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The prediction of laminar jet diffusion flame sizes: Part II. Experimental verification
COMBUSTION A N D F L A M E 2 9 , 2 2 7 - 2 3 4 (1977)
227
The Prediction of Laminar Jet Diffusion Flame Sizes: Part II. Experimental Verification F. G. ROPER,* C. SMITH, and A. C. CUNNINGHAM British Gas Corporation, Watson House, Peterborough Road, London SW6
This paper describes experiments to test the diffusion flame theory given in a previous paper. It is shown that diffusion flame sizes can be predicted for two different burner geometries (circular and slotted ports) by taking the diffusion coefficient of oxygen at a characteristic flame temperature of 1500 K. For the slot burner, the flame size is found to be controlled either by momentum or by buoyancy effects. The transition between the two regimes occurs, as predicted, when the modified Froude number is approximately one. In contrast, if the classical Burke-Schumann theory is used, the diffusion coefficient needed to predict the correct flame size varies by about a factor of six, depending upon the burner geometry and flame conditions. The paper goes on to show that gas compositions in the tail of a diffusion flame may be predicted by the theory already given. It also examines previous experimental work on diffusion flame size in relation to the present work.
I. INTRODUCTION The present trend towards compact burners and combustion chambers has caused much interest within the gas industry in the calculation of laminar diffusion flame sizes. This subject is of fundamental scientific interest, but also has many practical applications. The latter include: the prediction of minimum combustion chamber volume for compact gas appliances; the specification of safety margins needed in appliance design against possible overload conditions; and assessment of the interchangeability of fuel gases. It may seem that the many papers already published on laminar diffusion flame sizes, e.g., [1-3, 9, 10, 1 5 - 1 9 ] , have removed the need for further experimental work. However, the previous work has concentrated almost completely on the visible flame sizes o f circular port burners. Preliminary measurements showed that existing theories [1,2] gave order-of-magnitude errors when applied to
* Present address: British Gas Corporation, London Research Station, Michael Road, London, S.W.6.
non-circular burner geometries. A modified theory was therefore developed in part I of this paper. Experimental tests of the new theory are described in the following sections.
2. MEASUREMENT OF DIFFUSION FLAME SIZE
Previous workers, e.g., [1-3, 16, 17], have assumed that the diffusion flame ends at the same point as the visible flame. This assumption is often invalid for hydrocarbon flames, due to the slow decay of traces of soot or carbon monoxide [15, 1 9 - 2 1 ] . The diffusion flame height should therefore be found from the flame gas composition rather than visual observation. The end of the diffusion flame is the point on the flame axis where oxygen and fuel are in the stoichiometric ratio. This point can be found by gas sampling and analysis, using quartz microprobes and gas chromatography. However, the method was found to be too slow for general use. It was used to check the following rapid methods Copyright © 1977 by The Combustion Institute Published by Elsevier North-Holland, Inc.
228
F.G. ROPER, C. SMITH, and A. C. CUNNINGHAM
PUMP TO WASTE
which were developed for measuring diffusion flame size. 2.1. Diffusion Flame Size from Carbon Monoxide Concentrations Part I of this paper has shown how diffusion theory can predict the escape of carbon monoxide (CO) through a heat exchanger above the burner. For a heat exchanger at the end of the diffusion flame, the calculated CO concentrations were (dry-airfree basis): circular port 0.08%; slot burner 0.3%. These values were almost constant for the fuel gases and primary aerations used in the present work. The same method was used here in reverse; the diffusion flame heights were found from the measured concentrations of CO entering a heat exchanger at various heights above the burner. The method was tested experimentally as described in section 4.4. The heat exchanger was a water-cooled array of 2-ram-i.d. stainless-steel tubes. The combustion products passing through it were analysed for CO and CO 2 by nondispersive I.R. analysers. The sampling rate through the heat exchanger was high enough to minimise distortion of the flame impinging on the heat exchanger. The CO concentrations (corrected for dilution by excess secondary air) were then independent of the sampling rate. For the slot burner a double manifold was connected to the heat exchanger as shown in Fig. 1, so as to sample combustion products from above the central regions of the burner. This eliminated end effects, so that the flame heights corresponded to an infinitely long slot burner. A similar sampiing arrangement was used for the circular port burner, but without the inner manifold.
2.2. Diffusion Flame Size from Soot Concentrations Soot concentrations were measured using a sensitive dual-beam optical densitometer at a wavelength of 575 nm. The burner and flame containing soot were traversed automatically through one light beam of the densitometer, by a motorized traverse rig. The resulting absorption profiles were digitized and recorded on punched tape. They were then analysed on an IBM 1130 computer using data on the specific extinction coefficients
To J.R
4-
OUTERANALYSERS MANIFOLD .
Jl
II
71
II .~
VIEWING WINDOW
EXCHANGE~ VIEWING/ L~
WINDOW
DRAUGHT PROOF ENCLOSURE
H
I
ISL°r
SECONDARY AIR
I
BURNERI SECONDARY AIR
Fig. 1. Apparatus for measurement of diffusion flame height from the escape of carbon monoxide through a heat exchanger.
of soots formed from low molecular weight hydrocarbons [22]. This procedure yielded the soot concentrations integrated along the light beam of the densitometer. The flames studied in this way were axisymmetric. The results were deconvoluted to yield local soot concentrations, in a way similar to that used for axisymmetric flame interferograms [23]. The detection limit was better than 0.3 ng mm - a of soot, in a volume 1 mm a. The soot concentration profiles were found to show a common pattern. The soot oxidation zone moved inwards from the edge of the flame to cover its entire width, implying a large degree of chemical control. So the question arose of how the soot concentration profiles are related to the diffusion flame height. Obviously, the maximum soot concentration occurs at a point where net soot formation stops and oxidation starts. The axial soot maximum must be the point where hydrocarbons are replaced on the flame axis by oxygen. This conclusion was confirmed experimentally by flame gas composition measurements. In other words, if hydrocarbons were the only fuel species present in the flame, the axial soot maximum would be the end of the diffusion flame. But for the methane/air flame investigated, sufficient hydrogen and carbon monoxide were
PREDICTION OF FLAME SIZES
229
also present for the ratio (diffusion flame height/ height to axial soot maximum) to equal 1.15. For consistency, this correction was applied to all the flames containing soot, although it made slightly poorer the agreement between diffusion flame heights measured from soot and carbon monoxide concentrations.
