NBSIR 83-2807

Thermal Actuation of Extinguishing

Systems

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

March 1984

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U S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANOAROS

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83-2307

1384

NATIONAL BUREAU. OF STANDARDS

LIBRARY

NBSIR 83-2807

THERMAL ACTUATION OF EXTINGUISHING

SYSTEMS

1 co

. U5£>

IW

David D. Evans

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

March 1 984

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

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Director

TABLE OF CONTENTS

Page

LIST OF FIGURES iv

Abstract I

1. INTRODUCTION I

2. CHARACTERIZING THERMAL RESPONSE OF DETECTORS 3

3. CALCULATING CEILING-JET TEMPERATURES AND VELOCITIES 7

3.1 Uniform Ambient 7 3.2 Two-Layer Ambient 9

4. EXPERIMENT 13

5. DISCUSSION AND CONCLUSIONS 15

6. REFERENCES 15

7. NOTATION 18

iii
LIST OF FIGURES

Page

Figure 1. Calculated Temperature Rise of Sprinkler Links

(RTI 25, 100, and 400) in Response to Measured near Ceiling Temperature and Velocity Histories from the First

Large Scale NSF-Rann Bedroom Fire Test July 11, 1983... 20

Figure 2. Dimensionless Correlations for Maximum Ceiling-Jet

Temperatures and Velocities 21

Figure 3. Schematic Representation of the Substitute Plume

Calculation 22

Figure 4. Comparison of Dimensionless Maximum Ceiling-Jet

Temperature from Laboratory Experiment with Existing

Correlations 23
THERMAL ACTUATION OF EXTINGUISHING SYSTEMS

David D. Evans

Abstract

A brief review of the Response Time Index (RTI)

method of characterizing the thermal response of commercial sprinklers and heat detectors is presented. Measured ceiling layer flow temperature and velocity

histories from a bedroom fire test are used to illustrate

the use of RTI in calculating sprinkler operation

times. In small enclosure fires, a quiescent warm gas

layer confined by the room walls may accumulate below the

ceiling before sprinkler operation. The effects of this

warm gas layer on the fire plume and ceiling-jet flows are accounted for by substitution of an equivalent point

source fire. Relationships are given for the location

and strength of the substitute source relative to a point

source representation of the actual fire. Encouraging

agreement was found between measured ceiling-jet temperatures from steady fires in a laboratory scale cylindrical

enclosure put into dimensionless form, based on parameters of the substitute fire source, and existing empirical correlations from fire tests in large enclosures in

which a quiescent warm upper gas layer does not

accumulate.

Key Words: Fire models; fire plumes; fire protection;

heat detectors; sprinkler systems; zone models.

1 . INTRODUCTION

Over the past decade a great deal of research has been directed at making

quantitative predictions of fire growth in enclosures. Complementary efforts

to quantify and model fire suppression have also been initiated. Contribu1
tions to fire suppression and detection modeling have generally been made

under conditions where results are not influenced by any surrounding enclosure. Application of this research is generally limited to large spaces or short times after fire ignition in which enclosure effects are negligible.

In modeling the suppressive action of extinguishing systems, a primary

factor is the time delay between fire ignition and the start of fire suppression. In the case of typical automatic fire protection sprinkler systems,

suppression begins after actuation of thermal sensing elements heated to a predetermined temperature level predominately by convection from the fire

driven gas flow. These sensing elements are incorporated into the sprinkler

heads that will distribute the extinguishing agent. It is common to find

these sprinkler heads installed close to the ceiling of an enclosure.

Prediction of the time delay required for ceiling mounted thermal sensing

elements, such as those contained in sprinkler heads or heat detectors, to

respond to a growing fire has been studied by Heskestad and Delichatsios [1]*

for the special case of fires having heat release rates that increase proportionally with the second power of time from ignition. Experimental cor- relations of the fire driven ceiling-jet flow temperatures and velocities for

steady fires have been studied by Alpert [2]

,

Heskestad [3]

,

and Heskestad and

Delichatsios [4]. Alpert [5] also has performed a theoretical study of ceiling-jet flow.

In all of these studies, the ceiling layer flow is considered unconfined

by enclosure walls, and the enclosure ambient outside the ceiling-jet flow is

assumed to be uniform in temperature. This can be a useful approximation for

fires in large enclosures, such as warehouse or industrial facilities, where

the time to heat detector alarm or sprinkler operation may be small compared

to the time to fill the upper portion of the enclosure with recirculating

combustion products.

'Numbers in brackets refer to the literature references listed at the end of

this report.

