology, Volume 40, pp. 1–17, 1984. 

Cote, A., and P. Bugbee, Principle of Fire Protection, 2nd Edition National Fire Protection 

Association, Quincy, Massachusetts, 1988. 

Friedman, R., Principles of Fire Protection Chemistry and Physics, 3rd Edition, National Fire 

Protection Association, Quincy, Massachusetts, 1998. 

Fire Dynamics Course Guide, Federal Emergency Management Agency (FEMA), United States 

Fire Administration (USFA), National Emergency Training Center, Emmitsburg, Maryland, 1995. 

Icove, D.J., and J.D. DeHaan, Forensic Fire Science Reconstruction, 1st Edition, Pearson 

Education Inc., Upper Saddle River, New Jersey, 2004. 

Quintiere, J.G., Principles of Fire Behavior, Chapter 9, “Compartment Fires,”, Delmar 

Publishers, Albany, New York, pp. 169–195, 1997. 

Quinitiere, J.G., “A Simple Correlation for Predicting Temperature in a Room Fire,” NBSIR 83-

2712, National Bureau of Standards (NBS), U.S. Department of Commerce, Washington, DC, 

June 1983. 

American Gas Association (AGA), “LNG Safety Research Program,” Report IS 3–1, 1974. 

Barry, T.F., Risk-Informed, Performance-Based Industrial Fire Protection, T.F. Barry 

Publications and Tennessee Valley Publications, Knoxville, Tennessee, 2002. 

EPRI TR-100370, “Fire-Induced Vulnerability Evaluation (FIVE),” Final Report, Electrical 

Power Research Institute, Palo Alto, California, April 1992. 

Fay, J.A., and D.H. Lewis, “Unsteady Burning of Unconfined Fuel Vapor Clouds,” Sixteenth 

Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, Pennsylvania, 

pp. 1397–1404, 1977. 

Hasegawa, K., and K. Sato, “Study on the Fireball Following Steam Explosion of n-Pentane,” 

Second Symposium on Loss Prevention and Safety Promotion in the Process Industries, 

Heidelberg, pp. 297–304, 1977. 

Nolan, D.P., Handbook of Fire and Explosion Protection Engineering Principles for Oil, Gas, 

Chemical and Related Facilities, Noyes Publications, Westwood, New Jersey, 1996. 

Roberts, A., “Thermal Radiation Hazards from Release of LPG Fires from Pressurized Storage,” 

Fire Safety Journal, Volume 4, pp. 197–212, 1982. 

SFPE Engineering Guide, “Assessing Flame Radiation to External Targets from Pool Fires,” 

Society of Fire Protection Engineers (SFPE), Bethesda, Maryland, June 1999. 

Shokri, M., and C.L. Beyler, “Radiation from Large Pool Fires,” SFPE Journal of Fire 

Protection Engineering, Volume 1, No. 4, pp.141–150, 1989. 

Alpert, R.L., and E.J. Ward, “Evaluation of Unsprinklered Fire Hazard,” Fire Safety Journal, 

Volume 7, No. 177, 1984. 
References 

7-4 

Heskestad, G., “Fire Plumes,” Section 2, Chapter 2, SFPE Handbook of Fire Protection 

Engineering, 2nd Edition, P.J. DiNenno, Editor-in-Chief, National Fire Protection Association, 

Quincy, Massachusetts, 1995. 

George, W.K., R.L. Alpert, and F. Tamanini, “Turbulence Measurements in an Axisymmetric 

Buoyant Plume,” International Journal of Heat Mass Transfer, Volume 20, pp.1145–1154, 

1977. 
A-1 

A 

TECHNICAL DETAILS OF THE FDTS

 VALIDATION 

STUDY 

This appendix provides technical basis for the relative difference values listed in Chapter 6 of 

Volume 2 for the output parameters in the compilation of quantitative fire hazard analysis tools, 

FDTS

. This appendix is organized into sections for the parameters that have been verified and 

validated in this study for this specific tool. Not all of the spreadsheets included in FDTS have 

been subjected to verification and validation due to a lack of experimental data for comparison. 

Each section presents a graph of the experimental data and the model output and a table of 

relative differences at the peaks between experimental data and the model output. The sections 

also describe the process and the values selected for input to the model. Within each section, the 

graphs are grouped by experimental test series. Discussion and analysis of the relative 

differences can found in Chapter 6 of Volume 2. The Appendix is organized into four sections, 

as follows: 

A.1 Hot Gas Layer Temperature and Height 

A.2 Plume Temperature 

A.3 Flame Height 

A.4 Target Heat Flux 

Volume 7 includes detailed discussion of the uncertainties associated with both the experimental 

data and model predictions presented in this Appendix. 

A.1 Hot Gas Layer Temperature and Height 

Hot gas layer (HGL) temperatures in the experiments were estimated using data from ICFMP 

benchmark exercises (BE) 2, 3, 4, and 5, the FM/SNL test series, and the NBS multicompartment fire test series for the room of fire origin. Specifically, thermocouple tree data 

from those experiments was reduced to an instantaneous average temperature above the 

estimated layer interface height at a specific time step. The layer interface height is deduced 

from the continuous vertical profile of temperature indicated by the thermocouple tree data. 

Relative differences were calculated by comparing the peak HGL temperatures and heights 

estimated from the experiment to the peak predicted HGL temperatures calculated using FDTS. 

Peak or, where available, steady-state heat release rates were used as inputs to the spreadsheets. 

The heat release rate values for the different experiments are located in tables in this volume. 
Technical Details of the FDTS Validation Study 

A-2 

A.1.1 ICFMP BE # 2 

This test series consisted of three full-scale experiments with replicates. The experimental data 

reported here are averages of the replicate tests. In Cases 1 and 2 the test compartment was 

sealed with the exception of small openings incorporated as “infiltration ventilation,” which 

amounted to approximately 2 m2

 (22 ft2). Beyler’s method for calculating HGL temperature in a 

closed compartment was used for Cases 1 and 2 (02.3_Temperature_CC.xls). The “infiltration 

ventilation” was considered small enough compared to the volume of the space so that a natural 

ventilation condition would not exist and Beyler’s method would be appropriate. 

In Case 3, mechanical exhaust ventilation (11 m3

/s [388 ft3/s]) was employed, as well as two 

doorway openings (3.2 m2

 each [34 ft3/s]). Although there is no specific correlation for the 

scenario with forced ventilation and open doorways, the method of Foote, Pagni, and Alvares for 

forced ventilation was used (0.2.2_Temperature_FV.xls). 

A calculation method for HGL height is not found on the spreadsheets used for the predictions of 

BE #2. Also, the reduction method used to estimate experimental layer height from 

thermocouple trees does not apply to closed compartments. Therefore, no HGL height 

comparisons were made for BE #2.

For Cases 1 and 2, experimental HRR data at specific times was used as input to the spreadsheet. 

