Investigation of Combustion in Rocket Thrust Chambers C. H. TRENT Aerojet-General Corp., Azusa, Calif.
The results of an experimental investigation of the high pressure combustion of white fuming nitric acids and hydrocarbons is presented. The utilization of a water-cooled probe allows the measurement during steady state operation of the temperature, pressure, gas velocity, and chemical composition of the gases flowing through an operating rocket combustion chamber. Temperature and velocity profiles are presented and an attempt i s made to relate kinetic information through the V,/w parameter to combustion chamber design. The relationship between the injector and the combustion process i s discussed. Results indicate that heterogeneous combustion occurs for approximately the first 50% of propellant conversion. The design of the injector has little effect on the gas phase chemistry of the combustion process.
A
LTHOUGH research on combustion has been pursued with great vigor during the past few decades, the data available a t the present time contain little, if any, information pertinent to the combustion of white fuming nitric acid and hydrocarbons in rocket combustion chambers. The lack of knowledge of the phenomena occurring during the combustion process makes the development of rocket combustion chambers more of an a r t than a science; consequently, the development of such devices is almost entirely a trial-and-error procedure which is often timeconsuming and altogether too costly. Highly instructive information on the combustion of materials with white fuming nitric acid was obtained from the optical studies of the phenomenon in a “two-dimensional,” transparent thrust chamber ($), but these data were qualitative only. Recently the results of a combustion study on the liquid oxygenammonia propellant was published by Baker (4) wherein temperature and mixture ratio profiles were determined by a probing technique. Such information greatly aids propellant injector design. For purposes of rocket motor design, the most significant knowledge that can be gained from a study of rocket motor combustion is the determination of the rate a t which the propellants are being consumed, for, a t any given weight flow rate of propellants, the rate of propellant conversion determines the size of the combustion chamber. The successful development of a mechanical probe and of a mass spectrometric technique for the study of combustion in rocket engines has made i t possible t o secure more quantitative information on combustion. This experimental technique permits the measurement, under actual steady state operating conditions, of the temperature, velocity, flow direction, and chemical composition of the combustion gases in a combustion chamber. It is the purpose of this paper t o show how kinetic data usable for thrust chamber design can be obtained from measurements of combustion gas temperature, velocity, and chemical composition and to present the results of an experimental study of the combustion of hydrocarbons and white fuming nitric acids employing a probing technique.
Theoretical Discussion Conversion of Propellant. A useful criterion of rocket propellant performance is the characteristic exhaust velocity, c*, which can be determined from the thermodynamic properties of the fluid flowing through the motor and is related to the upstream temperature, gas molecular weight, and specific heat ratio
April 1956
(14). For a nonreacting gas Tyith constant specific heat, c* may be expressed as
For a reacting gas where M and k are no longer constant during the flow process Equation 1 should be modified to read
where c*
characteristic exhaust velocity, feet per sec.
= gravitational acceleration, 32.2 feet per sq. sec.
9
R =
T, = 1M = M
j
=
k = k’
universal gas constant, 1545 feet-lb. per 1b.-mole O R. combustion chamber temperature, O R. mean molecular weight of combustion gases mean molecular weight of combustion gases in the vicinity of the throat of rocket motor nozzle specific heat ratio, C,/C, specific heat ratio in the vicinity of the nozzle throat
On the other hand, c * can be determined from externally measured quantities such as combustion chamber pressure, p,, propellant weight flow rate, w, and nozzle throat area, At.
As defined in Equation 3, the characteristic exhaust velocity expresses the chemical energy liberated in terms of the force exerted on an area of the confining walls equivalent to the area A t , provided that the conversion of a unit mass of propellant into completely burned gases occurs in 1 second a t constant pressure. Therefore, the maximum obtainable value of this parameter can be calculated by means of thermochemical equations from the properties of the gases resulting from a complete adiabatic combustion of the propellant. For a completely adiabatic system free from such complicating phenomena as heat transfer, friction, shock effects, etc., the ideal theoretical value, cTh, given by Equation l is a true characteristic of the propellant, since it depends only upon the adiabatic flame temperature and the composition of the combustion products. I n such a system, the maximum value of the characteristic exhaust velocity corresponds to the
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
749
complete conversion of the injected propellants into the final equilibrium products, and any other value of c * corresponds to a less complete combustion process. Thus, the ratio of c * to c:, expresses the fractional conversion of the propellant. The fraction of the propellant injected into the combustion chamber that is converted into completely burned products obviously can be expressed also by the weight ratio of completely burned products to total propellant injected. I t follows then that this ratio equals the ratio of the actual value of characteristic eshaust velocity, c*, to the theoretical value, crh c*/& = wb/w
where
(4)
weight flow rate of completely burned gases in the combustion chamber, lb. per sec. w = propellant injection rate, lb. per see. Wb =
If it is assumed that the combustion in a rocket thrust chamber progresses in an axial direction in such a manner that the weight flow rate of completely burned gases is a function of the distance, 2,from the injection end of the chamber, and if the velocity of the reactants is also known to be a function of the distance, 2 , an equation can be derived which relates the Tyeight fioiv rate of completely burned products to the local values of c* and gas velocity and the axial distance x from the injector face.
Kinetics of Propellant Conversion. The usefulness of an experimental technique that permits measurements of the local temperature, velocity, specific heat ratio, and mean molecular weight of the gases present in an operating rocket motor cannot be ovelemphasized. From this body of data, the weight flow rate of completely burned gases, wb,and the percentage conversion of the incoming propellant into completely burned gases, 100 wb/w, ale readily calculated. I n addition, knowledge of wb as a function of time, which can be established from velocity measurements. permits the determination of the rate of consumption of unbuiiied propellant within the combustion chamber. I n general, the rate of a chemical reaction is proportional to powers of concentration of the reactants. For isothermal systems the rate of decrease in concentration of a reactant, - d c / d t , xith B concentration c at time t, can be expressed by the equation -dc/dt
where --dc/dt k C
n
= kc"
(6)
= rate of consumption of c = = =
specific reaction rate constant concentration of reactant at time t order of reaction
The general reaction rate equation, Equation 6, refers to a rcaction involving only one chemical substance or to a reaction in nhich the initial concentrations of all reactants are the same A possible kinetic analysis might start Kith an attempt to foice the observed data into an espreseion of the form rate where cos = cy = a,p =
=
kc,",cf
(7)
concentration of oxidant concentration of fuel order of reaction for the oxidant and fuel, respectively
I n actual practice, homever, it Tvould not be easy to determine the appropriate values for ,c, and e, experimentally in a rocket motor. However, if at an appreciable distance downstream from the injector, the fuel and oxidant would be so well mixed that the mixture could be considered to react as a monopropellant, the rate and reaction order of propellant consumption could be defined by means of Equation 6. The meaeurenient of gas velocity at various points within the combustion chamber permits the determination of the time history of the reacting gases. The time, At see , which elapses duiirig 350
the flow of the gases through the chamber, can be determined graphically by means of the equation dx/v
t =
At steady state operation, the weight flow rate of propellant, w, injected into the combustion chamber is constant, and the total weight of propellant injected during the time interval At is
w = wAt
(9)
From Equation 5 , the percentage conversion of injected propellant into completely burned gases can be calculated. Therefore, at any station the weight of unburned propellant is determined by
where
is calculated from experimentally determined data for T,. and M and k are calculated from the chemical composition of the gas samples extracted from the combustion chamber. Finally, the weight of unburned propellant can be expressed in terms of concentration
w: = Wu/7/lVc where
W',:
V, m
(11)
~.
