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NBSIR 80-2172

Estimating Safe Available Egress

Time From Fires

Occupational Safety and Health Administration (OSHA)

^S^epaitment of Labor

^tthington, DC 20210

National Bureau of Standards

ESTIMATING SAFE AVAILABLE EGRESS

TIME FROM FIRES

NBSIR 80-2172

Leonard Y. Cooper

Center for Fire Research

National Engineering Laboratory

U.S. Department of Commerce

National Bureau of Standards

Washington, DC 20234

February 1981

Final Report

Prepared for: The Occupational Safety and Health Administration (OSHA)

Department of Labor

Washington, DC 20210

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
A

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PREFACE

This report on estimating safe available egress time from fires is

one product of an ongoing joint research program of the Occupational

Safety and Health Administration (OSHA) of the Department of Labor and

the National Bureau of Standards (NBS), Center for Fire Research. The

program is entitled: Key Elements of Emergency Escape Requirements for

Employees in Workspaces Under OSHA Jurisdiction. Areas of research in

this program include: Fire tests of stairwell-sprinkler systems; the

relation of building design and human factors to emergency evacuation of

workspaces; and studies of the smoke leakage of door assemblies.

iii
TABLE OF CONTENTS

Page

PREFACE iii

LIST OF TABLES vi

LIST OF FIGURES vi

NOMENCLATURE vii

Abstract 1

1. INTRODUCTION 1

1.1 Objective of the Study 1

1.2 The Methodology 3

1.2.1 General Remarks 3

1.2.2 Rooms of Fire Origin . 5

1.2.3 Spaces Adjoining Rooms of Fire Origin 5

1.3 Order of the Remaining Sections 6

2. FREE BURN TESTING OF CHARACTERISTIC FUEL ASSEMBLIES AND ITS

UTILITIES 7

2.1 Uncoupling of the Combustion Problem and the Flow Dynamics

Problem 7 2.2 The History of the Fire’s Energy Release 7 2.3 The Practical Problem 8

3. QUALITATIVE DESCRIPTION OF THE PHENOMENA LEADING TO DETECTION

AND HAZARDOUS CONDITIONS 9

3.1 General Remarks 9

3.2 Setting the Scene 10

3.3 Ignition and Early Growth of the Fire 11

3.4 Detection 12

3.5 Intermediate Times - Between Detection and Hazard ... 14

3.6 The Approach of Hazardous Conditions 15

4. QUANTITATIVE DESCRIPTION OF THE MODEL - THE GOVERNING

EQUATIONS 16

4.1 General Remarks ..... 16

4.2 Formulation of the Initial Value Problem for Temperature

of the Upper Layer and Position of the Interface .... 17

4.3 Safe Available Egress Time from the Solution to the

Initial Value Problem 22

4.4 A Computer Program 23

iv
TABLE OF CONTENTS (Continued)

Page

5. AVAILABLE EGRESS TIME FROM ROOMS OF FIRE ORIGIN - SOME

EXAMPLE CALCULATIONS 24

5.1 An Introduction to Two Example Scenarios 24

5.2 Assimptions on the Disposition of Energy Release and

Their Implications 25

5.3 The First Scenario - An Indication of the Models

Predictive Capability 27

5.3.1 General Description of the Hospital Room - Corridor Scenario 27

5.3.2 The Room of Fire Origin . 28

5.3.3 The Adjacent Space 29

5.4 Available Egress Time in a Semi-Universal Fire 33

6. SUMMARY, CONCLUSIONS AND FUTURE DIRECTIONS 36

6.1 Summary 36

6.2 Conclusions and Future Directions 38

7. ACKNOWLEDGEMENTS 39

8. REFERENCES 40

APPENDIX A: HEAT TRANSFER TO THE BOUNDING SURFACES OF THE ROOM OF

FIRE ORIGIN 43

V
LIST OF TABLES

Page

Table 1. Various Factory Mutual Research Corporation fire data

fitted to the exponential growth law (from Friedman [1]) 49

LIST OF FIGURES

Page

Figure 1, Two examples of characteristic fuel assemblies of

Interest 50

Figure 2. History of the energy release rate from free burn

experiments 31

Figure 3. Scenario at the time of Ignition 52

Figure 4. Scenario at the time of detection 53

Figure 5. Scenario at Intermediate times - between detection

and hazard 54

Figure 6. Scenario at the onset of hazardous conditions ... 55

Figure 7. Simple Illustration of f Ire-ln-enclosure flow dynamics 56

Figure 8. Plan view of hospital room - corridor mockup space 57

Figure 9. Energy release rate of wastepaper basket - mattress

fuel assembly ..... 58

Figure 10. History of Interface position 59

Figure 11. History of average upper layer temperature 60

Figure 12. Optical densities measured by the photometers ... 61

Figure 13. Free bum energy release rate from a seml-unlversal

fire. A fictitious construct from the data of

Friedman [1] 62

Figure 14. Estimates of available egress times from the semlunlversal fire of figure 13 63

Figure 15. Plot of A /(1-A ) as a function of r/H .... 64 celling' ' r'

vl
NOMENCLATURE

g

h

H

•m

e

•m

• * Q

loss

^other

xeiling

EG

ad

area

constants defined below Eq, (4.8)

specific heat

a dimensionless heat transfer coefficient, see Eq. (A-1)

a dimensionless temperature, see Eq. (A-3)

acceleration of gravity

heat transfer coefficient

height of room

rate of mass leaking from room

rate of mass entrainment in plume

a dimensionless value of Q

dq/dx at T = 0

rate of fire's energy release

a dimensionless value of Q

amotmt of Q conducted out of room's bounding surfaces

a characteristic value of Q

convective heat transfer per Eq. (A-4)

radius

time

^HAZ

“ ^DET

temperature

ambient temperature

mixing cup temperature of plume crossection

temperature corresponding to

an adiabatic upper layer temperature

vii
T

c ceiling temperature

u rate of heat transfer

Z elevation

Z.

1

elevation of interface

A upper layer thickness

AT^

h

T, - T

h “

(new)

h

a newly computed AT^^

C dimensionless Z

X

C at T = 0

A c

^ (new)

c a new estimate for A c

^ceiling ^ceiling/^

other ^other'^^

A r effective fraction of Q radiated from combustion zone

P density

ambient density

Ph average upper layer density

T dimensionless t

^EG "^HAZ "

"^DET

4> TjT

h °o o ()) at C = 0

a dummy variable

Subscripts

DET at detection

HAZ at onset of hazardous conditions

viil
ESTIMATING SAFE AVAILABLE EGRESS TIME FROM FIRES

Leonard Y. Cooper

Abstract

A general technique for estimating the time

available for safe egress from a fire is presented.

By introducing a qualitative and quantitative model

of hazard development, the details of the technique

are formulated for the room of fire origin problem.

The inputs to the model are the area and ceiling

height of the room, data from free bum tests of

characteristic fuel assemblies likely to be found

therein, the anticipated mode of fire detection, and

a criterion for the onset of untenability . The output is an estimate of the length of time between

detection of a fire and the onset of untenable

conditions. Results of applying the estimation

technique are presented and discussed.

Key words: Combustion products; compartment fires;

egress; fire detection; fire growth; hazard analysis;

mathematical models; room fires; smoke movement;

tenabillty limits.

1. INTRODUCTION

1.1 Objective of the Study

The objective of this study is to develop a practical technique for

estimating safe available egress times subsequent to the detection of a

fire. Safe available egress time here means the interval between the

1
time of successful fire detection and alarm, and the time when hazardous

conditions prevail in the given building space of interest.

Having obtained safe available egress time estimates for different

spaces within a given building, a safe condition would be suggested if

these estimates are of sufficient duration that people can escape the

threatened space. The present study does not address the determination

of whether or not such a safe condition exists. Rather, it provides the

necessary input which, together with previous and ongoing research on human factors in egress, will allow such judgements to be made rationally.

To set the stage for the overall concept, assume that the following

estimates have been established by a technically based calculation

technique: For an ignition occuring in a given room located in a building equipped with a specific detector and alarm system, the available egress time from the room of fire origin is at least two minutes.

Further, the available egress time in a corridor connected to the room

of fire origin is at least four minutes. Finally, the available egress

time in a third space, connected to the corridor is arbitrarily long

(i.e., the third space is a place of refuge relative to a fire in the

specific room of fire origin). Then based on the results of human

factors studies, depending on the occupancy and dimensions of egress

paths in the room of fire origin, and depending on the corridor and

connecting doorway dimensions, it would be possible to determine whether

a safe condition exists vis a vis a fire in the considered room of fire

origin. A safe condition would exist if the time required for safe

egress was equal to or less than the time available for safe egress.

Determinations of this type when all spaces of the building are considered

as potential rooms of fire origin would hopefully lead to an overall

fire safe determination for the building.

It is the purpose of this study to develop a practical mechanism

to establish the type of egress time estimates which were assumed in the

above illustration.

2
It is appropriate to call attention to the work of Friedman [1]^

which, in a sense, serves as a prototype of the present investigation.

By assuming exponential growth of fire in a fuel assembly, Friedman, in

a simple but elegant manner, was able to tie together models for smoke

or product of combustion generation and spread, for detection and alarm

criteria, and for the development of untenable conditions. One result

is a technique for estimating the ratio of safe available egress times,

i.e., the relative hazard, of two different practical fuel assemblies.

The present study adds more detail to the models of the various physical

phenomena, thereby providing estimates for safe available egress times.

After briefly discussing overall concepts and methodology, this

work specifically addresses the egress time problem for the room of fire

origin. Future work will be devoted to detailing the adjacent (to room

of fire origin) space and the overall building egress problem.

1.2 The Methodology

1.2.1 General Remarks

Procedures to estimate available egress time are developed from

analytic models of fire development and smoke spread. The data base

from full scale fire tests reported in the literature is also used. The

analytic models are used to predict the significant features of growing

and fully developed (flashed over) enclosure or compartment fires. In

some practical way these models must take account of the characteristic

fuel loads, the significant dimensions of the compartment and the various

sorts of compartment openings which can affect fire ventilation; and

which impact on spread of smoke.

Available tools for predicting compartment fire growth are in

various stages of development. These tools can be divided into two

groups, viz., those which are reliable, relatively simple and well

^ Numbers in brackets refer to the list of references following this

report

3
supported by a strong data base, and those which are preliminairy and are on the fringes of the state-of-the-art of fire technology. For example,

while some quantitative predictions both of early growth stage and fully

developed stage compartment fire phenomena can be made in many instances,

simple but reasonably accurate predictions of transition state phenomena

2

(e.g., flashover) are not yet possible. Here, the transition state

(flashover) refers to the linking state of fire development which starts

when enclosure radiation feedback to the fuel significantly affects the

burning rate of fuel, and which ends at the onset of fully developed

fire conditions.

