Fire Safety Journal 41 (20

xetim

l N

Tu

d fo

Available online 18 September 2006

tunnel [1,2].The types of heat detectors that were not covered in the

work [1] were detectors activated by rate of rise of

scale re tests. As a convenience to the readers, portions ofthe early work [1] and data are summarized in this paper.Three types of heat detectors have been investigated in

ARTICLE IN PRESSthe overall program: xed-temperature rating, rate-of-rise,and rate-compensated detectors. Thermal sensitivities ofthe detectors were measured through bench-scale tests

0379-7112/$ - see front matter r 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.resaf.2006.06.004

Tel.: +1 781 255 4964; fax: +1 781 255 4024.E-mail address: soonil.nam@fmglobal.com.1. Introduction

As heat detectors are not only being used as a warningdevice but also widely used as a trip device of automaticre suppression systems, it is increasingly desirable for are safety engineer to have a reliable means of predict-ing heat detector activation times if a re growth rate canbe prescribed. Early work [1] established this goal byassigning response time index (RTI) to each xed-temperature-rating heat detector utilizing a plunge

temperatures and rate-compensated detectors. A studywas carried out in order to nd a way to nd detectorresponse times in connection with RTI values of thosedetectors. Five different models of detectors were chosenfor plunge-tunnel tests. In the plunge tunnel, the airtemperatures were varied with different rates of rise.Methods to extract the RTI from plunge-tunnel test datawere developed. Then the methods were validated bycomparisons of the estimated response times based on theassigned RTI values with measured response times in real-Abstract

A project was initiated to nd a way of assigning thermal response time index (RTI) of heat detectors and to see if a detector response

time could be estimated by utilizing the assigned RTI value. In phase 1 of the project, the concept was applied to xed-temperature rating

detectors and detector response times were successfully estimated. In the second part of the project, rate-of-rise detectors and rate-

compensated detectors were investigated. Test data employing a plunge tunnel of varying air temperatures were used to extract RTI

values of a rate-of-rise detector and rate-compensated detectors. In the nal stage of the project, adequacy of estimating detector

response times of rate-of-rise and rate-compensated detectors based on RTI values in conjunction with other threshold values for

activation was assessed. Twenty-seven real-scale re tests were conducted to see if the estimated response times match well with the

measured detector response times. Test results showed that the detector response time estimation based on RTI values matched well with

the measured ones. Having the ability of predicting detector response times in association of re scenarios provides a great exibility in

deploying heat detectors in eld operations. Detectors can be installed at performance-based spacing with respect to detector types and

anticipated re growth scenarios. Bench-scale tests to assign RTI values of detectors can replace the real-scale re tests for the maximum

spacing that are costly while less than reliable. Detector response sensitivity can be classied by the value of RTI and the maximum

spacing of a detector can be assigned based on its RTI value.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Heat detector; RTI; Response timePredicting response times ofand rate-compensated heat d

response

Sooni

FM Global, 1151 BostonProvidence

Received 20 April 2006; received in revise06) 616627

ed-temperature, rate-of-rise,tectors by utilizing thermale index

am

rnpike, Norwood, MA 02062, USA

rm 20 June 2006; accepted 27 June 2006

www.elsevier.com/locate/resaf

ARTICLE IN PRESSournusing plunge-type wind tunnels that provided an air ow ofa xed velocity with either a xed temperature ortemperatures increasing at a xed rate. Five restorableand four nonrestorable models of the xed-temperaturerating type were the subjects of the early study [1]. One

Nomenclature

A surface area of the heat sensing elementCr threshold rate of rise of temperature for

activation of a rate-of-rise heat detectorCDT0 plume coefcient for temperatureCVz0 plume coefcient for velocityK rate of rise of temperature (1C/s)_QT total heat release rate from a re_Qc convective heat release rate from a re

RTI response time indexTe temperature of the heat-sensing element in

detectorsTN ambient temperatureTg gas temperatureTr temperature rating of xed-temperature detec-

torsTe0 initial sensor temperatureTg0 initial gas temperatureTrv virtual temperature rating of rate-compen-

sated detectors

S. Nam / Fire Safety Jrestorable model of rate-of-rise type, and four restorablemodels of rate-compensated type detectors were used in thecurrent study. A small number of test samples per eachmodel were subjected to plunge-tunnel tests. In general,each test sample was exposed up to 10 plunge-tunneltests determining the thermal sensitivity of the sample inorder to reduce the inuence associated with possiblemeasurement variations. Then a RTI value wasobtained for each model of the detectors by averagingthe measured RTI values of the test samples belonging tothe same model.The detector models used in the program are given in

Table 1. The temperature ratings (the second column)in the table are the ones assigned by listing organizationsafter they were veried through the oven tests [3]. Therate-of-rise detectors do not have a temperature rating;thus, the value in the temperature rating column corre-sponding to rate-of-rise Model RR-A detector is thethreshold value of rate-of-rise of temperature in 1C/s forthe activation of the detector. The third column showswhether a detector is restorable or not. All the xed-temperature rating detectors in Table 1, Model FTR-Athrough FTR-K, were investigated in Ref. [1]; thus, theywill not be discussed in detail here. The rate-of-rise detectorand the rate-compensated detectors will be discussed in detail and some applications will be proposed based onthe study.2. Theory

If one can assume that detectors are activated byconvective heat transferred through the re plume, theenergy balance equation on the heat-sensing element of the

