t 83-2801

Ainob stoma , , , _. _, , _ me Induced Flows Through Room

Openings - Flow Coefficients

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

March 1984

QC

100

U56

33-2301

1934

Sponsored in part by:

Armstrong World Industries —ancaster, PA 17604

NATI< OF .

NBSIR 83-2801

€> FIRE INDUCED FLOWS THROUGH ROOM

OPENINGS - FLOW COEFFICIENTS

•'Tvef

ac

1 00

, U 50

% S "-?S6I

K. D. Steckler

H. R. Baum

J. G. Quintiere

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

March 1984

Sponsored in part by:

Armstrong World Industries

Lancaster, PA 17604

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director

TABLE OF CONTENTS

Page

LIST OF FIGURES iv

LIST OF TABLES vi

NOMENCLATURE vii

Abstract 1

1. INTRODUCTION 2

2. EXPERIMENTAL PROCEDURE 4

2.1 Actual Mass Flow Rates Through Room Openings 6

2.2 Idealized Mass Flows Through Room Openings 7

3. ORIFICE COEFFICIENT THEORY 11

4. RESULTS AND DISCUSSION 18

5. CONCLUSIONS 24

6. ACKNOWLEDGMENTS 25

7. REFERENCES 25

iii
LIST OF FIGURES

Page

Figure 1. Test room 31

Figure 2. Gas burner locations 32

Figure 3. Room opening configurations 33

Figure 4. Two-layer approximation of opening temperature profile 34

Figure 5. Transformations showing mappings from physical plane, to

hodograph plane, to n plane, to t plane . .... 35

Figure 6 . Transformation showing mapping of plan view of enclosure

from physical plane to hodograph plane 36

Figure 7. Vertical temperature profiles at different horizontal

locations within doorway; HQ = 1.829 m, WQ = 0.737 m,

Q = 63 kW 37

Figure 8 . Vertical velocity profiles at different horizontal

locations within doorway; H

Q = 1.829 m, WQ = 0.737 m,

Q = 63 kW 38

Figure 9. Horizontal velocity profiles at different vertical

locations within doorway; H

Q = 1.829 m, WQ = 0.737 m,

Q

= 63 kW 39

Figure 10. Vertical temperature profiles measured by aspirated

thermocouples in test room; HQ = 1.829 m, Q

= 63 kW 40

Figure 11. Mass flow rate vs. door width for fixed fire strength

and door height 41

Figure 12. Flow coefficients by Method A for a fixed door (0.74 x 1.83 m

high) as a function of fire strength 42

Figure 13. Outflow coefficients by Method B for a fixed doorway

(0.74 x 1.83 m high) as a function of fire strength 43

Figure 14. Flow coefficients by Method A for Q

= 63 kW as a function of

door width, HQ = 1.83 m 44

Figure 15. Flow coefficients by Method B for Q = 63 kW as a function of

door width, H

Q = 1.83 m 45

Figure 16. Flow # coefficients by Method A as a function of window size

for Q

= 63 kW and WQ = 0.73 m 46

Figure 17. Outflow coefficients by Method B as a function of window

size for Q

= 63 kW and W

Q = 0.73 ra 47

-iv-
Figure 18. Theoretical orifice coefficient C plotted as function of

opening to room width ratio b/h 48

Figure 19. Mass outflow rates predicted from temperatures 49

Figure 20. Mass inflow rates predicted from temperatures 50

-v-
LIST OF TABLES

Table 1. Summary of experimental results

Page

27

-vi-
NOMENCLATURE

b

C

i

C

C

c

g

h

H

c

l

m

m.xa

m.xi m

oa m . ox N

Q

•Q

t

T

T.

g*

gu

T

q

(z)

or

U

U

opening half width

inflow coefficient

theoretical orifice coefficient

outflow coefficient

gravitational acceleration

room or corridor half width

height of opening

length of line burner

average of actual mass inflow and outflow rates

mass inflow rate; actual

mass inflow rate; ideal

mass outflow rate; actual

mass outflow rate; ideal

height of neutral plane in the opening, Zn

-Z

g

theoretical volume flux through orifice

fire strength

complex variable defined in eq. ( 15 )

temperature within test room

ambient or reference temperature

temperature of lower gas layer

temperature of upper gas layer

average temperature within opening at height Z

temperature within outer room

approach flow speed

exit speed from orifice

magnitude of local velocity normal to opening

-vii-
v^ magnitude of velocity in opening jet

W complex potential function W = <f> + ii|>

W

Q width of opening

x coordinate in stream direction

y coordinate across enclosure, corridor or opening

z height above floor

Z complex variable x + iy

height above floor of interface between upper and lower gas layers in

room

Zn height above floor of neutral plane in opening

Z

Q height of soffit above floor

Z

g height of sill above floor

Ap(z) static pressure difference across opening at height Z

p local gas density within opening

p density of air at temperature T

a a

P q

(z) average density within opening at height Z

C complex hodograph variable £ = u - iv

n auxiliary complex variable

-viii-
FIRE INDUCED FLOWS THROUGH ROOM OPENINGS - FLOW COEFFICIENTS

K.D. Steckler, H.R. Baum and J.G. Quintiere

Abstract

A full-scale experimental and theoretical study was made of steady-state

fire-induced flows through doorway and window openings. Measurements included

two-dimensional temperature and pressure-difference profiles within the

opening and vertical temperature profiles within the rooms connected by the

openings. A floor-level gas burner served as the energy source. Mass flow

rates through the openings were calculated from the opening data. A staticpressure flow model was used to establish ideal orifice flows from different

combinations of the experimental temperature profiles. The opening and ideal

flow results were combined to form room-opening flow coefficients as a

function of fire energy release rate, opening geometry, and fire location.

Two calculation procedures were used to compute the ideal flow. An irrotational jet model for the flow coefficients was developed and found to be in

reasonable agreement with these and other measurements. Measured flow coefficient results show no significant dependence on fire strength, opening

geometry, or fire location, as long as the ideal mass flow rate was based on

measured gas temperatures. However, the theory indicates a significant variation in flow coefficient with opening widths larger than those used in the

experiments.

- 1 -
1 . INTRODUCTION

The flow of gas through openings in a room containing a fire represents a

key element in the fire-growth process. Therefore, it is important to

describe these flows correctly in mathematical models which simulate firegrowth in enclosures. In the zone modeling approach to fire growth

[e.g., 1-4], which represents phenomena in discrete physical zones, these

flows are computed based on conditions surrounding the opening. This computation requires knowledge of room-opening flow coefficients.

