orization of Li J
RI&JM AND RATE STUDIES GEORGE G. L.CvPB .iND LEO J. O’BRZES l o r t h m e s r s r n Technological r n s t i t t r t e , F c w n s t o n , I l l .
A study has been made of the equitibriurn and rate phenomena associated with the vaporization of fuel prior to combustion in an aircraft engine. Although lacking some pertinent experimental data directly applicable to aircraft engines, the authors believe that the rate concept as represented by mass transfer between phases across a laminar film resistance presents a ready means of defining fuel vaporization in terms of fuel composition, time available for the change in state, and the intenshe factors affecting vaporization-i. e., pressure and temperature. It is also indicated that the equilibrium between the vapor and liquid found in distillations is useful in learning the composition of a complex fuel to be studied in a similar analysis. I comparison is made betw-een experimentally deterinined A.S.T.M. and theoretical batch differential distillations, calculated equilibrium air distillations, and theoretical equilibrium flash distillations.
The quality of the air-fuel mixture-per cent of fuel vaporized ----within the precombustion zones of a jet propulsion burner and a t the intake ports of multicylinder reciprocating engines must be known for present aircraft-engine research. . The variation in rate and completeness of combustion i-iith different fuels cannot be completely understood unless the vaporization factors are given their proper emphasis in explaining the processes leading to combustion. In the reciprocating engine field, knorledge of mixture quality is needed for thc correlation of fuel knock ratings between multicplinder engines and single-cylinder laboratory engines for studying the performance of various engine component,a and for improving fuel distribution to cylinders. . . Socalled mixture temperatures and calculated equilibrium-airdistillation temperatures have been used for estimating mixture quality. Both methods are inadequate because important factors affecting mixture qualit,y and vaporization processes are neglect,ed. ~
~
I
The purpose of the work presented here is t’o examine the physical data t,hat, can be obtained readily on fuel blench, and to indicate the value of theoret,ical calculations in predicting the extent to which a fuel is vaporized prior to combustion in an aircraft engine.
URING World War I1 the need for aviation ga.soline increased nearly one hundredfold, and much effort was expended to increase the quantity of high ant,ikriock hydrocarbons obtained from a given amount of crude oil. With recent developments in synthetic petroleum processes such as alkylation, isomerization, catalytic cracking, polymerization, hydrogenation, hydroaromatizat,ion, aiid superfractionat,ion, yielding large amounts of high antiknock hydrocarbons of high boiling point, such as cumene, tmhexylenes, and catalytically cracked naphthas, an obvious means of increasing the production of aviation gnsoto increase the amount of high boiling point, materials included in any blend. The amount of such materials that could he added was controlled primarily b y the 907, point, of the A.S. T.M. clistillat,ion which v a s increased from 257“ to 302” F. Rowever, as service records of flights, both operational and test, showed that this mas at times a cost,ly procedure, additional control of “tail end” volatility became necessary. I t is known from experience that reducing the proportion of certain high boiling point materials in a blend yields a more satisfactory fuel, but t’he quantit,ative reason for this variance has not, been satisfactorily est ablished. This problem of bail end volatility stiinulated much interest’ during the recent Tyar, and several groups are now working on it. Holvever, the reports that have been published are limited. The Army, Navy, and National Advisory Committee for Aeronautics, working with various government agencies and industries through the Coordinating Research Council, have correlated a large amount of data from tests relative t,o this problem, but further analysis is nccessary. The University of Colorado has also been active in obtaining experiment,al data pertaining to fuel volat,ility, particularly a t as loiv temperatures as are possible to attain on this continent. Hull and Parker have reported on this work (19) The Nat’ional A4dvisoryCommitke for Aeronautics has pursued the problem under discussion, dealing almost entirely with empirical correlations ( 1 2 ) . An excerpt from t,his publication summarizes the importance of the problem concerning fuel vaporization and air-fuel mixture quality.
SURVEY O F POSSIBLE APPROkCHES TO PKOBLE\I
The term “gasoline” is usually associated with very complex hydrocarbon mixt,ures (13, 16),but, it is possiblc to have a reasonably acceptable aviation fuel of a single component, iso-octane (2,2,4- trirnethylpentane). However, for optimum utilization of the best, antiknock and perforniance characteristics of isoparaffins, aromatics, naphthenes, a,nd norihydrocarbori antiknock materials, aviation gasolines of highest quality may be blends ranging from three t o t,en cornponents. To simplify the aiislysis and yet deal nith a. satisfactory aviation fuel, four blends of throe and four components vc-ere chosen for this study. Thrir compositions are listed in Table I. Blends I[, 111,and I\; are uscd to show the effect of adding varying amounts of a heavy comlmncnt, t o an acceptable aviation fuel, represented by blend I.
