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Ceiling Jet Properties and Wall

Heat Transfer in Compartment

:;(0NS Fires Near Regions of Ceiling

Jet-Wall Impingement

Leonard Y. Cooper

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

January 1986

QC

100

• 1)56

86-3307

1986

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NBS

RESEARCH INFORMATION CENTER Q c*

/ oO

<?/ _ ? ^07

NBSIR 86-3307

CEILING JET PROPERTIES AND WALL

HEAT TRANSFER IN COMPARTMENT

FIRES NEAR REGIONS OF CEILING

JET-WALL IMPINGEMENT

Leonard Y. Cooper

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

January 1986

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director

TABLE OF CONTENTS

Esge

LIST Of FIGURES iv

Abstract 1

I INTRODUCTION 2

2. THE BASIC PHENOMENA 2

3. CEILING JET-WALL IMPINGEMENT 4

4. HEAT TRANSFER FROM IMPINGING TWO-DIMENSIONAL PLANE

AIR JETS 6

5. EQUIVALENCE BETWEEN THE PLANE JET AND THE CEILING JET

AT THE IMPINGEMENT POINT 8

6. STAGNATION POINT HEAT TRANSFER 10

7. COMPARISON WITH EXPERIMENTAL DATA 12

8. OTHER USEFUL PROPERTIES OF THE CEILING JET 12

9. AN ESTIMATE OF THE RANGE OF UTILITY OF THE RESULTS 15

10. REFERENCES 17

11. NOMENCLATURE 19

-iii-
LIST OF FIGURES

Rage

Figure 1. Early time ceiling jet- wall interaction 22

Figure 2. Ceiling jet-wall interaction with upper layer.

a) penetration of interface; b) no penetration of interface 23

Figure 3. Plane jet-wall impingement 24

Figure 4. A plot of stagnation line Nusselt number from Figure 2

of [ 10] and from Eq. (4) 25

Figure 5 Stagnation point heat transfer amplification from Eq.(9):

"typical" full-scale; reduced scale 26

Figure 6. A plot of the integral 1 defined in Eq. (28) 27

Figure 7. A plot of Q, oss /l( l -Xr )Q] per Eqs. (27) and (32) 28

-iv-
CEILING JET PROPERTIES AND WALL HEAT TRANSFER IN COMPARTMENT FIRES

NEAR REGIONS OF CEILING JET-WALL IMPINGEMENT

Leonard Y. Cooper

Abstract

The problem of heat transfer to walls from fire plume-driven ceiling jets during

compartment fires is introduced. An analogy is drawn between the flow dynamics

and heat transfer at ceiling jet-wall impingement and at the line impingement of a

wall and a two-dimensional, plane, free jet. Using the analogy, the literature on

plane, free jet flows and corresponding wall stagnation heat transfer rates leads to

readily useable estimates for the heat transfer from, and the mass, momentum,

and enthalpy fluxes of the turned compartment fire ceiling jet as it begins its

initial descent as a negatively buoyant flow along the compartment walls.

Available data from a reduced-scale experiment provides some limited

verification of the heat transfer estimate. Depending on the proximity of a wall to

the point of plume-ceiling impingement, the estimates indicate that for "typical"

full-scale compartment fires with energy release rates in the range

200-2000kW and fire- to-ceiling distances of 2-3m, the rate of heat transfer to

walls can be enhanced by a factor of 1-2.5 over the heat transfer to ceilings

immediately upstream of ceiling jet-wall impingement.
1. INTRODUCTION

In potentially hazardous compartment fires, the total heat transfer from fire plume-driven ceiling

and wall flows to enclosure ceiling and wall surfaces can be a significant fraction of the fire's total energy

release rate, Q. [1,2] This is especially true during the critical early times of such fires when events

which relate strongly to the ultimate safety of people and property are taking place, e.g. , during times of

significant fire detector and/or sprinkler link response; when fire compartment environments hazardous

to people are developing, and up to times when they are approached; up to the time when temperatures of

combustible ceiling and wall surfaces reach ignition temperatures, and when they are relatively low

compared to characteristic temperatures of the fire plume. Successful simulations of such critical events

must involve reasonably accurate mathematical models of the above-mentioned heat transfer and related

flow phenomena.

