REFERENCE

''mill

NBS

PUBLICATIONS

NBSIR 86-3442

A111D2 Limb?

NATL INST OF STANDARDS & TECH R. .C. itum Diffusion Flame

teristics and the Effects of

Water Spray

B. J. McCaffrey

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

November 1986

Sponsored by:

n«nartment of the Interior

-QC rals Management Service

100 on’ VA

. 1)56

# 86-3442

1986

RESEARCH

INFORMATION CENTER NBSIR 86-3442

a

MOMENTUM DIFFUSION FLAME

CHARACTERISTICS AND THE EFFECTS OF

WATER SPRAY

B. J. McCaffrey

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

November 1986

Sponsored by:

Department of the Interior

Minerals Management Service

Reston, VA

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

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director

TABLE OF CONTENTS

Page

List of Figures iv

Abstract 1

1. INTRODUCTION 2

2. EXPERIMENTAL 3

3. RESULTS AND DISCUSSIONS 5

3.1 Blowoff 5

3.2 Flame and Lift-Off Heights 9

3.3 Flame Temperature 15

3.4 Radiation 18

3.5 Effect of Water Spray 26

4. ACKNOWLEDGMENTS. 42

5. REFERENCES 43

6. NOMENCLATURE 45

-iii-
LIST OF FIGURES

Figure 1

Figure 2.

Figure 3®

Figure 4.

Figure 5.

Figure 6 .

Figure 7.

Figure 8 .

Figure 9.

Figure 10.

Figure 11.

Figure 12.

Figure 13.

Figure 14.

Figure 15.

Figure 16.

Figure 17.

Page

Schematic of experimental facility 47

Flame stability and blowoff characterization for methane 48

Flame and lift-off heights vs Froude number 49

Present and literature summary of methane lift-off

height data 50

Centerline temperature rise vs scaled height 51

Peak temperature vs nominal heat release rate (symbols

follow Fig. 5) 52

Incident radiant flux to two targets as a function of

fire size

Flame extinction coefficient and temperature for a fixed value of the other as a function of fire size 54

Derived extinction coefficient (upper portion) using

smoothed temperature data from Fig. 6 (lower portion)

vs heat release rate 55

Sensitivity analysis of flame radiation model to

various parameters 56

Predicted decreasing radiative fraction compared to

literature data plotted as a function of the square root

of Froude number 57

Centerline temperature rise vs height with and without

water spray (Q = 1.2 and 2.3 MW) 58

Centerline temperature rise vs height with and without

water spray (Q * 2.7 and 4.6 MW) 59

Reduction of peak temperature with water flow rate 60

Fractional increase in lift-off height due to water

spray as a function of mass flow ratio 61

Normalized incident flux and flame temperature reductions

vs Vc/'V 62

2 4

Increase in flame absorptivity as a function of both water

flow rate and the difference between the heat flux and

readings 63

-iv-
Figure 18. Water vapor emissivity and partial pressure plotted against

the water to gas flow ratio 64

Figure 19. Derived entrainment rates vs predictions of Ricou and

Spalding (1961) using effective source pV 65

-v-

Abstract

For water spray suppression of gas well blow-out fire applications,

reasonably large scale (1-10 MW) subsonic methane diffusion flames have been

investigated near the high Froude number limit. Characteristics of this limit

include constant flame height, increasing lift-off height, and decreasing

radiative fraction. Flame blow-off has been observed with pipe sizes to 30 mm

diameter. Flame and lift-off heights, centerline temperatures, and incident

radiative flux to nearby targets have been measured with and without water

spray suppressant. Using the Dayan- Tien formulation for a cylindrical flame

model an effective gray absorption coefficient approaching 0.2 m

- ^- was determined at the blow-off limit. Away from the limit, this number rises rapidly

as does flame temperature decrease. The derived shape of the functional

dependence of decreasing radiative fraction with increasing jet Froude number

in the limit is consistent with small scale literature. experiments

The effect of adding water spray to the gas flow below the base of a

lifted flame is to shift or raise the flame above its normal position, and to

lower peak flame temperature and radiation levels despite increased absorptivity due to the radiatively active steam. Extinguishment near blowoff is

thought to be due to the former effect, i.e., a shift in flame position.

Calculations of flame entrainment based on increased water vapor emission are

consistent with literature estimates of entrainment when account of the

effects of buoyancy due to the liquid spray is provided.

Key words: blow-off, blowout fires, diffusion flames, entrainment,

extinguishment, radiative fraction, suppression, water sprays.

- 1 -
1 . INTRODUCTION

Recent small scale studies (McCaffrey 1984) have demonstrated the

efficacy of using limited quantities of water in the form of sprays to

suppress and extinguish jet diffusion flames. Radiation reductions were

equivalent to those obtained using premixed gaseous diluents, and extinguishment with mass flow rates of water approximately equal to that of the fuel was

documented. Since part of that work was motivated by the desire to evaluate

the feasibility of using water sprays to control and extinguish off-shore gas

and oil well blow-out fires it is natural to inquire as to how far these small

scale results could be extrapolated. The present work is an attempt not only

to extend the size of the fire and determine any new scale-dependent

phenomenon but also to increase the understanding of high velocity jet diffusion flames. In this regime, flame heights become dependent on burner

diameter and the radiative fraction becomes dependent on gas flow rate. It is

felt that this regime together with the very buoyant end of the Froude number

scale, characteristic of the pool fire, contain more information about diffusion flame phenomena than is contained in the vast intermediate regime where

all flames appear similar, i.e., flame heights independent of burner size and

radiative fraction independent of flow (McCaffrey 1981).

The following describes an experimental program where large methane

diffusion flames (7 MW heat release rate and 7 m flame height) were studied in

an attempt to further extend the small scale findings about the effects of

water spray on jet diffusion flames.

-2 -
2 . EXPERIMENTAL

Figure 1 schematically depicts the experimental facility. The main

working area is the floor of an abandoned missile pit located about 5 m below

ground level. The flame is directed upward through opened silo doors somewhat

protecting the lower flame region from wind disturbances. The floor area of

the pit is sufficiently large and the whole space is in contact with an

adjacent stair tower open to ambient so as to provide (quiescently) sufficient

air for jet flame entrainment, i.e., air needn't be sucked down through the

silo door opening.

Uncoated twenty-four gauge (0.5 mm diameter) chromel-alumel thermocouple

wire was used for temperature measurements (T1-T6). Experience with smaller

diameter wire in this very abrasive environment indicated that the penalty in

terms of replacing thermocouples would be too severe for using finer gauge

materials. Steel wire and connectors for thermocouple supports were required.

Water cooled, wide angle, heat flux sensors (R1 & R2) were used for monitoring

incident radiant heat flux at the positions indicated. Standard rotameters

were used to measure water and the methane driver flow through the two-fluid

atomizing nozzle. The main CH^ burner flow rate was measured using a laminar

flow element mass flow rate device.

After reaching steady conditions at the operating point data channels for

the temperatures, radiation, and CH^ flow rate were scanned sequentially five

times and average values were determined for each data channel and used in

subsequent analysis.

-3 -
In determining blowoff velocity as a function of outlet diameter various

standard hardware items, pipe nipples and reducers, were used without further

preparation. For the temperature and radiation measurements the largest of

these, a 0.0292 mD pipe reducer complete with internal threads, and the

configuration seen in the highlighted ellipse on Fig. 1 were used. The latter

consisted of a 0.0318 mD circular hole cut straight through (as contrasted to

a sharp edged orifice, for example) a .008 m thick cap on the end of a

0.104 mD pipe which contained the spray nozzle. The top of the nozzle was

located 0.059 m from the top of the opening.

The nozzle was a two fluid or pneumatic atomizing nozzle, 1/2 J

designation from Spraying Systems Co.* Methane gas from a separate supply

served as the pneumatic atomizing fluid operating around 150 kPa. The flow of

methane was added to the main gas when calculating heat release rates, etc.

It constituted a small fraction of the total. The pneumatic nozzle was chosen

to provide relatively small water drops which it was hoped would optimize the

process of getting the drops into the combustion gases. Other methods of

spraying water at the flame, e.g., an external spray, might be compared to

this more idealized configuration. Differences may be then computed in terras

of a delivery efficiency.

*Implies no endorsement by NBS
3. RESULTS AND DISCUSSIONS

3.1 Blow-off

An interesting and significant feature of jet diffusion flames, generally

not encountered in smaller laboratories, involves blow-off and the concept of

absolute flame stability. When the flow rate of gas being supplied to a small

diameter pipe or burner, upon which is attached a free vertical jet diffusion

flame, is increased, the flame begins to separate from or to "exist" a small

distance above the exit of the burner. As the flow rate is further increased

this lift-off distance becomes larger until with further increase in flow rate

a point is reached - blow-off, whereby a flame cannot be sustained for that

particular gas burning in that particular geometric configuration. For a

variety of hydrocarbon gases and mixtures rather extensive compilations of

blow-off data have recently appeared (Kalghatgi 1981, 1982).

