2424
INDUSTRIAL AND ENGINEERING CHEMISTRY
now shown that under the conditions of his experiment rupture would be initiated a t the periphery. Hirnilarly Hassialis and JIyers (G)overlooked the lenslike shape of t,he ent,rapped film. Theae authors actually observed the fringe system corresponding to Figure 6, b u t were unable to intcrpret it. Sven-Nilsson ( I S ) used a method for measuring induction period whereby the bubble holder M-as vibrnted Tyhile the bubble was pressed against a plane hydrophobic surface. By observing thr fringe patt,ern during such i i n esperirnont, it, is seen that the tiisjoining film is of the type shown in Figure 6,d, and each vibration propagates a wave on the bublile surface which carries a siiiall amount of v,-at,er into the lens, thus opposing out,ward drain:ige. Contact occurs when the periph of the lens is able to thin to the rupt,ure thickness in the interval i)et,ween two sucwssive wave^. I’hilippoff has quest,ioncdthe rclevancy of Sven-Silssou’P results to practical flotation 011 the grounds that t,he duration of bubble-mineral contart is t,oo short t o Le influenced by such “longterm phenomena.” Sven-Silssoii‘s results are an excellent qualitative index of induction period, the high values obtained beiog simply the result, of using :I plane surface instead of a smnll mineral particle. Such R misunderst,aiiding arises from the vieTv, no longer t,enable, t,hat induction period is an int,rinxic property of the hydrophobic surface, whereas the present work shows t h a t for a given solid in a given liquid, only the rupture t,hickness is an intrinsic property of the interface, the induction period depending in addition on the size and shape of the particle and on the motion of the particle relative t,o the bubble.
Vol. 46, No. 11
ACKNOVI’LEDGM ENT
The author is indebted to IC. L. Sutherland, W. E, Ewerq, anti other members of the Physical Chemistry Section for their hclptu1 discussion and their criticism of the nianuscripi. LITER i’I’URE CITED
(1)
Dci.j:tgnin, 13., anti l., mici Jiyers, C . C . , Mining E,ig., 3 , 961 (t951). er, $1.C., .1. C‘olloid Sci., 7, 443 (1952). (2 f’hilippoff. \T., M i n i n g E?lg., 4, 386 (1952). ti Daiciiisicwics. ,J,, RdZ. Inst. M 3000 , I< ) by tho order oi tlifference shown in the last lines of Tables I and 11. Data alro exist that allow test of some of the assuinptionh macle in the derivations of Equations 5 and 8--naniclyJ Equations 3a and 4. TEST(2. With reference to Equation 3a, Dugger ( 1 ) merisureti the effect of initial temperature on burning wlocities of propitneair mixtures. By using these data on S,, and values of T , froni Table 11, calculations have been made of
Figure 5. Initial Temperature us. Critical Boundary Velocity Gradient for Blowoff of Methane-Air Flames
~
L
9
i0,OGC
r
5
9 10030 d aom
6
6,mC
9 2 4WO > 4
L
=
P
2,000
2 E
1,OCO
323
350
400
450
500 INITIAL TEfCFEPATJRE
550 'K
600
650
703
Figure 6. Initial Temperature us. Critical Boundary Velocity Gradients for Blowoff of Propane-Air Flames ( 1 )
Only an approximate constancy of T i j etc., is looked for in this treatment of the temperature dependence of flarnc stability limitk. The small variations of Ti, etc., in Tables I to IV with initial temperature are not,ed and judged negligihlc for the purpose at hand in view of the per cent deviations sl1oa.n in Tables I to IV and the agreement betiveen flash-hack and hlon-off data in Table I. The extent of inaccuracy caused by neglecting these variations may be judged from Figures 10, 1 I, and 12 and a comparison of predicted and experimental flame st,a\iility gradients. The t,lieory developed in this paper is shown in thcse figures t o be capable of approximately relating flash-hark and blon-off gradients a t room temperature t o t,hosrT coi,responding to several higher temperatures for two fuels and for nn estensivt~range of lean t o rich flames. If the assumptions, :tpprosimittions, and averages taken arc inadmispihle, i t seems most unlikely that these would cancel out so well in so many inptances. Equations 5 and 8 and values of Ti froni T ~ b l ( I3 may be used to calculate flash-back and blo~voffciirves for nicthane as a function of Tu, starting with the room temperature curves. Experimental curves and curves calculated in this way are compared in Figures 10 and 11. The agreement is satipfaetory, which it would not be if the average values of 5"; were not correct for all values of Tu. TESTB. The same procedure can bc followed for propane-air fuels, using data obtained by Dugger ( 1 ) . Values of Ti for propane-air are given in Table 11. Esperimcntal and calculated curves are compared in Figure 12, The agreement, is good. Corresponding calculations for other fuels rcquire flash-back and blowoff curves a t room temperature; which have not been published but are available from U. S. Bureau of Mines, Pitts-
These art: t a h l a t e d in Table 111for various values of T,. cz6 ; p is const~nt, enough t o j u d f y use of Equation 3a. TESTD. With reference to Equation 4, Friedman and Johnston ( 3 ) meamred quenching distances of propane-air mixtures Ixtween plane-parallel plates at, various initial temperatures. h l though quenching distances between plane-parallel plates are not nunierically equal to 2d,, the assumption that the temperature gradient in thc quenched zone is linear and independent of Tu
. . .
