NBSIR 83-2670

Calculating Fire Plume

Characteristics in A Two Layer

Environment

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

September 1983

100 U.s. DEPARTMENT OF COMMERCE

, U 5 6

national bureau of standards

33-2670

1933

NBSIR 83-2670

' * K CALCULATING FIRE PLUME

CHARACTERISTICS IN A TWO LAYER

ENVIRONMENT

RATIONAL BUPEAl! or STANDARDS UBJUAX

Oifioo

d/S%

no. H-iC

1983

David D. Evans

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

September 1983

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

NATIONAL BUREAU OF STANDARDS, EnwM Ambler Director
... ;y « 7,
TABLE OF CONTENTS

Page

List of Figures iv

Abstract 1

1. INTRODUCTION 1

2. BUOYANT PLUME IN A UNIFORM ENVIRONMENT 6

3. DETERMINATION OF WEAKLY BUOYANT PLUME PARAMETERS 10

4. TRANSITION ACROSS AN ABRUPT CHANGE IN AMBIENT DENSITY 12

5. PLUME FLOW WITH INITIAL BUOYANCY AND MOMENTUM 16

6. PLUME FLOW WITH INITIAL BUOYANCY, MOMENTUM AND MASS FLUX 18

7. APPROXIMATIONS FOR ENGINEERING APPLICATION 20

8. COMPARISON OF CALCULATION WITH EXPERIMENT 25

8.1 Point Source Solution for Lower Layer 27

8.2 Two Solutions for Sources with Initial Mass Flux 30

8.3 Engineering Approximation - Average Density Environment... 34

8.4 Engineering Approximation - Substitute Point Source 35

9. CONCLUSIONS 36

10. ACKNOWLEDGMENTS 36

11. REFERENCES 36

iii
LIST OF FIGURES

Page

A

5 —1/2 *1 Figure 1. Evaluation of integral I “ / (x - 1) x dx 41

1 Figure 2. 1.22 m diameter cylindrical enclosure apparatus 42

Figure 3. Calculated and measured plume centerline temperatures

for a 0.62 kW source 43

iv
Calculating Fire Plume Characteristics In a Two Layer Environment

David D. Evans

Abstract

Methods are developed to determine axial gas flow

conditions within a weakly buoyant plume that passes from

an ambient quiescent environment, in which the plume

originates, to an upper layer at elevated temperatures.

The methods are appropriate for inclusion in two layer

analysis of enclosure fire. In particular, they are a

first step in developing a prediction of actuation time

for thermally activated automatic sprinklers exposed to

an enclosure fire. Results obtained with various methods

are compared with measurements in a 1.22 m diameter

cylindrical enclosure.

Key words: Compartment fires; fire models; fire

plumes; room fires; sprinkler systems.

1 . INTRODUCTION

A primary objective of the suppression and extinguishment research group

in the Center for Fire Research is to develop methods to predict the performance of fire suppression systems. Current research includes efforts focused

on the study of light hazard automatic fire protection sprinkler systems.

1
To predict the fire suppression performance of a sprinkler system, it is

necessary to construct models for the various phenomena which influence system

performance. One must predict the time required for the system to respond to

the fire, the characteristics of the water spray discharged from the sprinkler

head, and the effects of this spray on the fire. This report is a contribution to the first of the objectives above, prediction of system actuation

time.

In the case of a typical water sprinkler system, the response of the

system is determined by the time required for the hot gases generated by the

fire to heat parts in the sprinkler head linkage. For typical sprinkler heads

in use today, actuation occurs after the rupture of either a frangible bulb or

solder link at a predetermined elevated temperature. The rupture of these

parts in the mechanical assembly of the sprinkler head allows water to flow

through the head.

In previous work, methods were developed to characterize the thermal

response of sprinkler heads to hot gas flow [1,2]*. It has been found that

the response of the sprinkler head can be characterized satisfactorily with a

single time constant. The time constant for the sprinkler head is calculated

from laboratory measurements of the time required to actuate the sprinkler

head in a controlled hot gas flow. The value of the time constant is sensitive to changes in the resistance to heat transfer from the hot gases to the

sprinkler head. For heat transfer dominated by convection from fire gases,

the product of the time constant and the square root of gas flow speed past

the sprinkler head is constant [2].

* Numbers in brackets indicate the literature references at the end of the

paper.

2
Using existing models of the thermal response of sprinkler heads, the

actuation time for the head could be predicted if it were possible to predict

the gas temperature and velocity histories at the sprinkler head generated by

specified fires. For enclosures large enough that accumulation of gases from

the fire into the quiescent hot gas layer under the ceiling is not significant, Alpert [3] has developed methods to determine the response of thermal

detectors to slowly varying fires using quasisteady approximations. Heskestad

and Delichatsios [4] have modeled the initial transient convective flows under

large flat ceilings.

Common light hazard fire protection sprinkler systems are often installed

to protect areas that are much smaller than the compartments for which the

results of the above two studies apply. In these small enclosures hot combustion products from a fire can quickly accumulate in the upper portion of the

enclosure after ignition, influencing the temperature of gases flowing near

the ceiling and walls of the enclosure. Therefore, for small enclosures

engineering methods must be developed to include the effects of an accumulated

hot gas layer in the prediction of gas flow temperatures and velocities near

ceilings and wall surfaces where sprinkler heads may be located. This is

currently an active area of fire research. As light hazard sprinklers have

activation temperatures in the range of 57°C to 77°C, it is important to

predict the initial gas flow temperatures accurately, to provide good

estimates of actuation times.

Difficulties exist in applying the present field equation models like

those of Baum et al. [5] and Liu and Yang [6], and global zone models like

those of Mitler and Emmons [7]

,

and Pape et al. [8] to predict the fire driven

3
gas flow temperatures and velocities within enclosures. The present field

equation models have the potential to calculate gae temperatures and velocities anywhere within an enclosure, but present codes require large computer

storage for execution and are generally not accurate near wall and celling

surfaces. The global zone fire models do not supply detailed Information

about flow conditions at any particular location within a zone, but simply the

average conditions for the zone. Without some means to include the effects of

boundary flows, zonal analysis is not capable of providing the detailed flow

information necessary for calculating sprinkler actuation times.