For Case 3, the spreadsheet requires a steady state HRR input. In this case, as a conservative 

assumption, the maximum HRR measured in the experiment was used as input. The interior wall 

material for all cases was assumed to be a 0.05 m layer of mineral wool. The experimental 

HRRs and wall thermal properties can be found in Table A-2. 

Table A-1: Input Values for ICFMP BE # 2 Case 1 and 2 

Case 1 Case 2 

Air 

 

Ambient Air Temperature (C) 20 20 

Ambient Air Density (kg/m3) 1.2 1.2 

 

Room Size 

 

Compartment Width (m) 27 27 

Compartment Length (m) 13.8 13.8 

Compartment Height (m) 15.9 15.9 

 

Wall Properties 

Interior Lining Thermal Inertia [(kW/m2-K)2-sec] 0.015 0.015 

Interior Lining Thermal Conductivity (kW/m-K) 0.0002 0.0002 

Interior Lining Specific Heat (kJ/kg-K) 0.15 0.15 

Interior Lining Density (kg/m3) 500 500 

Interior Lining Thickness (m) 0.05 0.05 
Technical Details of the FDTS Validation Study 

A-3 

Table A-2: Input Values for ICFMP BE # 2 Case 3 

Air 

Ambient Air Temperature (C) 20 

Ambient Air Density (kg/m3) 1.2 

Room Size 

Compartment Width (m) 27 

Compartment Length (m) 13.8 

Compartment Height (m) 15.8 

 

Wall Properties 

Interior Lining Thermal Inertia [(kW/m2-K)2-sec] 0.015 

Interior Lining Thermal Conductivity (kW/m-K) 0.0002 

Interior Lining Specific Heat (kJ/kg-K) 0.15 

Interior Lining Density (kg/m3) 500 

Interior Lining Thickness (m) 0.05 

 

Ventilation 

Forced Ventilation Flow Rate (cfm) 23500 

Heat Release Rate 

Fire Heat Release Rate (kW) 3640 
Technical Details of the FDTS Validation Study 

A-4 

HGL Temperature

ICFMP BE # 2, Case 1

0

20

40

60

80

100

120

0 2 4 6 8 10

Time (min)

Temp (C)

Case 1 FDTs

HGL Temperature

ICFMP BE # 2, Case 2

0

20

40

60

80

100

120

140

02468

Time (min)

Temp (C)

Case 2 FDTs

HGL Temperature

ICFMP BE # 2, Case 3

0

50

100

150

200

250

02468

Time (min)

Temp (C)

Case 3 FDTs

Figure A-1: Hot Gas Layer Temperature, ICFMP BE #2, Cases 1, 2, and 3 

A.1.2 ICFMP BE # 3 

The experiments in this test consisted of heptane and toluene spray fires varying nominally from 

350 kW to 2 MW. There were 15 tests conducted with more than 370 channels of data for each 

test. Six of the 15 tests were conducted with open doors (3, 5, 9, 14, 15, 18) and 9 with closed 

doors (1, 2, 4, 7, 8, 10, 13, 16, 17). One of the open door tests (5) and 3 of the closed door tests 

(4, 10, 16) also had mechanical ventilation of approximately 0.81m3

/s (29 ft3/s). The MQH 

model (02.1_Temperature_NV.xls) was used for open door tests without mechanical ventilation. 

The input values for these tests can be found in Table A-4. Beyler’s method for calculating HGL 

temperature in closed compartments (02.3_Temperature_CC.xls) was used for closed door tests 

without mechanical ventilation. The input values for these tests can be found in Table A-3. The 

FPA model was used for all tests with forced ventilation (02.2_Temperature_FV.xls). The input 

values for these tests can be found in Table A-5. For Test 5, the combination of mechanical 

ventilation and open doors cannot be directly modeled using FDTs

, so there are two predictions 

reported—one using the forced ventilation model, and another using the natural ventilation 

model. The HRRs used for inputs were taken from the experimental report issued by NIST. The 

wall material was assumed to be Marinite I and the thermal properties were taken from 

manufacturer’s data. 
Technical Details of the FDTS Validation Study 

A-5 

Table A-3: Input values for ICFMP BE#3 Closed Compartment Tests 

Test 1 Test 2 Test 7 Test 8 Test 13 Test 17 

Air 

 

Ambient Air Temperature (C) 21.1 23.9 22.2 28.9 32.2 25.6

Ambient Air Density (kg/m3) 1.2 1.19 1.2 1.17 1.16 1.18

 

Room Size 

Compartment Width (m) 7.04 7.04 7.04 7.04 7.04 7.04

Compartment Length (m) 21.7 21.7 21.7 21.7 21.7 21.7

Compartment Height (m) 3.82 3.82 3.82 3.82 3.82 3.82

 

Wall Properties 

Interior Lining Thermal Inertia 

[(kW/m2

-K)2-sec] 0.11 0.111 0.11 0.11 0.11 0.11

Interior Lining Thermal Conductivity 

(kW/m-K) 0.00012 0.00012 0.00012 0.00012 0.00012 0.00012

Interior Lining Specific Heat (kJ/kg-K) 1.26 1.26 1.26 1.26 1.26 1.26

Interior Lining Density (kg/m3) 737 737 737 737 737 737

Interior Lining Thickness (m) 0.0254 0.0254 0.0254 0.0254 0.0254 0.0254

 

Fire Heat Release Rate (kW) 

60 sec 410 1190 400 1190 2330 1160

120 sec 410 1190 400 1190 2330 1160

180 sec 410 1190 400 1190 2330 1160

240 sec 410 1190 400 1190 2330 1160

270 sec 1160

300 sec 410 1190 400 1190 2330 1160

360 sec 2330 

600 sec 410 1190 400 1190 2330 1160

900 sec 410 400 2330 1160

1200 sec 410 400 

1380 sec 410 400 
Technical Details of the FDTS Validation Study 

A-6 

Table A-4: Input values for ICFMP BE # 3 No Ventilation Tests 

Test 3 Test 9 Test 14 Test 15 Test 18 

Air 

 

Ambient Air Temperature (C) 27.8 28.9 25.6 23.3 24.4

Ambient Air Density (kg/m3) 1.2 1.2 1.2 1.2 1.2

 

Room Size 

Compartment Width (m) 7.04 7.04 7.04 7.04 7.04

Compartment Length (m) 21.7 21.7 21.7 21.7 21.7

Compartment Height (m) 3.82 3.82 3.82 3.82 3.82

 

Wall Properties 

Interior Lining Thermal Inertia [(kW/m2-K)2-sec] 0.11 0.11 0.11 0.11 0.11

Interior Lining Thermal Conductivity (kW/m-K) 0.00012 0.00012 0.00012 0.00012 0.00012

Interior Lining Specific Heat (kJ/kg-K) 1.26 1.26 1.26 1.26 1.26

Interior Lining Density (kg/m3) 737 737 737 737 737

Interior Lining Thickness (m) 0.0254 0.0254 0.0254 0.0254 0.0254

 