0'004
o []
~
0'003
:/
3. EXPERIMENTAL CONDITIONS
I
c 'tf 0
v J *
0"00: REF ,5) I
Z
r
0 /"
/
CH4 /,8"9/ /o CH4 [1%8 9~IT
/I
The burners used in this work were: (A) Circular port burner, diameter 0.36 to 10.2 mm; (B) straight slot burner, water cooled at 60°C. Length 90 ram, width 0.33 to 9.0 mm. The burners were placed within an enclosure, to control the secondary air flowrate and composition. Soot measurements were performed only on the circular port burner, with an enclosure crosssection which varied from 30 × 30 mm to 50 × 100 ram. The secondary air flow rate was varied from two to five times the stoichiometric requirements. These changes were found to have no effect on flame height. The apparatus for measurements of carbon monoxide escape is shown in Fig. 1. The enclosure had a cross-section 250 × 250 ram, with a secondary air velocity of 0.05 m/sec for the circular port and 0.075 m/sec for the slot burner.
/
2'0 CH4] t.-2 CH41] I)0"2 CH4II j
\
co I2o.9]+, ~ I ~
,4-0
¢
,
\
I
•,*
:, 27,0-3{,o,,.,,,,}-,
0 .ol
,Z; ° T©
I
I
1"0
2"0
3"0
I
In {1+1/s1 Fig. 2. Circular port diffusion flame sizes found from measurement of carbon monoxide escape. The fuel gas compositions are given in Table 1.
4. RESULTS AND DISCUSSION TABLE1
4.1. Circular Port Diffusion Flame Sizes
The equation derived in part I for the diffusion flame height (H) of a circular port burner was:
(H/Q) = {47rDo In (1
+
1/S)}-I(To/Tf) °'67,
(1)
where the symbols are defined in the nomenclature (Part I). The proportionality between H and flow rate Q was found to hold except at very low flow rates, where axial diffusion reduced flame size. Equation (1) was tested by plotting (H/Q) against {ln (1 + l/S)} - x for the fuel gases shown in Figs. 2 and 3. The flame sizes found from CO escape are shown in Fig. 2 for primary aerations from 25 to 95% of stoichiometric. The figure includes a value of H/Q for a CO/air diffusion flame, deduced from
Gas Mixture Letter
See Figs. No.
A B C D E F
3 3 2,3 3 3 3
G
2 2 2 3 3
Composition
95% CH4 + 5% C3H8 90% CH4 + 10 %C3H8 87% CH4 + 13% C3H8 50% CH4 + 50% AIR 33% C3H8 + 67% AIR 47% CH 4 + 35% H 2 + 10% C2H 6 + 4% C3H 8 + 4% N 2 30% CH 4 + 35% H 2 + 29% C3H 8 + 1% C4HIO + 5% CO2 65% CH4 + 35% H2 49%CH4+ 35% H2 + 16% C3H8 49% CH4 + 26% H2 + 25% C3H8 14% CH 4 + 48% H 2 + 14% C2H 4 + 24% N 2
F. G. ROPER, C. SMITH, and A. C. CUNNINGHAM
230 0-050
an average value in Eq. (2) below:
(H/Q) = (1.33
(2)
X
0,0t.0
X
A comparison of Eqs. (1) and (2) gave an estimate of Tf as 1500 K, which seems a reasonable mean temperature for the flame regions controlling diffusion. D O was taken as the diffusion coefficient of oxygen, calculated from LeonardJones viscosity fitted parameters [8]. (D O = 20 mm 2 sec - 1 at 293 K.)
r H/0=1"/,0
10-3{1-
0.030 'E E i
Tl__q L~
0'020
0.010
10 - 3 mm - 2 sec){ln (1 + I/S)} - 1 .
' SYMBOL FUEL GAS
,r'~
O A
//
X Y +
7 U
CH4 C2H6 C2 HL C2 H2 C3H8 C3H6 GAS A
4.2. Slot Burner Diffusion Flame Sizes
The values of Tf and Do found above may be used to calculate diffusion flame sizes for a straight slot burner. Substituting these values into Eqs. (23)(25) of part I.
OA$ B
GAS C GAS D
GAS E
0
!
tl 20
OAS K GAS L GAS F
Momentum Control." 30
In{ I "11s)
Fig. 3. Circular port diffusion flame sizes found from soot concentrations within the flame. The fuel gas compositions are given in Table 1.
HM = (.086
bQM4~2To I
/
(3)
Buoyancy Control: H B = (.20
the results of Hess [15]. For flames where H >> burner diameter (d), the points lie close to the straight line in Fig. 2. This linear relationship follows from Eq. (1) if Tf and Do are constant. The points which lie significantly below the line in Fig. 2 have ratios (H/d) less than about six, so that axial diffusion cannot be ignored. Vitiation of primary and secondary air had a large effect on the flame sizes in Fig. 2. A reduction of only 10% in oxygen concentration increased H by up to 60%, as predicted by Eq. (1). The flame sizes found from soot concentrations are plotted in Fig. 3, which again shows that (H/Q) ~ (in (1 + l/S)} - 1 . A change in burner diameter from 0.36 to 1.0 mm was found to reduce (H/Q) by 10%. In this case axial diffusion can be ignored, as (H/d) > 50. The effect seems to be due to buoyancy, and is discussed in Section 5. The equations of the lines in Figs. 2 and 3 differ only slightly, so it seems permissible to take
mm - 2 sec)
mm - 4 / 3 sec 213)(Q4(94/aL4)l/3
(4)
Transition Region: ~H = (4~(HB)
3
II1+v, / -] 338(HM~312/3 1
(5) The mean acceleration "a" of the flame gases due to buoyancy is needed in Eq. (4) to predict HB. We will treat "a" as an empirical constant. For fuel gases premixed with a substantial proportion of air, the maximum possible value of "a" is approximately g(Tf/To - 1) ~ 40 m sec - 2 . In practice, this value will be reduced by momentum losses to the surrounding air. The values of H observed and predicted from Eq. (5) are shown by the solid points in Fig. 4. The fuel gas was methane, with primary aerations from 30 to 80% of stoichiometric. H was determined as in section 2.1. For flames where buoyancy effects were small, the predicted and observed
PREDICTION OF FLAME SIZES
231
I/,0 E E 120
I
~100 o uJ :::) 80
x
+
Jr
•:.tl_~f
, I~
T.gORY
,•"
I I 0
4.3. Diffusion Flame Sizes from Burke- Schumann Theory
PART T
~la~"
LU
MOMENTUM BUOYANCY CONTROLLED CONTROLLED FLAMES FLAMES
THEORY
I 20
I 40
I I 60 80 CALCULATED
I 100 VALUE
width (b) for momentum control and independent of b for buoyancy controlled flames, as predicted from Eqs. (3) and (4). From part I, the criterion for buoyancy effects to be negligible is that the modified Froude number Fr >> 1. Figure 5 shows that the transition from momentum to buoyancy control occurs when Fr ~ 1.
