NIST Special Publication 1169

Verification and Validation

of Commonly Used

Empirical Correlations

for Fire Scenarios

Kristopher J. Overholt

http://dx.doi.org/10.6028/NIST.SP.1169

NIST Special Publication 1169

Verification and Validation

of Commonly Used

Empirical Correlations

for Fire Scenarios

Kristopher J. Overholt

Fire Research Division

Engineering Laboratory

http://dx.doi.org/10.6028/NIST.SP.1169

SVN Repository Revision : 19098

March 2014

UNITED STATES OF AMERICA

DEPARTMENT OF COMMERCE

U.S. Department of Commerce

Penny Pritzker, Secretary

National Institute of Standards and Technology

Patrick D. Gallagher, Under Secretary of Commerce for Standards and Technology and Director
Certain commercial entities, equipment, or materials may be identified in this

document in order to describe an experimental procedure or concept adequately.

Such identification is not intended to imply recommendation or endorsement by the

National Institute of Standards and Technology, nor is it intended to imply that the

entities, materials, or equipment are necessarily the best available for the purpose.

National Institute of Standards and Technology Special Publication 1169

Natl. Inst. Stand. Technol. Spec. Publ. 1169, 100 pages (March 2014)

CODEN: NSPUE2
Preface

In 2007, the U.S. Nuclear Regulatory Commission (NRC), together with the Electric Power Research Institute (EPRI) and the National Institute of Standards and Technology (NIST), conducted a research project to

verify and validate five fire models that have been used for nuclear power plant (NPP) applications. The results of this effort were documented in a seven-volume report, NUREG-1824 (EPRI 1011999), Verification

and Validation of Selected Fire Models for Nuclear Power Plant Applications [1].

In 2014, the verification and validation study was expanded, and this document was created to serve as a

verification and validation guide for the empirical correlations. The full details of this expanded verification

and validation study are summarized in NUREG-1824 Supplement 1 (EPRI 3002002182) [2].

The model evaluation process consists of two main components: verification and validation. Verification

is a process to check the correctness of the solution of the governing equations. Verification does not imply

that the governing equations are appropriate; only that the equations are being solved correctly.

Validation is a process to determine the appropriateness of the governing equations as a mathematical

model of the physical phenomena of interest. Typically, validation involves comparing model results with

experimental measurement. Differences that cannot be attributed to uncertainty in the measured quantities

in the experiment are attributed to the assumptions and simplifications of the physical model.

iii
iv
Contents

Preface iii

Contents v

List of Figures vii

List of Tables ix

List of Acronyms xi

1 Introduction 1

1.1 Scope of this Document . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Organization of this Document . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 List of Experimental Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Hot Gas Layer Temperature 3

2.1 Natural Ventilation (MQH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Forced Ventilation (FPA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Forced Ventilation (DB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 No Ventilation (Beyler) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3 Hot Gas Layer Depth 17

3.1 ASET Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2 Yamana and Tanaka Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4 Plume Temperature 23

4.1 Heskestad Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.2 McCaffrey Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5 Target Temperature 29

5.1 Cable Failure Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.2 Unprotected Steel Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5.3 Protected Steel Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

6 Target Heat Flux 39

6.1 Point Source Radiation Heat Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

6.2 Solid Flame Radiation Heat Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

7 Ceiling Jet Temperature 47

v
8 Sprinkler Activation Time 51

9 Smoke Detector Activation Time 55

10 Summary 59

Bibliography 61

A Validation Input Parameters 65

A.1 ATF Corridors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

A.2 CAROLFIRE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

A.3 Fleury Heat Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

A.4 FM/SNL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

A.5 LLNL Enclosure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

A.6 NBS Multi-Room . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

A.7 NIST/NRC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

A.8 NIST Smoke Alarms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

A.9 SP AST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

A.10 SP AST Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

A.11 Steckler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

A.12 UL/NFPRF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

A.13 USN Hawaii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

A.14 USN Iceland . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

A.15 Vettori Flat Ceiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

A.16 VTT Large Hall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

A.17 WTC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

vi
List of Figures

2.1 Summary of HGL temperature predictions for natural ventilation tests (MQH) . . . . . . . . . 5

2.2 Summary of HGL temperature predictions for forced ventilation tests (FPA) . . . . . . . . . . 9

2.3 Summary of HGL temperature predictions for forced ventilation tests (DB) . . . . . . . . . . 12

2.4 Summary of HGL temperature predictions for no ventilation tests (Beyler) . . . . . . . . . . 15

3.1 Summary of HGL depth predictions (ASET) . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 Summary of HGL depth predictions (Yamana and Tanaka) . . . . . . . . . . . . . . . . . . . 22

4.1 Summary of plume temperature predictions (Heskestad) . . . . . . . . . . . . . . . . . . . . 25

4.2 Summary of plume temperature predictions (McCaffrey) . . . . . . . . . . . . . . . . . . . . 28

5.1 Summary of cable failure time predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.2 Summary of target temperature predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

6.1 Summary of point source radiation heat flux predictions . . . . . . . . . . . . . . . . . . . . 41

6.2 Summary of solid flame radiation heat flux predictions . . . . . . . . . . . . . . . . . . . . . 45

7.1 Summary of ceiling jet temperature predictions . . . . . . . . . . . . . . . . . . . . . . . . . 50

8.1 Summary of sprinkler activation time predictions . . . . . . . . . . . . . . . . . . . . . . . . 53

9.1 Summary of smoke detector activation time predictions (Temperature Rise) . . . . . . . . . . 57

vii
viii
List of Tables

1.1 Experimental data sets used in this validation study . . . . . . . . . . . . . . . . . . . . . . 2

2.1 Verification case, HGL temperature, natural ventilation . . . . . . . . . . . . . . . . . . . . 4

2.2 Verification case, HGL temperature, forced ventilation . . . . . . . . . . . . . . . . . . . . 8

2.3 Verification case, HGL temperature, forced ventilation . . . . . . . . . . . . . . . . . . . . 11

2.4 Verification case, HGL temperature, no ventilation . . . . . . . . . . . . . . . . . . . . . . 14

3.1 Verification case, HGL depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2 Verification case, HGL depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.1 Verification case, plume temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.2 Constants used in McCaffrey plume temperature correlation . . . . . . . . . . . . . . . . . 26

4.3 Verification case, plume temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.1 Verification case, cable failure time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.2 Verification case, unprotected steel temperature . . . . . . . . . . . . . . . . . . . . . . . . 34

5.3 Verification case, protected steel temperature . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.4 Verification case, protected steel temperature (continued) . . . . . . . . . . . . . . . . . . . 37

6.1 Verification case, point source radiation heat flux . . . . . . . . . . . . . . . . . . . . . . . 40

6.2 Verification case, solid flame radiation heat flux . . . . . . . . . . . . . . . . . . . . . . . . 44

7.1 Verification case, ceiling jet temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

8.1 Verification case, sprinkler activation time . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

9.1 Verification case, smoke detector activation time . . . . . . . . . . . . . . . . . . . . . . . 56

10.1 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

A.1 Validation input parameters for ATF Corridors cases, ceiling jet temperature . . . . . . . . . 65

A.2 Validation input parameters for CAROLFIRE cases, cable failure time . . . . . . . . . . . . 67

A.3 Validation input parameters for CAROLFIRE cases, cable failure time (continued) . . . . . 68

A.4 Validation input parameters for Fleury Heat Flux cases, radiation heat flux . . . . . . . . . . 69

A.5 Validation input parameters for FM/SNL cases, HGL temperature . . . . . . . . . . . . . . 70

A.6 Validation input parameters for FM/SNL cases, plume temperature . . . . . . . . . . . . . . 71

A.7 Validation input parameters for FM/SNL cases, ceiling jet temperature . . . . . . . . . . . . 72

A.8 Validation input parameters for LLNL Enclosure cases, HGL temperature . . . . . . . . . . 74

A.9 Validation input parameters for NBS Multi-Room cases, HGL temperature . . . . . . . . . 76

A.10 Validation input parameters for NIST/NRC cases, HGL temperature and depth . . . . . . . 77

A.11 Validation input parameters for NIST/NRC cases, radiation heat flux . . . . . . . . . . . . . 78

ix
A.12 Validation input parameters for NIST/NRC cases, ceiling jet temperature . . . . . . . . . . 79

A.13 Validation input parameters for NIST Smoke Alarms cases, ceiling jet temperature . . . . . 80

A.14 Validation input parameters for NIST Smoke Alarms cases, smoke detector activation time . 81

A.15 Validation input parameters for SP AST cases, HGL temperature . . . . . . . . . . . . . . . 82

A.16 Validation input parameters for SP AST cases, unprotected steel temperature . . . . . . . . 83

A.17 Validation input parameters for SP AST cases, ceiling jet temperature . . . . . . . . . . . . 84

A.18 Validation input parameters for SP AST Column cases, plume temperature . . . . . . . . . 85

A.19 Validation input parameters for SP AST Column cases, unprotected steel temperature . . . . 86

A.20 Validation input parameters for Steckler cases, HGL temperature . . . . . . . . . . . . . . . 87

A.21 Validation input parameters for UL/NFPRF cases, ceiling jet temperature . . . . . . . . . . 89

A.22 Validation input parameters for UL/NFPRF cases, sprinkler activation time . . . . . . . . . 90

A.23 Validation input parameters for USN Hawaii cases, plume temperature . . . . . . . . . . . . 91

A.24 Validation input parameters for USN Hawaii cases, plume temperature . . . . . . . . . . . . 92

A.25 Validation input parameters for Vettori Flat cases, ceiling jet temperature . . . . . . . . . . 93

A.26 Validation input parameters for Vettori Flat cases, sprinkler activation time . . . . . . . . . 94

A.27 Validation input parameters for VTT Large Hall cases, plume temperature . . . . . . . . . . 95

A.28 Validation input parameters for WTC cases, HGL temperature . . . . . . . . . . . . . . . . 96

A.29 Validation input parameters for WTC cases, unprotected steel temperature . . . . . . . . . . 97

A.30 Validation input parameters for WTC cases, protected steel temperature . . . . . . . . . . . 98

A.31 Validation input parameters for WTC cases, radiation heat flux . . . . . . . . . . . . . . . . 99

A.32 Validation input parameters for WTC cases, ceiling jet temperature . . . . . . . . . . . . . 100

x
List of Acronyms

AST Adiabatic Surface Temperature

ATF Bureau of Alcohol, Tobacco, Firearms, and Explosives

CAROLFIRE Cable Response to Live Fire Test Program

CFAST Consolidated Model of Fire Growth and Smoke Transport

FDS Fire Dynamics Simulator

FM Factory Mutual Global

HGL Hot Gas Layer

HRR Heat Release Rate

LLNL Lawrence Livermore National Laboratory

NBS National Bureau of Standards (former name of NIST)

NFPRF National Fire Protection Research Foundation

NIST National Institute of Standards and Technology

NRC Nuclear Regulatory Commission

RTI Response Time Index

SNL Sandia National Laboratory

SP Statens Provningsanstalt (Technical Research Institute of Sweden)

THIEF Thermally-Induced Electrical Failure

UL Underwriters Laboratories

USN United States Navy

VTT Valtion Teknillinen Tutkimuskeskus (Technical Research Centre of Finland)

WTC World Trade Center

xi
xii
Chapter 1

Introduction

1.1 Scope of this Document

Various empirical correlations exist for calculating quantities of interest related to fire dynamics in a compartment (e.g., hot gas layer temperature, heat flux, plume temperature). The focus of this document is to

compare predictions made using empirical correlations to various experimentally measured quantities for a

fire in a compartment and to express the accuracy and uncertainty of the predictions in a consistent manner.

The empirical correlations selected for use in this document are based on the correlations that are used in

nuclear power plant (NPP) applications, and more details are provided in the verification and validation

report, NUREG-1824 Supplement 1 (EPRI 3002002182) [2].

A Fortran program was developed along with this document that implements the calculations for the

empirical correlations and automates the verification and validation process. This automated verification and

validation process is a method for maintaining the empirical correlations in the long term in a centralized

location and enables model verification and validation to be performed on the empirical correlations in a

systematic manner. As new empirical correlations are developed or relevant compartment fire experiments

are conducted, they can be added to this verification and validation suite and documented.

This document is complementary to the verification and validation guides for the Consolidated Model

of Fire Growth and Smoke Transport (CFAST) [3] and Fire Dynamics Simulator (FDS) [4, 5]. The experiments referred to in this study are described in more detail in the FDS Validation Guide [5] (Volume 3 of

the FDS Technical Reference Guide) and their respective test reports. The source code for the empirical

correlations calculation program, the verification and validation scripts used to generate this document, and

the experimental data shown in this document are freely available for download from the primary website

for FDS.1

1http://fire.nist.gov/fds

1
1.2 Organization of this Document

For each quantity and empirical correlation, Sections 2 through 9 provide a short description of the governing equations, a verification example, and a validation scatter plot that shows model predictions compared

to measured values. For each empirical correlation, the corresponding validation scatter plot lists the experimental relative standard deviation, model relative standard deviation, and bias factor.

Section 10 includes a table of summary statistics for each quantity and empirical correlation. These

statistical metrics can be used to summarize the uncertainty of model predictions and the tendency of a

model to underpredict or overpredict a given quantity. More detailed discussion on the application and

usage of these statistical metrics is provided in the “Quantifying Model Uncertainty” chapter of the FDS

Validation Guide [5].

For each of the experimental data sets, Appendix A lists the input parameters for the empirical correlations that were used in each of the the validation cases.

1.3 List of Experimental Data Sets

The experimental data sets included in this validation study are shown in Table 1.1. The experiments are

described in more detail in the FDS Validation Guide [5] (Volume 3 of the FDS Technical Reference Guide)

and their respective test reports.

Table 1.1: Experimental data sets used in this validation study.

