Reference

PUBLICATIONS

NBSIR 85-31

Methods to Calculate the

Response Time of Heat and

Smoke Detectors Installed Below

Large Unobstructed Ceilings

NAT'L INST. OF STAND & TECH

AlllDb 034^34

67

David D. Evans

David W. Stroup

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Gaithersburg, MD 20899

February 1985

issued July 1 985

~-QC100

• 1156

Prepared for the Sponsor:

I.S. Nuclear Regulatory Commission

Washington, DC 20555

85-3167

1985

national bureau

OF STANDARDS

I ’"NARY

NBSIR 85-3167

\ • * METHODS TO CALCULATE THE

RESPONSE TIME OF HEAT AND

SMOKE DETECTORS INSTALLED BELOW

LARGE UNOBSTRUCTED CEILINGS

David D. Evans

David W. Stroup

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Gaithersburg, MD 20899

February 1985

Issued July 1985

Prepared for the Sponsor:

U.S. Nuclear Regulatory Commission

Washington, DC 20555

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director

TABLE OF CONTENTS

Page

Abstract 1

1.0 Introduction 1

2 2.0 Detector Response to t - Fires 4

3.0 Detector Response to Arbitrary Fires 9

4.0 Smoke Detector Response 11

5.0 Summary 15

6.0 Acknowledgement 15

7.0 References 15

8.0 Notation 17

Appendix A - DETACT - T2 CODE 19

1) Example Calculation

2) Program Listing

Appendix B - DETACT - QS CODE 32

1) Example Calculation

2) Program Listing

i
1 /

-..f .
METHODS TO CALCULATE THE RESPONSE TIME OF HEAT AND SMOKE

DETECTORS INSTALLED BELOW LARGE UNOBSTRUCTED CEILINGS

Abstract

Recently developed methods to calculate the time required for ceiling

mounted heat and smoke detectors to respond to growing fires are reviewed. A

computer program that calculates activation times for both fixed temperature

and rate of rise heat detectors in response to fires that increase in heat

release rate proportionally with the square of time from ignition is given.

This program produces nearly equivalent results to the tables published in

Appendix C, Guide for Automatic Fire Detector Spacing, (NFPA 72E, 1984). A

separate method and corresponding program are provided to calculate response

time for fires having arbitrary heat release rate histories. This method is

based on quasi-steady ceiling layer gas flow assumptions. Assuming a constant

proportionality between smoke and heat released from burning materials, a

method is described to calculate smoke detector response time, modeling the

smoke detector as a low temperature heat detector in either of the two

response time models.

1. INTRODUCTION

Studies of the response of heat detectors to fire driven flows under

unconfined ceilings have been conducted since the early 1970's [1, 2, 3, 4],

Results of these largely experimental studies have been used to develop correlations of data that are useful under a broad range of fire conditions and

building geometries. These correlations have been used to construct engineering methods to determine heat detector spacing, sprinkler response time, ml

smoke detector alarm times for industrial buildings where large undivided

1
ceilings over storage and manufacturing facilities are common. The method for

calculation of heat detector spacing has been adopted by the National Fire

Protection Association (NFPA) as an alternate design method published in the

standard NFPA 72E, 1984 [5].

Although the NFPA heat detector spacing calculation is a well documented

method, it is not in a convenient form for use by the Nuclear Regulatory

Commission (NRC) in evaluating the response characteristics of existing

systems for two reasons. 1) Currently, the only available form of the information is the tabular form published in the NFPA 72E standard. An analytic

form or computer subroutine that produced equivalent answers would be more

flexible and of greater use to NRC. 2) The published tables are organized to

look-up spacing requirements for a given response time. In the evaluation of

existing systems, the opposite problem is of interest - for a given spacing

and detector determine the response time.

As part of this study, the basis for the calculation method published in

Appendix C of the NFPA 72E standard was determined. Alternative correlations

of the same experimental data that are the basis for the tables in Appendix C

of the NFPA 72E standard were used to construct a FORTRAN program (DETACT-T2

Code) to evaluate the response time of existing heat detector systems. Using

the program, calculated values for response time agree to within 5 percent of

those published in the tables contained in Appendix C of the NFPA 72E

standard. Although this calculation method is the most firmly based of those

to be discussed in this report, it is restricted to application in which the

fire to be detected increases in energy release rate proportionally with the

square of time from the ignition.

2
separate program (DETACT-QS Code), written in PC BASIC, is capable of

evaluating detector response for a fire with an arbitrary energy release rate

history. The only restriction is that the energy release rate must be represented as a series of connected straight lines, the end points of which are

entered as user input data. Inaccuracies may be introduced in the analysis of

rapidly varying fires because this code uses a quasi-steady approximation for

the fire driven gas flow. This means that changes at the fire source

immediately affect the gas flows at all distances from the fire. In reality,

time is required for the gases to travel from the fire to remote locations.

Generally, fire driven flows have a velocity the order of one meter per

second. Thus a quasi-steady analysis for locations close to the fire will

only be in error by a few seconds, while remote locations can be delayed by

tens of seconds. Keeping this approximation in mind, this program represents

the most flexible of available methods but has not been tested against experimental data.

Both of the codes discussed above analyze detector response at

installation sites under large unconfined ceilings. For smaller compartments,

in which confining walls will cause a layer of fire products to accumulate

under the ceiling, hence submerging the ceiling-jet flow before the heat

detector can respond, different calculations are necessary. The problem of

analyzing the response of heat detectors or sprinklers in a two-layer

environment (warm fire products over cool air) has been studied [6], but no

single code has been produced to facilitate analysis. This class of problem

will not be discussed in this report.

3
Analysis of smoke detector response is currently performed by

approximating the smoke detector as a low-temperature zero-lag-time heat

detector. Selection of the response temperature corresponding to a given

detector sensitivity also depends on the relative proportion of "smoke" and

energy released by the burning fuel. Test data of gas temperature rise at the

time of smoke detector alarm is presented in this report. An alternative

approximate method is given to determine this same temperature rise by using

fuel smoke and energy release rate measurements obtained in a laboratory scale

apparatus developed by Tewarson [7].

2. DETECTOR RESPONSE TO t

2 - FIRES

Appendix C of the NFPA 72E standard [5], "Guide for Automatic Fire

Detector Spacing," contains methods to determine the required heat detector

spacing that will provide alarms to growing fires before the fire has grown to

a user specified energy release rate. Tables provide information to evaluate

different fire growth rates, ceiling heights, ambient temperatures, detector

alarm conditions (fixed temperature or rate of rise), and detector thermal

time constant. The tables reflect the extensive experimental studies and

mathematical fire modeling performed by Heskestad and Delichatsios at Factory

Mutual Research Corporation [3, 4].

Beyler [8] uses a different correlation of Heskestad and Delichatsios*

data than was used to produce the tables in NFPA 72E Appendix C to obtain an

analytical expression for the gas flow temperature and velocity produced under

ceilings that can be used to evaluate heat detector response. Beyler's solutions are limited to evaluation of fires that increase in energy release rate

4
proportionally with the square of time from ignition. This class of fire is

commonly referred to as a "t-squared-f ire. " Briefly, the problem of the heat

detector response is solved using analytic solutions for the time dependent

temperature of the detector sensing element up to the point when it is heated

to the specified alarm conditions. The model for the detector sensing element

temperature is based on a convective heat transfer process. Characterization

of the thermal response of heat detector and sprinkler thermal sensing

elements is discussed by Heskestad and Smith [9], and Evans [10]. The first

order differential equation that describes the rate of temperature increase of

the sensing element is [6]:

dT

s dt

, 1/2

RTI

( 1 )

The notation for all equations is given in the notation section. The value of

RTI (Response Time Index), a measure of the thermal time constant of the

detector, is determined by testing [9]. Values of the time-dependent gas

temperature and velocity are obtained from the following correlations [8].