2OC
3:C
400
50:
bM
700
200
200
4CC
,5uy~K,EO>
I00
BCi
T , , K.
Figure 7 .
Flame Temperatures for Methane-Air ( 1 2 )
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
November 1954
2429
( 6 , 9 , IO). Two equations are involved-one
expresses the change in the fuel-air ratio and the second evaluates the change in boundary velocity gradients when fuel gases are exchanged. No change is required in the first equation by this theory of hot port burners. This is Equation 1 of (9) and is repeated in this paper as Equation 9. The second equation must be supplemented, I t is Equation 2 of (9) and is Equation 10 of this paper.
F2
+ d [ ( l - d0)SIz
Fz
-
4
=
0
(9)
Tvvhere
[FZS2d,] $ , = 200
?m
400
503
600
700
200
300
500 K'
EO0
?GO
800
and
Tv
1":H
Figure 8.
4W
[SZd,l,-[I-TjFd,)FSI,
Flame Temperatures for Propane-Air (1%)
must be equally acceptable for both situations. Friedman and Johnston quenching distances also include the width of the flame a t quenching. This width is assumed to be zero, an assumption that introduces a systematic error that is not involved in the deiivation of Equation 5 and that should not grossly affect this test of Equation 4. Table IV rontains values of T , - Tu divided by one half the quenching distances reported by Grumer (6). Values of T , were taken from Table 11. The quotient is found to be ioughly independent of Tu, which supports Equation 4. Tests A to D show that the> theory presented in this paper is adequate for approximate calculations of the ef! ect of initial teniperature on the critical flash back sild blowoff boundary velocity gradients of flames.
where subscript a designates fuel gas used for adjusting burners and subscript z designates new fuel gas.
PRLDICTING PERFORMANCE OF HOT PORT BURNERS
JVr?ri ONEFUEL.In practice, the initial temperatures of unburned mixtures flowing through hot ports are not readily evaluated. These will vary with thi, wall temperatures of the passages in the burner and the time available for transport of heat from the .sallq to the flowing mixture of gas and air. If the appliance is A Probable pmftle
8 Unedrued plollle
04
08
12
0 4
0.8
12
GAS C O N C E N T R A T I O N , FRACTION OF S T O l C H l O M E T R i C
Figure 10. Experimental Points and Calculated Curves for Flash Back of Methane-Air Flames at Various Initial Temperatures
i
W " M zone
I 7"
I
I
I
I
,
I
I
I
I
From unburnerl g a i to b u n &
mi
Figure 9. Temperature Profiles for a Flame
hot, the air and the gas may be heated before they enter the burner, and so forth. These considerations make it impractical to be exact and allow only consideration of the extremes that can be anticipated or consideration of a representative average temperature. The true performance of hot port burners will be somewhere in between the Aaine stability curves for room temperature and for some high initial temperature. Unless one is certain of the temperature range of the application, i t would be well to avoid designing burners that would operate in the areas below the high temperature flash-back curve or above the room temperature blowoff curve. IF'ITH EXCHANGED GASES. The theory of predicting the perCoImmce of burnerp ivith exchanged gases has been published
The exchangeability of burners a t room temperature is evaluated by following the procedure given by Grumer and associates (9). The performance of hot port burners may be predicted, too, by the supplementary use of Equations 5 and 8 of this paper. A high value of T , is selected, either as a good average value or as the maximum possible. Values of gz based on flash back are substituted in Equation 5 for ( g F ) l and the equation solved for (gZ):! Similarly, values of g2 base on blowoff are substituted in Equation 8 and solved for (g.)z. These are plotted as were the values of gz to form new curves of 1%and 2z (Figure 3 of Grumer and associates, 9). These curves should be compared with the high temperature flame stability diagram of fuel z obtained by application of Equations 5 and 8 to the room temperature flame stability diagram of fuel z. A high temperature exchangeability diagram is drawn (similar to Figure 3 of reference 9) and is usrd in conjunction with the room temperature exchangeability diagiam to predict exchangeability of fuels a and x in the conimuriity on hot and cold burners. SUMMARY
