Interaction of a water mist with a buoyant methane diffusion flame

ELSEVIER

Fire Safety Journal 24 (1995) 359-381 1995 Elsevier Science Limited

Printed in Northern Ireland. All rights reserved 0379-7112/95/$09.50

0 3 7 9 - 7 1 1 2 ( 9 5 ) 0 0 0 2 9 - 1

Interaction of a Water Mist with a Buoyant Methane Diffusion Flame

Bruce Downie,* Constantine Polymeropoulos

Department of Mechanical and Aerospace Engineering, Rutgers, The State University, P.O. Box 909, Piscataway, New Jersey, USA

&

George Gogos

Department of Mechanical Engineering, University of Nebraska-Lincoln, P.O Box 880656, Lincoln, Nebraska 68588-0656, USA

(Received 9 February 1995; revised version received 19 July 1995; accepted 26 July 1995)

ABSTRACT

This work describes observations and measurements from the interaction of a fine water spray from a hollow cone nozzle, with purely buoyant diffusion flames from a natural gas ceramic-plate burner located directly underneath the nozzle. The burner plate was instrumented with thermocouples cemented on its upper and lower surfaces to assess the influence of the spray on the burner temperature. A set of thermocouples was also used to measure plume centerline temperatures above the burner plate. An imaging system was used to record the presence of droplets near the burner surface, and a narrow angle total radiation detector was used to measure changes in local flame radiation. A limited number of measurements of the steady state O2 and CO concentrations along the plume centerline were also carried out.

For the conditions tested, the plume-to-spray thrust ratio was large, resulting in negligible direct penetration of the droplets into the fire region. A consequence of the low spray thrust was an almost droplet- free region above the flame. The observed cooling of the ceramic burner when the spray was applied was due to decreased radiant emission from the flame as well as deposition and evaporation of droplets entrained into the plume near the burner. The centerline plume temperatures did not change significantly upon application of the spray, at least within the error limits of thermocouple measurements. However, there was a

* Currently at General Dynamics Inc., Groton, CT, USA.

359

360 B. Downie et al.

significant decrease in 0 2 and an increase in CO concentrations along the plume centerline upon application of the spray. An energy balance on the ceramic-plate burner, together with the experimental data, yielded estimates of the water deposition rate on the burner surface.

Ap C Cpg

Cw D g hw2

kp

L I - v

m rr mg N Pr q;'

q"o t !

q rout t!

qcond

r! q stored

¢t qconv Q Ra Reg t

Zamb Te

Tm r. Tw,

X

NOTATION

Burner plate area Burner plate heat capacity Gas constant pressure specific heat Heat capacity of liquid water Hole diameter Acceleration of gravity Convection heat transfer coefficient for the burner surface at x = g Burner material thermal conductivity Water latent heat of vaporization Water deposition flux on the burner Gas mass flow rate Number of holes Gas Prandtl number, pgl.£g/Cpg Radiant heat flux Radiant heat flux into a surface element of the burner Radiant heat flux out of a burner surface element Conduction heat flux from a burner surface element to the burner interior Storage heat flux for a burner surface element Convective heat flux Heat release rate from the flame Gas Rayleigh number, eqn (A5) Gas Reynolds number, VgD/vg Time Ambient temperature Equivalent hemispherical temperature over the burner Gas inlet temperature Gas exit temperature (T,,,, + Tw2)/2 Burner plate temperature Burner temperature at the gas inlet side, at x = 0 Burner temperature on the flame side, at x = L Gas velocity Burner distance from the gas inlet

Greek symbols

tzg Vg

Parnb

Pg

Pp o"

A buoyant methane diffusion flame

Coefficient of volume expansion Thickness of a burner surface element Gas dynamic viscosity Gas kinematic viscosity Ambient air density Gas density Burner plate density Stefan-Boltzman constant

