INDUSTRIAL AND ENGINEERING CHEMISTRY
August 1953
Variation in Composition at Constant Temperature Unless
Main Burner Matches Pilot. Equation 13 shows that even for
*
a n isothermal, isobaric combustor the composition (fuel unburned to total fluid) varies with mass flow (and, consequently, axial position) unless the pilot is matched to the combustor by having the special composition pertinent to a constant temperature, constant pressure combustor. If this matching condition is not satisfied, a measurement of the amount of unburned fuel (or air) does not serve as a measure of temperature, because equilibrium concentration is not established. Stability Limits. A stationary-state, constant pressure, constant temperature combustor may exist, if the mass is injected into an exponential horn combustor a t a rate specified by Equation 18, subject to the approximations previously indicated. I n order to determine under what conditions of pressure, velocity, and temperature this combustor may operate in a stable stationary state, let the mass injection rate R (the ratio d h / d z ) be altered by a n amount AR. Because of the assumption of instantaneous mixing and energy transfer, the instantaneous effect of increasing the injection rate is to decrease the temperature throughout the combustor. The combustor will be stable against injection rate changes if the rate of heat production a t the reduced temperature is sufficient to maintain combustion. The heat generated per second per unit length a t the reduced temperature must be sufficient to raise the temperature of the injected mass (at the new rate) to the new temperature-i.e., the condition for injection-rate stability is that
where Am = @ -
? h R
I n the limit, Tu + 0,
-A =a _
1 - a
e + 0,
AR R
-AT AR T - T , = R
this inequality reduces to
Under these conditions the combustor is stable against smaIl changes in mass injection rate only if the tempgrature is greater than that corresponding to T,,t.. This minimum stable temperature is relatively insensitive to small values of T , and e. The combustor is stable for arbitrary changes in mass flow rate that do not instantaneously decrease the temperature below this amount.
1637
Conclusion
This analysis has been developed for instantaneous homogeneous mixing and heat transfer and indicates characteristics of a combustor in which the controlling rate process is a reaction kinetic rate. The analysis indicates how much might be gained in terms of performance, combustion efficiency, and combustor volume by improved mixing and heat transfer. The calculations emphasize the need for quantitative data on reaction rates a t high temperatures. Instantaneous homogeneous mixing may not be a n optimum situation. Although increased mixing homogeneity tends to cause an increase in the mean temperature of the reactant, leading to increased specific reaction rate, increased mixing homogeneity reduces the concentration of the reactant by diluting i t with combusted mdterial, thus tending to reduce the over-all reaction rate. Acknowledgment
The authors wish to acknowledge many helpful and stimulating discussions of the material presented in this paper with their colleagues engaged in the Bumblebee propulsion program. Discussions with J. P. Longwell of Standard Oil Development co. and with P. Rosen of this laboratory have been particularly helpful. Literature Cited
(1) Appleby, W. G., Avery, W. H., Meerbott, W. K., and Sartor, A. F., J. Am. Chem. SOC.,75, 1809 (1953). (2) Dugger, G. L., Ibid., 72, 5271 (1950). (3) Ibid., p. 5274, footnote. (4) Fristrom, R., Prescott, R., Neumann, R., and Avery, W. H., presented at the Fourth Symposium on Combustion, Cambridge, Mass., September 1952. ( 5 ) Xlaukens, H., and Wolfhard, H. G., Proc. Bog. SOC.,A193, 512 (1948). (6) Lewis, B., and Von Elbe, G., “Combustion Flames and Explosions,” pp. 152-3, New York, Academic Press, 1951. (7) Longwell, J. P., Frost, E. E., and Weiss, M. S . , IBD. ENG. CHEM.,45, 1629 (1953). (8) Mullen, J. W., 11, Fenn, J. B., and Garmon, R. C., Ibid., 43, 195 (1951). RECEIVED for review January 12, 1953. ACCEPTED May 28, 1953. This work wa8 supported by the Bureau of Ordnance under Contract NOrd 7386.
0
High Temperature
0
0
Combustion Chamber
0 0
ALEXANDER WEIR,
JR.
University o f Michigan Aircraft Propulsion laboratory, Ypsilanfi, Mich.