The simplest model that will yield useful engineering predictions for

actuation times of sprinkler heads in enclosures must contain a minimum of

three regions. Two of these regions are currently dealt with in the two zone

fire models - the lower or cold layer, and the upper or hot layer. The third

region that must be added to the two layer arrangement is a celling and wall

layer flow region that is driven by the fire plume. In this third region, gas

temperature and velocity will be a function of position within the enclosure.

This region would include the normal sites for ceiling and wall mounted sprinkler heads or other thermally actuated fire detection devices.

Although algorithms to treat special regions adjacent to enclosure

boundaries have not yet been included in two zone enclosure fire models,

Alpert [3]

,

and Heskestad and Delichatsios [4] have studied the behavior of a

fire plume and the induced flow under an unconfined ceiling. Useful predictive formulae for actuation time were found for heat detectors located in the

4
ceiling jet layer established by the fire plume. In Alpert’s calculations,

conditions of the plume flow near the ceiling, but prior to impingement on it,

were used as boundary conditions for a calculation of the ceiling jet flow.

Following Alpert's work, a first approximation calculation of flow

conditions in the ceiling jet layer within an enclosure may be performed,

provided that conditions within the fire plume prior to ceiling impingement,

including the effects of an accumulated hot gas layer, can be determined.

However, it should be recognized that buoyant flow within an enclosure is more

complex than flow under an unconfined ceiling. The walls of the enclosure

that lead to the accumulation of a stagnant hot gas layer in the upper portion

of the room may also affect the ceiling jet flow. As an example, Delichatsios

[9] has studied abrupt changes in the ceiling jet flow resulting from ceiling

beams.

In this report, methods are developed to determine axial gas flow

conditions within a weakly buoyant plume that passes from an ambient quiescent

environment, in which the plume originates, to an upper layer at elevated

temperatures. The models should be appropriate for inclusion in two layer

zonal analysis of enclosure fires. Results obtained using several methods to

calculate axial temperatures in a plume are compared to measurements made in a

1.22 m cylindrical enclosure, which is also described.

5
2. BUOYANT PLUME IN A UNIFORM ENVIRONMENT

A commonly used model for describing the flow in a fire plume was

developed by Morton, Taylor and Turner [10] . This model will be used to

describe plume flow conditions in the cold lower layer of a two layer environment. In the model, the weakly buoyant plume is assumed to originate at a

point source. Weakly buoyant plumes are those in which, everywhere, the

fractional density change from the ambient environment is assumed to be

small. These changes are small enough so that in writing conservation equations, density changes (or similarly, temperature in a constant pressure

system) need only be considered explicitly in buoyancy terms (i.e. where

Ap appears in combination with g)

.

A fire plume is assumed to be axisymmetric with radial distribution of

velocity in the vertical direction and density at any height, z, as follows:

where Ap = p - p , (p (z) is the ambient density at any height above the

o o source), b = b(z), and X is a dimensionless constant.

Using these assumed Gaussian profiles, equations may be written for

conservation of the flowing quantities mass, momentum, and density defect

(energy) integrated across the plume at each height. These take the form

u(z,r) = u(z,0) exp(-r^/b^) (la)

Ap(z,r) = Ap( z ,0) exp[-r2 /(X2 b

2

)

]

(lb)

6
(b

2 u(z,0)) - 2bau(z,0) (2a) ~ (b

2 u2 (z,0)) - 2X2

b

2

g (2b)

dz

(b

2

u(z,0)g Ap<° 0)

) - <1+1/A2

)b

2

„(z,0) «-

dz

° (2c)

where a is an entrainment constant and is the ambient density at the level

of the heat source z 0,* i.e. p.K • p (z * 0).

1 Ko

With the substitutions

P = Ap(z,0)/p

1 (3a)

U = u(z,0) (3b)

V = bU (3c)

W = b

2U (3d)

F = X

2 WgP (3e)

R * * p

0 /pl

the conservation equations become:

(3f )

2aV dz (4a)

dz =4FW (4b)

£ - + (4c)

7
The derivative of appearing in equation (4b) , results from the substitution of dvVdz for the term 2V^(dV^/dz) which appears after the use of

substitute variables.

The most widely used solution to the above equations is for a uniform

ambient density (dR/dz = 0) and a source at the level z = 0 of positive buoy2 2

ancy flux Trp^F^/(X +1) > 0, with no momentum flux (irp^V = 0), and no mass

flux (npjW =0). A useful shorthand notation for boundary conditions is the

form (F, V, W). The above conditions are written (Fp 0, 0).

For the boundary condition (F^, 0, 0), the equations (4a-c) may be solved

directly to describe conditions within the plume rising through a uniform

ambient density (dR/dz - 0). The solution is:

Using the definitions from equations

(5a)

(5b)

(5c)

(3a-f), the following are obtained:

(6a)

(6b)

(6c)

8
The buoyancy parameter for a weakly buoyant plume is related to the

heat release rate of the fire source Q by

00

o (7a)

where use has been made of the approximation T-T^ T^Ap/p^ in the constant

pressure ambient. With substitutions and integration equation (7a) becomes,

It is interesting to note that the plume width (b) for a constant value

of a, the entrainment coefficient, is simply proportional to height, z, above

the source (Eq. (6a)). Also the buoyancy parameter Fj , equation (7c), is

independent of changes in ambient density at the source in a constant pressure

system, because density only enters through the constant product of density

and temperature.

The equations (6a-c) are widely used to describe the plume above a fire

source. With the proper selection of a height for the source point, these

equations may be used to describe the plume in the cold or lower layer of a

two layer room fire model. The above solution does not continue correctly

across the sharp density change associated with the boundary between the upper

and lower layers in a two zone room fire model.

Q = Trp

1 T1 C

p

F

1 /g(A2

+l) (7b)

or Fj = Q g(A2+l)/irp

1 T1 C (7c)

9
3. DETERMINATION OF WEAKLY BUOYANT PLUME PARAMETERS

In recent publications, Zukoski [11,12] sets down several equations for

temperature, density, and velocity in weakly buoyant plume flows. Values of

several parameters used in the latter work [12], are refinements of estimates

used in the early paper [11]. All calculations performed in this paper are

based on the values of parameters given in the earlier work which differ only

slightly from the refined values. In the earlier work [11], Zukoski draws on

experiments performed by Yokoi [13] to obtain values for two empirical

constants that determine entrainment rate and relative width between the

temperature and velocity profiles. Values given in Zukoski' s paper [11]

of = 0.125 and = 1.15 can be translated into parameters used in this

paper of a = 0.1042 and X = 1.15. Using these two parameters, comparisons can

be made between weakly buoyant plume model discussed in section 2 and

Zukoski's formulae for plume centerline velocity and density.

