NBSIR 79-1910

Purely Buoyant Diffusion Flames:

Some Experimental Results

Bernard J. McCaffrey

Center for Fire Research

National Engineering Laboratory

National Bureau of Standards

Washington, D.C. 20234

October 1979

Final Report

U S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

not e*r -#e t

&&iCO

NBSIR 79-1910

PURELY BUOYANT DIFFUSION FLAMES:

SOME EXPERIMENTAL RESULTS

)C\~\C\ |Q

Bernard J. McCaffrey

Center for Fire Research

National Engineering Laboratory

National Bureau of Standards

Washington, D.C. 20234

October 1979

Final Report

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Luther H. Hodges, Jr., Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

TABLE OF CONTENTS

Page

LIST OF TABLES ' iv

LIST OF FIGURES iv

NOMENCLATURE . V

Abstract 1

1. INTRODUCTION 2

2. INSTRUMENTATION AND PROCEDURE 3

3. RESULTS AND DISCUSSION 5

3.1 Center Line Velocity and Temperature Rise 5 3.2 Radial Variation of the Data 11

3.3 Effect of Floor and Ceiling 17

3.4 Nature of the Signals 18

3.5 Entrainment and Heat Release 21

4. SUMMARY AND CONCLUSIONS 24

5. ACKNOWLEDGEMENTS 25

6. REFERENCES 25

iii
LIST OF TABLES

Page

Table 1. Summary of center line data 27

Table 2. Comparison to previous work, plume,

center line-axisymmetric 28

LIST OF FIGURES

Page

Figure 1. Center line velocity vs height 29

Figure 2. Center line temperature rise vs height 30

Figure 3. One-second time exposed flame photos vs heat release

rate 31

Figure 4. One and one-third seconds of cine film (24 frames/s)

showing 3 Hz (eight frames) oscillation 32

Figure 5. Width of velocity profile vs height 33

Figure 6. Velocity profile in plume 34

Figure 7. Velocity profile in intermittent region 35

Figure 8. Velocity profile in flame region 36

Figure 9. Temperature rise in space coordinates, Q = 22 kW 37

Figure 10. Temperature rise in space coordinates, Q = 45 kW 38

Figure 11. Velocity and temperature rise vs height for simulated

floor configuration 39

Figure 12. Unprocessed, time-averaged, RMS, and auto-correlation

signals of Ap output 40

Figure 13. Power density spectrum and energy distribution of

pressure signal vs frequency 41

Figure 14. Time-averaged and RMS component of pressure signal

axially and radially 42

Figure 15. Entrained mass flow vs height for various heat

release rates 43

Figure 16. Normalized convective flux vs height for various heat

release rates 44

iv
NOMENCLATURE

b intercept (at burner) of x

]_/ e vs z width line, m

0 ^ specific heat, J/kg K

C buoyancy constant = V/ ^

2gzAT/TQ

d diameter of burner, m

o

2 F source Froude number - u /g d

o o o

F

q

source buoyancy rate parameter - gQ/(p Q CpT

o

) 2 g gravitational acceleration, 9.8 m/s

2 h convective film coefficient, kW/m K

k coefficients for center line correlations, various dimensions

n exponent of center line correlations

m slope of x

]ye vs z width line

n exponent of exponential radial profiles

2 Ap total or stagnation pressure minus static pressure, N/m

Q nominal heat release rate or net calorific potential of fuel gas, kw

r radius of burner, m

oT absolute temperature, °K

AT temperature rise above ambient, °C

u

q velocity of gas leaving burner surface, m/s

V,v flow velocity, m/s

x traverse distance from center line, m

x l/e distance from center line where the value of the variable equals 1/e of

the value on the center line, m

z vertical height above burner, m

Eg effective gaseous emissivity

p density, kg/m^

t averaging time, s

x auto-correlation time delay, s a

V
Subscripts

o ambient

o center line values

o initial conditions at burner surface

v designating velocity profile when referenced to x

i/e AT designating temperature profile when referenced to x

±/e

c designating buoyancy profile when referenced to x

i/e

Superscripts

time-averaged values

' instantaneous values

vi
PURELY BUOYANT DIFFUSION FLAMES: SOME EXPERIMENTAL RESULTS

Bernard J. McCaffrey

Abstract

Measurements of temperature and velocity using

thermocouples and an impact probe were made in the near

field of a purely buoyant diffusion flame produced by

a porous refractory burner. Based on time-averaged

center line value of V and AT together with photographic

records the flame can be conveniently divided into three

distinct regimes: (1) a continous flame region, starting

from the surface of the burner with V equal to zero at

the surface and rising with the height above the burner,

z, to the 1/2 power. AT is constant over this regime.

Higher up is (2), an intermittent regime, with pulsating

flame ( ~ 3 Hz) exhibiting approximately constant V and

AT falling with z to the first power. Still higher is

(3) the plume region which is, most of the time, free of

-1/3 -5/3 flames with V ~ z ' and AT ~ z as predicted by

conventional plume theory. Throughout the three regimes

and indistinguishable among these is the consistency of

the buoyancy relation, V/ ^

2gzAT/T

Q which has a value

of approximately 0.9, a factor of 2.5 times previous

estimates in the flame region and confirming the recent

correlation measurements of Cox [ 1

]

1

. Different heat

release rates, Q, can be scaled to a "universal" fire if

2 /5 the length is normalized as z/Q and the velocity scale

as V/Q'*' 7^. The flame regime is thus independent of Q.

In the radial direction for time-averaged quantities

only the plume region appears reasonably Gaussian. The

data in the flame and intermittent regimes do not fall

as rapidly as that dictated by a Gaussian distribution.

In all three regimes the velocity profile is wider than

the temperature profile.

Large scale, low frequency Ap fluctuations are about 35% of the time-averaged signal on the center line

throughout the three regions. Radially the fluctuating

"''Numbers in brackets refer to literature references listed at the end of

this report.

1
to time-averaged signal ratio rises from the center line

value and approaches 100% in the wings. Elementary

spectral analysis indicates that most of this energy is

concentrated in a narrow band centered around 3 Hz.

Implications of these results for flame entrainment

calculations and heat release rates will be discussed.

Key words: Buoyancy; diffusion flames; fire entrainment;

flame oscillations; plume; scaling.

1. INTRODUCTION

Most studies of diffusion flames have been concerned with combustion

systems having fuel source injection rates characterized by high initial

momentum; the gas leaves the burner surface with substantial velocity in a jet-like manner. A free burning fire' such as would occur over a liquid

pool or slab of polymeric material, on the other hand, will be totally

dominated by buoyancy; the fuel leaves the surface with negligible velocity.

To date no satisfactory analytical scheme appears capable of accommodating

buoyancy with combustion and few experimental results exist for these

diffusion flames especially in the near field (the region immediately

adjacent to the fuel source) . Point source plume theory which is expected

to be valid far from the source will be inadequate in this region for most

finite-size fires, e.g., in an enclosure fire situation the flames will

extend to a significant portion of the height of the enclosure. The

region of interest in this case is the accelerating near field. Radiation,

the size of combustion zones and flame length, air entrainment, mixing and

other physiochemical processes governing the behavior of these fires are not well understood. Accurate knowledge of the flow in the accelerating

region may lead to better understanding of these phenomena.

Spatial and temporal non-uniformity due to large-scale, low frequency

eddy motion with little preferred direction, especially at the edges of the

flame, coupled with the tendency of these systems to be very susceptible to

ambient disturbances makes measurements and their interpretation extremely

difficult. Cox, at the Fire Research Station, Borehamwood, England where

most of the present measurements were made, is using cross correlation

techniques to probe the flame. Terai [2] also using cross correlation is

investigating the near field of finite-size pool fires. Heskestad [3] has

made some measurements using a pitot-static tube approaching the flame

2
region of both a wood crib and a methanol pan fire. Yokoi [4] in a classic

study of the subject has made temperature measurements in the flame above a finite area source.

The purpose of the present work is to add to and extend the utility of

the above collection of data. Modeling schemes will remain suspect until a reliable set of data becomes available which will provide comparisons at

least for the gross structure of buoyant diffusion flames. There are in

addition short term requirements of fire research which necessitate the

quantitative understanding of air entrainment in order to complete the flow

portion of Enclosure Fire Models [5]

.