= moles of unburned urooellant oer unit combustion
chamber volume = volume of combustion chamber up to the nozzle throat, cu. inches = mean molecular weight of the injected propellant
The rate of propellant consumption, --dW,/dt, can now be determined by plotting TV: versus t and taking the slope of the curve. By plotting such curves for each position, enough data can be obtained to determine the isothermal rate of propellant consumption a t various initial propellant concentrations, and an investigation can then be made of the chemical kinetics involved. V J w Parameter. The combustion chamber of a rocket motor serves merely to provide sufficient reaction volume for the combustion process to proceed to completion. In a liquid-propellant rocket motor, the combustion of the propellant occurs as a continuous flow process, usually taking place in a cylindrical reactor. A supply of liquid phase propellant is fed into the injector end of the reactor at a constant rate, and high temperature gases are discharged from the nozzle throat. The pertinent problem in the design or analpis of a flow process is the relationship between the reactor volume and the feed rate. If diffusion in the direction of flow is negligible and the etream of reacting propellant moves progressively through the chamber without longitudinal mixing, the relationship between chamber volume and feed rate may be resolved by consideration of an infinitesimal reactor volume. dV,,having the cross-sectional area of the combustion chamber and a length dx in the direction of flow (6). At the steady state condition, the number of moles of propellant converted in this elementary volume per unit of time is constant and equal to rdV,. The material balance for this volume requires that the conversion r d V , equal the reduction in the number of moles of unburned propellant in the stream passing through the section. Thus,
rdV, where r
=
wdn,
(12)
= rate of reaction, moles of propellant conveited per unit
volume of reacting system per unit time
V, = reactor volume occupied by the reacting system
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
Vol. 48,No. 4
ROCKET PROPELLANTS cooled, mechanically operated probe, fitted with orifices so that gas temperatures could be measured by the pneumatic method described by Blackshear (6),Moore (IO), and Wildhack ( 1 2 ) . A U I C O O U M RING The velocity of the combustion gases was measured utilizing a modified Pitot-tube technique. A sectional comW E E R NOZZLE PROBE PAVERSING DEVICE bustion chamber was used (Figure 1) and measurements were made a t various distances downstream from the injector; traversing the probe radially permitted the taking of measurements along the chamber diameter. Thus, i t was possible to obtain an extensive survey of conditions inside the combustion chamber. Representative data were obtained a t 3 72, 4.72, 6.72, and 8.72 inches downstream from the inFigure 1. Cutaway drawing of sectional thrust chamber with mechanical probe jector face At each axial distance, the thrust chamber was probed radially for a length of 0.891 inch measured w = propellant weight flow rate from the axis of the chamber. np = moles of propellant converted per unit weight of proIt should be emphasized that measurements obtained with the pellant fed probe are time average values. At each station the probe remained stationary for approximately 3 seconds during which The Combustion chamber volume required for a specified contime data was obtained. Consequently temperature, velocity, version, n,, a t a constant propellant injection rate, 20, is obtained and gas composition information reported herein are average by the integration of Equation 12. values measured over an approximately 3-second period. The present probing technique is effective only for measurements a t the steady state condition because of the instrumentation re= fnPdn,/r n, sponse times. A second limitation to the probing technique is the gas medium t o be sampled must be physically homogeneous. A plot of the nymber of moles of completely burned gases per The presence of liquid droplets or the deposition of solid particles unit volume, W b Jagainst elapsed time yields the time history in either of the two sonic orifices invalidates the data obtained. of the propellant within the combustjon chamber. The slope Because of the difficulty in calibrating such an instrument at t h e of that curve a t various values of W b gives the corresponding temperatures in question, the temperature data are most reliable rate of propellant conversion. The conversion np expresses the when considered as relative temperatures; however, the accuracy moles of propellant converted per pound of propellant injected of the temperature measurements is good. Operational experiinto the combustion chamber and can be determined from ence indicated the temperature measurements were obtained with Equation 14 an accuracy estimated to be within &200° F.; gas velocities &-eremeasured to between 0 and +20%, and the mass spectronp = W;/W (14) metric analysis of the combustion gases to within & l % . Temperature and Velocity Distribution. An inspection of t h e The parameter V,/w can then be determined by plotting the contemperature measurements revealed that, a t any one cross section version n, versus the respective rate l / r and measuring the area downstream from the injector, there was considerable variation under the curve. in temperature in the radial direction; this is further evidence of If the reaction rate, T , for a propellant feed of fixed composition the longitudinal flame striations or columnar burning zones obis a function only of the conversion np, Equation 13 expresses a served during optical studies of rocket combustion ( 2 ) . The relationship between V,/w and n, which is independent of reactor injector was so placed that the probe traversed along a row of size, shape, or propellant injection rate, so long as longitudinal pairs of fuel injection orifices. The greatest variation in temdiffusion in the combustion chamber is negligible. Thus, the perature occurred a t points approximately opposite and downVc/w ratio becomes an important combustion chamber design stream from the impingement point of a fuel injection pair. parameter which, within certain limitations, permits the deFrom the data obtained, the magnitude of the temperature termination of the required combustion chamber volume for a variations was greatest a t 3.72 inches from the injector; the rocket motor of any size to deliver a given characteristic exhaust variations became less pronounced further downstream, until, velocity. a t 0.52 inch from the entrance to the nozzle, the temperature profile was almost a smooth curve. Discussion of Experimental Data As would be expected, the combustion gas temperature increases as the gases regress from the injector end toward t h e The preceding discussion has shown that the percentage connozzle, indicating that the degree of completion of combustion version of injected propellant, the rates of propellant conversion, varies with axial distance from the injector. A representative and the combustion chamber volume required to convert a unit increase in gas temperature with axial distance is shown in weight flow rate of propellant can be readily calculated if experiFigure 2. mental measurements of combustion gas temperature, velocity, mean molecular weight, and specific heat ratio can be secured. The spatial temperature distribution throughout the sectional Such measurements have been obtained a t steady state on the combustion chamber produced by the like-on-like injector i s gases flowing through a 1000-pound thrust rocket motor equipped presented in Figure 3. The three-dimensional representation with a “like-on-like, impinging stream” injector and a waterwas obtained by plotting 1/T on the y-axis, distance downstream COOLANT WATER lRANSFEk8lQCKS
3
April 1956
INDUSTRIAL AND ENGINEERING CHEMISTRY
4500
4000
3500
3000 W' Q:
c 3
2 2500 W 0
2 I-
2000
fn
a
0
1500
1000
SO0
0
3
Figure 2.
