June 1952
INDUSTRIAL AND ENGINEERING CHEMISTRY
fall on one curve, showing that the decomposition properties of the two nitrocelluloses are practically identical. The data given in these tables are comparative only and are based on results obtained on one particular apparatus. Thus trinitrotoluene did not explode in the apparatus a t 360” C., whereas Robertson (8) under different conditions obtained explosions a t temperatures almost 100” lower. The authors believe, however, that the apparatus described is well suited for obtaining reproducible data on relative stability of explosives. LITERATURE CITED (1) Garner, W. E., and Gomm, A. S.,
J. Chem. SOC.,1931, 2123. Proc. Roy. SOC. (London),
(2) Garner, W. .E.,and Hailes, H. R.,
A139, 576 (1933).
1395
(3) Kostevitch, M., 2. ges. Schiess-Sprengstoffw., 23, 156 (1928). (4)Marshall, A., “Explosives,” Vol. 2, Philadelphia, P. Blakiston’s Son & Co., 1917. (5) Robertson, A. J. B., Trans. Faraday Soe., 44, 677 (1948). (6) Ibid., p. 977. (7) Roginsky, S., Physik. 2. Sowjetunion, 1, 640 (1932). (8) Semenov, N., “Chemical Kinetics and Chain Reactions,” Chap. 17, Oxford, Clarendon Press, 1935. (9) Urbanski, T., and Rychter, Compt. rend., 208, 900 (1939). RECEIVED for review April 30, 1951. ACCEPTEDFebruary 29, 1952. Work performed a t the Pittsburgh Station of the Bureau of Mines during World War 11, supported by a transfer of funds from the Office of Soientific Research and Development. I t was described in OSRD Report 1986, reoently deolassified by the Ordnance Department of the Army. The authors are grateful t o Colonel C. H. M. Roberts of the Ordnance Department for his assistance in having the report regraded.
Evaluation of Flame Speed at Burner Flame Tip L. C . LICHTY Yale University, New Haven, Conn.
T
H E Bunsen burner flame has long been used to determine the flame velocity of a combustible mixture of fuel and air. Usually, laminar flow conditions are maintained in order to eliminate the effect of turbulence on flame velocity. One of the common methods ( 4 )for evaluating flame velocity is to determine the velocity component of some lamina in the mixture stream perpendicular t o the flame surface the lamina enters. Usually, the velocity is determined for the lamina a t a radius of 0.707 of the inside radius of the burner tube as the velocity of this lamina is the mean flow velocity for the laminar burner stream. The assumption is made that in laminar flow the various stream laminas flow vertically out of the burner tube to the flame surface. The excellent work of Lewis and von Elbe ( I ) , in determining the direction of flow lines of the various laminas of mixture before entering the flame and of the products of combustion after leaving the flame, has shown that the customary angle method is inaccurate because of the bending of the flow lines as they approach the flame surface. Thus, the actual velocity with which the mixture stream enters the flame surface, except for the flame tip, is appreciably higher than usually computed on the assumption that all flow lines do not change direction before entering the flame surface. Only a t the flame tip does it appear that the unburned mixture actually enters the flame surface perpendicularly without changing its direction of flow. Consequently, Lewis and von Elbe concluded that the flame velocity at the burner tip is equal to the velocity of the unburned central lamina mixture velocity as it leaGes the burner tube. This indicates a very high velocity compared t o velocity determinations at various flame positions, even a t those very near the flame tip. Lewis and von Elbe found by their measurements that the flame velocity increased from 63 om. per second a t a distance of less than 0.02 cm. from the burner axis to 213 cm. per second a t the axis. It is this extremely large increase in flame velocity between two laminas only a short distance apart that ia under question and to which this study is directed. The relatively high flame velocity at the flame tip is usually accounted for by the assumption that the central mixture stream is heated appreciably before entering the flame surface and that this rise in mixture temperature increases the flame velocity very appreciably. The experimental evidence of Lewis and von Elbe ( I ) , for the flame of a mixture of 7.50% natural gas in air, shows an increase in stream velocity, except for the flame tip, as the unburned mix-
