Radiant Heat Transfer from Flames in a Turbojet Combustor LEONARD TOPPER D e p a r t m e n t of Chemical Engineering, T h e Johns Hopkins University, Baltimore 18, M d .
UASTITA4TIVEinformation concerning the rate of energy transfer from flames of turbojet combustors is necessary for evaluating such problems as combustor-wall cooling, application of flame-heated fuel prevaporizers, and vaporization of fuel droplete from atomizers. The total energy transfer is composed of convection and radiation from the flame to the fuel spray and the combustor liner, and conduction through the liner. When wall cooling is used, the outside and usually also the inside of the liner are cooled in a convective process by a film of air flowing along the liner. During normal operation, the combustion gases are highly turbulent, and heat is transferred by the movement of eddies of gae. The rate of this convective process can usually be expressed as a function of Reynolds number and Prandtl number, and it may be possible to estimate the convective transfer coefficientfor heat flowfrom the flame to thewall from one of the familiar relations developed for fluids flowing in pipes (3,5). Superposed on the convection process is that of thermal radiation. While the conduction and convection processes are affected only slightly by the temperature level, radiation increases rapidly with increase in temperature level. Thermal radiation may thus account for a large part of the total energy transfer, particularly in the primary zone, where gas temperatures are high, velocities are relatively low, and the flame emissivity is enhanced by the presence of incandescent soot particles (yellow “luminous” flame). Radiation from hydrocarbon flames can be of two distinct kinds. The nonluminous radiation consists of emission in certain regions of the infrared spectrum (due to simultaneous changes in the vibrational-rotational energy levels of heteropolar gas molecules) and also some visible and ultraviolet radiation. The luminous radiation is a continuous emission from flames made yellow by incandescent soot particles. Sonluminous radiation is always present and may be ascribed principally to carbon dioxide and water vapor. This type of radiation has been carefully studied a t a total pressure of 1 atmosphere (S), and there is some information on which to base extrapolation of the data to other total pressures (4, 6 ) . Such data may be used to predict the nonluminous radiation from flames. The prediction of the radiation to be expected from a luminous (yellow) flame is more difficult, as the soot concentration depends upon combustor design, degree of primary and secondary aeration, and combustor-inlet pressure. Useful information can best be obtained from experiments with combustors operated under actual conditions. The present investigation was undertaken a t the S A C A Lewis Laboratory to determine the effect of operating conditions on flame radiation in a single turbojet combustor that is typical in design of a class of combustors, operated with MILF-5624 (grade JP-4) fuel. The total radiation from a flame may be expressed by the equation
W
=
EUT~
where W is the total radiant energy emitted per unit area,
A single tubular combustor was modified by the addition of two pairs of sight holes (1.25 inches in diameter) in the inner liner (Figures 1 and 2). The first pair of holes was 5 inches from the fuel nozzle. The tapered shell was equipped with cross tubes 3 inches long having an inside diameter of 1.25 inches, which were located in line with the inner sight holes. Quartz windows 0.25 inch thick were attached by flanges to the cross tubes. The combustor was connected to the laboratory combustion air and exhaust service systems by ducting, as shown in Figure 1. The rate of air flow and combustor pressure were manually regulated by remote-control butterfly valves. Air flow and fuel flow to the combustor were measured by means of an adjustable orifice and calibrated rotameters, respectively. The temperature of the inlet air was measured by a single-junction iron-constantan thermocouple located a t instrumentation plane 3-3 (Figure 1). The inlet-air pressure was measured by a static-pressure tap a t plane 2-2. The combustoroutlet gas temperature was measured a t plane 1-1 by 12 ChromelAlumel thermocouples. The installation of thehe thermocouples is shown in Figure 2. All temperatures were indicated on selfbalancing potentiometers. The equivalent black-body temperature of the flame a t each of the two observation stations was measured with a portable total-radiation pyrometer which had been calibrated against a black-body furnace. The sensitive element of this instrument is a blackened thermopile on which the radiation is focused by a concave mirror. The thermopile responds nonselectively to radiation of all wave lengths. The red-brightness temperature was measured with a disappearing-filament optical pyrometer. An original method, based on the two-color principle ( 2 ) , was used to calculate average flame temperature and emissivity.