For the present purposes the details of transition stage phenomena

are not required. There are two basic reasons why it is reasonable to

assume that these details can be ignored. First, hazardous conditions

for humans occur at room temperatures which are far lower than the

levels that characterize the transition stage of fire development. In

other words, for the purpose of studying life safety the problem of the

room of fire origin is over (i.e,, the room is intolerable for human

occupancy) before the transition period is initiated.

Second, when available egress times from adjacent spaces are of

interest; and where hazardous conditions in these spaces occur during or subsequent to the transition stage of fire development (in the room of

fire origin) the time interval of the transition period is, in general,

relatively short compared to the overall available egress time Interval

of Interest. Accordingly, without loss of significant accuracy the

problem of uncertain predictive capability for transition stage phenomena

can be avoided by adopting a somewhat conservative model of real fire

development. This model would predict a "lower limit" or "assured"

available egress time. Such "lower limit" estimates would be obtained

by assuming that fully developed stage fire conditions immediately follow

Much progress has been made toward developing a capability for

successful prediction of the details of transition stage phenomena.

For example, see Emmons, et. al. [2].

4
early growth stage conditions (i.e., by conservatively shrinking the

relatively brief transition stage phenomenology to a jump condition at a relatively early time in the fire scenario).

1.2.2 Rooms of Fire Origin

With a physical description of available ventilation paths in a given room of fire origin together with fuel load per unit floor area,

reasonable models of fully developed fire energy release and its effect

in adjacent spaces are available or can be constructed from results in

the literature. However, for the early growth stages of fire development it is beyond the present stage of fire technology to calculate

theoretically the history of energy release in practical fuel assemblies.

Nevertheless, an existing data base from full scale free bum fire tests

will be seen to yield useful quantitative energy release rate history

estimates for a limited number of realistic fuel assemblies.

With a reasonable estimate of energy release rates during early

stages of fire growth, it is possible to describe the time-dependent

development of buoyancy driven plumes in fully or partially enclosed

room-of-f ire-origin spaces. Having first reached the ceiling, spreading

across it and setting off fire detectors, the time interval required for

the hot, smoky, toxic plume gases to drop to a hazardous elevation, one or one and a half meters (three or four feet) from the floor, or to

reach a hazardous temperature can be estimated. Such time intervals

will be taken as the safe available egress times for the room of fire

origin.

1.2.3 Spaces Adjoining Rooms of Fire Origin

Having solved the available egress time problem in the room of fire

origin, attention would be focused on solving the problem for adjacent

spaces. The fire in the room of origin would still be assumed to be the

source of hazardous combustion products. The rate at which these are driven into the adjacent space and the phenomenology of their dispersal

5
(e.g., stratification or uniform mixing) once they have entered this

space must be predicted quantitatively. This would be possible once the ventilation paths of the room of fire origin have been established

and appropriately described. These paths must include all significant

penetrations in partitions between the room of fire origin and adjacent

spaces

.

The character of the ventilation paths impact on the adjacent space

egress problem for two different reasons. First, the size of the fire

in the room of origin will eventually be totally dependent on a ventilating oxygen supply from adjacent spaces (e.g., from a broken outside

window). Second, the ventilation paths between the room of fire origin

and the adjacent space under study result in smoke or product of combustion migration into the adjacent space and, ultimately, to the development therein of hazardous conditions. Even if these latter ventilation

paths do not impact on the fire development, as in the case of securely

closed doors (with, say, a broken window in the room of origin for fire

ventilation), it is clear that they still affect the development of

hazard in adjacent spaces. Indeed, as discussed by Cooper [3], leakage

characteristics of door assemblies would play a key role in determining

available egress times for the favorable (for adjacent space egress)

circumstance of the "closed door" scenario.

The details of solution of the adjacent space problem are deferred

to future work where the room of origin results developed here and all

of the above ideas will be incorporated.

1.3 Order of the Remaining Sections

As noted above, the remainder of this report concentrates on a solution to the egress problem for the room of fire origin. Section 2

introduces the concept of characteristic fuel assemblies and explain the

general utility of their free bum test data. Following this, a detailed

description of the phenomenological model for hazard development is

presented in section 3. Section 4 presents the quantitative aspects of

6
the overall qualitative phenomenology. The result of this presentation

is an initial value problem, a (computer) solution of which yields the

desired safe available egress time from a specified room of fire origin.

Section 5 presents results obtained from using the latter, safe available

egress time estimation technique. These results are discussed and

compared to real fire scenarios. Finally, a summary of this investigation along with future directions is presented in Section 6.

2. FREE BURN TESTING OF CHARACTERISTIC FUEL

ASSEMBLIES AND ITS UTILITY

2.1 Uncoupling of The Combustion Problem and the

Flow Dynamics Problem

Heat and smoke sensitive fire detectors sound alarms and hazardous

conditions develop in a building space as a result of products of com- bustion (POC) migrating from the combustion zone. As discussed in

Section 1.2.1, for some significant time following ignition the development of the combustion process within this zone is essentially independent

of the physical characteristics of the compartment which encloses the

fire. This has an important implication in the solution to the problem

at hand; namely, it is possible to uncouple the dynamics of the fire

growth within the combustion zone from the flow dynamics occuring outside

of this zone. This is the fire growth phenomenon that is the topic of

this section.

2.2 The History of the Fire's Energy Release

For this analysis the most important characteristic of the fire is

the history of its energy release. In particular, the portion of the

energy which is convected away from the combustion zone provides the

buoyancy force which ultimately drives the POC throughout the building

space. In view of this, attention here is focused on the following

question: When a fire is initiated in an assembly of combustible

materials what is the history of the energy output as the fire develops

7
in a free bum situation? Free bum here is intended to suggest a bum

of the fuel assembly in a large (compared to the combustion zone) ventilated space which contains a relatively quiescent atmosphere.

There are presumedly two possible ways to answer the above question;

namely analytically or experimentally. As was Indicated in Section 1,

it is evident that for fire growth in practical fuel assemblies it is

beyond the state-of-the-art of fire technology to expect the analytic

approach to yield the required results. Thus, for the purpose at hand

experimental methods must be used to answer the above question. A full

scale free burn test of the fuel assembly is required.

2.3 The Practical Problem

If one seeks details of the growth of a fire in a specific fuel

assembly, where the position and mechanism of the ignition is known,

then no more need be added to the above approach. However, the objective

of the present investigation is to provide broad based, practical insight on egress. The tools used to meet this objective would require the

availability of data from fires developing from various possible ignitions

in an arbitrarily large number of the myriad of fuel assemblies to be

found in practice. However, for practical purposes the number of required

full scale free bum tests must be limited. Accordingly it is appropriate

to introduce the concept of limited numbers of fuel assemblies which are "characteristic" of occupancies of interest. Associated with each of

these characteristic fuel assemblies would be a definite Ignition

scenario (maybe two scenarios) which are considered to be characteristic

of the threat associated with the occupancy under consideration.

To illustrate. Figure 1 depicts a characteristic fuel assembly of

the "type A" variety that one might associate with an office space

occupancy (on the left), and an assembly of the "type A" variety that one might associate with a warehouse occupancy (on the right). With

agreement on an appropriate ignition location and mechanism for each of

these fuel assemblies, full scale free bums could be carried out in the

8
laboratory, and the desired energy release rate histories aquired. For

the two fuel assemblies of Figure 1, one example of this later test

process is depicted in Figure 2.

In practice, a data base for the energy release rate histories from

a variety of characteristic fuel assembly free burn fires will have to

be accumulated and catalogued. From a preliminary review of the literature of past full scale tests it is evident that the beginnings of this

data base already exists. For example, Friedman [1] presents a table,

reproduced here in Table 1, of exponential growth approximations to the

energy release rate during free bum tests of a variety of practical

fuel assemblies. Included in this table are the results of full scale

fire tests of commodities stacked on pallets to a height of 4.6 m (15.1

ft) where the type of commodity was varied in each of seven separate

tests. These results would prove useful in estimating safe available

egress times from warehouse occupancies. Another accumulation of useful

full scale test data on residential size fuel assemblies is provided by

Pape et. al. [4]. There are, however, many "important" fuel assemblies

whose energy release rates can not be reliably deduced from existing

data in the literature. Full scale test programs for these will have to

be formulated and carried out.

3. A QUALITATIVE DESCRIPTION OF THE PHENOMENA

LEADING TO DETECTION AND HAZARDOUS CONDITIONS

3 . 1 General Remarks

As noted in section 2.1, for the times of interest, i.e., at least

up to the time of untenable conditions in the room of fire origin, the

combustion zone dynamics of a hazardous fire are basically uncoupled

from POC migration. Also, from the ideas developed in sections 2.2 and

2.3 the energy release rate for a given fuel bed is known or obtainable.

With this knowledge in hand, a quantitative dynamic model for POC migration and for fire detection and hazard development can be constructed.

This section presents a qualitative description of this model.

9
3.2 Setting the Scene

For the purposes of the model, the geometry of the room of fire

origin can be adequately described by its area and the height of its

ceiling. The only restriction on the characteristic shape of the floor

plan is that the space not have an unduly large length to width, or aspect ratio. Thus, for example, the model of POC migration to be

adopted here may not be adequate for corridors with aspect ratios

considerably larger than, say, 10:1. With regard to height of the room,

it is consistent with the work of Baines and Turner [5] and with the

upper, stably stratified, smoke layer model to be adopted here, that

attention be restricted to spaces where the ratio of height to minimum

horizontal dimension not exceed the order of one. Where either of these

spatial restrictions are violated, it is possible that the phenomenological model to be adopted here will not be adequate.

It is assumed that all doors, windows and other significant partition

penetrations to adjacent spaces are closed. It is also assumed that,

prior to the onset of hazardous conditions, sufficient oxygen is available

for free-burning combustion. These assumptions turn out to be conservative in the sense that under the conditions of a fully enclosed space

and a free burning fire the model will generally estimate a more rapid

development of hazardous conditions in the room of fire origin than

would occur in practice if the room was unenclosed and/or if the effects

of oxygen depletion on the fire were taken account of.

Even with all penetrations secured, there will be some leakage from

the room of fire origin to adjacent spaces. This results from the

expansion of the air heated by the fire's energy release. Even if

sealed as tightly as practical, building enclosure partitions are generally unable to sustain significant overpressures without leaking.

It is assumed that all this leakage occurs through leakage gaps which

are close to the floor, i.e., the room leaks cool ambient air at a low

elevation rather than high temperature products of combustion at a near10
ceiling elevation. Consistent with the work of Zukoski [6] and with the

hazard development model to be adopted here, this latter assumption also

turns out to be conservative vis-a-vis rapidity of the development of

hazardous conditions.