2
However, for fires in enclosure sizes characteristic of residential

dwellings, the accumulation of a warm upper layer of gas confined by the room

walls occurs rapidly after ignition, and is a primary feature that must be

accounted for in fire models. Popular two-zone room fire models, such as the

Harvard Computer Fire Code [6]

,

predict enclosure fire conditions based on a division of the enclosure into a warm upper zone and a cool lower zone. To

provide useful methods to predict the time delay before operation of ceiling

mounted sprinklers and heat detectors in enclosures where an accumulated warm

upper layer of gas is present, existing methods must be extended to consider a two-layer ambient room environment.

This paper gives a brief description of a laboratory test method, the

Plunge Test [7], used to characterize the thermal response of commercial

sprinklers and heat detectors. An illustrative example is given of the use of

thermal characterizations from this test to estimate sprinkler operation times

in response to a specific room fire. Correlations of steady ceiling-jet flow

temperatures and velocities developed by Alpert [2] and Heskestad [3] are discussed. A technique is described that reduces the fire driven plume and

ceiling-jet flows in the upper portion of a two-layer ambient to the

equivalent single layer flow. Temperature measurements collected in the upper

portion of a laboratory scale cylindrical enclosure under steady fire conditions are used to test the technique.

2. CHARACTERIZING THERMAL RESPONSE OF DETECTORS

Either measurement or calculation of the fire driven gas flow temperature

and velocity history in the ceiling-jet provides information on the flow field

in which a sprinkler or detector is submerged and heated to operating temperature. In order to determine the time needed to raise the temperature of the

sensing element from the initial temperature at fire ignition to the operating

temperature, the thermal response characteristics of the hardware must be

known in such a way that they may be generalized for any given gas flow

history.

3
Heskestad and Smith [7] developed an approximate model for heating of

thermal sensing elements by fire driven flows. They found that for a wide

range of commercial sprinklers, the sensing elements may be considered uniform

in temperature when heated by the convective flow from a fire. Net radiative

effects during early fire growth were calculated to be less than 20 percent of

convective heating. Based on convective heating only, the equation for changing sensing element temperature is

d ( AT ) / d t r”

1 (AT - AT.) (1) L g L

where AT^ is the excess temperature of the sensing element above its initial

temperature, and AT is the excess temperature of the gas above the initial

8

sensing element temperature. The time constant, t, may be related to the

properties of the sensing element and the convective heating of the gas flow

it is exposed to according to:

T - m

L

cL

/h

cAL

(2)

where is the mass, c^ is the heat capacity per unit mass, is the area of

the sensing element, and h

c is the average convective heat transfer coefficient over area A^. The sensing element time constant, t, is not characteristic of the hardware alone because the value of h

c depends on the velocity of

the gas flow.

Typical fusible sprinkler sensing elements, links, in use today contain

solder material which must undergo phase transition before the sprinkler can operate. Strictly speaking, equation l governs the temperature response of

the sensing element up to the temperature at which phase transition of the

solder material begins. However, in practice, equation l is used to determine

an effective value of the time constant for a sensing element that includes a fusion process for the solder. In application, differences between the use of an effective time constant compared to explicit accounting of the phase transition process in a more complicated model have been studied by Evans [8] and were found to be minor even for elements with large solder contents.

4
Effective values of the time constant, t, for commercial devices are obtained from measurement of the time to operation for a sprinkler of known

initial temperature after suddenly immersed in a heated gas flow of known

uniform temperature and velocity. Operation is assumed to occur at the manufacturer's indicated operating temperature. Based on determination of the

link temperature history by equation l, the value of the time constant is

calculated from the solution for the known constant AT , and the measured time

g

to operation, t r

, as

t = -t /In (1 - ATt /AT ) (3)

r Lr g

where AT^

r is the manufacturer's indicated operation temperature minus the

initial temperature of the sensing element at the time of immersion. A test

apparatus designed to measure sprinkler time constants is described by

Heskestad and Smith [7].

The measured values of the time constant, t, are dependent on gas

velocity in the test apparatus. The greater the gas velocity, the larger the

value of convective heat transfer coefficient and smaller the value of t, from

equation 2. For blunt bodies in crossflows, over the range of interest for

application to sprinkler operation, variations of the convective heat transfer

coefficient are proportional to the square root of gas velocity and independent of the gas temperature [7,9]. Therefore, the product of t with gas

velocity to the half power is a quantity which compensates for variations in

gas velocity used in tests to measure the time constant and is a characteristic of the hardware alone. Heskestad [10] names this product the response

1/2 time index, RTI = t_U

q

» w^ere the subscript, o, identifies reference test

measurement conditions. The time constant at any gas velocity is calculated

from the RTI using

x = RTI/U 1 ^ 2 (4)

Customary units for the RTI are Values for the response time index

for ordinary sprinklers range from a low of 22 m^^s'V^ f or qUi ck operating

residential sprinklers to 375 m^^gl/2 f or filled bulb sprinklers [10].