Zukoski' s expression for maximum velocity, U

2uk» is

n _

. 1/3 -1/3 -1/3 r-l/3 -1/3 -1/3

U zuk

" Cv

g Q P

1 C

p

T

1

( 8 )

From the analysis in the previous section a similar expression for maximum

velocity, U, can be calculated

U =

[5 (9 (X

2 +l)a\ 1/3

1 _ 1 / 3 a 1/3 .-1/3 „-l/3 m-l/3 _-l/3

[_6^5 —)

J

g Q P

1 C

p

T

1 2 (9)

To produce equivalent answers, C v in Zukoski's work must be equal to the value

in brackets, or C

y

= 4.14. Zukoski suggests the use of a value in good agreement of C

y

= 3.8, based on experimental work performed by Yokoi [13].

10
Similarly, identical expressions for density defect Ap may be compared.

From Zukoski's work

An _ r -1/3 -2/3 1/3 -2/3

Ap . = C g Q p. T, zuk T

6 x

1 1 -2/3 -5/3

C# z p

( 10 )

From this analysis

5(A2

+1) / 9(>

2+l)q \

6aA

2 . V

5w /

To produce equivalent expressions Gp must be equal to the value in brackets,

or Gp = 8.64. This agrees well with the value of Crp = 9.1 obtained from

Yokoi's experiments.

-l/3j

g

-1/3 *2/3 1/3 -2/3 -2/3 -5/3

1 1 (ID

Using the above values for a and X in the calculation presented here, and

the corresponding calculated values for C

y

and Gp in Zukoski's formulation,

identical velocity and density distributions can be calculated. It should be

noted, that with the assumption of the weakly buoyant plume in a constant

pressure environment, density and temperature variables can be exchanged with

the use of

PT = Vi ( 12 )

Having examined the plume in the lower cold layer of gas, methods of

continuing the solution across an interface between cold and hot layers will

now be discussed.

11
4. TRANSITION ACROSS AN ABRUPT CHANGE IN AMBIENT DENSITY

In the usual room fire situation, shortly after a fire starts to grow, a

complex flow of hot combustion gases and cooler room air Is set Into motion.

The global features of this flow are modeled by dividing the room environment

away from the fire plume into a hot upper and a cold lower layer by determining an Interface height [8,9]. The height of the interface within the room

is determined by the size of the fire, the temperature of the hot and cold

layers and the geometry of openings in the room. Within each layer, temperature conditions are considered to be uniform.

The method described in section 2 enables one to determine density and

velocity profiles for a fire plume in the lower, cold region of the room

fire. This solution applies only up to the height of the interface between

the upper and lower layers. This height may be assumed to be a known quantity, for this paper, as various methods are available to calculate this

height.

Implicit in the use of radially integrated equations (2a-c) and assumed

radial distribution (la-b) is the requirement that the rate of change of

conditions in the environment, at the radial plume boundaries in the direction

of flow are slow with respect to rate of entrainment and mixing processes that

equilibrate the plume velocity and temperature distributions to new ambient

conditions. For slowly varying environmental conditions, the assumption that

Gaussian distributions of velocity and density defect within the plume asymptote to the ambient conditions at every height is appropriate. However, the

12
presence of an abrupt change in ambient density presents special problems f< r

the continuation of the solution found in the previous section to describe the

plume flow in the lower layer.

At the location of a sharp interface between two gas layers of differing

density, environmental conditions change rapidly. The radial distribution of

velocity and density defect within the plume is not expected to maintain a

simple Gaussian distribution in the radial direction. Cold gas from the lower

layer will be forced into the upper layer by the momentum of the gas at the

edge of the plume. This gas, being cooler than the ambient conditions in the

hot upper layer, can be expected to slow down after crossing into the upper

layer, and may then fall back towards the interface. These effects are

discussed in more detail by Jaluria [14] • The distance required for a buoyant

plume flow to recover a Gaussian distribution of density defect and velocity

adjusted to an abrupt increase in ambient temperature has not been studied.

Considering these effects, an exact solution to this problem of a plume

transition between the cold and hot layers would be prohibitively difficult

and inappropriate for the intended engineering applications. However, several

approximate solutions are possible, all of which retain the approximation of

Gaussian density defect and velocity profiles in the plume flow on both sides

of the interface. For example, a straight forward method to continue the

solution of the plume flow in the lower layer into the upper layer is to solve

equations (4a-c) in the upper layer using boundary conditions on F, V, and W

determined from conditions in the plume flow in the cold layer at the interface height. All solutions to be considered in this report include the

13
assumption that the entire plume flow from the lower layer continues into the

upper layer. This is a good assumption during the growth phase of the

enclosure fire of interest for prediction of sprinkler actuation. Other

cases, discussed by Jaluria [14], in which the entire lower layer plume flow

may not penetrate far into the upper layer may be calculated by adjusting the

F, V, and W boundary conditions at the interface.

In terms of conditions likely to be encountered in the growth stages of a

room fire, the interface between the hot and cold layers in a compartment may

be thought of as the limit of the mathematical processes by which relatively

small changes in layer density occur over a vanishingly small change in elevation. Equations (4a-c) show that only two terms may vary greatly in such a

region. Even though the overall change in the density between the cold and

hot layers may be small, the rate of change in hydrostatic parameter, dR/dz in

equation (4c), can be arbitrarily large. The only other term which may become

large in response to the rapid change in hydrostatic parameter, is the derivative of the buoyancy parameter, dF/dz. Consistent with equations (4a-c), one

may expect that changes in F will be as rapid as changes in layer gas density.

Changes in W and V may not be rapid. In the limit of a discontinuous change

in layer density, F will be discontinuous, but W and V will be continuous.

Physically continuous W and V requires that the plume width parameter and

velocity distribution be the same on both sides of a discontinuous change in

layer density. For the weakly buoyant plume, this is equivalent to mass flux

and momentum conservation across the interface.

14
From equation (4c), it is clear that within each layer of constant

density (dR/dz » 0), the value of F does not change. Crossing the interface

the value of F will change. The amount of change depends on the assumptions

made to describe how the density defect profile adjusts to the abrupt change

in ambient conditions.

