INDUSTRIAL AND ENGINEERING CHEMISTRY
1596 v
= component of convective velocity in z-direction. cciitimeters
per second = fraction of feed gas passing through diffusion harrier 2 = cvlindrical coordinate, centimeters R:
(i2),'(
a
= separation factor (common) =
p
= separation factor (this paper) =
1%)
A,, = n'th root of J I ( p n r ) pn =
E
An/%
= ( T H / Q ) ( R I / R ~seconds ) ~ , per square centimeter = gas densitv, cubic centimeters Der cubic centimeter
p PO.% =
gas density, romponent i in feed gas stream, cubic centimeters per cubic centimeter + ( L I Z ) = separation function, dimensionless
0
Vol. 45, No. 7
literature Cited (1) Arnold, J. H., IND. E m . CHEM.,22, 1091-5 (1930). (2) Benediot, M., a n d Boas, A , , Chem. Eng. PTOQT., 47, 51-62, 111-22 (1951 ). (3) Cichelli, h1. T., W e a t h e r f o r d , W. D., J r . , and B o w m a n , J. I b i d . , 47, 63-74, 123-33 (1951). (4) Inco Magazine, 16, 20-1 (1939). 15) MacGillavry, D., Trans. Faruduv Soc., 33, 433-9 (1937). (6) Schwertz, F. A , , Am. J . Phys., 15, 31-6 (1947). ( 7 ) Wilke, C. R., Chmn. Eng. Progr., 46,95-104 (1950).
R.,
RECEIVED for review August 2 5 , 1952. ACCEPTED February 12, 1953. Work done under industrial f e l l o x s h i p on coke-plant physical technology, sustained b y lioppers Co., I n c .
Material Transfer in Tur
0 0
A Coaxial Flame
0
V. J. BERRY', D. M. MASON,
AND
8. H. SAGE
California fnsfifufe o f Technology, Pasadena, Calif.
OMBUSTIOX in a homogeneous gas phase of uniform initia] composition has been the subject of many investigations.
C
compared the maximum fluctuating velocities with those calculated from experimental measurements. Fair agreement between experiment and theory \vas obtained. h marked influence of combustion upon the level of turbulence was indicated.
Jost (19) summarized bhe behavior of quiescent systems, and The present in.l,estigation w-as concerned lvith the study of the Hirschfelder and Curtiss (6,11) reviewed the status of knowledge effects of t'he combustion process in a cylindrical tube upon the aspects of the combustion process in flames and turbulent transfer of the react'ants and products. Earlier measof the problem from the standpoint of reaction kinetics. ;\luch experimental work was carried out upon the velocity of flames urements ( $ 6 ) Iyere made under nonburner conditions upon in quiescent fluids and laminar flowing streams. The laminar coaxial diffusion of streanis of natural gae and air and mith the diffusion flame has been studied in detail and Lewis, Von Elbe, equipment as m s employed here. Under nonburning and coworkers (19, 91) summarized information ahout, the staconditions reasonable correlation of the total Schmidt number bility and structure of burner flames. Lewis and Von Elbe also summarized :he literature (17) relating to the combustion in byith value8 obtained by Forstall and Shapiro ( 9 ) realized. burners, englnes, and jet-propulsion equipment. Scholefield Here the total Schmidt number, Sc, has been defined as the ratio and Garside (27) considered the behavior of the combustion process in the laminar, transition, and turbulent regions, T ~ % , ~of total viscosity to tot'al diffusivity. The measurements were made at' g r o s s approa,chvelocities of 10,25, and 50 feet per second symposia (8, 28) have served to summarize the work upon combustion before 1938. The problems of flame stabilization and and with a single ratio of natural gas t o air such as to yield apthe mechanism of combustion reactions, together with the therproximately a stoiclliometric reaction to carbon dioxide modynamics of the products of reaction, have been reported in end a recent symposium (50). The work of Zeldovich and Semenov (94) and of Wildenstein and Pannetier (92) upon the combustion of methane is of direct interest to the present problem, as is that Apparatus and Methods of Hoare and Linnett ( I d ) , who considered the mechanism of The apparatus employed in this investigation has been described flame propagation from a macroscopic standpoint. Damkohler (6) reviewed experimental work accomplished be(26). As shown schematically in Figure 1, it involved a cylindrical fore 1940 and presented results upon burner flames for low Reynolds numbers. Shelkin (29) investigated the influence of t'urcopper combustion tube having an inside diameter of 3.826 bulence upon the combustion of hydrocarbons and upon these inches. The air and natural gas were introduced a t a temperature of 100"F. and a t nearly at'mosphericprcssure. Thenatural studies based most of his practical discussions of the phenomma within internal combustion engines. The effect of Reynolds number upon t'urbulent combustion was considered by Rollr C O O L , W JKAET C inger and Williams (2). The work of Williams, Hottel, and Scurlock (95)upon flame stabilization and of Hawthorne, pyeddell, and Hot,tel (IO) upon combustlon in turbulent gas jets is of particular interest. Karlovitz (14) and coworkers (16) proposed a new theory for estimating open flame velocities under turbulent conditions. Their work considered the microscopic aspects of the flame front and 1 Present address, Stanolind Oil and Gas Co., Tulsa, Okla.