5
Application of the response time index to the prediction of sprinkler

operation times can be examined using published test data from a large scale

bedroom fire test. This fire test [11] was conducted on July 11, 1973 as part

of a broad fire research program conducted in part under the direction of

Professor Howard Emmons. In this test a bed mattress, in a fully furnished

room, was ignited by a small fire source. Among the many measurements, the

gas velocity and temperature 0.08 m below the ceiling, and 1.0 m from the axis

of the initial fire plume was measured in 20 second intervals after

ignition. Figure l shows the temperature and velocity histories. Velocity

measurements terminated with the failure of the sensitive fan anemometers at 9

minutes. Temperature measurements continue throughout the test.

The measured velocity and temperature histories provide the necessary

information to determine the temperature history of the sensing element of a sprinkler or heat detector that would be installed just below the ceiling at

the position where the measurement were taken. As an illustration, three

calculated curves produced by solving equation 1 numerically using the measured gas temperature and velocity histories are shown in figure l for sprinklers of different sensitivity: RTI = 25, 100, 400. As discussed an RTI of 25

is characteristic of current state-of-the-art quick operating sprinklers. The curves for RTI = 100 and 400 include the range of RTI values for most industrial sprinklers [10]. Selecting a typical operating temperature of 74°C, the

three sensor temperature curves may be used to estimate the time from ignition

of the mattress to sprinkler operation. In this case, the time to reach 74°C

for the RTI values of 25, 100 and 400 are 3.47 min, 4.27 min, and 5.77 min,

respectively.

In practice, it is unusual to have measured near ceiling temperature and

velocity histories available when making estimates of sprinkler or heat detector response times. It is more common to be given fire heat release rate

histories and fire locations. Therefore, ceiling-jet temperature and velocities must be calculated from this information. In the remaining portion of

this paper methods to perform these calculations will be examined.

6
3. CALCULATING CEILING-JET TEMPERATURES AND VELOCITIES

3.1. Uniform Ambient

Studies of fire driven ceiling layer flow were first performed to

characterize steady conditions by Alpert [2] and Heskestad [3]. Even though

steady fires are generally of limited practical interest, results of these

studies may be used to provide estimates of gas flow conditions in the ceiling

layer for slowly varying fires. For such quasi-steady fires, changes in heat

release rate are small over the time needed to adjust the flow field to new

conditions. Later, Heskestad and Delichatsios [A] studied a special class of

transient fires where the convective fraction of the heat release rate

increases proportionally with the time from ignition raised to a power (powerlaw fires). Results from selected experiments with fires that increased as the square of time from ignition have been the basis of current engineering

design calculations for fire detector spacing under large area ceilings [12].

Attention in this paper is limited to discussion and use of a series of

steady ceiling layer flow results to predict sprinkler and heat detector

operation for slowly growing fires. From experiments and use of dimensional

arguments, Heskestad [3] has provided a correlation of maximum steady temperatures and velocities for unconfined ceiling layer flow as a function of

radial distance from the axis of the fire plume impinging on an unobstructed

ceiling. These correlations of dimensionless maximum temperature rise,

are shown as solid line curves in figure 2, adapted from the work of Heskestad

and Delichatsios [4]. All symbols are defined in the Notation section of this

paper. The correlation of dimensionless maximum velocity is presented, com- bined with the dimensionless maximum temperature rise. The equation for the

solid line curve shown in figure 2 is:

(5)

and dimensionless maximum velocity

1/3

( 6 )

7
for (r/H > 0.3) (7)

* * 1/2

U /(AT ) lU

m m

0.68 (r/H)"

0,63

Both solid line curves in figure 2 are faired fits of data obtained from fire

tests with steady heat release rates in the range of 5 KW to 375 KW and ceiling heights from 1.2 m to 2.4 m [3].