Algorithms to estimate heat transfer to smooth ceilings during compartment fires, which are concise

enough to code into subroutines for use in practical zone- type compartment fire model computer codes, are

now available [1, 3-5]. Such is not the case for the potentially significant heat transfer to the

compartment walls. It is the purpose of this paper to develop a means of estimating the heat transfer from

ceiling jet driven wall flows to wall surfaces. Another goal of this work is to develop estimates for those

properties of ceiling jets, immediately upstream of wall impingement, which are required to predict the

characteristics of ensuing downward, negatively buoyant wall flows.

2. THE BASIC PHENOMENA

As a fire grows in an enclosure, the elevated temperature air and products of combustion which leave

the zone of the burning object form a plume and are convected upward by buoyancy. When the upward

movement of the plume constituents are blocked by the ceiling (a distance, H, above the fire) they spread

- 2

-
radially outward forming a relatively thin turbulent ceiling jet. Depending on the proximity, D, of

vertical surfaces, this ceiling jet either loses most of its momentum far out on its trajectory ( in the case

of an expansive ceiling with large D/H surfaces), or can be expected to interact vigorously with these

bounding surfaces (in the case of lower aspect ratio spaces with D/H of the order of 1) by forming a

downward wall jet flow which is eventually turned back upward by its own buoyancy. The flow scenario

for the latter case is depicted in Figure 1

.

Once the ceiling jet gases are blocked by bounding vertical surfaces, they begin to redistribute

themselves across the entire ceiling area of the enclosure. Eventually a relatively quiescent, stably

stratified, upper gas layer is formed below the continuing ceiling jet activity. The bottom of this layer is

defined by a distinctive material interface which separates the lower ambient air from the upper, heated,

product of combustion-contaminated gases. With increased time the level of the interface continues to drop

and the average absolute temperature, T U p, of the upper layer gases continues to rise. As depicted in

Figure 2, for small to moderate D/H, vigorous ceiling jet-wall flow interaction can still occur. Two cases

can be distinguished. In the first, depicted in Figure 2a, the downward wall jet penetrates the interface,

continues its downward flow in the lower layer, and is eventually buoyed back upward to interact with the

upper layer. In the second,depicted in Figure 2b, the downward flowing wall jet loses its downward

momentum , and is turned back upward prior to penetrating the two- layer interface.

An experimental program to isolate and study the type of wall flows depicted in Figures 1 and 2 is in

progress, and the first stage of this, which provides results for the flows of Figure 1 and 2b, has been

completed [6], To use the results of [6] and anticipated future results on wall flows requires an

under standing, not now available, of the ceiling jet turning region near ceiling jet-wall impingement It

is the objective of the present work to begin to develop such an understanding

The ceiling jet flow and heat transfer phenomena of Figure 2, which take place in the relatively

- 3

-
quiescent background environment of temperature T up , are similar to those of Figure 1 . Following ideas of

[3], where the upper layer is treated as an expansive environment with ambient temperature T up ,

quantitative descriptions of the latter phenomena would also be useable in predicting the former. For this

reason it is sufficient to focus attention here on the relatively simple Figure 1 configuration.

3. CEILING JET-WALL IMPINGEMENT

The goal of the present analysis is to develop estimares for ceiling jet properties and for the heat

transfer to the wall of Figure 1 near the ceiling- wall line of intersection, and where the radius vector, r,

is normal to the wall.

It is known that for small to moderate values of r/H inertial forces are generally large compared to

buoyancy forces ( i.e. , characteristic Richardson numbers, Ri , are small) in buoyant plume-driven ceiling

jets [7], This fact was used in [4] to argue that the flow and heat transfer characteristics of the buoyant

plume-driven ceiling jets depicted in Figures 1-2 could be directly related to the analogous

characteristics of wall or ceiling jets driven by heated or unheated free turbulent jets ( i.e. , flows with the

same configurations of Figure 1 , but with a turbulent jet replacing the fire and its buoyant plume).

