NIST Special Publication 1030

CFAST – Consolidated Model of Fire

Growth and Smoke Transport

(Version 5)

Technical Reference Guide

Walter W. Jones

Richard D. Peacock

Glenn P. Forney

Paul A. Reneke

CFAST – Consolidated Model of Fire

Growth and Smoke Transport

(Version 5)

Technical Reference Guide

Walter W. Jones

Richard D. Peacock

Glenn P. Forney

Paul A. Reneke

Fire Research Division

Building and Fire Research Laboratory

October 2004

U.S. Department of Commerce

Donald L. Evans, Secretary

Technology Administration

Phillip J. Bond, Under Secretary for Technology

National Institute of Standards and Technology

Arden L. Bement, Jr., 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 1030

Natl. Inst. Stand. Technol. Spec. Pub. 1030, 138 pages (October 2004)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 2004

_________________________________________

For sale by the Superintendent of Documents, U.S. Government Printing Office

Internet: bookstore.gpo.gov — Phone: (202) 512-1800 — Fax: (202) 512-2250

Mail: Stop SSOP, Washington, DC 20402-0001
iii

Bibliographic Information

Abstract

CFAST is a two-zone fire model capable of predicting the environment in a multi-compartment

structure subjected to a fire. It calculates the time evolving distribution of smoke and fire gases

and the temperature throughout a building during a user-prescribed fire. This report describes

the equations which constitute the model, the physical basis for these equations, and an

evaluation of the sensitivity and predictive capability of the model. 

This report is an assessment of the model following the outline set forth in ASTM E1355,

“Standard Guide for Evaluating the Predictive Capability of Deterministic Fire Models.”

Keywords

Model assessment, validation, verification, fire growth, smoke transport, computer models; fire

models; fire research; hazard assessment; toxicity
iv
v

DISCLAIMER

The U. S. Department of Commerce makes no warranty, expressed or implied, to users of -

CFAST and associated computer programs, and accepts no responsibility for its use. Users of

CFAST assume sole responsibility under Federal law for determining the appropriateness of its

use in any particular application; for any conclusions drawn from the results of its use; and for

any actions taken or not taken as a result of analyses performed using these tools.

CFAST is intended for use only by those competent in the field of fire safety and is intended

only to supplement the informed judgment of a qualified user. The software package is a

computer model which may or may not have predictive value when applied to a specific set of

factual circumstances. Lack of accurate predictions by the model could lead to erroneous

conclusions with regard to fire safety. All results should be evaluated by an informed user.

INTENT AND USE

The algorithms, procedures, and computer programs described in this report constitute a

methodology for predicting some of the consequences resulting from a prescribed fire. They

have been compiled from the best knowledge and understanding currently available, but have

important limitations that must be understood and considered by the user. The program is

intended for use by persons competent in the field of fire safety and with some familiarity with

personal computers. It is intended as an aid in the fire safety decision-making process.
vi
vii

Contents

Contents .................................................................. vii

Figures and Tables ........................................................... xi

Executive Summary ......................................................... xv

Nomenclature ............................................................. xvii

1 Introduction ............................................................... 1

1.1 History............................................................. 1

1.2 Model Evaluation .................................................... 2

2 Model and Scenario Definition ................................................ 5

2.1 Model Documentation ................................................ 5

2.1.1 Name and Version of the Model ................................. 5

2.1.2 Type of Model ............................................... 5

2.1.3 Model Developers ............................................ 6

2.1.4 Relevant Publications.......................................... 6

2.1.5 Governing Equations and Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.6 Input Data Required to Run the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.7 Property Data ................................................ 7

2.1.8 Model Results ............................................... 8

2.1.9 Uses and Limitations of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Scenarios for which the Model is Evaluated in this Document . . . . . . . . . . . . . . . . 10

2.2.1 Description of Scenarios of Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.2 List of Quantities Predicted by the Model . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.3 Degree of Accuracy Required for Each Output Quantity . . . . . . . . . . . . . 11

3 Theoretical Basis for CFAST ................................................ 13

3.1 Derivation of Equations for a Two-Layer Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.2 Equation Set Used in CFAST .......................................... 17

3.3 Limitations of the Zone Model Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.4 Source Terms for the Model ........................................... 19

3.4.1 The Fire ................................................... 19

3.4.2 Plumes .................................................... 25

3.4.3 Vent Flow .................................................. 29

3.4.4 Corridor Flow............................................... 47
viii

3.4.5 Heat Transfer ............................................... 52

3.4.6 Ceiling Jet ................................................. 64

3.5 Heat Detection ..................................................... 67

3.6 Sprinkler Activation and Fire Attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.7 Species Concentration and Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.7.1 Species Transport ............................................ 70

3.7.2 HCl Deposition ............................................. 71

3.8 Flame Spread ...................................................... 73

3.9 Single Zone Approximation ........................................... 74

3.10 Review of the Theoretical Development of the Model . . . . . . . . . . . . . . . . . . . . . . 74

3.10.1 Assessment of the Completeness of Documentation . . . . . . . . . . . . . . . . 76

3.10.2 Assessment of Justification of Approaches and Assumptions . . . . . . . . . 76

3.10.3 Assessment of Constants and Default Values . . . . . . . . . . . . . . . . . . . . . 77

4 Mathematical and Numerical Robustness ...................................... 79

4.1 Introduction ........................................................ 79

4.2 Structure of the Numerical Routines ..................................... 79

4.2.1 Subroutine Structure ......................................... 80

4.3 Code Checking ..................................................... 81

4.4 Numerical Tests..................................................... 82

4.5 Comparison with Analytic Solutions .................................... 83

5 Sensitivity of the Model ..................................................... 85

5.1 Factorial Design Studies .............................................. 85

5.1.1 Model Inputs and Outputs ..................................... 86

5.1.2 Sensitivity to Small Changes in Model Inputs . . . . . . . . . . . . . . . . . . . . . . 89

5.1.3 Sensitivity to Larger Changes in Model Inputs . . . . . . . . . . . . . . . . . . . . . 90

5.2 Response Surface Studies ............................................. 91

5.3 Latin Hypercube Sampling Studies ...................................... 95

5.4 Summary .......................................................... 95

6 Validation of the Model ..................................................... 97

6.1 Comparisons with Full-Scale Tests Conducted Specifically for 

the Chosen Evaluation ............................................. 97

6.2 Comparisons with Previously Published Test Data . . . . . . . . . . . . . . . . . . . . . . . . . 99

6.2.1 Experimental Data Selected for Comparison . . . . . . . . . . . . . . . . . . . . . . . 99

6.2.2 Layer Temperature and Interface Position . . . . . . . . . . . . . . . . . . . . . . . . 101

6.2.3 Gas Species ............................................... 106

6.2.4 Heat Release and Fuel Pyrolysis Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

6.2.5 Pressure .................................................. 111

6.2.6 Flow Through Openings ..................................... 114

6.2.7 Plume Model .............................................. 115
ix

6.2.8 Other Comparisons with Previously Published Test Data . . . . . . . . . . . . 115

6.3 Prediction of Flashover .............................................. 117

6.4 Comparison with Documented Fire Experience . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

6.5 Comparison with Experiments Which Cover Special Situations . . . . . . . . . . . . . . 120

6.5.1 Nuclear Facilities ........................................... 120

6.5.2 Small Scale Testing ......................................... 121

6.5.3 Unusual Geometry and Specific Algorithms . . . . . . . . . . . . . . . . . . . . . . 121

6.6 Summary ......................................................... 123

7 Conclusion .............................................................. 125

8 References ............................................................... 127
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xi

Figures and Tables

Figures

Figure 1. Zone model terms. ..................................................... 2

Figure 2. Schematic of control volumes in a two-layer zone model. . . . . . . . . . . . . . . . . . . . . . 14

Figure 3. Schematic of entrainment and burning regions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Figure 4. Notation conventions for two-layer model in two compartments

with a connecting vent. .................................................. 31

Figure 5. Flow patterns and layer numbering convention. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Figure 6. Some simple fan-duct systems............................................ 36

Figure 7. Network representation of a residential system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Figure 8. Typical fan performance at constant speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Figure 9. Some approaches to approximation of fan performance

for computer simulation ................................................. 42

F 10 igure 10. Log of the relative temperature excess downstream in a corridor using an adiabatic

temperature boundary condition for several inlet depths and inlet temperature boundary

condition. The inlet velocity 0, V , is given by eq (92). ........................... 51

Figure 11. Radiation exchange in a two-zone fire model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Figure 12. An example of the calculated two-wall (RAD2) and four-wall (RAD4) contributions

to radiation exchange on a ceiling and wall surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Figure 13. Setup for a configuration factor calculation between two arbitrarily oriented finite

areas ................................................................. 56

Figure 14. Radiative heat transfer from a point source fire to a target. . . . . . . . . . . . . . . . . . . . . 59

Figure 15. Radiative heat transfer from the upper and lower layer gas layers to a target in the

lower layer. ............................................................ 60

Figure 16. Convective heat transfer to ceiling and wall

surfaces via the ceiling jet. ................................................ 65

Figure 17. Schematic of hydrogen chloride deposition region. . . . . . . . . . . . . . . . . . . . . . . . . . 71

Figure 18. Subroutine structure for the CFAST Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Figure 19. Building geometry for base case scenario. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

Figure 20. Characterization of heat release rate of growing fires as t fires. . . . . . . . . . . . . . . . .

2

88

Figure 21. An example of time dependent sensitivity of fire model outputs to a 10 % change in

room volume for a single room fire scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Figure 22. Layer temperatures and volumes in several rooms resulting from variation in heat

release rate for a four-room growing fire scenario. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

Figure 23. Comparison of the time dependent heat release rate and layer temperatures in 

several rooms for a four-room growing fire scenario. . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

Figure 24. Sensitivity of temperature to heat release rate for a four-room growing fire scenario. 92
xii

Figure 25. Comparison of heat release rate and upper layer volume in several rooms for a fourroom growing fire scenario. ............................................... 93

Figure 26. Effect of both heat release rate and vent opening size on upper layer temperature for a

four-room growing fire scenario. ........................................... 94

Figure 27. Comparison of measured and predicted upper layer temperatures for several tests. 104

Figure 28. Comparison of measured and predicted lower layer temperatures for several tests. 105

Figure 29. Comparison of measured and predicted layer interface position for several tests. . 105

Figure 30. Comparison of measured and predicted gas species concentrations for several 

tests. ................................................................ 107

Figure 31. Comparison of measured and prescribed heat release rates for two selected tests. . 110

Figure 32. Comparison of measured and predicted pressures for several tests.

.................................................................... 112

Figure 33. Effect of leakage in an arbitrary single-room fire. . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Figure 34. Comparison of measured and predicted mass flow through vents for several tests.

(Numbers indicate comparable rooms in the test structure.) . . . . . . . . . . . . . . . . . . . . . 115

Figure 35. Comparison of correlations, CFAST predictions, and experimental data for the

prediction of flashover in a compartment fire. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

Tables

Table 1. Conservative zone model equations ........................................ 17

Table 2. Recommended compartment dimension limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Table 3. Absolute roughness values for common duct materials . . . . . . . . . . . . . . . . . . . . . . . . 46

Table 4. Transfer coefficients for HCl deposition from reference [70] . . . . . . . . . . . . . . . . . . . . 72

Table 5. Typical Inputs for a Two-Zone Fire Model. ................................. 87

Table 6. Typical Outputs for a Two-Zone Fire Model. ................................ 87

Table 7. Comparison of experimental measurements and model predictions

of upper layer temperature (°C) for several tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Table 8. Comparison of experimental measurements and model predictions

of lower layer temperature (°C) for several tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Table 9. Comparison of experimental measurements and model predictions

of layer interface position (m) for several tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Table 10. Comparison of experimental measurements and model predictions

of oxygen concentration for several tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Table 11. Comparison of measured and prescribed heat release rate for several tests . . . . . . . 110

Table 12. Comparison of experimental measurements and model predictions

of room pressure for several tests ......................................... 113

Table 13. Comparison of experimental measurements and model predictions

of mass flow through openings for several tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
xiii

Executive Summary

CFAST is a two-zone fire model used to calculate the evolving distribution of smoke, fire gases

and temperature throughout compartments of a constructed facility during a fire. In CFAST,

each compartment is divided into two gas layers.

The modeling equations used in CFAST take the mathematical form of an initial value problem

for a system of ordinary differential equations (ODEs). These equations are derived using the

conservation of mass, the conservation of energy (equivalently the first law of thermodynamics),

the ideal gas law and relations for density and internal energy. These equations predict as

functions of time quantities such as pressure, layer height and temperatures given the

accumulation of mass and enthalpy in the two layers. The CFAST model then consists of a set

of ODEs to compute the environment in each compartment and a collection of algorithms to

compute the mass and enthalpy source terms required by the ODEs. 

In general, this document provides the technical documentation for CFAST along with

significant information on validation of the model. It follows the ASTM E1355 guide for model

assessment. The guide provides several areas of evaluation:

 • Model and scenarios definition: CFAST is designed primarily to predict the

environment within compartmented structures which results from unwanted fires. These

can range from very small containment vessels, on the order of 1 m to large spaces on 3

the order of 1000 m . The appropriate size fire for a given application depends on the size

3

of the compartment being modeled. A range of such validation exercises is discussed in

chapter 6.

 • Theoretical basis for the model: Details of the underlying theory, governing equations,

correlations, and organization used in the model are presented. The process of

development of the model is discussed with reference to a range of NIST memorandums,

published reports, and peer-reviewed journal articles on the model. In addition to overall

limitations of zone-fire modeling, limitations of the individual sub-models are discussed.

 • Mathematical and numerical robustness: CFAST has been subjected to extensive use

and review both internal to NIST and by users worldwide in a broad range of

applications. In addition to review within NIST independent of the model developers, the

model has been published in international peer-reviewed journals worldwide, and in

industry-standard handbooks referenced in specific consensus standards. Besides formal

internal and peer review, CFAST is subjected to continuous scrutiny because it is

available to the general public and is used internationally by those involved in fire safety

design and post-fire reconstruction.
xiv

 • Model sensitivity: Many of the outputs from the CFAST model are relatively insensitive

to uncertainty in the inputs for a broad range of scenarios. Not surprisingly, the heat

release rate is the most important variable because it provides the driving force for firedriven flows. For CFAST, the heat release rate is prescribed by the user. Thus, careful

selection of the fire size is necessary for accurate predictions. Other variables related to

compartment geometry such as compartment height or vent sizes, while deemed

important for the model outputs, are typically more easily defined for specific design

scenarios than fire related inputs. 

 • Model evaluation: The CFAST model has been subjected to extensive validation studies

by NIST and others. Although some differences between the model and the experiments

were evident in these studies, they are typically explained by limitations of the model and

uncertainty of the experiments. Most prominent in the studies reviewed was the overprediction of gas temperature often attributed to uncertainty in soot production and

radiative fraction. Still, studies typically show predictions accurate within 10 % to 25 %

of measurements for a range of scenarios. Like all predictive models, the best predictions

come with a clear understanding of the limitations of the model and of the inputs

provided to the calculations.
xv

Nomenclature

A surface area of an object: the subscript denotes the application (m ); surface area 2

enclosing emitted gas (m )

2

Ag absorbance of gas (dimensionless)

AH20 absorbance 2 of H 0 (dimensionless)

ACO2 absorbance 2 of CO (dimensionless)

Ad duct surface area (m )

2

Ao area of the inlet, outlet, duct, contraction, or expansion joint, coil, damper, bend, filter,

and so on in a mechanical ventilation system. (m )

2

Aroom floor area of a room (m )

2

Assurface area (m )

2

Aslab cross-sectional area for horizontal flow (m )

2

Av area of ceiling or floor vent (m )

2

Aw wall surface area (m )

2

bi coefficients for adsorption and desorption of HCl (see table 3 for units)

C flow coefficient for horizontal flow of gas through a vertical vent (kg /Pa m s); 1/2 1/2 1/2

concentration of absorbing species (kg/m )

3

CLOLlLower oxygen limit (fraction, not percent)

Co characteristic flow coefficient (kg /Pa m s) 1/2 1/2 1/2

Cw wind coefficient – vector “dot” product of the wind vector and vent direction

(dimensionless)

c specific heat (J/kg K)

ck heat sources for the k'th wall segment (W)

cp heat capacity of air at constant pressure (J/kg K)

cv heat capacity of air at constant volume (J/kg K)

d0 depth of ceiling jet (m)

D effective diameter of ceiling or floor vent (m)

De effective duct diameter (m)

dHCl rate of deposition of HCl onto a wall surface (kg/s)

Eiinternal energy in layer i (W)

F friction factor (dimensionless)

Fk-j configuration factor, fraction of radiation given off by surface k intercepted by surface j

(dimensionless)

F1-2 configuration factor, fraction of radiation given off by surface 1 intercepted by surface 2

(dimensionless)

g gravitational constant (9.8 m/s )

2

G conductance (kg m )

1/2 2

Gr Grashof number for heat transfer (ratio of buoyancy to viscous forces - dimensionless)

Hc heat of combustion of the fuel (J/kg)
xvi

hc convective heat transfer coefficient (J/m K) 2

p

rate of addition of enthalpy into layer i (c T + ) (J/s)

hl convective heat transfer coefficient in ceiling boundary layer (J/m K) 2

h convective heat transfer coefficient (W/m K); 2

H height of the ceiling above a fire source (m); height of compartment (m); flame

height (m)

k equivalent thermal conductivity of air (W/m K); with subscripts c,e and s: mass transfer

coefficients for HCl deposition defined in text

L beam length (m); length of compartment (m); characteristic length of the geometry (m) -

specific use as a length for convection

mitotal mass in layer i (kg)

mi,j mass flow from node i to node j in a mechanical ventilation system (kg/s)

mb0 burning rate of the fuel (perhaps constrained by available oxygen) (kg/s)

mc0 production rate of carbon during combustion (kg/s)

md mass flow in duct (kg/s)

me0 rate of entrainment of air into the fire plume (kg/s)

mL0 mass flow rate into lower layer (kg/s)

mL mass of lower layer (kg)

mf0 pyrolysis rate of the fuel (before being constrained by available oxygen) (kg/s)

mtuhc 0 mass flow rate of total unburned hydrocarbons (kg/s)

mU0 mass flow rate into upper layer (kg/s)

mU mass of upper layer (kg)

mi0 rate of addition of mass into layer i (kg/s)

Nu Nusselt number (dimensionless)

P pressure (Pa)

Pref reference pressure (Pa)

Pr Prandtl number (dimensionless)

heat release rate per unit area (W/m )

2

flux per unit area from the flame (W/m )

2

total convective heat transfer (W)

plume strength at layer interface (dimensionless)

total heat release rate of the fire (W)

convection component of total heat release rate of the fire (W)

plume strength at the height H, a normalized heat release rate (dimensionless)

total radiative heat transfer (W)

total heat per unit area (W/m )

2

r radial distance from point source fire (m)

R universal gas constant (J/kg K)

Ra Rayleigh number (dimensionless)

Re Reynolds number (dimensionless)
xvii

RTI thermal characteristic of a sprinkler or heat detector (m s )

1/2 1/2

S vent shape factor for vertical flow (square or round) (dimensionless)

S distance between two radiating surfaces (m)

S/C ratio of the mass of soot to the mass of carbon in the pyrolysis of the fuel (kg/kg)

t time (s)

Tamb ambient temperature (K)

Tcj temperature of ceiling jet (K)

Td duct temperature (K)

Tetemperature of gas entrainment into the fire plume (K)

Tffilm temperature (K)

Tg bulk gas temperature (K)

temperature of adjacent gas layer - used in convection and radiation calculations (K)

Tssurface temperature (K)

minimum temperature at which lateral flame spread occurs. (K)

Titemperature of layer i (K)

surface ignition temperature (K)

Tktemperature of k’th wall segment (K)

TLtemperature of lower layer (K)

Tin duct inlet temperature (K)

Tktemperature of the k'th wall segment (K)

Tout duct outlet temperature (K)

Tptemperature of the plume as it intersects the upper layer (K)

surface temperature (K)

Tstransmittance of soot (dimensionless)

TTtotal transmittance (dimensionless)

TUtemperature of upper layer

Tw wall temperature (K)

v gas velocity (m/s)

V volume; subscript indicates usage (m )

3

V volume of emitted gas

Vd duct volume (m )

3

Vf velocity of fan (m/s)

Vi volume of layer i (m )

3

VL volume of lower layer (m )

3

vp height of virtual point source (m)

VU volume of upper layer (m )

3

W width of compartment (m)

burnout front position in the opposed flow direction (m)

pyrolysis front position in the opposed flow direction (m)
xviii

Y mass fraction of a species in a layer, with subscript O2 for oxygen and LOL as a lower

oxygen limit for oxygen constrained burning (dimensionless)

burnout front position in the wind aided direction (m)

flame tip position (m)

pyrolysis front position in the wind aided direction (m)

z height over which entrainment takes place (m)

Z general height (m)

" thermal diffusivity in conduction (m /s), absorption coefficient for gas radiation (m )

2 -1

" absorbance (dimensionless)

$ expansion coef fficient, 1/T (K )

-1

, emittance (dimensionless)

,k emittance of k’th wall segment (dimensionless)

)D change in density (kg/m )

3

)P pressure ref offset from reference pressure, P - P (Pa)

)Pf pressure drop across a fan (Pa)

effective heat of gasification (J/kg)

( p v ratio of c /c (dimensionless)

k

g emissivity of the k wall segment (dimensionless) th

g roughness factor (dimensionless)

6 thermal conductivity (J/m s K)

< kinematic viscosity (m /s) 2

B universal constant, ratio of circumference to diameter

D reflectivity (dimensionless)

Dcj density of ceiling jet (K)

Dd density of gas in a duct (kg/m )

3

Di density of gas in layer i (kg/m )

3

N flame heating parameter defined in eq. (168)

F Stefan-Boltzman constant (5.67 x 10 W/m K )

-8 2 4

J transmissivity (dimensionless)

11 angle between normal vector and direction vector another surface (Radians)

Pcfraction of the heat release rate of the fire which goes into convection (dimensionless)

Prfraction of the heat release rate of the fire which goes into radiation (dimensionless)
1

CFAST – Consolidated Model of Fire Growth and

Smoke Transport (Version 5)

Technical Reference Guide

Walter W. Jones, Richard D. Peacock, Glenn P. Forney, and Paul A. Reneke

Fire Research Division

Building and Fire Research Laboratory

1 Introduction

1.1 History

Analytical models for predicting fire behavior have been evolving since the 1960s. Over the

past decade, the completeness of the models has grown considerably. In the beginning, the focus

of these efforts was to describe in mathematical language the various phenomena which were

observed in fire growth and spread. These separate representations have typically described only

a small part of a fire. However, when combined they can create a complex computational model

that can predict the expected course of a fire. 

Once a mathematical representation of the underlying physics has been developed, the conservation equations can be re-cast into predictive equations for temperature, smoke and gas

concentration and other parameters of interest, and solved numerically. 

The equations are usually in the form of differential equations. A complete set of equations can

describe the conditions produced by the fire at a given time in a specified volume of air. 

Referred to as a control volume, the model assumes that the predicted conditions within this

volume are uniform at any time. Thus, the control volume has one temperature, smoke density,

gas concentration, etc. Different models divide the building into different numbers of control

volumes depending on the desired level of detail. The most common fire model, known as a

zone model, generally uses two control volumes to describe a compartment – an upper layer and

a lower layer. In the compartment with the fire, additional control volumes for the fire plume or

the ceiling jet may be included to improve the accuracy of the prediction (see figure 1).

This two-layer approach has evolved from observation of such layering in real-scale fire

experiments. Hot gases collect at the ceiling and fill the compartment from the top. While these

experiments show some variation in conditions within the layer, these are small compared to the
 ASTM International - formerly the American Society for Testing and Materials 1

2

Figure 1. Zone model terms.

differences between the layers. Thus, the zone model can produce a fairly realistic simulation

under many common and important conditions.

Other types of models include network models and field models. Network models use one

control volume per compartment and are used to predict conditions in spaces far removed from

the fire compartment where temperatures are near ambient and layering does not occur. The

field model goes to the other extreme, dividing the compartment into thousands or millions of

control volumes. Such models can predict the variation in conditions within the layers, but

typically require far longer run times than zone models. They are used when a highly detailed

prediction of the flow itself is of interest.

1.2 Model Evaluation

The process of model evaluation is critical to establishing both the acceptable uses and

limitations of fire models. It is not possible to evaluate a model in total; instead, available guides

such as ASTM E1355 are intended to provide a methodology for evaluating the predictive 1

capabilities for a specific use [1]. Validation for one application or scenario does not imply

validation for different scenarios. Several alternatives are provided for performing the evaluation

process including comparison of predictions against standard fire tests, full-scale fire

experiments, field experience, published literature, or previously evaluated models.

The use of fire models currently extends beyond the fire research laboratory and into the

engineering, fire service and legal communities. Sufficient evaluation of fire models is necessary
3

to ensure that those using the models can judge the adequacy of the scientific and technical basis

for the models, select models appropriate for a desired use, and understand the level of

confidence which can be placed on the results predicted by the models. Adequate evaluation will

help prevent the unintentional misuse of fire models. 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 implemented and 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 explained

by numerical errors in the model or uncertainty in the experiments are attributed to the

assumptions and simplifications of the physical model. These terms are used together to perform

a model assessment. The more general term, “model assessment,” encompasses both verification

and validation of a computer model.