I l 120 11.0 OF H-rnm
I 160
180
Fig. 4. Experimental and predicted diffusion flame heights for slot burner. The 45 ° line shows where the points should lie for complete agreement between theory and experiment.
values of H agreed well, regardless of the value taken for "a". When buoyancy effects were significant, good agreement was found if "a" was taken as 25 m sec - 2 , 60% of the maximum value. However, this value is not critical; a 50% increase in "a" decreases H e by only 12%. Figure 5 shows the transition from momentum to buoyancy control as the slot width increases. The curve in Fig. 5 shows the value of (H/Q) calculated from Eq. (5) taking a = 25 m sec- 2 . It can be seen that (H/Q) is proportional to the slot
The results given above can be used to test the Burke-Schumann (B-S) theory of diffusion flame size [1]. On this theory, the diffusion coefficient found from the circular port flame sizes is 60 mm 2 sec- 1 , equivalent to diffusion at 575 K. If this coefficient is used to predict flame sizes for the slot burner, the results are the crosses shown in Fig. 4. When buoyancy can be neglected, the observed flame sizes are about six times larger than predicted by the B-S theory. The results imply a diffusion coefficient for the slot burner (on the B-S theory) of 10 mm 2 sec- 1 , equivalent to diffusion at 190 K. The points for buoyancy controlled flames are scattered, but the ratios (Hexperimental/Hpredieted) are lower than for momentum controlled flames. In other words, buoyancy effects decrease flame size. The opposite effect would be expected by the B-S model, where an increase in gas velocity due to buoyancy should increase flame height.
4.4. Experimental and Calculated Flame Gas Compositions
500
z,O0
E
Io
~2oo
/ ° '~/I
! \l IBUOVANCV CONTROLLEDFLAM ,
~F r = l
~
-]
Fr > > 1 (MOMENTUM CONTROLLED FLAME) BURNER SLOT W I D T H - m m
Fig. 5. Transition from momentum to buoyancy control for slot burner flame. The solid line is the calculated curve.
The concentration profiles of CO, CO2, and 0 2 were calculated for the tail of a methane/air flame with primary aeration 60%. The method described in Part I was used, with the values of Do, Tf, and "a" from the present work. The results are compared with experiment in Figs. 6(a) and (b). In the region close to the flame axis and just above the primary flame zone, the measured CO and 0 2 concentrations are greater than calculated. This implies that conditions there have not yet reached equilibrium. But the remainder of the profiles show good agreement between theory and experiment. In particular, the width of the profiles agrees well with the calculated values. For
232
10
F.G. ROPER, C. SMITH, and A. C. CUNNINGHAM
/•
I
POSITION OF PRIMARY FLAME ZONE [] []
~
ENO OF
I
DIFFUSION] FLAME ]
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I
I
I Z
(I:
I
[]/~CALCULATED [
,--~7 06
[J 20 . . . .
.,/
P'5 Z
"~/" A
J;
%
ILl (..)
\
z/, O (J
A []
r
CO CO2
o
[
02
".o I
",, I o / '~~
o
,F~ ~,4w"~i, 60
- - 70
I
I
I
I
I
36
38
40
TIME
I /.2
l /./.
I
/.6
-millisecs
(a)
;\, -5
/
/ / /
/
o
100
]
CALCULATED LINE
/
o/o',,,,
¢
90
3/,
02
i:il"
-"r"--~._
80
o
16 - -
/
HEIGHT ABOVE BURNER-ram 32
181
i
%
o
I--I
EXPERIMENTAL POINTS [ SPECIES
LINE =limp
l
ol
CO2 EXPERIMENTAL POINTS CO2 CALCULATED LINE CO EXPERIMENTAL POINTSco CALCULATED LINE 02 EXPERIMENTAL POINTS
Td
"2,..
X
0
5
10
RADIAL DISTANCE -ram
(b)
Fig. 6. Concentration profiles for circular port burner-comparison of theory and experiment: (a) Axial profiles, (b) radial profiles 60 mm above the burner.
comparison, the classical Burke-Schumann theory would predict profiles less than half the observed width. The predictions of CO escape into a heat exchanger above the burner are compared with experiment for the circular port flame described above and for two slot burner flames. The diffusion flame height was found from the local gas compositions, as previously described. For the circular port flame the agreement between experiment and predictions is very good. For the slot burner, the experimental and calculated profiles are approximately parallel, and differ at most by 8% of the flame height (see Fig. 7).
5. C O M P A R I S O N WITH O T H E R W O R K
When a comparison was made with previous work for the visible flame size (HF) of a circular port burner, a linear relationship was found between (HF/Q) and (In (1 + l/S)} - 1 . The graph was similar to Fig. 3 (where H replaced HF) except that the linear relationship now extended from town gas to butane. The graph was restricted to flame sizes where soot was present, as the significance of "blue" flame sizes is doubtful. The results of the present work in general agreed well with Refs. [1, 3, 12, 15-17] for the laminar flow region where HF De Q. However, an anomaly occurred
PREDICTION OF FLAME SIZES
233
A Ill
1"0 SYMBOL BURNER
FLOW RATE, mls -1 METHANE
"--0--
C RCULAR
6ram I 0'
PRIMARY AIR
9"6
554.