(la)
CALCULATION O F TOTAL RADIATIOY, FLAME TEMPERATURE, AND EMISSIVITY
(1b)
ANALYSIS. A detailed discussion of heat transfer by radiation is given by XlcAdams ( 5 ) . Experimental data for the emissivities of carbon dioxide and water vapor are presented as a function of temperature and the product PGL,where PGis the partial presfiure
or
W = uTs4
Stefan-Boltzmann constant, and T is the absolute temperature. The emissivity, E , is the ratio of the actual emissive power to that of a perfect radiator or black body. The use of the parameter equivalent black-body temperature of the flame, T B , as in Equation l b , is a convenient index for W . W can be measured with a thermopile or a bolometer, and the flame temperature, by one of several different methods. Since the value of the StefanHoltzmann constant is accurately known, the emissivity can be calculated. In the study reported herein, the total radiation passing through a quartz window was measured n-ith a total-radiation pyrometer having a blackened thermopile as the sensitive element. This pyrometer was calibrated against a black-body furnace to permit evaluation of equivalent black-body temperature of the flame. The red-brightness temperature of the flame was measured with an optical pyrometer. A new modification of the two-color pyrometer method ( 2 ) was then used to compute the true flame temperature from the equivalent black-body temperature and the red-brightness temperature of the flame. The preceding measurements were obtained a t combustor inletair pressures from 13 to 96 inches of mercury absolute, air mass flows from 0.22 to 2.8 pounds per second, and fuel-air ratios from 0.008 to 0.035. The effects of these operating variables on blackbody flame temperature and flame emissivity are presented.
u is
the
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2552
INDUSTRIAL AND ENGINEERING CHEMISTRY
of the particular gab in atnioypheres and L is the equivalent bean1 length in feet for radiation. At temperatures above 2500" R., the gas emissivity decieases with increase in temperature and increases with increase in the teini P&. 111 these data were obtained a t total pressures of 1 atmosphere. Data at other pressures are limited hut indicate that pieysure broadening of the spectral lines makes Beer's law inapplicable ( 4 , 6 ) and that the value of the parameter PQLshould be multiplied by P l i abefore the chaits for gas emissivity presented by Foote and associates ( I ) are used.
The two-color method of flame pyrometry, as originally developed, is based on the simultaneous solution of the two equa-
_ 1 To
1
T =
AG
c,
1 2
4 '
4 T k J - r
It is possible to express E A as ex = 1 Iih =
II
PI?
log eo
dinicnsional constiint. 2.58 (cm.) ( " R.) true flame tempei ature green-brightness temperature (at wave length X G ) red-brightness ternpciature (at wave length An = 0.665 micron) spectral absorptivity (or emissivity) a t wave length XQ spectral absorptivity (or emiqsivity) a t wave length
FUEL
COMBUSTOR
Vol. 46, No. 12
II
e-RhL
(3a) (3b)
K/Aa
where
K L = absorption strength
2~ L CY
ORiFJCE
l..4 t -
= constants = constant dependent only on wave length =
equivalent beam length of flame
' I
Figure 1. Single Tuhular Combustor Installation Including Location of Instrumentation Planes The exact piediction of the emissivity of luminous flames on a theoretical basis is virtually impossible, but experimental evaluation has been simplified by the investigations of Hottel and Broughton ( 2 ) . Studies of the variation of the monochromatic absorptivity of luminous flames with wave length showed that the absorptivity and emissivity decrease with increase in wave length (Figure 3)) and that the total emissivity is lower than the emissivity in the visible spectrum. A relation between monochromatic brightness temperature and the true flame temperature and emissivity v a s developed ( 2 ) and made possible the determination of true flame temperature and emissivity from measurements of the brightness a t two wave lengths a i t h a special optical pyrometer. I n the present invefitigation, this method was modified to require only standard readily available equipment. A total-radiation pyrometer was used to determine equivalent black-body temperature, and a conventional optical pyrometer was used to measure red-brightness temperature. Temperature and emissivity were computed by a tiial-and-error procedure based on Hottel and Broughton's charts (Figures 4 and 5). This procedure assumes that all the radiant energy is from glowing soot particles and the energy-wave-length distribution corresponds t o that determined by Hottel and Broughton ( 2 ) . Equivalent black-body temperatures were adjuited for the contribution due to nonluminous radiation befoi e they were used for calculating average flame temperatures. The quartz window through which the flame was viewed absorbed and reflected some of the incident radiation and thus introduced a small error in the readings of both pyrometers. The reading of the optical pyrometer was adjusted as recommended by the National Bureau of Standards ( I ) . The observed equivalent black-body temperature was corrected on the basis of the actual transmittance-a-ave-lengthcharacteristics of the quartz. window (Figure 6 ) and the computed energy-wave-length characteristic of the flame (Figure 7 )based on (2). The total emissivity was computed as the fourth power of the ratio of corrected black-body temperature t o average flame temperature. As the flame is nonisotropic, this value is not of a fundamental naturc.
Dn SECTION . 1-1 0
8
Figure 2.