In general, this document follows the ASTM E1355 guide for model assessment and provides a

model assessment for the zone fire model CFAST. The guide provides four areas of evaluation

for predictive fire models:

 • Defining the model and scenarios for which the evaluation is to be conducted (chapter 2),

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

(chapter 3),

 • Assessing the mathematical and numerical robustness of the model (chapter 4), and

 • Quantifying the uncertainty and accuracy of the model results in predicting the course of

events in similar fire scenarios (chapters 5 and 6).
4
 ANSI - American National Standards Institute - The governing national standards body 2

for the United States. FORTRAN and C are two programming languages which are standardized

through the ANSI consensus process.

5

2 Model and Scenario Definition

Sufficient documentation of calculation models is necessary to assess the adequacy of the

scientific and technical basis of the model and the accuracy of the computational procedures for

scenarios of interest. In addition, adequate documentation will help prevent the unintentional

misuse of the model. The documentation in this document follows the guidelines in ASTM

E1355-04 [1].

2.1 Model Documentation

2.1.1 Name and Version of the Model

The name of the model is the Consolidated Fire Growth and Smoke Transport Model or CFAST.

The first public release was version 1.0 in June of 1990. This version was restructured from

FAST [2] to incorporate the "lessons learned" from the zone model CCFM developed by Cooper

and Forney [3], namely that modification is easier and more robust if the components such as the

physical routines are separated from the solver. chapter 4 (Mathematical and Numerical

Robustness) discusses this in more detail. Version 2 was released as a component of Hazard 1.2

in 1994 [4]. The first of the 3.x series was released in 1995 and included a vertical flame spread

algorithm, ceiling jets and nonuniform heat loss to the ceiling, spot targets, and heating and

burning of multiple objects (ignition by flux, temperature or time) in addition to multiple

prescribed fires. As it evolved over the next five years, version 3 included smoke and heat

detectors, suppression through heat release reduction, better characterization of flow through

doors and windows, vertical heat conduction through ceiling/floor boundaries, and

non-rectangular compartments. In 2000, version 4 was released and included horizontal heat

conduction through walls, and horizontal smoke flow in corridors. Version 5 improved the

combustion chemistry. The current version is 5.1.

Most of the code is written in FORTRAN 90, though some of the input/output routines as well as

those for handling objects, are written in ANSI C. 2

2.1.2 Type of Model

CFAST is a model that predicts the environment within compartmented structures resulting from

a fire prescribed by the user. It is an example of the class of models called finite element. This

particular implementation is called a zone model, and essentially the space to be modeled is
Naval Research Laboratory, Washington, DC 20375. 3

6

broken down to a few elements. The physics of the compartment fire phenomena is driven by

fluid flow, primarily buoyancy. The usual set of elements or zones are the upper and lower gas

layers, partitioning of the wall/ceiling/floor to an element each, one or more plumes and objects

such as fires, targets, and detectors. One feature of this implementation of a finite element model

is that the interface between the elements (in this case, the upper and lower gas layers) can move,

with its position defined by the governing equations.

2.1.3 Model Developers

CFAST was developed and is maintained primarily by the Fire Research Division of the

National Institute of Standards and Technology. The developers are Walter Jones, Richard

Peacock, Glenn Forney, Rebecca Portier, Paul Reneke, John Hoover , and John Klote. 3

There have been contributions through research and published papers at Worcester Polytechnic

Institute, University of California at Berkeley, VTT of Finland and CITCM of France. An

important guide to development of the model has been from many people around the world who

have provided ideas, suggestions, comments, detailed questions, opinions on what should happen

in particular scenarios, what physics and chemistry are needed and what types of problems must

be addressed by such a model in order to be useful for real world applications.

2.1.4 Relevant Publications

CFAST is documented by two publications, this Technical Reference Manual and the User’s

Guide [5]. The user’s guide describes how to use the model and this technical reference manual

describes the underlying physical principles, provides a comparison with other models and

includes a description of the limitations of this zone model. This technical reference guide

applies to version 5 and later and the user’s guide to versions 3 and later. Version 5 of CFAST

does not include a graphical user interface, so that portion of the user’s guide [5] is not

applicable. The remainder of the material on use of key words and data files is applicable. 

There are documents available (http://cfast.nist.gov) that are applicable to versions 2, 3, 4 and 5

of both the model and user interface.

2.1.5 Governing Equations and Assumptions

For CFAST, as for most zone fire models, the equations solved are for conservation of mass and

energy. The momentum equation is not solved explicitly, except for use of the Bernoulli

equation for the flow velocity at vents. Based on an integration over the volume of an element,

these equations are solved as ordinary differential equations. 
7

There are two assumptions which reduce the computation time dramatically. The first is that

relatively few zones or elements per compartment is sufficient to model the physical situation.

The second assumption is to close the set of equations without using the momentum equation in

the compartment interiors. This simplification eliminates acoustic waves. Though this prevents

one from calculating gravity waves in compartments (or between compartments), coupled with

only a few elements per compartment allows for a prediction in a large and complex space very

quickly.

The equations themselves and the algorithms and sub-models used are discussed in detail in

chapter 3.

2.1.6 Input Data Required to Run the Model

All of the data to run the model is contained in a primary data file, together with databases for

objects, thermophysical properties of boundaries, and sample prescribed fire descriptions [6].

These files contain information about the building geometry (compartment sizes, materials of

construction, and material properties), connections between compartments (horizontal flow

openings such as doors, windows), vertical flow openings in floors and ceilings, and mechanical

ventilation connections), fire properties (fire size and species production rates as a function of

time), and specifications for detectors, sprinklers, and targets (position, size, heat transfer

characteristics, and flow characteristics for sprinklers). Materials are defined by their thermal

conductivity, specific heat, density, thickness, and burning behavior. 

Sample data files are provided which encompass many of the validation exercises described in

chapter 6 and in the various articles and reports referenced in chapter 6. These examples range

from simple one-compartment simulations to a large multi-story hotel scenario that includes an

elevator shaft and stairwell pressurization. A complete description of the input parameters

required by CFAST can be found in the CFAST User’s Guide [5].

2.1.7 Property Data

Any simulation of a real fire scenario involves prescribing material properties for the walls,

floor, ceiling, and furnishings. CFAST treats all of these materials as homogeneous solids, thus

the physical parameters for many real objects can only be viewed as approximations to the actual

properties. Describing these materials in the input data file is a challenging task for the model

user. Thermal properties for the most common barrier materials used in construction, e.g.

gypsum wall board, are included in a database, thermal.df, included with the model. These

properties come directly from handbook values for typical materials [7].
8

2.1.8 Model Results

The output of CFAST are the sensible variables that are needed for assessing the environment in

a building subjected to a fire. These include temperatures of the upper and lower gas layers

within each compartment, the ceiling/wall/floor temperatures within each compartment, the

visible smoke and gas species concentrations within each layer, target temperatures and sprinkler

activation time. There is more extensive discussion of the output in chapter 6 of this technical

reference manual and the user’s guide. The output is always in the metric system of units.

2.1.9 Uses and Limitations of the Model

CFAST has been developed for solving practical fire problems in fire protection engineering,

while at the same time providing a tool to study fundamental fire dynamics and smoke spread. It 

is intended for system modeling of building and building components. It is not intended for

detailed study of flow within a compartment such as is needed for smoke detector siting. It

includes the activation of sprinklers, and fire suppression by water droplets.

The most extensive use of the model is in fire and smoke spread in complex buildings. The

efficiency and computational speed are inherent in the few computation cells needed for a zone

model implementation. Most of the use is for reconstruction of time-lines for fire and smoke

spread in residential, commercial and industrial fire reconstructions. Some applications of the

model have been for design of smoke control systems.

 • Compartments: CFAST is generally limited to situations where the compartment

volumes are strongly stratified. However, in order to facilitate the use of the model for

preliminary estimates when a more sophisticated calculation is ultimately needed, there

are algorithms for corridor flow, smoke detector activation and detailed heat conduction

through solid boundaries. This model does provide for non-rectangular compartments,

though the application is intended to be limited to relatively simple spaces such as attics

and ship corridors. There is no intent to include complex geometries where a complex

flow field is a driving force. For these applications, computational fluid dynamics (CFD)

models are appropriate.

There are also limitations inherent in the assumption of stratification of the gas layers.

The zone model concept, by definition, implies a sharp boundary between the upper and

lower layers, whereas in reality, the transition is typically over about 10 % of the height

of the compartment and can be larger in weakly stratified flow. For example, a burning

cigarette in a normal room is not within the purview of a zone model. While it is possible

to make predictions within 5 % of the actual temperatures of the gas layers, this is not the

optimum use of the model. It is more properly used to make estimates of fire spread (not

flame spread), smoke detection and contamination, and life safety calculations.
9

 • Heat Release Rate: There are limitations inherent in the assumptions used in application

of the empirical models. As a general guideline, the heat release should not exceed about

1 MW/m . This is a limitation on the numerical routines due to the coupling between gas 3

flow and heat transfer through boundaries (conduction, convection and radiation). The

inherent two-layer assumption is likely to break down well before this limit is reached.

 • Flame Spread: While there is a flame spread model included, it should only be used for

estimating such effects since it is a simplified empirical model developed to simulate

vertical flame spread in a wall-corner configuration.

 • Radiation: Since the model includes a sophisticated radiation model and ventilation

algorithms it has further use for studying building contamination through the ventilation

system, as well as the stack effect and the effect of wind on air circulation in buildings.

 • Ventilation and Leakage: In a single compartment, the ratio of the area of vents

connecting one compartment to another to the volume of the compartment should not

exceed roughly 2 m . This is a limitation on the plug flow assumption for vents. An -1

important limitation arises from the uncertainty in the scenario specification. For

example, leakage in buildings is significant, and this affects flow calculations especially

when wind is present and for tall buildings. These effects can overwhelm limitations on

accuracy of the implementation of the model. The overall accuracy of the model is

closely tied to the specificity, care, and completeness with which the data are provided.

 • Thermal Properties: The accuracy of the model predictions is limited by how well the

user can specify the thermophysical properties. For example, the fraction of fuel which

ends up as soot has an important effect on the radiation absorption of the gas layer and

therefor the relative convective versus radiative heating of the layers and walls, which in

turn affects the buoyancy and flow. There is a higher level of uncertainty of the

predictions if the properties of real materials and real fuels are unknown or difficult to

obtain, or the physical processes of combustion, radiation and heat transfer are more

complicated than their mathematical representations in CFAST. 

User feedback indicates that using CFAST to predict the transport of heat and combustion

products from a prescribed fire is straightforward, easily and quickly accomplished, and the

results are within expectations. Any user of a computer based (numerical) model must be aware

of the assumptions and approximations being employed. Except for those few materials supplied

in the property databases, the user must supply the thermal properties of the materials, and then

assess the performance of the model compared with experiments to ensure that the model is valid

for a specific application. Only then can the model be expected to predict the outcome of fire

scenarios that are similar to those that have actually been tested. 
10

In addition, there are specific limitations and assumptions made in the development of the

algorithms. These are detailed in the discussion of each of these sub-models:

 • section 3.3 on zone model assumptions, 

 • section 3.4.1 on prescribed fires,

 • section 3.4.1.3 on the relationship between fires and mass balance, 

 • section 3.4.2.1 on the plume entrainment model,

 • section 3.4.3.1 on doorway flows and entrainment at vents, 

 • section 3.4.4 on the assumptions made for corridor flow correlations,

 • section 3.4.5.1 on the assumptions made for radiation heat transfer,

 • section 3.6 on the suppression model, and 

 • section 3.7.2 on HCl deposition.

2.2 Scenarios for which the Model is Evaluated in this Document

CFAST is used for a wide range of buildings of interest, from “glove-box” size compartments, to

complex hotels to the vehicle assembly building at Cape Canaveral. The intended use of ASTM

E1355 [1] is to validate a specific scenario of interest so that the model can be used for scenarios

similar to the chosen scenario. The intent of this document, however, is to cover a much wider

range of scenarios which encompass the range of acceptable use of the model. Thus, this section

provides a description of this broader range of scenarios as discussed in this technical reference

guide rather than a single, specific scenario of interest for a validation exercise.

2.2.1 Description of Scenarios of Interest

CFAST is designed primarily to predict the environment within compartmented structures which

results from unwanted fires. These can range from very small containment vessels, on the order

of 1 m to large spaces on the order of 1000 m . As discussed in the section on limitations and 3 3

use (2.1.9), the appropriate size fire depends on the size of the compartment being modeled. A

range of such validation exercises is discussed in chapter 6.

2.2.2 List of Quantities Predicted by the Model

CFAST provides a prediction of the gas layer and boundary temperatures, target temperatures,

species concentration (including soot volume fraction), layer height, fire size and flame length,

floor pressure, flow and fire size at vents, and heat flux (both radiative and convective).

There is more extensive discussion of the output in chapter 6 and this technical reference manual

and the user’s guide.
11

2.2.3 Degree of Accuracy Required for Each Output Quantity

The accuracy required depends on the accuracy needed for the intended use. It is also very much

dependent on the care and completeness in specifying the input data, with the most sensitivity to

the heat release rate [8]. Further, the output is dependent on the accuracy of the data used for the

fire, and the thermophysical properties of boundaries and targets. However, a generalized

definition of the accuracy required with no regard as to the specifics of a particular scenario or

analysis is not practical and would be limited in its usefulness.

Studies typically show the predictions accurate within 10 % to 25 % of measurements for a

range of scenarios. In general, this is adequate for its intended uses which are life-safety

calculations and estimation of the environment to which building elements are subjected in a fire

environment. Applied design margins are typically larger than this level of accuracy and may be

appropriate to insure an adequate factor of safety.
12
13

3 Theoretical Basis for CFAST

Adequately detailed documentation of the theoretical basis of the model allows the model user to

understand the underlying theory behind the model implementation and thus be able to assess the

appropriateness of the model to specific problems. This chapter presents a derivation of the

predictive equations for zone fire models and explains in detail the ones used in CFAST [7], [9]. 

The modeling equations used in CFAST take the mathematical form of an initial value problem

for a system of ordinary differential equations. These equations are derived using the

conservation of mass, the conservation of energy (equivalently the first law of thermodynamics),

the ideal gas law. These equations predict as functions of time quantities such as pressure, layer

height and temperatures given the accumulation of mass and enthalpy in the two layers. The

assumption of a zone model is that properties such as temperature can be approximated

throughout a control volume by an average value. 

Many formulations based upon these assumptions can be derived. One formulation can be

converted into another using the definitions of density, internal energy and the ideal gas law. 

Though equivalent analytically, these formulations differ in their numerical properties. Each

formulation can be expressed in terms of mass and enthalpy flow. These rates represent the

exchange of mass and enthalpy between zones due to physical phenomena such as plumes,

natural and forced ventilation, convective and radiative heat transfer, and so on. For example, a

vent exchanges mass and enthalpy between zones in connected rooms, a fire plume typically

adds heat to the upper layer and transfers entrained mass and enthalpy from the lower to the

upper layer, and convection transfers enthalpy from the gas layers to the surrounding walls.

As discussed in references [10] and [9], the zone fire modeling ordinary differential equations

(ODEs) are stiff. The term stiff means that large variations in time scales are present in the ODE

solution. In our problem, pressures adjust to changing conditions more quickly than other

quantities such as layer temperatures or interface heights. Special solvers are required in general

to solve zone fire modeling ODEs because of this stiffness. Runge-Kutta methods or predictorcorrector methods such as Adams-Bashforth require prohibitively small time steps in order to

track the short-time scale phenomena (pressure in our case). Methods that calculate the Jacobian

(or at least approximate it) have a much larger stability region for stiff problems and are thus

more successful at their solution. 

3.1 Derivation of Equations for a Two-Layer Model

A compartment is divided into two control volumes, a relatively hot upper layer and a relatively

cool lower layer, as illustrated in figure 2. The gas in each layer has attributes of mass, internal

ene i i i i irgy, density, temperature, and volume denoted respectively by m , E , D , T , and V where i=L
14

Figure 2. Schematic of control volumes in a two-layer zone model.

for the lower layer and i=U for the upper layer. The compartment as a whole has the attribute of

pressure P. These 11 variables are related by means of the following seven constraints (counting

density, internal energy and the ideal gas law twice, once for each layer).

(22)

(23)

(24)

(25)

The spec v p ific heat at constant volume and at constant pressure c and c , the universal gas

constant, R p v p v, and the ratio of specific heats, (, are related by ( = c / c and R = c - c . For

ambient air p, c . 1 kJ/kg K and ( = 1.4. Four additional equations obtained from conservation of

mass and energy for each layer are required to complete the equation set. The differential

equations for mass in each layer are 
15

(26)

The first law of thermodynamics states that the rate of increase of internal energy plus the rate at

which the layer does work by expansion is equal to the rate at which enthalpy is added to the gas. 

In differential form this is

(27)

where cp is taken as constant in the enthalpy term, 

(28)

. 

A differential equation for pressure can be derived by adding the upper and lower layer versions

of U L eq (27), noting that dV /dt = -dV /dt, and substituting the differential form of eq (23) to yield

(29)

Differential equations for the layer volumes can be obtained by substituting the differential form

of eq (23) into eq (27) to obtain 

(30)

Equation (27) can be rewritten using eq (30) to eliminate dV/dt to obtain
16

(31)

A differential equation for density can be derived by applying the quotient rule to and

using eq (30) to eliminate dVi/dt to obtain

(32)

Temperature differential equations can be obtained from the equation of state by applying the

quotient rule to and using eq (32) to eliminate dD/dt to obtain

(33)

These equations for each of the 11 variables are summarized in table 1. The time evolution of

these solution variables can be computed by solving the corresponding differential equations

together with appropriate initial conditions. The remaining seven variables can be determined

from the four solution variables using eqs (22) to (25).

There are, however, many possible differential equation formulations. Indeed, there are 330

different ways to select four variables from eleven. Many of these systems are incomplete due to

the relationships that exist between the variables given in eqs (22) to (25). For example the

variables, DU U U U U U, V , m , and P form a dependent set since D = m / V .

The number of differential equation formulations can be considerably reduced by not mixing

variable types between layers; that is, if upper layer mass is chosen as a solution variable, then

L

lower layer mass must also be chosen. For example, for two of the solution variables choose m

and mU L U L U L U, or D and D , or T and T . For the other two solution variables pick E and E or P and

VL U or P and V . This reduces the number of distinct formulations to nine. Since the numerical

properties of the upper layer volume equation are the same as a lower layer one, the number of

distinct formulations can be reduced to six. 
17

Table 1. Conservative zone model equations

Equation Type Differential Equation

i'th layer mass

pressure

i'th layer energy

i'th layer volume

i'th layer density

i'th layer temperature

3.2 Equation Set Used in CFAST

The current version of CFAST is set up to use the equation set for layer temperature, layer

volume, and pressure as shown below. 

(34)

(35)

(36)
18

(37)

In these equations, the pressure is actually modeled with the pressure difference relative to an

ambient reference pressure to minimize numerical instability.

3.3 Limitations of the Zone Model Assumptions

The basic assumption of all zone fire models is that each compartment can be divided into a

small number of control volumes, each of which is uniform in temperature and composition. In

CFAST all compartments have two zones except for the fire room which has an additional zone

for the plume. Since a real upper/lower interface is not as sharp as this, one has a spatial error of

about 10 % in determining the height of the layer [10],[30].

The zone model concept best applies for an enclosure in which the width and length are not too

different. If the horizontal dimensions of the room differ too much (i.e., the room looks like a

corridor), the flow pattern in the room may become asymmetrical. If the enclosure is too

shallow, the temperature may have significant radial differences. The width of the plume may at

some height become equal to the width of the room and the model assumptions may fail in a tall

and narrow enclosure. Therefore, the user should recognize approximate limits on the ratio of the

length (L), width (W), and height (H) of the compartment. 

If the aspect ratio (length/width) is over about 10, the corridor flow algorithm should be used.

This provides the appropriate filling time. Similarly, for tall shafts (elevators and stairways), a

single zone approximation is more appropriate. It was found experimentally [11] that the mixing

between a plume and lower layer due to the interaction with the walls of the shaft, caused

complete mixing. The is the flip side of the corridor problem and occurs at a ratio of the height

to characteristic floor length of about 10. The following quantitative limits are recommended:

Group Acceptable Special consideration

required

Corridor flow

algorithm

max (L/W) L/W<3 3<L/W<5 L/W>5

max (L/H) L/H<3 3<L/H<6 L/H>6

min (W/H) W/H>0.4 0.2<W/H<0.4 W/H<0.2

Table 2. Recommended compartment dimension limits
19

3.4 Source Terms for the Model

This section discusses each of the sub-models in CFAST. In general, the sections are similar to

the way the model itself is structured. The sub-sections which follow discuss the way the actual

phenomena are implemented numerically. For each of the phenomena discussed below, the

physical basis for the model is discussed first, followed by a brief presentation of the

implementation within CFAST. For all of the phenomena, there are basically two parts to the

implementation: the physical interface routine (which is the interface between the CFAST

model and the algorithm) and the actual physical routine(s) which implement the physics. This

implementation allows the physics to remain independent of the structure of CFAST and allows

easier insertion of new phenomena.

3.4.1 The Fire

A fire in CFAST is implemented as a source of fuel mass which is released at a prescribed rate

(the pyrolysis rate). Energy is released by the fuel and combustion products are created as it

burns. The model incorporates two distinct types of fires: unconstrained and constrained. In

the unconstrained fire, the fire simply releases mass and energy at a rate prescribed by the user;

no calculation or tracking of products of combustion is included. In the constrained fire, species

production is calculated based on production yields prescribed by the user. In addition, for the

constrained fire, the pyrolysis rate and resulting energy and species generation may be limited by

the oxygen available for combustion. When sufficient oxygen is available for combustion, heat

release rate for the constrained fire is the same as for the unconstrained fire.

The model can simulate multiple fires in one or more compartments of the building. These fires

are treated as totally separate entities, with no interaction of the plumes. These fires are generally

referred to as “objects” and can be ignited at a prescribed time, temperature or heat flux.

CFAST does not include a pyrolysis model to predict fire growth. Rather, pyrolysis rates for

each fire are prescribed by the user. While this approach does not directly account for increased

pyrolysis due to radiative feedback from the flame or compartment, in theory these effects could

be prescribed by the user. In an actual fire, this is an important consideration, and the

specification used should consider the experimental conditions as closely as possible.

3.4.1.1 Unconstrained Fire

An unconstrained fire releases energy based on the pyrolysis rate of the fuel. This type of fire is

applicable to fuels for which there is always sufficient oxygen in the fuel for combustion to take

place and when the concentrations of products of combustion are not of interest.
20

The f b c pyrolysis rate is specified as m0 , the burning rate as m0 and the heat of combustion as H so

f

that the heat release rate, Q , is (total heat release less the energy necessary to heat the fuel)

(38)

where Tv a c and T are the fuel volatilization and ambient temperatures, respectively and H is the

heat of v combustion of the fuel. In CFAST, T is assumed to be the upper layer temperature in the

compar b f tment with a fire. For the unconstrained fire, m0 = m0 .

3.4.1.2 Constrained Fire

A constrained fire releases energy based on the pyrolysis of fuel, but may be constrained by the

oxygen available for combustion depending on the compartment conditions. Complete burning

will take place only where there is sufficient oxygen. When insufficient oxygen is entrained into

the fire plume, unburned fuel will be transported from zone to zone until there is sufficient

oxygen and a high enough temperature to support combustion. In general, CFAST uses a simple

definition of a combustion reaction that includes major products of combustion for hydrocarbon

fuels:

(39)

whe 1 2 re the coefficients m , m , etc. represent appropriate molar ratios for a stoichiometric balance

of the equation. For complete combustion of the simplest hydrocarbon fuel, methane reacts with

oxygen to form carbon dioxide and water. The only input required is the pyrolysis rate and the

heat of combustion. For fuels that contain oxygen, nitrogen, or chlorine, the reaction becomes

more complex. In this case, production yields for the species are prescribed by the user.

Stoichiometry is used to insure conservation of mass and elements in the reaction. The species

which are calculated are oxygen, carbon dioxide, carbon monoxide, water, total unburned

hydrocarbons (tuhc), and soot. Gaseous nitrogen is included, but only acts as a diluent.

Production of hydrogen cyanide and hydrogen chloride are tracked solely based on user

prescribed yields. 

The heat release rate for a constrained fire may be reduced below its prescribed value based

upon the oxygen available for combustion. For the constrained fire, the burning rate may be less

than the pyrolysis rate and eq (38) cannot be simplified as in the case of the unconstrained fire. 

As fuel and oxygen are consumed, heat is released and various products of combustion are

formed. The heat is released as radiation and convected enthalpy:

(40)
21

Figure 3. Schematic of entrainment and burning regions.

where, R , is the fraction of the fire’s heat release rate given off as radiation. The convective

enthalpy, then becomes the driving term in the plume flow. For a constrained fire there is

radiation to both the upper and lower layers, whereas the convective part contributes only to the

upper layer. 

3.4.1.3 Limiting Combustion by Available Oxygen

For a constrained fire, the heat release rate is limited by available oxygen. This limit is applied in

three places, which are shown schematically in figure 3. The first is burning in the portion of the

plume which is in the lower layer of the room of fire origin (region #1). The second is the

portion of the plume in the upper layer, also in the room of origin (region #2). The third is in the

vent flow which entrains air from a lower layer into an upper layer in an adjacent compartment

(region #3). The unburned hydrocarbons are tracked in this model. Further combustion of CO to

CO2 is not included in the model.

mf0 = pyrolysis rate of the source (kg/s) (region #1)

or mf tuhc 0 = m0 from a previous region (kg/s) (region #2 and #3).

and mtuhc f b0 = m0 - m0

where tuhc stands for total unburned hydrocarbons.