Presumably, a ceiling jet driven by a plume would have approximately identical flow properites as that

driven by an equivalent free jet, at least up to r/H of the order of 1. The criteria of equivalence proposed

in [4] was that the mass and momentum of the plume and of the free jet be identical at their respective

points of impingement. Applying these criteria, it has been possible to recorrelate results from the

literature on free jet-driven wall flows, to use them with results from buoyant plume-driven ceiling jet

experiments, and to obtain estimates for the ceiling jet flow and heat transfer characteristics of interest

in compartment fires [1,3-5],

Using the above ideas permits estimates for ceiling jet characteristics up to the point of wall

- 4-
impingement For example, upstream of this wall impingement point and outside of the ceiling

impingement stagnation zone defined by r/H < 0.2, results of [8] indicate that the radial velocity

distribution V(Z), is essentially self-similar, and rises very rapidly from zero at the ceiling to a

maximum , Ymax , at a distance Z=0.235 , 8 being the distance below the ceiling where V/Vmax

= 1 12 . Also,

V(Z/8= 1 6)/V

max

<«0.2. Finally, at any given radial position, and for Z/S>0.23, results of reference [9]

suggest that the V/Y

max

profile can be approximated by the velocity profile of half of a plane,

two-dimensional , free turbulent jet as depicted in F igure 3.

Define M 0

‘ as the momentum flux of the ceiling jet per unit width (assumed to be of near-constant

density, p, in the sense of the Boussinesq approximation)

oo Mo'-pVmax 2 M(V/VmM )2d(Z/6) (I)

0

As will be seen, an estimate of M0

’ immediately upstream of ceiling jet-wall impingement will lead to a

determination of the desired wall heat transfer at this Ixation.

Based on the above-mentioned character istics of the V/V

max

profile, it is assumed that the inner

layer of the ceiling jet, i.e. , from Z/ 8=0 to 0.23, is thin in the sense that the integral of Eq.( 1 ) between

0<Z/8<0.23 is expected to be a small fraction of M0

\ This together with the noted similarity between the

radially symmetric ceiling jet and half of the plane free jet suggests that the interaction of these two flows

with vertical surfaces in Figure 1 and 3 configurations, respectively, would be approximately reproduced

- 5

-
1^ appropriate criteria of equivalence between the two upstream flows were satisfied. Note that in the case

of the ceiling jet, the no-slip condition at the ceiling will lead to stagnation corner flows which are

significantly different than the flows in the immediate vicinity of plane jet-wall stagnation. However,

these corner Mows will likely be confined to a relatively small region with characteristic dimension

0.235, and, with regard to wall heat transfer, it is reasonable to expect that they will have an effect

primarily on a similarly small uppermost segment of the wall Stagnation heat transfer results to be

developed here are for the upper port, of the wai* which excludes such a segment

4. HEAT TRANSFER FROM IMPINGING TWO-DIMENSIONAL PLANE AIR JETS

Reference [10] presents data from an experimental study of heat transfer from an ambient

temperature plane jet to an isothermal wall (temperature, T w ) in a Figure 3-type configuration. For

X

r./B 1 4 and Reynold's numoer Re

e >2000, a correlation for the stagnation point heat, transfer coefficient,

n. , was found to be

= h c B/k = l.2Re.

n 55/ Y /R ) n

* ' -0.62 Re„ p , : O /II

t--’ p

whe' e is •“i? distance from the nozz'eof width S c a

is the uniform nozzle exit velocity, jj and k

are the gas viscosity and thermal conductivity, respectively, and h is cased on the temperature difference

( - T w

; Motivated Dy the expectation that for limiting large X

n /B (i.e , fully •developed jets* h

should depend explicitly on the characteristic length X, the distance from the virtual origin of the jet, and

not v" x

n or t , the data presented m [

! 0] were reanalyzed. Based on a review of the iMerature in [

i

! ] , X

was taren to oe
X = X (3)

n

I 95 B

The result was the following new correlation

lim Nu

5 = 1 74Re5 0 - 58 ( 4)

X/D ->

Nu

s = h5 X/k = (X/B)Nu0 . Re

s = (2M0 pX) w2/\l = (X/B) 1/2Re

e

where 2H0is the conserved momentum flux per unit width of the jet ( e.g. , 2M0

' = pBue 2

) , and h

s is the

stagnation point heat transfer coefficient based on the (T amb-Tw ) temperature difference. The Figure 2

data correlation plots of [ 10] are reproduced here in Figure 4 along with the approximation of Eq. (4).