4 5 6 7 8 A X I A L DISTANCE FROM INJECTOR, INCHES
9
Variation of combustion temperature and velocity with axial distance
from the injector on the z-axis, and radial distance from the chamber axis on the z-axis. The reciprocal of combustion temperature, l / T , was used since preliminary plotting of the data established that the concave shape of the curves was best suited for the three-dimensional representation. During several of the test runs, the combustion chamber Fas probed from the axis to 1.498 inches in order to obtain data near the combustion chamber wall. Both gas temperature and velocity were observed to decrease near the chamber walls. At 8.72 inches, the gas temperature near the nall was about 610' R. lower than the temperature near the chamber auis, and similarly, the gas
Figure 3. Spatial distribution of combustion g a s temperature within sectional combustion chamber, P, = 4 3 0 Ib. per sq. inch absolute
252
velocity near the wall TTaz about 100 feet per see. less than in the center of the chamber. Since the external cooling of the thrust chamber mas aided by fuel film-cooling, the large drop in temperature and velocity near the chamber walls is to be expected. The Combustion gases also exhibited a progressive increase in velocity during flow from near the injector to the nozzle. B typical axial variation in gas velocity is presented in Figure 2 . A t 3.72 inches and at 430 lb. per sq. inch absolute chamber pressure, the gas velocity was measured as 201 feet per sce. The velocity increased to 400 feet per see. in the remaining 5.28 inches of chamber length. The spatial distribution of gas velocity n-ithin the sectional combustion chamber produced by the like-on-like injector is presented in Figure 4. -it any one axial distance, the variation in velocity in the radial direction was very small. In accordance with the fluctuation in temperature, the greatest observed radial variation in velocity occurred at a distance 3.72 inches from the injector. The gas velocity at 300 lb. per sq. inch absolute was found to be higher than at 430 Ib. per sq. inch absolute, as would be predicted from the equation of continuity and equation of state for an ideal gas. Since both cross-sectional area of combustion chamber and propellant-weight flow rate were the samc for both chamber pressures, the gas velocity must vary inversely with the pressure, provided that the molecular weight and temperature of the gases remain constant. At 0.52 inches from the entrance to the nozzle, where gas temperature and gas molecular weight were approximately the same for both pressures, the ratio of gas velocities, V(300 ib. per sq. inoh absolute)/~(430 ib. per bg. inoh absolute), was 1.33 which is roughly the same as the pressure ratio 430/300, or 1.43. Gas Composition and Progress of Combustion. Samples of the combustion gases were obtained lor each location where temperature and velocity were measured. The following is a typical gas sample obtained from a position near the entrance to the nozzle. Compound Carbon dioxide, C O X Carbon monoxide, CO Water, HzO Hydrogen, Ha Nitrogen dioxide, XOz ic'itric oxide, NO Nitrogen, Nz Oxygen, Oz Small amounts of gaseous hydrocarbons
h!Io!e
.
Fraction 0.224 0,098 0 444 0.063 0.000
0.008
0.163 0,001
0.002
Figure 4. Spatial distribution of combustion g a s velocity within sectional combustion chamber, P, = 4 3 0 Ib. per sq. inch absolute
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 48, No. 4
ROCKET PROPELLANTS The variation in chemical composition as the gas stream travels downstream from the injector serves t o give some indication of t h e progress of combustion. For example, Figure 5 shows the variation in the corrected mole fraction with axial distance for nitrogen, nitric oxide, and oxygen. I n this figure i t can be noted that, as the gases progress toward the nozzle, the mole fractions of nitric oxide and oxygen decrease very sharply, the greatest decrease occurring between 3.72 and 4.72 inches. On the other hand, the concentration of nitrogen increases with decreasing nitric oxide concentration indicating that the nitrogen in the combustion gases in the region surveyed is derived from nitric oxide-for example, by a reaction such as
I-
3 0.20
3 0.16 U
; U.
0.18
0
4E
0.08
W
6 0.04 I 0
As shown later, nitrogen probably is not produced by the thermal dissociation of nitric oxide, but rather by the reaction of nitric oxide with some oxidizable substance in the combustion gases. The close relationship between nitric oxide and nitrogen suggests that the ratios between the nitric oxide and nitrogen concentrations would serve as useful criteria for judging the state of the combustion process. Large values of the nitric oxidenitrogen ratio imply that only a small amount of nitrogen has been produced and that, therefore, the combustion process is relatively incomplete, whereas small values of the nitric oxidenitrogen ratio indicate large concentrations of nitrogen, and therefore a more nearly complete reaction. Figure 6 shows the spatial distribution of the nitric oxide-nitrogen ratio calculated from gas composition throughout the combustion chamber. I n general, the value of the nitric oxide-nitrogen parameter exhibits a steady decline from the injector end to t h e nozzle end of the combustion chamber. The variations in the radial direction show marked differences in the progress of the combustion process for neighboring stream lines, further substantiating the belief that the gas f l o r through the chamber is stratified. T h e radial variation is most pronounced near the injector. The very steep gradient in this combustion parameter indicates t h a t a large amount of chemical activity occurred in the chamber between 3.72 and 4.72 inches from the injector. T h a t region could almost be visualized as the terminus of a broad “flame front.’’ The width of the zone of rapid propellant conversion is unknoa-n, since the chamber was not probed any nearer to the injector than 3.72 inches. The general shape of the combustion parameter Eurface indicates the combustion in the probe motor with the like-on-like injector as a progressive process.
