A 1110b Pb07El NBS

REFERENCE Publications

NBSIR 84-2856

Thermal Response of Unconfined

Ceilings Above Growing Fires

and the Importance of Convective

Heat Transfer

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

April 1984

-QC133

,U56

34-2355

1934

I S. DEPARTMENT OF COMMERCE

IATIONAL BUREAU OF STANDARDS

NBSIR 84-2856

THERMAL RESPONSE OF UNCONFINED

CEILINGS ABOVE GROWING FIRES

AND THE IMPORTANCE OF CONVECTIVE

HEAT TRANSFER

NATIONAL BUREAU CF ETAHDARCS

LIBRARY

. U5G

Leonard Y. Cooper

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

April 1984

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

NATIONAL BUREAU OF STANDARDS. Emm Ambler. Director

TABLE OF CONTENTS

Page

LIST OF TABLES iv

LIST OF FIGURES v

Abstract 1

1. INTRODUCTION 2

2. THE MODEL FOR THE CEILING RESPONSE 3

2.1 Heat Transfer at the Lower Ceiling Surface 4

2.2 Heat Transfer from the Upper Ceiling Surface 6

2.3 The Boundary Value Problem for the Ceiling, and the Method

of Its Solution 7 2.4 Convective Heat Transfer from the Plume Gases - Enthalpy

Flux in the Ceiling Jet 8

2.5 Radiative Flux from the Ceiling to Lower Targets 9

3. CALCULATIONS FOR THE RESPONSE OF A VARIETY OF DIFFERENT CEILING

CONSTRUCTIONS TO DIFFERENT FIRE THREATS 10

3.1 Descriptions of the Ceiling Constructions and Fire Threats 10

3.2 General Results of the Calculations 12

3.3 Discussion of Overall Results 12

4. ON THE IMPORTANCE OF CONVECTIVE HEAT TRANSFER 13

4.1 Predicting Ceiling Temperatures 14

4.2 Radiation to Remote Targets 15

4.3 Net Heat Transfer from the Enclosure Gases 17

5. SUMMARY OF CONCLUSIONS AND FUTURE WORK 18

6. ACKNOWLEDGMENTS 20

7. REFERENCES 20

8. NOMENCLATURE 21

-iil-
LIST OF TABLES

Page

Table l. Description of the four ceiling constructions 23

Table 2. Description of the six fire scenarios 24

-iv-
LIST OF FIGURES

Figure l

Figure 2

Figure 3

Figure 4

Figure 5

Page

The unconfined ceiling fire scenario 25

Responses of different ceiling constructions of Table 1

(insulation board , gypsum board concrete ,

steel .

. ) to fire scenarios of Table 2.

(a) Q,H=l01.2kW,2m; (b) Q,H=l000kW,2m; (c) Q,H=1000kW,5m;

(d) Q,H=9883kW,5m; (e) Q,H=0. 1054t 2 kW,2m;

(f) Q,H=0. l054t 2 kW,5m (t in seconds) 26

Plot of q"n T (r=0 ,t)/q"(r=0,t) for different ceiling conv,L L

constructions of Table l (see legend of Figure 2) to

the fire scenario Q,H=0 . l054t 2 kW, 2m (t in seconds) 28

Plot of T

g L (r=0

>

t )~Tamb ^ or different ceiling constructions

of Table I (see legend of Figure 2) to the fire scenario

Q,H=0. l054t 2 kW,2m with q^onv ^=0 (t in seconds) 29

Plots of radiant flux to remote targets from the gypsum board

O ceiling responding to the fire scenario Q,H=0.l054t kW,2m;

nonzero q;! onv>L ’ ^conv.L^ (t in seconds)

-v-

THERMAL RESPONSE OF UNCONFINED CEILINGS ABOVE GROWING FIRES

AND THE IMPORTANCE OF CONVECTIVE HEAT TRANSFER

Leonard Y. Cooper

National Bureau of Standards

Washington, DC 20234

Abstract

A procedure is developed to calculate the thermal

response of unconfined non-burning ceilings above growing

fires. The procedure uses an algorithm for conduction

into the ceiling material. It takes account of heat

transfer due to radiation from the combustion zone to the

ceiling surface, and due to reradiation from the ceiling

to the floor and furnishings. Finally, the procedure

uses a previously developed algorithm for convective heat

transfer to the ceiling from the fire-plume-driven

celling jet. The procedure is used to predict radialdependent surface temperature histories of typical

ceiling materials under a variety of different realistic

levels of hazardous fire energy generation rates and

combustion zone-ceiling separation distances. The

results give an indication of the influence of convective

heat transfer on peak ceiling thermal response, losses

from fire plume gases, and radial variations and peak

values of ceiling-to-f loor Irradiation during enclosure

fires
Key words: ceilings, compartment fires, fire

plumes, heat transfer, room fires.