Early work in the mathematical prediction of room fires, done by Kawagoe

[5] and Sekine [6], dealt with a fully-developed fire situation which was

approximated as uniform in temperature. They treated the buoyancy-driven gas

flow through the doorway or window opening as an orifice flow problem. A flow

coefficient of 0.7 — taken from pipe-flow technology — was assumed valid for

these room openings. Thomas, Heselden, and Law [7] examined the problem of

flow through both small and large openings in an enclosure containing a fullydeveloped fire. The small-opening flow was modeled as an orifice problem,

whereas the large-opening flow was treated as an entrainment problem.

The orifice concept was carried over to zone models for the developing

fire by Thomas, et al [8] who developed a two-layer model for gas flow through

a roof vent, and Emmons [9], Rockett [10], and Zukoski [11], who modeled the

doorway and window-opening versions of the problem. Here again, flow coefficients taken from pipe-flow technology were employed.

- 2-
Prahl and Emmons [12] studied flows through a single window and single

door opening with a reduced-scale kerosene/water analog experiment. Inflow

and outflow orifice coefficients were determined and found to be significantly

different at low Reynolds number (Re based on flow height), but tended to a

common value of approximately 0.68 as the Reynolds number increased. In

particular, they state that the outflow coefficient can be regarded as approximately 0.77 for 1000 < Re < 15,000; although their results at high R

g

tend to

be lower than 0.77. The inflow coefficient was lower, but appeared to

approach a value of 0.68 for Re > 4000 for the window and Re > 10,000 for the

door configuration. For most full-scale fire conditions (Re > 5000 in the

present study) , the large Reynolds number case should apply. Then their

results suggest the use of a constant coefficient value for both of approximately 0.68. The question remained, however, whether this flow coefficient,

which was obtained for two different constant density liquid layers, was

applicable to the flow of a variable density gas in a full-scale room geometry

and for various opening configurations.

In the case of gas flows, Shaw [13] studied full-scale natural convection

through rectangular openings in walls for space heating and ventilation applications. However, the temperature differentials in his work were limited to

12°C. His results show a flow coefficient of 0.65 ± .05 between temperature

differentials of 4 to 10°C with higher values outside this temperature range.

The present study describes full-scale experiments to measure fireinduced flows through room openings, and a theory for the attendant flow

coefficients. The experiments represent conditions of developing room fires,

before full involvement, and temperature differentials for the room gases

-3-
ranging from approximately 60 to 270°C. The effects on the coefficients of

opening geometry, fire strength, fire location and ideal-flow model selected

are examined. A discussion of the results of mass flow rate through the

opening and on fire plume entrainment characteristics has been reported elsewhere [14].

2 . EXPERIMENTAL PROCEDURE

Steady-state experiments were conducted in the 2.8 x 2.8 x 2.13 m test

room shown in figure 1. The ceiling and walls were covered with a ceramic

fiber insulation board to allow the room to reach quasi-steady test conditions

in approximately 0.5 hr. A door or window opening was located on one wall.

The vertical centerline of the opening either coincided with the centerline of

the wall or was located 6.25 cm to one side.

The test room was located in a small room of a one-story building. This

"outer-room" was maintained at nearly atmospheric conditions through the use

of two roof vents, several windows, and one door opening. No experiments were

conducted for external wind conditions in excess of 5 m/s.

A 0.305 m diameter floor-level diffusion gas burner served as the fire

source. Commercial grade methane was supplied at a low momentum rate typical

of natural fire pyrolysis rates. The burner was positioned in primarily three

locations: the center of the room, the back left corner and the center of the

rear wall relative to the wall with the opening. Other locations, with the

burner face raised 0.3 m above the floor, were also examined. These configurations are illustrated in figure 2.

-4 -
Movable bidirectional probes [15] with attached bare-wire thermocouples

were used to determine gas velocities and temperatures at points on a twodimensional grid which spanned the entire area of the room opening. The axes

of the bidirectional probe sensing heads were aligned normal to the opening.

The measurement plane was located at the mid-plane of the 102 ram deep jamb.

The horizontal spacing between grid points varied between 65.1 and 111 mm

depending on the width of the opening. With one exception the vertical

spacing was fixed at 114 mm. The exception was the smallest window in which

the spacing was reduced to 51 ram. These spacings produced between 64 and 144

measurement points depending on the area of the opening. The door and window

configurations selected for study are shown in figure 3«

Vertical gas temperature profiles were measured on both sides of the room

wall containing the opening. Aspirated thermocouples similar to those of

Newman and Croce [16] were used in the test room while bare-wire thermocouples

were used in the outer room. In both cases, vertical spacing between thermocouples was 114 mm.

All thermocouple junctions used in this study were formed by welding the

overlapping ends of 0.254 mm chromel and 0.254 mm alurael wires. No radiation

corrections were applied to the thermocouple data. Nevertheless, estimates of

the radiation error were used in assigning error bands to the flow coefficient

results.

Experiments were designed to determine the effect of room-opening

geometry, fire strength, and fire location on the opening flows and flow

coefficients. Fire strength, Q, is defined as the product of the fuel flow

-5-
rate and lower heating value of the fuel. The fire strength ranged from 31.6

to 158 kW.

Inflow and outflow coefficients, and C

Q

, were computed as the ratios

of experimental to idealized mass flow rates (see eqs. (10) and (11) below.

In this context, "idealized flows" are derived using Bernoulli's equation and

principles of hydrosatics. Two expressions will be examined for the idealized

mass flow rates.

2.1 Actual Mass Flow Rates Through Room Openings

Experimental or "actual" mass flow rates and velocities were calculated

from the opening temperature and bidirectional probe data. Actual mass flow

rates were obtained by integrating the local mass velocities, pv, over the

flow area. The local density p was obtained from the measured local temperature and the ideal gas law. Actual flow into the room, m. , occurs over the ° xa opening width, W-, and over the height between the sill, Z_, and neutral plane

o s or zero-velocity point within the opening, Zn

. Actual flow from the room,

m , occurs over the height between Z„ and the soffit, Z„. Therefore

oa n ’ o

W Z m. = / °

/ n

pv dz dy (1)

o Z

s

and

om

oa

o

Z

/ pv dz dy

Zn

( 2 )

- 6 -
These integrations were carried out numerically using the trapazodial rule in

the vertical direction and the rectangular rule in the horizontal direction.