Figure 6. Spatial distribution of nitric oxide-nitrogen ratio within sectional combustion chamber, P, = 430 Ib. per sq. inch absolute
April 1956
3 4 ‘ 5 6 7 8 9 AXIAL D I S T A N C E F R O M INJECTOR, I N C H E S
Figure 5. Variation of nitrogen, nitric oxide, and oxygen concentration with axial distance from injector
A comparison of Figure 6 with Figure 3 shows a remarkable correlation between the nitric oxide-nitrogen parameter and the temperature of the combustion gases. From these two figures, it is seen that at 3.72 inches from the injector and 0.272 inch from the axis, the nitric oxide-nitrogen ratio reaches a maximum value of 2.5, indicating t h a t the combustion process is less advanced a t t h a t point than a t any point within the combustion chamber surveyed by the probe. At the same position, the gas temperature is the minimum observed value of 2195’ R. and shows excellent qualitative agreement. The close correspondence between the nitric oxide-nitrogen parameter and gas temperature suggested t h a t some simple relationship might exist between the two factors. However, the curve of nitric oxide-nitrogen versus temperature is parabolic and the equation of the curve, determined by the method of least squares, demonstrates t h a t combustion gas temperature is related to the nitric oxide-nitrogen ratio in a complicated manner.
-NO _ iX2
exp. ( - 9 5 . 5 7 4 ) ~27.952 exp. [1.996(ln T ) 2 ]
where
NO = mole fraction of nitric oxide in combustion gases N 2
T
= mole fraction of nitrogen in combustion gases = combustion gas temperature, O F.
Figure 7. Distribution of unburned propellant throughout sectional combustion chamber, P, = 430 Ib. per sq. inch absolute
INDUSTRIAL AND ENGINEERING CHEMISTRY
153
Table I.
Propellant Conversion in Mechanical Probe Motor
(Operated v i t h like-on-like injector a t 300 a n d 430 lb. per sq. inch ahsolut,e chamber pressure; conversion w ~ / w ) ~ Axial Distance from from~ Axis of~Conibustion Chamber, Inches ~ ~ Radial j Distancc ~ ~ ~ , Inches 0.00 0.182 0 . 2 7 2 3 6 4 0 . 4 5 2 0 . 5 4 4 0.634 0 722
Pc = 300 lb. per sq. in. abs. 4.72 5.00 6.72 8.72
0.746 0.783 0.902
3.72 4.00 4.72 6.72 8.72
0.789
...
0:785 0.880 0.886
0.623 0.671 0,834 0.879
0.636 0.668 0.807 0.919
0.678 0.701 0.801 0,908
0 . 7 1 5 0 712 0 730 0 , 7 3 2 0.822 0,830 0.920 0.897
Po = 430 Ib. per sq. in. a b s , ,.. 0 677 0 609 0 . 6 6 8 0.734
0.786 0:834 0 . 8 5 3 0.889 0,930 0 . 9 5 6 0.986
0.732 0.913 0.903
0.896
0.800 0.855 0.918 0.932
0.777 0.832 0.922 0.910
0.670 0.698
...
...
0.822 0.920
... ...
... .._
0,786 0.804 0,823 0 837 0.830
,
..
,..
...
Nominal propellant weight flow r a t e at 300 Ib. per sq. inch abs. was 5.223 Ib. per s e e . , a n d a t 430 lb. per sq. inch abs. it was 5,059 Ib. per see. a
Since the magnitude of the nitric oxide-nitrogen ratio is an indication of the progress of combustion, the reciprocal of that ratio, nitrogen-nitric oxide, may be used in the same capacity. I n the initial stages of combustion-Le., a t temperatures near the ignition temperature-when only a small fragment of the available nitric acid oxidizing agent has been broken down, the concentration of nitrogen is extremely m a l l , and consequently, the nitrogen-nitric oxide ratio is small. Fortuitously, the minimum value of the ratio nitrogen-nitric oxide determined from the reciprocal of Equation 16, occurs a t a temperature of 637" F, which is slightly higher than the range of experimentally determined ignition temperatures for hydrocarbons and white fuming nitric acid. The minimum value of the nitrogen-nitric oxide ratio mas calculated to be 0.096. Conversion of Propellant within Combustion Chamber. The measurements of temperature, velocity, and combustion gas composition make it possible to compute the actual value of e* and, consequently, t o calculate a t any desired axial location nithin the chamber the R eight flow rate of completely burned gases, Wb, generated from the injected propellant. The local value of c* can be determined from the measured data by means of Equation 3 , and 2L'b can be calculated from Equation 5. Equation 5 n-as the working equation from which the over-all rate tub, and the propellant conversion, zc'b/w, were calculated from the temperature, velocity, and gas composition data obtained from test-firing the mechanical probe motor. Table I shows the percentage of conversion, w b / x , of the propellant into completely burned gascs at 300 and 430 Ib. pcr sq. inch absolute chamber pressure when the mechanical probe motor is operated with the like-on-like injector. T h e spatial distribution of propellant conversion within the combustion chamber is illustrated in the three-dimensional Figure 7. I n this figure, the fraction of injected propellant remaining unburned, (w - wb)/w, is plotted on the y-axis versus axial distance downstream from the injector (z-axis), and versus radial distance from the chamber axis toward the combustion chamber m.11 (z-axis). The various curves running the length of the surface represent the axial variation of the conversion for a particular streamline, whereas the curves traversing the breadth of the surface represent the radial variation of propellant conversion for a particular axial location. As in Figures 3 and 6, the large radial variations in propellant conversion a t 3.72 inches reflect the influence of the injector on the over-ail combustion process. The high rate of consumption of unburned propellant between 3.72 and 4.72 inches is in agreement with the large changes in gas temperature and nitric oxide-nitrogen ratio x-hich occur in the same region. The local characteristic velocity within the combustion chamher varies with the percentage of conversion of the injected
154
propellant. Figure 8 shon s the ielationship between propcllant conversion calculated from Equation 13 arid local ex, determincd by Equation 3 . A t 100% propellant conveision, the charactcristic velocity rorresponding to complete combustion predicted by the curve of Figure 8 mas found to be 4995 feet per scc. The ideal theoretical characteristic velocity a t an O/F mixture ratio of 3.85 is 5120 feet per see. Thus, the values of c * for complete combustion predicted from the data measured with the aid of the mechanical probe and that computed from thermochemical data agree to within 2 4%. The concentration of unburned propellant, W l , a t vat lous stations throughout the combustion chamber vas calculated by means of Equations 10 and 11. The rate of propellant consiuup; tion, -dlV:/dt, Tyas determined graphically by plotting lV,, veisus t [determined by integration of Equation 8 (Table 111 I ] and taking the slope of the curve. By plotting such curves ioi each radial position, sufficient data was obtained to determinr isothermal rate of propellant consumption a t various inii propellant concentrations. The rates of consumption a t different positions downstream from the injector for a typical streamline are presented in Table I1 for the temperature inteival froin 3300" to 4100" R a t 300 and 430 Ib. per sq. inch absolute chamlici pressure. Once the concentration of a reactant has been clctrrmined as a function of time, the order of reaction and thc specific reaction rate-constant may be calculated.
