REFERENCE NBS

PUBLICATIONS

NAT'L

AlllOb 053bbl

NBSIR 85-3144

ASET-B A Room Fire Program for

Personal Computers

William D. Walton

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

April 1985

Supported in part by:

National Park Service

Washington, DC

o r»rj -QC

100

. U56

85-3144

1985

partment of Health

ishington, DC

and Human Services

NBSIR 85-3144

0 * ' ASET-B A ROOM FIRE PROGRAM FOR

PERSONAL COMPUTERS

RATIONAL BUREAU

OF STANDARDS

library

AJ ClCIdd

William D. Walton

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

April 1985

Supported in part by:

National Park Service

Washington, DC

and

Department of Health and Human Services

Washington, DC

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

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Director

TABLE OF CONTENTS

Page

LIST OF FIGURES . . . iv

Abstract 1

1. INTRODUCTION . 2

2. DESCRIPTION OF THE MODEL ....... 4

3. SOLUTION OF THE EQUATIONS ....... 7

4. STRUCTURE OF THE COMPUTER PROGRAM ............ 10

4.1 General Structure ................. 10

4.2 Program Sections ......... 11

4.2.1 Input and Initialization Section 11

4.2.2 Equation Solving Section .......... 13

4.2.3 Subroutine to Calculate Heat Release Rate . 13

4.2.4 Output Subroutine ........ 14

5. RUNNING THE PROGRAM .............. 15

5.1 General Instructions .......... 15

5.2 Program Inputs .......... 16

5.2.1 Title ................... 16

5.2.2 Heat Loss Fraction ............. 16

5.2.3 Height if the Base of the Fire 17

5.2.4 Room Ceiling Height and Floor Area ..... 18

5.2.5 Maximum Time ........... 18

5.2.6 Heat Release Rate . 18

5.3 Program Outputs ............. 21

6. USE AND LIMITATIONS OF THE ASET-B RESULTS 21

6.1 Evaluating Fire Safety Objectives . 21

6.2 Using ASET-B for Multiple Rooms 23

6.3 Program Limitations 23

6.4 Program Verification 25

7. TRANSPORTING THE PROGRAM ........ 25

8. ACKNOWLEDGEMENTS ............ 27

9. REFERENCES ............. 27

APPENDIX A % ASET-B PROGRAM LISTING ............. 29

APPENDIX B: VARIABLE NAMES USED IN ASET-B 31

APPENDIX Cl SAMPLE RUN OF ASET-B PROGRAM 34

iii
LIST OF FIGURES

Figure 1. Schematic of fire phenomena

Page

. 28

iv
ASET-B A ROOM FIRE PROGRAM FOR PERSONAL COMPUTERS

William D. Walton

ABSTRACT

ASET-B, a personal computer program for predicting the fire

environment in a single room, is presented. ASET-B solves the

same differential equations as the previously developed computer

program, ASET (Available Safe Egress Time), using a simpler

numerical technique. ASET-B requires as input the height and area

of the room, the elevation of the fire above the floor, a heat

loss factor, and a fire specified in terms of heat release rate.

The program predicts the thickness end the temperature of the hot

smoke layer as a function of time. ASET-B is written in BASIC and

is not subject to copyright. This paper describes the program and

its use. Included are a listing of the program, program variable

name listing and a sample run. A discussion of user modifications

also is given.

Key Words? compartment fires; computer programs; evacuation; fire

growth; manuals; mathematical models; room fires; smoke.

1
1 . INTRODUCTION

In 1980 L. Y. Cooper of the Center for Fire Research,

National Bureau of Standards introduced ASET, a mathematical

1 model for estimating Available Safe Egress Time in fires Cl] . In

1982, Cooper with D. Stroup published a computer program to

perform the calculations in the mathematical model C23 , thus, the

computer program also became known as ASET. ASET was not

specifically written for the personal computer environment

because at the time it was being developed, personal computers

were ^ust emerging as a tool for use in the engineering office.

Since the introduction of ASET, the use of personal computers has

become widespread and there has been significant interest in

running ASET on personal computers «, In response to this interest,

this paper introduces ASET-B, a program for personal computers

based on the original ASET mathematical model. The B is used to

indicate basic, brief, BASIC and Beta.

Most larger personal computers, when properly configured,

can run the original ASET program. There are however, several

reasons why ASET is not the most appropriate program for the

personal computers widely used today. ASET is written in FORTRAN

and consists of over 1500 program lines. Although FORTRAN is

available on many personal computers, BASIC is by far the most

popular programming language. To make ASET-B easy to distribute

Figures in brackets indicate literature references at the end

of this report.

2
and allow the user to make modifications, it has been written in

BASIC. A second reason that ASET may not be appropriate for some

personal computers, is its size and run time. ASET has a wide

variety of features which allow the user to run multiple cases,

identify endpoints and calculate species concentrations. These

features increase program size, input , output and run time. In

developing ASET-B it was decided to make the program as simple

and fast as possible, while providing the same essential output

information produced by ASET. While ASET-B can be used to address

a wide variety of problems, it can also serve as an introduction

to the more comprehensive ASET.

ASET-B a© a program looks very different from the original

ASET. ASET-B consists of approximately 100 program lines in

BASIC. Most of the variable names have been changed in order to

make the program more compact and easier to follow. The multiple

run options have been eliminated as well as the ability to

calculate species concentrations and automatically identify

endpoints. With these exceptions, the primary equations solved by

ASET and ASET-B are identical. The most significant change in

ASET-B is the use of a different mathematical procedure to solve

the primary equations. ASET-B employs an equation solver that is

at least 5 times faster than that used in ASET, while retaining

mathematical agreement to within a fraction of a percent. It

reduces the time for an average run on a typical 16 bit personal

computer from over 5 minutes to under 1 minute.

