NAT L INST. OF STAND & TECH

A 111 Ob M 3 0 7 b b PUBLICATIONS PUBLICAI lONc REFERENCE

NBSIR 87-3535

Ceiling Jet-Driven Wall Flows in

Compartment Fires

Leonard Y. Cooper

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

April 1987

U.S. DEPARTMENT OF COMMERCE

£

100

J56

3.87-3535

387

mONAL BUREAU OF STANDARDS

NBSIR 87-3535

CEILING JET-DRIVEN WALL FLOWS IN

COMPARTMENT FIRES

Leonard Y. Cooper

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

April 1987

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director
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TABLE OF CONTENTS

Page

Abstract 1

Introduction 2

Characteristics of Ceiling Jet 3

Characteristics of the Wall Flow 7

Ceiling Jet Turning and Solution for m' out and fi p 9

Discussion of Results and Comparisons with Experiments 11

Summary and Conclusions 15

References 17

Nomenclature 20

List of Figures 22

ii
MC ;

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CEILING JET -DRIVEN WALL FLOWS IN COMPARTMENT FIRES

Leonard Y. Cooper

National Bureau of Standards

Gaithersburg, Maryland 20899

ABSTRACT

Analytic estimates are developed for depth of penetration and lateral

entrainment of negatively buoyant, ceiling jet-driven wall flows during early

times of compartment fire scenarios. When walls are not too far from the fire

source, of the order of the fire- to-ceiling distance, it is found that the

penetration of these downward wall flows is a large fraction of the fire - to -

ceiling distance, and that this fraction is relatively independent of the

details of fire size and fire-to-wall spacing. Also, net rate of entrainment

into the wall flow as it is buoyed back upward to the ceiling elevation is

found to be several times larger than the flow rate of the driving ceiling jet

flow immediately upstream of wall impingement. Data from five studies reported

in the literature are reviewed relative to the analytic results obtained. One

of these involved a field model simulation of the flow generated by a buoyant

source in an enclosure. Two experimental laboratory studies involved fires in

enclosures with characteristic dimension of the order of several meters. Two

others involved saltwater plumes in freshwater tanks with characteristic

dimension of the order of several tenths of a meter. These data are found to

be consistent generally with the analytic results, and, in particular, with

the notion that the wall flows in question provide the mechanism for mixing

which leads to the deep and rapid stratification typically observed in

enclosed compartment fire environments.
Introduction

A major source of wall flows in compartment fires is the fire plume -driven

ceiling jet which impinges on compartment walls at ceiling-wall junctures.

Figure 1 depicts the wall flow phenomenon at the early stage of such a fire of

total energy release rate, Q, before a significant upper smoke layer has

formed. Figures and text in [1] depict and discuss later generic stages;

first, when the wall flow of the type shown in Figure 1 penetrates an

established, growing upper layer, and second, when an upper smoke layer

completely submerges the ceiling jet and wall flow. As discussed in [1], at

least the latter of these two stages can be analyzed once a predictive

capability of the Figure 1 scenario is available. This paper will focus

attention on the Figure 1 phenomena.

As depicted in Figure 2, the problem of obtaining a description of the

characteristics of the wall flow can be broken into two isolated components.

One of these is the problem of estimating characteristics of the ceiling jet

immediately upstream of wall impingement. These characteristics must be

obtained as a function of fire and compartment parameters. The second

component is the problem of estimating the characteristics of a negatively

buoyant wall flow as a function of a specified, downward- directed, negatively

buoyant equivalent line- jet source positioned at the ceiling-wall juncture.

The wall flow characteristics of interest here are 6

p

, the extent of downward

penetration of the negatively buoyant wall jet, and (m' out - m' 0 )rjf the total

rate per unit radian (of a circle centered at the plume-ceiling impingement

point) at which far field ambient air is entrained laterally into the wall

2
flow as it is buoyed back upward to the original ceiling elevation. With the

solution to the two component problems in hand, a closure to the overall

problem is achieved once conditions of ceiling jet turning at the ceiling-wall

juncture are established and ceiling jet characteristics upstream of the

juncture are thereby related to the properties of the equivalent line -jet

source immediately downstream of the juncture.