361

1 I N T R O D U C T I O N

The use of water mists for fire extinguishment and control is currently receiving considerable attention as one of the potential methods for halon 1301 replacement) Water mists, which have been defined as sprays with water droplets less than 300 Izm in diameter, have also been considered for use in the control of fires in aircraft cabinsY In the latter application, full-scale cabin tests have shown that the use of mists with droplets having approximately 250/zm Sauter mean diameter and using relatively small amounts of water can effectively reduce cabin fire spread and thus provide sufficient time for passenger exit in post-crash fires. In applications where equipment is susceptible to water damage, one of the appealing aspects in using a mist, compared to the coarser spray produced by conventional sprinkler systems, is the relatively small quantity of water needed. This, however, poses stringent requirements of optimization in terms of droplet size, mass flux and droplet momentum. Moreover, there is currently insufficient knowledge for a quantitative assessment of which combination of mechanisms may best affect the suppression of a given fire, i.e. vaporization cooling within the flame, droplets that penetrate and cool the base of the fire, or droplets that cool the environment around the flame thus preventing flashover, etc.

Several investigators 4-14 have considered different aspects of the interaction between sprinkler sprays and fires in an enclosure. Most of this work involved sprays with relatively large-sized droplets and high water flow rates typical of those produced by conventional sprinkler systems. Experimental work using small-droplet-diameter water sprays is currently very limited. 15 The use of small droplets in a CFD code simulating the behavior of fires in an enclosure has recently been reported. 16

The present work was motivated by previous full-scale testing results obtained using water mists with aircraft cabin fires, 2 and involves


experimentat ion using the same type of spray nozzle located directly over the fire. The fire source was a ceramic-plate natural gas burner instrumented with thermocouples for measuring temperature changes upon application of the water spray. The conditions studied apply to cases where the plume-to-spray thrust ratio is relatively large resulting in large-scale deflection of the droplets away from the fire plume. The spray's influence on the fire was therefore primarily due to droplet entra inment into the fire plume and onto the burner surface. In the experimental configuration used, the fuel flow through the burner was maintained at a constant rate. This differed from an actual fire scenario, where the quantity of gaseous combustibles generated depends on the radiant flux feedback to a solid or liquid fuel surface. However, the use of a constant fuel supply provided a quasi-steady-state experimental platform which was convenient for the study of the general features of the spray-to-fire-plume interaction, and also for estimating the water deposition rate on the burner surface.

2 E X P E R I M E N T A L A P P A R A T U S

The experiments were performed in a 2 m x 2 m x 2 m glass-walled enclosure shown schematically in Fig. 1. A ceramic-plate natural gas

Double Flash Unit I I

Exhaust

Spray /~ Nozzle

Thermocouples Gas Sampling

/ T u b e

I /

[~ Pressurized Water Holding Tank

\ 1

Burner P l a t ~

" o r "

Fig. 1.

Dryers

Radiometer I I

E~]CCD Camera

---~ From House Gas

Schematic diagram of the experimental apparatus.

To CO and 0 2 Sensors

A buoyant methane diffusion flame 363

burner was located at the center of the chamber floor and at a distance of 1.87 m below the downward-pointing hollow cone spray nozzle.* The water flow through the spray nozzle was supplied from a pressurized holding tank and was measured using a calibrated rotameter. The delivery pressure was monitored at the nozzle inlet. The enclosure size was such that the estimated maximum radial dispersion of the largest expected droplets was 0-5 m. An extraction hood was located 10 cm above the chamber and exhausted with the aid of a low-volume fan. A 0.13 m high opening along the bottom of each wall allowed room air to be drawn into the fire. The burner, which was located 5 cm above the galvanized steel test chamber floor, was a clay bonded quartz ceramic plate 3 cm thick and 38cm × 38 cm in overall area. The actual burner was a 25 cm × 25 cm square area at the center of the ceramic plate where 449 holes, each of 8 mm diameter, were drilled in rows within the 2 5 c m X 2 5 c m square area. The burner was on top of a plenum chamber which was connected to the house natural gas supply. The gas flow rate was measured using a rotameter previously calibrated against a wet test meter. A series of layers of steel wool and fiberglass cloth within the plenum chamber generated a small but sufficient back pressure ( -- 100 Pa) to assure uniformity of gas flow through the holes.