Subject to the geometric restrictions and leakage assumptions, the

potential room of fire origin under investigation is of arbitrary size.

The space is assumed to be filled with fuel assemblies which are characteristic of the occupancy of interest. The potential fire threat is

assumed to become a reality and the following scenario develops.

3.3 Ignition and Early Growth of the Fire

Time t = 0 is taken to be the time when an ignition is initiated in

one of the fuel assemblies. The position and mechanism of the ignition

is assximed to be similar to the ignition which initiated the free bum

fuel assembly test referred to earlier. Indeed, for all t ^ 0, of

interest here, the combustion zone dynamics of the ensuing enclosure

fire are assumed to be substantially similar to the combustion zone

dynamics in the related free bum test. In other words, the energy

release rate history will remain close to that of the free bum test up

to, and somewhat beyond the time of hazardous conditions.

For the two different fuel assembly types of Figure 1, the scenario

at ignition is depicted in Figure 3. As suggested in that figures, the

power level of many common ignition sources will likely be in the order

of 10 kW. This corresponds to typical power levels of small wastepaper

basket type fires.

Time moves on. Because of the temperature of the POC, buoyancy

forces drive them out of the growing combustion zone and up toward the

ceiling. In this way a plume of upward moving elevated temperature

gases is formed above the fire. All along the axis of the plume relatively quiescent and cool gases are laterally entrained and mixed with

11
the plume gases as they continue their ascent to the ceiling. As a result of this entrainment the total mass flow in the plume continuously

increases and the average temperature in the plume continuously decreases

with increasing height. The plume dynamics at any instant of time can,

with reasonable accuracy, be quantitatively described by a simple function

of the rate of energy release from the combustion zone.

When the plume gases impinge on the celling they spread across it

forming a relatively thin, stably stratified upper layer. As the plume

gas upward filling process continues, the upper gas layer grows in depth

and the relatively sharp interface between it and the cool ambient air

layer below continuously drops. Thus, this interface separates a potentially hazardous mixture of POC and previously entrained air above,

from cool ambient air below which, as yet, is assumed not to have been

affected by the fire. It is possible to estimate the rate of drop of

this interface as a function of its Instantaneous vertical position and

of the then current picture of the plume dynamics, i.e., the current

rate of fire energy release. By making the reasonable engineering

assumption that the upper layer is always fully mixed or homogeneous, it

is also possible to estimate it's average temperature.

3.4 Detection

The fire and POC migration phenomena described in the last paragraph continue; and presumedly before hazardous conditions prevail in

the space, the fire is detected. The criteria by which one might model

the detection event would have to be based on the performance characteristics of the particular detector device being used, and on the characteristics of the changing POC environment which engulfs the device and

which leads to its activation.

With regard to the POC environment, the present phenomenological

model provides a dynamic description in terms of thickness and temperature of an asstjmed homogeneous upper layer. However, estimates for

12
these parameters during times when the layer is theoretically very thin

cannot be considered as reliable. Indeed, the "uniform upper layer"

concept is not even valid vintil such time during the course of the fire

that such a layer would totally submerge the ceiling jet. And these

ceiling jets can be of the order of ten percent of the ceiling height

[7]. In short, until such times during the course of the fire when

estimated upper layer thicknesses have reached the order of one foot

(assuming ceiling heights of the order of ten feet) such estimates and

their associated temperatures are unreliable for use in detection

criteria.

Where detectors are spaced with reasonable density and in a regular

grid (e.g., according to the specification of Benjamin, et al. [8])

across rooms with relatively smooth ceiling surfaces, detection criteria

of the type developed by Alpert [9] from results of his analysis of

ceiling jet flows [7] may be applicable. The experimental data of

Heskestad and Delichatsios [10,11] and their correlations [12,13] would

also be useful in this regard.

Analysis of detector response by using any of the latter references

[8-13] would be based on knowledge of the environment within the ceiling

jet and at the detector location. When the spacing of the detectors,

i.e., the distance of a detector from the fire, is too great (depending

on the fire growth rate, ceiling smoothness and the height of the room)

these environments are not generally well known. Under such sparsely

deployed detector scenarios, there are potentially useful and practical

detection criteria that can be constructed from the geometric specifications of the room of fire origin and from knowledge of the instantaneous

values of the fire energy release rate, layer thickness, and layer

temperature. For example, it may be reasonable to expect that an upper

smoke layer greater than some specified thickness would activate an appropriately sensitive smoke detector. Alternatively, if a heat sensitive detector were deployed its time of activation could be estimated

with the use of the history of the layer temperature. It is important

to point out that these latter types of detection are strictly speculative,

13
and, their reliability has not been evaluated in practice.

Detection without an actual detection and alarm device is also

possible. This could result from human sensitivity to, say, visual

obscuration due to smoke or downward directed thermal radiation both of

which would develop with increased overhead layer growth and fire

intensity. If appropriate levels of the effects can be identified, it

would be a simple matter to use these criteria for estimating the time

of fire detection.

Whatever detection criteria are finally used in practice, their

validity should clearly be verified with appropriate measurements. Such

verification would constitute a major future activity which will be

required to support the validity of the concepts being introduced here.

The results of applying some of the above hypothetical detection

criteria is discussed in a later section.

Figure 4 depicts a possible state of affairs within the overall

fire growth scenario at the time of detection. The actual condition

would be a function of the arrangement and type of detector. The

detection event could occur at an earlier or later state of fire development. What is important to this model is that detection does in fact

occur, thereby starting the "clock" which ultimately measures the available egress time.

3.5 Intermediate Times - Between Detection and Hazard

Having attained detection (and, presumedly, alarm) the "human

factors" aspect of egress would be initiated. In the meantime the upper

layer continues to grow in both depth and temperature. The energy

release rate of the fire continues to be very close to that of the free

burn test. Most important, safe evacuation is still possible. Figure 5

depicts the situation at some Intermediate time between detection and

hazard.

14
3.6 The Approach of Hazardous Conditions

The scenario continues to develop. Eventually the conditions in

the space become hazardous beyond human tolerability. As with the

situation for detection criteria, the criteria which define the onset of

hazardous conditions must be quantitatively related to those physical

parameters for which the model can provide reasonable estimates. Again,

the upper layer thickness (or the vertical position of it's interface),

and it's temperature can be used to provide the measures of whether or not the hazardous conditions prevail.

The implications of interface position on hazard are clear. Above

the Interface the gases are smoky, and, therefore, potentially obscure

beyond reasonable visibility. They are contaminated with toxic POC and,

therefore, they are themselves at toxicity levels potentially beyond

human tenabillty. Below the interface the gases are modeled as cool,

uncontaminated, ambient air. If the interface drops below some preassigned level, say some position between one to one and a half meters

(three to four feet), it is not practical to expect people to be capable

of keeping their faces out of the potentially hazardous upper layer.

Thus, a simple, albeit conservative, criterion for hazard can be established which is independent of the details of the toxicity and smoke

production properties of the constituent materials making up the fuel

assembly. Namely, once the upper layer - lower layer interface drops to

a preassigned level, hazardous conditions begin to prevail in the room

of fire origin and safe evacuation is no longer likely. Further work

will take account of the actual POC dilution and the resulting hazard

level of the upper layer gases.

As it happens, a high temperature upper layer condition can, in and

of Itself , lead to hazardous conditions even before the Interface drops

to a hazardous level. This would occur by virtue of its emission of

untenably high levels of thermal radiation. For example, Babrauskas

[14] has reviewed the literature and found that the threshold of human

15
tenabillty to heat fluxes for extended periods of time falls in the

2 2

range of 1.2 kW/m to 2.5kW/m , The latter value corresponds to radiation from a black body at 183° C (361°F). Thus, this general temperature

(radiation) level, which is well below temperature (radiation) levels

generally associated with flashover phenomena, would appear to form the

basis for a second Independent criterion for hazard. Namely, once the

upper gas layer temperature reaches some preassigned high value, hazardous conditions begin to prevail in the room of fire origin and safe

evacuation is no longer likely.

Taking the above two criteria together, the following overall

criterion for untenabllity results: The room of fire origin is assumed

to be untenable for safe evacuation at such time that either (1) the

upper layer interface drops to some specified, low hazardous level, or

(2) the temperature of the upper level grows to some specified, high,

hazardous value.

Figure 6 depicts the state of affairs in the room of fire origin at

the time when untenable conditions begin to prevail. In the left hand

office occupancy, the low level of the interface was the initiator of

hazardous conditions. In the right hand warehouse occupancy, however,

it was a hazardous level of radiation from the upper layer that triggered

the onset of untenabllity,

4. QUANTITATIVE DESCRIPTION OF THE MODEL - THE GOVERNING EQUATIONS

4 . 1 General Remarks

The previous section presented a qualitative description of the

events occurlng in a building space subsequent to the initiation of a fire and up to the time that hazardous conditions prevail. This section

constructs a quantitative description of this model. The major elements

of this will Include the turbulent buoyant plume theory of Morton et.

,al. [15] together with the experimental plume results of Yokoi [16], the

16
theory of Baines and Turner [5] on the dynamics of such plumes in confined

spaces, and Zukoski's [6] application of this latter theory to the fire

problem. Figure 7 presents a simple illustration of the flow dynamics

described.

4.2 Formulation of the Initial Value Problem for Temperature of

the Upper Layer and Position of the Interface

As noted earlier, the partitions of the room of fire origin are assumed to have all major penetrations (e.g., doors, windows, and vents)

closed. Any leakage from the room resulting from fire driven gas expansion is assumed to occur near the floor level. The sketch of Figure 7 is compatible with these assumptions, both of which lead to some conservatism in the eventual prediction of the time for onset of untenability

The fire's combustion zone is modeled as a point source of energy

release which is effectively located at the floor level. The mass rate

of fuel introduced from this zone into the plume is neglected compared

to the mass flow rate of entrained air. Except for the buoyancy forces

that they produce, density variations in the flow field are neglected

(e.g., the Boussinesq approximation is invoked in the usual manner).

Using the fact that the absolute pressure throughout the space varies

only Insignificantly from a constant uniform value [6], the density can

be related to the temperature at any time and spatial position through

the perfect gas law according to

pT = Constant = p T (4.1) a a

where p and T are the density and absolute temperature, respectively.

Si Si of the ambient air.

The total time varying energy release rate of the combustion zone

• • is defined by Q(t). The fraction of Q which effectively acts to heat

plume gases and to ultimately drive the plume's upward momentum is (1-X )

• IT where is approximately the fraction of Q lost by radiation from the

17
combustion zone and plume.