T.tR1-F:
1. COUPOSIT~ONY OF FUEL^ STCDIED
Corllyollnll
Isopentane Iso-octane
Cumene
Tetraethyllead 1,3-Diisogrop~lbeneerie m-Toluidine
Mole fraction Blcnd I Blend I1 0.2352 0,2383 0,6621 0.0997
.... ..., ....
0.6623
0.0086 0.0008
....
....
Blend I I I Blend r Y 0.2394 0,2367 0,6661 0,6581 0.0775 0.0783 0:01e0 ,,
, ,
.... , ,
.
t
0.0277
I n work associated mtli the internal combustion eiigine and its fuels, the A4.X.T.M. dietillation (D 86-45), ( 1 ) aiid equilibrium air distillation (3) have been generally used in studies of volatility and performance. The batch differential distillation and the equilibrium flash distillation may be considered the theoretical counterparts of the above two generally used distillation curves, and may be derived from data on the true boiling point distillation or from the actual composition of a fuel. The theoretical distillation calculations are particularly valuable, because they provide data on the composition of the fuel remaining in liquid 182
183
INDUSTRIAL AND ENGINEERING CHEMISTRY
January 1949
BLEND lS0PENTANE.t.
BLEND 2
I
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ISOOCTANE ISOOCTANE
ISOPENTANE
,CUMEN
I
300
,
ISOOCTANE
I
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.D.D.
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200.
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A.S.T.M. E. F. D.
E. A, 0. 200'
-
-
TRUE BOILING POINT DISTILLATION BATCH DIFFERENTIAL DISTILLATION STANDARD M E T H O D , EOUIUBRIUM
EQUILIBRIUM AIR
- 48
DISTILLATION
100
50
PERCENT
D86
FLASH DlSTlLLATlON
VAPORIZED
Figure 1
IO0
T B P -TRUE
BOlLlNQ P O I N T DISTILLATION
B 0.0- BATCH D I F F E R E N T I A L OISTILLATION A$T.M,-STANDARO E F.0.-
METHOD,
EPUILIBRIUM
E A D - EOUlLl BRIUM
droplets and of the fuel vaporized under the assumed conditions, whereas such information is usually not obtained in the A.S.T.M. and equilibrium air distillation tests. These distillations, presented graphically in Figures 1 to 4 for the four blends considered in this report, were obtained as follows: The A.S.T.X. distillation (standard test method D 56-45) (1) and the true boiling point distillation were determined experimentally. The apparatus used for these latter distillations consisted of a Shell Development Company jacketed column, using a Goldsbarry-Martin head and electrlcally controlled reflux and reboiler heat. This column contains thirty theoretical plates and was operated at a reflux ratio of 10 to 1. The true boiling point distillations were stopped at approximately 95% distilled owing to the holdup of liquid in the apparatus. However the data as presented are continued to 100% distilled by assuding that if it were possible to run the distillation to completion, the data would reflect the quantity and boiling point of the components included in the residue just as the lighter components were represented. The equilibrium air distillation data were calculated from Bridgeman's correlation (3), using the A.S.T.M. distillation curves mentioned above. The equilibrium flash distillation data were calculated by the method outlined by Brown (ZI),and the batch differential distillation data were calculated from equations derived by a n analysis similar to that first made by Rayleigh (29). These latter two distillation calculations are based on ideal conditions using vapor pressures for the calculation of vapor-liquid equilibrium constants. The volatility specifications of a fuel are based primarily on the A.S.T.M. distillation data with particular reference to the 10, 50, and 90% points, the initial boiling point, and the end point. As the end point is difficult to reproduce on a given fuel, most emphasis is placed on the 90% point to control the amount of high boiling point materials in a blend. The A.S.T.M. data presented in this paper indicate that addition of 2% heavy material to a blend has little influence on the 90% distilled temperature (Figures 1 to 4) Yet i t is known that 2% of a high boiling point component is sufficient to have a serious effect on performance of the fuel in aircraft engines under some operating conditions encountered in testing and use. The liquid composition data of the