A
GOOD jet combustor requires, in addition to high efficiency, low internal drag, and a wide range of operating conditions, that the combustion be completed in a minimum of space. This requirement has presented many problems and considerable effort has been expended during recent years on the problems of ram-jet combustion. One of the major problems is maintaining adequate flame stability in the combustion chamber. Current
ram-jet practice utilizes a bluff body, inserted in the high velocity gas stream, as a stabilizer or flame holder. A familiar example of a flame holder is the grid or screen on a Mdker laboratory burner. This grid allows more fuel and air to be burned than in an ordinary Bunsen burner before the flame lifts or blows off. Flame holders, however, have certain limitations. Previous work (16,17) has indicated that increasing the size of geometri-
1638
INDUSTRIAL AND ENGINEERING CHEMISTRY
cally similar flame holders brings diminishing returns-i.e., the increase in blowoff velocity becomes smaller and smaller. Several flame holders in series, however, have a higher blowoff velocity than a single flame holder (16). Other investigators have combined a hydrogen-oxygen pilot flame with a gutter flame holder to CERbHIClPLUMINAI RINGS
E2
0
0
INCUES
CERAMIC
COMBUSTION
CHAMBER
STbINLESS S T E E L GUTTER fLbMEROLDER
ljUTTER
FLAMEHOLDER
Figure 1.
COMBUSTION
experiments is shown in Figure 1. The rings, which were obtained from Massilon Refractories Co. , Massilon, Ohio, and cemented in place by alundum cement, were of a high alumina composition. Experiments with different lengths and thicknesses of ceramic were previously reported (8). The bevel on the ring was included a t the ceramic manufacturer's request for ease in removal from the mold. I n the previous experimental work (8) tests were made with the bevel facing upstream, downstream, and with the bevel filled with ceramic to form a smooth surface on the inside of the combustion chamber. KO observable difference in performance of the combustion chamber was obtained with the three different operating conditions. For the experiments described in this paper, the ceramic rings were oriented as shown in Figure 1 . Although a great amount of performance data has been obtained with many ram-jet combustion chambers containing flame holders, no spectroscopic data were readily available. Since it was desired to compare the emission spectra from the ceramic combustion chamber with the emission spectra from a combustion chamber containing a flame holder, the geometrically similar combustion chamber shown in the lower portion of Figure 1 was constructed. The flame holder used was a simple gutter flame holder, constructed of stainless steel and located at the inlet of the combustion chamber. It is true that more complicated flame-holder designs might be more effective under certain operating conditions, but it is believed that their emission spectra would not be too different from those with a gutter flame-holder design under the same operating conditions.
@)
&.%K
8 1-p
Vol. 45, No. 8
CHAMBER
Combustion Chambers
maintain a flame a t high mass velocities (IO). Electrically heated flame holders have been shown to have advantages (9, l a ) . Many other schemes have been proposed; the majority of these are classified for reasons of military security. Other work on a more basic level has indicated that the presence of a heat sink in the vicinity of a flame is unfavorable to combustion (1, a). Present day ram-jet combustion chamber walls are usually*metallic, and since the metal necessarily must be maintained at temperatures well below the flame temperature, the wall acts as a heat sink. The detrimental effects of a heat sink at the walls were deliberately minimized by using a ceramic lining whose temperature approached the flame temperature during operation. Preliminary tests with this ceramic lining indicated that flame holders inserted in the stream were not required for smooth operation at high mass velocities and blowoff did not occur a t the maximum mass velocity obtainable (60 pounds per second per square foot) from the available air supply (8). C2 and CH Spectra Were Obtained during Operation of Ceramic and Flame-Holder Combustors
The purpose of this paper is to present some additional experimental data obtained with this type of combustion chamber. A study of the spectra emitted was undertaken, in the course of which temperature, pressure, and performance data were simultaneously obtained. A simple Combustion chamber of comparable dimensions with a gutter flame holder was also operated with the same equipment, so that its emission spectra could be compared with those of the ceramic combustion chamber. The relative intensities of the spectra emitted by CZand CH in the 3700 to 5200 A. region were obtained for both combustion chambers under similar operating conditions. Equipment. The ceramic combustion chamber used in these
