Gas fires with pool-like boundary conditions

GAS FIRES WITH POOL-LIKE BOUNDARY CONDITIONS R. C. CORLETT Department of Mechanical Engineering, University of Washington, Seattle. Washington The consumption rate of a burning pool of liquid fuel is controlled by heat transfer to the liquid from the reaction zone, presumed to be in the gas phase. The object of this work was delineation ofimportam heat transfer mechanisms and determination of dependence of heat transfer on fuel vapour properties. As an approximation to the burmng pool, the burning of gas issuing uniformly from cool, horizontal, porous surfaces of 5, 10 and 19 cm diameter has been studied. Heat transfer to the cooled porous surface was the basic measurement. The use of gaseous fuel makes possible much greater experimental flexibility than the use of liquid fuel. The basic experiment and characteristic data patterns are described. The effects of burner geometry variations and of inert diluents are summarized, it is shown that the general magnitude of the heat transfer, and its variation with burner geometry, are consistent with corresponding data from burning pools. The radiative heat transfer component was determined by methods described in an Appendix. The basic radiation measurement was the output of a radiometer installed in the centre of each burner. This was supplemented by direct radiative heat transfer measurements, which were sometimes possible with a special burner configuration and with bolometer traverses of remotely projected images of the fires, The results suggest that fuel consumption rates, fo~ the diameter rat.le of interest, are determined primarily by non-radiative rather than radiative heat transfer.

F~l~i~,,utt~l~o pools of low,boiling liquid fuel e~hibit the basic features of malty fires of practiciil itltereit, ttiimely diffusive buftilttt~ free ¢iittveetiotl cetltrolled flii~ dyl~a~ics, aiid b~rtlittt tale control by heal ttii~ifet i?om the flame~ IO ii itasil~tiilt fuel louise, iilipeliiiietitiil dittii, ptiiiliirily liquid fell'el: liot~ r~le~, have b~tl r~,poried by ~vet~il itive~tiltator~t-~< The tteiieriil e~e~i of pool di,t~eter vatiittioti i~ rett~oiittltll+ w~ll iiiider .~iood iitid hti~ been ,~iimm,ri~e#: ~ pt:~ot di,melerv, rie,~ &ore ithOUl 4 fo lilO ~tii, Ilti~ fife flow field,~ l~olile ttlftlulittll tl,d Ihe doiiiinil,i heiil Ifiiiltfi~r to the liqliid, whi~l~ eOlitfol,~ Ihe v, pofi~itioil tlild hi~n~ hiirliilll

~o,v~tivet ,ieehtini,~m,~I~ ltldiilliOll. The lower I~rtio, of ihi,~ ritime, 4 io ~O ~m, i,~ ~f primtirt( iiitere,~i ill i~ w~rl~ r~t~ried hereitl, ttlifl~ ohje~iive.~ were d~li,~e,iil~n or imporllt,l m~httlll.~lll.~ of l~l~l ll'ltit~fer #t~m ~fl~fttttilttflo~ of thl ~ot of v~fi~iiion of f, ll

The fact that combustion and heat transfer in pool fires of low,boiling gels ~cur Pfl~fi!Y ifl the vapour phiise suggests the possible exploitatiori of suitiibiy desigtied gas burtiers for the study of ~ol fire heat li'atisfef, U~ tit t~ts httrnel',~avoids Ihe fuiidaiiieiitai difficulties thiit iifl~e withttttempted iteildy bufiiiiii ofliqukl fitel iiliilUres, tttid thus ittiili~ ~siihl~ ~Ottliiiuttiii viiiitttiotl or fuel tliptluf iloi~hiotti~ffy ~tli

wilti Iifltiitt hitflii~f.~ I~itj.~ ttl~ burttilii! ~t~ ithlt iilid tht pi.~ltltili {~tfiltTiTllfill~ !~iltitl t~v!t