"--"D----
0
SLOT
25.9
124
..°.°~
l, (3 mm SLOT
18" 0
103
....
8mm
(,o
t!
o ~°C. b 0_
V.. ~-
o
g
~t ~ IE O ~02
"~. ©
o w LIJ
CL
"~ %,%E]A °.%
X
z
0 0"6
\.
"...'... "
0"7
0"8
0-9
1'0
1-1 12 HEIGHT ABOVE BURNER DIFFUSION FLAME HEIGHT
-~
The effect of axial diffusion on flame size, found in section 4.1, is also confirmed by other workers. For short flames of butane, Savage [17] found that the ratio (Hp~eaietea/Hobservea) depended on the Reynolds number within the burner-which in turn is proportional to (H/d). When plotted in this way, the results of Savage and Barr (given in Ref. [17]) agree fairly well with the present work. The effect of buoyancy on flame size was investigated by Edelman et aL [9], using a numerical method which ignored axial diffusion. Their results show that a tenfold decrease in Fr reduces (H/Q) by only 7%, in the range 10- 1 > Fr > 10 - 5 . 5 . This agrees with the experimental results of the present work and those of Hess [15].
O
13
1''t
Fig. 7. Carbon monoxide concentrations in the combustion products sampled through a heat exchanger comparison of theory and experiment.
for propylene. The ratio (HF/Q) for this gas was much greater than for propane although the two diffusion coefficients should be similar. The effect did not occur for the values of (H/Q) in Fig. 3. The explanation is that, when soot concentrations are high, a soot oxidation zone follows the diffusion flame, causing a large increase in visible flame size. This point was shown clearly by Lee et al. [21]. Reed and Roper [20] have also shown that the length of the soot oxidation zone increases as the soot concentrations increase and as the secondary air supply decreases. Soot escape was found to occur when the ratio (soot oxidation length/H) reached a value close to one. The visible length of hydrocarbon flames at the point where air starvation just caused soot escape (//smoke) was measured by Vaerman [18]. He found that (Hsmoke/Q) cc S for olefins and paraffins up to C7. This is equivalent to two of the previous conclusions: that (H/Q) ~ {In (1 + l / S ) } - 1 , and that (soot oxidation length/H) is constant at the point of soot escape. (For the fuel gases concerned, (In (1 + l/S)} - 1 - S ) .
6. CONCLUSIONS (1) Experimental verification has been obtained for the theory given in part I for the diffusion flame sizes of axisymmetric and straight slot burners. (2) Concentration profiles in the tail of the flame may be predicted by diffusion theory, assuming the flame gases to be in thermodynamic equilibrium. This assumption is not valid in the region just above the primary flame zone. (3) Diffusion flame sizes may be found experimentally from measurements of soot or carbon monoxide within the flame. Visible flame sizes only approximate to the diffusion flame size when sufficient secondary air is present, and when small concentration of soot are present within the flame.
The authors are glad to acknowledge the help of Dr. M. E. Nolan, Dr. K. Thompson, and Mr. B. C. Dutton in the computation o f equilibrium flame gas compositions. They also wish to thank their colleagues at Watson House for many helpful discussions, and British Gas for permission to publish this paper.
REFERENCES 1.
B u r k e , S. P.,
and Schumann,
Chem. 20, 998 (1928).
T . E. W., Ind. Eng.
234 2. Hottel, H. C., and Hawthorne, W. R., Third Symposium on Combustion, Flame and Explosion Phenomena, Williams and Wilkins, Baltimore, 1949, p. 254. 3. Wohl, K., Gazley, C., and Kapp, N., Third Symposium on Combustion, Flame and Explosion Phenomena, Williams and Wilkins, Baltimore, 1949, p. 288. 4. Clarke, J. F.,Proc. Roy. Soc. A. 296, 519 (1967). 5. Melvin, A., Moss, J. B., and Clarke, J. F. Comb. Sci. Tech. 4, 17 (1971). 6. Williams, F. A., Combustion Theory, AddisonWesley, Massachusetts and London, 1965. 7. Carslaw, H. S., and Jaeger, J. C. Conduction of Heat in Solids, Oxford University Press, 1947. 8. Fristrom, R. M. and Westenberg, A. A., Flame Structure, McGraw-Hill, New York and London, 1965. 9. Edelman, R. E. Fortune, O. F., Weilerstein, G., Cochran, T. H., and Haggard, J. B., Fourteenth Symposium (International) on Combustion The Combustion Institute, Pittsburgh, 1973, p. 399. 10. Cochran, T. H., and Masiea, W. J., Thirteenth Symposium {International) on Combustion, The Combustion Institute, Pittsburgh, 1971, p. 821. 11. Fay, J. A., J. Aeronautical ScL 21,681 (1954). 12. Goudie, G. O., "Mixing and Combustion of Gas Jets," PhD Thesis, University of Glasgow, 1967.
F . G . ROPER, C. SMITH, and A. C. CUNNINGHAM 13. Goldburg, A., and Cheng, Sin-L, Comb. Flame 9, 259 (1965). 14. Powell, H. N., and Browne, W. G., Sixth Symposium Ilnternational) on Combustion, The Combustion Institute, Pittsburgh, 1956, p. 918. 15. Hess, K., "Flame Length and Flame Stability," Dissertation, Karlsruhe T.H., 1965. 16. Barr, J., Fourth Symposium {International) on Combustion, Williams and Wilkins, Baltimore, 1952, p. 765. 17. Savage,L. D., Comb. Flame 6, 77 (1962). 18. Vaerman, J.,Ind. Chem. Beige. 32,653 (1967). 19. Jones, J. M., and Rosenfeld, J. L. J., Combust. Flame 19,427 (1972). 20. Reed, S. B., and Roper, F. G., Gas Council Research Communication GC 186, presented to the Autumn Research Meeting of the Institute of Gas Engineers, 1971. 21. Lee, K. B., Thring, M. W., and B6er, J. M. Combust. Flame 6,137 (1962). 22. Dalzell, W. H., and Sarofim, A. F., Trans. ASME J. Heat Transfer 91,100 (1969). 23. Pearce, W. J., Optical Spectrometric Measurement o f High Temperatures, University of Chicago Press, 1960. Received 14 June 1976; revised 12 January 1977
227
The Prediction of Laminar Jet Diffusion Flame Sizes: Part II. Experimental Verification F. G. ROPER,* C. SMITH, and A. C. CUNNINGHAM British Gas Corporation, Watson House, Peterborough Road, London SW6
This paper describes experiments to test the diffusion flame theory given in a previous paper. It is shown that diffusion flame sizes can be predicted for two different burner geometries (circular and slotted ports) by taking the diffusion coefficient of oxygen at a characteristic flame temperature of 1500 K. For the slot burner, the flame size is found to be controlled either by momentum or by buoyancy effects. The transition between the two regimes occurs, as predicted, when the modified Froude number is approximately one. In contrast, if the classical Burke-Schumann theory is used, the diffusion coefficient needed to predict the correct flame size varies by about a factor of six, depending upon the burner geometry and flame conditions. The paper goes on to show that gas compositions in the tail of a diffusion flame may be predicted by the theory already given. It also examines previous experimental work on diffusion flame size in relation to the present work.