The present study consists of measurements made in the flame of a single burner where the amount of gas could be varied thus simulating

materials with different burning rates per unit area. Source Froude number

9 —6 —4

(Fv = u /g d ) varied from about 10 to 10 thus insuring a simulation

o o' ^ o of truly buoyant behavior.

2. INSTRUMENTATION AND PROCEDURE

The burner using natural gas (35 kJ/£) at various controlled rates was constructed of a porous refractory material 0.30 m square. It sat 0.75 m

above the floor and under a passive hood in a large laboratory. Visually

non-axisymmetric behavior could be observed only very close to the burner

surface. The instrumentation was located over the center line of the burner

using a plumb bob. Thereafter, vertical and side to side movement of the

instrument cluster was accomplished with a micrometer lathe-type movement

device which held the pressure probe and thermocouple.

Velocity was measured using a bidirectional pressure probe [ 6 ] which

responds like a pitot-static probe except the measuring area is quite large

(0.016 m diameter) which spatially averages the signals in order to obtain

the gross structure of the flame. In addition to the spatial averaging,

the output of the electronic manometer was time-averaged through a filtering

voltmeter where averaging times of up to 100 s were possible. This was

quite sufficient for a steady center line reading. In the wings of the

flame however, additional averaging was required due to ambient disturbances

and this was accomplished by taking the 100 s averaged output and displaying

it on a slow writing oscillograph and observing the signals for several

minutes until a faired signal could be obtained. No attempt was made to

totally isolate the flame from laboratory disturbances. The extent and

duration of disturbances could be monitored both visually and from the

oscillograph, and data recorded during these distrubances was not used.

3
Temperature rise was measured using a large thermocouple (1.0 mm SS

sheath) with the chromel-alumel junction welded to the sheath (nominal time

constant approx. 3s). No further damping was provided. The thermocouple

(mv) reading was displayed similar to the time-averaged pressure signal on

the slow writing oscillograph. Again, a faired averaged value of AT was then obtained. The majority of the results presented here are for timeaveraged quantities^ instantaneous values of pressure are discussed in the

appropriate section of the text.

There are notable difficulties with this kind of measurement of velocity,

i.e., using pressure and temperature for density. Firstly, in the high

temperatures of the flame the Reynolds number of the flow around the pressure

probe can go as low as a couple of hundred. Reference 6 contains a low

Reynolds number calibration which could be used to correct for these effects.

The results would be a maximum velocity error of about + 15% near the

burner surface with the error decreasing in going further above the surface

where velocities are rising. However, the calibration was not used due to

the strong oscillatory nature of the pressure signal (see "Nature of the

Signals" in Results Section) . The thickening boundary layer associated

with lower Reynolds numbers may not be sustained due to the strong pulsations

at 3 Hz present in the flow field.

Secondly, pulsations and turbulence can cause significant errors in

the measurement of velocity using pressure probes. For a nonlinear

2 relationship between signal and measurement property (Ap = KV ) an error

will be generated in the time-mean property of a fluctuating flow. For

constant density and when the pulsating frequency is low compared with the

turbulence frequencies this error can be shown to be small, e.g., 4% for a 40% RMS amplitude of velocity oscillation. However, the flame situation is

not so simple. At any position in a stationary flame the time-mean values

of density and velocity are constant but both may fluctuate independently

and in unknown correlation. Taking the time average of (Ap + Ap '

)

=

- - 2 K (

p

+ p '

)

(V + V') , for example, will lead to indeterminate correlations

even ignoring composition changes. The scale and intensity of turbulence

is virtually unknown in the lower regions of these systems.

The large size and slow time response of the instruments may tend to

help diminish the effects of this fine scale energy until some of these

effects may be resolved in future work.

Finally, thermocouple errors due to strong radiative interaction

will be difficult to assess. The center line value of temperature indicated

4
by the thermocouple will tend to be lower than the actual flame or gas

temperature due to radiation from the thermocouple through the gas to the

surroundings. These errors will be minimized in areas where the gaseous

absorption coefficient is high (thickest flames) and the convective coefficient is high (velocity high) . Coming up out of the flame the local

absorption coefficient will probably be decreasing whereas the velocity

will be increasing and hence the two will tend to compensate. Also radiation

error will decrease significantly still further up where the temperature is

falling significantly. The order of error for these typical flame conditions

2 will be about 20% at T = 1300 K assuming h ~ 0.1 kw/m K and e ~ 0.15.

gas g

The thermocouple will be reading about 1000 K.

In the wings the radiation error will be in the opposite direction,

the indicated temperature will be higher than the true gas temperature.

The thermocouple will be out of physical contact with the flames in the

slower moving entrained and mixed gases and will be dominated by radiation

from the nearby "wall" of flames. Future measurements using different size

thermocouple beads as well as an aspirated probe will be required to

accurately assess errors and effective gaseous emissivities in the radial

direction. Fortunately, in the calculation of velocity the square root of

the absolute temperature is used and hence in the wings, as the temperature

approaches ambient, the thermocouple errors will not be critical.

In spite of all these difficulties the pressure probe should provide a simple means of obtaining the gross structure of the flames in the form of

a consistent set of data which can be modified as more refined and detailed

information about buoyant combustion becomes available. Velocity will be

calculated as a constant times the square root of the product of the timeaveraged differential pressure and the time-averaged absolute temperature.

3. RESULTS AND DISCUSSION

3.1 Center Line Velocity and Temperature Rise

Figures 1 and 2 present the time-averaged center line velocity and

temperature against height above the burner, z, for five values of gas

flow, Q. (Hereafter Q will be referred to as the heat release rate or fire

size even though in fact it is only the calorific potential supplied to the

burner) . The scaling factors and for V and z are purely empirical

findings - coming directly from a consideration of log-log plots of V and

AT against z for the individual fire sizes. Upon plotting V and AT versus

z (not shown) , two regimes of data immediately become clear. For large

5
values of z, the plume region, the data exhibit the characteristic z

7 -5/3 and z variation for V and AT dependence. The other region is for the

points in the flame, small z, which show a remarkable tendency to cluster

around a line with slope plus 1/2 for V and zero for AT. Using cross correlation of temperature and flame ionization fluctuations Cox found the

identical behavior. Drawing a line through only points that are obviously

in the plume and another through only points which belong to the n = 1/2 or flame regime leads to an intersection falling higher than the intermediate

points which belong to neither regime. This intersection will define a velocity, which will be higher than the data and a height, z^. There

will be two z.'s: one from the velocity plot and one from the temperature

1 -5/3 plot (the constant flame temperature intersecting with the z

' plume line

will define another z^ but not a AT^ since that is the flame temperature

extended). The two z^'s turn out to be nearly identical. If this is done

for all the different Q's, and then and z^ for each are plotted against

Q the result will be that will vary with Q to the 1/5 power and z^ with

Q to the 2/5 power, thus establishing the proper scaling. If instead of a single z. two values of z for each Q are chosen corresponding to the location

1 1/2 where the data ceases to follow firstly, the flame z

' line, and secondly,

-1/3 the plume z line, then these can be plotted against Q. Both of these

2/5 again result in a Q

' relation. Like z^ there will be an additional set

of intersections from the temperature data. The agreement between the

velocity and temperature derived values of z^ at the intersections is good.

The functional relationship of V and AT with z in the intermittent

regime is not as straightforward as it is in the other two regions. For

convenience a zero slope for V and a slope of -1 for AT was arbitrarily

chosen. In reality these may vary, i.e., the actual velocity relationship

is probably a curving line or cap connecting the flame and plume rather

than the straight line with two sharp transitions. What is clear however

is that the buoyancy relation V/-J 2gzAT/T = constant must guide any choice

. ^ 2 ° m this regime as well as the other two . Substituting the data, i.e.,

values of V and AT, into this expression will result in a constant at all

values of z. The constant is preserved point by point throughout the

entire field and hence V(z) and AT(z) must be consistent.