* AT

2 = 0 for t* < (t*)

f

AT* = {[t* - 0.954(1 + r/H)] / [0. 188 + 0.313 r/H]} 4/3 for t* > (t*)

f

(t

2 ) f = 0.954 [1 + r/H] ( 2 )

* -0.63 * 1/2

U

2 = 0.59 [r/H]

U * bJ

[AT2 ] 1/Z

where

5
U

2 = U/[A Ct H]

1/5

AT* = AT/[A2/5

(T

a) /g) a 2/5

H~

3/5

]

* _ wrA_1/5 '1/5 h4/5 1 t 2 = t/[A a H i

A = g/(c T p ) P

00 00

AT = T - T

a = t /Q

The solutions to equation (1) for detector sensing element temperature, T_,

and rate of temperatue rise, dT

g

/dt, in response to the t^ - fire with growth

rate specified by the value of a are from Beyler [8] as follows:

AT

g = (AT/AT*) AT* [1 - (1 - e Y

)/Y] (3)

dT

s (4/3)(4T/4T*)( 4T*) 1/'‘

dt ” *

(^ “ e ) ^ ^ (t/t

2 )(0.188 + 0.313 r/H)

where

1/2 4T^

RTI (0.188 + 0.313 r/H)

assuming that AT

g = 0 initially. T and U in equation 1 are obtained from the

correlations in equation set (2) for AT

2 and U2 respectively. Equations 3 and

4 were programmed into a user interactive FORTRAN code called the DETACT-T2

6
Code. This code solves for the time required to reach a specified positive

value of AT or dT /dt representing detector alarm. Details of the DETACT-T2

s s Code use, a worked example, and program listing are given in Appendix A.

Briefly for a fixed temperature detector, the user enters values for:

Ambient air temperature

Detector response temperature or rate of temperature rise

Detector RTI

Fuel to ceiling distance

Radial distance of detector from the fire plume axis

Fire growth rate constant a (for t^ fires)

Outputs of the code are the time to detector response and fire energy

release rate at that time.

In Appendix A, use of the DETACT-T2 Code to calculate the response time

of a fixed temperature detector is demonstrated in a worked example using the

following program inputs:

Ambient air temperature 21.1°C (70°F)

Detector response temperature 54.44°C (130°F)

Detector RTI

Fuel to ceiling distance 3.66 m (12 ft.)

Radial distance of detector from

axis of fire 2. 16 m (7.07 ft.

)

11.71 J/s 3 (0.0111 BTU/s 3 Fire growth rate constant )

7
The calculated response time using the DETACT-T2 Code is 298 seconds and

corresponding fire energy release rate is 1.04 MW (986 BTU/s). This same fire

and detector combination can be seen in the table C-3-2. 1.1(e) in Appendix C

of NFPA 72E [5], (in the table notation, threshold fire size 1000 BTU/s, fire

growth rate, medium; DET TC = 300 As, AT = 60°F, ceiling height = 12 Aft,

installed spacing in the body of the table 10ft). All values in table C-3-

2.1.2(e) [5] are for detector response times of 300 seconds. This is in

agreement with the 298 s calculated with the DETACT-T2 Code given in Appendix

A of this report.

Eleven other randomly selected combinations of fires and detectors were

calculated using the DETACT-T2 Code and results compared to table values in

Appendix C of NFPA 72E [5]. Of these cases the greatest deviation was 7.5%

and least was 0.17%.

Use of the DETACT-T2 Code has two main advantages over the tables in

Appendix C of NFPA 72E [5]. One is that the code is specifically designed to

evaluate existing facilities. The other is that any t - fire growth rate can

be analyzed. The tables in Appendix C of NFPA 72E [5] contain only three

different fires. At present, an NBS special publication is being prepared

containing tabular results with the same information as those in the NFPA 72E,

Appendix C [5], but recast into a form useful for evaluation of existing

facilities. This publication "Evaluating Thermal Fire Detection Systems," by

Stroup, Evans, and Martin should become available in 1986.

8
3. DETECTOR RESPONSE TO ARBITRARY FIRES

The DETACT-T2 Code is useful for evaluating the response of specified

detectors to t 2 - fire growth rates. In some cases a fire of interest does

not follow an energy release rate that is proportional to the square of time

from ignition. For these cases use of the DETACT-T2 Code to evaluate the

responses of detector systems is inappropriate.

To evaluate detector response to an arbitrary energy release rate

history, an assumption of quasi-steady gas flow temperatures and velocities is

made. With this assumption, correlation for ceiling-jet temperatures and

velocities obtained from experiments using steady fire energy release rate

sources can be used to evaluate growing fires. The growing fire is represented in the calculation as a series of steady fires with energy release

rates changing in time to correspond to the fire of interest.

Correlations of ceiling-jet temperatures and velocities from experiments

using steady fire sources have been published by Alpert [1]. Recast into

metric form they are:

for r/H < 0.18

U = 0.95 (Q/H) 1/3 for r/H < 0.15 (5)

for r/H > 0.18

U = 0.2 Q

1/3

H

1/2

/ r 5/6 for r/H > 0. 1

5

9
where the metric units are T[°C], U[m/s], Q[kW], r[m], H[m].

A computer code to perform the integration of equation 1, the

differential equation for detector sensor temperature, using the quasi-steady

fire driven flow approximation and Alpert's correlations from equations in 5,

is listed in Appendix B. This code, called the DETACT-QS Code, is written in

PC BASIC. The code requires user input similiar to the DETACT-T2 Code in

Appendix A, with the one exception that the fire energy release rate is specified as a series of time, energy release rate data pairs.

The same fire and detector case used as an example of execution for the

DETACT-T2 Code was evaluated using the DETACT-QS Code. The example inputs and

results are given in Appendix B. The fire was input as time, energy release

o rate pairs at intervals of 5 seconds to match the t - fire with a = 11.7105

W/s . Other parameters were maintained the same. The resulting predicted

detection time using the DETACT-QS Code was 313 seconds with the corresponding

fire energy release rate at detection of 1147 kW. Remember that with the

DETACT-T2 Code the calculated time of detection was 298 seconds with fire

energy release rate at detection of 1040 kW. This example was chosen to

demonstrate specifically that there will be differences between the two

methods even in the evaluation of the same fire. The quasi-steady fire

analysis on which the DETACT-QS Code is based has the advantage that arbitrary

fire energy release rates can be input as a data set.

10
4. SMOKE DETECTOR RESPONSE

Both of the heat detector response models discussed are based on

predictions of the temperature and velocity of the fire driven gas flow under

the ceiling and models of the heat detector response. The same calculations

could be used to predict smoke detector response given a relationship between

smoke concentration and temperature rise in the fire driven gas flow and the

response characteristics of the smoke detector.

The response characteristics of smoke detectors are not as well

understood as thermal detectors. Smoke detector alarm conditions depend on

more than smoke concentration. Smoke particle sizes and optical or particle

scattering properties can affect the value of smoke concentration necessary to

reach alarm conditions. For thermal detectors, measured values of RTI

characterize the lag time between gas temperature and sensing element temperature. For smoke detectors there is no analogous method to characterize the

lag time between gas flow smoke concentration and the smoke concentration

within the sensing chamber. In the absence of understanding of the many

processes affecting smoke detector response, a smoke detector will be considered to

be a low temperature heat detector with no thermal lag, i.e. RTI = 0. The

analogy between smoke obscuration in the gas flow and temperature rise will be

developed in order to determine the corresponding temperature rise to use as a

model for a smoke detector known to alarm at a given smoke obscuration.

Similarity between temperature rise and smoke concentration will be

maintained everywhere within a fire-driven flow if the energy and smoke

continuity equations are similar. For the case of constant c

p

, k, and I) thosr

equations are:

11
: - k V

2 AT = O"

' p dt ( 6 )

2 - p D V Y

s m

t » ? ( 7 )

If the Lewis number k/pc^D = 1, then the ratio of temperature rise to

smoke concentration can remain constant throughout the fire driven flow, if

exchanged with the flow. Reactions in the flame over the burning fuel will

determine the ratio of temperature rise to smoke concentration throughout the

flow. Other energy exchanges in normal fire flows, convection to cool room

boundaries, and radiation from smokey gases decrease the ratio of temperature

rise to smoke concentration because energy is extracted from the flow without

a proportional decrease in smoke concentration. Mixing of hot combustion

products with cool smokey gases that may accumulate in an enclosure also

decrease the ratio of temperature rise to smoke concentration because smoke

mass is added to the flow without a proportional increase in energy. For fire

driven flows in which the effects that alter the ratio of temperature rise to

smoke concentration are not significant, the response of smoke detectors may

be calculated as if it were a fixed temperature heat detector. The temperature rise necessary for alarm of this substitute heat detector is calculated

from the product of smoke concentration needed to alarm the smoke detector and

the ratio of temperature rise to smoke concentration produced by the burning

material.

Generally the sensitivity of smoke alarms are given in terms of the

amount of obscuration by the smokey flow that is necessary to produce an alarm

and not directly in smoke concentration. The more sensitive the smoke

detector the smaller the amount of obscuration needed to alarm.