3
I

2. DESCRIPTION OF THE MODEL

The mathematical model which is the basis for ASET and thus

ASET-B has been presented in detail by Cooper Cl, 33, and will be

only summarized here. It is based on a single room or enclosure

with all doors, windows or vents closed except for a small leak

at floor level. This leak prevents the pressure from increasing

in the room. A fire starts at some point below the ceiling and

releases energy and products of combustion. The rate at which

energy and products of combustion are released may change with

time. The hot products of combustion form a plume, which due to

buoyancy, rises towards the ceiling. As the plume rises, it draws

in cool air from the room which decreases the plume's temperature

and increases it's volume flow rate. When the plume reaches the

ceiling it spreads out and forms a hot gas layer, which descends

with time as the plume's gases continue to flow into it. There is

a relatively sharp interface between the hot upper layer and the

air in the lower part of room, which in this model is considered

to be at ambient temperature. The only interchange between the

air in the lower part of the room and the hot upper layer is

through the plume. ASET could therefore be described as a two

layer or zone model. The basic fire phenomena are shown

schematically in figure 1.

The two unknowns in ASET-B are the height of the hot layer

interface above the fire, Z, and the average temperature of the

upper layer, P. It should be noted that the notation used here

to describe the model is consistent with the variable names used

4
in the computer program. The unknowns, Z and P, are often

referred to as the (dimensionless) height and temperature of the

smoke layer since, consistent with the model formulation, smoke

can only be found in the plume and the hot upper layer. The known

quantities are the area and height of the room, A and H, the

height of the base of the fire above the floor, F, and the

acceleration due to gravity, G. In addition, the ambient

temperature, PA, density, DA, and specific heat, CP, of air must

be known. The final known quantities are the rate at which heat

is released by the fire as a function of time, QT , the fraction

of the total heat release which is given off as radiation, LR,

and the fraction of total heat release rate which is lost to the

contents and surrounding surfaces of the room, LC.

The unknown height and temperature are determined by using

conservation of mass and energy in conjunction with equations

describing the plume. Since the height and temperature of the

smoke layer will vary with time, T, their solutions are obtained

by solving two differential equations. In developing the

original equations for ASET Cl, 33, two dimensionless groups of

problem parameters. Cl and C2, were introduced. Also introduced

were dimensionless forms of the variables time, height and

temperature of the smoke layer, initial height of the smoke

layer, height ©f the base of the fire and the rate of heat

release. These variables are made dimensionless by dividing them

by a characteristic quantity with the same dimensions or units.

Thus the dimensionless temperature, P, is the actual temperature

5
of the smoke layer, PF (converted to °R> , divided by the ambient

temperature, PA (°R) . Similarly, the dimensionless rate of heat

release, QT, is the actual rate of heat release, QA (kW) , divided

by the initial rate of heat release, QO (kW) . Finally, the

dimensionless variables, height of the smoke layer, Z, initial

height of the smoke layer, ZO, and height of the base of the

fire, F, are the dimensional values for these variables in feet

divided by a characteristic length CL which is also in feet. Here

as in the ASET program, CL is simply taken as one foot. Thus the

dimensionless lengths Z, ZO and F are the same as their physical

lengths in feet. The dimensionless time, T, is the actual time

divided by a characteristic time, CT, of one second. The

dimensionless time, T, is therefore numerically equal tb the

actual time in seconds. Since engineering units are used in

ASET, this convention has been continued here for consistency.

Conversion to SI units is provided in the computer program.

The differential equations for the dimensionless height of

the layer above the fire, Z, and average temperature of the

layer, P, are given below.

0<ZiZ0

-F<ZiO

Z="F

P CC1 • QT- ( P - 1 > C2 * QT

P • Cl QT/ (ZO+Z)

l/3

zS/3 3/CZ-ZO) 0<Z<Z0

-FlZiO

Cl - < 1 -LC) • QO • CT/ ( DA • CP a PA • A • CL

)

C2= (0.21 -CT/A) C(l-LR) • QO • G • CL2

/ ( DA • CP • PA )

1

1/3

6
In order to solve the equations for Z and P the initial

conditions must be known. One set of initial conditions which

were derived in Cl, 33, and will be used here, assume that the

fire starts with a small heat release rate, QO, at time T=0.

Under such conditions the initial conditions are.

z=zo

“5/3 P=1+Z0 C1/C2

Although dP/dT is indeterminate in the above equation at T=0 its

actual value has been found in Cl, 33 to be.

dP/dT* CC1/C2) C2-De0 + 5€C1+C2-Z05/3

) 3 /<6-Z08/3

) Where DQO=dQT/dT at time T~0.

3. SOLUTION OF THE EQUATIONS

In general, the differential equations for Z and P cannot be

solved explicitly, that is, an algebraic expression cannot be

written which describes Z and P at any time T. As a result, the

equations must be solved numerically. ASET solves the

differential equations using a variation of the fourth-order

Runge-Kutta method with variable time step. While this method has

a high degree of accuracy, it has been determined that the

improved Euler's method has sufficient accuracy for this problem.

The improved Euler's method is a simple predictor-corrector type

and is described in most books on numerical methods [43

.

The

improved Euler's method used in ASET-B requires substantially

fewer calculations than the method used in ASET, resulting in

ASET-B running much faster than ASET.

7
The improved Euler's method as applied in ASET-B is

basically a technique for stepping the solution forward in time.

Given the values of Z and P at a particular time, T, the method

is used to determine the values of Z and P at time, T + DT, where

DT is a small time increment. This process is started at time T=0

and continued until Z and P are known at all times of interest.

In the case of ASET-B an increment of 1 second has been found to

yield results which agree well with ASET for problems of

practical interest.

In ASET-B, Z1 and PI, are used to indicate the values of Z

and P at time, T. For the first step these are the initial values

at time, T=0. Z2 and P2 are used to indicate the values of Z and

P to be calculated at time, T+DT. To determine Z2 and P2 it is

observed that the differential equations for Z and P represent

the time rate of change of these quantities. The time rate of

change multiplied by the time step yields the change which occurs

over the time step. This would be an exact result if the

equations were linear or the time steps were infinitely small.