Test Series Description Reference

ATF Corridors Gas burner tests in a two-story structure with long hallways [6]

CAROLFIRE Electrical cables within a heated test apparatus [7]

Fleury Heat Flux Propane burner tests with measured heat flux [8]

FM/SNL Gas and liquid pool fire tests with forced ventilation [9, 10]

LLNL Enclosure Methane burner tests with various ventilation conditions [11]

NBS Multi-Room Gas burner tests in a three-room suite and corridor [12]

NIST/NRC Liquid spray burner tests with various ventilation conditions [13]

NIST Smoke Alarms Single-story manufactured home with furniture fire tests [14]

SP AST Gas burner tests in a compartment with a horizontal beam [15]

SP AST Column Pool fire tests with a vertical column in the center [16]

Steckler Compartment fire tests conducted at NBS (NIST) [17]

UL/NFPRF Spray burner tests in a large-scale facility with sprinklers [18, 19]

USN Hawaii Jet fuel fire tests in an aircraft hangar in a warm climate [20]

USN Iceland Jet fuel fire tests in an aircraft hangar in a cold climate [20]

Vettori Flat Ceiling Compartment tests conducted at NIST with residential sprinklers [21]

VTT Large Hall Heptane pool fire tests in a large-scale facility [22]

WTC Compartment spray burner tests conducted at NIST [23]

2
Chapter 2

Hot Gas Layer Temperature

The empirical correlations can predict an average hot gas layer (HGL) temperature. Because there are

different empirical correlations for compartments that are naturally ventilated, mechanically ventilated, or

unventilated, the results for HGL temperature are divided into three categories.

2.1 Natural Ventilation (MQH)

Description

For a compartment with natural ventilation, the correlation of McCaffrey, Quintiere, and Harkleroad (MQH) [24]

predicts that the hot gas layer (HGL) temperature rise, ∆Tg (

◦C), is given by

∆Tg = 6.85

Q ̇ 2

Ao

√

HohkAT

1/3

(2.1)

where Q ̇ is the total heat release rate (HRR) of the fire (kW), Ao is the area of the ventilation opening (m2),

Ho is the height of the ventilation opening (m), and AT is the total area of the compartment enclosing

surfaces (m2), excluding areas of vent openings, which is given by

AT = 2LW +2LH +2W H −HoWo (2.2)

where L, W, H are the length, width, and height of the compartment (m), respectively, and Wo is the width

of the ventilation opening (m). The heat transfer coefficient, hk (kW/(m2·K)), is given by

hk =

( p

kρc/t t ≤ tp

k/δ t > tp

(2.3)

where k is the thermal conductivity of the interior lining (kW/(m·K)), ρ is its density (kg/m3), c is its

specific heat (kJ/(kg ·K)), and δ is its thickness (m). The thermal penetration time, tp (s), is given by

tp =

ρc

k



δ

2

2

(2.4)

3
Verification

This example case is based on Test 51 from the Lawrence-Livermore National Laboratory (LLNL) [11]

series. This test involved a compartment with an open door, a methane burner, and natural ventilation.

Table 2.1: Verification case, HGL temperature, natural ventilation.

User-Specified Input

Parameter Value

Q ̇ (kW) 200

L (m) 6.0

W (m) 4.0

H (m) 3.0

Ho (m) 2.06

Wo (m) 0.76

k (kW/(m·K)) 0.000463

ρ (kg/m3) 1607

c (kJ/(kg ·K)) 1.0

δ (m) 0.10

T∞ (

◦C) 33

Calculated Output

Time HGL Temperature

(s) (

◦C)

0 33.00

60 111.45

120 121.05

180 127.21

600 148.14

1200 162.24

1800 171.28

2400 178.07

3000 183.57

This verification example serves as both a worked example case and a check on the mathematical implementation of this empirical correlation for software quality assurance (SQA) purposes, hence the extended

number of significant digits. The verification examples are similar for all of the remaining empirical correlations in this document.

4
Validation

A summary of the comparisons between peak predicted and measured compartment temperatures is shown

in Fig. 2.1.

0 200 400 600 800 1000

0

100

200

300

400

500

600

700

800

900

1000

Measured Temperature Rise (°C)

Predicted Temperature Rise (°C)

HGL Temperature, Natural Ventilation (MQH)

Exp. Rel. Std. Dev.: 0.07

Model Rel. Std. Dev.: 0.15

Model Bias Factor: 1.17

LLNL Enclosure

NBS Multiroom (Fire Room)

NIST/NRC

Steckler Compartment

WTC

Figure 2.1: Summary of HGL temperature predictions for natural ventilation tests using the MQH method.

5
Explanation of Statistical Metrics

In Fig. 2.1, the measured values are represented by the horizontal axis and the predicted values by the

vertical axis. If a particular prediction and measurement are the same, then the resulting point falls on the

solid diagonal line. To better make use of these results, two statistical parameters are calculated for each

empirical correlation and each predicted quantity. The first parameter, δ, is the bias factor, which indicates

the extent to which the empirical correlation, on average, under or over-predicts the measurements of a

given quantity. It is assumed that the experiments are unbiased; that is, the bias factor for the experimental

measurements is 1. For example, a bias factor of 1.02 indicates that the model over-estimates the measured

quantity by 2 %, on average. The bias factor is shown graphically by the solid red line.

The second parameter, σeM, is the relative standard deviation of the model, which indicates the variability

of the model. In Fig. 2.1, there are two sets of off-diagonal lines. The first set, shown as dashed black lines,

indicate the uncertainty of the experimental measurements in terms of a relative standard deviation, σeE.

The experimental relative standard deviation was determined by considering the systematic and random

uncertainty values for each measurement quantity, which is described in more detail in the “Experimental

Uncertainty” section of the FDS Validation Guide [5]. The slopes of the dashed black lines are 1 ± 2σeE,

which represents the 95 % confidence intervals. The set of red dashed lines indicate the model relative

standard deviation, σeM. The model relative standard deviation is reported as one standard deviation of the

predicted quantity. The slopes of these lines are δ ±2σeM. If the model was as accurate as the measurements

against which it is compared, then the two sets of off-diagonal lines would merge. The extent to which the

data scatters outside of the experimental bounds is an indication of the degree of uncertainty of the empirical

correlations.

These symbols and nomenclature are similar for all of the remaining scatter plots in this document.

More detailed discussion of the experimental and model relative standard deviations is provided in the FDS

Validation Guide [5] and in McGrattan and Toman [25].

6
2.2 Forced Ventilation (FPA)

Description

For a compartment with forced ventilation, the correlation of Foote, Pagni, and Alvares (FPA) [24] predicts

that the HGL temperature rise, ∆Tg (

◦C), is given by

∆Tg =

"

0.63

Q ̇

m ̇ gcpT∞

0.72 

hkAT

m ̇ gcp

−0.36#

T∞ (2.5)

where Q ̇ is the HRR of the fire (kW),  ̇mg is the compartment ventilation mass flow rate (kg/s), cp is the

specific heat of air (kJ/(kg ·K)), T∞ is the ambient air temperature (◦C), hk is the heat transfer coefficient (kW/(m2

·K)), and AT is the total area of the compartment enclosing surfaces (m2), excluding areas of

vent openings. The heat transfer coefficient, hk (kW/(m2·K)), is given by

hk =

( p

kρc/t t ≤ tp

k/δ t > tp

(2.6)

where k is the thermal conductivity of the interior lining (kW/(m·K)), ρ is its density (kg/m3), c is its

specific heat (kJ/(kg ·K)), and δ is its thickness (m). The thermal penetration time, tp (s), is given by

tp =

ρc

k



δ

2

2

(2.7)

7
Verification

This example case is based on Test 1 from the Factory Mutual and Sandia National Laboratories (FM/SNL) [9,

10] series. This test involved a compartment with an open door, a propylene burner, and forced ventilation.

Table 2.2: Verification case, HGL temperature, forced ventilation.

User-Specified Input

Parameter Value

Q ̇ (kW) 516

m ̇ (kg/s) 4.5

cp (kJ/(kg ·K)) 1.0

L (m) 18.3

W (m) 12.2

H (m) 6.1

k (kW/(m·K)) 0.00023

ρ (kg/m3) 1000

c (kJ/(kg ·K)) 1.16

δ (m) 0.025

T∞ (

◦C) 15

Calculated Output

Time HGL Temperature

(s) (

◦C)

0 15.00

60 53.07

120 58.13

180 61.39

240 63.86

300 65.86

360 67.56

420 69.04

480 70.35

540 71.54

600 72.62

8
Validation

A summary of the comparisons between peak predicted and measured compartment temperatures is shown

in Fig. 2.2.

0 100 200 300 400 500

0

50

100

150

200

250

300

350

400

450

500

Measured Temperature Rise (°C)

Predicted Temperature Rise (°C)

HGL Temperature, Forced Ventilation (FPA)

Exp. Rel. Std. Dev.: 0.07

Model Rel. Std. Dev.: 0.32

Model Bias Factor: 1.29

FM/SNL

LLNL Enclosure

NIST/NRC

Figure 2.2: Summary of HGL temperature predictions for forced ventilation tests using the FPA method.

Note that the LLNL Enclosure experiments were used to develop the FPA correlation.

9
2.3 Forced Ventilation (DB)

Description

For a compartment with forced ventilation, the correlation of Deal and Beyler (DB) [24] predicts that the

HGL temperature rise, ∆Tg (

◦C), is given by

∆Tg =



Q ̇

m ̇ gcp +hkAT



(2.8)

where Q ̇ is the HRR of the fire (kW),  ̇mg is the compartment ventilation mass flow rate (kg/s), cp is the

specific heat of air (kJ/(kg ·K)), T∞ is the ambient air temperature (◦C), hk is the heat transfer coefficient (kW/(m2

·K)), and AT is the total area of compartment enclosing surfaces (m2), excluding areas of

vent openings. The heat transfer coefficient, hk (kW/(m2·K)), is given by

hk = 0.4 max r

kρc

t

,

k

δ

!

(2.9)

where k is the thermal conductivity of the interior lining (kW/(m·K)), ρ is the density of the interior lining (kg/m3

), c is the specific heat of the interior lining (kJ/(kg ·K)), t is the exposure time (s), and δ is the

thickness of the interior lining (m). This model is only valid for times up to 2000 seconds.

10
Verification

This example case is based on Test 1 from the Factory Mutual and Sandia National Laboratories (FM/SNL) [9,

10] series. This test involved a compartment with an open door, a propylene burner, and forced ventilation.

Table 2.3: Verification case, HGL temperature, forced ventilation.

User-Specified Input

Parameter Value

Q ̇ (kW) 516

m ̇ (kg/s) 4.5

cp (kJ/(kg ·K)) 1.0

L (m) 18.3

W (m) 12.2

H (m) 6.1

k (kW/(m·K)) 0.00023

ρ (kg/m3) 1000

c (kJ/(kg ·K)) 1.16

δ (m) 0.025

T∞ (

◦C) 15

Calculated Output

Time HGL Temperature

(s) (

◦C)

0 15.00

60 34.60

120 40.88

180 45.16

240 48.47

300 51.17

360 53.47

420 55.46

480 57.23

540 58.81

600 60.24

11
Validation

A summary of the comparisons between peak predicted and measured compartment temperatures is shown

in Fig. 2.3.

0 100 200 300 400 500

0

50

100

150

200

250

300

350

400

450

500

Measured Temperature Rise (°C)

Predicted Temperature Rise (°C)

HGL Temperature, Forced Ventilation (DB)

Exp. Rel. Std. Dev.: 0.07

Model Rel. Std. Dev.: 0.25

Model Bias Factor: 1.18

FM/SNL

LLNL Enclosure

NIST/NRC

Figure 2.3: Summary of HGL temperature predictions for forced ventilation tests using the DB method.

12
2.4 No Ventilation (Beyler)

Description

For a compartment with no ventilation (closed doors) and constant HRR, the correlation of Beyler [24]

predicts that the HGL temperature rise, ∆Tg (

◦C), is given by

∆Tg =

2K2

K

2

1

(K1

√

t −1+e

−K1

√

t

) (2.10)

where t is the exposure time (s). K1 is given by

K1 =

2(0.4

p

kρc)AT

mcp

(2.11)

where k is the thermal conductivity of the interior lining (kW/(m·K)), ρ is the density of the interior lining (kg/m3

), c is the specific heat of the interior lining (kJ/(kg ·K)), AT the total area of compartment enclosing surfaces (m2

), m is the mass of gas in the compartment (kg), and cp is the specific heat of air (kJ/(kg ·K)).

K2 is given by

K2 =

Q ̇

mcp

(2.12)

where Q ̇ is the HRR of the fire (kW).

13
Verification

This example case is based on Test 1 from the Lawrence-Livermore National Laboratory (LLNL) [11] series.

This test involved a compartment with an open door, a methane burner, and no ventilation.

Table 2.4: Verification case, HGL temperature, no ventilation.

User-Specified Input

Parameter Value

Q ̇ (kW) 200

L (m) 6.0

W (m) 4.0

H (m) 4.5

cp (kJ/(kg ·K)) 1.0

k (kW/(m·K)) 0.000463

ρ (kg/m3) 1607

c (kJ/(kg ·K)) 1.0

T∞ (

◦C) 23

Calculated Output

Time HGL Temperature

(s) (

◦C)

0 23.00

100 59.33

200 76.72

300 90.07

400 101.33

500 111.24

14
Validation

A summary of the comparisons between peak predicted and measured compartment temperatures is shown

in Fig. 2.4.

0 100 200 300 400 500

0

50

100

150

200

250

300

350

400

450

500

Measured Temperature Rise (°C)

Predicted Temperature Rise (°C)

HGL Temperature, No Ventilation (Beyler)

Exp. Rel. Std. Dev.: 0.07

Model Rel. Std. Dev.: 0.37

Model Bias Factor: 1.04

LLNL Enclosure

NIST/NRC

Figure 2.4: Summary of HGL temperature predictions for no ventilation tests using the Beyler method.