SECTION 2-2
Single Tubular Combustor Modified for Radiation Studies
Arrangement of instrumentation planes of combustor installation] @ Static-prejsure tap 0 Thermocouple
Hottel and Broughton ( 2 ) studied the transmissivity of varioup flames and concluded that a value of 1.39 should be used for a between 0.3 and 0.8 micron, and 0.95 between 0.8 and 10 niicrons. Uyehara and associates ( 7 ) used values of 1.32 and 1.05 for CY. The computed flame temperature is irisensitive to sniall changc:~ in CY. Hottel and Broughton (2) showed that for moderately thick flames, a change in the value of CY used for the shorter wavo lengths from 1.7 to 1.39 resulted in a change in fla.me temperature of only 14" R. EVALUATION O F LIGHT TRANSLIITTAKCE O F QCARTZ \~ISDOTV. The fraction of the incident light which will be transniit,tod,:hy the quartz. window is given as
December 1954
INDUSTRIAL AND ENGINEERING CHEMISTRY
2553
independent of wave length, these curves would coincide; as 2 microns is close to the effective wave length, the areas subtended by a given curve over and under 2 microns are approuimately equal. The variation of the spectral transmittance of the quartz window for light from hydrocarbon flames is shown in Figure 8, and was calculated by use of Equation 4 and Figures G and 7. These computations were made for flame temperatures of 2960' and 3460' R. and are summarized in Table I.
TABLE I. LIGHTTRANSMITT-4NCE Temp.,
R.
Emissivitya 1.0 0.5
OF
QUARTZWINDOW
Transmittance of Window, Tray.
Effective Wave Length of Flame Radiationa, @
0.1 1.0 0.7 0.5
a
0.1 A t wave length of 2 microns.
Wave length above which half radiant energy of flame lies.
0
1
3
2
4
5
Figure 3. Variation of Spectral Emissivity of Hydrocarbon Flames as Function of Wave Length For flames having certain spectral emissivities at 2-micron wave length
where
J A = intensity of incident radiation a t wave length X T r A = light transmittance of quartz window a t wave length X = wave length of radiation
X
A plot of Tr>against h for the quartz plate used in this investigation is shown in Figure 6. An infrared spectrophotometer was used to obtain these data. Figure 7 indicates the variation of the ~ ~ ,wave length, A, for flames relative luminous intensity, J A / E with having a temperature of 3460" R. and having emissivities of 0.1, 0.5, 0.7, and 1.0 a t X of 2 microns. If the spectral emissivity were
2200
2600
1.0
.B
-----
.6
.4
.2
0
Figure 4.
.5
1.0
1.5
2 0
2.5
3.0
3000
3400
3600
Figure 5. Effect of True Temperature and Red-Brightness Temperature on Absorption Strength (2)
5.5
4.0
Effect of Absorption Strength and Temperature on Luminous Emissivity (6)
The "cutoff" of the quartz window a t about 4.0 microns is not a eerious difficulty, since only a relatively small portion of the total radiation is of longer wave length. Thus, more than SO% of the luminous radiation is generally transmitted (see Table I). The nonluminous r a d i a t i o n d u e t o c a r b o n dioxide and water vapor is only a smail fraction of the total radiation. When the combustion is complete, the emissivities for this radiation may be computed ( 5 ) from the partial pressures of carbon dioxide and water vapor. When the combustion efficiency was less than loo%, the partial pressures of carbon dioxide and water were estimated to be the product of the combustion efficiency and the respective partial pressures corresponding to a combustion efficiency Of loo%* It was assumed that all of the gases present in incomplete
INDUSTRIAL AND ENGINEERING CHEMISTRY
2554
combustion, other than carbon dioxide and water vapor, are transparent to radiation a t those wave lengths where most of the flame energy is contained. It can be shown that the trial-and-error procedure used herein converges to the same values that would be obtained if Hottel's method based on red- and green-brightness temperatures were employed. SAMPLE CALCUL4TION OF EQUI%4LENT BLACK-BODY TEMPERATURE, TRUE TERIPERdTURE, &ND EMISSIVITY OF FLA3lE
The procedure used for computing the iadiation characteristics of the flame is illustrated in the following paragraphs. The experimental data are those for point 1 (Table 11).
EXPERIMEXTAL D~TA 28.8 2800 1810
Combustor inlet pressure, inches of mercury, abs Red-brightness temperatuLe, R. Black-body temperature, R .
CALCULATIONS. As a first estimate of T , use T = T R = 2800" R. Bv Eauations 1, the first estimate of emissivitv is = = 0,175'. 2800 For E = 0.175 and T = T R = 2800" R..the first estimate of K L (Figure 4) is 0.42.
(!%j4
TABLE 11.