Kalghatgi' s data answers the question of what fuel flow rate expressed as

the exit gas velocity just causes the flame from a given sized burner to blowoff. Kalghatgi (1981) was able to correlate all his data in terms of a nondimensional blow-off velocity, U

g as a function of Reynolds number, RH» based

on a characteristic lift-off distance, H

g

, which in turn depends on an

effective burner diameter. Both U and RH contain S„, the maximum laminar

flame speed, which accommodates the data from such gases as diverse in their

burning velocity characteristic as hydrogen and methane. Figure 2 presents

the results of the correlation in terms of dimensional velocity at blowoff

versus actual pipe diameter for methane gas both for a low and a high range of

Ry (solid and dashed curves). Note from the equations shown on the figure for

-5-
both ranges of R^, the velocity-Reynolds number (or diameter) relation appears

to be linear and, in fact, the solid curve for the lower velocities, smaller

diameters (R^ < 30,000) is indeed linear. The interesting phenomenon however

takes place at larger diameters, higher flowrates where compressibility

effects associated with choked flow and underexpanded jet behavior begin to

dominate. The near linear relationship in non-dimensional space exhibits the

“doubling back" behavior in dimensional space.

When the gas flowrate through a pipe, hole or other aperature not

specifically designed with supersonic effects in mind is increased to sonic

conditions at the exit plane the pressure there will generally be higher than

atmospheric and the flow will have to expand in some form of a supersonic

plume above the exit. In order to estimate the flow conditions in such a

situation the pipe or burner exit is generally conceived to be replaced by a

convergent-divergent nozzle having sonic conditions occur at the throat and at

the exit of which the flow has expanded supersonically to atmospheric

pressure. The relationship between this effective diameter, d

g

, and the

actual pipe or burner diameter, d^, comes directly from standard isentropic

flow equations and is:

where M is the exit Mach number after expansion and y is the ratio of specific

heats. The quantity d

e /d^ is greater than one and increases raonotonical Ly

with M. In order to observe the behavior of the dashed line on Fig. 2 we

simply solve the inverse problem, i.e., find d^ as a function of U

e

. It can

be shown that for linear or near linear U » f (R„), that is, U„ almost linear

e H e

(I)

-6-
with d

e , db

is basically equal to M or U

e divided by d

e /d^, and the quantity

M

-

j-r- goes through a maximum at about a Mach number of 2, thereafter the ratio

d / d, e b

falls in magnitude, i.e., the effective diameter is growing more rapidly with

Mach number than simple proportionality.

The data used by Kalghatgi (1981) for which the curve on Fig. 2 is a

correlation only extend out to pipe sizes of diameter equal to 12 mm for

CH^. The turning back behavior noted near 40 mm and M ~ 2 is therefore based

on a significant extrapolation of that data. However, Annushkin and Sverdlov

(1979) have given an analysis and some data for hydrogen which confirms the

general shape of Fig. 2. That shape is extremely important since it demarks

blowoff stability, exhibiting a dual significance. Firstly, for small to

moderate size holes or cracks in pipes there is another stable regime where if

the stagnation pressure is high enough diffusion flames can again be

supported. They will be supersonic jet flames. This is for diameters where

at low velocity the flames could easily be blown off if the velocity were

increased up to the lower curve on Fig. 2. By further increasing the velocity

or pressure we intersect the upper half of the stability envelope and presumably again can sustain a flame. Only for hydrogen has this been confirmed

since it turns out that the critical diameter (the maxima of the d^ vs U

g

plot) for H2 is small and hence the experiments can be performed with a

relatively small apparatus and modest quantities of hydrogen.

The second aspect to the stability curve on Fig. 2 is the existence of

the critical diameter beyond which flames cannot be blown off for any flow,

supersonic or subsonic. Seen on the figure by crosshatched vertical lines are

two estimates of the critical diameter for methane gas - approximately 40 mm,

-7 -
due to Kalghatgi (1981) from extrapolation of small diameter blowoff results;

and approximately 25 mm, from the analysis of Annushkin and Sverdlov (1979).

No data exists at present to check these results because of the difficulties

associated with producing and burning supersonic methane flows from orifices

about 40 mm in diameter.

The present data shown by circles and sexagons are blow-off results of

flames from gas flow through ordinary plumbing components - pipe nipples:

relatively smooth sections of straight pipe or tube with a length to diameter

ratio of about 2, and threaded reducers: converging sections of pipe hardware

ending in internal coarse, pipe thread. These would represent, at least for

circular openings, a range of exit, flow conditions which might be encountered

in practice. It is not evident from the figure that a significant difference

exists between the results of the two exit configurations nor is it evident

why the present values are falling lower than Kalghatgi’ s (1981) extrapolation. Those results were for blow-off from straight tubes 65 mm long and

would represent somewhat different exit flow field conditions even for the

largest of the methane results which was a diameter of 12 mm.

What is evident from the figure is that the Annushkin and Sverdlov (1979)

analytical findings will need to be modified since their predicted diameter

for absolute flame stability was exceeded by the last two data points, 26.2 mm

and 29.2 mm. Also, if the trend of the present data persists with further

experiments, i.e., continues to fall below and exhibits a gradually decreasing

slope compared to the small diameter extrapolation, then the estimate of

critical diameter for CH^ must be increased. The absolute value at this

juncture is not as important as the understanding of, or at least, some

-8 -
knowledge of blowoff and absolute flame stability. In subsequent studies of

the suppression and extinguishment of large jet flames using water sprays the

relative stability of the flame with regard to blow-off must be known in order

to separate momentum effects of the spray (liquid drops plus entrained air)

from purely thermodynamic ones. Are we in fact just "pushing off" a

marginally stable flame at small diameters which at prototype scale could not

be blown off so easily?

3.2 Flame and Lift-Off Heights

Figure 3 presents flame height (measured from pipe outlet) and lift-off

height, both normalized by outlet diameter, as a function of source Froude

number, U^/gD. Shown with this 30 mm diameter data are various literature

correlations. The vertical arrow indicates the position where blow-off

occurred. The Froude number regime here is such that the flames are lifted,

loud, and turbulent by most researchers' definition with a noticeable

decreased luminosity as blowoff is approached. The pipe exit Reynolds number

(UD/v) ranges from 30,000 through 500,000 for the data points shown. For

flame height, the break in the Suris, et al. (1977) correlation at a Froude

number approximately equal to 3 x 10^ is to mark the beginning of the Froude

number independent regime for flame height. This recommended value is based

on a considerable body of data. The transition value suggested by Becker and

Liang (1978) is quite a bit higher - orders of magnitude higher (£ > 1 in

1j their notation vs. about + 8.6. Froude number is inversely proportional to

this number cubed, a Richardson number using flame height as the length

scale). Their resulting flame height/diameter at the limit is about 420 vs.

about 220 for the Suris et al. (1977) recommendation. The present three data

-9-
points in this region could not differentiate or give support to either correlation seen on Fig. 3. To go beyond this data in Froude number however would

require some H

2 or O

2 or other stabilizing gas to keep the flame from blowing

off the end of the pipe. For the present, either representation is sufficient, although from a practical point of view, the Suris et al. (1977) result

might be preferred for this subsonic case. There is probably more theoretical

justification for the Becker & Liang (1978) correlation but the classical 2/5

Froude number power represented by the Suris et al. (1977) correlation is

computationally easier. The dotted line shown on the figure prior to the

limit is for methane,

H

f

/D - 28 Fr

0,2

(2)

For other fuels the numerical constant will vary with the square root of

the density ratio, the simple manifestation of conservation of momentum.

Irrespective of which flame height representation is chosen the important

point here is that no scale effect is evident. That is, for pipe diameters to

30 mm and velocities to blowoff, small scale laboratory flame height correlations dp an adequate job in representing the large scale flame height data.

Neither does the pipe exit configuration, i.e., flat-edged orifice or reducer,

appear to make a difference in flame height.

The lift-off data, though scattered, rises more or less consistent with

the literature prediction of lift-off height being proportional to gas

velocity or here, a square root dependence upon Froude number, with blowott

coming near Lf/D * 50. Peters and Williams (1983), using scalar dissipation

arguments recommend the following:

- 10-
L (3)

f

/D = 0.0036 /i7D Fr

1/2

with the numerical .0036 having units of seconds. Or

L

f /U = 3.6 ms (4)

Note that is therefore independent of D. (The scaling on Fig. 3 for Lf is

permissible since all the data are for essentially a single diameter.)

Kalghatgi (1984) correlated lift-off data from a variety of fuels and pipe

sizes to 10 mm in terms of dimensionless variables derived from his previous

blowoff studies:

with C£ approximately equal to 50. Substituting kinematic viscosity and

laminar flame speed appropriate to methane yields a constant equal to

0.0022 s, somewhat less than the Peters and Williams (1983) value of .00365.

It is interesting to note that Kalghatgi’s (1984) variables are based on the

more conventional arguments involving the extinction point being near the

absence of an appropriate stoichiometry for reaction or the inequality of gas

flow velocity and turbulent burning flame speed as opposed to the flame

stretching argument of Peters and Williams (1983). Both correlations are

shown on Fig. 3.

The disagreement between the correlations for lift-off seen in the figure

as well as the high degree of scatter in the data led to further study and an

assembly of previous literature lift-off data. Figure 4 is the result.

(5) u

- 11 -
(There are far less experimental data available for lift-off height compared

to flame height.) What is critical for the present study is the determination

of how well one can scale to very large fires. The appropriate parameter here

is burner diameter and the object then, is to see how things vary with it.