Since the equations are nonlinear, and it is impractical to make

the time step infinitely small, an approximation must be used. In

the improved Euler's method, Z2 and P2 are first predicted using

the derivatives evaluated at time, T. Using Z2 and P2 the

derivatives are then evaluated at time, T+DT. Corrected values of

Z2 and P2 are then calculated using the average of the

derivatives evaluated at times T, and, T+DT

.

Z2 and P2 are

predicted by

8
Z2=Z1+DZ1 • DT

P2=Pl-*-DPl DT

where DZl=dZ/dT and DPl»dP/dT are evaluated using Z=Z1 and P=P1

.

The derivatives at time T+DT, DZ2~dZ/dT and DP2-dP/dT, are then

evaluated using Z=Z2 and P=P2. Corrected values for Z2 and P2 are

calculated using the average derivatives.

Z2C=Z1 [ (DZ1+DZ2) /23 • DT

P2C=P1 4- C (DP1+DP2) /23 «DT

The predicted values of Z and P are then compared to the

corrected values

.

In ASET-B if the absolute value of the

difference between the predicted and corrected values is leas

than 0.001, the solution is considered to have converged and the

program proceeds to the next time step. If the difference is

greater than 0.001 the predicted values become the corrected

values and the derivatives at time, T + DT, are recalculated. New

corrected values are then calculated. In ASET-B this procedure is

repeated for a maximum of thirty times. If the differences are

still greater than 0.001, a warning is printed, and the program

proceeds to the next time step.

The evaluation of the derivatives of Z and P requires the

dimensionless heat release rate, 0T, be known for all times, T.

For heat release rates which ere not constant with time, A5ET-B

requires the heat release be specified for each one second time

interval. To simplify this procedure, ASET-B uses point specified

heat release rates with linear interpolation. Heat release rates

9
can be specified at as many as 100 different times. Linear

interpolation is then performed to determine the heat release

rate at each time step.

4. STRUCTURE OF THE COMPUTER PROGRAM

4.1 General Structure

ASET-B is structured to be easy to understand and modify,

while being adaptable to a variety of computers. In some cases

these objectives conflict since BASIC is not a structured

programming language and the implementation of BASIC varies among

computers. As a result, some of the so called rules of structured

programming have not been followed in favor of a program that can

be adapted to most forms of the BASIC programming language. A

listing of the program is given in appendix A and an index of

variable names in appendix B. In order to make the listing

compact, all documentation is provided in the text of this paper.

ASET-B is designed to be easy to modify as well as easy to

use. It is intended to serve as a base program which the user can

modify to meet a particular set of needs. Although the number of

possible user modifications is almost unlimited, comments on

several typical modifications have been provided with the program

description. If user modifications are made to the program, a

comment should be added to the header printed in lines 10 and

440. This will indicate that the program has user modifications

and is not the standard program.

10
4.2 Program Sections

The program consist of four major sections. The first, lines

10-530, reads and writes the required input data, sets initial

parameters and performs initial calculations. The second, lines

540-870, consist of the calculations required to step the

solution through time. Finally, lines 880 to 9S0 are a subroutine

which calculates the rate of heat release of the fire, and lines

970 to 1080 a subroutine which writes results. A brief

description of each of the sections is provided below.

4.2.1 Input and Initialization Section

The first section of the program can be subdivided by

function. The input data is read, and unit conversions performed,

in lines 10-250. The units of input lengths and area are feet and

square feet respectively with conversion to meters and square

meters in lines 110-130. The units of these inputs may be changed

to meters and square meters by reversing the input variable names

and conversion factors in lines 80-130. In line 60, the fraction

of the heat release rate of the fire which is instantaneously

lost by radiation for the combustion zone, LR, is set equal to

0o35. A discussion of this parameter which is called ALAMR in

ASET can be found in E13

.

The input heat release rates are read and stored in lines

150-250. The rate of heat release at time zero, Q0, has been set

11
at 0.1 kilowatts in line 150, corresponding to an initial fire

size which approaches zero. This value can be increased by the

user if needed. ASET-B can accommodate 100 pairs of input times

and heat release rates. While this number should be adequate for

most cases it can be changed by substituting the new number for

100 in lines 40, 170 and 230. The units for the input heat

release rates are kilowatts and may be changed to other units by

placing conversion factors in lines 200 and 210.

Lines 260-420 initialize variable values and perform initial

calculations. Several of the variables defined in these lines may

be modified to suit the user. This may be accomplished by either

changing the values within the program or by creating new prompt

questions and assigning the variables with input values. In lines

260 and 270 the ambient temperature, PA, and density, DA, of air

may be changed to reflect an initial temperature other than

o 70 F. In line 410 the time interval for printing, 01, may be

changed from its default value of 5 seconds. The results are

calculated for every second but are printed only at the time

interval specified by 01.

Lines 430-530 write out a summary of the input data, the

column headings for the subsequent output and the initial output.

Some users may desire this output to be sent to a printer or disk

file in addition to, or in place of, the output to the screen.

The techniques for accomplishing this vary with computer but the

most common are the use of LPRINT and PRINT#. Similar techniques

may be used to read the input data from a disk file.

12
4.2.2 Equation Solving Section

The second section of the program, lines 540-870, solves the

differential equations following the methodology outlined earlier

in this report. This section consists of two primary loops. The

outer loop beginning at line 540 and ending at line 880

corresponds to a single time step. The inner loop beginning at

line 620 and ending at line 800 is repeated only if the absolute

value of the difference between the predicted and corrected

values of either 2 or P is greater than 0.001. This comparison is

made in line 750.

At the beginning of the outer loop are two checks to

determine if the solution process should be terminated. In line

560 the current time, T2, is compared to the maximum input time,

TL, and in line 570 t© the last time for which a heat release

rate is specified, TQ(NQ) . If the current time is greater than

either of these two time limits the run is terminated with

transfer to line 870.