Figure
1.
Combustion Tube
INDUSTRIAL AND ENGINEERING CHEMISTRY
July 1953 COO-INS
BRASS
%ATER
-JBE
COPPER -USE
RUBBER SEAL
SAMPLE PORT-
-8
Figure 2.
Cross Section of Combustion Tube and Sample Port
gas entered along the axis through a tube, A , which was nearly 1 mch in diameter, as shown in Figure 1. The air was admitted COaxially through the annular space between the copper tube, B, and the gas tube, A. The exterior of tube B was with water circulating through the jacket, C. Piezometer rings were provided at D and D' to permit the change in pressure &~ros8 the combustion zone to be measured with an uncertainty of approximately 0.001 inch of kerosene. Ports were provided at ll downstream positions to permit the atomic composition and apparent velocity and temperature of the combustion zone to be investigated as a function of the distance along the combustion zone. The arrangement of these ports is shown in Figure 2, which includes a cross section of the combustion tube. The flow of air was measured by a Venturi meter, utilizing equipment that has been described ( 4 ) . It is believed that the rate of flow was known with a standard deviation of less than 1yo. The flow of natural gas was determined by means of a roundedged orifice of conventional design, and the rate of introduction was known within a standard deviation of 1.2% as determined from direct calibration of the orifice. Combustion was maintained by means of a small spark-type flame holder depicted in Figure 3. The spark was located 0.625 inch downstream from the point of injection of the natural gas. The flame holder was introduced into the combustion chamber through a port such as shown in Figure 2.
/,
I
The apparent velocities were measured in the same fashion as in the investigation of the nonburning stream (16). A small, water-cooled Pitot tube of conventional design as shown in Figure 4 was provided. Kerosene-in-glass manometers were employed in conjunction with a cathetometer for the measurement of dynamic pressure. The difference in elevation of the interfaces on the arms of the manometer was established with an uncertainty of not more than 0.0015 inch. The dynamic head reached a maximum value of 0.04 inch of kerosene in the combustion tube. Samples of gas were taken through the Pitot tube a t such a rate that the time average velocity in the entrance was comparable to the time average velocity of the stream a t the point in question. It was found that variations in the time average velocity by as much as a factor of 2 did not influence the measured composition by as much as the probable error in analysis. For this reason i t is believed that the fluctuating velocities a t the entrance to the Pitot tube did not influence the sampling process significantly. The composition of the samples withdrawn was determined with conventional analytical equipment. The quantity of hydrocarbon was established by combustion analysis (3). It is believed that the standard deviation in the mole fraction of carbon dioxide, carbon monoxide, oxygen, and hydrocarbon in each sample was 0.002. Reproducibility of the measurements upon samples withdrawn a t the same point confirmed such estimates of probable error. The composition of the gas sample as
1597
analyzed undoubtedly differed materially from the molecular composition in the combustion zone at the time of sampling. This difference resulted from changes in molecular composition during the cooling of the gases from the combustion temperature to that a t which it was stored for analysis. As this cooling was carried out rather slowly, some molecular changes toward chemical equilibrium at a temperature lower than that in the combustion tube occurred. However, the atomic composition is not changed during such a sampling process. With a known atomic composition, nitrogen affords a convenient means of following the characteristic of the transfer process, since its molecular identity is not modified within the temperature range investigated. The apparent temperature at different points in the combustion tube was determined by means of a shrouded, 2-mil, platinum-platinumiridium thermocouple. The arrangement of the quartz shroud of the thermocouple is shown in Figure 5. For the measurements of apparent temperatures encountered in this study the shroud was not heated as has been suggested by Mullikin and Osborn (23)for the measurement of high temperature gases. From the work of Kreisinger and Barkley ( 1 6 ) it was improbable that the apparent temperatures were more than 500 F. removed from the actual values. T~ avoid catalytic effects upon the nonequilibrium mixtures of natural gas and air, the platinum-platinum-iridium thermocouple was coated with a thin layer of quartz. The entire shroud, which was approximately 0.12 inch in diameter and 0.4 inch in length, was mounted with its axis parallel to that of the flowing stream.
WATER COOLING
PRESSURE
Figure 4.