I. INTRODUCTION The present trend towards compact burners and combustion chambers has caused much interest within the gas industry in the calculation of laminar diffusion flame sizes. This subject is of fundamental scientific interest, but also has many practical applications. The latter include: the prediction of minimum combustion chamber volume for compact gas appliances; the specification of safety margins needed in appliance design against possible overload conditions; and assessment of the interchangeability of fuel gases. It may seem that the many papers already published on laminar diffusion flame sizes, e.g., [1-3, 9, 10, 1 5 - 1 9 ] , have removed the need for further experimental work. However, the previous work has concentrated almost completely on the visible flame sizes o f circular port burners. Preliminary measurements showed that existing theories [1,2] gave order-of-magnitude errors when applied to
* Present address: British Gas Corporation, London Research Station, Michael Road, London, S.W.6.
non-circular burner geometries. A modified theory was therefore developed in part I of this paper. Experimental tests of the new theory are described in the following sections.
2. MEASUREMENT OF DIFFUSION FLAME SIZE
Previous workers, e.g., [1-3, 16, 17], have assumed that the diffusion flame ends at the same point as the visible flame. This assumption is often invalid for hydrocarbon flames, due to the slow decay of traces of soot or carbon monoxide [15, 1 9 - 2 1 ] . The diffusion flame height should therefore be found from the flame gas composition rather than visual observation. The end of the diffusion flame is the point on the flame axis where oxygen and fuel are in the stoichiometric ratio. This point can be found by gas sampling and analysis, using quartz microprobes and gas chromatography. However, the method was found to be too slow for general use. It was used to check the following rapid methods Copyright © 1977 by The Combustion Institute Published by Elsevier North-Holland, Inc.
228
F.G. ROPER, C. SMITH, and A. C. CUNNINGHAM
PUMP TO WASTE
which were developed for measuring diffusion flame size. 2.1. Diffusion Flame Size from Carbon Monoxide Concentrations Part I of this paper has shown how diffusion theory can predict the escape of carbon monoxide (CO) through a heat exchanger above the burner. For a heat exchanger at the end of the diffusion flame, the calculated CO concentrations were (dry-airfree basis): circular port 0.08%; slot burner 0.3%. These values were almost constant for the fuel gases and primary aerations used in the present work. The same method was used here in reverse; the diffusion flame heights were found from the measured concentrations of CO entering a heat exchanger at various heights above the burner. The method was tested experimentally as described in section 4.4. The heat exchanger was a water-cooled array of 2-ram-i.d. stainless-steel tubes. The combustion products passing through it were analysed for CO and CO 2 by nondispersive I.R. analysers. The sampling rate through the heat exchanger was high enough to minimise distortion of the flame impinging on the heat exchanger. The CO concentrations (corrected for dilution by excess secondary air) were then independent of the sampling rate. For the slot burner a double manifold was connected to the heat exchanger as shown in Fig. 1, so as to sample combustion products from above the central regions of the burner. This eliminated end effects, so that the flame heights corresponded to an infinitely long slot burner. A similar sampiing arrangement was used for the circular port burner, but without the inner manifold.
2.2. Diffusion Flame Size from Soot Concentrations Soot concentrations were measured using a sensitive dual-beam optical densitometer at a wavelength of 575 nm. The burner and flame containing soot were traversed automatically through one light beam of the densitometer, by a motorized traverse rig. The resulting absorption profiles were digitized and recorded on punched tape. They were then analysed on an IBM 1130 computer using data on the specific extinction coefficients
To J.R
4-
OUTERANALYSERS MANIFOLD .
Jl
II
71
II .~
VIEWING WINDOW
EXCHANGE~ VIEWING/ L~
WINDOW
DRAUGHT PROOF ENCLOSURE
H
I
ISL°r
SECONDARY AIR
I
BURNERI SECONDARY AIR
Fig. 1. Apparatus for measurement of diffusion flame height from the escape of carbon monoxide through a heat exchanger.
of soots formed from low molecular weight hydrocarbons [22]. This procedure yielded the soot concentrations integrated along the light beam of the densitometer. The flames studied in this way were axisymmetric. The results were deconvoluted to yield local soot concentrations, in a way similar to that used for axisymmetric flame interferograms [23]. The detection limit was better than 0.3 ng mm - a of soot, in a volume 1 mm a. The soot concentration profiles were found to show a common pattern. The soot oxidation zone moved inwards from the edge of the flame to cover its entire width, implying a large degree of chemical control. So the question arose of how the soot concentration profiles are related to the diffusion flame height. Obviously, the maximum soot concentration occurs at a point where net soot formation stops and oxidation starts. The axial soot maximum must be the point where hydrocarbons are replaced on the flame axis by oxygen. This conclusion was confirmed experimentally by flame gas composition measurements. In other words, if hydrocarbons were the only fuel species present in the flame, the axial soot maximum would be the end of the diffusion flame. But for the methane/air flame investigated, sufficient hydrogen and carbon monoxide were
PREDICTION OF FLAME SIZES
229
also present for the ratio (diffusion flame height/ height to axial soot maximum) to equal 1.15. For consistency, this correction was applied to all the flames containing soot, although it made slightly poorer the agreement between diffusion flame heights measured from soot and carbon monoxide concentrations.