What is plotted is the average value of the constant referred to above, i.e.,

the ratio of the lift-off distance to the exit gas velocity - the time for a

gas parcel to travel from the burner exit to the bottom of the flame, as a

function of diameter. For a given diameter the average of reported L^/U

values is calculated and plotted on Fig. 4. High and low values are shown by

the vertical lines on the symbols. The number of experiments for any average

is shown by the number beside the symbol. Note that all of the data is for

ch4

.

Contact can be made between the values of L^/U quoted above and the

previous figure and what one observes on Fig. 4. The open circles clustered

around 2. 4-2. 5 ms represents the data of Kalghatgi (1984). The 2.2 ms quoted

above is derived from correlating all his data involving several different

gases. Those gases will have lower L^/U values and weight the average lower.

Observation of Fig. 3 indicates that this result falls below most of the

present data points and the correlation due to that of Peters and Williams

(1983). Their value, 3.6 ms, has been determined from the open square symbols

representing the data of Horch.

Based on Fig. 4 the question to ask is: is there a systematic dependence

of Lf/U upon D? The implication of such a dependence could be extremely

important in trying to extrapolate lift-off data to larger scale. Like blowoff, lift-off is critical in attempting to understand diffusion flame stabil-

- 12 -
ity, and therefore in trying to understand flame suppression and ultimate

extinguishment with water sprays. Theoretical implications for the presence

or absence of a D dependence are quite significant. Within any particular

group of points no dependence on D is apparent, however, one might argue,

especially if one included the filled or present results, that, in fact, some

overall dependence might be present.

There is another relevant piece of work, not included in Fig. 4 involving

propane flames from burner diameters 10 to 80 mm, although the data from the

larger D are for quite small Froude numbers. Schuller, et al. (1983) found

the following expression could correlate their lift-off data:

0.05 Fr

1/2

( 6 )

Interestingly, this result for propane flames falls precisely midway between

the two lines shown on Fig. 3 for CH^ flames from 30 mm pipes. This result is

interesting for two reasons. Firstly, based on small scale results, there

ought to be a fuel dependency which this result suggests is missing in the

larger scale results, at least for these two paraffins. This is to be

contrasted with flame height where the normal square root of fuel density

dependence in large scale has been noted (Schuller, et al. 1983). Secondly,

converting Eq. (6) to the L^/U form will result, not in a constant residence

time but in a half power dependence on diameter, i.e.,
Bringing this result back to a further observation of Fig. 4 might cause one

to speculate even more strongly about a diameter effect.

The 1.8 nun data of Vanquickenborne and Van Tiggelen (1966) are also

interesting regarding the diameter effect. Two different positions of the

lifted flames were obtained with that diameter burner. From the "high

position" the flame could drop back to the "low position" and vice versa; this

happens in a seemingly random fashion. Whether this phenomenon is related to

the hysteresis noted in lifted flame position when the flow rate is increasing

vs. the position assumed by the flame when the flow rate is decreasing is not

clear (see, for example, Fig. 2 of Gunther, Horch, and Lenze 1981). To

confuse matters even more there appears to be some evidence of an additional

dependence of Lj/U upon U in some of the data sets - again in a seemingly

random fashion.

What is beginning to emerge is the fact that diffusion flame stability

phenomena like lift-off are poorly understood and even the empirical information at small scale is not complete enough to pursue with any degree of

certainty extrapolations to larger flames. A systematic study of lift-off

using the present or similar experimental facility should be undertaken. For

present data reduction purposes of scaling the temperature and radiation data,

use will be made of the Peters and Williams (1983) recommendation which seems

on Fig. 3 at least, a reasonable representation for estimating lift-off

distances. The Suris et al. (1977) suggested correlation will be used for

flame height. (Note that above a Froude number of about 3x10"* the actual

length of the flame decreases with Froude number, a result consistent with

observation - Lf approaches as blowoff is approached.) No further general-

- 14-
ization, however on the lift-off data beyond this can reasonably be made at

this time.

3.3 Flame Temperature

Figure 5 presents the uncorrected centerline temperature rise above

ambient, AT = T - T , from the six thermocouples (TC) plotted as a function of

scaled height, (z-L^ )/(Hf-Lf ) , where z is the height of the TC measured from

the burner exit. The attempt here is to make all the flames similar. As Q is

increased or decreased both lift-off and flame height change relative to the

fixed thermocouple tree. The numerator gives the length or distance the

thermocouple is from the beginning of the luminous region. The denominator

gives the entire length of luminosity. This scaling then gives the relative

position in the flame irrespective of length or lift-off. At the flame tip,

(z-Lf )/(Hf-Lf ) equals 1 and at the lift-off height it equals zero. How

successful this scaling is in making all flames similar has yet to be

determined.

The two lines on the figure represent, for the threaded reducer, the

extremes in heat release rates and offer a very graphic view of the scaling.

The lower solid line, 494 kW flame, contains 6 data points representing a

reading from each of the 6 thermocouples and spans most of the flame and to

40% beyond. As Q is increased the flame height and lift off height increase

until near blowoff, represented by the upper dashed curve, i.e., the 6.99 MW

case, the TC at 1/2 and 1 m from the exit actually miss the flame - the lift

off distance is beyond 1 meter. Those latter 4 TC’s now only see the midportion or peak temperature region of this nearly transparent flame. The last

- 15-
point at a AT = 1140 K is determined from the same TC which registered for the

lower heat release rate case a AT * 110 K. The 6.99 MW case is about the best

pre-blow off experiment that can be obtained. Even at this setting methane

gas bottles are being used up at an excessive rate.

Overall, the scaling has been successful in pulling together data

representing nearly a 15-fold change in heat release rate. In detail, however, there remains systematic variations of the data among the scatter. The

most obvious one and the one that will offer new information, regarding these

decreasing radiative fraction - high momentum jet flames, is the increase in

flame temperature with heat release rate. The data in that portion of the

figure from (z-Lf) / (Hf-Lf) equal to about 0.2 out to approximately 0.75

bounded on the bottom by the line of the lowest heat release fire and on the

top by the 6.99 MW line exhibit a weak but systemmatic variation of temperature rise with heat release rate. The length scaling of (z-Lf )/(Hf-Lf ) may

have brought the data for both the rising and falling temperature portions of

the flame, i.e., small and large values of abscissa, into a crude correlation

but It doesn't and cannot be expected to do anything about the high

temperature central portion of the flame.

All these flames are therefore not similar. In a previous report

(McCaffrey 1981), correspondence was made between the flame height and radiative fraction of non-laminar diffusion flames over the entire Froude number

spectrum. There exists a large intermediate range of Froude number where for

a given fuel the radiative fraction is a constant, independent of burner

diameter and fuel flow rate. In this regime flame height is independent ot

diameter varying with Q to the 2/5's power. This is a kind of similarity

- 16-
region, the portion on the H^/D plot. Fig. 3, prior to the "transition" at

3xl04

. (Lf is still a small fraction of Hf up until this point.) In this

regime temperature data might be expected to be independent of Q. On the

other hand, at very low Froude numbers (H^/D + 0) is the buoyancy controlled

pool fire regime where similarity breaks down both for radiative fraction and

flame height. Similarly at the opposite end (H^/D + constant), the present

interest, flame height no longer varies with Q

2//5 and the radiative fraction

is no longer constant. It continuously decreases with increasing fuel flow

reaching a non-zero value just prior to blow-off. Visually, as the flame is

lifting off it gets more and more bluish and transparent until finally at

blow-off all traces of yellow luminosity are gone. The ghostly bit of emission remaining up near the position where the flame height was maximum

disappears with the ultimate increase in flow which brings blow-off. (There

is a parallel here with the behavior of bench-top scale laminar diffusion

flames. Santoro (1986) reports that his laminar C

2H2 flame can be made almost

totally blue by inerting. However, just before the last bit of yellow

disappears, the flame becomes highly unstable or blows off.)

Like the non-similar buoyant end of the Froude spectrum little is known

in this Hf/D = constant region. The soot formation-oxidation process is too

strongly coupled to the fluid mechanical process in these regimes to study a

single representative flame and be able to generalize the behavior much beyond

the particular parameters of the experiment. Here we look to empiricism to

garner any bit of information possible. The rising temperature with heat

release is plotted on Fig. 6 in the chemical kinetic form of the logarithm of

the process rate as a function of inverse temperature. The form is purely

arbitrary - any reasonable function which relates the increasing temperature

- 17 -
rise in the middle portion of the flame with the heat release rate as seen on

Fig. 5 would be adequate. Coupled with the radiation measurements in the

following section an attempt will be made to relate the results of Fig. 6 with

the soot formation-oxidation processes taking place in diffusion flames at the

high momentum limit. The line on the figure represents a least squares data

fit in the Arrhenius form, exp(-E/RT) with the activation energy, E, given as

30.8 kcal/mole.

3.4 Radiation

Figure 7 presents the incident radiative flux from large methane

diffusion flames to nearby targets as measured by two water-cooled, wide angle

heat flux sensors located several meters from the flame as indicated by the

schematic on the figure. They, in fact, were located in different longitudinal planes but for time-mean purposes the flames are considered to be axisynrmetric. Not only are these measurements useful for estimating the flux from

these flames incident to any other target once the data has been generalized,

but also, they will provide a baseline for estimating the suppressing effects

of water spray once that data is considered. On the figure are shown for each

sensor two sets of data for two different exit geometries - an internally

threaded ordinary pipe reducer of exit diameter 29.2 mm and a circular hole or

slot, 31.8 mm diameter, cut straight in an 8 mm thick cap which is the end or

top of a 100 mm diameter pipe section. The large section allows placement of

the spray nozzle in the pipe for study of the effects of internal water spray

on the flame behavior. The top of the spray nozzle is located 6 cm below the

exit. This, coupled with the fact that the conditions in the large section

are practically stagnation, makes the presence of the nozzle less likely to

significantly affect the exit flow field (see fig. 1).