Vol. 12 used for the exveriments reported in this paper were propane, methane and carbon monoxide. Both CP and less pure grades of each fuel were burned. No effect of fuel purity variation was dis~rned. Additional experiments with a much L~roaderassortment of fuel will be reported in a ,,ubs~uent paper. For reasons discussed below, I d ~ + 6.4 rnm (¼in.) was adopted as a standard configuration. For this elevation and for D = 10 Knife-edge Uniformlf,~ flux ~t~n , cm, total heat transfer data for the three fuels are presented in Figure 2. For purposes of interpretation, latent heat requirements for acetone and methanol, based on supply velocity U, are included. Corrections *'6 for heating these liquids from room temperature to the pool surface temperature, which is near boiling point, have not been added to these latent heat requirements, Such corrections would increase the latent heat requirements of acetone and W~ter- cooled Burner mount (rigidly methanol from 10 to 15 per cent depending on burner attached to coltar) assumed liquid surface temperatures. Values of FIGURE l, Burner installation, schematic elevation cross U corresponding to intersections of the latent section heat requirement lines with the curves of QT versus U are interpreted as apparent pool water maintained the surface temperature near burning rates in vapour volume units. For ambient and made possible calorimetric deter- reasons discussed below the indicated acetone mination of the time average total heat transfer, burning rate is based on propane heat transfer, QT, from the flames. (Fuel and water were and the indicated methanol burning rates are distributed by channelling, not shown in Figure based on methane and carbon monoxide heat 1; a complete description of experimental transfer. details is given in a thesist6.) The knife.edge The validity of these liquid burning rate mount shown in the diagram was an effectively estimates depends on several assumptions. First. adiabatic interface between the burner and she it is assumed that molecular, as opposed to collar. The collar was also wate;:-cooled and radiative, heat transfer mechanisms exercise the heat transfer, Qo to it could be measured dominant control over burning rates in the independently. Apart from the diameter D, the range of diameters of interest. On the basis of only geometric variable was the burner surface experiments described in the Appendix, this was elevation d, which was adjustable over the range shown to be true {except possibly for diameter of approximately - 7 to + 13 mm. D = 19 cm} for the fuel gases used in the work The basic experimental measurement was discussed here. A second and tentative assumpQT as a function of the cold vapour supply tion is that the beat transfer Qz is independent of velocity U at the burner surface, with geometry chemical kinetic differences among the fuels. and fuel composition fixed. The radiative con- The qttestioa of chemical kinetic influence is a tribution QK was determined by measurements major problem area of the investigation and is wi;h a thermocouple radiometer installed in not fully resolved. The data presented in this the ~.'entre of the burner. Justification of this paper are consistent with the followingview: technique is given in the Appendix. The fuels Among a large class of C--H--O fuels, chemical kinetic differences do not greatly influence the non-radiative heat transfer. An * Machined from ~ in. thick, $ mi,~on {iltrat.,on grade stock exception is carbon monoxide, whose fires oL,tain~.~fromCurioEn~inwringCorporaliO~.Mmrklm,Ctmeecticut It, C. COItLffrT

L ~ j . ~ n q m m =~ f a t e d ltmd= T ~ gas burners of nominal 5, 10 and 19 cm diameter were used. The arrangement is illustrated schematically in F~ure I. A uniform flux of pt~'ous fuel issued from the-porous stainless steel* upper face. Internally flowing cooling

Fehruary 1968

(~,xs FilRES WITH POOL-LIKEBOUNDARYCONDITIONS

21

;Hi Latentheat )zCO

t,l e

2e

C3HI

0

Apparentburningrate:mmliquidlmin p/

....

I

~

|

.....(CH3)2C0 : 1"6 CH30H: 1.2-1"t. ,

I

2"0

1,o U, crn Isec

I"t(iURE2. Tctal heat transferversusfuel suppl.,,'~'docity, +9= 10cm, standardelevationd

transfer unusually large amounts of heat to cold burner surfaces. Aim additional assumption is that the gas burners adequately simulated the vapour phase boundary condition of a pool fire. The gas burners provided a steady, uniform flux of fuel at ambient temperature {usually 20'~' to 30C) instead of the presumably unsteady, non-uniform flux of fuel vapour evaporating from a burning liquid pool surface at some temperature generally not ambient. Published data s indicate that the time average fuel flux from a real pool fire is relatively low near +he rmo] centre. That these differences in boundary conditions are not fundamental are suggested by three things: the reasonable agreement of real and apparent pool burning rates, as discussed below; results of experiments with damaged or corroded burners ~6 that resulted in only moderate distortion of heat transfer characteristics: and similarity of flame geometries as revealed by direct and shadow observations and of flame dynamics as revealed by direct and shadow motion pictures.

Discrepancies between gas burner surface temperature and those of boiling acetone and methanol are about 30 to 40 deg.C As the flame-to-liquid, and probably also reaction zone-to-liquid, driving temperature differentials greatly exceed 40 deg.C, it is expected that burner surface temperature is a secondary variable. This view is supported by the fact that reasonably reproducible results were obtained despite nearly 20 deg,C fluctuations in ambient temperature. If the above assumptions are true, gas and liquid fires will be similar if the vapour parameters listed, in Table. 1 !hence.forth called gros~s parameters) are sufficiently well matched+ From the kinetic theory of gases, correspondence in viscosity implies a rough corresponden~ in mass diffusion coefficients. Table I suggests that propane and acetone arc roughly comparable in their gross properties, and that methanol falts somewhere in between methane and carbon monoxide. It is shown below, on the basis of experiments with inert diluents, that the effects of variation of the air requirement L and of

Vol.12

R, C. COKLETT

TABLE I. Gross properties of fl~,~lvapour* t,t~ Vapour

Air . Acetone Methanol Propane Methane Carbon monoxide

t~

k

~

b

Mol. ~

1410 0.38 0.52 0,43 0,54 0-96

1.00 0-42 0.65 0,77 1.20 1,02

-19.1 72 23.8 9.5 2.38

-9.8 9.6 9.6 8.9 9.9

29 58 32 44 16 28

tt is dynamic viscosity relative to air at standard conditions, k is thermal conductivity relative to air at standard conditions. ~. is the sloichiometric requirement, moles air per mole fuel. b is heat of reaction per mole stoiehiometric reactants normalized by ambient thermal enthalpy: b = AH/[O. + t)CtTo]