For Re

e >2750 and Xn /B>15, Eq. (4) estimates all hs data in the figure to within approximately five

percent.

It is of interest here to extend the results of [

1 0] in order to estimate heat transfer rates, q, from

elevated temperature jets to nonuniform temperature walls. In a manner analogous to analyses in

[ 1 ,3-5,12- 13] the adiabatic wall temperature, T

ad , is introduced as a characteristic temperature, and it

is assumed that an estimate for q can be obtained from

q = h(T

ad -Tw

) (5)

where T w

would generally vary with position from the stagnation point. Here, T adis the temperature

- 7-
distribution adjacent to an adiabatic wall on which a plane jet from an elevated temperature source is

impinging. T ad = T amb in [10], and for this reason the assumed formulation of Eq.( 5) is equivalent to the

assumption that its h is identical to the h obtained in [10]. This is of particular interest here near the

stagnation point where h = h

s

5. EQUIVALENCE BETWEEN THE PLANE JET AND THE CEILING JET AT THE

IMPINGEMENT POINT

In the Figure 3 configuration, h

s can be estimated by using the plane jet's impingement point values

X and M0

‘ in Eq.(4). These will be chosen in a manner that would simulate the Figure 1 ceiling jet flow

immediately upstream of the r=D wall impingement point.

Reference [ 1 4] proposes the following for the plane jet velocity distribution

V/V

max = exp[-cx(Z/X) 2

] ;Vmax = 0[2MQ 7( pX)] 1/2 (6)

where conservation of momentum along the X axis requires

$

2

= (2cx/7T) 1/2 (7)

Taking cx in Eq.(6) to be the average of the two values, 75.0 and 70.7, found for the two

experiments of [1 4]

,

and using this in Eq.( 7) leads to

- 8-
c* = 72.8, 3

= 2.61 ( 8 )

where the above value for 3 compares favorably with values of 3 which are consistent with three other

plane jet models reviewed in [ 11 ] , viz., 3

= 2.56, 2.45 and 2.83.

As in Eq.(6) for the plane jet, for the purpose of estimating impingement wall heat transfer it is

now assumed that the ceiling jet velocity immediately upstream of r=D can also be simulated by a Gaussian

distribution in Z. Then, immediately upstream of their respective impingement points, the flow

distribution of the plane jet and ceiling jet would be equivalent if

^•plane jet at V=Vmax/2 "

^ceiling jet at V=Vmax/2

= °

Vmax of plane jet = Ymax of ceiling jet = Ymax

For plume-driven ceiling jets, results from [4] and [8] lead to

V

rriax /Y = 0 85( D/H)' 1 1

S/H = 0. 1 0( D/H )° 9

Y = g 1/2 H

1/2 Q* 1/3

, Q* = (

1 -Xr )Q/( pC

p T ambg 1/2 H

5/2

)

where gis the acceleration of gravity, C

p

is the specific heat and X • is the fraction of Q radiated from the

fire's combustion zone.

Using Eq.( 12) and the first of Eqs. (6) in Eq.( 9), andEq. (11) and the second of Eqs (6) in Eq ( 10)

( 11 )

( 12 )

( 9 )

( 10 )

- 9

-
leads to the following respective properties of the equivalent plane jet

X/H = 1 0( D/H)° 9 (13)

M0 '/(pHV 2

) = 0.053(D/H)

-1 ' 3 (H)

6. STAGNATION POINT HEAT TRANSFER

Eqs. ( 1 3) and ( H) in Eqs. ( 4) yield the following relationship for h

s

in terms of compartment fire

parameters

h

5 /h = 0.89ReH

"° ‘:12 Pr~ 1 ( D/H)“' 02

( 15)

h = pC

pg 1/2 H

1/2 Q* 1/3

; ReH = pg

1/2 H3/2 Q* 1/3 /|i

where h and ReH are a normalizing heat transfer coefficient and the characteristic impingement point

Reynold's number , respectively, and where Pr is the Prandtl number

To use Eq.( 15) in Eq.(5) requires T

a(j

. This would be identical to T ad (r=D) for the ceiling jet [5]