Other empirical correlations for maximum temperature rise and velocity in

the ceiling-jet layer have been reported by Alpert [2]. Data for these correlations was obtained from tests of a larger scale than those used by Heskestad

[3] ranging in heat release rate from 670 kW to 100 MW with ceiling heights

from 4.6 m to 13.7 m. The correlations obtained by Alpert [2] have been

recast into dimensionless variables using an ambient air temperature of 293°K

and pressure of 1.0 atmosphere. They are •

•

AT* = 6.18 mfor r/H < 0.18 (8)

* . -2/3

AT = 1.97 (r/H) /J mfor r/H > 0.18 (9)

U* = 3.16 m

for r/H < 0.15 (10)

U* = 0.65 (r/H)" 5/6

m for r/H > 0.15 (ID

These values are shown as the broken-line curves in figure 2, in the same form

used by Heskestad and Delichatsios [4]. For the graph of velocity correla-

* * ]/2 tion, equation 11 was extended to calculate U /(AT ) over the range 0.133 < m m

r/H < 0.18.

The correlations, equations 8-11 determined from large scale tests were

found to be in good agreement with theoretical predictions also performed by

Alpert [5] for weakly buoyant flows. Using both top-hat and half-Gaussian

distributions of temperature and velocity for steady flow in the ceiling

layer, Alpert calculated temperatures, velocities, and layer depths as a function of radial position from the axis of the fire plume impinging on the

ceiling.

8
Results from either of the steady-state correlations presented above may

be used to determine gas flow temperatures and velocities in the ceiling layer

where sprinklers and heat detectors are typically located. For cases of

slowly growing fires where quasi-steady assumptions may be reasonable, the

results of these studies may be used to estimate transient conditions and

provide a basis for calculation of response time. In enclosures where fires

may produce an accumulated warm layer of gas above a cool lower layer before

fire detector response, results from the above studies do not apply

directly. However, methods have been developed to make use of these correlations to predict conditions in the two layer ambient characteristic of small

enclosure fires.

3.2. Two-Layer Ambient

Soon after fire starts in small enclosures a quiescent layer of warm gas

accumulates in the upper portion of the room. Zukoski [13] has developed

methods to estimate the filling rate of this upper layer for closed rooms. To

take advantage of the research described in the previous section where the

accumulation of this quiescent upper warm layer of gas is unimportant, a method needs to be found to determine the plume flow in the warm layer from

conditions given for the fire in the cool lower layer.

Plume flow above fires is often characterized by the weakly buoyant flow

analysis from a virtual point source as described by Morton et al. [14] and

Zukoski et al. [15]. The former has been used by Alpert [5] as part of his

analysis of ceiling-jet flows in a uniform ambient. In a room fire in which

warm gas has accumulated above cooler gas forming a two layer ambient , weakly

buoyant point source plume flow calculations are just as applicable in the

lower layer containing the fire as in a totally uniform ambient. However,

adjustments are needed to describe the plume flow after penetration into the

upper layer.

In a study of heat transfer to ceilings, Cooper [16] was the first to

propose approximations to calculate steady plume flow in the upper warm layer

by formulating a substitute virtual point source fire. The location of the

second source relative to the one used to calculate flow in the lower layer,

9
depends on the upper and lower layer temperatures, fire heat release rate, and

distance of the interface between the cool and warm layers above the source

point for the lower layer plume flow. Other methods to approximate plume flow

in the upper layer have been proposed by Sargent [17], Evans [18] and Cooper

[19]. Although several of these methods have shown good agreement with presently available two-layer ambient plume flow temperature data, a recently

developed method intended specifically for use in models to estimate detector

and sprinkler response to growing fires will be described.

Starting with plume flow equations developed by Zukoski et al. [15] a substitute virtual point source strength and location for plume flow in the

upper layer can be determined by conserving axial temperature and excess enthalpy flux for the entire plume flow across the interface between the

quiescent cool lower layer and warm upper layer. Using this substitute point source for plume flow in the upper layer, the problem of flow in the two layer

ambient is reduced to flow in a uniform temperature ambient with temperature

equal to the upper layer. For cases where the ceiling-jet flow, generated by

impingement of the fire plume on the ceiling, remains in the warm layer, the

correlations (equations 8-11) when used with the substitute source apply to

the prediction of sprinkler or heat detector activation in the upper layer.

Zukoski et al. [15] proposed the following equations to describe fire

plume temperature and velocity distributions, which will be taken as the

starting point for this analysis.

AT/ AT = exp (-e

2 r2 /b2

) m

(12)

W/W = exp (-r

2 /b2

) m

(13)

b = C „Z

l (14)

4VT - - S'}*

273

(15)

W = C g

1/2

Z l/2

Q*

l/3 m w

(16)

Q* = Qc/(p„c p>c Ty/2

z 5/2

) (17)

10
kukoski et al. [15] recommended the use of the following values for constants

determined directly or indirectly from experiments:

C- = 9.115, C = 3.87, C 0 = 0.131, 0

2 = 0.913

T w l

Equations 12-17 can be used directly to calculate the plume flow in the

lower cool gas layer containing a fire that can be characterized using a point

source of heat at some distance below the interface. At the interface adjustments must be made.