12
The obscuring ability of a smoke laden gas flow is measured by the

attenuation of a light beam. The measure of the attenuation is the optical

density per unit beam length, OD, [3]

OD = (log

1Q “|)/L (8)

By testing, Seader and Einhorn [11] found that the attenuating abilities of

smokes produced from many different materials undergoing flaming combustion

were similar. For flaming combustion they found that the optical density per

unit length was proportional to the mass concentration of "smoke" in a gas

flow as:

OD = 3330 C

s (9)

where OD is optical density per meter and C

g

is smoke mass concentration in

kilograms per cubic meter.

The ratio of temperature rise in a fire driven flow to smoke

concentration may be recast in terms of optical density using equation 9 as

AT = pAT = 3330pAT

Y C OD

s s

( 10 )

Under the assumption discussed at the beginning of this section, this

. " ' .

» » ' ratio will be equal to the ratio Q ' C

pm

s

* The la8t ratio may be approximated by a volume average over the combustion region so that

3330 D AT

OD

c m

P s

13
or OP

AT

3330pc m

P

s

•Q

( 11 )

As an example, literature values for oak wood may be used to obtain a

representative value. For oak

Q

= 7600 kJ/kg fuel consumed per unit time

m = 0.017 kg smoke/kg fuel consumed per unit time

s air Cp = 1 kJ/kg °C

air p = 1.165 kg/m^ at 30°C

From equation (11) 7^7 = 8.68 x 10 ^ (m°C) *

. Ai

Heskestad and Delichatsios [3] have reported representative optical

density per meter for smoke detector alarm and corresponding temperature rise

in the gas flow. For wood crib (unknown type) fires, the ratio of these

-3

values was OD/aT = 1.2 x 10 [l/m°C]. This is the same order of magnitude as

the number calculated in the analysis given above and may be representative of

the expected accuracy given no knowledge of wood type. Heskestad and

Delichatsios [3] report that an ionization detector will alarm in response to

a wood fire at OD = 0.016 1/m.

Using the OD/aT value for wood of 1.2 x 10-^(m°C)“^ the corresponding

change in gas temperature would be 13°C, (0.016/1.2 x 10“^). For the purpose

of response time calculation using the heat detector models, this ionization

smoke detector would be represented as a low temperature heat detector

alarming at 13°C above ambient for a wood fire.

[ 12 ]

[ 12 ]

14
Other measurements of the ratio OD/aT are obtained for burning materials

in a laboratory scale apparatus developed by Tewarson [7]. Values for a large

number of plastics and wood under many environmental conditions are given by

Tewarson [12].

5.

SUMMARY

Two methods have been presented to calculate the response of heat

detectors installed under large unobstructed ceilings in response to growing

fires. Smoke detector response is calculated using the same thermal calculations by approximating the smoke detector as a low temperature, zero lag time

thermal detector.

6.

ACKNOWLEDGMENT

The authors are grateful to Mr. Doug Walton for coding DETACT-QS version

1.1 for exection in PC BASIC.

7.

REFERENCES

1. Alpert, R. L. , Calculation of response time of ceiling-mounted fire

detectors. Fire Technology , 8, 1972, p 181.

2. Alpert, R.L. , TXirbulent ceiling-jet induced by large-scale fires,

Combustion Science and Technology , 11, 1975, p 197.

3. Heskestad, G. and Delichatsios , M. A. , Environments of fire detectors

phase 1; Effects of fire size, ceiling height and material, Volume II - Analysis. Technical Report Serial No. 22427, RC 77-T-ll, Factory Mutual

Research Corporation, Norwood Massachusetts 02062, 1977.

4. Heskestad, 6, and Delichatsios, M. A. , The initial convective flow in

fire, Seventeenth Symposium (International) on Combustion , The Combustion

Institute, Pittsburgh, Pennsylvania, 1978, pp 1113-1123.

15
5. Standard on Automatic Fire Detectors, NFPA 72E-1984, Appendix C, National

Fire Protection Association, Batterymarch Park, Quincy, MA, 02269.

6. Evans, D.D. , Calculating Sprinkler Actuation Time in Compartment, to be

published in Fire Safety Journal, 1985.

7. Tewarson, A., and Pion, R. , "A Laboratory-Scale Test Method for the

Measurement of Flammability Parameters, FMRC serial No. 22524, Factory

Mutual Research Corporation, Norwood, Mass. 02062, Oct 1977.

8. Beyler, C.L. , A design method for flaming fire detection, Fire Technology,

20, 4, 1984, p 5.

9. Heskestad, G. , Smith, H. , Investigation of a New Sprinkler Sensitivity

Approval Test: The Plunge Test FMRC Technical Report 22485, Factory

Mutual Research Corporation, Norwood, Mass. 02062, 1976.

10. Evans, D. D. , Madrzykowski, D. , Characterizing the Thermal Response of

Fusible-Link Sprinklers, NBSIR 81-2329, U. S. Department of Commerce,

National Bureau of Standards, Washington, D.C. 20234, (1981).

11. Seader, J. and Einhorn, I., ’’Some Physical, Chemical, Toxicological, and

Physiological Aspects of Fire Smokes”, Sixteenth Symposium

(International) on Combustion , The Combustion Institute, Pittsburgh,

Penn. 1976, pp 1423-1445.

12. Tewarson, A. , Physico-Chemical and Combustion/Pyrolysis Properties of

Polymeric Materials. FMRC J. I. OEONG. RC, Factory Mutual Research

Corporation, Norwood, Mass 02062, Nov. 1980, p 27.

16
8. NOTATION

A

c

p

Cs

D

g

H

I

X o

L

ft”'

s OD

0

Q* ' *

r

RTI

t *

t 2

, * V ( t2 )f

T00

T

TsAT

AT.

g/( C

p

Too Poo }

specific heat capacity of ambient air

smoke mass concentration

effective Binary diffusion coefficient

acceleration of gravity

vertical distance from fuel to ceiling

light intensity

initial Light intensity

light beam length

smoke gas mass production rate per unit volume

optical density per unit length (see eq. 8)

fire energy release rate

energy release rate per unit volume.

radial distance from fire axis to the detector

response time index, the product of the detector thermal time

constant and the square root of the gas speed used in the test

to measure the time constant [9].

time

dimensionless time t/[A

dimensionless time for time delay for gas front travel.

ambient temperature

gas temperature at detector location

temperature of detector sensing elements

T - T

00 dimensionless temperature difference AT/[A^^(T^/g) a

5

)

gas speed at the detector location

dimensionless gas speed U/[A a

17
local ratio of smoke mass to total mass in flow

proportionality constant for t^- fire growth = Q/t

ambient air density
APPENDIX A - DETACT-T2 CODE

FORTRAN Program to Calculate

2 Detector Response to t - Fires

1) Example Calculation

2) Program Listing

19
APPENDIX A. DETACT-T2 CODE

A FORTRAN Program to Calculate Detector Response to X?- ~ Fires

This appendix describes the theory and use of a computer program which

determines the response of fixed temperature and rate of rise heat detectors

2 to fires with energy release rates described by the expression Q = at . The

program is designed for use in evaluating detectors installed at known

spacings.

The activation time of a given detector is a function of fire growth

rate, ceiling height, detector spacing, detector activation temperature,

ambient temperature, and detector response time index (RTI). The program

prompts the user to provide this information. These input data are converted

to a dimensionless form for use in the calculations. Equations for the

activation time of a fixed temperature detector and a rate of rise detector

are set up. The two equations are then solved using a Newton-Raphson

technique. Once the activation times are known, the lire energy release rates

at those times are calculated. Finally, the results for each detector type

are printed as well as some appropriate input data.

In the following example, input prompts from the

printed in all capital letters while user responses cir

(where possible) and proceed ed by the character ">".

computer program are

e printed in lower case

20
EXAMPLE

Calculate the activation times for fixed temperature and rate of rise

heat detectors installed, using a 3.05 meter spacing, in an area with a

ceiling height of 3.66 meters. The detectors have an RTI of 370.3 (msec)^^. The detector activation temperature is 54.4°C, and the activation

rate of rise is 8.33°C/min. Ambient temperature is 21 °C.

ENTER 1 FOR ENGLISH UNIT INPUT

2 FOR METRIC UNIT INPUT

>2

ENTER THE AMBIENT TEMPERATURE IN DEGREES C.

>21

ENTER THE DETECTOR RESPONSE TIME INDEX (RTI) IN (M-SEC)**1 /2.