- 18 -
If indeed the two geometries represent extremes in exit flow conditions,

at least for circular apertures, then any differences between the radiative

results of the two as evidenced by Fig. 7 are too subtle to discriminate - the

results of the orifice appear to fall within the bounds of the scatter

exhibited by the reducer. Both signals from both of the two transducers rise

with gas flow rate or fire size, a not unexpected result, up to a level of

about 1/2 W/cnr at a lateral distance of 2-3 m and for flow conditions of

imminent blowoff, i.e., about a 7 MW methane diffusion flame from a 30 mm

nozzle.

The data contained on Fig. 7 can be generalized in terms of a model for

the flame radiation, useful for estimating the flux to targets at any location

and orientation. There are several methods available, none of which is

totally satisfactory due to the nature of thermal radiation from flames. For

jet flames the most simple geometry that immediately comes to mind to model

the shape is a cylinder. Very recent compilations have appeared (Schuller et

al. 1983) where effective flame heights, flame diameters, and lift off heights

were determined from photographs of hydrocarbon flames from circular as well

as rectangular burners of similar scale to those of interest here. Their

results, in terms of source Froude number (U^/gD), are:

Height ( 8 )

Diameter (9)

Lift-Off Height ~ = 0.05 Fr

1/2

( 10 )

-19-
Note in comparing Eq. (2) with Eq. (8) that the effective flame height

based on photographs is considerably less than the normal extent-of-flame-tip

value* Since later a single value of temperature will be used to characterize

the flame region the smaller (completely luminous volume) height may turn out

to be more appropriate*

Dayan and Tien (1974) have presented a convenient analysis for a

radiatively participating cylindrical fire column of uniform temperature and

species concentration. It is a two parameter model of effective flame temperature, Tf, and an effective gray flame emittance a. The flux to an external

target is given as

q” =» F a aT^ (11)

where F is the shape factor. The absorption coefficient is usually expressed

in terms of an extinction coefficient, kf(m~*) independent of geometry, and

flame geometry,

a = 1 - exp[-kf * f (D ) ] (12)

where f(D) accommodates the flame geometry, e.g., mean beam length. The

measurements of q" seen on Fig. 7 together with the assumed cylinder model

(Eqs. 8-10), a function of Q, can now be substituted into the above expressions and a flame temperature and extinction coefficient derived. These now

are considered "properties" of these flames and could be used to calculate the

flux to an arbitrary target.

-20-
Figure 8 shows the derived flame properties, absorptivity and flame

temperature, as a function of Q for single values of the other property. The

points represent the mean of the two sets of data from the two instruments

shown on Fig. 7. From Eq. (11) it is obvious that an unlimited number of

combinations of and kf will satisfy the data of Fig. 7. For the present,

"reasonable” values of each are chosen. Note the relative sensitivity of the

ordinate scales of Fig. 8 - temperature dependence to the fourth power, and

kf, a much milder dependence, i.e., a linearly dependent upon kf for thin

flames. What is attempted in any two parameter model is to relate the results

to some other independent measurement of either flame temperature or

absorptivity.

First it is worthwhile observing some overall characteristics of the

radiation from these jet diffusion flames. Without additional information.

Fig. 8 on its own would indicate that as Q is increased the relative radiation

decreases, which is reflected either in decreased temperature with Q or, for

fixed flame temperature, a decreasing k

f with Q. Whether it makes sense to

hold either parameter constant throughout such a range of fuel flow rate is

not obvious. The observation of decreasing radiation with Q or gas flow rate

for jet flames however, has been observed and somewhat quantified previously

in terms of a decreasing radiative fraction.

The independent piece of information that can be used in the radiation

model is the centerline temperature discussed in the previous section.

Although the model assumes a homogeneous volume of absorbing-emitting material

and certainly Fig. 5 indicates no such conformity, even axially, those

measurements will nevertheless reflect the temperature variation with fire

-21 -
size in the central portion of the flame. Figure 9, exhibiting the same

scales as Fig. 8, shows the derived values of kf given the now variable

temperature variation shown on the lower portion of the figure by a solid

line. This is the least squares analysis of peak temperature shown in Fig.

6. Although the general shape of kj vs Q is similar to the constant temperature result of Fig. 8, i.e., decreasing kf with Q, the range from low to high

values has increased something like a factor of two and the minimum absorptivity is now around 0.2 m”^. Having the two figures, 8 and 9, in hand will

aid in evaluating not only the changes in the levels that can be expected but

also the effect of the variation on the derived property. The curve through

the k^ data is simply a least squares fit.

Figure 10 shows additional sensitivity analysis for an experiment in the

middle of the group of data, i.e., the threaded reducer, 3.3 MW flame. Here

the sensitivity to the cylindrical model chosen with regards to height and

diameter of the flame as well as Tf, seen previously, can be observed. The

abscissa plots the change in the independent variables, e.g., 1.1 would

indicate a 10% increase in flame height over the base value. The ordinate

gives the relative change in k^ due to that change, e.g., k^ has decreased by

about 6% to approximately 0.94. This way one is able to judge how critical

the dimensions of the cylindrical model of the flame, for example, would be to

the calculated absorptivity. From the figure it would appear that flame

height is not very important since the flames are quite tall already relative

to the height of the sensor and that flame diameter is more critical, D and k*

come as a product (see Eq. 12). Flame temperature is quite critical as one

would suspect basically due to thermal radiation's fourth power dependence on

T. A 140 K temperature differential at a level of 1400 K is 10% and would

-22-
correspond to a 60% increase in k^ on the low side or a 35% decrease in kf on

the high temperature side. Still when these numbers get fed back to Eq. (12),

the expression for flame emittance, a much milder variation results - provided

the flame diameter is of order 1 m or less which is true in the present case.

This is not the case for more usual extinction coefficients which are on the

order of 1 m”*, the point where the exponential function is changing rapidly.

The present model of the quite optically thin high momentum CH^ flames is

therefore quite robust as regards temperature changes.

We now have a "model" for the radiative field associated with high

momentum CH^ diffusion flames. Recall from Fig. 9 the lower portion represents an independent measurement of the way a representative flame temperature

varies with heat release rate. That information coupled with the radiometer

measurements and the cylindrical flame model yields the upper portion of the

figure, the extinction coefficient, kf, as a function of fire size. There is

another way of expressing the information contained on Fig. 9 which is useful

and is such that direct comparison with the literature can be made. One can

calculate the radiative fraction, using the flame temperature, geometry and

absorption coefficient data of the model.

Using Eq. (11), the view factor for a surface element very far, x, from

the flame is:

F

1 Df H£ (13)

The flame emittance, a, can be expressed (see Dayan and Tien 1974) for far

distances as:

-23 -
a - 1 - exp [-0.7 • D^j (14)

The definition used here for the radiative fraction is the total radiative

power output, obtained from the flux to the surface element far from the flame

2 multiplied by the total surface area of the hemisphere, 4ttx , divided by the

nominal heat release rate of the fire. This assumes a point source and

uniform flux at the surface of the sphere of radius x, even though to calculate the flux at x we will use the cylindrical model of the flame. The radiative fraction, x is therefore:

‘rad 4 4

Q

D

f

H

f

aT

f

[1 - -0.7k

f

D

f ] 05)

where Eq. (11), (13) and (14) are substituted for q". Using the cylindrical

model for Df and H^, Eq . (8) and (9),

T

4

X - 1.124 x 10“ 12

-jjj [l - exp(-0.0196 k

fQ

2/5

)] (15a)

where T^ is in K, Q in kW, and kf in m

*

. The least squares expression for T

f

and kf as a function of Q from Fig. 9 can be substituted to obtain the final

result.

A plot of this derived or semi-calculated model radiative fraction result

is shown on Fig. 11 along with literature measurements. In place of Q the

abscissa is the square root of Froude number. (For the present pure methane

gas from a 30 mm exit diameter U//gD = 0.0769 Q, Q in kW.) What ts seen on

Fig. 11 is the high end of the buoyancy-momentum Froude number spectrum

(McCaffrey 1981). The left portion is the intermediate region, Becker's

-24-
(1982) "natural convection limit". Here flame height is independent of

diameter and the radiative fraction is constant. Although not evident from

the data shown on the figure this region of constant radiative fraction

extends down, using larger and large diameter burners, many orders of magnitude in Froude number (McCaffrey 1981). At higher Froude numbers ~ 0(10^)

flame height becomes constant, lift off becomes significant and the radiative

fraction begins to decrease as blowoff is approached. That is the region

where most of the data on Fig. 11 is contained. The decreasing radiative

fraction corresponds visibly to less yellow luminosity and hence indicates

perhaps some interference with the soot formation-oxidation process. Recall

that temperatures are rising in this regime. Flame particulate decrease with

rising temperature or jet velocity has been noted previously by Brzustowski,

et. al. (1975) for smaller diffusion flames.