The gas velocities at the surface interface were taken as zero.

2.2 Idealized Mass Flows Through Room Openings

A static pressure ideal gas flow model was used to establish the

idealized opening flows in terms of the room and/or opening experimental

temperature profiles. Two methods of calculation were employed. The first,

designated Method A, follows the analysis of Quintiere and DenBraven [17].

This method uses the ideal gas law to express the differences between the

static pressure profiles in the rooms connected by the opening, Ap(z), in

terms of the vertical temperature profiles measured in these rooms; T(z) in

the test room and TQr (z) in the outer room. Variables at the opening are

considered to depend only on z. Hence horizontally averaged temperatures in

the opening, T

Q (z), will be used in computing the idealized flow. The opening

gas density, p q

(z), is accordingly computed from T

Q(z) since pT is a constant.

The idealized velocity profile at the opening, v^(z), is obtained by applying

Bernoulli's equation along assumed horizontal streamlines which start from

rest at points "far" from the opening and terminate at the opening where

v^z) = /2Ap(z)/p

Q

(z) (3)

The static pressure difference Ap(z) is computed from the temperature distributions on either side of the opening, T(z) and TQr (z), and the neutral plane

height, ZR

. One temperature, or pressure, distribution refers to the fluid

in the rest state, the other distribution refers to the fluid surrounding the

-7-
jet as it enters or leaves the room through the opening. For concurrent flow

in a simple orifice, the latter pressure distribution strictly applies just

downstream of the orifice at the vena contracta of the jet. The flow coefficient, to a large extent, then reflects the difference between the flow area

at the orifice opening and the flow area at the vena contracta. In computing

the idealized flow for the countercurrent case, the flow area at the opening

is used. The mass velocity, P Q

V ^» is then formed and integrated over the area

of flow within the opening to produce the ideal mass outflow rate

m . 01

= W p T /2g / o a a

Jz (4)

and ideal mass inflow rate

m. . n

- w„p>t. fig / "

z o a a

(5)

The fact that the velocity profile at the opening differs from v^, or alternatively, that the area of flow at the vena contracta differs from the flow area

within the opening is accounted for in the flow coefficient.

__ The second calculation method was based on a two-layer temperature

profile as defined by Emmons [18]. This is designated as Method B. The

motivation for this approach was to provide some compatiblity between the flow

coefficient and its use in zone modeling wherein the room gas temperature

distribution is represented as constant in the upper and lower regions. This

method requires an interpretation of the experimental data into a two-step

profile. The idealized outflow, defined by this two-layer temperature profile

is

m . 01 W p T

o a a /2g ( 6 )

-8-
where T represents the temperature of a uniform upper gas layer within the

o room and T represents the temperature of a uniform single gas layer located

a outside the room. Equation (6) follows directly from eq. (4) for this twostep temperature profile.

Effective values for T..,,, T_, and Z„ are obtained from the experimental

gu a n data taken within the opening by constructing a two-layer approximation to the

opening temperature profile as depicted in figure 4. First T

a is set equal to

the average of the temperatures measured in the lower opening. Then TgU and

Zn are established subject to the physical condition that the experimental and

idealized opening temperature profiles represent equal masses of gas per unit

horizontal area,

Z

/ ° i

Z Vz)

s

dz = (zv - Z )/T + (Z - Z )/T , n s' a

v o n' gu* (7)

and the arbitrary condition that the temperature integrals are equal such that

Zo

Z

s

T (z) dz = (z - Z ) T + (z - Z ) T

o

v n s' a

v o n' gu

( 8 )

The integrations in equations (4), (5), (7), and (8) were carried out

numerically.

A corresponding ideal inflow mass flow rate can also be defined in terms

of a two-layer temperature model. It becomes more difficult, however, to

convert the experimental profiles into equivalent two-step temperature

profiles. For a room temperature represented by a step profile (T , T ) , the

a o u ideal inflow rate follows from eq. (5) as follows:

-9 -
f "oVa

^

Jf (f * xM

1 a \

a gu/

2

(

• ( Zn

- h

]U2 Zn + / - f

Z

s

; when Z

d i Z

s (9a)

4

ii •

, I

W

o

P a T

a ^Vf (f -

' i-) f a \ a gu/

• (z - Z ) 3/2

v ; when Z, < Z (9b) n s' d — s

where Z^ is the height of the interface between the upper and lower layers

within the room. In this case, the corresponding two-step profile can be

determined from the room temperature data and equations (7) and (8). The

inability of this procedure to provide a good approximation to the temperature

data and its impact on the flow coefficient will be discussed later.

For both methods, the flow coefficients are defined as

Co

• / • m /m

oa oi ( 10 )

for outflow, and

C

i = 4

ia/4ii ( 11 )

for inflow.

For both Method A and Method B, the extent to which the assumptions used

to develop the ideal flows deviate from reality will be reflected in differences between the ideal and actual flows; namely, the flow coefficients.

- 10 -
3. ORIFICE COEFFICIENT THEORY

The use of orifice models to predict room opening mass flows in zone

models suggests that the underlying physics might be used to calculate the

orifice coefficient itself. The flow in the doorway or window is assumed to

be dominated by the horizontal contraction and acceleration induced by the

hydrostatic pressure drop at a given height across the opening. The effects

of variable density, three dimensionality, turbulence, viscosity, and thermal

conductivity on the motion are omitted. The problem then reduces to the

calculation of a two dimensional irrotational jet. The jet is generated when

a uniform approach flow of speed U in a room or corridor of half width h is

accelerated through an opening of half width b < h (see figure 5a). The

uniform flow originates either outside the room or corridor, or in the buoyant

plume generated by the enclosure fire. In the latter case, the conditions

under which the uniform flow assumption is reasonable are examined by a separate analysis.

The flow can be described in terms of a complex potential function W(Z),

defined by the following relations:

W(Z) = <|> (x,y) + ii|» (x,y)

= ? = u (x,y) - iv (x,y) (12)

Z = x + iy

- 11 -
Here <J> is the velocity potential, \J^ is the stream function, while u and v are

the velocity components in the x and y coordinate directions respectively.