>370.3

ENTER THE DETECTOR ACTIVATION TEMPERATURE IN DEGREES C.

>54.4

ENTER A DETECTOR RATE OF RISE IN DEGREES C/MIN.

>8.33

ENTER THE CEILING HEIGHT IN METERS.

>3.66

ENTER THE DETECTOR SPACING IN METERS.

>3.05

ENTER: S FOR SLOW FIRE GROWTH RATE

M FOR MEDIUM FIRE GROWTH RATE

F FOR FAST FIRE GROWTH RATE OR

0 FOR OTHER

>m

21
RESULTS:

CEILING HEIGHT = 3.66 METERS ( 12.0 FEET)

DETECTOR SPACING = 3.05 METERS ( 10.0 FEET)

DETECTOR RTI = 370.3 (M-SEC)**l/2 ( 670.8 (FT-SEC)**1 /2

)

FIRE GROWTH CONSTANT = .1171+002 WATTS/SEC**2)

(.1111-001 BTU/SEC**3)

FOR TEMPERATURE ACTUATED DETECTOR:

ACTIVATION TEMPERATURE = 54.4 DEGREES C (129.9 DEGREES F)

TIME OF ACTIVATION = 297.88 SECS

HEAT RELEASE RATE = .1038+007 WATTS (.9840+003 BTU/SEC)

FOR RATE OF RISE ACTUATED DETECTOR:

ACTIVATION RATE OF RISE = 8.33 DEGREES C/MIN

(14.99 DEGREES F/MIN)

TIME OF ACTIVATION = 182.75 SECS

HEAT RELEASE RATE = .3908+006 WATTS (.3704+003 BTU/SEC)

22
The results show that the heat detector would activate approximately 298

seconds after the fire reaches a flaming state. The heat release rate at this

time would be 1038 kilowatts. A rate of rise detector would activate at about

183 seconds with a corresponding heat release rate of 391 kilowatts.

If English units had been selected, the input requests would have called

for data in English units instead of metric units.

The program is written in ANSI 77 FORTRAN. A PC BASIC version is being

coded. Each is in a form which makes it easy to incorporate into existing

computer fire models as a subroutine.

23
****** PROGRAM DETACT-T? ******

PROGRAM DEI ACT

C

c **************** *********** *******************************************

c

C DETACT-T2 CODF

CC A FORTRAN pRGGR

m FOR CALCULATING DETFCTOR RESPONSE

C TO TIME SQUARED FIRES.

C£  4 «** **** 4 ******* ************ ************************* ****** *******

CQ****************   ** ********** **************************************

cC THIS IS A PROGRAM FOR CALCULATING ACTIVATION TI*E AND HFAT

C RELEASE RATE FOR A GIVEN DETEC1CR. iHE pROGRAw CALCULATES RESULTS

C FOR BOTH TEMPERATURE AND RATE OF RISE ACTUATED DETECIORS. T HE

C PROGRAM REGIURES DATA DFSCRIBING THE DETECTCR, ROOM, AND F IPE

C CHAR ACT ERIST ICS . CC PROGRAM WRITTEN BY P • U. STROUP 1/4/85

C FINAL REVISION 1/9/85

C

£ 4644 * 4 * 644*44444 ******************************************************

cC====> VERSION 1.0 <==================================s=s

C

C INPUT:

C J - UNITS CODE (1 OR 2 > C 1 ~ INFUT DATA IN ENGLISH UNITS

C 2 - INPUT DATA IN METRIC UMTS

C IAMB - AMBIENT TEMPERATURE

C R 1 I - DETECTOR RFSPONSF TIME INDEX

C TACT - DETECTOR ACTIVATION TEMPERATURE

C ROR - DETECTCR ACTIVATION RATE OF RISE

C HF - C EILIN G HE IGHT

C 2 F - DETE CT CR S PAC ING CM - GROWTH FACTOR CODE, CHARACTER VARIABLE (S, M, F, OR 0)

C ALPHA - FIRE GROWTH RATE FACTOR

C II fl = 0, ALPHA SHOULD CONTAIN THe GROWTH FACTORR TO BF USFD.

c

r IF M <> 0, ALPHA MAY BE SET TO ZERO.

Lc OUTPUT:

c T T IME OF ACTIVATION FOR A TEMPERATURE DETECTOR

c QD HEAT RELEASE RATE AT TIME OF ACTIVATION, T c TR T IME OF ACTIVATION FOR R A 1

OF RISE DETECTOR

c Q DR HEAT RELEASE RATE AT TIME OF ACT IV AT TONt T R

c I ERR - ERROR CODE (0 OR 1)

c 0

- SU ccrs S FUL

c 1 - UN SU CC ESS FUL

CE*************************************,***.****************************

C CHARACTER M

DATA IRTT Y, IWTT Y/5 ,6/

DATA G E ,C PE , R HO F / 3 2 . 2 t C. 2 4 t 0. 07 35 / DATA GM, C PM ,R HO M/9. P,1.CC35 , 1.1768/

I E R R= 0

24
PROGRAM DE1ACT-1? ******

WRITE (IW1T Y, 10)

10 FORMAT f' ENTER: 1 FOR ENGLISH UNIT I N F ti 1 '/ T9 , ' ? F OP METRIC UNIT I RNPUT')

READ ( I R 1 T Y ,*) J IF (J.EQ.1) THEN

WRITE (IWTTY,?0)

20 FORMAT (' ENTER THE AMBIENT TEMFERATUR6 IN DEGREES F.')

READ < IR1TY ,*) T AMB

WRITE OWTTY t 30)

30 FORMAT (' ENTFR THE DETECTOR RESPONSE TIME INDEX (R7I) IN (FT-SEC)

R**1/2.'>

READ < IRTTY ,*) RT I IF (RT I. LT. C. 000001) RTI=0. 000001

RTI R=R1I

WRITE (IWIT Y , 40 ) 40 FORMAT (' ENTER THE DETECTOR ACTIVATION TEMPERATURE IN DEGREES F

.

f )READ (IRTTY,*) TACT

WRITE (IWTTY,50)

50 FORMAT (' ENTER A DETECTOR RATE OF RISE IN DEGREES E/M IN. ^)

RFAD (IRTTY ,* ) ROR

WRITE (IWTTY.60)

60 FORMAT (' ENTER THE CEILING HEIGHT IN FEET.')

READ (IRTTY ,*) Hf

WRITE (IWTT Y,70 ) 7 C FORMAT (' ENTER THE DE1ECT0R SPACING IN FEET.')

READ (IRTTY ,*) Zf

WRITE (IWTT Y f 80 ) 80 FORMAT (' ENTER: S FOR SLOW FIRE GROWTH RATE'/

8 ' M FOR MEDIUM FIRE GROWTH RATE'/

8

' F FOR FAST FIRE GROWTH RATE OR'/

8 ' 0 FOR OTHER ')

READ ( IR T TY ,410 ) M

IF ((M.E W. ' s'). OR . CM .EG . 'S ')) ALPHA =0 .0C27777P

IF < < M.EO in'). OH . (M.E W. 'M ')) AL PH A =0 . 0 1 1 1 1 1

IF ((M.ECi.'f').OR.(M.EQ.'F')) AL PH A =Q .0^44445

IF (M.NE .'0') GO 7 C 100

WRITE (IwTTY,90)

90 FORMAT (' ENTER THE FIRE GROWTH RATE CONSTANT (ALPHA) IN PTU/SFc/S

EEC/SEC .'

)

READ (IRTTY ,*> ALP HA

TOO CONTINUE

ELSE

WRITE (IWTT Y, 11 0)

110 FORMAT (' EMFR THE AMBIENT TEMPERATURE IN DEGREES C.')

READ (IRTTY,*) TAME

WRITE Own Y , 12 0)

1 20 FORMAT (' ENTER THE DETECTOR RESPONSE TIMF INDEX (RTI) TN <»-$£()

£* 1 / 2 .' ) READ URT1Y ,*) RT I IF (RT I. LT. C. 000001 ) R1I=0. 000001

R 1 I R=RT

WRITE (IWTT Y, 130)

1 3 C FORMAT (' ENTER THE DETECTOR ACTIVATION 1FMPERA TURE IN ffU'f r C.'