CONNECTION
Water-Cooled
Pitot Tube
It was not necessary to employ spectral line-reversal methods of temperature measurement, as proposed by FBry ( 7 ) and discussed by Lewis and Von Elbe ( g o ) , because the apparent temperature was used only to establish the regions in which rapid rates of chemical reaction mere experienced. Such line-reversal methods with the modification suggested by Penner (84, 26) would be applicable to nonisothermal situations such as were encountered in this study. The thermocouple of Figure 5 was compared up t o a temperature of 500' F. with a platinum resist-
Table 1. Radius, Inches
Carbon Dioxide
Carbon Monoxide GROSS
l.5b
0.005c
1.0 0.5 0.0 -0.0 -1.0 -1.5
0.012 0.020 0.028 0.037 0.033 0.023
1.5 1.0
0.019 0.029 0.036
Oxygen
Water
VELOCITY10 F E E T
11.70Inchesa 0.181 0.154 0.126 0.102 0.092 0.123 0.167
Composition of Gases in Combustion Tube Hydrocarbon
Kitrogen
0.009 0.018
0.048 0.079
0 737
0.028
0.087
0.016
0.011 0.000
0.016 0.034
0.054 0.078 0.098 0.081 0.042
Carbon Monoxide
-1.0 -1.5
1.5 1.0 0.5 0.0
-0.5 -1.0 -1.5 1.5 1.0 0.5 0.0
-0.5 -1.0 -1.5
0.042
0.044 0.041 0.033 0.034
0.039 0.043 0.046 0.047 0.045 0.039 0.049 0.050 0.050 0.051 0.050 0.048
0.044
0.032 0.028 0.016 0.002 0.011 0.021 0.030 0.034 0.031 0.018 0.004 0.012 0.023 0.030 0.033 0,029 0.017 0.004
0.075 0.054 0.028 0.012 23.70Inches 0.103 0.077 0.059 0.050 0.054 0.082
n
113
35.70Inches 0.074 0.054 0 044 0.042 0.050 0.072 0.097
0 0 0 0
1.5 1.0 0.5 0.0
-0.5 -1.0 -1.5
0.0
-0.5 -1.0 -1.5
0.054 0.054 0.053 0.053 0.052 0.051 0.048
655 651 678 n 715 0 753
0.0
-0.5 -1.0 -1.5
0.063 0.060
0.058 0.057 0.056 0 065
0.062
0 082
0.109 0.134 0.146 0.142 n 115 0 077
1 3 1.0
0,068 0.065
0.012
0 0 0 0 0 0 0
0.034
0 721
0.044 0.064 0.072 0,066 0.049 0.026
0.088
0.050
0.057 0.053
0.040 0.022 0.009
727 689 662 659 677 714 755
0.5 0.0
0.063 0.061
0 671 670 0 686
n 722 0 757
0 724 0 695
0.043 n.031 o.ni8
n
0.045
n ,007
-1.0
0,058 0.056
-0.5
-1.5
1.5 1.0
0.5 0.0 -0.5 -1.0
-1.6 1.5 1.0 0.5 0.0 -0.5
-1.0 -1.5 1.5 1.0
n,s
0.0 -0.5 -1.0 -1.5
0.060
0 0
n
0 0
n
0
0.017
n . 005
0.011
0.025 n.028
0.027
0.014
0 , nzo
0.001
0,002
0.015
0.019 0.015 0.006 0.001 0.000
0.137 0.143 0 149 0.139 n.118 0.107 0 102
0 008 0.013 0.015 0.014 0.012 0.005 0.000
GROSSVELOCITY 25 FEETP E R S E L O A D 17 70 Inchen 0.0'19 0.041 0 169 010 n on0 0.069 0 132 0.058 021 0 010 0.089 0.089 0 102 029 o 019 0.091 0.102 0 064 034 0 022 0,064 0.097 0 087 035 0 018 0.028 0 109 0.080 033 o 011 0.052 0.009 0 143 02,5 0 003
0.022 0.032 0.038 0.042 0.043 0.041 0.035
23 70 Inches 0 135 0 051 0.006 0 089 0 103 0.017 o os1 n 117 0.026 0 069 0 125 0.027 o 073 o 11s 0.022 0 100 0 086 0.014 o 114 n 074 0.005
35 70 Inchw 0 097 0 094 n 073 o 120
o
n ias
05q
0 053
0
o o
142
n 136 o 120
056 068 0 088
0 096 a
h c
1.0 0 5 0.0
-0.5 -1.0 -1.5 1 3
1.0 0.5 0.0 -0.5
-1.0 3
-1
n 691
n
0.027 n 041
0,009 0.018 0.024 0.022
0.007
Hydro carbon
Kitrogcn
n
n
0 015
047 o5n
o
n
0 052 0 053 o 053
022 027
0 028 n 025
o 052 0 050
n 017 0 008
0.058
0
0.057 0.057
0.016 0,021 0.022 n 019 0 011
0.056
n 057
0 057 n 05s
o
nin
no0
47.70Inches 0.076 0.114 0.069 0 132 0.047 0.144 0.044 0.147 0.049 0.142 0.059 0.127 0.078 0.105 71.70 Inches 0 063 o 051 0 046 n 045 0 051 0 063 0 080