The first step is to limit the actual burning which takes place in the combustion zone. In each

combustion zone, there is a quantity of fuel available. At the source this results from the
 The units for oxygen consumption calorimetry are J/kg. The value 1.31x10 J/kg is 4 7

representative of typical fuels such as furniture (see reference [14]) and implies these units. The

variation or uncertainty (2F) associated with this value is on the order of ± 5 %.This is a fixed

parameter in CFAST version 5 and earlier.

22

py frolysis of the material, m0 . In other situations such as a plume or door jet, it is the net

unburned fuel ava tuhc ilable, m0 . In each case, the fuel which is available but not burned is then

deposited into the “mtuhc 0 ” category. This provides a consistent notation. In the discussion below,

mf0 is the amount of fuel burned. This value is initially specified as to the available fuel, and then

reduced if there is insufficient oxygen to support complete combustion. Subsequently, the

available tuhc f fuel, m0 , is reduced by the final value of m0 . Thus we have a consistent description in

each burning region, with an algorithm that is invoked independent of the region being analyzed.

(41)

with the mass of oxygen required to achieve this energy release rate of

(42)

where E is the heat release per mass unit of oxygen consumed, taken to be 1.31 x 10 J/kg (based 7

on oxygen consumption calorimetry [12],[13], [14] for typical fuels). If the fuel contains oxygen 4

(available for combustion), the oxygen needed to achieve full combustion is less:

(43)

If sufficient oxygen is available, then it is fully burned. However, if the oxygen concentration is

low enough, it will constrain the burning and impose a limit on the amount of fuel actually

burned, as opposed to the amount pyrolyzed. The actual limitation is discussed below and is:

(44)

(45)

The relationship between oxygen and fuel concentration defines a range in which burning will

take place. In the CFAST model, a limit is incorporated by limiting the burning rate as the

oxygen level decreases until a “lower oxygen limit” (LOL) is reached. The lower oxygen limit is

incorporated through a smooth decrease in the burning rate near the limit:
23

(46)

where me is the mass entrainment flow rate, is the mass fraction of oxygen, and the lower

oxygen limit coef LOLficient, C , is the fraction of the available fuel which can be burned with the

available oxygen and varies from 0 at the limit to 1 above the limit. The functional form that

utilizes the hyperbolic tangent was determined empirically to provide a smooth cutoff of the

burning over a narrow range above the limit.

(47)

A temperature criterion is also imposed so that no burning will take place when the temperature

is below a user prescribed temperature. 

In summary, it is possible to follow the formation of the major products of combustion (carbon

dioxide, carbon monoxide, soot, water, hydrogen cyanide, and hydrogen chloride) using

appropriate measured product yields (e.g., [15]) to define product yields for eq (39). Actual

combustion chemistry is not considered in CFAST due to the complexities associated with

detailed kinetics and transport.

3.4.1.4 Flame Height

CFAST includes a calculation of average flame height based on the work of Heskestad [16].

Valid for a wide range of hydrocarbon and gaseous fuels, the correlation is given by

(48)

where H f is the average flame height and Q is the fire size. The mean flame height is defined as

the distance from the fuel source to the top of the visible flame where the intermittency is 0.5. A

flame intermittency of 0.5 means that the visible flame is above the mean 50 % of the time and

below the mean 50 % of the time. This average flame height is included in the printed output

from CFAST.

3.4.1.5 Limitation of the Algorithm for Fires and Mass Balance

CFAST depends on pyrolysis data for the source term for a fire. The usual way to obtain this

data is a large-scale calorimeter, e.g., reference [17]. Generally, a product (e.g., chair, table,

bookcase) is placed under a large collection hood and ignited by a burner (.50 kW simulating a

wastebasket) placed adjacent to the item. The combustion process then proceeds under assumed

“free-burning” conditions, and the heat release rate is measured. Potential sources of uncertainty

include measurement errors related to the instrumentation and the degree to which “free-burning” conditions are not achieved (e.g., radiation from the gases under the hood or from the hood
24

itself, and restrictions in the air entrained by the object causing locally reduced oxygen

concentrations affecting the combustion chemistry). There are limited experimental data for

upholstered furniture which suggest that prior to the onset of flashover in a compartment, the

influence of the compartment on the burning behavior of the item is small. The differences

obtained from the use of different types or locations of ignition sources have not been explored. 

These factors are discussed in reference [18].

Where small-scale calorimeter data are used, procedures are available to extrapolate to the

behavior of a full-size item. These procedures are based on empirical correlations of data which

exhibit significant scatter, thus limiting their accuracy. For example, for upholstered furniture,

the peak heat release rates estimated by the “triangular approximation” method averaged 91 %

(range 46 % to 103 %) of values measured for a group of 26 chairs with noncombustible frames,

but only 63 % (range 46 % to 83 %) of values measured for a group of 11 chairs with

combustible frames [19]. Also, the triangle neglects the “tails” of the curve; these are the initial

time from ignition to significant burning of the item, and the region of burning of the combustible frame, after the fabric and filler are consumed.

The provided data and procedures only relate directly to burning of items initiated by relatively

large flaming sources. Little data are currently available for release rates under smoldering

combustion, or for the high external flux and low oxygen conditions characteristic of postflashover burning. While the model allows multiple items burning simultaneously, it does not

account for the synergy of such multiple fires. Thus, for other ignition scenarios, multiple items

burning simultaneously (which exchange energy by radiation and convection), combustible

interior finish, and post-flashover conditions, the model can give estimates which are often

nonconservative (the actual release rates would be greater than estimated). At present, the only

sure way to account for all of these complex phenomena is to conduct a full-scale compartment

burn and use the pyrolysis rates directly. 

Burning can be constrained by the available oxygen. However, this “constrained fire” is not

subject to the influences of radiation to enhance its burning rate, but is influenced by the oxygen

available in the compartment. If a large mass loss rate is entered, the model will follow this

input until there is insufficient oxygen available for that quantity of fuel to burn in the

compartment. The unburned fuel (sometimes called excess pyrolysate) is tracked as it flows out

in the door jet, where it can entrain more oxygen. If this mixture is within the user-constrained

flammable range, it burns in the door plume. If not, it will be tracked throughout the building

until it eventually collects as unburned fuel or burns in a vent. The enthalpy released in the fire

compartment and in each vent, as well as the total enthalpy released, is detailed in the output of

the model. Since mass and enthalpy are conserved, the total will be correct. However, since

combustion did not take place adjacent to the burning object, the actual mass burned could be

lower than that specified by the user. The difference will be the unburned fuel.
25

An oxygen combustion chemistry scheme is employed only in constrained fires. Here userconstrained hydrocarbon ratios and species yields are used by the model to predict concentrations. A balance among hydrogen, carbon, and oxygen molecules is maintained. Under some

conditions, low oxygen can change the combustion chemistry, with a resulting increase in the

yields of products of incomplete combustion such as carbon momoxide. However, not enough is

known about these chemical processes to build this relationship into the model at the present

time. Some data exist in reports of full-scale experiments (e.g., reference [20]) which can assist

in making such determinations.

3.4.2 Plumes

A plume is formed above any burning object. It acts as a pump transferring mass and enthalpy

from the lower layer into the upper layer. A correlation is used to predict the amount of mass

and enthalpy that is transferred. A more complete plume model would predict plume

entrainment by creating a separate zone and solving the appropriate equations.

Two sources exist for moving enthalpy and mass between the layers within and between

compartments. Within the compartment, the fire plume provides one source. The other source

of mixing between the layers occurs at vents such as doors or windows. Here, there is mixing at

the boundary of the opposing flows moving into and out of the compartment. The degree of

mixing is based on an empirically-derived mixing relation. Both the outflow and inflow entrain

air from the surrounding layers. The flow at vents is also modeled as a plume (called the door

plume or jet), and uses the same equations as the fire plume, with two differences. First, an

offset is calculated to account for entrainment within the doorway and second, the equations are

modified to account for the rectangular geometry of vents compared to the round geometry of

fire plumes. All plumes within the simulation entrain air from their surroundings according to

an empirically-derived entrainment relation. Entrainment of relatively cool, non-smoke laden air

adds oxygen to the plume and allows burning of the fuel. It also causes it to expand as the plume

moves upward in the shape of an inverted cone. The entrainment in a vent is caused by bidirectional flow and results from vortices formed near a shear layer. This phenomenon is called

the Kelvin-Helmholtz instability [21]. It is not exactly the same as a normal plume, so some

error (not measured) arises when this entrainment is approximated by a normal plume

entrainment algorithm.

While experiments show that there is very little mixing between the layers at their interface,

sources of convection such as radiators or diffusers of heating and air conditioning systems, and

the downward flows of gases caused by cooling at walls, will cause such mixing. These are

examples of phenomena which are inconsistent with the two-zone approximation. Also, the

plumes are assumed not to be affected by other flows which may occur. For example, if the

burning object is near the door the strong inflow of air will cause the plume axis to lean away

from the door and affect entrainment of gases into the plume. Such effects are not included in

the model.
26

As discussed above, each compartment is divided into an upper and lower layer. At the start of

the simulation, the layers in each compartment are initialized at ambient conditions and by

default, the upper layer volume set to 0.001 of the compartment volume (an arbitrary, small

value set to avoid the potential mathematical problems associated with dividing by zero). Other

values can be set. As enthalpy and mass are pumped into the upper layer by the fire plume, the

upper layer expands in volume causing the lower layer to decrease in volume and the interface to

move downward. If the door to the next compartment has a soffit, there can be no flow through

the vent from the upper layer until the interface reaches the bottom of that soffit. Thus in the

early stages the expanding upper layer will push down on the lower layer air and force it into the

next compartment through the vent by expansion. 

Once the interface reaches the soffit level, a door plume forms and flow from the fire

compartment to the next compartment is initiated. As smoke flow from the fire compartment

fills the second compartment, the lower layer of air in the second compartment is pushed down. 

As a result, some of this air flows into the fire compartment through the lower part of the

connecting doorway (or vent). Thus, a vent between the fire compartment and connecting

compartments can have simultaneous, opposing flows of air. All flows are driven by pressure

and density differences that result from temperature differences and layer depths. The key to

getting the correct flow is to distribute correctly the fire and plume’s mass and enthalpy between

the layers.

Buoyancy generated by the combustion processes in a fire causes the formation of a plume. 

Such a plume can transport mass and enthalpy from the fire into the lower or upper layer of a

compartment. In the present implementation, we assume that both mass and enthalpy from the

fire are deposited only into the upper layer. In addition the plume entrains mass from the lower

layer and transports it into the upper layer. This yields a net enthalpy transfer between the two

layers. 

A fire R generates energy at a rate . Some fraction, P , will exit the fire as radiation. The

C

remainder, P , will then be deposited in the layers as convective energy or heat additional fuel

which may then pyrolyze. McCaffrey [22] estimated the mass entrained by the fire/plume from

the lower into the upper layer. This correlation divides the flame/plume into three regions as

given in eq (50). This prescription agrees with the work of Cetegen et al. [23] in the intermittent

regions but yields greater entrainment in the other two regions. This difference is particularly

important for the initial fire since the upper layer is far removed from the fire.
27

(51)

(50)

McCaffrey's correlation is an extension of the common point source plume model, with a

different set of coefficients for each region. These coefficients are experimental correlations. 

Within CFAST, the radiative fraction defaults to 0.30 [24]; i.e., 30 % of the fire’s energy is

released via radiation. For other fuels, the work of Tewarson [25], McCaffrey [26], or Koseki

[27] is available for reference. The typical range for the radiative fraction is from about 0.05 to

0.4.

In CFAST, there is a constraint on the quantity of gas which can be entrained by a plume arising

from a fire. The constraint arises from the physical fact that a plume can rise only so high for a

given size of a heat source. Early in a fire, when the energy flux is very small, the plume may

not have sufficient energy to reach the compartment ceiling. The correct sequence of events is

for a small fire to generate a plume which does not reach the ceiling or upper layer initially. The

plume entrains enough cool gas to decrease the buoyancy to the point where it no longer rises. 

When there is sufficient energy present in the plume, it will penetrate the upper layer. To this

end the following prescription has been incorporated: for a given size fire, a limit is placed on

the amount of mass which can be entrained, such that no more is entrained than would allow the

plume to reach the layer interface. The result is that the interface falls at about the correct rate,

although it starts a little too soon, and the upper layer temperature is over predicted, but follows

experimental data after the initial phase.

For the plume to be able to penetrate the inversion formed by a hot gas layer over a cooler gas

layer, the density of the gas in the plume at the point of intersection must be less than the density

of the gas in the upper layer. In practice, this places a maximum on the air entrained into the

plume. From conservation of mass and enthalpy
28

(55)

(52)

(56)

(53)

(54)

where the subscripts p, f, e, and l refer to the plume, fire, entrained air, and lower layer,

respectively.

The criterion that the density in the plume region be lower than the upper layer implies that

p

. Solving eq (52) for T and eliminating using eq (51) yields

or

Substituting the convective energy released by the fire,

into eq (54) yields the final form of the entrainment limit used in the CFAST model:

which is incorporated into the model. It should be noted that both the plume and layers are

assumed to be well mixed with negligible mixing and transport time for the plume and layers.

3.4.2.1 Limitation of the Plume Algorithm

The entrainment coefficients are empirically determined values from the work of McCaffrey

[27]. Small errors in these values will have a small effect on the fire plume or the flow in the

plume of gases exiting the door of that compartment. In a multi-compartment model such as

CFAST, however, small errors in each door plume are multiplicative as the flow proceeds

through many compartments, possibly resulting in a significant error in the furthest

compartments. The data available from validation experiments [28] indicate that the values for
29

entrainment coefficients currently used in most zone models produce good agreement for a

three-compartment configuration. More data are needed for larger numbers of compartments to

study this further.

In real fires, smoke and gases are introduced into the lower layer of each compartment primarily

due to mixing at connections between compartments and from the downward flows along walls

(where contact with the wall cools the gas and reduces its buoyancy). Doorway mixing has been

included in CFAST, using the same empirically derived mixing coefficients as used for

calculating fire plume entrainment. Downward wall flow has not been included. This could

result in underestimates of lower layer temperatures and species concentration. 

Entrainment at a vent (doors, windows, ...) yields mixing into the lower and upper layers. The

latter has been studied more extensively than the former. The door jets are not symmetric for

these mixing phenomena, however. We have constrained the phenomenon for CFAST to be in

the range as predicted by Zukoski et al. [29].

3.4.3 Vent Flow

Flow through vents is a dominant component of any fire model because it is sensitive to small

changes in pressure and transfers the greatest amount of enthalpy on an instantaneous basis of all

the source terms (except of course for the fire and plume). Its sensitivity to environmental

changes arises through its dependence on the pressure difference between compartments which

can change rapidly. 

CFAST models two types of vent flow, vertical flow through horizontal vents (such as ceiling

holes or hatches) and horizontal flow through vertical vents (such as doors or windows). 

Horizontal flow is the flow which is normally thought of when discussing fires. Vertical flow is

particularly important in two disparate situations: a ship, and the role of fire fighters doing roof

venting.

Horizontal vent flow is determined using the pressure difference across a vent. Flow at a given

elevation may be computed using Bernoulli’s law by first computing the pressure difference at

that elevation. The pressure on each side of the vent is computed using the pressure at the floor,

the height of the floor and the density. 

Atmospheric pressure is about 100 000 Pa. Fires produce pressure changes from 1 Pa to 1000 Pa

and mechanical ventilation systems typically involve pressure differentials of about 1 Pa to

100 Pa. The pressure variables are solved to a higher accuracy than other solution variables

because of the subtraction (with resulting loss of precision) needed to calculate vent flows from

pressure differences.
30

Mass flow (in the remainder of this section, the term “flow” will be used to mean mass flow) is

the dominant source term for the predictive equations because it fluctuates most rapidly and

transfers the greatest amount of enthalpy on an instantaneous basis of all the source terms

(except of course the fire). Also, it is most sensitive to changes in the environment. Horizontal

flow encompasses flow through doors, windows and so on. Horizontal flow is discussed in

section 3.4.3.1. Vertical flow occurs in ceiling vents. It is important in two separate situations:

on a ship with open hatches and in house fires with roof venting. Vertical flow is discussed in

section 3.4.3.2.

Flow through vents can be forced (mechanical) or natural (convective). Force flow can occur

through either vertical or horizontal vents. The differences are primarily the selection rules for

the source of the gases or whether the resultant plume enters the lower or upper layer of each

compartment.

There is a special case of horizontal flow for long corridors. A corridor flow algorithm is

incorporated to calculate the time delay from when a plume enters a compartment to when the

effluent is available for flow into adjacent compartments.

3.4.3.1 Horizontal Flow Through Vertical Vents

Flow through normal vents such as windows and doors is governed by the pressure difference

across a vent. A momentum equation for the zone boundaries is not solved directly. Instead

momentum transfer at the zone boundaries is included by using an integrated form of Euler's

equation, namely Bernoulli's solution for the velocity equation. This solution is augmented for

restricted openings by using flow coefficients [30] to allow for constriction from finite size

doors. The flow (or orifice) coefficient is an empirical term which addresses the problem of

constriction of velocity streamlines at an orifice.

Bernoulli's equation is the integral of the Euler equation and applies to general initial and final

velocities and pressures. The implication of using this equation for a zone model is that the

initial velocity in the doorway is the quantity sought, and the final velocity in the target

compartment vanishes. That is, the flow velocity vanishes where the final pressure is measured. 

Thus, the pressure at a stagnation point is used. This is consistent with the concept of uniform

zones which are completely mixed and have no internal flow. The general form for the velocity

of the mass flow is given by

(57)
31

Figure 4. Notation conventions for two-layer model in two compartments

with a connecting vent.

where C is the constriction (or flow) coefficient (.0.7), D is the gas density on the source side,

and P is the pressure across the interface. (Note: at present we use a constant C for all gas

temperatures)

The simplest means to define the limits of integration is with neutral planes, that is the height at

which flow reversal occurs, and physical boundaries such as sills and soffits. By breaking the

integral into intervals defined by flow reversal, a soffit, a sill, or a zone interface, the flow

equation can be integrated piecewise analytically and then summed. 

The approach to calculating the flow field is of some interest. The flow calculations are

performed as follows. The vent opening is partitioned into at most six slabs where each slab is

bounded by a layer height, neutral plane, or vent boundary such as a soffit or sill. The most

general case is illustrated in figure 4.

The mass flow for each slab can be determined from

(58)

where t b , and . P and P are the cross-vent pressure differential at the

slab top and bottom of the slab respectively and A is the cross-sectional area of the slab. The value

of the density, D, is taken from the source compartment.
32

(59)

A mixing phenomenon occurs at vents which is similar to entrainment in plumes. As hot gases

from one compartment leave that compartment and flow into an adjacent compartment a door jet

can ex 13 ist which is analogous to a normal plume. Mixing of this type occurs for m0 > 0 as shown

43 in figure 5. To calculate the entrainment (m0 in this example), once again we use a plume

description consistent with the work of McCaffrey, but with an extended point source. The

estimate for the point source extension is given by Cetegen et al. [23]. This virtual point source

is chosen so that the flow at the door opening would correspond to a plume with the heating for a

equivalent doorway fire source (with respect to the lower layer) given by

where is the heat release rate of the doorway fire. The concept of the virtual source is that

the enthalpy flux from the virtual point source should equal the actual enthalpy flux in the door

jet at the point of exit from the vent using the same prescription. Thus the entrainment is

calculated the same way p as was done for a normal plume. The reduced height of the plume, z , is

[22]
33

Figure 5. Flow patterns and layer numbering convention.

(61)

(60)

where vp, the virtual point source, is defined by inverting the entrainment process to yield 

Although outside of the normal range of validity of the plume model, a level of agreement with

experiment is apparent (section 6 includes discussion of validation experiments for the plume

model). Since a door jet forms a flat plume whereas a normal fire plume will be approximately

circular, strong agreement is not expected.

The other type of mixing is much like an inverse plume and causes contamination of the lower

42 layer. It occurs when there is flow of the type m0 > 0. The shear flow causes vortex shedding

into the lower layer and thus some of the particulates end up in the lower layer. The actual

amount of mass or energy transferred is usually not large, but its effect can be large. For
34

example, even minute amounts of carbon can change the radiative properties of the gas layer,

from negligible to something finite. It changes the rate of radiation absorption significantly and

invalidates the simplification of an ambient temperature lower layer. This term is predicated on

the Kelvin-Helmholz flow instability and requires shear flow between two separate fluids. The

mixing is enhanced for greater density differences between the two layers. However, the amount

of mixing has never been well characterized. Quintiere et al. [30] discuss this phenomena for the

case of crib fires in a single room, but their correlation does not yield good agreement with

experimental data in the general case [31]. In the CFAST model, it is assumed that the incoming

cold plume behaves like the inverse of the usual door jet between adjacent hot layers; thus we

have a descending plume. It is possible that the entrainment is overestimated in this case, since

buoyancy, which is the driving force, is not nearly as strong as for the usually upright plume.

3.4.3.2 Vertical Flow Through Horizontal Vents

Flow through a ceiling or floor vent can be somewhat more complicated than through door or

window vents. The simplest form is uni-directional flow, driven solely by a pressure difference. 

This is analogous to flow in the horizontal direction driven by a piston effect of expanding gases. 

Once again, it can be calculated based on the Bernoulli equation, and presents little difficulty. 

However, in general we must deal with more complex situations that must be modeled in order

to have a proper understanding of smoke movement. The first is an occurrence of puffing. 

When a fire exists in a compartment in which there is only one hole in the ceiling, the fire will

burn until the oxygen has been depleted, pushing gas out the hole. Eventually the fire will die

down. At this point ambient air will rush back in, enable combustion to increase, and the

process will be repeated. Combustion is thus tightly coupled to the flow. The other case is

exchange flow which occurs when the fluid configuration across the vent is unstable (such as a

hotter gas layer underneath a cooler gas layer). Both of these pressure regimes require a

calculation of the onset of the flow reversal mechanism.

Normally a non-zero cross vent pressure difference tends to drive unidirectional flow from the

higher to the lower pressure side. An unstable fluid density configuration occurs when the pressure alone would dictate stable stratification, but the fluid densities are reversed. That is, the

hotter gas is underneath the cooler gas. Flow induced by such an unstable fluid density

configuration tends to lead to bi-directional flow, with the fluid in the lower compartment rising

into the upper compartment. This situation might arise in a real fire if the room of origin

suddenly had a hole punched in the ceiling. No pretense is made of being able to do this

instability calculation analytically. Cooper's algorithm [32] is used for computing mass flow

through ceiling and floor vents. It is based on correlations to model the unsteady component of

the flow. What is surprising is that we can find a correlation at all for such a complex

phenomenon. There are two components to the flow. The first is a net flow dictated by a

pressure difference. The second is an exchange flow based on the relative densities of the gases. 

The overall flow is given by [32]
35

(65)

(62)

where ( p v = c /c is the ratio of specific heats and

(63)

(64)

and f is a weak function of both ( and g [32]. In the situation where we have an instability, we

use Cooper's correlations for the function f. The resulting exchange flow is given by

where

(66)

and S is 0.754 or 0.942 for round or square openings, respectively [32].

3.4.3.3 Forced Flow

Fan-duct systems are commonly used in buildings for heating, ventilation, air conditioning,

pressurization, and exhaust. Figure 6(a) shows smoke management by an exhaust fan at the top

of an atrium, and figure 6(b) illustrates a kitchen exhaust. Cross ventilation, shown in figure

6(c), is occasionally used without heating or cooling. Generally systems that maintain comfort

conditions have either one or two fans. Residences often have a system with a single fan as

shown in figure 6 and 7(a). In this system return air from the living quarters is drawn in at one

location, flows through filter, fan and coils, and is distributed back to the residence. This system

does not have the capability of providing fresh outside air. These systems are intended for
36

Figure 6. Some simple fan-duct systems.

applications where there is sufficient natural air leakage through cracks in walls and around

windows and doors for odor control. Further information about these systems is presented in 

Klote and Milke [33] and the American Society of Heating, Refrigerating and Air Conditioning

Engineers (ASHRAE) [34].

The model for mechanical ventilation used in CFAST is based on the theory of networks and is

based on the model developed by Klote [35]. This is a simplified form of Kirchoff's law which

says that flow into a node must be balanced by flow out of the node. Adapting Ohm’s law,

voltage = current × resistance,

to HVAC flow, we have
37

pressure change = mass flow × resistance 

which can then be written equivalently

mass flow = conductance × (pressure drop across a resistance) .

1⁄2

For each node, this flow must sum to zero. There are several assumptions which are made in

computing this flow in ducts, fans, elbows, etc. First, we assume unidirectional flow. Given the

usual size of ducts, and the nominal presence of fans, this is quite reasonable. Also, the

Figure 7. Network representation of a residential system
38

particular implementation used here [35] does not allow for reverse flow in the fans. The

difficulty lies in describing how a fan behaves in such a case.

Each fan-duct system is represented as a network of nodes, each at a specific temperature and

pressure. The nodes may be connected by fans, ducts, fittings and other components. Except for

fans, air flows through these components from nodes of higher pressure to nodes of lower

pressure. For example, the residential system illustrated in 7(a) is represented in 7(b) as a

network of a fan, eight resistances and ten nodes. These resistances incorporate all the resistance

1

to flow between nodes. For instance, the equivalent resistance, R , between nodes 1 and 2

accounts for resistances of the inlet, duct, filter and connection to the fan. 