4.2.3 Subroutine to Calculate Heat Release Rate

The third section of the program consist of a subroutine , lines 880-960, which calculates the rate of heat release of the

fire end is called from the outer calculation loop at line 580.

This subroutine utilizes the input rates of heat release at

13
specified times and performs linear interpolation to determine

the rate of heat release at each time step. Although this method

of specifying the heat release rate is the most general, the user

may wish to modify the program to accept other models of fire

heat release. The ASET program for example can accommodate multipoint exponential fire growth input. Other fire growth models can

be inserted in place of, or in addition to, the existing point

specified model. This is accomplished by modifying the input

section in lines 160-250 and subroutine in lines 880-960.

4.2.4 Output Subroutine

The second subroutine, lines 970-1080, is called from the

outer calculation loop at line 850. This subroutine converts the

dimensionless variables to ones with units and writes the

results. The particular variables printed in this subroutine have

been selected to satisfy the needs of most users. The speed of

program execution may be affected by the quantity of the output,

particularly if a printer is used. As a result, the user may want

to reduce the quantity of output to reduce the run time. This is

accomplished by eliminating the variables to be printed in line

1070 and the corresponding column headings in lines 510 and 520.

There are two values calculated in this subroutine which have not

been printed. These are the rate of rise of temperature in the

upper layer in degrees Fahrenheit, RRF, and Celsius, RRC, per

minute. These values may be printed by adding their variable

names to the output list and including the appropriate column

14
headings. It should be noted that rate of rise of the upper layer

is not the sane as the rate of rise in a heat detector. The

temperature of the heat sensing element is a function of the heat

transfer between the hot gas and the element.

ASET-B produces only tabular output and has no specific

provisions for graphics. The reason is that graphics commands are

generally dependent on the device which produces the graphics.

There are however several methods by which graphics can be added

to ASET-B. The user may writ© the tabular results to a file which

can be read as input by a commercial graphics routine. The

results can then be presented using the graphics commands in the

commercial routine. Alternatively, the user may write a graphics

routine into the ASET-B program.

Sc RUNNING THE PROGRAM

5.1 General Instructions

ASET -B is written as an interactive program. that is. the

program prompts the user with questions. The mechanics of

answering the questions- is very straightforward

,

however the

selection of the input data requires further explanation. The

procedure for loading and running the program will not be covered

in this paper, but can be found in the user's guide included with

the computer. When the program is started it will initially print

the program name, a version number and a copyright notice. The

program will then print the first of seven questions and wait for

15
a response to that question. After the user has answered a question, a return or enter key is typed to register the answer

and proceed to the next question. No special error checking is

provided in the program so the user should carefully verify all

entries. If an error is detected after the data has been entered,

the program must be terminated and restarted.

5.2 Program Inputs

5.2.1 Title

The first prompt question or input is a run title. This

title is used to identify the run and may consists of characters

and/or numbers. The title will be printed at the beginning of the

output

.

5.2.2 Heat Loss Fraction

The second input is the heat loss fraction. This quantity

is the instantaneous faction of the heat release rate of the

fire which is lost to the bounding surfaces of the room and its

contents. Cooper has provided guidelines for selecting this

parameter which is called Lamda C or ALMAC in ASET Cl, 33. He has

determined that the approximate range is 0.6 - 0.9. The lower

value corresponds to high aspect ratio spaces (ratio of ceiling

span to room height) with smooth ceilings and fires positioned

far away form the walls. The intermediate to high values

16
correspond to low aspect ratio spaces, rooms with irregular

surfaces or rooms in which the fire is within one ceiling height

of the wall. The temperature of the upper layer is a function of

the heat loss fraction and the heat release rate of the fire. The

greater the heat loss fraction the lower the temperature in the

upper layer. The heat loss fraction for a room with insulated

walls will be lower than the fraction for the same room with

uninsulated walls.

Both ASET and A5ET-B treat the heat loss parameter as a constant. That is, the heat lost from the room is a constant

fraction of the heat release rate of the fire. As the heat

release rat© of the fire change© the quantity of heat lost will

also change but in direct proportion to the fire. Therefore the

room will not cool down even thought the heat release rate of the

fire goes to zero.

5.2.3 Height of the Base of the Fire

The third input is the height of the base of the fire above

the floor in feet. For fuel items of relatively uniform surface

height, such as beds, this is simply the height of the surface.

For three dimensional fuel items, such as sofas, an average

height weighted to reflect the distribution of surfaces should be

used. The rate of growth of the upper layer is strongly dependent

on the difference between the height of the base of the fire and

the height of the smoke layer interface.

17
5.2.4

Room Ceiling Height and Floor Area

The fourth and fifth inputs are the room ceiling height in

feet and the floor area in square feet. According to references

Cl, 3] the calculations may not be valid when applied to room

length-to-width aspect ratios greater than 10:1, or with a ratio

of height to minimum horizontal dimension exceeding one. The

equations are based on the assumption that the upper layer is

well mixed and at a uniform temperature. Therefore the results

for a square room and a rectangular room of equal height and area

will be the same.

5.2.5

Maximum Time

The sixth input is the maximum time for the simulation in

seconds. The results of the calculations will be printed at five

second intervals until the maximum time or until the end of the

heat release data.

5.2.6

Heat Release Rate

The final input is the description of heat release rate of

the fire. As described earlier the program can accommodate up to

100 pairs of times and corresponding heat release rates. The

program performs a linear interpolation between the specified

points to determine the heat release rates at the required times

18
during the calculations. The data is entered by typing the time

in seconds, followed by a comma, followed by the heat release

rate in kilowatts. A return or enter is then typed to proceed to

the next line. Heat release rates entered as less than 0.1

kilowatts will be converted to that value. The program will

automatically assume a starting value 0.1 kilowatts at time zero.

A heat release rate at time zero does not have to be entered

unless a greater initial heat release rate is required. When all

of the desired times and heat release rates have been entered a -9,-9 followed by a return is entered to terminate the data entry

and begin the calculations. Actually any negative time followed

by a heat release rate will result in the same action.