1 . INTRODUCTION

In reference [l] an algorithm was developed to estimate the radial- and

time-dependent convective heat transfer to unconfined ceilings above growing

fires. Together with an account of radial-dependent radiant heat transfer to

and from the ceiling, it would appear that such an algorithm is required to

predict the thermal response of the ceiling material from the time of fire

initiation (when the ceiling and lower gas temperature is at a uniform ambient

temperature, Tam^), to critical times during the course of hazardous fires

(when the temperature field of the ceiling material can have significant

variation in both thickness and radial position, r, from the ceiling-fire

plume impingement point). Examples of such critical times might be those

times when near-ceiling fire detectors and/or fusible sprinkler links are

actuated, when the ceiling surface reaches an ignition or failure temperature,

and when radiation from the ceiling to occupants or combustible furnishings

below, reaches critical levels.

The importance of position-dependent ceiling response, to an understanding of hazardous fire phenomena, in general, does not appear to have been

previously studied. To do so is a major objective of this work.

As pointed out in [l], at relatively early times subsequent to the

ignition of a fire the unconfined celling fire scenario depicted in figure 1

- 2-
is relevant to enclosure fire scenarios where ceiling surfaces are inherently

confined. Also, as discussed in [2] and [3], even at later times during

enclosure fires when the inevitable upper layer of elevated temperature gases

has partially filled the enclosure, analytic methods for describing the unconfined ceiling fire scenario can still be directly used to predict continuing

changes in the fire-generated enclosure response.

This work represents the first stage of an investigation of the response

of real ceiling materials above typical hazardous fires. This first stage

effort deals with the response of ceilings in the unconfined ceiling fire

scenario. Subsequent stages will use the present procedures together with the

ideas of [2] and [3] to study confined ceiling, enclosure fire scenarios.

2. THE MODEL FOR THE CEILING RESPONSE

Figure l is a sketch of the fire scenario under consideration. A fire,

modeled as a point source of total time-dependent energy release rate Q(t), is

initiated a distance H below an expansive (unconfined) ceiling. Because of

their elevated temperature the products of combustion of the fire are driven

upwards by buoyancy. These products generate a turbulent plume of upward

moving, elevated temperature gases. The fraction of Q which effectively acts

to heat the plume gases and drive the plume's upward momentum is taken to

be 1-A^, where A^ is approximately the fraction of Q lost by radiation from

the combustion zone.

- 3-
2.1 Heat Transfer at the Lower Ceiling Surface

As indicated in figure l, the radiant energy, X^Q, is assumed to be

radiated uniformly outward from the fire. The radiant flux, q" , , rad-fire

Incident on the lower surface of the ceiling at a distance r from the plumeceiling impingement point is, therefore,

The fire plume gases continue to rise and entrain air from the ambient

environment. When their upward movement is blocked by the ceiling, they

spread radially outward forming a relatively thin, turbulent, ceiling jet.

As was done in eq. (1), radiation absorption and emission of the ceiling

jet will be neglected throughout this paper. In the case of the early time,

unconfined ceiling, fire scenario under consideration, this neglect is

justified, for example, if one anticipates effective ceiling jet thicknesses

of the order of a few tenths of a meter and absorption coefficients of the

order of a few tenths of an inverse meter.

Heat is transferred by convection from the ceiling jet to the lower

surface of the ceiling. At an arbitrary time after ignition, this radialdependent heat flux, q” T , can be estimated from [l] conv,L

^rad-fire = [X

rQ/(4TTH

2 )][l + (r/H)

2

] 3/2

( 1 )

<Cconv ,L = h. (T . - T _ ) L'' ad s,L'

( 2 )

- 4-
where T T Is the then-current, absolute temperature of the lower surface of

S y Ll

the ceiling, and T

a<^ is the temperature of the gas that would be measured

adjacent to the lower ceiling surface under the condition of an adiabatic

ceiling. hL and Tad of eq. (2) can be estimated [l] from

7.75 Re"°*

5

[l - (r/H) (

5

0.213 Re"

0,3 (r/H)"

0,65

0.217 Re"

0,3 (r/H)“ l/2

,

- 0.390 Re

0,2

)], 0 < r/H <_ 0.2;

0.2 j< r/H < 1.03;

1.03 < r/H

(3)