Sargent [15] assumes that the plume flow equilibrates immediately to the

Gaussian distribution of temperature adapted to the increased ambient temperature while maintaining the lower layer velocity distribution. Conservation of

excess enthalpy flux with respect to the lower layer ambient temperature is

assumed across the interface. This assumption results in an abrupt change in

maximum plume temperature as the flow crosses the interface.

Using the assumed Gaussian density defect profile, equation (lb), a

similar result may be obtained by requiring that the flux of excess density

defect with respect to the lower layer ambient density, p^, be conserved

crossing the interface between the cold and hot layers. The expected abrupt

change in centerline density defect at the interface is

[ p 2 " P 2,I (z,0 ^"[ p

l “ p i,i(

z »°)] * ( p

2 " p j) U + */*

2

) 03)

where subscript I indicates values at the interface height, and subscripts 1

and 2 represent variables in the lower and upper layer, respectively. The

value of F

2 may be calculated using equation (3c) with Ap„ (z,0) from equation (13) and w

2 j = W

1 I*

15
Alternately the value of F

2 may be calculated assuming that the centerline density defect is continuous, p 0

_ (z,0) - p. (z,0). Using equation

(3c) the value for F

2 is calculated using either approximation for p. (z,0)

2 »

I

as

F„ - X Wjg

p

2 - lii

(z,0)

(14)

In the following section, a solution will be constructed by the method

used by Morton [16] that continues the plume into the upper layer using

boundary conditions at the interface determined from calculated flow at the

interface elevation in the lower layer and assumed transition conditions.

5. PLUME FLOW WITH INITIAL BUOYANCY AND MOMENTUM

Solutions to the weakly buoyant plume equations for boundary conditions

other than (F^, 0, 0) have been calculated by Morton [16]. The solution for

the (F

2

, Vj, 0) boundary condition must be obtained in order to solve the

equations for the boundary condition (F

2

, Vj, Wj) needed to continue the plume

flow solution across the interface between the hot and cold gas layers. The

(^2* ^i» 0) boundary conditions requires that the plume have both initial

buoyancy and momentum, but zero mass flux at the source.

With the change of coordinates Z

2 = z - z^ where Zj is the height of the

interface above the source in the lower layer, equations 4a-c, to be solved in

the upper layer Z

2 > 0, become:

= 2aV (15a)

dz_

16
with the boundary condition (F2

, Vj, 0) at Z

2

0.

(15b)

(15c)

For this problem, explicit formulas cannot be written for V and W in

terms of position z as found for the simple buoyant plume calculation with the

(Fp 0, 0), boundary condition. Following Morton [16], the solution takes the

form

F = Fr

W =

V/V.

/

1

1 (x

5

-l)

-1/2 3, x dx

(16a)

(16b)

(16c)

Equation (16a) is found by direct integration of equation (15c).

Equation (16b) is found by eliminating variable Z 2 using equations (15a) and

(15b) before integration to determine the relationship between W and V. The

relationship between Z

2 and V in equation (16c) is found by eliminating the

variable W using equations (15a) and (15b).

The integral of the type in equation (16c) can be evaluated numerically.

Values are shown graphically in figure 1. For large values of the upper

integration limit A in figure 1, the integral grows like To determine

17
flow conditions near the interface, and over a range of distances appropriate

for hot layer depths in room fires, values of A V/yV^ close to 1.0 must be

considered.

To continue the plume into the hot, upper layer of a two layer environment, the boundary conditions (F

2

, Vj, Wj) must be satisfied by the plume in

the hot layer at the interface with the cold layer, Z

2 0. These boundary

conditions represent the presence of buoyancy, momentum and mass flux at the

interface Z

2 0.

The solution to this problem has also been found by Morton [16]. In his

solution, a source of the type (F

2

, y V^, 0) is placed at a position z

2 - - z2 below the interface, Z

2 “ 0. Then the unknown parameters z

2 and y are determined by requiring the flow from the virtual (F

2

, y V^, 0) source at z

2 - z2 match the desired (F

2

, Vj, Wj) conditions identically at Z

2 ” 0. This is the

solution to the equations for the boundary conditions (F

2

, Vj, Wj) for Z 2 > 0

or z > Zj.

The solution developed in section 5 for the plume from a (F2> y V^, 0)

source, can be used directly if a displaced coordinate system Z 2 is introduced.

6. PLUME FLOW WITH INITIAL BUOYANCY, MOMENTUM AND MASS FLUX

(17a)

(17b)

18
where z£ = + z

2

an(* W ' an<* are vari able8 with respect to the displaced

coordinates. Applying the desired conditions at the interface

W' = Wj at z

2 = z 2

(18a)

V' = Vj at z£ = z

2

(18b)

values for the parameters y and z

2

may be calculated as

(&) •?]'"

:

2 - (^2)"

1/2

(yVi ) 3/2

; l/Y(x5

.

0

-l/2

x

3dx

(19a)

(19b)

Substitution of z 2

and y into equations (17a) and (17b) yields the desired

solution for the plume in the hot upper layer. This solution is awkward

because the independent variable is V' V(z

2

) instead of the distance z

2

.

As with the solution for the point source solution (Fj, 0, 0) boundary conditions, values for plume width, velocity, and density may be calculated from

the definitions of the F, V and W variables given in equations (3a-f).

Crossing the interface between the lower and upper layer, the plume width and

velocity distributions are preserved. Peak density defect may be preserved or

may change abruptly depending on the assumptions used to calculate F

2 (see

section 4). The distribution of density defect remains Gaussian but decays to

the upper layer density far from the axis of the plume.

19
7. APPROXIMATIONS FOR ENGINEERING APPLICATION

Although the solution for plume flow In a two layer environment presented

In the previous section may be a good closed form analytic solution possible,

it is certainly not convenient to use. For engineering applications, simpler

formulations may be desirable. However, the previous solution, although

complex, is valuable because it provides a bench mark to which approximations

may be compared.

The problem of determining approximations to continue the buoyant plume

from the cold to the hot layer has been addressed recently by Cooper [17], in

a study of heat transfer to ceilings. In that work, the integrated plume

properties of mass flux and mass average temperature in the lower ambient

environment are computed from Zukoskl's [11] point source plume equations.