The flames with and without the spray were recorded using a video camera with side illumination against a black background. Centerline plume temperatures were measured using a set of six type K (chromel- alumel) bare junction stainless steel sheathed thermocouples located between 0.15 m and 1-4 m above the burner. Most of the data were obtained using 500 /zm diameter thermocouple wire. Temperature readings at selected centerline locations using 130 and 25 p~m diameter thermocouple wires were used to assess the radiation error. For this purpose, the thermocouple junctions were assumed to be spheres of size equal to twice the wire diameter, the convective heat loss was estimated using the correlation of Incropera and De Witt, 17 and the radiative transfer from the thermocouple junction was expressed in terms of heat loss to the ambient surroundings and heat exchange with the hot burner surface. Radiative exchange with soot in the flame was neglected. A trial-and-error procedure was then used to show that an effective total junction emissivity of 0-6 resulted in the same (within 20°C) corrected temperature for all three thermocouple sizes used. Using this emissivity value, the estimated temperature correction for the 500 /zm thermocouple wire ranged from approximately 160°C at reading levels of 900°C, to less than 50°C for readings less than 600°C.

* Spraying Systems Inc., No. 1/4 TD-23, 89 ° hollow cone nozzle, 0.013 kg/s nominal flow rate at 380 kPa.

364 B. D o w n i e et al.

The burner surface temperature was monitored using three type K stainless steel sheathed grounded junction thermocouples. These thermocouples, with 500 ~m diameter sheaths and 100/xm diameter wire, were flush with the burner surface and were cemented into grooves cut between the holes of the burner The locations of these thermocouples were 0, 5, and 10 cm from the burner plate's center. Two additional thermocouples were used to monitor the upstream (gas inlet side) surface temperature of the burner plate, placed 0 and 9 cm from the burner plate's center. The gas inlet temperature was measured using a type K thermocouple placed approximately 1 cm upstream from the burner.

A water-cooled, nitrogen-purged, linear-output, ellipsoidal radiometer, configured for an 11 ° field of view using a water-cooled extension tube, was used for registering uncalibrated relative radiation readings which were proportional to the total flame radiation from a distance of 50 cm from the burner center. For each flame tested, the radiometer was positioned at a height equal to the transition between the continuous and intermittent flame regions as defined in McCaffrey. 18. The burner surface was not in the radiometer field of view. An upper limit estimation of the influence of radiant energy attenuation due to water vapor absorption can be made assuming that all the injected water was evaporated and was then mixed with the fire plume flow 8 at the height of the radiometer. The resulting gas mixture emittance was then estimated 19 to be less than 0.1, leading to the conclusion that radiant energy measurements with the mist operating were not significantly affected by the evaporated water.

Mean CO and 02 concentrations along the centerline of the plume region were measured using a water-cooled sampling probe. The gas samples were dried and then collected into a 31 glass mixing vessel from where they were drawn for analysis using electrochemical sensor cells. All data was transferred to disk storage using a PC-controlled data acquisition system.

Of interest to the present study was whether the cooling of the burner surface upon application of the spray was due to changes in the flame radiation alone, or was also due to cooling by deposition of water droplets on the surface. The existence of droplets, and their trajectories, near the burner were qualitatively verified by an imaging system consisting of a double flash arc source with controllable separation between flashes, and a video camera connected to a high-speed frame grabber. The optical components were positioned outside the test

* This corresponds to the point z / Q °4 = 0.2 in Fig. 6.


enclosure, and the image plane was 2 cm above the burner and at various distances from its center.

The total heat release rates from the three flames tested were 26-5, 40.0 and 53-0 kW, based on the mean specific gravity (0.58) and higher heating value (54.9 MJ/kg) of the house gas used. For these flames, using computed gas temperatures at the burner surface, the Richardson number , (g~/---~p/pgV2g)(Pamb--pg), based on the burner diagonal distance, was between 2500 and 8500, indicating a buoyancy-dominated flame. The burner Reynolds number, 4rhg/rc ~ V ~ p ~ , was between 106 and 220, and the mean gas velocity was between 3 and 5 cm/s. The thermal inertia of the burner plate required approximately 30 min before its surface reached a steady temperature. Application of the water spray was initiated only after a steady burner thermal state was reached. The water from the spray nozzle was initially collected into a small container placed directly underneath the nozzle until the desired steady water flow rate was established.