( T

ad “ T ) HO. 22 exp (-1.77 r/H), 0 <_ r/H < 0.750;

T u Q* 2/3 (2.10 (r/H)"

0,88

, 0.750 < r/H

amb^H —

where

h~

pamb

C

p8 1/2H

' /2 %

1/3

; 116 " s'

/2H

3/ V

/3 /v

QJ - (l-Xr )Q/[pamb

C

p

Tamb

(gH)

l/2

H

2

]

amb ’

(4)

(5)

and where p , , C and v , are the density, specific heat, and kinematic

amb p amb

viscosity of the ambient air. In the above, Q* is a dimensionless number

representing the relative strength of the fire, and Re is a characteristic

Reynold's number of the fire plume at the elevation of ceiling Impingement

As time goes on, T

g b

, initially at Tam^> begins to increase. At all

times this surface is assumed to diffusely radiate to the initially ambient

temperature, expansive, lower floor surface and to exposed surfaces of furniture or other items. In response to this radiation the temperatures of these

surfaces also increase with time. For times of interest here, it is assumed

that these "floor" temperature increases are always relatively small compared

to the characteristic increases of T

g Accordingly, at a given radJal

- 5 -
position of the lower ceiling surface, the net radiation exchange between the

ceiling and the floor/furniture/etc. surfaces below can be approximated by a

net reradiation flux

‘rerad ,L

( 6 )

where a is the Stephan-Boltzmann constant and e is the emittance/

Li absorptance of the assumed grey, lower ceiling surface.

2.2 Heat Transfer from the Upper Ceiling Surface

Heat is transferred through the ceiling, and eventually the temperature

of its upper surface, which is also assumed to be exposed to a constant Tam^ environment, begins to rise.

The rate of heat transfer from the upper surface has convective and

radiative components, H conv p

and q rera(j respectively, which can be estimated from

^conv,U ^ T

s,U

T

amb^’ ^rerad,U e U

0 ^ T

s,U

T

amb^ (7)

where T

g ^

is the instantaneous, radius-dependent upper surface temperature,

hjj is an effective heat transfer coefficient, and is the emittance/

absorptance of the assumed grey, upper ceiling surface. The value for hy to

be used in the present calculations, will be [4]

h = 1.675 It „

- T , | 1/3 W/m2 (T in °K)

U I s , U amb

I

( 8 )

-6 -
2.3 The Boundary Value Problem for the Ceiling, and the Method of Its Solution

The absolute temperature field, T(r,t), in the ceiling material is

assumed to be governed by the Fourier heat conduction equation. Initially,

the ceiling is taken to be of uniform temperature, Tam^. The rates of heat

transfer to the lower and upper surfaces, and q^, respectively, are given

by

q L ^rad-fire

+ ^conv,L ^rerad,L ’ ^conv,U ^rerad,U

For times of interest here, radial gradients of variables of the problem

are assumed to be small enough so that conduction in the ceiling is quasi-one

dimensional in space, i.e., T = T(Z,t;r), where Z is the indepth ceiling

coordinate

.

An algorithm for solving the above problem was developed. Q, X^, H,

properties of the ambient environment, ceiling thickness and material

properties are specified along with the position of radial locations of

interest. The solution to the heat conduction equation for the ceiling at

every specified radial position is by finite differences. The algorithm for

this was taken from [5] and [6]. For a given calculation, N <_ 20 equally

spaced points are positioned at the surfaces and through the thickness of the

ceiling. The spacing, 6Z, is selected to be large enough (based on a maximum

time step) to insure stability of the calculation. Throughout a calculation,

time steps are made small enough so that, at a given lower surface node, the

temperature increase for each time step never exceeds one percent of the then

current value of T at that node.

- 7 -
2.4 Convective Heat Transfer from the Plume Gases - Enthalpy Flux in the Ceiling Jet

A key parameter in enclosure fire modeling is the net rate of heat

transfer from the plume-ceiling jet gases to the enclosure boundaries. The

value of this can play a very important role in a determination of the temperature history of the upper "smoke" layer of enclosure fires. For the

unconfined ceiling scenario, one anticipates that convection dominates this

heat transfer and, as mentioned earlier, that it is reasonable to neglect

radiative transfer to and from the relatively thin ceiling jet.

The rate of convective heat transfer to the lower ceiling surface out to

radius r will be expressed as a fraction, ^ conv > °f Q according to

X (r,t) Q(t) = 2 tt / q (r,t)rdr

conv ’ x J n conv,L

o

( 10 )

Thus, of the total instantaneous energy release rate, Q, of the fire, X^Q is

lost to bounding surfaces of the enclosure by radiation from the combustion

zone and, within a circle of radius r, X Q is lost by convection from the convx

ceiling jet.