Given that we can describe mass flow in terms of pressure differences and conductance, the

conservation equation for each node is

(67)

The index “j” is a summation over connections to a node, and there is an equation “i” for each

node. The remaining problem is to specify the boundary conditions. At each connection to a

compartment, the pressure is specified. Then, given that flow at each connection is

unidirectional (at a given instant of time, the flow is either all into or all out of a given

connection), the mass and enthalpy flow into or out of a room can be calculated explicitly. Thus

we end up with a set of equations of the form

(68)

This is an algebraic set of equations that is solved simultaneously with the equations for flow in

the compartments.

The equations describe the relationship between the pressure drop across a duct, the resistance of

a duct, and the mass flow. The pressure can be changed by conditions in a compartment, or a fan

in line in the duct system. Resistance arises from the finite size of ducts, roughness on surfaces,

bends and joints. To carry the electrical analog a little further, fans act like constant voltage

sources. The analogy breaks down in this case because the pressure (voltage) is proportional to

the square of the velocity (current) rather than linearly related as in the electrical case. Since we
39

are using the current form of the conservation equation to balance the system, the flow can be

recast in terms of a conductance

(69)

The conductance can be expressed generally as

(70)

where C0 0 is the flow coefficient, and A is the area of the inlet, outlet, duct, contraction or

expansion joint, coil, damper, bend, filter, and so on. Their values for the most common of these

items are tabulated in the ASHRAE Handbook [36].

The mechanical ventilation system is partitioned into one or more independent systems. 

Differential equations for species for each of these systems are derived by lumping all ducts in a

system into one pseudo tank. This set of equations is then solved at each time step. Previously

the mechanical ventilation computations in CFAST were performed as a side calculation using

time splitting. This could cause problems since time-splitting methods require that the split

phenomenon (the pressures and temperatures in this case) change slowly compared to other

phenomenon such as room pressures or layer heights. The pressures at each internal node and

the temperatures in each branch (duct, fan) are now determined explicitly by the solver, once

again using conservation of mass and energy discussed in this section.

 Ducts. 

Ducts are long pipes through which gases can flow. They have been studied much more extensively than other types of connections. For this reason, eq (70) can be put into a form which

allows one to characterize the conductance in more detail, depending on the type of duct (e.g.,

oval, round, or square) and is given by

(71)

where F e is the friction factor, L and D are the length and effective diameter of the duct

respectively. The temperature for each duct d is determined using the following differential

equation:

accumulated heat = (heat in - heat out) - convective losses through duct walls
40

Figure 8. Typical fan performance at constant speed. 

(72)

where cv p d d, c are the constant volume/pressure specific heats; V is the duct volume, D is the duct

gas density d d , dT /dt is the time rate of change of the duct gas temperature, m is the mass flow

in out d d

rate,T and T are the gas temperatures going into and out of the duct, h , A are the convective

hea ambt transfer coefficient and surface area for duct d and T is the ambient temperature. The

first term on the right hand side of eq (72) represents the net gain of energy due to gas

transported into or out of the duct. The second term represents heat transferred to the duct walls

due to convection. Heat loss through the duct walls is assumed to be zero. The differential and

algebraic (DAE) solver used by CFAST solves eq (72) exactly as written. A normal ordinary

differential equation solver would require that this equation be solved for dT/dt. By writing it

this way, the duct volumes can be zero which is the case for fans.

 Fans. 

This section provides background information about fan performance. For more information

about fans, readers are referred to Jorgensen [37] and ASHRAE [34]. Normal fan operating

f

range is represented by the line segment AB in figure 8. In this figure, )P is the static pressure

of the fan, and is the volumetric flow of the fan. The point B represents a margin of safety

selected by the fan manufacturer in order to avoid unstable flow.
41

Fans operating in the positively sloping portion (CD of figure 8) of the fan curve exhibit unstable

behavior called surging or pulsing. Unstable flow consists of violent flow reversals

accompanied by significant changes in pressure, power and noise. There is little information

about how long a fan can operate in the unstable region before it is destroyed.

Backward flow through a fan occurs when the static pressure is greater than that at point D. This

is also called second quadrant flow. Quadrant terminology is customarily used in description of

fan performance. The horizontal axis and the vertical axis divide a plane into four quadrants

which for convenience are labeled Q I, Q II, Q III and Q IV on figure 8. Backward flow can be

exhibited by all types of fans. The wind blowing into the outlet of a propeller fan can result in

backflow, and pressures produced by fires could also produce backflow. Fourth quadrant flow is

probably f representative of all fans. As )p becomes negative, the flow increases with decreasing 

)pf until a choking condition develops at point E. 

It is common practice in the engineering community and fan industry to represent fan

performance with )pf on the vertical axis and on the horizontal axis. Probably the reason is

f

that can be thought of as a single valued function of )p for flow in the first and second

quadrants. Fan manufacturers generally supply flow-pressure data for the normal operating

range, and they often supply data for the rest of the fan curve in the first quadrant. Specific data

are not available for either second or fourth quadrant flow. No approach has been developed for

simulation of unstable fan operation, and numerical modeling of unstable flow would be a

complicated effort requiring research. 

Numerical Approximation of Fan Performance: Figure 9 illustrates four approaches that can

be used to approximate fan performance without simulation of unstable flow. For all of these

approaches, the fan curve is used for the normal operating range of AB. Also for all of the

approaches, flows above the normal operating range are approximated by a straight line tangent

to the fan curve at point A. This results in fourth quadrant flow that is similar to the expected

f

flow provided that )p is not overly far below the horizontal axis. In figure 9(a), flows below the

normal range are approximated by a linear curve tangent to the fan curve at point B. This avoids

simulation of unstable flows, but the approximated flow is higher than expected in the first

quadrant and lower than expected for much of the fourth quadrant. 

The approach of figure 9(b) reduces the approximated flow in the first quadrant. In this

approach, the fan curve is also used for the range BF, and flows above the normal operating

range are approximated by a straight line tangent to the fan curve at point F. To increase the
42

Figure 9. Some approaches to approximation of fan performance

for computer simulation 

flow in the second quadrant, figure 9(c) uses a line passing through point D with the slope of the 
43

(73)

fan curve at point A. Both of the modifications of figure 9(b) and figure 9(c) are combined in the

approach of figure 9(d). 

Fan manufacturer data are routinely either in tabular or graphical form. As indicated by

Jorgensen [37], the use of a polynomial form of fan curve is common within the industry. 

The units for f and Îp in CFAST are m /s and Pa respectively. Therefore the units for the 3

coe ifficients B (i=1, ... , 5) are m /(s Pa ). The coefficients can be entered as data or calculated

3 i-1

by least squares regression from flow and pressure data. For constant volumetric flow

app 1lications, the only non-zero coefficient in eq (73) is B (n = 1). For incompressible fluids, eq

(73) is independent of temperature and pressure. For fan data at 20 °C, compressibility effects

amount to an error of about 6 % at a temperature of 200 °C. 
44

(74)

(75)

(76)

(77)

(78)

(79)

Effective Resistance: The resistance, R, of a flow element can be defined as

where )p is the pressure loss through the element corresponding to a mass flow rate, . The

effective resistance between two nodes is always positive, however, sometimes one of the

resistances between nodes can be negative as will be explained later. To account for this, R = K

1⁄2

can be substituted into eq (74) to give

The total pre t i ssure loss, )p , from one node to the next is the sum of the losses, )p , through each

flow element, i, between the nodes.

The e effective value, K , relates the total pressure loss to the mass flow rate as , and

Ki relates the pressure loss through element i as . These pressure losses can be

substituted into eq (76), and canceling like terms yields

Values of Ki e can be calculated for each element using equations developed later, and K can be

calculated by eq (77).

Resistance of Ducts: For a straight section of duct with constant cross sectional area, the

Be fr rnoulli equation incorporating pressure loss, )p , due to friction is commonly written

where the subscripts 1 and 2 refer to the duct inlet and outlet respectively, p is pressure, Z is

elevation, g is the acceleration due to gravity, and D is the density of the gas. The pressure loss

due to friction is expressed by the Darcy equation in most elementary treatments of flow in pipes

and ducts [36], [38], [39].
45

(80)

(81)

(82)

(83)

(84)

(85)

where ef is the friction factor, L is the duct length, D is the effective diameter of the duct and U is

the average velocity in the duct ( where A is the cross-sectional area of the duct). For

a circular duct, the effective diameter is the duct diameter. For rectangular duct, Huebscher [40]

developed the relationship 

where a is the length of one side of the duct, and b is the length of the adjacent side. For flat

oval duct, Heyt and Diaz [41] developed the relationship

where A and P are the cross-sectional area and the perimeter of the flat oval duct. The area of a

flat oval duct is

and the perimeter of a flat oval duct is

where a is the major dimension of the flat oval duct, and b is the minor dimension of the duct. 

Combining eqs 74 and 78 results in

Combining eqs 75 and 79 results in

where A is the cross sectional area of the duct. Colebrook developed the following equation for

the friction factor [42].
46

(86)

Duct Material Roughness

Category

Absolute Roughness,

g

mm ft

Uncoated Carbon Steel, Clean. PVC Plastic Pipe.

Aluminum.

Smooth 0.03 0.0001

Galvanized Steel, Longitudinal Seams, 1200 mm

Joints.

Galvanized Steel, Continuously Rolled, Spiral

Seams, 3000 mm Joints.

Galvanized Steel, Spiral Seam with 1, 2 and 3

Ribs, 3600 mm Joints.

Medium

Smooth 0.09 0.0003

Galvanized Steel, Longitudinal Seams, 760 mm

Joints.

Average 0.15 0.0005

Fibrous Glass Duct, Rigid.

Fibrous Glass Duct Liner, Air Side With Facing

Material.

Medium

Rough 0.9 0.003

Fibrous Glass Duct Liner, Air Side Spray Coated.

Flexible Duct, Metallic.

Flexible Duct, All Types of Fabric and Wire.

Concrete.

Rough 3.0 0.01

Table 3. Absolute roughness values for common duct materials 

(87)

where Re e is the Reynolds number (UD /L where L is the kinematic viscosity) and g is the

roughness of the inside surface of the duct. Data on roughness of duct materials are listed in

table 3. A graphical presentation of the Colebrook equation developed by Moody [43] was used

for decades to calculate friction factors. However, today it is practical to solve the Colebrook

equation with computers.

Local Loss Resistances: The pressure loss, )p, through many other elements can be expressed

as

where Uo o is the average velocity at cross section o within the element, and C is a local loss

coefficient. This equation is commonly used for inlets, outlets, duct contractions and
47

(88)

expansions, heating and cooling coils, dampers, bends and many filters. For a large number of

o

these elements, values of C have been empirically determined and are tabulated frequently as

functions of geometry in handbooks [34],[44]. Manufacturers’ literature also contains some

values of Co. The value of K for these resistances is

where Ao is the area at cross section o.

3.4.4 Corridor Flow

A standard assumption in zone fire modeling is that once hot smoke enters a compartment, a

well defined upper layer forms instantly throughout the compartment. This assumption breaks

down in large compartments and long corridors due to the time required to fill these spaces. A

simple procedure is described for accounting for the formation delay of an upper layer in a long

corridor by using correlations developed from numerical experiments generated with the NIST

fire model Large Eddy Simulation Model (LES) [45], which is now the Fire Dynamic Simulation

Model (FDS) [46]. FDS is a computational fluid dynamics model capable of simulating fire

flow velocities and temperatures with high (.0.1 m) resolution. Two parameters related to

corridor flow are then estimated: the time required for a ceiling jet to travel in a corridor and the

temperature distribution down the corridor. These estimates are then used in CFAST by

delaying flow into compartments connected to corridors until the ceiling jet has passed these

compartments.

FDS was used to estimate ceiling jet characteristics by running a number of cases for various

inlet layer depths and temperatures. The vent flow algorithm in CFAST then uses this

information to compute mass and enthalpy flow between the corridor and adjacent

compartments. This is accomplished by presenting the vent algorithm with a one layer

environment (the lower layer) before the ceiling jet reaches the vent and a two layer environment

afterwards. Estimated ceiling jet temperatures and depths are used to define upper layer

properties.

The problem is to estimate the ceiling jet temperature and depth as a function of time until it

reaches the end of the corridor. The approach used here is to run a field model as a

pre-processing step and to summarize the results as correlations describing the ceiling jet's

temperatures and velocities. The steps used in this process are as follows:

 1. Model corridor flow for a range of inlet ceiling jet temperatures and depths. Inlet

velocities are derived from the inlet temperatures and depths.
48

 2. For each model run calculate average ceiling jet temperature and velocity as a function of

distance down the corridor.

 3. Correlate the temperature and velocity distribution down the hall.

The zone fire model then uses these correlations to estimate conditions in the corridor as follows:

 1. Estimate the inlet temperature, depth and velocity of the ceiling jet. If the corridor is the

fire room then use a standard correlation. If the source of the ceiling jet is another room

then calculate the inlet ceiling jet flow using Bernoulli's law for the vent connecting the

source room and the corridor.

 2. Use correlations in 3. above to estimate the ceiling jet arrival time at each vent.

 3. For each vent in the corridor use lower layer properties to compute vent flow before the

ceiling jet arrives at the vent and lower/upper layer properties afterwards.

Assumptions: The assumptions made in order to develop the correlations are:

 • The time scale of interest is the time required for a ceiling jet to traverse the length of the

corridor. For example, for a 100 m corridor with 1 m/s flow, the characteristic time

would be 100 s.

 • Cooling of the ceiling jet due to mixing with adjacent cool air is large compared to

cooling due to heat loss to walls. Equivalently, we assume that walls are adiabatic. This

assumption is conservative. An adiabatic corridor model predicts more severe conditions

downstream in a corridor than a model that accounts for heat transfer to walls, since

cooler ceiling jets travel slower and not as far.

 • We do not account for the fact that ceiling jets that are sufficiently cooled will stagnate.

Similar to the previous assumption, this assumption is conservative and results in over

predictions of conditions in compartments connected to corridors (since the model

predicts that a ceiling jet may arrive at a compartment when in fact it may have stagnated

before reaching it).

 • Ceiling jet flow is buoyancy driven and behaves like a gravity current. The inlet velocity

of the ceiling jet is related to its temperature and depth.

 • Ceiling jet flow lost to compartments adjacent to the corridor is not considered when

estimating ceiling jet temperatures and depths. Similarly, a ceiling jet in a corridor is

assumed to have only one source.
49

(89)

 • The temperature and velocity at the corridor inlet is constant in time.

 • The corridor height and width do not effect a ceiling jet's characteristics. Two ceiling jets

with the same inlet temperature, depth and velocity behave the same when flowing in

corridors with different widths or heights as long as the ratio of inlet widths to corridor

width are equal.

 • Flow entering the corridor enters at or near the ceiling. The inlet ceiling jet velocity is

vent room vent room reduced from the vent inlet velocity by a factor of w /w where w and w are the

width of the vent and room, respectively.

Corridor Jet Flow Characteristics: Ceiling jet flow in a corridor can be characterized as a one

dimensional gravity current. To a first approximation, the velocity of the current depends on the

difference between the density of the gas located at the leading edge of the current and the gas in

the adjacent ambient air. The velocity also depends on the depth of the current below the

ceiling. A simple formula for the gravity current velocity may be derived by equating the

po 0 0tential energy of the current, mgd /2, measured at the half-height d /2 with its kinetic energy,

mV /2 to obtain 2

where m 0 is mass, g is the acceleration of gravity, d is the height of the gravity current and V is

the velocity. When the density difference, between the current and the ambient fluid is small, the

velocity amb amb, V, is proportional to where D and T are the ambient

density cj cj and temperature and D and T are the density and temperature of the ceiling jet and 

)T = Tcj amb - T is the temperature difference. Here use has been made of the ideal gas law,

DambTamb . DcjTcj. This can be shown using an integrated form of Bernoulli's law noting that the

pre bssure drop at the bottom of the ceiling jet is P = 0, the pressure drop at the top is

vent and using a vent coefficient c of 0.74, to obtain
50

(94)

(92)

Formulas of the form of the above equation lead one to conclude that a ceiling jet's

characte 0ristics in a corridor depend on its depth, d , and relative temperature difference,

. Therefore, as the jet cools, it slows down. If no heat transfer occurs between the ceiling

jet and the surrounding walls, then the only mechanism for cooling is mixing with surrounding

cool air.

Twenty numerical experiments were performed using FDS in order to better understand the

effects of the inlet ceiling jet temperature and depth on ceiling jet characteristics downstream in

a corridor. These cases were run with five different inlet depths and four different inlet

0 0 temperatures. The inlet ceiling jet temperature rise, )T , and depth, d , were used to define an

0 0 inlet velocity, V using eq (92). The inlet ceiling jet depths, d , used in the parameter study are

0.15 m, 0.30 m, 0.45 m, 0.60 m and 0.75 m. The inlet ceiling 0 jet temperature rises, T , used in the

parameter study are 100 °C, 200 °C, 300 °C and 400 °C.

Correlations: Ceiling jet functions were plotted as a function of distance down a corridor for

each of the 20 test cases. These results are shown in figure 10. Note that all but the 0.15 m

ceiling jet data lie on essentially the same line. 

The best fit line is given in the form of
51

(95)

(96)

This is equivalent to

where C1 1/2 1/2 = 10 and h = - log(2)/b. The parameter h has a physical interpretation. It is the a

distance down the corridor where the temperature rise T , falls off to 50 % of its original value or

equivalently 1/2 , T (x + h ) = T (x)/2.

The ha 1/2 1/2 lf-distance, h , can be approximated by h = log(2)/0.018 = 16.7 m where b = -0.018 is

g 1 1 iven in figure 10. Similarly, the coefficients C is approximated by C = 10 = 10 . 1 where

a -0.003

a can be determined from figure 10. Therefore the temperature rise, )T , may be approximated

by 

Figure 10. Log10 of the relative temperature excess downstream in a

corridor using an adiabatic temperature boundary condition for several

inlet depths and inlet temperature boundary condition. The inlet velocity,

V0, is given by eq (92).
52

The numerical experiments with FDS [46] demonstrated that for the cases simulated, ceiling jet

characteristics depend on the relative inlet temperature rise and not the inlet depth. Flow in long

corridors (greater than 10 m) need to be better characterized due to the flow stagnation which

may occur because of the ceiling jet's temperature decay.

3.4.5 Heat Transfer

This section discusses radiation, convection and conduction, the three mechanisms by which

heat is transferred between the gas layers and the enclosing compartment walls. This section

also discusses heat transfer algorithms for calculating target temperatures.

Gas layers exchange energy with their surroundings via convective and radiative heat transfer. 

Different material properties can be used for the ceiling, floor, and walls of each compartment

(although all the walls of a compartment must be the same). Additionally, CFAST allows each

surface to be composed of up to three distinct layers. This allows the user to deal naturally with

the actual building construction. Material thermophysical properties are assumed to be constant,

although we know that they actually vary with temperature. The user should also recognize that

the mechanical properties of some materials may change with temperature, but these effects are

not modeled.

Radiative transfer occurs among the fire(s), gas layers and compartment surfaces (ceiling, walls

and floor). This transfer is a function of the temperature differences and the emissivity of the

gas layers as well as the compartment surfaces. Typical surface emissivity values only vary over

a small range. For the gas layers, however, the emissivity is a function of the concentration of

species which are strong radiators, predominately smoke particulates, carbon dioxide, and water. 

Thus errors in the species concentrations can give rise to errors in the distribution of enthalpy

among the layers, which results in errors in temperatures, resulting in errors in the flows. This

illustrates just how tightly coupled the predictions made by CFAST can be.

3.4.5.1 Radiation

Radiation heat transfer forms a significant portion of the energy balance in a zone fire model,

especially in the fire room. Radiative heat transfer is computed from wall and gas temperatures,

emisivities and fire heat release rates. To calculate the radiation absorbed in a zone, a heat

balance must be done accounting for all surfaces that radiate to and absorb radiation from a zone. 

A radiation heat transfer calculation can easily dominate the computational requirements of any

fire model. Approximations are then required to perform these calculations in a time consistent

with other zone fire model sources terms. For example, it is assumed that all zones and surfaces

radiate and absorb like a gray body, that the fires radiate as point sources and that the plume does

not radiate at all. Radiative heat transfer is approximated using a limited number of radiating

wall surfaces, four in the fire room and two everywhere else. The use of these and other
53

approximations allows CFAST to perform the radiation computation in a reasonably efficient

manner [47]. 

Modeling Assumptions: The following assumptions are made in order to simplify the radiation

heat exchange model used in CFAST and to make its calculation tractable.

Iso-thermal - Each gas layer and each wall segment is assumed to be at a uniform

temperature. 

Equilibrium - The wall segments and gas layers are assumed to be in a quasi-steady

state. In other words, the wall and gas layer temperatures are assumed to change slowly

over the duration of the time step of the associated differential equation.

Point Soure Fires - The fire is assumed to radiate uniformly in all directions giving off a

R

fraction, P , of the total energy release rate. This radiation is assumed to originate from a

single point. Radiation feedback to the fire and radiation from the plume is not modeled

in the radiation exchange algorithm.

Diffuse and gray surfaces - The radiation emitted is assumed to be diffuse and gray. In

other words, the radiant fluxes emitted are independent of direction and wavelength. 

These assumptions allow us to infer that the emittance, ,, absorptance, " and reflectance,

D, are related via ,="=1-D. 

Geometry - Rooms or compartments are assumed to be rectangular boxes. Each wall is

either perpendicular or parallel to every other wall. Radiation transfer through vent

openings is lost from the room.

4-Wall and 2-Wall Radiation Exchange: When computing wall temperatures, CFAST

partitions a compartment into four parts; the ceiling, the floor, the wall segments above the layer

interface and the wall segments below the layer interface. The radiation algorithm then

computes a heat flux striking each wall segment using the surface temperature and emissivity. 

The four wall algorithm used in CFAST for computing radiative heat exchange is based upon the

equations developed in Siegel and Howell [48] which in turn is based on the work of Hottel [49].

Siegel and Howell model an enclosure with N wall segments and a homogeneous gas. A

radiation algorithm for a two layer zone fire model requires treatment of an enclosure with two

uniform gases. Hottel and Cohen [50] developed a method where the enclosure is divided into a

number of wall and gas volume elements. An energy balance is written for each element. Each

balance includes interactions with all other elements. Treatment of the fire and the interaction of

the fire and gas layers with the walls is based upon the work of Yamada and Cooper [51]. They

model fires as point heat sources radiating uniformly in all directions and use the Lambert-Beer

law to model the interaction between heat emitting elements (fires, walls, gas layers) and the gas
54

Figure 11. Radiation exchange in a two-zone fire model.

layers. By implementing a four wall rather than an N wall model, significant algorithmic speed

increases are achieved. This is done by exploiting the simple structure and symmetry of the four

wall problem.

The nomenclature used in this section follows that of Siegel and Howell [48]. The radiation

exchange at the k'th surface is shown schematically in figure 11. For each wall segment k from

1 to N, a net heat flux, )q "k, must be found such that the energy balance,

(97)

at each wa kll segment k is satisfied, where F is the Stefan-Boltzman constant, A is the area of the

k’th wall segment , k kg is the emissivity of the k’th wall segment, T is the temperature of the k’th

wall segment and qk is the energy arriving at the k’th wall segment from all other wall segments in

and heat sources.

Radiation exchange at each wall segment considers the emitted, reflected, incoming and net

k

radiation terms. The unknown net radiative fluxes, )q " , are found by solving the modified net

radiation equation

(98)

where k-j , F is the configuration factor, J is the transmittance and other terms are

de kfined previously. The parameters c represent the various sources of heat, namely the fire

itself and the gas layers. 
55

Figure 12. An example of the calculated two-wall (RAD2) and

four-wall (RAD4) contributions to radiation exchange on a ceiling

and wall surface.

The walls can be modeled using two surfaces or four. The four wall model is necessary for fire

rooms because the temperatures of the ceiling and upper walls differ significantly. The two wall

model is used for compartments that contain no fires.

To simplify the comparison between the two and four wall segment models, assume that the

emissivities of all wall segments are one and that the gas absorptivities are zero. Let the room

dimensions be 4 m × 4 m × 4 m, the temperature of the floor and the lower and upper walls be

300 K, and the ceiling temperature vary from 300 K to 600 K. Figure 12 shows a plot of the heat

flux to the ceiling and upper wall as a function of the ceiling temperature [47], [52]. The two

wall model predicts that the extended ceiling (a surface formed by combining the ceiling and

upper wall into one wall segment) cools, while the four wall model predicts that the ceiling cools

and the upper wall warms. The four-wall model moderates temperature differences that may

exist between the ceiling and upper wall (or floor and lower wall) by allowing heat transfer to

occur between the ceiling and upper wall. This problem does not arise when a fire is not present.

Reference [47] documents how to minimize the work required to compute the 16 configuration

factors, , required in a 4 wall model.
56

(99)

(100)

Figure 13. Setup for a configuration factor calculation

between two arbitrarily oriented finite areas

(101)

Conf 1-2 iguration Factors: A configuration factor between two finite areas denoted F is the

fraction of radiant energy given off by surface 1 that is intercepted by surface 2 and is given by

where L 1 2 is the distance along the line of integration, 2 and 2 are the angles for surface 1 and 2

between the re 1 2 spective normal vectors and the line of integration, and A and A are the areas of

1 2 the two surfaces. These terms are illustrated in figure 13. When the surfaces A and A are far

apa 1 2 rt relative to their surface area, eq (99) can be approximated by assuming that 2 , 2 and L are

constant over the region of integration to obtain

Transmittance and Absorptance: The transmittance of a gas volume is the fraction of radiant

energy that will pass through it unimpeded and is given by
57

where a is the absorption coefficient of the gas volume and L is a characteristic path length.

The absorptance, ", of a gas volume is the fraction of radiant energy absorbed by that volume. 