The boundary conditions are:

G (—) = U

ip ( x , o) = 0

= Uh along ABCD

2 2 2 u + v = along CD

(13)

Note that neither the location of the curve CD nor the limiting downstream

speed UMare known a priori. Once they are determined as part of the solution, then the orifice coefficient C is given by:

C

Uh

U b

00 (14)

The solution procedure rests on the fact that the flow boundaries have a

very simple shape in the £ (hodograph) plane (figure 5b). The velocity on

streamline ip = Uh decreases horizontally along the wall from A to B. The

corner B at Z = ih is a stagnation point Z, = 0. The velocity on this

streamline then increases along the wall in the negative y direction until the

unknown speed U^ is reached at the opening point C, where Z = ib. The

streamline then turns at constant speed until the direction parallel to the xaxis is reached at D. Thus, in the £ plane, the curve CD is the arc of a

circle of radius U^. The velocity on the streamline ip - 0 increases

- 12-
». t izontally from A to D, as the flow is accelerated from velocity U

at x = -«> to UBat x = -H». The restriction to a symmetrical geometry is not

essential, but it greatly simplifies the algebra with little loss in basic

understanding or ability to compare theory and experiment.

The use of the hodograph plane to solve problems of this type dates back

over a century to Kirchhoff, who solved this problem in the limit h -»• ®. This

and subsequent developments are described in Lamb [23]. The sequence of

conformal mappings and "solution by inspection" needed for the present problem

are as follows:

i) b = £ 2

2 This maps the domain in the £ plane into a semicircle of radius in

the b plane (figure 5c).

ii) t = -(b + U^/b)

This maps the domain in the b plane into the upper half t-plane

(figure 5d).

iii) The complex potential W(t) must vanish at infinity and satisfy the

following conditions on the real axis in the t plane.

- 13-
Im {w(t)} - Uh; Re(t) > -2 U

2

Im {w( t) } = 0; - (u

2 + U*/U2

) < Re(t) < - 2U

2

Im {w(t)J = Uh; Re (t) < - (u

2 + U^/U

2

)

The unique non-singular function satisfying these conditions is:

W(t) = ~ {log [t + (u

2 + ut/U2 )] - log [t + 2U

2

] + i*}

t = -(c

2 + Ut/C

2

). (15)

The physical coordinate can be recovered by noting that the point Z * ih is a

stagnation point (see figure 5a). Thus

z=lh + /

? «i£ ( 16 )

Inserting eq. (15) in eq. (16), the solution can be written in dimensionless

form as

- 14-
f

* i + 7

(U/Uj (| log [(1 + 0/(1 " C)1

- \

(UjU) log [(1 + uj/o/ci - uj/u)]

- i

(u/uj lQg Id + UC/UJ/O - uc/uj]} (17)

^ - 7

{log [(u/uj 2 + (uju) 2 - (c

2 + 1/C2 )]

- log [2 - (c

2 + l/c

2

)] + iir]

C = (u - iv)^

The final step in the analysis is the calculation of the ratio U/U^,

which determines the orifice coefficient (see eq. 14). This is done by

enforcing the condition (see figure 5a)

Z - ib @ C = iUro

. (18)

This is most conveniently done using eqs. (15) and (16) directly and noting

that C is imaginary along the integration path. The result is

£

= 1 + 7 (U/UJ {£ - {

(Uju) tan~

1 (UCB/U)

- \

(U/UJ tan”

1 (U/UJ]

(19)

- 15 -
Eqs. (14) and (19) together are a formula for the orifice coefficient C

as a function of b/h, expressed parametrically in terms of the velocity ratio

U/U*, The two limiting cases provide ready checks on the analysis. When

b/h = 1, the problem degenerates to a uniform flow in a channel, i.e.:

b/h = U/U*, = C = 1

When b/h - 0, with Uh = Q fixed, then the classical Kirchhoff result [23] is

recovered.

b = (Q/UJ (1 + 2/w)

C = tt/(tt +2)

Finally, some assessment of the conditions under which the approach flow

in horizontal planes might be reasonably uniform for the case of an outflow

can be made. Let the outflow from the fire plume at a given height be represented by a point source of strength 2Uh located at the point x

Q

, yQ in the

enclosure (figure 6a). The flow is assumed to be a plane potential flow.

While this is certainly unrealistic, all the neglected effects will tend to

make the actual flow uniform more quickly than in this calculation. Hence,

the distance between the fire plume and the opening needed for the approach

flow to be considered uniform can be estimated from this calculation with

confidence that the estimate is conservative.

The solution is obtained by noting that the transformation defined by

- 16 -
( 20 )

C = £ + in = sinh (~)

Z = x + iy

maps the interior of the enclosure in the Z plane into the right half C plane

(figure 6b). The complex potential then is the sum of the original source

plus its image at (-5

Q

,n o

)

W(C) = + i* = y

1

l lo8 + log

n =

sinh (S) cos ($

cosh (S) sin (l£)

( 21 )

C = p(x , y ) = K + in

o

v o’ 3 o' o o

C = K - in

o o o

Now suppose that x-xQ

> 2h; i.e. the point under consideration is at least one

room width away from the center of the plume. Then, the complex velocity

field dW/dZ can be approximated to better than one percent by:

u - iv : !

{

<

i—? o /o

—

1

+ u+co/o-1

} ( 22 )

However, under these circumstances

r I < I -r I < e"

- 17 -
Thus, if the door opening is more than one room (or corridor) width from the

fire plume, the approach velocity should be reasonably uniform in a horizontal

plane. The effects of vertical mixing and density variations of all kinds

remain unaccounted for, however.

4. RESULTS AND DISCUSSION

Before considering the results for the flow coefficients, some characteristics of the temperature and flow fields will be examined. The room corner

and center fires will be used for illustration since those results tend to

bracket the data for all the conditions. Detailed listings of the temperatures, velocities, and mass flows for all experiments conducted in this study

can be found in ref. [19]. Representative vertical temperature profiles

within a room opening for both center and corner 63 kW fires are displayed in

figure 7. These typical data show a shift from a fairly well defined twolayer flow to a much more stratified flow as the burner is moved from the

center to corner position. The Zn values shown in these and subsequent

figures represent the experimental zero-velocity heights within the openings.

Attendant velocity profiles presented in figures 8 and 9 show that the

opening flow velocities are lower for the corner fire than for the center

fire. Throughout this study, for a given opening geometry and fire strength,

the opening velocities were lower for the corner fire.