15
16
Chapter 3

Hot Gas Layer Depth

The HGL depth is defined as the distance between the ceiling and the HGL height.

3.1 ASET Method

Description

For a compartment with no ventilation (closed doors) and constant HRR, the available safe egress time

(ASET) [26] correlation predicts that the HGL height, z (m), is given by [27]

As

dz

dt

=

dVul

dt

= V ̇

ul (3.1)

where Asis the area of the boundary surfaces (m2), and Vul is the volume of the HGL (m3). The change in

volume of the upper layer, V ̇

ul (m3

/s), is given by

V ̇

ul = V ̇

exp +V ̇ent (3.2)

The volumetric expansion rate, V ̇

exp (m3

/s), is given by [28]

V ̇

exp =

Q ̇

net

ρgcpTg

≈

(1− χl)Q ̇

f

353 ; Q ̇

net = Q ̇

f −Q ̇l = Q ̇f(1− χ ̇l) (3.3)

where Q ̇

net, Q ̇

f

, and Q ̇

l are the net HRR, total HRR, and HRR loss to the boundaries (kW), respectively,

ρg, cp and Tg are the density (kg/m3), specific heat (kJ/(kg ·K)), and temperature (K) of air in the HGL,

respectively, and χlis the heat loss fraction to the enclosure boundaries. The volumetric entrainment rate,

V ̇

ent (m3

/s), is given by [29]

V ̇

ent = kvQ ̇

1/3

z

5/3 =

0.21

Kf



g

ρ∞T∞

1/3

(KfQ ̇)

1/3

(z−zf)

5/3

(3.4)

where kv is the volumetric entrainment coefficient, g is the acceleration due to gravity (m/s2), ρ∞ and T∞ are

the density (kg/m3) and temperature (K) of ambient air, respectively, Kfis the location factor, and zfis the

fuel height (m). The location factor has a value of 1, 2, or 4, which corresponds to a fire away from walls or

corners, a fire adjacent to a wall, or a fire located in a corner, respectively.

The HGL height, z, in Eq. 3.1 can be calculated iteratively using

z|t+1 = z|t −

V ̇

ul

LW

∆t (3.5)

where L and W are the length and width of the compartment (m), respectively, and ∆t is the time step size (s).

17
Verification

This example case is based on Test 1 from the NIST and Nuclear Regulatory Commission (NIST/NRC) [13]

series. This test involved a compartment with a closed door, a heptane spray burner, and no ventilation.

Table 3.1: Verification case, HGL depth.

User-Specified Input

Parameter Value

Q ̇ (kW) 410

L (m) 21.66

W (m) 7.04

H (m) 3.82

k (kW/(m·K)) 0.00012

ρ (kg/m3) 737

c (kJ/(kg ·K)) 1.42

T∞ (

◦C) 22

Location Factor 1

χl 0

zf 0

Calculated Output

Time HGL Depth

(s) (m)

0 0.00

10 0.35

20 0.65

30 0.93

40 1.17

50 1.40

60 1.60

100 2.26

200 3.34

300 3.82

1000 3.82

1350 3.82

18
Validation

A summary of the comparisons between peak predicted and measured HGL depths is shown in Fig. 3.1.

0 5 10 15 20

0

2

4

6

8

10

12

14

16

18

20

Measured Layer Depth (m)

Predicted Layer Depth (m)

HGL Depth (ASET)

NIST/NRC

Figure 3.1: Summary of HGL depth predictions using ASET.

This correlation is only valid for closed room tests, and the NIST/NRC tests are the only closed room

data set with reduced HGL depth data. Note that the bias and standard deviation are not calculated for these

cases because of the limited amount of data.

19
3.2 Yamana and Tanaka Method

Description

For a compartment with no ventilation (closed doors) and constant HRR, the correlation of Yamana and

Tanaka [30] predicts that the HGL height, z (m), is given by

z =

 

2kQ ̇ 1/3t

3Ac

+

1

h

2/3

c

!−3/2

(3.6)

where Q ̇ is the HRR (kW), t is the time after ignition (s), Ac is the compartment floor area (m2), and hc is

the compartment height (m). The constant k is given by

k =

0.076

(353/Tg)

(3.7)

where Tg is the HGL temperature (K).

20
Verification

This example case is based on Test 1 from the NIST and Nuclear Regulatory Commission (NIST/NRC) [13]

series. This test involved a compartment with a closed door, a heptane spray burner, and no ventilation.

Note: In this verification case, the Beyler method (see Section 2.4) is used to calculate the HGL temperature, Tg.

Table 3.2: Verification case, HGL depth.

User-Specified Input

Parameter Value

Q ̇ (kW) 410

L (m) 21.66

W (m) 7.04

H (m) 3.82

k (kW/(m·K)) 0.00012

ρ (kg/m3) 737

c (kJ/(kg ·K)) 1.42

T∞ (

◦C) 22

Calculated Output

Time HGL Depth

(s) (m)

0 0.00

10 0.28

20 0.53

30 0.75

40 0.96

50 1.15

60 1.31

100 1.86

200 2.64

300 3.04

1000 3.67

1350 3.73

21
Validation

A summary of the comparisons between peak predicted and measured HGL depths is shown in Fig. 3.2.

0 5 10 15 20

0

2

4

6

8

10

12

14

16

18

20

Measured Layer Depth (m)

Predicted Layer Depth (m)

HGL Depth (Yamana and Tanaka)

NIST/NRC

Figure 3.2: Summary of HGL depth predictions using Yamana and Tanaka method.

This correlation is only valid for closed room tests, and the NIST/NRC tests are the only closed room

data set with reduced HGL depth data. Note that the bias and standard deviation are not calculated for these

cases because of the limited amount of data.

22
Chapter 4

Plume Temperature

The fire plume transports hot gases into the HGL. Its temperature is greater than the ceiling jet and HGL

temperature. It is particularly important scenarios that involve targets directly above a potential fire.

4.1 Heskestad Method

Description

For a fire plume, the correlation by Heskestad [31] predicts that the increase in centerline temperature,

∆T0 (

◦C), is given by

∆T0 =

9.1



T∞

gc2

pρ

2

∞

1/3

Q ̇

2/3

c

(z−z0)

5/3

(4.1)

where T∞ is the ambient air temperature (◦C), g is the acceleration of gravity (m/s2), cp is the specific heat of

air (kJ/(kg ·K)), ρ∞ is the ambient air density (kg/m3), and z is the elevation above the fire source (m). The

convective HRR, Q ̇

c (kW), is given by

Q ̇

c = Q ̇(1− χr) (4.2)

where Q ̇ is the total HRR (kW), and χris the radiative fraction. Note that the total HRR Q ̇ is the actual

HRR, not the idealized HRR. The hypothetical virtual origin of the fire, z0 (m), is given by

z0 = −1.02D+0.083Q ̇

2/5

(4.3)

where D is the diameter of the fire source (m) and is given by

D =

r

4A

π

(4.4)

where A is the area of the fire source (m2). Note that this plume temperature correlation is only valid above

the mean flame height.

23
Verification

This example case is based on Test 1 from the VTT [22] series. This test involved a large test hall with

closed doors, a heptane pool fire, and no ventilation.

Table 4.1: Verification case, plume temperature.

User-Specified Input

Parameter Value

Q ̇ (m) 1245

cp (kJ/(kg ·K)) 1.0

z (m) 6

A (m2) 1.075

χr 0.40

T∞ (

◦C) 22

Calculated Output

Plume Temperature

(

◦C)

133.78

24
Validation

A summary of the comparisons between peak predicted and measured plume temperatures is shown in

Fig. 4.1.

0 200 400 600 800 1000

0

100

200

300

400

500

600

700

800

900

1000

1100

Measured Temperature Rise (°C)

Predicted Temperature Rise (°C)

Plume Temperature (Heskestad)

Exp. Rel. Std. Dev.: 0.07

Model Rel. Std. Dev.: 0.33

Model Bias Factor: 0.84

FM/SNL

SP AST Column

USN Hangars, Hawaii

USN Hangars, Iceland

VTT

Figure 4.1: Summary of plume temperature predictions using the Heskestad method.

25
4.2 McCaffrey Method

Description

For a fire plume, the correlation by McCaffrey [32] predicts that the increase in centerline temperature,

∆T0 (

◦C), is given by

∆T0 =

"

κ

0.9

√

2g

2 

z

Q ̇ 2/5

2η−1

#

T∞ (4.5)

where g is the acceleration of gravity (m/s2), z is the elevation above the fire source (m), Q ̇ is the HRR (kW),

and T∞ is the ambient air temperature (◦C). The constants η and κ are a function of the height z within the

plume and are listed in Table 4.2.

Table 4.2: Constants used in McCaffrey plume temperature correlation.

Region z/Q ̇ 2/5 η κ

Continuous < 0.08 1/2 6.8

Intermittent < 0.08 – 0.2 0 1.9

Plume > 0.2 -1/3 1.1

26
Verification

This example case is based on Test 1 from the VTT [22] series. This test involved a large test hall with

closed doors, a heptane pool fire, and no ventilation.

Table 4.3: Verification case, plume temperature.

User-Specified Input

Parameter Value

Q ̇ (m) 1245

z (m) 6

T∞ (

◦C) 22

Calculated Output

Plume Temperature

(

◦C)

153.21

27
Validation

A summary of the comparisons between peak predicted and measured plume temperatures is shown in

Fig. 4.2.

0 200 400 600 800 1000

0

100

200

300

400

500

600

700

800

900

1000

1100

Measured Temperature Rise (°C)

Predicted Temperature Rise (°C)

Plume Temperature (McCaffrey)

Exp. Rel. Std. Dev.: 0.07

Model Rel. Std. Dev.: 0.31

Model Bias Factor: 0.90

FM/SNL

SP AST Column

USN Hangars, Hawaii

USN Hangars, Iceland

VTT

Figure 4.2: Summary of plume temperature predictions using the McCaffrey method.

28
Chapter 5

Target Temperature

The calculation of target temperature is a common objective of fire modeling analyses. The targets in this

validation study include electrical cables as well as unprotected and protected steel members.

5.1 Cable Failure Time

Description

Even though an electrical cable is considered a “target”, the cable failure time quantity is included in this

study to assess the models’ ability to predict the time to cable failure. This is an indirect way of assessing

the model prediction of temperature. The model only predicts the interior temperature of the cable, and

the failure time is considered as the time at which the predicted temperature rises above an experimentally

determined value.

The thermally-induced electrical failure (THIEF) of a cable can be predicted via a simple one-dimensional

heat transfer calculation, under the assumption that the cable can be treated as a homogeneous cylinder [7].

The governing equation for the cable temperature, T(r,t) (

◦C), is given by

ρc



∂T

∂t



=

1

r

∂

∂ r

kr

∂T

∂ r



(5.1)

where ρ, c and k are the effective density (kg/m3), specific heat (J/(g ·K)), and thermal conductivity (W/m·K)

of the solid, respectively, and r is the radius of the cable (m). The boundary condition at the exterior boundary, r = R, is defined as

q ̇

00 = k



∂T

∂ r



(R,t) (5.2)

where  ̇q

00 is the assumed axially-symmetric heat flux to the exterior surface of the cable (kW/m2

). The net

heat flux at the surface of the cable is determined from the exposing gas temperature surrounding the cable

at the n-th time step, Tg(t

n

)

q ̇

00(tn

) = εσ(Tg(t

n

)

4 −(Tn

s

)

4

) +h(Tg(t

n

)−T

n

s

) (5.3)

where ε is the emissivity of the cable surface (assumed to be 0.95), σ is the Stefan-Boltzmann constant

(5.67×10−8 W/(m2·K

4

)), h is the convective heat transfer coefficient (assumed to be 10 W/(m2·K), which

is typical of free convection), Tg(t

n

) is the effective gas temperature at the n-th time step (K), and T

n

s

is the

surface temperature of the cable (K).

29
A slight complication of the solution methodology described above is in situations where the cable

is surrounded by a protective layer like a conduit, armor jacket, or tray covering. In CAROLFIRE, only

conduits were considered in the modeling, but other protective measures can be handled in similar fashion,

assuming test data is available to validate the various physical assumptions.

A conduit forms a thermal barrier between the hot gases of a fire and the cable itself. A simple way

to incorporate its effect into the THIEF model is to replace the “exposing” gas temperature, Tg, in Eq. 5.3

by the conduit’s temperature, Tc. In other words, the cable no longer “sees” the hot gases from the fire, but

rather the interior surface of the conduit.

A steel conduit may be assumed to exhibit thermally-thin behavior; that is, its conductivity is so large

that for all practical purposes it can be assumed that its exterior and interior surface temperatures are equal.

Its temperature increases due to the heat flux from the hot gases at its exterior surface, which is given by

q ̇

00

ext(t

n

) = εcσ(Tg(t

n

)

4 −(Tn

c

)

4

) +h(Tg(t

n

)−T

n

c

) (5.4)

where T

n

c

is the conduit temperature at the n-th time step (K), and εc is the emissivity of its surface (assumed

to be 0.85, which is typical of non-polished steel). Heat is transferred from the interior surface of the conduit

to the cable surface via radiation and convection

q ̇

00

int(t

n

) = Fσ((T

n

c

)

4 −(Tn

s

)

4

) +h(T

n

c −T

n

s

) (5.5)

where

F =

Rc

R



1

ε

+

1−εc

εc

−1

(5.6)

where Rc is the inner radius of the conduit (m). The view factor, F, was based on the assumption that the

conduit and cable are concentric cylinders [7].

30
Verification

This example case is based on Penlight Test 7 from the Cable Response to Live Fire (CAROLFIRE) [7]

series. This test involved a cable inside of conduit that was located in a heated cylindrical enclosure.

Table 5.1: Verification case, cable failure time.