In a previous study of plume flow across abrupt changes in ambient

temperature by Evans [20], it was found that sharp decreases in calculated

plume temperatures could occur when substitute plume sources are determined by

matching at the interface only quantities that are integrated over the entire

plume flow; such as mass flux, excess enthalpy flux, and momentum flux. These

abrupt changes have not been observed in experiments. For calculation of

ceiling mounted sprinkler and heat detector operation times, this abrupt

decrease in calculated temperature is undesirable. In applying the substitute

plume technique only two properties of the plume flow from the cool lower

layer arriving at the interface can be preserved in calculating the new source

location and strength representing plume flow above the interface. To calculate heat detector and sprinkler response, the best choice of quantities to

preserve may be maximum temperature, and excess enthalpy flux. Preserving the

maximum temperature prevents dramatic changes in the temperature profile.

Conserving excess enthalpy flux is equivalent to energy conservation. Preserving velocity and closely associated plume mass and momentum fluxes are not

considered as important as preserving temperature elevations and excess energy

flux in calculating sprinkler operation times, because thermal detectors

primarily respond to temperature rise and not gas velocity. The velocity of

the gas flow does affect heat transfer rates, but only proportionally with the

half-power of velocity.

At the interface between the lower cool layer, (1), and upper warm layer,

(2), the calculated flow from the source in the lower layer is matched to

11
plume flow from an imagined source point totally within a warm layer such

that;

T , T « m,l m,2 (18)

and

/

2ttc p . W. AT. rdr

n P °°»1 1 l 2l' c

p

p-,2

W

2

[

T

-,2

- T

-,l + AT2

]

rdr (19)

Equation 18 requires that the maximum plume temperatures be equal. Equation

19 requires that the excess enthalpy flux with respect to the reference temperature T . be equal in both layers. Specific heat capacity is assumed to

be constant. Radial temperature and velocity profiles in both layers are assumed to be Gaussian. Using equations 12-17 to represent the plume flow,

substitutions are made in equations 18 and 19. The resulting two equations

are solved for the relationships between the strength and location of the source points relative to the interface for flow in the lower and upper

layers. They are:

‘ 1,2

‘ 1,2

2/3

(1 + S: Q

i,i )/?C

T " 1/C

T

]

3/2

T7T

g Ql,l

C

T

‘1,2 [«- DCS2

*!) + 5 C

T

Q*

>2

2/3

]

2/5

Z

I,

l

( 20 )

( 21 )

where £ = T^

\ anc* subscript * represents conditions at the interface

between cool and warm quiescent layers. A schematic representation of the

calculated plume flow in the two layer environment divided into its two components is shown in figure 3. In the lower layer, flow is calculated from

* source in an ambient with uniform temperature T^

^ for < Z^. In the

upper layer, plume flow is calculated from source in an ambient with uniform temperature T 0 for Z 9 > Z „ which corresponds to positions measured

from the elevation of source as Z = Z - Z

^ + Z ^

.

12
After a substitute source for plume flow in the warm upper layer has been

calculated, the correlations developed for ceiling layer flow by Alpert (equations 8-11) and Heskestad (figure 2) may be applied to calculate maximum

temperatures and velocities in the ceiling-jet flow using upper layer ambient

* conditions to form dimensionless variables for the substitute source Q^.

4. EXPERIMENT

A simple laboratory scale cylindrical enclosure was built to study the

flow produced by steady axisymmetric fires. This enclosure consisted of a 1.22 ra diameter, 13 mm thick ceramic fiber board circular ceiling surrounded

by a 0.29 m deep clear rigid plastic curtain. This enclosure is supported by

rods so that gas may flow freely out around the lower edge of the plastic

curtain sidewall into the laboratory. The commercial laboratory burner that was used had a 0.0365 m diameter screened outlet and was located directly

under the center of the circular ceiling and below the lower edge of the

sidewall. Flow from the burner outlet would entrain laboratory air until it

reached the warm layer of gas accumulated under the ceiling within the sidewall. Laboratory natural gas was burned, premixed with laboratory air to

minimize flame heights. Protective screening was installed around the apparatus to help dampen room air drafts.