density ,"re mild at supply velocities U charac- thesized numbers are raw data, the others are teristic of pool fire burning rates, with trends corrected for transient, pan energy storage predictable. effects. Akita and Yumoto s experimented with The parameter b is a dimensionless heat of steady burners surrounded by cooling water. reaction per mole stoichiometric fuel-air mix- Corlett and Fu t° obtained their data with ture. None of the data available suggest a steadily fed, thin.walled stainless steel pans stronger than linear heat transfer dependence exposed to ambient air all around. In viewof the on b. It is noted that large variations of b are approximate nature ofthe gas burner simulation, unattainable in a normal ambient atmosphere. tile apparent burning rates of acetone and One expects a relatively weak direct dependence m~thanol are considered to be in satisfactory on fuel viscesity and thermal conductivity agreement with the directly measured regression because of the high concentration of nitrogen in rates. regions where .tiffusive transport is important. Moreover, general experience with convective Variation of GeometrkParameters heat transfer processes is that small discrepancies Composites of acetone and methanol burning in transport properties are almost never ampli- • rate data e's't° are presented as Figure 3,',ogethcr fied in measured heat transfer. with apparent burning rates (round symbols) Directly measured liquid fuel regression rates inferred from gas burner data (elevation d - 64 are compared with corresponding apparent mm}. Small extrapolations were required for burning rates inferred from gas burner data in the 19 cm diameter apparent burning rates from Table 2. Emmons6 gave burning rates from propane and carbon monoxide data. It is noted transient pan burning experi.men!s.The pardn- that the variation of liquid burning rates with TABU: 2. Regression rate comparison ID = t0 cml

Liquid blm~im3rate, ram~rain i"tM E#tlAlOtl.¢ ~

Methanol Acelone

1'1 ~I.0) I'8-2"0

(1.5)

Akita and YlitttOto8

Corlett

and/.~to

Apptlr~',t!

0-95

I'10 + 0"01 1"2 IMethan¢ data)

--

1,42 +_ 0.02 1.6 (Propane data)

1.4 (Carbon monoxide dalai

February 1968

23

GASFIRESWITH POOL-LIKEBOUNDARYCONDITIONS

It 6---

1-0 '[ 0"8 0"6 O

0.4 1.(~ 0'8

23

0.2 ..J

0'6

o.,

"'

0e1'0

'

. . . . . . .

'

:;

2 ~, 6 8 10 0 30 POOl diameter, cm FIr~L,AL 3. Comparison of real and apparent pool burning tales

diameter D differs considerably between data sources,especiallytowards lowerdiameters.This variation evidently depends on thermal, geometric and other details of the experimental arrangement. (The data taken from Emmonse are for the flush mounted pans, corrected for storage effects.) The burners of Corlett and Fu were designed to correspond with the edge conditions of the gas burners. The variation of apparent acetone burning rates with D is in qualitative agreement with the steady liquid burning rate data ~°, The apparent methanol burning rates based on methane data show virtually no variation with D, in contrast with steady pool burning data s'l° Those based on carbon monoxide data are ii', rough agreement with the pool burning data of Corlett and Fu. The authoz believes that the latter correspondence is to some extent fortuitous in view of the poor ~natch between air requirements/, of methanol and carbon monoxide !Tah!e l,~ ~.4 :,~.eseeming differences in chemical kinetics, discussed subsequently. The failure of the apparent methanol burning rates based on methane data to increase with decreasing D cannot be conclusivelyexplained. Tentatively, this is ascribed to the low density

of methane on the basis of the following reasoning. At sufficiently low diameter D, the effect of buoyancy can be shown by similarity arguments to be~,omenegligible. In the absence of other characteristic lengths, the burning taie must then vary inverselytv with D. This is observed with appropriate burner designst'4"t°. Flattening of the burning rate versus D characteristic evidently marks the onset of buoyancy effects. Now a low density fuel gas such as methane tends to enhance the buoy,ant effec,t of the hot flame gases. The flamestend to be sucked in over the pool surface resulting in a general increase of heat transfer {Figure 7). It thus appears that buoyancy effects should become significant at relatively low D with a light fuel gas such as methane. Ti~e [~s~t ~u!d be relatively flat burning rate versus D characteristics. The variable burner elevation d {Figure I) makes possible limited exploration of the effect of edge geometry variation. Typical data are shown in Figure 4; the uncorrected data are heat transfer measured with the burner cooling circuit only, and the corrected data were obtained by adding to the uncorrected data the convective heat transfer from the flames to the

24

g. C, CORLETr

collar. This correction, which is not purported to be precise, was developed by subtracting from the measured -,~o,,~r '~ heat transfer" Qc the corresponding value of Qcwith d = + 6.4ram, but otherwise with identical operating conditions. The validity of this procedure depends on two assumptions, First, that convective heating of the collar by the flames was zero when d = + 6.4 ram. Repeated observations

0

...................

CH4

U=1"4cmlsec'

i t

0

I I I L[II

1 t i t I I i ~ lal I I

co u1

L

i"1.7 I

o 5

Vol. 12

tion that flame configurations were substantially independent of d. It is observed that the corrected heat transfer generally varies less with elevation d than the uncorrected heat transfer. Evidently the con. v~tive heat transfer from the hot flame gases is split between burner and collar, when d < + 3 ram, in a complicated way which depends on edge construction, fuel supply rate and fuel ~density. The corrected heat transfer is relatively insensitive to such details and can be determined simply by measurement of burner heat transfer in a slightly elevated configuration. For this reason d - + 6'4 nun was adopted as a standard configuration tor subsequent experiments. On the basis of negative elevation d heat transfer data, apparent burning rates were computed as functio~3s of liquid level elevation below pan rim. Pool burning rates fall off rapidlySwith decreasing liquid surface elevation at small diameter D. As D increases the effect is less pronounced, a decrease in burning rate of five to ten per cent being observed in the first 6 mm of liquid level drop at L'~- 10 cm t°'t3, Apparent burning rate data exhibited trends in qualitative agreement with the~ observations.