DT0 excess temperature at the plume centerlineb plume half-widthc specic heat of the heat-sensing element in

detectorscp specic heat of airg gravitational accelerationh convective heat transfer coefcientm mass of the heat-sensing element in detectorsr radial distance from a plume centerline axist timetif elapsed time from the beginning of temperature

rise to activation of a detectoru gas ow velocityx log (r/b) in a ceiling-jet correlation or (Tg T e)y log DT=DT0

or log V r=Vr0

in a ceiling-jet

correlationz elevation from a re sourcez0 virtual origin of re plumeZc convective portion of heat transferrN density of ambient airt time constant (mc/hA)

al 41 (2006) 616627 617detector can be given as

mcdT e

dt hA Tg Te

, (1)

where m is the mass of the heat-sensing element, c thespecic heat of the element, Te the sensing-elementtemperature, t the time, h the convective heat transfercoefcient, A the sensing-element surface area, and Tg thesurrounding hot air temperature. By introducing the timeconstant t(mc/hA) [2] and t RTI= up [2], Eq. (1) canbe transformed to

dT e

dt Tg T e

t

u

p

RTITg T e

. (2)

Note that the energy balance in Eq. (1) assumes no loss dueto conduction in contrast to [2]. Here RTI is the responsetime index of a detector that indicates a thermal responsesensitivity of the sensing element to the surrounding hotgas (mostly air) originated by a re plume, and u is the owvelocity at the detector. As the sensing elements of mostheat detectors inside protective casings have shapes ofblunt objects, such as cylinder or sphere, the time constantcan be expressed as t / 1= up , as is the case in sprinklers.The RTI can be measured through plunge-tunnel tests [1,2].Once the RTI of a heat detector is known, detectorresponse times can be computed by obtaining Te vs. tthrough the integration of Eq. (2). Tg and u in the equation

ARTICLE IN PRESSourneither can be estimated by re scenarios or measuredthrough re tests.If the air temperature increases at a xed rate inside a

plunge tunnel, then the temperature of the owing air owbecomes

Tg Kt Tg0, (3)where K is the rate of rise of temperature, t the time, andTg0 the initial gas temperature. By dening x(TgTe), Eq.(2) can be converted to

dx

dt dTg

dt dTe

dt

K dT edt

. 4

By combining Eqs. (2) and (4),

dT e

dt K dx

dt

xt. 5

Table 1

Test detector models

Detector model ID Temperature rating (1C)

Fixed temp. rating model FTR-A 57

Fixed temp. rating model FTR-B 77

Fixed temp. rating model FTR-C 57

Fixed temp. rating model FTR-D 93

Fixed temp. rating model FTR-E 88

Fixed temp. rating model FTR-H 57

Fixed temp. rating model FTR-I 90

Fixed temp. rating model FTR-J 57

Fixed temp. rating model FTR-K 93

Rate-of-rise model RR-A 0.139 1C/sRate-compensated model RC-B 57

Rate-compensated model RC-C 57

Rate-compensated model RC-D 71

Rate-compensated model RC-E 88

S. Nam / Fire Safety J618Integrating Eq. (5) yields

Te Tg Kt Tg0 Te0 Kt exp t=t, (6)

where Te0 is the initial detector sensor temperature. Eq. (6)shows that

dT e

dt K 1 et=t

Tg0 Te0

tet=t. (7)

For the convenience of measuring t, the last term in Eq. (7)can be deleted by having the test sample exposed tosurrounding gas ow for a long enough time before a teststarts, thus, making Tg0 Te0. Then, Eq. (7) for activationof a rate-of-rise detector can be solved as

Cr K 1 et=t

, (8)

where Cr is the threshold rate of rise of temperature thatwould activate the detector.Then

t tif

ln 1 Cr=K , (9)

where tif is the elapsed time from the beginning oftemperature rise to activation of the detector at the plungetunnel. Once t is known, the RTI can be computed [2] as

RTI t up , (10)where u is the constant air ow velocity inside the plungetunnel during the test.A xed-temperature rating detector activates when Te

becomes the temperature rating, Tr. A rate-of-rise detectoractivates when

Tg T e

=t

XCr. (11)

A rate-compensated detector is modeled as activating whenTe becomes the virtual temperature rating, Trv, which willbe discussed shortly. Activation mechanisms of rate-compensated detectors are in general more complex than

Restorable/nonrestorable Reference

Restorable Type A in Ref. [1]

Restorable Type B in Ref. [1]

Restorable Type C in Ref. [1]

Restorable Type D in Ref. [1]

Restorable Type E in Ref. [1]

Nonrestorable Type H in Ref. [1]

Nonrestorable Type I in Ref. [1]

Nonrestorable Type J in Ref. [1]

Nonrestorable Type K in Ref. [1]

Restorable Current study

Restorable Current study

Restorable Current study

Restorable Current study (Type F in Ref. [1])

Restorable Current study (Type G in Ref. [1])

al 41 (2006) 616627that of rate-of-rise detectors. The adequacy of using RTI inprediction of detector response times is shown below.

3. Assigning RTI values to various detector types based onthe bench-scale test data

3.1. Fixed-temperature-rating detectors

The RTI of a xed-temperature-rating heat detector(Model FTR-A through Model FTR-K in Table 1) wasmeasured by plunging the detector samples into a tunnel, inwhich air ow has a xed temperature and velocity, untilthe test samples activated [1]. Eq. (2) was numericallyintegrated with known Tg (197 1C) and u (1.55m/s) andfound the RTI value that made Te become the temperaturerating, Tr, at the measured activation time. For eachrestorable-detector model, ve samples were chosen andten tests were conducted for each sample. Then the averagevalue of the 50 data points (5 samples 10 tests) was

started to increase. Note that the numbers in the abscissa ofthe gure correspond to 0.1 s intervals. During the periodof the rst 446 s, the ambient temperature inside the tunnelwas well maintained at a constant temperature so that itwould not affect the test outcome. Also the time was longenough to treat the initial sensor temperature as the sameas the ambient air temperature inside the tunnel.As the air temperature started to rise at ti 446 s, and

the detector sample activated at tf 578 s, the temperaturevariation between that period had to be analyzed in detail.The average air ow velocity between ti and tf measured bya Pitot tube came out as 1.53m/s. The temperature at ti was22.4 1C and that at tf was 48.9 1C, which were denoted as Tiand Tf in the following equations, respectively.The rate of rise K can be found as