The integrated plume properties in the upper hot layer are similarly described

in terms of flow from a new point source located in a hot layer which, for the

purpose of computation of plume conditions in the upper layer, is assumed to

be extended below the interface in an imaginary manner. The strength and

location of the new point source are chosen so that the mass flux and mass

average temperature of the plume flow is continuous across the interface.

While these two integrated plume properties are maintained continuous across

the interface, the momentum flux, excess enthalpy flux referenced to the lower

ambient temperature and the radial distribution of temperature and velocity

are not modeled as being continuous. In particular, an abrupt change in

centerline plume temperature is allowed as the flow crosses the interface.

20
For the purpose of determining sprinkler actuation times, it is important

to make accurate estimates of gas flow temperatures and velocities near the

ceiling. As shown by Alpert [18] , gas temperatures and velocities in this

flow are directly related to temperatures and velocities in the plume flow

before ceiling impingement. It is probable that the ability to predict temperatures along the axis of a plume, particularly near the ceiling, will be an

important step towards predicting sprinkler actuation in room fires.

The engineering approximations used by Cooper [17], as discussed above,

to calculate heat transfer to ceilings, do not attempt to preserve the distribution of temperature and velocity in the region about the axis of the plume.

Instead close attention is given to matching only integrated plume

quantities. For the purpose of calculating heat transfer from fire plumes to

enclosure ceilings, this approximation appears to be adequate [17]. For the

calculation of sprinkler actuation times, where greater accuracy in the prediction of fire plume temperatures may be necessary, this approximation may

not suffice.

Consistent with the discussion of plume flow across a rapid change in

ambient density in section 4, it may be desirable to preserve the plume width

b, and gas velocity on the plume axis across the interface between the lower

and upper layers. This corresponds to continuous V and W variables. Note that

preserving plume width and maximum velocity on the plume axis also preserves

the entire velocity distribution for the flow.

21
To obtain useful engineering approximations to the plume flow in the

upper layer, Cooper [17] has chosen to make changes in the plume source location and strength while maintaining fixed environmental boundary conditions.

An alternate choice for approximate solutions, to be discussed below, is to

maintain the plume source strength and location fixed and modify the environmental boundary conditions to account for the effects of the two layer

environment on the plume flow. This method has the important advantage that

the plume width and velocity profiles can easily be made continuous through

the interface because the location of the source is not changed.

In general, for the prediction of sprinkler actuation in a room containing a two layer environment, one must account for the cumulative effect of

entrained gases from the environment over the distance from the source to the

ceiling. It should be observed that using the point source plume flow equations discussed in section 2, all the flow in the plume is entrained from the

environment. Therefore, temperature and velocity distributions in the plume

depend directly on the entrained mass. One way to replace the two layer

environment with a suitable average environment is to determine an equivalent

average value of environment density, p^, through which the plume from the

given fire source is imagined to pass. The environmental density p^, is

chosen such that, at any height above the source, the mass flow in the plume

flowing through the two layer environment is equal to that in the plume flowing through the imaginary constant density environment. Thus the average

environment density, p^, becomes a function of height above the source at

every elevation in the upper layer, but remains equal to the constant density

of the lower layer at every elevation in the lower layer.

22
In order to determine a value for the equivalent average environment

density, the plume mass flow at all heights in the two layer environment must

be calculated. This can be done by integrating the entrained mass flow from

the source to the elevation of interest. To do this, it must be assumed that

entrainment at the interface and in the upper hot layer is characterized by

the same process as in the lower layer. Using equation (2a) the rate of mass

per unit height entrained into the plume is proportional to the product of

bu(z,0) and the local ambient density, pQ

(z).

Integrating the entrained mass flow from the source to any height, z in

both the two layer environment and the equivalent average density environment

and equating them at every height yields

pm

(z) m

/^P

Q

(z)bu(z,0)dz

o

(z) V(z) dzj| two layer environment

/*bu(z,0)dz i |/qV( z) dzj average environment

( 20)

The product bu(z,0) is by definition the variable V, (equation (3c)).

From equation (5b), for flow from a point source

V(z) ( 21 )

As discussed in section 2, the value of Fj is independent of changes in

density in a constant pressure system. So, evaluating the mean density for

elevations in the plume below the interface z < z^, the values of V(z) in the

two integrals will be equal and the mean density will equal the lower level

density p = p, . m 1

23
The values of flow velocity and plume width reflected in V(z) above the

interface z > z^ will not be equal to those calculated in a uniform environment at the same distance above the source. In large part this is due to the

choice of assumptions used to calculate the change in variable F crossing the

Interface as discussed In section 4.

Fortunately, for many practical enclosure fire growth problems the

changes in the velocity and plume width parameter b, because of the change In

ambient density associated with the initial stages of a fire may not be

rapid. A suitable approximation for the purpose of calculating a mean density

is simply to assume that the variable V(z) be equal to values calculated for a

uniform environment. With this assumption, equation (21) can be used for all

elevations and equation (20) simplifies to

Equations (22a-b) provide a convenient method to calculate approximate

plume flow conditions in the upper and lower layer of the two layer environment using the solution of the flow from a weakly buoyant point source,

equations (5a-c) or (6a-c) with variables defined in (3a-f). For flow in the

lower layer, the calculation is straight forward, using the lower layer

density p^. For positions in the upper layer, the same solution may be used,

except that ambient density is replaced by the mean values P m

( z ) given in

equation (22b).

p (z) - p. m i for z <. (22a)

(22b)

24
In practice, the above method may be used to calculate flow conditions on

the axis of the plume at the ceiling elevation for room size fires. It is

expected that the assumptions used in the development of the approximate

method will not introduce great inaccuracies in the calculation of plume flow

in the region close to the axis for fire sizes and layer depths encountered in

room fire situations. Since the calculation may generally be used to determine conditions at only one elevation in the upper layer, the ceiling elevation, the fact that the mean density is a function of elevation in the upper

layer does not add a significant burden to the calculation.

At present, testing is being conducted to measure impingement conditions

in the flow over a range of fire sizes, ceiling elevations, and layer depths.

These measurements are being made in a 1 .22 m diameter cylindrical enclosure

using a steady fire source. In the next section, the application of both the

detailed solutions and various approximation to prediction of plume centerline

temperatures are illustrated and comparison is made with one set of measurements collected in the cylindrical enclosure.