I

0

iilli

Itlll

III

II!III,

,, C3He

',

15

Standard-~ I

~Ol-

O[LLI

"10

es6',

~

t I J I

5

o Corrected

i I i.l.1

0 d, mm

L]

.5

i'i

I t

",10

=, Uncorrected

FIGU'~E4, Heat transfer versus burner elevation, D = 5 ¢m, standard elevation d

showed that the hot flame gases were then out of contact with the,collar. Second, all extraneous heat transfer to the water-cooled collar {i.e. flame radiation and heat exchange with in. flowing fresh air) was substantially independent of d with supply velocity U, fixed. The justification of this second assumption was the observa-

Experiments with Inert Diluents One of the primary reasons for studying small gas fires was the opportunity to use diluents in a simple yet meaningful way. The motivation for use of diluents depends on theoretical con. sid,~rationswhich may be summarized as follows. Radiative transport is ignored in the energy equation, a single overall reaction (pure fuel plus oxygen) is assumed, and the diffusive flux j~ of each species i is taken to be - (p~)V~ (where Y~is the mass fraction of species i) and (pY) is a function of local temperature and mean molecular weight only, Then the mathematical formulation of the flow and molecular heat transfer problem for a diluted fuel burning in air is formally the same as that of a pure fuel burning in air, provided the air requirement and the dimensionless heat of reaction b are calculated as if the fuel--diluelit mixture were a pure substance, e.g. ,[ is the number of moles air per mole fuel-diluent mixture. In particular, if subscript pfis used to denote

February 1968

GAS Flgl~ WITH POOL-MICEBOUNDARYCONDITIONS

pure fuel values, it is easily seen from the defmition in Table 1 that, for a fixed combustible component,

b a// (~.,~+ I) b~,f A//Ps (~. + I)

~. (2,s + I) ~.pj. 12 + I)

which is nearly unity if 2 ~, t. Hence the gross parameter b is substantially invariant among pure and diluted hydrocarbons. By adding to a combustible gas an inert diluent of equal density, it was possible to vary the stoichiometric air requirement ). with only slight variation of the remaining gross parameters listed in Table 1. Hopefully, the controlling chemical kinetics remained unchanged upon addition of inert diluents.

25

addition. This su$gcsts that the presence of neither diluent appreciably affected the overall controlling chemical kinetic rates, and that radiation from the flame was uninfluenced by diluent addition, The data pattern shown reflects mainly molecular as opposed to radiative heat transfer phenomena. This is illustrated by Figure 6, which presents the propane--carbon dioxide data of Figure 5 after subtraclion of the radiative heat transfer Qa as determined by procedures described in the Appendix.

30

p~:23.8

40

d•z•

"8

Oituent

x

0

..... I

0"5

~:

t-"

1.0

t-5

U, cml sec FIGURE6. Molecular heat transfer Q = Qr - QR, propa~e-carbon dioxide system, D = I0 cm, standard elevation d

V-

0

/ _._=.__

0.5

I~0

1.5

U,cm/seC FIGURE5. rotal heat transfer Qr, propane--carbon dioxide and propane-argon systems, D = I0 cm, standard eleva. tion D (NOTE: Diluent mole fraction = I-~..!/'Ps: lbr propane ,;,J,/= 23.8)

The results of nearly constant density diluent addition to propane in the diameter D = 10 cm burner are shown in Figure 5. A similar but less well resolved data pattern was obtained for D = 5 cm. Propane (molecular weight 44) was diluted with carbon dioxide (tool. wt = 44) and argon (tool. wt = 40). The argon addition ez~riments were conducted to provide con. trast in possible chemical kinetics or radiative effects of diluent addition. As indicated in Figure 5, the effect of argon addition to propane up to at least 40 per cent (2 = 14.3) appears substantially the same as that of carbon dioxide

Similar patterns were obtained from fires of methane (mol. wt = 16) diluted with a I: 1 by volume helium-nitrogen mixture(tool, wt - 16), designated Hc-N 2, and carbon monoxide (tool wt = 28) diluted with nitrogen (tool. wt = 28). The propane, methane and carbon monoxide data patterns exhibit common features. At low fuel supply velocities ~J" me heat transfer for each system tends to correlate when plotted against UA, which is proportional to the supply rate of the combustible gas. Such a low sl;pply velocity correlation was observed for each fuel studied (see discussion of Figure 8, below). This is readily explained on grounds that the flow field at low supply velocities is dominated everywhere by combustion products or air: ":fso the combustion processes ought to proceed independently of the fue! diluent concentration. At high U, the heat transfer for each system tends roughly to correlate as a function of U only. No convincing ,-xplanation of the latter tendency has been put forward. Both tendencies