ARTICLE IN PRESSournal 41 (2006) 616627 6190

10

20

30

RTI

(m.s)

1/2

Average RTI of each sample Average RTI of all five samples

S. Nam / Fire Safety Jassigned as the RTI value of the given model [1]. Fig. 1shows one such example. The black dots in the gure arethe average values of 10 data points per each sample andthe red dots correspond to the average value of the 50 datapoints described above.

3.2. Rate-of-rise-type detectors

Among the ve models of the test samples used in thecurrent study, only one detector model, RR-A, was foundto be activated solely by the rate of rise of temperature. Atotal of 34 plunge-tunnel tests were conducted at threedifferent rates (K) with four test samples. The average airvelocities used in the tests were varied from 1.53 to 2.2m/s.Fig. 2 shows the air temperature variation with respect totime during a test. The test sample was inside the tunnel for446 s before the air temperature inside the plunge tunnel

K T f T i 48:9 22:4 0:201 C=s . (12)0 1 2 3 4 5 6

Sample ID Number

Fig. 1. Average RTI value of xed-temperature-rating-type detector

samples FTRC1-C5.

4400 4600 4800 5000 5200 5400 5600 580020

25

30

35

40

45

50

55

Air T

empe

ratu

re in

Tun

nel (

C)

Time (s x 10)

ti =446 stf =578 s

Fig. 2. Air temperatures inside the plunge tunnel between ti and tf.tf ti 578 446Now t can be calculated by Eq. (9). Once t is determinedafter nding a proper Cr, RTI can be obtained byRTI t up . Although the listed Cr value was 0.139 1C/s(15 1F/min), no independent measurement data on Cr wereavailable. Thus, a way to nd the Cr value consistent withthe RTI model of the test results had to be devised. FMApprovals conducts tests for a rate of rise detector insidean oven [3], in which temperature of air ow increases atthe rate of 0.185 1C/s until the detector sample activates. Itis, therefore, reasonable to assume that Cr value must beless than 0.185 1C/s. RTI values associated with the testedsamples were computed using Eq. (9) with the Cr variedbetween 0.12 and 0.18 1C/s with an increment of 0.01 1C/sin conjunction with the measured plunge-tunnel test data.It is reasonable to assume that the best estimate of Cr valuecorresponding to the smallest standard deviation of RTIvalues would be the closest to the real Cr value that thetested detector samples had. The analysis based on thecollected data shown in Fig. 3 indicates that Cr 0.15

0.12 0.13 0.14 0.15 0.16 0.17 0.1822

23

24

25

Sand

ard

Devia

tion

of R

TI (m

.s)1/

2

Cr (C/s)Fig. 3. Standard deviation of RTI values per varying Cr values.

provides the minimum standard deviation; thus,Cr 0.15 1C/s was chosen for Model RR-A detectors.With Cr 0.15 1C/s, Eq. (9) provides the value of t andeventually RTI values.

3.3. Rate-compensated heat detectors

Detector Models RC-BE in Table 1 were all identiedas rate-compensated detectors by screening tests, which willbe discussed later. Fig. 4 shows the air temperatures insidethe tunnel at activation of the tested samples vs. variousinitial air temperatures. The gure indicates that eachdetector model activates at a xed air temperatureregardless of the differences in the initial air temperatures.Fig. 5 shows the air temperatures at activation of test

ARTICLE IN PRESS

20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 5020

25

30

35

40

45

50

55

60

65

70

75

80

Air t

empe

ratu

re a

t det

ecto

r act

ivatio

n (C

)

Initial air temperature (C)

Rate-compensated type Model RC-BRate-compensated type Model RC-CRate-compensated type Model RC-DRate-compensated type Model RC-E

Fig. 4. Initial air temperature inside the plunge tunnel vs. the air

temperature at detector activation.

30

80

tem

p

Rate-compensated type Model RC-C

S. Nam / Fire Safety Journ6200.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.272025Ai

r

Rate of temperature rise, K (C/s)

Rate-compensated type Model RC-DRate-compensated type Model RC-E354045

5055

60657075

erat

ure

at d

etec

tor a

ctiva

tion

(C)

Rate-compensated type Model RC-BFig. 5. Rate of rise of air temperature inside the plunge tunnel (K) vs. air

temperature at detector activation.samples vs. various Ks used in the tests. The gureindicates that each detector model activates at a xed airtemperature regardless of the differences in the rate of riseof the air temperatures K adopted in the tests. Figs. 4 and 5clearly show that the test samples activate at thetemperatures far below the listed temperature ratings ofeach detector model, which were obtained through thestandard oven tests [3] at listing organizations. The averageair temperature at activation of each model in Fig. 4, whichmust be higher than the temperature at the detector sensingelement, was 50 1C for Model RC-B, 47 1C for Model RC-C, 62 1C for Model RC-D, and 74 1C for Model RC-E,while the corresponding temperature ratings in Table 1 aresubstantially higher. The plunge-tunnel test results shownin Figs. 4 and 5 strongly suggest that the test samplesbehave as if they were xed-temperature-rating detectors;however, their true temperature ratings, which are denotedas virtual temperature ratings, Trv, would be lower than thecorresponding listed temperature ratings.As the RTI value and the virtual temperature rating of