The derived curve on Fig. 11, designated "present calculation",

encouragingly splits the available data indicating both a reasonable level

of X as well as variation of x with jet velocity. On the top of the figure

are some reference benchmarks. The quoted flame height transition at

Fr = 3x10^ is seen and appears to be well into the decreasing x regime rather

than coinciding exactly with the start of the regime. Another reason for the

call for a systematic study of lift off would be to exactly determine where

that feature of the region begins relative to these other two, i.e., the start

of the decreasing radiative fraction and blowoff. The end of the region is

marked by the "blow off" designation - the 5 mm is from Kalghatgi (1981); the

30 mm is the present result. The variation from 5 to 30 ought to go as the

1/2 power if lift off velocity is linear with diameter. (Becker (1982) has

data for smaller diameter burners which are not shown since a stabilizing gas

-25-
was used to prevent lift off and hence that data extends well beyond the

normal blow-off for pure CH^«)

Using the least squares expression for and as a function of Q from

4 Fig. 9 the quantity c(o can be calculated. This emissive power varies only

slightly with Q or fire size: equal to about 2.9 W/cm2 at 1 MW rising to

about 3.3 W/ cnr at 7 MW, or at blow-off for this 30 mmD configuration. This

is a much milder variation with size and a somewhat higher level than that

found by Sonju and Hustad (1985). They chose to correlate their data in terras

of the radiating height of a cylindrical surface emitter

acrT4 - 0.5 + 0.39 (H

f - Lf

) (15b)

in W/cmr with the heights in m. The present absorbing-emit ting results come

out to be significantly higher at small fire sizes but with little variation

with increasingly larger scale, i.e.,

acrT4 - 2.6 + 0.13 (H

f - L

f

) (15c)

Note that Eqs. (8) and (10) were used for the present calculations.

3.5 Effect of Water Spray

The effect of water spray on the centerline thermocouple readings can be

seen in Figs. 12 and 13 which show temperature as a function of height for .i

variety of fire sizes. For clarity, faired curves are drawn between the dots

representing the data points. (For repeated runs vertical lines are used, the

-26-
extremities of which span the data scatter.) The parameter is the ratio of

the mass flow rate of water to that of the gas, q/®ch » a natural scaled

quantity used previously in small scale studies.

In general there appear to be two dominant effects emerging from the

figures: peak temperatures are lowered and relative positions in the flame

have been shifted to higher z, i.e., the flame is being pushed off or lifted

above its non-sprayed position. Both effects tend to increase with the amount

of spray. For certain experiments, notably the 2.3 MW flame there exists

confusion regarding a temperature inversion when viewed in a physical height

coordinate. A portion of this can be accounted for by the shift of the flame,

i.e., hotter portions are at higher elevations. Evans (1985) in a subsequent

study using external sprays found that the remainder of the anomalies in the

upper regions disappeared with longer sampling times and more restrictions on

what constituted acceptable weather variations for running the experiments.

The lower and peak temperature regions appear unaffected.

The first of the effects, the lowering of the temperatures, is more

easily quantified on Fig. 14 which shows the peak temperature plotted against

water flow for the data from the previous two figures. In general the temperature data appear to decrease with scaled water flow rate as a group, i.e.,

there is no obvious ordering of the data aside from the small T increase with

Q noted earlier for the case of the zero water flow base line, seen here at

the ordinate. The one exception is the largest, 4.6 MW flame which extinguished slightly beyond the last recorded data on the lower portion of Fig.

13. At q^CH e9ual t0 0»23 the flame was suppressed but stable; at

2 4

c/TMCH e9ua-^ t0 0»34 the flame went out. Based on the small size of the

2 4

-27 -
temperature reduction at these water flow rates it appears that extinguishment

resulted not from a thermodynamic-like cooling effect to some lower limit

temperature but rather to the slight, further lift or push to an already

lifted flame beyond some flame stabilization distance. There would be a

strong analogy in this interpretation in going to blow-off for an unsprayed

flame. Presumably those suppressed flames which did not extinguish even with

rates of water flow ten times that amount, as seen on the figure, were that

much more stably configured. These observations are quite similar to small

scale H

2 flame extinguishment with sprays seen previously (McCaffrey 1984)

where temperature measurements alone would not have indicated an unstable

situation.

Shown in Fig. 14 by the solid lines are equilibrium calculations for the

CH^/air/I^O (£) system for arbitrary equivalence ratios of 0.45 and 2.15.

These were chosen on each side of stoichiometry in order to approximately

match the unsprayed temperature results. As one might travel with the gas

from very fuel rich at the pipe exit through a variety of <j> to very lean

conditions near the flame tip the peak temperature region of the flame might

straddle those <J>» The trend of the data sort of matches the trend of the

calculation even though the relationship between a real diffusion flame

sprayed with water and an adiabatic perfectly mixed system calculation is not

clear. [Recent work by Jeng, Chen, and Faeth (1982) have shown that partial

equilibrium methods have yielded some reasonable success regarding the

characterization of CH^ jet flames.] The calculated temperature will tend to

decrease without limit as the relative amount of water is increased. Perhaps

the data would indicate a weakening of the trend to decrease, i.e., reach an

asymptote and then perhaps the flame would go out. Thermodynamics is certainly not going to explain the 4.6 MW extinguishment at m^

0 ^CH " 0.34.

2 4

-28 -
Some quantification of the second effect of sprays seen on Figs. 12 and

13, namely that of the "push off" effect, can be estimated from Fig. 15. Two

arbitrary positions in the flame, the height where AT = 500 K, the filled

symbols, and the height where AT = 0, that is the extrapolation to AT = 0 from

Figs. 12 and 13, the open symbols, are plotted against scaled water flow

rate. The ordinate is the ratio of the positions of the sprayed, or wet (W),

to the unsprayed, or dry (D). The presumption is that the same temperature

would be representative of similar reaction regions in the flame and that the

water has not otherwise perturbed the flame. We are tacitly assuming that the

two effects are distinct. The similarity between the AT = 0 data and the data

for the temperature in the reaction zone is encouraging in this regard. The

ordinate has been normalized by the heights or the flame positions corresponding to the loci of AT » 500 and AT = 0 for the situation without water spray

which does a reasonable job of pulling together different fire sizes. Those

zero water flow values for AT = 0 are consistent with Fig. 3 which shows liftoff height vs. Froude number thus strengthening the confidence in the results

of the rather liberal extrapolation made of the data on Figs. 12 and 13.

The results seen on Fig. 15 can be used to estimate the degree of

additional lift-off height the spray will provide to an otherwise undisturbed

flame. In fact a model can easily be constructed of the process involved in

the kind of extinguishment discussed previously concerning the 4.6 MW flame on

Fig. 14. From Fig. 3 the lift-off height for a given fire size will be known.

(The need for a systematic study of large fire lift-off in order to improve

the accuracy of what is to follow ought to be evident.) This height is then

increased by the results of Fig. 15, i.e..

-29-
( 16 )

(L

f

/D)

where subscripts W and D refer to conditions with (wet) and without (dry)

water spray, respectively. The function f is a suitable representation of the

increased lift data seen on the figure. It should be able to be calculated

through a sufficiently detailed model of the momentum exchange between a jet

encompassing a spray. When (Lf/D)w

is increased to the critical value by the

spray, blowoff results. Using Eq. (4) for (Lf/D) D, in terms of heat release,

For Lf/D critical equal to a constant, say 50 (see Peters and Williams, 1983),

and a linear approximation to the data of Fig. 15 (the straight line on the

figure), the required flowrate of water for the kind of extinguishment

discussed above is:

where 0.64 is the slope of the fourteen data of Fig. 15. That number (and the

linear approximation) together with the critical Lf/D, i.e., 50 and the variation of Lf/D with Fr number, the 3.6 ms number, constitute considerable experimental information whose accuracy and range are yet to be established,

especially for large flames. Nevertheless, Eq . (18) may provide for first

order effects with regards to the expected variation of water requirements

with scale. Note that the 3.6 ms could be replaced by Kalghatgi's (1984)

expression for Lf/U, i.e., Eq. (5), for different gas mixtures.

(17)

(18)

-30-
For the present 0.03 mD burner using CH^ gas, the critical water flow

rate becomes

(19)

CH

4

For the data show on Fig. 14, the three smaller fires all would require flow

kind of extinguishment. Only for the 4.6 MW fire would extinguishment be

visible in the range of the abscissa of Fig. 14. The number calculated by Eq.

(19) is about 1.8 whereas extinguishment occurred at a flow rate ratio of

0.34. We might perhaps expect the analysis to be conservative in requiring

more water since any dilution or cooling effects have been ignored. However,

given the small amount of experimental information and the contention of

isolated effects used to generate the above, the qualitative agreement seen in

the four fire sizes is probably all that can be expected and speculation about

any quantitative differences, at this stage, is probably fruitless.

The final effect of water spray observed during this work was that of a

reduction in radiation as observed by the heat flux sensors. Figure 16 shows

solid symbols. Shown by open symbols are the temperature data seen on Fig. 14

normalized by the value for zero water flow raised to the fourth power. Both

the heat flux and the gas temperature fall as the amount of water sprayed

increases. The very large decrease in temperature to the fourth power is not,

however, being reflected in the sensor output. Something is preventing the

radiation sensors from realizing the tremendous cooling that is being observed

by the thermocouples due to the water. And that something appears to be

increasing with increased water flow.