8. COMPARISON OF CALCULATION WITH EXPERIMENT

Measurement of the gas temperature along the axis of a plume flowing

through both a uniform and quiescent cold and then hot layer environment would

be the ideal test conditions for comparison with these calculations. Experimentally this is difficult to do. A less ideal comparison, but closer to

conditions that would exist in room fires, would be to establish a hot gas

layer in an enclosure, by containing the hot combustion products from the

25
plume flow. The upper layer, formed by the circulation of these hot gases

before eventually flowing from the enclosure, will not be perfectly uniform or

quiescent but may be thought of as such.

To study the axisymmetric plume, a particularly useful enclosure shape to

maintain axisymmetric flow is a cylinder. A 1.22 m diameter enclosure formed

by the 0.29 m deep PMMA curtain around a 13 mm thick ceramic fiber board

ceiling was constructed as shown in figure 2. The 0.0365 m outlet of the

burner is located 0.58 m directly under the center ceiling of the enclosure.

Protective screening that shields the apparatus from room air drafts is not

shown in figure 2.

A steady flow of laboratory gas premixed with air to minimize flame

height was burned in the enclosure. Combustion products from the plume flow

accumulated into an upper hot gas layer contained by the curtain. To compare

various methods of calculating temperatures along the axis of the fire plume

temperature measurements were made in the enclosure after steady conditions

were established by a 0.62 kW total heat release rate (assuming complete

combustion) methane fire. Measurements of gas temperatures along the plume

axis and in the upper gas layer outside the plume flow are shown in figure

3. The range indicated by the bars attached to each data point for the

centerline plume temperatures indicate the amount of signal fluctuation

associated with the measurement at each position. Temperatures nearer the

burner outlet show greater fluctuations than temperatures measured at positions further away. The average value for the upper layer temperatures used

in calculations is shown in figure 3.

26
8.1 Point Source Solution for Lower Layer

For the purpose of calculation, the interface between the cold and hot

layers is located at the bottom edge of the enclosed wall. For the configuration tested, this is at mid-height between the burner outlet and the ceiling,

(z’/H = 0.5). The upper gas layer is imagined to be large enough so that a

region of quiescent, uniform temperature gas at 30 K above the lower layer

ambient can be said to exist far from the axis of the plume.

For the test conditions corresponding to the data in figure 3 parameters

for the weakly buoyant plume flow model are as follows

Q

= 0.62 kW (23a)

g = 9.8 m/s^ (23b)

T

x = 296 K (23c)

P

: = 1.1923 kg/m3 (23d)

Cp = 1.0 kj/kg K (23e)

X = 1.15 (23f)

a = 0.1042 (23g)

27
In order to calculate plume flow conditions In the lower cold layer

region using the above parameters and the analysis of weakly buoyant plume

flow from section 2, it is necessary to determine a location for the position

of the imaginary point source that best represents the flaming heat source*

In the absence of any data, one approximation to locate this position has been

suggested by Alpert [18]* Using this approximation, a position for the

virtual point source of heat below the burner face is calculated such that the

diameter of the plume is equal to the burner diameter at the elevation of the

burner surface above this virtual point source.

For the test conditions corresponding to the data in figure 3, a virtual

point source located 0.09 m below the actual burner outlet reproduces well the

centerline plume temperature data in the lower cold layer. This value differs

from the 0.07 m distance that would be calculated by direct application of

Alpert *s formula [18]. In any event, the portion of the plume calculation

that applies to the lower cold layer will be common to all methods of calculating conditions in the upper layer.

Using the above parameters for the heat source strength and conditions in

the lower layer given in equations (23a-f), the value of the buoyancy parameter Fj in the lower layer can be calculated using equation (7c). The result

is

F

1 = 0.0127 m

4 /s 3 (24)

28
Using this value of F^ , and a point source location 0.09 m below the burner

outlet, conditions along the plume centerline anywhere in the lower layer can

be calculated.

Besides the experimental data shown in figure 3, five separate calculations of plume centerline temperatures are shown. Each will be discussed in

detail. For now, attention should be directed at the single curve corresponding to the predicted centerline temperature in the lower layer (z’/H < 0.5).

This curve is based on calculated centerline densities from equation (6c)

using the value of Fj given in equation (24). Density and temperature variables are exchanged using equation (12).

At this point it is worth noting, that for this example calculation,

plume conditions in the lower layer will be extending into an upper gas layer

with an ambient temperature 30 K above the lower layer temperature. This

temperature was determined from test data as discussed previously. In

practice, application of these calculations will depend on temperatures for

the upper and lower gas layers in the room and the elevation of the interface

being established by separate calculations. It is assumed that this information can be supplied by developing two-zone models of room fire dynamics.

To make the transition from the lower layer to upper layer values of

variables are needed at the elevation of the interface 0.29 m above the burner

outlet (z' = 0.29 m) or 0.38 m above the point source (z = 0.38 m). Values of

the key plume variables at the interface, indicated by subscript I, are

calculated using equations (5a-c) and (6a-c). For the given test conditions

these values are

29
V (25a) r - 0.0701 m

2

/

s

Wj 0.00333 m^/s (25b)

bj = 0.0475 m (25c)

Uj = 1 .475 m/s (25d)

Pj - 0.2943 (25e)

As a baseline to judge other methods of continuing the plume flow solution from the lower to the upper layer, the calculation performed in the lower

layer can simply be extended to greater elevations completely ignoring the

change in ambient temperature. The broken curve A in figure 2 shows the

calculated plume centerline temperatures using this method. As would be

expected the predicted results fall below measured values, with the difference

increasing with increasing elevation in the upper layer.

To continue the plume flow into the upper layer using solutions for plume

flow from sources with initial mass flux, based on work by Morton [16]

discussed in sections 5 and 6, values of additional parameters need to be

determined. The upper hot gas layer is imagined to be at a uniform temperature of 326 K, 30 K above the lower layer temperature, with corresponding gas

3 density = 1.0826 kg/m . To calculate an estimated value for the buoyancy

parameter in the upper layer, F£ » using equation (14), a value for the density

8.2 Two Solutions for Sources with Initial Mass Flux

30
of the gas flowing along the centerline of the plume at the elevation of the

interface in the upper layers, p_ (z,0), is needed. This value may be calcu4 »1

lated using either of the two methods discussed in section 4. If the plume

centerline density is assumed to be preserved crossing the interface then this

value of p (z,0) is obtained directly from the analysis of flow in the

z »

I

lower layer. Using the definition of variable P, equation (3a), and the

calculated value of Pj from equation (25e), the density of gas on the centerline of the plume flow entering the interface is

P

2 jCz.O) = 0.8414 kg/m3

(26)

Using equation (14) and the above information, the buoyancy variable for the

upper layer is found to be

F

2 = 0.008731 m

4 /s 2 (27)

As found for the lower layer, this value of F is constant for all elevations

in the upper layer.