R )read < irt ty ,*) t act

WRITE (IWTT Y, 14 G)

140 FORMAT (' E M pR A DETECTOR RATE OF PISE IN DEGREES C/«IN'.')

25
****** pRoGRAp DETACl-T? ******

READ (IR 1 TY ,*) ROR

WRITE (IWll Y, 15 C)

150 FORMAT (' EN1FR THE CEILING HEIGHT IN METERS.')

READ (1RTTY ,*) H

WRI TE (IWTT Y , 1 60)

160 F OR PA 7 (' EMFR THE DETECTOR SPACING IN METERS.')

READ ( IRTTY ,*) Z F WRITE (IWTT Y, 80)

READ < IRT TY ,A10 ) M IF ((M.E G

• ' s'). OR . CM.EQ.'S')) AL PH A = 2 . 9 3C5 5 55 5

6

IF ((M.EG.'ir').OR.(M.FG.'M'>> AL PH A = 1 1 . 7222 222 2 IF ((M.FG.'f ').OR.(M.EG.'F')) ALPHA =A6 . 8886889

IF (M.NE .'0') GO T C 180

WRITE (I*TTY,17C)

170 FORMAT (' ENTER THE FIRE GROWTH RATE CONSTANT (ALPHA) IN VATT/SEc'

8SEC .' ) READ (IRTTY,*) ALP M

180 CONTINUE

END IF

C

£ ************************ calculations *****************************

c R = C . 5* SORT ( ? • )* 2 F RCH=R/ HF

ROR = RO R/60

IF (J.EQ.1) THEN

1 AMB=T AMfcj+4 60 . 1AC T = 1ACT + 460.

A=GE/(CPE*T AMP* RHOE)

G = 6 E ELSE

T A MB = T A MB + 2 7 3 • T AC T = TAC T+2 73 . A=6M/ (CPK*1 AMP*RH0M*10C0«>

G=GM

END IF

T0TS2=A**(-1./5.)*ALPHA**(-1./5.)*HF**(A.Z5.)

DL10DL=A ** ( ?• /5 •)* (TAMB/G)* ALPHA** (2. /5 .)*HF** (-3 • / 5 •

)

U0US2 = A**(1 ,/5.)*ALFHA**(1. /5.)*HF**(1./5.)

DE LTD = TA CT- T A MB

IF (R0H.GT.0.3) THEN

UOD LT H = 0 . 59 *R OH * * C - 0 .6 3 ) ELSE

UCDLTH = 3.87 /(9. 115 **0.5)

ENDI F 1 S2F = 0.9 5 A* (1 . POH)

A2=(A./3.)*DLTOPL*UOUS2**(-0.5 ) *UOD L 1 H * * ( -0 .5 ) * RT 1/

8 (1 01 S2 *(0 .188 *0.313*R0H))

C = 1 .O+DELTD /A 2 CALL NWTN ( C , Y, I EP R , I W 1 T Y ) IF (IERR.EQ .1) GC TO 380

DELTS2=(4./3.)* IIOUS?** C-0.5)*U0DLTH**(-r.S)*RTl*Y/

8 < T0TS?*(0. 188+0. 313*R0H))

TS2=0.954*( 1.+R0H) *(Q. 186 +0 . 3 1 3 *ROH )*D E t T S

2 ** ( 3 ./ 4 .

TS2 = 1S2+1S2 F T=1S2*A** (- 1 • / 5 „)* ALPHA** (-1. /5 .)*HF** ( 4 • / 5 • ) OD = A LP HA * 1**1

IF (HI IR .LE .2 .0 ) RT IR = 2.0

26
PROGRAM DE1AC1-T2 ****** Dl=(4./3.)*ELTODL/(TOTS?M0.18B+D.313*RCH)>

D 2 = < 3 ./4 . )* UOUS 2**C.5*U0DLTH**0.5*(1./RTIP)*T0TS2

8 * (0.188+Q. 313* ROH)

CALL BISECT < Dl ,D2,RGR f DELT S2,I ERR ,IWTT Y)

If (IERR.EG.1) CO 10 3 80

TS2R=0.954*fl.+RCH)+(0.l68*0.3l3*RCH)*DELTS2**c3./4.)

1 S^R = 1 S?R*T S Z F TR=TS2R*A** ( - 1 • / 5 , )*ALPHA** (-1./5.)*HF**<4./5.)

QD R = A LPHA *1 P**2

C

C ****** FRIN7 OUT RESULTS * ** * * ** * *********************************** * c ROR^ROR* 6 0.

WRITE (IWnY.190)

190 FORMAT ('1 RESULTS :')

IF ( J .EQ .1) 1 HE K HF 2 = HF *C. 30 48

ZF 2=2 F *0.30 4 8

WRITE (TWIT Y,?00) HF,H F? ,7 f ,ZF 2 200 F CROAT ('0 CEILING HEIGHT = ',F6.2,' FEET (',F6.2,' METERS)'/

8 TC, “'DETECTOR SPACING = ',F6.2 1 ' FEET <',F6.2,' f» E T E R S ) ' ) RTI2 = RTI* (0 .304 8**0.5)

WHITE (IWTT Y, 21 D R1 I, RTI?

z 1 c format ("o detector rti = ',F6.i,' < ft-sec ) **t /

i',f6.i,' ( v -s

»FC >** 1/?)")

ALEHA2 = AlPHA *10 5 5.

WRITE (IWTT Y , ?2 C ) ALP H A , AL PH A?

220 FORMAT ('0 FIRE GROWTH CONSTANT = ',E1?.4,' P T U / < S E C * * 3 ) '/

8

' (',El?.4,' WATTS/Srf**2 >')

WRITE (IW TTY ,400)

READ (IRTTY ,4 10) * WRITE (IWTT Y, 23 0)

230 FORMAT </'0 FOR TEMPERATURE ACTUATED DETECTOR:')

TACT=TACT-46u.

TACT2=(5./9 .) *(T ACT -3? .)

WRITE ( I w T T Y , 2 4 0 ) TACT.TACT?

24 0 FORMAT ('0 ACTIVATION TEMPERATURE = ',F6.1,' DEGREES F ( f6.1 ,

f: ' DEGRFES O')

WRITE ( I W T T Y , ? 5 0 ) T 250 FORMAT C'O TIRE TO ACTIVATION = SECONDS')

QD 2 = UD *1 C 55 . WRITE (IWTT Y, 26 0) QO,Q D2

260 FORMAT t'C Heat RELEASE RATE = ',E12.4,' BTU/SFC'/

E

' (',E 12. 4, 'WAITS)')

WRITE <IwTTY,40r>

RFAD (IPTTy, 410) f* WRITE ( IWTT Y , 27 p)

270 FORMAT <//'0 FOR RATE OF RISE ACTUATED DETECTOR:')

ROR 2= R 0 P * (5 . / 9 . ) WRITE <IWTTY,?9p) ROR,ROR2

29 0 FORMAT f'O ACTIVATION RATE CF RISE = ',F6.?,' r E f R F F S F /•'IK ( '

. 8 F 6 • 2 , ' DEGREES C / M I N ) ' ) WRITE ( U T T Y , 2 5 0 ) TR

QDR2 = QDP* 10 c 5 . WRITE (IWTT Y, 2 60) GPR»UDR2

WRITE < I W T T Y , 4C 0

)

READ (IRTTY ,410 * ELSE

27
****** PROGRAM DETACl-l' ****** HF2=HF*(1./C.3C48)

If 2= If Ml ./p.30 48)

WRJU Clwm.lCO) H F ,H F2 ,7 F ,ZF 2! 300 FORMAT ("0 COILING HEIGHT = ',F6.2,' RF1ERS <',F6.?,' FEE!)'/

! If, 'DETECTOR SPACING = ',F6.2,' METERS (',F6.?,' f E E 1

”> ' > R T I 2 = R T I * < < 1 . /G . 3(1 4 fi ) * * 0 . 5 ) WRITE (IWTT y y 320 RT I,RTI2

3 2 0 FORMAT ('0 DfTfCTOR RTI = '

, F6 . 1 ( V - S E C

)

* * 1/ 2 ('

t F6.1,' (FT-S

K E C ) * * 1/?)')

ALPHA2=A LPH A* (1 ./1()55.)

WRITE (IWTTY,33D ALPHA, ALPHA2

33 C FORMAT ('0 F IRp GROWTH CONSTANT = ',012.4,' VATTS/(SEC**?)'/

S ' C',E1?.4,' B"! U /S E C * *3 ) '

)

WRITE < IwTT Y, 400)

READ (IRTTY ,41C ) N

WRITE (IWTT Y

f 23 C)

T A CT = T ACT -2 73.

T A C T 2= (9 ./5 .)*T ACT «32.

