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Reference

IMBSIR 83-2789

A Buoyant Source in the Lower of

Two, Homogeneous, Stably

Stratified Layers - A Problem of

Fire in an Enclosure

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

December 1 983

-QC

100 U S DEPARTMENT OF COMMERCE

,U56 NATIONAL BUREAU OF STANDARDS

83-2739

1933

NBSIR 83-2789

A BUOYANT SOURCE IN THE LOWER OF

TWO, HOMOGENEOUS, STABLY

STRATIFIED LAYERS - A PROBLEM OF

FIRE IN AN ENCLOSURE

JIATIO LI _ _ J OF STA'.IDAHLj LIBRARY "ReT

I GO

• uS (o

1^23

Leonard Y. Cooper

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

December 1983

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director

f HAT!0

' OF ST/.-iOAKUS

TABLE OF CONTENTS

Page

LIST OF FIGURES iv

Abstract 1

1. INTRODUCTION 1

2. THE MODEL EQUATIONS 5

2.1 The Point Source Plume and the Model Equations 7

3. COMPARISONS BETWEEN MODEL RESULTS AND EXPERIMENTAL DATA 9

3.1 Upper Layer Centerline Plume Temperatures 9

3.2 Heat Transfer to the Ceiling 10

4. SUMMARY AND CONCLUSIONS 11

5. ACKNOWLEDGMENTS 11

6. REFERENCES 12

7. NOMENCLATURE 13

-iii-
LIST OF FIGURES

Page

Figure 1. Environment near the plume in a room of fire involvement ..... 15

Figure 2. The early time, or unconfined ceiling fire environment 16

Figure 3. An equivalent unconfined ceiling fire environment for

describing the upper layer plume and ceiling jet dynamics

of Figure l 17

Figure 4. Sketches of real and idealized flows 18

Figure 5. Plots of solutions to eqs. ( 25)— ( 32) 19

Figure 6. Comparisons between measured [9] and calculated plume

centerline temperatures for a Figure I scenario 20

Figure 7. A comparison of predicted [7] and calculated ceiling heat

transfer for a Figure 1 scenario 21

-iv-
TABLE OF CONTENTS

Page

LIST OF FIGURES iv

Abstract 1

1. INTRODUCTION 1

2. THE MODEL EQUATIONS 5

2.1 The Point Source Plume and the Model Equations 7

3. COMPARISONS BETWEEN MODEL RESULTS AND EXPERIMENTAL DATA 9

3.1 Upper Layer Centerline Plume Temperatures 9

3.2 Heat Transfer to the Celling 10

4. SUMMARY AND CONCLUSIONS 11

5. ACKNOWLEDGMENTS 11

6. REFERENCES 12

7. NOMENCLATURE 13

-ill-
LIST OF FIGURES

Page

Figure 1. Environment near the plume in a room of fire involvement 15

Figure 2. The early time, or unconfined ceiling fire environment 16

Figure 3. An equivalent unconfined ceiling fire environment for

describing the upper layer plume and ceiling jet dynamics

of Figure l 17

Figure 4. Sketches of real and idealized flows 18

Figure 5. Plots of solutions to eqs. (25)— (32) 19

Figure 6. Comparisons between measured [9] and calculated plume

centerline temperatures for a Figure 1 scenario 20

Figure 7. A comparison of predicted [7] and calculated ceiling heat

transfer for a Figure 1 scenario 21

-iv-
A BUOYANT SOURCE IN THE LOWER OF TWO, HOMOGENEOUS, STABLY

STRATIFIED LAYERS - A PROBLEM OF FIRE IN AN ENCLOSURE

Leonard Y. Cooper

Abstract

A point source of buoyancy is located at a specified

elevation within the lower of two, homogeneous, stably

stratified layers. A turbulent buoyant plume is formed

above the source, and it impinges on the layers' interface. Depending on the strength of the source, its

position below the interface and on the density difference of the two layers, it is conjectured that either:

(1) a central portion of the impinging plume flow will

penetrate and continue upward into the far field of the

upper layer as a buoyant plume, the outer portion of the

flow penetrating but then dropping down toward the interface because of negative relative buoyancy; or (2) none

of the impinging plume flow will penetrate the upper

layer (indepth) because of its being uniformly of

negative relative buoyancy. Associated with these

possible conditions will be an effective horizontal

outflow of fluid at the interface. The paper derives and

solves a set of model equations for these plume-interface

interactions, and the results are applied to a generic

heat transfer problem related to fires in enclosures.