For a gray gas, " + J = 1.

Calculating absorption for broad band gas layer radiation: In general, the transmittance and

absorptance are a function of wavelength. This is an important factor to consider for the major

gaseous products (CO2 2 and H O); however soot has a continuous absorption spectrum which

allows the transmittance and absorptance to be approximated as “gray” [48] across the entire

spectrum.

The gas absorptance G 2 2, " , is due to the combination of the CO and H O

and is given by

where C is a correction for band overlap. For typical fire conditions, the overlap amounts to

about half of the CO2 absorptance [53] so the gas transmittance is approximated by

The total transmittance of a gas-soot mixture is the product of the gas and soot transmittances

Substitution of eqs (101) and (103) into eq (104) yields

In the optically thin limit the absorption coefficient, a, may be replaced by the Planck mean

absorption coefficient and in the optically thick limit, it may be replaced by the Rosseland mean

absorption coefficient. For the entire range of optical thicknesses, Tien et al. [53] report that a

reasonable approximation is

(102)

(103)

(104)

(105)

(106)
58

where k v is a constant which depends on the optical properties of the soot particles, f is the soot

volume fraction and T is the soot temperature in Kelvin. Values of a, have been found to be

about constant for v a wide range of fuels [54]. The soot volume fraction, f , is calculated from

the soot mass, soot density and layer volume. The soot is assumed to be in thermal equilibrium

with the gas layer.

Edwards' 2 2 absorptance data for H O and CO are reported [55] as log(emissivity) versus

log(pressure-pathlength), with log(gas concentration) as a parameter. For each gas, these data

were incorporated into a look-up table, implemented as a two-dimensional array of

log(emissivity) values, with indices based on temperature and gas concentration. It is assumed

that absorptance and emittance are equivalent for the gaseous species as well as for soot.

An effective path length ( mean beam length, L) treats an emitting volume as if it were a

hemisphere of a radius such that the flux impinging on the center of the circular base is equal to

the average boundary flux produced by the real volume. The value of this radius is approximated

as [53],[56]

where L is the mean beam length in meters, c is a constant (approximately 0.9, for typical

geometries), V is the emitting gas volume (m ) and A is the surface area (m ) of the gas volume. 3 2

The volume and surface area are calculated from the dimensions of the layer.

For each gas, the log(absorptance) is estimated from the look-up table for that gas by 

interpolating both the log(temperature) and log(concentration) domains. In the event that the

required absorptance lies outside the temperature or concentration range of the look-up table, the

nearest acceptable value is returned. Error flags are also returned, indicating whether each

parameter was in or out of range and, in the latter case, whether it was high or low. This entire

proce 2 2 ss is carried out for both CO and H O.

3.4.5.2 Computing Target Heat Flux and Temperature

The calculation of the radiative heat flux to a target is similar to the radiative heat transfer

calculation discussed previously. The main difference is that CFAST does not compute

feedback from the target to the wall surfaces or gas layers. The target is simply a probe or

sensor not interacting with the modeled environment. 

(107)
59

Figure 14. Radiative heat transfer from a point source fire

to a target.

(108)

The net flux striking a target can be used as a boundary condition in order to compute the

temperature of the target. If the target is thin, then its temperature quickly rises to a level where

the heat flux to and from the target are in equilibrium.

There are four components of heat flux to a target: fires, walls (including the ceiling and floor),

gas layer radiation and gas layer convection.

Heat Flux from a Fire to a Target: Figure 14 illustrates terms used to compute heat flux from a

t t fire to a target. Let n be a unit vector perpendicular to the target and 1 be the angle between the

vector ts and n .

Us f,r ing the definition that q is the radiative portion of the energy release rate of the fire, then the

heat flux on a sphere of radius L due to this fire is . Correcting for the orientation of

the target and accounting for heat transfer through the gas layers, the heat flux to the target is
60

(109)

(110)

(111)

Figure 15. Radiative heat transfer from the upper and lower

layer gas layers to a target in the lower layer.

Radiative Heat Flux from a Wall Segment to a Target: Figure 15 illustrates terms used to

compute hea w,t t flux from a wall segment to a target. The flux, q" , from a wall segment to a target

can then be computed using

where q"w,out w t is the flux leaving the wall segment, A , A are the areas of the wall segment and

w-t target respectively, F is the fraction of radiant energy given off by the wall segment that is

U U L L intercepted by the target (i.e., a configuration factor) and J (L ) and J (L ) are defined as before.

Equation (109) can be simplified using w w-t t t-w the symmetry relation A F = A F to obtain

where

Tw w w is the temperature of the wall segment, g is the emissivity of the wall segment and )q " is

the net flux striking the wall segment.

Radiation from the Gas Layer to the Target: Figure 15 illustrates the setup for calculating the

heat flux from the gas layers to the target. The upper and lower gas layers in a room contribute

to the heat flux striking the target if the layer absorptances are non-zero. 
61

(112)

(113)

(114)

(115)

(116)

Le w,t,gas t q" denote the flux striking the target due to the gas g in the direction of wall segment w.

Then

The total target flux due to the gas (upper or lower layer) is obtained by summing eq (112) over

each wall segment or

Comput ting the Target Temperature The steady state target temperature, T can be found by

solving an energy balance on the target; namely

Le tt f(T ) be the difference between the left and right hand side of equation (114). Then this

equation may be solved using the Newton iteration 

Equation (115) is iterated until the dif new old ference T - T is sufficiently small.

3.4.5.3 Convection

S

In general, convective heat transfer, q”, across a surface of area A , is defined as

The convective heat transfer coefficient, h, is a function of the gas properties, temperature, and

velocity. The Nusselt number is defined as , which for natural convection is

related to the Rayleigh number,
62

(118)

(119)

where L is a characteristic length of the geometry, g is the gravitational constant (m/s ), k is the 2

S g thermal conductivity (W/m K), $ is a volumetric expansion coefficient (K ), T and T are the 2 -1

temperatures of the surface and gas, respectively (K), < is the kinematic viscosity (m /s), and " is 2

f

the thermal diffusivity (m /s). All properties are evaluated at the film temperature, T /

2

s g (T +T )/2. The typical correlations applicable to the problem at hand are available in the

literature. The table below gives the correlations used in CFAST [57]:

Geometry Correlation Restrictions

Walls none

Ceilings and floors

(hot surface up or

cold surface down)

2 LA10 # Ra # 10 8 11

Ceilings and floors

(cold surface up or

hot surface down)

10 # L Ra # 10 8 10

The Prandtl number, Pr, is the ratio of the kinematic viscosity and the thermal diffusivity. The

thermal diffusivity, ", and thermal conductivity, k, of air are defined as a function of the film

temperature from data in reference [57]. 

3.4.5.4 Conduction

Procedures for solving 1-d heat conduction problems are well known, (e.g., backward difference

(fully implicit), forward difference (fully explicit) or Crank-Nicolson [58]). A finite difference
63

approach [59] using a non-uniform spatial mesh is used to advance the wall temperature

solution. The heat equation is discretized using a second order central difference for the spatial

derivative and a backward differences for the time derivative. The resulting tri-diagonal system

of equations is then solved to advance the temperature solution to time t+ T. This process is

repeated , using the work of Moss and Forney [59], until the heat flux striking the wall

(calculated from the convection and radiation algorithms) is consistent with the flux conducted

into the wall calculated via Fourier’s law

(120)

where k is the thermal conductivity. This solution strategy requires a differential algebraic

(DAE) solver that can simultaneously solve both differential and algebraic equations. With this

method, only one or two extra equations are required per wall segment (two if both the interior

and exterior wall segment surface temperatures are computed). This solution strategy is more

efficient than the method of lines since fewer equations need to be solved. Wall segment

temperature profiles, however, still have to be stored so there is no decrease in storage

requirements. Conduction is then coupled to the room conditions by temperatures supplied at

the interior boundary by the differential equation solver. The exterior boundary condition types

(constant flux, insulated, or constant temperature) are specified in the configuration of CFAST.

A non-uniform mesh scheme was chosen to allow breakpoints to cluster near the interior and

exterior wall segment surfaces. This is where the temperature gradients are the steepest. A

breakpoin b b pt x was defined by x =MIN(x ,W/2),where and erfc-1

denotes the inve prse of the complementary error function. The value x is the location in a

final semi-infinite wall where the temperature rise is 5 % after t seconds and is sometimes called

b

the penetration depth. Eighty percent of the breakpoints were placed on the interior side of x

and the remaining 20 % were placed on the exterior side.

To illustrate the method, consider a one room case with one active wall. There are four gas

equations (pressure, upper layer volume, upper layer temperature, and lower layer temperature)

and one wall temperature equation. Implementation of the gradient matching method requires

that storage be allocated for the temperature profile at the previous time, t, and at the next time, t

+ *t. Given the profile at time t and values for the five unknowns at time t + *t (initial guess by

the solver), the temperature profile is advanced from time t to time t + *t. The temperature

profile gradient at x = 0 is computed followed by the residuals for the five equations. The DAE

solver adjusts the solution variables and the time step until the residuals for all the equations are

below an error tolerance. Once the solver has completed the step, the array storing the temperature profile for the previous time is updated, and the DAE solver is ready to take its next step.
64

(121)

3.4.5.5 Inter-compartment Heat Transfer

Heat transfer between vertically connected compartments is modeled by merging the connected

surfaces for the ceiling and floor compartments or for the connected horizontal compartments. A

heat conduction problem is solved for the merged walls using a temperature boundary condition

for both the near and far wall. As before, temperatures are determined by the DAE solver so that

the heat flux striking the wall surface (both interior and exterior) is consistent with the

temperature gradient at that surface. This option is implemented with the CFCON (for vertical

heat transfer) and the HHEAT (for horizontal heat transfer) keywords. 

For horizontal heat transfer between compartments, the connections may be between partial wall

surfaces, expressed as a fraction of the wall surface. CFAST first estimates conduction fractions

analogous to radiative configuration factors. For example, if only one half of the rear wall in

one compartment is adjacent to the front wall in a second compartment, the conduction fraction

between the two compartments is 1/2. These fractions can be prescribed on the HHEAT

keyword line. Once these avg fractions are determined, an average flux, q” , is calculated using

where F ij wallj is the fraction of flux from wall i that contributes to wall j, q is the flux striking wall

j.

3.4.6 Ceiling Jet

Relatively early in the development of a fire, fire-driven ceiling jets and gas-to-ceiling convective heat transfer can play a significant role in room-to-room smoke spread and in the

response of near-ceiling mounted detection hardware. Cooper [60] details a model and computer

algorithm to predict the instantaneous rate of convective heat transfer from fire plume gases to

the overhead ceiling surface in a room of fire origin. The room is assumed to be a rectangular

parallelepiped and, at times of interest, ceiling temperatures are simulated as being uniform. 

Also presented is an estimate of the convective heat transfer due to ceiling-jet driven wall flows. 

The effect on the heat transfer of the location of the fire within the room is taken into account. 

This algorithm has been incorporated into the CFAST model. In this section, we provide an

overview of the model. Complete details are available in reference [60].

A schematic of a fire, fire plume, and ceiling jet is shown in figure 16. The buoyant fire plume

fire rises from the height Z toward the ceiling. When the fire is below the layer interface, its mass

and layer enthalpy flow are assumed to be deposited into the upper layer at height Z . Having penetrated the interface, a portion of the plume typically continues to rise toward the ceiling. As it

impinges on the ceiling surface, the plume gases turn and form a relatively high temperature,

high velocity, turbulent ceiling jet which flows radially outward along the ceiling and transfers
65

Figure 16. Convective heat transfer to ceiling and wall

surfaces via the ceiling jet.

heat to the relatively cool ceiling surface. The convective heat transfer rate is a strong function

of the radial distance from the point of impingement, reducing rapidly with increasing radius. 

Eventually, the relatively high temperature ceiling jet is blocked by the relatively cool wall

surfaces [61]. The ceiling jet then turns downward and outward in a complicated flow along the

vertical wall surfaces [62], [63]. The descent of the wall flows and the heat transfer from them

are eventually stopped by upward buoyant forces. They are then buoyed back upward and mix

with the upper layer.

The average convective heat transfer from the ceiling jet gases to the ceiling surface, , can

be expressed in integral form as

(122)

The instantaneous convec ceil tive heat flux, q" (X,Y) can be determined as derived by Cooper [60]:

(123)

where Tad, a characteristic ceiling jet temperature, is the temperature that would be measured

adjacent to an adiabatic lower ad ceiling surface, and h is a heat transfer coefficient. h and T are

given by
66

(124)

(125)

where

(126)

(127)

(128)

(129)

(130)
67

(132)

(133)

(134)

(131)

fire fire In the above, H is the distance from the (presumed) point source fire and the ceiling, X and Y

are u the position of the fire in the room, Pr is the Prandtl number (taken to be 0.7) and < is the

kinematic viscosity of the upper layer gas which is assumed to have the properties of air and can

be u u u estimated from < = 0.04128(10 )T /(T +110.4). and are dimensionless numbers and 7 5/2

are measures of the strength of the plume at the ceiling and the layer interface, respectively.

When the ceiling jet is blocked by the wall surfaces, the rate of heat transfer to the surface

increases. Reference [60] provides details of the calculation of wall surface area and convective

heat flux for the wall surfaces.

3.5 Heat Detection

Heat detection is modeled using temperatures obtained from the ceiling jet [60]. Rooms without

fires do not have ceiling jets. Sensors in these types of rooms use gas layer temperatures instead

of ceiling jet temperatures. The characteristic detector temperature is simply the temperature of

the ceiling jet (at the location of the detector). The characteristic heat detector temperature is

modeled using the differential equation [64]

where TL g , T are the link and gas temperatures, V is the gas velocity, and RTI (response time

index) is a measure of the sensor's sensitivity to temperature change (thermal inertia). The heat

detector differential eq (132) may be rewritten to
68

(136)

(137)

(138)

(139)

(140)

(141)

(142)

where

Equation (134) may be solved using the trapezoidal rule to obtain

whe ire the subscript i denotes time at t . Equation (137) may be simplified to

which has a solution

Equation (141) reduces to the trapezoidal rule for integration when b(t) = 0. When a(t) and b(t)

are g constant (the gas temperature, T , and gas velocity, V are not changing), eq (132) has the

solution 
69

(143)

(144)

(145)

(146)

(147)

3.6 Sprinkler Activation and Fire Attenuation

For suppression, the sprinkler is modeled using a simple model [65] generalized for varying

sprinkler spray densities [66]. It is then modeled by attenuating all fires in the room where the

act sensor activated by a term of the form e where t is the time when the sensor activated

-(t-tact)/trate

and rate rate t is a constant determining how quickly the fire attenuates. The term t can be related to

spray density of a sprinkler using a correlation developed in [66]. The suppression correlation

was developed by act modifying the heat release rate of a fire. For t>t the heat release is given by 

where is the spray density of a sprinkler. Note that decay rate can be formulated in terms

of either rate the attenuation rate or the spray density. Both options are available. t can be

expressed in terms of as 

and the decay time (time to 50 % attenuation) as the input line allows the specification of either

the spray density of the sprinkler or the time required to reduce the fire heat release rate by 50 %,

t

50%. A calculation is done to make sure that the fuel burned is consistent with the available

oxygen. Once detection has occurred, then the mass and energy release rates are attenuated by

rate the term e =t to obtain -(t-tact)

There are assumptions and limitations in this approach. Its main deficiency is that it assumes that

sufficient water is applied to the fire to cause a decrease in the rate of heat release. This
70

suppression model cannot handle the case when the fire overwhelms the sprinkler. The

suppression model as implemented does not include the effect of a second sprinkler. Detection of

all sprinklers are noted but their activation does not make the fire go out any faster. Further,

multiple fires in a room imply multiple ceiling jets. It is not clear how this should be handled,

i.e.,how two ceiling jets should interact. When there is more than one fire, the detection

algorithm uses the fire that results in the worst conditions (usually the closest fire) in order to

calculate the fire sensor temperatures. Finally, the ceiling jet algorithm that we use results in

temperature predictions that are warmer (for a given heat release rate) than those used in the

correlation developed by Madrzykowski [67], which will cause activation sooner than expected.

3.7 Species Concentration and Deposition

CFAST uses a combustion chemistry scheme based on a carbon-hydrogen-oxygen balance. The

scheme is applied in three places. The first is burning in the portion of the plume which is in the

lower layer of the compartment of fire origin. The second is the portion in the upper layer, also

in the compartment of origin. The third is in the vent flow which entrains air from a lower layer

into an upper layer in an adjacent compartment. This is equivalent to solving the conservation

equations for each species independently.

3.7.1 Species Transport

The species transport in CFAST is primarily a matter of bookkeeping to track individual species

mass as it is generated by a fire, transported through vents, or mixed between layers in a

compartment. When the layers are initialized at the start of the simulation, they are set to

ambient conditions. These are the initial temperature prescribed by the user, and 23 % by mass

fraction (21 % by volume fraction) oxygen, 77 % by mass fraction (79 % by volume fraction)

nitrogen, a mass concentration of water prescribed by the user as a relative humidity, and a zero

concentration of all other species. As fuel is burned, the various species are produced in direct

relation to the mass of fuel burned (this relation is the species yield prescribed by the user for the

fuel burning). Since oxygen is consumed rather than produced by the burning, the “yield” of

oxygen is negative, and is set internally to correspond to the amount of oxygen used to burn the

fuel (within the constraint of available oxygen limits discussed in sec. 3.4.1.3).

Each unit mass of a species produced is carried in the flow to the various rooms and accumulates

in the layers. The model keeps track of the mass of each species in each layer, and knows the

volume of each layer as a function of time. The mass divided by the volume is the mass

concentration, which along with the relative molecular mass gives the concentration in volume

percent or parts per million as appropriate.

There are two separate radiation calculations done by CFAST. The first is for broadband

radiation transfer for energy balance. The way this calculation is done is discussed in section

3.4.51. The second is a visible light calculation to answer the question of whether exit signs will
71

Figure 17. Schematic of hydrogen chloride deposition region.

be visible. The absorption of broadband radiation depends on the concentration of water, carbon

dioxide and soot. The visibility calculation depends solely on the soot concentration For soot, the

2

input for C/CO is used to calculate a “soot” yield from the fire (assuming all the excess carbon

goes to soot). This soot generation is then transported as a species to yield a soot mass

concentration to use in the optical density calculation based originally on the work of Seader and

Einhorn [68]. The most recent work is by Mulholland and Croakin[69]. Based on their

experimental measurements, the soot mass density is multiplied by 3,817 m /kg/m (formerly

-1 3

3,500) to obtain an optical density per meter which is the value reported by the model.

3.7.2 HCl Deposition

Hydrogen chloride produced in a fire can produce a strong irritant reaction that can impair

escape from the fire. It has been shown [70] that significant amounts of the substance can be removed by adsorption by surfaces which contact smoke. In our model, HCl production is treated

in a manner similar to other species. However, an additional term is required to allow for

deposition on, and subsequent absorption into, material surfaces.

The physical configuration that we are modeling is a gas layer adjacent to a surface (figure 17). 

The gas layer is at some tempera g HCl ture T with a concomitant density of hydrogen chloride, D . 

The mass transport coefficient is calculated based on the Reynolds analogy with mass and heat

transfer; that is, hydrogen chloride is mass being moved convectively in the boundary layer, and

some of it simply sticks to the wall surface rather than completing the journey during the

convective roll-up associated with eddy diffusion in the boundary layer. The boundary layer at

the wall is then in equilibrium with the wall. The latter is a statistical process and is determined

by evaporation from the wall and stickiness of the wall for HCl molecules. This latter is greatly

influenced by the concentration of water in the gas, in the boundary layer and on the wall itself.

The rate of addition of mass of hydrogen chloride to the gas layer is given by

(148)

where source is the production rate from the burning object plus flow from other compartments. 
72

For the wall concentration, the rate of addition is

(149)

where the concentration in the boundary blHCl layer, D , is related to the wall surface concentration

by e the equilibrium constant k ,

(150)

We never actually solve for the concentration in the boundary layer, but it is available, as is a

boundary layer temperature if it were of interest. The transfer coefficients are

(151)

(152)

(153)

The only values currently available [71] for these quantities are shown in table 4. The “b” coefficients are parameters which are found by fitting experimental data to eqs (148) through (153). 

These coefficients reproduce the adsorption and absorption of HCl reasonably well. Note though

that error bars for these coefficients have not been reported in the literature. 
73

 Surface

b1 b2 b3 b4 b b 5 6 b7

(m) (m /kg) (s ) (J/g mol) (note a) (note b) (note c)

3 -1

Painted Gypsum 0.0063 191.8 0.0587 7476. 193 1.021 0.431

PMMA 9.6×10 0.0137 0.0205 7476. 29 1.0 0.431 -5

Ceiling Tile 4.0×10 0.0548 0.123 7476. 30 1.0 0.431 -3 b

Cement Block 1.8×10 5.48 0.497 7476. 30 1.0 0.431 -2 b

Marinite® 1.9×10 0.137 0.030 7476. 30 1.0 0.431 -2 b

a units of b5 are

b very approximate value, insufficient data for high confidence value

c non-dimensional

Table 4. Transfer coefficients for HCl deposition from reference [70]

(154)

(155)

The experimental basis for poly(methyl methacrylate) and gypsum cover a sufficiently wide

range of conditions that they should be usable in a variety of practical situations. The parameters

for the other surfaces do not have much experimental backing, and so their use should be limited

to comparison purposes.

3.8 Flame Spread

The Cleary-Quintiere flame spread model [72] incorporated into CFAST is based on five simple

differential equations. One each for concurrent (eq (154)) and opposed flow flame spread

(eq (155)). One each (eqs (157) and (156)) for the two burn-out fronts, and the last one for burnout at the ignition point (eq (158)).
74

(156)

(157)

(158)

and

where y is the wind-aided coordinate direction, x is the opposed flow coordinate direction, kDc is

ig the thermal inertia (thermal conductivity x density x specific heat), T is the ignition

s s,min temperature, T is the surface temperature, T is the minimum surface temperature for

pyrolysis, q” is heat flux, and N is a flame heating parameter defined in eq (168). The subscripts

p, b, f, and TOT refer to pyrolysis front, burnout front, flame, and total respectively.

p

 The equations describe the growth of two rectangles. At ignition a single rectangle, R , is

defined and its growth is determined by eq (154) for spread up the wall and eq (155) for lateral

b p spread as well as spread down the wall. When q” < 0, a second rectangle, R , the same size as R

was orig binally starts growing. It is governed by eqs (157) and (156). After R starts to be tracked

p b the pyrolysis area is R – R .

When a flame spread object is defined, CFAST adds five additional differential equations to the

equation set. A target is also placed at the prescribed location on the prescribed wall surface and

the maximum time step is set to 1 s. This allows the temperature of the target to be tracked and

the ignition temperature and time to be calculated. Once the object ignites, its mass loss and heat

release rate are calculated and then treated like any other fire by CFAST.

3.9 Single Zone Approximation

A single zone approximation is appropriate for smoke flow far from a fire source where the twozone layer stratification is less pronounced than in compartments near the fire. In this situation, a

single zone approximation may be derived by using the normal two-zone source terms and the

substitutions:
75

(159)

This is used in situations where the stratification does not occur. Examples are elevators shafts,

complex stairwells, and compartments far from the fire. In addition to a slight decrease in

computing time, it allows one to benchmark simpler models such as CONTAM [73] and other

network models.

3.10 Review of the Theoretical Development of the Model

The current version of ASTM E 1355-04 includes provisions to guide in the assessment of the

theoretical basis of the model that includes a review of the model “by one or more recognized

experts fully conversant with the chemistry and physics of fire phenomenon, but not involved

with the production of the model. Publication of the theoretical basis of the model in a peerreviewed journal article may be sufficient to fulfill this review” [1].

CFAST has been subjected to independent review in two ways, internal and external. First, all

documents issued by the National Institute of Standards and Technology receive three levels of

internal review by members of the staff not involved in the preparation of the report or

underlying research. The theoretical basis of CFAST is presented in this document, and is

subject to internal review by staff members who are not active participants in the development of

the model, but who are members of the Fire Research Division and are considered experts in the

fields of fire and combustion. The same was true of previous versions of the technical reference

guide over the last decade [2],[74],[75]. Externally, the theoretical basis for the model has been

published in peer reviewed journals [76],[77],[78] and conference proceedings [79]. In addition,

CFAST is used worldwide by fire protection engineering firms who review the technical details

of the model related to their particular application. Some of these firms also publish in the open

literature reports documenting internal efforts to validate the model for a particular use. Many of

these studies are discussed in more detail in the present document.

In addition to the formal review, procedures were in place during the development of CFAST to

assure the quality of the model. These procedures included several components:

 • Review of proposed changes to the code by at least two others involved in the

development process to insure that a proposed change was consistent with the rest of the

CFAST code and was implemented correctly. These reviews, while informal in nature,

provided a comprehensive review of the changes to the model during its development. 

Significant changes were documented in internal memorandums covering such areas as
76

the numerics and structure of the model [80], improvements in the chemistry [81]

convection [82], HCl deposition [83] algorithms, and output formats for the model [84].

Comparisons of the impact of the changes on the output results were often described in

internal memorandums (see, for example, reference [80]).

 • Internal review of the model prior to public release. In addition to the normal NIST

document review process, the CFAST software was circulated internally to Fire Research

Division Staff to allow interested staff members to test the model [85],[86],[87]. These

memorandums detail changes to the model since the last public release of the model and

provide documentation of the history of the model development.

