Mollier Diagrams for Theoretical AlcoholAir and Octane-Water-Air Mixtures Northern Regional Research Laboratory,
U.S. Department OF Agriculture, Peoria, Ill.
Charts are presented to show the thermodynamic quantities necessary to calculate the temperatures, pressures, mean effective pressures, work, and efficiencies for the possible cycles for mixtures of alcohol-air and octane-water-air (35 pounds of water for each 100 pounds of fuel). Sample calculations show that lower temperatures prevail during the combustion of alcohol-air and octanewater-air than with octane-air mixtures, when full advantage is taken of the heat of vaporization of alcohol and water. Maximum temperatures during combustion give no indication regarding preignition. According to the data presented, there i s no reason why water injection alone should be more beneficial than the injection of an alcohol-water mixture with the identical amount of water as shown b y Kuhring. Additional experimental and theoretical work will be required to give more information regarding the behavior of alcohol-air and octane-water-air mixtures in engines.
NO, 02, OH, CO, as well as the undissociated portion of COO, and H20, is plotted against temperature a t three pressures. The data were taken from octane-water-air mixture calculations. It is interesting to note the considerable amount of OH, as well as the trend of dissociation with pressure and temperature. Thermodynamic Properties
Since this laboratory is interested in investigations of motor fuels from agricultural products, it was considered important to determine the thermodynamic properties of a theoretical alcohol-air mixture according to the following equation: CiHlOH 301 (79.08/20.92)3Ne = 2C02 3Hz0 11.34Nz (1)
+
+
+
+
The hydrogenlcarbon ratio for ethyl alcohol is 3, while that for octane is 2.25. Tsien and Hottel (W), in their note on the effect of hydrogen/carbon ratio on the validity of Mollier diagrams for internal combustion engines, computed a chart for octene having a ratio of 2 and compared their results with those previously obtained for octane (4)- They found that a calculation of the cycle efficiency for octene fuel, using the octane diagram, would result in a 3 per cent error, while the difference between octane and octene from their charts was only 2 per cent. Since alcohol has an oxygen atom in addition t o hydrogen and carbon, the difference between its Mollier diagram and that for octane was expected to be more significant. Because alcohol has a considerably higher heat of vaporization than octane, we assumed the former as a liquid a t our base temperature, 520" R., and believe that this will form a reasonable basis of comparison with similar calculations on octane (4),and octane-water-air mixtures, where octane is in the vapor state at this temperature. Kuhring (9),in his work on water and water-alcohol manifold injection in a supercharged Jaguar aircraft engine, found that water injection resulted in lower cylinder and charge temperatures and slightly lower specific fuel consumption; the minimum fuel was consumed when about 40 pounds of water were used per 100 pounds of fuel; the brake horsepower was a t a maximum at around 60 pounds of water per 100 pounds of fuel. On the other hand, while water-alcohol injection lowered the charge and cylinder temperatures, actually an increase in specific fuel consumption resulted; the maximum brake horsepower was obtained when about 20 pounds of water were used in a mixture containing 46.25 per cent or 17.2 pounds of alcohol by weight. Kuhring admitted that the alcohol-water question had not been fully examined. Therefore, the thermodynamic effect was investigated of adding water to a theoretical octane-air mixture at a ratio of 35 pounds of water to 100 pounds of fuel, according to the following equation:
IN
RECENT years the importance of accurate thermodynamic analyses for various fuels used in internal combustion engines has become apparent (1, 4, 6, 8,14, 17, 20,66, 83)- Unfortunately most of the work was based on older and incomplete thermal data, so that many of the conclusions are uncertain though not necessarily incorrect. Kuhl (8) used the most recent data available (&IO, 11, IS),but his work involves considerable additional calculations. Hershey, Eberhardt, and Hottel (4) overcame these di$culties in their work on the thermodynamic properties of the working fluid in internal combustion engines, and their data have been followed closely in the present calculations. The limitations of calculations of this sort when translated to actual engine operations have been discussed before-e. g., by Taylor and Taylor (61). They pointed out that the fuel-air cycle must be corrected for combustion, time, and direct heat losses as well as for leakage, etc., in order to become the actual cycle; also, that the latter must be corrected for friction losses to give the useful work. Even with these limitations the results give the actual limiting conditions, in normal combustion, of temperature, pressure, work, and efficiency for the various cycles. The importance of making allowance for dissociation is clearly shown in Figure 1 where the volume of 0, H, Hz, 575
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15
10 8.0
I
6P
I
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I P.2000 L E
3200
TEMP, 'R
Figure
CsHls
3500
I
4000 4500 TEMP. 'R.