“31 -
From Eq. (11) which is the expression which quantifies what the sensor

ought to read, one can immediately postulate that either the flame emissivity

or the view factor or both must be increasing in order to compensate for the

decreased temperature levels. Since it is known that the spray lifts the

flame vertically, which for the present locations of the sensors will not

significantly improve the view and may, in some cases, tend to decrease the

view factor, we will look to increased absorptivity in order to reconcile this

apparent dilemma. It ceases to be a dilemma when it is realized that water

when sprayed into a flame, besides disturbing the flame, will be evaporated

and heated to a significant temperature and itself then becomes a significant

IR radiator. And the more water the more radiating volume. This is exactly

true for a non-sooting flame. However, for flames with appreciable soot the

water may exhibit a far greater influence by interfering with the soot formation-oxidation process. Since it is expected that the amount of soot will be

controlling the optical properties of these very luminous diffusion flames the

emissivity will decrease and not increase with the amount of water sprayed.

Presumably the steam will still be radiating but not sufficiently to be able

to overcome the decrease due to the reduced particulate emission. (In subsequent calculations the additional lift due to the spray has been incorporated

into the radiation model.) However, we need not be too concerned here with

interfering with the soot formation-oxidation process since our high velocity

CH^ jet flames are almost soot free.

Returning to the simple gray, cylindrical model of the flame an effective

absorptivity can be determined. Recall that the fire size, Q (for flame

dimensions and view factors) and the measured heat flux are input to a calculation which then produces a variety of temperatures and absorptivities which

-32-
will satisfy the model (see Fig. 8). Now, the experimental temperatures shown

on Fig. 14 are used to determine the appropriate kf for both the dry base line

and the sprayed data. The results are shown on Fig. 17 in the form of

kfy/kfD» that is, the increase in absorptivity due to the water spray as a

function of water flow (solid symbols) or the difference between q^/q” and

(1^/T^)^ seen on Fig. 16 (open symbols). That increased kf is what is going

to be required in order to reconcile the very low temperature data with the

only moderately low heat flux data. At m^ q^CH ~ ^ » f°r example, a factor

of 2 increase in absorptivity will be required.

Knowing the size and variation of the increased k^ it is now a matter of

simply obtaining water vapor emissivities from the literature in order to

confirm the above. That is, the increased emissivity required to reconcile

the temperature data is determined from the radiation model of the flame,

i.e., Fig. 17. An attempt will be made to predict that increase based on an

emissivity chart for water vapor (Hottel 1967) which requires knowing the

temperature and path length and will yield a partial pressure of water for a

given emissivity. That partial pressure can then yield information about

flame entrainment which can be checked or at least compared with small scale

jet flame entrainment measurements of Ricou and Spalding (1961). For that, a

model will be constructed which attempts to determine an "equivalent” fluid

for the configuration of a water spray inside the CH^ jet to be used for

source conditions needed for the entrainment calculation. The idea of

increased emissivity due to flame suppression by water spray can then rest on

firmer ground.

-33 -
The following calculation will utilize a range of flame diameter or path

length so as to set brackets on the final result. High and low values of D

are chosen since the result is quite dependent on the value of D and it is

difficult to assess, a priori, what value of D is appropriate. The reason for

the difficulty is the counter effects of increasing flame volume due to the

increased mass injected (steam volume is 1700 times that of liquid water). It

will be seen that the entrained flow is proportional to the injected flow.

This is countered by the tendency of the flame to entrain at a lower rate due

to buoyancy effects brought about by the increased density of the fluid, i.e.,

liquid drops, at the source of the jet.

Even if the additional mass or volume of fluid entrained were known, a

priori, how it is proportioned between diameter and height would be still

unknown. From Fig. 10 it is obvious that putting all the volume into an

increased diameter would result in a far different kf then having all the mass

increase the flame height. The characteristics of the spray and jet-spray

interaction and a host of other things would have to be known in a much more

detailed manner than is currently available in order to do this problem.

A scheme for determining a reasonable range of D which avoids some of

these difficulties is as follows: let D extend from a base line established

solely by the heat release rate of the fire, Eq. (9) to a maximum value of D

determined from Fig. 10, the sensitivity analysis of the radiation model.

(Figure 17, for example, uses the base line or the "dry” value of D in the

calculation.) From Fig. 10 as D is increased k^ decreases. A natural upper

limit on D, therefore, would occur when k^ drops to such a value as to eliminate the advantage of the radiating steam, i.e., k^ falls to the dry value

-34-
predicted by the model. From Fig. 10 and the data on Fig. 17, a D was determined which will be designated Dw

for wet, maximum diameter. A crude fit to

those results relative to D which is the value if no change in volume results

from the spray, i.e., Eq. (9), is:

D

= 1 + 2.33 x 10

-6

( 20 )

where Q is in kW. This is purely a data fit and as yet of unknown physical

significance. (A form similar to this would be suitable for representing the

solid symbols of Fig. 17.) Most of the data yields an incremental increase in

diameter of about 10% with the larger water flow rates rising to about 30%.

These values are quite a bit smaller than ones calculated by assuming that the

diameter is taking up most of the increased volume and that the entrained flow

is directly proportional to injected flow, i.e., Dw

/D from Eq. (20) is much

less than ^

1 + m^ • We cannot at this juncture put the rest of the

additional volume into an increased flame height because the total is still

unknown

Having now a seemingly reasonable range over which D might vary, the

radiation model is run again, this time with the larger D (recall that Fig. 17

used the heat release rate calculated for a dry value of D). For both

diameters the procedure is the same. Assume for convenience an expression

like Eq. (12) for absorptivity for both dry and. wet cases. The difference

between the two will be assumed due to the water vapor:

Op = 1 - exp (-0.7 • D • k

f

) (21)

-35-
( 22 ) = 1 - exp (-0.7 • D •

) w

where kf now includes the additional emitter or k- = k^ + k, , and hence w w

f D

f H

2 0

the separate contribution to the radiation due to water vapor is:

(23)

Figure 18 shows the calculated

^ for both extremes of diameter.

With that absorptivity (assumed equal to emissivity) and temperature, a

value of the product of path length and partial pressure is obtained from the

water vapor emissivity chart (Hottel 1967). Dividing this number by path

length yields the derived vapor pressure of water in the flame. Figure 18

shows a plot of water vapor pressure, Pw , versus m^ o^TMCH * The s >rmbols

2 4

represent a simple average, the lines extend to the two diameter results with

the upper extent corresponding to the calculation using the small or ’dry"

diameter. Like the necessity of a being larger, one would require more

emitting vapor if the optical path were smaller. Judging by the amount of

vapor required the amount of entrained fluid will turn out to be small.

is,

Figure 18 now allows an estimate of the amount of flame entrainment,

normalized by the source flow, m

Q = m

CH

+

“Hi o»

e9 ua^ to:

It

^NT

m.

29/1

PT [}

+ 1/(’V/i

CH4

"I " 1 (24)

assuming total pressure is 1 atm and that most of the total gas consists of

entrained air. This estimate of entrainment can now be compared with an

-36-
independent calculation of flame entrainment which ought to validate somewhat

the determined partial pressure of water vapor seen on Fig. 18.

Ricou and Spalding (1961) have correlated small scale flame entrainment

data in the following form*:

*ENT

Fr

~l/2

. c m

o

= 0.165 i Gf 5/3

(25)

where H is the entrainment length and Frc is a Froude number which includes

buoyancy effects due to combustion.

Fr

c y.

“CH,

7i

o “

(26)

for injected fluids at ambient temperature. Eq. (25) can be written in the

following form:

= 0.165 m

o

“ent rj (27)

From Eq. (25) it is clear that entrainment varies inversely with source Froude

number to the 1/3 power and here, Eq. (27), the explicit dependence upon the

product P q U

q

at the source is seen. For a pure gas there is no difficulty,

for a gas encapsulating a water spray the situation is not so clear. Perhaps

an effective p U could be developed, oo

*The slope and intercept are given by Putnam, A. A. and Speich, C.F. (1963), A

Model Study of the Interaction of Multiple Turbulent Diffusion Flames, Ninth

Combustion Symposium (Int.), Pittsburgh, USA, p. 867.

-37 -
For the dry case of pure CHa, m,TM /m - 1, flame height varies with

o Froude number to the 1/5 [Eq® (8)] and hence source conditions for the dry

case drop out of the equations. Equation (27) predicts » 146 for all the

m

cases of interest here. The stoichiometric air requirement for CH^ is 17.3 kg

air/kg CH^ and therefore 146/17.3 = 8.4 times the necessary air has been

entrained up to the flame tip. This is about half the value obtained for CH^

diffusion flames burning in a pool configuration where buoyancy is much more

dominant (McCaffrey 1983). Note for the buoyant case the flame length is only

several diameters high versus several hundred for the jet.

It is interesting to go the other way and eliminate buoyancy and estimate

entrainment. The Ricou and Spalding (1961) result in the absence of buoyancy

(but allowing for different source density than the surroundings) is:

°*ENT

«m

o

(28)

which for CH^ is 0.43 H/D. For the larger fires H/D ~ 220 (Fig. 3) yielding

an entrained to source flow of about 94 compared to 146 for the flame case.