At a given radius, the total enthalpy flux of the ceiling jet is

fl-X -X 1 q. A reliable estimate for the enthalpy flux of these diluted

products of combustion is required in enclosure fire modeling since these are

the ceiling jet gases which, when eventually blocked by a vertical wall, will

be turned back to develop into the potentially hazardous upper smoke layer.

-8-
In the present calculations the value of X at an arbitrary value of r

r conv

Is obtained as follows:

At a given instant of time in the calculation, q" is

approximated by a piecewise linear function of r which passes

through the q^onv Lvalues previously computed at the selected

radial positions. This function is then integrated according to

eq. (10) to yield ^conv

as a piecewise quadratic function of r.

2.5 Radiative Flux from the Ceiling to Lower Targets

One measure of the hazard of an enclosure fire is the radiative flux to

nonburning combustible target items. The main concern is the onset of remote

ignitions which could rapidly lead to flashover. Radiation from the combustion zone contributes to the remote target flux, but even for items shielded

from direct fire radiation, illumination from lower ceiling surface radiation

alone can lead to flashover. This latter radiative flux will decrease with

distance from the fire and will vary with the orientation of the target

surface

.

The present algorithm includes a capability for calculating downward

radiative flux from the ceiling to horizontal target surfaces. This is

obtained with the use of the commonly available view factor between a disc

(and, from this, an annulus), and a parallel but otherwise arbitrarily positioned target surface element. At a given instant of time in a calculation,

this view factor is used to compute the total celllng-to-target radiant flux

as follows

-9 -
The ceiling is divided into a disc (center at the plume impingement

point) of radius 0.1H, and 99 concentric, contiguous annuli of ring

width O.IH. The temperature of the disc and of each annulus is

assumed uniform at the position of its average radius, at which

location the temperature is estimated from linear interpolations

between previously computed, current ceiling temperatures.

Appropriate view factors are used, and the radiative flux from the

disc and from each annulus to the target location of interest is

computed and summed sequentially starting from the plume axis. The

summation is stopped when the flux contribution of an annulus is

less than one percent of the largest of the previous single annuli

contributions at the current time step. If the latter condition is

still not achieved by the outermost annulus (i.e., at r/H=10.), then

the entire calculation for that target location is assumed to be

invalid. In this calculation, a black body lower ceiling surface is

assumed.

3. CALCULATIONS FOR THE RESPONSE OF A VARIETY OF DIFFERENT

CEILING CONSTRUCTIONS TO DIFFERENT FIRE THREATS

3.1 Descriptions of the Ceiling Constructions and Fire Threats

The algorithm described in the last section was exercised for fire

scenarios involving four typical ceiling constructions Identified by ceiling

material and thickness in table 1, and six fire scenarios identified by the

x'ed pairs of Q and H in table 2. The response of each of the ceiling

constructions to each of the fire scenarios was calculated. Each of these 24

calculations was carried out to 300s, or was terminated if the peak ceiling

- 10-
temperature at r=0 exceeded 1300°K. In all calculations Tam^ , P am^> Cp>

and v , were taken as 300°K, I.177kg/m^, 1004. Ws/ (kg°K) and 0.1568(10 ^)m^/s,

amb

respectively; £^=£^=1 (black body surfaces); and Xr =0.35. This latter value

for X^_ is a reasonable choice for typical hazardous, flaming fires [7]. The

ceiling response was computed at 28 values of r, where the r/H for these were

r/H = 0., 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.25, 1.50, 1.75,

2.00, 2.25, 2.50, 2.75, 3.00, 3.5, 4.0, 4.5, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0.

The fire scenarios of table 2 involve the two fire-to-ceiling distances

2m and 5m, and four different Q's. H=2m would relate, say, to slightly

elevated fires in residential-type occupancies, where a typical floor-toceiling height is 2.4m. H=5m relates to fires in larger spaces such as places

of assembly or commercial storerooms.

Besides the Q,H pair which defines a given fire scenario, the

corresponding value of Q* is also displayed in table 2. Note that the "odd"

values Q=101.2kW at H=2m and 9883kW at H=5m were chosen to exactly reproduce

the two Q* values of 0.01048 and 0.1035, which correspond to the lOOOkW fires

of H=5m and H=2m, respectively. Thus, for example, effects of a dimensionless

Q*=0. 01048 fire strength is predicted here for two dramatically different

physical fire scenarios.