User-Specified Input

Parameter Value

Time Ramp 0, 80, 820, 1240, 1800, 1900

Temperature Ramp 24, 460, 460, 460, 460, 0

Cable Diameter (mm) 16.3

Mass per Unit Length (kg/m) 0.529

Jacket Thickness (mm) 1.5

Conduit Diameter (mm) 50

Conduit Thickness (mm) 4.9

T∞ (

◦C) 24

Calculated Output

Exposing Cable Conduit

Time Temperature Temperature Temperature

(s) (

◦C) (◦C) (◦C)

0 24.0 24.0 24.0

24 155.0 24.0 25.6

50 296.3 24.1 32.4

80 460.0 24.6 52.3

130 460.0 27.5 98.7

240 460.0 44.7 186.9

370 460.0 81.5 265.9

500 460.0 130.5 320.6

740 460.0 227.3 379.1

900 460.0 282.8 401.3

1140 460.0 345.8 422.8

1300 460.0 375.9 432.5

1460 460.0 398.4 439.8

1473 460.0 400.0 440.3

1800 460.0 428.6 449.6

31
Validation

A summary of the comparisons between predicted and measured cable failure times (the time at which the

cable reaches its threshold failure temperature, which corresponds to 200 ◦C for thermoplastic cables and

400 ◦C for thermoset cables) is shown in Fig. 5.1.

0 200 400 600 800 1000 1200 1400 1600 1800

0

200

400

600

800

1000

1200

1400

1600

1800

Measured Time to Threshold Temperature (s)

Predicted Time to Threshold Temperature (s)

Cable Failure Time (THIEF)

Exp. Rel. Std. Dev.: 0.11

Model Rel. Std. Dev.: 0.11

Model Bias Factor: 0.90

CAROLFIRE

Figure 5.1: Summary of cable failure time predictions.

32
5.2 Unprotected Steel Temperature

Description

The temperature rise, ∆Ts (

◦C), of an unprotected steel member exposed to fire can be predicted using [33]

∆Ts =

F

V

1

ρscs



hc(Tf −Ts) +σε(T

4

f −T

4

s

)



∆t (5.7)

where F/V is the ratio of heated surface area to volume (m−1), ρsis the density of steel (kg/m3), csis the

specific heat of steel (J/(kg ·K)), hc is the convective heat transfer coefficient (W/(m2·K)), Tfis the exposing

fire temperature (K), Tsis the steel temperature (K), σ is the Stefan-Boltzmann constant (W/(m2·K

4

)), ε

is the flame emissivity, and ∆t is the time step (s). Note that the HGL temperature, plume temperature, or

other exposing temperature can be used as the fire temperature, Tf.

33
Verification

This example case is based on the 1.1 m Diesel Fire Test from the SP AST Column [16] series. This test

involved a large test hall with a steel column located in the middle of a diesel pool fire.

Note: In this verification case, the McCaffrey method (see Section 4.2) is used to calculate the exposing

fire temperature, Tf.

Table 5.2: Verification case, unprotected steel temperature.

User-Specified Input

Parameter Value

F/V (1/m) 205

ρs (kg/m3) 7833

cs (kJ/(kg ·K)) 0

ε 0

hc (W/(m2·K)) 25

Correlation for Tf McCaffrey

Q ̇ (kW) 1434

Height (m) 1

T∞ (

◦C) 20

Calculated Output

Fire Steel

Time Temperature Temperature

(s) (

◦C) (◦C)

0 872.81 20.0

15 872.81 89.7

30 872.81 162.4

45 872.81 232.8

60 872.81 300.6

120 872.81 536.6

180 872.81 700.6

240 872.81 793.6

300 872.81 838.7

600 872.81 872.4

900 872.81 872.8

1200 872.81 872.8

1500 872.81 872.8

34
5.3 Protected Steel Temperature

Description

The temperature rise, ∆Ts (

◦C), of a protected steel member exposed to fire can be predicted, but we must first

determine if the thermal capacity of the insulation layer should be accounted for or if it can be neglected [33].

∆Ts =







ki



Tf−Ts

csh

W

D



∆t cs

W

D > 2ciρih

ki

h



Tf−Ts

cs

W

D +

1

2

ciρih



∆t cs

W

D < 2ciρih

(5.8)

where kiis the thermal conductivity of the insulation material (W/(m·K)), Tfis the exposing fire temperature (K), Ts

is the steel temperature (K), csis the specific heat of steel (J/(kg ·K)), ciis the specific heat of the

insulation material (J/(kg ·K)), h is the thickness of the insulation (m), W/D is the ratio of the weight of steel

section per unit length to the heated perimeter (kg/m2), ρiis the density of the insulating material (kg/m3),

and ∆t is the time step (s). Note that the HGL temperature, plume temperature, or other exposing temperature can be used as the fire temperature, Tf

.

35
Verification

This example case examines the temperature of a bar structural element in Test 4 of the World Trade Center (WTC) [23] series. This test involved a simple compartment with a heptane spray burner and various

structural elements with varying amounts of sprayed fire-resistive materials.

Note: In this verification case, the MQH method (see Section 2.1) is used to calculate the exposing fire

temperature, Tf.

Table 5.3: Verification case, protected steel temperature.

User-Specified Input

Parameter Value

cs (kJ/(kg ·K)) 0.450

W/D (kg/m2) 50.1

ki (W/(m·K)) 0.10

ρi (kg/m3) 208

ci (kJ/(kg ·K)) 2.0

hi (m) 0.0191

Correlation for Tf MQH

Q ̇ (kW) 3200

L (m) 7.04

W (m) 3.60

H (m) 3.82

Ho (m) 2.82

Wo (m) 2.4

k (kW/(m·K)) 0.00012

ρ (kg/m3) 737

c (kJ/(kg ·K)) 1.42

δ (m) 0.0254

T∞ (

◦C) 20

36
Table 5.4: Verification case, protected steel temperature (continued).

Calculated Output

Fire Steel

Time Temperature Temperature

(s) (

◦C) (◦C)

0 25.9 20.00

50 378.7 24.14

100 422.6 29.24

200 471.9 40.51

300 503.5 52.54

400 527.3 65.00

500 546.5 77.72

600 562.7 90.60

700 576.9 103.56

800 589.4 116.55

840 594 121.74

37
Validation

For the unprotected and protected steel cases, a summary of the comparisons between peak predicted and

measured target temperatures is shown in Fig. 5.2.

0 200 400 600 800 1000

0

100

200

300

400

500

600

700

800

900

1000

Measured Temperature Rise (°C)

Predicted Temperature Rise (°C)

Target Temperature

Exp. Rel. Std. Dev.: 0.07

Model Rel. Std. Dev.: 0.45

Model Bias Factor: 1.29

SP AST

SP AST Column

WTC (Immersed)

Figure 5.2: Summary of target temperature predictions.

38
Chapter 6

Target Heat Flux

Thermal radiation is an important mode of heat transfer in fires. The empirical correlations include simple

estimates of flame radiation from a point or cylindrical source.

6.1 Point Source Radiation Heat Flux

Description

The point source model assumes that radiative energy is concentrated at a point located within a flame [34].

Here, the point source is located at a point one-third the height of the flame. The radiative heat flux,

q ̇

00

r

(kW/m2), at any distance R (m) from this point can be predicted using

q ̇

00

r = cosθ



χrQ ̇

4πR2



(6.1)

where the cosθ term (equal to x/R for targets facing sideways, or z/R for gauges facing upward or downward) accounts for a target that is at an angle θ from the source. In the Fortan implementation of this

empirical correlation, the IOR orientation parameter is used to specify which direction the target or gauge

is facing: 1 or -1 for the positive or negative x direction, 2 or -2 for the positive or negative y direction, and

3 or -3 for the positive or negative z direction. In Eq. 6.1, χris the radiative fraction (unless provided in the

test report, a value of 0.35 was used), Q ̇ is the HRR of the fire (kW), and R is the radial distance from the

point source to the edge of the target (m) and is given by

R =

s

x

2 +



z−

Lf

3

2

(6.2)

where x is the horizontal distance from the point source to the edge of the target (m), and z is the height of

the heat flux target (m). The flame height, Lf (m), is given by

Lf = D(3.7Q

∗

2/5

−1.02) (6.3)

where D is the diameter of the fire source (m) and is given by

D =

r

4A

π

(6.4)

where A is the area of the fire source (m2). The nondimensional HRR, Q

∗

, is given by

Q

∗ =

Q ̇

ρ∞cpT∞

√gD5/2

(6.5)

39
where ρ∞ is the ambient air density (kg/m3

), cp is the specific heat of air (kJ/(kg ·K)), T∞ is the ambient air

temperature (K), and g is the acceleration of gravity (m/s2).

Verification

This example case is based on Test 7 from the Fleury Heat Flux [8] series. This test involved a 100 kW

propane burner with dimensions of 0.3 m by 0.3 m and heat flux measurements at various distances from

the burner.

Table 6.1: Verification case, point source radiation heat flux.

User-Specified Input

Parameter Value

Q ̇ (kW) 100

χr 0.35

A (m2) 0.09

x (m) 0.50, 0.75, 1.0

z (m) 0.0

IOR 2

Calculated Output

Radius Heat Flux

(m) (kW/m2)

0.50 6.01

0.75 3.65

1.00 2.33

40
Validation

A summary of the comparisons between peak predicted and measured heat fluxes is shown in Fig. 6.1.

0 20 40 60 80 100 120

0

20

40

60

80

100

120

Measured Heat Flux (kW/m2)

Predicted Heat Flux (kW/m

2

)

Target Heat Flux (Point Source)

Exp. Rel. Std. Dev.: 0.11

Model Rel. Std. Dev.: 0.47

Model Bias Factor: 1.44

Fleury Heat Flux

NIST/NRC

WTC (Non−Immersed)

Figure 6.1: Summary of point source radiation heat flux predictions.

41
6.2 Solid Flame Radiation Heat Flux

Description

The solid flame model predicts the heat flux to a target based on the effective emissive power from a flame

and a view factor calculation [34]. The radiative heat flux,  ̇q

00

r

(kW/m2), at any distance R (m) from the center

of the flame can be predicted using

q ̇

00

r = EF12 (6.6)

where E is the effective emissive power of the flame (kW/m2), and F12 is the view factor between the target

and the flame. The effective emissive power of the flame, E, is given by

E = 58(10−0.0823D) (6.7)

where D is the effective fire diameter (m).

Ground-Level Target

For a heat flux target that is at the same level as the base of the flame, the view factor between the target and

the flame, F12, is given by

F12 =

q

F

2

12,H +F

2

12,V

(6.8)

where F12,H and F12,V are given by

F12,H =



B−

1

S



π

√

B2 −1

tan−1

s

(B+1)(S−1)

(B−1)(S+1)

−



A−

1

S



π

√

A2 −1

tan−1

s

(A+1)(S−1)

(A−1)(S+1)

(6.9)

F12,V =

1

πS

tan−1



H

√

S

2 −1



−

H

πS

tan−1

r

S−1

S+1

+

AH

πS

√

A2 −1

tan−1

s

(A+1)(S−1)

(A−1)(S+1)

(6.10)

where H, S, A, and B are given by

H =

2Lf

D

(6.11)

S =

2x

D

(6.12)

A =

H

2 +S2 +1

2S

(6.13)

B =

1+S

2

2S

(6.14)

where x is the horizontal distance from the center of the flame to the edge of the heat flux target (m), and Lf

is the flame height given in Eq. 6.3 (m).

42
Elevated Target

For a heat flux target that is elevated from the base of the flame, the view factor between the target and the

flame, F12, is given by

F12 = F12,V1 +F12,V2 (6.15)

where F12,V1 and F12,V2 are given by

F12,V1 =

1

πS

tan−1



H1

√

S

2 −1



−

H1

πS

tan−1

r

S−1

S+1

+

A1H1

πS

q

A

2

1 −1

tan−1

s

(A1 +1)(S−1)

(A1 −1)(S+1)

(6.16)

F12,V2 =

1

πS

tan−1



H2

√

S

2 −1



−

H2

πS

tan−1

r

S−1

S+1

+

A2H2

πS

q

A

2

2 −1

tan−1

s

(A2 +1)(S−1)

(A2 −1)(S+1)

(6.17)

where H1, H2, S, A1, and A2 are given by

H1 =

2z

D

(6.18)

H2 =

2(Lf −z)

D

(6.19)

S =

2x

D

(6.20)

A1 =

H

2

1 +S

2 +1

2S

(6.21)

A2 =

H

2

2 +S

2 +1

2S

(6.22)

where x is the horizontal distance from the center of the flame to the edge of the heat flux target (m), z is the

height of the target from the base of the flame (m), and Lfis the flame height given in Eq. 6.3 (m).

43
Verification

This example case is based on Test 7 from the Fleury Heat Flux [8] series. This test involved a 100 kW

propane burner with dimensions of 0.3 m by 0.3 m and heat flux measurements at various distances from

the burner.

Table 6.2: Verification case, solid flame radiation heat flux.

User-Specified Input

Parameter Value

Q ̇ (kW) 100

A (m2) 0.09

x (m) 0.50, 0.75, 1.0

z (m) 0.0

Calculated Output

Radius Heat Flux

(m) (kW/m2)

0.50 11.18

0.75 6.90

1.00 4.69

44
Validation

A summary of the comparisons between peak predicted and measured plume temperatures is shown in

Fig. 6.2.

0 20 40 60 80 100 120

0

20

40

60

80

100

120

Measured Heat Flux (kW/m2)

Predicted Heat Flux (kW/m

2

)

Target Heat Flux (Solid Flame)

Exp. Rel. Std. Dev.: 0.11

Model Rel. Std. Dev.: 0.44

Model Bias Factor: 1.17

Fleury Heat Flux

NIST/NRC

WTC (Non−Immersed)

Figure 6.2: Summary of solid flame radiation heat flux predictions.

45
46
Chapter 7

Ceiling Jet Temperature

The ceiling jet is the shallow layer of hot gases below the ceiling that spreads radially from the centerline

of the fire plume. The ceiling jet has a higher temperature than the overall temperature of the HGL, and

therefore it is important where targets are located just below the ceiling.