1 . INTRODUCTION

The environment which develops within a fire-containing enclosure space

is driven by the fire-generated buoyant plume. The fire products and the air

entrained into the plume flow upward from the fire's combustion zone to the

elevation of the initially ambient temperature ceiling surface. There, plumeceiling impingement leads to an outwardly moving ceiling jet flow of the plume

gases. These gases are eventually redistributed across the entire area of the

-l-
enclosure celling, and an upper layer of elevated temperature, product-ofcombustion-laden air (smoke) starts to fill the space from above. At some arbitrary time, t, into the fire, when the convected portion of the energy

release rate is Q(t), the environment in the space of fire involvement and near the plume can be depicted as in Figure 1. The thickness of the upper

smoke layer which submerges the continuing ceiling jet flow is A(t), and its

lower interface is at an elevation, Z(t) above the fire. Data from many full

scale fire experiments (e.g., references 1 and 2) indicate that it is reasonable to describe the bulk of the upper layer, outside the plume and boundary

flows, as being of uniform composition, e.g., of uniform absolute temperature,

T

Up(t). Indeed, this assumption is key to rendering tractable the problem of

predicting the overall fire generated enclosure environment, and it has been

used in almost every one of the several zone fire models which have been

developed in recent years.

Mathematical modeling of the ceiling jet flow is very important in the

development of rational design methods for fire safety. For example, it is

the ceiling jet flow which would interact with properly deployed fire

detectors, and with thermally actuated sprinklers, smoke vents and other fire

intervention hardware. The rate of convective heat transfer from the ceiling

jet to the ceiling surface material is also important, and it can be a significant fraction of Q(t) [2]. In designing for fire safety, reasonable quantitative estimates of this heat transfer are required for at least two reasons.

First, the rate of heat transfer will determine the temperature and the

eventual failure response of the ceiling structure. Second, the rate of heat

transfer will determine the temperature and spread characteristics of the

smoke layer. This is the smoke which eventually leads to an environment which

is hazardous to life and/or property.

To describe the ceiling jet it is necessary to be able to estimate plume

properties prior to ceiling impingement.

Prior to the time when the ceiling jet is submerged by the upper layer,

or at times when ceiling jet temperatures are significantly larger than T

up , the Figure 1 scenario can be approximated by the unconfined ceiling problem

depicted in Figure 2, i.e., the upper layer thickness and temperature rise

- 2 -
above ambient do not greatly affect the ceiling jet properties, and the upper

layer, whatever its thickness, can be assumed to have the properties of the

ambient. Such situations would occur relatively early into the fire, later

into the fire for very expansive ceilings, or when the fire strength is

growing at a sufficiently rapid rate. Analytic descriptions of the ceiling

jet for the unconfined ceiling problem have been presented in [3-5], where the

fire in [3] and [5] was modeled as a point source of buoyancy.

A method for describing the ceiling jet for the more general Figure 1 scenario was presented in [6]. There, the concept of an "extended upper layer

equivalent point source" is combined with the unconfined ceiling analysis of

[5]. As depicted in Figure 3, the plume dynamics in the upper layer are described as being generated by a point source fire of strength Q’ , located a distance H' below the ceiling, and in an infinite "ambient" environment of

temperature, T

Up. The values Q' and H' are computed by invoking a principle

of continuation which conserves plume mass and enthalpy flux across the upper

layer interface. With Q' and H' in hand, the unconfined ceiling solution of

[5] is used to predict heat transfer to the ceiling. This method gave

analytic results which compared favorably to experimental data reported in

[7].

Although it is reasonable to expect that the above method will provide

excellent results when relatively strong plumes penetrate the layer interface,

it will be inadequate when the plumes are relatively weak. Weak here refers

to situations where the penetrating lower plume flow, having, say, a Gaussian

distribution of temperature and velocity, is such that a significant outer

portion, possibly the entire flow, is at a lower temperature than T

Up» As

such a plume enters the upper layer, this outer portion of the flow will be

negatively buoyant relative to the "new" ambient, and it will tend to be

separated off from the core flow, never to penetrate to the ceiling. The core flow will be positively buoyant relative to the upper layer, and it can be

expected to continue its ascent to the ceiling as a buoyant plume. It is also

possible that the negatively buoyant portion of the plume flow will shear off some of the core flow as it separates, or visa versa. If the excess enthalpy

flux, H , of the penetrating plume flow relative to the upper, T environment

is negative, and if even its maximum temperature, T is less than or equal

- 3 -
to T

U p (as may be the case subsequent to decay phases of the fire), then It is

reasonable to expect that all of thlB flow will be effectively redirected

laterally near the Interface. For large enough A, none of It will rise to the

celling. The resulting flows In the upper layer near the Interface would be

similar to those studied In [8]. Here, H

R

Is defined as

00 Hr

- 2ir C / p'u" <T“ - T )rdr (1)

p o

p

where u , p , and T are the flow velocity, density, and temperature,

respectively, In the plume directly below the Interface. Also, C

p is the

specific heat which is assumed constant.