Heat release data for some furniture items can be found in

C5]

o

These data can be entered directly by selecting a number of

the points which represent the general shape of the curve.

Equations for the growth rate of a number of industrial

commodities can be found in NFPA 72E and 204M [6,7]. These

equations can be solved to yield the heat release rate at

selected times, which can then be entered into the program. In

addition, correlations of pool and crib fires have been

summarized in appendix B of reference C8]

.

In many cases there is insufficient knowledge of the fuel or

no data on which to determine a heat release rate for the fuel.

One possibility in this case is to use the so called semiuniversal fire developed by Cooper [1,33. Moat fires, other than

19
rapid growth fires such as flammable liquids have heat release

rates less than the semi-universal fire. The semi-universal fire

is based on the same Factory Mutual data used in NFPA 204M and

72E . Initially it simulates a fire on a polyurethane mattress,

at 148 seconds it begins to simulate burning wood and

polyurethane pallets, and at 349 seconds a fire spreading

through commodities in paper cartons and stacked on pallets. The

mathematical description of the semi-universal fire is provided

in appendix C. The semi-universal fire will generally provide

conservative results when used in ASET-B to predict the height

and temperature of the upper layer. If the semi-universal fire is

used to predict time to detection, it may predict detection too

quickly

.

ASET-B cannot change the burning rate of the fire as a function of the conditions in the room. ASET-B cannot determine

if there is sufficient oxygen present for the fire to burn as

prescribed and it cannot increase the burning rate as a result of

thermal radiation to the fuel. The burning rate data referenced

above is based on free burn conditions, that is with a free

supply of ambient air and no thermal enhancement from the

surroundings. The use of free burn data should prove satisfactory

at least up to the time when ASET-B predicts upper layer

temperatures of approximately 350-450°C. Beyond that time ASET-B

will continue to calculate layer heights and temperatures based

on the input fire even though the results may be physically

impossible

.

20
5.3 Program Outputs

The output of the ASET-B program is a summary of the input

data and a table of the conditions in the room as a function of

time. The first column in the table is the simulation time in

seconds. The second and third columns are the temperature in the

upper layer in degrees Fahrenheit and Celsius. The fourth and

fifth columns are the height above the floor of the interface

between the upper and lower layers. The sixth and seventh columns

are the heat release rate of the fire in kilowatts and BTU per

second. Because of the formatting limitations in the BASIC

language, some columns may show more significant digits than are

meaningful

.

6. USE AND LIMITATIONS OF THE ASET-B RESULTS

6.1 Evaluating Fire Safety Objectives

Fire simulation computer programs such as ASET-B generally

provide a description of the environment within an enclosure and

not a direct evaluation of the fire safety. While a complete

discussion of the use of these programs in evaluating fire safety

is beyond the scope of this paper a few examples will be given.

A common objective in fire safety design is to determine the

time available for safe egress. In fact, ASET was originally

written with this objective in mind C93

.

Although the design

objective may be stated in different ways, one such statement la

21
as follows. Given a particular room and fire, how long does it

take to reach untenable conditions within the room? To evaluate

this objective, the limits of tenability must be established in

terms of the program results. For example, the room will become

untenable when the smoke layer reaches head height, or when the

temperature in the layer reaches a particular value. Using these

tenability limits and the program results, the time to untenable

conditions can be evaluated.

A second common fire safety design objective is to determine

if equipment or products will sustain damage in the fire

environment. Equipment damage thresholds can be established in

the same manner as human tenability limits. The damage thresholds

can be compared to the predictions to determine if equipment will

be damaged and the time to the onset of damage. The results can

then be evaluated based qn estimates of detection time,

suppression effectiveness and salvage capability.

In addition to determining the time to untenable conditions

or damage, ASET-B can be used to evaluate the impact of changing

one or more of the input variables. For example, the sensitivity

of the resultant fire environment to room size can be examined by

making multiple runs with different room sizes while holding the

other input values constant.

22
6.2 Using ASET-B For Multiple Rooms

Although the ASET-B program is based on a single room with

closed doors and windows, it is possible to use the program to

make approximations for rooms with open doors or windows or even

multiple rooms. The results of the closed room ASET- program are

generally valid for rooms with open doors or windows until the

interface drops to the top of the door or window. For the case of

a door opening into another closed room, a second run can be made

using the area of the two rooms combined. The first run (with

floor area of single room) is used to predict conditions until

the interface drops to the top of the door. The second run (with

floor area of combined rooms) is used from the time the newly

computed interface drops to the top of the door until the end of

the simulation. Although there will be a time gap between the two

runs, this technique will provide satisfactory results in many

cases, especially where door openings are relatively large and

where fire heat release rates are relatively small.

6.3 Program Limitations

The use of ASET-B or any design aid requires the design

engineer to make the final evaluation as to the appropriateness

of the design. ASET-B is based on certain engineering

approximations of the fire environment and should be used to

supplement rather than replace sound engineering judgement. The

program results should be treated as approximate and the user

encouraged to become familiar with how changes in the input

23
variables effect the program reeulte. The temperature of the

upper layer and the height of the interface respond differently

to changes in the input data. Appropriate factors of safety

should be applied to either the input data or the program

results

.

Some of the limitations of the program have been presented

in conjunction with the input data requirements. There are

however , some additional limitations. The mathematical procedure

used in ASET-B is very hardy, that is, the procedure will

normally converge and produce results. There are combinations of

input data for which the program will either fail to converge or

halt due to an illegal mathematical operation. If the procedure

for solving the equations fails to converge, a warning will be

printed and the solution will continue. The results following

this message may be in error and should be treated as such. The

failure to converge is usually a result of a heat release value

which changes too rapidly. In most cases this problem can be

corrected by minor smoothing of the input heat release curve.