ture passes through the flame surface and emerges as products of reaction. This increase in velocity of products compared to mixture indicates a momentum effect. von Elbe and Mentser (6) have made use of this momentum effect to evaluate the mean flame velocity for an acetylene-oxygen burner flame from the pressure build-up beneath the flame as measured in the burner tube. The usual assumption, made by them and others, was that the flow area does not increase in passing through the flame. This is equivalent t o assuming that the flame thickness is very small, The same assumption is used in this paper to determine the limiting or minimum value for the tip flame speed. However, the increase in flow area that may be caused by heat transfer into the unburned lamina before it reaches the flame, the increase in flow area that may result from appreciable flame thickness, and the effect of each on the computed tip flame speed are indicated. The flow of the burner central mixture stream t o and through the burner flame tip should be subject to the usual momentum effects that were observed for other mixture laminas in passing through the flame cone at positions other than the flame tip. This would indicate a products velocity immediately above the flame tip appreciably higher than the c e n t r a l m i x t u r e velocity leaving the burner , depending on the amount of heat transfer to the unburned mixture before entering the flaine. This is not in accord with the experimental eviHEATING 1 -% dence mentioned. However, ---It* the equality of the velocities of the burner central stream RAM SECTION before and after the flame surface can be reconciled with the inherent momentum effects if the following proc-- 4, esses occur: CENTRAL BLRN,ER STREAM‘,, \
Figure 1. Central Burner Stream
1. The central mixture stream is rammed from pl and TIto p z and TI’(Figure 1) as it approaches the tip. This decreases the stream velocity from o1 to 2r2. This ram-
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
1396
ming of the stream does not change the temperature or pressure appreciably because of the low velocities involved. 2. After or during ramming, the central stream is heated at constant pressure p , from TI' to Tz by the flame. Actually, this process and the ram process may occur simultaneously, the net result being the same, except for a negligible difference in heat transfer. 3. The central stream undergoes the usual momentum effect in passing through the flame and has its velocity increased from v2 to 213, which is equal to the original stream velocity, VI, as indicated by the experimental evidence for the case in question. Pressure and temperature change from pz to p a , and from T2 to respectively. 212 is the flame velocity, as this is the velocity with which the combustible mixture actually enters the flame front. FUNDAMENTAL RELATIONS FOR ANALYSIS
The adiabatic reversible ram equation for compressible flow is ~12/2g-- ~2'/2g = 778cp(T:' - T I ) = 778cpTi[(pz/p:)
(IC
-
1)I.k
-
I ] (1)
If u2 is assumed to be zero, then Ti' - Ti
=
u12/2 g 778 cp
(2)
Thus, for a ram temperature rise of 1' F., v I would be about 110 feet per second for air. Consequently, rain temperature rise may be neglected in cases in which the stream velocity is less than 100 feet per second. The adiabatic reversible ram equation for incompressible flow, Vi2/28 - 2'22/29
=
lAh? = Vl(ZAP1)
(la)
is used in the following analysis, because the specific volume, V , of the mixture undergoes a negligible change during the ram process. The momentum equation for the lamina in question, for a constant flow area through the flame, is (3)
The continuity equation for flow through the flame, for the assumed constant flow area, is
udV3
h/Vz
=
(4)
Then, neglecting the effect of the very small pressure drop through the flame front on the change in specific volume of the medium, M3T3/NzTz
03/1>2
(5)
Combining Equations l a , 3, and 5, and assuming that 2Ap1 and are equal, which is equivalent to assuming that the pressure build-up in the burner tube for the low flow velocity is negligible compared to l A p z , the ram effect beneath the flame tip,
If the pressure build-up above atmospheric in the burner tube were known, then 2A.m =
or
2Apl
+ - I p in burner tube
~ A p i=
d24p3)
Combining this relation with Equations la, 3, and 5 results in
HEAT TRANSFER FROM FL4\1E TO UNBURNED MIXTURE
The assumption of heat transfer from the section of the flame to the mixture stream which will enter this flame section tndicates the following energy relation for the heating and combustion processes:
C,,, 5
(Hmtxhi'
+
Qtn
=
Cmx
+
(Hrnn.)~~ = (ffprodh
The foregoing heat-transfer assumption indicates that Q,, = and that the temperature of the products, Talis the same regardless of the amount of this heat transfer. However, T z depends on this heat transfer. Thus, &,,t
T z - 2'1' = AT = Q l n / M ~ p
(8)
DATA FOR MIXTURE
-4mixture of 7.50% natural gas in air was used by Lewis and von Elbe for their track particle photographs. The central lamina velocity was 213 cm. per second (6.99 feet per second). The mixture mole relationship, neglecting the small amount of nitrogen is 7.5 (0.818 CH4
+ 0.177 CzHb + 0.005 Xi) + 92.5 air = 1 CHa + 0.216 CZHB+ 15.09 air
The molecular weight of this mixture is 28.2 pounds per mole. At a temperature of 27" C. the specific heat of this mixture is 7.17 B.t.u. per mole per F. difference, or 0.254 B.t.u. per pound per F. difference. Also, a t 27" C. and a pressure of 14.7 pounds per square inch absolute, the specific volume of the mixture is 14.0 cubic feet per pound. Then,
V2 = 14.0 TS/T1
(9)
DETERMINATION O F ADIABATIC FLAME TEYIPERATUI