Ventilation 

Vent Width (m) 2 2 2 2 2

Vent Height (m) 2 2 2 2 2

Top of Vent from Floor (m) 2 2 2 2 2

 

Heat Release Rate 

Fire Heat Release Rate (kW) 1190 1170 1180 1180 1180
Technical Details of the FDTS Validation Study 

A-7 

Table A-5: Input values for ICFMP BE # 3 Forced Ventilation Tests 

Test 4 Test 5 Test 10 Test 16 

Air 

 

Ambient Air Temperature (C) 26.7 25 24.4 21.1

Ambient Air Density (kg/m3) 1.2 1.2 1.2 1.2

 

Room Size 

 

Compartment Width (m) 7.04 7.04 7.04 7.04

Compartment Length (m) 21.7 21.7 21.7 21.7

Compartment Height (m) 3.82 3.82 3.82 3.82

 

Wall Properties 

Interior Lining Thermal Inertia [(kW/m2-K)2-sec] 0.11 0.11 0.11 0.11

Interior Lining Thermal Conductivity (kW/m-K) 0.00012 0.00012 0.00012 0.00012

Interior Lining Specific Heat (kJ/kg-K) 1.26 1.26 1.26 1.26

Interior Lining Density (kg/m3) 737 737 737 737

Interior Lining Thickness (m) 0.0254 0.0254 0.0254 0.0254

 

Ventilation 

Forced Ventilation Flow Rate (cfm) 1907 1907 1907 1907

Heat Release Rate 

Fire Heat Release Rate (kW) 1200 1190 1190 2300
Technical Details of the FDTS Validation Study 

A-8 

HGL Temperature

ICFMP BE # 3, Test 1

0

50

100

150

200

250

0 10 20 30 40

Time (min)

Temp (C)

Exp FDTs

HGL Temperature

ICFMP BE # 3, Test 7

0

50

100

150

200

250

0 10 20 30 40

Time (min)

Temp (C)

Exp FDTs

HGL Temperature

ICFMP BE # 3, Test 2

0

50

100

150

200

250

300

350

400

0 10 20 30 40

Time (min)

Temp (C)

Exp FDTs

HGL Temperature

ICFMP BE # 3, Test 8

0

50

100

150

200

250

300

350

400

0 10 20 30 40

Time (min)

Temp (C)

Exp FDTs

HGL Temperature

ICFMP BE # 3, Test 4

0

50

100

150

200

250

300

0 10 20 30 40

Time (min)

Temp (C)

Exp FDTs

HGL Temperature

ICFMP BE # 3, Test 10

0

50

100

150

200

250

300

0 10 20 30 40

Time (min)

Temp (C)

Exp FDTs

HGL Temperature

ICFMP BE # 3, Test 13

0

100

200

300

400

500

600

0 10 20 30 40

Time (min)

Temp (C)

Exp FDTs

HGL Temperature

ICFMP BE # 3, Test 16

0

100

200

300

400

500

600

0 10 20 30 40

Time (min)

Temp (C)

Exp FDTs

Figure A-2: Hot Gas Layer Temperature, ICFMP BE #3, closed door tests 
Technical Details of the FDTS Validation Study 

A-9 

HGL Temperature

ICFMP BE # 3, Test 17

0

50

100

150

200

250

0 5 10 15 20

Time (min)

Temp (C)

Exp FDTs

Figure A-3: Hot Gas Layer Temperature, ICFMP BE #3, closed door tests (cont.) 
Technical Details of the FDTS Validation Study 

A-10 

HGL Temperature

ICFMP BE # 3, Test 3

0

50

100

150

200

250

300

0 10 20 30 40

Time (min)

Temp (C)

Exp FDTs

HGL Temperature

ICFMP BE # 3, Test 5

0

50

100

150

200

250

300

350

400

0 10 20 30 40

Time (min)

Temp (C)

Exp FDTs FV FDTs NV

HGL Temperature

ICFMP BE # 3, Test 15

0

50

100

150

200

250

300

350

400

0 10 20 30 40

Time (min)

Temp (C)

Exp FDTs

HGL Temperature

ICFMP BE # 3, Test 9

0

50

100

150

200

250

300

350

400

0 10 20 30 40

Time (min)

Temp (C)

Exp FDTs

HGL Temperature

ICFMP BE # 3, Test 14

0

50

100

150

200

250

300

350

0 10 20 30 40

Time (min)

Temp (C)

Exp FDTs

HGL Temperature

ICFMP BE # 3, Test 18

0

50

100

150

200

250

300

350

400

0 10 20 30 40

Time (min)

Temp (C)

Exp FDTs

Figure A-4: Hot Gas Layer Temperature, ICFMP BE #3, open door tests 

A calculation method for HGL height is only found on the spreadsheet for open door conditions. 

However, this calculation method is only valid before the layer descends to an opening and spills 

out of the fire room. The graphs for HGL height comparisons for open door rooms only depict 

the early times of the test, before the layer spills out of the room. A relative difference 

comparison is not made due to the restricted application of layer height calculation. 
Technical Details of the FDTS Validation Study 

A-11 

HGL Height

ICFMP BE #3, Test 3

0

1

2

3

4

5

024

Time (min)

Height (m)

Test 3 FDTs

HGL Height

ICFMP BE #3, Test 9

0

1

2

3

4

5

024

Time (min)

Height (m)

Test 9 FDTs

HGL Height

ICFMP BE #3, Test 14

0

1

2

3

4

5

01234

Time (min)

Height (m)

Test 14 FDTs

HGL Height

ICFMP BE #3, Test 15

0

1

2

3

4

5

01234

Time (min)

Height (m)

Test 15 FDTs

HGL Height

ICFMP BE #3, Test 18

0

1

2

3

4

5

01234

Time (min)

Height (m)

Test 18 FDTs

Figure A-5: Hot Gas Layer Height, ICFMP BE #3, open door tests w/o ventilation 
Technical Details of the FDTS Validation Study 

A-12 

A.1.3 ICFMP BE # 4 

This experiment included a relatively large fire in a relatively small compartment. The 

compartment included a doorway of about 2.1m2 (23 ft2) and no mechanical ventilation. The 

spreadsheet in FDTS

 used to estimate the HGL temperature for this exercise was 

02.1_Temperature_NV.xls. The maximum experimental HRR was input as a steady-state value 

for the spreadsheet as a conservative assumption. The experimental HRR, thermal properties of 

the wall materials, and other input values can be found in Table A-6. 

Experimental data for HGL Height during this test is not available for comparison. 