0.022
0.028 0.032 0.033 0.027 0.020 n.015
n.013
0.019 0.022 0,023
0.018 0.011
n ,002
0 . 72fi
0.710
n . 897 n . GRG
0,705 n. 725 0.747 n.73n
n. 722
0.713 0.701) 0.718 0.736 0.758
0 061
n
060 0 059 0 059 0 059 0 050
o
058
0 on2 o 010 0 015 0 017
0 . 734
0.722 0716 0.710 0.726
0 012
n
003 0 no0
0,718 0.756
Y m o c I w 50 FEETP E R SECOXD 11.70Inches 0 . no0 0.194 0.000 0.027 0 000 0.174 0.008 0.173 0 . nnn 0.147 0.017 0.354 0 . no3 0.123 0.031 0.484 n . 004 0.137 0.037 0.188 0.001 0 163 0 028 0.036 0 000 0 186 n 015 0.000
GROSS
0,111 0.133 0.148 0.152 0.144 0.119
0.012 0.022 0.029 0.029 0.024 0.014 0.004
0 6 . 7 0 Inc1ic.s 0.051 0.053 0.055 0 060 0 068 0.074 0 078
Water
95.70Incl1cs
1.5 1.0
0.5 0.0 -0.5
-1.0 -1.5 1.5
0 679
681 0 699
0 728 0 761
71.70Inclios 1.5 1.0 0.5
1 3
688
4 7 . 7 0 Inches
1.5 1.0 0.5
Oxygen
GROSSVELOCITY25 FEETPEB SECOND (Contd.) 0 752 0 689 0 655 0 666 0 695 0 722 0 757
0,010 0.015
Carbon Dioxide
PER SECOND
0.041 0.104 0.135 0.111 0.061 0.030 0.011
0.004 0.006
Radius, Inches
17.70Inches 0.5 0.0 -0.5
Vol. 45, No. 7
INDUSTRIAL AND ENGINEERING CHEMISTRY
1598
0 7.27 0 704 n 691 0 697 0 719 0 745 0 765
1.0 0.5
0.0 5 -1.0 -1.5
-0
0 000
0 004 009 014 016 014 0 008
0 0 0 0
n
009 0 013
0 018 0 022 0 024 0 022
0 016
0 710 0 737 0 754 0 764
0,085
0.173 0,265 0 . 280
0.172 0.087 n ,060
0.618
0.759 0.791 0 . m 0 638 0.544 0.525 0 617 0.697 0.732
23 70 Inches
1.5 1.0 0 5
00 -0.5 -1.0 -1 5
0 013 n 020 0 024 0 027
n 029 0 027 n 022
0 729 0 710 n 699
17 7 0 Inches 0 174 n 016 o 151 n 024 0 124 n 043 o io4 n 069 0 113 0 063 0.011 0 005 o 139 n 050 0 on0 n 162 0 n3o 0,000
0 . non n on6 0 010
0.778 0.641 0,473 0.344
1 3 1.0 0.5 0.0 -0.5 -1.0 -1.5
n
OLJ
0 027 0 031
n o
033 035 0 034 0 030
(7.000 0.004 0.011 0.016 0.015 0.010
n.noi
o
161
0 136
n
io7 0 093 0 101 0 122 o 147
33.70Inches 0.141 0.001 n.nio 0.115 0.017 0.092 0.021 0.080 0.019 0.087 0.014 0.103 n . no5 0.127
n
0.-2 ~ 0 042
o
064 0 078 0 081 0 068
n
043
0.099
0.151 0.206 0.209 0.150
n. io2
0.079
0.698 0.648
0.588 0 578
0.624 0.671 0,707
0.045 0.068 n.088 0,100
0.057 0.093 0.120 0.117 0.088
n . 087 0,652 0.649
0.087 0.063
0.061
0.701
n.ion
n ,043
0.733
0.674 0.732
17.70Inches 0 0 0 0 0
n n
760 711 671 666 699 740 768
1 5
1.0 0.5 0.0
-0.6 -1.0
-1.5
n
030 0 034 0 036 0 038 0 039 0 038 n 035
n.000 0.013
0.097
0.064 0.079 0.072
0.020
n . 023
0.021 0.015 0 007
0.052 0.037 0.020
0.737 0.702 0.679 0.681 0 700 0 721
0.746
i l .70 Inchce 0 040 0 058 o 066 0 067
n
049 0 027 o 016 0 030 o 036 0 041 0 041 o 0x5
n
024
0 018
0 0 0 0 0
745 702 672 669
695 n 731 0 756 0 728 n 706 0 687 0 686 0 698 0 721 0 745
1 .3 1.0 0.5 0.0 -0.5
-1.0 -1.5
1. 3 1.0 0.5
0.0 -0 5
-1.0 -1.5
0 038 0 042 0 044 0 035 0 045 0 044 0
0 0 0 0 0 0 0
042 043 047 048 049
050 049 046
n.006
0.013 0.021 0.024 0.022 0.016 o on9
95 70 Inclic3 n 004 n 095 o 086 0.012 0 079 0 090 n.oio n 066 o 123 0.022 n mi n iai o om 0 065 n 127 0.014 n 07.5 n 115 n . no6 0 089 0 096
Distance downstream from point of initial mixing. Positive values are above center line of radius and negativr helow Compositions expressed in niole fraction.