Of the different Q's, the 101. 2kW level is characteristic of fires in

small chairs or large wastepaper baskets; the lOOOkW level is characteristic

of peak levels of fires in bedding or in upholstered couches; and the 9883. -W

level is characteristic of a 1-1. 5m fuel spill fire, or of peak levels of

fires in a variety of typical arrangements of stacked commodities, as idonti-
fled in table 4.1 of [8]. Finally, as identified in table 4.2 of [8], the t^

fire of table 2 is characteristic of the growth stages of fires in various

diverse arrangements of combustibles, e.g., wood pallets stacked 3m high.

3.2 General Results of the Calculations

Some results of the aforementioned calculations are presented in figure

(groups) 2a-f. Each one of the six figure groups are associated with the

ceiling responses to one of the six fire threats. Plots of three of the

several variables of the ceiling responses, which were obtained during the

course of a calculation, are presented in each figure group, one variable for

each figure of the group. The left-hand figures present plots of the peak

ceiling temperature increase T

g L (r=0

t )"Tam^ vs t. The center figures

present plots of the radial distribution of the normalized T ' s,

S , L

[tL T (r,t)-T 1 /[t T (r=0,t)-T 1, for t=10s and 300s. The right-hand

s,L amb J L s,L amb J &

figures present plots of X (r,t), also for 10s and 300s. conv

3.3 Discussion of Overall Results

The results of figures 2a-f provide insight into the early time response

of real and significantly different ceiling constructions to typical hazardous

fires developing in expansive enclosure geometries. Within the specific

limitations discussed above, the computation algorithm can be used to estimate

the response of any other non-burning ceiling construction to arbitrarily

specified H,Q combinations.

- 12 -
Results for the two pairs of identical Q* fire scenarios can be compared

in figures 2a and 2c (Q*=0. 01048) and in figures 2b and 2d (Q*=0.1035).

Considering the significant differences in the values of Q and H, the lower

ceiling surface temperature responses (i.e., the left and center figures) for

a given Q* are remarkably similar. This is especially true for the r=0

temperature histories. Thus, it appears that for constant Q fires, and for a

fairly wide range of H values, it may be possible to describe the unconfined

ceiling impingement point temperature response with reasonable accuracy by

specifying Q* alone instead of the Q,H (or Q*,H) pair.

rl

The response of the ceilings is strongly influenced by the characteristic

dimension H of the enclosure fire problem. Thus, the center plots of figures

2 indicate significant variation of T_ T with r/H variations of the order of

l. When attempting to model enclosure fire environments, this suggests that

calculations of the ceiling response in terms of a simple spatial average may

not be adequate.

4. ON THE IMPORTANCE OF CONVECTIVE HEAT TRANSFER

The significant impact of radiation heat transfer on enclosure fire

environments is well known. The corresponding importance of convective heat

transfer, however, is not clear and enclosure fire models have taken this

effect into account in only the most rudimentary manner.

- 13-
4.1 Predicting Ceiling Temperatures

The importance of ceiling surface temperatures to fire hazard analyses Is

mentioned in the introduction. The present calculations indicate that, in

general, lower ceiling surface convective heat transfer is significant in the

sense that reliable estimates of its values are required if such temperature

predictions are to be made with reasonable accuracy.

To illustrate this, plots of q^onv ^(r=0,t)/q£(r=0,t) are presented in

O figure 3 for the previously calculated 2m, Q~t fire scenario. The result is

typical of that of the other fire scenarios considered here, in that at all

times considered, q" T (r,t) at r=0 (and, indeed, at all r) is generally of

conv,L

the order of q"(r,t).

Li

To further illustrate the significance of qconv ^on T

g the ceiling

O responses to the 2m, Q~t fire scenario was calculated a second time under a

condition of q conv l

=0* The resul ts for T

g L

(r=0 are plotted in

figure 4, which is to be compared to the left-hand plots of figures 2e. For

example, consider a papered gypsum board ceiling with an ignition temperature

O of 700°K. Then, for the 2m, Q~t fire scenario, the left-hand gypsum board

plot of figure 2e indicates that ignition of the ceiling will occur at approximately 120s while the calculations of figure 4, which neglect convection,

indicate that ignition will occur at 190s.

- 14-
4.2 Radiation to Remote Targets

Another key to successful fire hazard analysis is prediction of the

Ignition of target surfaces removed from the immediate vicinity of a fire's

combustion zone. Such ignition would typically occur on account of radiant

fluxes from the hot ceiling surface, from the upper hot smoke layer, and from

the flame itself.