Characteristics of the Ceiling Jet

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

generally large compared to buoyancy forces in buoyant plume-driven ceiling

jets [2]. This fact was used in [3] to argue that the flow and heat transfer

characteristics of buoyant plume-driven ceiling jets, like the one depicted in

Figure 1, could be related directly to the analogous characteristics of wall

or ceiling jets driven by unheated or weakly heated free turbulent jets (i.e.,

flows with the same configuration as Figure 1, but with a turbulent free jet

replacing the fire and its buoyant plume). Thus, for the limited but important

range of r/H up to the order of one, a ceiling jet driven by a plume would

presumedly have approximately identical flow properties as that driven by an

equivalent free jet. (This limitation on the r/H range is assumed throughout

this work.) The criteria of equivalence proposed in [3] 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 and to

apply the new correlations to data from buoyant plume -driven ceiling jet

3
experiments, thereby obtaining estimates for the ceiling jet flow and heat

transfer characteristics of interest in compartment fires [3-6]. Thus, results

of [7-9] indicate that outside of the plume/ceiling impingement stagnation

zone, defined approximately by r/H > 0.2, the radial velocity distribution,

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

ceiling to a maximum, Vmax , at a distance Z = 0.235, 5 being the distance

below the ceiling where V/Vmax = 1/2.

Applying further the above ideas, the following estimate for the velocity

distribution of free jet-driven wall jets can be used directly for the

analogous velocity distribution of the ceiling jet

v/vn

' (8/7) [Z/(0.236)] 1/7 {1- [Z/(0 . 235) ] /8 } , 0 < Z/(0.236) < 1

b cosh" 2

{ (0 .23/0 . 77)arccosh(2 1 /2 )[Z/ (0.236)-!]}, 1 Z/(0.235)

( 1 )

The above result for the outer portion of the jet, 1 < Z/(0.23 6), is obtained

from [9], and the inner jet velocity distribution is simply chosen to satisfy

V . Z

1/7 at Z = 0 and dV/dZ = 0 at V - Vmax . Finally [1],

Vmax /V = 0. 85 (r/H )" 1 • 1

; 6/H - 0.10(r/H)°- 9 (2)

V = g

i/2 Hi/2 Q*i/3 . Q

* = (l-Ar )Q/(p amb C

p Tamb g

1/2 H

5 / 2

) (3)

where g is the acceleration of gravity, A r is the fraction of Q radiated from

4
the fire's combustion zone, and C

p is the specific heat at constant pressure,

assumed to be constant.

Reference [10] reports results of measured V/Vmax distributions in the range

0.2 < r/H < 1.5 under steady state conditions in reduced- scale , unconfined

ceiling, plume -driven ceiling jets. Experimental parameters were in the range

H = 0.28-0.91 m, Q - 0.1-0. 6 kW, Q* = 0. 3(10’ 2

) -0. 6(10‘ 3

) , and the heat

sources used to drive the the plumes were an electric heater, an ethane pool

fire or a methane - air burner. The plume flow immediately upstream of ceiling

impingement was turbulent in all experiments. Data plotted in Figure 10 of

[10] are reproduced here in Figure 3 along with a plot of the present result

of Eq. (3). H in Figure 3 is defined by

The far field plume description of [11] was used in the derivation of Eqs

(2). This includes the following estimate, which will be used below, for the

mass flow rate of the plume at the elevation of ceiling impingement

V/Vmax (Z - i) - 1/e (4)

where use of Eqs. (1) and (4) leads to the result

£ = 1.177935 (5)

( 6 )

5
Equations (l)-(3) provide a detailed velocity distribution of the ceiling jet.

Once verified experimentally, this should prove useful in a variety of

applications, e.g., for predicting the response of near-ceiling sprinkler

links deployed at small- to -moderate r/H, and for specifying initial conditions

in integral analyses of ceiling jets for larger r/H where buoyancy forces

become comparable to and ultimately dominate inertial forces.