1/2 The points on figures 1 and 2 which fall below the z

' line of V and

the constant AT vs z line were for z very close to the burner surface

2 r

z For a simple hydrostatic pressure variation p = p -g / pdz or Ap ~ -gApz,

° Jo

Using Bernoulli's equation and the ideal gas relation, this becomes:

2 AT i 1/2 pV ~ gp Q — z or V/ yj 2gzAT/T

Q

= C.

6
(0.045 m) where a very fuel-rich condition exists in the center. It is

actually possible to see a cone-shaped region or core of non- luminous gas

just above the burner surface surrounded by a flame envelope near the

edges. The larger the gas flow the greater the deviation from the behavior

of the flame region further up, i.e., the greater the fuel-rich volume

above the burner.

Reiterating and relating the results to what one observes visually,

the purely buoyant diffusion flame above a finite area source can be

divided into three distinct regimes. In terms of time-averaged center line

velocity and temperature the lowest regime of continuous flame is characterized by constant temperature and a velocity starting off with a value of zero at the burner surface and rising proportional to the height above the

burner to the 1/2 power. Above this zone the flame is intermittent in

appearance and clumps of visible flame are seen to rise periodically from

the continuous flame zone at a regular frequency of a few Hz. Velocity in

this region is nearly constant and temperature drops with height at a rate

proportional to the first power of z. At about the point where the "broken

off pieces" of flame of the intermittent region cease to be visible the

-1/3 -5/3 third region begins. Conventional plume theory (V ~ z '

, AT ~ z '

) describes this non-luminous region adequately.

Time-averaged center line velocity in all three regimes can therefore

be derived from static pressure differences due solely to buoyancy, i.e.,

^2gzAT/T

Q

. The value of the proportionality constant is very high,

V/ ^

2gzAT/T

Q ~ 0.9 and virtually invariant throughout, from the plume

region through the intermittent zone right down through continuous flames

to the base of the burner.

For larger and smaller fires from the same size source scaling with

the heat release rate, Q, will reduce all data to a universal curve. The

length scale becomes z/Q and velocity is normalized as V/Q^^ with AT

invariant with Q when viewed in the proper length coordinate. The three

regimes then will be distinguished by two intersections or constant values

2/5 of z/Q . For the flame region alone both V and AT are independent of

fire size, Q, and presumably only dependent on burner area and fuel type.

Fire size enters only in determining how high or long this continuous flame

region will be.

Table 1 presents a summary of all the center line data and the weighted

average values of the coefficients of the various expressions found for the

three regimes from the five fire sizes. The solid lines on figures 1 and 2

7
are taken from table 1. Use of a third significant figure in the numbers

is probably optimistic here but perhaps might be useful in picking out

slight trends in such a large array of data.

In the flame region, which is independent of Q, the precision is

excellent, on the order of 1%. Note that those points in the fuel-rich

region very near the surface of the burner which fall below the major trend

of the data have been ignored. In the intermittent and plume regime there

exists a tendency for both temperature correlations, ATz/Q 2 ^and ATz^/^/q^/-^

to increase slightly with fire size resulting in a decrease in the buoyancy

relation, V/ ^2gzAT/T

Q

. This tendency can be seen on figure 2 where the

higher Q points rise above the solid line. A possible reason for this

anomaly could be thermocouple (TC) radiation error decreasing with fire

size. Recall that center line temperature will read low. The width or base

of flames "seen" by the thermocouple from above will increase with Q. The

effect of this component will be more pronounced in the intermittent and

plume regimes. Note that velocity, as expected, appears to be little

affected by temperature error since V varies with the square root of the

absolute temperature whereas the buoyancy relation varies with the square

root of the temperature difference. The averages will be heavily weighted

toward the smallest fire (Q = 14.4 kW) since more data is available for it.

The errors in the final averages for temperature will therefore be in that

direction. A summary of the center line data is:

Flame

Intermittent

Plume

6.8

1.9

1.1

m

1/2

m

s kW

m

175

4/3

s kW173

n

1/2

0

-1/3

z/Q2/5 m/kW2//5

<0.08 .

0.08-0.2

[ C

> 0.2 '

0.9

Both the flame-intermittent intersection z/Q 2 ^ 5 = 0.08 m kW 2//5 and

the intermittent-plume intersection z/Q 2//5 = 0.20 m kW 2/^ 5 show good agreement as calculated by velocity and temperature correlations. How well this

demarkation of regimes relates to what one might observe visually can be seen in figure 3 where z is plotted against Q for the two intersections.

The lines are superimposed on 1 s time exposed photographs of the five

flames. One second exposure appears to be a good compromise between the

exposure being too fast and getting too few representative cycles of the

pulsating motion, and too slow and emphasizing atypical bursts of flame

8
outside a representative or average envelope. The 45 kW fire for example

shows a large protrusion of flame beyond the marking stick on the right

hand side of the picture, which is rarely present.

The tip of visible flame in the 1 s exposure comes just about equal

or slightly lower than the velocity measurement-determined intermittentplume intersection, z/Q^5 = 0.2 m kW 2// ^, and hence this definition or criterion might lead to a less subjective or more quantitative measurement

of flame length. Substituting this intersection into the correlation for

temperature rise in either the intermittent or the plume region leads to a flame tip temperature rise of AT = 320° C which compares very favorably

with previous work [7] . In that same study with a larger fire (250 kW) using

a similar burner Thomas presents a flame height of 190 cm using mean

values of the location of the flame tip from photographs. The present

2/5 correlation would yield 0.2 x (252) ' = 1.83 m which is again slightly

lower but probably within the scatter of the photographic records. Extrapolation of these flame length relationships to larger fires then would seem

reasonable to at least a factor of five on heat release rate or source

Froude number basis.

Nothing distinguishable, like flame height, can be observed on figure 3 2/5 -2/5 for the lower, flame-intermittent intersection, z/Q = 0.08 m kW /

, since the intermittent region will be completely exposed in a one-second

photograph even for these low frequency pulsations. Consider, rather,

figure 4 which shows a series of about one and one-third seconds of con- secutive frames of motion-picture (24 frames/s) film of the flame. The

heat release rate for this fire is 33 kW and the two intersections will be

at 0.3 and 0.8 m. These can be located by the black flags on the measuring

stick seen on the right side of the picture. The flags are 0.2 m apart.

Most of the motion then should range midway between the first and second

flag up to the fourth flag. Given the small sample size and the fact that

the flame is seen in two dimensions, the contention that continuous flame

exists up to 0.3 m is somewhat demonstrated in the photos. The nature of

the intermittent regime is clearly illustrated. Mote that the photos have

been deliberately arranged in groups of eight each. (But they are consecutive, the first frame on the left in any row follows in time the last frame

on the right in the previous row.) Across any row is one cycle of the

eruption, stretching, and finally breaking of the flame envelope - the

pulsation or oscillation associated with large diffusion flames. Eight

frames per cycle corresponds to a period of about one-third second. If the

length of the intermittent region, (0.20 - 0.08) m kW

2 / 5

, i s divided by

the period, the velocity of flame travel will be obtained. (This is the

9
flame movement as viewed in a picture, not a flame propagation velocity)

For the data here this number ranges from 1.1 to 1.8 m/s. From table 1 the

gas velocity in the intermittent region ranges from 3.3 m/s to 4.3 m/s, a factor of 2-1/2 to 3 times larger. Hence measurements based on photographing

flame travel will be considerably low [12]. (For the buoyancy constant, C,

0.9/0.36 = 2-1/2. The constant 0.36 is an often quoted literature value.)

For a non-luminous flame the intersection of the two lower flame regimes

may be visually quite indistinguishable. The inward necking or pinching

and separation from the anchored fuel-rich core near the burner may be

difficult to observe without the naturally occurring soot "tracer" seen in

the present photographs (see reference 16)

A comparison of the present data with some previous work is shown on table 2. Only the plume region has been investigated to any extent with

the exception of Heskestad's work whose measurements extended into the

flames. The results are presented in terms of a source buoyancy rate

parameter [9] , F

q = gQ/p oCpTQ

. Note the third column is independent of heat

release rate, Q, whereas the fourth column is independent of distance from

the source. This is a result of some practical importance and is discussed

in detail by Heskestad who has collected data for a large range of fire

sizes, Q = 40-25000 kW. The present results indicate that V/ (QAT)

ceases to be a constant in the intermittent regime and is a function of z equal to (1. 93/62 . = 0.843) or 0.843 (z/Q 3//3

) (see table 1). Between

the two intersections, z/Q 3// ~* = 0.08 to 0.2 m kW v/(QAT)^3 will rise

from 0.51 at the flame-intermittent intersection to 0.61 in the plume.