Table II. Rates of Consumption of Unburned Propellant in, Sectional Thrust Chamber with Like-on-Like Injector Distance from InJector, Inches 4.00 4.15 4.21 4.34 4.52 5.97 6.29 6.57
Distance from Chamber lixis, Inch 0 372 0 272 0 272 0 272 0 272 0 272 0 272 0 272 0 272 0 272
6 86
7.17
Table 111.
R.
3300 3500 3700 3900 4100 3300 3500 3700 3900 4100
Lb. per 8s. Inch Abs. 430 430 430 430 430
dW:/dt, Lb. l I o l e / Cu. Inch/Rec. ( X 10-4) 5.0
3.7 3.1 2 4 1.8 1.81
300 300 300 300 300
1.77 1.74 1.71 l.b9
Order of Reaction for Consumption of Unburned Propellant
Temp.,
" R.
x. n~o . . 3300 3.500 3700 3900 2900 3100 3300
pc,
Temp.,
p c, L b . per Sq. Inch Abs. 4.10 ~. . 430 430 430 430 300 300 300
Ordei of Reaction, It
3 R
2 2 2 3 3
0 67 89 00 2fi 2 53 2 09
By plotting curves of TV: and temperature against time, it m-as possible to determine a t a given temperature the rates of piopellant consumption a t various values of initial propellant concentration; and, by employing the differential method, the ordei of reaction, n>for the consumption of unburned propellant n a s calculated. The data of Table I11 present the order of reaction, n, a t various temperaturrs and a t the two pressures investigatd The rate of change in partial pressure of nitric oxide in the combustion gases and the order of reaction for the change ale now considered. Employing the technique described, the ordei of reaction for the consumption of nitric oxide was determined to be 1.73, 2.09, and 2.31 a t 3iOO0, 3900", and 4100' R. a t 430 lh. per eq. inch absolute, the average being 2.04. I n view of t h r apparent second-order change in concentration of nitric oxide it does not seem unreasonable t h a t the kinetics of over-all propcllant consumption in the temperature range above 3100" R.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 48, No. 4
ROCKET PROPELLANTS are approximately third order. Originally, the assumption was made t h a t t h e unburned propellant reacted as a single substance; however, a reaction mechanism which involves a three-body collision for the decomposition of a single substance appears improbable. I n reality, the unburned propellant is a mixture of fuel and oxidant. The apparent orders of reaction for consumption of unburned propellant (3rd) and nitric oxide (2nd) indicate that, in the temperature range investigated, the propellants are consumed in part by reaction between oxidizable material and nitric oxide. This conclusion is strengthened by two facts.
conversion. It is also possible t h a t some of the unburned propellant is oxidized by a simpler mechanism, such as a secondorder reaction between fuel and oxygen, the oxygen being produced by thermal dissociation of the oxides of nitrogen. A combination of the two mechanisms proceeding simultaneously could well result in the fractional order observed for propellant conversion listed in Table 111. However, the observed orders are nearer three than two, indicating that the rate-limiting reaction for the combustion process above 3100' R. may be the thirdorder reaction between propellant and nitric oxide.
Most of the known gaseous reactions of the third order involve nitric oxide as one of the reacting molecules (8). For an exception to this rule see Stephens and Pease (11). There is a large difference between the calculated and the measured rate of disappearance of nitric oxide. Using the kinetic data obtained a t high temperatures by Daniels ( 1 ) for the decomposition of nitric oxide according t o the second-order reaction kx0
2 s o 3 n-,
+
0 2
ICNO = 109 exp. ( -70,00O/RT)
(17) (18)
the rates of change in partial pressure of nitric oxide were calculated and compared with the rates obtained from chemical composition data. [More recent data on the kinetics of the thermal decomposition of nitric oxide published by X s e and F r e c h ( I S ) indicate t h a t above 2295" R. the kinetic equation for t h e process is k s o = 3.1 X 1015exp. (-82,0OO/RT) (mole/ml.)-l set.-'
Table IV. Comparison of Calculated and Measured Rate of Change in Nitric Oxide Content of Combustion Gases DNO . -dUNO/dt. - d D N 0 /at Temp., O
R.
3500 3700 3900 4100
'NO
Atm.'-' See.-' 13.68 37.13 82.62
183.9
Lb. per Sq. Inch Abs. 83,50 77.70 74.50 60.7
Lb.'per Sq. Inch Abs./Sec., Cnlcd. 6 . 5 x 103 1.5 x 1 0 4 2 . 1 x 104 4 . 6 x 104
Lb.'per Sq. Inch Abs./Sec., Meas. (X10-') 30.2 28.5 26.8 24 0
However, the use of Wise and Frech's data does not alter the conclusion reached based on Equation 18.1 The data of Table IV show t h a t the measured rate of disappearance of nitric oxide, - d p N o / d t , is 46 times as large as the calculated value a t 3500" R. T h e large difference indicates t h a t nitric oxide probably is not reacting according to Equation 17 but, instead, by some other reaction, notably t h e reduction of nitric oxide b y unburned propellant. As the temperature is increased, the difference between measured rate and calculated rate for the consumption of nitric oxide decreases, until a t some elevated temperature the two rates should become equal. T h e equality of the two rates mould mean t h a t the disappearance of nitric oxide could be attributed either to thermal dissociation of nitric oxide or t o reduction of nitric oxide by oxidizable material. Since the measured rate of nitric oxide disappearance decreases with increasing temperature (the combustion reaction becomes more complete; therefore, the rate of combustion becomes less), the equality of t h e measured and calculated rates of nitric oxide disappearance would correspond to a near-thermal equilibrium condition in the combustion gases. By plotting the calculated and measured rates against temperature, the temperature of the intersection of the two curves was found to be 4710" R. The average combustion gas temperature measured a t 0.52 inch from t h e entrance to the nozzle of the sectional thrust chamber was found t o be 4650' R. T h e conversion of unburned propellant into completely burned gases by a third-order reaction between fuel and nitric oxide should be considered only as a possible mechanism for propellant
April 1956
L O C A L CHARACTERISTIC VELOCITY, C: FT./SEC.