26

R,C CORLETT

to correlate were noted for all three systems, and broke down only near diluent concentrations too high for the mixtures to burn. Up to this point, the effect of systematic variation of the mixture air requirement is clear and regular. The quantitative explanation of extinction diluent concentrations for free.burning fires apparently requires much further work. Unless an extreme, and probably unlikely, sensitivity to transport property variations is responsible, the basis of the extinction phenomenon must involve parameters other than the gross parameters (as characterizing the fuel gas mixture) listed in Table 1. Otherwise the fact that diluted propane or methane would not burn with ,:, < 5 implies that carbon monoxide should not burn at all (i.e. except for kinetic parameters, the mathematical formulation of the problem ~:)r a hydrocarbon mixture of mol. wt = 28 and /~ = 2.38 is substantially the same as that for pure carbon monoxide). Presumably chemical kinetics are important in the determination of the extinction diluent concentrations. The role of chemical kinetics appears clearer when one considers the heat transfer data in the limit of low supply 'velocity U. in the limit U -, 0 excess air would be available everywhere. If the chemical kinetic rate were infinite, complete combustion would occur in an infini. tesimally thick zone immediately abo,,.e the burner surface and all of the available heat of combustion would be transferred back to the burner surface. In fact, the heat transfer at,low U approaches roughly a tenth of this maximum for propane and methane, and roughly a third of the maximum for carbon monoxide. This suggests strongly that the controlling kinetics of carbon monoxide fires are, relatively rapid near the cold burner surface. This interpretation is consistent with evidence, based on deflagration velocity data t4, that carbon monoxide reaction rates at normal flame temperatures are slower than those of hydrocarbons. Computed overall activation energies t4 and flammability limit theory and data ts imply that carbon monoxide reaction rates are much less temperature ~ensitive than are those of hydrocarbons, In custjunction with the data of Table 1, the data patterns such as those exhibited in Figure 5 assist in interpretation of ~he ~,ppetent

Voi. 12

burning rates shown in Figure 2. If one assumes that the controlling reactions of propane and acetone combustion are identical, then the small difference in air requirements ~. of these two fuels should, according to Figure 5, have negligible effect on the burning rate comparison. However, an analogous methane-methanol comparison indicates that, due to the difference in air requirements ;., the pure methane heat transfer data should lead to a significant overestimate of the methanol burning rate. As shown in Table 2, a modest overestimate does occur. The latter interpretation is complicated by two additional factors. First, the buoyancy effects discussed earlier should enhance still further the overestimate of the methanol burning rate. Secondly, for methanol the heat of reaction parameter b (Table 1) is somewhat higher than that of methane. Interpretation of the overestimate of methanol burning rate on the basis of the carbon menoxide data in Figure 2, in terms of differences in air requirement A, fails entirely. This is further evidence that. heat transfer from carbon monoxide fires cannot be related to heat transfer from hydrocarbon fires solely in terms of gross parameters listed in Table 1. To strengthen the arguments, given above, regarding the effect of density variation, that parameter was varied independently of/, by use 40

o

3C

u

i I Io IC).,-co l,. I,,lC~:Co,

l 4, •

IS,t

~o I

1.0 2,0 U, cm/sec FtGURE7. Effect of density variation, D = 10 cm, standard elevation d 0

c,,h .....

CONDITIONS GAS FIRES WITH POOL-LIKE BOUNDARY

!OI;R

of alternative dihents for propane and methane. The data are shown in Figure 7. For sufficiently high fuel supply velocities, the figure indicates, for both propane and methane, a clear trend of increasing heat transfer with independently decreasing mixture densities. Also shown in Figure 7 are data for a propanemethane mixture (2 = 16.7). Within ~catter, these data agree with data from a propane(He--N2) mixture of the same density and nearly the same air requirement (2--11.9). This suggests that among propane-diluent and methane-diluent systems, the heat transfer is a function only of the gross parameters listed in Table 1. The foregoing idea is further borne out by Figure 8 in which the data of Figure 7,

40 ~

monoxide

~J 111

3C f,,.)

(:}

20Hydrocarbon-inemritxtures Symbols as for FIGURE7 10

F=O',JRE 8.

I 2

L I 4 6 U ),,, c m / s e c

Flamegeometry Motion pictures show that the flame motions of a pool.like gas fire are similar to those of a real pool fire, provided gas supply velocity U and gross physical parameters are of appropriate magnitude. At very low U many different rotating and axisymmetrically oscillating flan~e patterns have been observed; these are beyond the scope of the present paper. Similarly, the competition between jet momentum transport and buoyancy forces at very large U is not of interest here. In the diameter range of interest, the dynamics of fires are dominated by buoyancy when U corresponds to pool burning. At low U a gas fire concentrates unsteadily over the centre region of the burner. With increasing U the fire grows in size and the heat transfer increases until a cold fuel core appears over the centre. The core grows and the heat transfer decreases with further increase of U. In general, the extent of the core increases with increasing supply velocity U, increasing air requirement ,L and decreasing fuel density. Flame geometries of liquid pool fires and those of corresponding pool-like gas fires are in reasonable agreement. However, the cores of the liquid pool fires tend to be somewhat weaker. This last observation is consistent with physical reasoning and experimental data 8 to the effect that vaporization near the centre of a burning pool is lower than that near the edge.