WRITE (IWTT Y,34D TACT, TACT?

34 C FORMAT ('0 ACTIVATION TEMPERATURE = *,F6.1,' DEGREES C ('

f F6.1,

R

' DEGREES F) ')

WRITE (IWTT Y, 35 0) T 350 FORMAT ('0 TIME TO ACTIVATION = ',F8.2,' SECONDS')

GD2 = QD *( 1 ./ 1055 .> WRITE (IWTTY.360) 0 D ,G D?

36 0 FORMAT ('0 H p AT RELEASE RATE = ',El?.4 t ' WATTS'/

£ ' (' ,E 12.4,' BTU /SEC)')

WRITE (IWTTY,400)

READ (IRTTy ,410 > M

WRITE (IWTT Y t ?7 C)

ROR?=ROR* (9 . / 5 .

)

WRITE (IWTT Y, 37 0) RCR,R0R2

370 FORMAT C'O ACTIVATION RATE OF RISE = ',F6.2,' DEGRFES C/«IN (',

K Ft.?,' DEGREES F /MIN)')

WRITE (I W T T Y , 3 5 0 > TR

GDk?=QDP* (1 . / 10 5 5 • ) WRITE (IwTT Y , 3 6 0 ) 0 PH , G OK 2 WRITE (IWTT Y, 400)

READ ( IR 1 TY ,410 ) M END IF

STOP 'FRGGRAM CCNPLF1ED'

380 CONTINUE

WRITE (IWTTY.79 0)

390 F C R V A T (' ******0 ERROR IN D F T ACT ROUTTNF <**« ')

ACC FORMAT (//' <RETURN> TO CONTINUE')

410 FORMAT ( A 1

)

STOP 'PROGRAM ABORTED'

END

28
SUBROUTINE NW'lN ** ****

SUBROUTINE NWTN C C , P , I £R R , I W T T Y ) CC***** *********** ******* ****** **************************************

cc NE *1 ON” RAPHSON SUBROUTINE

C

c this subroutine is used to evaluate the tine expression for the

C FIXED TEMPERATURE DETECTOR.

C

c * ***************   ** ***** ***** ************************   ** * *** *

c PC=0.1

1CL=G. 00001

NC=1000

1 = 1

I ERR = 0

10 CONTINUE

IF (I.LE.KO) THEN

IF (P0.G1.5 r .) THEN

X = 0 .0

ELSE

X = E X P (-P0)

E N D I

F Y=PG+X-C

FPMX=1 .C-X

IF (F PMX .LT .0 .0 COOCCGl ) 00 TO 30

P = P n ~ (FX/ f P MX ) IF (ABS(P-Pn) .LT.TCL) THEN

IE R R = 0

RETURN

ELSE

1 = 1+1

F’C = P END IF

GO TO 10

END IF

IE NR=1

WRITE ( I W T T Y , ?0 > I 20 FORMAT (' NFUTON-R APHSON FAILED AFTER N 0 ITTRATTCNSt NC = '.14)

RETURN

30 WRITE Own V, 40)

40 FORMAT (' SLOPE OF EQUATION TOO CLOSE TC 7EP0 FOR '/

n ' NEWT ON-R APHSON METHOD.'/

R

' ERROP RETURN')

I F R R= 1 RE TURN

END

29
****** SUBROUTINE BISECT ******

SUbROUl INF BISECT ( D 1 , D? , RO R , P , I E R R , I W IT Y

C£* 44444444 * 4 * 4444444 * 44444 * 4444444 * 4444444 * 4444444 * 44444444444 * 4444 * 4 *

c

c BISECTION SUbROUT IN

C

c this subroutine evaluates the time expression for the rate of

C RISE DETECTOR USING A BISECTION M F T HOD

C£

4 ** 444**44444444 444 * 44 * 44*4 44*44 4444444444 * 44 ****** 44 * 44 ** 44*44 44444 *

C

I ERR=D

TOL=0. COCCI

NC= 1000

A=c .0

B = 1C0C .0

RLKT=TCL/20 .Q

10 CONTINUE

If CCD 2*b ). C l .50.) T HE N

x =0 «0

ELSE

X = E X P (~D t *B ) END If

F XB=D1*B **C .2 5- D1* E**0.?5* X-ROR

If Cf MB. LT. r. 0) THEN

A =6

B = b + 500

.

GO TO 10

E NO IF

1 = 1 20 CONTINUE

IF (I .LF .NO > THEN

P = A + (8 “A )/2 .0

If < <D2*P). GT .50.) THEN

X = 0 .0

EL S E X =E XP (-D <_*P ) END I F FX = D1*P**0. Z 5 “ D 1*P**G.25*X-ROP

IF ( C ( F X .GT ,-RL NT ) . AND .< F X.LT . RLMT )).0R.(<(R-A)/2.).LT.T0L)) THEN

IF RR = 0

RETURN

ELSE

1=1 +1

IF C CD 2* A ). H .50.) THEN

x=o .0

ELSE

X = E XP ( ~D c * A ) E ND IF FXA = D1*A**C ,2 5-Dl*A**0.25*X-R0R

IF ( ( F X A * FX ). OT .0.0 T Hf N

A = P ELSE

B = P

E N D I F END I F GO TO 20

30
****** SUBROUTINE bisect ******

ENl> I F IF RR = 1 WRITE <IWTTV,30) I 3Q FORMAT (' BISECT ROUTINE FAILED AFTER NC ITERATIONS, NO = ',14)

RETURN

END

31
APPENDIX B - DETACT-QS CODE

PC BASIC Program to Calculate

Detector Response to Fire with Arbitrary

Energy Release Rate Histories

1) Example Calculation

2) Program Listing

32
DETACT-QS Code Sample Calculation

DETACT-QS VERSION 1.1 WRITTEN BY D.D. EVANS 1985

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

NOT SUBJECT TO COPYRIGHT.

QUASI-STEADY FIRE CALCULATION OF DETECTOR ACTUATION TIME

BELOW AN UNCONFINED CEILING BASED ON ALPERT ' S EQUATIONS

AS PUBLISHED IN FIRE TECHNOLOGY AUGUST 1972.

USER SUPPLIED INPUT

HEIGHT OF CEILING ABOVE FUEL (METERS) ? 3.6576

DISTANCE OF DETECTOR FROM AXIS OF FIRE (METERS) ? 2.155

INITIAL ROOM TEMPERATURE (CELSIUS) ? 21.111

DETECTOR ACTUATION TEMPERATURE (CELSIUS)

(140 F = 60 C 160 F = 71 C 165 F = 74 C) ? 54.444

DETECTOR RESPONSE TIME INDEX (RTI ) (m*s)~(l/2) 370.34

NEXT A DESCRIPTION OF THE FIRE HEAT RELEASE RATE AS A

AS A FUNCTION OF TIME MUST BE CONSTRUCTED. THIS WILL BE

DONE BY THE USER ENTERING KEY HEAT RELEASE RATES ALONG

THE DESIRED FIRE CURVE. FOR THE USERS INFORMATION THE

MINIMUM HEAT RELEASE RATE NECESSARY TO ACTUATE THE

DETECTOR AT THE LOCATION GIVEN IS 232 kW

ENTER KEY HEAT RELEASE RATES THAT DETERMINE THE SHAPE OF THE

DESIRED FIRE DEVELOPMENT CURVE. USUALLY THE FIRST DATA

PAIR WILL BE ( TIME 0 HEAT RELEASE 0 ) . UP TO 100

PAIRS CAN BE ENTERED. TO STOP ENTERING DATA ENTER ANY

NEGATIVE TIME VALUE. THE PROGRAM WILL GENERATE HEAT

RELEASE RATE VALUES BETWEEN THE VALUES ENTERED AS NEEDED

BASED ON A STRAIGHT LINE INTERPOLATION BETWEEN POINTS AT

ONE SECOND INTERVALS

1 . .

2 . .

TIME (SEC) ? O

HEAT RELEASE (kW)? O

TIME (SEC) ? 5

HEAT RELEASE (kW)? 0.2928

33
3 . . TIME (SEC) ? 10

HEAT RELEASE (kW) ? 1.1711

4 . . TIME (SEC) ? 15

HEAT RELEASE (kW) ? 2.635

5 . . TIME (SEC) ? 20

HEAT RELEASE (kW) ? 4.684

6 .

.