Fundamental research on the performance of fuels on gas burners has been extended in this paper to include the effect of initial
INDUSTRIAL AND ENGINEERING CHEMISTRY
2430
GAS COhCENTKATIOU, FRACT8ON O F STO C ~ I O H E i R , C
GAS COUCEhTRATlON, FRACTlON OF S T O I C i O>.lET2lC
iJ*k+?*I
40
Vol. 46, No. liil
20 0 3 0
10000 e,ooo 6,000
2 4030
40 030
s
--
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ic 000
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ioco
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z
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100
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v
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> >
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8
800
i
400
p-
600
a 200
4 6 l ? 16 20 GAS CCNCERTFAT ON C9SC'Oh O F >TO ;HICLIETRIC
100 21
Figure 11. Blowoff of Methane-Air Flames at Various Initial Temperatures
temperature of the unburned gas on flame stabilization. The problem is of practical concern since most burners operate hot. I t is shovn that the room temperature values of critical boundary velocity gradients for flash hack and blowoff are related to those for hot burnws by theoretical rquations involving the unburned gas temperature., the flame temperature, and the lon est temperature in the primary combustion zone. The last temperature is presently obtained empirically from data on variation of flashback and blowoff gradirnts viith unburned gas temperature, Experiments have included flames of methane and propane only, hut the theory is applicable to all flames. NORf ENCLATURE
c p = specific heat capacity at constant pressure, cal./(gram) (0 C.)~ d~ = quenching distance, depth of penetration of secondary air to form noncombustible boundary layer, cm. d o = specific gravity of fuel gas d, = quenching distance, depth of penetration of chilling effect of Fvall on flame, cni. g = boundary velocity gradient, sec.-] p. = fuel gas line preysure, em. water t = time, see. D = diffusion coefficient, sq. cm./sec. F = fuel-gas concentration, fraction of stoichiometric R = radius of port, cm. Re = Reynolds number S = stoichiometric fuel gas concentration, % divided by 100 S , = burning velocity, cm./sec. 7' = temperature, O K. V = volumetric flow, cc./sec. 6 = flame thickness, em. k = friction coefficient p = coefficient of thermal conductivity, cal./(ser.)(cm.)( C.) p = density, grams/cc.
4 8 12 16 20 G S S C O h C E N l RATION FRACTiON OF STO1CHIOMETL:IC
400 24
Figure 12. BlowoR of Propane-Air Flames at Various Initial Temperatures ( I )
Subscripts a refers to adjustment fuel gas b refers to burned gas u refers to unburned gas x refers to substitute fuel gas B refers to blowoff F refers t o flash back i refers to point of minimum temperature in primary combastion zone LITERATURE CITED
(1) Dugger, G. L., Natl. Advisory Comm. Aeronaut., Tech. Kate, 2170, 1950.
( 2 ) Friedman, R., Fourth Symposium (International) on Combustion, 1952, p. 259, Williams and Wilkins, Baltimore, 1953. (3) Friedman, R., and Johnston, IT. C., J . AppZ. Phys., 21, 798
(1950). (4) Fristrom, R. M., Prescott, R., and associates. Fourth Symposium (International) on Combustion, 1952, p. 267, Williams and TTilkins, Baltimore, 1953. (5) Grumer, J., Am. Gas Assoc., Project PDC-3-GU, Inbrim Rep$. 1, October 1951. (6) Grumer, J., IXD. EXG.CHERI.,41, 2756 (1949). ( 7 ) Grumer, J., and Harris, 1 1 ~ E., ISD. E m . C H E X , 44. 1543 (1962). (8) Grumer, J., Harris, h l . E., and Schults, H., Fourth Symposium (International) on Combustion, 1952, p. 695, Williams and Williins, Baltimore, 1953. (9) Grumer, J., Harris, A I . E., and Schulta, R.,ISD. EKG.CHBM.. 44, 1554 (1952). (10) Lewis, B., and Grumer, J., Gas Age, 105, 25 (1950). (11) Lewis, B., and von Elbe, G., Trans. Am. SOC.M e c h . Ennrs., 70, 307 (1948). (12) Smith, R. W.,Jr., Edwards, H. E., and Brinkley, S. R.,.TI,. LT. S. Bur. Mines, Rept. Invest. 4938, January 1953. ACCEPTEDJuly 10. 1854. RECEIVED January 14, 1054. ?resented before the Division of Gas and Fuel Chemistry at the 121th Meet. ing of the AMERICAN CHEMICAL SOCIETY,Chicago, Ill. This work is B ~ B . ported i n part by the American Gas Association, Projoct PDC-8-GU.