10.22-14.9 r/H , 0 < r/H <0 2,

lT ad(r/H)-T,ambmJJ

T 0*2/3

amfcr

f( r/H) ( 16 )

8.39 [1 - 1 . 1 0( r/H) 0 8 + 0.808( r/H) '

-

6

)

, r/H >0.2

[ 1 - 1 . 1 0( r/H)°-0 + 2.2O( r/H) 1 - 6 + 0.690( r/H) 2 4}

- 10 -
Assuming identical wall and ceiling temperatures near the ceiling-wall junction, it is of interest to

compare q=qs to the wall at the stagnation point to qcej | jng , the heat transfer rate to the ceiling,

immediately upstream of the stagnation point. This would provide insight into the expected level of any heat

transfer enhancement due to stagnation point flow conditions. Using Eq.(5) for both wall and ceiling,

Eq ( 6) of [5] for h

ce) | jng

and Eq.( 15), and taking Pr=0.7 leads to

Qs^Qceiling^ ~^s^ceiling^

= S.SRe^0 12 (D/H) 01 (D/H+0.279)/( D/H-0.0771); D/Hk0.2 (17)

where h

cej | jng

is the ceiling heat transfer coefficient.

"Typical" full-scale compartment fires with ( 1-X )Q in the range 200-2000kW and H in the

range 2- 3m are in the ReH

range 2( 1

0

5 )- 5( 10 5

), i.e., ReH

-0 - 12 * 0.2. The reduced-scale fires of

[2- 13] and [ 15] [Q=0( IkW), H=0( 1m)] were in the ReH

range 7( 103 )-2( 10 4

), i.e., ReH

"° 12 « 0.3

For identical D/H, Eq.( 1 7) therefore predicts that the magnitude of heat transfer amplification near the

stagnation point is approximately 1.5 greater in the reduced-scale compartment fires than in a "typical"

full-scale compartment fire. Results of Eq.( 1 7) are plotted in Figure 5 for the two classes of fire. As can

be seen, the results predict that in the "typical" full-scale fire, heat transfer amplification, i.e.,

qs /qcej ij ng (r=D) > 1, will only occur for D/H's less than 1-1.5, while for the reduced-scale fires,

amplification by a factor of 1.4 or greater will alwer/s occur in the small to moderate D/H range of

interest.
7. COMPARISON WITH EXPERIMENTAL DATA

An experiment was carried out with a convective buoyant plume of strength Q=0. 1 17kW whose

source was centrally located H= 1.22m below the ceiling of a tightly sealed, rectangular- plan enclosure

(2. 13mx2.44m) with controlled leakage from below [16]. For the experiment, Q*=0.657( 10

-4

) and

ReH =0 123( 105

). Dataaquired included time-temperature measurements of the insulated, 0.79( 10~3 )m

thick, galvanized steel walls and ceiling on a line from the plume impingement point and normal to the

D= 1.22m ceiling-wall junction. Data near this junction led to the estimated experimental fluxes

qs =8 W/m2

, qce ,| jng ( r=D)=4 W/m 2 This is to be compared to the Eqs.( 15)-( 1 7) theoretical estimates

qs =6.46W/m2 and qceiijng (r=D)=4.04W/m 2

, respectively. While these preliminary comparison are

favorable, it is evident that more data, especially from stronger Q" , ReH

buoyant sources, are required to

validate the utility of the Eqs. ( 1 5)-( 1 7) results of this paper.

8. OTHER USEFUL PROPERTIES OF THE CEILING JET

A determination of M0

' per Eq. ( 14) was key to an estimate of the ceiling jet stagnation heat

transfer. M0

‘ will also be useful for future reference in characterizing the initial properties of the ceiling

jet-driven wall flows of Figure 1 , e. g. , for use in applying the results of [6]. The ceiling jet mass flux

per unit width, m0 ',and enthaply flux per unit width, H0

‘ would also be useful in this regard. These are

defined by

- 12 -
oo

">„• = pV ( 18 ) max

Sj(V/Vmax )d(Z/S)

0

H„' pC0 T

amtJVmax SJ ( V/V

max

)( T / 7amb

- 1 )(K Z/ S

)