PERFORMANCE A N D
Vol. 46, No, 12
For K L = 0.42 and T B = 2800" R., the first computed flame t,einperature(Figure 5) is 2920" R. For c2 = 0.175 and 1' = 2920" It., the first estimate of the light transmitt'ance of the quartz plate (Figure 8) is 86%. 1810 The correct black-body temperature is -?= 1870" R. (0.8b) l '4 Corrected red-brightness temperature is 2820" R . (1). The black-body temperature associated with the radiation from carbon dioxide and wat,er vapor (5)is 1020" It. The black-body temperature for luminous radiation alone is ( B i o i - 10204)1'1= 1830" R . For T g = 1830" R. and T = 2920" R., the first estimate of the luminous emissivit,y is (1"") ' = 0.151. 2920 For c = 0.154 and T = 2920" R.,the second estimate of K L (Figure 4)ie 0.33. For K L = 0.33 and T B = 2820" R., the second computed flame temperature (Figure 5) is 2990" R. The second estimate of luminous emissivity is ( 2 g g ) h = 0.140. For E = 0.140 and T = 2990" R.. t'he third estimate of K L (Figure 4) is 0.30. For KL = 0.30 and T R = 2820" R., the third computed flame temperature (Figure 5 ) is 3040" R. = 0.132. The third estimate of luminous emissivity is
(go)'
For 6 = 0.132 and T = 3010" R., the fourth estimate of K L (Figure 4) is 0.28.
FLAME-RADIATION DATAO B
SIXGLE
TUBULAR CO\.lBUSTOR
Equiv. Black-
Bod\,
Combustor Inlet Pressure, Inches Hg
Abs.
28.8 20.5 15.5 51.0 51 . 0 62.0 28.0 21.0 13.1 13.4 16.0 20.0 26.0 28.5 26.5 26.5 46.0 51 . o 61.0 72.0 92.0 81 .O 37.0 73.0 85.0
86.0 76.0 77.0 96.0 95.0 80.0 63.0 77.0 92.0 94.0 22.0 32.0 36.0 41 .O 50.0 62 0 33.0 45.0 62.0 42.0 52.0 65.0 a
Teind. of
Air
Fuel Flow Flow Lb./Seo. Lb / H r 0.22 0.22 0.22 0.46 0.46 0.44 0.45 0.45 0.45 0.45 0.58 0.58 0.65 0.64 1.25 1.25 1.51 1.51 1.43 1.43 1.43 1,47 0.97 2.81 2.81 2.81 2.81 2.81 2.81 2.81 2.81 1.81 1.81 1.81 2.81 1.81 1.81 1.81 1.81 1.81 1.81 2.81 2.81 2.81 2.81 2.81 2.81
28.0 28.0 28.0 25.0 30.0 29.0 21.0 28.0 30.0 36.0 33.0 33.0 36.5 57,s 54.0 59.0 45.0 41.0 42.0 42.0 41.0 44.0 28.0 94.0 95.0 80.0 82 0 80.0 97.0 49.0 96.0 92 0 97.0 97.0 170.0 97.0 97.0 97.0 147,O 97.0 92.0 92.0 92.0 92.0 170.0 170.0 170,O
hIean CombusCombustor tion Fuel-Air Outlet EfEcieiicS Ratio Temp., R. % 48 1585 0.0350 43 1510 0.0360 37 1360 0.0380 58 1160 0.0161 66 1385 0.0182 08 1410 0,0180 33 860 0,0130 43 1085 0.0180 41 1060 0.0180 44 1210 0.0220 0.0160 0.0160 0.0156 0,0248 0.0120 0.0130 0.0083 0.0073 0.0082 0 0082 0.0080 0.0083 0 . ooao 0,0094 0,0094 0.0080 0,0081 0.0080 0.0096 0,0098 0,0005 0.0140 0 0150 0.0160 0.0169 0.0150 0.0150 0.0150 0.0225 0.0180 0.0142 0.0091 0.0091 0.0091 0,0169 0.0169 0,0169
1060 1085 1060 1010 1100
47 49 47 65 61
1160 935 935 960 985 1010 1035 1070 1260 1260 1270 1120 1260 1220 1310