Concludingremarks

I

B

27 ~one are significant in the determination of heat transfer from small fires.

lO

Low velocitycorrelationof hydrocarbondata, D = 10cm, standardelevationd

together with those for pure carbon monoxide, are plotted against U2. In substance the low U correlation discussed above is common to both propane-diluent and methane-diluent systems, But for the anomalously high heat transfer from carbon monoxide, one would be tempted to conclude that generally the gross parameters

The principal conclusions of the work reported are as follows: (1) Cooled, uniform flow gas burners in the range of diameters studied provide heat transfer data that are consistent with the heat transfer implications of liquid pool burning data. (2) Variable burner geometry experiments showed that the heat transfer from gas fires, when completely accounted for, is a fairly well defined experimental quantity. These data suggest a simple experimental configuration for which measured heat transfer can be interpreted unambiguously.

28 lCc. COnt,E~ Vol. 12 (3) By systematic addition of inert diluents to absorptivit)' was determined to be in the range propane, methane and carbon monoxide clear 0"6 to 0"8. Both the absorptivity and the radiodata patterns showing the effect of independent meter response fell off moderately as the variation of fuel mixture stoichiometric air incidenceangle increased to 450, and much more requirement and density were obtained. The rapidly the.re,after. For reasons discussed below, effectofindependent density decreaseis increased radiation at large incidence angles is unimheat transfer, due apparently to enhancement of portant. free convection. An alternative and more reaiistic calibration In general, these res,lts are regarded as was obtained with ~ special burner mount necessary preliminary evidence that gas fires (Figure 9). For high ~ ,pply velocity U of fuels with pool.like boundary conditions sufficiently resemble pool fires to make possible meaningful Iollar ;~c~,~:hment interpretation of results. Through the use of ~:,c~+i,~oft flame i diluents to control physical parameters, and because of their general experimental conveni. er~ce,gas bu~.ers provide a usefultool for fur,daI mental studies of free-burning fires. ,,.rner [

.+J

'APPENDIX

Experimental Estimation of Radiative Heat Transfer QR* ~ e centre radiometer In practice the radiative .heat transfer contribution QR was determined by using a black thermocouple radiometer mounted in a cavity in the centre of the burner, The cavity wall was polished brass. A small upward stream of argon injected below the detector protected against contaminants and provided a nearly uniform temperature environment for the detector. The complete radiometer assembly occupied about 1 cm 2 in the centre of the burner. Outside this area the fuel flux was uniform, as indicated in Figure 1. In general, the radiometer was calibrated by using the burner cooling water circuit as a calorimeter. The responses of the porous burner surface and the radiometer were checked, using lamps as heat sources. The true magnitude of the radiation from the lamps was determined calorimetrically with the burner surface blackened. During burning experiments the burner surfaces tended toward a specific equilibrium condition for each fire studied. For the fuels of interest in this paper, the burner surface A morethoroughdiscussionof this topicts foundm Relerences 16and 17.

O-rings

, I

i

t

FIoug~ 9. Modified burner mount for direct radiative heat transfer measurement, elevation cross section through centre line

denser than air, the flameswould attach to a rim out of thermal contac~ with the burner. This could be verified by the examination of shadowgraphs. The burner calorimetric circuit then gave a direct measurement of the incident radiative heat transfi:,r QR. Such direct calibrations with carbon m~,,noxideand propane fires, and lamp calibrations, were in approximate but not preciseagreement,presumablyindicating a mild sensitivity of burner absorptivity to wavelength. Radiometer response was slightly sensitive also to the total heat transfer Qr as cooling water temperature variation~ affected the tern. perature of the radiometer housing. Appropriate corrections were determined with the radiometer shielded. Before proceeding with justifica. tion of the centre radiometer output as a practical measure of QR, it is advisable to put the problem in perspective. A posteriori comparison of total heat transfer Qr and the

GASFIRESWITH POOL-LIKEBOUNDARYCONDITIONS

February 1968

molecular component Q-- Q ~ - Qs as functions of supply velocity U (e.g. Figures 5 and 6) shows that Q rather than Qk exercisesdominant control over the apparent burning rate. The Qa measurements would have to be quite seriously in error to invalidate this conclusion. The acceptable fractional error in QR increases with decreasing U. The conclusionshold also for carbon monoxide and methane fires. Now consider the accuracy of the measured Q~ at high U. For high U, most of the radiation incident on the burner surface is assumed to originate high enough such that the incident flux may be considered uniformly distributed and at normal incidence. On the basis of remote bolometer traverses discussed later, it can be demo:tstrated that this assumption is very good for hydrocarbor/fires and reasonable for carbon monoxide fires. Thus the principal sources of error are minimal at high U. As U decreases, the flame shortens and the incident radiation tends to originate closer to the burner surface. Problems of non-uniform distribution and non.normal incidence become increasingly severe. The essential problem is one of extrapolating a method that is very good at large supply velocity U into a r~gime of lower U where the method is not obviously valid, but where

~.,~~..~ Z/D=3

2

_ j~

increasing error is tolerable. To support this extrapolation, a series of auxiliary measurements was made with a remote bolometer. Remote bolometersurveys