TIME (SEC) ? 25

HEAT RELEASE (kW) ? 7.319

7 . . TIME (SEC) ? 30

HEAT RELEASE (kW) ? 10.539

8 . . TIME (SEC) ? 35

HEAT RELEASE (kW) ? 14.345

9 . . TIME (SEC) ? 40

HEAT RELEASE (kW) ? 18.737

10 . . TIME: (SEC) ? 45

HEAT RELEASE (kW) ? 23.71

11 . . TIME: (SEC) ? 50

HEAT RELEASE (kW) ? 29.28

12 . . TIME: (SEC) ? 55

HEAT RELEASE (kW) ? 35.42

13 . . TIME (SEC) ? 60

HEAT RELEASE (kW) ? 42.16

34
14 .

15 .

16 .

17 .

18 .

19 .

20 .

21 .

22 .

23 .

24 .

TIME (SEC) ? 65

HEAT RELEASE (kW)? 49.48

TIME (SEC) ? 70

HEAT RELEASE (kW)? 57.38

TIME (SEC) ? 75

HEAT RELEASE (kW)? 65.87

TIME (SEC) ? 80

HEAT RELEASE (kW)? 74.95

TIME (SEC) ? 85

HEAT RELEASE (kW)? 84.61

TIME (SEC) ? 90

HEAT RELEASE (kW)? 94.86

TIME (SEC) ? 95

HEAT RELEASE (kW)? 105.69

TIME (SEC) ? 100

HEAT RELEASE (kW)? 117.11

TIME (SEC) ? 105

HEAT RELEASE (kW)? 129.11

TIME (SEC) ? 110

HEAT RELEASE (kW)? 141.70

TIME (SEC) ? 115

HEAT RELEASE (kW)? 154.87

35
25

26

27

28

29

30

31

32

33

34

35

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

? 120

(kW)? 168.63

? 125

(kW)? 182.98

? 130

(kW)? 197.91

? 135

(kW)? 213.4

? 140

(kW)? 229.5

? 145

(kW)? 246.2

? 150

(kW)? 263.5

? 155

(kW)? 281.3

? 160

(kW)? 299.8

? 165

(kW>? 318.8

? 170

(kW)? 338.4

36
36 .

37 .

36 .

39 .

40 .

41 .

42 .

43 .

44 .

45 .

46 .

TIME (SEC) ? 175

HEAT RELEASE (kW)? 358.6

TIME (SEC) ? 180

HEAT RELEASE (kW)? 379.4

TIME (SEC) ? 185

HEAT RELEASE (kW)? 400.8

TIME (SEC) ? 190

HEAT RELEASE (kW)? 422.7

TIME (SEC) ? 195

HEAT RELEASE (kW)? 445.3

TIME (SEC) ? 200

HEAT RELEASE (kW)? 468.4

TIME (SEC) ? 205

HEAT RELEASE (kW)? 492.1

TIME (SEC) ? 210

HEAT RELEASE (kW)? 516.4

TIME (SEC) ? 215

HEAT RELEASE (kW)? 541.3

TIME (SEC) ? 220

HEAT RELEASE (kW)? 556.8

TIME (SEC) ? 225

HEAT RELEASE (kW)? 592.8

37
47 .

48 .

49 .

50 .

51 .

52 .

53 .

54 .

55 .

56 .

57 .

TIME (SEC) ? 230

HEAT RELEASE <kW>? 619.5

TIME (SEC) ? 235

HEAT RELEASE <kW>? 646.7

TIME (SEC) ? 240

HEAT RELEASE (kW)? 674.5

TIME (SEC) ? 245

HEAT RELEASE (kW)? 702.9

TIME (SEC) ? 250

HEAT RELEASE (kW)? 731.9

TIME (SEC) ? 255

HEAT RELEASE (kW)? 761.5

TIME (SEC) ? 260

HEAT RELEASE (kW>? 791.6

TIME (SEC) ? 265

HEAT RELEASE (kW)? 822.4

TIME (SEC) ? 270

HEAT RELEASE (kW)? 835.7

TIME (SEC) ? 275

HEAT RELEASE (kW)? 885.6

TIME (SEC) ? 280

HEAT RELEASE (kW)? 918.1

38
58

59

60

61

62

63

64

65

66

67

68

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

TIME (SEC)

HEAT RELEASE

? 285

(kW)? 951.2

? 290

(kW)? 984.9

? 295

(kW)? 1019.1

? 300

(kW)? 1053.9

? 305

(kW)? 1089.4

? 310

(kW)? 1125.4

? 315

(kW)? 1162.0

? 320

(kW)? 1199.2

? 325

(kW)? 1236.9

? 330

(kW)? 1275.3

? 335

(kW)? 1314.2

39
69 . . TIME (SEC) ? 340

HEAT RELEASE <kW>? 1353.7

70 . . TIME (SEC) ? 345

HEAT RELEASE <kW)? 1393.8

71 .. TIME (SEC) ? 350

HEAT RELEASE (kW)? 1434.5

72 . . TIME (SEC) ? 355

HEAT RELEASE (kW)? 1475.8

73 . . TIME (SEC) ? 360

HEAT RELEASE (kW)? 1517.7

74 .. TIME (SEC) ? -1

SEND OUTPUT TO PRINTER (Y OR N) ? N

CEILING HEIGHT = 3.6576 RADIUS= 2.155 DET ACT TEMP= 54.444 RTI = 370.34

TIME FIRE GAS TEMP DET TEMP

sec kW C C

0.0 0.0 21 .

21.1

10.0 1.2 22.0 21 .

20.0 4.7 23.4 21 .

30.0 10.5 25.2 21.2

40.0 18.7 27.1 21.3

50.0 29.3 29.3 21.4

60.0 42.2 31.6 21.6

70.0 57.4 34.0 21.9

80.0 75.0 36.5 22.2

90.0 94.9 39.2 22.6

100.0 117.1 41.9 23.1

110.0 141.7 44.8 23.6

120.0 168.6 47.7 24.2

130.0 197.9 50.8 24.9

140.0 229.5 53.8 25.7

150.0 263.5 57.0 26.6

160.0 299.8 60.3 27.6

170.0 338.4 63 .

6

28.7

180.0 379.4 67.0 29.8

190.0 422.7 70.4 31 .

200.0 468.4 73.9 32.4

40
210.0 516.4 77.5

220.0 556.8 80.6

230.0 619.5 84.8

240.0 674.5 88.5

250.0 731.9 92.3

260.0 791.6 96.2

270.0 835.7 99.2

280.0 918.1 104.0

290.0 984.9 108.0

300.0 1053.9 112.0

310.0 1125.4 116.1

* * * * DETECTOR ACTUATION

33.9

35.4

37.1

38.8

40.6

42.6

44.6

46.7

48.9

51.2

53.6

AT 313.4 SECONDS **** TYPE A CARRIAGE RETURN TO CONTINUE?

ANALYZE SAME FIRE WITH DIFFERENT DETECTOR <Y OR N) ? N

41
DETACT-QS Code Listing

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

210

220

230

240

250

260

270

280

290

300

310

320

330

340

350

360

370

380

390

400

410

420

430

440

450

460

470

480

490

500

510

520

530

540

550

DIM 3(101)

K= 10

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

INPUT

PRINT

PRINT

INPUT

PRINT

PRINT

INPUT

PRINT

PRINT

PRINT

INPUT

PRINT

PRINT

INPUT

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

Q ( 101

)

"DETACT-QS VERSION 1.1 WRITTEN BY

"CONTRIBUTION OF THE NATIONAL BUREAU

"NOT SUBJECT TO COPYRIGHT."

D.D. EVANS 1985"

OF STANDARDS (U.S

"QUASI-STEADY FIRE CALCULATION OF DETECTOR ACTUATION TIME"

"BELOW AN UNCONFINED CEILING BASED ON ALPERT'S EQUATIONS"

"AS PUBLISHED IN FIRE TECHNOLOGY AUGUST 1972."

USER SUPPLIED INPUT"

HEIGHT OF CEILING ABOVE FUEL (METERS)

H

• • i "DISTANCE

R

i § oa "INITIAL

T1

0 0 I • "DETECTOR

"(140 F = T9

OB SB "DETECTOR

L

OF DETECTOR FROM AXIS OF FIRE (METERS)

ROOM TEMPERATURE (CELSIUS)

ACTUATION TEMPERATURE

60 C 160 F = 71 C

(CELSIUS)"

165 F = 74 C)

RESPONSE TIME INDEX ( RTI ) (m*s)~(l/2)

"NEXT A DESCRIPTION OF THE FIRE HEAT RELEASE RATE AS A"

"AS A FUNCTION OF TIME MUST BE CONSTRUCTED. THIS WILL BE"

"DONE BY THE USER ENTERING KEY HEAT RELEASE RATES ALONG"

"THE DESIRED FIRE CURVE. FOR THE USERS INFORMATION THE"

"MINIMUM HEAT RELEASE RATE NECESSARY TO ACTUATE THE"

"DETECTOR AT THE LOCATION GIVEN IS";

X= ( (T9-T1) *H/5.38*R~ (2/3) ) ^ (3/2)

IF R/H> . 18 THEN 390

X=( (T9-Tl)*H~(5/3)/16.9)~(3/2)

X = X .5

X= INT (X)

PRINT X;

PRINT " kW."