Perhaps the low value, 0.50 of reference 3 represents some kind of average

of both plume and intermittent data.

The present data are most like those of Yokoi, falling about 5% lower

in velocity and 12% lower in temperature. One major difference between the

two experiments is flame radiation - alcohol burns with little soot radiation

while the present gas flame was very luminous. Significant flame radiation

could decrease the amount of energy available for buoyancy in the plume.

Since V and AT depend on heat release rate differently it is possible to

estimate the effective or buoyancy component of Q: comparing Yokoi and the

present results from table 2 (3. 7/3. 9)

3 = 0.85 and ( 8 . 0/9 .

) 3 ^2 = 0.82.

(Note that a small increase in ATz 3//3

/Q

3//3 from table 1 could bring the

reduction in Q up to 0.85. Recall that the mean values in table 1 are weighted in favor of the smallest fire where center line temperature errors

due to radiation are suspected to be largest.) This indicates that in the

order of 15 to 20% of the heat release is lost in the form of flame radiation

in the present experiments and does not contribute to buoyancy. Note that

10
Yokoi's temperature data has recently been confirmed by Zukoski [10] for a completely premixed flame system and hence the data of reference 8 appears

to be high. The value of 20% appears reasonable for a radiative component

for this system. Reference 11 presents measurements which yield, for a simple pipe burner, radiation loss of 3.3 kW/SCFM of CH

4 (1 CFM = 0.472 1/s)

and hence 3.3/(0.472 x 35) = 0.2. Obviously much more detailed analysis of

flame radiation including RMS volume and absorptivity measurements are required for more precise calculations.

3.2 Radial Variation of the Data

Horizontal traverses of time-averaged V and AT were made at various

heights above the burner spanning the three vertical regimes for two different

heat release rates, Q = 22 and 45 kW. With the exception of perhaps the

plume no single line through the data was judged to be an adequate fit to a

2 3/2 Gaussian representation of the data using x or x ' as independent variables.

As x increases away from the center line (bulk of flames) the data would

fall above a line determined by the near center data.

In order to obtain first a broad view of the spreading of the fire the

width where the velocity falls to 1/e of the value on the center line ( x

]ye

) was determined at each height. This was accomplished by interpolation of a faired line through the data since no single analytical characterization

using all the data for a single traverse could be found, i.e., x±/e will

be heavily weighted by the data in the "wings". On a plot of the width,

x l/e vs the height, z, no recognizable difference between the flame and the

intermittent regime was apparent due to the considerable scatter in the

data. So both regimes were lumped into one and a linear least squares fit

of x. , vs z was made for both sets of heat release data. The results 1/e

indicate that the larger fire has a larger x

±/e intercept, i.e., wider

base, and a smaller slope, i.e., it does not spread as rapidly, as compared

to the smaller fire. From the center line analysis the appropriate scaling

2/5 for height was determined to be z/Q '

. If that length scale is used the

2/5 linear fit can be expressed as x^/e

= mZ//<^ + b for both sets of data.

In this form the values of the two slopes, m, turn out to be remarkably

similar, within a few percent. This would indicate that the spread rate is

independent of heat release in the scaled coordinate and depends only on Q

through the initial width.

The intercept or initial width, b, at the same time, comes out to be a function of Q to very close to the 1/2 power. This is an important result

since most materials burning under the influence of their own flame radiation

11
will exhibit a constant burning rate per unit area, the so-called burning

velocity. That is, except for small samples, the larger the sample area

2 the greater the heat release rate, and Q ~ A ~ x , where x is a charactero o' o istic dimension of the source. Yokoi proposed for finite area sources the

scaling relation between the radius of the source, rQ

and the strength of

it as: Q/r2 and then showed by comparing data in the plume region for

alcohol lamps its validity for sources larger than about 10 cm. Terai has

flame height varying with r 4/5

intersections, z

for methanol pool fires. The present

2 Q

2//5

, will also follow x

q

4//5 if Q

1/2 -2/5 The present results, x

]ye Q ~ Q and slope ~ Q , means a smaller

fire starts from a smaller area but diverges at a faster rate than a larger

fire, perhaps because the smaller fire has less buoyancy generated momentum

in the wings. This result in fact may be more general than the use of a single sized burner might indicate. Here heat release ranged from 15 to 60

2 kW which corresponds to about 150 to 600 kW/m . This value for given

circumstances is fixed for a given material and depends on a multitude of

2 parameters. Cellulosics range from about 100 to 200 kW/m ; for ethyl

2 alcohol it is about 650 kW/m , and a commonly studied polymer, PMMA, is

2 about 530 kW/m for a large pool. Instead of using different materials in

different sizes which should yield, if the sample is large enough, similar

results, since the burning rate per unit area is constant, the burner can simulate different materials of a similar size by changing the gas flow or heat release rate. The flame shape above the burner appears to neck down

for small flow rates and to broaden for higher flows. Obviously the partition of radiative and convective energy will vary from material to material

and hence care must be exercised in interpretating the present results.

The radial results can be seen in figure 5 which is a plot of x, , vs 2/5 L ' e z/Q for the two fires. The solid lines through the data are the least

squares fit discussed above and only include the points in the flame and

intermittent regime. It is doubtful whether the lines are valid as drawn on

the figure very close to the surface of the burner since flow asymmetry may

begin to dominate here. Also some necking of the flow may be occurring as seen on the flame photographs (figure 3) . Recall that the time-averaged

results will include flame as well as cold entrained air passing the probes.

Since both sets of points yield the same slope the question arises about

the statistical significance of having two lines. By subjecting the

intercepts to Student-t statistics and also comparing two standard deviation

bands around the intercepts it can be shown that the lines are indeed

distinct. Note that it is not possible to obtain a single universal curve

of the width data as was done for the vertical direction data in terms of

heat release rates due to the area dependence of Q.

12
The plume data which horizontally appears moderately self similar is

shown by dashed lines originating from the center of the surface of the

burner. Recall that for distances far enough away from the source a plume

will behave independently of the source. The slopes, x-^/z, of the five

plume points average 0.195 with a scatter of + 6% which corresponds to an entrainment constant, a = 0.195 x 5/6 = 0.16, a rather high value. As

expected these values are independent of Q and will therefore not fall on a single curve in a z/Q 2 ^ 5 coordinate. Note that if the plume were not

totally developed and the five points were included in the least squares

analysis performed previously the conclusions reached there will not be

1/9 — 9/S

very different, that is, x n ~ Q and slope ~ Q

In terms of a virtual source, a position where the flow originates

below the burner, the distance will be almost a linear function of Q, the

exponent equal to 0.9. In this framework the entrainment coefficient (5/6

times the slope) for the flame-intermittent regime would be about 0.15 for

the smaller fire, decreasing to 0.10 for the larger fire. The numbers will

shift slightly if the plume points are included but the tendency for lowering

of a with increasing fire size will remain.

The plume radial data is shown on figure 6 where the velocity V at any

width x is plotted in similarity form, V/V

q vs x/z, where VQ

is the center

line value and z is the height above the burner. The lines represent a Gaussian distribution with three different entrainment coefficients which

bracket most of the data. With the considerable amount of scatter present

the futility of identifying a particular entrainment coefficent unequivocally

is obvious.

Figure 7 shows the intermittent velocity data where the x coordinate

has been normalized by the least squares expression for x^e

, not the individually determined values. With considerably more data than in the plume

regime the results appear to exhibit less scatter. An appropriate representation of the data might be the function exp [- (x/x^^

g

) 2//2] . There is not

a great deal of difference between the overall shape of the decaying

exponential function using 3/2 as opposed to 2 as the power of x. The

former will decay more quickly for values of x < x^/e

an<3 will decrease less

rapidly for x > x -]y e

a tendency noted in both the intermittent and flame

data. Yokoi actually proposes a 3/2 expression multiplied by a power

series of x/z for the distribution of velocity and temperature.