0'004
o []
~
0'003
:/
3. EXPERIMENTAL CONDITIONS
I
c 'tf 0
v J *
0"00: REF ,5) I
Z
r
0 /"
/
CH4 /,8"9/ /o CH4 [1%8 9~IT
/I
The burners used in this work were: (A) Circular port burner, diameter 0.36 to 10.2 mm; (B) straight slot burner, water cooled at 60°C. Length 90 ram, width 0.33 to 9.0 mm. The burners were placed within an enclosure, to control the secondary air flowrate and composition. Soot measurements were performed only on the circular port burner, with an enclosure crosssection which varied from 30 × 30 mm to 50 × 100 ram. The secondary air flow rate was varied from two to five times the stoichiometric requirements. These changes were found to have no effect on flame height. The apparatus for measurements of carbon monoxide escape is shown in Fig. 1. The enclosure had a cross-section 250 × 250 ram, with a secondary air velocity of 0.05 m/sec for the circular port and 0.075 m/sec for the slot burner.
/
2'0 CH4] t.-2 CH41] I)0"2 CH4II j
\
co I2o.9]+, ~ I ~
,4-0
¢
,
\
I
•,*
:, 27,0-3{,o,,.,,,,}-,
0 .ol
,Z; ° T©
I
I
1"0
2"0
3"0
I
In {1+1/s1 Fig. 2. Circular port diffusion flame sizes found from measurement of carbon monoxide escape. The fuel gas compositions are given in Table 1.
4. RESULTS AND DISCUSSION TABLE1
4.1. Circular Port Diffusion Flame Sizes
The equation derived in part I for the diffusion flame height (H) of a circular port burner was:
(H/Q) = {47rDo In (1
+
1/S)}-I(To/Tf) °'67,
(1)
where the symbols are defined in the nomenclature (Part I). The proportionality between H and flow rate Q was found to hold except at very low flow rates, where axial diffusion reduced flame size. Equation (1) was tested by plotting (H/Q) against {ln (1 + l/S)} - x for the fuel gases shown in Figs. 2 and 3. The flame sizes found from CO escape are shown in Fig. 2 for primary aerations from 25 to 95% of stoichiometric. The figure includes a value of H/Q for a CO/air diffusion flame, deduced from
Gas Mixture Letter
See Figs. No.
A B C D E F
3 3 2,3 3 3 3
G
2 2 2 3 3
Composition
95% CH4 + 5% C3H8 90% CH4 + 10 %C3H8 87% CH4 + 13% C3H8 50% CH4 + 50% AIR 33% C3H8 + 67% AIR 47% CH 4 + 35% H 2 + 10% C2H 6 + 4% C3H 8 + 4% N 2 30% CH 4 + 35% H 2 + 29% C3H 8 + 1% C4HIO + 5% CO2 65% CH4 + 35% H2 49%CH4+ 35% H2 + 16% C3H8 49% CH4 + 26% H2 + 25% C3H8 14% CH 4 + 48% H 2 + 14% C2H 4 + 24% N 2
F. G. ROPER, C. SMITH, and A. C. CUNNINGHAM
230 0-050
an average value in Eq. (2) below:
(H/Q) = (1.33
(2)
X
0,0t.0
X
A comparison of Eqs. (1) and (2) gave an estimate of Tf as 1500 K, which seems a reasonable mean temperature for the flame regions controlling diffusion. D O was taken as the diffusion coefficient of oxygen, calculated from LeonardJones viscosity fitted parameters [8]. (D O = 20 mm 2 sec - 1 at 293 K.)
r H/0=1"/,0
10-3{1-
0.030 'E E i
Tl__q L~
0'020
0.010
10 - 3 mm - 2 sec){ln (1 + I/S)} - 1 .
' SYMBOL FUEL GAS
,r'~
O A
//
X Y +
7 U
CH4 C2H6 C2 HL C2 H2 C3H8 C3H6 GAS A
4.2. Slot Burner Diffusion Flame Sizes
The values of Tf and Do found above may be used to calculate diffusion flame sizes for a straight slot burner. Substituting these values into Eqs. (23)(25) of part I.
OA$ B
GAS C GAS D
GAS E
0
!
tl 20
OAS K GAS L GAS F
Momentum Control." 30
In{ I "11s)
Fig. 3. Circular port diffusion flame sizes found from soot concentrations within the flame. The fuel gas compositions are given in Table 1.
HM = (.086
bQM4~2To I
/
(3)
Buoyancy Control: H B = (.20
the results of Hess [15]. For flames where H >> burner diameter (d), the points lie close to the straight line in Fig. 2. This linear relationship follows from Eq. (1) if Tf and Do are constant. The points which lie significantly below the line in Fig. 2 have ratios (H/d) less than about six, so that axial diffusion cannot be ignored. Vitiation of primary and secondary air had a large effect on the flame sizes in Fig. 2. A reduction of only 10% in oxygen concentration increased H by up to 60%, as predicted by Eq. (1). The flame sizes found from soot concentrations are plotted in Fig. 3, which again shows that (H/Q) ~ (in (1 + l/S)} - 1 . A change in burner diameter from 0.36 to 1.0 mm was found to reduce (H/Q) by 10%. In this case axial diffusion can be ignored, as (H/d) > 50. The effect seems to be due to buoyancy, and is discussed in Section 5. The equations of the lines in Figs. 2 and 3 differ only slightly, so it seems permissible to take
mm - 2 sec)
mm - 4 / 3 sec 213)(Q4(94/aL4)l/3
(4)
Transition Region: ~H = (4~(HB)
3
II1+v, / -] 338(HM~312/3 1
(5) The mean acceleration "a" of the flame gases due to buoyancy is needed in Eq. (4) to predict HB. We will treat "a" as an empirical constant. For fuel gases premixed with a substantial proportion of air, the maximum possible value of "a" is approximately g(Tf/To - 1) ~ 40 m sec - 2 . In practice, this value will be reduced by momentum losses to the surrounding air. The values of H observed and predicted from Eq. (5) are shown by the solid points in Fig. 4. The fuel gas was methane, with primary aerations from 30 to 80% of stoichiometric. H was determined as in section 2.1. For flames where buoyancy effects were small, the predicted and observed
PREDICTION OF FLAME SIZES
231
I/,0 E E 120
I
~100 o uJ :::) 80
x
+
Jr
•:.tl_~f
, I~
T.gORY
,•"
I I 0
4.3. Diffusion Flame Sizes from Burke- Schumann Theory
PART T
~la~"
LU
MOMENTUM BUOYANCY CONTROLLED CONTROLLED FLAMES FLAMES
THEORY
I 20
I 40
I I 60 80 CALCULATED
I 100 VALUE
width (b) for momentum control and independent of b for buoyancy controlled flames, as predicted from Eqs. (3) and (4). From part I, the criterion for buoyancy effects to be negligible is that the modified Froude number Fr >> 1. Figure 5 shows that the transition from momentum to buoyancy control occurs when Fr ~ 1.