(19)

where T is the temperature in the ceiling jet, and where the above integrals can be estimated with use of

V/V

max = exp[ -ln(2) (Z/S) 2

] (20)

Using Eqs. ( 1 1)-( 12) and (20) in Eq. ( 18) leads to

m0 /(pHY) = 0.088 (D/H)“0 - 2 (21)

Beside depending on XrQ, the T distribution on which H

0

’ is dependent will vary during the course of

a given fire according to the heat transfer losses from the ceiling jet between r=0 and r=D. This can be

estimated with use of

Veiling "^ceiling ^ ^ad

” ^ceiling

where T

cej]jng

is the local ceiling surface temperature, and where h

cej , jng

and T

ad can be estimated from

Eq. (6) of [5] andEq.( 16), respectively. Assuming the ceiling jet to be thin enough and/or the jet gases to

-13-
be transparent enough as to not play a significant role in radiative transfer, bounds for H

0

‘ are easy to

estimate. Thus, from r=0 to D the total rate of heat transfer from the ceiling jet, Q| oss , and then H

0

‘ can be

obtained from

D

°loss = 2l, l Veiling r dr (23)

0

H

0

’ = [( 1-X

p )Q - Qloss ]/(2ttD) (24)

The maximum possible value for H

0

', H

0

'( max) , would be for ceilings which behaved in an

approximately adiabatic manner, i.e. , negligible conduction into the surface, with limiting low effective

surface emissivity, and, therefore, with T

cej , jng * Tad . Under such conditions all enthalpy converted from

the fire's combustion zone would reach the r =D wall location with Q, oss

= 0, and

^una *> = < , -VQ/t2nD) (2S)

The minimum value for H

‘ H

0

' (min)l would be for a ceiling which, from the initiation of the fire,

had not yet been heated to temperatures significantly above its initial T amb temperature. Under such

circumstances, Q| 055 can be estimated from Eqs (22) and (23). The result of the indicated integration

leads to

H

o'(mm)

= Ho(max){'-Qioss / f( 1 -\)Qn (26)

- 14 -
where, for the applicable D/H range of interest

Q^/tO-VO] = 2tt[0.513 ReH

~ 1/2 Pr~2/3 + Re^Pr'273 l(D/H)], 0.2 < D/H (27)

l( Tj ) = 0.0533 J [(£-0.0771)/(£ + 0.279)][f(O/£°'2 ]d?

0.2 (28)

and f is given in Eq. ( 16). l(Tj) has been computed, and is plotted in Figure 6. Also, taking Pr = 0.7,

0loss /[( l - X )Q] is plotted in Figure 7 for different values of ReH

. As can be seen, this figure indicates

that for any D/H the relative rate of ceiling heat transfer is significantly larger in reduced scale fires than

in "typical" full scale fires.

The results developed here are based on the analogy drawn between free jet and buoyant

plume-driven ceiling flows. While the analogy is strong for ceiling jet flow locations where Ri, the ratio

of buoyancy to inertial forces, is small, the analogy and corresponding results are unreliable for

moderate-to- large Ri. Such regions of unreliability can be established from an estimate of Ri(D/H) Ri

can be defined and obtained with the use of a characteristic temperature, T ch.of the ceiling jet. This is

taken here to be

9. AN ESTIMATE OF THE RANGE OF UTILITY OF THE RESULTS

ATd-Trt-WtV'tW) ch 1 amb (29)

- 15 -
and Ri is defined as

( 30 )

Using Eqs. ( 1 1), ( 12). (21), (25) and (29) in Eq. (30) leads to

Ri^Wt'-Q^/UI-ArW max (31)

Ri max

= 1 6( D/H) 2 3

/( 2tt ) (32)

where Ri

ma;<

is the maximum possible value for Ri . corresponding to the adiabatic ceiling, l. e. . Q| oss =0.

The upper abscissa of Figure 7 is presented in units of Ri max

. Based on the above observations it is

therefore evident from this figure that in the approximate range D/H of 2.-5 and larger, corresponding to

Ri

rnax of 2.- 1 0 and larger, the reliability of the 0

(oss results, and, indeed, of all the results of this work

must be brought into question on theoretical grounds. Finally, even for smaller D/H. experimental

validation is required before the results presented here can be applied with confidence.