each model detector had yet to be determined, the datacollected with the plunge tunnel with the variable airtemperature alone were not sufcient to extract both RTIand Trv. Thus, more data were collected with the plungetunnel with a xed temperature. Then potential RTI valuescorresponding to possible Trv values were computed. Thenumerical integration of Eq. (2) was used to extract RTIand Trv values from the data collected with the xed-temperature plunge tunnel, while Eq. (4) was used for thedata collected with the varied-temperature plunge tunnel.As the virtual temperature rating of a RC detector is not

known a priori, the RTI values from xed-temperatureplunge-tunnel test data cannot be computed directly. Thus,a range of possible temperature ratings had to be initiallyguessed and the RTI values corresponding to each possibletemperature rating were to be assessed. Using the possibleRTI values obtained above, possible range of Trv were thencalculated by utilizing the data obtained in plunge-tunneltests conducted with varying air temperatures. To do so,Eq. (6) was utilized. When Te in Eq. (6) becomes Trv, thedetector activates, and Tg0Te0 becomes zero if the testsamples are exposed to the ambient tunnel temperature fora long-enough period prior to the increase of tunnel airtemperature. For the t and K in the equation, the activationtime and rate of rise, respectively, should be used. The t inthe equation can be obtained by t RTI= up .The results are shown in Fig. 6. The average value of the

two sets of RTI values, one from the xed air temperatureplunge-tunnel data and the other from the varied airtemperature plunge-tunnel data, at each potential Trv isgiven. As the RTI curves obtained from the two sets ofplunge-tunnel test data share the same principle, the RTIvalues from the two data sets must meet. The intersectionpoint of the two sets of RTI values is most likely the realRTI value of the detector samples, and the corresponding

al 41 (2006) 616627Trv value is also most likely the real temperature rating Trvof the detector samples. Fig. 6 indicates that Trv and RTI of

4. Comparisons of estimated with measured response times

In order to see if the RTI model and the processesemployed to obtain the RTI values of the detectorsdescribed in Section 3 are valid, detector response times

ARTICLE IN PRESSournal 41 (2006) 616627 6219

10

S. Nam / Fire Safety JModel RC-B detectors would be 49.1 1C and 5.5 (m s)1/2,respectively.Similar processes were used to obtain RTI and Trv values

of the other rate-compensated detectors and the values aregiven in Table 2. For the sake of completion, the RTI andTr values of the other detector samples used in the studyare given in Table 3.

estimated based on the obtained RTI values werecompared with the response times actually measured inre tests. A total of 27 tests were conducted under themovable ceiling of the Research Laboratory at FM GlobalResearch Campus, West Glocester, Rhode Islands, USA.The following is a brief description of re tests.

4.1. Fire test configuration

Ten detector samples (two samples per each model of46.0 46.5 47.0 47.5 48.0 48.5 49.0 49.5

5

6

7

8

RTI

(m.s)

1/2

Virtual temperature rating (C)

Average RTI with varied air temperatureAverage RTI with fixed air temperature

Fig. 6. Average RTI values obtained through plunge-tunnel tests with

xed air temperatures and with varied air temperatures of Model RC-B

detectors.

Table 2

RTI and Trv values of rate-compensated-type detectors

Detector test

samples

RTI (m s)1/2 Virtual temperature

rating Trv (1C)Listed temperature

rating Tr (1C)

Model RC-

B

5.5 49.1 57

Model RC-

C

8.5 48.3 57

Model RC-

D

33.1 57.5 71

Model RC-

E

32.1 71.4 88

Table 3

RTI and Tr or Cr values of xed-temperature-rating and rate-of-rise-type

detectors

Detector test samples RTI (m s)1/2 Listed temperature

rating (1C)

Fixed temp. rating model FTR-A 65.1 57

Fixed temp. rating model FTR-B 69.0 77

Fixed temp. rating model FTR-C 14.4 57

Fixed temp. rating model FTR-D 12.7 93

Fixed temp. rating model FTR-E 8.8 88

Rate-of-rise model RR-A 156 Cr 0.15 1C/sRR and RCs), two velocity probes, and two sprinklers wereinstalled on the ceiling along the circumference of a 3.4-mradius circle in the eastwest direction. The re source wasto be located at the center of the circle. As shown in Fig. 7,the detector samples were installed in the following orderfrom the east to the west direction: Sprinkler 1, DetectorRR-A1, Detector RC-B1, Detector RC-C1, Velocity Probe1, Detector RC-D1, Detector RC-E1, Sprinkler 2, DetectorRR-A2, Detector RC-B2, Detector RC-C2, Velocity Probe2, Detector RC-D2, and Detector RC-E2.The dimension of the room where the tests were

conducted was 30m (eastwest) by 42m (northsouth) by9m high. The dimension of the movable ceiling was 24 by12m. The ceiling heights were varied few times in the testprogram. The location of the re source, which was theorigin of the 3.4m radius circle, was 7.5m from the southwall and 5.7m from the north wall. The distance betweeneach detector/velocity probe/sprinkler sample was main-tained at 0.15m edge to edge. When detector responsetimes were estimated, the temperatures and velocitiesmeasured at Velocity Probe 1 were used for DetectorRR-A1 through Detector RC-E1, and those at VelocityProbe 2 were used for Detector RR-A2 through DetectorRC-E2. Note that although the sprinklers were installed as

0.15m

Origin of Fire

R = 3.4 m

S1A1

B1C1

V1D1 E1

W A2 B2 C2 V2D2

E2S2

Fig. 7. Schematic of the test sample locations. They were placed at 0.15m-

edge-to-edge distance between the samples. Here S1 and S2 denote

Sprinklers 1 and 2; V1 and V2 denote Velocity Probes 1 and 2; and A1through E2 correspond to, respectively, Detector RR-A1 through