Experimental Air Flows Were Obtained from High Pressure Blowdown System
The large mass flows of air required for these experiments were obtained from a high pressure blowdown system. Air is compressed to 2500 pounds per square inch by means of two Ingersoll-Rand compressors (70 cubic feet per minute each), and this compressedair is storedin two tanks with a totalvolume of 170 cubic feet. Approximately 1 ton (mass) of air is thus available for use a t any rate desired during the experiments. Air from the storage tanks is reduced to a pressure of 300 pounds per square inch in the test stand, metered with an ASME orifice in 3-inch pipe, and passed through a manually controlled valve. The temperature of the air entering the combustion chamber is approximately 0 to 40" F. Commercial propane (Phillips Petroleum Co.) is obtained in the vapor state from a 1000-gallon tank, metered with an ASME orifice in 2-inch pipe, and passed through a manually controlled valve. A sketch of the equipment used in this investigation is shown in Figure 2. The air and propane are mixed downstream of their respective control valves and the mixture flows in 3-inch pipe through the 45" Y shown in Figure 2 to the combustion chamber. Immediately upstream of the combustion chamber an automotive spark plug provides ignition. The spark plug is not used after ignition has been achieved. -4 static pressure measurement is made at the inlet of the combustion chamber, and the ceramic wall temperature is measured at the exit of the combustion chamber by means of a Leeds and Northrup optical pyrometer. A Plexiglas window, 3 inches in diameter and 1 inch thick, is located behind the 45" Y connection so that a view from the u p stream end through the entire length of the combustion chamber
August 1953
INDUSTRIAL AND ENGINEERING CHEMISTRY
1639
corresponds to thermal choking conditions (Mach number a t exit of combustion chamber equal to one) for a fuelair ratio of 0.060 pound of propane per pound of air. The maximum pressure occurs a t the stoichiometric ratio of 0.063 pound of propane per pound of air. The ceramic wall temperature a t the exit of the combustion chamber for steady state conditions versus mass velocity is plotted in Figure 5 for a constant fuel-air ratio of 0.060 pound of propane per pound of air. The temperature of the wall increases as the mass velocity increases. A warm-up time of 3 minutes is required for the wall temperature to reach 2500" F. a t a mass velocity of 5 pounds per second per square foot. After this preheat a period of 10 to 20 seconds is required to establish these steady state temperatures. In Figure 6, the ceramic wall temperature is plotted versus the fuel-air ratio for a constant mass velocity of 32 pounds per second per square foot. The maximum temperature occurs a t the stoichiometric fuel-air ratio. The shape of the experimental curve is similar to the calculated adiabatic flame temperature curve shown in Figure 6. These optical pyrometer temperatures at this mass velocity are 500' to 600" F. lower than the adiabatic flame temperature. The experimental temperatures plotted are the optical pyrometer readings, and calculations based on assumed emissivities would indicate higher temperatures. Of course, one would not expect to attain the adiabatic flame temperature.
7
Figure 2.
Experimental Equipment
is obtained. Inside the test stand, a Cenco grating spectrograph is mounted on ways so located that the optical axis of the spectrograph is always coincident with the center line of the pipe. This permits observation of the combustion prior to the time the spectrograph is moved into position. The spectrograms were examined with a Leeds and Northrup recording microphotometer. Ceramic Wall Temperature Reached 3000' F. during Operation
The combustion chamber inlet pressure for the ceramic combustion chamber versus mass velocity of the gaseous fuel-air mixture is plotted in Figure 3 for a constant fuel-air ratio of 0.060 pound of propane per pound of air. Since there is no bluff body inserted in the flow, most of the pressure drop through the combustion chamber is that due to combustion; the pressure drop due to friction is of the order 1 pound per square inchfor the range of mass velocities used here.
4 v) a INLET
I
PRESSURE
ui
P
FUEL-AIR
FUEL-AIR
RATIO
-
RATIO
LB. PROPANE / LB. AIR
Figure 4
MASS
VELOCITY
- LBS/ SEC./
SP. FT.