0.023 0.046 0.050 0.039 0.026
0.013 0 . no0
0.018 0.034 0.036 0.027 0,016 0.004
0.000
0.744 0.711 0 600
0.700 0.716 0.737 n 760 0,758 0.738 0,708 0.701) 0.722 0.742 0.782
INDUSTRIAL AND ENGINEERING CHEMISTRY
July 1953
Table II. Radius, Inches
l.5b 1.0 0.5 0.0
-0.5 -1.0 -1.5
c
1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 1.5 1.0 0.5 0.0
-0.5 -1.0
-1.5 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5
Apparent Temperatures, Volumes, and Velocities in Combustion Tube
Temp., Volume, Velocity, Temp., Volume Velocity, p F. Cu. Ft./Lb. Ft./Sec. F. Cu. F t . / i b . Ft./Sec. GROSS VELOCITY 10 FEETP E R SECOND 17.70Inches 11.70Inchesa 31.50 36.65 280 43,OO 44.19 495 45.60 52.56 840 46 75 57.82 1356 47.10 59.07 1438 45.00 57.49 1301 38.85 44.02 908
1320 1590 1729 1812 1849 1801 1488 1704 1830 1896 1920 1909 1813 1536 1532 1676 1758 1695 1622 1514 1295
23.70Inches 47 80 56 02 60 53 63 01 63 54 60 96 51 53 58.47 62.71 64.94 65.55 64.70 61.30 53.16 95.70Inches 53.47 57.69 60.14 58.18 55.75 52.57 46.64
1599
43 15 48 30 61 45 52 70 52 35 50 30 45 55 52.75 59.75 62.15 62.75 62.55 60 65 56.38
1638 1762 1852 1912 1926 1858 1562
35,70Inches 56.62 60.89 64.01 65.65 65.49 62.56 53.70 57.77 61.89 63.54 63.00 60.90 57.00 50.16
Radius Inches’
1.5 1.0 0.5 0.0
-0.5 -1.0 -1.5
Temp., Volume, Velocity, Temp., Volume, Velocity F. Cu.Ft./Lb. Ft./Sec. O F. Cu.Ft./Lb. Ft./Seo: GROSSVELOCITY 25 FEETPER SRCOND 17 70 Inches 23.70Inches 660 29,14 69.7 1188 43.51 91.4 922 88.1 1562 102.4 1282 47:23 97.3 1760 60181 107.8 1559 , . 100.8 1864 .. , 109.8 1656 ... 100.7 1866 .. . 109.8 1526 96.0 1770 107.5 1238 44:is 87.4 1538 52:62 101.1
35.70 Inches 49.70 55.50 58.65 59.80 59.40 57.75 53.95 53.35 59.55 61.80 62.20 61.m 58.20 51.00
1.5
1816 2053 2156 2176 2147 2044 1771
1.0
0.5 0.0 -0.5
-1.0 -1.5 71 70 Inches 1.5
1726
1.0 0.6
47.70Inches 61.51 118.7 68.58 126.0 71.94 128.6 72.62 128.9 127.2 68101 123.2 59.84 115.7 95.70Inches
.. .
...
1652
0.0
-0.5
-1.0 -1.6 50.50 56.85 60.58 60.95 59.40 55.20 45.00
GROSSVELOCITY 50 FEETPER SECOND
1.5 1 .o
0.5 0.0
-0.5 -1.0 -1.5
w
1.5 1.0 0.5 0.0
-0.5 -1.0 -1.5
168 348 364 390 564 596 428
11.70Inches 15.23 ... 20.63 ... 22.34 , . . 24.28 .., 26.57 ... 26.06 . .. 21.56 ...
710 888 932 1012 1218 1172 918
23.70Inches 29.72 ... ... 35.13 ... 37.35 39.64 ... 44.43 42.35 ... 34.98 . . I
17.70Inches 452 624 638 696 868 918 696
1.5 1.0 -0.5 -1.0 -1.5
1272 1505 1602 ‘1646 1651 1584 1292
5i:60 54.84 56.01 55.55 53.27
139:1 139.2 133,7 129.4 124,s 115.0
67.9 62.8 57.1 58.7 63.0
...
35.70Inches 1084 1290 1418 1500 1578 1520 1204
47.70Inches 0.5 0.0
, . .
27197 29.35 31.50 35.00 35.27 ...
1414 1660 1742 1760 1718 1604 1336
...
45.66 49.69 52.08 53.57 51.40
...
90.0 101.5 97.7 88.8 88.8 89.8 81.4
71.70Inches 49.08 191.0 56.40 208,7 59.10 220.3 59.57 222.6 58.11 216.9 54.59 204.0 46.98 183.5
95.70Inches
Figure 5.
1.5 1.0 0.5
Shrouded Thermocouple
0.0
-0.5 -1.0 -1.5
a
ance thermometer of the strain-f.ree type which had been calibrated by the National Bureau of Standards. Above this temperature the characteristics of platinum-platinum-iridium thermocouples from available tabulations were employed (68). The electromotive force from the thermocouple was measured with a potentiometer of the White type, having a range of 1000 microvolts. It is believed that the temperature of the junction of the shrouded thermocouple was known with a probable error of 1 O F. However, because of the uncertainties from radiation and possible catalytic effects, all temperatures have been designated as “apparent temperatures.” Experimental Results
A total of 20 traverses were made a t gross approach velocities of 10, 25, and 50 feet per second, which corresponds to the flow rates used in the investigation under nonburning conditions (66). For each gross velocity and downstream position the apparent temperature, composition, static pressure, and impact pressure
a b
1522 1794 1920 1952 1916 1786 1392
60: 29
65.04 65.39 64,06 60.01
...