There are combinations of input data which will result in

the program attempting to execute mathematical operations which

are invalid in the BASIC language. These operations include

dividing by zero and raising numbers to very small or large

powers . Operations of this type will be flagged by the computer

and subsequent results should be considered in error. Invalid

operations are usually caused by errors in input data. ASET-B

24
does not check the input data for possible errors which can cause

illegal machine operations or produce unrealistic results such as

negative temperatures or interface heights above the ceiling. As

indicated previously ASET-B may predict physically impossible

temperatures if very large fires are placed in small rooms.

6.4 Program Verification

Results of the ASET program have been compared to data from

a limited number of actual fire experiments Cl, 3]. These

comparisons can be extended to the ASET-B program since it

produces results which are within a few percent of those produced

by ASET. The fire experiments considered a mockup of a hospital

room-corridor building space. Comparisons were found to be

generally favorable. This does not necessarily mean that the

comparison will be favorable in all cases. Clearly additional

studies are required in this area and that work is ongoing.

7. TRANSPORTING THE PROGRAM

An important aspect of using any computer program is

obtaining a copy of the program for the computer where it is to

be used. The program must not only run, but it must produce the

correct results. Although a listing of ASET-B is given in

appendix A, it is not recommended the user attempt to type in the

program. A typographical error is generally very difficult to

track down and may result in a program error that occur* only

with certain combinations of input data. Instead the user should

25
obtain the program in machine readable form. Since ASET-B is in

the public domain it may be freely copied.

A sample run of the ASET-B program is shown in appendix C.

Although the program cannot be thoroughly tested by comparing the

output of a single run, this example has been selected to

exercise most of the computer program. Results from a copy of the

program which do not compare exactly with this sample output

probably indicate the program is in error.

The output of the ASET-B program will not agree exactly with

the output of the ASET program. This results from the difference

in the mathematical procedures used. Also, the ASET program

listed in C23 contains an error which causes the calculated

temperatures to be approximately one percent too high.

2 ASET-B was written for Microsoft interpreted and complied

3 BASIC and has run successfully on IBM and compatible personal

2 computers operating under MS-DOS . ASET-B has not yet been tested

on other personal computers, but it should run with no

difficulties

.

Microsoft and MS are trademarks of Microsoft Corporation and

do not represent an endorsement by the National Bureau of

Standards

IBM is a trademark of International Business Machines

Corporation and does not represent an endorsement by the

National Bureau of Standards

26
8. ACKNOWLEDGEMENTS

Appreciation is extended to Dr. Leonard Cooper and Mr. David

Stroup for their assistance in preparing this report.

9. REFERENCES

[13 Cooper

,

L.Y

Fires Nat. Bur

72 p.

[23 Cooper

,

L.Y

(ASET) - A Computer

(U.S.) NBSIR 82-2578

Estimating Safe Available Egress Time from

Stand. (U.S.) NBSIR 80-2172; 1981 February.

Stroup, D.W. Calculating Safe Egress Time

Program and User's Guide. Net. Bur. Stand.

; 1982 September. 137 p. also to appear in

Fire Safety Jour.

[33 Cooper, L.Y. A Mathematical Model for Estimating Available

Safe Egress Time in Fires. Fire Mater. 6(3/4 )

%

135-144; 1982

September/December

.

[43 Carhanan, B.; Luther, H.A.; Wilkes, J.O. Applied Numerical

Methods. New York; John Wiley & Sons; 1969. 604 p.

[53 Lawson, J.R.; Walton, W.D.; and Twilley, W.H. Fire

Performance of Furnishings As Measured in the NBS Furniture

Calorimeter. Part 1. Nat. Bur. Stand. (U.S.) NBSIR 83-2787; 1983

August. 133 p.

C63 Standard on Automatic Fire Detectors 72E. Boston; Nat. Fire

Prot. Assn.; 1984.

[73 Guide for Smoke and Heat Venting 204M. Boston; Nat. Fire

Prot. Assn.; 1982.

[83 Quintiere J.G.; Baum H.R.; Lawson J.R. Fire Growth In Combat

Ships. Nat. Bur. Stand. (U.S.) NBSIR; To be published.

C93 Cooper L.Y. A Concept for Estimating Available Safe Egress

Time in Fires. Fire Safety Jour. 5(2); 135-144; 1983.

27
28

Figure

1.

Schematic

of

fire

phenomena
APF A: ASET-B PROGRAM LISTING

10 PRINT" ASET-B VERSIO WRITTEN BY W. D. WALTON 1985"

20 PRINT "CONTRIBUTION OPTIONAL BUREAU OF STANDARDS ( U. S. ) . " 30 PRINT" NOT SUBJECT TClGHT. " 40 DIM TQ( 100) , Q( 100)

50 INPUT” ENTER RUN TITLES

60 LR = . 35

70 INPUT" HEAT LOSS FRA(LC

80 I NPUT" FIRE HEIGHT ( l 90 INPUT" ROOM CEILING ]( ft) H 100 I NPUT" ROOM FLOOR A) f t) A 110 FM=F*. 3048

1 20 HM=H*. 3048

1 30 AM=A A . 0929

140 INPUT"MAXIMUM TIME'; TL

150 Q0=. 1 160 PRINT” INPUT FIRE T*D HEAT RELEASE RATES (use -9,-9 to end input)"

170 FOR N=1 TO 100

180 INPUT"TIME (sec), 2LEASE RATE ( kW) TQ( N) , QX

190 IF TQ( N) < 0 GOTO

200 IF QX < QO THEN Q(

210 Q( N) =QI/QO

220 NEXT N 230 PRINT"MAXIMUM OF 1UT ?ALUES REACHED"

240 NQ=N-1

250 IF TQ( 1) <. 1 THEN D

260 PA=530!

270 DA = . 0735

280 CP = . 24

290 Cl =( 1 ! -LC) *Q0/( DA*A*1. 054)

300 C2=. 21 / A A ( ( 1! -LR) V( DA*CP*PA A 1. 054) ) '( 1! / 35 ) 31 0 DQO = ( Q( 1) — 1! ) /TQ( 1 320 ZO=H-F

330 Z1=Z0

340 DZ1 =-C1 -C2 A Z0 '( 5! - 350 PI =1 ! +C1 /C2*Z0~( -* 360 DPI =C1 /C2 A ( 2! A DQ0'+C2*Z0 '( 5! / 3! ) ) > /( 6! A Z0^( 8! /3! ) ) 370 T1 =0!