Many of the horizontal velocity profiles mapped in this study exhibit

centerline velocities which are low relative to velocities closer to the jamb

for the same height. The result is the "dished" appearance shown in most of

- 18 -
f.ure 9a and to a lesser extent in figure 9b. This concave appearance of the

profiles has an explanation offered by potential flow theory [20], and is a

result of the theory presented herein; however, other variations must be

attributed to the velocity probe or non-uniform ambient conditions.

Figure 10 shows typical test room temperature profiles for both center

and corner 63 kW fires as a function of door width. In contrast to the doorway temperature profiles of figure 7, these profiles show a uniform temperature in the upper and lower regions more consistent with the idealized

profiles of the two-layer zone models. Although upper and lower layers might

be defined by these uniform temperature regions, the transition between them

is not sharp and the lower layer temperature is greater than the inlet air

temperature. For either fire location, the temperature and depth of the upper

layer increases as the door width decreases. However, for a given opening

geometry and fire strength, the corner fire produces a hotter and thinner

upper layer. These variations are similar to those reported by McCaffrey and

Rockett [21], and may be a general effect of fire location.

Doorway neutral plane heights, Zn , are also displayed in figure 10. Note

that for the center burner configuration (figure 10a) Zn

is either within or

above the transition zone or "interface" between the upper and lower layer.

However, for the corner fire configurations (figure 10b) Zn

is below the

interface. The position of Zn relative to the interface is important when one

attempts to compute the idealized mass inflow rate for Method B. Also it has

been shown [21] that the actual temperature in the lower layer, necessarily

greater than the inlet air, must be used to predict more accurately the

pressure difference across the room opening. Since this pressure difference

- 19-
controls the flow rate, it is easy to see why an overly constrained stepprofile for Method B can lead to poor results.

Examples of actual mass flow rates are illustrated in figure 11 as a

function of width for the door configuration. Inflow and outflow rates for a

given test fall within ± 3.1% of the average of these two values. Indeed,

with the exception of the smallest window, all configurations examined in this

study yielded deviations between inflow and outflow within this range. The

deviation is ± 7% for the smallest window. In general, the mass flow rates

are smallest for the corner fire location because the fire plume entrains less

gas in this position [14]. It is significant to note that the mass flow rate

in figure 11 is not directly proportional to WQ nor W as is frequently

assumed.

In addition to these experiments, more recent results have been added for

a line-burner fire, positioned at the rear wall on the floor (see figure 2).

A summary of results for all the experimental conditions are listed in table 1

(4 pages). The zero-velocity neutral plane position, relative to the bottom

of the opening, N = Z_ - Z_ , is fairly constant at approximately half of the

opening height. This position was determined from the velocity data. In

contrast, the thermal interface between the upper and lower layers in the room

varies significantly. This height, Z^, was estimated at the mid point of the

transition region between the approximate uniform upper and lower temperature

regions. The extent of the transition zone is also noted, and the average

- 20-
£

values of the experimental upper and lower temperatures are tabulated. Thus,

approximate temperature profiles could be constructed from these data in a

form similar to those of figure 10. Finally, the flow coefficients are listed

for Methods A and B. Only the outflow coefficient is shown for Method B

because the results for the inflow coefficient showed a significant dependence

on door width and this computation was not pursued further [22]. The inflow

coefficient decreased nearly linearly from 0.62 to 0.48 from the smallest to

largest door width. Moreover, the two-step temperature profile used in Method

B was a poor approximation to the measured room temperatures.

The results for the flow coefficients will now be examined in more

detail. Also, in the following figures, "error bars" are included which

represent the maximum uncertainty in the results. These uncertainties were

determined by estimating errors in the velocity and temperature measurements

and then computing the maximum deviations of the flow rates and coefficients

about their measured values [19]. The most significant uncertainty is due to

estimates of radiation error in the temperature measurements at near ambient

temperature; however, the error estimate is most conservative in that temperature range. The flow coefficients were computed by eqs. (10) and (11) using

the average value of the measured in and outflows. Hence, some uncertainty in

the coefficients results from descrepancies between these flow measurements.

Figures 12 and 13 display the flow coefficients computed by both methods

as a function of the fire size. This is shown for three burner locations -

center, wall and corner - for a fixed door opening - 0.74 x 1.83 m high.

Note that these temperatures are arithmetic averages of the experimental data

and not effective values computed by eqs. (7) and (8).

-21-
Method A yields essentially constant values: 0.70-0.75 for C

Q

and 0.65-0.73

for C

i

. The large uncertainty in at small fires is due to the conservative

estimate of radiation error on the thermocouples which in turn causes significant variations in the ideal mass flow rate. Indeed, this reflects the sensitivity of the ideal flows to the temperature profile and contributes to the

wider variation of results by Method B: 0.76 <_ C

Q <_ 1.0 as shown in figure

13.

Similar results are shown in figures 14-17 when the effect of door and

window size are examined for a fixed fire strength, Q

= 63 kW. The flow

coefficients by Method A appear to remain fairly constant, independent of fire

location and opening size, with the outflow values slightly higher than the

inflow coefficients. Considerably more variation is shown for Method B.

The calculated orifice coefficient is plotted as a function of b/h in

figure 18. The experimentally determined coefficients are also replotted here

in terms of the b/h ratio appropriate to the room of origin of the flow. To

permit the most appropriate comparison between experiment and theory, only

coefficients from experiments involving symmetric geometries consistent with

the uniform-flow assumption are displayed. The slow upward trend predicted by

potential flow theory is clearly observeable, although the calculated results

are about 15 percent low. This result is highly encouraging, considering the

simplicity of the approach. Further support for the theory comes from the

shape of the profiles in figure 9. It is well known [20] that in a potential

flow the speed is greatest at a flow boundary. This requirement, together

with the assumption of flow symmetry with respect to the doorway centerline

leads to the dish shaped speed profiles seen in figure 9.

- 22-
In order to gain insight into the sources of the discrepancy shown in

figure 18, it is useful to examine the experiments of Prahl and Emmons [12]

•

Their experiments were performed with opposed uniform kerosene and water

streams, eliminating both variable density and non-uniform flow effects. The

reported orifice coefficients are strongly dependent on Reynolds number, due

to the small scale of the experiments. If one restricts attention to the data

corresponding to Reynolds numbers above 10^, as displayed in figure 9 of ref.