Following Zukoski [6], and Zukoski, Kubota, and Cetegen [17], the

total mass flow in the plume, m , and the mass mixing cup temperature of

the plume, T^, at a distance Z above the fire (but below the layer

interface) can be estimated by — ** 2/3

T /T - 1 = (Q )^'-^/0.210

P a

m = 0.210P (gZ)^^V(Q*)^/^

Si

0 < Z £ Z^(t) (4.2)

* * where Q is defined as

Q* = d-x^)Q/[p^CpT^(gZ)^^^z^]

and where g is the acceleration of gravity and is the specific heat

of the ambient air. The mass flow rate of ambient air, m^, leaking out

of the room's lower leakage paths is given by [6]

m = (1-X^)Q/(C T ) = [(1-X^)/(1-X )]Q% (gH)^/V

e c p a c r a

(4.3)

where X is the instantaneous fraction of Q lost to the bounding surfaces

c • • •* of the room and it's contents (i.e., X^ = Qj^^gg/Q) where Q is

evalxiated at Z = Z^(t); Z^(t) being the time varying distance of the

interface above the fire. This total energy loss characterized by X^ occurs as a result of a variety of different convective and radiative

heat transfer interchanges between the room's gases and the above

mentioned surfaces.

A mass balance for the lower (shrinking) volume of ambient air

results in

d (P AZ.)

a 1

dt

+ m +m(Z = Zj=0 e p i

18
where A is the area of the room of fire origin, and where estimates for

m^ and m^ are provided in Eqs. (4.2) and (4.3).

An energy balance for the upper layer results in

/^(l-X^)Qdt = pA(C T-C T )dZ

o c p p a

where H is the height of the room. Using Eq. (4.1) in the above, and

defining the average upper layer density, p^, as

the following results

1 - p, /p^ ha = 1 - Tah/T, = [/*'(1-X oc)Qdt]/[p C T A(H-Z.)] (4.6) apa x

Here, T, is defined as the temperature corresponding to p, through

h h

Eq. (4.1). When the upper layer is well mixed,

p^^

and T^, computed in

accord with the above, should provide a reasonable estimate for the hot

layer's actual density and temperature. This uniformly mixed upper

layer model will be assumed to provide an accurate representation of the

actual phenomena under investigation.

For the present purpose it is convenient to introduce the following

• dimensionless forms for t, Z., T, , and Q

1 h

T = t/t^ ; ; = z^/L^

where t and L are a characteristic time and length, respectively.

• o Also, Q represents some characteristic energy release rate. For example,

provided it is nonzero, will be taken as Q(t=0). These are now

introduced into Eqs. (4.2) - (4.4) and (4.6), where Eq. (4.6) is recast

19
Into differential form. After some manipulation the following pair of

governing equations for the dimensionless interface position, and

upper layer temperature, (p, results

^ ^ ^ — .1/3 5/3 - -c^q-c^q C

where C = H/L = ?(t = 0) o c

and where c, =

(1-X )Q t c o c

1 p C T AL

a p a c

0.210t

^2 “ a-xpq_^gL;

p C T

a p a

1/3

For p , T , C and g values of

a 3.^ p

”

p = 0.0735 Ib/ft^ = 1.18 kg/m^

a

T = 530“R = 294°K

a

C =0.24 BTU/(lb“F) = 240 cal/(kg®C)

g = 32 ft/sec = 9.80 m/sec‘‘

(4.8)

the values of and C

2 are

c, = 0.107 (1-X )(Q /kW)(t /sec)(ft/L )^/(A/L^)

1 c o c c c

C

2 = 0.314(t^/sec)[(l-X^)(Q^/kW)(ft/L^)^]^^^/(A/L^)

The problem now becomes one of simultaneously solving the above

pair of differential equations subject to the appropriate initial

conditions. For the present purposes these initial conditions can be

taken as those relating to one of two different cases.

Case 1: q(x=0) = 1, i.e., Q(t=0) 0.

20
Here define

q = Q(t)/Q(t=0) (4.10)

and assume

lim q = 1 + T + O(t^) (4.11)

T^O

I where q^ = dq/dt at t = 0

Then solve Eqs. (4.8) subject to

<;(t=0) = ^

4>(t=0) = (^>^ = 1+C (4.12)

O O 12

where analysis of the apparent singularity of the second of Eqs. (4.8)

leads to the result that the initial value of d(f)/dT can be obtained from

lim d*/dT = {(c,/c,)[ 24

'+

5 (c,+c,C }[1+0 (t) 1 (4.13)

1 2 o 1 2 o o

t-K)

Case 2: 4 (t=0) = 0, i.e., Q(t=0)=0

Here assume

lim q = q^T+0(x^) (4.14)

T->0

Then solve Eqs. (4.8) subject to the initial conditions

?(t=0) = ?^, (|)(t=0)=(|)^=1 (4.15)

21
Here analysis of the problem reveals the following small time estimates

for ? and (|)

11m C = C -(3/4)c (d ^''\^''^[1+0 (t^/^)]

o z o o

lim (|> = 1 + (2/3)(c /c

1 z o o

t-K)

(4.16)

4.3 Safe Available Egress Time From the Solution

to the Initial Value Problem

The above initial value problem for cj) and ? would be solved by a numerical integration procedure. Compatible with the hazard criterion

of the type described in section 3.6, the actual solution procedure

would be terminated in a given problem at that time,

^HAZ 1 0 * 9 ^HAZ ^HAZ^^c (4.17)

when

\(HAZ) - *HAZ ° \(HAZ)^’^a

(layer temperature reaches a hazardous value)

or

(4.18)

^i - ^i(HAZ) ^ - ^HAZ

“ ^i(HAZ)^^c

(interface reaches a hazardous elevation)

(4.19)

From the computed history of tf> and C, and compatible with the

detection criterion which is Invoked, the time of detection would be

obtained. This would be defined as that time.

'DET

i. e. , T = t /

1

DET DET' c (4.20)

when e.g.

,

22
H-Zi ^

i.e., Cl

(layer thickness detection criterion)

and/ or

\ ~ \(DET) - ‘*’dET ' \(DET)^^a

(layer temperature detection criterion)

and/or

(4.21)

(4.22)

dT^/dt 1 (dT^Zdt)j^g^ i.e., (4.23)

d4>/« i = (t^/T^) (d\/dt)pj,j

(layer rate of temperature rise detection criterion)

The time of detection corresponding to other detection criteria

which were similarly related to (}> or C, etc. could also be obtained.

From all the above the desired value for safe available egress time,

"EG

i.e..

”^EG ^EG^^c

would be computed from

(4.24)

^EG ^HAZ"^DET x.e •

"^EG "^HAZ "^DET (4.25)

4.4 A Computer Program

A computer program was written to solve the problem outlined in the

above paragraphs. The code accepts representations of Q in one of three

possible forms, viz, digital data points with linear interpolation,

digital data points with exponential interpolation, and analytic representation. Hazardous conditions are determined per Eqs. (4.18) and

(4.19) where arbitrary choices for \(HAZ) made.

23
Detection criteria per Eqs. (4.21), (4.22) or (4.23) can be chosen where

arbitrary choices for assigned.

Safe available egress times for some example fire scenarios were

obtained with the use of this computer code. The results of these

computations are presented in the next section,

5. AVAILABLE EGRESS TIME FROM ROOMS OF FIRE ORIGIN - SOME

EXAMPLE CALCULATIONS

5.1 An Introduction to Two Example Scenarios

This section presents results of the use of the quantitative model

developed in the previous section. In particular the model has been

used to investigate the available egress times that would result from

fires in two different types of fuel assemblies.

One of the fuel assemblies that was studied was a particular mattress

construction and adjacent igniting wastepaper basket whose combined free

burn energy release had been previously determined from weight loss

measurements. The development of the hazardous environment generated by

this fuel assembly as it burned in a full scale hospital patient room- corridor mockup had also been observed experimentally. Data from this

latter test were therefore available for the purpose of a partial

evaluation of the model's general predictive capability.

A free bum in the second fuel assembly was assumed to release

energy according to a composite semi-universal fire constructed from

free burn data summarized in [1]. A set of calculations using this as the threatening fuel assembly was carried out. The results of these

calculations are presented here for the purpose of providing a hint of

the model's utility in presenting building designers with practical

estimates of safe available egress time, e.g., when the fuel assemblies

in the room or building of Interest are (anticipated to be) characteristic

of a given type of occupancy.

24
5.2 Assumptions on the Disposition of Energy Release

and Their Implications

In order to use the model for any given free burn energy release

data, values of X and A (the effective fraction of the energy release

r c that is radiated out of the combustion zone, and the net fraction of

*0(t) that is transferred to the room boundaries, respectively; c.f,,

section 4.2) are required. While appropriately chosen constant A values should prove to be adequate for most engineering applications,

the method described can, through specified dynamic variations in these

A's, readily accept more detailed characterizations of the gas-to-room

surface heat transfer phenomena.

Depending on the fuel and its configuration Burgess and Hertzberg

[18] and DeRis [19] report that the total radiant power output in fire

combustion zones tend to fall in the range of 15-40 percent of the total

rate of heat release. Based on this and, for example, on recent data

presented by Modak and Croce [20] it appears that the use of a figure of

A^ = .35 in Eq. (4.2) is a reasonable choice for the type of growing

hazardous fires under consideration. This value was used in all calculations to be described below.

Using the .35 value for A^ and taking account of convective heat

transfer considerations an appropriate value for A^ was developed in

Appendix A. This was found to lie in the approximate range 0.6 - 0.9.

The lower, 0.6 value would relate to high aspect ratio spaces (ratio of

ceiling span to room height) with smooth ceilings and with fires positioned far away from walls. The intermediate values and the high 0.9

value for A^ would relate to low aspect ratio spaces, fire scenarios

where the fire position is within a room height or so from walls, and/or

to spaces with highly irregular ceiling surfaces. In the latter types

of situations, which are representative of most realistic fire scenarios,

it is not presently possibly to provide general rules to accurately

estimate A^ within this 0.6 - 0.9 range. This fact has especially

strong Implications on the capability for establishing accurate estimates

25
for the average upper layer temperature. This can be seen from the

second of Eq. (4.8) where, early in the fire and at times of relatively

cool upper layer temperatures ((j> close to 1), dT^^/dt and, ultimately,

= AT^ are seen to be proportional (through the factor c^) to

(1 - A^) . In contrast to the upper layer temperature estimate and during

the early growth stages of the fire, the upper layer - lower layer

interface position history is not nearly as sensitive to inaccuracies in

A . At such early times q is of the order of 1 and ^ is close to H/L . c c A study of the first of Eq. (4.8) together with the c^, values of Eq.