Finally, figure 8 presents the flame region velocity data. The scatter

is considerable. Near the center line the data indicate that a less rapidly

13
2 decaying function, e. g. , ( x/x i/e

) would be more appropriate. In the wings

the opposite condition is indicated, i .e. , 3/2 is too large. The data near

the center line and close to the burner show the same tendency as the center

line data did previously, i.e., the velocity and temperature in the fuelrich region fall below the tendency shown by data further away from the

burner. Likewise here when one moves horizontally away from the center line

into a more uniformly mixed region, V and AT rise above the center line

values before falling. This would be similar to probing the flame sheath

of a high velocity diffusion flame where the boundary of fuel and air is

sharply distinct.

In the flame and the intermittent region to some extent there is

confusion as to the shape of the profile in the wings. For example, on figure 8 for z = 0.287 (filled squares) the velocity falls away from the

center line up to x/Xjy

e = 0.86. The next data point, x/x

]ye = 1.03 is

actually at a higher velocity than the previous points. This is an exaggerated case but, in this region, there is a tendency for the curve to

"flatten out" before falling. That is, the velocity (and temperature)

remains nearly constant for a short radial distance before decreasing. It

is not clear if this phenomenon is associated with the large-scale eddy

motion seen at the edges but perhaps it might shed some light upon the

mixing process since these are long time averaged results. At present it

makes the determination of a distinct width parameter, x

±/e in this region

difficult.

In order to remove some of the arbitrariness of the above data

interpretation a numerical scheme was applied to the radial data. It consisted

of assuming that the data follows a decaying exponential, i.e., V/V

q

= exp [- (x/Xjy

e

) n

] whose n and xi/e are unknown. By taking logarithms twice a linear least squares fit could be made of the data yielding both n and x

±/e at each vertical position. The determined n was interesting. Near the

burner n was approximately 2.5 (indicative of the high values just off the

center line seen in figure 8) and fell with z to approximately 1.5 at the

start of the intermittent regime. In the plume it rises with z from 1.5 to

about 2 for the large z points. The values of x ]ye were not very different

from those obtained by visual interpolation except for some distortion

noted near the burner surface resulting from the "flattened" profiles noted

above. These results indicated that the previous data handling is probably

sufficiently accurate for the present overall view of the fire.

The temperature rise distribution in the radial direction is very

similar to the velocity distribution. If temperature rise at any x is

14
normalized by the center line value and plotted as in figures 6, 7, and 8 the results will be similar to the velocity results shown on those figures

with one exception. Throughout the three regimes and for both fire sizes

the velocity profile is wider than the AT profile. By finding the 1/e

value of the temperature rise distribution as was done for the velocity

distribution the two widths can be quantitatively compared. The mean for

all values at each height and fire size yields ( xi/e

)

x l/e^ AT

= 1,2 with

a standard deviation of 0.13. The difference in the widths is more or less

uniform throughout the plume and intermittent regime and becomes somewhat

less (~1.1) in the flame region. Thermocouple radiation error may be most

severe in the wings of the flame regime causing high readings and thus

appearing to bring the temperature profile close to the velocity profile.

The fact that the velocity profile turns out to be wider than the

temperature is contrary to the classical plume results [8] but recent work by

George et al . in the plume region of a heated jet also has (x^^

e

) v

/

(

x

i /e ) at

greater than one. There it was equal to 1.09 for a limited number of measurements. Also Terai finds the ratio to be about 1.3 for methanol pool fires

of this size. Plumes along walls also exhibit this behavior.

V

Since, on the center line, the buoyancy relation C 2gz AT/T

q

' remarkably consistent throughout the three regimes it will be worthwhile to

investigate its off-axis behavior in the radial direction. It might be

possible to estimate the loss of z-direction momentum to large-scale mixing

in the wings. The plume results of Rouse etal. can be recast in terms of

the buoyancy constant as:

and for George et aL [9]

For ease of comparison the previous expressions can be given in terms of an actual width, the xi/e value of the various distributions, e.g., ~ ——

z =0.102 z, etc. Also let the width of the C distribution be x. . /_,.

V96 1/e c From the definition of C and the assumed exponential profiles

15
xl/e/C xl/e/V

1/n

1 - 1/2 l/e^v

1/e^ATy

where n is the exponent of the width scale, x, in the exponential which is

equal to 2 in the expressions above. This will give an idea of how closely

the decay in buoyancy follows the decay in velocity. The present results

are compared with the previous two references in the following:

xl/e^V x l/e/C xl/e/AT

x l/eA/

YIH 1/1.16

George 1.09

Present 1.2

1.3

1.6

1.9 n = 2 2.0 n = 3/2

It appears then that the decay in C is significantly less than the decay in

velocity, the C profile being about twice as wide. Any radiation error

will tend to bring C closer to V but the high value for reference 9 where

no flame was present tends to indicate that more exact radiation corrections

X / would not alter this conclusion. Note the limits on l/e/ C for various

*1777

x / X / 1/e' V . The upper limit, C / C (x) , i.e., x ±/e ^

00 is for 1/e' V equal

Xl/e// AT xl/e// AT

to 2^' //n

, e. g. , 1.4 for n = 2. Going the other way,

xl/eA/ decreasing

x l/e^AT

through 1 (reference 8) toward 0,

approaches that of velocity.

x

x 1/e^C approaches

1/eA/

1 , the decay rate of C

Instead of plotting AT in the x direction for the three regions which

will be virtually identical to the velocity figures 6, 7, and 8, except for

the smaller width, it might be more instructive to plot isotherms in actual

space coordinates, z vs x. Figures 9 and 10 do this for both fire sizes.

The x-axis is greatly exaggerated (5x) so that the detail at the base of

the burner can be distinguished. The dots on the figures are interpolated

values at hundreds of degrees, the curves are simply faired representations

through the dots. Interpolated values from the center line scanning are also shown by dots on the ordinate. The three vertical regimes are marked

on the figures. For the larger fire, figure 10, the fuel-rich region near

the base of the burner characterized by lower AT close to the center line can be clearly distinguished. The maximum temperature occurs some distance

16
from the origin. For the smaller fire it would probably take a traverse

closer to the face of the burner before this behavior could be seen.

Comparing figures 9 and 10 to figure 3 which shows the 1 s time

exposed photographs, it is possible to sketch the visible flame envelope.

For the smaller fire (figure 9) the envelope will nearly coincide with an isotherm of about 320 - 350° C starting from the center line down to a height of about 0.2 m. Below this height it begins to bend across the 300

and 200° C isotherms approaching the burner edge at the surface. The

larger fire shows similar behavior except the envelope crosses through

higher temperature regions midway down toward the surface . With the increased

scatter on figure 10 it is difficult to draw conclusions about this behavior.

3.3 Effect of Floor and Ceiling

In order to investigate the effect of locating the burner surface

flush with a floor, a noncombustible sheet was placed around the burner

edge for a distance of one burner width (W) on all sides. The entire

square had dimensions then of 3 W x 3 W. The entrained flow field would

conceptually be completely different than the previous configuration where

the burner could suck flow from below and up along the sides of the burner.

With the simulated floor in place this vertical flow would be cut off and

air would be required to come in horizontally before turning upward into

the flame.

Figure 11 shows the result of center line traversing with the floor in

place, the points representing two fire sizes and the lines represent the

previous correlations for no floor. There are some differences, notably

the flame temperatures appear slightly higher and plume temperatures slightly

lower, with velocity differences in the same directions. However, in

general, these differences are slight for such a radical change in configuration. A few radial scans were made with the "floor" in place and

like the center line no significant changes were recorded. The radial

scatter, though, is considerable in any case.

One noteworthy observation concerns the stability of the floor

configuration. The flame was much more sensitive to disturbances than when

there was no floor. With the floor in place if one walked by the burner at a pace and distance that would not noticeably disturb the flame in the normal

configuration, the flame was apt to behave wildly, leaning far to one side

with a tendency to form fire whirls at one of the corners of the burner.

After some time in the absence of further disturbance the flame would again

become symmetric.