Figure 3
The inlet pressure to the ceramic combustion chamber versus fuel-air ratio a t a constant mass velocity of 32 pounds per second per square foot is plotted in Figure 4. This mass velocity closely
As shown in Figure 2, the spectrograph was mounted so that a view lengthwise through the combustion chamber was obtained. Before the combustion chamber was ignited, an iron arc was placed a t the exit of the combustion chamber 80 that a calibra$ion spectrogram of iron could be obtained on the same film as the combustion chamber spectrogram. This, together with a mercury spectrogram, served to establish the wave lengths of bands obtained from the combustion chamber. Typical spectrograms are shown in Figure 7, in which mercury is a t the top, iron in the center, and a spectrogram of the ceramic combustion chamber on the bottom. Since the grating in the instrument used was an inexpensive plastic replica grating, good resolution was difficult to obtain. Exposure times of 2 minutes were used t o ob-
1640
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 45. No. 8
LOCITY THROUG
MASS VELOCITY- LES/SEC./SQ.FT. OF JET-AREA
Figure
FUEL-AIR
5
RATIO
-
LB. PROPANE / LB. AIR
Figure 6
tain pictures on Du Pont 428 film. The spectrograms were obtained at night inasmuch as daytime operation superimposed the sun’s spectrum on the spectrum obtained from the combustion chamber. Up to twelve exposures could be obtained on one strip of film so that differences in developing technique were not important in determining relative intensities. A Microphotometer Showed Relative Intensities of Cp and CH Bands
Relative intensities were determined by placing the negative in a microphotometer and measuring the relative blackness of the bands. A sample tracing for the ceramic combustion chamber is shown in Figure 8. On such a graph, clear film is zero, and infinite blackness is slightly greater than a relative intensity of 1.7. As may be seen from Figure 8, the Swan bands of C2(5165 to 5129 A., etc.) and bands of C H (4315 to 3871 A . ) ( 7 , I S ) were obtained in the spectrum from the ceramic combustion chamber in the wave length region studied. I n Figure 9, the relative intensity of the strong CH lines versus fuel-air ratio is plotted a t a mass velocity of 32 pounds per second per square foot. The curves for both wave lengths have similar shapes with a maximum around the stoichiometric fuel-air ratio. I n Figure 10, the relative intensity of three strong Cz lines versus
Figure 7.
fuel-air ratio is plotted a t a mass velocity of 32 pounds per second per square foot. These curves do not have a maximum a t the stoichiometric fuel-air ratio but increase as the fuel-air ratio is increased. In both these figures, the data were obtained with the ceramic combustion chamber. At lean fuel-air ratios, the relative intensity is quite sensitive to fuel-air ratio-for example, as the fuel-air ratio increases from 0.054 to 0.060, the relative intensity of C H increases about 20% and the relative intensity of C2 increases about 60%. For consistent results, the fuel-air ratio must be held constant in those esperiments in which the mass velocity is varied. I n Figures 11 and 12, the relative intensities of the strong CH lines versus mass velocity are plotted for the two combustion chambers shown in Figure 1. For both curves, the intensity of the CH band is much greater in the ceramic combustion chamber than in the combustion chamber containing a gutter flame holder. This is true under the same conditions of pressure and mass velocity. I n Figure 12, the 4315 A. CH line for the ceramic combustion chamber seems to become asymptotic to a relative intensity of 1.7. This is due to the relatively long exposure times used. In Figures 13, 14, and 15, the intensity of various CZlines versus mass velocity are plotted for the ceramic combustion chamber as well as for the combustion chamber containing a gutter flame holder. -4t the same mass velocity (and inlet pressures), the in-
Typical Spectrograms
Top = Mercury vapor lamp Center = iron arc Bottom = Ceramic combustion chamber
INDUSTRIAL AND ENGINEERING CHEMISTRY
August 1953
a
I
0
Figure 8.
s
2
Microphotometer Tracing
0,
FUEL-AIR RATIO
0.
As indicated in Figure 11, the relative intensity of C pis extremely sensitive to fuel-air ratio, and the relative intensities of CZin the dotted region should be some 50 to 60% greater due to the lower fuel-air ratio. However, in the absence of data in this region, the actual points obtained were plotted as shown with no correction for the low fuel-air ratio. The intensity of C:!in the ceramic conibustion chamber, therefore, seems to increase as the mass velocity is increased.
RATIO
- LE PROP.ANE/LB AIR
.04
FUEL - A I R
Figure 9
.05 RATIO
-
.06 .07 LE. PROPANE / LE. AIR
Figure 10
RELATIVE INTENSITY
MASS
VELOCITY-
LBS / SEC / S a FT.