(4.9) reveals that under such q, C conditions the second term on the

right side of Eq. (4.8), which is independent of A^, strongly dominates

the first term.

The above discussion leads to the following guidelines for selection

and use of a value for A , when a reliable estimate of it*s actual value

c is not otherwise available:

a. For the purpose of computing a conservative estimate of the time

when a hazardous temperature or a hazardous interface elevation

will be attained (i.e. , the predicted t„._ will be less than the

nAZ

observed should select A^ = 0,6.

b. For the purpose of a conservative estimate of detection time when

detection is by temperature or rate of temperature rise of the

upper layer (i.e,, the predicted tp.„„ will be greater than the

Dhil

actual t^.TM) one should select A =0.9.

DET c

c. When fire detection is by temperature or rate of temperature rise

an accurate (as compared to a conservative) estimate of detection

time is achievable only 1) in large aspect ratio, smooth ceiling

spaces where detection is based on a A^ = 0.6 computation of average

upper layer temperature; and 2) in other configurations where

detectors are deployed near the ceiling in some regular grid array

and where the time of detection is based on estimates of actual

ceiling jet temperature (i.e., predictions of average upper layer

26
temperature are not the basis determining likely times of detection)

Such estimates are provided, for example, in references [8,9,11 and

13].

5.3 The First Scenario - An Indication of

the Model’s Predictive Capability

5.3.1 General Description of the Hospital Patient

Room-Lobby Scenario

This section covers some comparisons between the results of a practical full scale fire experiment and calculations based on the

concepts developed above. The actual experiment considered is one of a series of full scale tests of a mockup hospital patient room-corridor

building space. The test series, described in detail by O’Neill and

Hayes [21], was for the purpose of evaluating the utility of sprinkler

systems in hospitals. The specific test rtm from that series which will

be considered here does not involve sprinkler operation.

It is noteworthy that the test data that was acquired, although

appropriate and adequate for the original test objective, only provides

a minimal base for the comparisons that are of interest in the present

work. Nevertheless, the experimental vs theoretical comparisons to

follow verify, indeed extend, the utility of the ideas developed in this

investigation.

A plan view of the building space is presented in Figure 8. The

2 2

space is made up of a room of area 155 ft (14.4 m ) connected by an

2

open doorway to a corridor-lobby configuration of area 800 ft (74.3

2 . m )

A fire is initiated in a wastepaper basket next to the comer of a polyurethane mattress covered with bedding. The wastepaper basketmattress fuel assembly and its mode of ^ignition was carefully reproduced

in most runs of the test series referred to above including the test run under present consideration. The bum characteristics of this assembly

27
were studied in detail prior to the room burns of this series [14]. The

history of the energy release rate as derived from weight loss measurements is plotted in Figure 9, For the purpose of the present analysis it

is assumed that this energy release rate was reproduced in the actual

test run under review. However, some significant deviations from the

Figure 9 energy release rates are a distinct possibility especially

during the early growth stage of the fire, say, 0-100 seconds, during

which time the wastepaper basket involvement dominates the fire development.

The model which has been quantitatively detailed in section 4 is a single room or room of fire origin model. Thus, it may not be immediately

obvious at what point, if any, it will have relevance to the present

fire scenario. Together with the general ideas of sections 1-3, it

would appear that a two room or multi-room flow dynamics model of the

type developed by Zukoski and Kubota [22] or Tanaka [23] would generally

be required to study the room-corridor-lobby scenario under consideration,

(For example, a two room example flow calculation for a set of fire and

room size parameters which somewhat correspond to the present scenario

has been considered in [22]), Nevertheless, it is possible that a simple, single room modeling approach to fire scenarios involving

relatively free-flowing multi-space configurations can be adequate for

# t

.

the purpose of obtaining engineering estimates of available egress time

in the range of conditions that occured in the referenced hospital

patient room-corridor test,

5,3,2 The Room of Fire Origin

For early times into the fire, prior to the time when the layer

interface drops to the level of the connecting doorway soffit, the

single room model is completely relevant for the burn room. Up to that

point the open doorway acts as the lower leakage path referenced in

section 4.2. Using the energy release data of Figure 9, the model was

2 2 therefore used to compute the POC filling history of a 155 ft (14.4 m )

28
room up to the time that the layer thickness exceeded the existing

ceiling to soffit dimension of 1.33 ft (.41m). A value of X = .72 was

c used in Eqs. (4.8). This estimate for X^ is based on a calculation

which is presented in section A. 3 of the appendix. In this calculation

the contribution to convective heat transfer was taken from the reduced

scale room fire studies of Zukoski and Kubota [24]. The contribution to

radiative heat transfer was taken to be consistent with the X = . 35 r value discussed in section 5.2. The time for the Interface to reach the

soffit was computed to be 21 seconds following ignition.

5.3.3 The Adjacent Space

Once the smoke flows under the soffit and starts to fill the large

corridor-lobby space, a two room model is required to describe the gas

migration and exchange between the two spaces. This would continue to

be true for at least some intermediate time interval. Following this,

the single room model* can again be relevant as discussed below.

If the fire is small enough or the doorway is large enough so that

flows through the doorway remain relatively weak the adjacent space will

eventually attain and maintain a smoke layer thickness essentially

identical to that of the burn room. After some time interval the

histories of the elevations of the layer interfaces in both spaces will

be similar and can be computed from a single room model, where the

single room has an area equal to the combined area of both spaces. Time

intervals when the upper layer thicknesses of the two rooms are not

similar would encompass 1) the initial time when the room of origin

fills up with smoke to the level of the dooirway soffit, and 2) the

subsequent time interval when the upper layer thickness of the adjacent

space grows from zero to a value close to that of the room of fire

origin.

For fire scenarios where the above is applicable, significant

simplifications occur in that the relatively simple single room of fire

origin model can be used to study the significant effects of fire growth

29
when far more complicated multi-room models would, at first hand, appear

to be required.

In an attempt to test the utility of the above ideas the single room

model was used to predict the history of a single interface elevation

and the average upper layer temperature within the combined patient

room-corridor space. Using the energy release rate of Figure 9 and a

2 2

total room area of 955 ft (88.7 m ) the history of the interface

elevation and of the average upper layer temperature was computed. An

effective for this combined space scenario is expected to be greater

than the above - *72 value used for the single room of fire origin.

This is the case because of the additional heat transfer to the corridor

surfaces. A value of X = .85 was selected for the calculation. This

c was done with the anticipation that comparisons between computed and

experimental average upper layer temperatures would reveal an appropriate

correction to this X^ value. (Recall from section 5.2 that the upper

layer temperature difference, AT, - T , is approximately proportional to

n Si 1 - X^) . The results of the computation for Interface position and

layer temperature are presented in Figures 10 and 11 respectively.

For the purpose of comparing results for the analytic and experimental interface position an operational definition of the experimental

Interface position was required. This definition was based on the

outputs of a total of 6 photometers placed at three different elevations

and at one to three different positions (indicated in Figure 8) in the

corridor and lobby. The measured optical density (OD) outputs of these

photometers are indicated in Figure 12. From these latter outputs, and

for the purpose of defining a time when the smoke layer interface

position passes the elevations of these photometers, there is still

ambiguity as to what value of OD should constitute the presence of a smoke layer. Four different OD values .01, .02, .03, and .04 were used

as possible definitions for a minimum upper layer OD. Using the photometer outputs, the result of these four possible interface definitions

leads to four possible sets of experimental data points for the interface elevation vs time. These are plotted in Figure 10 together with

30
the theoretical results of the interface motion.

The agreement between the results of theoretical and experimental

interface position at the lower two of the three photometer locations

illustrates the capability of the model in the present Instance to

predict the growth of the potentially hazardous upper smoke layer thickness. As discussed earlier, a favorable comparison at the uppermost

photometer elevation located .20 ft (.06 m) from the ceiling was not to

be expected. This is because of the fact that in the present multispace

configuration the single room model implemented in the manner described

is clearly not adequate to predict the early layer growth in the corridorlobby portion of the test space.

Gas temperatures were measured by two thermocouple trees located in

the center of the corridor 15 ft (4.6 m) on either side of the bum room

doorway. No temperature data was acquired in the lobby space. At any

given time the equi-level thermocouples of these two trees measured

temperature differences, T-T which agreed to within 20 percent of one

Si another. For the purpose of comparing analytic and experimental average

layer temperature histories an appropriate instantaneous weighting of

the measured temperatures of the limited ntiinber of these corridor thermocouples was required. At a given instant of time this weighting had to

be consistent with the estimate/ measurement of the interface position

as well as the relative position of the thermocouples in question. A

plot of the measured average layer temperature history deduced from such

a data reduction scheme is presented along with the plot of the computed

temperature history in Figure 11. As noted earlier, if a different

had been used in the computation then, to a first approximation (i.e.,

using the "principle of proportionality" between AT, and 1-X ) , one would

_

h c anticipate a shift from the originally computed ATj^(t) (with X^ = .85)

to a new temperature history, (t) (with X = where h c c

^^(new) ^

31
In view of the above It is possible to bring the predicted analytic

plot into coincidence with the experimental plot for at least one

(n©w) instant of time by a new choice, X , for X . Such coincidence is

c c attained at t = 330 seconds [when the computed layer Interface is at the

potentially hazardous position 3 ft (.91 m) from the corridor floor] by

the specific choice of = 0.947. Using this latter value of

in Eq. (5.1) an adjusted average upper layer temperature history was computed and plotted in Figure 11.

The single room model was also used to recompute the interface

position and temperature histories corresponding to X^ = .947. These

are plotted in Figures 10 and 11, respectively. For the parameters of

the present scenario, the proximity of the - *85 and X^ = .947 plots

of Figure 10 illustrates the relative insensitivity of the interface

position history to changes in X^. The variations between the two X^ =

.947 temperature history estimates are so small that they cannot be

discerned in Figure 11. For this scenario this fact Illustrates the

validity of the "principle of proportionality" as expressed through Eq.

(5.1).

As can be noted in Figure 11, the overall comparison between the

experimental and newly calculated estimates for the upper layer temperature histoi^r is good in the time interval 175-330 seconds but poor at

earlier times. One would hope that these temperature comparisons would

be favorable for a longer time interval if the spatial distribution of

the corridor thermocouples had been more refined, i.e., if a more

accurate estimate of experimentally determined average upper layer

temperature was available. It is possible, however, that the relatively

complicated nature of the energy transfers which are being simulated may

preclude sharper estimates of T^ with the use of a single, constant

value of X^. Also, as noted earlier, the single room simulation of the

multi-room flow dynamics must inevitably break down during some initial

Interval.