Integrated, rather than detailed ceiling jet properties will be used to

resolve the present ceiling jet turning problem. For this reason the mass and

momentum flux per unit width of the ceiling jet, m' and M' , respectively, are

defined and computed from Eqs. ( 1

)

- ( 3 ) and (6) as

where near-constant density, p ~ P &mh , in the sense of the Bousinesq

approximation, is assumed here and throughout the rest of this paper. The

enthalpy flux per unit width, H' , is also of interest. Thus

00 - ^„ t V„. x «J(V/V„„)d(Z/«) - 0.093,>, lnb HV<r/H)-°- 2

0 (7)

- 2.8(r/H)-"- 2 mplulIS /(2^H)

M' ~ f.»bVn,. I

2 «;(V/VI„ ]t ) 2 ci(Z/S) - 0 ,059palnb HV2 (r/H)' 1 • 3

0

( 8 )

H' “ P amb (9)

ceiling rdr (10)

6
where H' max is the maximum possible value of H ; A c is the fraction of the

plume's rate of convected enthalpy which is transferred out of the ceiling jet

within a radius, r, of interest; and q" cei i ing is the local flux of heat

transfer out of the ceiling jet. A c will typically be at its maximum (H' at

its minimum) at early times in a fire when the ceiling is uniformly near its

initial temperature, Tamb . At such times, an estimate for Ac as a function of

r/H has been obtained in [1], For the moderate r/H range of applicability, it

will not exceed 0.3 for "typical" full-scale compartment fires with (l-Ar )Q in

the range 200-2000 kW and H in the range 2-3 m.

Using m' , M' and H' , it will be useful to define a characteristic thickness,

L* • temperature difference, AT*- and velocity, V* ’ of the ceiling jet

Characteristics of the Wall Flow

References [12] and [13] report the following correlations of experimental

results for turbulent wall flows driven by negatively buoyant jet sources

configured as in Figure 2.

m'o Ut /m'o “ f (Ri) - 0. 037+60. 968R1-238 . 056Ri2 +485 . 018Ri3 -381. 35RiA (13)

( 11 )

6

p /D = 4.424Ri"°

389

( 12 )

0.02 < Ri < 0.5

7
where m' 0 is the mass flux per unit width of the jet source, Ri is the jet

Richardson's number based on the jet width, D, uniform exit velocity, V , and

temperature, T0

,

Ri - Gr/Re2 = gATo D/(Vo

2 TQ ) ; Gr - gATo D3 /(T0

i/ 0

s

2

) ; Re - V0 D/»/0 (14)

and where ATQ = T0

- Tamb and uQ is the kinematic viscosity at the jet source.

Re, the jet Reynold's number, and Ri of the referenced experiments were in the

range 1400 < Re < 4700 and 0.02 < Ri < 0.5, respectively. Presumedly the

limits on Re are significant in the sense that the results are restricted to

conditions of turbulent flow at the jet source. Thus, within the above

experimental Ri range it is expected that the results of Eqs . (12) and (13)

can be extended to jet sources with arbitrary Re greater than some minimum

value which would distinguish between a laminar and turbulent source. In this

regard, it is reasonable to expect this transition at Re ~ 1000 [14].

For the purpose of studying the properties of the wall flow, Z in the

integrals of Eqs. (7)-(9) is now interpreted as the distance from the wall.

Then m' , M' and H' , now designated as m' 0 , M' c and H' 0 , respectively, are

computed for the wall jet at its source. The definitions of Eqs. (11) are then

applied to these results to obtain the following corresponding characteristic

width, velocity and temperature of the source

8
L’ source “ *'

0

2 /(P amb M' 0 ) “ D ; V' source - M' 0 /m' 0 - V0

;

( 15 )

AT* source source

The global properties of the finite thickness, negatively buoyant experimental

jet source, m' 0 , M' Q and H' 0

, can be thought of as defining the properties of

an equivalent line source of mass, momentum and enthalpy flux.

Ceiling Jet Turning and the Solution for m' out and 6 p

Attention is focused at the position along a ceiling/wall juncture which is

normal to a ray and at a distance, rj , from the plume/ceiling impingement

point There, the turning downward of the ceiling jet is assumed to occur in

such a manner as to preserve the magnitude of its mass , momentum and enthalpy

flux, and, as a result, its characteristic jet thickness, velocity and

temperature difference. Thus

Using the Eq . (15) results for D, VQ , ATC and TQ in terms of m' 0 , M' 0 and H' 0

,

<S p /D of Eq. (12) and Ri and Re of Eq. (14) can be rewritten as

(16)

Ri - gH' 0 m' 0

3 /(/?

