COMBUSTION
JST
NOTE:
0-NEEDLE VALVE
8
Q-SEAT SEAL
XI-BACK
-HAND REGULATOR
VALVE
Figure 1,
1
-@--
FLOWMETER
O-REDUC~NG REG.
PRESSURE REG. I-RESTRICTOR Equipment layout for producing high-pressure Bunsen burner flames
LOREN E. BOLLINGER, WILLIAM A. STRAUSS, and RUDOLPH EDSE Rocket Laboratory, Department o f Aeronautical Engineering, The Ohio State University, Columbus 10, Ohio
Burning Velocities of Bunsen Burner Flames by the Flame-Pressure Method The theoretical relationship between flame pressure and burning velocity cannot be used to calculate burning velocities from flame pressures measured somewhere in the burner tube T H E efficiency of all jet engines depends, among other factors, largely on the rate of combustion of the fuel-oxidizer combination. T o effect further reductions in engine weight and volume of today’s engines, it is necessary to have propellants with faster burning velocities. Unfortunately, our present understand-
768
ing of the mechanism of flame propagation is rather scant, and it is not known how to increase the burning velocities of jet fuels. To fill this gap a program of flame studies was started at this laboratory. Because of the indistinct flame structure of hydrogen-oxygen flames burning
INDUSTRIAL AND ENOlNEERlNO CHEMISTRY
a t pressures above 20 atm., the measurements of burning velocities by the burner method became extremely difficdt and erratic. To establish reliable results it was decided to obtain the burning velocities of these flames from other methods. The flame-pressure method was selected because theoretical calcula-
0
tions indicated that hydrogen-oxygen flames produce a flame pressure sufficiently large for easy measurement. Furthermore, this method required only minor modifications of existing equipment. I n a continuation of the studies of the effect of pressure on burning velocities, Stevens’ soap-bubble method has been adapted to pressures up to 1500 pounds per square inch absolute. These measurements are in progress at present and the results will be published later. The theoretical relationship between flame pressure and burning velocity is derived by applying the continuity equation and the laws of conservation of momentum and energy to the gas flowing through the flame front. According to these expressions, the pressure difference across the combustion wave is $u
-Pb
= Pus:
[E -
I]
REG. SUPPLY PRESS., 600 PSI
I 1-600 PSI
9
(I)
where subscripts u and b refer to unburned and burned gas, respectively, p is the absolute pressure of the gases, p is the density, and Su is the burning velocity. The difference p , - pb represents the flame pressure, A@. The ratio of unburned to burned gas density is obtained from theoretical calculations of the composition and temperature of the flame gases for an adiabatic, isobaric process. The calculation is based on the assumption that complete chemical and thermodynamic equilibrium prevails in the flame gases. With the perfect gas law, the density ratio across the flame front can be written as
I
2
;5
CHAMBER PRESSURE MANOMETER
CHAMBER PRESSURE
I because the pressure difference across the combustion wave is very small in comparison with the gas pressure. Here X ‘C is the molecular weight and T is the absolute temperature. The adiabatic flame temperature, Tb, and the density ratio given by Equation 2 for hydrogen-oxygen mixtures burning at 1and 14.6-atm. pressure are listed in Table I. Experimental Method
14.6-Atm. Pressure. A schematic diagram of the apparatus used to produce stable high-pressure Bunsen burner flames is given in Figure 1. The gases were taken from standard cylinders at 2200 pounds per square inch. By reducing regulators, a constant pressure of each gas was maintained in the metering section where the gas flow rates were obtained from empirically determined relationships between the mass flow of the gas and the corresponding pressure loss occurring in the restrictors. Before
Figure 2.