PERCENT
FLASH AIR
088-45
DISTILLATION
DISTILLATION
VAPORIZED
Figure 2
equilibrium flash distillation, batch differential distillation, and diffusion controlled vaporization (Figures 5 to 12 and 14) show that the material of high boiling point present in a fuel in small amounts is not vaporized appreciably until more than 95y0 of the liquid is vaporized. This indication, plus the slight difference noted between the experimental A.S.T.M. 90% distilled temperature of the four blends considered, is a strong argument in favor of placing more emphasis upon the 98% distilled or the end point of the A.S.T.M. distillation in specifying aviation fuels, with respect to tail end volatility. These points, with reproducibility as required by A.S.T.M. standards ( I ) , are a better indication of the presence and possibly the effect of small amounts of a heavy component in a fuel than the 90% point. Brown recognized the relationship of fuel volatility in an auto engine to ease of engine starting, etc., by his exhaustive work in correlation of engine performance with the front end of the A.S.T.M. distillation and equilibrium air distillation curves (4, 6). However, when one studies the latter portion (from 70% distilled to dew point) of the equilibrium air distillation curves presented in this report, i t does not appear that they can be correlated as neatly to give a working tool for the study of the latter stages of fuel vaporization in a n aircraft engine, as this distillation will not ordinarily reflect the presence of small amounts of high boiling point components in a blend. These curves are primarily considered in this discussion because they reflect the influence of air in the equilibrium affecting hydrocarbons which are vaporizing into an air stream, even though they do not include data on compositions of liquid and vapor. Another major objection to their use is that gathering experimental equilibrium air distillation data on an endless variety of fuel blends is very timeconsuming, while a correlation such as Bridgeman's is a t best an approximation and cannot be used too exactly.
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INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY BLEND 3 ISWENTANE
,
Vol. 41, No.
BLEND
ISOOCTANE
CUMLNE
DIISOPROPY;h&E ,OOi
ISOPENTANE
n
4
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- EOUILIBR1UH
E AD-
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-~
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Figure 3
STANDARD METHOD, D8e-45
EFD.-
EPUlLl0RlUM FLASH
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EOUILl8RIUM
AtR
PERCENT
Figure 5
100
VAPOR1 2 ED
Figure 4
VAPORIZED
MOL
DISTILLATIOW DISTILLATIO~I
50
- P : 0.017ATM. --_ p=0.027 ATM.
MOL
DISTILLATION
ASTW-
P E RC,E NT
VAPORIZED
BOILING P O I N ? DISTILLATIC+@
TBP-
ma-
PERGENT
Figure 6
VAPORIZED
B
INDUSTRIAL A N D ENGINEERING CHEMISTRY
January 1949
The equilibrium air distillation data calculated in this report by the Bridgeman correlation (3) have the 90% distilled ordinate lower than the SO% point, an impossible condition. Probably this resulted from the extremely high tail of the A.S.T.M. distillations, and perhaps because any empirical correlation is never completely infallible. By ignoring the 90% ordinate a smooth curve was drawn in this instance. The equilibrium air distillation data Bridgeman possessed were lacking in bubble and dew points; these were obtained in his work by extrapolation of data.