By using outer surface mirrors, an elevation image of each fire investigated was projected. Each image was traversed horizontally at a series of elevations with a thermistor bolometer. The bolometer was sensitive to total incident radiation over the wavelength range of interest, as was verified by a black source at variable temperature and at variable distance. Frequ,:nt recalibrations were made with a referencelarap. Traces of typical data are shown in Figure 10. Fires of the type investigated are subject to random fluctuations of considerable magnitude but are symmetrical about a vertical axis in a time average sense. Traverse velocity and signal damping were such that at low elevations the results may be interpreted as approximate time average emission profiles. At higher elevations there occurred long period excursions that were not fully averaged out. Nevertheless, it was possible to make reasonable inferences of time average emission profiles at such elevations. For purposes of data reduction, an idealized model was adopted. In this model, all relevant optical paths are optically thin and, at each

/,~ropane^ U=0,4¢m/sec

1'5"~1.0"-~0,5~.,~2~p ~ ~

CaLibration] LI ..~.~C

~D(to state of traverse data as shown)

F~Gu~

10.Typicalremotebolomcterrawoutput

~

30

VoL 12 a direct measurement using a carbon monoxideargon mixture, the fuels were pure. The points designated centre corrected remote bolometer are calculations of what the centre radiometer should read if it absorbed uniformly at all incidence angles. The source distribution as a function of elevation for the eight remote bolometer surveys used in Figure 12 is given in Tables 3 and 4. In these tables, ~ is the elevation of the ith traverse, in units of burner diameters, (AOi is the elevation increment a~igned to the traverse at ~i for purposes of numerical integration, and Q~.i is the contribution to Qa from

R, C, CORLETT

elevation, the time average volumetric emission intensity is uniform over a horizontal annulus and zero elsewhere. (The interior of the annulus is a cold fuel core as evidenced by shadowgraph observation and probing re, and indirectly by doubly peaked remote bolometer traverses as in Figure I0.) At elevations where a cold fuel core does not exist, the annulus degenerates to a disc. For burner diameters D -- 5 and 10 cm, the optical thinness assumption appears to be quite accurate with saturated hydrocarbon fuels and a rough but quantitatively meaningful approximation with carbon monoxide, provided carbon 0"15

o Carbon monoxide o Propane

Tu

o a O

'Eu 0.10

O O

0"05 ~

' (3'5

1.0 H FIGURE l i, Test of remote bolometer data reduction procedure

dioxide is not used as a diluent. After making the above assumptions it was possible to evaluate from the bolom©ter traverse data a numerical integral H theo~'etically proportional to the radiative heat transfer QK.Figure 11 shows results for fires amenable to direct Qx measuren~t by using the configuration of Figure 9. Although the data are considerably scattered, a linear correlation is well enough approximated to justify the remo*,ebolometer method as a semiquantitative tool for studying the source distribution of radiation incident on the burner. " The remote bolometvr data also !made it possible to determine formt.lly the distribution of radiation on the burner surface. Specifically, it was possible to compute the error in the centre radiometer output due to the non.uniform distribution of incident radiant energy. Results for propane and carbon monoxide fires on the diameter D = 10 cm burner arc shown in Figure 12. Except for the indicated data point denoting

* Cer~tre corrected remote botometer o Remote botometer .4 A Centre radiometer

o

Propane ,

1 0-5

I 1,o

l°F---" ,":=., , ] 5~

0

. A~~ ~'" "

1.5

-)

-A-~

o

,, ' a ! Q--With argon (Z= 1'/~

1

2 3 U, cm/sec FIGURE12. Compositesof radiation data for propane and

carbon monoxidefires, D = 10 cm, standarde|¢vationd

February 1968

GAS F I ~ WITH I:~OL-LIKE BOUNDARY coNDITIONS

TABLE3, Radiationsourcedistributionfor propanefires{D= 10cm) U, cm/see

0.10

0.30

0-65

1.20

i

~,

qAO,

QR.~

AQR.+

Q..~

AQR,,

Q.,,

AQ..i

Q..,

aQ~.+

1 2 3 4 5 6 7 8 9

0.1 0-3 0,6 1,0 1,5 2,5 4 6 9

0"20 0"25 0-35 0.45 0-75 1-25 1.75 2,5 4

0"8 0'7 0.5 0-3 0.3 . . . .

0"6 I~ 0.4 0.1 -. . .

I'0 1-7 l.l 0.8 @4

-0"7 + i'2 ~,5 0.3 --

0"8 1-2 0.8 0.9 1.2 0-7 0.3

- 1t} -0.4 +0.8 0.4 0-3 0.1 --

0'2 !'0 i.O I-3 !.3 I-2 !-2 1.2 0.6

-0-4 -0-4 +0.1 0-1 0.4 0.t 0-1 ---

5,9

0-2

9~

Qt and AQa

. . . .

. . . .

2,1

2.6

. .

.

.

.

5~

. 2.3

(col~see)

TAnK 4. Radiation source distribution for carbon monoxide fires (D = 10 cm)

U, cm/sec

0,42

0-76

1-10

1-85

i

(,i

(A~)i

Qa,+

AQa.+

Qa,+

AQ~,,

Qa,i

AQ~,+

Q~.~

AQa,~

1 2 3 4 S 6 7

0-1 0"3 0'6 !'0 t.5 2"5 4

0'20 0"25 0.35 0.45 0.75 1'25 1"75

!'3 1'2 0.4 . . .

l't !'9 0.4 . .