380 T2 = 0! 390 DT-1

!

400 QT=1

410 01 = 5! 420 0T = 0! 430 PRINT" " 440 PRINT" ASET-B VER 0"

450 PRINT TITLES

460 PRINT"HEAT LOSS FN="; LC

470 PRINT"FIRE HEIGHTTt ";FM;"m"

480 PRINT" ROOM HEIGHTTt " ; H M ; " m

490 PRINT" ROOM AREA = " ft ";AM;"sq m" 500 PRINT" " 510 PRINT" TIME ? TEMP LAYER LAYER FIRE

520 PRINT" sec F C ft m kH BTU/s

530 GOSUB 970

29
540 T1=T2

550 T2=T1+DT

560 IF T2> TL THEN PRINT"RUN COMPLETE": GOTO 870

570 IF T2> TQ( NQ) THEN PRINT" END OF INPUT FIRE": GOTO 870

580 GOSUB 880

590 Z2=Z1+DZ1*DT

600 P2=P1 +DP1 A DT

610 I ER=0

620 IF Z2< =0! GOTO 670

630 K=C2 A QT ~( 1! / 3! ) A Z2~( 5! /3! ) 640 DZ2=-C1 A QT-K

650 DP2=P2A ( Cl A QT-( P2-1! ) A K) /( Z0-Z2)

660 GOTO 720

670 DP2=( P2 A C1 A QT) /( Z0-Z2)

680 IF Z2< =~F GOTO 710

690 DZ2=-C1 A QT

700 GOTO 720

710 DZ2 = 0! 720 Z2C = Z1 +( DZ1 +DZ2) /2! A DT

730 P2C = P1 +( DPI +DP2) /2! A DT

740 IF Z2C< -F THEN Z2 = -F: Z2C=-F

750 IF ABS( Z2C-Z2) <. 001 AND ABS( P2C-P2) < . 001 GOTO 810

760 TF IER> 30 THEN PRINT" HARNING! SOLUTION DID NOT CONVERGE": GOTO 310

770 7T- 7 7 r 730 P 2 = P 2 C

?<>0 IER-IER<-1

;j 0 u GOTO 620

310 Z 1 -- Z 2 C 320 P1-P2C

330 DZ 1 =DZ2

340 DPI =DP2

350 GOSUB 970

860 GOTO 540

370 END

380 IF T2> TQ( 1) GOTO 910

890 QT=Q( 1 ) -( ( Q( 1 ) -1 ! ) /TQ( 1 ) ) A < TQ( 1 ) -T2)

900 RETURN

910 FOR N=1 TO NQ

920 IF T2> TQ( N) GOTO 950

930 QT=Q( N) -( ( Q( N) -Q( N-1 ) ) /( TQ( N) -TQ( N~1 ) ) ) A ( TQ( N) -T2)

940 RETURN

950 NEXT N 960 RETURN

970 IF T2< OT THEN RETURN

980 OT=OT +01

990 QK=QTA QO

1000 QB=QKA . 9485

1010 PF=( PI A PA) -460!

1020 PC=( PF-32! ) / I. 8 1030 RRF = DP1 A 31 800!

1040 RRC=RRF/1 .

3

1050 X=Z 1 +F

1060 XM = X

A . 3048

1070 PRINT USING"#**###.# "; T2; PF; PC: X; XM; QK; QB

1080 RETURN

30
APPENDIX B: VARIABLE NAMES USED IN ASET-B

Quantities without unite are dimensionless

2

A area of room (ft ) 2 AM area of room (ft )

Cl dimensionless group 1

C2 dimensionless group 2

CP specific heat of air (BTU/lb ,G

F)

DA density of air (lb/ft^)

DPI derivative of upper layer temperature with respect to

time at the present time step

DP2 derivative of upper layer temperature with respect to

time at the next time step

DQO derivative of the rate of heat release with respect to

time at the initial time

DT time step

DZ1 derivative of height of upper layer above fire with

respect to time at present time step

DZ2 derivative of height of upper layer above fire with

respect to time at next time step

F height of base of fir© (ft)

FM height of base of fir© (m>

H height of room (ft)

HP! height of room (m)

XER counts number of predictions-correct ions

K intermediate value used in evaluating derivatives

LC fraction of heat release lost to contents and surroundings

LR fraction of heat release radiated from fire

N counts number of input rates of heat release

NQ number of input rates of heat release

01 output time interval (s)

31
OT

PI

P2

P2C

PA

PC

PF

Q

GO

QB

01

OK

QT

RRC

RRF

T1

T2

TITLES

TL

TO

X

XM

20

21

22

22C

time for next output <s)

temperature of upper layer at pre.ent time etep

predicted temperature of upper layer at next time etep

corrected temperature of upper layer at next time step

ambient temperature <°R)

temperature of upper layer <°C)

temperature of upper layer <°F)

rate of heat release specified at time TO

rate of heat release at initial time step <kW>

rate of heat release at next time step <BTU/s)

rate of heat release specified at time TO CkW)

rate of heat release at next time step <kW>

rate of heat release at next time step

rate of rise of temperature in upper layer <°C/minJ

rat© of rise of temperature in upper layer <°F/min)

present time step

next time step

run title

limit of simulation time («)

time for specified rate of heat release 0 (*)

height ©f interface above floor <ft>

height of interface above floor (m)

height of interface above fir© at initial time step

height of interface above fire at present time step

predicted height of interface above fire at next time step

corrected height of interface above fire at next time step

32
Variable names used in report but not in program

CL characteristic length (1 ft)

CT characteristic time (1 8)

P temperature of upper layer

2 height of interface above the fire

Note: The symbol 0 is the number zero and the symbol 0 is the

letter 0

33
APPENDIX C SAMPLE RUN OF ASET-B PROGRAM

ASET-B VERSION 1.0 WRITTEN BY W.D. WALTON 19B5

CONTRIBUTION OF THE NATIONAL BUREAU OF STANDARDS (U.S.).