Table A-6: Input Values for ICFMP BE # 4 

Air 

Ambient Air Temperature (C) 20 

Ambient Air Density (kg/m3) 1.2 

Room Size 

Compartment Width (m) 3.6 

Compartment Length (m) 3.6 

Compartment Height (m) 5.7 

 

Wall Properties 

Interior Lining Thermal Inertia [(kW/m2-K)2-sec] 9.45 

Interior Lining Thermal Conductivity (kW/m-K) 0.0075 

Interior Lining Specific Heat (kJ/kg-K) 0.84 

Interior Lining Density (kg/m3) 1500 

Interior Lining Thickness (m) 0.3 

 

Ventilation 

Vent Width (m) 0.7 

Vent Height (m) 3 

Top of Vent from Floor (m) 3.6 

 

Heat Release Rate 

Fire Heat Release Rate (kW) 3518 
Technical Details of the FDTS Validation Study 

A-13 

HGL Temperature

ICFMP BE # 4, Test 1

0

100

200

300

400

500

600

700

800

0 10 20 30 40

Time (min)

Temp (C)

Exp FDTs

Figure A-6: Hot Gas Layer Temperature, ICFMP BE #4 

A.1.4 ICFMP BE # 5 

This experiment was conducted in the same compartment as ICFMP BE #4, except the doorway 

was small, about 1.5m2 (16ft2), again with no mechanical ventilation. The spreadsheet in FDTS

used to estimate the HGL temperature for this exercise is 02.1_Temperature_NV.xls. The 

maximum experimental HRR was input as a steady-state value for the spreadsheet as a 

conservative assumption. The HRR and other input values can be found in Table A-7. 
Technical Details of the FDTS Validation Study 

A-14 

Table A-7: Input Values for ICFMP BE # 5 

Air 

 

Ambient Air Temperature (C) 20 

Ambient Air Density (kg/m3) 1.2 

 

Room Size 

Compartment Width (m) 3.6 

Compartment Length (m) 3.6 

Compartment Height (m) 5.7 

 

Wall Properties 

 

Interior Lining Thermal Inertia [(kW/m2-K)2-

sec] 9.45 

Interior Lining Thermal Conductivity (kW/mK) 0.0075 

Interior Lining Specific Heat (kJ/kg-K) 0.84 

Interior Lining Density (kg/m3) 1500 

Interior Lining Thickness (m) 0.3 

 

Ventilation 

 

Vent Width (m) 0.7 

Vent Height (m) 2.2 

Top of Vent from Floor (m) 3.6 

 

Heat Release Rate 

 

Fire Heat Release Rate (kW) 716 

Experimental data for HGL Height during this test is not available for comparison. 
Technical Details of the FDTS Validation Study 

A-15 

HGL Temperature

ICFMP BE # 5, Test 4

0

50

100

150

200

250

0 10 20 30 40

Time (min)

Temp (C)

Exp FDTs

Figure A-7: Hot Gas Layer Temperature, ICFMP BE #5 

A.1.5 The FM-SNL Test Series 

This test series was conducted in a large closed room with mechanical ventilation. Tests 4 and 

21 had a ventilation rate of approximately 0.37 m3/s (13 ft3/s), while Test 5 had a ventilation rate 

of approximately 3.7 m3/s (131 ft3/s). The FPA model was used for these tests with forced 

ventilation (02.2_Temperature_FV.xls). A steady-state HRR of 516 kW based on experimental 

data was used as input to the spreadsheets. The input values used for these three tests can be 

found in Table A-8. 
Technical Details of the FDTS Validation Study 

A-16 

Table A-8: Input values for FM/SNL Tests 

Test 4 Test 5 Test 21 

Air 

 

Ambient Air Temperature (C) 20 20 20 

Ambient Air Density (kg/m3) 1.2 1.2 1.2 

 

Room Size 

Compartment Width (m) 12.2 12.2 12.2 

Compartment Length (m) 18.3 18.3 18.3 

Compartment Height (m) 6.1 6.1 6.1 

 

Wall Properties 

Interior Lining Thermal Inertia [(kW/m2-K)2-sec] 0.108 0.108 0.108 

Interior Lining Thermal Conductivity (kW/m-K) 0.00012 0.00012 0.00012 

Interior Lining Specific Heat (kJ/kg-K) 1.25 1.25 1.25 

Interior Lining Density (kg/m3) 720 720 720 

Interior Lining Thickness (m) 0.0127 0.0127 0.0127 

 

Ventilation 

Forced Ventilation Flow Rate (cfm) 800 8000 800 

Heat Release Rate 

Fire Heat Release Rate (kW) 516 516 516 
Technical Details of the FDTS Validation Study 

A-17 

HGL Temperature

FM/SNL Test 4

0

50

100

150

200

250

0 5 10 15 20

Time (min)

Temp (C)

Exp FDTs

HGL Temperature

FM/SNL Test 5

0

20

40

60

80

100

120

0 5 10 15

Time (min)

Temp (C)

Exp FDTs

HGL Temperature

FM/SNL Test 21

0

50

100

150

200

250

0 10 20 30

Time (min)

Temp (C)

Exp FDTs

Figure A-8: Hot Gas Layer Temperature, FM/SNL tests 

A.1.6 The NBS Test Series 

This test series involved a three compartment configuration with two smaller rooms opening off 

of a long corridor. One of the smaller rooms contained the fire source. All experimental data 

used to compare with FDTs

 came from the fire room because FDTs does not have the capability 

to model conditions in rooms other than the fire room. The three tests considered are labeled 

100A, 100O and 100Z, respectively. The differences between these three tests concerned 

ventilation conditions in the corridor. Test 100A involved closed doors from the corridor to the 

outside and from the corridor to the third room. Test 100O involved an open door from the 

corridor to the outside and a closed door from the corridor to the third room. Test 100Z involved 

open doors from the corridor to the outside and from the corridor to the third room. Since all 

tests involved an open door between the fire room and the corridor, the spreadsheet with the 

MQH model (02.1_Temperature_NV.xls) was used to estimate HGL temperature for the NBS 

tests. All three tests used a HRR of 110 kW, based on experimental HRR data. Material 

properties and other input values can be found in Table A-9. 
Technical Details of the FDTS Validation Study 

A-18 

Table A-9: Input Values for NBS Tests 

Air 

 

Ambient Air Temperature (C) 22.8 

Ambient Air Density (kg/m3) 1.19 

 

Room Size 

Compartment Width (m) 2.34 

Compartment Length (m) 2.34 

Compartment Height (m) 2.16 

 

Wall Properties 

Interior Lining Thermal Inertia [(kW/m2-K)2-sec] 0.012 

Interior Lining Thermal Conductivity (kW/m-K) 0.00009 

Interior Lining Specific Heat (kJ/kg-K) 1.04 

Interior Lining Density (kg/m3) 128 

Interior Lining Thickness (m) 0.05 

 

Ventilation 

 

Vent Width (m) 0.8 

Vent Height (m) 1.6 

Top of Vent from Floor (m) 1.6 

 

Heat Release Rate 

Fire Heat Release Rate (kW) 110 
Technical Details of the FDTS Validation Study 

A-19 

HGL Temperature

NBS Test 100A

0

75

150

225

300

375

0 5 10 15 20

Time (min)

Temp (C)

NBS 100A FDTs

HGL Temperature

NBS Test 100O

0

75

150

225

300

375

0 5 10 15 20

Time (min)