17
2 Also in the spirit of looking for gross effects, aim noncombustible

sheet was placed horizontally and centrally above the burner to simulate

the effect of a ceiling on the fire, i.e., to evaluate any far field elliptic

characteristics. Again the results were not affected at least as regards

the center line behavior up to a height of about 70% of the height of the

ceiling.

3.4 Nature of the Signals

In order to obtain the overall gross structure of a typical diffusion

flame analysis up to this point has involved time-averaged quantities.

Long-time integration has masked naturally occurring pulsations, turbulence,

or ambient disturbances. In order to try to understand the gross structure

more detailed information will be required. Cox has investigated thermal

and electrostatic probe fluctuations for this flame system and in this

section the nature of the pressure signal which is related to velocity

fluctuations will be described. Recall that the probe volume is considerable

so fine scale information will not be sensed but rather the macroscopic

structure of the flame may be further elucidated.

Figure 12 shows the unprocessed dc output of the electrical manometer

on a fast-writing recorder (through an oscilloscope the signal appears

identical) . This record is from the center line at the upper edge of the

flame region. Within the vertical lines, corresponding to a 1 s time

interval, periodic activity of approximately 3 Hz can be observed consistently.

The size of the fluctuations are not trivial and the need for conditioning

in determining the time-averaged velocity behavior is obvious. To the left

of the unprocessed signal is shown the result of conditioning through an integrating voltmeter for an averaging time (x) of 100 s. For the center line

all but the very low frequencies associated with large laboratory disturbances

are eliminated for even smaller averaging-time settings, i.e., x = 10 s and

Is. In the wings however, activity still persists at higher x's as the

fire sways about. The average dc level is about 1.9 volts. (The question

of instrument frequency response will be addressed below.)

The same signal was also passed through a true root mean square (RMS)

meter with variable high pass filters on the input. The dc is thus removed

so the resulting RMS is essentially a standard deviation measurement. With

the meter set for acceptance of the lowest possible frequency range, i.e.,

f > 0.1 Hz the RMS pressure value determined was 0.0073 torr at a dc level

of 0.019 torr or ^fAp ,2 /Ap = 0.38. For higher minimum frequency settings of

18
the meter the RMS value decreases indicating that most of the energy is at

low frequencies. Mote that since these are high pass filters the upper end

of the frequency spectrum is unaffected by minimum frequency cutoff.

Also on figure 12 is the auto-correlation function for a similar

center line signal. The auto-correlation function compares or correlates a given signal with a delayed version of itself for different delay time,

(t ) the abscissa on the photo in figure 12. At t = 0 the two signals are

cl ^ obviously most similar and the ordinate is the mean square value of the

signal. In this case Ap'

2 = 0.00005 torr 2 or V AP'

2 = 0.0071 torr , similar to

the voltmeter result. The useful property of correlation here is the fact

that the auto-correlation function of a periodic signal is periodic and has

the same period as the signal. Hence the raw signal seen in the unprocessed

chart recorder plot on the lower part of figure 12 can be interpreted not

as random noise but as a repetitive signal of period approximately 0.33 s. Where the auto-correlation function goes to a maximum, i.e., t = 0.33, 0.68,

a. etc. on the picture the signal is most like itself. For longer and longer

delay times the amplitude of the correlation function will decrease at each

of the maxima due to finite statistics and deviations from a pure sinusoid,

i.e., broadening of the spectrum. The number of samples for the 100 point

trace shown was 8 x 1024.

Taking the Fourier transform of the auto-correlation function leads to

its equivalent in the frequency domain, the power density spectrum. Figure

13 (provided by Cox) is a plot for a similar Ap signal of the relative

power spectrum (maximum equals 1) and the amount contained at each frequency

interval, seen in the lower linear trace for the frequency range of 0.5 to

50 Hz. During the previous discussion concerning the RMS results it was determined qualitatively that most of the energy appeared to be at lower

frequencies. Figure 13 gives a quantitative answer to the energy distribution

question. The dominance at 3 Hz (or slightly less) is quite unequivocal in

both plots. A second two decade scan from 5 to 500 Hz shows similar results

as that seen in the figures up to 50 Hz. Unfortunately there appears to be

an instrument response problem at about 20 Hz (the 5 to 500 Hz scan exhibits

another at 40 Hz)Determination of frequency response for a transducertubulation (probe, tubing, valves, manometer) system like the present is

not a simple matter [13] and without further information detailed interpretation of figure 13 would be of questionable value. Fortunately Cox has

obtained spectra for AT' for this burner at similar conditions and that result

is practically identical (except for the sharp attenuation at 20 Hz) to figure

13 thus strengthening somewhat the contentions about the low frequency

activity.

19
The 3 Hz frequency is a factor of three lower than the classical

results for oscillations or "flame flicker" of laminar diffusion flames

such as candle flames. These have been found to be always of the order of

10 Hz and are unaffected by the dimensions or type (including square) of

burner, the fuel flow rate or fuel type [14]

On the other hand, in a study of large-scale diffusion flames McCamy [15]

measured flicker frequencies optically and found peak amplitudes at frequencies

between 3 and 10 Hz. These were sharp maximums with peaks 100 times the

average amplitude over the range from 2.5 to 750 Hz. Diffusion flames over

lubricating oil and hydraulic fluid contained in a 0.15 m diameter pan

yielded precisely 3 Hz. A natural gas diffusion flame above a small burner

exhibited a peak at slightly less than 5 Hz. Like the 10 Hz results above,

the initial momentum may not be negligible due to the small size of the

burner and hence the flames may not be truly buoyant. For this case the

flicker was so regular that second and third harmonics were detectable. A

gasoline diffusion flame exhibited two peaks of similar magnitude at 5 and

8 Hz. A further summary discussion of flame oscillations can be found in

reference 16 where a variation of frequency with pool size has been observed

for methanol fires. The present 3 Hz result is not inconsistent with those

findings for similar size pools. (Terai also finds peaks at about 3-4 Hz

in his power density spectrum of temperature fluctuations.)

How this fluctuating structure varies throughout the flame can be seen

on figure 14 where the voltmeter RMS reading (f > 0.1 Hz) is plotted along

with the dc component and also the ratio of the two. The upper portion of

the figure gives center line results throu ’ "rom the

almost an order of magnitude and yet the ratio of the two remains virtually

constant at about 0.35. Judging by the voltmeter results with the variable

high pass input filter the frequency distribution is probably similar to

figure 13 everywhere. That is, a spectrum analysis was not obtained at

each and every point of figure 14 but the RMS voltmeter was used at three

minimum frequency cutoffs during those traverses and the lower frequency

dominance was maintained throughout. The 3 Hz frequency then is something

fundamental throughout the entire flame to plume structure and the ejection

of flame "tongues" in the intermittent region is just one manifestation of

the phenomenon.

The radial scan at z = 0.267 m, near the tip of the flame region shown

on the lower portion of figure 14, is more interesting regarding this behavior.

The time-averaged signal falls with radial distance, x, as was seen previously

base of the burner to well into the plume

20
in the velocity profiles. The fluctuating components on the other hand

decrease much less with distance into the wings. The net result is that

the ratio of the two signals starts at about 0.35 at the center line and

increases radially until at the extremities the RMS almost constitutes the

entire signal. The RMS portion has not changed very much throughout x, but

Ap representing a net upward flux, decreases such that at the extremes

there is no longer a preferred upward tendency. It is this lack of strong

direction coupled with significant fluctuations that makes the wing measurements difficult. Note again that these are large-scale pulsations and make

the truly buoyant diffusion flame subject to even minor ambient disturbances.

3.5 Entrainment and Heat Release

The mass flow rate, m, at any height above the burner assuming axial

symmetry is given by:

oo m(z)

= J

pv(z,x) 2 it x dx

o Since any correlation between p and v is presently not well understood for

these systems it will be assumed that pv = p" x v. Using an ideal gas with

2 AT (z , x) = AT (z

)

exp[- (x/x1/e ) ]

V (z ,x) = V (z) exp[- (x/x

1 ^e

) 2]

the mass flow rate expression can be easily integrated. The exponent 2 was

chosen as well as a single characteristic width, x±/

e for both the velocity

and temperature profiles in order to obtain a perfect differential. Mass

flow becomes:

m(z) p o

(x l/e ) 2 V(z)

AT (z) /T' O

Note that if x±/e was used as an upper limit of integration instead of » the In term would become slightly more complex leading to a significant

reduction in mass flow rate, e.g., a factor of two in the flame region.