Using values for the various variables and ambient properties in the

lower layer, at the interface, and in the upper layer as given above, parameters to describe the source for plume flow in the upper layer, y and can

be calculated using equations (19a) and (19b), respectively. For this

example, they are

Y = 0.7931 (28)

31
Z 0.258 m (29)

2

using a value of I - 0.53 for the Integral in equation (19b) as read from the

graph in figure 1, for A - 1/y- 1.261

Using these two parameters, values for W' and V’ (W and V variables in z£

coordinates) can be calculated using equations (17a) and (17b). As discussed

in section 6 the determination of W' and V' as a function of elevation is not

straight forward because the independent variable in equation (17a) and (17b)

is V’.

Corresponding values for z£, W' , and V' were calculated using equations

(17a) and (17b) for various elevation in the upper gas layer. The variable

dependence on elevation z£ above the source for flow in the upper layer is

changed to dependence on z' the elevation above the burner face with the

relation

z' = z'

2 - 1

2 + 0.29 m (30)

where 0.29 m is the distance of the burner face below the interface for the

test condition calculated. Values of centerline flow density are calculated

using the values of F^, anc* W(z') in equations (3c) and (3a). Corresponding values of temperature are calculated using equation (12). The result of

the calculation for centerline temperature in the plume flow in the upper

layer is shown as curve B in figure 3.

32
Alternately, the value of F

2 may be calculated assuming that excess

density defect flux is preserved across the interface (equation (13)). In

this case

P

2 l (z ,0) = 0.9243 kg/m3

(31)

All other parameters would then be calculated as above. The relevant values

are.

F

2 = 0.005730 m

4

/s

3

(32)

Y = 0.8872 (33)

Z

2 = 0.220 m (34)

I = 0.31 (with A = 1/y) (35)

The result of this alternate calculation for centerline temperature in

the plume flow in the upper layer is shown as curve C in figure 3.

The agreement of both curves B and C with the experimental data is good

away from the interface. Just above the interface the solutions differ

greatly, largely because of the abrupt change in density produced by the

method conserving excess density defect flux. Predicted values are consistently higher than measured values for method B, which may in part be due to

an increase in excess density defect flux introduced by preserving centerline

33
density deieet end the veieeliy profiie. predieted values are eensistently

lower than measured values for method C, which reflects the continued

influence of the abrupt decrease Introduced st the interface*

8.3 Engineering Approximation - Average Density Environment

Considerable simplification over the method Just described can be

achieved by using the approximate, average environment method of calculating

conditions in the upper layer as described in section 7. To apply the method

a mean density P m

(<) 1> determined for each elevation of interest in the upper

layer using equation (22b). Each elevation z is measured from the location of

the virtual point source for flow in the lower layer* For each location in

the upper layer, the solution for the lower layer is continued exactly as

described in section 8.1 except that the layer density is replaced by pm(r)

in definition 3a. Notice that the change In mean density does not affect the

functional form of the solution or the value of the buoyancy variable for

the flow, if a mean temperature corresponding to Pm

( z ) i n the constant pressure system is used in equation (7c) replacing Tj. Therefore, values of P are

taken for all elevations in the lower and upper level from equation (6c).

Centerline density values are calculated using Pm

(z) i n place of in equation (3a) for elevations in the upper layer. Corresponding values of centerline temperature are then calculated using equation (12).

» «• ,. i 7

The results of this procedure are shown in figure 3 as curve D. As with

the more complex solution curve B, the predicted values of centerline temperature in the upper layer is continuous from the lower layer. The predicted

values are close to, but consistently slightly below the previous solution B.

34
8.4 Engineering Approximation - Substitute Point Source

For completeness in this discussion, it is interesting to apply the

method used by Cooper [17] as discussed in section 7 of this report, to predict centerline temperatures in the upper hot layer. Using this method the

plume flow in the upper layer is imagined to originate at a point source at

both an elevation and with a heat release rate differing from the point source

used to predict conditions in the lower layer. For the test case being

studied here, the 0.62 kW source located 0.38 m below the interface used to

predict centerline plume flow conditions in the lower layer at 296 K must be

replaced by a 0.246 kW source located 0.484 m below the interface in a uniform

326 K environment in order to calculate flow conditions above the interface.

Again the solution to the weakly buoyant plume flow equations (5a-c), (6a-c)

,

and (7c) apply.

Carrying out the calculation produces curve E as shown in figure 3. This

calculation has features very similar to curve C, having an abrupt change in

centerline above the interface. In this example, an abrupt decrease of 60 K

in centerline temperature is predicted as the plume crosses the interface from

cold lower layer to the hot upper layer. As a result of assumptions at the

interface, a larger temperature decrease is predicted than for curve C in

which density defect flux was preserved. The offset between curves C and E is

maintained throughout the upper layer. This results in calculated values for

curve E remaining significantly below measured values even near the ceiling

elevation which is relatively far from the interface.

35
9.

CONCLUSIONS

Various methods to calculate the continuation of plume flow across an

abrupt change In ambient density characteristic of conditions that occur In

the Initial stages of fire growth In enclosures have been examined. An

approximate method to calculate plume conditions both In the lower and upper

layer of the two layer environment using the common solution to buoyant flow

from a point source with a suitable average ambient has been shown to be at

least as accurate as other methods for the single case examined. Accurate

prediction of plume temperature is an important step toward prediction of

sprinkler actuation times in response to the flow of hot combustion products

generated by fires within small enclosures. Although the results of comparing

calculations with experiment presented in this report are encouraging, the

calculation method requires evaluation over a range of fire heat release rates

and layer depths.

10.

ACKNOWLEDGMENTS

The author wishes to thank Mr. Richard Zile for the careful construction

and instrumentation of the cylindrical enclosure apparatus and Dr. Howard Baum

for his help in interpreting the calculations of Morton.

1 1

.