(Using Eq. 8 for effective flame height the 94 would be correspondingly

lower.) By lighting-off the methane jet, therefore, one can increase the

entrainment by 50%. By burning it in a more buoyant configuration by, for

example, increasing D, even much larger entrainment rates are available.

These examples illustrate the importance of buoyancy and the range of values

that could be expected. Anything that changes the source conditions like Che

introduction of a heavy fluid such as a water spray into the gas stream will

obviously then have a significant effect on flame entrainment.

-38-
The question now arises as to how to estimate an "effective" source p U oo

for use in Eq. (27). Probably the simplest method is to find a uniform

"equivalent" fluid the properties of which reflect the liquid spray (the

details of which little is known) in the methane stream.

Consider an equivalent stream of mass flow equal to the sum of the mass

flows of the methane and water spray streams

4

o = *CH, + Vo (29)

4 2

Similarly, let the momentum of the equivalent stream equal the sum of the

individual momenta of the two streams.

m V

o o m

CH

4

V

CH

4 + TMH

2 0

V

H

2

0 (30)

We can immediately solve for the velocity of our hypothetical equivalent

stream. It is the mass flow rate-weighted velocity.

V

o 1 + r CH,

1 + r

-1 h

2 o

where r is the mass flow rate ratio, r

(31)

In steady flow the density of a mixture of two simple fluids is, again,

the mixture fraction-weighted density, i.e.,

P o 1 + r CH.

1 + r-1 H2°

(32)

-39-
Taking the product and simplifying

p V = p V

o o

m CH. CH.

4 4

(1 + <j>r)(l + At / 4>

(1 + r)

2

( 33 )

where A is the ratio of the individual stream outlet areas, i.e.,

A “ anc* ^ is the ratio °f density of water (or soon to be, spray) to

gas, 4> = PH

q/

Cy

. The reason <J> will be a parameter in what is to follow is

2 4

that the water stream is not a simple fluid but rather a spray of very complex

properties, e.g., unknown mean drop size, size distribution, particle

velocities, volume fraction of liquid, etc. For two simple fluids Eq. (33),

utilizing the two appropriate conservation laws, Eqs . (29) and (30), would be

perfectly general, with <j> equal to a constant. Here we will allow 4> to vary

within reasonable limits and observe the behavior of the final result.

As r approaches zero the value of PQ

V

0

from Eq. (33) approaches that of

GH^ and as r grows extremely large P Q

V

0 approaches that of ^0, both results

independent of the parameters <f> and A. For simplicity we will fix A at 21.97,

the ratio of the squares of diameters of the two outlets, and only vary $.

The largest value of 4> would be that of a solid stream of water, the actual

density of liquid water to that of methane, i.e., 1000/. 679. The value of the

real spray will be less since the stream will contain not a solid stream but

individual drops surrounded by methane gas. The lower limit for $ would

approach 1 as the volume fraction of the liquid drops approaches zero - the

density of the water stream approaches that of the CH^ gas. For <J> 1, Eq

(33) is the same as a mass flow rate-weighted calculation of p V , a strong

o o function of r. For <p m 1473, P Q

V

Q

is obviously very large and Is weakly

dependent on r.

-40-
The final step is to calculate m^^/m^ from Eq. (27) using the range

of 4> described above for determining the hypothetical equivalent source

function, p^V^. Figure 19 shows the comparison of m^^/m^ determined from the

radiation and temperature measurements through derived water vapor partial

pressure (ordinate) as against m^^/m calculated from the Ricou and Spalding

formulation (abscissa) using the range of <J>. The symbols represent simple

arithmetic averages of the high and low value of each calculation, the lines

extend to the full range of the calculations. Vertically, the larger or "wet"

diameter corresponds to the upper extent and the lower extent to the smaller

or "dry" D used in the radiation calculation. Again, larger path lengths

require less mass of radiating material and less participating material means

more entrainment. Horizontally, the left size of the <p range corresponds to a

solid stream, very large values of PQ

V

0

with little variation with either heat

release rate or water flow rate ratio. On the right, approaching larger void

volumes, the variation with water flow rate is picked up. Also on the figure,

for reference, is the entrained values of a jet and two flames without spray

as discussed above.

Judging by the figure the entrainment rate for sprayed flames is

extremely low vs. non-sprayed flames and decreases with increasing m^ /m . ri- 0 Cn,

2 4

Recall, however, that m in the denominator contains water flow as well as

o methane. To convert the numbers on Fig. 19 to m^^/m^ , the entrainment to

4

flame gases only, multiply by 1 + m^ q^CH • If that is done all the data

2 4

will yield an entrained flow beyond the stoichiometric value for methane

although just barely for the higher values of spray.

-41 -
Although Fig. 19 is certainly supportive of the increased emissivity with

water spray idea it should be approached with caution. As previously

mentioned for sooty flames the water will probably have a more profound effect

on the particulate creation-destruction processes and hence affect radiation

differently for those cases. Also there is a great deal of quantitative

uncertainty built into both the ordinate and abcissa of Fig. 19. Most notably

the use of variable f as a representative for spray dynamics as well as the

homogeneous radiation model for a sprayed flame must be included. Obviously,

further experimentation is warranted. In the meantime, the "reasonableness"

of Fig. 19 remains intriguing.

4. ACKNOWLEDGMENTS

Thanks are due R. Zile and W. Hayes who assisted with the construction of

the test facility, instrumentation and data taking; as are thanks due H. Baum

for fruitful discussions. Portions of this work was sponsored by the Department of the Interior, Minerals Management Service, John Gregory and Ed

Tennyson, contract monitors.

-42-
5 . REFERENCES

Annushkin, Y.M. and Sverdlov, E.D. (1979). Stability of Submerged Diffusion

Flames in Subsonic and Underexpanded Supersonic Gas-Fuel Streams, Combust.

Explosion and Shock Waves 14, 597.

Becker, H.A. and Liang, D. (1978). Visible Length of Vertical Free Turbulent

Diffusion Flames, Combustion and Flame 32, 115.

Becker, H.A. and Liang, D. (1982). Total Emission of Soot and Thermal

Radiation by Free Turbulent Diffusion Flames, Combustion and Flame 44, 305.

Brzustowski, T.A., Gollahalli, S.R., Gupta, M.P., Kaptein, M. and

Sullivan, H.F. (1975). Radiant Heating from Flares, American Society of

Mechanical Engineers, New York, Paper 75HT4.

Dayan, A. and Tien, C.L. (1974). Radiant Heating from a Cylindrical Fire

Column, Combustion Science and Technology 9, 41.

Evans, D. (1985). To be published

Gunther, R. , Horch, K. and Lenze, B. (1981). "The Stabilization Mechanism of

Free Jet Diffusion Flames", Colloque International Berthelot-VieilleMallard-Le Chatelier, First Specialists Meeting (International) of the

Combustion Institute, p. 117.

Hottel, H.C. and Sarofim, A.F. (1967). Radiative Transfer, McGraw-Hill Book

Company, New York, p. 232.

Jeng, S.M., Chen, L-D., and Faeth, G.M. (1982). "The Structure of Buoyant

Methane and Propane Diffusion Flames, Nineteenth Symposium (International)

on Combustion, The Combustion Institute, pp. 349-358.

Kalghatgi, G.T. (1981). Blow-Out Stability of Gaseous Jet Diffusion

Flames. Part I: In Still Air. Combustion Science and Technology 26, 233;

Part II: Effect of Cross Wind, ibid, p. 241; Part III: Effect of Burner

Orientation to Wind Direction, ibid 28, 241 (1982).

Kalghati, G.T. (1984). Lift-Off Heights and Visible Lengths of Vertical

Turbulent Jet Diffusion Flames in Still Air, paper presented at 9th

(International) Colloquium on Gas Dynamics of Explosions and Reactive

Systems, Poitiers, France, July 4-8, 1983 (Combustion Science and

Technology 41, 17).

Lockwood, F.C. and Moneib, H.A. (1982). Fluctuating Temperature Measurements

in Turbulent Jet Diffusion Flames, Combustion and Flame 47, 291.

McCaffrey, B.J. (1981). Some Measurements of the Radiative Power Output of

Diffusion Flames, Paper No. WSS/CI 81-15, Western States Section,

Combustion Institute, Pullman, WA.

-43-
McCaffrey, B.J. (1983). Momentum Implications for Buoyant Diffusion Flames,

Combustion and Flame 52, 149.

McCaffrey, B.J. (1984). Jet Diffusion Flame Suppression Using Water Sprays,

Final Report, NBSIR 84-2812-1, U.S. Dept, of Commerce, Washington, DC,

July 1985; also, Combustion Science and Technology 40, 107.

Peters, N. and Williams, F.A. (1983). Liftoff Characteristics of Turbulent

Jet Diffusion Flames, AIAA J. 21, 423.

Ricou, F.P. and Spalding, D.B. (1961). Measurements of Entrainment by

Axisymmetric Turbulent Jets, J. Fluid Mechanics 11, 21.

Santoro, R.J. (1986). Personal communication.

Schuller, R.B., Nylund, J., Sonju, O.K. and Hustad, J. (1983). Effect of

Nozzle Geometry on Burning Subsonic Hydrocarbon Jets, in Fire Dynamics and

Heat Transfer, Ihe 21st National Heat Transfer Conf., Seattle, July 1983,

p. 33.