This is because although velocity is getting smaller density is getting

larger, approaching ambient, and hence pv

- is not falling as rapidly as v. The integration limits are therefore important. This is in contrast to

constant density flows where there is a smaller fraction of flow from x i/e to 00

.

21
The equation for m(z) states that the mass flow rate is basically the

cold density times the area within times the center line velocity.

. V ln(AT/T + 1) The modifying factor of temperature, i.e., ' o accounts for the

AT/T

q

variable density. Far into the plume with AT -* 0 the factor equals 1.0.

Toward the other extreme in the flame the factor equals about 0.5 and hence

the mass flow is almost independent of temperature and consequently it is

not so sensitive to radiation error in the thermocouple measurement.

Substituting for V and AT into the expression for m yields

m (z) = c

1

( x

1// e ) 2 Q

1//5

(*>) - In (M 2 "‘ *

2 2 where C. = 2girp C and C~ = (k/C)

-L O Z n -t

2 g

and x. , =az + 3 Q 1/2

values of k and n are given previously for the three different regimes. C

is constant throughout and due to the limited amount of plume data a and 3 can also be considered constant throughout. Figure 15 shows the resulting

flow rate, m, of the above calculation plotted against normalized height

above the burner for various fire sizes. A useful simplifying expression

valid in the near field is:

m = 0.055 z Q

1//2 [kg. s -1

] z [m] , Q [kW]

which states that the flow rate is proportional to the height above the

burner to the first power and depends on heat release rate to a significant

degree. Both of these effects are missing in most formulations based on plume theory [5]. Of course, in the above expression x. , for the flame and /e

v intermittent region was used in the plume due to limited plume data and

hence these results will not be valid far away from a small fire where

plume theory will apply, i.e., m will be a stronger function of z and a weaker function of Q.

The convective energy flux at any height for a given fire size is:

22
00 H(Z) = C /

pv AT 2 it x dx

Using the same assumptions as before, namely: the time-averaged of the

product is equal to the product of the time-averaged quantities, and a square power Gaussian for both V and AT having equal widths. The integration

results in:

H = ’ C

p

°° <X l/e 4T

> 2 V(z) A T ~ T

° ln

ft * j

AT/T

or comparing to the equation for mass flow:

t, m C T

H = E_°

(1 . 2 ) 2

AT/T

ln

(€

+ *)

- 1

Note that for H, x, , is chosen as the appropriate width since the ±/e AT

multiplication by AT which falls much faster than pV will control the H

profile. For mass flow x. , was used since pv was on the wider side of

^V either the AT or V profile.

Figure 16 shows the convective energy flux normalized by the nominal

2/5 heat release rate, H/Q, plotted against z/Q '

. Since Q is the energy

originally supplied to the burner H/Q indicates how much energy is realized

convectively and therefore cannot exceed 1.0. Previously it was estimated

that 15 to 20% of Q is radiated away in the luminous zones so perhaps more

realistically H/Q cannot exceed about 0.8. Except for the very small fires

H/Q reaches about 0.55 independent of Q at the flame-intermittent intersection. In the intermittent regime for the larger fires H/Q rises weakly

or not at all. Thereafter, in the plume region H/Q begins to fall as combustion ceases and dilution begins to dominate. The results for the

majority of the present data, i.e., 20 to 50 kW envelop a region around 0.8

at the top of the intermittent regime indicating roughly the validity of

the previous experimental results and the above analytical approximations

Although there may exist some tendency for radiation to increase with fire

size and hence result in lower H/Q the high values (H/Q >_ 1) for the small

fire point out the need for further refinement. Extrapolation to Q below

the range of measurements will lead to errors due to the form of x., 2/5 i.e., the first term, a z/Q , will begin to dominate.

‘1/e'

23
4. SUMMARY AND CONCLUSIONS

A pressure probe and thermocouple have been used to determine the near field characteristics of a buoyant, area source, diffusion flame. The

validity of this technique, for velocity measurement in buoyant flames

appears to be demonstrated. This contention is based on agreement with

previous measurements in the less severe plume region where different

instruments, e.g., hot wires have been utilized. There is also consistency

between the present results and a number of cross correlation measurements

in the flame regime.

The results of center line probing have established the time-averaged

fluid mechanical and thermal fields or gross structure of the flame. In

addition the scaling relations in terms of a nominal heat release rate,

i.e., V~Q1//5 and z ~ Q

2//5 have been established. The measured demarkation

of the fire into flame-intermittent-plume regimes as well as the visual

identification of each have been seen to characterize the phenomena. The

dominant role played by buoyancy is shown by the consistency of V/^ 2gzAT/T

Q

in all three regimes.

2/5 1/2 A tentative scaling for width, x

±/e ~ a z/Q + 6 Q has been

proposed and it is in this area that definite further study is required.

More refined radial scanning of different sized burners/pool fires will be

necessary in order to demonstrate proper scaling.

Having found the center line and radial behavior of the flame system,

expressions for mass entrainment and heat release were determined. Assessment

of H/Q can provide a simple check of overall accuracy.

Additional experiments should include an evaluation of radiation from

the flames. Various methods are available whereby the total radiative

power output of the flame can be ascertained with a minimum of straightforward

flux measurements.

Finally, on the analytical side, information like the dominance of 3 Hz

and future finer scale spectral measurements, especially in the mixing

regions, can provide guidelines for modeling characterization.

24
5 . ACKNOWLEDGEMENTS

Sincere thanks are due to Geoffrey Cox and the staff of the Fire

Research Station at Borehamwood, England where these experiments were

performed while the author was a guest worker during the past year.

6. REFERENCES

[1] Cox, G., to be published.

[2] Terai, T., Experiments on Plume Rising from Burning Heat Source with

Finite Sizes, to be published.

[3] Heskestad, G. , Optimization of Sprinkler Fire Protection Progress Report

No. 9, Factory Mutual Research Corporation, Norwood, Mass., March 1974.

[4] Yokoi, S., Study on the Prevention of Fire-Spread Caused by Hot Upward

Current, Report of the Building Research Institute, Ministry of

Construction, Japan, No. 34, Nov. 1960.

[5] McCaffrey, B. J. and Rockett, J. A., Static Pressure Measurements of

Enclosure Fires, Journal of Research of the National Bureau of

Standards, 82^2

, 107 (1977).

[6] McCaffrey, B. J. and Heskestad, G. , A Robust Bidirectional Low Velocity

Probe for Flame and Fire Application, Combustion and Flame 26, 125

(1976).

[7] Thomas, P. H. , Baldwin, R. and Heselden, A. J. M. , Buoyant Diffusion

Flames: Some Measurements of Air Entrainment, Heat Transfer, and Flame

Merging, Tenth Symposium (Int.) on Combustion, The Combustion Institute,

1965, pp. 983-996.

[8] Rouse, H., Yih, C. S. and Humphreys, H. W. , Gravitational Convection

from a Boundary Source, Tellus 4, 201 (1952).

[9] George, W. K. , Alpert, R. L. and Tamanini , F. , Turbulence Measurements

in an Axisymmetric Buoyant Plume, Factory Mutual Research Technical

Report No. 22359-2, Norwood, Mass., Jan. 1976.

25
[10] Veldman, C. C., Kubota, T. and Zukoski, E. E. , An Experimental Investigation of the Heat Transfer from a Buoyant Gas Plume to a Horizontal

Ceiling, Nat. Bur. Stand. (U.S.), NBS-GCR-77-97 (1975).

[11] Powers, R. M. , Calorimetry of Luminous Natural Gas Flames, 2nd AIAA/ASME

Thermophysics and Heat Transfer Conference, Palo Alto, Calif., May 1978.

[12] Thomas, P. H. , The Size of Flames from Natural Fires, Ninth Symposium

(Int.) on Combustion, The Combustion Institute, 1963, p. 844.

[13] Iberall, A. S., Attenuation of Oscillatory Pressure in Instrument

Lines, Research Paper RP 2115, Journal of Research of the National

Bureau of Standards, £5, 85 (1950)

.