Temp (C)

NBS Test 100O FDTs

HGL Temperature NBS

Test 100Z

0

75

150

225

300

375

0 5 10 15 20

Time (min)

Temp (C)

NBS Test 100Z FDTs

Figure A-9: Hot Gas Layer Temperature, NBS tests 

A.1.7 Summary: Hot Gas Layer Temperature and Height 

The following chart lists the relative differences between experimental data and model results for 

HGL temperature. “∆ E” is the difference between the experimental peak and the experimental 

initial condition. “∆ M” is the difference between model peak and experimental peak. Since 

FDTs

 does not have an appropriate calculation method for layer height for the experimental 

conditions in these tests, no relative differences are given. 
Technical Details of the FDTS Validation Study 

A-20 

Table A-10: Hot Gas Layer Temperature Relative Differences 

Hot Gas Layer Temperature (C) 

 ∆ E ∆ M % Difference 

Case 1 55 14 25% 

Case 2 86 22 25% 

ICFMP 

BE # 2 

Case 3 83 124 150% 

Test 1 123 75 61% 

Test 2 229 108 47% 

Test 3 207 113 54% 

Test 4 204 56 27% 

Test 5 175 180 (144) 103% (82%) 

Test 7 117 75 65% 

Test 8 218 116 53% 

Test 9 204 111 55% 

Test 10 198 62 31% 

Test 13 290 178 61% 

Test 14 208 108 52% 

Test 15 211 107 51% 

Test 16 268 88 33% 

Test 17 135 61 45% 

ICFMP BE # 3 

Test 18 194 123 64% 

BE # 4 Test 1 701 -201 -29% 

BE # 5 Test 4 186 26 14% 

Test 4 60 124 209% 

Test 5 47 32 69% 

FM/SNL 

Test 21 66 113 170% 

Test 1 248 12 5% 

Test 2 310 -32 -10% 

NBS 

Test 4 284 -7 -2% 

A.2 Plume Temperature 

Plume temperatures are measured with thermocouple trees above the fire source. The test series 

that included an arrangement for collecting plume temperature data include ICFMP benchmark 

exercises number 2, 4, and 5, and FM-SNL. During benchmark exercises 4 and 5, the fire and 

the plume tilted away from the plume thermocouples, therefore, that data will not be used. The 

following figures present the experimental observations as well as FDTS

 predictions for plume 

temperature using Heskestad’s plume temperature correlation (FDTS spreadsheet: 

09_Plume_Temperature_Calculations.xls). 

A.2.1 ICFMP BE # 2 

In the experiment, the two thermocouples in the fire plume were located 7 m (23 ft) and 13 m (43 

ft) above the fire source, respectively. Heat release rates were calculated from fuel mass loss 

rates during the experiments, modified by an efficiency factor of 0.85. The convective heat 

release fraction used was 0.65. The input values for this experiment can be found in Table A-11 

while the heat release rates can be found in Table A-12. 
Technical Details of the FDTS Validation Study 

A-21 

Table A-11: Input values for ICFMP BE # 2 Plume Temperature Calculations 

TG1 TG2 

Air 

 

Ambient Air Temperature (C) 20 20 

Ambient Air Density (kg/m3) 1.2 1.2 

 

Fire Characteristics 

Elevation Above the Fire Source (m) 7 13 

Area of Combustible Fuel (m2) 0.5 0.5 

Convective Heat Release Rate Fraction (xc) 0.65 0.65 

Table A-12: ICFMP BE #2 Heat Release Rates 

Case 1 Case 2 Case 3 

Time (sec) HRR (kW) Time (sec) HRR (kW) Time (sec) HRR (kW) 

0 0 0 0 0 0

13.2 1251 13.8 2161 13.2 2426

90 1706 30 2540 63 3184

288 1858 91.2 3071 166.2 3601

327 1782 193.2 3260 256.2 3639

409.2 1365 282 3146 292.2 3450

438 0 340.2 2729 330 2654

372 2275 345 0

394.8 0
Technical Details of the FDTS Validation Study 

A-22 

Plume Temperature at 7 meters

ICFMP BE#2 Case 1

0

50

100

150

200

02468

Time (min)

Temperature (C)

Exp. TG.1

FDTs TG.1

Plume Temperature at 7 meters

ICFMP BE#2 Case 2

0

50

100

150

200

250

300

350

02468

Time (min)

Temperature (C)

Exp. TG.1

FDTs TG.1

Plume Temperature at 7 meters

ICFMP BE#2 Case 3

0

50

100

150

200

250

300

02468

Time (min)

Temperature (C)

Exp. TG.1

FDTs TG.1

Plume Temperature at 13 meters

ICFMP BE#2 Case 1

0

20

40

60

80

100

120

140

160

02468

Time (min)

Temperature (C)

Exp. TG.2

FDTs TG.2

Plume Temperature at 13 meters

ICFMP BE#2 Case 2

0

20

40

60

80

100

120

140

160

02468

Time (min)

Temperature (C)

Exp. TG.2

FDTs TG.2

Plume Temperature at 13 meters

ICFMP E#2 Case 3

0

20

40

60

80

100

120

140

160

02468

Time (min)

Temperature (C)

Exp. TG.2

FDTs TG.2

Figure A-10: Plume Temperature, ICFMP BE #2, Cases 1, 2, and 3 

A.2.2 The FM-SNL Test Series 

The thermocouple for measuring plume temperatures was located 5.66 m (18.6 ft) above the base 

of the fire, approximately 5.95 m (19.5 ft) above the floor. The HRRs used as inputs were 

calculated using a t2

 curve with a peak of 516 kW, which matches the experimental data. The 
Technical Details of the FDTS Validation Study 

A-23 

convective heat release fraction used was 0.65. Additional input values can be found in Table 

A-13. 

Table A-13: Input values for FM/SNL Tests Plume Temperature Calculations 

Air 

 

Ambient Air Temperature (C) 20 

Ambient Air Density (kg/m3) 1.2 

 

Fire Characteristics 

Elevation Above the Fire Source (m) 5.66 

Area of Combustible Fuel (m2) 0.17 

Convective Heat Release Rate Fraction (xc) 0.65 
Technical Details of the FDTS Validation Study 

A-24 

Plume Temperature at 5.95 meters 

FM/SNL Test 4

0

20

40

60

80

100

120

140

0 5 10 15 20

Time (min)

Temperature (C)

Exp.

FDTs

Plume Temperature at 5.95 meters 

FM/SNL Test 5

0

20

40

60

80

100

120

140

0 5 10 15 20

Time (min)

Temperature (C)

Exp.

FDTs

Plume Temperature at 5.95 meters 

FM/SNL Test 21

0

20

40

60

80

100

120

0 10 20 30

Time (min)

Temperature (C)

Exp.