Detector RC-E2.

reference detectors, estimating sprinkler response timeswere not pursued as the information provided for thesprinkler characteristics were deemed unreliable. It wasalso learned after Test 17 that the direction of the installedDetector RC-C1 and RC-C2 were 901 off from thedirection used in the plunge-tunnel tests. Thus, all the dataassociated with Model RC-C detectors in Tests 117 weredeleted. Additional ten re tests were carried out afterModel RC-C detector samples were installed properly.Detector activation times were estimated by using the

RTI and Trv (or Cr in the cases of RR-A1 and RR-A2) ofeach detector model, which are shown in Table 2. Thedetector response times were found by numericallyintegrating Te in Eq. (2) with the measured values of uand Tg in re tests. When, Tg Te

=t becomes greater

than Cr, Detector samples RR-A1 and RR-A2 willactivate. For all the other detector samples, a detector willactivate when Te becomes greater than Trv of the detector.

4.3. Overall comparisons of the estimated and the measured

response times per each detector model

The estimated detector response times based on the RTIand Trv (or Cr) of test detector samples in conjunction withthe measured air temperatures and velocities at detectorsample locations in each test were compared with themeasured ones in the actual rel tests.Fig. 10 shows the cases with the rate-of-rise detectors,

Model RR-A. The estimated response times match well

ARTICLE IN PRESS

Fig. 9. One of the crib res used in the test program. Depending on the

test, one or two cribs were used.

0 100 200 300 400 500 6000

100

200

300

400

500

600

Mea

sure

d Re

spon

se ti

me

(s)

Estimated response time (s)

MeasuredEstimated

Fig. 10. Comparison of the measured and the estimated response times of

rate-of- rise heat-detector samples of the same model.

S. Nam / Fire Safety Journ6224.2. Test fires

The test re was a heptane spray re for Tests 19,1317, and 2227. The ow rate of heptane was designed tobe 1.894 105m3/s (15GPH), which would generateapproximately 480 kW re, while the fuel pump wasdesigned to maintain a 0.791MPa (100 psig) pressure forthe duration of the test. Fig. 8 shows a typical spay re thatwas used in the test program. The test res for the othertests were wood-crib res, one of which is shown in Fig. 9.The expected maximum heat release rate from each cribwas approximately 300 kW.Fig. 8. Heptane spray re used in tests. Test detector samples can be seen

in the right.al 41 (2006) 616627with the measured ones. The comparisons for the caseswith slow growing res, such as crib res used in the test

program, look more favorable than those in the tests withspray res, which reached their maximum heat release rateswith almost no inception periods.Fig. 11 shows the ambient air temperatures at activation

of RC-B detectors in re tests. They all look random andwould not be possible to predict when the detector willactivate just based on the air temperature at activationalone. Fig. 12 shows the air temperature at activation vs.the average rate of rise of air temperature for RC-Bdetectors in re tests. Here the average rate of rise of airtemperature K was calculated as (air temperature atactivationinitial air temperature in a re test)/activationtime. The gure does not reveal any specic trend ofactivation temperatures with respect to the average rate of

rise of temperatures. Similar behaviors of air temperaturesat activation were observed in cases with the otherdetectors too. Again, predicting detector activation justbased on air temperature at activation alone would not bepossible. However, when the RTI and Trv of Detector RC-B were utilized, the prediction came out quite good asshown in Fig. 13.Fig. 14 shows the test results of the cases with RC-C,

RC-D, and RC-E detectors. The results with RC-B werealso included for comparison. The gure shows that thepredicted response times match reasonably well with themeasured ones for Model RC-C detectors. Note that thecomparison of the measured and estimated response timesfor Model RC-C detector samples are only in re tests1827. The gure indicates that the match in tests usingspray res are more favorable than those in the tests using

ARTICLE IN PRESS

0 10 20 30 40 50 6030

40

50

60

70

80

Air t

emp

at a

ctiva

tion

(C)

Test ID

Detector RC-B

Fig. 11. Air temperature at activation of RC-B detector samples in re

tests.

80

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 7500

100

200

300

400

500

600

700

Mea

sure

d Re

spon

se T

ime

(a)

Estimated Response Time (s)

MeasuredEstimated

Fig. 13. The measured vs. the estimated response times of RC-B detectors

in re tests.

S. Nam / Fire Safety Journal 41 (2006) 616627 6230 2 4 6 8 1030

40

50

60

70

Air t

empe

ratu

re a

t act

ivatio

n (C

)

Average rate of rise of temperature (C/s)

Detector RC-BFig. 12. Air temperature at activation vs. K of RC-B detector samples in

re tests.0 100 200 300 400 500 600 700 8000

100

200

300

400

500

600

700

800

Mea

sure

d re

spon

se ti

me

(s)

Estimated response time (s)

Rate-Compensated Detector RC-BRate-Compensated Detector RC-CRate-Compensated Detector RC-DRate-Compensated Detector RC-EEstimatedFig. 14. Comparison of the measured and the estimated response times of

rate-compensated heat-detector samples from four different models.

predicting response times will provide larger exibility tore safety engineers in choosing detector types andassigning the maximum detector spacing than currentlybeing practiced.