26212 214.9 217.0 209,6 183.5 168.0
Distance downstream from point of initial mixing. Positive values are above center line and negative values are below.
were determined a t seven symmetrically located points above and below the axis of the stream within a maximum radius of 1.5 inches. From these data the apparent temperature and mole fractions of carbon dioxide, carbon monoxide, oxygen, water, hydrocarbon, and nitrogen were determined as a function of position in the flow channel. The smoothed results are shown in Table I and the experimental data are available (88). The apparent specific volume was computed from the measured, apparent, molal composition of the samples, the apparent temperature, and the pressure within the combustion tube on the basis that the components were perfect gases and formed ideal solutions ( 2 1 ) . These specific volumes together with the Pitot tube measurements of dynamic pressure yielded values of the apparent velocity in the combustion tube. A tabulation of apparent temperatures, volumes, and velocities of the gas in the combustion tube is given in Table 11. These data are all subject to uncertainty because of the relatively large possible error in the meas-
urement of the actual temperature and molecular weight of the gases in the combustion zone. These apparent values are a t least indicative of the changes in conditions from point to point within the combustion zone. The standard error of the smoothed temperatures from the experimental, apparent values was 24.9' F. and that of the smoothed mole fractions was 0.00188. A detailed study of the deviation of the experimental data from the smoothed curves used in the preparation of Tables I and I1 is available ( 2 2 ) . The distribution of apparent temperature in a vertical plane through the axis of the tube is shown in Figure 6 for a gross approach velocity of 10 feet per second. There is some asymmetry
(L
g
1.0
3
?
r
0
m
3
(L 4
53
Vol. 45, No. 7
INDUSTRIAL AND ENGINEERING CHEMISTRY
1600
1.0
as a result of the effect of gravity upon the horizontal flow of this nonisothermal system. The use of a point flame holder adds to the asymmetry. The same information is shown on a somewhat different basis in Figure 7 . The lack of symmetry is again evident. The variation in position of the isotherm corresponding t o an apparent temperature of 1600' F. is shown in Figure 8 for three approach velocities. There is but little difference in the apparent temperatures found for gross approach velocities of 10 and 25 feet per second near the injection tube, thus indicating that the flame velocity increased almost proportionately with the approach velocity. However, it required nearly twice the downstream distance to obtain the same apparent teniperature for an approach velocity of 50 feet per second, indicating that there was but little change in flame velocity between approach conditions of 25 and 50 feet per second. This behavior is in accord with the results found by Karlovitz and coworkers (1,5)and other investigators (2, SO). The apparent velocity in the combustion zone is shown in Fiqure 9 as a function of position for an approach velocity of 10 feet per second. The asymmetry of the flow is indicated particularly for conditions near the end of the injection tube. A comparison of the data for higher approach velocities indicates similar behavior a t 25 and 50 feet per second. The variation in the mole fraction of carbon dioxide with position is shown in Figure 10. There was a regular increase in the apparent mole fraction of carbon dioxide with downstream dis-
0
I
I
I
800
I200
I600
WALL 400
,
TEMPERATURE
I
g
O F
Figure 6. Apparent Temperature Distribution at Gross Approach Velocity of 10 Feet per Second
1.0
3
Lo
Y
2 0 VI
a K d
53
s
1.0
10
20
30
40
POINT VELOCITY
Figure 0
20
00
43
DtSTANCE
60
50 PER
SECOND
Apparent Velocity as Function of Position for Approach Velocity of 10 Feet per Second
9.
100
80
DOVJNSTREALI
FfCT
INCHES
Figure 7. Apparent Temperature Distribution in Combustion Tube at Gross Approach Velocity of 10 Feet per Second a:
k2
1.0
3
8z 0 vl
2 K
U
$
10 .
0
0
1 20
I 40
I 60
DISTANCE DOWNSTREAM
Figure 8.
1 80
100
M X E FRPCTION
INCHES
Effect of Gross Approach Velocity upon Position of Combustion Zone at 1600" F.
Figure I O .
CARBON DIOXIDE
(DRY
BASIS)
Distribution of Carbon Dioxide at Gross Approach Velocity of 10 Feet per Second
July 1953
INDUSTRIAL AND ENGINEERING CHEMISTRY
1601
lo-'Q
IO-"
ro-14
lo-"
20
60
40
80
DISTANCE DOWNSTREAM MOLE FRACTION NITROGEN
Figure 11.