Data is available from a small series of tests conducted to map the

radial distribution of temperatures within and just below the upper layer of

gas contained by the sidewall [21]. This data may be used to determine an average temperature for the warm layer contained by the plastic sidewall and

ceiling, temperatures in the fire plume before entering the warm gas layer,

and the maximum temperatures in the ceiling-jet flow. In all cases, a steady

fire was established for at least 20 minutes before data sampling was started.

Figure 4 shows data from four tests having different combinations of two

heat release rates and three burner to ceiling heights. For this modest

series of tests, the depth of the plastic sidewall was fixed at 0.29 m. Average warm layer temperatures established naturally by the plume flow from

the burner impinging on the ceiling and circulating through the enclosure

ranged from 21 °C to 56°C above the lower layer (laboratory) ambient of 20°C.

13
The depth of the warm gas layer was assumed for calculation purposes to be

equal to the depth of the sidewall curtain. Heat release from the burner was assumed to be totally convective and equal to the value obtained from complete

combustion of the metered natural gas flow.

Virtual source locations for all fires were checked using temperature

measurements on the plume axis in the laboratory ambient. For all of the 0.63

kW fires the virtual source was calculated to be within 0.01 m of the actual

burner outlet. For the 1.25 kW fire, Nixon’s [21] recorded temperature in the

plume before entering the upper layer is labeled with large uncertainty

because of signal fluctuations and is 100 K greater than expected from extrapolation of the adjacent measurement. The calculated virtual source location

using this measurement was 0.04 m above the burner outlet. Using the adjacent

measured value 0.04 m into the warm layer, the virtual source location was found to be at the burner outlet elevation, as in the 0.63 kW fire tests. In

all calculations of ceiling layer flow, to be presented in this paper, the

virtual source location was assumed to be at the burner outlet.

Using the above characterizations of the enclosure fire; upper and lower

layer temperatures, the heat release rate of the burner, and upper layer depth

of 0.29 m corresponding to the curtain depth, a substitute source

* location Z T

„ and strength Q „ for the flow in the upper layer were calculated using equations 20 and 21. Values of dimensional Q

c and H

calculated from these substitute source parameters were used to form values

* of AT^ following equation 5 from the measured values of maximum temperature in

the ceiling-jet, AT = T - T _ for radial positions no closer than 0.20 m to m m 00

, z the sidewall. At distances within 0.20 m of the sidewall the ceiling-jet flow

enters the ceiling-sidewall corner region which is not modeled. These dimensionless maximum excess temperatures are shown plotted vs. dimensionless

radius in figure 4. Other data obtained in a 0.91 m diameter enclosure by

Zukoski and Kubota [22] were reduced in the same manner as Nixon's data with

the exception that the upper layer temperature was determined from the average

of only one vertical traverse in the upper layer at mid-radius. These data

from three experiments are shown in figure 4. For comparison, the two

temperature correlations developed by Alpert [2]

,

and Heskestad and

Delichatsios [4] are also shown in figure 4.

14
Measurements from the laboratory scale tests (Q

c

“ l kW and H * 0.5 m) are seen to fall close to, but at consistently higher temperatures than would be

expected from the correlations obtained in much larger tests

(Q

c

» 1 MW, H » 10 m) . This could be simply a result of the relatively weaker

turbulent mixing of the plume flow with ambient air in these laboratory scale

tests compared with the much larger fires and ceiling heights used to develop

the empirical correlations. Therefore, it is recommended that the existing

correlations developed by Alpert [2] and Heskestad and Delichatsios [4] be

used in application to fires that are larger then those used in these

laboratory experiments.

5. DISCUSSION AND CONCLUSIONS

A method has been demonstrated to estimate maximum excess temperature and

maximum velocity for steady axisymmetric ceiling-jet flow in an upper warm

layer, from a fire source in a lower cool layer of a two-layer ambient. The

method involves calculating an equivalent single layer source and using existing correlations. When combined with measured thermal response characteristics, such as the Response Time Index, and warm upper layer temperatures and

depths from a zone fire model, this method may be a useful tool for calculating operation times of convectively heated thermally activated sprinklers and

heat detectors that are often installed near ceilings. It is expected that

the steady-state results may be useful in estimating conditions for slowly

growing fires in enclosures where a quiescent warm gas layer can accumulate

below the ceiling before operation of a thermally activated device, although

limitations have not been quantified. Large scale tests with both steady and

growing fires are needed to test the limitations of these calculation methods.

6. REFERENCES

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

Phase I: Effects of Fire Size, Ceiling Height and Material, Volumes II - Analysis, Technical Report Serial No. 22427, RC 77-T-ll, Factory Mutual

Research Corporation, Norwood, MA 02062, 1977.