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

PRINT

N= 1

ENTER KEY HEAT RELEASE RATES THAT DETERMINE THE SHAPE OF THE"

DESIRED FIRE DEVELOPMENT CURVE. USUALLY THE FIRST DATA"

PAIR WILL BE ( TIME O HEAT RELEASE 0 ) . UP TO 100"

PAIRS CAN BE ENTERED. TO STOP ENTERING DATA ENTER ANY"

NEGATIVE TIME VALUE. THE PROGRAM WILL GENERATE HEAT"

RELEASE RATE VALUES BETWEEN THE VALUES

BASED ON A STRAIGHT LINE INTERPOLATION

ONE SECOND INTERVALS"

ENTERED

BETWEEN

AS NEEDED"

POINTS AT"

42
560 FOR 1=1 TO 101

570 S ( I ) = 1 . 701412E+38

580 Q ( I ) =0

590 NEXT I 600 PRINT N;

610 PRINT TIME (SEC) "

620 INPUT S(N>

630 IF S ( N ) <0 THEN 710

640 PRINT " •' 650 PRINT " HEAT RELEASE ( kW ) "

660 INPUT Q(N)

670 PRINT ° " 680 N = N-*-

690 PRINT " " 700 GOTO 600

710 S ( N ) =S ( N- 1 ) +1

720 PR = 0

730 PRINT " •* 740 PRINT "SEND OUTPUT TO PRINTER <Y OR N) "

750 INPUT A£

760 IF AS="Y" OR AS="y" THEN PR=1

770 PRINT " " 780 PRINT "CEILING HEIGHT =

" ; H

; " RADIUS = ";R;" DET ACT TEMP=";T9;" RTI

790 PRINT " " 800 PRINT " TIME FIRE GAS TEMP DET TEMP"

810 PRINT " sec kW C C"

820 IF PR=0 THEN 920

330 LPRINT

840 LPRINT

850 LPRINT

860 LPRINT

870 LPRINT

880 LPRINT

890 LPRINT

900 LPRINT

910 LPRINT

920 I = N -

930 P = K

940 N=0

950 T4=T1

960 T5=T1

970 T6=T1

980 J=1

990 IF N<S(J+1) THEN 1020

1000 J= J+l

1010 GOTO 990

1020 0=(N-S(J))/(S(J-*-l)-S(J))*(Q(J + l)-Q(J))-a(J)

1030 T4=T5

1040 S6=T6

1050 T6 = 16.9*0''(2/3)/H''(5/3)-*-Tl

1060 IF R/H<=.18 THEN 1080

1070 T6=5.38* (0/R) ~ (2/3) /H+Tl

1080 V6= . 95* (O/H) ~ (1/3)

1090 IF R/H < = . 15 THEN 1110

1100 V6=.2*0~(l/3)*H~(l/2)/R~(5/6)

"DETACT-QS VERSION 1.1"

• 8 t • "CEILING HEIGHT=" ; H

; " m"

"DETECTOR DISTANCE FROM AXIS OF FIRE= " ; R

; " m"

"DETECTOR ACTUTATION TEMP=";T9;" C"

"RTI =

" ; L

; " (m*s)~(l/2)”

ii •• " TIME FIRE GAS TEMP DET TEMP"

" sec kW C C"

43
Hi

0

1120

1130

1140

1150

1160

1170

1180

1190

1200

1210

1220

1230

1240

1250

1260

1270

1280

1290

1300

1310

1320

1330

1340

1350

1360

1370

1380

1390

1400

1410

1420

1430

1440

1450

1460

1470

1480

1490

1500

1510

1520

1530

1540

1550

1560

1570

1580

1590

1600

1610

1620

1630

1640

1650

IF Vb>.i THEN 1130

V6 = . 1 L1=L/V6" .5

B=T6-S6

T5 = T4- (S6-T4) * (1-EXP (- 1/Ll) ) -*-B*Ll*<EXP(-l/Ll ) +1/L1-1)

IF P<K THEN 1200

PRINT USING "########. #";N,0,S6,T4

IF PR = 1 THEN LPRINT USING "######## N , 0 , S6 , T4

P = 0

N = N+ 1 p = p + l

IF T5<T9 THEN 990

GOSUB 1680

PRINT '* " PRINT ’* **** DETECTOR ACTUATION AT";

PRINT USING "######. #";E;

PRINT " SECONDS  " PRINT " " IF PR = 0 THEN 1350

LPRINT " " LPRINT " ** ** DETECTOR ACTUATION AT";

LPRINT USING "######.#"; E

LPRINT " SECONDS ***«”

LPRINT " " PRINT "TYPE A CARRIAGE RETURN TO CONTINUE";

INPUT AS

PRINT " " PRINT "ANALYZE SAME FIRE WITH DIFFERENT DETECTOR <Y OR N) ";

INPUT AS

IF AS="Y" OR AS= "y " THEN 1420

END

PRINT "CHANGE RTI VALUE CY OR N) ";

INPUT AS

IF AS< > " Y" AND ASO"y" THEN 1470

PRINT "NEW VALUE = ";

INPUT L

PRINT "CHANGE ACTUATION TEMPERATURE <Y OR N) ";

INPUT AS

IF ASO"Y" AND ASO"y" THEN 1520

PRINT "NEW VALUE = ";

INPUT T9

PRINT "CHANGE FUEL TO CEILING HEIGHT (Y OR N) ";

INPUT AS

IF ASO"Y" AND AS< > "y " THEN 1570

PRINT "NEW VALUE= ";

INPUT H

PRINT "CHANGE RADIUS OF DETECTOR FROM FIRE AXIS <Y OR N) ";

INPUT AS

IF ASO"Y" AND AS < > "y " THEN 1620

PRINT "NEW VALUE= ";

INPUT R

PRINT "CHANGE PRINTOUT INTERVAL <Y OR N) ";

INPUT AS

IF ASO"Y" AND ASO"y" THEN 1670

PRINT "NEW VALUE = ";

44
1660

1670

1660

1690

1700

1710

1720

INPUT K

GOTO 770

E=N-lf (T9-T4) /(T5-T4)

E = E* 100+ .

5

E=INT(E)

E = E/ 100

RETURN

45
NBS-114A (rev. 2-00

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR-85/3167

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

July 1985

4. TITLE AND SUBTITLE

Methods to Calculate the Response Time of Heat and Smoke Detectors

Installed Below Large Unobstructed Ceilings

5. AUTHOR(S)

David D. Evans, David W. Stroup

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7 . Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

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

U.S. Nuclear Regulatory Commission

Washington, D.C. 20555 ,

10.

SUPPLEMENTARY NOTES

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

11.

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

bi bl iography or literature survey, mention it here) Recently developed methods to calculate the time required for ceiling mounted

heat and smoke detectors to respond to growing fires are reviewed. A computer program, that calculates activation times for both fixed temperatures and rate of

rise heat detectors in response to fires that increase in heat release rate

proportionally with the square of time from ignition is given. This program produces

equivalent results to the tables published in Appendix C, Guide for Automatic

Fire Detector Spacing, (NEPA 72E, 1984). A separate method and corresponding program are provided to calculate response time for fires having arbitrary heat release

rate histories. This method is based on quasi—steady ceiling layer gas flow

assumptions. Assuming a constant proportionality between smoke and heat release

from burning materials, a method is described to calculate smoke detector response

time modeling the smoke detector as a low temperature heat detector in either of the

two response time models.

12.

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

ceilings; computer program; egress; escape; fire alarms; fire detection; fire

suppression; heat detectors; smoke detectors; sprinkler systems

13. AVAILABILITY

^ | Uni i mi ted

| | For Official Distribution. Do Not Release to NTIS

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

20402.

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

14. NO. OF

PRINTED PAGES

49

15. Price

$8.50

USCOMM-DC 6043-P80