 • For each major release of CFAST, NIST has maintained a history of the source code

which goes back to March 1989. While it is not practical to reconstruct the programs for

each release for use with modern software tools and computer operating systems, the

source code history allows the developers to examine what changes were made at each

release point. This provides detailed documentation of the history of model development

and is often useful to understand the impact of changes to submodels over the

development of the model.

 • Once a release of CFAST was approved by NIST, it was announced with a letter to

model users which provided a summary of model changes and available documentation. 

In essence, these were a condensation of the internal memorandums, without details or

printout of specific code changes. These memorandums provide documentation of the

history of the model development [88], [89], [90], [91], [92].

Finally, CFAST has been reviewed and included in industry-standard handbooks such as the

SFPE Handbook [93] and referenced in specific standards, including NFPA 805 [94] and NFPA

551 [95].

3.10.1 Assessment of the Completeness of Documentation

There are two primary documents on CFAST, this Technical Reference Guide and a Model

User’s Guide [96]. This document is the Technical Reference Guide and provides

documentation of the governing equations, assumptions, and approximations of the various

submodels. It also includes a summary description of the model structure, and numerics. The

Model User’s Guide includes a description of the model input data requirements and model

results.

The extensive formal review process for all NIST publications in part insures the quality of the

CFAST Guides. In addition, the model developers routinely receive feedback from users on the

completeness of the documentation and add clarifications when needed. It is estimated that there

are several thousand users of CFAST. Before new versions of the model are released, there is a
77

“beta test” period in which the users test the new version using the updated documentation. This

process is similar, although less formal, to that which most computer software programs

undergo. Training courses for use of the model in fire hazard analysis have been developed from

the model documentation and presented at training courses worldwide [97].

3.10.2 Assessment of Justification of Approaches and Assumptions

The technical approach and assumptions of the model have been presented in the peer reviewed

scientific literature and at technical conferences. Also, all documents released by NIST are

required to go through an internal editorial review and approval process. This process is

designed to ensure compliance with the technical requirements, policy, and editorial quality

required by NIST. The technical review includes a critical evaluation of the technical content

and methodology, statistical treatment of data, uncertainty analysis, use of appropriate reference

data and units, and bibliographic references. CFAST manuals are always first reviewed by a

member of the Fire Research Division, then by the immediate supervisor of the author of the

document, then by the chief of the Fire Research Division, and finally by a reader from outside

the division. Both the immediate supervisor and the division chief are technical experts in the

field. Once the document has been reviewed, it is then brought before the Editorial Review

Board (ERB), a body of representatives from all the NIST laboratories. At least one reader is

designated by the Board for each document that it accepts for review. This last reader is selected

based on technical competence and impartiality. The reader is usually from outside the division

producing the document and is responsible for checking that the document conforms with NIST

policy on units, uncertainty and scope. This reader does not need to be a technical expert in fire

or combustion. 

Besides formal internal and peer review, CFAST is subjected to continuous scrutiny because it is

available to the general public and is used internationally by those involved in fire safety design

and postfire reconstruction. The source code for CFAST is also released publicly, and has been

used at various universities worldwide, both in the classroom as a teaching tool as well as for

research. As a result, flaws in the theoretical development and the computer program itself have

been identified and fixed. The user base continues to serve as a means to evaluate the model,

which is as important to its development as the formal internal and external peer review

processes.

3.10.3 Assessment of Constants and Default Values 

A comprehensive assessment of the numerical parameters (such as default time step or solution

convergence criteria) and physical parameters (such as empirical constants for convective heat

transfer or plume entrainment) used in CFAST is not available in one document. Instead,

specific parameters have been tested in various verification and validation studies performed at

NIST and elsewhere. Numerical parameters are described in this Technical Reference Guide and

are subject to the internal review process at NIST, but many physical parameters are extracted
78

from the literature and do not undergo a formal review. In addition, default values for the various

model inputs have been specifically reviewed by a professional fire protection engineering

university professor to insure appropriate default values and suggested limits for the various

input values. The model user is expected to assess the appropriateness of default values provided

by CFAST and make changes to the default values if need be. 
79

4 Mathematical and Numerical Robustness

4.1 Introduction

The mathematical and numerical robustness of a deterministic computer model depends upon

three issues: the code must be transparent so that it can be understood and modified by visual

inspection; it must be possible to check and verify with automated tools; and there must be a

method for checking the correctness of the solution, at least for asymptotic (steady state)

solutions (numerical stability and agreement with known solutions).

In order to understand the meaning of accuracy and robustness, it is necessary to understand the

means by which the numerical routines are structured. In this chapter, details of the

implementation of the model are presented, including the tests used to assess the numerical

aspects of the model. These include

 • the structure of the model, including the major routines implementing the various

physical phenomena included in the model,

 • the organization of data initialization and data input used by the model, 

 • the structure of data used to formulate the differential equations solved by the model,

 • a summary of the main control routines in the model that are used to control all input and

output, initialize the model and solve the appropriate differential equation set for the

problem to be solved,

 • the means by which the computer code is checked for consistency and correctness,

 • analysis of the numerical implementation for stability and error propagation, and

 • comparison of the results of the system model with simple analytical or numerical

solutions.

4.2 Structure of the Numerical Routines

A methodology which is critical to verification of the model is the schema used to incorporate

physical phenomena. This is the subroutine structure discussed below. The method for

incorporating new phenomena and insuring the correctness of the code was adopted as part of

the consolidation of CCFM and FAST. This consolidation occurred in 1990 and has resulted in a

more transparent, transportable and verifiable numerical model. This transparency is crucial to a

verifiable and robust numerical implementation of the predictive model as discussed in the

sections on code checking and numerical analysis.
80

Figure 18. Subroutine structure for the CFAST Model.

4.2.1 Subroutine Structure

The model can be split into distinct parts. There are routines for reading data, calculating results

and reporting the results to a file or printer. The major routines for performing these functions

are identified in figure 18. These physical interface routines link the CFAST model to the actual

routines which calculate quantities such as mass or energy flow at one particular point in time

for a given environment.

The routines SOLVE, RESID and DASSL are the key to understanding how the physical

equations are solved. SOLVE is the control program that oversees the general solution of the

problem. It invokes the differential equation solver DASSL [98] which in turn calls RESID to

solve the transport equations. Given a solution at time t, what is the solution at time t plus a

small increment of time, )t, (where the time increment is determined dynamically by the

program to insure convergence of the solution at t + )t) ? The differential equations are of the

form

(160)

where y is a vector representing pressure, layer height, mass and such, and f is a vector function
 Cleanscape Software, 445 Sherman Ave, Ste. Q, Palo Alto, CA 94306 5

 Typically one part in 10 , which is the error limit used for DASSL. 6 6

81

0

that represents changes in these values with respect to time. The term y is an initial condition at

0

the initial time t . The subroutine RESID computes the right hand side of eq (160) and returns a

set of residuals of that calculation to be compared to the values expected by DASSL. DASSL

then checks for convergence. Once DASSL reaches an error limit (defined as convergence of

the equations) for the solution at t+)t, SOLVE then advances the solution of species concentration, wall temperature profiles, and mechanical ventilation for the same time interval.

Note that there are several distinct time scales that are involved in the solution of this type of

problem. The fastest will be chemical kinetics. We avoid that scale by assuming that the

chemistry is infinitely fast. The next larger time scale is that associated with the flow field. 

These are the equations which are cast into the form of ordinary differential equations. Then

there is the time scale for mechanical ventilation, and finally, heat conduction through objects. 

Chemical kinetic times are typically on the order of milliseconds. The transport time scale are

on the order of 0.1 s. The mechanical ventilation and conduction time scales are typically

several seconds, or even longer. The time step is dynamically adjusted to a value appropriate for

the solution of the currently defined equation set. In addition to allowing a more correct solution

to the pressure equation, very large time steps are possible if the problem being solved

approaches steady-state.

4.3 Code Checking

There are two means to automate checking the correctness of the language used by a numerical

model. The first is the use of standard methods for checking the structure and interface.

Programs such as Flint and Lint are standard tools to do such checking. They are applied to the

whole model. There are three aspects of the model checked by this procedure: correctness of the

interface, undefined or incorrectly defined (or used) variables and constants, and completeness

of loops and threads. It does not check for the correctness of the numerical use of constants or

variables only that they are used correctly in a syntactical sense. Lint is part of most C language

distributions of Unix. Flint is the equivalent for the FORTRAN language. Though it is not

usually included with FORTRAN distributions Flint is generally available . Both have been used 5

with CFAST.

The second is to use a variety of computer platforms to compile and run the code. Since

FORTRAN and C are implemented differently for various computers, this represents both a

numerical check as well as a syntactic check. CFAST has been compiled for the Sun (Solaris),

SGI (Irix), the windows-based PCs (Lahey, Digital, and Intel FORTRAN), and the Concurrent

Computer platforms. Within the precision afforded by the various hardware implementations, the

answers are identical

6
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As discussed in section 6.5 , many others have used the source for special applications, which

provides another check that the paradigm discussed in section 4.1 provides high reliability and

robustness.

4.4 Numerical Tests

There are two components to testing the numerical solutions of CFAST. First, the DASSL

solver is well tested for a wide variety of differential equations, and is widely used and accepted

[97]. Also, the radiation and conduction routines are tested with known solutions. These are not

analytical tests, but physical limits, such as an object immersed in a fluid of constant

temperature, to which the temperature must equilibrate. The solver(s) must show that the

differential equations asymptotically converge to these answers.

The second is to insure that the coupling between algorithms and the solver is correct. Most

errors are avoided because of the structure discussed in section 4.1. The error due to the

numerical solution is far less than that associated with the model assumptions. Two examples of

this are the coupling of mechanical ventilation with buoyant flow, and the Nusselt number

assumption for boundary layer convection. For the former, the coupling of a network of

incompressible flow with an ODE for compressible flow has to deal with disparate calculations

of pressure. For the latter, a very small time step occurs when a floor is heated and the thermal

wave reaches the far (unexposed) side. This is a limitation of the physical implementation of the

heat flow algorithm (convection). The solver arrives at the correct solution, but the time step

becomes very small in order to achieve this.

Numerical error can be divided into three categories: roundoff, truncation and discretization

error. Roundoff error occurs because computers represent real numbers using a finite number of

digits. Truncation error occurs when an infinite process is replaced by a finite one. This can

happen, for example, when an in finite series is truncated after a finite number of terms or when

an iteration is terminated after a convergence criterion has been satisfied. Discretization error

occurs when a continuous process such as a derivative is approximated by a discrete analog such

as a divided difference. CFAST is designed to use 64-bit precision for real number calculations

to minimize these effects.

Implicit in solving the equations discussed in chapter 3, is that the solver will arrive at a solution.

 Inherent in the DASSL solver are convergence criteria for the mass and energy balance within

CFAST to insure mass and energy conservation within 1 part in 10 . There are, however, 6

limitations introduced by the algorithmic realization of physical models, that can produce errors

and instabilities. Using the example above, if a mechanical ventilation system injects or removes

mass and enthalpy from a small duct, then there can be a stability issue with the layer interface

bobbing up and down over the duct. These are annoyances to the user community and

shortcomings of the implementation of algorithm rather than failure of the system model.
83

Problems of this sort are noted in the “frequently asked questions” on the CFAST web site

(http://cfast.nist.gov).

4.5 Comparison with Analytic Solutions

There do not exist general analytic solutions for fire problems, even for the simplest cases. That

is, there are no closed form solutions to this type of problem. However, it is possible to do two

kinds of checking. The first type is discussed in the section on the theoretical basis of the model,

for which individual algorithms are validated against experimental work. The second is simple

experiments, especially for conduction and radiation, for which the results are asymptotic. For

example, for a simple, single compartment test case with no fire, all temperatures should

equilibrate asymptotically to a single value. Such comparisons are common and not usually

published.
84
85

5 Sensitivity of the Model

A sensitivity analysis considers the extent to which uncertainty in model inputs influences model

output. For a sensitivity analysis, this uncertainty includes not only that inherent in the input of

data for specific scenarios by the model user, but also uncertainty in empirical data or numerical

parameters in the model such as the time step size used by the model to obtain a solution.

Among the purposes for conducting a sensitivity analysis are to determine

 • the important variables in the models,

 • the computationally valid range of values for each input variable, and

 • the sensitivity of output variables to variations in input data.

Conducting a sensitivity analysis of a complex model is not a simple task and it will differ

depending on the application. CFAST typically requires the user to provide numerous input

parameters that describe the building geometry, compartment connections, construction

materials, and description of one or more fires. 

Iman and Helton [99] studied the sensitivity of complex computer models developed to simulate

the risk of severe nuclear accidents which may include fire and other risks. Consistent with the

work of Iman and Helton [98], ASTM E1355 [1] provides overall guidance on typical areas of

evaluation of the sensitivity of deterministic fire models. These areas may involve one or more

of the following techniques: finite difference or direct analysis methods that provide an explicit

solution of the sensitivity equations associated with the governing equations of the model,

factorial design or Latin hypercube sampling studies that investigate the effect of varying the

input parameters and consequential interactions between parameters that may be deemed

important, and global or response surface methods that investigate the overall behavior of model

outputs for a desired range of inputs.

This chapter provides a review of the sensitivity studies that have been conducted using CFAST

with an emphasis on uncertainty in the input. Other sensitivity investigations of CFAST are also

available [100],[101],[102].

5.1 Factorial Design Studies

Khoudja [103] has studied the sensitivity of an early version of the FAST [2] (predecessor to

CFAST) model with a fractional factorial design involving two levels of 16 different input

parameters. The statistical design, taken from the texts by Box and Hunter [104], and

Daniel [105] reduced the necessary model runs from more than 65 000 to 256 by studying the

interactions of input parameters simultaneously. The choice of values for each input parameter

represented a range for each parameter. The analysis of the FAST model showed sensitivity to
86

heat loss to the compartment walls and to the number of compartments in the simulation.

Without the inclusion of surface thermophysical properties, this model treats surfaces as

adiabatic for conductive heat transfer. Thus, consistent sensitivity should be expected.

Sensitivity to changes in thermal properties of the surfaces were not explored.

Walker [106] discussed the uncertainties in components of zone models and showed how

uncertainty within user-supplied data affects the results of calculations using CFAST as an

example. The study systematically varied inputs related to the fire (heat release rate, heat of

combustion, mass loss rate, radiative fraction, and species yields) and compartment geometry

(vent size and ceiling height) ranging from ± 1 % to ± 20 % of base values for a onecompartment scenario. Heat release rate and ceiling height are seen to be the dominant input

variables in the simulations. Upper layer temperature changed ± 10 % for a ± 10 % change in

heat release rate. Typical variation of ± 10 s in time to untenable conditions for a 20 % variation

in the inputs was noted for the scenarios studied.

Peacock et al. [99] studied the sensitivity of CFAST for a range of input parameters. They used

simple factorial designs for model inputs deemed important to investigate local behavior of

important model outputs along with response surface methods to evaluate overall model

behavior. Results of the parametric investigations are discussed below and the application of

response surface methods is summarized in section 5.2. Both are discussed in more detail in

reference [99].

5.1.1 Model Inputs and Outputs

Most studies of modeling related to fire hazard and fire reconstruction present a consistent set of

variables of interest to the model user [107],[108],[109]: upper and lower gas layer temperatures,

gas species concentrations, and layer interface position. Other variables of interest include

 • mass pyrolysis and heat release rate,

 • room pressure, and

 • vent flow.

Although there are certainly other comparisons of interest, these will provide evidence of the

sensitivity of the model to most model inputs. Tables 5 and 6 show typical inputs and outputs

for the CFAST model

Consider the following fire scenario: The building geometry (figure 19) includes four rooms on

two floors with horizontal, vertical, and mechanical vents connecting the rooms and venting to

the outdoors. The fire source in one of the rooms on the lower floor is a medium growth rate t2

fire [110] chosen to simulate a mattress fire [111] (figure 20).
87

Parameter Inputs (Items in bold are inputs that may vary due to error in measurements)

Ambient Conditions Inside temperature and pressure

Outside temperature and pressure

Wind speed

Relative humidity (0 % to 100 %)

Building Geometry Compartment width, depth, height, and surface material properties (conductivity,

heat capacity, density, thickness)

Horizontal Flow Vents: Height of soffit above floor, height of sill above floor, width

of vent, angle of wind to vent, time history of vent openings and closings

Vertical Flow Vents: Area of vent, shape of vent

Mechanical Ventilation, Orientation of vent, Center height of vent, area of vent,

length of ducts, diameter of ducts, duct roughness, duct flow coefficients,

fan flow characteristics

Fire Specification Fire room, X, Y, Z position in room, fire area

Fire Chemistry: Molar Weight, Lower oxygen limit, heat of combustion, initial fuel

temperature, gaseous ignition temperature, radiative fraction

Fire History: Mass loss rate, heat release rate, species yields for HCN, HCl, H/C,

O /2 2 C 2, C/CO , CO/CO

Table 5. Typical Inputs for a Two-Zone Fire Model.

Parameter Output (typically time histories)

Compartment

Environment

for each

compartment

Compartment pressure and layer interface height

for each layer

and

compartment

Temperature, 

Layer mass density, layer volume, heat release rate, gas concentrations

2 2 2 2

(N , O , CO , CO, H O, HCl, HCN, soot optical density), radiative heat

into layer, convective heat into layer, heat release rate in layer

for each vent

and layer

Mass flow, entrainment, vent jet fire

for each fire Heat release rate of fire, mass flow from plume to upper layer, plume

entrainment, pyrolysis rate of fire

for each

compartment

surface

Surface temperatures

Tenability Temperature

Fractional Exposure Dose (FED)

Table 6. Typical Outputs for a Two-Zone Fire Model.
88

Figure 19. Building geometry for base case scenario.

Figure 20. Characterization of heat release rate of growing fires as t fires. 2
89

Figure 21. An example of time dependent sensitivity of fire model

outputs to a 10 % change in room volume for a single room fire scenario

5.1.2 Sensitivity to Small Changes in Model Inputs

To investigate the sensitivity of the model, a number of simulations were conducted varying the

input parameters about the base scenario discussed in the previous section. Both small (±10 %)

and larger (up to an order of magnitude) variations for selected inputs were studied. Varying

most of the inputs by small amounts had little effect on the model outputs. Figure 21 presents an

example of the time dependent sensitivity of several outputs to a 10 % change in room volume

for the fire compartment in the scenario described above. For example, the pair of dotted-line

curves labeled “Upper Layer Volume” were created by comparing the base case scenario with a

scenario whose compartment volume was increased and decreased by 10 %. The resulting curves

presented on the graph are the relative difference between the variant cases and the base case

defined by (Variant value - Base value) / Base value for each time point. The graph shows that

temperature and pressure are insensitive to changes in the volume of the fire room since a 10 %

change in room volume led to smaller relative changes in layer temperature and room pressure

for all times. Upper layer volume can be considered neutrally sensitive (a 10 % change in room

volume led to about a 10% change in layer volume). Further, this implies that there is negligible

effect on the average layer interface height. This is consistent with both experimental
90

observations in open compartment room fires [112] and analytical solutions for single

compartment steady-state fires [113]. For transient conditions early in the fire or when the fire

burns out (illustrated in the figure at 300 s when the gas burner fire heat release rate goes to zero)

higher uncertainties are noted. While these are transient effects, the early phases of the fire, in

particular, may be important in calculating tenability for occupants during egress. While an

uncertainty in the compartment volumes results in an equivalent uncertainty in calculated

outputs, accurate specification of compartment dimensions within 5 % is often easily obtained.

In addition, figure 21 shows a somewhat constant relative difference for the changes as a

function of time. As suggested by Iman and Helton [98], an average relative difference could

thus be used to characterize the model sensitivity for comparing individual inputs and outputs.

5.1.3 Sensitivity to Larger Changes in Model Inputs

To investigate the effects of much larger changes in the inputs, a series of simulations was

conducted where the inputs were varied from 10 % to 400 % of base values. Simulations

changing the heat release rate inputs from the base peak heat release rate of 750 kW are shown

in figure 22. 

Each set appears as families of curves with similar functional forms. This indicates that the heat

release rate has a monotonic effect on the layer temperatures, with not as clear an effect on upper

layer volume due to compartment filling and flow between compartments. Like the sensitivity to

compartment volume in the previous section, changing the heat release rate by a factor of two

results in a factor of two change in the upper layer temperature. Thus, in absolute terms, heat

release rate and compartment volume are equally sensitive. However, compartment volume is

easily determined accurately while heat release rate is typically estimated with far less accuracy

and may be uncertain to within an order of magnitude or larger. 

In the majority of fire cases, the most crucial question that can be asked by the person responsible for fire protection is: “How big is the fire?” Put in quantitative terms, this translates to:

“What is the heat release rate of this fire?” Recently the National Institute of Standards and

Technology (NIST) examined the pivotal nature of heat release rate measurements in detail [8].

Not only is heat release rate seen as the key indicator of real-scale fire performance of a material

or construction, heat release rate is, in fact, the single most important variable in characterizing

the “flammability” of products and their consequent fire hazard. Much of the remainder of this

paper focuses on heat release rate as an example for examining sensitivity analysis.
91

Figure 22. Layer temperatures and volumes in several rooms resulting from

variation in heat release rate for a four-room growing fire scenario.

5.2 Response Surface Studies

A next step beyond the simple plots presented in figure 22 is a cross-plot of outputs of interest

against heat release rate. Figure 23 presents plots of the upper (presented in figure 22) and lower

layer temperatures plotted against the heat release rate for all the simulations. The shaded areas

on figure 23 shows the locus of all the individual data points representing all the layer

temperature time points for all the simulations shown in figure 22. For each room, a regression

fit to the data for each room overlays the locus. The temperature curves for both upper and lower

layer temperature in all four rooms (figure 23) show a strong functional dependence on heat

release rate. Even for the wide variation in inputs, the heat release rate provides a simple
92

Figure 23. Comparison of the time dependent heat release rate and layer

temperatures in several rooms for a four-room growing fire scenario.

predictor of the temperature in the rooms. In addition, this relationship allows calculation of the

sensitivity of the temperature outputs to the heat release rate inputs as a simple slope of the

resulting correlation between heat release rate and temperature. 

Figure 24, simply a plot of the slope of the regression curves in figure 23, shows this sensitivity,

M(T)/M(heat release rate), for the four-room scenarios studied and represents all time points in all

Figure 24. Sensitivity of temperature to heat release

rate for a four-room growing fire scenario.
93

the simulations in which the peak heat release rate was varied from 0.1 to 4.0 times the base

value. Except for relatively low heat release rate, the upper layer temperature sensitivity is less

than 1 K/kW and usually below 0.2 K/kW. Not surprisingly, the layer that the fire feeds directly

is most sensitive to changes. The lower layer in the fire room and all layers in other rooms have

sensitivities less than 0.2 K/kW. This implies, for example, that if the heat release rate for a

1 MW fire is known to within 100 kW, the resulting uncertainty in the calculation of upper layer

temperature in the fire room is about ± 30 K.

For upper layer volumes (figure 25) of both rooms 1 and 2, it is again a simple correlation

between heat release rate and volume fraction (upper layer volume expressed as a fraction of the

total room volume). The shaded gray area on the graph shows the locus of all individual time

point values of temperature and volume in the four compartments of the simulation. The

correlations for the upper layer volumes of room 1 and room 2 could also be differentiated as

was done for the temperature correlations to obtain sensitivities for the upper layer volume. For

rooms 3 and 4, the relationship is not as clear. The flow into the layers of these rooms is more

complicated than for rooms 1 and 2, resulting from flow from the first floor through a vent in the

floor of room 3 and from a vent to the outside in room 4. However, even these rooms approach a

constant value for higher heat release rate values, implying near zero sensitivity for high heat

release rate.

Figure 25. Comparison of heat release rate and

upper layer volume in several rooms for a fourroom growing fire scenario.
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Figure 26. Effect of both heat release rate and vent

opening size on upper layer temperature for a four-room

growing fire scenario.

Figure 26 presents the effect of both peak heat release rate and vent opening (in the fire room) on

the peak upper layer temperature. In this figure, actual model calculations, normalized to the

base scenario values are indicated by circles overlaid on a surface grid generated by a spline

interpolation between the data points. At high heat release rate and small vent openings, the fire

becomes oxygen limited and the temperature trails off accordingly, but for the most part, the

behavior of the model is monotonic in nature. Although more laborious, the approaches used to

calculate sensitivities for single variable dependencies illustrated earlier are thus equally

applicable to multivariate analyses.

From the surface, it is clear that heat release rate has more of an effect on the peak temperature

than does the vent width. Until the fire becomes oxygen limited, the trends evident in the surface

are consistent with expectations – temperature goes up with rising heat release rate and down

with rising vent width. The effects are not, of course, linear with either heat release rate or vent

opening. Plume theory and typically used algorithms for estimating upper layer temperature in a

single room with a fire [114] suggest that the dependence is on the order of for heat release

rate and for the vent opening where A is the area of the vent and h is the height of the vent.

Although these correlations are based on a simple analysis of a single room fire, the dependence

suggested is similar to that illustrated in figure 26.
95

5.3 Latin Hypercube Sampling Studies

Notarianni [101] developed an iterative methodology for the treatment of uncertainty in firesafety engineering calculations to identify important model parameters for detailed study of

uncertainty. She defines a nine-step process to identify crucial model inputs and parameters,

select sampling methods appropriate for the important parameters, and evaluate the sensitivity of

the model to chosen outcomes. Both factorial designs and Latin hypercube sampling are

included in a case study involving the CFAST model. In a performance-based design of a

16 story residential structure, the impact of model uncertainty on a chosen design and inclusion

of residential sprinklers in the design would effect the resulting safety of the design. For a

seven-compartment scenario representing one living unit in the structure, distributions of input

variables based on Latin hypercube sampling of selected ranges of the inputs were developed

and used as input for a series of 500 CFAST simulations for the scenario. The results of the

calculations are presented in a series of cumulative distribution functions which show the

probability that a chosen criterion of the design is exceeded within a given time. Depending on

the evaluation criterion chosen, times to unacceptable designs varied by as little as 10 s to as

much as 470 s. To determine important input variables, Notarianni used a multivariate

correlation of the input and output variables to determine statistical significance at a 95 %

confidence level. Input variables deemed important in the analysis included fire-related inputs

(growth rate, heat of combustion, position of the base of the fire, and generation rates of products

of combustion) and door opening sizes. Other inputs were determined to be less important.