It is extremely difficult to obtain data exactly at the dew point, as the latter few per cent of the distillation require laboratory
technique that is almost impossible to attain. These shortcomings appear t o eliminate the equilibrium air distillation as an absolute and ready means of correlation with tail end volatility. For a complete discussion of the value of the various distillations in studies of fuel vaporization, it becomes necessary to examine the conditions of pressure and trniperature that prevail in an aircraft engine from the instant the fuel is injected into the air stream until it is burned by the flame advance across the conibustion zone in the cylinder. Ttirsc conditions may vary from 0.5 to 60 atmospheres pressure and 150" to 5000" F. vapor-air temperature, but the following values approximated from the charts of Hottel et al. (I?"), except as noted, appear acccptable for the present problem To help define the problem a specific aircraft engine under specified operating conditions is chosen for analysis-i. e., the Pratt and Whitney R-2800 engine, operating a t 10 000 feet altitude and 2000 revolutions per minute with an air-fuei ratio of 16 to 1 ( P I A = 0.0625). The fuel is injected into the supercharger so that it strikes the impeller blades in meeting the air stream. The mixture in the supercharger and intake manifold of this engine will be at approximately 1 atmosphere pressure and a temperature of about 170" F. (88). The air-vapor mixture, still at 170" F. as it enters the intake port of the cylinder, will be met by the residual
I
-P *
185
gas at approximately 1740' F. from the previous combustion. Assuming 5% residual gas and 95% fresh intake, the temperature of the resulting mixture will be 260" F. prior to compression With a compression ratio of 6.5 to 1-the temperature of the airvapor-gas mixture will be about 940' F. at a pressure of approximately 15 atmospheres after compression. During combustion, the flame temperature exceeds 4600" F. (the unburned gases will not reach this temperature), and the pressure increases to about 60 atmospheres. The expansion of the gases during the power and exhaust stroke cools them to the temperature initially assumed for the residual gas (1740' F.). In comparing the temperatures concerned with the various distillations of the four fuel blends with those temperatures encountered by the air-fuel mixture in the aircraft engine, one may conclude that these latter temperatures are more than adequate to cause complete vaporization of the fuel b y boiling, if one assumes instantaneous heat transfer to the fuel. However, from the work on fuel vaporization mentioned below, and other accepted facts (intake manifold wall of an engine wetted b y unvaporixed fuel, for example), i t is known that the fuel is not completely vaporized as it enters the cylinders. Commercial aircraft engines are designed to include drain lines from the intake manifold pipeb on the bottom cylinders to prevent a n accumulation of the unvaporized fuel during starting which could cause a disastrous back-fire. Hull and Parker in their work on fuel volatility in aircraft engines report that even after combustion, condensable liquid, other than the water vapor one would naturally expect, was found in the exhaust gases (19). Variation in the fuel-air ratio and composition of fuel delivered to the various cylinders 111 multicylinder aircraft engines has been reported (19). Engine service performance indicates that liquid fuel may be present at the time of combustion, and experimental engine work confirms
QOt7 ATH.
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ATM
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BLEND 4 EQUILIBRIUM
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DISTILLATION
ISOPENTANE
MOL
PERCENT
Figure 7
VAPORIZED
'
MOL
PERCENT
Figure 8
VAPORIZED
.
.
Vol. 41, No. 1
INDUSTRIAL AND ENGINEERING CHEMISTRY
186
{
1.0
I
BLEND
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DIFFERENTIAL
CUMENE
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= IoATM.
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Figure 10
Figure 9
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Figure 11
MOL
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Figure 12 RATE CONCEPTS
It is indicated above that distillation data ale riot coinplctely adequdtc t o define fuel performance. One additional variable that can be considered is time. Hon much time do?\ the fuel require for completr vaporization? Does the injected fuel have sufficient tiine to vaporize completely in thc intake system or prior to conibustion in an aircraft engine? For this investigation of the rate phenomenon involved in fuel vaporization, the concept of inteiphase mass transfer was usrd as developed for a binary system from the fundamental analysis of true diffusion po-tulatrd by Vax~vell( 2 3 ) and Stefan (32)
where Xa= rate of niass transfer, pound-nioles per hour D = a diffusivity coefficient, squaro feet per h o w m-i r , ~ ~ ~ ~ ~ _ _ = ().0()68(j ' 1_ _ (Isj 1
I" R
=
T
=
X
=
=
pressure on system in atinospheres absolute gas constant in atmospheres absolute, cubic feci pw pound mole, R. temperature of diffusing vapor, O It. thicknes? o f film resistant diffusion, \ w t
January 1949
187
INDUSTRIAL AND ENGINEERING CHEMISTRY
of diffusing gas at interface between liquid and air pa2 = partial pressure of diffusing gas in main gas stream = mean partial pressure of inert gas from the interface to main stream V Aand V B = molecular volumes of diffusing gas and inert gas, respectively M ~ a i i dM B = molecular weights of diffuiing and inett gases, respectively 'pa, = partial pressure