By adding and subtracting Tam^ in the above parentheses and regrouping

terms it is possible to rewrite eq. (1) as

where m

face

,

Q - C T , (T /T . -1) m“

p amb up amb ( 2 )

is defined as the mass flux in the plume Immediately below the inter00 m => 2 tt / p u rdr (3)

o

and where, by conservation of energy, Q is the enthalpy flux of the plume

below the interface,

00 Q

= 2ir C / p"u“ (T~ - T . ) rdr (4)

pK amb

o

By defining the following dimensionless variables

H*-= H^/Q; *»- = n-'CpTamb/qi a - T

up

/Tamb

Eq. (2) becomes

(5)

H* = 1 - (a - 1) m*

K

( 6 )

-4 -
It is the purpose of this paper to extend the method of [6] in such a wav

that the ceiling jet problems related to the scenario of Figure 1 can be

described quantitatively for fires of arbitrary strength.

2. THE MODEL EQUATIONS

Consistent with the above discussion, sketches of the real and idealized

flow are presented in Figure 4. The outflowing arrows in the idealized sketch

represent two components of the outward-moving mass flow, I* and 1^, above and

below the interface, respectively. These flows are taken to be at the respective ambient temperatures, Tam^ and T

Up, of the local environments into which

they are flowing. Note that the two distinct outward flowing mass sources,

I* and 1^, can be thought of as representing either a single idealized source,

at some temperature between T

Up

and Tam^, or as an actual outward moving flow

with some nonuniform temperature distribution. It is also noteworthy that the

model being proposed does not distinguish possible flows involving portions

of I* and/or Im turning back, and being entrained into the plume either above

fl+

v

] or below fl 1 the interface.

nr v nr

When T < T , all of the penetrating lower plume flow has negative

max — up

buoyancy relative to the upper layer, and it will all eventually be turned

downward, back toward the interface and away from the axis as in Figure 4a.

For such completely turned flows, it is not useful to invoke conservation of

vertical momentum in the present global model. To do so would lead to an equation which relates momentum flux of the plume at the interface to an integral of the pressure distribution along the upper boundary of some control

volume, e.g., along the ceiling surface. Using the same reasoning when

T^ax > T (and the incoming lower layer plume is partially overturned near

the interface and partially continued as an upper layer buoyant plume) , continuity of momentum will still not provide, here, useful additional information.

As in Figure 4b, when T > T the portion of the penetrating plume max up

_L flow which continues upward in the upper layer is designated by m , where

00 m

+

= m

+

(z > Z) = 2 tt / p+u+rdr (7)

o

- 5 -
and where p+ and u+ are the density and upward velocity, respectively above

the interface. The ceiling is assumed to be far enough above the interface so that, at the elevation of ceiling impingement this upper layer buoyant plume

can be adequately described as being equivalent to a flow driven by a point source of some unknown buoyant strength Q’ = H+ located a distance H' below

the ceiling in an extended infinite environment of uniform temperature, T

Up.

Here, Q

1 is defined by

00 Q’ = 2ttC / pV (T

+

- T ) rdr (8)

P

JQ up

where T+is the temperature distribution above the interface, p +

, u+ and T+

are also the values of the variables that would occur at z < Z as a result of

the equivalent buoyant source being located in the extended upper layer, i.e.,

as in the scenario depicted in Figure 3.