Description

For a steady-state fire, the correlation of Alpert [35] predicts that the ceiling jet temperature rise, ∆Tjet (

◦C),

from a fire plume is given by

∆Tjet =







16.9Q ̇ 2/3

H5/3

r/H <= 0.18

5.38(Q ̇/r)

2/3

H

r/H > 0.18

(7.1)

where Q ̇ is the total HRR (kW), H is the height of the ceiling above the fuel (m), and r is the radial distance

to the detector (m).

Note that some of these cases assume a quasi-steady approach for a fire source Q ̇ that follows a specified

t-squared growth rate, which is given by

Q ̇ = αt

2

(7.2)

where α is the t-squared growth rate parameter (kW/s2), and t is time (s).

For cases in which the fire was located against a wall or corner, these correlations are adjusted based

on the method of reflection. For a fire adjacent to a flat wall, 2Q ̇ is substituted for Q ̇; and for a fire in a

90-degree corner, 4Q ̇ is substituted for Q ̇. This adjustment is denoted in the input parameters as the location

factor. For a given case, the location factor has a value of 1, 2, or 4, which corresponds to a fire away from

walls or corners, a fire adjacent to a wall, or a fire located in a corner, respectively.

47
Verification

This example case is based on Test 1 from the NIST and Nuclear Regulatory Commission (NIST/NRC) [13]

series. This test involved a compartment with a closed door, a heptane spray burner, and no ventilation.

Table 7.1: Verification case, ceiling jet temperature.

User-Specified Input

Parameter Value

Q ̇ (kW) 410

Location Factor 1

r (m) 5.90

H (m) 3.72

T∞ (

◦C) 22

Calculated Output

Ceiling Jet Temperature

(

◦C)

46.45

48
Validation

A summary of the comparisons between peak predicted and measured ceiling jet temperatures is shown in

Fig. 7.1.

It is important to note that this ceiling jet temperature correlation was developed using data from tests

that were conducted in a large facility in which the distant walls and large compartment size did not allow for

the development of a significant hot gas layer. In a more typical fire scenario (i.e., a smaller compartment),

the HGL develops relatively quickly, and temperatures at the ceiling are affected by the ceiling jet as well

as the accumulating HGL. Thus, when compared to experimentally measured ceiling temperatures in a

compartment fire, this correlation tends to underpredict the temperatures because it is not accounting for the

development of the HGL. This is an important consideration when using this correlation to predict detector

or sprinkler activations.

For the reasons stated above, two scatter plot comparisons are shown in Fig. 7.1. One scatter plot shows

the results for unconfined tests that were conducted under a false ceiling in which the hot plume gases

did not accumulate to form an HGL, but were allowed to spill out from under a false ceiling. The other

scatter plot shows the results of underpredicted temperature comparisons for compartment fire tests. The

use of the ceiling jet correlation in a confined compartment with the presence of an HGL can result in an

underprediction of the measured ceiling jet temperature by approximately 70 %. Therefore, the model bias

factor and model relative standard deviation were only calculated for the unconfined ceiling jet cases that

the correlation was developed for. In the unconfined ceiling cases, the ceiling temperature predictions are in

better agreement with experimental data because this scenario is more representative of a temperature rise

due to only ceiling jet flow from the fire plume.

49
0 200 400 600 800 1000

0

100

200

300

400

500

600

700

800

900

1000

Measured Temperature Rise (°C)

Predicted Temperature Rise (°C)

Ceiling Jet Temperature, Unconfined (Alpert)

Exp. Rel. Std. Dev.: 0.07

Model Rel. Std. Dev.: 0.11

Model Bias Factor: 0.86

UL/NFPRF, Series I

0 200 400 600 800 1000

0

100

200

300

400

500

600

700

800

900

1000

Measured Temperature Rise (°C)

Predicted Temperature Rise (°C)

Ceiling Jet Temperature, Compartment (Alpert)

ATF Corridors

FM/SNL

NIST Smoke Alarms (Fire Room)

NIST/NRC

SP AST

Vettori Flat Ceiling

WTC

Figure 7.1: Summary of compartment (top) and unconfined (bottom) ceiling jet temperature predictions.

50
Chapter 8

Sprinkler Activation Time

Much like an electrical cable, a sprinkler is merely a “target” with a particular set of thermal properties, such

as the response time index (RTI) that indicates the sensitivity of the fusible link or glass bulb. Activation is

assumed to occur when the link or bulb temperatures reaches a predetermined threshold temperature.

Description

For a steady-state fire, the correlation of Alpert [35] predicts that the activation time of a sprinkler, tact (s),

is given by [36]

tact =

RTI

√ujet

ln

Tjet −T∞

Tjet −Tact 

(8.1)

where RTI is the response time index of the sprinkler ((m·s)1/2), T∞ is the ambient air temperature (◦C), and

Tact is the activation temperature of the sprinkler (◦C). The ceiling jet temperature, Tjet (

◦C), is given by

Tjet =







16.9Q ̇ 2/3

H5/3 +T∞ r/H <= 0.18

5.38(Q ̇/r)

2/3

H +T∞ r/H > 0.18

(8.2)

where Q ̇ is the total HRR (kW), H is the height of the ceiling above the fuel (m), and r is the radial distance

to the detector (m). The ceiling jet velocity, ujet (m/s), is given by

ujet =







0.947

Q ̇

H

1/3

r/H <= 0.15

0.197Q ̇ 1/3H

1/2

r

5/6

r/H > 0.15

(8.3)

Note that some of these cases assume a quasi-steady approach for a fire source Q ̇ that follows a specified

t-squared growth rate, which is given by Eq. 7.2.

For cases in which the fire was located against a wall or corner, these correlations are adjusted based

on the method of reflection. For a fire adjacent to a flat wall, 2Q ̇ is substituted for Q ̇; and for a fire in a

90-degree corner, 4Q ̇ is substituted for Q ̇ [35]. This adjustment is denoted in the input parameters as the

location factor. For a given case, the location factor has a value of 1, 2, or 4, which corresponds to a fire

away from walls or corners, a fire adjacent to a wall, or a fire located in a corner, respectively.

51
Verification

This example case is based on Test 1 from the Vettori Flat Ceiling [21] series. This test involved residential

quick response sprinklers located on a flat ceiling in a compartment with a closed door, a methane burner,

and no ventilation.

Table 8.1: Verification case, sprinkler activation time.

User-Specified Input

Parameter Value

α (kW/s2) 0.105

Location Factor 1

RTI ((m·s)1/2) 55

Tact (

◦C) 68

r (m) 2.20

H (m) 2.09

T∞ (

◦C) 16.6

Calculated Output

Time HRR Activation Time

(s) (kW) (s)

50 262.5 98.2

52
Validation

A summary of the comparisons between predicted and measured sprinkler activation times is shown in

Fig. 8.1.

0 50 100 150 200 250 300

0

50

100

150

200

250

300

Measured Activation Time (s)

Predicted Activation Time (s)

Sprinkler Activation Time

Exp. Rel. Std. Dev.: 0.06

Model Rel. Std. Dev.: 0.41

Model Bias Factor: 1.11

UL/NFPRF, Series I

UL/NFPRF, Series II

Vettori Flat Ceiling (Unobstructed)

Figure 8.1: Summary of sprinkler activation time predictions.

53
54
Chapter 9

Smoke Detector Activation Time

Smoke detector activation can be modeled in a variety of ways. A common method is to assume that the

detector behaves like a very sensitive sprinkler with a low activation temperature and RTI.

Description

For this method, the prediction of smoke detector activation time is identical to that for a sprinkler (as described in Chapter 8). Equations 8.1, 8.2, and 8.3 are used to calculate the time at which the detector reaches

its activation temperature, and the input parameters are the same as described in Chapter 8. Bukowski and

Averill [37] suggested an activation temperature that corresponds to a temperature rise above ambient, ∆Tc,

of 5 ◦C to be typical of many residential smoke alarms. It is assumed that the smoke detectors are low-RTI

devices (RTI = 5 (m·s)

1/2

).

Note that some of these cases assume a quasi-steady approach for a fire source Q ̇ that follows a specified

t-squared growth rate, which was specified as Q ̇ = αt

2 up to a cutoff time of tfire. In this approach, for a

given time and HRR, Eq. 8.1 was used to calculate the time that the detector would activate. If the calculated

activation time was less than the current time, then the detector was assumed to activate. After the time tfire,

the fire HRR was steady.

55
Verification

This example case is based on Test SDC02 from the NIST Smoke Alarms [14] series. This test involved

ionization and photoelectric smoke alarms located in a single-story manufactured home with a closed door,

an upholstered chair fuel source, and no ventilation. If the fire size is not sufficiently large enough to activate

the detector, then the activation time is denoted as not applicable (N/A).

Table 9.1: Verification case, smoke detector activation time.

User-Specified Input

Parameter Value

α (kW/s2) 0.00463

Location Factor 1

RTI ((m·s)1/2) 5

∆Tc (

◦C) 5

r (m) 1.3

H (m) 2.1

tfire (s) 300

T∞ (

◦C) 21

Calculated Output

Time HRR Activation Time

(s) (kW) (s)

25 2.90 N/A

26 3.10 N/A

27 3.40 N/A

28 3.63 35.0

29 3.89 23.3

56
Validation

A summary of the comparisons between predicted and measured smoke detector activation times is shown

in Fig. 9.1.

0 50 100 150 200 250 300

0

50

100

150

200

250

300

Measured Activation Time (s)

Predicted Activation Time (s)

Smoke Detector Activation Time (Temperature Rise)

Exp. Rel. Std. Dev.: 0.34

Model Rel. Std. Dev.: 0.57

Model Bias Factor: 0.66

NIST Smoke Alarms (Fire Room)

Figure 9.1: Summary of smoke detector activation time predictions using the Temperature Rise method.

57
58
Chapter 10

Summary

Summary of Uncertainty Statistics for Empirical Correlations

For each quantity of interest, the experimental relative standard deviation, σeE, model relative standard deviation, σeM, and model bias factor are shown in Table 10.1, which are taken from each of the scatter plots in the

corresponding chapters of this document. The latter two values indicate the average scatter and bias of the

model predictions. For example, for a given quantity, a model relative standard deviation of 0.15 indicates

that one standard deviation of all of the model predictions is equal to 15 %, and a model bias factor of 1.05

indicates that, on average, the model tends to overpredict that quantity by 5 %. The number of datasets and

data points are also listed for each quantity.

For quantities with only a small number of experimental data points, additional experimental data is

needed to justify the model uncertainty and bias. Note that some quantities exhibit a large amount of model

uncertainty or are significantly under- or over-predicted, and some caution should be exercised when applying these empirical correlations. More detailed discussion on the application and usage of these statistical

metrics is provided in the “Quantifying Model Uncertainty” chapter of the FDS Validation Guide [5].

Table 10.1: Summary statistics for all quantities of interest

Quantity Section Datasets Points σeE σeM Bias

HGL Temperature, Natural Ventilation (MQH) 2.1 5 78 0.07 0.15 1.17

HGL Temperature, Forced Ventilation (FPA) 2.2 3 66 0.07 0.32 1.29

HGL Temperature, Forced Ventilation (DB) 2.3 3 66 0.07 0.25 1.18

HGL Temperature, No Ventilation (Beyler) 2.4 2 18 0.07 0.37 1.04

Plume Temperature (Heskestad) 4.1 5 156 0.07 0.33 0.84

Plume Temperature (McCaffrey) 4.2 5 162 0.07 0.31 0.90

Cable Failure Time (THIEF) 5.1 1 35 0.11 0.11 0.90

Target Temperature 5.2 3 72 0.07 0.45 1.29

Target Heat Flux (Point Source) 6.1 3 658 0.11 0.47 1.44

Target Heat Flux (Solid Flame) 6.2 3 658 0.11 0.44 1.17

Ceiling Jet Temperature, Unconfined (Alpert) 7.1 1 103 0.07 0.11 0.86

Sprinkler Activation Time 8.1 3 60 0.06 0.41 1.11

Smoke Detector Activation Time (Temperature Rise) 9.1 1 24 0.34 0.57 0.66

59
60
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63
64
Appendix A

Validation Input Parameters

This appendix lists all of the input parameters that were used for each test in each data set. The input

parameters are arranged alphabetically by data set, then by experimental quantity.

A.1 ATF Corridors

Ceiling Jet Temperature (Alpert) [35]

Table A.1: Summary of validation input parameters used for ATF Corridors cases [6], ceiling jet temperature.

Input Parameter Value

Location Factor 1

r (m) 2, 9, 14.5

H (m) 2.03

T∞ (

◦C) 20

Test Q ̇

(kW)

ATF Corridors 50 kW 48

ATF Corridors 100 kW 97

ATF Corridors 240 kW 242

ATF Corridors 250 kW 250

ATF Corridors 500 kW 485

65
A.2 CAROLFIRE

Cable Failure Time [7]

The cable and conduit targets were not completely surrounded by the Penlight apparatus, which had openings at its ends. Therefore, the exposing temperature ramp Tramp was calculated using a view factor of 0.90

and the experimentally measured shroud temperature.