- 16 -
10. REFERENCES

: Cooper

, L Y , Thermal Response of Unconfined Ceilings Above Growing Fires and the Importance of

Convective Heat Transfer, 22nd Nat'l Heat Trans Conf, ASME paper 84-HT-105( 1984).

[2] Cooper, L Y., Harkleroad, M., Quintiere, J.,and Rinkinen, W., An Experimental Study of Upper Hot

Layer Stratification in Full-Scale Multiroom Fire Scenarios, J Heat Trans, 104, p741( 1982).

[3] Cooper, L.Y., Convective Heat Transfer to Ceilings Above Enclosure Fires, 19th Symp (Inter) on

Combustion, p933( 1 982).

[4] Cooper, L.Y., Heat Transfer from a Buoyant Plume to an Unconfined Ceiling, J Heat Trans,

104, p446( 1982).

[5] Cooper, L.Y. and Woodhouse, A., The Bouyant Plume-Driven Adiabatic Ceiling Temperature

Revisited, 23rd Nat'l Heat Trans Conf, ASME HTD-Y0145, p 1 67( 1 985) , to appear in J. Heat

Trans

[6] Jaiuria, Y. and Goldman, D. , An Experimental Study of Negatively Buoyant Flows Generated in

Enclosure Fires, Rutgers Univ, Nat'l Bur Stand (US) NBS-0CR-85-487( 1985).

[7] Alpert, R.L., Turbulent Ceiling-Jet Induced by Large-Scale Fires, Comb Sci and Tech,: :

p197( 1975).

- 17 -
Co

] Pcsreh. M., Tsuei, Y.G., and Cermak, J.E., investigation of a Turbulent Radial Wall Jet, J Appl

Mech, p457( 1957).

[9] Glauret, M.B., The Wall Jet, J FI Mech, 1

, p.625( 1 956)

[ 10] Garden, R. and Akfirat, J.C., Heat Transfer Characteristics of Impinging Two-Dimensional Air

Jets, J Heat Trans, p!01( 1966).

[11] Abramovich, ON.. The Theory of Turbulent Jets. MIT Press, p75( 1963).

[ 12) Yeldman, C.C. , Kubota, T. andZukoski, E.E.,An Experimental Investigation of the Heat Transfer

from a Buoyant Gas Plume to a Horizontal Ceiling - Part 1. Unobstructed Ceiling, Cal Inst

Tech, Nat'l Bur Stand (US) NBS-OCR-77-97 ( 1 975).

[ 13] Zukoski , E.E. and Kubota, T., An Experimental Investigation of the Heat Transfer from a

Buoyant Gas Plume to a Horizontal Ceiling - Part 2. Effects of Ceiling Layer, Cal Inst Tech,

Nat'l Bur Stand (US) NBS-GCR-77-98 ( 1975).

[ 14] HegqeZijnen, B.G., Measurements of the Velocity Distribution in a Plane Turbulent Jet of Air,

Appl Sci Res, A, 7, p256( 1958).

[

1 5] You, H-Z. and Faeth, G.M. .Ceiling Heat Transfer During Fire Plume and Fire Impingement,

Fire and Materials, 103, p140( 1979).

[ 1 6] Mulholland, G. , National Bureau of Standards, private communication.

- 18 -
1 1. NOMENCLATURE

B Nozzle width

C

P Specific heat at constant pressure

D Wall-to-fire distance

f Function in Eq. ( 16)

g

Acceleration of gravity

H Ceil ing-to-fire distance

H

o' Enthalpy flux per unit width, Eq. ( 1 9)

H ' H

' n

o (max) ' no (min) Max , min possible values of H0

‘

h Heat transfer coeficient, Eq. ( 5)

h Characteristic heat transfer coefficient

^ceiling

1

h at wall stagnation, ceiling

An integral, Eq. (28)

k Thermal conductivity

"o' Momentum flux per unit width, Eq. ( 1

)

mo' Mass flux per unit width, Eq. ( 18)

Nu0 ,Nu

s Nusselt numbers. , Eqs. ( 2) and ( 4)