SUMP
Flow diagram for flame-pressure measurements at 14.6 atmospheres
entering the mixing chamber, the gases were passed through back-pressure regulators to eliminate mutual interference of the gas flows. The combustion chamber in which the burner tube was installed consisted of a 25-inch length of %inch diameter, colddrawn carbon steel pipe. I t was provided with three ?/s-inch quartz windows through which the flames could be observed and photographed. Air, used as the ambient gas, was passed through the chamber at the rate of 300 cc. per second (NPT). This air was directed against the windows through short tubes mounted on the window flanges to prevent water vapor from condensing on the windows. A constant chamber pressure was maintained by a back-pressure regulator installed between the exit of
the combustion chamber and the exhaust line. The burners used for the experiments were made of copper or Type 304 stainless steel in the form of convergent tubes whose inner diameters at the port were 0.0747 and 0.0650 cm. They were cooled by passing water through a jacket surrounding the tubes. The auxiliary equipment for measuring the flame pressure of flames burning in a closed chamber is shown in Figure 2. The flame pressure was obtained by measuring the pressure difference between a point (Figure 2, A ) l l inches upstream of the burner tip and the chamber (Figure 2, B ) . This difference was measured twice to eliminate the effect of the pressure gradient in the gas flow in the burner tube. The first measurement was made as a stable flame VOL. 49, NO. 4
APRIL 1957
796
RESSVRE TAP 030 OD MONEL
IN INCHES MATERIAL-COPPER
t
Figure 3. Converging nozzle-type burner used in hydrogen-oxygen flame experiments a t atmospheric pressure
was burning, and the second reading was taken after the flame was blown out while the gas flow through the burner tube remained unchanged. During the starting operation of the flames, the valves of the flame-pressure apparatus leading to the combustion chamber and flame-pressure tap were closed. Then, after equilibrium of the flows was established, the chamberpressure manometer and sump were equalized to the chamber pressure while the flame-pressure manometer and its sump were equalized to the pressure a t the flame-pressure tap. As soon as pressure equilibrium was reached: valves 1, 2, 3, 4, and 5 (Figure 2) were closed. The flame was then extinguished by mo-
Table I.
mentarily injecting nitrogen gas into the combustible gas mixture in the burner tube. After all nitrogen had cleared from the burner tube (requiring approximately 20 seconds), valves 1 and 2 were opened and the flame pressure was read. The pressure in the reservoir of the flame-pressure manometer was kept constant by maintaining the mercury level in the pressure-equalizing sight a t a fixed height. Corrections necessitated by changes of the chamber pressure were ascertained by reading the chamberpressure manometer. Atmospheric Pressure. Figure 3 illustrates the nozzle-type burner used for some of the hydrogen-oxygen experiments. With this burner the inner flame
cone was laminar for Reynolds numbers up to 10,000 at the burner port. A shadowgraph of a flame on this burner is shown in Figure 4 ; the Reynolds number is 9400. A straight-tube burner having practically the same diameter as the throat of the nozzle burner was used to afford a comparison between the flame pressures obtained with laminar and turbulent gas-flow patterns. A water-cooled burner having an inside diameter of 0.0495 cm. was used for the acetylene-oxygen tests. One pressure tap was located 0.2 cm. upstream of the burner port, while for another series of experiments the tap was installed 26.5 cm. upstream. Use of the pressure tap immediately upstream of the burner port eliminated the inaccuracy involved in determining the flame pressure from the difference of two large static pressures. In addition, a few experiments were carried out with an uncooled, nozzle-type burner whose port diameter was 0.0794 cm. A 6-inch water manometer \vas used to measure the flame pressure with the three burners where the pressure tap was located immediately upstream of the flame. Extreme care was taken to ensure that the inside of the burner tube was smooth. Cooling the burners was unnecessary when the pressure tap was located very close to the burner tip, as, in this case, the pressure difference due to the gas flow in the burner tube from the tap to the exit is small in comparison with the flame pressure. The flame pressures were determined in the following way: After the gas flows were adjusted to the desired values, a reading was takm Tvith the water manometer when equilibrium was attained. Next, the gas mixture was
Calculated Adiabatic Flame Temperatures and Density Ratios for Constant-Pressure Combustion of Hydrogen-Oxygen Flames"
30.14 55.40 66.67 75.00 84.20
2343 2963 3058 2976 2551
6.705 8.025 8.279 8.154 7.268
Tu = 300' K.
2407 3270 3423 3290 2649
6.859 8.619 8.927 8.750 7.483
Figure 4. Shadowgraph of laminar hydrogen-oxygen flame on nozzletype burner a t atmospheric pressure Reynolds number = 9400
770
INDUSTRIAL AND ENGINEERING CHEMISTRY
ignited and another manometer reading secured. Approximately 10 seconds were required for the manometer to reach equilibrium. Thereafter, no change in pressure occurred even over a period of 5 minutes. The difference between the initial and final manometer readings was taken as the flame pressure. The acetylene used in the experiments was obtained from Linde Air Products Co.; analysis of the gas specified 0.35% air, 0.04% (max.) oxygen, 0.00025% phosphine, 0 . 0 0 0 7 ~ 0 hydrogen sulfide, 2.5% acetone, 0.1% water vapor, and acetylene as the balance. The acetylene was purified by passing it through an ice-cooled trap filled with activated
Hydrogen-Oxygen Flames at Atmospheric Pressure. The burning velocities as derived from the flame pressure of hydrogen-oxygen flames on straight and nozzle-type burners are presented in
Table II. Vol. % H2 in
Mixture 50.7 53.1 53.1 55.1 56.7 57.9 59.3 61.0 62.8 63.7 64.0 64.1 64.1 64.7 65.4 65.5 66.5 66.6 67.9 67.9 68.0 69.1 70.8 72.6 74.1 75.4 76.7 79.7
40
A
35
-
30
,-REFERENCE I (14 6 ATM, BURNER METHOD)
2s
\
bW
3 I
to=
9
40
so
70
60
90
80
PERCENT HYDROGEN IN MIXTURE
Figure
5.