Figure 8. Relationship between local characteristic velocity and percentage conversion of propellant
I n view of the preceding discussion, the kinetic equation for the conversion of unburned propellant into completely burned gases has been assumed to be
The specific reaction rate constants (IC;,) for this reaction of 430 lb. per sq. inch absolute and a t 3500", 3700", and 3900" R. were and 6.17 X 10'6 (inch3)* calculated t o be 4.30 X 10'6, 5.1 X mole-2 sec.-l A plot of In kh, against l / T yielded a straight line. Thus, the data obeyed the Arrhenius law. The slope of the straight line gave a n apparent activation energy E, of -24,433 B.t.u. per 1b.-mole. T h e over-all kinetic equation for propellant conversion above 3100" R. becomes kku = 1.4 X 1019 exp. (-24,433/RT) (inchs)2mole-a sea-1
(20)
Since there was no evidence for the presence of liquid propellant beyond 3.72 inches from the injector, Equation 20 represents the kinetics for t h e gas phase combustion reactions. T h e material in the gas mixture capable of being oxidized probably consists of carbon monoxide, hydrogen, vaporized hydrocarbons and the respective atoms and free radicals. T h e small quantities of hydrocarbons present in the gas samples consisted of acetylene, ethylene, benzene, and much smaller quantities of
INDUSTRIAL AND ENGINEERING CHEMISTRY
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butane and isobutane. Near the injector (3.72 inches) the mole fraction of hydrocarbons was observed to be less than a t 6.72 inches; however, a t the shorter distances, a resinous deposit collected in the sample-bottle valves during the test operation. Such deposits indicate t h a t high molecular neight organic material was present in combustion gases but, because of low volatility, escaped analysis.
0
IO
20 30 4 0 50 6 0 70 BO 90 100
PERCENT CONVERSION OF INJECTED P R O P E L L A N T
Figure 9. Percentage conversion of propellant into completely burned gases at various V,/w ratios The unburned propellant within the portion of the thrust chamber surveyed by the probe probably consists of carbon monoxide, hydrogen, vaporized hydrocarbons, oxygen, and nitric oxide. The kinetic equations indicate t h a t the energy is released from the unburned propellant by t h e reaction of oxidizable substances with nitric oxide. The following reactions of nitric oxide are known to be termolecular ( 7 ) .
2N0 2NO
+
+ 2Hz
0 2
.-f
2N0*
2Hz0
+ Nz
(21, (22)
Since the decomposition of nitrogen dioxide is complete above 619' C., reactions involving nitrogen dioxide appear unlikely t o occur in the investigated region of the probe motor. On the other hand, the reduction of nitric oxide by hydrogen proceeds at high temperatures and probably occurs along n i t h the oxidation of organic material. Combustion Chamber, Injector, and Combustion Process. The parameter V , l w expresses the combustion chamber volume required to allow a specified conversion of unit n-eight flow rate of propellant. The propellant conmision rate, r , and the conversion per pound of injected propellant. n,, were calculated from the temperature, velocity, and combustion gas composition data and were utilized for the graphical integration of Equation 13. By determining the areas under the curve required for various conversions, n,, a representation of the parameter V , / w required for a specified degree of propellant conversion was obtained and is presented as Figure 9. The integration of Equation 13 yields a V,/w of 26.83 cu. inches-see. per lb. required for 100% conversion of propellant a t a mixture ratio of 3.84 into completely burned gases; in other words, required to yield ideal theoretical performance. It is of interest to determine the applicability of the parameter V,/w for predicting the combustion chamber volume of the probe 756
motor.
The volume of the probe motor from the injector face
to the plane of the nozzle throat is calculated to be 114 cu. inches. The average operating propellant weight flow rate was 5.059 lb. per see., giving a V,/w of 22.53 cu. inches-see. per lb. From Figure 9 a V,/w of 22.53 cu. inches-sec. per lb., equivalent to that of the probe motor, yields a propellant conversion of 9770. The propellant conversion calculated from data measured in the probe motor a t a position 0.52 inch from the entrance t o the nozzle was found to be 9670. The characteristic exhaust velocity corresponding to 96% propellant conversion is 4940 feet per see. whereas the average c * obtained during the test-firings of the section thrust chamber with the like-on-like injector (calculated from measured data for propellant flow rate, chamber pressure and throat area) was 4673 feet per see. and differs by only 5.4% from the c* predicted from the V,/w ratio for the probe motor. Further inspection of Figure 9 leads to an interesting conclusion with respect to the relationship between a rocket motor combustion chamber and the combustion process proceeding inside it. For the like-on-like injector, only a small fraction of the total combust,ion chamber volume is required to produce an 80% conversion of the injected propellant. Conversely, most of the chamber volume is required to extract the remaining 20% of the available energy from the propellant'. Since data sufficient for the computation of the V,/w parameter were available only for the like-on-like injector, the exact effect of other injectors on the combustion volume required for a given conversion is unknown. However, by employing the data obt'ained from testing six different repetitive pattern injectors, some indication can be obtained of the effect of injector design on the necessary combustion chamber volume. This testing RTas performed under conditions comparable to those employed during the testing of the probe motor-namely, a t the same thrust and same chamber pressure-in a thrust chamber of dimensions identical to those of the probe motor. The objective of the foregoing test program was to compare the relative merits of injectors of different design and to establish the effects on operational characteristics of different chamber diameters which in turn affect the distance between sets of injection holes. The injectors tested are showerhead injector, modification I; showerhead injector, modification 11; 1 t o 1 impinging stream injector; 2 to 1 impinging stream injector; 1 to 1 impinging stream injector with splash wall; and like-on-like injector. The characteristic exhaust velocity of each injector was found to vary with the combust'ion chamber volume. If a conipa,rison of the coinbustion chamber volumes required to produce a c * of 4500 feet per see. a t 300 lb. per sq. inch absolutc chamber pressure and a t a propellant flow rate of 5 lb. per see. is made for these injectors, it may be determined that the following combustion chamber volumee are required:
Type of Injector 2 : 1 impinging stream injector
1 : 1 impinging stream injector with splash wall 1: 1 impinging stream injector Like-on-like injector Showerhead injector, mod. I1 Showerhead injector, mod. I
Vol. Required,
C u . Inches 31.5 47 78 80
126.5
145.0
Thus, the design of the injector and the hole spacing, as exemplified by the modification I and I1 showerhead injectors, which differ only in the distance between adjacent orifices, appear to affect the combustion volume required to produce a prescribed value of c*. The fact that, for the same propellant combination, injectors of different design require different combustion volumes for the same performancea as known from the earlydags of both ilmerican and German liquid-rocket power-plant development (3, 9). Since that time the reasons for the different operational characteristics of the various injector designs have been a subject of speculation. The major arguments have ccntered around the
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
voi. 48, N ~ 4.