9
( 17 )

L* Q - L* ; V* 0 = V* ; AT* 0 = AT*

Based on Eqs . (17), m' , M' and H' from Eqs. (6) -(9) are substituted for m' Q ,

M' c and H' Q , respectively, in Eqs. (16) to yield

Ri = 0 . 62 (r^ /H) 2 • 3 (1 - A c

) (18)

Re ~ 0.093(r

j /H)‘°

-

2 ReH . ReH - g

1 / 2 h3 ' 2Q*1

1

3 /uBmh (19)

fi p /H = 0.78(1 - A c

) -0 - 39 a 0.8 for "typical" full-scale fires (20)

m 'out/m 'o - {m' out /[mplume /(27rr

J )]}/[2.8(r

J /H)°- 8

] = f(Ri) (21)

where ReH is a characteristic Reynold's number of the plume at its ceiling

impingement point [3], and where the a replaces the - in the first of Eq. (19)

on account of the replacement of uQ with v&mh in the definition of Re. As a

point of reference, the "typical" full-scale compartment fires mentioned

earlier are in the ReH range 2(10 5

) -5(10 5

)

.

It is evident from the first of

Eq. (19) that for these, and even for significantly smaller-scale fires, Re

will exceed the 1000 < Re constraint mentioned below Eq. (14).

It is noteworthy that the results of Eqs. (17) -(21), including the 6

p /H a 0.8

estimate of Eq . (20), would also hold in the small-Ri, large-Re range of

buoyancy- conserving ceiling jets generated, for example, when salt water

10
plumes are introduced into tanks of fresh water. For such situations, A

c = 0

and (1 - A

r )Q/(C

p Tamb ) of Eq. (3) is replaced by (pplume source - P amb ) X

(volume flow rate of plume source)

Plots of Ri per Eq.(18) are presented in Figure 4 for the two extreme ReH values lO*1 and 106

, and for the two cases, A c = 0 and A c (rj/H) = A c (max)

, its

maximum possible value. In the latter case, A c (inax) was calculated according

to Eqs. (27) and (28) of [1] which are based on an estimate of heat transfer

from the ceiling jet to an ambient temperature ceiling. The Figure 4 results

were used to generate plots of m' oufc per Eqs. (13), (18) and (21). These are

presented in Figure 5.

Discussion of Results and Comparisons with Experiments

There are three surprising aspects to the results of Eq. (20) and Figure 5.

These should be applicable for ceiling jet - wall impingement in the small -Ri

range, which according to Eq. (18) and Figure 4 is to be expected in spaces

with tj/H up to 1 and possibly greater.

First, is the result of Figure 5. Compared to initial rates of smoke filling

which would be estimated conventionally from mp lume , it is found that the

smoke filling due to m' out will be exceedingly large, approximately 5-20 times

as great for a compartment with an effective r

j /H in the range 0. 5-1.0. This

result is always independent of source strength for buoyancy conserving flows

11
and is relatively insensitive to source strength even when ceiling jet

buoyancy losses due to ceiling heat transfer are at their highest levels.

Second is the result of Eq. (20) that 8 /H is approximately independent of all

fire and compartment parameters.

The final surprise is again found in the result of Eq. (20) which indicates

that 8

p is almost as large as H itself. This suggests that the wall flow can

be a significant mechanism for mixing throughout most of the horizontal slab

of the compartment bounded by the elevation of the fire, i.e., the source of

buoyancy, and the ceiling.

Indirect theoretical and laboratory experiment results having relevance to the

current phenomenon are available in reports of studies involving a buoyant

source in initially uniform ambient, enclosed compartments. The one

theoretical work involved numerical experiments with a compartment fire field

model. In two of the laboratory experiment studies, the buoyant source was a

fire in an enclosure, while two others involved salt water - fresh water

flows

.

Of the two laboratory experiment fire studies, one [15] involved tests with H

= 2.1m and Q* between l.(10 -3

) and 3.(10-3

). The other [16] included a series

of tests with H = 6.0m and Q* between 0.2(10-3

) and l.(10" 3 ). For all of these

experiments ReH > 6.(10A

) and predicted conditions of the ceiling jet at rj

were such that all results of the previous sections should be applicable.