FDTs

Figure A-11: Plume Temperature, FM/SNL tests

A.2.3 Summary: Plume Temperature

The following chart lists the relative differences between experimental data and model results for 

plume temperature. “∆ E” is the difference between the experimental peak and the experimental 

initial condition. “∆ M” is the difference between model peak and experimental peak. 

Table A-14: Plume Temperature Relative Differences 

Plume Temperature (C) 

 Sensor ∆ E ∆ M % Difference 

TG1 166 -25 -15% 

Case 1 TG2 77 -32 -41% 

TG1 288 -62 -22% 

Case 2 TG2 128 -60 -47% 

TG1 252 2 1% 

ICFMP BE # 2 

Case 3 TG2 128 -51 -40% 

Test 4 5.66 m above fire 116 -34 -29% 

Test 5 5.66 m above fire 94 -16 -17% 

FM/SNL 

Test 21 5.66 m above fire 79 3 4% 
Technical Details of the FDTS Validation Study 

A-25 

A.3 Flame Height 

Flame height is recorded by visual observations, photographs or video footage. Photographs 

from the ICFMP BE #2 test series and video from BE #3 test series are available. It is difficult to 

precisely measure the flame height, but the photos and videos allow one to make estimates 

accurate to within a pan diameter. Such observations can be compared with outputs from 

Heskestad’s flame height correlation. Although no accuracy can be calculated, this comparison 

may provide insights about the capabilities and limitations of the model. The spreadsheet in 

FDTS used to calculate the flame height was 

03_HRR_Flame_Height_Burning_Duration_Calculations.xls. 

A.3.1 ICFMP BE # 2 

Figure 1 contains photographs of the actual fire. The height of the visible flame in the 

photographs has been estimated to be between 2.4 and 3 pan diameters (3.8 m (12.5 ft) to 4.8 m 

(15.7 ft)). Using Heskestad’s method for estimating the height of a pool fire flame FDTs 

estimated flame height to be 4.3 m (14.1 ft). 
Technical Details of the FDTS Validation Study 

A-26 

Figure A-12: Photographs of heptane pan fires, ICFMP BE #2, Case 2. Courtesy, Simo 

Hostikka, VTT Building and Transport, Espoo, Finland.

A.3.1 ICFMP BE # 3 

No measurements were made of the flame height during BE #3, but numerous photographs were 

taken through the 2 m by 2 m doorway. Figure 2 is one of these photographs. During BE #3, Test 

3, the peak flame height is estimated to be 2.8 m, roughly consistent with the view through the 
Technical Details of the FDTS Validation Study 

A-27 

doorway in the figure below. FDTS

 results in a flame height of 3.0 m (9.8 ft) using Heskestad’s 

flame height prediction. 

Figure A-13: Photograph and simulation of ICFMP BE #3, Test 3, as seen through the 2 m 

by 2 m doorway. Photo courtesy of Francisco Joglar, SAIC. 

A.4 Target Heat Flux 

A.4.1 ICFMP BE #3 

The experimental results for radiant heat flux were obtained from Benchmark Exercise #3. The 

spreadsheet in FDTS used to calculate the radiant heat flux is 

05.1_Heat_Flux_Calculations_Wind_Free.xls. The Point Source Radiation model was used. 

The heat flux measurements were taken using ten different gauges located at varying distances 

from the fire. Five gauges measured total heat flux, and five measured radiant heat flux. Since 

FDTs

 calculates radiant heat flux, just that data was compared. Also, one of the five radiant heat 

flux gauges was oriented in the horizontal direction and not with the proposed targets, so that 

data will not be compared. 

The heat release rates used as inputs are listed in Table A-3, Table A-4, and Table A-5 and are 

consistent with the experimental measurements of HRR. The radiation fraction for all tests 

except test 17 was 0.44. The radiation fraction used for test 17 was 0.40. The following table 

lists the distances to targets for each test. The position of the fire was different for three of the 

fifteen tests in BE #3, so the distances to targets are different for those tests. 
Technical Details of the FDTS Validation Study 

A-28 

Table A-15: Distance from Fire to Radiant Heat Flux Gauges, meters 

Gauge Test 14 Test 15 Test 18 All Others 

1 5.23 2.20 2.78 4.07 

3 4.73 2.52 2.96 3.39 

7 4.45 3.13 3.43 3.40 

10 2.38 5.87 5.77 3.77 
Technical Details of the FDTS Validation Study 

A-29 

Radiative Heat Flux to Power Cable F

ICFMP BE #3 Test 1

0.0

0.3

0.5

0.8

1.0

0 10 20 30 40 50

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 1

FDTs Rad Gauge 1

Radiative Heat Flux to Cable B 

ICFMP BE#3 Test 1

0.0

0.5

1.0

1.5

0 10 20 30 40 50

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 3

FDTs Rad Gauge 3

Radiative Heat Flux to Tray D

ICFMP BE#3 Test 1

0.0

0.5

1.0

1.5

0 10 20 30 40 50

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 7

FDTs Rad Gauge 7

Radiative Heat Flux to Tray G 

ICFMP BE#3 Test 1

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 10

FDTs Rad Gauge 10

Radiant Heat Flux to Power Cable F

ICFMP BE#3 Test 7

0.0

0.3

0.5

0.8

1.0

0 10 20 30 40 50

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 1

FDTs Rad Gauge 1

Radiant Heat Flux to Cable B

ICFMP BE#3 Test 7

0.0

0.5

1.0

1.5

0 10 20 30 40 50

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 3

FDTs Rad Gauge 3

Radiant Heat Flux to Tray D

ICFMP BE#3 Test 7

0.0

0.5

1.0

1.5

0 10 20 30 40 50

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 7

FDTs Rad Gauge 7

Radiant Heat Flux to Tray G

ICFMP BE#3 Test 7

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 10

FDTs Rad Gauge 10

Figure A-14: Radiant Heat Flux, ICFMP BE #3, Tests 1 and 7 
Technical Details of the FDTS Validation Study 

A-30 

Radiative Heat Flux to Power Cable F 

ICFMP BE#3 Test 2

0

1

2

3

0 5 10 15 20 25

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 1

FDTs Rad Gauge 1

Radiant Heat Flux to Cable B 

ICFMP BE#3 Test 2

0

1

2

3

4

0 5 10 15 20 25

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 3

FDTs Rad Gauge 3

Radiant Heat Flux to Tray D 

ICFMP BE#3 Test 2

0

1

2

3

4

5

0 5 10 15 20 25

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 7

FDTs Rad Gauge 7

Radiant Heat Flux to Tray G

ICFMP BE#3 Test 2

0

2

4

6

8

0 5 10 15 20 25

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 10

FDTs Rad Gauge 10

Radiant Heat Flux to Power Cable F

ICFMP BE#3 Test 8

0

1

2

3

0 5 10 15 20 25

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 1

FDTs Rad Gauge 1

Radiant Heat Flux to Cable B

ICFMP BE#3 Test 8

0

1

2

3

4

0 5 10 15 20 25

Time (min) 

Heat Flux (kW/m2

)