[12], the doorway coefficients converge asymptotically within a band between

0.6 and 0.7, with an average value of about 0.65. Since the corresponding

theoretical value for this configuration is 0.62, the non-uniformity of the

approach flow and density variations in each stream seem to be the principal

sources of error.

Finally all of the circular burner results for the center, wall, corner

and elevated locations are displayed in figures 19 and 20 where the measured

mass flow rates are plotted against the idealized mass flow rates by Method A

for the outflow and inflow respectively. These results follow a linear dependence with the slope representing a nominal flow coefficient. A linear fit to

the data yields an average outflow coefficient of 0.73 and an average inflow

coefficient of 0.68. Additional results, presented in table 1 for the line

burner at the rear wall, show flow coefficients consistent with these average

values. Moreover Method A gives results that differ little from these mean

values.

- 23-
5. CONCLUSIONS

For the range of conditions in this study, the flow coefficients derived

by Method A are fairly invariant with fire size, location and opening configuration. The mean value of the inflow coefficient is 0.68 and 0.73 for the

outflow coefficient. The variation of the data about these mean values is

less than ± 0.05. Although the uncertainty in the results is greater than

this deviation in some instances, this is due to the sensitivity of the error

analysis on thermocouple corrections at low temperatures.

The measured coefficients agree reasonably well with predictions based on

two dimensional potential flow. The most important discrepancies between

theory and experiment appear to be due to density variations in three dimensions. The theory predicts a systematic variation of orifice coefficient with

ratio of vent width to room of origin width. However, this variation is small

in the parameter range investigated in most fire experiments to date.

Within the range of the opening configurations and fires studied the

derived flow coefficients could be used together with the idealized equations

given here to calculate door or window flows in fire experiments. Hence

temperature data, without the expenditure of numerous velocity probes, are

sufficient to calculate the flow. This technique could be of significant

value in fire experiments.

The results for flow coefficients also provide improved data for use in

the current zone models to predict room fire growth [1-4]. Although a question of consistency between Methods A and B and a two-layer room fire model

-24-
remains, the results presented provide improved insight on the variations of

and C

Q under realistic fire conditions. As long as the predictions of

temperature from models are in good agreement with the data, then the flow

calculations for the flow coefficients of Method A will give accurate results.

6. ACKNOWLEDGMENTS

We are grateful to Armstrong World Industries for their partial support

of this project through the National Bureau of Standards Research Associate

Program. We are indebted to William Rinkinen and cooperative-education

interns Cho Sze, Wendy Wussow, Adalberto Maldonado and Michael Beaupre for

their assistance with the experiments and data reduction.

7. REFERENCES

1. Quintiere, J.G., Growth of Fire in Building Compartments, Fire Standards

and Safety, ASTM STP 614, 1977, p. 131.

2. Emmons, H.W., Mitler, H.E. and Trefethen, L.N. , Computer Fire Code III,

Horae Fire Project Technical Report No. 25, Harvard Univeristy, 1978.

3. Pape, R. and Waterman, T., Modification to the RFIRES Preflashover Room

Fire Computer Model, IITRI Project J6400, IIT Research Institute,

Chicago, IL, March 1977.

4. MacArthur, C.D. and Myers, J.F., Dayton Aircraft Cabin Fire Model

Validation, Phase I, Report No. FAA-RD-78-57 , University of Dayton

Research Institute, Dayton, OH, March 1978.

5. Kawagoe, K. , Fire Behavior in Rooms, Report No. 27, The Building Research

Institute, Japan, Sept. 1958.

6. Sekine, T. , Room Temperature in Fire of a Fire-Resistive Room, Report No.

29, The Building Research Institute, Japan, March 1959.

7. Thomas, P.H. , Heselden, A.J.M. and Law, M. , Fully-Developed Compartment

Fires — Two Kinds of Behavior, F.R. Technical Paper No. 18, Fire

Research Station, Borehamwood, England, Oct. 1967.

-25-
8. Thomas, P.H. , Hinkley, P.L. , Theobald, C.R. and Simms, D.L.

,

Investigations into the Flow of Hot Gases in Roof Venting, F.R. Technical

Paper No. 7, Dept, of Scientific and Industrial Research and Fire

Offices' Committee Joint Research Organization, London, 1963.

9. Emmons, H.W. , Natural Convective Flow Through an Opening, Part I, Home

Fire Project Technical Report No. 1, Harvard University, 1973.

10. Rockett, J.A. , Combustion and Flame, 12:165-175 (1976).

11. Zukoski, E.E., Convective Flows Associated with Room Fires, Semi-Annual

Progress Report, NSF GI 31892X1, California Institute of Technology,

Pasadena, CA, June 1975.

12. Prahl, J. and Emmons, H.W. , Combustion and Flame, 25:369-385 (1975).

13. Shaw, B.H., Heat and Mass Transfer by Combined Forced and Natural

Convection, Institution of Mechanical Engineers Symposium, University of

Manchester, Owens Park, England, Sept. 15, 1971, Paper C117/71, p. 31-39.

14. Steckler, K.D., 19th Symposium (Int.) on Combustion, The Combustion

Institute, 1983.

15. McCaffrey, B.J. and Heskestad, G. , Combustion and Flame, 26:125-127

(1976).

16. Newman, J.S. and Croce, P.A. , Journal of Fire and Flammability,

10:326-336 (1979).

17. Quintiere, J.B. and DenBraven, K. , Some Theoretical Aspects of Fire

Induced Flows Through Doorways in a Room-Corridor Scale Model,

NBSIR 78-1512, National Bureau of Standards, Washington, DC, Oct. 1978.

18. Emmons, H.W. , Personal Communication, 1979.

19. Steckler, K.D. , Quintiere, J.G. and Rinkinen, W.J., Flow Induced by Fire

in a Compartment, NBSIR 82-2520, National Bureau of Standards,

Washington, DC, Sept. 1982.

20. Batchelor, G.K. , An Introduction to Fluid Dynamics, Cambridge University

Press 1967, p. 384.

21. McCaffrey, B.J. and Rockett, J.A. , Journal of Research of the National

Bureau of Standards, 82:107-117 (1977).

22. Steckler, K.D., "Fire Induced Flows Through Room Openings", Tech. Res.

Rep. Project 203005-003, Armstrong Cork Co., Research and Development,

May 13, 1981.