3 RESULTS A ND DISCUSSION

3.1 Plume-to-spray thrust ratio

The Sauter mean droplet diameter from a similar nozzle operated under the same flow conditions as in the present work 3 was between 250 and 270 /xm, and the maximum droplet speed near the nozzle was 15 m/s. Using the applied water flow rate (0.013 kg/s), an upper limit of the vertical spray thrust at the nozzle was estimated to be 0.2 N, assuming that all of the spray mass was moving vertically at the maximum droplet velocity of 15 m/s. For the flames tested and using the plume region correlations in Heskestad, 2° the plume thrust at the nozzle position was between 1 and 2 N. The resulting plume-to-spray thrust ratio at the nozzle for the conditions of the present work was therefore at least in the range 5-10, which is larger than the ratios considered in previous work on sprinkler-spray interactions. The experimental configuration was therefore expected to yield results showing a strong influence of the plume thrust on the droplet trajectories. Without the flame, it was shown 21 that the largest and fastest moving droplets originating on the spray periphery (45 ° with respect to the vertical direction) reached a terminal free-fall velocity of


about lm/s at a vertical distance of about 1 m and a horizontal distance of about 0.5 m from the nozzle.

3.2 General features without the spray

Without the spray, the flames immediately above the burner were blue, quickly changing to the characteristic yellow diffusion flame color for the balance of the visible portion. The overall appearance, the mean flame heights and the frequency of the flame pulsations were in agreement with previous results. 22 Because of the well-known sensitivity of such flames to external disturbances, care was exercised to accept only the experimental runs which did not show irregular fluctuations in the mean values of the collected data.

The measured steady-state upper (flame side) and lower (gas plenum side) burner surface temperatures and the corresponding gas inlet temperatures for the three flames tested are shown in Table 1, where the positions indicated are from the center of the burner surface. It should be noted that the magnitude of the recorded temperatures on the flame side was above the Liedenfrost point of water, which for single droplets is approximately 570K. 23

Appendix A presents a description of a model of steady-state heat transfer in the burner plate, based on one-dimensional conduction in the ceramic material with appropriate terms in the equation to account for convective heat transfer io the gas, as well as radiation to the burner. Numerical solution of the equations in Appendix A was used to calculate the temperature distribution within the burner and the gas exit temperature, Tg2. The effective hemispherical temperature of the surroundings, Tf, which is necessary to provide the radiant energy for

TABLE 1 Steady State Burner and Gas Inlet Temperalures

Burner surface temperature (K)

Flame side Gas inlet side Gas inlet Flame size temperature

(kW) 0* 5* 10" 0* 9* (K)

26.5 1159 886 713 648 543 458 37 1016 743 688 633 498 383 53 996 723 673 588 463 333

*Distance from burner center (cm).


existence of the orange region, except to note that it may be related to changes in the vaporization rate of impinging liquid droplets as the burner surface was cooled by the spray through a temperature range which includes the Leidenfrost temperature 23 for droplets contacting a hot surface. The observed reduction in soot radiation can be partly attributed to a decrease in soot temperature accompanying the cooling of the burner (and of the natural gas) by the vaporization of droplets entrained into the flame and onto the burner surface. It is also possible that increasing OH radical concentrations, because of the presence of water vapor, interfered with the soot production process near the burner and, in addition, increased soot destruction in the flame. 24'2s Both processes would result in there being less soot present and a reduction in soot radiation. Figure 3 shows radiometer readings from the 26.5 and 53 kW flames for a period of approximately 3 min after application of the spray. The readings, which were proportional to the received total flame radiation, show considerable fluctuation because of turbulence. However, the mean received total radiation decreased with time, which is in agreement with the previous visual observations regarding the reduction of soot radiation. The results in Fig. 3 show an initial relatively rapid decrease in mean radiation after application of the spray, followed by a period of diminishing rate of decrease. The

n-"

.=_o

m n.-

2.5 of Spray

21 53 kW Flame

1.5

1

0.5

0

0 50 100 150 200 250 300 350 400 450

Time Sec

Fig. 3. Relative total flame radiation at the end of the continuous flame TM region°


Fig. 4. Photograph of the spray on the 53 kW flame. 1/30 s exposure.

latter can be attributed to the gradual reduction of the inlet methane temperature as the burner surface temperature was reduced by the vaporization of impinging droplets.