67 67 68 73 74 78 78 88 100 97 100 94 98 95 100 100 100 100 100 100 76 87 91 90 100 90 79 90 100 83 91 97
1235 1585 1620 1685 1760 1310 I410 1485 1910 1585 1610 1080 1160 1240 1520 1620 1710
Red-Brightness R. -Temp., Obsd. Corr. 2820 2800 2650 2630 2630 2610 2900 2880 2930 29 10 2860 2880 2770 2790 2560 2580 2110 2120 2140 2150 2170 2160 2480 2400 2450 2430 2695 2673 2160 2150 2203 2215 2820 2840 2840 2860 3010 3030 3060 3080 3060 3080 3060 3080 2710 2730 3080 2100 3110 3130 3130 3110 3100 3120 3050 3070 3175 3155 3180 3210 3100 3120 2900 2880 2860 2880 2930 2950 2870 2850 2010 2030 2620 2600 2600 2620 2600 2620 2640 2660 2780 2160 2 120 2750 2180 2420 2590
2800 2170 2460 2770 2190 2440 2610
COll
1810 1610 1460 2040 2160 2160 1670 1550 1190 1290 1290 1480 1510 1700 1410 1460 1650 1790 1910 2050 2260 2160 1660 2040 2280 2320 2180 2210 2360 2490 2220 2170 2415 2600 2190 1360 1530 1670 1680 2040 2280 1410 1700 2060 1530 1675 1885
1870 1660 1500 2140 2260 2260 1730 1600 1220 1330 1340 1520 1565 1760 1460 1520 1720 1855 1985 2130 2330 2250 1720 2120 2370 2410 2230 2290 2440 2580 2300 2270 2550 2790 2300 1420 1690 1730 1730 2150 2400 1460 1770 2160 1605 1755 1976
True flame temperature, equivalent black-body temperature, and emissivity values are uncertain
1020 HI0 865 1000 1160 1210 1000 950 800 800 800 860 950 1020 800 930 1200 1200 1230 12YO 1370 1320 1010 1290 1315 1315 1320 1270 1380 1380
3060 2800 2860 2990 2970 2960 2980 2700 2250 2280 2290 2550 2530 2840 2250 2300 3140 3070 3180 3250 3170 3190 2930 3250 3220 3170 3270 3120 3270 3220
1325 1222 1260 1310 1310
3250 2950 2895 2960 2890 2035 2540 2740 2740 2670 2810 2180 2465 2530 2200 2470 2650
800 950 1020 1060 1100 1370
...
1050 1200
...
1070 1170
Totpl Emissivity 0.090 0.122 0.070 0.200 0.320 0.330 0.117 0.125 0.085 0.116 0.117 0.126 0.140 0.145 0.178 0.180 0.090 0.134 0.152 0.185 0,290 0,250 0,119 0.181 0.293 0,335 0,215 0.286 0.310 0.110 0.250 0.345 0.625 0.790 0.405 0.240 0.155 0.190 0.190 0.420 0,530 0.200 0.265 0.340 0.288 0,200 0.300
Ratio of Total Radiation t o Nonlumi. nous Radiarion 6.6 11.1 9.0 21.0 14.1
Comments
12.2 9.0 8.1
... ,..
...
10.2 7.4 8.8
...
...
4.2 5.8 6.8 7.5 8.0 8 4 8.4 7.3 10.5 11.6 8.1 10.8 9.9 12.3
Blue flamen Blue flamea Blue flamea
Blue flamea Blue flamea
9.2 12.0 16.8 21.2 9.5
... 7.8 7.7 7.2 14.5 9.3
...
7.6 10.6
...
7.4 8.2
Blue flamea
Blue flamea CTnsteady flamen
December 1954
INDUSTRIAL AND ENGINEERING CHEMISTRY
2555
Figure 6. Spectral Transmittance of Quartz Window Used i n Study of Flame Radiation For K L = 0.28 and T = 2820" R., the fourth computed flame temperature (Figure 5 ) is 3060' R. As the fourth estimate is very close to the third, T = 3060' R. is used.
Then the total emissivity is
=
0.141.