5. Other applications of bench-scale tests to heat detectors

5.1. Bench-scale tests in classification of detector types

Plunge-tunnel tests with varied air temperatures wereuseful for classifying whether certain detectors were a rate-of-rise type or a rate-compensated type. Simple testsrevealed that one of the most widely circulated rate-of-rise detectors was in fact not a rate-of-rise-type detector.Figs. 16 and 17 show how one can identify a rate-of-risedetector from other detector types. Fig. 16 shows that theair temperatures at detector activation of a rate-of-risedetector linearly increase with the initial air temperatureswhile those of a rate-compensated detector show no cleardependence on the initial air temperatures. Fig. 17 showsthat while the detector activation times of a rate-of-rise

ARTICLE IN PRESS

Detector Model

ourncrib res for Model RC-C detectors. The degrees ofdiscrepancies in the re tests using crib res, slow growingres, are greater than that in the tests with spray res.For RC-D detector samples, the estimated response

times are within an acceptable range of the measured onesfor practical applications. The gure shows that thematches are excellent when detector response times aregenerally short, i.e., under fast growing res, but lessaccurate when the response times are long, i.e., under slowgrowing res. For the tests with Model RC-E detectors,except for a few cases of poor matches, the estimatedresponse times match well with the measured ones. It wasnoticed that when Model RC-E detector samples wereexposed to repeated re tests, they sometimes either took aconsiderably longer time before responding than normallyexpected, or did not respond at all. There was a possibilitythat if the tests were conducted with a much slower phase,thus provided longer pauses between the tests, the detectorsamples might have responded differently.Overall, the body of test results indicate that predicting

detector response times using the model developed in thecurrent study works reasonably well. The relatively largedeviations associated with rate-compensated-type detectorModels RC-D and RC-E in Fig. 14 are related to the caseswhere the test re sizes with respect to the detectorlocations were marginal to activate the detectors in therst place. Also the heat release rates of the test resalready had peaked at some point before the end of thetest; thus, prolongation of the test did not signicantlycontribute to the increase of temperature and velocity of airsurrounding the detector samples. In those cases, instead ofa comparison of response times, a comparison of estimatedand measured re sizes at activation could have been abetter indicator of the precision of the prediction. In all theother cases, where the re sizes were not marginal fordetector activation or res grew continuously, as expectedin most eld operations, the comparisons of the responsetimes show good matches. Comparisons of predictedresponse times of xed-temperature rating detectors withthe measured response times in re tests are given inRef. [1].

4.4. Two fire tests in Ref. [1]

Two sets of detectors, Models RC-D and RC-E, wereexposed to two re tests conducted in Ref. [1]. Instead ofvirtual temperature rating Trv, it was assumed then that thelisted temperature rating Tr was the true temperaturerating. Based on that assumption, the corresponding RTIvalues were obtained. The estimated response times basedon that assumption did match poorly with the measuredtimes and that prompted new sets of analyses carried out inthis study. Using the RTI values and the Trv valuesestablished in Section 3, new estimation of the responsetimes were conducted and are shown in Fig. 15.

S. Nam / Fire Safety J624The re source was a heptane pan re [1]. The ceilingclearance for the re source was 3.05m and the re waslocated at the center of the 3.34-m radius circle for Test 1and 3.05m for Test 2. Fig. 15 shows the comparisons of themeasured response times and estimated ones of DetectorModels RC-D and RC-E, which were denoted as Type Fand G detectors, respectively, in Ref. [1]. The newlyestimated response times provide much improved matchescompared with the old estimated values.In summary, the concept of modeling detector response

times by using the RTI of heat detectors and themethodology of assigning the RTI values through bench-scale tests seem to be acceptable. The capability of

Fig. 15. Comparison of old- and new-estimated response times with the

measured response times for RC-D and RC-E detectors in Tests 1 and 2 of

Ref. [1].RC-D (Type F) RC-E (Type G)0

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Test 1: MeasuredTest 1: Current EstimationTest 1: Old EstimationTest 2: MeasuredTest 2: Current EstimationTest 2: Old Estimation

al 41 (2006) 616627detector are relatively constant regardless of the initialair temperatures, those of a rate-compensated detector

ARTICLE IN PRESSourn30

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S. Nam / Fire Safety Jdecrease with increasing initial air temperatures. Duringthe tests in Figs. 16 and 17, K was maintained at 0.2 1C/s.

5.2. Bench-scale test application for product quality control

It is important that manufactured detectors maintain areliable quality control so that the end users can expectconsistent performance under similar circumstances. How-ever, there is no reliable test method or enforced standardto guarantee this consistency. The bench-scale testsutilizing a plunge tunnel similar to the one used in thisstudy can be used as a good screening tool to measure adegree of the quality control of products. Fig. 18 shows theRTI values obtained through the data utilizing a xed-temperature plunge tunnel. The test samples were two

18 20 22 24 26 28 30 32 34 360

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Activ

atio

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Initial air temperature (C)

Rate-of-rise detectorRate-compensated detector

Fig. 17. Initial air temperature inside the plunge tunnel vs. detector

activation time (K 0.2 1C/s).

20 25 30 35 40 4520

25

Initial air temperature (C)

Rate-compendated detector

Fig. 16. Initial air temperature inside the plunge tunnel vs. the air

temperature at detector activation (K 0.2 1C/s). different models of xed-temperature-rating nonrestorabletypes, FTR-I and FTR-H. Twenty samples per each modelwere used in the tests. Based on Fig. 18, one can deductthat Model FTR-I would provide more consistent perfor-mance than Model FTR-H might. A listing organizationcan suggest an acceptable tolerance in the quality ofproducts and verify the tolerance through bench-scale tests.