Burning velocities of hydrogen-oxygen flames
Burning Velocities of Hydrogen-Oxygen Flames a t 14.6 Atm. as Obtained b y Flame-Pressure Method Vol. Flow Rate of Mixture (NPT), Inner Diameter of Flame Pressure, Burning Velocity, Burner Port, Cm. Cc./Seo. Inches Hg M./Sec. 1060 1120 1120 1170 1210 1240 1270 1320 1220 1180 1030 1070 978 1240 1240 1240 1210 1210 1130 906 909 1100 1170 953 672 917 836 671
0.0747 0.0650 0.0650 0.0747 0.0747 0.0747 0.0747 0.0747 0.0747 0.0650 0.0650 0.0650 0.0650 0.0747 0.0747 0.0747 0.0747 0.0747 0.0747 0.0650 0.0650 0.0747 0.0747 0.0747 0.0650 0.0747 0.0747 0.0747
3.28 3.23 4.33 1.56 3.82 2.47 3.04 3.94 3.89 3.04 3.87 2.04 2.97 2.78 4.89 3.04 1.91 1.58 2.19
12.3 12.5 14.3 8.7 13.8 11.4 12.5 14.5 16.6 13.1 14.8 10.7 13.0 12.6 16.9 13.3 10.7 9.7 11.6 13.6
3.00 1.65 1.17 1.14 0.85 0.34 0.12 0.90 0.23
10.1
8.6 8.7 8.2 5.0 3.1 8.6 4.7
VOL. 49, NO. 4
0
APRIL 1957
771
PERCENT HYDROGEN IN MIXTURE
Figure 6. Comparison of burning velocities of hydrogen-oxygen mixtures as derived b y Bunsen burner and flame-pressure methods a t atmospheric pressure
Table HI. TO].7 0 Hz in
Mixture
Flame Pressures of Hydrogen-Oxygen Flames a t Atmospheric Pressure Vol. Flow Rate of Mixture (NPT), Flame Pressure, Cc./Sec. Cm. HaOa
22.4 25.1 29.8 33.9 37.5 40.7 43.2 47.0 49.6 52.0 57.3 61.8 64.4 66.8 68.7 69.7 71.1 74.0 77.6 80.0 81.2 82.4 85.4 87.7 90.5
704 729 778 826 873 921 961 1031 1084 1138 1280 1188 1140 1159 1127 1166 1032 906 763 469 501 535 643 764 986
0.467-cm. diameter straight-tube burner. I, 0.470-cm. diameter converging-nozzle burner.
772
Figure 6 ; Table I11 contains the experimental data. The burning velocities derived from flame-pressure measurements are approximately one half of the values obtained by the Bunsen burner method. For mixtures containing less than 70"/c hydrogen the nozzle-type burner produced somewhat smaller flame pressures than the straight-tube burner of the same diameter. Whereas the flames on the nozzle-type burner were laminar, all flames on the straight burner were turbulent. For both burners, however, the observed flame pressures were independent of the linear gas velocities at the burner port. The flow velocities in these experiments ranged from those at flash back to values more than twice as large. Acetylene-Oxygen Flames at Atmospheric Pressure. According to the measurements of von Elbe and Mentser ( 4 ) , the burning velocities of acetyleneoxygen mixtures as derived by the Bunsen burner method are identical with those derived from flame-pressure measurements. To find out whether the behavior of hydrogen-oxygen flames differs from that of acetylene-oxygen flames, von Elbe's measurements were repeated in this laboratory. Their results together with the present observations are given in Figure 7; the experimental data are listed in Table IV. According to the present measurements the burning velocities based on flame-pressure measurements are much lower than those derived from cone dimensions. In one series of experiments the flame pressure was measured 26.5 cm. up-
INDUSTRIAL AND ENGINEERING CHEMISTRY
0.08 0.08 0.20 0.32 0.41 0.54 0.66 0.76 0.90 0.96 1.06 1.07 1.01 0.96 0.89
...