23. Lamb, H. , Hydrodynamics, Dover, NY, p. 94, 1945.

- 26-
Table

1*

Summary

of

Experimental

Results

Sn'SSSSSSKSSSSSJ css 0 0 9 0 0

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w a> H • if

~

v£i on m v£> s s

a. « .-4 O' 00 *-4 m n r*> m «<y r- m sy

85 s s

eft r>* r* © o eft eft 4 N N N # 00 •*

60 a

> a. < o

a s a 3 a s

e x

m oc *c^

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oiovoocor^r^^.

OO»Hft0ft0iHOCO

I -PI -U ! O r» f". »h <0 O' O' O'

•O *0 *H

0'*^^o<ses«HOr«.fO oit— vymLftmmmmmmm •cftfftm'O'Oiftinf** n h m co o 00 m *n ^

«ft O' P*

co m •£> >»

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m eft r> c

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O' O' O' O' O' O' O' NNNNNNNNNNNNNN CN <N rs 'C >0 «©

a 8 S 8

«o >o «o n n >j n w «c »H SO ooooooooooo-HCceooo u u u

o Q o

v. — \ CM Cft >0

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CM vO sC P>- m in in in dodo m in in m dodo

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< (fa H H »B M

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CMCMCMCMCMCMCMCMCM AM CM CM CM CM CM CM CM

a) oc oo

Q. -H *rM O **- (fa 5 §

<o <0 <0 tO H V V N. — 3

n© \© p^. ao bu

i© i© v©

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IP2uI

O u

2

2

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a u «o u <u <u h o •HO.

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oo a is

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$3t

o o o o o o *

h» in e* * r* r*» «

o * » * « «o o* o«Hoddooo

o n o o o n o n n n o r« n

o o d o o o o

o o OK N l> O odd

o h m n h

r» o o h> o d o d o

s* «n o <n m «n mminom^c*** r*. r-* o» r* r*« r>» n» ddddodd dddooooo

o •» o> « oo ! o >£) r^. rs.

N m 00 ^ N CO O

<n <n sr m oi «n m nn.nnnnnh

n « ® « 4 n » soOfHmO'O'r^o m m r» ao a © oo <no»*o»n^M^Hm ^•HtHCM Old rHf-4-4<HiH~4<H~H

o o n n n n n f*.Noooono

o o c o c

M fl +1 ! *1 sO 'O 04 04

C O C O O C C C

0 -H -fl

•n *> s

PIo>mOo(p2«« tft ® lA H 00 O O. mtnmintninmm oooooooo

O »H ^ d iH O d on oi © O' &> >r\ *j n h n irt >o ddddodd o o o es no

o u o o o o u

sc «n o m 9i9ta»9tOi»» NNNNNNNN 'X>'0'0'«'0sCv0'£>

•§§?*

3 5 2 2

3 3 S 5 fc.bt.h.bfc.b.t.

I 1 2 1 2 2 2 2 2 2 2 2 2

^ tnc .h >e •& VVV>»V>.N.V p«o<o<op«o<o>o

29
to « 9 N S ^ N N C X ooooocco

ooooocoo

NNNNKNKSr» coococoo

C w /-* t c c u

k- H • H

-

tt 0 . .5

a y-s E c M U

1 c fit! H C H W

c — P* r*. f* C — oc “ * 4 w w i N ^ ?*

«S

E 3 V

l &

ac>Cf'w''-y—'*c-<T —

—

— —— C<N*^C« — r^pjpi —

coco

r* r*. - - N COO

C « «H U C w wee 3^0 *. 5- C Z J

WN *> «"> o c o o o

* €

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O C O — — — —

U. U w coo^ m

t*> *3 © —

c o o o

1.5 5

o o o 2 2 2

-30-
MOVABLE BIDIRECTIONAL VELOCITY

PROBES AND THERMOCOUPLES

ASPIRATED THERMOCOUPLES

2.13 m

Fig. 1. Test room.
2.80

k— 0.42 —

'— 0.42 —»

[*- 0.30 —

|

|— 0.30 —

~0.02

L-

'

Floor -n

=i \

S

o.: 10 7// fi

1

1 ///////////

\ _

NEAR FLUSH RAISED

Fig. 2. Gas burner locations with dimensions in meters.

-32 -
0.24 0.36 0.49 0.62

WINDOW OPENINGS

Fig. 3. Room opening configurations with dimensions in meters.

- 33 -
- 34 -

Fig.

4.

Two-layer

approximation

of

opening

temperature

profile.
a. Physical plane b. Hodograph plane

lm(t)

c. 77 - plane d. t-plane

Fig. 5. Transformations showing mappings from physical plane (a), to hodograph

plane (b) , to n plane (c)

,

to t plane (d)

.

The point B is at infinity

in the t^plane. The coordinates of points A, D, and C in the t plane

are - (U + U^/U ), - 211^, and 2Uot respectively.

- 35-
y

a. Physical plane

-6

0 '%

/

/

/

/

/

/

/

/V

/

;

/

/

/

;

/

f

'So’%

b. £

- plane

Fig. 6. Transformation showing mapping of plan view of enclosure from physical

plane (a) to hodograph plane (b) . The source representing the plume

is at x , y . o o

- 36-
CENTER

BURNER

(uij 1H9I3H

'UJ) 1H9I3H

- 37 -

Fig.

7.

Vertical

temperature

profiles

at

different

horizontal

locations

within

doorway;

H

=

1.829

m,

W

=

0.737

m, Q

=

63

kW;

(a)

center

burner,

(b)

corner

burner.
CENTER

BURNER

hsl

c/> e;

O (J

r= ts

00 2 SZ,’ I 03 ‘ i S2‘ t G&’ I M 1H9I3H

sz/e GS’G S2‘0 00-0

00 2 Si’ I 03" l S2 ’ I 00“ t SZ/0 0S ‘ 0 32 0 00-0

(uj) 1H9I3H

38

Fig.

8.

Vertical

velocity

profiles

at

different

horizontal

locations

within

doorway;

H

=

1.829

m,

W

=

0.737

m, Q

=

63

kW;

(a)

center

burner,

(b)

corner

burner.
CORNER

BURNER

Q>©

©G'ti

8 E

i I

r i

i

f ; ///.*

i /////.

f ( ; i til si

i i i f ;;;/;

f i i i it//;

i r / 1////

I l I I LVl/

i i i i in.