Figure 4 shows a 1/30 s duration photograph of a 53 kW flame with the spray. The existence of an almost droplet-free region above the flame and the transport of droplets through the spray sheath by the upward mot ion of the plume are clearly seen, and they are a consequence of the previously discussed large plume-to-spray thrust ratio. Examinat ion of video records of such f lame-spray interactions showed (a) intermittent billowing motions of different parts of the spray as droplets were carried upwards through the spray envelope by buoyant flame eddies; (b) negligible direct penetrat ion of droplets into the flame region; and (c) that droplets falling near the flame plume were influenced by the entra inment flow around the plume and moved towards the flame near the base of the burner plate. Droplet mot ion due to the entrained flow towards the flame, as well as incipient


105

1 0 0 -

, <

95

c

Fig . 5 .

9 0 ¸

8 5 ! i i I i

0 10 20 30 40 50 60

Heat Release Rate, kW

Effect of flame heat release rate on initial spray angle.

deposition of droplets on the burner surface, were also qualitatively observed using the double-flash imaging system described in Fig. 1.

The spray angle, which was approximately 89 ° without the flame, increased considerably with the flames as shown in Fig. 5. This was because of the pressure difference generated by the upward plume flow across the spray sheath. The resulting spray angle increase resulted in a larger dispersion of the droplets within the test chamber.

Figure 6 shows 2rain-averaged centerline temperatures (not corrected for radiation) plotted against the normalized distance from the

J~ E

I - -

I - -

1000.0

100.0

10.0 0.01

A

13

nnEI

ref. 18

with spray

without spray . . . . . . | 1

O.lO

7./QO.4

| | | | | • . ,

1.00

Fig. 6. Average (2 min) plume centerline temperatures with and without spray.


burner employed by Heskestad. 18 The empirical predictions of temperature vs burner distance from this work, which were derived using uncorrected temperatures, are also shown as solid lines in the same figure, and they are in good agreement with the present results without the spray. There also appears to have been no significant difference in centerline temperatures with and without the spray. This supports the previous observation regarding the absence of droplets above the fire, since droplets directly impinging on the thermocouple junctions would depress the measured temperatures. The uncorrected centerline temperature results in Fig. 6 suggest that the amount of cooling due to vaporization of the entrained water droplets, and subsequent dilution due to the addition of water vapor, was not sufficient to cause significant changes in the flame temperature, but was enough to suppress soot radiation. A similar result for laminar flames was reported in Shug et al . 26 It should be noted that the interpretation of the centerline temperature results was made under the assumption that the thermocouple radiation error was similar with and without the spray° This assumption, however, may require further examination.

Figure 7(a) and (b) shows measured (dry basis) 02 and CO concentrations with and without spray at the centerline of the 40 kW flame plume region and for distances between 0.6 and 0.9 m above the burner. It is noted that the application of the spray resulted in a decrease in 02 concentrat ion but in an increase in CO concentration. The presence of droplets increases the total amount of water present in the plume, and the local distribution of water vapor within the plume is expected to influence the flame chemistry. Entra inment of combustion products into the flame by the downwards flow induced by the spray may also contribute to the observed changes in CO and 02 concentration. However, the absence of a significant decrease in centerline flame temperature indicates that the effect of product recirculation may not be significant. It appears that more detailed measurements are needed to relate the the observed behavior to the presence of water vapor and its effect on centerline species measurements .

3.4 Interaction with the burner surface

Figure 8 is an example of the temperature variation with respect to time from the three thermocouples cemented onto the burner surface. The period 0 < t <120 s was without spray and, as expected, the mean burner temperatures were constant with time. The fluctuations in the readings were due to variations in flame radiant energy from the 26.5


Fig. 7.