l
5000
/
J
1. Effect of Pressure and of Temperature o n Composition of Combustion Products of O n e Pound of Air w i t h Theoretical Fuel (GH18) Plus A d d e d W a t e r (35 Pounds p e r 100 Pounds Fuel)
+ 12.602 + 47x2 + 2Hz0 (liquid) + 0.22H20 (gas) = 8COZ + 11.22H20(gas) + 47x2
S
(2)
As a compromise for the possible presence of residual gases, nine tenths of the added water was assumed-to be liquid, and one tenth to be in the gaseous state a t 520" R. Use of Charts Following the example of Hershey, Eberhardt, and Hottel (4),we prepared two charts for each of the two reactionsalcohol, Equation 1, and octane, Equation 2 (Figures 2 and 3). For many details the paper of Hershey, Eberhardt, and Hottel should be consulted. The symbols used on these charts are as follows:
V
= volume, cu. ft. T = temperature, R. P = pressure, lb./sq. in. E = internal energy, B. t. u. S = entropy, B. t. u . / O R. O
E and S for liquid ethyl alcohol, gaseous oxygen, nitrogen, carbon dioxide, and water (in addition to liquid water added as explained previously) are zero a t the reference temperature of 60" F. or 520" R. and 14.7 pounds per square inch, while for all other components a t the reference temperature they are equal to the energies and entropies of formation, E, and S,, respectively. The sensible internal energy, E,, was calculated from the equation,
while the internal energy of combustion, E,, was added a t the base temperature; for any other temperature
+ L2:
Ecr = ECWG
where C,
=
ZC. resultants
AC, dt
- ZC, reactants
The entropy a t any point is equal to:
=
S,
J2r
C, d In T
- nR In N
is defined by the equation: N=E+PV
The values for the heats of combustion a t constant volume and constant pressure for alcohol as a liquid and water as a gas were calculated from Rossini's value (It?), giving E, = 11,560B. t. u. per pound and H , = 11,537 B. t. u. per pound. Similarly, for gaseous octane and liquid water in the product the data were calculated from Jessup's work (6),giving E , = 19,316 and He = 19,284 €3. t. u. per pound. I n our work a correction was made for the heat of vaporization of 0.001163 mole of water added a t the base temperature. Since the amount and atomic composition of the mixture remains constant, the process involves a system with two degrees of freedom, and all thermodynamic quantities will be completely determined by pressure and temperature. The method used in calculating the data may be briefly outlined as follows; TABLEI. COMPARISON OF THREEFUELMIXTURES IN THREE FUELAIRCYCLES OctaneOctaneAir Water-Air Unthrottled Cyolea 463 468 Work B. t . u . 37.7 38.0 E5ci;ncy % Mean effective ressure, Ib./sq. in. 193 205 4840 Mar. temp. OR. 4990 Throttled Cvcleb 439 443 Work, B . t . u. 36.3 36.6 E5ciency % Mean effebtive rtssure, lb./sq. in. 114 119 4950 4800 Max. temp. (T$, R. Supercharged Cycles Work B. t . u. 499 502 39.8 40.0 Efficidncy 3 ', Mean effebtive ressure. Ib./aq. in. 468 467 M a x . tsrnn. (Ta?. 6070 4900 . ~ -O -. ,R ., a Initial conditions were a8 follows: PI = 14.7, temperature compression ratio = 6. exhaust pressure 14.7. b PI = 10: other odnditions same as a. c PI P 30; other Conditions same as a. Mixture
AlcoholAir 509 39.9 210 4760
(TX
-
480 38.3 119
4700
-
544 41.8 498 4810
520" R.,
May, 1942
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
Figure 2
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1
17
16
15 14 I3
12 II
IO 9 8
-
CHEMICAL
EO UI L l BR IUM
~ ~ i t l l i i ~ ~ i i i i / i I i I lU i I tI Ii I I I I I I 0.35
0.40
0.45
0.50 0.55 0.6 0 T O T A L ENTROPY, B.T. U. 'R,?
T = TEMPERATURE, O R . P = P R E S S U R E , LBS./INe (Solid Lines) v = VOLUME, CU. FT. ( D a s h e d Llnes)
I 0.65 I I ~ ~0.7 0I I I I.75I I ~ I I I I9
I
2
t-
m v)
0
2
> (3
K
w
z
w
_I
4
z K
w
c
E -1
a
t0 I-
] 0
Y W
z e
'0 I-
AIR
2bih
0.35
0.40
FUEL PLUS
WITH T H E THEORETICAL 0.45 TOTAL
0.5 0
0.55
ENTROPY,
0.60 B.T.U.
Figure 3
O R - '
~
WATER 0.65
/ 0.70
0.75
E
m
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l8OC
loo( SUPERCHARGED O T T O CYCLE
THROTTLED OTTO CYCLE
UNTHROTTLED O T T O CYCLE
P
501
IO'
R
.