I I I I iui

I I I I tiV v it vtiJ

t (IKS

I I I I SO

J l I IUD

/ i I U.u T V T i Tia

I I I I’lltt

I I I I U Ui

i IIIO Dl \ T 7 \ b7v%

V l i \ Cl w

\ \ 1 \\\ w

VI I \ \

00

G<r t £2*G

(s/ui) AJJ0013A

&s e>- se

- 1- &£ ’ d39

Fig.

9.

Horizontal

velocity

profiles

at

different

vertical

locations

within

doorway;

H

=

1.829

W

=

0.737

m,

Q

=

63

kW;

(a)

center

burner,

(b)

corner

burner.

Horizontal

distance

is

measured

from

the

left

side

of

the

jamb

as

viewed

from

outside

the

room.
o

in

cooo

coo ^ m Q <n o oo

CMomooo

in

(W) 1H0I3H

m

QC=3 ~ < W

cc

LU

0.

LUI- 0OoM

4Ja3 0)

4-1

a,3 M ooog

0) 4=

4-1

a>E3

42

J-i a) T)

a)

toU /-s •H 42 a.'-'

CO

to -n o <u in *° 5

co T3 3

<D -Q oo M3 V4

C0 CD co CO 4-» QJ 3 0 <U o

in o o

CO

0) /—v CM o

s-/ r-H CO •H LU

t4HO o oc U S o =>

C2u 4«S CM H a) co O <

DC

CO 3 lO 3

4J II in LU

0.

(0U'Cr

0) oo 2

LUhO - «\ 0 0

<D 4J CTs CM T“ rH 00

CO • O rH

iH

O 4J II in 4-1 0) < > 32 o O

CM (W) 1H0I3H

00

•H

40-
0.8

0.6

<S)

0.4

oo

GO

0.2

0

6

&

a

3 4

o

A

O OUTFLOW

A INFLOW

OPEN - CENTER BURNER

SOLID - CORNER BURNER

H = 1.829m

Q = 63 kW

i i

o

A

0.2 0.4 0.6 0.8

DOOR WIDTH, W0

(m)

1.0 1.2

Fig. 11. Mass flow rate vs. door width for fixed fire strength and door height.

-41-
OUTFLOW

COEFFICIENT,

C

0

1.3

1.2

1.1 -

1.0

METHOD A

Inflow

i i i—

50 100 _ 150

FIRE STRENGTH, Q (kW)

Fig. 12. Flow coefficients by Method A for a fixed door (0.74 x 1.83 m high)

as a function of fire strength.

- 42 -
FIRE STRENGTH, Q (kW)

Fig. 13. Outflow coefficients by Method B for a fixed doorway

(0.74 x 1.83 m high) as a function of fire strength.

-43-
OUTFLOW

COEFFICIENT,

C

0

1.1

1.0

0.9

0.8

0.7

0.6

8=:- 8- -

0.5 -

0.4

0.3

METHOD A

Outflow

0.2 -

0.1 -

i I I I l o 0.2 0.4 0.6 0.8 1.0 DOOR WIDTH, W0 (m)

Fig. 14. Flow coefficients by Method A for Q

= 63 kW as a function of

door width, H = 1.83 m.

o

-44-
Fig. 15. Flow coefficients by Method B for Q

= 63 kW as a function of

door width, H = 1.83 m.

o

-45-
OUTFLOW

COEFFICIENT,

C

0

1.1 r

1.0

0.9

0.8

0.7 W

0.6

0.5

0.4

0.3

0.2

0.1

Q

8: : O!fj

METHOD A

Outflow

JL 0.5 1.0 1.5

SILL HEIGHT, Z s

(m)

oo

( H1.1 r

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

METHOD A

Inflow

±

0.5 1.0 1.5

SILL HEIGHT, Z s (m)

Fig. 16. Flow coefficients by Method A as a function of window size for

Q

= 63 kW and W =0.73 m.

o

-46-
oo

o

1.5

1.4

1.3 h

1.2

1.1

1.0 f

0.9

0.8

0.7 h

0.6

0.5

0.4

0.3

0.2

0.1

METHOD B

O- - o

sj Do •

0.5 1.0 1.5

SILL HEIGHT, Zs |m)

Fig. 17. Outflow coefficients by Method B as a function of window size

for Q

= 63 kW and W =0.73 m.

o

- 47 -
FLOW

COEFFICIENT,

C

0.0 0.2 0.4 0.6 0.8 1.0

b/h

Fig. 18. Theoretical orifice coefficient C plotted as function of opening

to room width ratio b/h. The experimental data obtained by

Method A is replotted above.

- 48 -
OUTFLOW

(S/3M) 31VH MOld SSVN ONINddO lVfUOV

-49-

Fig.

19.

Mass

outflow

rates

preui.

ted

from

temperatures.
INFLOW

(S/8'1] 31VH MOU SSVW 9NIN3dO 1VIU3V

- 50-

Fig.

20.

Mass

inflow

rates

predicted

from

temperatures.
U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 83-2801

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

March 1984

4. TITLE AND SUBTITLE

Fire Induced Flows Through Room Openings - Flow Coefficients

3. AUTHOR(S)

K.D. Steckler, H.R. Baum and J.G. Quintiere

^

S. PERFORMING ORGANIZATION (If joint or other than N BS, see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8

.

Type of Report & Period Covered

9.

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

10.

SUPPLEMENTARY NOTES

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

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a sjgnifJ cant . bi bi iography or literature survey, mention it here) A full-scale experimental and theoretical study was made of steady-state fire-induced flows through doorway and window openings. Measurements included two-dimensional temperature and pressure-difference profiles within the

opening and vertical temperature profiles within the rooms connected by the openings.

A floor-level gas burner served as the energy source. Mass flow rates through the

openings were calculated from the opening data. A static-pressure flow model was used

to establish ideal orifice flows from different combinations of the experimental temperature profiles. The opening and ideal flow results were combined to form room- opening flow coefficients as a function of fire energy release rate, opening geometry,

and fire location. Two calculation procedures were used to compute the ideal flow.

An irrotational jet model for the flow coefficients was developed and found to be

in reasonable agreement with these and other measurements. Measured flow coefficient

results show no significant dependence on fire strength, opening geometry, or fire

location, as long as the ideal mass flow rate was based on measured gas temperatures.

However, the theory indicates a significant variation in flow coefficient with

opening widths larger than those used in the experiments.

12.

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

air flows; compartment fires; flow coefficients; opening flows; orifice

coefficients

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