Typical test results from thermocouple trees in each of these studies indicate

12
that from an elevation outside of the ceiling jet region down to near the

floor, and away from walls and the fire plume, the temperature distribution in

the compartments could be reasonably described by a linear function of

elevation. In general, low elevation thermocouples responded far more rapidly

than would be predicted by a conventional, two -layer smoke- filling theory

which didn't include a mechanism for upper layer - lower layer mixing. Also,

it was reported in [15] that in some experiments, smoke movement down the

walls was indicated by way of early increases in smoke concentration measured

at the lowest smoke meter position located near the elevation of, but away

from the burner source. All of these effects are consistent with the present

results which predict an initial, deep, ceiling jet- driven wall flow which

would likely lead to an early and continuing stratified distribution of the

fire's products of combustion throughout most of the compartment height.

One of the two salt water studies [17] involved a buoyant source with Q*

between 0.9(10" 5

) and 5.(10" 5 ), and with Re > 1100 In all experiments. In all

test runs reported in Table IV of [17], flow visualization indicated that

throughout the compartment, a turbulent region driven by the ceiling jetdriven wall flow grew quickly from the ceiling down to a thickness of about

0.55H. Below this, further gradual filling continued, but with laminar

layering of a type described at length in [17]. The 0.55H result was

insensitive to changes in Q* , or in r^/H, the latter of which varied between

0.5 -1.0. It is possible to see the turbulent and laminar regions in Figure 6,

which is a photograph of one of the experiments of [17] at a relatively late

stage of filling.

13
The second of the salt water studies [18] involved a source with Q* between

2.6(10-7

) and 24. (10" 7

) and with 0.5 < r\ /H < 1.1. From the data presented, Re

was computed to be between 260 and 610. As in the previous study, it appears

that a well-mixed near-ceiling layer was also formed rapidly. However, in

these experiments the layer thickness varied significantly from test to test.

The depth of wall flow overturning, which in [18] manifested itself in a nonuniform ring vortex motion, ranged from being non-discernable in the largest

r,/H cases to 0 . 8H in the smallest r./H cases. The difference between these

data and the result of the present work, which predicts the well -mixed ceiling

layer thickness to be a constant fraction of H independent of tj/H, can be

explained by the low values of Re. For the r

i /H range of approximately 1 or

less, these are estimated to be significantly lower than Re values to be

expected in most fire conditions of real interest and for which the present

analysis is applicable As mentioned earlier, a Re of less than 1000 is not

likely to lead to the initially turbulent downward wall flow for which the

data of [12], used in this study, are relevant.

Consistent with all the above results, it is noteworthy that [18] includes an

order-of -magnitude estimate which concludes that significant wall overturning

of plume driven flows is to be expected in relatively small r^ /H sourceenclosure configurations.

The one theoretical study presents results for the transient development of a

plume from a distributed source [19]. Calculations are carried out for

different compartment configurations. Figure 12 of [19] presents results for a

cubical compartment with energy source distributed near the floor. Prior to

14
its expected overshoot and eventual upturn, this figure indicates a deep

initial drop of the negatively buoyant wall flow to an elevation consistent

with results of Eq. (20).

Summary and Conclusions

The main results of this work are in Eqs . (20) and (21). These provide

estimates for the early depth of penetration of and the lateral entrainment

into negatively buoyant, ceiling jet- driven wall flows which are generic to

compartment fire scenarios.

When walls are not too far from the fire, of the order of the fire- to-ceiling

distance, it is found that the penetration of the downward flow near such

walls can be approximated by 0.8 of the fire- to-ceiling distance itself, and

that this result is relatively independent of the details of fire size,

spacings, etc. Also, net rate of entrainment into the wall flow as it is

buoyed back upward to the ceiling elevation is found to be several times

larger than the flow rate of the driving ceiling jet flow immediately upstream

of ceiling jet - wall impingement.

Data from one theoretical and four experimental studies reported in the

literature were reviewed relative to the analytic results obtained here. The

theoretical study involved a field model simulation of conditions in a fully

enclosed space with a distributed volumetric heat source near the center of

the floor surface. Two of these studies involved fires in enclosures with

15
characteristic dimension of the order of several meters. The other two

involved saltwater plumes in freshwater tanks with characteristic dimension of

the order of several tenths of a meter.