Exp. Rad Gauge 3

FDTs Rad Gauge 3

Radiant Heat Flux to Tray D

ICFMP BE#3 Test 8

0

1

2

3

4

5

0 5 10 15 20 25

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 7

FDTs Rad Gauge 7

Radiant Heat Flux to Tray G

ICFMP BE#3 Test 8

0

2

4

6

8

0 5 10 15 20 25

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 10

FDTs Rad Gauge 10

Figure A-15: Radiant Heat Flux, ICFMP BE #3, Tests 2 and 8 
Technical Details of the FDTS Validation Study 

A-31 

Radiant Heat Flux to Power Cable F

ICFMP BE#3 Test 3

0

1

2

3

0 10 20 30 40 50 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 1

FDTs Rad Gauge 1

Radiant Heat Flux to Cable B

ICFMP BE#3 Test 3

0

1

2

3

4

5

0 10 20 30 40 50 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 3

FDTs Rad Gauge 3

Radiant Heat Flux to Tray G

ICFMP BE#3 Test 3

0

1

2

3

4

5

6

0 10 20 30 40 50 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 10

FDTs Rad Gauge 10

Radiant Heat Flux to Tray D ICFMP 

BE#3 Test 3

0

1

2

3

4

0 10 20 30 40

Time (min)

Heat Flux (kW/m2

)

FDTs Rad Gauge 7

Rad Gauge 7 malfunctioned

Radiant Heat Flux to Power Cable F 

ICFMP BE#3 Test 9

0

1

2

3

0 10 20 30 40 50 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 1

FDTs Rad Gauge 1

Radiant Heat Flux to Cable B 

ICFMP BE#3 Test 9

0

1

2

3

4

5

0 10 20 30 40 50 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 3

FDTs Rad Gauge 3

Radiant Heat Flux to Tray D 

ICFMP BE#3 Test 9

0

1

2

3

4

5

6

0 10 20 30 40 50 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 7

FDTs Rad Gauge 7

Radiant Heat Flux to Tray G

ICFMP BE#3 Test 9

0

1

2

3

4

5

6

0 10 20 30 40 50 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 10

FDTs Rad Gauge 10

Figure A-16: Radiant Heat Flux, ICFMP BE #3, Tests 3 and 9 
Technical Details of the FDTS Validation Study 

A-32 

Radiant Heat Flux to Power Cable F

ICFMP BE#3 Test 4

0

1

2

3

0 20 40 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 1

FDTs Rad Gauge 1

Radiant Heat Flux to Cable B 

ICFMP BE#3 Test 4

0

1

2

3

4

0 20 40 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 3

FDTs Rad Gauge 3

Radiant Heat Flux to Tray D 

ICFMP BE#3 Test 4

0

1

2

3

4

0 20 40 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 7

FDTs Rad Gauge 7

Radiant Heat Flux to Tray G 

ICFMP BE#3 Test 4

0

1

2

3

4

5

6

7

0 20 40 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 10

FDTs Rad Gauge 10

Radiant Heat Flux to Power Cable F

ICFMP BE#3 Test 10

0

1

2

3

0 20 40 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 1

FDTs Rad Gauge 1

Radiant Heat Flux to Cable B ICFMP 

BE#3 Test 10

0

1

2

3

4

0 20 40 60

Time (min) 

Heat Flux (kW/m2

)

Exp. Rad Gauge 3

FDTs Rad Gauge 3

Radiant Heat Flux to Tray D ICFMP BE#3 

Test 10

0

1

2

3

4

0 20 40 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 7

FDTs Rad Gauge 7

Radiant Heat Flux to Tray G ICFMP 

BE#3 Test 10

0

1

2

3

4

5

6

7

0 20 40 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 10

FDTs Rad Gauge 10

Figure A-17: Radiant Heat Flux, ICFMP BE #3, Tests 4 and 10 
Technical Details of the FDTS Validation Study 

A-33 

Radiant Heat Flux to Power Cable F 

ICFMP BE#3 Test 5

0

1

2

3

0 10 20 30 40

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 1

FDTs Rad Gauge 1

Radiant Heat Flux to Cable B 

ICFMP BE#3 Test 5

0

1

2

3

4

5

0 10 20 30 40

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 3

FDTs Rad Gauge 3

Radiant Heat Flux to Tray D 

ICFMP BE#3 Test 5

0

1

2

3

4

5

6

0 10 20 30 40

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 7

FDTs Rad Gauge 7

Radiant Heat Flux to Tray G 

ICFMP BE#3 Test 5 

0

2

4

6

8

10

12

0 10 20 30 40

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 10

FDTs Rad Gauge 10

Radiant Heat Flux to Power Cable F 

ICFMP BE#3 Test 14

0

1

2

3

0 10 20 30 40

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 1

FDTs Rad Gauge 1

Radiant Heat Flux to Cable B ICFMP 

BE#3 Test 14

0

1

2

3

4

5

0 10 20 30 40

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 3

FDTs Rad Gauge 3

Radiant Heat Flux to Tray D

ICFMP BE#3 Test 14

0

1

2

3

4

5

6

0 10 20 30 40

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 7

FDTs Rad Gauge 7

Radiant Heat Flux to Tray G

ICFMP BE#3 Test 14

0

2

4

6

8

10

12

0 10 20 30 40

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 10

FDTs Rad Gauge 10

Figure A-18: Radiant Heat Flux, ICFMP BE #3, Tests 5 and 14 
Technical Details of the FDTS Validation Study 

A-34 

Radiant Heat Flux to Power Cable F 

ICFMP BE#3 Test 13

0

1

2

3

4

5

6

0 10 20 30 40

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 1

FDTs Rad Gauge 1

Radiant Heat Flux to Cable B

ICFMP BE#3 Test 13

0

1

2

3

4

5

6

7

8

0 10 20 30 40

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 3

FDTs Rad Gauge 3

Radiant Heat Flux to Tray D

ICFMP BE#3 Test 13

0

1

2

3

4

5

6

7

8

0 10 20 30 40

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 7

FDTs Rad Gauge 7

Radiant Heat Flux to Tray G

IDFMP BE#3 Test 13

0

2

4

6

8

10

12

14

0 10 20 30 40

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 10

FDTs Rad Gauge 10

Radiant Heat Flux to Power Cable F 

ICFMP BE#3 Test 16

0

1

2

3

4

5

6

0 10 20 30 40

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 1

FDTs Rad Gauge 1

Radiant Heat Flux to Cable B

ICFMP BE#3 Test 16

0

1

2

3

4

5

6

7

8

0 10 20 30 40

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 3

FDTs Rad Gauge 3

Radiant Heat Flux to Tray D

ICFMP BE#3 Test 16

0

1

2

3

4

5

6

7

8

0 10 20 30 40

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 7

FDTs Rad Gauge 7

Radiant Heat Flux to Tray G

ICFMP BE#3 Test 16

0

2

4

6

8

10

12

14

0 10 20 30 40

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 10

FDTs Rad Gauge 10

Figure A-19: Radiant Heat Flux, ICFMP BE #3, Tests 5 and 14 
Technical Details of the FDTS Validation Study 