6. Application of the RTI concept to eld operations

Currently, heat detectors are approved through two setsof tests: Oven tests and real-scale re tests [3]. Oven testsverify the posted temperature rating of heat detectors whilereal-scale re tests are employed to determine themaximum spacing that is to be assigned to detectors. TheRTI values obtained through the bench-scale tests can beused to assign the maximum spacing of a detector without

0 5 10 15 200

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Fig. 18. RTI values of nonrestorable xed-temperature-rating detector

Models H and I.

al 41 (2006) 616627 625going through real-scale re tests. Assigning the maximumspacing based on the RTI value has the followingadvantages over the current method: (1) Determinationof the maximum spacing based on real-scale re dependson a device that is adopted for the reference detector (asprinkler is commonly used), the size of a standard test re,the size of room where tests are conducted, or an ambienttemperature while tests are conducted; Thus, the tests canprovide wide range of different results for an identical typeof detectors. The spacing values based on RTI values ofdetectors will eliminate these inconsistencies. (2) Replacingreal-scale re tests with bench-scale tests will reduce thecosts associated with detector approvals. (3) Detectorspacing can be exibly adjusted to meet custom-tailoredspecic demands, if it deemed appropriate.A practical guide to the use of the RTI concept for

detectors can be illustrated through demonstrations ofpredicting detector response times under various rescenarios. Once RTI and Trv (or Cr for the rate-of-risedetectors) are known, the response can be predicted with aknown re scenario. The following examples will show how

the relationship of the detector spacing to activation can becalculated for given re scenarios.Detector response times with respect to threshold re

sizes were estimated by utilizing RTI and Trv (or Tr or Cr)of ten detector models in Table 1. The temperature ratingTr of the detectors in Ref. [1] are given in Table 1 and theRTI values are: 65.1, 69.0, 14.4, 12.7, and 8.8 in (m s)1/2,respectively, from FTR-AE [1]. The RTI values and Trv(or Cr) values of the detector used in the current work aregiven in Table 2. The detector response time of eachdetector was calculated with the following three differentspacing values3.0 by 3.0, 9.1 by 9.1, and 15.2 by 15.2m.The re growth rate was assumed the same as that of the

temperature is 20 1C, virtual origin z0 is close to zero, andthe detectors are mounted on a 9.1-m-high ceiling, which isthe ceiling height of many warehouses.The ceiling mounted detectors are located at 2.16, 6.47,

and 10.78m radial distances from the re plume axis. Inorder to estimate the re plume velocities and thetemperatures at the detector locations, the correlationsthat show the velocities and the temperatures as a functionof a radial distance r from a plume centerline axis need tobe known, preferably in functional forms. The ceiling jetow correlations in Ref. [6] are used here. The correlationof the ceiling jet temperatures in Ref. [6] is

p h i 2n o

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S. Nam / Fire Safety Journal 41 (2006) 616627626medium growing re of NFPA 72 [4]. The following willshow how detector response times at different spacingvalues can be estimated.The re scenario described in NFPA 72 as the medium

growing re has the following heat release rate:

_QT 0:0117t2, (13)where _QT is the total heat release rate from a re in kW andt the time after ignition in s. To stay in a conservative side,it can be assumed that the re source is directly below thecenter of the specied maximum detector spacing, which isthe most remote location from the detectors.The plume correlations can be given as follows [5]:

DT0 CDT0 T1 = gC2pr21 h i1=3

_Q2=3c z z0 5=3, (14)

Vz0 CV z0 g= Cpr1T1 1=3 _Q1=3c z z01=3, (15)

where DT0 is the excess temperature at the plume centerline(K), TN the ambient temperature (K), g the gravitationalacceleration (m/s2), Cp the constant pressure specic heatof air (kJ/kgK), rN the density of ambient air (kg/m

3), _Qcthe convective heat release rates (kW) calculated as Zc _QT(here Zc is the convective portion of HRR and chosen as0.65) , z is the elevation from the source of the plume (m),and z0 the virtual origin of the plume (m). The plumecoefcient for temperature, CDT0 , was taken as 9.1 and forvelocity, CVz0 3:1 [5]. It is assumed that the ambient

Table 4

Detector response times in the given re scenario

Detector model ID R1 (3.0 by 3.0m)

tactivation (s) _QT (kW)

RR-A 282 929

RC-B 254 754

RC-C 250 734

RC-D 319 1192

RC-E 395 1830

FTR-A 332 1294

FTR-B 441 2283

FTR-C 306 1100FTR-D 495 2874 740

FTR-E 469 2579 704y y0 a= w p=2 exp 2 x xc =w , (16)

where y log DT=DT0

, y0 0.00781, a 1.279,w 1.239, x log r=b, and xc 1.51. Here DT(r) is theexcess ceiling ow temperature at location r, normalized byDT0, which is the excess temperature of an unobstructedre plume axis at the elevation corresponding to a ceilingheight h. The radial distance, r, was normalized by b, whichis a plume half-width of an unobstructed re plume at theelevation corresponding to the ceiling height h. The plumehalf width can be calculated as [5]

b 0:12 T0=T1 1=2

z z0 , (17)where T0 is DT0+TN. Ref. [6] also shows a collection ofdata showing Vr/Vz0 vs. (r/b). Vr is the radial directionalow velocity at r and Vz0 is the centerline axial velocity ofan unobstructed re plume at the elevation correspondingto a ceiling height h. The correlation curve given in thegure is the same as Eq. (16), however, with differentvalues of the parameters. Here y log V r=V z0

,

y0 0.0551, a 0.799, w 0.791, and xc 1.318.The temperature and velocity variations with time at

r 2.16, 6.47 and 10.78m can be obtained by applyingEqs. (14)(17). Then Eq. (2) can be numerically integrateduntil Te reaches the virtual detector temperature rating,Trv, in Table 2 for rate-compensated detectors (ordTe=dt

XCr in the case of rate-of-rise detectors) or Trin Table 1 for xed-temperature-rating detectors. Table 4