I l 120 11.0 OF H-rnm
I 160
180
Fig. 4. Experimental and predicted diffusion flame heights for slot burner. The 45 ° line shows where the points should lie for complete agreement between theory and experiment.
values of H agreed well, regardless of the value taken for "a". When buoyancy effects were significant, good agreement was found if "a" was taken as 25 m sec - 2 , 60% of the maximum value. However, this value is not critical; a 50% increase in "a" decreases H e by only 12%. Figure 5 shows the transition from momentum to buoyancy control as the slot width increases. The curve in Fig. 5 shows the value of (H/Q) calculated from Eq. (5) taking a = 25 m sec- 2 . It can be seen that (H/Q) is proportional to the slot
The results given above can be used to test the Burke-Schumann (B-S) theory of diffusion flame size [1]. On this theory, the diffusion coefficient found from the circular port flame sizes is 60 mm 2 sec- 1 , equivalent to diffusion at 575 K. If this coefficient is used to predict flame sizes for the slot burner, the results are the crosses shown in Fig. 4. When buoyancy can be neglected, the observed flame sizes are about six times larger than predicted by the B-S theory. The results imply a diffusion coefficient for the slot burner (on the B-S theory) of 10 mm 2 sec- 1 , equivalent to diffusion at 190 K. The points for buoyancy controlled flames are scattered, but the ratios (Hexperimental/Hpredieted) are lower than for momentum controlled flames. In other words, buoyancy effects decrease flame size. The opposite effect would be expected by the B-S model, where an increase in gas velocity due to buoyancy should increase flame height.
4.4. Experimental and Calculated Flame Gas Compositions
500
z,O0
E
Io
~2oo
/ ° '~/I
! \l IBUOVANCV CONTROLLEDFLAM ,
~F r = l
~
-]
Fr > > 1 (MOMENTUM CONTROLLED FLAME) BURNER SLOT W I D T H - m m
Fig. 5. Transition from momentum to buoyancy control for slot burner flame. The solid line is the calculated curve.
The concentration profiles of CO, CO2, and 0 2 were calculated for the tail of a methane/air flame with primary aeration 60%. The method described in Part I was used, with the values of Do, Tf, and "a" from the present work. The results are compared with experiment in Figs. 6(a) and (b). In the region close to the flame axis and just above the primary flame zone, the measured CO and 0 2 concentrations are greater than calculated. This implies that conditions there have not yet reached equilibrium. But the remainder of the profiles show good agreement between theory and experiment. In particular, the width of the profiles agrees well with the calculated values. For
232
10
F.G. ROPER, C. SMITH, and A. C. CUNNINGHAM
/•
I
POSITION OF PRIMARY FLAME ZONE [] []
~
ENO OF
I
DIFFUSION] FLAME ]
Io 22
I
I
I Z
(I:
I
[]/~CALCULATED [
,--~7 06
[J 20 . . . .
.,/
P'5 Z
"~/" A
J;
%
ILl (..)
\
z/, O (J
A []
r
CO CO2
o
[
02
".o I
",, I o / '~~
o
,F~ ~,4w"~i, 60
- - 70
I
I
I
I
I
36
38
40
TIME
I /.2
l /./.
I
/.6
-millisecs
(a)
;\, -5
/
/ / /
/
o
100
]
CALCULATED LINE
/
o/o',,,,
¢
90
3/,
02
i:il"
-"r"--~._
80
o
16 - -
/
HEIGHT ABOVE BURNER-ram 32
181
i
%
o
I--I
EXPERIMENTAL POINTS [ SPECIES
LINE =limp
l
ol
CO2 EXPERIMENTAL POINTS CO2 CALCULATED LINE CO EXPERIMENTAL POINTSco CALCULATED LINE 02 EXPERIMENTAL POINTS
Td
"2,..
X
0
5
10
RADIAL DISTANCE -ram
(b)
Fig. 6. Concentration profiles for circular port burner-comparison of theory and experiment: (a) Axial profiles, (b) radial profiles 60 mm above the burner.
comparison, the classical Burke-Schumann theory would predict profiles less than half the observed width. The predictions of CO escape into a heat exchanger above the burner are compared with experiment for the circular port flame described above and for two slot burner flames. The diffusion flame height was found from the local gas compositions, as previously described. For the circular port flame the agreement between experiment and predictions is very good. For the slot burner, the experimental and calculated profiles are approximately parallel, and differ at most by 8% of the flame height (see Fig. 7).
5. C O M P A R I S O N WITH O T H E R W O R K
When a comparison was made with previous work for the visible flame size (HF) of a circular port burner, a linear relationship was found between (HF/Q) and (In (1 + l/S)} - 1 . The graph was similar to Fig. 3 (where H replaced HF) except that the linear relationship now extended from town gas to butane. The graph was restricted to flame sizes where soot was present, as the significance of "blue" flame sizes is doubtful. The results of the present work in general agreed well with Refs. [1, 3, 12, 15-17] for the laminar flow region where HF De Q. However, an anomaly occurred
PREDICTION OF FLAME SIZES
233
A Ill
1"0 SYMBOL BURNER
FLOW RATE, mls -1 METHANE
"--0--
C RCULAR
6ram I 0'
PRIMARY AIR
9"6
554.