66
Table A.2: Summary of validation input parameters used for CAROLFIRE cases [7], cable failure time.

Cable Mass per Jacket Conduit Conduit

Test Diameter Unit Length Thickness Diameter Thickness T∞ tend

(mm) (kg/m) (mm) (mm) (mm) (

◦C) (s)

Penlight Test 1 16.3 0.529 1.5 - - 24 1800

Penlight Test 2 16.3 0.529 1.5 - - 24 1800

Penlight Test 3 16.3 0.529 1.5 - - 24 1800

Penlight Test 4 15.2 0.459 1.5 - - 20 1800

Penlight Test 5 15.2 0.459 1.5 - - 20 1800

Penlight Test 6 15.2 0.459 1.5 - - 20 1800

Penlight Test 7 16.3 0.529 1.5 50 4.9 24 1800

Penlight Test 8 15.2 0.459 1.5 50 4.9 30 1800

Penlight Test 9 16.3 0.529 1.5 - - 24 1800

Penlight Test 10 15.2 0.459 1.5 - - 20 1800

Penlight Test 11 15.0 0.410 1.5 - - 24 1800

Penlight Test 12 15.0 0.410 1.5 - - 24 1800

Penlight Test 13 15.0 0.410 1.5 - - 24 1800

Penlight Test 14 15.0 0.380 1.1 - - 24 1800

Penlight Test 15 15.0 0.380 1.1 - - 24 1800

Penlight Test 16 15.0 0.380 1.1 - - 24 1800

Penlight Test 17 15.1 0.400 1.5 - - 24 1800

Penlight Test 18 14.5 0.358 1.0 - - 24 1800

Penlight Test 19 12.2 0.321 0.9 - - 24 1800

Penlight Test 20 15.1 0.388 1.5 - - 24 1800

Penlight Test 21 12.4 0.324 1.1 - - 24 1190

Penlight Test 22 10.2 0.292 0.5 - - 24 1640

Penlight Test 23 15.0 0.410 1.5 50 4.9 24 1800

Penlight Test 24 15.0 0.410 1.5 50 4.9 24 1800

Penlight Test 25 15.0 0.380 1.1 50 4.9 24 1800

Penlight Test 26 15.0 0.380 1.1 50 4.9 24 1800

Penlight Test 27 15.0 0.410 1.5 - - 24 1800

Penlight Test 28 15.0 0.410 1.5 - - 24 1800

Penlight Test 29 15.0 0.380 1.1 - - 24 1640

Penlight Test 30 15.0 0.380 1.1 - - 24 1800

Penlight Test 31 19.0 0.500 2.0 - - 24 1800

Penlight Test 62 12.7 0.231 1.1 - - 24 1190

Penlight Test 63 11.3 0.195 1.1 - - 24 710

Penlight Test 64 7.9 0.097 1.1 - - 24 890

Penlight Test 65 7.0 0.076 1.0 - - 24 770

67
Table A.3: Summary of validation input parameters used for CAROLFIRE cases [7], cable failure time

(continued).

Test tramp Tramp

(s) (

◦C)

Penlight Test 1 0, 70, 820, 1240, 1600, 1800 24, 460, 460, 275, 178, 0

Penlight Test 2 0, 80, 800, 1220, 1600, 1800 24, 460, 460, 275, 178, 0

Penlight Test 3 0, 80, 700, 950, 1600, 1800 24, 460, 460, 334, 178, 0

Penlight Test 4 0, 60, 820, 1470, 1800, 1900 24, 290, 290, 290, 188, 0

Penlight Test 5 0, 60, 820, 1080, 1600, 1800 24, 290, 290, 290, 139, 0

Penlight Test 6 0, 60, 820, 1080, 1600, 1800 24, 290, 290, 290, 139, 0

Penlight Test 7 0, 80, 820, 1240, 1800, 1900 24, 460, 460, 460, 460, 0

Penlight Test 8 0, 55, 820, 1080, 1800, 1900 24, 290, 290, 290, 290, 0

Penlight Test 9 0, 80, 820, 1240, 1800, 1900 24, 451, 451, 451, 451, 0

Penlight Test 10 0, 60, 820, 1500, 1800, 1900 24, 285, 285, 285, 188, 0

Penlight Test 11 0, 80, 820, 1320, 1800, 1900 24, 456, 456, 456, 266, 0

Penlight Test 12 0, 80, 820, 1320, 1800, 1900 24, 460, 460, 460, 266, 0

Penlight Test 13 0, 80, 820, 1320, 1800, 1900 24, 460, 460, 460, 266, 0

Penlight Test 14 0, 60, 820, 1470, 1800, 1900 24, 290, 290, 290, 290, 0

Penlight Test 15 0, 60, 820, 1470, 1800, 1900 24, 314, 314, 314, 188, 0

Penlight Test 16 0, 60, 820, 1470, 1800, 1900 24, 314, 314, 314, 314, 0

Penlight Test 17 0, 80, 660, 1240, 1600, 1800 24, 460, 460, 275, 178, 0

Penlight Test 18 0, 70, 820, 1240, 1600, 1800 24, 675, 675, 675, 675, 0

Penlight Test 19 0, 80, 820, 1050, 1500, 1800 24, 460, 460, 460, 236, 0

Penlight Test 20 0, 70, 600, 1240, 1600, 1800 24, 460, 460, 275, 178, 0

Penlight Test 21 0, 60, 930, 1200 24, 290, 290, 197

Penlight Test 22 0, 80, 1440, 1650 24, 460, 460, 295

Penlight Test 23 0, 80, 1801 24, 456, 456

Penlight Test 24 0, 80, 1801 24, 456, 456

Penlight Test 25 0, 50, 1801 24, 309, 309

Penlight Test 26 0, 60, 1801 24, 309, 309

Penlight Test 27 0, 80, 1500, 1801 24, 456, 456, 305

Penlight Test 28 0, 80, 1801 24, 451, 451

Penlight Test 29 0, 60, 1260, 1650 24, 309, 309, 188

Penlight Test 30 0, 50, 1350, 1800 24, 309, 309, 188

Penlight Test 31 0, 70, 820, 1240, 1600, 1801 24, 675, 675, 675, 675, 0

Penlight Test 62 0, 80, 300, 480, 1200 24, 451, 451, 334, 207

Penlight Test 63 0, 70, 720 24, 309, 309

Penlight Test 64 0, 80, 240, 900 24, 451, 451, 207

Penlight Test 65 0, 65, 540, 780 24, 309, 309, 217

68
A.3 Fleury Heat Flux

Point Source and Solid Flame Radiation Heat Flux [34]

Table A.4: Summary of validation input parameters used for Fleury Heat Flux cases [8], radiation heat flux.

Input Parameter Value

χr 0.35

x (m) 0.5, 0.75, 1.0, 1.5, 2.0

z (m) 0.0, 0.5, 1.0, 1.5

IOR 2

Test Q ̇ A

(kW) (m2)

100 kW, 1:1 Burner 100 0.09

150 kW, 1:1 Burner 150 0.09

200 kW, 1:1 Burner 200 0.09

250 kW, 1:1 Burner 250 0.09

300 kW, 1:1 Burner 300 0.09

100 kW, 2:1 Burner 100 0.18

150 kW, 2:1 Burner 150 0.18

200 kW, 2:1 Burner 200 0.18

250 kW, 2:1 Burner 250 0.18

300 kW, 2:1 Burner 300 0.18

100 kW, 3:1 Burner 100 0.27

150 kW, 3:1 Burner 150 0.27

200 kW, 3:1 Burner 200 0.27

250 kW, 3:1 Burner 250 0.27

300 kW, 3:1 Burner 300 0.27

69
A.4 FM/SNL

HGL Temperature [24]

Table A.5: Summary of validation input parameters used for FM/SNL cases [9, 10], HGL temperature.

Input Parameter Value

L (m) 18.3

W (m) 12.2

H (m) 6.1

cp (kJ/(kg ·K)) 1.0

k (kW/(m·K)) 0.00023

ρ (kg/m3) 1000

c (kJ/(kg ·K)) 1.16

δ (m) 0.025

Test Correlation Q ̇ m ̇ T∞ tend

(kW) (kg/s) (

◦C) (s)

Test 1 FPA, DB 516 4.5 15 600

Test 2 FPA, DB 516 4.5 14 600

Test 3 FPA, DB 2000 4.5 15 300

Test 4 FPA, DB 516 0.45 15 600

Test 5 FPA, DB 516 4.5 19 600

Test 6 FPA, DB 500 0.45 15 600

Test 7 FPA, DB 516 0.45 15 600

Test 8 FPA, DB 1000 0.45 21 720

Test 9 FPA, DB 1000 3.6 24 840

Test 10 FPA, DB 1000 2.0 18 600

Test 11 FPA, DB 500 2.0 16 600

Test 12 FPA, DB 2000 2.0 17 600

Test 13 FPA, DB 2000 3.6 21 600

Test 14 FPA, DB 500 0.45 15 600

Test 15 FPA, DB 1000 0.45 18 1380

Test 16 FPA, DB 500 0.45 18 720

Test 17 FPA, DB 500 4.5 10 1380

Test 21 FPA, DB 500 0.45 14 1200

Test 22 FPA, DB 1000 0.45 14 840

70
Plume Temperature (Heskestad and McCaffrey) [31, 32]

Table A.6: Summary of validation input parameters used for FM/SNL cases [9, 10], plume temperature.

Input Parameter Value

z (m) 5.98

A (m2) 0.64

χr 0.35

cp (kJ/(kg ·K)) 1.0

Test Q ̇ T∞

(kW) (

◦C)

Test 1 516 15

Test 2 516 14

Test 3 2000 15

Test 4 516 15

Test 5 516 19

Test 6 500 15

Test 7 516 15

Test 8 1000 21

Test 9 1000 24

Test 10 1000 18

Test 11 500 16

Test 12 2000 17

Test 13 2000 21

Test 14 500 15

Test 15 1000 18

Test 16 500 18

Test 17 500 10

Test 21 500 14

Test 22 1000 14

71
Ceiling Jet Temperature (Alpert) [35]

Table A.7: Summary of validation input parameters used for FM/SNL cases [9, 10], ceiling jet temperature.

Input Parameter Value

r (m) 3.05, 9.15

H (m) 5.9

Test Q ̇ Location T∞

(kW) Factor (

◦C)

Test 1 516 1 15

Test 2 516 1 14

Test 3 2000 1 15

Test 4 516 1 15

Test 5 516 1 19

Test 6 500 2 15

Test 7 516 1 15

Test 8 1000 1 21

Test 9 1000 1 24

Test 10 1000 2 18

Test 11 500 2 16

Test 12 2000 2 17

Test 13 2000 2 21

Test 14 500 2 15

Test 15 1000 2 18

Test 16 500 4 18

Test 17 500 4 10

Test 21 500 1 14

Test 22 1000 1 14

72
A.5 LLNL Enclosure

HGL Temperature [24]

For the cases with natural ventilation (MQH), the door size was 2.06 m high by 0.76 m wide.

73
Table A.8: Summary of validation input parameters used for LLNL Enclosure cases [11], HGL temperature.

Input Parameter Value

cp (kJ/(kg ·K)) 1.0

k (kW/(m·K)) 0.000463

ρ (kg/m3) 1607

c (kJ/(kg ·K)) 1.0

δ (m) 0.1

Location Factor 1

Heat Loss Fraction 0

Fuel Height 0

Test Correlation Q ̇ L W H m ̇ T∞ tend

(kW) (m) (m) (m) (kg/s) (

◦C) (s)

Test 1 Beyler 200 6.0 4.0 4.5 - 23 500

Test 2 Beyler 200 6.0 4.0 4.5 - 27 500

Test 3 Beyler 400 6.0 4.0 4.5 - 27 200

Test 4 Beyler 300 6.0 4.0 4.5 - 24 300

Test 5 Beyler 50 6.0 4.0 4.5 - 28 2500

Test 6 Beyler 100 6.0 4.0 4.5 - 29 1000

Test 7 Beyler 100 6.0 4.0 4.5 - 35 1000

Test 8 Beyler 200 6.0 4.0 4.5 - 35 500

Test 9 FPA, DB 200 6.0 4.0 4.5 0.565 33 4000

Test 10 FPA, DB 200 6.0 4.0 4.5 0.118 28 6000

Test 11 FPA, DB 200 6.0 4.0 4.5 0.240 18 4000

Test 12 FPA, DB 200 6.0 4.0 4.5 0.366 21 5000

Test 13 FPA, DB 200 6.0 4.0 4.5 0.474 28 5000

Test 14 FPA, DB 200 6.0 4.0 4.5 0.472 28 5000

Test 15 FPA, DB 100 6.0 4.0 4.5 0.352 24 4000

Test 16 FPA, DB 200 6.0 4.0 4.5 0.356 21 6000

Test 17 FPA, DB 200 6.0 4.0 3.0 0.587 26 3000

Test 18 FPA, DB 200 6.0 4.0 3.0 0.463 21 4000

Test 19 FPA, DB 200 6.0 4.0 3.0 0.351 18 5000

Test 20 FPA, DB 200 6.0 4.0 3.0 0.240 16 6000

Test 21 FPA, DB 200 6.0 4.0 3.0 0.116 23 6000

Test 22 FPA, DB 200 6.0 4.0 3.0 0.225 30 500

Test 23 FPA, DB 200 6.0 4.0 3.0 0.249 28 4000

Test 24 FPA, DB 200 6.0 4.0 3.0 0.235 26 1000

Test 25 FPA, DB 200 6.0 4.0 3.0 0.233 25 2000

74
Test Correlation Q ̇ L W H m ̇ T∞ tend

(kW) (m) (m) (m) (kg/s) (

◦C) (s)