\ I
14.
Figure 4.
Ideal Pressure-Volume Diagrams for Various Engine Cycles
corrections to be applied in case of throttling and supercharging have been described (4, 21). INDUCTION STROKE.P = constant: (alcohol air)To (residual gas)T, = (alcohol air residual gas)n Hs, = HTO(1 - f ) H n . f wheref = weight fraction of residual gas in mixture COMPRESSION STROKE.S = constant: (alcohol air residual gas)E,TlV, = (alcohol air residual
+
+ +
+
+
+ + + + V = constant: (alcohol + air + residual gas)E2T1vd+ (heat of combustion) = F)E~T*V*
OMBUSTION.
(products of combustion)Z,T,va heat of combustion = E, (1 f) EXPANSION STROKE.S = constant: (products of combustion)E,T3va= (products of combustion)x,T,v,
-
EXHAUST. S = constant: (productsof COmbUStiOn)E,T,v,
=
(products of COmbUStiOn)e,.r,vs
where k = C,/C. = 1.4, and is a function of the compression ratio only. To obtain more nearly the actual limiting efficiencies, i t is necessary to assume a ratio lower than 1.4. Lichty (11) suggested 1.246. Table I1 gives the values of efficiency for a number of compression ratios when using three different values for k (see also citation 3). Table I shows that the actual limiting efficiencies under the stated conditions fall between the values obtained when using 1.3 and 1.246. The use of values other than k = 1.4 makes Equation 3 an empirical relation which is useful only to indicate roughly the increase of efficiency which can be obtained with increase of compression, though in actual practice the relative efficiency increases faster due to reduction of heat losses and decrease in dissociation a t the higher pressures ( 7 ) . Other empirical equations taking into account fuel-air ratios are given by Taylor (21,page 47).
Efficiencies
Table I compares three fuel-air cycles and three fuel mixtures in each fuel-air cycle, and Figure 4 shows the diagrammatic outline of each. As a result of the lowering of the cycle temperatures, the efficiencies of alcohol-air and alcoholwater-air mixtures are greater than for octane, particularly of alcohol-air. No correction for supercharger work has been made, but this can also be obtained from Figure 2. It is both of theoretical and practical interest to calculate efficiencies by means of an air-standard constant volume cycle, which is approached when infinitely lean mixtures are being used. The efficiency of the cycle is given by efficiency = 1 - EO--)) (3)
TABLE 11. EFFICIENCY AT VARIOUS COMPRESSION k 1.4 1.3 1.246
c = 2 0.24
0.18 0.17
e - 4 0.42 0.34 0.29
R.kTIOs
Efficiency
€ 3 6 a = - 8 0.51 0.56 0.42 0.46 0.36 0.40
~ - 1 0 e - 1 2 ~ = 1 4 e = 1 6 0.60 0.63 0.65 0.67 0.50 0.53 0.55 0.57 0.43 0.46 0.48 0.49
That high compression ratios are a possibility even for spark ignition engines was recently demonstrated by Prescott (16),whose two-cylinder compound engine had a maximum compression ratio of 15.05. (Prescott used a two-stage expansion to a final ratio of 15.05/1.)
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TABLE 111. MAXIMUM COMBUSTION TEMPERATURES AND PRESSURES OF
MIXTURES
Max. Temp., Max. Pressure, Theoretical >:Mixtures O R. Lb./Sq. In. Benzene-aira 5337 605 CsHia-air 5 5149 605 5067 590 CaHIeair b 5359 635 Cl~Hse(kerosene)-airs Alcohol-air= 4900 587 4950 CaHls-water-air 0 693 4971 605 CaHis-water-aird a From Goodenough and Felbeck (8, Tables IX and X). b Calculated from d a t a of Hershey, Eberhardt, and Hottel (4),using similar initial Conditions. 0 From the writers’ data. d From Goodenough and Felbeck (8, Table II), talcjng the value for 0.4 Ib. of liquid water per lb. of fuel a t 672’ R. compared with 0.35 lb. of gaeeous weter a t 672’ R. in our case.
TABLEIV. DECREASE IN TEYPERATURE OF INCOMINQ MIXTURE DUETO HEATOF VAPORIZATION H e i t of Vaporization
Fuel Octane Benzene Cyclohexane He tylene EtRyl aloohol Methyl alcohol
B.T. U . / L i .
Correct Air/ Fuel Ratio
Fall in Temp.,
128 172 156 167 397 512
15.05 13.2 14.7 14.7 8.95 6.44
29.0 46.8 38.7 41.4 148.8 252,o
O
F.