Depending on target orientation and elevation, direct flame radiation,

which diminishes inversely as the square of the distance from the combustion

zone, could be significant for targets close to the fire. This component of

radiant flux to remote targets will not be considered here.

At early times during enclosure fires when smoke layer accumulations are

still not significant and when the present type of unconfined ceiling calculations are directly applicable, radiation from these layers will be negligible.

Even when smoke layer thicknesses become a significant fraction of H, they can

still be optically thin to the extent that gas radiation to remote target

surfaces will not be significant. Under the two latter circumstances (at

least), and at targets sufficiently removed from walls, overhead radiation

will be determined by the temperature distribution of the lower ceiling

surface

.

In predicting remote ignition of targets under expansive ceilings, the

fact that ceiling temperature distributions are distinctly nonuniform Is

key. Thus, one expects that the peak value of T_ T at r=0, as well as its r

distribution is important in establishing the levels of remote target irradln-

- 15 -
tion. Also, one anticipates that significant reductions of T

g ^ with r,

suggested in the center plots of figure 2, lead to a significantly reduced

threat of remote ignition far from the fire.

Based on these observations and on earlier remarks, it would appear that

the radial dependence of convective heat transfer to the lower ceiling surface

can play an important role in predicting remote ignition/flashover threats

during enclosure fires.

To illustrate this conclusion quantitatively, the overhead radiant flux

to horizontal remote targets a distance H below the gypsum board ceiling is

O plotted vs r/H and at different times in figure 5 for the 2m, Q~t fire.

These fluxes were obtained using the T„ T presented in the left and center

plots of figure 2e, and the target radiation calculation scheme described

earlier. For comparison, the radiation flux for the same ceiling construction

and fire, but q conv ^=0 (i.e., corresponding to the gypsum T

g ^

of figure 4),

is also plotted in figure 5.

As can be seen in figure 5, there is a significant reduction of overhead

flux to targets which are removed distances of the order of H from the fire.

Also, neglect of convection appears to lead to serious underestimates of peak

O fluxes when they reach typical hazardous levels of 2W/cm4 and above. For

O example, at 300s, the peak predicted flux level of 3.67W/cm is reduced to 67

O percent of its value (2.44W/cm ) if convection is neglected.

- 16-
4.3 Net Heat Transfer from the Enclosure Gases

When X is a significant fraction of l-X (which, as assumed here, is conv r typically equal to 0.65) then the net rate of heat transfer from the enclosure

gases to ceilings would definitely be required to predict temperature

histories of enclosure fire environments. However, if X is relatively

conv

small, then such heat transfer estimates may not be important.

The right-hand plots of figure 2 indicate that ^conv

Is °f the order of

0.1 or less for small to moderate r/H. Except for very early times, this is

also true for larger r/H. For the purposes of estimating net enthalpy flux in

the ceiling jet this would seem to suggest that accurate estimates of the

convective loss to the ceiling may not be critical in the calculation of

average, enclosure smoke layer temperatures. Careful scrutiny of the situation does not, however, provide any real confidence in such a conclusion:

For early times, when the present unconf ined-ceiling-type of calculation

hopefully provides reliable estimates of ceiling response, modeling of fire

growth is key. In this regard early time ceiling responses to the Q~t fires

of figures 2e and f are particularly relevant. But it is exactly for these

fire scenarios, and at early times, that the values of X are relatively

conv

large. Furthermore, the most direct practical use for early time calculations

would be for prediction of fire detector/sprinkler link response. It is

9 exactly for such a purpose that the details of the convection problem (i.e.,

the time-dependent temperature and velocity field of the ceiling jet) are

likely to play an important role.

- 17 -
For later times, when upper layer growth becomes a prominent feature of

the enclosure environment, there is an indication in figures 4 and 5 of [2]

that there may be a significant enhancement in values of X over unconfined

conv ceiling values. As indicated in the introduction, by using the procedures

developed here together with ideas presented in [2] and [3]

,

the next stage of

this investigation will, hopefully, provide more definitive insight into this

question.

5. SUMMARY OF CONCLUSIONS AND FUTURE WORK

The algorithm developed here was used to predict the response of a

variety of realistic ceiling constructions to different fire scenarios. The

algorithm is designed to be useful at times subsequent to ignition which are

small enough (dependent on the size of the enclosure, and on the size and

location of the fire) that the unconfined ceiling scenario of figure 1 is

still relevant. Besides the specific results presented in the figures, the

following is a summary of some general results which were indicated by the

calculations

.

Significant variations in ceiling response and lower target irradiation

occur over intervals of radial distance from the fire of the order of H.