ROCKET PROPELLANTS relative importance of t h e physical processes, such as propellant jet disintegration (atomization), mixing, and propellant evaporation, in comparison with the chemical processes comprising t h e actual oxidation phenomena. Prior t o the study reported herein, insufficient knowledge of the phenomena occurring within a rocket combustion chamber prevented determination of t h e relative importance of these processes, and therefore the criteria necessary for the design of a n optimum injector were unknown. On the basis of the data obtained, both from combustion studies in the probe motor and the testing of repetitive pattern injectors, an insight into the relationship between the chemistry of combustion and the injector was achieved. T h e ultimate approach to a comparison of the effects of different injectors on the combustion process is to investigate the magnitude of the V,/w parameter required for each injector t o produce a given characteristic velocity. Consider for the various injectors the additional combustion chamber volume required t o increase t h e characteristic exhaust velocity from 4500 t o 5000 feet per sec., t h a t is, t o achieve approximately the last 12% of theoretical performance. This comparison can be accomplished by determining t h e difference between V , / w ratio required for 5000 and 4500 feet per sec. e*. The additional chamber volumes required for a thrust chamber operating a t 5 lb. per sec. propellant flow rate are presented in Table V. Within reasonable limits, the additional combustion chamber volume required is the same for all the injectors compared.
Table V.
Additional Combustion Chamber Volume Required b y Different Injectors to Boost Performance (From 4500 to 5000 feet per sec. c*)
Injector Type Showerhead, mod. I Showerhead, mod. I1 Splash wall Like-on-!ik? 1 :1 Impinging stream 2: 1 Impinging stream
VdW
13.8 12.6 13.5 13.2 11.8 10.4
Vol. Required a t 5 Lb./Sec. Flow Rate, Cu. Inch 69 63 67.5 66 59
52
In the region of temperature and gas molecular weight corresponding t o 3000 feet per sec. e* and above, the data from the probe motor with the like-on-like injector indicate that the processes occurring in this region are mostly chemical. Therefore the additional volume required is apparently governed solely by the chemical processes of combustion, and since the volume required for the additional gain in performance appears t o be the same for all injectors, i t can be concluded t h a t the injector exerts little, if any, effect on the chemical reactions occurring in t h e region considerably downstream from the injector face. Unfortunately, there was insufficient reliable data t o extend the foregoing comparison t o determine where the different injectors cease to resemble one another. From the present data obtained with t h e probe motor the effects of differently designed injectors on the physical processes of jet disintegration, mixing, and vaporization cannot be clearly demonstrated. So far as probe data are concerned, there is a n unexplored region for the first 3.72 inches of t h e probe motor. Since a t 3.72 inches from the injector face no evidence was uncovered for the existence of liquid droplets, i t must be concluded t h a t these physical processes were being completed in t h e volume bounded by the injector face and a plane 3.72 inches downstream. Thus at present, the region from 0 feet per sec. t o 3000 feet per sec. e* (the local value of e* at 3.72 inches) represents the region of heterogeneous combustion, t h a t is, combustion reactions occurring where both t h e liquid phase and gas phase coexist. This may be expressed in another manner by stating that, on the basis of present knowledge, heterogeneous combustion occurs for approximately the April 1956
first 50% of propellant conversion. Undoubtedly, further experimentation by probing closer t o the injector face would reduce the foregoing e* and propellant conversion range. Effect of Chamber Pressure on Combustion Process. The 1000-lb. sectional thrust chamber coupled t o the like-on-like injector was test-fired at combustion chamber pressures of 300 and 430 lb. per sq. inch absolute in order t o obtain data for chamber temperature, gas velocity, and combustion gas composition a t different pressures. An increase of 130 Ib. per sq. inch absolute did not seriously alter the temperature distribution in the probe motor. At 0.52 inch from the entrance t o the nozzle, the combustion gas temperature was found to be approximately the same for the two pressures. This is t o be expected since the variation of equilibrium flame temperature with pressure is small. T h e performance calculations indicate t h a t the combustion temperature would be increased only 70" F. b y increasing the chamber pressure from 300 t o 600 lb. per sq. inch absolute. T h e effect of chamber pressure on gas velocity has been noted. T h e most significant effect of increasing chamber pressure was the apparent increase in the rate a t which the propellant was converted into completely burned products. For example, a t 3.77 inches downstream from the injector face, 66.4% of the propellant was converted at 430 lb. per sq. inch absolute chamber pressure, whereas at 300 lb. per sq. inch absolute a n additional 1.12 inch of chamber length was required t o obtain approximately the same conversion of the propellant. At 66% conversion the respective rates of conversion were 0.0024 mole per cu. inch-see. at 430 lb. per sq. inch absolute and 0.000215 mole per cu. inchsec. at 300 lb. per sq. inch absolute. It is to be pointed out again t h a t the gas velocities were higher at 300 lb. per sq. inch absolute than a t 430 lb. per sq. inch absolute. T h e larger velocity a t 300 lb. per sq. inch absolute resulted in a shorter stay time for the gases in the combustion chamber. Thus the large increase in rate of propellant conversion on increasing chamber pressure from 300 to 430 lb. per sq. inch absolute must be attributed to both increased pressure and increased stay time. T h e various rates of propellant conversion at the two pressures are presented in Table VI. I n general, increasing the pressure a t which t h e combustion process occurs decreases the axial distance required for a specified conversion of the propellant.
Table VI. Rate o f Propellant Conversion in 1000-Lb. Thrust Sectional Chamber Coupled with Like-On-Like injector Axial Radial Distance Distance from from Injector, Chamber Axis, Inches Inch 3.77 3.85 3.95 4.26 5.70 8.02 4.89 5.46 6.04
7.46 8.35
Chamber Pressure,
Rate of Conversion,
Inch -4bs.
Inch-Sec.
430 430 430 430 430 430 300
0.0024 0.0014 0.00087 0.00025 0.00013
Lb. per Sq. Mole per Cu.