None of the above experimental studies were designed specifically to

investigate the ceiling jet-driven wall flow phenomenon studied here. Also the

analytic results were strictly valid only very early in a fire scenario, prior

to any significant upper layer development, additional analysis being required

to place quantitatively the ideas introduced here into the developing fire

scenario. Yet, consistent with the results of this work and with the limited

and indirect available data discussed above, it is reasonable to attribute to

these wall flows the mechanism for mixing which leads to the deep and rapid

stratification typically observed in enclosed compartment fire scenarios. Such

rapid filling, heretofore unexplained by existing zone-type compartment fire

models, can have a significant impact on parameters which characterize the

dynamic compartment fire environment. Reasonably accurate estimates for such

parameters are necessary if one is to predict, for example, the interactions

between fire growth and the upper layer and the response of sprinkler links

and smoke detectors. These are the predictions which must be used to resolve

quantitatively issues of fire safety. In this regard, further analysis and

more focused experimental study, e.g., using full- and reduced-scale enclosure

fires and/or saltwater experiments, are required for confident application of

ideas and results of this work to practical compartment fire modeling.

16
References

[1] Cooper, L.Y.

Ceiling Jet Properties and Wall Heat Transfer in

Compartment Fires Near Regions of Ceiling- Jet Wall Impingement, National

Bureau of Standards NBSIR 86-3307, 1986.

[2] Alpert, R.L.

Turbulent Ceiling-Jet Induced by Large-Scale Fires,

Combustion Science and Technology, 11, p 197, 1975.

[3] Cooper, L.Y.

Heat Transfer from a Buoyant Plume to an Unconfined

Ceiling, Journal of Heat Transfer, 104, p446 , 1982.

[4] Cooper, L.Y.

,

Thermal Response of Unconfined Ceilings Above Growing

Fires and the Importance of Convective Heat Transfer, 22nd National Heat

Transfer Conference, ASME paper 84-HT-105, 1984; to appear in Journal of

Heat Transfer.

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

Ceiling Temperature Revisited, Journal of Heat Transfer, 108, p822,

1986.

[6] Cooper, L.Y.

Convective Heat Transfer to Ceilings Above Enclosure

Fires, 19th International Conference on Combustion, p933, 1982.

[7] Poreh, M. , Tsuei, Y.G. and Cermak, J.E., Journal of Applied Mechanics,

p457

1967.

17
[8] Bakke, P. , An Experimental Investigation of a Wall Jet, Journal of Fluid

Mechanics, 2, p467, 1957.

[9] Glauret.M.B. , The Wall Jet, Journal of Fluid Mechanics, 1, p625, 1956.

[10] Alpert, R.L., Fire Induced Turbulent Jet, Factory Mutual Research

Corporation, Norwood, MA, Report Number 19722-2, 1971.

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

Fire Safety Journal, 3, p 107, 1980/81.

[12] Goldman D. and Jaluria, Y. , Effect of Opposing Buoyancy on the Flow in

Free and Wall Jets, Journal of Fluid Mechanics, 166, p41, 1986.

[13] Jaluria, Y. , private communication.

[14] Schlicting, H. , Boundary Laver Theory . p571, McGraw Hill, 6th Edition,

1968.

[15] Mulholland, G. et al , Smoke Filling in an Enclosure, ASME paper 81-HT-8,

1982.

[16] Hagglund, B., Jansson, R. and Nireus, K. , Smoke Filling Experiments in a

6X6 Meter Enclosure, Swedish National Defense Research Institute, FOA

Report C 20585-D6, Stockholm, 1985.

18
[17] Tangren, E.N., Sargent, W.S. and Zukoski, E.E., Hydraulic and Numerical

Modeling of Room Fires, Report prepared by the California Institute of

Technology for the National Bureau of Standards, Grant No. 5-9004,

1978.

[18] Baines, W.D., and Turner, J.S., Turbulent Buoyant Convection from a

Source in a Confined Region, Journal of Fluid Mechanics, 37, p51, 1969.

[19] Baum, H.R. and Rehm, R.G.

Calculations of Three Dimensional Buoyant

Plumes in Enclosures, Combustion Science and Technology, 40, p55, 1984.