Sonju, O.K. and Hustad, J. (1985). An Experimental Study of Turbulent Jet

Diffusion Flames, in Dynamics of Flames and Reactive Systems, ed.

Bowen, J.R. , et al., Vol. 95, Progress in Astronautics and Aeronautics.

Suris, A.L., Flankin, E.V. and Shorin, S.N. (1977). Length of Free Diffusion

Flames, Combustion Explosion and Shock Waves 13, 459.

Vanquickenbome, L. and van Tiggelen, A. (1966). The Stabilization Mechanism

of Lifted Diffusion Flames, Combustion and Flame 10, 59.

-44-
6 . NOMENCLATURE

A

c

2

D

f

D

d

b

d

e f(D)

F

Fr

8

Hf

H

s

AH

k

f

Lf

•m

M

• •• q

Q

qrad

r

R

H

Su

T

T

f

area ratio, A^/A^q

constant in Kalghatgi's lift-off correlation, Eq. (5)

flame diameter

burner diameter

burner diameter

effective burner diameter in chocked flow situations, Eq. (1)

flame geometric factor, e.g., mean beam length

radiative view factor

Froude number U^/gD

gravitational acceleration

flame height

distance from burner exit where mean fuel concentration falls to

stoichiometric level H = [72.7 ( P / P^)

1 / 2 + 5.8] d for a pure CHa

jet

heat of combustion

extinction coefficient

lift-off height

mass flow rate

exit Mach number after expansion

incident radiant flux to a target

nominal heat release rate, net calorific potential of fuel

that portion of Q radiated away

water to gas mass flow rate ratio

Reynolds number based on lift-off height = S,Use • H /v

maximum laminar flame speed (0.39 m/s for CH^)

temperature

flame temperature (radiation model)

-45-
AT T-T^ temperature rise above ambient

U exit gas velocity

U

g

blowoff velocity

1.5

V general stream velocity

x lateral distance from flame

z vertical distance above burner exit plane

a flame emittance or absorption

Y ratio of specific heats (1.31 for CH^)

p density

Becker & Liang's flame height correlation parameter

a Stef an-Boltzmann constant

v kinematic viscosity (110 yp for CH^ near ambient)

<J> variable density ratio of spray to gas

X radiative fraction

Subscripts

d, D dry conditions, i.e., no spray

e conditions at jet exit

“ ambient

CH^ referring to methane

H

2 O referring to water

w, W wet conditions, i.e., being sprayed with water

o source flow in sprayed systems, gas plus water

ent entrained

U /p

non-dimensional gas velocity at blowoff = TM ( —

u ' P

-46-
Figure 1. Schematic of experimental facility

47
09

U

09 3

5" 09

fO

(0 09 M09

«*

3 >» O .

</» “

3 «0

</i

cn

v

LA

3

09

s

co

i

*

B (Q

LA

co O 0

c mmai

3 O0 +

LA

cn

JS CD cn

8) ii ii 15 09 09

is is

CO

II CO

II09

3

o»

CD

1A

E

E

cn

04

00 CO

^

04

Figure 2. Flame stability and blowoff characterization for mechd
inO

'tO

coO

CM

q/*h

Figure 3. a/ ,_

i Flame and lift-off heights vs Froude number

49

U

2

/(gD)
Lf/U

(ms)

10 1 I TT - cm 4 -

2<>i

1.0

^

10

A9 j

11

'f* t

7 5 | ^3 Q3

02

^ <> 5

'f

1

'j59

O4

>1

18

0.5

0.2

As

> Present

Horch (Peters & Williams)

O Annushkin & S\/erdlo\/

O Kalghatgi

V Lockwood & Moneib

A Vanquickenborne & Van Tiggelen

0.1 J I L , - 1 LL

5 10

D (mm)

20

Figure 4. Present and literature summary of methane lift-off

height data

50
CSj

CO

6

CD

o

6

CVJ d

o

_i

i N

(X) IV

Figure 5. Centerline temperature rise vs scaled height

51

H,-L,
1600

1500

1400

1300

1200

(MW) O

Figure 6. Peak temperature vs nominal heat release rate (symbols

follow Fig. 5)

52

1/Tmax

x

10

4

(K"

1)
90

( 2 luo/m) xmd iNdaiONi

Figure 7. Incident radiant flux to two targets as a function of

fire size

53

Q

(MW)
80 6

co in CO O O o O

6 o

• o

• o O O o o

in CO C\J

T— T“ T— y—

(t-W)

(») *1

Figure 8. Flame extinction coefficient and temperature for a fixed value of the other as a function of fire size

54

Q

(MW)
90

( t _ui) 1>)

(>0 *1

Figure 9. Derived extinction coefficient (upper portion) using

smoothed temperature data from Fig. 6 (lower portion)

vs heat release rate cc

Q

(MW)
*>) Nl 3DNVH0 3AI1V13H

Figure 10. Sensitivity analysis of flame radiation model to

various parameters

56

0.7

0.8

0.9

1.0

1.1

1

RELATIVE

CHANGE

IN

H

f>

D

f>

T,
0.25

COO

o o m

C\J *“ T” o

6 o d o

Figure 11. Predicted decreasing radiative fraction compared to

literature data plotted as a function of the square root

of Proud e number r 7

U//gD
1200

1000

800

600

400

200

0

1200

1000

800

600

400

200

0 1 2 3 4 5

Z (m)

Figure 12. Centerline temperature rise vs height with and without

water spray (Q 1.2 and 2.3 MW)

58
1200

1000

800

600

400

200

0

1200

1000

800

600

400

200

0 1 2 3 4 5

Z (m)

Figure 13. Centerline temperature rise vs height with and without

water spray (Q 2.7 and 4.6 MW)

59
1600

O

00

o

c\j

in co C\J O) oo co lo CO

(>l) 1

Figure 14. Reduction of peak temperature with water flow race

60

mH

2

o/mcH4
4.0

a Z/M Z

. Fractional increase in lift-off height due to water

spray as a function of mass flow ratio

61

Figure 15

^houi/oZhui
o

CO

o

c\i

o

co co

6 6

Tj" CM

d 6

o

*( a l/ M±) ‘a

( b/M

<(

b

Figure 16. Normalized incident flux and flame temperature reductions

TS VO^CH, 2 4 62

rhH

2

o/riicH4
> 1 1 1 © I O o o

°

co c\i

Figure 17. Increase in flame absorptivity as a function of both water

flow rate and the difference between the heat flux and

T* readings

63

0.2

0.3

0.4

q'W/q'D

-

(Tw/T

d)

4
Pw

(ATM)

1.0

0.8

0.6

0.4

0.2 -

0.1

0.08

0.06

0.04

0.02 -

0.01

0

0

*6

r a

1.0

Pw (solid symbol) -

::

a h2 o (open symbol)-

2.0 3.0

mH2 0/^CH4

Figure 18. Water vapor emissivity and partial pressure plotted against

the water to gas flow ratio

64
1000 ooo OOO o oooo o o oo co CM O O 00 CD Tf CM *-

00 CD

^

CM T-

(siu0iuajnsB0^ 0jn;Bj0dui0i $ uoiiBipBy) 0 qj/in3uj

Figure 19. Derived entrainment rates vs predictions of Ricou and

Spalding (1961) using effective source pV

65

rhENT^o

(Calculated)

14A 'REV.

U.S. DEPT. OF COMM. 1. PUBLICATION OR

REPORT NO.

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

BIBLIOGRAPHIC DATA

SHEET (See instructions) NBSIR-86/3442 * November 1986

4. TITLE AND SUBTITLE

Momentum Diffusion Flame Characteristics and the Effects of Water Spray

5. AUTHOR(S)

B. J. McCaffrey

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

National Bureau of Standards

Department of Commerce

Gaithersburg, MD 20899

7. Contract/Grant No.

8. Type of Report & Period Covered

9.

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Department of Interior

Minerals Management Service

Res ton, VA

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 literature survey, mention it here)

For water spray suppression of gas well blowout fire applications^ reasonably

large scale (1-10 MW) methane diffusion flames have been investigated near the high

Froude number limit. Flame blow-off has been observed with pipe sizes to 30 mm

diameter. Flame and lift-off heights, centerline temperatures and incident radiative

flux to nearby targets have been measured with and without water spray suppressant.

Using the Dayan-Tien formulation for a cylindrical flame model an effective gray

absorption coefficient approaching 0.2 m was determined at the blow-off limit. The

derived shape of the functional dependence of decreasing radiative fraction with jet

Froude number in the limit is consistent with small scale experiments.

The effect of spraying water internal to the flame envelope at the base is to

shift or raise the flame above its normal position and to lower peak flame temperature

and radiation levels despite increased absorptivity due to the radiativelv active

steam. Extinguishment near blowoff is thought due to te former effect. Calculations

of flame entrain.ment based on increased water vapor emission are consistent with

literature estimates of entrainment when account of the effects of buoyancy due to

the liquid spray is provided.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

blow-off, blowout fires, diffusion flames, entrainment, extinguishment,

radiative fraction, suppression, water sprays

13. availability

[jy<jUnlimited

i For Official Distribution. Do Not Release to NTIS

| Order From Superintendent of Documents, U.S. Government Printing Office, Washington, Q.C.

20402.

[XI Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

71

15. Price

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