Figure 11
1
of Typical Ceramic Combustion Chamber Spectrogram
tensities of CZ bands in the ceramic combustion chamber are about double the intensities of CZin the combustion chamber containing a gutter flame holder. In Figures 14 and 15 the curves for the ceramic combustion chamber are dotted for mass velocities lower than 25 because the fuel-air ratios in this region were about 0.054. A fuel-air ratio of 0.060 was used to obtain the higher mass velocity data for the ceramic combustion chamber as well as for all the gutter flame-holder combustion chamber data.
FUEL- AIR
a
2
1
1641
MASS
VELOCITY
-
LBS /SEC. / SQ F T
Figure 12
INDUSTRIAL AND ENGINEERING CHEMISTRY
1642
Efficiency of Ceramic Chamber Was Evaluated by Specific Air Impulse Method
The specific air impulse or Sa method was used to evaluate the efficiency of the ceramic combustion chamber. Briefly, Sa is the stream thrust divided by the mass flow of air when the combustion chamber is choked. A correction factor involving the exit Mach number is employed for other than choking conditions. With this method of evaluating combustion chamber performance, the combustion chamber is penalized for any decrease in momentum resulting from unequal flow distributions. The determination of Sa as a criterion for ram-jet combustion chamber performance has been used by other invcstiyators and the method is adequately described in the literature (3, 4,6, 8, 10, li, 15).
OF
5129
a
Vol. 45, No. 8
K i t h the ceramic combustion chamber, Sa \$as computed by assuming that the temperature of the ceramic ~ a 1 1a, t the exit of the combustion chamber and as measured bj the optical pyrometer, to be equal to the stagnation temperature of the exit gases. The Sa obtained with the ceramic combustion chamber was divided by the theoretical maximum Sa and plotted versus mass velocity in Figure 16 and against fuel-air ratio in Figure 17. I n these figures some performance data obtained with a stainless steel ram-jet combustion chamber containing an orifice flame holder with 40% blockage is also plotted. These data were obtained by D. R. Glass a t this laboratory in an earlier investigation, and the Sa Tvas computed from internal drag measurements made during his investigation (4). A few scattered points obtained with the gutter flame-holder combustion chamber are also plotted. These indicate that the performance of the gutter flame-holder design (36y0 blockage) shown in Figure 1is probably similar to the performance of the orifice flame-holder (40Y0 blockage) combustion chamber. A coniparison of Figure 16 with Figures 13, 14, and 15 s h o w that the efficiency as well as the intensity of the (3%bands increases as the mass velocity in the ceramic combustion chamber is increased. With the t v o flame-holder designs tested, as the mass velocity is increased, the efficiency and the intensity of Cz reach a maximum at a mass velocity of about 15 pounds per second per square foot. Further increase in mass velocity results in a derrease in efficiency and in Cz intensity. Due to the similarity of behavior, one might suspect some correlation between (2%intensity and efficiency. Figures 16 and 17 are not intended to imply that all flameholder combustion chambers have performance characteristics similar to the gutter flame holder and orifice flame-holder com-
c,
vs
1.2
z Ln
z
1.0 0.8
MASS
VELOCITY
-
LBS./
SEC. / SP. FT.
Figure 14
+
5
Figure 16
06 0.4
K W 02
0.0 MASS
VELOCITY
- LBS./ SEC
Figure 75
/ SO. FT.
FUEL- AIR
Figure 17
RATIO
August 1953
INDUSTRIAL AND ENGINEERING CHEMISTRY
1643
portant from a practical standpoint but are believed to be outside the scope of this paper which is intended to indicate the possibility of a mechanism of flame stabilization other than that of drag stabilization with flame holders. Combustion Efficiency Reached 90% in Ceramic Chamber at Mass Velocity of 50 Lb./Sec./Sq. Ft.