5.4 Summary

Many of the outputs of the CFAST model are quite insensitive to uncertainty in the input

parameters for a broad range of scenarios. Not surprisingly, heat release rate was consistently

seen as the most important variable in a range of simulations. Heat release rate and related

variables such as heat of combustion or generation rates of products of combustion provide the

driving force for fire-driven flows. For CFAST, all of these are user inputs. Thus, careful

selection of these fire related variables are necessary for accurate predictions. Other variables

related to compartment geometry such as compartment height or vent sizes, while deemed

important for the model outputs, are typically more easily defined for specific design scenarios

than fire related inputs. For some scenarios, such as typical building performance design, these

vents may need to include the effects of leakage to insure accurate predictions. For other

scenarios, such as shipboard use or nuclear power facilities, leakage (or lack thereof) may be

easily defined and may not be an issue in the calculations.
96
 The 1997 Uniform Building Code has been superceded by the International Building 7

Code, 2003 Edition, International Code Council, Country Club Hills, Illinois.

97

6 Validation of the Model

There are two ways of comparing predictive capability with actual events. The first is simply

graphing the time series curves of model results with measured values of sensible variables such

as temperature. Another approach is to consider the time to critical conditions such as flashover.

Making direct comparisons between theory and experiment gives a good sense of whether

predictions are reasonable. This chapter provides a review of CFAST validation efforts by NIST

and others to better understand the quality of the predictions by the model.

6.1 Comparisons with Full-Scale Tests Conducted Specifically for the Chosen

Evaluation

Several studies have been conducted specifically to validate the use of CFAST in building

performance design. Dembsey [115] used CFAST to predict the ceiling jet temperatures, surface

heat fluxes and heat transfer coefficients for twenty compartment fire experiments in a

compartment that is similar in size, geometry, and construction to the standard fire test

compartment specified in the Uniform Building Code[116] . Results from 330 kW, 630 kW, and 7

980 kW fires were used. In general, CFAST made predictions which were higher than the

experimental results. In these cases, the temperature prediction is typically 20 to 30% higher

than measured values. Much of this can be attributed to not knowing the species production

(soot) and relative absorption of radiation by the gas layers which highlights the importance of

scenario specification. This is the most common cause of “over prediction” of temperature by

CFAST. A secondary source of discrepancy is correcting for radiation from thermocouple beads.

The authors do this, but the corrections cited are not as large as has been reported in similar fire

experiments [117].

He et al. [118] describe a series of full-scale fire experiments that were designed to investigate

the validity of two zone models including CFAST. The experiments, involving steady state

burning rates and a number of ventilation conditions, were conducted in a four-story building.

Temperature, pressure, flow velocity, smoke density and species concentrations were measured

in various parts of the building. The stack effect and its influence on temperature distribution in a

stair shaft were observed. Comparisons were then made between the experimental results and the

model predictions. Early in the fire there is very good agreement (a few percent difference)

between the predictions and measurements, beyond 10 min, there are significant variations. Both

the experiment and the model are internally consistent; that is, higher flow leads to a higher

interface height (figure 13 in this paper). Once again, the difference is about 25 %. The authors
98

discuss the effect of fuel composition and correction for radiation from thermocouple beads but

cannot draw firm conclusions based on their measurements of fuel products.

A series of experimental results for flaming fires, obtained using realistic fires in a prototype

apartment building were performed by Luo et al. [119]. Fuel configurations in the fire test

included a horizontal plain polyurethane slab, mock-up chair (polyurethane slabs plus a cotton

linen cover), and a commercial chair. CFAST typically over-predicted upper layer temperatures

by 10 % to 50 % depending on the test conditions and measurement location in that test. The

predicted and experimental time dependent upper layer temperatures were similar in shape. The

time to obtain peak upper layer temperatures was typically predicted to within 15 % of the

experimental measurements. The authors concluded that CFAST was conservative in terms of

life safety calculations, and that in these experiments, the layer was not uniform.

In order to optimize fire service training facilities, the best use of resources is imperative. The

work reported by Poole et al. [120] represents one aspect of a cooperative project between the

city of Kitchener Fire Department (Canada) and the University of Waterloo aimed at developing

design criteria for the construction of a fire fighter training facility. One particular criterion is

that realistic training with respect to temperature, heat release and stratification be provided in

such a facility. The purpose of this paper was to compare existing analytical heat release and

upper and lower gas temperature rise correlations and models with data from actual structures

which were instrumented and burned in collaboration with the Kitchener Fire Department. The

CFAST model was used successfully to predict these conditions and will be used in future

design of such facilities.

A report by Bailey et al. [121] compares predictions by CFAST to data from real scale fire tests

conducted onboard ex-USS SHADWELL, the Navy’s R&D damage control platform. The

phenomenon of particular interest in this validation series was the conduction of heat in the

vertical direction through compartment ceilings and floors. As part of this work, Bailey et al.

[122] compared CFAST temperature predictions on the unexposed walls of large metal boxes,

driven by steady state fires. This tested the model’s prediction of radiation and conduction in

both the vertical and horizontal directions. Indirectly it quantifies the quality of the

conduction/convection/radiation models. The model and experiment compared well within

measurement error bounds of each. The comparison was particularly good for measurements in

the fire compartment as well as for the compartment and deck directly above it, with predictions

typically agreeing with experiments within measurement uncertainty. The model under-predicted

the temperatures of the compartments and decks not directly adjacent to the fire compartment

early in the tests. Most of the error arose due to uncertainty in modeling the details of the

experiment. The size of the vent openings between decks and to the outside must be included,

but these were not always known. Cracks formed in the deck between the fire compartment and

the compartment above due to the intense fire in the room of origin, but a time dependent record

was not kept. The total size of the openings to the outside of warped doors in both compartments

was not recorded. As can be seen in figures 7 and 8 of reference [120], the steady state
99

predictions are identical (within error bounds of the experiment and prediction). The largest

error is after ignition (uncertainty in the initial fire) and during development of the cracks

between the compartments. While this does not affect the agreement in the room of origin, it

does lead to an error of about 30 % in the adjacent compartment.

6.2 Comparisons with Previously Published Test Data

A number of researchers have studied the level of agreement between computer fire models and

real-scale fires. These comparisons fall into two broad categories: fire reconstruction and

comparison with laboratory experiments. Both categories provide a level of verification for the

models used. Fire reconstruction, although often more qualitative, provides a higher degree of

confidence for the user when the models successfully simulate real-life conditions. Comparisons

with laboratory experiments, however, can yield detailed comparisons that can point out

weaknesses in the individual phenomena included in the models.

NIST has studied the predictive capability of CFAST in detail for several scenarios where

experimental data were available. In this section, we will consider these variables for

comparison:

 • upper and lower layer gas temperature,

 • layer interface position,

 • gas species concentration.

 • fire pyrolysis and heat release rate,

 • room pressure, and

 • vent flow.

Although there are certainly other comparisons of interest, these will provide an indication of the

match of the model to the experimental data. The intent is to do a general comparison of each of

the sensible output variables with full scale experiments. Additional comparisons for additional

specific applications are discussed later.

6.2.1 Experimental Data Selected for Comparison

Peacock et al. [123] compared the performance of the CFAST model with experimental

measurements for the variables presented above. Using a range of laboratory tests, they

presented comparisons of peak values, average values, and overall curve shape for a number of

variables of interest to model users. A total of five different real-scale fire tests were selected for

the comparisons to represent a range of challenges for the CFAST model. Details of the

experimental measurements and procedure for model calculations are available in the original

paper [122]. Five sets of tests were considered for comparison:
100

 1) A single-room test using upholstered furniture as the burning item was selected for its

well-characterized and realistic fire source in a simple single-room geometry [124]. Heat

release rate, mass loss rate, and species yields measurements were made available for the

test. This should allow straightforward application of the model. Peak fire size was

about 2.9 MW with a total room volume of 21 m .

3

 2) Like the first test, this test was a single-room fire test using furniture as the fire source

[125]. It expanded upon that data set by adding the phenomenon of wall burning. Peak

fire size was about 7 MW. Room size was similar to the first test. 

 3) This data set is actually an average of a series of 11 replicate tests in a three-room configuration with simple steady-state gas burner fires [28]. It provides a basic set of

measured quantities for small to medium size fires. Since all fires were gas burner fires,

simulation should be straightforward. It is of particular interest since it was undertaken

as a part of a program to develop a methodology for the evaluation and accuracy assessment of fire models. Fire size was about 100 kW with a total volume of 100 m .

3

 4) This data set is part a series of tests conducted in a multiple room configuration with

more complex gas burner fires than the three-room configuration [120] , [126]. This

study was included because it expands upon that data set by providing larger and timevarying gas burner fires in a room-corridor configuration. Fire size was about up to

1 MW with a total volume of 200 m .

3

 5) By far the most complex test, this data set is part of a series of full-scale experiments

conducted to evaluate zoned smoke control systems, with and without stairwell pressurization [11]. It was conducted in a seven story hotel with multiple rooms on each floor

and a stairwell connecting all floors. This data set was chosen because it would be considered beyond the scope of most current fire models. Measured temperatures and pressure differences between the rooms and floors of the building are extensive and consistent. Peak fire size was 3 MW with a total building volume of 140 000 m . 

3

All of the simulations were performed with version 4 of the CFAST model. For each of the data

sets, the model data were developed from the building and fire descriptions provided in the

original reports. Obtaining building geometry, construction materials, and room interconnections was straightforward. Usually, description of the fire source was more difficult. Where

freeburn data were available, such data were used to describe the heat release rate, pyrolysis rate,

and species yields. In other cases, estimates from tests of similar materials or textbook values

were used to determine missing quantities.
101

6.2.2 Layer Temperature and Interface Position

Arguably the most frequent question asked about a fire is, ?How hot did it become?” Temperature in the upper layer of a compartment is an obvious indicator to answer this question. Peak

temperature, time to peak temperature, or time to reach a chosen temperature tenability limit are

typical values of interest. Quality of the prediction (or measurement) of layer interface position

is more difficult to quantify. Although observed valid in a range of experiments, the two-layer

assumption is in many ways just a convenience for modeling. From a standpoint of hazard, time

of descent to a chosen level may be a reasonable criterion (assuming some in the room will then

either be forced to crawl beneath the interface to breathe the ?clean” atmosphere near the floor or

be forced to breath the upper layer gases). Minimum values may also be used to indicate general

agreement. For the single-room tests with furniture or wall-burning, these are appropriate

indicators to judge the comparisons between model and experiment. For the more-closely

steady-state three- and four-room tests with corridor or the multiple-story building tests, a

steady-state average better characterizes the nature of the experiment.

Figures 27 – 29 and tables 7 – 9 show the upper layer temperature, lower layer temperature, and

interface position for the tests studied. Like all zone-based fire models, CFAST calculates

conditions within each room as an upper and a lower volume (layer), each with uniform conditions throughout the volume at any instant of time. Thus, for the model, the temperature environment within a room can be described by an upper and lower layer temperature and by the

position of the interface between these two layers. By contrast, experimental measurements

often take the form of a vertical array of measurement points describing a profile of temperature. 

Techniques for collapsing these profiles to data that can be compared to zone fire models are

available [111] and are used here to facilitate the comparison. 

For the single-room tests, predicted temperatures and layer interface position show obvious

similarities to the measured values. Peak values occurred at similar times with comparable rise

and fall for most comparisons. Interface height for the single-room with wall-burning is a

notable exception. Unlike the model prediction, the experimental measurement did not show the

rise and fall in concert with the temperature measurement. Peak values were typically higher for

upper layer temperature and lower for lower layer temperature and layer interface position. For

all the tests, including the single-room tests, times to peak values and times to 100 °C predicted

by the model were within 25 s of experimentally measured values on average.
102

Numbers in parentheses are

model predictions

Peaka

Value

(°C)

Time to

Peak

(s)

Time to

100°C

(s)

SteadyState

Value

(°C)

Similar

Shape?

Single-room furniture testsb

(Tests 1 and 6)

790 (780)

920 (780)

500 (510)

450 (510)

290 (250)

290 (250) – T

c

590 (660)

900 (660)

510 (520)

510 (520)

330 (260)

330 (260) -- T

Single-room tests with wall

burning

(Tests 1 and 2)

750 (620) 710 (230) 100 (140) -- T

810 (1190) 520 (470) 100 (80) -- T

Three-room tests with corridord

(SET 4, 11 replicates) -- --

100 (120)

830 (n.r. )

e

n.r.

230 (215)

75 (90)

45 (50)

Four-room tests with corridord

(Tests 19 and 21)

-- --

195 (195)

n.r.

n.r.

n.r.

240 (370)

70 (90)

55 (35)

40 (35)

T

-- --

200 (195)

n.r. (240)

n.r.

n.r.

260 (370)

80 (100)

65 (50)

50 (50)

Multiple-story building

(Test 7) -- --

390 (180)

210 (390)

n.r.

270 (340)

110 (110)

15 (15)

T

a Experimental data for these comparisons come from references [28],[123], [124],[125],[11] discussed in section

6.2.1.

b Two measurement positions within the room were available from the experimental data.

c Not appropriate for the experiment.

d Multiple entries indicate multiple measurements were available for comparison with model predictions.

e not reached in the experiment

Table 7. Comparison of experimental measurements and model predictions

of upper layer temperature (°C) for several tests
103

Numbers in parentheses are

model predictions

Peak

Value

(°C)

Time to

Peak

(s)

Time to

100°C

(s)

SteadyState

Value

(°C)

Similar

Shape?

Single-room furniture testsa

570 (430)

590 (430)

500 (510)

420 (510)

370 (400)

390 (400) – T

c

230 (230)

590 (230)

510 (520)

500 (520)

410 (460)

390 (460) -- T

Single-room tests with wall burning

710 (240) 710 (230) 240 (220) -- T

700 (950) 520 (470) 290 (290) -- T

Three-room tests with corridorc

-- --

n.r.

n.r.

n.r.

70 (50)

30 (30)

23 (30)

Four-room tests with corridorc

-- --

n.r.

n.r.

n.r.

75 (50)

21 (22)

21 (17)

T

-- --

n.r.

n.r.

n.r.

70 (52)

20 (22)

20 (17)

Multiple-story building -- --

520 (n.r.)

n.r.

n.r.

85 (95)

40 (45)

14 (16)

T

See notes for Table 7.

Table 8. Comparison of experimental measurements and model predictions

of lower layer temperature (°C) for several tests

Numbers in parentheses are

model predictions

Peak

Value

(m)

Time to

Peak

(s)

Time to

1 m

(s)

SteadyState

Value

(m)

Similar

Shape?

Single-room furniture testsa

0.8 (0.3)

0.8 (0.3)

420 (480)

450 (480)

400 (390)

380 (390) – T

c

0.8 (0.5)

0.9 (0.5)

480 (510)

460 (510)

420 (430)

430 (430) -- T

Single-room tests with wall burning

0.2 (0.7) 710 (220) 120 (210) -- T

0.1 (0.6) 500 (410) 80 (280) -- T

Three-room tests with corridorc

-- --

360 (n.r.)

1210 (n.r.)

90 (n.r.)

1.0 (1.7)

1.2 (1.6)

0.9 (1.3)

T

Four-room tests with corridorc

-- -- n.a.

0.7 (1.7)

1.0 (1.8)

1.0 (1.7)

0.7 (1.7)

-- -- n.a.

0.8 (1.5)

0.9 (1.4)

0.8 (1.2)

0.6 (1.2)

Multiple-story building -- -- n.a.

0.3 (0.6)

0.8 (0.8)

1.8 (0.9)

See notes for Table 7.

Table 9. Comparison of experimental measurements and model predictions

of layer interface position (m) for several tests
104

Figure 27. Comparison of measured and predicted upper layer temperatures for several tests.
105

Figure 28. Comparison of measured and predicted lower layer temperatures for several tests.

Figure 29. Comparison of measured and predicted layer interface position for several tests.

Systematic deviations exist for the remaining three data sets. Differences between model

predictions and experimental measurements changed monotonically over time (rising for the

three-room test and falling for the four-rooms tests. Modeling of heat conduction (losing too
106

much or too little heat to the surfaces) or lack of modeling of leakage (rooms in CFAST are

presumed perfectly sealed unless vents are included to simulate leakage) may account for the

trends. The comparison of interface position for the four-room test with corridor seems an

anomaly. Although a nearly closed space, the roughly level interface position from the experiment seems more typical of a test more open to the ambient. The model calculations appear to

better represent the mixing which would occur in a closed volume. Again, leakage may be a

factor. With some leakage in the space, lower temperatures for both the lower and upper layers

and higher (and more uniform) interface position would be calculated.

In general, upper layer temperature and interface position predicted by the model were somewhat higher than the experimental measurements [127], with the differences ranging from

-140 °C to 380 °C for the temperature and -0.5 m to 0.8 m for the interface position. Conversely, the lower layer temperature was somewhat lower for the model than for the experiments

(-470 °C to 250 °C). Presuming conservation of energy (an underlying assumption in all fire

models), these three observations were consistent. A higher interface position gives rise to a

smaller upper volume (and larger lower volume) within a room. With the same enthalpy in a

smaller upper volume, higher temperatures result. This lends credence to the assumption of

enthalpy conservation. Layer interface position is primarily affected by entrainment by the fire

or at vents. Plume entrainment in CFAST is based on the work of McCaffrey [22] on circular

plumes in relatively small spaces. For large fires in small spaces where the fire impinges on the

ceiling (such as the single room tests with wall burning) or very small fires in large spaces (such

as atria), these correlations may not be as valid.

6.2.3 Gas Species

The fire chemistry scheme in CFAST is essentially a species balance from user-prescribed

species yields and the oxygen available for combustion. Once generated, it is a matter of

bookkeeping to track the mass of species throughout the various control volumes in a simulated

building. It does, however, provide another check of the flow algorithms within the model. 

Since the major species (CO and CO2) are generated only by the fire, the relative accuracy of the

predicted values throughout multiple rooms of a structure should be comparable. Figure 30 and

2 2 table 10 show measured and predicted concentrations of O , CO , and CO in two of the tests

studied.
107

Figure 30. Comparison of measured and predicted gas species concentrations for several tests.
108

Oxygen Concentration

Numbers in parentheses are

model predictions

Peak

Valuea

(%)

Time to

Peak

(s)

SteadyState

Value

(%)

Similar

Shape?

Single-room furniture fire tests

0.01 (6.7) 510 (490) -- T

a

6.9 (10.6) 490 (510) -- T

Four-room tests with corridorc

-- --

17.9 (12.8)

18.0 (15.4) T

-- --

16.1 (11.8)

18.1 (16.5) T

Multiple-story building test -- --

c 15.5 (11.1)

20.9 (20.3)

Carbon Dioxide Concentration

Single-room furniture fire tests

17.0 (5.6) 480 (510) – T

b

10.6 (4.1) 490 (510) -- T

Four-room tests with corridorc

-- -- 2.3 (4.1) T

-- -- 2.4 (4.8) T

Multiple-story building test -- -- 2.0 (0.5) c

Carbon Monoxide Concentration

Single-room furniture fire tests

2.2 (0.2) 490 (510) -- T

a

0.6 (0.1) 440 (510) -- T

Multiple-story building test -- -- 0.8 (0.04) c

a Experimental data for these comparisons come from references [28],[123], [124],[125],[11] discussed in section

6.2.1.

b not appropriate for the test.

c multiple entries indicate comparable rooms in the test structure.

Table 10. Comparison of experimental measurements and model predictions

of oxygen concentration for several tests

For the single-room tests with furniture, the predicted concentrations are lower than those

measured experimentally (averaging 5 % low). This is probably due to the treatment of oxygen

limited burning. In CFAST, the burning rate simply decreases as the oxygen level decreases. A

user prescribed lower limit determines the point below which burning will not take place. This

parameter could be finessed to provide better agreement with the experiment. For the present

comparisons, it was always left at the default value of 14 %. 
109

For the four room test with corridor, the asymptotic values of the gas concentrations agree quite

well. At first glance, the model predictions reach this equilibrium more quickly. An

appreciation of the differences between the modeled parameters and the experimental

measurements put this in perspective. From figure 29, it takes about 100 s for the upper layer to

descend to the level of the gas sampling port in the test. In addition, it is assumed than this point

measurement is the bulk concentration of the entire upper layer. In reality, some vertical distribution not unlike the temperature profile (figure 29) exists for the gas concentration as well. 

Since this measurement point is near the lower edge of the upper layer for a significant time, it

should underestimate the bulk concentration until the layer is large in volume and well mixed.

For 2 2 the multiple-story building test, predicted values for CO , CO, and O are far lower than

measured experimentally. Both the lower burning rate limit as well as leakage in the 100 yearold structure probably contributed to the differences between the experiments and model. In

addition, values for species yields were simply literature values since no test data were available.

6.2.4 Heat Release and Fuel Pyrolysis Rate

Heat release rate and its intimately related pyrolysis rate are key indicators of fire hazard [8]. 

Peak values and time to reach peak values are typical scalar estimates used to represent the timevariant heat release rate and fire pyrolysis rate. For the single-room tests with furniture or wallburning, these are appropriate indicators to judge the comparisons between model and

experiment. For the three- and four-room tests with corridor or the multiple-story building tests,

a steady state average is more appropriate.

Table 11 and figure 31 compare measured and predicted heat release rates for the tests. In the

CFAST model, the fire is prescribed as a series of straight line segments describing the pyrolysis

rate, heat release rate, and species yields. Thus, the model predictions could be expected to

agree quite well with experimental measurements. For tests where experimental data were

available, the agreement is excellent – usually within 5 % of the peak experimental values. 

Since this effectively just shows how well a series of line segments reproduces experimental

measurement, this level of agreement is expected. 

Times to peak values are always close. For two tests (the single-room with furniture and wall

burning and the multiple-story building), the heat release rate in the room is limited by the available oxygen. Additional burning outside the room (seen in the single-room with furniture) accounts for the remainder of the heat released.

For the three-room test with corridor, multiple replicate tests put the agreement between the

model and experiments in perspective. For all tests in the original study [28], the coefficients of

variation (the standard deviation expressed as a percentage of the mean) ranged from 4 % to

52 %. In another study, precision to within 15 % for fires of 2.5 MW was noted [123]. Thus, the
110

Figure 31. Comparison of measured and prescribed heat release rates for two selected tests.

Numbers in parentheses are

model predictions

Peak

Valuea

(kW)

Time to

Peak

(s)

SteadyState

Value

(kW)

Similar

Shape?

Single-room furniture fire tests

2450 (2200) 480 (480) – T

b

2600 (2350) 500 (510) -- T

Single-room tests with wall-burning

2050 (2000) 230 (200) -- T

4000 (3150) 420 (370) -- T

Three-room test with corridor -- -- 86 (87) T

Four-room tests with corridor

-- -- n.r. T

c

-- -- n.r T

Multiple-story building test -- -- n.r T

a Experimental data for these comparisons come from references [28],[123], [124],[125],[11] discussed in section

6.2.1.

b not appropriate for the test.

c not available from experimental data.

Table 11. Comparison of measured and prescribed heat release rate for several tests

simplification of specifying the fire growth as a series of straight lines is easily justified with the

expected accuracy of experimental measurements.
111

For the multiple-story building test, no pyrolysis rate or heat release rate data were available. 

Estimates of the “steady-state” burning rate, time to reach “steady-state,” and duration of

“steady-state” burning were made from available correlations for wood cribs [128], [129]. 

Although the comparisons for this test should be considered approximate, it was included since,

if successful, the scope of the model is extended considerably to a large multiple-story building

with mechanical ventilation.

6.2.5 Pressure

The differential pressure across an opening drives the flow through the opening. For each room,

the CFAST model calculates a differential pressure at floor level, referenced to ambient. Noting

that the ambient pressure is approximately 100 kPa, typical pressure drops across openings

induced by fires are but a small fraction of the ambient pressure – typically from less than 1 Pa

to perhaps a few hundred Pascals in well-sealed enclosures. The ability to model these

extremely small differential pressures provides another check on the flow algorithms in the

model. These are, however, expected to be difficult to model and measure accurately. Thus,

agreement within a few pascals is often considered acceptable. In four of the five experimental

test series, measurements (corrected to floor level) were available which could be compared to

these predicted values (measurements were not available for the single room tests with

furniture). 

Figure 35 and table 12 show the comparisons. For most cases, the agreement is reasonable, with

the difference between measured and predicted values typically less than 2 Pa and for some

experiments, less than 0.5 Pa. Trends displayed in the experimental data are replicated by the

model predictions. Some interesting exceptions are apparent however. In major part, these are

due to quantities unknown in the experiments (leakage). Not all of the onus for agreement

should be placed on the model, however. Only one of the test series included any estimate of

leakage through cracks in the buildings. Logically, unless directed otherwise, the model

assumes no leakage from any room. This leakage can have a dramatic effect on the results

predicted by the model. Figure 33 illustrates the effect of leakage for a single room with a single

doorway and an upholstered chair used as the fire source. Leakage areas from 0 % to 100 % of

the vent area were simulated with a second vent of appropriate size and placed at floor level

(much of the leakage in rooms take place at floor level). Both temperatures and pressures

change by more than a factor of two (other variables can be expected to change with similar

variation). Temperature changes by about 20 % with only a 10 % leakage area. The effect on

pressure is not quite as straightforward, but for larger leakages changes in concert with the

temperature. For the four-room tests with corridor, leakage from the “well sealed rooms” was

estimated via measurement at not more than 25 % of the total vent area.
112

Figure 32. Comparison of measured and predicted pressures for several tests.
113

Numbers in parentheses are

model predictions

Peak

Value

Time to

Peak

SteadyState

Value

Similar

Shape?