32
5.4 Available Egress Time in a Semi-Universal Fire

If the present concept on estimating egress time is to have utility

to practitioners of fire safety it will be necessary that the significant elements of potentially threatening fire scenarios be identified.

It will also be necessary for the results of egress time analyses to be

presented in a concise and practical manner. This paragraph provides an example of how the whole concept might proceed in practice.

First, one must deal with quantitative characteristics of a particular, potentially threatening, free bum fire of concern. Paragraph

2.3 dealt with some practical considerations that would be useful in

deducing such characteristics. For the present purpose a composite,

semi-universal type fire has been constructed from the data of Table 1.

The fire's energy release history is plotted in Figure 13. The fire is

assumed to be initiated from a 10 kW (9.5 BTU/sec) ignition source. Initially, it grows exponentially at a growth rate which is characteristic

of a fire initiated in a polyurethane mattress with bedding. This early

growth rate would be characteristic of the early growth of threatening

fires in a variety of occupancies which typically contain upholstered

polyurethane cushioning, e.g., hospital patient and lobby rooms, residential spaces and auditoriums. From Table 1, it would also appear to

be consistent with the (unreported) early growth stage of fires in large

assemblies of commodities stacked on pallets. Beyond 400 kW (380 BTU/sec)

and consistent with Table 1, the fire of Figure 13 is assumed to grow at a rate which is similar to and/or which bounds the anticipated growth of

fires initiated in a variety of different types of commodities stacked

on pallets. This latter portion of the semi-universal fire is no doubt

also representative of other threatening fires in large merchantlle

and/or business occupancies.

The fire of Figure 13 was assumed to be initiated in a variety of

different size spaces. The geometries of these spaces are characterized

by areas ranging from 300-10,000 ft^ (28-929 m^) and by heights ranging

from 8-20 ft (2.4 - 6.1 m).

33
Various possible criteria for fire detection were considered in the

analysis of available egress time. These included instantaneous detection (by whatever means), i.e., at a time when the upper hot layer

thickness = 0; detection by smoke detectors which is assumed to

DET

occur at a time when AZ = 1 ft = .3 m, and detection when the upper

gas layer reaches an average temperature of 135°F (54°C) . As noted at

the end of section 3.4, the utility of the latter two detection criteria

are at present strictly speculative. They are included here only to

illustrate the type of results which one might hope to generate by

applying the methodology under discussion.

The criterion for the onset of hazardous conditions is an upper

layer interface position 3 ft (.91 m) above the floor, or an average

2

upper layer temperature of 361°F (183°C) (corresponding to .25 W/cm ),

whichever comes first.

It is assumed that 35 percent of the fire's instantaneous energy

release rate is radiated from the combustion zone (A^ = .35) and that a total of 60 percent of this energy release rate is transfered to the

surfaces of the room and it's contents, i.e., 40 percent of this energy

is retained in the upper layer products of combustion (A^ = .60).

Recall that the latter choice of A^ would be appropriate for large

aspect ratio spaces with smooth ceilings, but, in any event the choice

of A^ would have a minor impact on estimated egress times in cases where

criteria of detection or hazard are not dependent on upper layer gas

temperature.

With the above range of parameters the quantitative particulars of

section 4 were used to compute estimates for available egress times.

The results of these computations are presented in Figure 14. In that

figure, available egress time (t - t^_^) is plotted as a function of

nAZ DjCj 1

•k The technology now exists to produce a temperature sensitive detection

device which would respond in a manner consistent with this detection

criterion [25].

34
room area for different parametric values of room height and for different detection criteria.

As an example of the utility of Figure 14 consider a scenario where

2 2 a fire is initiated in an occupied, 5,000 ft (465 m ) nominal 20 ft

(6.1 m) high ceiling auditorium outfitted with polyurethane cushion

seats (which are assximed to be the most significant fuel load). Then,

from Figure 14 one would estimate an available egress time of approximately seven minutes. This assumes immediate detection as a result of

occupant recognition and verbal alarm to fellow occupants at the time of

fire initiation. If the auditorium is to be considered safe relative to

successful egress, then a further study would have to reveal that the

time required for a capacity crowd to evacuate the auditorium is less

than these seven minutes.

The following general features of the results of Figure 14 are noteworthy:

a) As is well known, for life safety as it relates to safe

egress, temperature detectors are far less effective than

smoke detectors.

b) For a given curve, moving up in room area eventually leads to

an abrupt reduction in the curve's slope. This is the result

of a shift in the triggering mechanism for onset of hazardous

conditions. On the left side of the change in slope (smaller

areas) , untenability occurs as a result of the layer interface

dropping to the 3 ft (.91 m) level. On the right side (larger

areas), untenability occurs as a result of thermal radiation

from a hot upper layer.

c) For some curves [e.g., 8 ft (2.4 m) ceiling height, A = 1

Dili 1 ft (.3 m)] the available egress time actually decreases with

increasing area for areas in excess of some critical area. This occurs because the specified Figure 13 fire will take a

35
longer time to fill a larger area room to a given

specified upper layer thickness (A__„) . But, the longer this

time of detection, the higher will be the upper layer temperature at the time of detection. Accordingly, with increasing

area a diminishing amount of egress time is available beyond

t^„„ before the hazardous upper layer temperature T „ is

achieved. Beyond some (large) area this phenomenon of

shrinking available egress time with larger area will not

represent a realistic sequence of events. For example, the

phenomenon would break down when, say, detection by inevitable

human response to high, but not yet hazardous, upper layer

radiation occurs prior to the buildup of upper layer thickness

to the specified

6. SUMMARY, CONCLUSIONS AND FUTURE DIRECTIONS

6 . 1 Summary

The introductory section to this work presented the concept of

attaining life safety in fires by means of safe egress. The concept

involves two basic elements, namely, the time available for safe egress,

t (i.e., the time between fire detection and the onset of hazardous

conditions), and the time required for safe egress, (i.e., the time

required for occupants to evacuate a threatened space) . A safe condition would be indicated if t ^- > t . General ideas on estimating

avail — req

safe available egress time from rooms of fire origin and from adjacent

spaces were discussed. Actual estimates would be based on a model of

the development of hazardous conditions in a specified space subsequent

to the initiation of a specific fire. Appropriate criteria for both

fire detection and onset of untenability would be used to identify these

two events within the simulated tlme-varying-description of the degrading

environmental conditions.

Relative to the task of estimating available egress time. Section 2 was devoted to a discussion of the significance and utility of free bum

36
testing of practical fuel assemblies. Such tests would be carried out

on fuel assemblies which are characteristically found in different

occupancies. The data from the tests would be used as inputs to the

safe available egress time estimation scheme.

By introducing a definite qualitative and quantitative model of

hazard development, the details of an available egress time estimation

technique were formulated in Sections 3 and 4 for the room of fire

origin problem. The model basically assumes that the products of

combustion rise in a plume which forms above a threatening fire, and

that these products fill the room from above with a hot, potentially

toxic, obscuring, and ever-thickening smoke layer.

In Section 5 the room of fire origin model was used in two example

problems. First, results from the model were compared to actual test

data which were generated in a full scale test of a hospital patient

room-corridor mockup fire scenario. Favorable comparisons between the

computed and measured evolution of the upper layer depth suggest that

for some practical problems the use of the (single) room of fire origin

model can be extended to freely connected multiple space configurations.

Comparisons between computed and measured results also suggested that

the limited nature of available estimates in overall heat transfer to

ceilings and walls can lead to serious errors in estimates of average

upper layer temperature.

The second example problem of Section 5 presented a hint of the

ability of the room of fire origin egress model, indeed, of the overall

egress concept, to provide building designers with practical estimates

of available egress time. There, a hybrid, semi-universal fire (Figure

13) was analytically constructed from data acquired in diverse, practical

fuel assembly free bums. Rooms of different areas and heights were

assumed to contain this fictitious fire, and for a specific realistic

hazard criterion, available egress times were estimated for different

detection criteria.

37
6.2 Conclusions and Future Directions

From the above it is concluded that the concept of achieving life

safety in fires through safe egress is not only qualitatively useful,

but it can be quantitatively applied to real building problems by means

of practical and rational engineering calculations. This work has

suggested general ideas on formulating the essential elements of a physical fire development model that would be the basis for such calculations. These elements would be constructed from a variety of well

established, experimentally and theoretically derived enclosure fire

phenomena.

Fire growth models that are developed to provide fire protection

practitioners with available egress time estimates are likely to represent

compromises between accuracy in simulation and practicality in implementation. With regard to "optimizing" such compromises in the specific

model adopted here, somewhat more modeling detail can readily be brought

into play without seriously detracting from the model's practicality.

For example, it is anticipated that near term future embellishments of

the room of fire origin model will include dynamic estimates of product

of combustion concentrations in the upper layer. This capability would

allow both detection and untenability to be realistically based on such

concentrations

.

Room of fire origin results were shown to have some applicability

to freely communicating, multiple space fire scenarios. However, the

application of such results to multiple space problems is not generally

appropriate. Accordingly, there is a clear requirement to develop a practical, generalized technique to solve the (available egress time

from) adjacent space egress problem, and utlimately, to solve the

overall building egress problem. This work has outlined guidelines for

such solution techniques. The major new directions for future work on the available egress time problem clearly lie in the implementation of

these guidelines.

38
7 . ACKNOWLEDGEMENTS

Throughout the entire course of this work the author received the

enthusiastic support of Mr. Harold Nelson who, while helping to provide

a stimulating environment on a regular basis, freely shared his vast

experience and keen insight into fire safety engineering technology, in

general, and fire protection engineering, in particular.

Most calculations reported in this work were performed by Mr.

Steven West who took the original room-of-fire-origin computer program

and revised it in a manner as to significantly increase its versatility.

All of the above is gratefully acknowledged.

39
8 . REFERENCES

[1] Friedman, R. , Quantification of Threat from a Rapidly Growing

Fire in Terms of Relative Material Properties, Fire and Materials,

Vol. 2, No. 1, 1978.

[2] Emmons, H.W. , Mitler, H.E. , and Trefethen, L.N. , Computer Fire

Code III, Home Fire Project Tech. Rpt., No. 25, Div. Appl.

Sciences, Harvard Univ. , Jan., 1978.

[3] Cooper, L.Y., The Measurement of Smoke Leakage of Door Assemblies

During Standard Fire Exposures, NBSIR 80-2004, U.S. Dept.

Commerce, Nat'l. Bur. Standards, Center for Fire Research,

June, 1980.

[4] Pape, R. , Mavec, J., Kalkbrenner, D. , and Waterman, T., Semistochastic Approach to Predicting the Development of a Fire in a Room from Ignition to Flashover. Program Documentation and

User's Guide, 111. Inst. Tech. Research Inst. Report NBS-GCR-77-111

prepared for U.S. Dept, Commerce, Nat'l. Bur. Standards, 1977.