The first estimate of quartz light transmittance is now checked and found t o be correct. RESULTS
The flame-radiation data obtained over a range of combustor inlet-air pressure, rate of air flow, and fuel-air ratio a t the first station (5 inches from the fuel nozzle) in the single combustor are presented in Table I1 and in Figures 9 and 10. Figure 9 compares the effect of combustor inlet-air pressure on equivalent black-body flame temperature a t various air-flow rates and two fuel-air ratio ranges: 0.008 to 0.010 and 0.014 to 0.018. These and other data are combined in Figure 10 to compare this effect a t various fuel-air ratios and three ranges of air-flolT rate: 0.22 to 0.65, 1.4 to 1.8, and 2.8 pounds per second (Figure 10, A , B , and C, respectively). The greatest effect on black-body temperature of the flame was observed with variations in inlet-air pressure. Thus, a t fuel-air ratios of 0.008 to 0.010 and an air flow of 2.8 pounds per second, an increase in pressure from 35 to 95 inches of mercury absolute was accompanied by a n increase in black-body temperature from 1520" to 2490" R. (Figure 9, A ) , which is equivalent t o a sevenfold increase in radiant energy. Similar increases were observed a t the other fuel-air ratios and air-flow rates. The black-body temperature of the flame was influenced t o a lesser degree by fuel-air ratio and by mass flow rate of air. At fuel-air ratios of 0.008 to 0,010, an increase in air flow from 1.4 to 1.5 to 2.8 pounds per second (Figure 9, A ) resulted in a slight increase in radiant intensity a t pressures above 40 inches of mercury absolute. At fuel-air ratios of 0.014 to 0.018, however, the equivalent black-body temperature decreased very slightly with a n increase in air flow from 0.45 to 0.65 to 1.8 pounds per second (Figure 9, B ) ; however, a further increase in air flow to 2.8 resulted in a marked decrease in black-body temperature. At mass flows of air from 0.22 t o 1.8 pounds per second, the flame blackbody temperature generally increased with an increase in fuel-air ratio (Figure 10). At the highest air-flow rate (2.8 pounds per second) a reverse trend was observed; thus, a n increase in fuel-air ratio from 0.008 to 0.010 to 0.017 resulted in a significant decrease in black-body temperature. Calculated values of the average flame temperature in the primary zone (Figure 11) remained essentially independent of air flow and of pressure a t pressures greater than 80 inches of mercury absolute, but were more than 200" F. higher a t fuel-air ratios of
0
1
2
4
5
Figure 7. Variation of Relative Luminous Jntensity of Hydrocarbon Flames with Wave Length Flame temperature, 3460' R .
Figure 8. Variation of Average Light Transmittance of Quartz Window Used in Study of Flame Radiation with Temperature and Emissivity of Flame Emissivity assumed equal to average emissary
0.008 to 0.010 than a t fuel-air ratios of 0.014 to 0.017. The calculated flame temperature decreased rapidly as pressure was reduced. Computed total emissivities of the flame are presented in Figure 12. The effects of pressure, air flow, and fuel-air ratio are similar to those observed for the black-body temperatures. The highest value of emissivity observed was 0.79 (at a pressure of 92 inches of mercury absolute, fuel-air ratio of 0.015, and air flow of 1.8 pounds per second), corresponding to a n equivalent black-body temperature of 2790" R.; the lowest value of emissivity observed was 0.09. Figures 11 and 12 present sufficient
2556
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
A
Figure 9.
Vol. 46, No. 12
B
Effect of Combustor Inlet-Air Pressure on Corrected Black-Body Flame Temperature at Various Combustor Air-Flow Rates in Single Tubular Combustor A. B.
Fuel-air ratio 0.008 to 0.010 0.014 to 0.018
26W
Fuel-air ratio Air-flow rate LL
3
0.035 0.015-0 .Ole
G,450.65
22W
2003
1200
1600
iirc
20
IC
80
C O M B U S T O R I N L E T - A I R PRESSURE, I N C H E S HG ABS.
Figure 10.
Effect of Combustor Inlet-Air Pressure on CorrecLed Black-Body Flame Temperature a t Various Combustor Fuel-Air Ratios in Single Tubular Combus tor Air mass A. B.
flow
0.22 to 0.65 pound per sccond 1.4 to 1.8 pounds per second C. 2.8 pounds per second
INDUSTRIAL AND ENGINEERING CHEMISTRY
December 1954
2557
Combustor air-flow
2200 20
60
100
60
20
Figure 11. Effect of Combustor Inlet-Air Pressure, Fuel-Air Ratio, and Air-Flow Rate on Computed Average Flame Temperature in Single Tubular Combustion
60
100
Figure 12. Effect of Combustor Inlet-Air Pressure, Fuel-Air Ratio, and Air-Flow Rate on Computed Total Emissivity of Flames i n Single Tubular Combustor
Fuel-air ratio 0.008 t o 0.010 0.014 to 0.017
Fuel-air ratio A . 0.008 to 0.010 B . 0.014 to 0.017
A. B.
data to indicate the variation in flame temperature and emissivity. The pressure a t which the flame in the primary zone became blue dcpended on the fuel-air ratio and the mass flow of air. At a fuel-air ratio of 0.035 and a n air flow of 0.22 pound per second, it was still yellow (red-brightness temperature, 2630" R.) a t a pressure of 15.5 inches of mercury absolute. At a fuel-air ratio of 0.016, a pressure of 20 inches of mercury absolute, and a n air flow of 0.58 pound per second, the flame luminosity was low (redbrightness temperature of 2480" R.).At a fuel-air ratio of 0.009, a pressure of 45 inches of mercury absolute, and an air flow of 2.8 pounds per second, the red-brightness temperature observed was only 2460' R. Only data for the upstream station are reported here. The flame a t the downstream station always had an equivalent blackbody temperature too low for accurate measurement (below 1300" R.) and was blue, so that the two-color method for computing true flame temperature was not applicable.