Some quantitative similarity in celling response is obtained for constant

Q fire scenarios which have identical Q*. For such scenarios, and for a

ri fairly wide range of H, it appears that unconflned ceiling impingement point

temperature response can be predicted with reasonable accuracy by specifying

the single, dimensionless, fire strength parameter, Q*.

- 18 -
Convective heating along with radiative heating and cooling has a significant effect on the magnitude of the ceiling's lower surface temperature,

and, as a result, on the magnitude of heat transfer by radiation from this

surface to targets below.

Net convective heat transfer to enclosure ceilings can be a significant

fraction of Q at early times during growing fires. At later times, when an

elevated temperature, upper smoke layer starts to fill an enclosed space, the

situation in this regard is unclear. It will hopefully be clarified in the

next stage of this investigation.

In general, the results of the calculations presented here are plausible,

and they provide useful Insight into the response of real ceilings to

hazardous fires. Nevertheless, no data presently exist to compare theory with

experiment. In this regard, a program at the National Bureau of Standards to

measure ceiling response in reduced scale fire experiments has been recently

initiated.

The next stage in this investigation will use the algorithm of this paper

in a new calculation procedure for estimating the ceiling response and firegenerated environment in expansive, but fully enclosed spaces. (If D is the

fire-to-wall distance in an enclosure fire, then, as discussed in [2], an

expansive enclosure is one where D/H is large enough that vigorous ceiling

jet-wall interactions do not occur.)

- 19 -
6 . ACKNOWLEDGMENTS

The author gratefully acknowledges Mr. D. Stroup for his assistance in

preparing the computer-generated plots. 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.

7. REFERENCES

[1] Cooper, L.Y., Heat Transfer from a Buoyant Plume to an Unconfined

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

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

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

[3] Cooper, L.Y., A Buoyant Source in the Lower of Two, Homogeneous, Stably

Stratified Layers, U.S. Nat'l Bur. Standards, NBSIR 83-2789, (1983), and

paper 83-WA/FE-4, 1983 Annual ASME Mtg., Boston.

[4] Yousef, W.W. , Tarasuk, J.D., and McKeen, W.J., Free Convection Heat

Transfer from Upward-Facing Isothermal, Horizontal Surfaces, J. Heat

Transfer, 104, p. 493 (1982).

[5] Emmons, H.W. , The Prediction of Fires in Buildings, 17th Symp. (Inter.)

on Combustion, p. I l 0 1 (1979).

[6] Mitler, H.E. and Emmons, H.W. , Documentation for the Fifth Harvard

Computer Fire Code, Home Fire Project Tech. Rpt. 45, Harvard Univ.

(1981).

[7] Cooper, L.Y., A Mathematical Model for Estimating Available Safe Egress

Time in Fires, Fire and Materials, 6, p. 135 (1982).

[8] NFPA 204M, Guide for Smoke and Heat Venting, Nat'l. Fire Protection

Assoc. (1982).

[9] Thomas, P.H. and Bullen, M.L., On the Role of kpC of Room Lining

Materials in the Growth of Room Fires, Fire and Materials, 3, p. 68

(1979).

[10]

Carslaw, H.S. and Jaeger, J.C., Conduction of Heat In Solids , Oxford,

2nd Ed. (1959).

- 20-
8 . NOMENCLATURE

C

P

specific heat at constant pressure

g acceleration of gravity

H fire-to-ceiling distance

h characteristic heat transfer coefficient

h

L» hU convective heat transfer coefficient at lower and

upper surface

k thermal conductivity

N number of ceiling node points

Q fire’s energy release rate

O' *1 a dimensionless value of Q

q" , q"

conv,L conv,U

convection from the lower and upper surface

q L» net incident flux to lower and upper surface

q rad-f ire

direct radiation from the fire

it it q rerad,L’ q rerad,U

net reradiation from the lower and upper surface

Re plume Reynold ’ s number

r radius from plume-ceiling impingraent point

T absolute temperature field of ceiling

Tamb ambient temperature

Ts,L» Ts,U absolute temperature of lower and upper surface

t time from ignition

z indepth ceiling coordinate

a thermal diffusivity

<5Z distance between node points in ceiling

e . e L* U emittance/absorptance of lower and upper grey surface

Xr fraction of Q radiated from fire

Xconv fraction of Q convected to ceiling

- 21 -
ambient kinematic viscosity

amb

p , ambient density

amb

o Stephan-Boltzmann constant

-22-
Table 1. Decription of the four ceiling constructions

Thickness

Material (m)