[5] Baines, W.D. and Turner, J.S., Turbulent Buoyant Convection

from a Source in a Confined Region, Journal Fluid Mech., Vol.

37, Part I, 1969.

[6] Zukoski, E.E., Development of a Stratified Ceiling Layer in

the Early Stages of a Closed-Room Fire, Fire and Materials,

Vol. 2, No. 2, 1978.

[7] Alpert, R.L. , Turbulent Ceiling Jet Induced by Large Scale

Fires, Tech. Report FMRC 22347-2, Factory Mutual Research

Corp., 1974.

[8] Benjamin, I., Heskestad, G. , Bright, R. , Hayes, T., An Analysis

of the Report on Environments of Fire Detectors, Fire Detection

Institute, 1979.

[9] Alpert, R.L., Calculation of Response Time of Ceiling-Mounted

Fire Detectors, Fire Technology, Vol. 3, 1972.

[10] Heskestad, G. , and Delichatsios, M.A., Environments of Fire

Detectors - Phase I: Effect of Fire Size, Ceiling Height, and

Materials, Volume 1. Measurements, Factory Mutual Research

Corp. Report NBS-GCR-77-86 prepared for U.S. Dept. Commerce,

Nat'l. Bur. Standards, 1977.

[11] Heskestad, G. , and Delichatsios, M.A., Environments of Fire

Detectors - Phase I: Effect of Fire Size, Ceiling Heights,

and Material. Volume 2. Analysis, Factory Mutual Research

Corp. Report NBS-GCR-77-95 prepared for U.S. Dept. Commerce,

Nat'l. Bur. Standards, 1977.

40
[12] Heskestad, G. , and Delichatsios , M.A., Environments of Fire

Detectors - Phase 11° Effect of Ceiling Configuration.

Volume I. Measurements, Factory Mutual Research Corp. Report

NBS-GCR-78-128 prepared for U.S. Dept. Commerce, Nat’l. Bur.

Standards, 1978.

[13] Heskestad, G. , and Delichatsios, M.A., Environments of Fire

Detectors - Phase II: Effect of Ceiling Configuration.

Volume II. Analysis, Factory Mutual Research Corp. Report

NBS-GCR-78-129 prepared for U.S. Dept. Commerce, Nat'l. Bur.

Standards, 1978.

[14] Babrauskas, V. , Combustion of Mattresses Exposed to Flaming

Ignition Sources. Part I. Full-Scale Tests and Hazard Analysis,

Center for Fire Research, NBSIR 77-1290, U.S. Dept. Commerce,

Nat’l. Bur. Standards, 1977.

[15] Morton, B.R. , The Choice of Conservation Equations for Plume

Models, Journal Geophysical Research, Vol. 76, No. 30, 1971.

[16] Yokoi, S., On the Heights of Flames from Burning Cribs, BRI

Report 12, Ministry of Construction, Japanese Government,

1963.

[17] Zukoski, E.E., Kubota, T. , Cetegen, B. , Entrainment in Fire

Plumes, Calif. Inst, of Tech. Report supported through Grant

No. G8-9014 of U.S. Dept. Commerce, Nat’l. Bur. Standards,

April, 1980.

[18] Burgess, D. , and Hertzberg, M. , Radiation from Pool Fires,

Chapter 27 of Heat Transfer in Flames, Afgan, N.H., and Beer,

J.M., Eds., Wiley, 1974.

[19] DeRis, J. , Fire Radiation - A Review, Tech. Report FMRC RC 78-

BT-27, Factory Mutual Research Corp., 1978.

[20] Modok, A.T., and Croce, P.A., Plastic Pool Fires, Combustion

and Flame, Vol. 30, 1977.

[21] O’Neill, J.G., and Hayes, W.D. , Full-Scale Fire Tests with

Automatic Sprinklers in a Patient Room, Center for Fire

Research, NBSIR 79-1749, U.S. Dept. Commerce, Nat’l. Bur.

Standards, 1979.

[22] Zukoski, E.E. , and Kubota, T. , A Computer Model for Fluid

Dynamic Aspects of a Transient Fire In a Two Room Structure

(Second Edition), Calif. Inst. Tech. Report prepared for U.S.

Dept. Commerce, Nat’l. Bur. Standards, 1978.

[23] Tanaka, T. , A Model on Fire Spread in Small Scale Building,

Third Joint Meeting U.S. -Japan Panel on Fire Research and

Safety, U. J.N.R. , Wash., D.C., March 13-17, 1978.

41
[ 24 ] Zukoskl, E.E. , Kubota, T. , An Experimental Investigation of

the Heat Transfer from a Buoyant Plume to a Horizontal Ceiling - Part 2, Effects of Ceiling Layer, Calif. Inst, of Tech. Report

NBS-GCR-77-98 prepared for U.S. Dept. Commerce, Nat’l. Bur.

Standards, 1975.

[25] Bukowski, R. , private communication.

[26] Veldman, C.C., Kubota, T. and Zukoski, E.E. , An Experimental

Investigation of the Heat Transfer from a Buoyant Gas Plume to

a Horizontal Ceiling - Part 1, Unobstructed Celling, Calif.

Inst. Tech. Report NBS-GCR-77-97 prepared for U.S. Dept.

Commerce, Nat*l. Bur. Standards, 1975.

[27] Cooper, L.Y. and O’Neill, J.G., Fire Tests of Stairwell Sprinkler

Systems to Appear as Center for Fire Research NBSIR, U.S.

Dept, Commerce, Nat’l. Bur. Standards.

42
APPENDIX A. HEAT TRANSFER TO THE BOUNDING SURFACES OF

THE ROOM OF FIRE ORIGIN

A.l Introduction

This appendix is for the purpose of establishing an appropriate

value for X to use in Eqs. (4.8). As noted in section 4.2, X is

c . c defined as the combined instantaneous fraction of Q lost by the combustion zone, the plume gases, and the hot upper layer gases to the bounding

surfaces of the room and it’s contents. X is made up of radiation

c losses and convection losses.

As discussed in section 5.2, for the present purposes it is reasonable to assume that 35 percent of the fire's energy release rate,

Q(t), is radiated from the combustion zone. During the relatively early

times under consideration here when exposed surfaces are still relatively

cool, of the order of half of this energy "shines” on and is absorbed by

the floor and by surfaces of furniture, hardware, etc.

,

contained within

the room. The remaining half of this . 35 Q irradiates the upper portions

of the room. At very early times when the upper layer is relatively

transparent because of it’s small thickness and/or optical density, most

of this upper radiant energy is actually absorbed by the ceiling.

Somewhat later, a significant portion of this .35 Q/2 energy delivery

may be trapped by the upper gas layer because of it’s growing effective

absorbtivity . With regard to energy transfer from the upper layer

itself, it is reasonable to assume that for the times of interest here

convective losses will dominate those energy losses which are due to

upper layer reradiation. This latter assumption along with the above

transparent upper layer assumption will be made below. To complete the

picture and to eventually draw all the pieces together and finally

select an appropriate effective X^, it is necessary to estimate the

magnitude of the convective losses.

43
A. 2 Convective Heat Transfer to the Celling

Assuming rooms with smooth surface, characteristic celling spans of

the order of several room heights and with fires away from the walls,

the losses from the upper layer to the celling will be the result of

convection heat transfer from an axlsymmetrlc celling jet. Alpert [7]

has studied the celling jet problem both analytically and experimentally

for the case of a constant fire size and for zero upper layer thickness.

Veldman, Kubota and Zukoskl [26] have added more experimental data to

the heat transfer aspects of the problem. Zukoskl and Kubota [24] have

studied the heat transfer problem experimentally for configurations

having upper layer thicknesses which grow to fixed values In the steady

state. The latter work concluded that the heat transfer coefficients,

h, for both the zero layer and finite layer thickness cases are substantially similar. The following correlates the heat transfer coefficient

data of [26]

f.(o.

070(1-2.39 r/H); 0 £ r/h £ 0.2

0124(r/H)"^’^^; 0.2 < r/H < 0.72

(A-1)

Here the rate of heat transfer to the celling, u, Is defined as

U = h[T^^ - TJ (A-2)

where T^^ Is the near-celling jet temperature for an adiabatic celling.

and T^ Is the celling temperature.

An analytic estimate of the effective celling jet temperature,

In the zero layer thickness case which fits the data of [26] Is given by

, , ** 2/3

f^ = 10.2 exp(-1.77 r/H); 0 _< r/H £ 0.72

44

(A- 3)
In the case of a finite layer thickness the plotted results of

Figure 11 of [24] indicate that the values of will be larger than

indicated by the above equation. This is due to the fact that instead

of entraining ambient air the plume entrains heated gases of the upper

layer once it passes through the upper layer-lower layer interface. In

terms of actual data, the enhanced T , measurements of [24] for the

ad

finite layer are peculiar to the particular configurations used in that

study. As it turns out, a general expression for say as a function

of Z^/H, fire size, room aspect ratio (charcteristic ceiling span

divided by H) , and room lining materials, is not yet available. Since

the zero layer result of Eq. (A- 3) will be valid for early times and

possible for later times in the case of rapidly growing fires (where, at

a given instant, plume temperatures will tend to be significantly larger

than the average upper layer temperature) , it is reasonable to use it in

the present calculations.

Using the above ideas together with the results of Eqs. (A-1) and

(A- 3) in Eq. (A-2) , the rate of heat transfer can be computed from

u(r/H) = p^CpT^(gH)^^Vfjj[fT - " D/(Q*)^^^]

where f, , f„ and T are all functions of r/H. The convective heat

h T c transfer to the ceiling,

Q(,gjLij[ng* ^ circle of radius r can be

computed from

r/H

• * or, using the above result for u and the definition of Q [below Eq.

(4.2)],

^ceiling^^ ^ceiling

= 2tt(1-A ) / r

•' o

r/H

f (C){f (.Q-(T /T -l)/(Q*)^/^}^dC

n i c a

45
For the present problem it will be assumed that the ceiling

temperature has not increased significantly above an initial T value in

Si the relatively short times of interest. Thus

r /H

^celllng/Q

= (A-4)

Using the analytic expressions of Eqs. (A-1) and (A-3) , and assuming

that the validity of these equations can be extended up to r/H = 2, the

value of ^ceiling the range 0 _< r/H _< 2. has been computed

from a numerical integration of Eq. (A-4). The results of this is

presented in Figure 15.