Defining the dimensionless variables

I*

f = I+ /nf ; 1*' = r/m";

m ra m m

’

m*

f = m

+

/ra ; H*

+

= Q'/Q

R

(9)

continuity of mass and energy across the interface leads to

m*

+

( z = Z) + I* + + I* = 1 (10) m m

11* + + (a -1 ) ( 1 - I*“)m*“ = 1 (11) R m

m*

+

= H*

+

= 0 if T" < T (12) R max — up

Eqs . (10) and (11) are for the four variables I*

+

, I* , m*

+ (Z), H*+ mm . For

R

the case T > T , when the latter two of these are expected to be nonzero, max up

two more equations are required. In this case it is assumed that the continuing flow, m

+ (Z), is all from a radial core region, r <_ r

Q

, of the plume mass

flux, m

-

. Then the first of the additional equations will reflect the assumption that the enthalpy flux between this core flow and m

+

(Z) is conserved

across the interface. Thus, r Q is defined by

-6 -
m ( 13 ) +

(Z) = 2ir J ° p u rdr

o

and the conserved enthalpy flux assumption leads to

r

Ll* ++(a-l)m* m* +(Z)=2ir(C /Q) / °p u (T -T , )rdr (14) R p amb

o

The second equation will require that the peak temperature of the plume (i.e.

at the axis) be continuous across the interface, viz,

T~ = t” (r = 0) = T+

(Z, r = 0) > T (15) max up

It is noteworthy that in the work of [9], which treats aspects of the upper

layer plume dynamics in some detail, considerable importance is attached to

this requirement which was ignored in [6].

2.1 The Point Source Plume and the Model Equations

The model equations ( 10)— ( 15) will now be developed further with the use

of the point source buoyancy plume description of [10], viz,

(T-TJ/(Tmax-Tj - exp [-8r2 /(C2

;

2

)

]

u/umax

“ exp

where

T = (1 + C ft* 2/3

) T max X oo

u = C g

l/2

5 l/2a*l/3 max V

ft* = n/(p C T ; 5/2

g

1/2

) OO p

oo °

6cJ = 3 C

t

/2; (1+S)/C

v

=

C

T

= 9.115; 3 = 0.913

(16)

(17)

(18)

(19)

( 20 )

( 21 )

-7 -
In the above, T and u are the absolute temperature and vertical velocity In a plume at a distance C above a point source of convected enthalpy of strength ft which Is submerged In an ambient environment of uniform density, , and

absolute temperature, T^. Also, g Is the acceleration of gravity, and Tmax

and umaxare the maximum (centerline) values of T and u.

If mgp Is the mass flux in the buoyant plume, then the above description,

together with the Boussinesq approximation in the form p(Z,r) " p(Z,®) leads

to

m

Bp = [(l+0)/C

T

) Poo g

1/2

C 5/2 n* l/3

(22)

where, from eq. (21), (1+S)/C

T

= 0.210

Define

T = T" /T - 1 > T ,/T - 1 = -(a-1 )/a max up arab up

Then, from eq. (18)

T = (1 + C

T

Q* 2/3 )/a - 1

(23)

(24)

where Q* is defined by eq. (20) with 0, p^, Tm

and X, replaced by Q, P am^»

T amb and Z, respectively. Using the plume equations further, eqs. (10 )— ( 15)

lead to

If r < 0 : m* +(Z) = 0

If T > 0 : m*+

(Z) is the solution to

(0+l+a)m*

+ (Z)/(l+a) = l-[ l-m*+

(Z)

1+3

(25)

(26)

where

- 1 < a = af/(a-l) (27)

-8 -
Also

I* = {3 - o [ l+m*+

(Z) ] } /( 1+3) (28) m

I*

+ = 1 - I*”- m*+

(Z) (29) m m

H*~ = (a - 3)/( 1 + a) (30)

Q'/Q = am*+

(Z) /( 1 + a) (31)

( H'-A)/ ( H-A) = a

3/5

[m*+

(Z)] 2/5 [(l+a)/a] l/5 (32)

2.2 Solution

A numerical solution to eq. (26) for m* +

(Z), a > 0 has been obtained and

is plotted up to moderate values of a in Figure 5. From the numerical

results, the following analytic estimate for m* +

(Z), accurate to within 0.05%

in the entire range a > 0, (well beyond any fire modeling requirements) has

also been obtained

1.04599a + 0.360391a2 m* (Z) (33)

1. + 1.37748a + 0.360391a

The remaining variables in the model were found from eqs. (28)-(32), and are plotted in Figure 5.