Fibre insulation board 0.0127

Gypsum board 0.0127

Concrete 0.0508

Steel 0.003175

k a

(Wra

-1

“K” 1 ) (m2

s -1

) Reference

0.04 1 . 2 ( 1 0~7

) [8]

0.134 1.577(10“7

) [6]

0.92 4 . 2 ( 10 —

7

) [8]

46. O • H-* o1

N-/ [9]

23
Table 2. Description of the six fire scenarios

Q (kW) « H (m) = 101.2 1000. 9883. 0.1054 (t/s) 2 (t in seconds)

2.0 X

Q* = 0.01048

n

X

Q* = 0.1035

X

5.0 X

Q* = 0.01048

X

Q* = 0.1035

H.

X

24
j~7 7 7 7 7 7 7 7 7 7 T'

Figure 1. The unconfined ceiling fire scenario

25
(T(R/H=0)-T(AMB)1,

DEGS K

(T{R/H=0)-T(AMB»,

DEGS K

(T(R/H=0)-T(AMB)),

DEGS K

(T(R/H=0)-T(AMBM,

DEGS K

(a) Q,H=101.2kW,2m;

TIME (s) R/H R/H

(b) Q,H=100QkWr 2m;

TIME (s)

(c) Q,H=1000kW,5m;

500

400

300

200

100

0 -0.05

2.0 3.0 4.0 TIME (s) R/H R/H

(d) Q,H=9883kW,5m;

Figure 2. Responses of different ceiling constructions of Table 1 (insulation board

gypsum board concrete , steel ) to fire scenarios of Table 2

26
(T(R/R=0)-T(AHB)).

BEGS K

(T(R/H=0)-T{ABIB)).

BEGS K

0 60 100 160 200 269 300 6.0 0.4 0.0 1.2 1.6 2.0 0.0 1.0 2.0 3.0 4.0 6.0 TIME is) R/H R/H

(e) Qr H = 0.1054 kW, 2m (t an seconds);

(f) Q,H = 0.1054 kWf 5 m (t in seconds).

Figure 2. Responses of different ceiling constructions of Table 1 (insulations i>

(Cont'd.) gypsum board ...., concrete , steel .

. ) to fire scenarios of I o'.

27
(r/H

=0)/q'

(r/H

=0)

Figure 3. Plot of q" (r»0,t)/q"(r»0,t) for different ceiling

conv y L L

constructions of Table l (see legend of Figure 2) to

the fire scenario Q,H»0. l054t^kW,2m (t in seconds)

28
Q —I J I 1 I I I 1 I I l l l i I l l I l 0 50 100 150 200 250 300

TIME (s)

figure 4. Plot of T

g ^(r-OjO—T^k for different ceiling constructions

of Table 1 (see legend of Figure 2) to the fire scenario

Q,H=0. 1054t 2kW,2m with q^onv,L“0 ^ ln seconds)

29
AT

FIRE

ELEVATION

(W/cm

2)

0 1.0 2.0 3.0

r/H

Figure 5. Plots of radiant flux to remote targets from the gypsum board

O ceiling responding to the fire scenario Q,H=0.1054t kW,2m;

nonzero q^onv >L , ^conv,^0 (t ln seconds)

30
NBS-1 14A (REV. 2*80) U.s.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

1. PUBLICATION OR

REPORT NO.

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

SHEET (See Instructions) NBSIR 84-2856 April 1984

4. TITLE AND SUBTITLE

Thermal Response of Unconfined Ceilings Above Growing Fires and the Importance

of Convective Heat Transfer

5. AUTHOR(S)

I pnnard Y. Cooper

S. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions) 7. Contract/Grant No. national bureau of standards

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

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

bibliography or literatwe survey, mention it here)

A procedure is developed to calculate the thermal response of unconfined ceilings

above growing fires. The procedure uses an algorithm for conduction into the

ceiling material. It takes account of heat transfer due to radiation from the

combustion zone to the ceiling surface, and due to reradiation from the ceiling

to the floor and furnishings. Finally, the procedure uses a previously developed

algorithm for convective heat transfer to the ceiling from the fire-plume-driven

ceiling jet. The procedure is used to predict radial-dependent surface temperature

histories of typical ceiling materials under a variety of different realistic levels

of hazardous fire energy generation rates and combustion zone-ceiling separation

distances. The results give an indication of the influence of convective heat

transfer on peak ceiling thermal response, losses from fire plume gases, and radial

variations and peak values of ceiling-to-floor irradiation during enclosure fires.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by se^.co on; ceilings; compartment fires; fire plumes; heat transfer; room fires

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