As seen in Figure 15 1 appears to be approaching a large r/H asymptotic value of approximately 0.40. In view of the

earlier X = . 35 estimate, it is therefore concluded that for rooms with

r ceiling spans of the order of 4H or larger the convective heat transfer

to the ceiling can be estimated from

X ,,, (r/H>2) = 0.40 (1-X ) = .40 (1 - .35) = .26 ceiling r

For rooms of smaller ceiling spans, appropriate smaller values of

^ceiling estimated with the use of the results of Figure 15.

A. 3 Constructing a Value for X

It is Important to note that the above estimate for X does ceiling

not account for convective heat transfer to ceilings with deep surface

irregularities (e.g., greater than .02H in depth). Nor does this estimate account for variations in ceiling heat transfer that come about as

a result of strong ceiling jet-wall interactions which can occur in the

vicinity of ceiling-wall junctions. It is also apparent that the above

result does not take account of heat transfer to wall surfaces themselves.

The total amount of all of these potential variations in convective heat

transfer rates can be a significant fraction of Q. This would be

46
particularly true in a scenario where (1) the fire is close enough to a wall so that strong flow interactions occur between the ceiling jet and

the wall (this would always occur in rooms with span to height ratios

smaller than 2-4) or (2) the ceiling has deep irregularities (e.g., deep

beams) which are generally closer together than 2H - 4H.

Define the rate of convective heat transfer over and above Q

[defined in Eq. (A-4) ] as ceiling

Now in a room with a smooth ceiling where the fire distance from

the wall is several multiples of H or greater the value of X other

Qother^^ may be negligible compared to ~ .40(1-X^). For such

scenarios

,

X + X +X^^ =^.35 +.26 + X^^ ==0.6

r ceiling other other

On the other hand, where ^other significant, the total

value of X^ can be as large as 0.9. For example, in a series of large

scale experiments reported by Cooper and O'Neill in [27] (1.5 and 4.0 MW

propane diffusion flames in 3.7 m high space with deep ceiling beams and

an aspect ratio of the order of two) X^ was measured to be in the range

. 74 - .89. Also, in the small scale circular room experiments (.58 m

high and . 91 m in diameter) reported in [24], where radiation loss from

a premixed propane burner (1.17 and 1.53 kW) was measured to be negligible

[26], (X + ^ ..u )/(l - X ) was estimated to be .57. It is noteworthy that data from these latter experiments were taken in the steady

state. It is likely that a number larger than .57 would have been

observed at early times into the experiments when ceiling and wall

surfaces were near the original ambient temperature and when the energy

content of the growing upper layer was increasing. For the large

threatening fires of interest here where X^ = .35 is assumed and where

the other considerations of paragraph A.l were valid, the above .57

value for ^

47
A. 4 Summary

To summarize all the above: X for fire scenarios of interest here

c will generally fall within the approximate range

0. 6 < A <0.9 — c —

The lower, 0.6 value would relate to high aspect ratio spaces with

smooth ceilings and with fires positioned far away from walls. The

intermediate values and the high 0.9 value for A^ would relate to low

aspect ratio spaces, fire scenarios where the fire position is within a room height or so from walls and/or to spaces with highly irregular

ceiling surfaces.

48
Table 1. Various Factory Mutual Research Corporation fire

the exponential growth lay (from Friedman [1]):

data fitted to

• • Q

= exp [a(t-t^)].

Doubling

Time

Range of Fire Size Fitted

^ 0.693/a

Fire Description (kW) a (sec ) (sec)

1. flex. PU foam 0.6 m x 0.6 m 1-20 0.033 21

X 0.1 m high, ignited at top

center

2. NSF bedroom fire 1975, PU 10 - 400 0.024 29

mattress covered with sheet on bed in 8’ x 12' room

3. wood crib, 0.76 m square, 0.38 m 150 - 1,000 0.018 38

high, made of 120 pine sticks

3.2 cm. sqxiare, ignited at bottom

center

4. Commodities on pallets in array

2.4mx2.6mx4.6m high, ignited

at bottom:

a. paper cartons with metal

liners 4,000 - 18,000 0.0029 240

b. toy parts in cartons 2,500 - 15,000 0.0040 170

c. polypropylene tubs in, cartons 1,500 - 22,000 0.0045 150

d. compartmented paper cartons,

empty 7,000 - 20,000 0.0057 120

eair-cond. units on polyethylene

pallets 2,000 - 40,000 0.0088 79

f

polystyrene meat trays, paperwrapped 3,000 - 60,000 0.025 28

g- polystyrene insulation boards 7,000 - 100,000 0.029 24

49
50

Figure

1.

Two

examples

of

characteristic

fuel

assemblies

of

interest
aseaiay

A6j9U3

51

Figure

2.

History

of

the

energy

release

rate

from

free

burn

experiments
•

Fire

is

initiated *

See

restrictions

in

section

3.2 *

Energy

release

rate

history

will

remain

close

to

that

of

free

burn

test

beyond

predicted

times

of

intolerably

hazardous

conditions
•

Plume

has

formed

•

Layer

has

developed

and

grown

in

thickness

and

temperature

0)

>«

(0

53
0) o

(DOaE

0)

“DC

(0

LU

1-<

(/)

(/> 0)

O c

LUs o

cc

LUHZ o

>*

(0

II • $ooo

0) o is

(/> 0) 3Ccoo

0)

c3

0)

(0

(0 —0) o

0> </)

0)

0)o%

0) ^ c.E o>oc

LU

©

JQ

’3

(0oa

(0

(/) o *:o3

(U oo

>%

k»

0)> o

(0>

0)

0)

O)

54

Figure

5.

Scenario

at

intermediate

times

between

detection

and

hazard
L—

IHAZ

•

Conditions

become

hazardous

beyond

human

tolerability

•

Hazard

criteria:

55

height

-

conditions

(may

be)

becomes

critical

-

radiatioi

intolerable

for

safe

evacuation

exceeds

bounds

of

human

tolerability
56 0) 3

(0oaE0)

-2

(0

(00) co

‘3c0) E

"O

II8

II 0)

(0

CD0) 0)

O)oc0)

(0

(0oco

<0 £ 2 - "O

IIO’

CO

T*

k. I T

CM o01 To c

•HI<UU

•H

M-l mo

flo

•H

4-1 n)U

•U

Cfi t—I

iH (U •H Md

QJ

W

iH

OI—I e o

•H

p

W (U

cuu3

bO

"HP4

I'

flow

dynamics
57

Figure

8.

Plan

view

of

hospital

room

corridor

mockup

space
000‘0l lM>i) udij JO indino AOdJNj - o

58

Figure

9.

Energy

release

rate

of

wastepaper

basket

-

mattress

fuel

assembly
LAYER

THICKNESS

(ft)

Figure 10. History of interface position

0 50 100 150 200 250 300 350

TIME (sec)

59
TEMPERATURE

DIFFERENTIAL

OF

UPPER

LAYER

AT|,/°C

Figure 11. History of average upper layer

temperature

60
T

^ -- -o ® a> c S

ITS ^ +- ' lO CO

«« ts 111 to +i* S w «« S o> o> C So> ^a>

ir> S ^

lo lo o>

**“ - - «-«io

- - _ a»

i= fc- o i_r •-I' o o o o O

o o oCP oo

oo

CM CO

o> oo «

k«o> Q> Q> o> o>

•«-> *-• .»

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E E E E E E

CO CO CO CO CO CO < < o • O

-

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< ^

0

lO

CO

CO

ir> CM

CM

in

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cs

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CO

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mm H3d AiiSN3a ivoiido

61

Figure

12.

Optical

densities

measured

by

the

photometers
\

10000 r

1000 -

as

Figure 13. Free burn energy release rate from

a semi-universal fire. A

fictitious construct from the data

of Friedman [1]

. .

. T

^ r Q/Qo=300 EXP[005 (TIME/sec-349|]

(COMMODITIES IN PAPER CARTONS

AND STACKED DN PALLETS)

Q/Qo=40 EXP[010 (TIME/sec-147.6)]

("BETWEEN” WODD CRIBS AND SOME

COMMODITIES ON PU PALLETS)

Q/Qo=EXP[.025 TIME/sec]

(PU MATTRESS COVERED WITH

SHEET ON BED)

Qo=10 kW=Q IMMEDIATELY AFTER IGNITION

100 200 300 400 500

TIME FROM (10 kW) FIRE IGNITION (secj

62
CM

CO

CO CO

II II

IMI l*sl

INI

CO m

130 j- ZVHJ

a- CO CM

(38S) 3IMI1 ss3d93

63

300

400

500

700

1000

1500

2000

3000

4000

5000

7000

10000

ROOM

AREA

(ft

2)*

Figure

lA.

Estimates

of

available

egress

NBS-114A (REV. 9-78)

u.s. DEFT. OF COMM. 1. PUBLICATION CR hii.’ORT NO. BIBLIOGRAPHIC DATA I ^

SHEET 1 NBSIR 80-2172

3. .to.

'4

4. TITLE AND SUBTITLE

j

ESTIMATING SAFE AVAILABLE EGRESS TIME FROM FIRES

5. Publication Date February 1981

7. AUTHOR(S)

Leonard Y. Cooper

8. Performing Organ. Report No.

i ^-^FRFORM'NG ORGANIZATION NAME AND ADDRESS

! NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS rsfreef, aty, state, zip)

The Occupational Safety and Health Administration (OSHA)

Department of Labor

Washington, D. C. 20210

13. Type of Report & Period Covered

Final

15. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

16. ABSTRACT (A 200-word or leas factual summary of moat aignificant information. If document includes a significant bibliography or

literature survey, mention it here.)

A general technique for estimating the time available for safe egress from a fire

is presented. By introducing a qualitative and quantitative model of hazard

development, the details of the technique are 'formulated for the room of fire

origin problem. The inputs to the model are the area and ceiling height of the

room, data from free burn tests of characteristic fuel assemblies likely to be

found therein, the anticipated model of fire detection, and a criterion for the

onset of untenabil ity. The output is an estimate of the length of time between

detection of a fire and the onset of untenable conditions. Results of applying

the estimation technique are presented and discussed.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons)

Combustion products; compartment fires; egress; fire detection; fire growth;

hazard analysis; mathematical models; room fires; smoke movement; tenability

J-imits ] 18. AVAILABILITY [^Unlimited 19. SECURITY CLASS

(THIS REPORT)

21. NO. OF

PRINTED PAGES

r~l For Official Distribution. Do Not Release to NTIS UNCLASSIFIED 72

n Order From Sup. of Doc., U.S. Government Printing Office, Washington, DC

20402, SD Stock No. SN003-003-

20. SECURITY CLASS

(THIS PAGE)

22. Price

[X~l Order From National Technical Information Service (NTIS), Springfield,

VA. 22161 UNCLASSIFIED

$8.00

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