"--"D----
0
SLOT
25.9
124
..°.°~
l, (3 mm SLOT
18" 0
103
....
8mm
(,o
t!
o ~°C. b 0_
V.. ~-
o
g
~t ~ IE O ~02
"~. ©
o w LIJ
CL
"~ %,%E]A °.%
X
z
0 0"6
\.
"...'... "
0"7
0"8
0-9
1'0
1-1 12 HEIGHT ABOVE BURNER DIFFUSION FLAME HEIGHT
-~
The effect of axial diffusion on flame size, found in section 4.1, is also confirmed by other workers. For short flames of butane, Savage [17] found that the ratio (Hp~eaietea/Hobservea) depended on the Reynolds number within the burner-which in turn is proportional to (H/d). When plotted in this way, the results of Savage and Barr (given in Ref. [17]) agree fairly well with the present work. The effect of buoyancy on flame size was investigated by Edelman et aL [9], using a numerical method which ignored axial diffusion. Their results show that a tenfold decrease in Fr reduces (H/Q) by only 7%, in the range 10- 1 > Fr > 10 - 5 . 5 . This agrees with the experimental results of the present work and those of Hess [15].
O
13
1''t
Fig. 7. Carbon monoxide concentrations in the combustion products sampled through a heat exchanger comparison of theory and experiment.
for propylene. The ratio (HF/Q) for this gas was much greater than for propane although the two diffusion coefficients should be similar. The effect did not occur for the values of (H/Q) in Fig. 3. The explanation is that, when soot concentrations are high, a soot oxidation zone follows the diffusion flame, causing a large increase in visible flame size. This point was shown clearly by Lee et al. [21]. Reed and Roper [20] have also shown that the length of the soot oxidation zone increases as the soot concentrations increase and as the secondary air supply decreases. Soot escape was found to occur when the ratio (soot oxidation length/H) reached a value close to one. The visible length of hydrocarbon flames at the point where air starvation just caused soot escape (//smoke) was measured by Vaerman [18]. He found that (Hsmoke/Q) cc S for olefins and paraffins up to C7. This is equivalent to two of the previous conclusions: that (H/Q) ~ {In (1 + l / S ) } - 1 , and that (soot oxidation length/H) is constant at the point of soot escape. (For the fuel gases concerned, (In (1 + l/S)} - 1 - S ) .
6. CONCLUSIONS (1) Experimental verification has been obtained for the theory given in part I for the diffusion flame sizes of axisymmetric and straight slot burners. (2) Concentration profiles in the tail of the flame may be predicted by diffusion theory, assuming the flame gases to be in thermodynamic equilibrium. This assumption is not valid in the region just above the primary flame zone. (3) Diffusion flame sizes may be found experimentally from measurements of soot or carbon monoxide within the flame. Visible flame sizes only approximate to the diffusion flame size when sufficient secondary air is present, and when small concentration of soot are present within the flame.
The authors are glad to acknowledge the help of Dr. M. E. Nolan, Dr. K. Thompson, and Mr. B. C. Dutton in the computation o f equilibrium flame gas compositions. They also wish to thank their colleagues at Watson House for many helpful discussions, and British Gas for permission to publish this paper.
REFERENCES 1.
B u r k e , S. P.,
and Schumann,
Chem. 20, 998 (1928).
T . E. W., Ind. Eng.
234 2. Hottel, H. C., and Hawthorne, W. R., Third Symposium on Combustion, Flame and Explosion Phenomena, Williams and Wilkins, Baltimore, 1949, p. 254. 3. Wohl, K., Gazley, C., and Kapp, N., Third Symposium on Combustion, Flame and Explosion Phenomena, Williams and Wilkins, Baltimore, 1949, p. 288. 4. Clarke, J. F.,Proc. Roy. Soc. A. 296, 519 (1967). 5. Melvin, A., Moss, J. B., and Clarke, J. F. Comb. Sci. Tech. 4, 17 (1971). 6. Williams, F. A., Combustion Theory, AddisonWesley, Massachusetts and London, 1965. 7. Carslaw, H. S., and Jaeger, J. C. Conduction of Heat in Solids, Oxford University Press, 1947. 8. Fristrom, R. M. and Westenberg, A. A., Flame Structure, McGraw-Hill, New York and London, 1965. 9. Edelman, R. E. Fortune, O. F., Weilerstein, G., Cochran, T. H., and Haggard, J. B., Fourteenth Symposium (International) on Combustion The Combustion Institute, Pittsburgh, 1973, p. 399. 10. Cochran, T. H., and Masiea, W. J., Thirteenth Symposium {International) on Combustion, The Combustion Institute, Pittsburgh, 1971, p. 821. 11. Fay, J. A., J. Aeronautical ScL 21,681 (1954). 12. Goudie, G. O., "Mixing and Combustion of Gas Jets," PhD Thesis, University of Glasgow, 1967.
F . G . ROPER, C. SMITH, and A. C. CUNNINGHAM 13. Goldburg, A., and Cheng, Sin-L, Comb. Flame 9, 259 (1965). 14. Powell, H. N., and Browne, W. G., Sixth Symposium Ilnternational) on Combustion, The Combustion Institute, Pittsburgh, 1956, p. 918. 15. Hess, K., "Flame Length and Flame Stability," Dissertation, Karlsruhe T.H., 1965. 16. Barr, J., Fourth Symposium {International) on Combustion, Williams and Wilkins, Baltimore, 1952, p. 765. 17. Savage,L. D., Comb. Flame 6, 77 (1962). 18. Vaerman, J.,Ind. Chem. Beige. 32,653 (1967). 19. Jones, J. M., and Rosenfeld, J. L. J., Combust. Flame 19,427 (1972). 20. Reed, S. B., and Roper, F. G., Gas Council Research Communication GC 186, presented to the Autumn Research Meeting of the Institute of Gas Engineers, 1971. 21. Lee, K. B., Thring, M. W., and B6er, J. M. Combust. Flame 6,137 (1962). 22. Dalzell, W. H., and Sarofim, A. F., Trans. ASME J. Heat Transfer 91,100 (1969). 23. Pearce, W. J., Optical Spectrometric Measurement o f High Temperatures, University of Chicago Press, 1960. Received 14 June 1976; revised 12 January 1977