NOT SUBJECT TO COPYRIGHT.

ENTER RUN TITLE? SAMPLE RUN OF ASET-B

HEAT LOSS FRACTION? .8

FIRE HEIGHT (ft)? 1

ROOM CEILING HEIGHT (ft)? 9

ROOM FLOOR AREA (sq ft)? 225

MAXIMUM TIME (sec)? 180

INPUT FIRE TIMES AND HEAT RELEASE RATES (us® -9,-9 to end input)

TIME (sec), HEAT RELEASE RATE (kW)? 20,40

TIME (sec), HEAT RELEASE RATE (kW)? 100,200

TIME (sec), HEAT RELEASE RATE (kW)? 180,500

TIME (sec), HEAT RELEASE RATE (kW)? -9,-9

ASET-B VERSION 1.0

SAMPLE RUN OF ASET-B

HEAT LOSS FRACTION® .8

FIRE HEIGHT® 1 ft .3048 m

ROOM HEIGHT® 9 ft 2.7432 m

ROOM AREA® 225 sq ft 20.9025 sq m

TIME TEMP TEMP LAYER LAYER FIRE FIRE

sec F C ft m kW BTU/s

0.0 70.3 21.3 9.0 2.7 0.1 0.1

5.0 74.2 23.4 8.7 2.7 10.1 9.6

10.0 76.7 24.9 8.3 2.5 20.0 19.0

15.0 79.3 26.3 7.8 2.4 30.0 28.5

20.0 81.8 27.7 7.3 2.2 40.0 37.9

25.0 84.6 29.2 6.9 2.1 50.0 47.4

30.0 87.5 30.8 6.5 2.0 60.0 56.9

35.0 90.6 32.6 6.0 1.8 70.0 66.4

40.0 93.9 34.4 5.7 1.7 80.0 75.9

45.0 97.5 36.4 5.3 1.6 90.0 85.4

50.0 101.4 38.6 5.0 1.5 100.0 94.9

55.0 105.6 40.9 4.7 1.4 110.0 104.3

60.0 110.0 43.3 4.4 1.3 120.0 113.8

65.0 114.7 46.0 4.1 1.2 130.0 123.3

70.0 119.8 48.8 3.9 1.2 140.0 132.8

75.0 125.2 51.8 3.6 1.1 150.0 142.3

80.0 130.9 55.0 3.4 1.0 160.0 151.8

85.0 137.0 58.3 3.2 laO 170.0 161.2

90.0 143.5 61.9 3.0 0.9 180.0 170.7

95.0 150.4 65.8 2.8 0.9 190.0 180.2

100.0 157.6 69.8 2.6 0.8 200.0 189.7

105.0 165.5 74.2 2.5 0.8 218.8 207.5

110.0 174.2 79.0 2.3 0.7 237.5 225.3

115.0 183.7 84.3 2.1 0.7 256.3 243.1

120.0 194.0 90.0 2.0 0.6 275.0 260.8

125.0 205.1 96.2 1.8 0.6 293.8 278.6

130.0 217.2 102.9 1.7 0.5 312.5 296.4

135.0 230.1 110.1 1.5 0.5 331.3 314.2

34
140.0 243.9 117.7

145.0 258.7 125.9

150.0 274.3 134.6

155.0 290.7 143.7

160.0 307.9 153.3

165.0 325.9 163.3

170.0 344.6 173.7

175.0 364.2 184.5

160.0 384.7 195.9

RUN COMPLETE

1.3 0.4 350.0 332.0

1.2 0.4 368.8 349.8

1.0 0.3 387.5 367.5

0.8 0.2 406.3 385.3

0.6 0.2 425.0 403.1

0.4 0.1 443.8 420.9

0.2 0.1 462.5 438.7

0o0 0.0 481.3 456.5

0.0 0.0 500.0 474.3

Note: The input heat release rate wei selected to exercise

various sections o£ the pregre* and dees not necessarily

represent an actual fire*

35
NBS-1 1 4 A REV. 2-8C! U.S. OEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. Publication Date

NBSIR 85-3144 April 1985

4. TITLE AND SUBTITLE

ASET-B A Room Fire Program for Personal Computers

5. AUTHOR(S)

William D. Walton

6. PERFORMING ORGANIZATION (If joint or other than NBS. see in struction s)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8 . Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

National Park Service Dept, of Health & Human Services

Washington, D.C. and Washington, D.C.

10. SUPPLEMENTARY NOTES

| | Document describes a computer program; SF-185, rlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a si gnificant

bibliography or literature survey, mention it here)

ASET-B, a personal computer program for predicting the fire environment in a single

room, is presented. ASET-B solves the same differential equations as the previously

developed computer program, ASET (Available Safe Egress Time) , using a simpler

numerical technique. ASET-B requires as input the height and area of the room, the

elevation of the fire above the floor, a heat loss factor, and a fire specified in

terms of heat release rate. The program predicts the thickness and the temperature

of the hot smoke layer as a function of time. ASET-B is written in BASIC and is

not subject to copyright. This paper describes the program and its use. Included

are a listing of the program, program variable name listing and a sample run. A

discussion of user modifications also is given.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

compartment fires; computer programs; evacuation; fire growth; manuals;

mathematical models; room fires; smoke

13. AVAILA8ILITY

iY~! Unl imited

|

i For Official Distribution. Do Not Release to NTIS

I

I Order From SuDerintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

[^2 Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

40

15. Price

<£S. 50

USCOMM-OC 8043 -P 90

)

JI

]

I

H