19
Nomenclature

C

P specific heat

D thickness of wall flow source

Gr Grashoff number of wall flow source, Eq. (12)

f function of Ri , Eq. (10)

g acceleration of gravity

H distance from buoyant source to ceiling

H' enthalpy flow per unit length of ceiling jet

H

' max maximum possible H'

V enthalpy flow per unit length of wall flow source

L

A; ^source characteristic thickness of ceiling jet; width of the

wall flow source

z Z where V/Vmax = 1/e, Eqs . (3) and (4)

M' ; M' 0 momentum flow rate/unit lenght of ceiling jet; wall

flow source

m

p 1 u m e mass flow rate of plume at ceiling

m '; m

' 0 ; “'out mass flow rate/unit length of ceiling jet, Eq.(5);

wall flow source; and wall flow, Fig. 2

Q energy release rate of fire

Ql OSS rate of heat transfer from ceiling jet

Q* dimensionless Q, Eq.(3)

1 ceiling flux of heat transfer from ceiling jet

Re ; ReH Reynold's number of wall flow source, Eq. (12); plume

at impingement, Eq . (17)

Ri Richardson's number of wall flow source, Eq.(12)

20
r radial distance from plume impingement

r

j r at ceiling-wall juncture

Tamb ambient temperature

T0 temperature of wall flow source

rp* • rp* source characteristic temperature of ceiling jet; wall flow

source

V velocity distribution of ceiling jet

Vmax maximum of V

V-’ V* •

’ V* source characteristic velocity of plume, Eq. (3); ceiling

jet; wall flow source

Vo velocity of wall flow source

z distance below ceiling

AT* T* - T . amt)

AT0 T - T 0 amb

^T source

rp* rp 1 source

" i amb

5 Z where V - Vma3C /2

5

P penetration depth of wall flow

*c fraction of (1 - Ar )Q transferred from ceiling jet

\ ( max

)

A c maximum of Ac

A

r fraction of Q radiated from fire

^amb * *0 dynamic viscosity of ambient; wall flow source

^amb ’ ^plume source density of ambient; plume source

21
List of Figures

Figure 1. Early time ceiling jet-wall interaction

Figure 2

.

Components of the ceiling jet-wall flow problem

Figure 3. Normalized ceiling jet velocity profiles: Symbols - measured values

from Figure 10 of [10]; Curve - predicted values from Eq.(l)

Figure 4, Plots of Ri(rj/H) for extreme values of ReH and A c = 0, A c (max)

Figure 5

.

Plots of for extreme values of ReH and A

c = 0, A c (max)

Figure 6. Photograph of a saltwater simulation of a closed-room fire

illustrating the turbulent and laminar regions of the upper layer;

Figure 43 of [17]

22
NBS-114A (pev. 2 -ec) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

4. TITLE AND SUBTITLE

PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. NBSIR-87/3535

Publication Date

April 1987

CEILING JET-DRIVEN WALL FLOWS IN COMPARTMENT FIRES

5. AUTHOR(S)

Leonard Y. Cooper

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7 . Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE 8 . Type of Report & Period Covered

Gaithersburg, Maryland 20899

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 significant

bi bliography or literature survey, mention it here) Analytic estimates are developed for the early depth of penetration of and the lateral

entrainment into negatively buoyant, ceiling jet-driven wall flows which are generic

to compartment fire scenarios. When walls are not too far from the fire source, of the

order of the fire-to-ceiling distance, it is found that the penetration of the downward

flow near such walls is a large fraction of the fire-to-ceiling distance itself, and

that this fraction is relatively independent of the details of fire size, spacings, etc.

Also, net rate of entrainment into the wall flow as it is buoyed back upward to the

ceiling elevation is found to be several times larger than the flow rate of the driving

ceiling jet flow immediately upstream of ceiling jet - wall impingement. Data from

five studies reported in the literature are being reviewed relative to the analytic

results obtained. One of these involves numerical experiments with a field model of

the problem of a buoyant source in an enclosure. Two laboratory experimental studies

involve fires in enclosures with characteristic dimensions of the order of several

meters. Two others involve saltwater plumes in freshwater tanks with characteristic

dimensions of the order of several tenths of a meter.

12.

KEY WORDS (Six to twelve entries ; alphabetical order; capitalize only proper names; and separate key words by semicolon s) ceilings; compartment fires; convective heat transfer; enclosure fires; fire plumes;

fire modeling; heat transfer; room fires; walls

13. AVAILABILITY 14. NO. OF

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