Test 26 FPA, DB 200 6.0 4.0 3.0 0.586 24 4000

Test 27 FPA, DB 200 6.0 4.0 3.0 0.116 23 500

Test 28 FPA, DB 150 6.0 4.0 3.0 0.174 31 1000

Test 29 FPA, DB 250 6.0 4.0 3.0 0.298 28 1000

Test 30 FPA, DB 250 6.0 4.0 3.0 0.349 34 4000

Test 31 FPA, DB 250 6.0 4.0 3.0 0.576 36 4000

Test 32 FPA, DB 100 6.0 4.0 3.0 0.110 33 4000

Test 33 FPA, DB 100 6.0 4.0 3.0 0.230 23 5000

Test 34 FPA, DB 100 6.0 4.0 3.0 0.342 34 4000

Test 35 FPA, DB 100 6.0 4.0 3.0 0.455 22 4000

Test 36 FPA, DB 100 6.0 4.0 3.0 0.582 29 4000

Test 37 FPA, DB 170 6.0 4.0 3.0 0.111 20 500

Test 38 FPA, DB 200 6.0 4.0 3.0 0.346 29 4000

Test 39 FPA, DB 250 6.0 4.0 3.0 0.107 18 500

Test 40 FPA, DB 200 6.0 4.0 3.0 0.467 28 4000

Test 41 FPA, DB 150 6.0 4.0 3.0 0.126 20 500

Test 42 FPA, DB 200 6.0 4.0 3.0 0.206 30 5000

Test 43 Beyler 200 6.0 4.0 3.0 - 32 500

Test 44 FPA, DB 200 6.0 4.0 3.0 0.213 19 2000

Test 45 Beyler 200 6.0 4.0 3.0 - 30 500

Test 46 FPA, DB 200 6.0 4.0 3.0 0.201 19 500

Test 47 Beyler 200 6.0 4.0 3.0 - 19 500

Test 48 Beyler 165 6.0 4.0 3.0 - 21 500

Test 49 FPA, DB 200 6.0 4.0 3.0 0.208 26 500

Test 50 FPA, DB 200 6.0 4.0 3.0 0.222 21 4000

Test 51 MQH 200 6.0 4.0 3.0 - 33 3000

Test 52 MQH 200 6.0 4.0 3.0 - 23 4000

Test 53 FPA, DB 200 6.0 4.0 3.0 0.214 33 1000

Test 54 FPA, DB 200 6.0 4.0 3.0 0.248 21 4000

Test 55 MQH 100 6.0 4.0 3.0 - 31 4000

Test 56 FPA, DB 200 6.0 4.0 3.0 0.221 20 1000

Test 57 FPA, DB 200 6.0 4.0 3.0 0.247 29 5000

Test 58 FPA, DB 200 6.0 4.0 3.0 0.220 18 4000

Test 59 FPA, DB 200 6.0 4.0 3.0 0.214 24 4000

Test 60 MQH 400 6.0 4.0 3.0 - 22 2000

Test 61 MQH 200 6.0 4.0 4.5 - 31 2000

Test 62 MQH 400 6.0 4.0 4.5 - 22 2000

Test 63 MQH 50 6.0 4.0 4.5 - 28 3000

Test 64 MQH 100 6.0 4.0 4.5 - 17 3000

75
A.6 NBS Multi-Room

HGL Temperature [24]

Table A.9: Summary of validation input parameters used for NBS Multi-Room cases [12], HGL temperature.

Input Parameter Value

Q ̇ (kW) 100

L (m) 2.34

W (m) 2.34

H (m) 2.16

Ho (m) 1.6

Wo (m) 0.81

k (kW/(m·K)) 0.00017

ρ (kg/m3) 128

c (kJ/(kg ·K)) 1.04

δ (m) 0.05

tend (s) 1200

Test Correlation T∞

(

◦C)

Test 100A MQH 23

Test 100O MQH 21

Test 100Z MQH 22

76
A.7 NIST/NRC

HGL Temperature and Depth [24, 26, 30]

For the cases with natural ventilation (MQH), the door size was 2.0 m high by 2.0 m wide.

Table A.10: Summary of validation input parameters used for NIST/NRC cases [13], HGL temperature and

depth.

Input Parameter Value

L (m) 21.66

W (m) 7.04

H (m) 3.82

cp (kJ/(kg ·K)) 1.0

k (kW/(m·K)) 0.00012

ρ (kg/m3) 737

c (kJ/(kg ·K)) 1.42

δ (m) 0.0254

Location Factor 1

Heat Loss Fraction 0

Fuel Height 0

Test Correlation Q ̇ m ̇ Ho Wo T∞ tend

(kW) (kg/s) (m) (m) (

◦C) (s)

Test 1 Beyler 410 - - - 22 1350

Test 2 Beyler 1190 - - - 26 625

Test 3 MQH 1190 - 2.0 2.0 30 1380

Test 4 FPA, DB 1200 1.3 - - 27 816

Test 5 MQH 1190 - 2.0 2.0 28 1380

Test 7 Beyler 400 - - - 24 1330

Test 8 Beyler 1190 - - - 25 610

Test 9 MQH 1170 - 2.0 2.0 27 1380

Test 10 FPA, DB 1190 1.3 - - 27 826

Test 13 Beyler 2330 - - - 31 265

Test 14 MQH 1180 - 2.0 2.0 28 1380

Test 15 MQH 1180 - 2.0 2.0 18 1380

Test 16 FPA, DB 2300 1.3 - - 26 380

Test 17 Beyler 1160 - - - 29 272

Test 18 MQH 1180 - 2.0 2.0 27 1380

77
Point Source and Solid Flame Radiation Heat Flux [34]

Table A.11: Summary of validation input parameters used for NIST/NRC cases [13], radiation heat flux.

Input Parameter Value

x (m) 3.14, 2.33, 2.18, 1.58, 3.27

z (m) 2.05, 2.52, 2.54, 3.04, 1.76

IOR -3, -3, 2, -3, -2

Test Q ̇ χr A

(kW) (m2)

Test 1 410 0.44 0.671

Test 2 1190 0.44 1.028

Test 3 1190 0.44 1.028

Test 4 1200 0.44 1.032

Test 5 1190 0.44 1.028

Test 7 400 0.44 0.665

Test 8 1190 0.44 1.028

Test 9 1170 0.44 1.021

Test 10 1190 0.44 1.028

Test 13 2330 0.44 1.345

Test 14 1180 0.44 1.025

Test 15 1180 0.44 1.025

Test 16 2300 0.44 1.338

Test 17 1160 0.40 1.018

Test 18 1180 0.44 1.025

78
Ceiling Jet Temperature (Alpert) [35]

Table A.12: Summary of validation input parameters used for NIST/NRC cases [13], ceiling jet temperature.

Input Parameter Value

Location Factor 1

r (m) 5.9

H (m) 3.72

Test Q ̇ T∞

(kW) (

◦C)

Test 1 410 22

Test 2 1190 26

Test 3 1190 30

Test 4 1200 27

Test 5 1190 28

Test 7 400 24

Test 8 1190 25

Test 9 1170 27

Test 10 1190 27

Test 13 2330 31

Test 14 1180 28

Test 15 1180 18

Test 16 2300 26

Test 17 1160 29

Test 18 1180 27

79
A.8 NIST Smoke Alarms

Ceiling Jet Temperature (Alpert) [35]

Table A.13: Summary of validation input parameters used for NIST Smoke Alarms cases [14], ceiling jet

temperature.

Input Parameter Value

Location Factor 1

H (m) 2.1

tend (s) 300

Test α r T∞

(kW/s2) (m) (

◦C)

Test SDC02 0.00463 1.15 21

Test SDC05 0.00617 1.25 22

Test SDC07 0.01080 1.25 24

Test SDC10 0.00463 1.15 26

Test SDC33 0.00309 1.15 26

Test SDC35 0.00309 1.15 26

Test SDC38 0.00370 1.25 25

Test SDC39 0.00617 1.25 25

80
Smoke Detector Activation Time (Temperature Rise) [35, 37]

The fire growth was specified as Q ̇ = αt

2 up to a cutoff time of tfire. After the time tfire, the fire HRR was

steady.

Table A.14: Summary of validation input parameters used for NIST Smoke Alarms cases [14], smoke

detector activation time.

Input Parameter Value

Location Factor 1

tfire (s) 300

∆Tc (

◦C) 5

RTI ((m·s)1/2) 5

Test α r H T∞

(kW/s2) (m) (m) (

◦C)

Test SDC02 0.00463 1.3 2.1 21

Test SDC05 0.00617 1.8 2.0 22

Test SDC07 0.01080 1.8 2.0 24

Test SDC10 0.00463 1.3 2.1 26

Test SDC33 0.00309 1.3 2.1 26

Test SDC35 0.00309 1.3 2.1 26

Test SDC38 0.00370 1.3 2.1 25

Test SDC39 0.00617 1.8 2.0 25

81
A.9 SP AST

HGL Temperature [24]

Table A.15: Summary of validation input parameters used for SP AST cases, HGL temperature.

Input Parameter Value

Q ̇ (kW) 450

L (m) 3.6

W (m) 3.6

H (m) 2.4

Ho (m) 2.0

Wo (m) 0.8

k (kW/(m·K)) 0.0001

ρ (kg/m3) 600

c (kJ/(kg ·K)) 0.8

δ (m) 0.2

T∞ (

◦C) 20

Test Correlation tend

(s)

Test 1 MQH 2400

Test 2 MQH 2400

Test 3 MQH 3600

82
Steel Temperature (Unprotected) [33]

The HGL temperatures from the MQH HGL temperature correlation were used as the input fire temperature Tf

.

Table A.16: Summary of validation input parameters used for SP AST cases [15], unprotected steel temperature.

Input Parameter Value

ρs (kg/m3) 7833

cs (kJ/(kg ·K)) 0.465

ε 0.7

hc (W/(m2·K)) 25

Test Correlation F/V tend

for Tf (1/m) (s)

Test 1 MQH 125 2400

Test 2 MQH 157 2400

Test 3 MQH 157 3600

83
Ceiling Jet Temperature (Alpert) [35]

Table A.17: Summary of validation input parameters used for SP AST cases [15], ceiling jet temperature.

Input Parameter Value

Q ̇ (kW) 450

H (m) 1.65

T∞ (

◦C) 20

Test Location Factor r

(m)

Test 1 4 1.22

Test 2 4 1.22

Test 3 2 0.70

84
A.10 SP AST Column

Plume Temperature (Heskestad and McCaffrey) [31, 32]

Note that the Heskestad correlation did not use heights of 1 m and 2 m because it is valid only above the

flame region.

Table A.18: Summary of validation input parameters used for SP AST Column cases [16], plume temperature.

Input Parameter Value

z (m) 1, 2, 3, 4, 5

χr 0.35

cp (kJ/(kg ·K)) 1.0

T∞ (

◦C) 20

Test Q ̇ A

(kW) (m2)

Diesel, 1.1 m 1434 0.95

Diesel, 1.9 m 1873 0.95

Heptane, 1.1 m 2275 2.83

85
Steel Temperature (Unprotected) [33]

The HGL temperatures from the McCaffrey plume temperature correlation were used as the input fire temperature Tf

.

Table A.19: Summary of validation input parameters used for SP AST Column cases [16], unprotected steel

temperature.

Input Parameter Value

F/V (1/m) 205

ρs (kg/m3) 7833

cs (kJ/(kg ·K)) 0.465

ε 0.7

hc (W/(m2·K)) 25

Test Correlation Q ̇ tend

for Tf (kW) (s)

Diesel, 1.1 m McCaffrey 1434 1620

Diesel, 1.9 m McCaffrey 1873 1080

Heptane, 1.1 m McCaffrey 2275 900

86
A.11 Steckler

HGL Temperature [24]

Table A.20: Summary of validation input parameters used for Steckler cases [17], HGL temperature.

Input Parameter Value

L (m) 2.8

W (m) 2.8

H (m) 2.13

k (kW/(m·K)) 0.0001

ρ (kg/m3

) 200

c (kJ/(kg ·K)) 1.0

δ (m) 0.013

Test Correlation Q ̇ Ho Wo T∞

(kW) (m) (m) (

◦C)

Test 10 MQH 62.9 1.83 0.24 22

Test 11 MQH 62.9 1.83 0.36 25

Test 12 MQH 62.9 1.83 0.49 19

Test 612 MQH 62.9 1.83 0.49 19

Test 13 MQH 62.9 1.83 0.62 20

Test 14 MQH 62.9 1.83 0.74 28

Test 18 MQH 62.9 1.83 0.74 29

Test 710 MQH 62.9 1.83 0.74 13

Test 810 MQH 62.9 1.83 0.74 15

Test 16 MQH 62.9 1.83 0.86 23

Test 17 MQH 62.9 1.83 0.99 19

Test 22 MQH 62.9 1.38 0.74 26

Test 23 MQH 62.9 0.92 0.74 23

Test 30 MQH 62.9 0.92 0.74 23

Test 41 MQH 62.9 0.46 0.74 14

Test 19 MQH 31.6 1.83 0.74 29

Test 20 MQH 105.3 1.83 0.74 29

Test 21 MQH 158. 1.83 0.74 29

Test 114 MQH 62.9 1.83 0.24 31

Test 144 MQH 62.9 1.83 0.36 30

Test 212 MQH 62.9 1.83 0.49 25

Test 242 MQH 62.9 1.83 0.62 29

Test 410 MQH 62.9 1.83 0.74 21

87
Test Correlation Q ̇ Ho Wo T∞

(kW) (m) (m) (

◦C)

Test 210 MQH 62.9 1.83 0.74 30

Test 310 MQH 62.9 1.83 0.74 20

Test 240 MQH 62.9 1.83 0.86 28

Test 116 MQH 62.9 1.83 0.99 29

Test 122 MQH 62.9 1.38 0.74 27

Test 224 MQH 62.9 0.92 0.74 26

Test 324 MQH 62.9 0.92 0.74 22

Test 220 MQH 31.6 1.83 0.74 25

Test 221 MQH 105.3 1.83 0.74 25

Test 514 MQH 62.9 1.83 0.24 8

Test 544 MQH 62.9 1.83 0.36 8

Test 512 MQH 62.9 1.83 0.49 20

Test 542 MQH 62.9 1.83 0.62 20

Test 610 MQH 62.9 1.83 0.74 18

Test 510 MQH 62.9 1.83 0.74 22

Test 540 MQH 62.9 1.83 0.86 13

Test 517 MQH 62.9 1.83 0.99 14

Test 622 MQH 62.9 1.38 0.74 9

Test 522 MQH 62.9 1.38 0.74 13

Test 524 MQH 62.9 0.92 0.74 8

Test 541 MQH 62.9 0.46 0.74 7

Test 520 MQH 31.6 1.83 0.74 17

Test 521 MQH 105.3 1.83 0.74 13

Test 513 MQH 158. 1.83 0.74 14

Test 160 MQH 62.9 1.83 0.74 6

Test 163 MQH 62.9 1.83 0.74 6

Test 164 MQH 62.9 1.83 0.74 6

Test 165 MQH 62.9 1.83 0.74 6

Test 162 MQH 62.9 1.83 0.74 6

Test 167 MQH 62.9 1.83 0.74 6

Test 161 MQH 62.9 1.83 0.74 6

Test 166 MQH 62.9 1.83 0.74 6

88
A.12 UL/NFPRF

Ceiling Jet Temperature (Alpert) [35]

Table A.21: Summary of validation input parameters used for UL/NFPRF cases [18, 19], ceiling jet temperature.