(9.1 by 9.1m) R3 (15.2 by 15.2m)

ivation (s) _QT (kW) tactivation (s) _QT (kW)

6750 1316 20307

1829 522 3189

1777 514 3099

2772 637 4754

4172 777 7067

2935 653 5000

5059 851 8482

2602 619 44856411 956 10709

5807 912 9742

shows the response times of the detectors at the threespacing locations. The re growth was simulated for

conducted with the tunnel that provided air ow of a xedtemperature. Possible combinations of RTI and T values

measured temperatures and velocities of the re plumes

The author gratefully acknowledge Dr. Chris Wieczorek

ARTICLE IN PRESSS. Nam / Fire Safety Journal 41 (2006) 616627 62730min. When the computation showed that a detectorwould activate, then the response time and the HRR at theactivation are given.Ref. [6] shows how the maximum spacing of a xed-

temperature-rating detector can be assigned when thedetector works as a device tripping a pre-action valve in adry-pipe system. The example in the reference shows thatby having the ability of predicting the detector responsetime, it was possible to assign the maximum detectorspacing without compromising on the full benet of havingthe pre-action valve in the given dry-pipe sprinkler system.There can be more similar examples of performance-basedspacing once all detectors are approved with their knownRTI values, rather than the current practice of assigningthe maximum spacing value of a detector that has a limitedvalue in practical applications. In case a listing organiza-tion wants to maintain the current way of assigning themaximum spacing values that are linked to activation of acertain reference device, it can be achieved in a similar waydescribed above. By computing response times of thereference device using its own RTI and Tr values under thegiven re scenario, one can decide the maximum spacingvalues of a detector by comparing the response times of thedetector at a few radial locations with that of the referencedevice at the specied locations.

7. Summary and conclusion

Three subjects covered in this paper are: obtaining RTIvalues of rate-of-rise and rate-compensated heat detectorsthrough bench-scale tests, validating through real-scale retests the methodology of assigning RTI values, andapplying the RTI concept to product approvals and eldoperations.Detector samples from ve different modelsone rate-

of-rise and four rate-compensated detector typeswereexposed to plunge-tunnel tests to measure response timeswhere hot air was circulated with the temperature varyingat a xed rate. The RTI and Cr (threshold rate of rise foractivation) of the rate-of-rise detector, Model RR-A, wereobtained by analyzing the test data. However, rate-compensated detectors needed more plunge-tunnel tests.Plunge-tunnel test data indicated that rate-compensateddetectors behave as if they were xed-temperature-ratingdetectors albeit that their true temperature rating values(virtual temperature rating) would be substantially lowerthan their corresponding listed temperature rating values.Finding the RTI and the virtual temperature rating valuesof rate-compensated detectors (Trv) required additionalsets of plunge-tunnel test data. One more set of tests werefor his contributions in setting up the bench-scale testapparatus and selecting the proper test detectors, and Mr.Steve DAniello for his contributions in conducting thebench-scale tests. He is also grateful to Mr. Jeff Chaffeeand his group for contributions in carrying out the re testsand to Dr. Robert Bill, Jr., for his encouragements andmany valuable suggestions in carrying out this project.

References

[1] Nam S, Donovan LP, Kim JG. Establishing heat detectors thermal

sensitivity index through bench-scale tests. Fire Saf J 2004;39:191215.

[2] Heskestad G, Bill RG. Quantication of thermal responsiveness of

automatic sprinklers including conduction effects. Fire Saf J

1988;14:11325.

[3] Thermostats for automatic re detection, Class no 3210, FM

Approvals, 1151 BostonProvidence Turnpike, Norwood, Massachu-

setts, 1978.

[4] NFPA 72, National re alarm code, 2002 ed. , 1 Batterymarch Park,

Quincy, Massachusetts:National Fire Protection Association;2002.

[5] Heskestad G. Engineering relations for re plumes. Fire Saf J

1984;7:2532.

[6] Nam S. A case study: determination of maximum spacing of heat

detectors. J Fire Prot Eng 2005;15:518.were compared with the measured ones. The comparisonswere favorable and thus provided condence in themethodology and the concept. The ability of predictingdetector response times by utilizing the RTI values thatwould be obtained through bench-scale tests will provide agreat exibility for eld operations in choosing detectortypes and maximum spacing values of a chosen detector.

Acknowledgmentsobtained from the two sets of test data were plotted to nda common value. The intersection point of the potentialRTI and Trv values estimated from the two sets of data waschosen as the RTI and the virtual Trv values of the rate-compensated detectors.Once the RTI and Trv (or Cr) values were obtained, the

validity of the concept and the methodology were testedthrough 27 real-scale re tests. Ten detector samples, twoeach from the ve models, were installed on a movableceiling and exposed to either heptane spray res or cribres. Detector response times were recorded together withthe temperatures and velocities of the ceiling jet ows atdetector locations. The estimated detector response timesthat were calculated by utilizing the RTI and Trv (or Cr)values of the detector samples in conjunction withrv

Predicting response times of fixed-temperature, rate-of-rise, and rate-compensated heat detectors by utilizing thermal response time indexIntroductionTheoryAssigning RTI values to various detector types based on the bench-scale test dataFixed-temperature-rating detectorsRate-of-rise-type detectorsRate-compensated heat detectors

Comparisons of estimated with measured response timesFire test configurationTest firesOverall comparisons of the estimated and the measured response times per each detector modelTwo fire tests in Ref. [1]

Other applications of bench-scale tests to heat detectorsBench-scale tests in classification of detector typesBench-scale test application for product quality control

Application of the RTI concept to field operationsSummary and conclusionAcknowledgmentsReferences