(a) 20

1 9 . 5 -

1 9 - &

O 1 8 . 5 -

18

17.5 0.5

(b) IOO0

~" 1 0 0 - d o

10 0.5

without spray

with spray r - n ~ E I O~

~ 0 ¢ 0 kW Flame o16 o17 o18 oi,

Distance from Burner, m

[]

t-

+..~,~ 40 kW Flame

without spray -- ~ ' ~

w i I h spray

0'6 o17 o18 oi, Distance from Burner, m

Average plume centerline concentrations with and without spray for the 40 kW flame. (a) O2 concentration; and (b) CO concentration.

k W turbulent flame. At a time corresponding to 120 s in Fig. 8, the spray was started and the burner surface tempera tures began decreasing with time. The t empera tu re decrease was due to a combinat ion of the decrease in soot radiation and also to evaporat ive cooling from water droplets whose trajectories were influenced by flow entra inment towards the flame, resulting in water deposi t ion on the burner surface. The measured surface tempera tures in Fig. 8 showed an initial relatively rapid decrease (especially at the point further away from the center) as the surface and the flame were first subjected to the sudden cooling by


Fig. 8.

600

0 500

~=. 400

E p-

3(10

200 0

|

- - A A A . ~ L ' ~ - ~ - A . _ _ i . _ a ~ L _ _

0 5cm Start of Spray

0 10 cm , / . , f .

I I

100 200 300

Time, sec

Burner surface temperature variation before and after the spray. Distances are measured from the burner center, for the 26-5 kW flame.

the droplets. This was followed by a more gradual cooling period during which the thermocouple furthest from the center registered the largest tempera ture drop, presumably because it was closer to the path of entrained droplets impinging on the burner surface. The temperature readings appear to approach a constant value. Testing was, however, interrupted approximately 3-4 min after application of the spray because of water accumulation near the burner edges which interfered with the flow of gas through the burner holes.

Appendix B describes a model for the transient heat transfer in the burner plate which requires measured burner temperature and radiometer data to generate the different energy fluxes and the water deposition rate for a surface element of the burner. Using this model, the computed water deposition rates for the 26.5 and 53 kW flames are shown in Fig. 9. After an initial period of approximately 25 s, which is denoted by a dashed line in Fig. 9, the computed water deposition fluxes were almost constant with time. The magnitude of the computed fluxes was also smaller than the flux without a fire (measured using a collection method) whose magnitude is shown in the figure. The slow increase of the deposition rate for times less than 25 s is considered physically unrealistic and was due to the sensitivity of eqn (B3) to precision errors in the competing parameters during the initial period of relatively rapid changes after the start of the spray.

Figure 10 shows computed energy fluxes at the surface of the burner for the 26.5 kW flame. The energy flux for vaporization of the


Fig. 9.

Od E

I./. c 0

8

_=

0.0025

0 .002-

0 .0015-

0.001

0.0005

. f °o

.#

/ ,o°"

,o

Y

26.5 kW

53 kW

Deposition Flux without Fire: 0.0083 kg/rn2 sec

I I I

0 5 0 1 O0 1 5 0 2 0 0

Time, sec

Computed water deposition flux at the burner surface, 26.5 kW, and 53 kW flames.

impinging droplets, q"ap, c a m e primarily from the net radiation flux into the burner, q'r'in -- q'r'ot, and from conduction, q'c'o.d, to the interior of the burner. The energy associated with conduction changed sign as the surface cooling eventually resulted in local surface temperatures below those of the burner 's interior. The relative magnitudes of the energy fluxes due to convection, q'c'nv, and heat storage in the surface element,

Od E

x

t t .

,,5

10000

°o." o,

50O0- ¢.;

:: . . . . . . . _ ~ q'conv

-5000

q"vap

q"rin " q"roul

q"oond I ! i

0 50 100 150 200

Time, sec

Fig. 10. Computed energy fluxes at the burner surface. 26.5 kW flame.


q's'tored, were relatively small, so that the energy flux for vaporization was essentially the sum of the net radiant energy flux into the burner, and the conduction between the surface element and the burner interior. Similar results were also obtained for the 53 kW flame.

4 CONCLUSIONS

The interaction of the spray produced by a hollow cone nozzle with buoyant diffusion flames from a ceramic-plate burner located directly undernea th the spray was examined experimentally. The experimental configuration employed a constant rate of gas supply through a ceramic burner and is therefore not directly applicable to a fire extinguishment scenario where the rate of fuel supply depends on the energy feedback from the flame to the a liquid or solid fuel surface. The plume-to-spray thrust ratio was large, resulting in a strong deflection of the spray away from the fire. Application of the spray to the fire did not result in appreciable changes in the mean plume centerline temperatures. The mean 02 concentrations at the plume centerline were reduced when the spray was applied while the mean CO concentrations were increased. The spray produced a decrease in soot radiation which was observed visually and also using a narrow angle radiometer aimed at the end of the continuous flame zone. The spray did not result in an appreciable change in visible flame height.