Some indication of combustion intensity may be obtained by examining the photographs shown in Figure 18. In these photographs, the mass velocity is 20 pounds per second per A C square foot, and the fuel-air ratio is 0.060 pound of propane per pound of air. Figures 18A and 18B mere taken through the Plexiglas window-Le., the view obtained by the spectrograph. Figure 188 is the gutter flame-holder combustion c h a m b e r , and Figure 18B is the ceramic combustion chamber. Both 18h and 18B are to the same scale, thp ceramic combustion chamber appearing larger because light from the incandescent walls is reflected from the upstream piping. In both cases, the upstream piping is not hot. Side views of both combustion chambers in operation a t the same conditions are shown in Figures 18C and 18D; 18C the gutter B D flame-holder combustion c h a m b e r , Figure 18. Combustion Chambers in Operation 18D the ceramic combustion chamber. As may be seen from these Fuel-air ratio = 0.060 Ib. propane/lb. o f air Mass velocity = 20 Ib./sec./sq. ft. photographs, the gutter flame-holder A = View through gutter flame-holder combustion chamber design allows a great deal of combusB = View through ceramic combustion chamber tion to occur outside the combustion C = Side view o f gutter flame-holder combustion chamber chamber itself, as evidenced by the D = Side view o f ceramic combustion chamber .long luminous flame. Figure 18D of the ceramic combustion chamber a t bustion chambers tested. For example, Mullin el al. ( 1 1 ) have, the same operating conditions indicates that most of the combusby combining a hydrogen-oxygen pilot flame with a gutter flame tion occurs inside the combustion chamber itself. holder and by preheating the air 200' or 300' higher than used in In these photographs, neither combustion chamber is thermally the present experiments, maintained a flame a t mass velocities as choked, the mass velocity being 20 pounds per second per square high as is indicated here for the ceramic combustion chamber foot. This gutter flame-holder combustion chamber, as shown in and obtained comparable efficiencies. Figures 16 and 17 are inFigure 1, was not capable of being operated under thermal chokcluded so that the relationship between performance data and ing conditions. spectroscopic data could be observed at the same operating conditions. Conclusions In propulsive devices, it is desirable to operate a t Q high level of combustion intensity. Combustion intensity levels for different The spectroscopic data indicated that no new bands were obtypes of combustion chambers are shown below: tained in the ceramic combustion chamber, but the bands of CZ and CH were more intense in the ceramic combustion chamber B.t.u./Sec./ B.t.u./Sec./ than in the gutter flame-holder combustion chamber tested a t the Cu. Ft. Cu. Ft./Atm. same operating conditions. The ceramic combustion chamber Domestic coal furnace (14) 1.5-3.0 1.5-3.0 was operable over a wide'range of fuel-air ratios a t a mass velocShipboard installation (14) 15-20 15-20 ity over 50 pounds per second per square foot with a high imTurbojet combustion chamber (6) 2500-3500 410-580 pulse efficiency. The high level of combustion intensity obCeramic combustion chamber used Over 50,000 Over 12,500 tained with the ceramic combustion chamber indicates potentialiin this investigation ties in propulsive devices. The intensity figures for the ceramic combustion chamber are based on the inside diameter of the combustion chamber. The Acknowledgment thickness of the ceramic used presumably could be reduced. The questions of minimum ceramic thickness, minimum warm-up The writer wishes to express his appreciation to R. J. Kelley time, minimum internal drag, maximum ceramic life, etc., are imand R. E. Cullen as well as to R. B. Morrison for aid in this work. I
INDUSTRIAL AND ENGINEERING CHEMISTRY
1644
Discussions of spectroscopic procedures with G. B. B. A I , Sutherland were extremely valuable. Literature Cited . .
Cullen, R. E., Trans. Am. Soc. ikfech. Engrs., 75, 43 (1953). Cullen, R. E., Univ. Mich. Eatern. Memo. 81 (December 1950). Davis, T., and Sellars, J., Johns Hopkins University, Applied Physics Laboratory, Project Bumblebee, R e p t . 32 (March 1946). Dodge, R. A., Hagerty, W. W., Luecht, J. W.,York, J. L., Glass, D. R., Stubbs, H. E., and Yagle, R. A., Air Force Tech. R e p t . 6067, Part 2, Wright-Patterson Air Force Base, Dayton, Ohio (Sovember 1950). Ethyl Corp., Detroit, blich., “Aviation Fuels aiid Theii Effect on Engine Performance.” SAVAER-06-5-501, USAF T.O. S o . 06--5-4, 1961. Ganiiett, J. R., Univ. M i c h . Estern. Memo. 7 (July 1947). Gaydon, A. G., “Spectroscopy and Combustion Theory,” 2nd ed., London, England, Chapman and Hall, Ltd., 1948. Hicks, H. H., Jr., and Weir, A . , Jr., Uniu. Mich. Extern. Memo. 73 (December 1950). l\Iorrison, R. E., and Dunlap, R. A, Ibid., 21 (May 1948).