Input Parameter Value

Location Factor 1

r (m) 2.12, 4.74, 6.36, 10.61, 12.90, 13.58, 14.23, 14.85, 17.10, 19.09, 21.32

H (m) 7.1

T∞ (

◦C) 18

Test Q ̇

(kW)

I-17 4600

I-18 3700

I-19 4600

I-20 4200

I-21 4600

I-22 4600

89
Sprinkler Activation Time [35]

The fire growth was specified as Q ̇ = αt

2 up to a cutoff time of tfire. After the time tfire, the fire HRR was

steady.

Table A.22: Summary of validation input parameters used for UL/NFPRF cases [18, 19], sprinkler activation

time.

Input Parameter Value

α (kW/s2) 1.778

Location Factor 1

RTI ((m·s)1/2) 148

Tact (

◦C) 74

H (m) 7.0

T∞ (

◦C) 18

Test tfire r Test tfire r

(s) (m) (s) (m)

I-1 50 2.12 II-1 75 1.5

I-2 50 2.12 II-2 75 1.5

I-3 50 2.12 II-3 75 1.5

I-4 50 2.12 II-4 75 1.5

I-5 50 2.12 II-5 75 1.5

I-6 50 2.12 II-6 75 1.5

I-7 50 2.12 II-7 75 1.5

I-8 50 2.12 II-8 75 1.5

I-9 50 2.12 II-9 75 2.12

I-10 50 2.12 II-10 75 2.12

I-11 50 2.12 II-11 75 1.5

I-12 50 2.12 II-12 75 1.5

I-13 58 2.12 1.5

I-14 57 2.12 1.5

I-15 57 2.12 1.5

I-16 106 2.12 1.5

I-17 51 2.12 1.5

I-18 47 2.12 1.5

I-19 51 2.12 1.5

I-20 49 2.12 1.5

I-21 51 2.12 1.5

I-22 51 2.12 1.5

90
A.13 USN Hawaii

Plume Temperature (Heskestad and McCaffrey) [31, 32]

The fire growth was specified as Q ̇ = αt

2 up to a cutoff time of tfire. After the time tfire, the fire HRR was

steady.

Table A.23: Summary of validation input parameters used for USN Hawaii cases [20], plume temperature.

Input Parameter Value

z (m) 8.7, 11.8, 13.3, 14.5

χr 0.35

cp (kJ/(kg ·K)) 1.0

Test α tfire Q ̇ A T∞

(kW/s2) (s) (kW) (m2) (

◦C)

Test 1 0.00694 120 100 0.09 27

Test 2 0.02222 150 500 0.36 28

Test 3 0.04889 150 1100 0.81 27

Test 4 0.09133 180 2959 1.69 27

Test 5 0.48597 120 6998 3.24 27

Test 6 0.33773 150 7599 4.84 25

Test 7 0.17799 180 5767 3.24 30

Test 11 0.00444 150 100 0.09 30

91
A.14 USN Iceland

Plume Temperature (Heskestad and McCaffrey) [31, 32]

Table A.24: Summary of validation input parameters used for USN Hawaii cases [20], plume temperature.

Input Parameter Value

z (m) 15.7, 17.2, 18.8, 20.3, 21.5

χr 0.35

cp (kJ/(kg ·K)) 1.0

Test Q ̇ A T∞

(kW) (m2) (

◦C)

Test 1 88 0.09 10

Test 2 60 0.09 10

Test 3 720 0.36 11

Test 4 684 0.36 14

Test 5 1134 0.81 17

Test 6 1296 0.81 16

Test 7 2736 1.44 16

Test 9 153 0.09 9

Test 10 612 0.36 9

Test 11 648 0.36 9

Test 12 1512 0.36 9

Test 13 2700 1.44 11

Test 14 7802 4.84 12

Test 15 15300 9.00 12

Test 17 15750 9.00 11

Test 18 4918 3.24 10

Test 19 8712 4.84 13

Test 20 14850 9.00 14

92
A.15 Vettori Flat Ceiling

Ceiling Jet Temperature (Alpert) [35]

Table A.25: Summary of validation input parameters used for Vettori Flat cases [21], ceiling jet temperature.

Only the smooth, unobstructed ceiling tests were included in this study. The fire growth was specified as

Q ̇ = αt

2 up to a cutoff time of tfire. After the time tfire, the fire HRR was steady.

Input Parameter Value

H (m) 2.075

Test α tfire r Location T∞

(kW/s2) (s) (m) Factor (

◦C)

Test 1 0.105 50 2.2, 2.2 1 16.6

Test 2 0.105 50 2.2, 2.2 1 19.0

Test 3 0.105 50 2.2, 2.2 1 20.8

Test 6 0.017 80 2.2, 2.2 1 17.1

Test 7 0.017 80 2.2, 2.2 1 21.6

Test 8 0.017 80 2.2, 2.2 1 21.8

Test 11 0.0041 100 2.2, 2.2 1 18.1

Test 12 0.0041 140 2.2, 2.2 1 21.0

Test 13 0.0041 130 2.2, 2.2 1 22.0

Test 16 0.105 45 2.4, 2.4 2 20.7

Test 17 0.105 42 2.4, 2.4 2 20.4

Test 18 0.105 35 2.4, 2.4 2 20.3

Test 21 0.017 70 2.4, 2.4 2 21.1

Test 22 0.017 70 2.4, 2.4 2 21.7

Test 23 0.017 70 2.4, 2.4 2 21.8

Test 26 0.0041 130 2.4, 2.4 2 21.5

Test 27 0.0041 130 2.4, 2.4 2 22.5

Test 28 0.0041 120 2.4, 2.4 2 22.7

Test 31 0.105 37 2.1, 6.59 4 20.2

Test 32 0.105 30 2.1, 6.59 4 21.9

Test 33 0.105 30 2.1, 6.59 4 21.7

Test 36 0.017 50 2.1, 6.59 4 22.3

Test 37 0.017 47 2.1, 6.59 4 22.3

Test 38 0.017 50 2.1, 6.59 4 21.7

Test 41 0.0041 100 2.1, 6.59 4 21.6

Test 42 0.0041 85 2.1, 6.59 4 22.4

Test 43 0.0041 85 2.1, 6.59 4 21.6

93
Sprinkler Activation Time [35]

The fire growth was specified as Q ̇ = αt

2 up to the time of the first sprinkler activation.

Table A.26: Summary of validation input parameters used for Vettori Flat cases [21], sprinkler activation

time.

Input Parameter Value

RTI ((m·s)1/2) 55

Tact (

◦C) 68

H (m) 2.09

Test α r Location T∞

(kW/s2) (m) Factor (

◦C)

Test 1 0.105 2.2 1 16.6

Test 2 0.105 2.2 1 19.0

Test 3 0.105 2.2 1 20.8

Test 6 0.017 2.2 1 17.1

Test 7 0.017 2.2 1 21.6

Test 8 0.017 2.2 1 21.8

Test 11 0.0041 2.2 1 18.1

Test 12 0.0041 2.2 1 21.0

Test 13 0.0041 2.2 1 22.0

Test 16 0.105 2.4 2 20.7

Test 17 0.105 2.4 2 20.4

Test 18 0.105 2.4 2 20.3

Test 21 0.017 2.4 2 21.1

Test 22 0.017 2.4 2 21.7

Test 23 0.017 2.4 2 21.8

Test 26 0.0041 2.4 2 21.5

Test 27 0.0041 2.4 2 22.5

Test 28 0.0041 2.4 2 22.7

Test 31 0.105 2.1 4 20.2

Test 32 0.105 2.1 4 21.9

Test 33 0.105 2.1 4 21.7

Test 36 0.017 2.1 4 22.3

Test 37 0.017 2.1 4 22.3

Test 38 0.017 2.1 4 21.7

Test 41 0.0041 2.1 4 21.6

Test 42 0.0041 2.1 4 22.4

Test 43 0.0041 2.1 4 21.6

94
A.16 VTT Large Hall

Plume Temperature (Heskestad and McCaffrey) [31, 32]

The fire ramp was specified as Q ̇

ramp with a corresponding tramp. For example, a fire growing linearly over

time 0 s to 100 s from 0 kW to 500 kW would be specified with a tramp of [0, 100] and a Q ̇

ramp of [0, 500].

Table A.27: Summary of validation input parameters used for VTT Large Hall cases [22], plume temperature.

Input Parameter Value

z (m) 6, 12

χr 0.40

cp (kJ/(kg ·K)) 1.0

Test tramp Q ̇

ramp A T∞

(s) (kW) (m2) (

◦C)

Test 1 13, 90, 288, 327, 409 1245, 1309, 1858, 1783, 1356 1.075 25

Test 2 14, 30, 91, 193, 282, 340, 372 2151, 2542, 3063, 3259, 3129, 2737, 2281 2.01 22

Test 3 13, 63, 166, 256, 292, 330 2437, 3201, 3601, 3638, 3456, 2656 2.01 22

95
A.17 WTC

HGL Temperature [24]

Table A.28: Summary of validation input parameters used for WTC cases [23], HGL temperature.

Input Parameter Value

L (m) 7.04

W (m) 3.60

H (m) 3.82

Ho (m) 2.82

Wo (m) 2.4

k (kW/(m·K)) 0.00012

ρ (kg/m3) 737

c (kJ/(kg ·K)) 1.42

δ (m) 0.0254

Test Correlation Q ̇ tend T∞

(kW) (s) (

◦C)

Test 1 MQH 2000 870 24

Test 2 MQH 2400 380 25

Test 3 MQH 2000 990 20

Test 4 MQH 3200 840 20

Test 5 MQH 3000 3080 20

Test 6 MQH 3000 3030 20

96
Steel Temperature (Unprotected) [33]

The HGL temperatures from the MQH HGL temperature correlation were used as the input fire temperature Tf

. The inputs for the MQH correlation are described in the WTC HGL temperature section.

Table A.29: Summary of validation input parameters used for WTC cases [23], unprotected steel temperature.

Input Parameter Value

ρs (kg/m3) 7860

cs (kJ/(kg ·K)) 0.450

ε 0.7

hc (W/(m2·K)) 25

Test Correlation Structural F/V

for Tf Element (1/m)

Test 1 MQH Bar 157

Test 2 MQH Bar 157

Test 3 MQH Bar 157

Test 1 MQH Column 159

Test 2 MQH Column 159

Test 3 MQH Column 159

Test 1 MQH Truss A 156

Test 2 MQH Truss A 156

Test 3 MQH Truss A 156

Test 1 MQH Truss B 156

Test 2 MQH Truss B 156

Test 3 MQH Truss B 156

97
Steel Temperature (Protected) [33]

The HGL temperatures from the MQH HGL temperature correlation were used as the input fire temperature Tf

. The inputs for the MQH correlation are described in the WTC HGL temperature section.

Table A.30: Summary of validation input parameters used for WTC cases [23], protected steel temperature.

Input Parameter Value

cs (kJ/(kg ·K)) 0.450

ki (W/(m·K)) 0.10

ρi (kg/m3) 208

ci (kJ/(kg ·K)) 2.0

Test Correlation Structural hi W/D

for Tf Element (m) (kg/m2)

Test 4 MQH Bar 0.0191 50.1

Test 5 MQH Bar 0.0191 50.1

Test 6 MQH Bar 0.0191 50.1

Test 4 MQH Column 0.0381 49.4

Test 5 MQH Column 0.0381 49.4

Test 6 MQH Column 0.0381 49.4

Test 4 MQH Truss A 0.0191 50.3

Test 5 MQH Truss A 0.0191 50.3

Test 6 MQH Truss A 0.0191 50.3

Test 4 MQH Truss B 0.0381 50.3

Test 5 MQH Truss B 0.0381 50.3

Test 6 MQH Truss B 0.0381 50.3

98
Point Source and Solid Flame Radiation Heat Flux [34]

Table A.31: Summary of validation input parameters used for WTC cases [23], radiation heat flux.

Input Parameter Value

x (m) 0.90, 0.82, 0.71, 0.77, 1.23, 1.34, 1.23, 1.34, 1.07, 1.56, 0.57, 0.35, 0.87, 2.58

z (m) 3.3, 3.3, 3.15, 3.15, 3.46, 3.27, 0.92, 1.02, 0.13, 0.13, 3.82, 3.82, 3.82, 3.82

IOR 3, 3, -3, -3, 1, 2, 1, 2, 3, 3, -3, -3, -3, -3

Test Q ̇ χr A

(kW) (m2)

Test 1 2000 0.44 1.258

Test 2 2400 0.39 1.455

Test 3 2000 0.39 1.258

Test 4 3200 0.44 1.832

Test 5 3000 0.44 1.739

Test 6 3000 0.44 1.739

99
Ceiling Jet Temperature (Alpert) [35]

Table A.32: Summary of validation input parameters used for WTC cases, ceiling jet temperature.

Input Parameter Value

Location Factor 1

r (m) 2, 3

H (m) 3.72

Test Q ̇ T∞

(kW) (

◦C)

Test 1 2000 24

Test 2 2400 25

Test 3 2000 20

Test 4 3200 20

Test 5 3000 20

Test 6 3000 20

100