for the basic measurements, rather than a single optical pyrometer with two interchangeable filters, as in the original procedure of Hottel and Broughton. The two techniques are subject t o different errors, although they are both based on the same principle. Both depend on the assumption of a simple law (Equations 3a and 3b) relating spectral emissivity and wave length. The original method measures two-color temperatures t h a t are ordinarily relatively close to each other and to the true flame temperature. The proposed method measures one color temperature and the blackbody temperature; these are often hundreds of degrees apart. The modified method makes i t possible t o estimate the flame emissivity even when the assumed variation of spectral emissivity is inaccurate, while the original procedure mould be less successful in such a case. On the other hand, the calibration of the additional pyrometer may be more tedious. Calculations indicate that the rate of radiant heat transfer to the combustor liner in the primary zone may be as large as a convective transfer corresponding t o a heat-transfer coefficient of 50 B.t.u. per hour per square foot per O F.
DISCUSSION
The variation in emissive power of the flame with pressure, fuel-air ratio, and air mass flow cannot be predicted on any purely theoretical grounds. It is reasonable, however, to assume that it will vary, at least qualitatively, in the same manner as does the local smoke density of the zone which has the emissive power under consideration. A11 the observed trends in radiant energy reported herein follow trends in smoke density of turbojet-combustor exhaust gas observed in unpublished work of this laboratory. Molecular radiation from carbon dioxide, water vapor, and other optically active molecules and radicals makes a much smaller contribution to the over-all transfer of energy than does radiation from luminous soot particles. I n most cases, the observed total radiant energy was 4 to 21 times that estimated for a mixture of carbon dioxide and water vapor at the flame temperature and a t partial pressures corresponding to complete conversion of the air in the primary combustion zone. The actual ratio would be even higher, as it is probable that some of the oxygen passes through the primary zone without being utilized for burning. The modified two-color method presented here for measurement of flame temperatures uRes two pyrometers of different kind3
APPLICATION O F EMISSIVITY DATA
The use of emissivities in computing radiant heat transfer from gases is as follows:
'
Consider a cylinder of flame 6 inches in diameter and of infinite length, and aBsume an average flame temperature of 3200" R. and emissivity of 0.50. Suppose the cylinder of flame is to be enclosed in a metal shell with temperature of 1800' R. and emissivity equal to 0.90. Then the net transfer of heat from the flame envelope per foot of length is q = U A E J E ~( TTa4) /~
where
A
= area of flame, square feet T I = flame temperature, R. T , = shell temperature, R. = emissivity of flame E* = emissivity of shell u = Stefan-Boltzmann constant, 0.173 X lo-* B.t.u./(sq. foot) (hour)(' Rj4 4 = (0.173 X (a/2)(0.50) (0.90) (104 X 1OI2 - 10.5 X 1012j O
q = 11.4 X lo4 B.t.u./(hour)(foot)
INDUSTRIAL AND ENGINEERING CHEMISTRY
2558
T o transfer this quantity of heat by convection would require a film coefficient of a t least 5 2 [B.t.u./(hour) (sq. foot) ( " F.)]. If the flame and shell diameters are increased to 8 inches, the emissivity of the flame will be approximately 0.68 (Equation 3al. Then p =
0.68 8 - (11.4 X 10') 0.50 6
~
=
Over the observed range of operating conditions, measurablc radiant energy was observed only in the primary zone; in this region the greater part of the total energy transfer to the liner may consist of radiation from the flame. Flame emissivities of 0.09 to 0.79 were observed.
18.2 X lo4 B.t,.u,i(hour) (foot) ACKNOWLEDGMENT
Since the flame volume has increased as
(8)'
=
1.78
The experimental work reported here was completed while t h c author xyas associat,ed with the Lewis Laboratory of the Sational .4dvisory Committee for Aeronautics.
the radiant heat loss per unit volume is 907, of the former value. S U V M A R Y OF R E S U L T S
The folloiiing results were obtained from an investigation of the effects of combustor operating variables on the thermal radiation from the flame of a turbojet combustor. The intensity of radiation from the flame increased rapidly with an increase in combustor inlet pressure and was affected to a lesser degree by variations in fuel-air ratio and air mass flow. The total radiation of the luminous flames (containing incandescent soot particles) was much grcater (4 to 21 times) than the niolccular nonluminouq radiation due to carbon dioxide and water vapor.