0.73 0.60 0.40
... ... 0.17 ...
0.06
...
Flame Pressure, Cm. Haoh
0.06 0.05 0.14 0.21 0.28 0.41 0.51 0.63
...
0.79 0.90 0.95 0.94 0.89 0.87 0.76 0.73 0.59 0.41 0.36 0.22 0.16 0.06 0.05 0.05
BURNING V E L O C I T I E S little higher, in view of the fact that the evaluations were based on theoretical flame temperatures which are somewhat higher than the actual flame temperature. Probably this correction would increase the burning velocities by only a few per cent. According to Figure 7, the present burning velocities of acetylene-oxygen flames as derived from flame-pressure measurements are much lower than those obtained by von Elbe and Mentser. O n the other hand, the burning velocities obtained by the burner method in this investigation are somewhat higher than those published by von Elbe and Mentser. Concl usion s
30
20
40
PERCENT ACETYLBNE
50
60
IN MIXTURE
Figure 7. Comparison of burning velocities of acetylene-oxygen mixtures as derived by Bunsen burner and flame-pressure methods at atmospheric pressure
Table IV. Flame Pressures of Acetylene-Oxygen Flames at Atmospheric Pressure on 0.0495-Cm. Diameter Straight-Tube Burner Vol. Flow Rate of MixVol. % CzH2 ture (NPT), Flame Presin Mixture Cc./Sec. sure, Cm. H20 30.7 35.9 45.3 51.5 63.5
5.84 5.38 4.30 4.84 7.40
’
2.59 3.00 2.13 0.71 0.41
stream of the burner tip, while in later tests the tap was located only 0.2 cm. upstream. The same burner was employed for both series of experiments. Data taken at the former location showed a moderate amount of scatter; this probably resulted from the fact that the flame pressure was obtained from the difference of two fairly large pressures. Since the burner tip was water-cooled, the pressure drop that the gases experience when flowing through the tube was not affected by the heat from the flame. Discussion
For both hydrogen-oxygen and acetylene-oxygen flames, the burning velocities derived from flame-pressure measure-
ments a r e much lower than those obtained by the burner method. This discrepancy may be caused by the radial escape of unburned gas at the burner rim without haying passed through the flame front. The relationship between the true flame pressure, A@, the measured flame pressure, A@,,,,,, and the escape velocity, u,,, is given by Bernoulli’s equation (3)
The volume flow rate of gas escaping through the dead space, u,,, depends on the escape velocity and the width of the dead space, h, that is, the distance between the burner rim and the base of the flame cone : ueS = u,,irdh
(4)
where d is the diameter of the burner port. For the flow velocities investigated it appears that the escape velocity is independent of the linear gas velocity a t the burner port. Since the dead space increases with increasing velocity of the unburned gas, it is obvious that the amount of gas escaping through the dead space also increases as shown in Equation 4. T h e burning velocities derived from flame-pressure measurements might be a
I n view of the results obtained with hydrogen-oxygen and acetylene-oxygen flames, it is concluded that the theoretical relationship between flame pressure and burning velocity cannot be used to calculate burning velocities from flame pressures measured somewhere in the burner tube because of the radial escape of unburned gas through the dead space. A more exact relationship between flame pressure and burning velocity should be obtained by adding the term ‘/z p,uzs to the observed flame pressure according to Equation 3, provided that a reliable value for the escape velocity could be established. T h e particle track method introduced by Lewis and von Elbe might be suitable for measuring u,, ( 2 ) . However, no experiments were carried out to investigate the relationship expressed in Equation 3 because of other commitments. Acknowledgment
The authors express their thanks to
M. C. Fong and H. E. Smeck for their assistance in conducting the experimental observations. Literature Cited (1) Edse, R., “Proceedings of the Second Midwestern Conference an Fluid Mechanics,” pp. 441-57, Ohio State University Press, Columbus, Ohio, 1952. ( 2 ) Lewis, B., von Elbe, G., “Combustion, Flames and Explosions of Gases,” pp. 266-7, Academic Press, New York, 1951. ( 3 ) Zbid., p. 460. (4) von Elbe, G., Mentser, M., J . Chem. Phys. 13, 89-100 (1945).
RECEIVED for review April 27, 1956 ACCEPTED October 29, 1956 Work sponsored in part by Chemistry Branch, Aeronautical Research Laboratory, Wright Air Development Center, under contract with The Ohio State University Research Foundation. VOL. 49, NO. 4
APRIL 1957
773