(DRY
Figure 12. Com arison of Constant at Thermodynamic Equiligrium with Apparent Constant
8AS15)
Variation in M o l e Fraction of Nitrogen for Gross Approach Velocity of 10 Feet per Second
tance, indicating a gradual approach to chemical equilibrium as the gases traversed the channel. Similar information is presented in Figure 11 for the mole fraction of nitrogen. These data all apply to an approach velocity of 10 feet per second. The asymmetry in Figures 10 and 11 is evident. Similar but more complex diagrams can be prepared for the apparent mole fractions of carbon monoxide and oxygen. Such data for each of the three approach velocities are recorded in Table I. One reaction which was of importance in the course of the combustion is as follows:
2co + 02 * 2c02
Assuming ideal solutions and perfect gases, the equilibrium constant usually used in combustion work for Equation 1 may be expressed as follows for a total pressure of 1 atmosphere: I~col2[no*l
k'E =
-[;;;F
Values of the corresponding apparent constant, KA, may be established for a pressure of 1 atmosphere from the experimental data of Table I. The equilibrium data of Lewis and Von Elbe (18) were used as a basis of comparison. The ratios of the constant of Equation 2 for thermodynamic equilibrium and the apparent value a t the same temperature are shown in Figure 12. These ratios have been presented for conditions along the center line of the combustion tube and indicate large deviations from thermodynamic equilibrium. There is uncertainty in determining the proper equilibrium constant to employ, since the point temperatures in the combustion zone undoubtedly v a r y markedly from the apparent temperatures recorded in Table I. For this reason the data of Figure 12 are only indicative of the lack of approach to equilibrium and should not be considered as more than a qualitative comparison. The deviations from equilibrium indicate? in Figure 12 may have re-
5% :I3
sulted from large microscopic variations in composition and temperature with time within the combustion zone. . Tnese variations may well extend over a significant region and thus introduce marked deviations from the behavior that would be experienced in a nonturbulent phase. At chemical equilibrium much higher temperatures would have been obtained than the apparent values reported. It is possible that local equilibrium may have been approached a t a point during reaction. The subsequent transport of oxygen into this local region by a turbulent mixing process with an associated lowering of temperature may have contributed to the large macroscopic deviations from equilibrium indicated. Hawthorne, Weddell, and Hottel (IO) correlated some of the characteristics of the combustion process by means of a characteristic width defined by the locus of points a t which the concentration of one component was one half that of the maximum. Such a method of correlation has been employed here, except that nitrogen was used as the tracer component, and a reference concentration corresponding to that for nitrogen in air was employed as a basis of comparison. Under these circumstances the concentration of nitrogen a t the boundary of the wake is defined by the following equation, in which CE is the reference concentration:
c, 0
5 BF
2 w
2!
OCL
08
1.2
F A A C T I W WlDTH OF WAKE
Figure 13.
INCHES
18
L
RC
Relative Concentration of Nitrogen in Reaction Zone
=
Cm ~
+ CR 2
~
nm 4- nR 2
(3)
If variations in temperature and pressure are neglected, mole fractions may be substituted for concentration as indicated in the proportion shown. The relative mole fraction of nitrogen is presented as a function of the relative radial position in the channel in Figure 13. The shaded areas include all of the experimental points obtained in this investigation. It has been found (26) that the total Schmidt number, Sc, is approximately 0.8 for the conditions encountered in the central part of the channel. On this basis it is possib*eto estimate from the 'Ow conditions the distribution of nitrogen
Vol. 45, No. 7
INDUSTRIAL AND ENGINEERING CHEMISTRY
1602
in the channel. Following methods which have been described for the estimation of the temperature distribution in the wake of a sphere (I), the variations in the concentration of a nonreacting component may be approximated. The continuity equation for the component of interest may tie written for symmetrical, cylindrical, steady flow in the following way if radial velocity is neglected :
bd
sd
= eddy diffusivity,
ern = = v = = =
snL
Bd
iD, q u a r e feet per second
= total diffusivity, square jeet per second
eddy viscosity, square feet per second total viscosity, eVa Y, square feet per second kinematic viscosity, square feet per second proportional to
+
Subscripts k w
= component k , 171 = minimum, = boundary of the wake
R
= reference state
literature Cited
If the velocity and total diffusivity, _td, are assumed to be constant throughout that portion of the flowing stream of intereet, and if the eddy transport along the axis is neglected, Equation 4 may be integrated. I n case the stream of natural gas is taken a s a point source in infinite media, thc integration of Equation 4 yields (5)
Equation 5 assumes that the flow is symmetrical and therefore does not take into account the gravitational effects which have been found to be of importance in the experimental work. I n integrating Equation 4 it was assumed that the concentration of nitrogen at a distance from the axis of the stream was equal t o that in air. Relative mole fractions may be substituted for relative concentration if the variations in temperatures and pressures are neglected. Under such circumstances Equation 4 predicts the relative change in mole fraction to be a single-valued function of the relative position in the wake based upon the characteristic width as fixed by Equation 3. The full lines shown in Figure 13 were obtained from such predictions. The relative standard error of the experimental points which are included within the shaded area from the three curves shoivn in Figure 13 was 2.90/,. The axis of the combustion zone was taken a8 the locus corresponding to the minimum mole fraction of nitrogen. Types of correlations similar to those shown in Figure 13 may be made for the other components, or if desired the pertinent differential equations ($6) may be integrated to permit the actual concentration of the components t o be estimated. However, until the mechanism of combustion is better understood it does not appear worth while t o pursue further the correlation of the associated transfer processes. Acknowledgment
This work was supported by the Ordnance Corps of the Department of the Army through the Jet Propulsion Laboratory of the California Institute of Technology. The assistance of Betty Kendall and Olga Strandvold in preparing the data in a form suitable for publication is acknowledged. W. H. Corcoran reviewed the manuscript.