The measured burner plate surface temperature decrease with the start of the spray was attributed to the deposition and evaporation of water droplets on the burner surface. The available data were used to estimate the deposition rate of water droplets on the burner. The results showed a relatively constant deposition rate which was considerably smaller than the measured deposition rate without fire.

Future work will consider different nozzle types, as well as liquid injection directions different to that opposing the fire plume.

A C K N O W L E D G E M E N T

This work was supported by a research grant from the Fire Safety Branch of the Federal Aviation Administrat ion Technical Center, Atlantic City, NJ, USA


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24. Haynes, B. S. & Wagner, H. G., Soot formation. Prog. Energy Combust. Sci., 7 (1981) 229-73.

25. Zhang, C., Atreya, A. & Lee, K., Sooting structure of methane coun- terflow diffusion flames with preheated reactants and dilution by products of combustion. Twenty-fourth Symp. (Int.) on Combustion. The Combus- tion Institute, Philadelphia, PA, USA, 1992, pp. 1049-57.

26. Schug, K. P., Manheimer-Timnat, Y., Yaccarino, P. & Glassman, I., Sooting behavior of gaseous hydrocarbon diffusion flames and the influence of additives. Comb. Sci. and Tech., 22 (1980) 235-50.

27. Kays, W. M., Convective Heat and Mass Transfer. McGraw-Hill, New York, 1966, p. 121.

A P P E N D I X A: S T E A D Y - S T A T E B U R N E R E N E R G Y B A L A N C E W I T H O U T S P R A Y

Figure A1 is a schemat ic diagram of the burner plate showing two of the N holes of d iameter D which were drilled for passage of the gas. Natura l gas with an initial t empera ture Tgl en tered the burner at x = 0, and was heated by convect ion as it flowed through the holes exiting at a higher t empera ture Tg2. The burner surface t empera tu re was Twl at x = 0, and Tw2 at x = L. The surface at x = L exchanged radiant energy with the hemispherical surroundings which are at an effective temperature, T~, not necessarily equal to the flame temperature .* There was also

* The burner material was assumed to be black, a result confirmed by comparing measured surface temperatures with the reading from a total radiation pyrometer with adjustable total emissivity setting.


/ 449 holes, 8mmD

Tw2\

FLAME

] / Twl

GAS INLET

Tg'2i i I/ir"rc Ddx

i.;...1

/ Ceramic Burner

Tg I 25x25 cm 3.1 cm thick

Fig. A1. Schematic diagram of the burner plate.

an exchange of radiation between the lateral hole surfaces and the hole bases at x = 0 and x = L, which were taken to be at temperatures Twl and Tf, respectively. The following equation and boundary conditions were therefore used to describe heat transfer in the burner plate.

d2Vp reD - - - N[q'r '(X) - q'(x)] ~ - - = 0 (A1) dx 2 kpAp

for x = 0, Tp = Tw~ (0), x = L, Tp = T~2(0)

where the first term represents conduction heat transfer with Tp(x) the temperature distribution in the burner material. The second term is the difference between convective, q " ( x ) , and radiative, q; ' (x ) , heat transfer through the N holes. The convective heat flux, q ' ( x ) , from the hole surfaces was expressed using Duhamel 's integral and the solution for laminar, hydrodynamically fully developed flow in a tube with variable surface temperature: 27

kp x+ dTp q " ( x + ) = 4 ~ { f 0 ~[G.e A~'x+-"]-~d~+(Tw,-Tg,)~[Goe "~+]} (12)

where An and Gn are the eigenvalues and eigenfunctions for the thermally developing flow, and

x x + = 2

D RegPrg

Reg = vg

e r = jl.KgCpg

02


The radiative heat flux to the lateral hole surface was expressed as follows by considering each hole as a cylindrical black isothermal cavity at a t empera tu re Tm= (Twl + Twz)/2:

q " ( x +) = o'[T4m - T ~ l ] d F , ~ _ b - o'[r4m - T ~ l d F , ~ _ : (A3)

where the configuration factors to the surfaces at x = 0 and x = L were given by the following relations:

( L - x ] 2 A _ O . 5 L - x \ D /

dFdx- : - f D ( L - x ) 2 + 1

\ D /

x ( - ~ ; + 0 " 5

d F ~ - b -

Finally, the energy balance at the burner surface at x = L was used as a closure to the problem formulat ion, and was expressed as:

k dTp x=L t r ( T ~ - T4wE) - hwz(Tw2 -- Tg2) "q- p ~ = 0 (A4)

where the first te rm is the net radiat ion f rom the surface, the second te rm is the convective heat transfer to the gas and the last te rm is the conductive heat transfer into the burner . The Nusselt number for the convective heat transfer f rom the burner surface to the hot gas at x = L was expressed using the following correlat ion for free convection f rom horizontal surfaces: 17

h w z D N u - - - - 0.54Ra °'25 (A5)

kg

where

gfl(Tw2- Tg2)A~ "5 IZgCpg R a -

Solution of the system of equations [eqn ( A 1 ) - e q n (A5)] was obta ined numerical ly using an iterative process to de termine Tf. The input parameters were (a) the mean surface tempera tures Twl and Tw2, which were est imated by area averaging the local surface tempera tures in Table 1; (b) the measured values of Tgl, also shown in Table 1; (c) the measured gas flow rates; (d) the propert ies of natural gas at the mean


temperature Tin; and (d) kp = 1-3 W/mZK for the ceramic burner. The exit gas temperature, Tg2, was obtained using the total convective heat transfer from the hole surfaces.

A P P E N D I X B: T R A N S I E N T B U R N E R E N E R G Y B A L A N C E U P O N A P P L I C A T I O N OF T H E S P R A Y

Upon application of the spray, the heat transfer in the burner was expressed using the t ime-dependent form of eqn (A1) and its boundary conditions:

6Tp d2Tp JrD (B1) at - ap--~- + [q~(x,t) - q"(x,t)] ppcA------ 7

x = 0, rp = Two(0, t), x = L, Tp = Tw2(L, t)

The initial burner temperature distribution Tp(x,O) was obtained from the steady state solution of eqn (A1). Assuming that there was no droplet penetrat ion into the burner holes, numerical integration of eqn (B1) requires the radiant and convective heat fluxes q"(x, t) and q"(x, t), which were obtained at each time step using eqns (A2) and (A3), respectively. The effective temperature of the hemispherical surroundings, Tf(t), which is required in the expression for q"(x, t), was computed, assuming that the effective radiation to the plate surface varied in a manner proportional to the radiation received by the narrow angle radiometer used in the experimentation:

T~(t) 4= Tf(O)4g(t) (B2)

where g(t) is the radiometer response normalized to yield g(0) = 1. The water deposition flux on the burner surface was given by the

following energy balance around a burner surface element of thickness zXx located at x -- L.

m"[L,_v + cw(Tw2 - Tamb)]

zXX dTp(L, T) (B3) t! -(q~'in q r o u , ) - " " + - - q~onv ppC 2 dt q c o n d - -

where the left-hand side of the equation represents the energy flux needed to vaporize a mass flux, m", of droplets initially at a temperature Tam b which is deposited on the burner surface and instantly evaporates, generating water vapor at the plate temperature Tw> The first term in parentheses on the right-hand side of eqn (B3) represents the net radiation flux into the burner, the second term is the conductive


flux from the surface element to the interior of the burner, the third term is the convective flux from the surface of the burner, the fourth term represents the energy flux due to the change in element internal energy, and the last term is the heat flux due changes in stored energy. Starting with steady-state initial conditions, the system of eqns (B1) and (B2) was solved numerically to generate the temperature distribution Tp(x, t). The boundary conditions at the burner surface were area averaged mean temperatures Twl(t) and Twz(t) obtained from experimental thermocouple data such as shown in Fig. 8. Averaged radiometer data similar to those shown in Fig. 3 were used for obtaining g(t) in eqn (B2). The specific heat of the burner material was 700 J/kg K and the density was 1750 kg/m 3. The results of this computation were then used in eqn (B3) for estimating the water deposition rate.

Interaction of a water mist with a buoyant methane diffusion flame

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