Single-room tests with wall-burning

-1.9 (-4.5) 730 (230) – T

a

-1.9 (-6.4) 520 (490) -- T

Three-room test with corridor -- -- -1.1 (-0.6)

-0.2 (-0.5) T

Four-room tests with corridor

-- -- -1.0 (-2.1) T

-- -- 36 (22)

Multiple-story building test -- -- 2.4 (1.3) T

Experimental data for these comparisons come from references [28],[123], [124],[125],[11] discussed in section

6.2.1.

 not appropriate for the test. a

Table 12. Comparison of experimental measurements and model predictions

of room pressure for several tests

Figure 33. Effect of leakage in an arbitrary single-room fire.
114

Numbers in parentheses are

model predictions

Peak

Value

Time to

Peak

SteadyState

Value

Similar

Shape?

Single-room furniture fire tests

1.2 (1.3) 380 (410) -- T

a

1.9 (1.9) 560 (460) -- T

Three-room test with corridor -- -- 0.4 (0.3) T

Experimental data for these comparisons come from references [28],[123], [124],[125],[11] discussed in section 6.2.1.

 not appropriate for the test. a

Table 13. Comparison of experimental measurements and model predictions

of mass flow through openings for several tests

6.2.6 Flow Through Openings

In the control volume approach, the differential form of the momentum equation for the zones is

not solved directly. Rather, the momentum transfer at the zone boundaries is included by using

Bernoulli's approximation for the velocity equation. This solution is augmented for restricted

openings by using flow coefficients [30], [57] to allow for constriction in vents. The flow coefficients allow for an effective constriction of fluid flow which occurs for vents with sharp edges. 

In CFAST, these coefficients are for rectangular openings in walls whose surfaces are much

larger than the opening.

Figure 34 and table 13 compare measured and predicted mass flows through doorways in two of

the tests studied. For the three-room test with corridor, flow through two doorways of the same

test are shown (one between the fire room and the corridor and one between the corridor and the

outdoors). Not surprisingly, the flow is typically somewhat underpredicted by the model

(averaging 0.1 kg/s). The vent flow in CFAST includes mixing phenomena at the vents. As hot

gases from one compartment leave that compartment and flow into an adjacent compartment, a

door jet can exist which is analogous to a normal fire plume, but with an extended flat plume

similar to a waterfall. This places its use outside the normal range of the plume model [22] and

perhaps beyond its range of validity. However, no reliable correlation yet exists for the extended

flat plume which occurs in vent flow. Examining the trends of prediction of upper layer

temperature in tests with multiple rooms (Tables 7 and 8), the typical over-prediction in the

room of fire origin is far greater than for other rooms in the structures. The under-prediction of

the mass flows probably accounts for this as a cascading effect with distance from the room of

fire origin.

Sections 6.2.2 through 6.2.6 show comparisons of the experiments with the model predictions.

The differences are quantified based on time to peak (e.g. temperature), closeness of the two

curves in a time varying sense, and the steady state predictions. The latter are valuable since they
115

Figure 34. Comparison of measured and predicted mass flow through vents for several tests.

(Numbers indicate comparable rooms in the test structure.)

iron out impreciseness of the explanation of the experiment. In addition to these comparisons, it

is possible to quantify the relative difference between the time dependent curves and the relative

shape of the curves. For these experiments such a detailed quantification was done by Peacock

et. al. [130].

6.2.7 Plume Model

Davis compared predictions by CFAST (and other models) for high ceiling spaces [131]. In this

paper, the predictive capability of two algorithms designed to calculate plume centerline

temperature and maximum ceiling jet temperature in the presence of a hot upper layer were

compared to measurements from experiments and to predictions using CFAST’s ceiling jet

algorithm. The experiments included ceiling heights of 0.58 m to 22 m and heat release rates of

0.62 kW to 33 MW. When compared to the experimental results CFAST’s ceiling jet algorithm

tended to over-predict the upper layer temperature by 20 %. With proper adjustment for radiation

effects in the thermocouple measurements, some of this difference disappears. The effect of

entrainment of the upper layer gases needs to be improved.

6.2.8 Other Comparisons with Previously Published Test Data

Jones and Peacock [132] presented a limited set of comparisons between the FAST model and a

multi-room fire test. The experiment involved a constant fire of about 100 kW in a three-
116

compartment configuration of about 100 m . They observed that the model predicted an upper

3

layer temperature that was too high by about 20 % with satisfactory prediction of the layer

interface position. These observations were made before the work of Pitts et al. [116] showed

that the thermocouple measurements need to be corrected for radiation effects. Convective

heating and plume entrainment were seen to limit the accuracy of the predictions. A comparison

of predicted and measured pressures in the rooms showed within 20 %. Since pressure is the

driving force for flow between compartments, this agreement was seen as important.

Levine and Nelson [133] used a combination of full-scale fire testing and modeling to simulate a

fire in a residence. The 1987 fire in a first-floor kitchen resulted in the deaths of three persons in

an upstairs bedroom, one with a reported blood carboxyhemoglobin content of 91 %. Considerable physical evidence remained. The fire was successfully simulated at full scale in a fullyinstrumented seven-room two-story test structure. The data collected during the test have been

used to test the predictive abilities of two multiroom computer fire models: FAST and HARVARD VI. A coherent ceiling layer flow occurred during the full-scale test and quickly carried

high concentrations of carbon monoxide to remote compartments. Such flow is not directly

accounted for in either computer code. However, both codes predicted the carbon monoxide

buildup in the room most remote from the fire. Prediction of the pre-flashover temperature rise

was also good. Prediction of temperatures after flashover that occurred in the room of fire origin

was less good. Other predictions of conditions throughout the seven test rooms varied from

good approximations to significant deviations from test data. Some of these deviations are

believed to be due to phenomena not considered in any computer models.

Deal [134] reviewed four computer fire models (CCFM [8], FIRST [6], FPETOOL [135] and

FAST) to ascertain the relative performance of the models in simulating fire experiments in a

small room (about 12 m in volume) in which the vent and fuel effects were varied. Peak fire 3

size in the experiments ranged up to 800 kW. All the models simulated the experimental

conditions including temperature, species generation, and vent flows quite satisfactorily. With a

variety of conditions, including narrow and normal vent widths, plastic and wood fuels, and

flashover and sub-flashover fire temperatures, competence of the models at these room

geometries was demonstrated.

Duong [136] studied the predictions of several computer fire models (CCFM, FAST, FIRST, and

BRI [6]), comparing the models with one another and with large fires (4 MW to 36 MW) in an

aircraft hanger (60 000 m ). For the 4 MW fire size, he concluded that all the models are 3

reasonably accurate. At 36 MW, however, none of the models did well. Limitations of the heat

conduction and plume entrainment algorithms were thought to account for some of the

inaccuracies.
117

6.3 Prediction of Flashover

A chaotic event that can be predicted by mathematical modeling is that of flashover. Flashover is

the common term used for the transition a fire makes from a few objects pyrolyzing to full room

involvement. It is of interest to the fire service because of the danger to fire fighters and to

building designers because of life safety and the attendant impact on occupants. Several papers

have looked at the capability of CFAST to predict the conditions under which flashover can

occur. 

Chow [137] concluded that CFAST correctly predicted the onset of flashover if the appropriate

criteria were used. The criteria were gas temperature near the ceiling, heat flux at the floor level

and flames coming out of the openings. This analysis was based on a series of compartment

fires.

A paper by Luo et al. [138] presents a comparison of the results from CFAST against a

comprehensive set of data obtained from one flashover fire experiment. The experimental results

were obtained from a full-scale prototype apartment building under flashover conditions. Three

polyurethane mattresses were used as fuel. It was found that the predicted temperatures from the

CFAST fire model agreed well with the experimental results in most areas, once radiation

corrections are applied to the thermocouple data.

Collier [139] makes an attempt to quantify the fire hazards associated with a typical New

Zealand dwelling, a series of experiments. These tests, done in a three-bedroom dwelling,

included both non-flashover and flashover fires. The predictions were consistent with the

experiments within the uncertainty of each.

Post-flashover fires in shipboard spaces have a pronounced effects on adjacent spaces due to

highly conductive boundaries. The CFAST model predictions for the gas temperature and the

cold wall temperature were compared with shipboard fires [140]. The comparisons between the

model and experimental data show conservative predictions. The authors attribute this to an

overestimation of the average hot wall temperature and an underestimation of external

convective losses due to wind effects.

Finally, a more general comparison of CFAST with a number of simple correlations was used by

Peacock and Babrauskas [141], [142] to simulate a range of geometries and fire conditions to

predict the development of the fire up to the point of flashover. The simulations represent a

range of compartment sizes from 8 m to 1327 m , with ceiling height varying from 2.4 m to 3 3

12.2 m and vent openings from 10 % to 100 % of the length of the short wall (plus a “standard”

door, 0.76 m in width). For most of the simulations, the surface lining material was gypsum

wallboard, 12.7 mm in thickness, consistent with the values used in the correlations. A simple

constant fire size was varied until the calculated upper layer temperature reached 600 /C at the

end of the simulation. For some simulations, the surface linings ranged from aluminum to a
118

highly insulating foam and the fire source diverged from the simple steady-state fire to more

complex shapes.

The important test of all these prediction methods is in the comparison of the predictions with

actual fire observations. Figure 35 presents estimates of the minimum energy required to achieve

flashover for a range of room and vent sizes. This figure is an extension of the earlier work of

Babrauskas [143] and includes additional experimental measurements from a variety of sources,

most notably the work of Deal and Beyler [144]. In addition, figure 35 includes predictions from

the CFAST model.

As with some of the experimental data defining flashover as an upper layer temperature reaching

600 /C, many experimental measures were reported as peak values rather than minimum values

necessary to achieve flashover. Thus, ideally all the predictions should provide a lower bound

for the experimental data. Indeed, this is consistent with the graph – the vast majority of the

experimental observations lie above the correlations and model predictions. For a considerable

range in the ratio , the correlations of Babrauskas [123] Thomas [145], and the MQH

correlation of McCaffrey et al. [146] provide similar estimates of the minimum energy required

to produce flashover. The estimates of Hägglund [147] yields somewhat higher estimates for

values of greater than 20 m .

-1/2

Figure 35. Comparison of correlations, CFAST predictions, and

experimental data for the prediction of flashover in a compartment fire.
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The results from the CFAST model for this single compartment scenario provide similar results

to the experiments and the correlations for most of the range of . For small values of

, the CFAST values rise somewhat above the values from the correlations. These small

va Tlues of result from either very small compartments (small A ) or very large openings

(large ), both of which stretch the limits of the assumptions inherent in the model. For very

small compartments, radiation from the fire to the compartment surfaces becomes more

important, enhancing the conductive heat losses through the walls. However, the basic two-zone

assumption may break down as the room becomes very small. For very large openings, the

calculation of vent flow via an orifice flow coefficient approach is likely inaccurate. Indeed, for

such openings, this limitation has been observed experimentally [123]. The estimates are close

to the range of uncertainty shown by the correlations which also diverge at very small values of

.

Perhaps most significant in these comparisons is that all the simple correlations provide

estimates similar to the CFAST model and all the models are consistent with a wide range of

experimental data. For this simple scenario, little is gained with the use of the more complex

models. For more complicated scenarios, the comparison may not be as simple.

6.4 Comparison with Documented Fire Experience

There are numerous cases of CFAST being used to adjudicate legal disputes. Since these are

discussed in courts of law, there is a great deal of scrutiny of the modeling, assumptions, and

results. Most of these simulations and comparisons are not available in the public literature. A

few of the cases which are available are discussed below. In these scenarios, there are, of course, 

no detailed measurements. The metric for how good the model performed is its ability to

reproduce the time-line as observed by witnesses and the death of occupants or the destruction of

property as was used in evidence in legal proceedings.

As mentioned in section 6.2.8, Levine and Nelson describe the use of CFAST for understanding

the deaths of two adults in a residence in Sharon, Pennsylvania in 1987 [132]. The paper

compared the evidence of the actual fire, a full scale mockup done at NIST and the results from

CFAST (FAST 18 [76]) and Harvard VI [148]. The most notable shortcoming of the models was

the lower than actual temperatures in the bedrooms, caused by loss of heat through the fire

barriers. This led to the improvement in CFAST in the mid-90s to couple compartments together

so that both horizontal and vertical heat transfer occur to adjacent compartments.

Bukowski used CFAST to analyze a fire in New York City [149] in 1994 which resulted in the

death of three fire fighters. The CFAST model was able to (very accurately) reproduce the
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observable conditions and supported the theory as to how the fire began and the cause of death

of the three fire fighters.

Chow describes the use and comparison of CFAST simulations with a recent (circa 1996) highrise building fire in Hong Kong [150]. CFAST simulations were performed to help understand

the probable fire environment under different conditions. Three simulations were performed to

study the consequences of a fire starting in the lift shaft. Smoke flow in the simulations

qualitatively matched those observed during the incident.

In the early morning hours of March 25,1990 a tragic fire took the lives of 87 persons at a

neighborhood club in the Bronx, New York [151]. The New York City Fire Department

requested the assistance of the Center for Fire Research (CFR) in understanding the factors

which contributed to this high death toll and to develop a strategy that might reduce the risk of a

similar occurrence in the many similar clubs operating in the city.

These are examples of CFAST being validated by corroboration with eye witness accounts, and

forensic evidence.

6.5 Comparison with Experiments Which Cover Special Situations

There are several sets of comparisons used in the development of the model or specific

applications beyond those discussed more generally above.

6.5.1 Nuclear Facilities

Floyd validated CFAST by comparing the modeling results with measurements from fire tests at

the Heiss-Dampf Reaktor (HDR) facility [152]. The structure was originally the containment

building for a nuclear power reactor in Germany. The cylindrical structure was 20 m in diameter

and 50 m in height topped by a hemispherical dome 10 m in radius. The building was divided

into eight levels. The total volume of the building was approximately 11 000 m . From 1984 to 3

1991, four fire test series were performed within the HDR facility. The T51 test series consisted

of 11 propane gas tests and three wood crib tests. To avoid permanent damage to the test facility,

a special set of test rooms were constructed, consisting of a fire room with a narrow door, a long

corridor wrapping around the reactor vessel shield wall, and a curtained area centered beneath a

maintenance hatch. The fire room walls were lined with fire brick. The doorway and corridor

walls had the same construction as the test chamber. Six gas burners were mounted in the fire

room. The fuel source was propane gas mixed with 10 % air fed at a constant rate to one of the

six burners.

In general, the comparison between CFAST and the HDR results was good, with two exceptions.

The first is the over estimate of the temperature of the upper layer, typically within about 15 %

of the experimental measurements. This is common and generally results from the using too low
121

a value for the production of soot, water (hydrogen) and carbon monoxide. The other exception

consists of predictions in spaces where the zone model concept breaks down, for example in the

stairways between levels. In this case, CFAST has to treat the space either in the filling mode

(two layer approximation) or as a fully mixed zone (using the SHAFT option). Neither is quite

correct, and in order to understand the condition in such spaces in detail (beyond the transfer of

mass and energy), a more detailed CFD model must be used, for example, FDS [46].

6.5.2 Small Scale Testing

As an implementation of the zone model concept, CFAST is applicable to a wide range of

scenarios. One end of this spectrum are small compartments, one to two meters on a side.

Several research efforts have looked at small scale validation. There are three papers by Chow

[153],[154],[155] which examine this issue. The first is the use of an electric heater with

adjustable thermal power output was to verify results predicted by CFAST. The second was

closed chamber fires studied by burning four types of organic liquids, namely ethanol, Nheptane, thinner and kerosene. The burning behavior of the liquids was observed, and the hot gas

temperature measured. These behaviors along with the transient variations of the temperature

were then compared with those predicted by the CFAST model. Finally, in another series of

experiments, three zone models, one of which was CFAST, were evaluated experimentally using

a small fire chamber. Once again, liquid fires were chosen for having better control on the mass

loss rate. The results on the development of smoke layer and the hot gas temperature predicted

by the three models were compared with those measured experimentally. According to Chow,

fairly good agreement was found if the input parameters were chosen properly.

6.5.3 Unusual Geometry and Specific Algorithms

A zone model is inherently volume calculation. There is an assumption in the derivation of the

equations that gas layers are strongly stratified. This allows for the usual interpretation that a

volume can then be thought of as a rectangular parallelepiped, which allows the developers to

express the volume in terms of a floor area and height of a compartment, saying simply that the

height times the floor area is the volume. However, there are other geometries which can be

adequately described by zone models. Tunnels, ships, and attics are the most common areas of

application which fall outside of the usual scope.

6.5.3.1 Railway and Vehicle Tunnels 

Altinakar et al. [156] used a modified version of CFAST for predicting fire development and

smoke propagation in vehicle or railroad tunnels. The model was tested by simulating several

full-scale tests carried out at memorial Tunnel Ventilation Test Program in West Virginia, and

the Offeneg Tunnel in Switzerland. His article compares simulated values of temperature,

opacity and similar sensible quantities with measured values and discusses the limits of the

applicability of zone models for simulating fire and smoke propagation in vehicle and railroad
122

tunnels. The two major modifications made to the model dealt with mixing between the upper

and lower layers and friction losses along the tunnel.

Peacock et al. [157] compared times to untenable conditions determined from tests in a

passenger rail car with those predicted by CFAST for the same car geometry and fire scenarios. 

For a range of fire sizes and growth rates, they found agreement that averaged approximately

13 %.

6.5.3.2 Non-Uniform Compartments

In January 1996, the U.S. Navy began testing how the CFAST model would perform when

tasked with predicting shipboard fires. These conditions include mass transport through vertical

vents (representing hatches and scuttles), energy transport via conduction through decks,

improvement to the radiation transport sub model, and geometry peculiar to combat ships. The

purpose of this study was to identify CFAST limitations and develop methods for

circumnavigating these problems [158]. The approach taken was to apply CFAST to the

modeling of a full-scale shipboard fire test and then compare to model conditions. A retired ship

representing the forward half of a USS LOS ANGELES class submarine was used during this

test. Compartments in combat ships are not square in floor area, nor do they have parallel sides.

Application of CFAST to these scenarios required a direct integration of floor area over height to

interpret the layer interface and provide correct predictions for flow through doors and windows

(vertical vents). The most vexing part of this was development of the user specification

(ROOMA and ROOMH) to provide a description for the model to use. For most applications of

CFAST, the effort required for the input outweighs any additional precision in the calculated

results.

6.5.3.3 Long Corridors

Prior to development of the corridor flow model, the implementation of flow in compartments

assumed that smoke traveled instantly from one side of a compartment to another. The work of

Bailey et al. [159] provided the basis for the corridor flow model discussed in the section 3.4.4.

It shows good agreement for the delay time calculated using CFAST and measured flow along

high aspect ratio passageways.

6.5.3.4 Mechanical Ventilation

There have been two papers which have looked at the effectiveness of the mechanical ventilation

system. The first considered a fire chamber of length 4.0 m, width 3.0 m and height 2.8 m with

adjustable ventilation rates [160]. Burning tests were carried out with wood cribs and methanol

to study the preflashover stage of a compartmental fire and the effect of ventilation. The mass

loss rate of fuel, temperature distribution of the compartment and the air intake rate were
123

measured. The heat release rates of the fuel were calculated and the smoke temperature was used

as a validation parameter. A scoring system was proposed to compare the results predicted by

the three models. CFAST does particularly well, though there are some differences which can be

attributed to the zone model approach.

A second series of experiments by Luo [161] indicate that the CFAST model generally over

predicts the upper layer temperature in the burn room because the zonal assumption is likely to

break down in the burn room. It was found that the room –averaged temperatures obtained from

CFAST were in good overall agreement with the experimental results. The discrepancies can be

attributed to the correction needed for thermocouple measurements. The CO concentration,

however, was inconsistent. CFAST tended to overestimate CO concentration when the air

handling system was in operation. This is probably due to inconsistencies in what is measured

(point measurements) and predicted (global measurements).

6.5.3.5 Sprinkler Activation

A suppression algorithm [65] was incorporated into CFAST. This paper [162] evaluates the

predictive capability for a sprinkler installed in an atrium roof. There were three main points

being considered: the possibility of activating the sprinkler, thermal response, and water

requirement. The zone model CFAST was used to analyze the possibility of activation of a

sprinkler head. Results derived from CFAST proved to be accurate, that is, providing good

agreement with experimental measurements.

6.5.3.6 t Fires 2

In this study, a series of full-scale experiments [163] were carried out using t fires. Fire room 2

and corridor smoke filling processes were measured. The size of the corridors and arrangements

of smoke curtains were varied in several patterns. Comparisons were then made between the

experimental results and those predicted by CFAST. The author concludes that while the model

does a good job of predicting experimental results, there are systematic differences which could

be reduced with some revision to zone model formulation to include the impact of smoke

curtains.

6.6 Summary

How to best quantify the comparisons between model predictions and experiments is not

obvious. The necessary and perceived level of agreement for any variable is dependent upon

both the typical use of the variable in a given simulation (for instance, the user may be interested

in the time it takes to reach a certain temperature in the room), the nature of the experiment

(peak temperatures would be of little interest in an experiment which quickly reached steady

state), and the context of the comparison in relation to other comparisons being made (a true

validation of a model would involve proper statistical treatment of many compared variables).
124

Insufficient experimental data and understanding of how to compare the numerous variables in a

complex fire model prevent a true validation of the model. Thus, the comparisons of the

differences between model predictions and experimental data discussed here are intentionally

simple and vary from test to test and from variable to variable due to the changing nature of the

tests and typical use of different variables.

In general, upper layer temperatures predicted by the CFAST model are higher than experimental measurements, with the differences typically in the 10 % to 25 % range. Conversely, the

lower layer temperature is somewhat lower for the model than for the experiments. Presuming

conservation of energy (an underlying assumption in all fire models), these observations are consistent. Limitations inherent in the model also account partially for these trends. In the current

version of CFAST, energy exchange in the lower layer is only by mixing or convection from

surfaces. Adding radiative exchange to the lower layer would reduce the upper layer

temperature and increase the lower layer temperature. Layer interface position is primarily

affected by entrainment by the fire or at vents. Underestimation of the conduction would also

account for the effect. Plume entrainment in CFAST is based on the work of McCaffrey [22] on

circular plumes in relatively small spaces. For large fires in small spaces where the fire

impinges on the ceiling (such as the single room tests with wall burning) or very small fires in

large spaces (such as atria), these correlations may not be as valid.
125

7 Conclusion

CFAST is a collection of data, computer programs, and documentation which are used to

simulate the important time-dependent phenomena describing the character of a compartment

fire. The major functions provided include calculation of the buoyancy-driven as well as forced

transport of energy and mass through a series of specified compartments and connections (e.g.,

doors, windows, cracks, ducts), and the resulting temperatures, smoke optical densities, and gas

concentrations after accounting for heat transfer to surfaces and dilution by mixing with clean

air.

CFAST is a zone model. The basic assumption of all zone fire models is that each compartment

can be divided into a small number of control volumes, each of which is internally uniform in

temperature and composition. Beyond these basic assumptions, the model typically involves a

mixture of established theory (e.g., conservation equations), empirical correlations where there

are data but no theory (e.g., flow and entrainment coefficients), and approximations where there

are neither (e.g., post-flashover combustion chemistry) or where their effect is considered

secondary compared to the “cost” of inclusion (e.g., temperature dependent material properties)..

The predictive equations are based on the fundamental laws of conservation of mass and energy.

Empirical correlations are employed to bridge gaps in existing knowledge. Since the necessary

approximations required by operational practicality result in the introduction of uncertainties in

the results, the user should understand the inherent assumptions and limitations of the programs,

and use these programs judiciously – including sensitivity analyses for the ranges of values for

key parameters – in order to make estimates of these uncertainties.

As discussed in this report, the CFAST model has been subjected to extensive evaluation studies

by NIST and others. Although differences between the model and the experiments were evident

in these studies, most differences can be explained by limitations of the model as well as of the

experiments. Like all predictive models, the best predictions come with a clear understanding of

the limitations of the model and of the inputs provided to do the calculations.

CFAST has proven to be fast, robust and reliable. While the focus of the development of the

model has been whole building simulations for assessing the effect of fire on a building

environment, principally to calculate threats to life safety of occupants and insults to the building

structure, it has been used for a wide variety of building and fire scenarios. The simplest use has

been to ascertain the sufficiency of an air handling system to extract smoke. The most complex

has been an assessment of fire propagation in a high-rise complex. It is also widely used as the

fire model in egress calculations and is described as the basis in the Simulex [164] and Exodus

[165] egress models.
126

Because of the speed of the model, it is possible to do real parameter studies of the building

environment. It is reasonable to do actual parameter studies including the tens of thousands of

variations needed for a proper hazard and risk calculation. Even in those cases where more

detailed predictions are needed (e.g., smoke detector and sprinkler head siting), CFAST provides

the capability to scope the problem, in essence doing parameter studies to determine what

specific scenario should be addressed by more detailed calculations.
127

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