3. COMPARISONS BETWEEN MODEL RESULTS AND EXPERIMENTAL DATA

3.1 Upper Layer Centerline Plume Temperatures

Reference [9] provides one set of experimental data for upper layer

centerline plume temperatures in a Figure 1 scenario. In that experiment, the

energy source was a 0.62 kW fire from a preraixed (to minimize flame length)

burner with 36.5 mm exit diameter. The experimental conditions along with the

temperature data are presented in Figure 6. Consistent with these conditions

a = 1.098; T = 0.286; a = 3.20 (34)

-9 -
Using these in the results of the previous section leads to an analytic

estimate for the plume centerline temperature distribution, which is also

plotted in Figure 6. The agreement between measured and calculated results is

such that |(Tmeas

-Tcalc )/(Traea8-Tamb )| never exceeds 0.14 in the upper layer.

3.2 Heat Transfer to the Ceiling

Reference [7] provides data for the radial and time-dependent convective

heat transfer, qraeasureci> t0 an initially ambient temperature ceiling in a Figure 1 scenario. Measurements were taken at seven r/H values ranging from

0-0.72 and at 1, 2, 3 and 5 minutes into the test. The time-dependent values

of the ceiling surface temperatures were also reported at these locations and

times. The basic experimental conditions for the test were

H = 0.584 m; A = 0.31 m; (35)

Q^ = 1.530 kW; T , = 290°K ’ amb

Describing the upper layer environment according to the unconfined

ceiling scenario of Figure 3, estimating Q * ( t ) and H’(t) with the use of the

results of eqs. (31 )— (33) and estimating the ceiling heat transfer according

to the method developed in [5] leads to estimates of ceiling heat transfer

rates, ^predicted*

The above procedure was followed, and the resulting values for

^predicted ^measured are plotted in Figure 7. The values of q predicted and

^measured at t *ie seven radial positions were used to estimate the instantaneous total rates of convective heat transfer, 2Tr/qp redic ted rc^ r anc*

2‘rr /qcalculated r<^ r * to t ^e experimental ceiling surface. For l, 2, 3 and 5 minutes into the test the values of /qpredicted rdr //qmeasured r<^ r were 0.82,

0.88, 0.93, and 0.92, respectively. Predicted values for m*+ were also

obtained at these four times. These were found to be 0.89, 0.87, 0.85, and

0.83, respectively (a = 7.56, 6.18, 5.43, and 4.64).

- 10-
The present comparisons between predicted and measured heat transfer

results are not significantly different from those obtained in [6]. In view

of the above estimates of m*+

>_ 0.83 (i.e., m* + close to 1), this comes as no particular surprise since the model of [6] includes the assumption that

m*+

= 1. However, in contrast to the present model, the reference (6) model

must eventually fail for small m*+ (i.e., small a) fire scenarios.

While it is reasonable to hope that the presently proposed calculation

scheme will provide useful ceiling heat transfer results even for fire

scenarios with moderate and small values of a, further experimental verification of its utility is clearly required.

When - 1 < a <_ 0, the present model predicts a quiescent upper layer with

no plume rising to the elevation of the ceiling. In such cases the

convective/conductive heat transfer to the ceiling surface would be relatively

small, the result, say, of a thick slab of quiescent, TUp

gas which is cooled

and/or heated from above by a relatively nonuniform ceiling surface.

4. SUMMARY AND CONCLUSIONS

Consistent with the sketches of Figure 4, a set of model equations to

describe the plume dynamics in enclosure fire scenarios was derived. The

solutions to the equation are plotted in Figure 5, and they are algebraically

represented by eqs. (25 )— ( 32 )

where eq. (26) is replaced by eq. (33).

Although the model equations and their solutions are remarkably simple,

they were found to provide useful predictions to plume centerline temperatures, and to convective ceiling heat transfer in Figure 1 fire scenarios. In

this regard, further experimental verification of the results over a broader

range of model parameters is encouraged.

5. ACKNOWLEDGMENTS

This work was supported by the U.S. Department of Health and Human

Services, the Bureau of Mines and the National Park Service of the U.S.

Department of Interior, and the Federal Aviation Administration of the U.S.

Department of Transportation.

- 11 -
6. REFERENCES

[1] Mullholland, G., Handa, T., Sugawa, 0., and Yamamoto, H., Smoke Filling

in an Enclosure, Fire Science and Technology, 1, p. 1 (1981).

[2] Cooper, L.Y., Harkelroad, M., Quintiere, J., Rinkinen, W., An Experimental Study of Upper Hot Layer Stratification in Full-Scale Multiroom

Fire Scenarios, J. Heat Transfer, 104, p. 741 (1982).

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

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

[4] You, H-Z. , and Faeth, G.M. , Ceiling Heat Transfer During Fire Plume and

Fire Impingement, Fire and Materials, 103, p. 140 (1979).