A-35 

Radiant Heat Flux to Power Cable F 

ICFMP BE#3 Test 15

0

2

4

6

8

10

12

14

16

18

20

0 20 40 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 1

FDTs Rad Gauge 1

Radiant Heat Flux to Cable B

ICFMP BE#3 Test 15

0

10

20

30

40

50

0 20 40 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 3

FDTs Rad Gauge 3

Radiant Heat Flux to Tray D

ICFMP BE#3 Test 15

0

1

2

3

4

5

0 20 40 60

Time (min)

Heat Flux (kW/m2

)

FDTs Rad Gauge 7

Rad Gauge 7 malfunctioned

Radiant Heat Flux to Tray G

ICFMP BE#3 Test 15

0

1

2

3

4

0 20 40 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 10

FDTs Rad Gauge 10

Radiant Heat Flux to Power Cable F 

ICFMP BE#3 Test 18

0

1

2

3

4

5

6

0 20 40 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 1

FDTs Rad Gauge 1

Radiant Heat Flux to Cable B

ICFMP BE#3 Test 18

0

1

2

3

4

5

6

0 20 40 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 3

FDTs Rad Gauge 3

Radiant Heat Flux to Tray D

ICFMP BE#3 Test 18

0

1

2

3

4

0 20 40 60

Time (min)

Heat Flux (kW/m2

)

FDTs Rad Gauge 7

Rad Gauge 7 malfunctioned

Radiant Heat Flux to Tray G

ICFMP BE#3 Test 18

0

1

2

3

0 20 40 60

Time (min)

Heat Flux (kW/m2

)

Exp. Rad Gauge 10

FDTs Rad Gauge 10

Figure A-20: Radiant Heat Flux, ICFMP BE #3, Tests 15 and 18 
Technical Details of the FDTS Validation Study 

A-36 

Radiant Heat Flux to Power Cable F 

ICFMP BE#3 Test 17

0

1

2

3

0 5 10 15 20

Time (min)

H eat Flux (kW/m2

)

Exp. Rad Gauge 1

FDTs Rad Gauge 1

Radiant Heat Flux to Cable B

ICFMP BE#3 Test 17

0

1

2

3

4

0 5 10 15 20

Time (min)

H eat Flux (kW /m2

)

Exp. Rad Gauge 3

FDTs Rad Gauge 3

Radiant Heat Flux to Tray D

ICFMP BE#3 Test 17

0

1

2

3

4

0 5 10 15 20

Time (min)

H eat Flux (kW/m2

)

Exp. Rad Gauge 7

FDTs Rad Gauge 7

Radiant Heat Flux to Tray G

ICFMP BE#3 Test 17

0

1

2

3

0 5 10 15 20

Time (min)

H eat Flux (kW /m2

)

Exp. Rad Gauge 10

FDTs Rad Gauge 10

Figure A-21: Radiant Heat Flux, ICFMP BE #3, Test 17 

A.4.2 Summary: Radiant Heat Flux 

The following chart lists the relative differences between experimental data and model results for 

radiant heat flux. “∆ E” is the difference between the experimental peak and the experimental 

initial condition. “∆ M” is the difference between model peak and experimental peak. 

Table A-16: Relative Differences, Radiant Heat Flux 

Radiant Heat Flux (kW/m2) 

BE # 3 Sensor 

∆ E ∆ M % Difference 

Gauge 1 0.87 0.00 0% 

Gauge 3 1.12 0.13 12% 

Gauge 7 1.43 -0.19 -13% 

Test 1 Gauge 10 1.51 -0.50 -33% 

Gauge 1 1.99 0.53 27% 

Gauge 3 2.88 0.75 26% 

Gauge 7 4.16 -0.56 -13% 

Test 2 Gauge 10 5.97 -3.04 -51% 

Gauge 1 2.95 -0.43 -15% 

Gauge 3 4.45 -0.82 -18% 

Test 3 

Gauge 7 
Technical Details of the FDTS Validation Study 

A-37 

Radiant Heat Flux (kW/m2) 

BE # 3 Sensor 

∆ E ∆ M % Difference 

Gauge 10 5.36 -2.43 -45% 

Gauge 1 2.02 0.52 26% 

Gauge 3 2.92 0.74 25% 

Gauge 7 3.26 0.37 11% 

Test 4 Gauge 10 6.00 -3.04 -51% 

Gauge 1 2.65 -0.13 -5% 

Gauge 3 3.88 -0.25 -7% 

Gauge 7 4.78 -1.18 -25% 

Test 5 Gauge 10 5.45 -2.52 -46% 

Gauge 1 0.82 0.03 4% 

Gauge 3 1.21 0.01 1% 

Gauge 7 1.35 -0.14 -10% 

Test 7 Gauge 10 1.47 -0.48 -33% 

Gauge 1 1.93 0.59 30% 

Gauge 3 2.92 0.71 25% 

Gauge 7 3.56 0.04 1% 

Test 8 Gauge 10 6.02 -3.09 -51% 

Gauge 1 2.72 -0.25 -9% 

Gauge 3 4.27 -0.71 -17% 

Gauge 7 5.23 -1.69 -32% 

Test 9 Gauge 10 5.10 -2.22 -44% 

Gauge 1 1.92 0.60 31% 

Gauge 3 2.68 0.95 36% 

Gauge 7 2.91 0.69 24% 

Test 10 Gauge 10 5.42 -2.49 -46% 

Gauge 1 2.90 2.03 70% 

Gauge 3 4.77 2.33 49% 

Gauge 7 6.58 0.48 7% 

Test 13 Gauge 10 10.06 -4.32 -43% 

Gauge 1 2.12 -0.60 -28% 

Gauge 3 2.84 -0.99 -35% 

Gauge 7 3.32 -1.23 -37% 

Test 14 Gauge 10 10.50 -3.21 -31% 

Gauge 1 18.02 -9.48 -53% 

Gauge 3 45.88 -39.37 -86% 

Gauge 7 

Test 15 Gauge 10 3.65 -2.45 -67% 

Gauge 1 2.73 2.13 78% 

Gauge 3 4.05 2.96 73% 

Gauge 7 4.74 2.23 47% 

Test 16 Gauge 10 11.79 -6.12 -52% 

Gauge 1 0.88 1.35 153% 

Gauge 3 1.30 1.91 147% 

Gauge 7 1.53 1.66 108% 

Test 17 Gauge 10 2.42 0.18 8% 

Test 18 Gauge 1 5.18 0.17 3% 
Technical Details of the FDTS Validation Study 

A-38 

Radiant Heat Flux (kW/m2) 

BE # 3 Sensor 

∆ E ∆ M % Difference 

Gauge 3 5.24 -0.52 -10% 

Gauge 7 

Gauge 10 2.84 -1.60 -56%