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

Detectors, Fire Technology, 8, pp. 181-195, 1972.

15
[3] Heskestad, G. , Physical Modeling of Fire, J. Fire and Flammability, 6,

pp. 253-265, 1975.

[4] Heskestad, G. and Delichatsios , M.A. , The Initial Convective Flow in

Fire, Seventeenth Symposium (International) on Combustion, The

Combustion Institute, Pittsburgh, PA, pp. 1113-1123, 1978.

[5] Alpert, R.L., Turbulent Ceiling-Jet Induced by Large-Scale Fires,

Combustion Science and Technology, 11, pp. 197-213, 1975.

[6] Mitler, H. and Emmons, H.W., Documentation for CFC V, The Fifth Harvard

Computer Fire Code, NBS-GCR-8 1-344 , National Bureau of Standards,

Washington, D.C. 20234, 1981.

[7] Heskestad, G. and Smith, H.F., Investigation of a New Sprinkler

Sensitivity Approval Test: The Plunge Test, Technical Report Serial No.

22485, RC 76-T-50, Factory Mutual Research Corp., Norwood, MA 02062,

1976.

[8] Evans, D.D., Characterizing the Thermal Response of Fusible-Link

Sprinklers, NBSIR 81-2329, National Bureau of Standards, Washington,

D.C. 20234, 1981.

[9] Young, M.F., LaRue , J.C. and Koency, J.E., Effect of Fire-Stream

Velocity Vector on the Output of a Circular Disk Heat Flux Gauge, Paper

83-HT-58 American Society of Mechanical Engineers, New York, NY 10017,

1983.

[10] Heskestad, G., The Sprinkler Response Time Index (RTI), Paper (RC 81-TP3) presented at the Technical Conference on Residential Sprinkler

Systems, Factory Mutual Research Corp., Norwood, MA, April 28-29, 1981.

[11] Croce, P.A. and Emmons, H.W., The Large Scale Bedroom Fire Test, July

11, 1973, Technical Report Serial No. 21011.4, RC 74-T-31, Factory

Mutual Research Corp., Norwood, MA 02062, 1974.

[12] NFPA 72E-M, Guide for Automatic Fire Detector Spacing, proposed NFPA

72E-M, Supplement to NFPA 72E, Standard for Automatic Fire Detectors,

National Fire Protection Assn., Quincy, MA 02269, 1983.

[13] Zukoski, E.E., Development of a Stratified Ceiling Layer in the Early

Stages of a Closed-Room Fire, Fire and Materials, 2, pp. 54-62, 1978.

[14] Morton, B.R., Taylor, G. and Turner, J.S., Turbulent Gravitational

Convection from Maintained and Instantaneous Sources, Proc. Roy. Soc.,

Lond. A. 234, pp. 1-23, 1956.

[15] Zukoski, E.E., Kubota, T. and Cetegen, B., Entrainment in Fire Plumes,

Fire Safety Journal, 3, pp. 107-121, 1980.

[16] Cooper, L.Y., Convective Heat Transfer to Ceilings above Enclosure

Fires, Nineteenth Symposium (Internationa) on Combustion, The Combustion

Institute, Pittsburg, PA, pp. 933-939, 1982.

16
[17] Sargent, W.S., Natural Convection Flow and Associated Heat Transfer

Processes in Room Fires, Ph.D. Thesis, California Institute of

Technology, Pasadena, CA, 1983.

[18] Evans, D.D., Plume Flow in a Two-Layer Environment, The 21st National

Heat Transfer Conference, Fire Dynamics and Heat Transfer HTD, Vol. 25,

Book No. H00269, American Society of Mechanical Engineers, New York, NY

10017, 1983.

[19] Cooper, L.Y., A Buoyant Source in the Lower of Two, Homogeneous Stably

Stratified Layers - A Problem of Fire in an Enclosure, National Bureau

of Standards, Washington, D.C. 20234, NBSIR in preparation.

[20] Evans, D.D., Calculated Fire Plume Characteristics in a Two-Layer

Environment, NBSIR 83-2670, National Bureau of Standards, Washington,

D.C. 20234, 1983.

[21] Nixon, B.M., Small-Scale Study of the Temperature Profile of FireInduced, Near-Ceiling Gas Flow in a Compartment where the Wall-to-Wall

Distance is not Large when Compared to the Ceiling Height, Senior

Research Project Report, Department of Fire Protection Engineering,

University of Maryland, College Park, MD 20742, 1983.