Octane Values
The value of ethyl alcohol lies principally in its high octane value. Rothrock (19) points out that octane numbers of certain aromatics and alcohols are somewhat meaningless with present rating methods, since there is no conclusive evidence that methanol, benzene, and toluene (ethyl alcohol belongs to this class) have ever been shown to knock but have always failed through preignition (ignition of the charge before the spark jumps the gap). The fact that preignition is caused by hot spots within the cylinder and that the so-called temperature plugs (thermocouple indicating devices) showed higher relative (not true) temperatures-e. g., for benzene than for octane-indicated the possibility that the combustion temperatures under similar conditions would be higher in one case than in the other (19). Table I11 shows that benzene-air mixtures have a higher maximum combustion temperature than octane-air; but so has kerosene, which fails through detonation. The results for alcohol-air and for octane-water-air mixtures show the cooling effect of the heats of vaporization of alcohol and water. These data do not bear out the contentions of higher maximum cylinder temperatures for alcohols at any rate. That the whole question is far from simple was indicated by experiments at the laboratory of the National Advisory Committee for Aeronautics (19) showing that benzene, toluene, and commercial iso-octane plus tetraethyllead preignited on a heated wire within an engine a t about the same temperature, and that the temperature required to ignite methanol was considerably lower; i. e., the absolute magnitude is not significant. Thermodynamic analysis may assist in solving the problem of detonation or that of preignition, but they are primarily questions of kinetics and of local temperature distribution. The relatively high heat of vaporization has an advantage in practical operation since it lowers the mixture temperature; this effect is of particular importance in supercharging operations and, in any case, increases the volumetric efficiency and lowers the maximum temperature in the combustion cycle. This point was brought out in our calculations. Table IV, taken from Ricardo’s work (16),shows the decrease in temperature of the incoming mixture due to the heats of vaporization of different fuels. The large temperature drops obtainable with methyl and ethyl alcohols have been utilized in fuel mixtures for racing purposes (12).
Vol. 34, No. 5
Literature Cited Goodenough and Baker, Univ. Illinois Eng. Expt. Sta., Bull. 160 (1927). Goodenough and Felbeck, Ibid., 139 (1924). Hersey. D. S., S. A . E. Journal, 44, 235T (1939). Hershey, Eberhardt, and Hottel, Ibid., 39, 409T (1936). Hottel and Eberhardt, Chem. Rev., 21, 439 (1937). Jessup, J. Research Natl. B u r . Standards, 18, 115 (1937). Jost, “Explosions- und Verbrennungsvorgange in Gasen” p. 495, Berlin, Julius Springer, 1939. Kuhl, Forsch. Gebiete Ingenieurw., 6 , Forsohungsheft 373 (1936). Kuhring, Can. J. Research, 16A, 149 (1938). Lewis, E.,and Von Elbe, G., “Combustion, Flames and Explosions of Gases”, Cambridge Univ. Press, 1938. Liohty, “Internal Combustion Engines”, 5th ed., Chap. IV, p , 59, New York, McGraw-Hill Book Co., 1939. Kash and Howes, “Principles of Motor Fuel Preparation and Application”, paragraphs 425, 426, 816, New York, John Wiley & Sons, 1935; Automotive Ind., 32, 268 (1940) Parks and Huffman, “Free Energies of Some Organic Compounds”, A. C. S. Monograph 60, New York, Chemical Catalog Co., 1932. Pflaum, W. W., “IS-Diagramme fur Verbrennungsgase und ihre Anwendung auf die Verbrennungsmaschine”, Berlin, V. D. I. = Verlag, 1932. Prescott, S. A. E. Journal, 49, 3261‘ (1941). Ricardo, “High-speed Internal Combustion Engines”. p. 15, London and Glasgow, Blackie and Son, 1931. Rosecranz and Felbeck, Univ. Illinois Eng. Expt. Sta., Bull. 150 (1925). Rossini, J . Research Natl. Bur. Standards, 8, 119 (1932). Rothrock, S. A. E. Journal, 48 51T (1941). Tanaka and Awano, Rept. Aeronaut. Research Inst., TdkyB I m p . Univ., 118, 128 (1935). Taylor and Taylor, “The Internal Combustion Engine”, Scranton, Penna., Int. Textbook Co., 1938. Tizard and Pye, Rept. Empire Motor Fuels Comm., 18, Part 1 (1924). Tsien and Hottel, J . Aeronaut. Sci., 5, 203 (1938).
Courtery, Texdr
Gulf Sulphur Compdnv
Elaborate System of Controls for Regulating Temperatures and Pressures a t a Field Station on Sulfur Dome