[5] Cooper, L.Y., Heat Transfer From a Buoyant Plume to an Unconfined

Ceiling, J. Heat Transfer, 104, p. 446 (1982).

[6] Cooper, L.Y., Convective Heat Transfer to Ceilings Above Enclosure

Fires, 19th Symp. (Inter.) on Combustion, p. 933 (1982).

[7] 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, Calif. Inst. Tech. /Nat. Bur. Stand. (U.S.)

NBS-GCR-77-97 (1975).

[8] Turner, J.S., Jets and Plumes with Negative or Reversing Buoyancy,

J. Fluid Mech., 26, p. 779 (1966).

[9] Evans, D.D., Plume Flow in a Two-Layer Environment, 1983 ASME/AIChE

National Heat Transfer Conference, Fire Dynamics and Heat Transfer, ASME

HTD Vol . 25, p. 89.

[10]

Zukoski, E.E., Kubota, T. , Cetegen, B. , Entrainment in Fire Plumes, Fire

Safety Journal, 3, p. 107 (1981).

- 12 -
7 . NOMENCLATURE

C o > » Cn

H

H'HR

H£

Xm

I*mm

m*“

m*^

Q

Q'

Q*

T

T

max

tu

umax

Z

za

0

r

A

c

pa

Q.

constants, eq. (21)

specific heat

distance between ceiling and Q source distance between ceiling and Q* source enthalpy flux of plume relative to T

up

Hr/Q, dimensionless

outward mass flux near interface

Im

/m

-

, dimensionless

mass flux of plume

dimensionless m

-

, eq. (5)

dimensionless m , eq. (9)

convected portion of energy release rate

an upper layer equivalent source strength

dimensionless Q, c.f. below eq. (24)

distance from plume axis

absolute temperature

maximum (axial) T of plume

time

upward velocity

maximum u of plume

z of interface

elevation above buoyant source

T /T

up' amb

a constant, eq. (21)

a parameter, eqs. (23) and (24)

upper layer thickness

elevation above point source of buoyancy

density

a parameter, eq. (27)

strength of a point source of buoyancy

- 13-
Subscripts

arab , 00 ambient

up upper layer

BP buoyant plume

Superscripts

+ above interface

- immediately below interface

- 14-
- 15 -

Figure

1.

Environment

near

the

plume

in

a

room

of

fire

involvement.
- 16 -

Figure

2.

The

early

time,

or

unconfined

ceiling

fire

environment
-17 -

Figure

3.

An

equivalent

unconfined

ceiling

fire

environment

for

describing

the

upper

layer

plume

and

ceiling

jet

dynamics

of

Figure

1.
//////////////

///////////////

-18 -

Figure

4.

Sketches

of

real

and

idealized

flows
CO

CM

M

-19 -
Mor'i-i

-20 -

Figure

6.

Comparisons

between

measured

[9]

and

calculated

plume

centerline

temperatures

for

a

Figure

1

scenario.
oo

CO

CO

CM

pajnseaui b

/pai3!pajd b

- 21

Figure

7.

A

comparison

of

predicted

[7]

and

calculated

ceiling

heat

transfer
NBS-114A tREv. 2 -ec> U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR83-2789

2. Performing Organ. Report No. 3. Publication Date December 1983

4. TITLE AND SUBTITLE

A Buoyant Source in the Lower of Two, Homogeneous, Stably Stratified Layers - A

Problem of Fire in an Enclosure

5. AUTHOR(S)

Leonard Y. Cooper

6. PERFORMING ORGANIZATION (If joint or other than NBS, 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 significant

bi bl iography or literature survey, mention it here) A point source of buoyancy is located at a specified elevation within the lower of

two homogeneous, stably stratified layers. A turbulent buoyant plume is formed

above the source, and it impinges on the layers’ interface. Depending on the strength

of the source, its position below the interface and on the density difference of the

two layers, it is conjectured that either: (1) a central portion of the impinging

plume flow will penetrate and continue upward into the far field of the upper layer

as a buoyant plume, the outer portion of the flow penetrating but then dropping down

toward the interface because of negative relative buoyancy; or (2) none of the

impinging plume flow will penetrate the upper layer (indepth) because of its being

uniformly of negative relative buoyancy. Associated with these possible conditions

will be an effective horizontal outflow of fluid at the interface. The paper derives

and solves a set of model equations for these plume- interface interactions, and the

results are applied to a generic heat transfer problem related to fires in enclosures

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

mathematical models; smoke

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