(1) Baer, D. H., et al., “Temgeraturc Distribution in the Wake of a Heated Sphere,” accepted by J . A p p l . Mech. ( 2 ) Bollinger, L. M., and Williams, D. T., Natl. Advisory Comm. Aeronaut., Tech. Rept. 932 (1944). I Boomer, E. H., and Johnqon, C. A., Can. J . Research., 15B, 363
(1937). Corcoran, W. H., et al., ISD.ENG.CHEM.,44,410 (1952). Curtiss, C. F., and Hirschfelder, J . O., J. Chem. Plaus., 1 7 , 550 (1949). Damkohler, G., 2. Elektrochem., 46, 601 (1940); Xatl. Advisory Comm. Aeronaut., Tech. M e m . 1112 (1947). FQry,C., Compt. rend., 137,909 (1903). “First Symposium 01% Combustion, Flame, and Explosion Phenomena,” IXD.ENG.CHEX.,20,998 (1928). Forstall, W., Jr., and Shapiro, A. H., J . A p p l . Mech., 17, 399 (1950). Hawthorne, W. R., Weddell, D. S., and Hottel, H. C . , i n “Third Symposium on Combustion, Flame, and Explosion Phenomena,” p. 266, Baltimore, Williams and Wilkins Co., 1949. Hirsehfelder, J. O., and Curtiss, C. F., J. Chem. Pirys., 17, 1076 (1949). Hoare, kl. F., and Linnett, J. W., Ibid.,16,747 (1948). Jost, W., “Explosion and Combustion Processes in Gases,” New York, MoGraw-Hill Book Co., 1946. Karlovitz, B., Phys. Rea., 77,574 (1950). Karlovita, B., et al., J . Chem. Phys., 19,541 (1951). Kreisinger, H., and Barkley, J. F., Bur. Mines, BuZE. 145 (1918). Lewis, B., and Van Elbe, G., IXD.ENG.CHEM.,40, 1590 (1948). Lewis, B., and Von Elbe, G., J . Am. Chem. SOC.,57, 612 (1935). Lewis, B., and Von Elbe, G., J . Chem. Phys., 11, 75 (1943), Lewis, B., and Von Elbe, G., in “Temperature, Its Measiircmcnt and Control in Science and Industry,” p. 707, N e x York, Reinhold Publishing Corp., 1941. Lewis, G. N., J . Am. Chem. SOC.,30, 668 (1908). Mason, D. M., et al., Washington, D. C., American Dociuiicntation Institute, Document 3848 (1952). Mullikin, H. F., and Osborn, M‘. J., in “Temperaturc, Ita Rfeasurement and Control in Science and Industry,” p. 805, New York, Reinhold Publishing Corp., 1941. Penner. S. S.. Am. J. Phvs., 17,422 (1949). Ibid., p. 491. Schlinper, W. G., and Sage, B. H., IND.EKG.CHEM.,45, 657 (1953). Scholefield, D. A,, and Garside, J. E., “The Structure a n d Stability of Diffusion Flames,” London, Gas Research Board, Communication GRB-48 (1949). “Second Symposium on Combustion, Flame, and Explosion Phenomena,”Chem. Revs.,21, 209 (1937); 22, 1 (1938). K. I., Natl. Advisors Comm. Aeronaut., Tech. R c p t . Ahelkin. . . 1110 (1947). “Third Symposium on Combustion, Flame, and Explosion Phenomena.” Baltimore, R‘illiams and Wilkins Co.. 1949 Von Elbe, G., and Mentser, M., J . Chem. Phys., 13,89 (1945). Wildenstein, R., and Pannetier, G., Rea. inst. franc. phtrole et Ann. combustibles liquides, 4, 424 (1949). Williams, G. C., et al., in “Third Symposium on Combustion, Flame, and Explosion Phenomena,” p. 21, Baltimore, Williams and Wilkins Co., 1949. Zeldovich, Y . , and Semenov, N., Xatl. Advisory C o m m . Aeronaut., Tech. M e m . 1084 (1946?. ~~
Nomenclature
C
D e
= concentration, pounds per cubic foot = diffusion coefficient, square feet per eecond = exponential
K A = apparent experimental constant K E = thermodynamic equilibrium constant
weight rate of flow, pounds per second
7%
=
n
= mole fraction
T
R,
= radius, feet = characteristic width of wake, feet or inches
Sc = total Schmidt number
U u
X A
fmE d
=
‘%i+-Y Jr D
Bd
= gross velocity, feet per second
= point velocity, feet per second = downstream distances, feet or inches = difference in
RECEIVED for review December 2 , 1952.
ACCEPTEDMarch 1 3 , 1953. Material supplementary t o this article has been deposited as Document 3848 with the AD1 Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washinpt,on 2 5 , D. C. A copy may be Becured by citing the document number and remitting $3.75 for photoprintn or $2.00 for 35-mm. microfilm. Advance payment is required. Make, cthecks or money order payable t o Chief, Photoduplication Service Library of Congress,