[22] Zukoski, E.E., and Kubota, T., An Experimental Investigation of the Heat

Transfer from a Buoyant Gas Plume to a Horizontal Ceiling - Part 2.

Effects of Ceiling Layer, NBS-GCR-77-98 , National Bureau of Standards,

Washington, D.C. 20234, 1977.

17
7 . NOTATION

A

b

C V

c

g

h< Hm%

Q*

rT

T*

RTI

AT

tU

u*w

z

3

5

PT

area

half width in Gaussian profile for velocity

constants in equations 14-16

specific heat

gravitational constant

convective heat transfer coefficient

heat source to ceiling distance

mass convective fraction of heat release rate from flame

• 1/2 5/2 dimensionless heat addition parameter Q /p c T_g Z c 00 p , 00 radius

temperature

dimensionless temperature, T(c^

Response Time Index

2

P V/T Q

2

) 1/3

O 00 ° CO 'Q

T - T

00 time

radial velocity

* 1/3 dimensionless velocity, U(c T p H/g Q ) P J oo 00 00 C

vertical velocity in the plume

distance above point source

ratio of the Gaussian profile half widths, velocity to

temperature

ratio of upper to lower layer ambient temperatures

density

thermal response time constant

Subscripts

c convective portion

I interface

g gas

L sensing element, link

m maximum value at given height for plume or given radius

for ceiling-jet

18
0 reference values

p constant pressure

r of reaction or operation

1 lower, cool layer

2 upper, warm layer

00 ambient conditions

19
Do auruvuBdwai

S/UI 001. X A1I0013A

o

<U a>

CO t—

I

a nj o o a to

CO

20

3.47 J

l

4.27 l

5.77

TIME

(min.)

Figure

1.

Calculated

Temperature

Rise

of

Sprinkler

Links

(RTI

=

25,

100,

and

400)

in

Re:

Measured

near

Ceiling

Temperature

and

Velocity

Histories

from

the

First

Large

NSF-Rann

Bedroom

Fire

Test

July

11,

1983
21
1I

<N4m N oN' * W • O so « o

>»

<9 c

a> 5E< so *

k. 8

0)

H

>1 +*c

L. <D 3 s E o

_i <

22

Figure

3.

Schematic

Representation

of

the

Substitute

Plume

Calculation
Heskestad

and

Delichatsios

N

Z

N*

0>

T“

•o £

*

<0 o * 0) (0 CM <0

CM CO T“ * o i* A

« CO <0 CO CO CO CO

CO CO CO CO A o

0> 0> 0) 0* 0> 9 0> cm CM cm CM CM CM CM

o> * * 0) T“ CO

cm A A CM

o o o o o o o

CO CO CO CO r* r* A

3 * N A CO CO A

o o o o o o o

CO CO CO A N CO CO

<o

• A A CS T“ A A

o o o T" T“ r*

111

i nJ- V

23

0.1

1

r/H

Figure

4.

Comparison

of

Dimensionless

Maximum

Ceiling-Jet

Temperature

from

Laboratory

^vne'-jment

with

Existing

Correlations
U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See Instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 83-2807

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

March 1984

4. TITLE AND SUBTITLE

THERMAL ACTUATION OF EXTINGUISHING SYSTEMS

5. AUTHOR(S)

David D. Evans

6. PERFORMING ORGANIZATION (If joint or other than SIB S. see Instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

I. Type of Report & Period Covered

9.

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

)

10.

SUPPLEMENTARY NOTES

J 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 significant

bibliography or literature survey, mention it here)

A brief review of the Response Time Index (RTI) method of characterizing the

thermal response of commercial sprinklers and heat detectors is presented.

Measured ceiling layer flow temperature and velocity histories from a bedroom fire

test are used to illustrate the use of RTI in calculating sprinkler operation times.

In small enclosure fires, a quiescent warm gas layer confined by the room walls may

accumulate below the ceiling before sprinkler operation. The effects of this warm

gas layer on the fire plume and ceiling-jet flows are accounted for by substitution

of an equivalent point source fire. Relationships are given for the location and

strength of the substitute source relative to a point source representation of the

actual fire. Encouraging agreement was found between measured ceiling-jet

temperatures from steady fires in a laboratory scale cylindrical enclosure put into

dimensionless form based on parameters of the substitute fire source, and existing

empirical correlations from fire tests in large enclosures in which a quiescent

warm upper gas layer does not accumulate.

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

fire models; fire plumes; fire protection; heat detectors; sprinkler systems; zone models

13. AVAILABILITY 14. NO. OF

PRINTED PAGES

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