Natura
Vol. 46, No. 12
as
LITERATURE C I T E D
(1) Foot,e, P. D., Fairchild, C. O., a n d Harrison, T. R., Natl. I3ur. Standards, T e c h . Paper 170 (Feb. 16, 1921). ( 2 ) Hottel, H. C., and Broughton, F. P., IKD, E s c . CHEM.. AS.^,.
ED.,4, 1W-75 (1932). ( 3 ) Humble, L. V., Lowderniilk, W.H., and Desmon. L. G.. S a t l . Advisory Cornm. Aeronaut., R e p t . 1020 (1951). ( 4 ) Kaplan, L. D . , J . M e t e o r o l . , 9, 1-12 (1952). (5) McAdams. W.H., "Heat Transmission," 2nd ed., S e l r Y o r k ,
McGraw-Hill Book Co.. 1.942. (6) Mtttossi, Frank, and Rauacher, Emma, 2. P / I ~ .125, \ . , S o s . 7-10, 418-22 (1949).
(7) Uyehara, 0. h.,and as?ociates, Tmns. A m . S o c . X ~ c h E. t i g i s . , 68, 17-30 (1946).
1 2 r . c e i v t ~ior review- J a n u a r y 2 9 , 19:4.
A c c r ~ . i i r September , 17, 1P531.
osions a
DETONATION VELOCITIES AND PRESSURES MELVIN GERSTEIN, EDWARD R . CARLSON, ~ N D FRANCIS U. HILL iVational Adcisory Committee for Aeronautics, Lewis F l i g h t Propulsion Laborutory, Clezeland, Ohio
XP1,OSIOhX in a given system ma?- lead to two different combustion processes: Under some conditions, the explosion results in a flame or combustion wave which mag travel at several hundred feet per second; under other conditions, a detonation wave may result which travels a t several thousand feet per second ( 2 ) . Higher pressures and greater destructiveness are associated with the detonation wave. .llthough many systems that may contain unburned combustible mixtures-Le., exhaust ducts and mixture feed pipes-are designed to withstand the sloiver and lower pressure rise of a combust,ion wave, these systems are often not designed t o ITithstand the greater pressures and deetructiveness of a detonation vave. I t is therefore desirable to knoJT the conditions under which an explosion may develop t,he characterist,ics of a detonation. Much work has been done on the occurrence of detonations in fuel-oxygen mixtures and in some fuel-air mixtures a t atmospheric or elevated pressures ( 2 ) ,but little work has been reported 011 the possibilities of detonation in hydrocarbon-air mixtures a t reduced pressures. This report presents the results of an investigation a t the SXCA Lewis Laboratory to determine whether a stoichiometric natural gas-air mixture a t pressures from 0.4 to 0.2 atmosphere may give rise to explosions with velocities and pressures characteristic of detonation. Natural gas mas chosen as the fuel because of its wide use and availability. I n addition, the relat,ively low flame velocity of methane ( I ) , a major constituent of natural gaE, suggested that it might be less likely t o form detonable mixtures, so that the existence of a detonation hazard in natural gas-air mixtures might imply the existence of such a hazard in other hydrocarbon-air mixtures. The experiments \Yere performed in a pipe 2 feet in diameter and approximately 300 feet
long. The great length was used to ensure suEcient distancc: for build-up of the detonat,ion, and the large diameter was U P C ~ t o minimize wall effects a t the low pressures. The velocity arid pressure of the explosion were measured to determine the nature of the wave, but no attempt' was made to obtain precise research data. Additional experiments were performed to determine thquantity of water required t o extinguish the explo3ion. EXPERX4IEXThL
While t,he velocity and pressure of a fully developed detountion are relatively insensitive to the apparatus and conditions oi the test, the likelihood that detonation with result from a flame is very dependent on the experimental variables ( 2 ) . For this reason, a rakher complete description is given of those parts of the experiment which could influence the occurrence of a detonation. PIPISGSYSTELI.A photograph of the pipe used in this study is shown in Figure 1, and a diagram showing ewential feat>uresof the apparatus in Figure 2 . The pipe consisted of sections of 3i8-inch seamless and '/l-inch spiral-weld pipc 2 feet in diarn welded together to form the desired length. The longest run of pipe was 305 feet, followed by a %-foot run a t right. angles. A. tee was used to change the direction of trawl, so that an aluminum rupture disk could be placed a t the end of the long run. -4 neoprene rupture disk closed the inlet of the 305-foot section. The 25-foot section was followed by another tee and a section leading to a large plenum. This tee held an aluminum rupture disk, and the plenum shown in Figure 3 contained two ncoprenc rupture disks. The short length of pipe leading to the plenum, and the plenum itself, which was 11 feet long and 7 feet