Vol. 45, No. 8
(10) l,Iullen, J. IT’., 11,IXD. EXG.CHEM.,41,1935 (1949). (11) Mullen, J. W., 11, Fenn, J . B., and Garmon, R . C., Ibid., 43, 195 (1951). (12) Mullen, J. W., 11, Benn, J. B., and I r h y , 31. R., “Third Symposium on Combustion. Flame. and ExDlosion Phenomena.” 13. 317, Baltimore, I\Id.,’Williamsand Wilkins Co., 1949. (13) Pearse, R. W. B., and Gaydon, A. G., “Identification of Llolecular Spectra,” 2nd ed., New York, John Wiley 8: Sons, Inc., 1950. (14) Perry, J. IT7., ”Chemical Engineer’s Handbook,’’ 3rd ed., 12. 1600, Ken- York, McGraw-Hill Book Co., 1950, (15) Rudnick, J . Aeronaut. Sei., 14, 540 (1947). (16) Weir, A,, Jr., Rogers, D . E., aiid Cullen, R. E., C n i ~ Mich. , Estern. Memo. 74 (September 1950). (17) Williams, G. C., Hottel, H . C., and Scurlock, il. C., “Third Symposium on Combustion, Flame, arid Explosion Phenomena,” p. 21, Baltimore, h l d . , Killiarns and Wilkins Co., 1949. RECEIVED for review October 27, 19.52. ACCEPTEDMarcli 1.5, 195.3 Presented as past of the Symposium on Chemisisg.of Combustion before the Division of G a s and Fuel Chemistry at the 122nd Meeting, . ~ Y E R I C A N CHEXICALSOCIETY, Btlantic City, N. J. This work was sponsored by the Office of Ordnance Research, U. S. Army.
e e e
e
Relation of Space Velocity and Space Time Yield
e SHlNJlRO KODAMA, KENlCHl FUKUI, A N D AKlRA MAZUME Foculfy of Engineering, Kyofo Universify, Kyofo, Japan
s
EVERAL authors have discussed the relation of space velocity and space time yield in catalytic react,ors of the fixed-bed type (10, 14). Some have treated this problem through considerable simplification and others have considered special cases. I n the present paper the space velocity-space time yield relation is discussed more generally-Le., all the factors that possibly affect this relation are taken into consideration. For this purpose the exact expression for t’he over-all reaction rate must first be obtained preliminarily by a flow method in a laboratory scale experiment. This rate equation can be expressed in terms of the partial pressure of each component of the reaction mixture, the temperature, and the linear velocity, which is related to the reaction rate only implicitly in the material transfer term. I n order to obtain the space velocity-space t,inie yield relation, therefore, the following factors must be considered : Change of partial pressures Change of reaction temperature Change of material transfer rate The third factor, the change of material transfer rate, which is principally due to the change of linear velocity of feed gas, is considered important in some heterogeneous processes, but in most chemical reactions this factor is not so serious as the other two, if the reaction temperature is not extremely high or linear velocity is not extremely small. Accordingly, in the present treat,ment, this factor may be left out of consideration. The second factor, the change of reaction temperature, depends on the type or structure of the reactor-Le., on whether it. is an isothermal reactor, an adiabatic reactor, a heat-erchanger type of reactor, or a self-heat-exchanger type of reactor. I n addition to these three factors, in a practical sense, another
factor det,erniines the quaiitit,?. of desired product that is actually recovered: This factor m a y be called recovery efficiency, defined as the number of moles of desired product recovered per number of moles o i desired product produced in the reactor. The recovery efficiency is considered to be a function of the linear velocity and the temperature of effluent gaa from the reactor and the partial pressure of the desired product in the final reitntion mixture. This functional relation is not, the same in all recovery equipment, and if information concerning this relation is sufficiently complete in a certain piece of equipment,, it is not difficult to take the influence of recover>-efficiency into account in obtaining the actual space time yield-space velocity relation. It is, therefore, rather a meaningless effort than a laborious work t o attempt to discuss this influence generally. Fundamentals. For discussing the phenomena occurring in a reactor in geqeral, a reaction represented by the following st>oichiometric equation is considered : viAi
+ vnA, + V ~ A+S
=o
(1)
Then, the equat,ioiis of mat,erial balance and of heat halarice are
(i
=
1>2,
. . . . .)
and
where
-++ =v o is
-
-+-+
the reaction rate and v, v mean the forward xntl