Some of the experimental data needed for a rigorous application of these equations were not available for this work, and the necessary values were assumed, using pertinent published experimental data (however remote from this particular problem) as a guide whenever possible. The conditions in the supercharger of the engine chosen for study have been defined as 1 atmosphere pressure and air temperature of 170 F., which is also considered as the temperature of the diffusing vapor. To evaluate the partial pressure driving force affecting mass transfer, a fuel temperature of 80" F. was chosen and assumed constant throughout vaporization-Le., heat flow across stagnant film just equals the energy needed t o transfer material across film from liquid t o vapor. The corresponding partial pressures were found from Raoult's' law, using vapor pressure data obtained by extrapolation and interpolation of the data published by Rossini (SO) and various data of other investigators (2, Y,8, 20, 29, 24,26,SJ). The value used for film thickness is probably most questionable, as little is known of the variables in an aircraft engine induction system affecting this resistance to mass transfer. However, by using the straight line relationship between film thickness and liquid-gas ratio found by Gilliland and Sherwood (24)a value of x = 0.03 cm. was chosen for this particular problem. Whereas little is known of the degree of turbulence between air and liquid in the supercharger as compared to that prevalent in the wetted wall column of the above investigators, the molecular volumes and weights of liquids vaporizing into air in both instances are comparable. On this basis, and in place of more exact data, the above value of film thickness is used. It is obvious that the value of iVadecreases throughout the process of vaporization, as the fuel is associated with a finite quantity of air. An exact solution of Equation 1 throughout vaporization would require the use of calculus, the resulting equation being solved by electronic instruments. However, the method of trial and error can be used with good results if small increments (1 to 2% vaporized) are used in the calculations. The complete solution for blend I using this method is shown in the plot of N , against per cent vaporized in Figure 13. The fuel can be considered to form droplets upon injection into the supercharger, but their size is not easily evaluated. Some work has been done on droplet size of Diesel fuel injected under pressure (fO),and the National Advisory Committee for Aeronautics used droplet size varying from 0.001 t o 0.1 inch in its study of aircraft engine fuel vaporization ( I d ) . Droplets 0.005 inch in diameter were selected for the study presented in this paper. The time required for the vaporization of a fuel is found in terms of droplet size and rate of vaporization by an application of the integral calculus. This equation is
where t = time for a given vaporization in seconds, YO and rf = initial and final radii of droplet, respectively, in inches, and N ; = mass transfer in cubic inches per square inch per second. The derivation of this equation required the assumption that the rate of mass transfer is constant over thp range of vaporization desirrd. Thii: is not true oi thr instantaneous value of the rate vaporization, but the average Safound from the area under
25
BLEND I*
\
VAPORIZATION
OF
DROPLETS
20 v)
I w
z e IS "0 X
v)
\
~AVERAGE
MOL
PERCENT
2
0 LT 4
VAPORIZED
Figure 13
the desired portion 01 the total mass transfer curve can be considered constant over the desired range of vaporization. This average rate of mass transfer is also shown in Figure 13 as a function of per cent vaporized. If, in addition, the radius of the remaining droplet is plotted as a function of per cent vaporized, the time for a given vaporization, or the vaporization that can be expected in a given time, is readily found from Equation 2 and a series of plots as shown in Figure 13. To determine the degree of vaporization one must know the time a given quantity of air-fuel mixture remains in the intake system of the aircraft engine. The speed of the engine and its piston displacement will define the quantity of air-fuel mixture required by an engine per unit time. Exact measurement or an approximation from working drawings (this latter method was used in this study) will define the volume of the intake system ($7). The desired value of time available for fuel vaporization is then the result of dividing the volume of the intake system by the volume of air-fuel mixture required by the engine per unit time. For the Pratt and Whitney R-2800 engine under the conditions specified above, this time was found to be 0.152 second. From an application of Equation 2 and with the aid of Figure 13 it was found that this time permits but 31y0of blend I t o vaporize. The numerical value of per cent vaporized will be markedly affected by the assumed liquid fuel temperature; 80" F. was used in these calculations. This analysis cannot be applied as simply to the vaporization that takes place in the engine cylinders during compression and just prior to combustion, for the changes in pressure and temperature are so marked that reaction kinetics, flame advance, and radiant heat transfer must be considered. However, a simple application of the effects of these pressures and temperatures encountered in the cylinder to the mass transfer conwpt indicates that an additional vaporization of only 3% viould result, sinw the
XNDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
188
conibined timw of compression and combustion a t 2000 revolutions per minute is of the order of 0.018 second. Comparing the results of these calculations with what is normally expected to occur in an engine, it appears that the results of the additional fact