[14] Grant, A. J. and Jones, J. M. , Low-Frequency Diffusion Flame Oscillations,

Combustion and Flame 2_5, 153 (1975) .

[15] McCamy, C. S., A Five-Band Recording Spectroradiometer , Journal of

5 Research of the National Bureau of Standards, _56 , 293 (1956).

[16] Hertzberg, M., Cashdollar, K. , Litton, C. and Bugess, D., The Diffusion

Flame in Free Convection, U.S. Bureau of Mines Report RI 8263 (1978).

[17] Beuther, P. D. , Capp, S. P. , George, W. K. , Momentum and Temperature

Balance Measurements in an Axisymmetric Turbulent Plume, American

Society of Mechanical Engineers Paper No. 79-HT-42 (1979)

.

26
Table 1. Summary of center line data

Weighted

Fire Size Q(kW) 14.4 21.7 33.0 44.9 57.5 Average

Flame AT (°C) 791 800 807 790 800 797

1/2 , 1/2 -1. V/z (m s ) 6.87 6.83 6.89 6.77 6.80 6.84

V

I 2gATz 0.943 0.932 0.936 0.930 0.928 0.936

\ T

o (22). (n) (8 (12) (e) (61/

Intermittent ATz 171 221 277 326 353

(°C m)

ATz/Q2/5

(°C m kW ' > 58.8 64.5 68.4 71.2 69.8 62.9

V , 3.29 3.59 3.92 4.10 4.24

(ms

A

)

V/Ql/5

-1 -1/5

(ms kW ) 1.93 1.94 1.95 1.92 1.89 1.93

V

1 2gATz 0.971 0.932 0.909 0.877 0.871 0.940 * T

o (39 (10) (=) .lo)

' 5

) (69/

Plume -V3

5/3

('CmV )

122 166 240 314 357

ATZ

5/ V/3

(»Cm 5/3 kw'2/3

) 20.6 21.3 23.3 24.9 24.0 21.6

Vz

1/3

, 4/3 , (m s) 2.72 3.10 3.61 3.98 4.12

-VVf4/3 -1 -1/3, 1.12 1.11 1.13 1.12 1.07 1.12

V

[2gATz ' T

o

0.951 0.929 0.900 0.867 0.842 0.928

(27) (8) (**) Uj (3) (46)

V/ 1 2q ATz All Q All z .935 > T

o

(176;

AT V

Intersections

Flame- Intermittent

62.9

797 0789 (±21\

2

\ 6.84/

= .0796 .0793

z/Q (m«kW

2/5, IntermittentPlume /21.6' 3/2

\ 62 .9 ) -201 (—)

3

} 1.93 / = .195 .198

( ) number of data points

27
Table 2. Comparison to previous work, plume,

center line-axisymmetric

Velocity

V = A F

1/3

z- 1/3

o

Temperature Rise

AT D „ 2/3 -5/3 g—3 = B F z T o

o

A B V/^2gATz/T

Q

1/5 V/ ‘«4T> (kw K) 1/5

Yokoi (4) 3.9 9.1 .90 .62 Alcohol Point

Source

Yih (8) 4. 7 11.0 1.0 .72 Bunsen Burner

George (9)

(17)

3.4

3.6

9.1

9.5

.80 .83

.54 .57 Heated Air Jet

Plume

(3) Heskestad < .50> Best Estimate

into Flame

Region for

Q = 40-25000 kW

Present 3.7 8.0 .93 .61 Natural Gas with

Radiation Loss

(A/^IzT ) (.25 A/B1/5

)

28
in

isi

(s/i-M>l*i-s*iti| s/iO/A

29

Figure

1.

Center

line

velocity

vs

height
(9.1 IV

30

Figure

2.

Center

line

temperature

rise

vs

height
31

Figure

3.

One-second

time

exposed

flame

photos

vs

heat

release

rate
32

Figure

4.

One

and

one-third

seconds

of

cine

film

(24

frames/s)

showing

3

Hz

(eight

frames)

oscillation
CM

in

(UI) s/lx

33

Figure

5.

Width

of

velocity

profile

vs

height
PLUME

_M

°A/A

34

Figure

6.

Velocity

profile

in

plume
CO

CM

CO

en

r— o o <3 o

. r

LO LO C-3 E oo CM CO CM

PM CM CO

c=> C=> CO

to

CM

CM

o

o

9

a>.°

X

X

Irt

°A/A

35

Figure

7.

Velocity

profile

in

intermittent

region
X

X

°A/A

36

Figure

8.

Velocity

profile

in

flame

region
Figure 9. Temperature rise in space coordinates, Q = 22 kW

37
N

Figure 10. Temperature rise in space coordinates, Q = 45 kW

38
(Oo)iV

(s/i MM'i s-m) 5/iO/a

39

Figure

11.

Velocity

and

temperature

rise

vs

height

for

simulated

floor

configuration
SOOOO'O z(UUOl)

CO

40

100s

PRESSURE

SIGNAL

UNPROCESSED

RMS

|f*0.1

Hz)
ENERGY/Af

POWER

DENSITY

SPECTRUM

AP' 2

/Hz

f|Hz)

Figure 13. Power density spectrum and energy distribution

of pressure signal vs frequency

41
ARBITRARY

UNITS

ARBITRARY

UNITS

X|m|

Figure 14. Time-averaged and RMS component of

pressure signal axially and radially

42
(i-s*3)|) ui

43

Figure

15.

Entrained

mass

flow

vs

height

for

various

heat

release

rates
Figure

16.

Normalized

convective

flux

vs

height

for

various

heat

release

rates
NBS-114A (REV. 9-78)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 79-1910

4. TITLE AND SUBTITLE

PURELY BUOYANT DIFFUSION FLAMES: SOME EXPERIMENTAL RESULTS

5. Publication Date October 1979

1 Organization Code MM

7. AUTHOR(S)

Bernard J. McCaffrey

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

M. ask^terfc Unit No.

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, state, ZIP)

(same as above)

13. Type of Report & Period Covered

Final

14. SpiwjKJrtfig Agency Code

15. SUPPLEMENTARY NOTES

| | Document describes a computer program; SF-185, FIPS Software Summary, is attached.

16. ABSTRACT (A 200-word or teas {actual summary of moat s i ghi fi cant information. If document includes a significant bibliography or

literature survey, mention it here.) Measurements of temperature and velocity using thermocouples ancj an impact probe were made in the near field of a purely buoyant diffusion flame produced by a porous refractory burner. Based on time-averaged center line value of V and

AT together with photographic records the flame can be conveniently divided into three

distinct regimes: (1) a continous flame region, starting from, the surface of the burner with V equal to zero at the surface and rising with the height above the burner,

z, to the 1/2 power. At is constant over this regime. Higher up is (2) , an intermittent regime, with pulsating flame (~3 Hz) exhibiting approximately constant V and AT falling with z to the first power. Still higher is (3) the plume region which is, most

of the time, free of flames with v ^z- l/3 and AT~z-5 / 3 as predicted by conventional

plume theory. Throughout the three regimes and indistinguishable among these is the consistency of the buoyancy relation, V/ V2gz AT/T0 which has a value of approximately

0.9, a factor 2.5 times previous estimates in the flame region and confirming the recent, correlation measurements of Cox1

. Different heat release rates, Q, can be scaled to a "universal" fire if the length is normalized as z/Q2 / 5 and the velocity scale as V/q1/5

, The flame regime is thus independent of Q. In the radial direction for time-averaged quantities only the plume region appears

reasonably Gaussian. The data in the flame and intermittent regimes do not fall as rapidly as that dictated by a Gaussian distribution. In all three regimes the velocity

profile is wider than the temperature profile.

Large scale, low frequency Ap fluctuations are about 35% of the time-averaged

signal on the center line throughout the three regions. Radially the fluctuating

to time-averaged signal ratio rises from the center line value and approaches 100%

in the wings. Elementary spectral analysis indicates that most of this energy is concentrated in a narrow band centered around 3 Hz. Implications of these results for flame entrainment calculations and heat release

rates will be discussed.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the firat letter of the firat key word unless a proper name;

separated by semicolons)

Buoyancy; diffusion flames; fire entrainment; flame oscillations;

plume; scaling.

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