Pr Prandtl number

Q Fire's energy release rate

^loss Rate of heat loss to ceiling, Eq. ( 23)

Q* Dimensionless Q, Eq. ( 1 1

)

- 19 -
Veiling Convective heat transfer rate to wall , ceiling

% q near wall stagnation

Reg.Re

5 .ReH Reynold's numbers, Eqs. (2), (4), and (5)

Ri Richardson number, Eq. (30)

^'max Maximum possible Ri

r Distance from fire

T Temperature in ceiling jet

T ch Characteristic T

^ceiling T at ceiling surface

^up 1 ^amb’ V^ad Upper layer , ambient , wall . and adiabatic temperatures

V Plane or ceiling jet velocity

V

e Nozzle exit velocity

Vmax Maximum of V

V Characteristic velocity, Eq. (11)

X Distance from jet's virtual origin

X

n Distance from nozzle

Z Distance below ceiling

«, J3 Constants, Eqs. ( 6 )-( 8 )

ATch Eq. (29)

S Z where V/Vm =1 /2

IllaA

- 20 -
F raction of Q radiated from combustion zone

P

P

Viscosity

Density

- 21 -
- 22 -

Figure

1

Early

time

ceiling

jet-wall

interaction.
Figure 2. Ceiling jet-wall interaction with upper layer

- 23-
- 24 -

Figure

3

Plane

jetwall

impingement
80

70

60

50

40

30

20

10

0

Dl

re 4

Slot Width B (in.)

---1/4 — 1/8

1/16 Normal Operation

1/16 With Noise

Common

This work

10

/IENSIONLESS

20 30 40

NOZZLE-TO-PLATE SPACING, X n /B

plot of stagnation line Nusselt number from Figure 2 of [ 10] and from Eq ( 4)

- 25 -
(q = J) / s

q

- 26-

Figure

5.

Stagnation

point

heat

transfer

amplification

from

Eq.(9):

"typical"

full-scale.
- 27 -

Figure 6A

plot

of

the

integral 1

defined

in

Eq.

(28)
0.1

0.2

0.5

O-dodo 00 CD Tt CM o

[ 0 (

J V - 0]/ SSO| 0

- 28 -

Figure

7

A

plot

ofQ

)oss

/[

(

1

-Xp

)Qj

per

Eqs.

(27)

and

(32).
NBS-114A irev. 2-8ti U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR-86/3307

2. Performing Organ. Report No 3. Publication Date January 1986

4. TITLE AND SUBTITLE

Ceiling Jet Properties and Wall Heat Transfer in Compartment Fire Near Regions of

Ceiling Jet-Wall Impingement

5. author(S) Leonard Y. Cooper

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

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

Gaithersburg, MD 20899

7. Contract/Grant No.

8. Type of Report & Period Covered

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

10. SUPPLEMENTARY NOTES

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

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

bi bl iography or literature survey, mention it here)

The problem of heat transfer to walls from fire plume-driven ceiling jets during

compartment fires is introduced. An analogy is drawn between the flow dynamics and

heat transfer at ceiling jet-wall impingement and at the line impingement of a wall

and a two-dimensional, plane, free jet. Using the analogy, the literature on plane

free jet flows and corresponding wall stagnation heat transfer rates leads to

readily useable estimates for the heat transfer from, and the mass, momentum, and

enthalpy fluxes of the turned compartment fire ceiling jet as it begins its initial

descent as a negatively buoyant flow along the compartment walls. Available data

from a reduced-scale experiment provides some limited verification of the heat

transfer estimate. Depending on the proximity of a wall to the point of plumeceiling impingement, the estimates indicate that for "typical" full-scale

compartment fires with energy release rates in the range 200-2000kW and

fire-to-ceiling distances of 2-3m, the rate of heat transfer to walls can be

enhanced by a factor of 1-2.5 over the heat transfer to ceilings immediately

upstream of ceiling jet-wall impingement.

fire plumes; fire modeling; heat transfer; room fires; walls

12. KEY WORDS (Six to twelve entries ; alphabetical order; capitalize o ceilings; compartment fires;

13. AVAILABILITY

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| | For Official Distribution. Do Not Release to NTIS

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