RERERENCES

[1] Evans, D.D. , Characterizing the Thermal Reponse of Fusible-Link

Sprinklers, U.S. Department of Commerce, Washington, DC, NBSIR 81-2329,

August 1981.

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

Sensitivity Approval Test: The Plunge Test, FMRC RC76-T-50, December

1976 .

36
[3] Alpert, R. L. , Calculation of Response Time of Ceiling-Mounted Fire

Detectors, Fire Technology , August 1972.

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

Seventeenth Symposium (International) on Combustion, The Combustion

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

[5] Baum, H. , Rehm, R. , Barnett, P. and Corley, D. , Finite Difference

Calculations of Buoyant Convection in an Enclosure, Part 1. The Basic

Algorithm, U.S. Department of Commerce, Washington, DC, NBSIR 81-2385,

December 1981.

[6] Liu, V. and Yang, K. , UNDSAFE-II - A Computer Code for Buoyant Turbulent

Flow in an Enclosure with Thermal Radiation, U.S. Department of

Commerce, Washington, DC, NBS-GCR-78-150 , July 1978.

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

Computer Fire Code, U.S. Department of Commerce, Washington, DC,

NBS-GCR-8 1-344, October 1981.

[8] Pape, R. , Waterman, T. and Eichler, T. , Development of a Fire in a Room

from Ignition to Full Room Involvement - RFIRES, U.S. Department of

Commerce, Washington, DC, NBS-GCR-8 1-301 , January, 1981.

[9] Delichatsios, M. , The Flow of Fire Gases Under a Beamed Ceiling,

Combustion and Flame , Vol. 43, pp. 1-10, 1981.

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

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

,

Lond. A., Vol. 234, January 1956.

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

Stages of a Closed-Room Fire, Fire and Materials, April 1978.

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

Fire Safety Journal , Vol. 3 (1980/81) pp. 107-121.

[13] Yokoi, S. , Study on the Prevention of Fire-Spread Caused by Hot Upward

Currents, Report of the Building Research Institute (Japan), No. 34,

November 1960.

[14] Jaluria, Y. , "Fire Plume Penetration into the Hot Upper Layer in a Room

Fire", paper no. 57 presented at 1982 Technical Meeting, Eastern Section

of the Combustion Institute, December 14-16, Atlantic City, New Jersey.

[15] Sargent, W., "Natural Convective Flows and Associated Heat Transfer

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

Technology, 1983.

[16] Morton, B., Forced Plume, J. Fluid Mechanics, Vol. 5, pp. 151-163, 1959.

37
[17] Cooper, L. , Convective Heat Transfer to Confined Ceilings Above

Enclosure Fires, presented at Nineteenth International Symposium on Combustion, August 8-12, 1982.

[18] Alpert, R. L. , Fire Induced Turbulent Ceiling-Jet, FMRC Technical

Report, No. 19722-2, FM Research Corporation, Norwood, MA, May 1971,

Appendix B.

38
Notation

c*t/c

*

g

H

I

P

•Q

u

U

V, V*

w, w'

r

R

T

x

z

Z

I

z

2

characteristic width of plume [m]

proportionality constant from reference [11]

rate of thermal to velocity profile width from reference [11]

heat capacity [kW«s/kgK]

constant from reference [11] (equation (8))

constant from reference [11] (equation (10))

buoyancy flux parameter (equation (3e)) [m4 /s J

] O gravitational acceleration [m/s z

]

ceiling height above burner outlet [m]

value of integral (figure 1)

density defect parameter (equation (3a))

convective heat release rate [kW]

velocity in plume [m/s]

centerline velocity u(z,0) [m/s]

momentum flux parameter (equation (3c)) [m /s]

mass flux parameter (equation (3d)) [mJ /s]

radial distance [m]

o hydrostatic parameter (equation (3f)) [m/s z

]

temperature [K]

integration variable

axial distance above source [m]

height of interface above source [m]

distance above interface - z - z^ [m]

distance of plume source, for upper layer flow below the interface [m]

displaced coordinate system z

2 = z

2 + z 2

^

39
z ' axial distance above burner outlet [m]

a entrainment constant (equation (2a))

Y parameter for substitute plume modifying Vj

X ratio of thermal to velocity profile width

p plume density [kg/nr]

P q ambient density at any elevation

Ap density defect (p

Q - p)

p^ mean density for approximate flow calculation (equation (22a-b))

Subscripts

I interface conditions

1 conditions in lower layer

2 conditions in upper layer

zuk taken from reference [11] (Zukoski)

40
A

A

Figure 1. Evaluation of integral I =

1

/

f 5 ,

v -1/2

(X -1) 5

41
Figure 2. 1.22 m diameter cylindrical enclosure apparatus

42
ISI

U3AV1

(Ml

a3M01 l - i

43

Figure

3.

Calculated

and

measured

plume

centerline

temperatures

for

a

0.62

kW

source
NBS-1 14A a-t U.9. DEPT. OF . O 1. BIBLIOGRAPHIC DATA

SHEET (See Instructions)

1. PUfc .ICATION 2. P' 'mlnf Organ. Report Nr*.}

i REPORT I.J. NBSIR 83-2670

4.

TITLE AND SUBTITLE

CALCULATING FIRE PLUME CHARACTERISTICS IN A TWO LAYER ENVIRONMENT

September 1983

5.

AUTHOR(S)

David D. Evans

6.

PERFORMING ORGANIZATION (If Joint or other than NBS, tee Initructlont)

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

QJ Document describes a computer program; SF-185, FIPS Software Summary, Is attached. Hi ABSTRACT (A 200-word or less factual summary of most significant Information. If document Includes a significant

bibliography or literature survey, mention It here)

Methods are developed to determine axial gas flow conditions within a weakly

buoyant plume that passes from an ambient quiescent environment, in which the plume

originates, to an upper layer at elevated temperatures. The methods are appropriate

for inclusion in two layer analysis of enclosure fire. In particular, they are a first step in developing a prediction of actuation time for thermally activated

automatic sprinklers exposed to an enclosure fire. Results obtained with various

methods are compared with measurements in a 1.22 m diameter cylindrical enclosure.

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

Compartment fires; fire models; fire plumes; room fires; sprinkler systems.

13. AVAILABILITY 14. NO. OF

Qx] Unlimited

[^] For Official Distribution. Do Not Release to NTIS

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