0.272 0.272 0.272 0.272 0.272 0.272 0.272 0.272 0.272 0.272 0.272
300 300
300 300
0.00010
0.000215 0.00020 0.000186 0.000169 0.000158
Percentage Conversion of Propellants 66.4 71.5 76.6 81.7 89.4 97.0 65.3 70.95 75.7 85.1 89.9
Conclusions As the result of a theoretical and experimental evaluation of t h e combustion of hydrocarbons and white fuming nitric acid in an operating thrust chamber, the following conclusions may be drawn. The temperature, velocity, and chemical composition of t h e combustion gases flowing through a rocket thrust chamber during steady state operation can be measured by a probing technique with sufficient precision to permit a kinetic analysis of the combustion process.
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The characteristic velocity calculated from the temperature, mean molecular weight, and specific heat ratio of the combustion gases at’ the entrance to the nozzle deviated by only 1.3% from the characteristic velocity calculated from propellant weight flow rate, chamber pressure, and throat area. Thus, the data obtained by the mechanical probe were considered representative of the phenomena occurring vithin the combustion chamber of the probe mot,or. The radial variations in temperature, velocity, and gas composition indicated that the flow through the combustion chamber consisted of longitudinal strata of different temperatures and gas compositions. The stratification of the flow was found to diminish v i t h increasing distance from the injector face. The ratio of the mole fraction of nitric oxide to the mole fraction of nitrogen present in the combustion gases %-asfound t o be an excellent qualitative measure of the completeness of combustion. T h e relationship between nitric oxide-nitrogen ratio and gas temperature is not simple. The curve of nitric oxide-nitrogen ratio versus temperature is parabolic and the equation for t h a t curve has the form
NO/& =
exp. (-96.574)~ 27.952 exp. [1.996 (In T ) z ]
The percentage conversion and the rate of conversion of the propellants into completely burned combustion products \vas found to depend upon axial distance from the injector and radial distance from the chamber axis. With the like-on-like injector and a t 430 lh. per sq. inch absolute chamber pressure, approximately BO$& of the propellant was converted into completely burned gases in the volume bounded by t,he injector face and a plane 3.72 inches downstream from it. I n general, increasing the pressure of combustion from 300 to 430 lb. per sq. inch absolute decreases the axial distance required for conversion of the propellant. The data indicate that increasing the combustion pressure also increases the rate of propellant conversion. Above 3100” R., the unburned propellant, consisting of both fuel and oxidizer within the probe motor, was found to be consumed by a process a t present indicated t o be of third order. I n the same region, second-order kinetics were observed for the disappearance of nitric oxide from the combustion gases. In the region beyond approximately 4 inches from the injector face, combustion with white fuming nitric acid as oxidizer is believed to involve, as the rate-controlling step, terinolecular reactions bet\\-een nitric oxide and incompletely burned fuel. At 430 Ib. per sq. inch absolute chamber pressure and a t 3600°, 3700”, and 3900” R., t’he specific reaction rate-constants for the consump5.1 X lolo, 6.17 X tion of unburned propellant are 4.30 X 10’6 (inchee3)2mole+ set.-' The variation of t,he rate constant with temperature obeyed the Arrhenius law.
kkU = 1.4 X l O l Q exp. ( - 24,433/RT) The kinetic data obtained by probing the sectional thrust chamber were employed in the computatiori of the parameter V J w cu. inch-sec. per Ib. n-liich expresses the combustion chamber
758
volume required to allow a specified conversion of a unit weight flowrate of propellant. The V C / wratio for the propellant burning in the sectional combustion chamber, equipped with the likeon-like injector to produce the theoretical characteristic velocity, was 26.82 cu. inches-see. per lb. B s long as the rate of propellant conversion a t a particular temperature depends only on the moles of propellant converted per pound of feed a t that temperature, the parameter V,/wis independent of combustion chamber s i x , shape, and propellant injection rate. The comparison of six different repetitive pattern injectors was made on the basis of the combustion chamber volume required t o produce a characteristic velocity of 4500 fect per sec. from the, combustion of the hydrorarbon-white fuming nitric acid propellant. This comparison indicated that the cIe5ign of an injector has little. if any, effect on the chemistry of the combustion process. Acknowledgment
This mork was done in connection with a pioject sponsored by the United States Air Force. The author nishes to thank them and the various inembers of the Aerojet organization ~1ho helped with this work. Acknodedgments are especially made to J. D. Thackrey who developed the mechanically operated combiistion probe, t o P. P. Datner for his derivation of Cqiiation 5, and to T. B 1,nzer who made the mass spectrometiic analyses of the combustion gas samples. Operation of the equipment mas a t various times under the supervision of IT. D. Stinnett, .J. C. LTcConahay, and H 1%. 1Iurphy Literature Cited
(1) Altman, D., Peniier, S. S., J . Chena. Phgs. 17, 59 (1949). (2) Altsiemer, J. H., J . Am. Rocket Soc. 22, 86 (1952). (3) “Analysis and Evaluation of German -4ttainments and Rescarcli in The Liquid Rocket Engine Field,” vol. 1, Combustion Chambers (available from Central Air Documents Office, AII, 86003, January 1962). (4) Baker, D. I., Jet Propulsion 25, 217 (1985). (5) Blackshear, P. L., Jr., Natl. Advisory Comm. aeronaut,.,Tech. Kote 2167, September 1950. (6) Hougen. 0 . A . , Watson, K. RI.,“Chemical Process Principles,” p. 832, Wiley, Kew York, 1947. (7) Laidler, K. J., “Chemical Kinetics,” p . 14, IIcGraw-Hill, New York, 1950. ( 8 ) Ibid., p. 96. (9) Lutz, O., “R-dntriebe,” 1943 (available from Central -4ir Documents Ofice, Order N o . FWB/DdL/1071-43). (10) b)Ioore, P. W., Jr., Aeronaut. Eng. Rea. 7, KO.5, 30 (1948). (11) Stephens, E. R., Pease, R. X., J . -4?n. Chem. Soc. 74, 3480 (1952).
(12) Wildhack, W. A., Rev. Sci. Instr. 21, 1 (1950). (13) Wise, H., Prech, 21. P., J . Chem. Phus. 20, 22 (1982). (14) Zucrow, hI. J., “Principles of Jet Propulsion and Gas Turbines,” p. 506, Wiley, New York, 1948. R E C E I T Efor D review September 23, 1955.
INDUSTRIAL AND ENGINEERING CHEMISTRY
ACCEPTEDMaroh 2 , 1956
Voi. 48, No. 4