1'4 2'! 1"i 0,4

-0'9 + 2'0 1"0 0+2

1,0 I-7 1,2 1,0 0.7 0-2

- F0 + I'0 1,1 0.4 0.2 -

0,9 1+6 1,3 1-0 1.4 07 0.1

- 1,4 +if! 1-6 0-9 0-3 0-1 --

5,8

1.7

7,0

1.6

QR and AQa

2,9

. . .

. . .

3.4

.

5,0

.

.

2.3

(cal/sec)

the elevation increment (A~)~about ~+.AQs is the correction that must be added to Qs to yield radiation flux at the burner ~ntre, and AQR.+is the contribution to AQ~ from (AO+about ~i. For the propane fires the agreement is excellent. At very low supply velocity U, the rues tend to concentrate over the burner centre, causing the centre radiometer to indicate a fictitious hump in Qa versus U. In view of the fact that relatively large error is tolerable at low U, it is permissible to extrapolate centre radiometer output smoothly as shown in the figure. Examination of data such as are shown in the

tables, in conjunction with photographs and remote bolometer raw data, shows that for propane fires a large fraction of the radiation falling on the burner centre is nearly at normal incidence, i,e. it originates either at high elevations or near the vertical axis of the fire. For carbon monoxide fires, the agreement is less precise, One mason is that carbon monoxkt¢ fires are shorter than corresponding propane fires and radiate strongly even at very low elevations. Furthermore, becauseofabsorptioneffects, the data reduction mode! is only approximately valid. Nevertheless, the extent of agreement

32

R. C, CORLETT

obtained for carbon monoxide fires shows that Qa, as inferred from centre radiometer output, cannot be seriously in error.

Coednfm In general, interpretation along the lines outlined above indicates that, for diameter D = 5 and 10 cm, the centre radiometer gives reasonably accurate estimates of QR. For D = 19 cm, all sources of error are enhanced and alternative estimates of Qa do not agree very well. However, none of the estimates obtained indicates that Qa dominates the heat transfer even for D = 19 cm. This las~: finding is consist~,nt with the conclusion of Corlett and Fu ~°, that the radiative heat transfer fraction in real pool fires increases only gradually with pool diameter. 7he work reported was supported by AFOSR Contract No. AF-49{638)-29 and NSF Grant 9445. This ;;~rk comprises a portion of the author's Harvard University doctoral dissertation. 7he author is indebted to Professor H. W. Emmons for many helpful sugoestions and stimu. lating discussions.

( ~eceived March 1967; revised August i%7) Referenees KHUDIAI~OY,G. N. hrest, Akad. Nauk S.S.S,R.. Otdel. Tekh Nauk. 10, (11), I 115-.!126 (1945) Busov, V. 1. Doi'd. Akad. Nauk S.S.S.R. 89, 101-104 (1953).

VÜI. 12

3 Bu~v, V. I. hvest. Akad, Naul $,$,$.R,, OtdeL Tekh Nauk, 4,115-127 (19~6) BLINOV, V. 1. and KI.IUDIAKOV,G, N. DOkL Akad, Nauk $.S.$.R. 113, 1094--1098(1957) s Bt,INOV,V. l. inzh.fiz. Zh, S.$.$.R, 8,15.-22 (1959) 6 EMaom, H. W. 'Some observation on pool burni.~g'. International Symposium on the Use of Models in Fire Research. National Academy of Sciences--National Research Council, Washington (I%!) 7 Felt, W. L. Combustion& Flame,5, 233-.236(1961) s AKITA, K. and YUMOTO,T. Tenth Symposium (International) on Combustion,pp. 943-948. The Combustion Institute: Pittsburgh (1965) 9 HOI'Tr:L, H. C. Fire Research Abstracts and R~viewsl National Academy of Sciences--National Re,arch Council, I, 41-..44(1959) ~o CORIZrT,R, C, and Fu, T, M 'Some recent experiments with pool fires', Pyrodynamics,4, 253-269 (1966) It Handbookof Chemistryand Physics,44th edn. Chemical Rubber Publishing Company: Cleveland (1961) t' LANoI~,N. A, (Ed,) Handbook of Chemistry, 8th edn, Handbook Publishers: Sandusky, Ohio (1952) t~ E~oh~, H. W, Combustion Project Final Summary Report, pp 10-16. Harvard Um~versity, Division 6f Engineering and Appli,~ Physics: Cambridge, Mass, (1961) to, FENN, J, B. and CALCOTt~, H, F. Fourth Symposium (International)on Combustion,pp 231-239. Williamsand Wilkins: Baltimore (1953) ts EOI/R'rON,A. C. Fourth Symposium (international) on Combustion, pp. 4--13. Williamsand Wiikin~:Baltimore (1953) t6 CORL~'rr,R. C. 'Heat translbr phenomena in small pool fires', Doctoral Thesis, Harvard University (1%2) "~CoRt~'rr, R. C. 'Pool fire data summary repor':, Engineerins Sciences Laboratory Technical Report No. I9, Division of Engineering an.:l Applied Physics, Harvard University: Cambridge, Idass. Ouiy !%5) 4.